,Topic,Count,Name,Representation,Representative_Docs,Keywords
0,0,2007,0_reed solomon codes_solomon codes_codes constructed_linear codes,"['reed solomon codes', 'solomon codes', 'codes constructed', 'linear codes', 'codes finite', 'cyclic codes', 'reed muller codes', 'codes length', 'binary codes', 'dual codes']","['AG Codes Achieve List-decoding Capacity over Constant-sized Fields   The recently-emerging field of higher order MDS codes has sought to unify a\nnumber of concepts in coding theory. Such areas captured by higher order MDS\ncodes include maximally recoverable (MR) tensor codes, codes with optimal\nlist-decoding guarantees, and codes with constrained generator matrices (as in\nthe GM-MDS theorem).\n  By proving these equivalences, Brakensiek-Gopi-Makam showed the existence of\noptimally list-decodable Reed-Solomon codes over exponential sized fields.\nBuilding on this, recent breakthroughs by Guo-Zhang and Alrabiah-Guruswami-Li\nhave shown that randomly punctured Reed-Solomon codes achieve list-decoding\ncapacity (which is a relaxation of optimal list-decodability) over linear size\nfields. We extend these works by developing a formal theory of relaxed higher\norder MDS codes. In particular, we show that there are two inequivalent\nrelaxations which we call lower and upper relaxations. The lower relaxation is\nequivalent to relaxed optimal list-decodable codes and the upper relaxation is\nequivalent to relaxed MR tensor codes with a single parity check per column.\n  We then generalize the techniques of GZ and AGL to show that both these\nrelaxations can be constructed over constant size fields by randomly puncturing\nsuitable algebraic-geometric codes. For this, we crucially use the generalized\nGM-MDS theorem for polynomial codes recently proved by Brakensiek-Dhar-Gopi. We\nobtain the following corollaries from our main result. First, randomly\npunctured AG codes of rate $R$ achieve list-decoding capacity with list size\n$O(1/\\epsilon)$ and field size $\\exp(O(1/\\epsilon^2))$. Prior to this work, AG\ncodes were not even known to achieve list-decoding capacity. Second, by\nrandomly puncturing AG codes, we can construct relaxed MR tensor codes with a\nsingle parity check per column over constant-sized fields, whereas\n(non-relaxed) MR tensor codes require exponential field size.\n', 'Many Non-Reed-Solomon Type MDS Codes From Arbitrary Genus Algebraic\n  Curves   It is always interesting and important to construct non-Reed-Solomon type MDS\ncodes in coding theory and finite geometries. In this paper, we prove that\nthere are non-Reed-Solomon type MDS codes from arbitrary genus algebraic\ncurves. It is proved that MDS algebraic geometry (AG) codes from higher genus\ncurves are not equivalent to MDS AG codes from lower genus curves. For genus\none case, we construct MDS AG codes of small consecutive lengths from elliptic\ncurves. New self-dual MDS AG codes over ${\\bf F}_{{2^s}}$ from elliptic curves\nare also constructed. These MDS AG codes are not equivalent to Reed-Solomon\ncodes, not equivalent to known MDS twisted Reed-Solomon codes and not\nequivalent to Roth-Lempel MDS codes.\n  Hence many non-equivalent MDS AG codes, which are not equivalent to\nReed-Solomon codes and known MDS twisted-Reed-Solomon codes, can be obtained\nfrom arbitrary genus algebraic curves. It is interesting open problem to\nconstruct explicit longer MDS AG codes from maximal curves.\n', 'New Constructions of MDS Twisted Reed-Solomon Codes and LCD MDS Codes   Maximum distance separable (MDS) codes are optimal where the minimum distance\ncannot be improved for a given length and code size. Twisted Reed-Solomon codes\nover finite fields were introduced in 2017, which are generalization of\nReed-Solomon codes. Twisted Reed-Solomon codes can be applied in cryptography\nwhich prefer the codes with large minimum distance. MDS codes can be\nconstructed from twisted Reed-Solomon codes, and most of them are not\nequivalent to Reed-Solomon codes. In this paper, we first generalize twisted\nReed-Solomon codes to generalized twisted Reed-Solomon codes, then we give some\nnew explicit constructions of MDS (generalized) twisted Reed-Solomon codes. In\nsome cases, our constructions can get MDS codes with the length longer than the\nconstructions of previous works. Linear complementary dual (LCD) codes are\nlinear codes that intersect with their duals trivially. LCD codes can be\napplied in cryptography. This application of LCD codes renewed the interest in\nthe construction of LCD codes having a large minimum distance. We also provide\nnew constructions of LCD MDS codes from generalized twisted Reed-Solomon codes.\n']","[('reed solomon codes', 0.6646755337715149), ('solomon codes', 0.6306332945823669), ('codes constructed', 0.616558849811554), ('linear codes', 0.6121247410774231), ('codes finite', 0.607392430305481), ('cyclic codes', 0.5927842855453491), ('reed muller codes', 0.5909152626991272), ('codes length', 0.575136125087738), ('binary codes', 0.5728431940078735), ('dual codes', 0.555058479309082)]"
1,1,1557,1_nonlinear schr odinger_schr odinger equations_nonlinear schrodinger_nonlinear schr,"['nonlinear schr odinger', 'schr odinger equations', 'nonlinear schrodinger', 'nonlinear schr', 'odinger equations', 'cubic nonlinear schr', 'well posedness scattering', 'nonlinear schr dinger', 'posedness scattering', 'soliton solutions']","['Decay estimates for nonlinear Schr\\""odinger equations   In this short note, we present some decay estimates for nonlinear solutions\nof 3d quintic, 3d cubic and 2d quintic NLS (nonlinear Schr\\""odinger equations).\n', 'Scattering for the dispersion managed nonlinear Schr\\""odinger equation   We consider the dispersion managed nonlinear Schr\\""dinger equations with\nquintic and cubic nonlinearities in one and two dimensions, respectively. We\nprove the global well-posedness and scattering in $L_x^2$ for small initial\ndata employing the $U^p$ and $V^p$ spaces.\n', 'Global well-posedness and scattering of the two dimensional cubic\n  focusing nonlinear Schr\\""odinger system   In this article, we prove the global well-posedness and scattering of the\ncubic focusing infinite coupled nonlinear Schr\\""odinger system on\n$\\mathbb{R}^2$ below the threshold in $L_x^2h^1(\\mathbb{R}^2\\times\n\\mathbb{Z})$. We first establish the variational characterization of the ground\nstate, and derive the threshold of the global well-posedness and scattering.\nThen we show the global well-posedness and scattering below the threshold by\nthe concentration-compactness/rigidity method, where the almost periodic\nsolution is excluded by adapting the argument in the proof of the mass-critical\nnonlinear Schr\\""odinger equations by B. Dodson. As a byproduct of the\nscattering of the cubic focusing infinite coupled nonlinear Sch\\""odinger\nsystem, we obtain the scattering of the cubic focusing nonlinear Schr\\""odinger\nequation on the small cylinder, this is the first large data scattering result\nof the focusing nonlinear Schr\\""odinger equations on the cylinders. In the\narticle, we also show the global well-posedness and scattering of the two\ndimensional $N-$coupled focusing cubic nonlinear Schr\\""odinger system in\n$\\left(L^2(\\mathbb{R}^2) \\right)^N$.\n']","[('nonlinear schr odinger', 0.7245205640792847), ('schr odinger equations', 0.709191620349884), ('nonlinear schrodinger', 0.634990394115448), ('nonlinear schr', 0.6349025368690491), ('odinger equations', 0.5982327461242676), ('cubic nonlinear schr', 0.5895614624023438), ('well posedness scattering', 0.5350183844566345), ('nonlinear schr dinger', 0.49812424182891846), ('posedness scattering', 0.4957127273082733), ('soliton solutions', 0.48148131370544434)]"
2,2,1483,2_von neumann algebras_von neumann algebra_neumann algebras_ast algebras,"['von neumann algebras', 'von neumann algebra', 'neumann algebras', 'ast algebras', 'operator algebras', 'group algebras', 'banach algebras', 'unital algebras', 'groupoid algebras', 'neumann algebra']","['The weak tracial Rokhlin property for finite group actions on simple\n  C*-algebras   We develop the concept of weak tracial Rokhlin property for finite group\nactions on simple (not necessarily unital) C*-algebras and study its properties\nsystematically. In particular, we show that this property is stable under\nrestriction to invariant hereditary C*-algebras, minimal tensor products, and\ndirect limits of actions. Some of these results are new even in the unital case\nand answer open questions asked by N. C. Phillips in full generality. We\npresent several examples of finite group actions with the weak tracial Rokhlin\nproperty on simple stably projectionless C*-algebras. We prove that if $\\alpha\n\\colon G \\rightarrow \\mathrm{Aut}(A)$ is an action of a finite group $G$ on a\nsimple C*-algebra $A$ with tracial rank zero and $\\alpha$ has the weak tracial\nRokhlin property, then the crossed product $A \\rtimes _{\\alpha} G$ and the\nfixed point algebra $A^{\\alpha}$ are simple with tracial rank zero. This\nextends a result of N. C. Phillips to the nonunital case. We use the machinery\nof Cuntz subequivalence to work in this nonunital setting.\n', 'Amenable and inner amenable actions and approximation properties for\n  crossed products by locally compact groups   Amenable actions of locally compact groups on von Neumann algebras are\ninvestigated by exploiting the natural module structure of the crossed product\nover the Fourier algebra of the acting group. The resulting characterisation of\ninjectivity for crossed products generalises a result of Anantharaman-Delaroche\non discrete groups. Amenable actions of locally compact groups on\n$C^*$-algebras are investigated in the same way, and amenability of the action\nis related to nuclearity of the corresponding crossed product. A survey is\ngiven to show that this notion of amenable action for $C^*$-algebras satisfies\na number of expected properties. A notion of inner amenability for actions of\nlocally compact groups is introduced, and a number of applications are given in\nthe form of averaging arguments, relating approximation properties of crossed\nproduct von Neumann algebras to properties of the components of the underlying\n$w^*$-dynamical system. We use these results to answer a recent question of\nBuss-Echterhoff-Willett.\n', 'A von Neumann algebraic approach to self-similar group actions   We study some relations between self-similar group actions and operator\nalgebras. We consider KMS states on the Cuntz--Pimsner algebras constructed by\nNekrashevych from self-similar actions and the GNS representations of the KMS\nstates. The KMS states are given by the Bernoulli measure. We also consider the\nvon Neumann algebras on the GNS spaces and show that the von Neumann algebras\nare type III factors.\n']","[('von neumann algebras', 0.6377335786819458), ('von neumann algebra', 0.5751657485961914), ('neumann algebras', 0.5746338963508606), ('ast algebras', 0.5306749939918518), ('operator algebras', 0.524013102054596), ('group algebras', 0.5180414319038391), ('banach algebras', 0.5093449950218201), ('unital algebras', 0.5085675716400146), ('groupoid algebras', 0.5026136636734009), ('neumann algebra', 0.4977380335330963)]"
3,3,1449,3_partially hyperbolic_topological entropy_uniformly hyperbolic_singular hyperbolic,"['partially hyperbolic', 'topological entropy', 'uniformly hyperbolic', 'singular hyperbolic', 'anosov diffeomorphisms', 'ergodic measures', 'diffeomorphisms', 'measures maximal entropy', 'ergodic measure', 'invariant measures']","['SRB measures for mostly expanding partially hyperbolic diffeomorphisms\n  via the variational approach   By using the variational approach, we prove the existence of\nSinai-Ruelle-Bowen measures for partially hyperbolic $\\mathcal C^1$\ndiffeomorphisms with mostly expanding properties. The same conclusion holds\ntrue if one considers a dominated splitting $E\\oplus F$, where $\\dim E=1$ and\n$F$ is mostly expanding. When the diffeomorphisms are $\\mathcal C^{1+\\alpha}$,\nwe prove the basin covering property for both cases.\n', 'Unstable Entropy and Unstable Pressure for Partially Hyperbolic\n  Endomorphisms   In this paper, unstable metric entropy, unstable topological entropy and\nunstable pressure for partially hyperbolic endomorphisms are introduced and\ninvestigated. A version of Shannon-McMillan-Breiman Theorem is established, and\na variational principle is formulated, which gives a relationship between\nunstable metric entropy and unstable pressure (unstable topological entropy).\nAs an application of the variational principle, some results on the\n$u$-equilibrium states are given.\n', 'Minimality of Strong Foliations of Anosov and Partially Hyperbolic\n  Diffeomorphisms   We study the topological properties of expanding invariant foliations of\n$C^{1+}$ diffeomorphisms, in the context of partially hyperbolic\ndiffeomorphisms and laminations with $1$-dimensional center bundle.\n  In this first version of the paper, we introduce a property we call\n*s-transversality* of a partially hyperbolic lamination with $1$-dimensional\ncenter bundle, which is robust under $C^1$ perturbations. We prove that under a\nweak expanding condition on the center bundle (called *some hyperbolicity*, or\n""SH""), any s-transverse partially hyperbolic lamination contains a disk tangent\nto the center-unstable direction (Theorem C).\n  We obtain several corollaries, among them: if $f$ is a $C^{1+}$ partially\nhyperbolic Anosov diffeomorphism with $1$-dimensional expanding center, and the\n(strong) unstable foliation $W^{uu}$ of $f$ is minimal, then $W^{uu}$ is\nrobustly minimal under $C^1$-small perturbations, provided that the stable and\nstrong unstable bundles are not jointly integrable (Theorem B).\n  Theorem B has applications in our upcoming work with Eskin, Potrie and Zhang,\nin which we prove that on ${\\mathbb T}^3$, any $C^{1+}$ partially hyperbolic\nAnosov diffeomorphism with $1$-dimensional expanding center has a minimal\nstrong unstable foliation, and has a unique $uu$-Gibbs measure provided that\nthe stable and strong unstable bundles are not jointly integrable.\n  In a future work, we address the density (in any $C^r$ topology) of\nminimality of strong unstable foliations for $C^{1+}$ partially hyperbolic\ndiffeomorphisms with $1$-dimensional center and the SH property.\n']","[('partially hyperbolic', 0.5368204116821289), ('topological entropy', 0.5126826763153076), ('uniformly hyperbolic', 0.5120298862457275), ('singular hyperbolic', 0.5108306407928467), ('anosov diffeomorphisms', 0.506287157535553), ('ergodic measures', 0.49570387601852417), ('diffeomorphisms', 0.48167508840560913), ('measures maximal entropy', 0.46082785725593567), ('ergodic measure', 0.4517849087715149), ('invariant measures', 0.44821715354919434)]"
4,4,1371,4_enriched categories_infty categories_monoidal categories_monoidal infty,"['enriched categories', 'infty categories', 'monoidal categories', 'monoidal infty', 'categories enriched', 'monoidal category', 'infty categorical', 'infty category', 'functors', 'adjunctions']","[""An equivalence between enriched $\\infty$-categories and\n  $\\infty$-categories with weak action   We show that an $\\infty$-category $\\mathcal{M}$ with a closed left action of\na monoidal $\\infty$-category $\\mathcal{V}$ is completely determined by the\n$\\mathcal{V}$-valued graph of morphism objects equipped with the structure of a\n$\\mathcal{V}$-enrichment in the sense of Gepner-Haugseng. We prove a similar\nresult when $\\mathcal{M}$ is a $\\mathcal{V}$-enriched $\\infty$-category in the\nsense of Lurie, an operadic generalization of the notion of $\\infty$-category\nwith closed left action. Precisely, we prove that sending a\n$\\mathcal{V}$-enriched $\\infty$-category in the sense of Lurie to the\n$\\mathcal{V}$-valued graph of morphism objects refines to an equivalence $\\chi$\nbetween the $\\infty$-category of $\\mathcal{V}$-enriched $\\infty$-categories in\nthe sense of Lurie and of Gepner-Haugseng. Moreover if $\\mathcal{V}$ is a\npresentably $\\mathbb{E}_{\\mathrm{k+1}}$-monoidal $\\infty$-category for $1 \\leq\nk \\leq \\infty$, we prove that $\\chi$ restricts to a lax\n$\\mathbb{E}_{\\mathrm{k}}$-monoidal functor between the $\\infty$-category of\nleft $\\mathcal{V}$-modules in $\\mathrm{Pr}^L$, the symmetric monoidal\n$\\infty$-category of presentable $\\infty$-categories, endowed with the relative\ntensor product, and the tensor product of $\\mathcal{V}$-enriched\n$\\infty$-categories of Gepner-Haugseng. As an application of our theory we\nconstruct a lax symmetric monoidal embedding of the $\\infty$-category of small\nstable $\\infty$-categories into the $\\infty$-category of small spectral\n$\\infty$-categories. As a second application we produce a Yoneda-embedding for\nLurie's notion of enriched $\\infty$-categories.\n"", ""The higher algebra of weighted colimits   We develop a theory of weighted colimits in the framework of weakly\nbienriched $\\infty$-categories, an extension of Lurie's notion of enriched\n$\\infty$-categories. We prove an existence result for weighted colimits, study\nweighted colimits of diagrams of enriched functors, express weighted colimits\nvia enriched coends, characterize the enriched $\\infty$-category of enriched\npresheaves as the free cocompletion under weighted colimits, prove a\nBousfield-Kan formula for weighted colimits and an enriched adjoint functor\ntheorem and develop a theory of universally adjoining weighted colimits to an\nenriched $\\infty$-category. Via the latter we construct for every presentably\n$\\mathbb{E}_{k+1}$-monoidal $\\infty$-category $\\mathcal{V}$ for $1 \\leq k \\leq\n\\infty$ and set $\\mathcal{H}$ of weights a presentably $\\mathbb{E}_k$-monoidal\nstructure on the $\\infty$-category of $\\mathcal{V}$-enriched\n$\\infty$-categories that admit $\\mathcal{H}$-weighted colimits. Varying\n$\\mathcal{H}$ this $\\mathbb{E}_k$-monoidal structure interpolates between the\ntensor product for $\\mathcal{V}$-enriched $\\infty$-categories and the relative\ntensor product for $\\infty$-categories presentably left tensored over\n$\\mathcal{V}$. Studying functoriality in $\\mathcal{H}$ we deduce that taking\n$\\mathcal{V}$-enriched presheaves is $\\mathbb{E}_k$-monoidal with respect to\nthe tensor product on small $\\mathcal{V}$-enriched $\\infty$-categories and the\nrelative tensor product on $\\infty$-categories presentably left tensored over\n$\\mathcal{V}.$ As key applications we construct for every $n \\geq 1 $ and set\n$\\mathcal{K}$ of $(\\infty, n)$-categories a tensor product for\n$(\\infty,n)$-categories that admit $\\mathcal{K}$-indexed (op)lax colimits, a\ntensor product for Cauchy-complete $\\mathcal{V}$-enriched $\\infty$-categories\nand tensor products for (Cauchy complete) $n$-stable, $n$-additive and\n$n$-preadditive $(\\infty,n)$-categories.\n"", ""On bi-enriched $\\infty$-categories   We extend Lurie's definition of enriched $\\infty$-categories to notions of\nleft enriched, right enriched and bienriched $\\infty$-categories, which\ngeneralize the concepts of closed left tensored, right tensored and bitensored\n$\\infty$-categories and share many desirable features with them. We use\nbienriched $\\infty$-categories to endow the $\\infty$-category of enriched\nfunctors with enrichment that generalizes both the internal hom of the tensor\nproduct of enriched $\\infty$-categories when the latter exists, and the free\ncocompletion under colimits and tensors. As an application we construct\nenriched Kan-extensions from operadic Kan-extensions, compute the monad for\nenriched functors, prove an end formula for morphism objects of enriched\n$\\infty$-categories of enriched functors and a coend formula for the relative\ntensor product of enriched profunctors and construct transfer of enrichment\nfrom scalar extension of presentably bitensored $\\infty$-categories. In\nparticular, we develop an independent theory of enriched $\\infty$-categories\nfor Lurie's model of enriched $\\infty$-categories.\n""]","[('enriched categories', 0.5784633159637451), ('infty categories', 0.5609920024871826), ('monoidal categories', 0.5609633326530457), ('monoidal infty', 0.5506011843681335), ('categories enriched', 0.5311741828918457), ('monoidal category', 0.5300876498222351), ('infty categorical', 0.5235422849655151), ('infty category', 0.5138448476791382), ('functors', 0.48752516508102417), ('adjunctions', 0.474403440952301)]"
5,5,1366,5_randomized kaczmarz_sparse matrix_krylov subspace methods_iterative methods,"['randomized kaczmarz', 'sparse matrix', 'krylov subspace methods', 'iterative methods', 'large sparse', 'low rank approximation', 'subspace methods', 'krylov methods', 'solving linear systems', 'singular value decomposition']","['Parallelization Strategies for the Randomized Kaczmarz Algorithm on\n  Large-Scale Dense Systems   The Kaczmarz algorithm is an iterative technique designed to solve consistent\nlinear systems of equations. It falls within the category of row-action\nmethods, focusing on handling one equation per iteration. This characteristic\nmakes it especially useful in solving very large systems. The recent\nintroduction of a randomized version, the Randomized Kaczmarz method, renewed\ninterest in the algorithm, leading to the development of numerous variations.\nSubsequently, parallel implementations for both the original and Randomized\nKaczmarz method have since then been proposed. However, previous work has\naddressed sparse linear systems, whereas we focus on solving dense systems. In\nthis paper, we explore in detail approaches to parallelizing the Kaczmarz\nmethod for both shared and distributed memory for large dense systems. In\nparticular, we implemented the Randomized Kaczmarz with Averaging (RKA) method\nthat, for inconsistent systems, unlike the standard Randomized Kaczmarz\nalgorithm, reduces the final error of the solution. While efficient\nparallelization of this algorithm is not achievable, we introduce a block\nversion of the averaging method that can outperform the RKA method.\n', 'A Novel Greedy Kaczmarz Method For Solving Consistent Linear Systems   With a quite different way to determine the working rows, we propose a novel\ngreedy Kaczmarz method for solving consistent linear systems. Convergence\nanalysis of the new method is provided. Numerical experiments show that, for\nthe same accuracy, our method outperforms the greedy randomized Kaczmarz method\nand the relaxed greedy randomized Kaczmarz method introduced recently by Bai\nand Wu [Z.Z. BAI AND W.T. WU, On greedy randomized Kaczmarz method for solving\nlarge sparse linear systems, SIAM J. Sci. Comput., 40 (2018), pp. A592--A606;\nZ.Z. BAI AND W.T. WU, On relaxed greedy randomized Kaczmarz methods for solving\nlarge sparse linear systems, Appl. Math. Lett., 83 (2018), pp. 21--26] in term\nof the computing time.\n', 'Mixed Precision Iterative Refinement with Adaptive Precision Sparse\n  Approximate Inverse Preconditioning   Hardware trends have motivated the development of mixed precision algo-rithms\nin numerical linear algebra, which aim to decrease runtime while maintaining\nacceptable accuracy. One recent development is the development of an adaptive\nprecision sparse matrix-vector produce routine, which may be used to accelerate\nthe solution of sparse linear systems by iterative methods. This approach is\nalso applicable to the application of inexact preconditioners, such as sparse\napproximate inverse preconditioners used in Krylov subspace methods. In this\nwork, we develop an adaptive precision sparse approximate inverse\npreconditioner and demonstrate its use within a five-precision GMRES-based\niterative refinement method. We call this algorithm variant BSPAI-GMRES-IR. We\nthen analyze the conditions for the convergence of BSPAI-GMRES-IR, and\ndetermine settings under which BSPAI-GMRES-IR will produce similar backward and\nforward errors as the existing SPAI-GMRES-IR method, the latter of which does\nnot use adaptive precision in preconditioning. Our numerical experiments show\nthat this approach can potentially lead to a reduction in the cost of storing\nand applying sparse approximate inverse preconditioners, although a significant\nreduction in cost may comes at the expense of increasing the number of GMRES\niterations required for convergence.\n']","[('randomized kaczmarz', 0.5546283721923828), ('sparse matrix', 0.5349823236465454), ('krylov subspace methods', 0.5323358178138733), ('iterative methods', 0.5034121870994568), ('large sparse', 0.47312769293785095), ('low rank approximation', 0.45638352632522583), ('subspace methods', 0.4484175145626068), ('krylov methods', 0.43034589290618896), ('solving linear systems', 0.4274519681930542), ('singular value decomposition', 0.4176044464111328)]"
6,6,1125,6_banach lattices_operators banach spaces_banach lattice_banach spaces,"['banach lattices', 'operators banach spaces', 'banach lattice', 'banach spaces', 'banach space', 'spaces banach', 'dimensional banach space', 'operators banach', 'dimensional banach', 'properties banach']","['Unbounded continuous operators and unbounded Banach-Saks property in\n  Banach lattices   Motivated by the equivalent definition of a continuous operator between\nBanach spaces in terms of weakly null nets, we introduce unbounded continuous\noperators by replacing weak convergence with the unbounded absolutely weak\nconvergence ( $uaw$-convergence) in the definition of a continuous operator\nbetween Banach lattices. We characterize order continuous Banach lattices and\nreflexive Banach lattices in terms of these spaces of operators. Moreover,\nmotivated by characterizing of a reflexive Banach lattice in terms of unbounded\nabsolutely weakly Cauchy sequences, we consider pre-unbounded operators between\nBanach lattices which maps $uaw$-Cauchy sequences to weakly ( $uaw$- or norm)\nconvergent sequences. This allows us to characterize $KB$-spaces and reflexive\nspaces in terms of these operators, too. Furthermore, we consider the unbounded\nBanach-Saks property as an unbounded version of the weak Banach-Saks property.\nThere are many considerable relations between spaces possessing the unbounded\nBanach-Saks property with spaces fulfilled by different types of the known\nBanach-Saks property. In particular, we characterize order continuous Banach\nlattices in terms of these relations, as well.\n', 'Free Banach lattices over pre-ordered Banach spaces   We define the free Banach lattice over a pre-ordered Banach space in a\ncategory of Banach lattices of a given convexity type, and show its existence.\nThe subsumption of a pre-ordering necessitates an approach that differs\nfundamentally from the known one for the free Banach lattice over a Banach\nspace under a given convexity condition, which is a special case. The relation\nbetween the free vector lattice over a pre-ordered Banach space and the free\nBanach lattice of a given convexity type over it is made explicit. It is\ndetermined when precisely the free Banach lattice has a canonical realisation\nas a lattice of homogeneous continuous functions on the positive part of the\nunit ball of the dual space. For free $p$-convex Banach lattices with convexity\nconstant 1 over pre-ordered Banach spaces, realisations as function lattices\nare obtained that generalise those for free Banach lattices of that type over\nBanach spaces.\n  A characterisation of $p$-convex Banach lattices in terms of vector lattice\nhomomorphisms into $\\mathrm{L}_p$-spaces or into the real numbers is included.\n', 'On Subspaces of Indecomposable Banach Spaces   We address the following question: what is the class of Banach spaces\nisomorphic to subspaces of indecomposable Banach spaces? We show that this\nclass includes all Banach spaces of density not bigger than the continuum which\ndo not admit $\\ell_\\infty$ as a quotient (equivalently do not admit a subspace\nisomorphic to $\\ell_1(\\cc)$). This includes all Asplund spaces and all weakly\nLindel\\""of determined Banach spaces of density not bigger than the continuum.\nHowever, we also show that this class includes some Banach spaces admitting\n$\\ell_\\infty$ as a quotient. This sheds some light on the question asked in [S.\nArgyros, R. Haydon, \\emph{Bourgain-Delbaen $L^\\infty$-spaces, the\nscalar-plus-compact property and related problems}, Proceedings of the\nInternational Congress of Mathematicians (ICM 2018), Vol. III, 1477--1510. Page\n1502] whether all Banach spaces not containing $\\ell_\\infty$ embed in some\nindecomposable Banach spaces. Our method of constructing indecomposable Banach\nspaces above a given Banach space is a considerable modification of the method\nof constructing Banach spaces of continuous functions with few$^*$ operators\ndeveloped before by the first-named author.\n']","[('banach lattices', 0.7167437672615051), ('operators banach spaces', 0.6922822594642639), ('banach lattice', 0.6896278262138367), ('banach spaces', 0.6819224953651428), ('banach space', 0.6386907696723938), ('spaces banach', 0.6321093440055847), ('dimensional banach space', 0.6247883439064026), ('operators banach', 0.6192137002944946), ('dimensional banach', 0.6020046472549438), ('properties banach', 0.5831128358840942)]"
7,7,1085,7_coloring graphs_edge colorings_vertex coloring_chromatic number graph,"['coloring graphs', 'edge colorings', 'vertex coloring', 'chromatic number graph', 'coloring graph', 'coloring edges', 'edge coloring', 'chromatic number', 'chromatic index', 'chromatic']","['New bounds on the anti-Ramsey numbers of star graphs   The anti-Ramsey number $ar(G,H)$ with input graph $G$ and pattern graph $H$,\nis the maximum positive integer $k$ such that there exists an edge coloring of\n$G$ using $k$ colors, in which there are no rainbow subgraphs isomorphic to $H$\nin $G$. ($H$ is rainbow if all its edges get distinct colors). The concept of\nanti-Ramsey number was introduced by Erd\\""os, Simanovitz, and S\\\'os in 1973.\nThereafter several researchers investigated this concept in the combinatorial\nsetting. Recently, Feng et al. revisited the anti-Ramsey problem for the\npattern graph $K_{1,t}$ (for $t \\geq 3$) purely from an algorithmic point of\nview due to its applications in interference modeling of wireless networks.\nThey posed it as an optimization problem, the maximum edge $q$-coloring\nproblem. For a graph $G$ and an integer $q\\geq 2$, an edge $q$-coloring of $G$\nis an assignment of colors to edges of $G$, such that edges incident on a\nvertex span at most $q$ distinct colors. The maximum edge $q$-coloring problem\nseeks to maximize the number of colors in an edge $q$-coloring of the graph\n$G$. Note that the optimum value of the edge $q$-coloring problem of $G$ equals\n$ar(G,K_{1,q+1})$. In this paper, we study $ar(G,K_{1,t})$, the anti-Ramsey\nnumber of stars, for each fixed integer $t\\geq 3$, both from combinatorial and\nalgorithmic point of view. The first of our main results presents an upper\nbound for $ar(G,K_{1,q+1})$, in terms of number of vertices and the minimum\ndegree of $G$. The second one improves this result for the case of\ntriangle-free input graphs. For a positive integer $t$, let $H_t$ denote a\nsubgraph of $G$ with maximum number of possible edges and maximum degree $t$.\nOur third main result presents an upper bound for $ar(G,K_{1,q+1})$ in terms of\n$|E(H_{q-1})|$. All our results have algorithmic consequences.\n', 'Introduction to dominated edge chromatic number of a graph   We introduce and study the dominated edge coloring of a graph. A dominated\nedge coloring of a graph $G$ is a proper edge coloring of $G$ such that each\ncolor class is dominated by at least one edge of $G$. The minimum number of\ncolors among all dominated edge coloring is called the dominated edge chromatic\nnumber, denoted by $\\chi_{dom}^{\\prime}(G)$. We obtain some properties of\n$\\chi_{dom}^{\\prime}(G)$ and compute it for specific graphs. Also we examine\nthe effects on $\\chi_{dom}^{\\prime}(G)$ when $G$ is modified by operations on\nvertex and edge of $G$. Finally, we consider the $k$-subdivision of $G$ and\nstudy the dominated edge chromatic number of these kind of graphs.\n', 'A polynomial time algorithm to find star chromatic index on bounded\n  treewidth graphs with given maximum degree   A star edge coloring of a graph $G$ is a proper edge coloring with no\n2-colored path or cycle of length four. The star edge coloring problem is to\nfind an edge coloring of a given graph $G$ with minimum number $k$ of colors\nsuch that $G$ admits a star edge coloring with $k$ colors. This problem is\nknown to be NP-complete. In this paper, for a bounded treewidth graph with\ngiven maximum degree, we show that it can be solved in polynomial time.\n']","[('coloring graphs', 0.7209494113922119), ('edge colorings', 0.6942355632781982), ('vertex coloring', 0.6914392709732056), ('chromatic number graph', 0.6857175827026367), ('coloring graph', 0.6821513772010803), ('coloring edges', 0.6717137098312378), ('edge coloring', 0.6575759053230286), ('chromatic number', 0.6307727694511414), ('chromatic index', 0.5741596221923828), ('chromatic', 0.5573487281799316)]"
8,8,1025,8_elliptic equations_laplacian_normalized solutions_state solutions,"['elliptic equations', 'laplacian', 'normalized solutions', 'state solutions', 'ground state solutions', 'positive solutions', 'nonlinearities', 'solutions following', 'elliptic', 'delta lambda']","['Positive normalized solutions of Schr\\""{o}dinger equations with Sobolev critical growth in bounded domains This paper investigates the existence of positive normalized solutions to the Sobolev critical Schr\\""{o}dinger equation: \\begin{equation*} \\left\\{ \\begin{aligned} &-\\Delta u +\\lambda u =|u|^{2^*-2}u \\quad &\\mbox{in}& \\ \\Omega,\\\\ &\\int_{\\Omega}|u|^{2}dx=c, \\quad u=0 \\quad &\\mbox{on}& \\ \\partial\\Omega, \\end{aligned} \\right. \\end{equation*} where $\\Omega\\subset\\mathbb{R}^{N}$ ($N\\geq3$) is a bounded smooth domain, $2^*=\\frac{2N}{N-2}$, $\\lambda\\in \\mathbb{R}$ is a Lagrange multiplier, and $c>0$ is a prescribed constant. By introducing a novel blow-up analysis for Sobolev subcritical approximation solutions with uniformly bounded Morse index and fixed mass, we establish the existence of mountain pass type positive normalized solutions for\n  $N\\ge 3$. This resolves an open problem posed in [Pierotti, Verzini and Yu, SIAM J. Math. Anal. 2025].', 'Multiplicity of normalized solutions for a Schr\\""{o}dinger equation with\n  critical growth in $\\mathbb{R}^{N}$   In this paper we study the multiplicity of normalized solutions to the\nfollowing nonlinear Schr\\""{o}dinger equation with critical growth\n\\begin{align*}\n  \\left\\{ \\begin{aligned} &-\\Delta u=\\lambda u+\\mu |u|^{q-2}u+f(u), \\quad \\quad\n\\hbox{in }\\mathbb{R}^N,\\\\ &\\int_{\\mathbb{R}^{N}}|u|^{2}dx=a^{2}, \\end{aligned}\n\\right. \\end{align*} where $a,\\mu>0$, $\\lambda\\in \\mathbb{R}$ is an unknown\nparameter that appears as a Lagrange multiplier, $q \\in (2,2+\\frac{4}{N})$ and\n$f$ has an exponential critical growth when $N=2$, and $f(u)=|u|^{2^*-2}u$ when\n$N \\geq 3$ and $2^{*}=\\frac{2N}{N-2}$.\n', 'Normalized ground states for a biharmonic Choquard system in\n  $\\mathbb{R}^4$   In this paper, we study the existence of normalized ground state solutions\nfor the following biharmonic Choquard system \\begin{align*}\n  \\begin{split}\n  \\left\\{\n  \\begin{array}{ll}\n  \\Delta^2u=\\lambda_1 u+(I_\\mu*F(u,v))F_u (u,v),\n  \\quad\\mbox{in}\\ \\ \\mathbb{R}^4,\n  \\Delta^2v=\\lambda_2 v+(I_\\mu*F(u,v)) F_v(u,v),\n  \\quad\\mbox{in}\\ \\ \\mathbb{R}^4,\n  \\displaystyle\\int_{\\mathbb{R}^4}|u|^2dx=a^2,\\quad\n\\displaystyle\\int_{\\mathbb{R}^4}|v|^2dx=b^2,\\quad u,v\\in H^2(\\mathbb{R}^4),\n  \\end{array}\n  \\right.\n  \\end{split}\n  \\end{align*} where $a,b>0$ are prescribed, $\\lambda_1,\\lambda_2\\in\n\\mathbb{R}$, $I_\\mu=\\frac{1}{|x|^\\mu}$ with $\\mu\\in (0,4)$, $F_u,F_v$ are\npartial derivatives of $F$ and $F_u,F_v$ have exponential subcritical or\ncritical growth in the sense of the Adams inequality. By using a minimax\nprinciple and analyzing the behavior of the ground state energy with respect to\nthe prescribed mass, we obtain the existence of ground state solutions for the\nabove problem.\n']","[('elliptic equations', 0.4259313642978668), ('laplacian', 0.41863712668418884), ('normalized solutions', 0.3873852491378784), ('state solutions', 0.3728928864002228), ('ground state solutions', 0.3410762548446655), ('positive solutions', 0.3221206068992615), ('nonlinearities', 0.30490800738334656), ('solutions following', 0.2973612844944), ('elliptic', 0.2876700162887573), ('delta lambda', 0.2798498570919037)]"
9,9,1016,9_singular integral operators_maximal operators_integral operators_maximal operator,"['singular integral operators', 'maximal operators', 'integral operators', 'maximal operator', 'weighted lebesgue spaces', 'besov spaces', 'integral operator', 'morrey spaces', 'operators', 'triebel lizorkin spaces']","['Extrapolation for multilinear compact operators and applications   This paper is devoted to studying the Rubio de Francia extrapolation for\nmultilinear compact operators. It allows one to extrapolate the compactness of\n$T$ from just one space to the full range of weighted spaces, whenever an\n$m$-linear operator $T$ is bounded on weighted Lebesgue spaces. This result is\nindeed established in terms of the multilinear Muckenhoupt weights $A_{\\vec{p},\n\\vec{r}}$, and the limited range of the $L^p$ scale. To show extrapolation\ntheorems above, by means of a new weighted Fr\\\'{e}chet-Kolmogorov theorem, we\npresent the weighted interpolation for multilinear compact operators. To prove\nthe latter, we also need to bulid a weighted interpolation theorem in\nmixed-norm Lebesgue spaces. As applications, we obtain the weighted compactness\nof commutators of many multilinear operators, including multilinear\n$\\omega$-Calder\\\'{o}n-Zygmund operators, multilinear Fourier multipliers,\nbilinear rough singular integrals and bilinear Bochner-Riesz means. Beyond\nthat, we establish the weighted compactness of higher order Calder\\\'{o}n\ncommutators, and commutators of Riesz transforms related to Schr\\""{o}dinger\noperators.\n', 'The multilinear Littlewood-Paley square operators and their commutators\n  on weighted Morrey spaces   In this paper, we prove the boundedness of the multilinear Littlewood-Paley\nsquare operators and their commutators on weighted Morrey spaces, then we give\nthe boundedness and weak-type $L\\log L$ estimates for the commutators of\nmultilinear Littlewood-Paley g-functions and multilinear Marcinkiewicz\nintegrals on weighted Morrey spaces in the form of corollaries.\n', ""A class of multilinear bounded oscillation operators on measure spaces\n  and applications   In this paper, we develop a comprehensive weighted theory for a class of\nBanach-valued multilinear bounded oscillation operators on measure spaces,\nwhich merges multilinear Calder\\'{o}n-Zygmund operators with a quantity of\noperators beyond the multilinear Calder\\'{o}n-Zygmund theory. We prove that\nsuch multilinear operators and corresponding commutators are locally pointwise\ndominated by two sparse dyadic operators, respectively. We also establish three\nkinds of typical estimates: local exponential decay estimates, mixed weak type\nestimates, and sharp weighted norm inequalities. Beyond that, based on Rubio de\nFrancia extrapolation for abstract multilinear compact operators, we obtain\nweighted compactness for commutators of specific multilinear operators on\nspaces of homogeneous type. A compact extrapolation allows us to get full range\nof exponents, while weighted interpolation for multilinear compact operators is\ncrucial to the compact extrapolation. These are due to a weighted\nFr\\'{e}chet-Kolmogorov theorem in the quasi-Banach range, which gives a\ncharacterization of relative compactness of subsets in weighted Lebesgue\nspaces. As applications, we illustrate multilinear bounded oscillation\noperators with examples including multilinear Hardy-Littlewood maximal\noperators on measure spaces, multilinear $\\omega$-Calder\\'{o}n-Zygmund\noperators on spaces of homogeneous type, multilinear Littlewood-Paley square\noperators, multilinear Fourier integral operators, higher order Calder\\'{o}n\ncommutators, maximally modulated multilinear singular integrals, and\n$q$-variation of $\\omega$-Calder\\'{o}n-Zygmund operators.\n""]","[('singular integral operators', 0.5150975584983826), ('maximal operators', 0.5139108896255493), ('integral operators', 0.5090199708938599), ('maximal operator', 0.4837888479232788), ('weighted lebesgue spaces', 0.4723037779331207), ('besov spaces', 0.4702804982662201), ('integral operator', 0.4377456307411194), ('morrey spaces', 0.43089646100997925), ('operators', 0.42896440625190735), ('triebel lizorkin spaces', 0.4198434054851532)]"
10,10,993,10_persistent homology_homology persistent_persistence diagrams_persistence diagram,"['persistent homology', 'homology persistent', 'persistence diagrams', 'persistence diagram', 'persistence modules', 'space persistence', 'persistent', 'persistence', 'persistence module', 'topological information']","['Persistent Homology and Applied Homotopy Theory   This paper is a survey of persistent homology, primarily as it is used in\ntopological data analysis. It includes the theory of persistence modules, as\nwell as stability theorems for persistence barcodes, generalized persistence,\nvectorization of persistence barcodes, as well as some applications.\n', 'Approximating Persistent Homology for Large Datasets   Persistent homology is an important methodology from topological data\nanalysis which adapts theory from algebraic topology to data settings and has\nbeen successfully implemented in many applications. It produces a statistical\nsummary in the form of a persistence diagram, which captures the shape and size\nof the data. Despite its widespread use, persistent homology is simply\nimpossible to implement when a dataset is very large. In this paper we address\nthe problem of finding a representative persistence diagram for prohibitively\nlarge datasets. We adapt the classical statistical method of bootstrapping,\nnamely, drawing and studying smaller multiple subsamples from the large\ndataset. We show that the mean of the persistence diagrams of subsamples --\ntaken as a mean persistence measure computed from the subsamples -- is a valid\napproximation of the true persistent homology of the larger dataset. We give\nthe rate of convergence of the mean persistence diagram to the true persistence\ndiagram in terms of the number of subsamples and size of each subsample. Given\nthe complex algebraic and geometric nature of persistent homology, we adapt the\nconvexity and stability properties in the space of persistence diagrams\ntogether with random set theory to achieve our theoretical results for the\ngeneral setting of point cloud data. We demonstrate our approach on simulated\nand real data, including an application of shape clustering on complex\nlarge-scale point cloud data.\n', 'Persistent Homology Analysis for Materials Research and Persistent\n  Homology Software: HomCloud   This paper introduces persistent homology, which is a powerful tool to\ncharacterize the shape of data using the mathematical concept of topology. We\nexplain the fundamental idea of persistent homology from scratch using some\nexamples. We also review some applications of persistent homology to materials\nresearches and software for persistent homology data analysis. HomCloud, one of\npersistent homology software, is especially featured in this paper.\n']","[('persistent homology', 0.7719906568527222), ('homology persistent', 0.744110107421875), ('persistence diagrams', 0.7337721586227417), ('persistence diagram', 0.699025571346283), ('persistence modules', 0.6252869367599487), ('space persistence', 0.5914064049720764), ('persistent', 0.5803965330123901), ('persistence', 0.5683341026306152), ('persistence module', 0.5662754774093628), ('topological information', 0.5057733058929443)]"
11,11,865,11_physics informed neural_neural networks solving_neural networks pinns_neural network pinn,"['physics informed neural', 'neural networks solving', 'neural networks pinns', 'neural network pinn', 'informed neural networks', 'neural operators', 'operator networks', 'neural networks', 'informed neural network', 'deep learning']","['Physics-Informed Neural Networks for Solving Forward and Inverse PDEs\n  with Limited and Noisy Data: Application to Solar Corona Modeling   I will demonstrate the effectiveness of Physics-Informed Neural Networks\n(PINNs) in solving partial differential equations (PDEs) when training data are\nscarce or noisy. The training data can be located either at the boundaries or\nwithin the domain. Additionally, PINNs can be used as an inverse method to\ndetermine unknown coefficients in the equations. This study will highlight the\napplication of PINNs in modeling magnetohydrodynamic processes relevant to\nstrongly magnetized plasmas, such as those found in the solar corona.\n', 'Operator Learning Enhanced Physics-informed Neural Networks for Solving\n  Partial Differential Equations Characterized by Sharp Solutions   Physics-informed Neural Networks (PINNs) have been shown as a promising\napproach for solving both forward and inverse problems of partial differential\nequations (PDEs). Meanwhile, the neural operator approach, including methods\nsuch as Deep Operator Network (DeepONet) and Fourier neural operator (FNO), has\nbeen introduced and extensively employed in approximating solution of PDEs.\nNevertheless, to solve problems consisting of sharp solutions poses a\nsignificant challenge when employing these two approaches. To address this\nissue, we propose in this work a novel framework termed Operator Learning\nEnhanced Physics-informed Neural Networks (OL-PINN). Initially, we utilize\nDeepONet to learn the solution operator for a set of smooth problems relevant\nto the PDEs characterized by sharp solutions. Subsequently, we integrate the\npre-trained DeepONet with PINN to resolve the target sharp solution problem. We\nshowcase the efficacy of OL-PINN by successfully addressing various problems,\nsuch as the nonlinear diffusion-reaction equation, the Burgers equation and the\nincompressible Navier-Stokes equation at high Reynolds number. Compared with\nthe vanilla PINN, the proposed method requires only a small number of residual\npoints to achieve a strong generalization capability. Moreover, it\nsubstantially enhances accuracy, while also ensuring a robust training process.\nFurthermore, OL-PINN inherits the advantage of PINN for solving inverse\nproblems. To this end, we apply the OL-PINN approach for solving problems with\nonly partial boundary conditions, which usually cannot be solved by the\nclassical numerical methods, showing its capacity in solving ill-posed problems\nand consequently more complex inverse problems.\n', '$PINN - a Domain Decomposition Method for Bayesian Physics-Informed\n  Neural Networks   Physics-Informed Neural Networks (PINNs) are a novel computational approach\nfor solving partial differential equations (PDEs) with noisy and sparse initial\nand boundary data. Although, efficient quantification of epistemic and\naleatoric uncertainties in big multi-scale problems remains challenging. We\npropose \\$PINN a novel method of computing global uncertainty in PDEs using a\nBayesian framework, by combining local Bayesian Physics-Informed Neural\nNetworks (BPINN) with domain decomposition. The solution continuity across\nsubdomains is obtained by imposing the flux continuity across the interface of\nneighboring subdomains. To demonstrate the effectiveness of \\$PINN, we conduct\na series of computational experiments on PDEs in 1D and 2D spatial domains.\nAlthough we have adopted conservative PINNs (cPINNs), the method can be\nseamlessly extended to other domain decomposition techniques. The results infer\nthat the proposed method recovers the global uncertainty by computing the local\nuncertainty exactly more efficiently as the uncertainty in each subdomain can\nbe computed concurrently. The robustness of \\$PINN is verified by adding\nuncorrelated random noise to the training data up to 15% and testing for\ndifferent domain sizes.\n']","[('physics informed neural', 0.5689100623130798), ('neural networks solving', 0.5453101992607117), ('neural networks pinns', 0.5199720859527588), ('neural network pinn', 0.507737398147583), ('informed neural networks', 0.46342530846595764), ('neural operators', 0.43872472643852234), ('operator networks', 0.43652039766311646), ('neural networks', 0.4260292053222656), ('informed neural network', 0.4212857186794281), ('deep learning', 0.4172765016555786)]"
12,12,864,12_eigenvalue adjacency_eigenvalue adjacency matrix_eigenvalue graph_maximum spectral radius,"['eigenvalue adjacency', 'eigenvalue adjacency matrix', 'eigenvalue graph', 'maximum spectral radius', 'maximum spectral', 'spectral graph', 'spectral radius among', 'alpha spectral', 'spectral radius', 'laplacian spectral radius']","[""On the eigenvalues and energy of the $A_\\alpha$-matrix of graphs   For a graph $G$, the generalized adjacency matrix $A_\\alpha(G)$ is the convex\ncombination of the diagonal matrix $D(G)$ and the adjacency matrix $A(G)$ and\nis defined as $A_\\alpha(G)=\\alpha D(G)+(1-\\alpha) A(G)$ for $0\\leq \\alpha \\leq\n1$. This matrix has been found to be useful in merging the spectral theories of\n$A(G)$ and the signless Laplacian matrix $Q(G)$ of the graph $G$. The\ngeneralized adjacency energy or $A_\\alpha$-energy is the mean deviation of the\n$A_\\alpha$-eigenvalues of $G$ and is defined as\n$E(A_\\alpha(G))=\\sum_{i=1}^{n}|p_i-\\frac{2\\alpha m}{n}|$, where $p_i$'s are\n$A_\\alpha$-eigenvalues of $G$. In this paper, we investigate the\n$A_\\alpha$-eigenvalues of a strongly regular graph $G$. We observe that\n$A_\\alpha$-spectral radius $p_1$ satisfies $\\delta(G)\\leq p_1 \\leq \\Delta(G)$,\nwhere $\\delta(G)$ and $\\Delta(G)$ are, respectively, the smallest and the\nlargest degrees of $G$. Further, we show that the complete graph is the only\ngraph to have exactly two distinct $A_\\alpha$-eigenvalues. We obtain lower and\nupper bounds of $A_\\alpha$-energy in terms of order, size and extremal degrees\nof $G$. We also discuss the extremal cases of these bounds.\n"", 'On the sum of the largest $A_{\\alpha}$-eigenvalues of graphs   For every real $0\\leq \\alpha \\leq 1$, Nikiforov defined the\n$A_{\\alpha}$-matrix of a graph $G$ as $A_{\\alpha}(G)=\\alpha\nD(G)+(1-\\alpha)A(G)$, where $A(G)$ and $D(G)$ are the adjacency matrix and the\ndegree diagonal matrix of a graph $G$, respectively. The eigenvalues of\n$A_{\\alpha}(G)$ are called the $A_{\\alpha}$-eigenvalues of $G$. Let\n$S_k(A_{\\alpha}(G))$ be the sum of $k$ largest $A_{\\alpha}$-eigenvalues of $G$.\nIn this paper, we present several upper and lower bounds on\n$S_k(A_{\\alpha}(G))$ and characterize the extremal graphs for certain cases,\nwhich can be regard as a common generalization of the sum of $k$ largest\neigenvalues of adjacency matrix and signless Laplacian matrix of graphs. In\naddition, some graph operations on $S_k(A_{\\alpha}(G))$ are presented.\n', 'The $A_\\alpha$ spectral radius with given independence number $n-4$   Let $G$ be a graph with adjacency matrix $A(G)$ and degree diagonal matrix $D\n(G)$. In 2017, Nikiforov [Appl. Anal. Discrete Math., 11 (2017) 81--107]\ndefined the matrix $A_\\alpha(G) = \\alpha D(G) + (1-\\alpha)A(G)$ for any real\n$\\alpha\\in[0,1]$. The largest eigenvalue of $A(G)$ is called the spectral\nradius of $G$, while the largest eigenvalue of $A_\\alpha(G)$ is called the\n$A_\\alpha$ spectral radius of $G$. Let $\\mathcal{G}_{n,i}$ be the set of graphs\nof order $n$ with independence number $i$. Recently, for all graphs in\n$\\mathcal{G}_{n,i}$ having the minimum or the maximum $A$, $Q$ and $A_\\alpha$\nspectral radius where\n$i\\in\\{1,2,\\lfloor\\frac{n}{2}\\rfloor\\,\\lceil\\frac{n}{2}\\rceil+1,n-3,n-2,n-1\\}$,\nthere are some results have been given by Xu, Li and Sun et al., respectively.\nIn 2021, Luo and Guo [Discrete Math., 345 (2022) 112778] determined all graphs\nin $\\mathcal{G}_{n,n-4}$ having the minimum spectral radius. In this paper, we\ncharacterize the graphs in $\\mathcal{G}_{n,n-4}$ having the minimum and the\nmaximum $A_\\alpha$ spectral radius for $\\alpha\\in[\\frac{1}{2},1)$,\nrespectively.\n']","[('eigenvalue adjacency', 0.5817904472351074), ('eigenvalue adjacency matrix', 0.5783923864364624), ('eigenvalue graph', 0.5597145557403564), ('maximum spectral radius', 0.553380012512207), ('maximum spectral', 0.5523805618286133), ('spectral graph', 0.5423811078071594), ('spectral radius among', 0.5341256856918335), ('alpha spectral', 0.5182501673698425), ('spectral radius', 0.5051199197769165), ('laplacian spectral radius', 0.49834445118904114)]"
13,13,844,13_iterative regularization_total variation regularization_variation regularization_regularization methods,"['iterative regularization', 'total variation regularization', 'variation regularization', 'regularization methods', 'variational regularization', 'image reconstruction', 'image restoration', 'regularization', 'regularization parameters', 'reconstruction methods']","['Feature reconstruction from incomplete tomographic data without detour   In this paper, we consider the problem of feature reconstruction from\nincomplete x-ray CT data. Such problems occurs, e.g., as a result of dose\nreduction in the context medical imaging. Since image reconstruction from\nincomplete data is a severely ill-posed problem, the reconstructed images may\nsuffer from characteristic artefacts or missing features, and significantly\ncomplicate subsequent image processing tasks (e.g., edge detection or\nsegmentation). In this paper, we introduce a novel framework for the robust\nreconstruction of convolutional image features directly from CT data, without\nthe need of computing a reconstruction firs. Within our framework we use\nnon-linear (variational) regularization methods that can be adapted to a\nvariety of feature reconstruction tasks and to several limited data situations\n. In our numerical experiments, we consider several instances of edge\nreconstructions from angularly undersampled data and show that our approach is\nable to reliably reconstruct feature maps in this case.\n', 'Convergent regularization in inverse problems and linear plug-and-play\n  denoisers   Plug-and-play (PnP) denoising is a popular iterative framework for solving\nimaging inverse problems using off-the-shelf image denoisers. Their empirical\nsuccess has motivated a line of research that seeks to understand the\nconvergence of PnP iterates under various assumptions on the denoiser. While a\nsignificant amount of research has gone into establishing the convergence of\nthe PnP iteration for different regularity conditions on the denoisers, not\nmuch is known about the asymptotic properties of the converged solution as the\nnoise level in the measurement tends to zero, i.e., whether PnP methods are\nprovably convergent regularization schemes under reasonable assumptions on the\ndenoiser. This paper serves two purposes: first, we provide an overview of the\nclassical regularization theory in inverse problems and survey a few notable\nrecent data-driven methods that are provably convergent regularization schemes.\nWe then continue to discuss PnP algorithms and their established convergence\nguarantees. Subsequently, we consider PnP algorithms with linear denoisers and\npropose a novel spectral filtering technique to control the strength of\nregularization arising from the denoiser. Further, by relating the implicit\nregularization of the denoiser to an explicit regularization functional, we\nrigorously show that PnP with linear denoisers leads to a convergent\nregularization scheme. More specifically, we prove that in the limit as the\nnoise vanishes, the PnP reconstruction converges to the minimizer of a\nregularization potential subject to the solution satisfying the noiseless\noperator equation. The theoretical analysis is corroborated by numerical\nexperiments for the classical inverse problem of tomographic image\nreconstruction.\n', 'Plug-and-Play image reconstruction is a convergent regularization method   Non-uniqueness and instability are characteristic features of image\nreconstruction processes. As a result, it is necessary to develop\nregularization methods that can be used to compute reliable approximate\nsolutions. A regularization method provides of a family of stable\nreconstructions that converge to an exact solution of the noise-free problem as\nthe noise level tends to zero. The standard regularization technique is defined\nby variational image reconstruction, which minimizes a data discrepancy\naugmented by a regularizer. The actual numerical implementation makes use of\niterative methods, often involving proximal mappings of the regularizer. In\nrecent years, Plug-and-Play image reconstruction (PnP) has been developed as a\nnew powerful generalization of variational methods based on replacing proximal\nmappings by more general image denoisers. While PnP iterations yield excellent\nresults, neither stability nor convergence in the sense of regularization has\nbeen studied so far. In this work, we extend the idea of PnP by considering\nfamilies of PnP iterations, each being accompanied by its own denoiser. As our\nmain theoretical result, we show that such PnP reconstructions lead to stable\nand convergent regularization methods. This shows for the first time that PnP\nis mathematically equally justified for robust image reconstruction as\nvariational methods\n']","[('iterative regularization', 0.6654669642448425), ('total variation regularization', 0.6452040672302246), ('variation regularization', 0.6424564123153687), ('regularization methods', 0.6273462176322937), ('variational regularization', 0.6228638887405396), ('image reconstruction', 0.6172869801521301), ('image restoration', 0.6093907952308655), ('regularization', 0.5960000157356262), ('regularization parameters', 0.577573835849762), ('reconstruction methods', 0.5735197067260742)]"
14,14,813,14_hermitian random matrices_random matrix theory_hermitian random_random matrix ensembles,"['hermitian random matrices', 'random matrix theory', 'hermitian random', 'random matrix ensembles', 'unitary ensemble', 'random matrices', 'spectral statistics', 'spectral distribution', 'gaussian unitary', 'empirical spectral distribution']","[""Towards the bulk universality of non-Hermitian random matrices   We consider the non-Hermitian analogue of the celebrated Wigner-Dyson-Mehta\nbulk universality phenomenon, i.e. that in the bulk the local eigenvalue\nstatistics of a large random matrix with independent, identically distributed\ncentred entries are universal, in particular they asymptotically coincide with\nthose of the Ginibre ensemble in the corresponding symmetry class. In this\npaper we reduce this problem to understanding a certain microscopic regime for\nthe Hermitized resolvent in Girko's formula by showing that all other regimes\nare negligible.\n"", 'Edge Universality for non-Hermitian Random Matrices   We consider large non-Hermitian real or complex random matrices $X$ with\nindependent, identically distributed centred entries. We prove that their local\neigenvalue statistics near the spectral edge, the unit circle, coincide with\nthose of the Ginibre ensemble, i.e. when the matrix elements of $X$ are\nGaussian. This result is the non-Hermitian counterpart of the universality of\nthe Tracy-Widom distribution at the spectral edges of the Wigner ensemble.\n', 'Universal eigenvector correlations in quaternionic Ginibre ensembles   Non-Hermitian random matrices enjoy non-trivial correlations in the\nstatistics of their eigenvectors. We study the overlap among left and right\neigenvectors in Ginibre ensembles with quaternion valued Gaussian matrix\nelements. This concept was introduced by Chalker and Mehlig in the complex\nGinibre ensemble. Using a Schur decomposition, for harmonic potentials we can\nexpress the overlap in terms of complex eigenvalues only, coming in conjugate\npairs in this symmetry class. Its expectation value leads to a Pfaffian\ndeterminant, for which we explicitly compute the matrix elements for the\ninduced Ginibre ensemble with $2\\alpha$ zero eigenvalues, for finite matrix\nsize $N$. In the macroscopic large-$N$ limit in the bulk of the spectrum we\nrecover the limiting expressions of the complex Ginibre ensemble for the\ndiagonal and off-diagonal overlap, which are thus universal.\n']","[('hermitian random matrices', 0.6939499378204346), ('random matrix theory', 0.62031489610672), ('hermitian random', 0.5967514514923096), ('random matrix ensembles', 0.5674776434898376), ('unitary ensemble', 0.549867570400238), ('random matrices', 0.5347515940666199), ('spectral statistics', 0.530767023563385), ('spectral distribution', 0.5011853575706482), ('gaussian unitary', 0.4785281717777252), ('empirical spectral distribution', 0.4635581970214844)]"
15,15,778,15_minimal surface_minimal surfaces_minimal hypersurfaces_minimal hypersurface,"['minimal surface', 'minimal surfaces', 'minimal hypersurfaces', 'minimal hypersurface', 'curvature hypersurfaces', 'curvature surfaces', 'mean curvature hypersurfaces', 'boundary minimal', 'surfaces euclidean space', 'surfaces euclidean']","[""Contributions to the theory of free boundary minimal surfaces   In this thesis, we present various contributions to the study of free\nboundary minimal surfaces. After introducing some basic tools and discussing\nsome delicate aspects related to the definition of Morse index when allowing\nfor a contact set, we divide the thesis in two parts. In the first part of this\ndissertation, we study free boundary minimal surfaces with bounded Morse index\nin a three-dimensional ambient manifold. More specifically, we present a\ndegeneration analysis of a sequence of such surfaces, proving that (up to\nsubsequence) they converge smoothly away from finitely many points and that,\naround such `bad' points, we can at least `uniformly' control the topology and\nthe area of the surfaces in question. As a corollary, we obtain a complete\npicture of the way different `complexity criteria' (in particular: topology,\narea and Morse index) compare for free boundary minimal surfaces in ambient\nmanifolds with positive scalar curvature and mean convex boundary. In the\nsecond part, we focus on an equivariant min-max scheme to prove the existence\nof free boundary minimal surfaces with a prescribed topological type. The\nprinciple is to choose a suitable group of isometries of the ambient manifold\nin order to obtain exactly the topology we are looking for. We recall a proof\nof the equivariant min-max theorem, and we also prove a bound on the Morse\nindex of the resulting surfaces. Finally, we apply this procedure to show the\nexistence of a new family of free boundary minimal surfaces with connected\nboundary and arbitrary genus in the three-dimensional unit ball.\n"", 'On free boundary minimal hypersurfaces in the Riemannian Schwarzschild\n  space   In contrast with the 3-dimensional case (cf. \\cite{RaMo}), where rotationally\nsymmetric totally geodesic free boundary minimal surfaces have Morse index one;\nwe prove in this work that the Morse index of a free boundary rotationally\nsymmetric totally geodesic hypersurface of the $n$-dimensional Riemannnian\nSchwarzschild space with respect to variations that are tangential along the\nhorizon is zero, for $n\\geq4$.\n  Moreover, we show that there exist non-compact free boundary minimal\nhypersurfaces which are not totally geodesic, $n\\geq 8$, with Morse index equal\nto $0$. Also, it is shown that, for $n\\geq4$, there exist infinitely many\nnon-compact free boundary minimal hypersurfaces, which are not congruent to\neach other, with infinite Morse index.\n  We also study the density at infinity of a free boundary minimal hypersurface\nwith respect to a minimal cone constructed over a minimal hypersurface of the\nunit Euclidean sphere. We obtain a lower bound for the density in terms of the\narea of the boundary of the hypersurface and the area of the minimal\nhypersurface in the unit sphere. This lower bound is optimal in the sense that\nonly minimal cones achieve it.\n', 'Geodesic boundary of constant mean curvature surfaces in\n  $\\mathbb{H}^2\\times \\mathbb{R}$   Some results about the geodesic boundary of minimal surfaces in\n$\\mathbb{H}^2\\times \\mathbb{R}$ are generalized for surfaces of constant mean\ncurvature surfaces $H$, with $0\\le H\\le 1/2$.\n']","[('minimal surface', 0.6928406357765198), ('minimal surfaces', 0.6897007822990417), ('minimal hypersurfaces', 0.6710419058799744), ('minimal hypersurface', 0.6568589806556702), ('curvature hypersurfaces', 0.6564315557479858), ('curvature surfaces', 0.6536926031112671), ('mean curvature hypersurfaces', 0.6350403428077698), ('boundary minimal', 0.6231570243835449), ('surfaces euclidean space', 0.5849295258522034), ('surfaces euclidean', 0.5756801962852478)]"
16,16,760,16_electricity market_electricity markets_energy storage_renewable energy,"['electricity market', 'electricity markets', 'energy storage', 'renewable energy', 'optimal power flow', 'distributed energy resources', 'ac optimal power', 'bidding', 'microgrids', 'economic dispatch']","['Strategic Bidding in Electricity Markets with Convexified AC\n  Market-Clearing Process   This paper presents a framework to solve the strategic bidding problem of\nparticipants in an electricity market cleared by employing the full AC Optimal\nPower Flow (ACOPF) problem formulation. Traditionally, the independent system\noperators (ISOs) leveraged DC Optimal Power Flow (DCOPF) problem formulation to\nsettle the electricity market. The main quest of this work is to find what\nwould be the challenges and opportunities if ISOs leverage the full ACOPF as\nthe market-clearing Problem (MCP)? This paper presents tractable mathematical\nprogramming with equilibrium constraints for the convexified AC market-clearing\nproblem. Market participants maximize their profit via strategic bidding while\nconsidering the reactive power dispatch of generation units. The equilibrium\nconstraints are procured by presenting the dual form of the relaxed ACOPF\nproblem. The strategic bidding problem with ACOPF-based MCP improves the\nexactness of the location marginal prices (LMPs) and profit of market\nparticipants compared to the one with DCOPF. It is shown that the strategic\nbidding problem with DCOFP-based MCP is unable to model the limitations of\nreactive power support. The presented results display cases where the proposed\nstrategic bidding method renders $52.3\\%$ more profit for the Generation\nCompany (GENCO) than the DCOPF-based MCP model. The proposed strategic bidding\nframework also addresses the challenges in coupling real and reactive power\ndispatch of generation constraints, ramping constraints, demand response\nimplications with curtailable and time shiftable loads, and AC line flow\nconstraints. Therefore, the presented method will help market participants\nleverage the more accurate ACOPF model in the strategic bidding problem.\n', 'Electricity Market Bidding for Renewable Electrolyzer Plants: An\n  Opportunity Cost Approach   Hydrogen produced through electrolysis with renewable power is considered key\nto decarbonize several hard-to-electrify sectors. This work proposes a novel\napproach to model the active electricity market participation of co-located\nrenewable energy and electrolyzer plants, based on opportunity-cost bidding.\nWhile a renewable energy plant typically has zero marginal cost, selling power\nto the grid carries a potential opportunity-cost of not producing hydrogen when\nit is co-located with a hydrogen electrolyzer. We first consider only the\nelectrolyzer, and derive its revenue of consuming electricity based on the\nnon-convex hydrogen production curve. We then consider the available renewable\nenergy production and form a piece-wise linear cost curve representing the\nopportunity cost of selling (or revenue from consuming) various levels of\nelectricity. This cost curve can be used to model a stand-alone electrolyzer or\na co-located hydrogen and renewable energy plant participating in an\nelectricity market. Our case study analyzes the effects of market-bidding\nelectrolyzers on electricity markets and grid operations. We compare two\nstrategies for a co-located electrolyzer-wind plant; one based on the proposed\nbid curve and one with a more conventional fixed electrolyzer consumption. The\nresults show that electrolyzers that actively participate in the electricity\nmarket lower the average cost of electricity and the amount of curtailed\nrenewable energy in the system compared with a fixed consumption case. However,\nthe difference in total system emissions between the two strategies is\ninsignificant. The specific impacts vary based on electrolyzer capacity and\nhydrogen price, which determines the location of the co-located plant in the\nelectricity market merit order.\n', 'Towards Low-carbon Power Networks: Optimal Integration of Renewable\n  Energy Sources and Hydrogen Storage   This paper proposes a new optimization model and solution method for\ndetermining optimal locations and sizing of renewable energy sources and\nhydrogen storage in a power network. We obtain these strategic decisions based\non the multi-period alternating current optimal power (AC OPF) flow problem\nthat considers the uncertainty of renewable output, electricity demand, and\nelectricity prices. We develop a second-order cone programming approach within\na Benders decomposition framework to provide globally optimal solutions. To the\nbest of our knowledge, our paper is the first to propose a systematic\noptimization framework based on AC OPF that jointly analyzes power network,\nrenewable, and hydrogen storage interactions in order to provide optimal\nlocations and sizing decisions of renewables and hydrogen storage. In a test\ncase, we show that the joint integration of renewable sources and hydrogen\nstorage and consideration of the AC OPF model significantly reduces the\noperational cost of the power network. In turn, our findings can provide\nquantitative insights to decision-makers on how to integrate renewable sources\nand hydrogen storage under different settings of the hydrogen selling price,\nrenewable curtailment costs, emission tax prices, and conversion efficiency.\n']","[('electricity market', 0.6624227166175842), ('electricity markets', 0.6622233390808105), ('energy storage', 0.511863648891449), ('renewable energy', 0.487198144197464), ('optimal power flow', 0.48545706272125244), ('distributed energy resources', 0.466025173664093), ('ac optimal power', 0.43247517943382263), ('bidding', 0.4297572672367096), ('microgrids', 0.427568644285202), ('economic dispatch', 0.4235292077064514)]"
17,17,756,17_prime gaps_number primes_prime conjecture_goldbach conjecture,"['prime gaps', 'number primes', 'prime conjecture', 'goldbach conjecture', 'primes arithmetic progressions', 'prime numbers', 'number prime', 'primes', 'prime counting', 'almost primes']","['The ternary Goldbach problem with a prime with a missing digit and\n  primes of special types   Let $$\\gamma^*:=\\frac{8}{9}+\\frac{2}{3}\\:\\frac{\\log(10/9)}{\\log 10}\\:(\\approx\n0.919\\ldots)\\:,\\ \\gamma^*<\\frac{1}{c_0}\\leq 1\\:.$$\n  Let $\\gamma^*<\\gamma_0\\leq 1$, $c_0=1/\\gamma_0$ be fixed. Let also\n$a_0\\in\\{0,1,\\ldots, 9\\}$. In [23] we proved on assumption of the Generalized\nRiemann Hypothesis (GRH), that each sufficiently large odd integer $N_0$ can be\nrepresented in the form $$N_0=p_1+p_2+p_3\\:,$$ where for $i=2, 3$ the primes\n$p_i$ are Piatetski-Shapiro primes - primes of the form $p_i=[n_i^{c_0}]$,\n$n_i\\in\\mathbb{N}$ - whereas the decimal expansion of $p_1$ does not contain\nthe digit $a_0$. In this paper we replace one of the Piatetski-Shapiro primes\n$p_2$ and $p_3$ by primes of the type $$p=x^2+y^2+1\\:.$$\n', 'The importance of finding the upper bounds for prime gaps in order to\n  solve the twin primes conjecture and the Goldbach conjecture   ABSTRACT. In this article we present a point of view that highlights the\nimportance of finding the upper bounds for prime gaps, in order to solve the\ntwin primes conjecture and the Goldbach conjecture. For this purpose, we\npresent a procedure for the determination of the upper bounds for prime gaps\ndifferent from the most famous and known approaches. The proposed method\nanalyzes the distribution of prime numbers using the set of relative numbers.\nUsing negative numbers too, it becomes intuitive to understand that that the\narrangement of 2P+1 consecutive numbers that goes -P to P, is the only\narrangement that minimizes the distance between two powers having the same\nabsolute value of the base D, with |D|<=P. This arrangement is considered\nimportant because by increasing the number of powers of the prime numbers\nwithin a range of consecutive numbers, it is presumed to decrease the overlap\nbetween the prime numbers considered. Consequently, by reducing these overlaps,\nwe suppose to obtain an arrangement, in which the prime numbers less than and\nequal to P and their multiples occupy the greatest possible number of positions\nwithin a range of 2P+1 consecutive numbers. If this result could be\ndemonstrated, would imply not only the resolution of the Legendre conjecture,\nbut also a step forward in the resolution of the twin primes conjecture and the\nGoldbach conjecture.\n', 'The prime number theorem for primes in arithmetic progressions at large\n  values   Assuming the Riemann hypothesis, we prove the latest explicit version of the\nprime number theorem for short intervals. Using this result, and assuming the\ngeneralised Riemann hypothesis for Dirichlet $L$-functions is true, we then\nestablish explicit formulae for $\\psi(x,\\chi)$, $\\theta(x,\\chi)$, and an\nexplicit version of the prime number theorem for primes in arithmetic\nprogressions that hold for general moduli $q\\geq 3$. Finally, we restrict our\nattention to $q\\leq 10\\,000$ and use an exact computation to refine these\nresults.\n']","[('prime gaps', 0.6675330996513367), ('number primes', 0.6480919122695923), ('prime conjecture', 0.6419015526771545), ('goldbach conjecture', 0.6226076483726501), ('primes arithmetic progressions', 0.6190563440322876), ('prime numbers', 0.605564534664154), ('number prime', 0.5766497254371643), ('primes', 0.5702134966850281), ('prime counting', 0.5620697140693665), ('almost primes', 0.5605617165565491)]"
18,18,754,18_epidemic models_epidemic dynamics_covid 19 pandemic_covid 19,"['epidemic models', 'epidemic dynamics', 'covid 19 pandemic', 'covid 19', 'spread covid 19', 'disease dynamics', 'spread covid', 'covid', '19 pandemic', 'epidemic']","['A novel analysis approach of uniform persistence for a COVID-19 model\n  with quarantine and standard incidence rate   A coronavirus disease 2019 (COVID-19) model with quarantine and standard\nincidence rate is first developed, then a novel analysis approach for finding\nthe ultimate lower bound of COVID-19 infectious individuals is proposed, which\nmeans that the COVID-19 pandemic is uniformly persistent if the control\nreproduction number $\\mathcal{R}_{c}>1$. This approach can be applied to other\nrelated biomathematical models, and some existing works can be improved by\nusing it. In addition, the COVID-19-free equilibrium $V^0$ is locally\nasymptotically stable (LAS) if $\\mathcal{R}_{c}<1$ and linearly stable if\n$\\mathcal{R}_{c}=1$, respectively; while $V^0$ is unstable if\n$\\mathcal{R}_{c}>1$.\n', 'Analysis of COVID-19 Infection Dynamics: Extended SIR Model Approach This paper presents a detailed mathematical investigation into the dynamics of COVID-19 infections through extended Susceptible-Infected-Recovered (SIR) and Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological models. By incorporating demographic factors such as birth and death rates, we enhance the classical Kermack-McKendrick framework to realistically represent long-term disease progression. Using empirical data from four COVID-19 epidemic waves in Orange County, California, between January 2020 and March 2022, we estimate key parameters and perform stability and bifurcation analyses. Our results consistently indicate endemic states characterized by stable spiral equilibria due to reproduction numbers (R0) exceeding unity across all waves. Additionally, the inclusion of vaccination demonstrates the potential to reduce the effective reproduction number below one, shifting the system towards a stable disease-free equilibrium. Our analysis underscores the critical role of latency periods in shaping epidemic dynamics and highlights actionable insights for public health interventions aimed at COVID-19 control and eventual eradication.', 'Dynamics of COVID-19 models with asymptomatic infections and quarantine\n  measures   Considering the propagation characteristics of COVID-19 in different regions,\nthe dynamics analysis and numerical demonstration of long-term and short-term\nmodels of COVID-19 are carried out, respectively. The long-term model is\ndevoted to investigate the global stability of COVID-19 model with asymptomatic\ninfections and quarantine measures. By using the limit system of the model and\nLyapunov function method, it is shown that the COVID-19-free equilibrium $V^0$\nis globally asymptotically stable if the control reproduction number\n$\\mathcal{R}_{c}<1$ and globally attractive if $\\mathcal{R}_{c}=1$, which means\nthat COVID-19 will die out; the COVID-19 equilibrium $V^{\\ast}$ is globally\nasymptotically stable if $\\mathcal{R}_{c}>1$, which means that COVID-19 will be\npersistent. In particular, to obtain the local stability of $V^{\\ast}$, we use\nproof by contradiction and the properties of complex modulus with some novel\ndetails, and we prove the weak persistence of the system to obtain the global\nattractivity of $V^{\\ast}$. Moreover, the final size of the corresponding\nshort-term model is calculated and the stability of its multiple equilibria is\nanalyzed. Numerical simulations of COVID-19 cases show that quarantine measures\nand asymptomatic infections have a non-negligible impact on the transmission of\nCOVID-19.\n']","[('epidemic models', 0.6135826110839844), ('epidemic dynamics', 0.5887249112129211), ('covid 19 pandemic', 0.5673967599868774), ('covid 19', 0.5290824174880981), ('spread covid 19', 0.5087593793869019), ('disease dynamics', 0.46155285835266113), ('spread covid', 0.4544823169708252), ('covid', 0.45442166924476624), ('19 pandemic', 0.4410402774810791), ('epidemic', 0.43481525778770447)]"
19,19,716,19_differential privacy_differentially private_privacy utility_privacy constraints,"['differential privacy', 'differentially private', 'privacy utility', 'privacy constraints', 'privacy preserving', 'privacy leakage', 'privacy', 'privacy guarantees', 'privacy preservation', 'information privacy']","[""A Statistical Viewpoint on Differential Privacy: Hypothesis Testing,\n  Representation and Blackwell's Theorem   Differential privacy is widely considered the formal privacy for\nprivacy-preserving data analysis due to its robust and rigorous guarantees,\nwith increasingly broad adoption in public services, academia, and industry.\nDespite originating in the cryptographic context, in this review paper we argue\nthat, fundamentally, differential privacy can be considered a \\textit{pure}\nstatistical concept. By leveraging David Blackwell's informativeness theorem,\nour focus is to demonstrate based on prior work that all definitions of\ndifferential privacy can be formally motivated from a hypothesis testing\nperspective, thereby showing that hypothesis testing is not merely convenient\nbut also the right language for reasoning about differential privacy. This\ninsight leads to the definition of $f$-differential privacy, which extends\nother differential privacy definitions through a representation theorem. We\nreview techniques that render $f$-differential privacy a unified framework for\nanalyzing privacy bounds in data analysis and machine learning. Applications of\nthis differential privacy definition to private deep learning, private convex\noptimization, shuffled mechanisms, and U.S.\\ Census data are discussed to\nhighlight the benefits of analyzing privacy bounds under this framework\ncompared to existing alternatives.\n"", ""Randomized Privacy Budget Differential Privacy   While pursuing better utility by discovering knowledge from the data,\nindividual's privacy may be compromised during an analysis. To that end,\ndifferential privacy has been widely recognized as the state-of-the-art privacy\nnotion. By requiring the presence of any individual's data in the input to only\nmarginally affect the distribution over the output, differential privacy\nprovides strong protection against adversaries in possession of arbitrary\nbackground. However, the privacy constraints (e.g., the degree of\nrandomization) imposed by differential privacy may render the released data\nless useful for analysis, the fundamental trade-off between privacy and utility\n(i.e., analysis accuracy) has attracted significant attention in various\nsettings. In this report we present DP mechanisms with randomized parameters,\ni.e., randomized privacy budget, and formally analyze its privacy and utility\nand demonstrate that randomizing privacy budget in DP mechanisms will boost the\naccuracy in a humongous scale.\n"", 'Privacy-Utility Trade-Off   In this paper, we investigate the privacy-utility trade-off (PUT) problem,\nwhich considers the minimal privacy loss at a fixed expense of utility. Several\ndifferent kinds of privacy in the PUT problem are studied, including\ndifferential privacy, approximate differential privacy, maximal information,\nmaximal leakage, Renyi differential privacy, Sibson mutual information and\nmutual information. The average Hamming distance is used to measure the\ndistortion caused by the privacy mechanism. We consider two scenarios: global\nprivacy and local privacy. In the framework of global privacy framework, the\nprivacy-distortion function is upper-bounded by the privacy loss of a special\nmechanism, and lower-bounded by the optimal privacy loss with any possible\nprior input distribution. In the framework of local privacy, we generalize a\ncoloring method for the PUT problem.\n']","[('differential privacy', 0.8331697583198547), ('differentially private', 0.7061411142349243), ('privacy utility', 0.6955509185791016), ('privacy constraints', 0.6809157133102417), ('privacy preserving', 0.6730833053588867), ('privacy leakage', 0.6569550633430481), ('privacy', 0.6513382792472839), ('privacy guarantees', 0.6435558199882507), ('privacy preservation', 0.6347290277481079), ('information privacy', 0.6130636930465698)]"
20,20,682,20_sparse random graphs_enyi random graphs_inhomogeneous random graphs_random graphs,"['sparse random graphs', 'enyi random graphs', 'inhomogeneous random graphs', 'random graphs', 'graphs random', 'inhomogeneous random graph', 'enyi random graph', 'random graph', 'random geometric graph', 'binomial random graph']","[""Counting cliques in a random graph   We show that the expected number of cliques in the Erd\\H{o}s-R\\'enyi random\ngraph $G(n,p)$ is $n^{\\frac1{-2\\log p}(\\log n-2\\log\\log n+O(1))}$.\n"", ""The friendship paradox for sparse random graphs   Let $G_n$ be an undirected finite graph on $n\\in\\mathbb{N}$ vertices labelled\nby $[n] = \\{1,\\ldots,n\\}$. For $i \\in [n]$, let $\\Delta_{i,n}$ be the\nfriendship bias of vertex $i$, defined as the difference between the average\ndegree of the neighbours of vertex $i$ and the degree of vertex $i$ itself when\n$i$ is not isolated, and zero when $i$ is isolated. Let $\\mu_n$ denote the\nfriendship-bias empirical distribution, i.e., the measure that puts mass\n$\\frac{1}{n}$ at each $\\Delta_{i,n}$, $i \\in [n]$. The friendship paradox says\nthat $\\int_{\\mathbb{R}} x\\mu_n(\\mathrm{d}x) \\geq 0$, with equality if and only\nif in each connected component of $G_n$ all the degrees are the same.\n  We show that if $(G_n)_{n\\in\\mathbb{N}}$ is a sequence of sparse random\ngraphs that converges to a rooted random tree in the sense of convergence\nlocally in probability, then $\\mu_n$ converges weakly to a limiting measure\n$\\mu$ that is expressible in terms of the law of the rooted random tree. We\nstudy $\\mu$ for four classes of sparse random graphs: the homogeneous\nErd\\H{o}s-R\\'enyi random graph, the inhomogeneous Erd\\H{o}s-R\\'enyi random\ngraph, the configuration model and the preferential attachment model. In\nparticular, we compute the first two moments of $\\mu$, identify the right tail\nof $\\mu$, and argue that $\\mu([0,\\infty))\\geq\\tfrac{1}{2}$, a property we refer\nto as friendship paradox significance.\n"", ""Scaling limits of random graph models at criticality: Universality and\n  the basin of attraction of the Erd\\H{o}s-R\\'enyi random graph   A wide array of random graph models have been postulated to understand\nproperties of observed networks. Typically these models have a parameter $t$\nand a critical time $t_c$ when a giant component emerges. It is conjectured\nthat for a large class of models, the nature of this emergence is similar to\nthat of the Erd\\H{o}s-R\\'enyi random graph, in the sense that (a) the sizes of\nthe maximal components in the critical regime scale like $n^{2/3}$, and (b) the\nstructure of the maximal components at criticality (rescaled by $n^{-1/3}$)\nconverges to random fractals. To date, (a) has been proven for a number of\nmodels using different techniques. This paper develops a general program for\nproving (b) that requires three ingredients: (i) in the critical scaling\nwindow, components merge approximately like the multiplicative coalescent, (ii)\nscaling exponents of susceptibility functions are the same as that of the\nErd\\H{o}s-R\\'enyi random graph, and (iii) macroscopic averaging of distances\nbetween vertices in the barely subcritical regime. We show that these apply to\ntwo fundamental random graph models: the configuration model and inhomogeneous\nrandom graphs with a finite ground space. For these models, we also obtain new\nresults for component sizes at criticality and structural properties in the\nbarely subcritical regime.\n""]","[('sparse random graphs', 0.6838136315345764), ('enyi random graphs', 0.6805925369262695), ('inhomogeneous random graphs', 0.6747233271598816), ('random graphs', 0.6644832491874695), ('graphs random', 0.6533709168434143), ('inhomogeneous random graph', 0.6371763944625854), ('enyi random graph', 0.6254574656486511), ('random graph', 0.5861456990242004), ('random geometric graph', 0.5233210921287537), ('binomial random graph', 0.5006449818611145)]"
21,21,644,21_intuitionistic logic_classical logic_modal logic_propositional logic,"['intuitionistic logic', 'classical logic', 'modal logic', 'propositional logic', 'logics', 'kripke semantics', 'linear logic', 'axiomatizations', 'logic', 'first order logic']","[""Wijesekera-style constructive modal logics   We define a family of propositional constructive modal logics corresponding\neach to a different classical modal system. The logics are defined in the style\nof Wijesekera's constructive modal logic, and are both proof-theoretically and\nsemantically motivated. On the one hand, they correspond to the\nsingle-succedent restriction of standard sequent calculi for classical modal\nlogics. On the other hand, they are obtained by incorporating the\nhereditariness of intuitionistic Kripke models into the classical satisfaction\nclauses for modal formulas. We show that, for the considered classical logics,\nthe proof-theoretical and the semantical approach return the same constructive\nsystems.\n"", 'Undecidability and non-axiomatizability of modal many-valued logics   In this work we study the decidability of a class of global modal logics\narising from Kripke frames evaluated over certain residuated lattices, known in\nthe literature as modal many-valued logics. We exhibit a large family of these\nmodal logics which are undecidable, in contrast with classical modal logic and\npropositional logics defined over the same classes of algebras. This family\nincludes the global modal logics arising from Kripke frames evaluated over the\nstandard Lukasiewicz and Product algebras. We later refine the previous result,\nand prove that global modal Lukasiewicz and Product logics are not even\nrecursively axiomatizable. We conclude by solving negatively the open question\nof whether each global modal logic coincides with its local modal logic closed\nunder the unrestricted necessitation rule.\n', 'Goldblat-Thomason Theorems for Fundamental (Modal) Logic   Holliday recently introduced a non-classical logic called Fundamental Logic,\nwhich intends to capture exactly those properties of the connectives ""and"",\n""or"" and ""not"" that hold in virtue of their introduction and elimination rules\nin Fitch\'s natural deduction system for propositional logic. Holliday provides\nan intuitive relational semantics for fundamental logic which generalizes both\nGoldblatt\'s semantics for orthologic and Kripke semantics for intuitionistic\nlogic. In this paper, we further the analysis of this semantics by providing a\nGoldblatt-Thomason theorem for Fundamental Logic. We identify necessary and\nsufficient conditions on a class K of fundamental frames for it to be\naxiomatic, i.e., to be the class of frames satisfying some logic extending\nFundamental Logic. As a straightforward application of our main result, we also\nobtain a Goldblatt-Thomason theorem for Fundamental Modal Logic, which extends\nFundamental Logic with standard Box and Diamond operators.\n']","[('intuitionistic logic', 0.6555971503257751), ('classical logic', 0.6389921307563782), ('modal logic', 0.635036826133728), ('propositional logic', 0.5318912863731384), ('logics', 0.5301538705825806), ('kripke semantics', 0.5282455682754517), ('linear logic', 0.5247777104377747), ('axiomatizations', 0.4690765142440796), ('logic', 0.46435263752937317), ('first order logic', 0.4517408013343811)]"
22,22,628,22_distributed optimization_distributed optimization algorithms_distributed stochastic gradient_consensus optimization,"['distributed optimization', 'distributed optimization algorithms', 'distributed stochastic gradient', 'consensus optimization', 'distributed optimization problems', 'distributed gradient', 'optimization distributed', 'decentralized optimization', 'distributed algorithms', 'distributed stochastic']","['Decentralized Riemannian Gradient Descent on the Stiefel Manifold   We consider a distributed non-convex optimization where a network of agents\naims at minimizing a global function over the Stiefel manifold. The global\nfunction is represented as a finite sum of smooth local functions, where each\nlocal function is associated with one agent and agents communicate with each\nother over an undirected connected graph. The problem is non-convex as local\nfunctions are possibly non-convex (but smooth) and the Steifel manifold is a\nnon-convex set. We present a decentralized Riemannian stochastic gradient\nmethod (DRSGD) with the convergence rate of $\\mathcal{O}(1/\\sqrt{K})$ to a\nstationary point. To have exact convergence with constant stepsize, we also\npropose a decentralized Riemannian gradient tracking algorithm (DRGTA) with the\nconvergence rate of $\\mathcal{O}(1/K)$ to a stationary point. We use multi-step\nconsensus to preserve the iteration in the local (consensus) region. DRGTA is\nthe first decentralized algorithm with exact convergence for distributed\noptimization on Stiefel manifold.\n', 'Distributed Stochastic Gradient Tracking Methods   In this paper, we study the problem of distributed multi-agent optimization\nover a network, where each agent possesses a local cost function that is smooth\nand strongly convex. The global objective is to find a common solution that\nminimizes the average of all cost functions. Assuming agents only have access\nto unbiased estimates of the gradients of their local cost functions, we\nconsider a distributed stochastic gradient tracking method (DSGT) and a\ngossip-like stochastic gradient tracking method (GSGT). We show that, in\nexpectation, the iterates generated by each agent are attracted to a\nneighborhood of the optimal solution, where they accumulate exponentially fast\n(under a constant stepsize choice). Under DSGT, the limiting (expected) error\nbounds on the distance of the iterates from the optimal solution decrease with\nthe network size $n$, which is a comparable performance to a centralized\nstochastic gradient algorithm. Moreover, we show that when the network is\nwell-connected, GSGT incurs lower communication cost than DSGT while\nmaintaining a similar computational cost. Numerical example further\ndemonstrates the effectiveness of the proposed methods.\n', 'Compressed Gradient Tracking Methods for Decentralized Optimization with\n  Linear Convergence   Communication compression techniques are of growing interests for solving the\ndecentralized optimization problem under limited communication, where the\nglobal objective is to minimize the average of local cost functions over a\nmulti-agent network using only local computation and peer-to-peer\ncommunication. In this paper, we first propose a novel compressed gradient\ntracking algorithm (C-GT) that combines gradient tracking technique with\ncommunication compression. In particular, C-GT is compatible with a general\nclass of compression operators that unifies both unbiased and biased\ncompressors. We show that C-GT inherits the advantages of gradient\ntracking-based algorithms and achieves linear convergence rate for strongly\nconvex and smooth objective functions. In the second part of this paper, we\npropose an error feedback based compressed gradient tracking algorithm\n(EF-C-GT) to further improve the algorithm efficiency for biased compression\noperators. Numerical examples complement the theoretical findings and\ndemonstrate the efficiency and flexibility of the proposed algorithms.\n']","[('distributed optimization', 0.6905539035797119), ('distributed optimization algorithms', 0.6812353730201721), ('distributed stochastic gradient', 0.680627703666687), ('consensus optimization', 0.679185688495636), ('distributed optimization problems', 0.6634774208068848), ('distributed gradient', 0.6421706676483154), ('optimization distributed', 0.6395581364631653), ('decentralized optimization', 0.59379643201828), ('distributed algorithms', 0.5768039226531982), ('distributed stochastic', 0.5120251774787903)]"
23,23,615,23_knot floer homology_classical knots_knots links_space knots,"['knot floer homology', 'classical knots', 'knots links', 'space knots', 'alternating knots', 'ribbon knots', 'knots', 'knot diagrams', 'torus knots', 'bridge knots']","[""On unknotting fibered positive knots and braids   The unknotting number $u$ and the genus $g$ of braid positive knots are\nequal, as shown by Rudolph. We prove the stronger statement that any positive\nbraid diagram of a genus $g$ knot contains $g$ crossings, such that changing\nthem produces a diagram of the trivial knot. Then, we turn to unknotting the\nmore general class of fibered positive knots, for which $u = g$ was conjectured\nby Stoimenow. We prove that the known ways to unknot braid positive knots do\nnot generalize to fibered positive knots. Namely, we prove that there are\nfibered positive knots that cannot be unknotted optimally along fibered\npositive knots; there are fibered positive knots that do not arise as trefoil\nplumbings; and there are positive diagrams of fibered positive knots of genus\n$g$ that do not contain $g$ crossings, such that changing them produces a\ndiagram of the trivial knot. In fact, we conjecture that one of our examples is\na counterexample to Stoimenow's conjecture.\n"", ""Knot cobordisms, bridge index, and torsion in Floer homology   Given a connected cobordism between two knots in the 3-sphere, our main\nresult is an inequality involving torsion orders of the knot Floer homology of\nthe knots, and the number of local maxima and the genus of the cobordism. This\nhas several topological applications: The torsion order gives lower bounds on\nthe bridge index and the band-unlinking number of a knot, the fusion number of\na ribbon knot, and the number of minima appearing in a slice disk of a knot. It\nalso gives a lower bound on the number of bands appearing in a ribbon\nconcordance between two knots. Our bounds on the bridge index and fusion number\nare sharp for $T_{p,q}$ and $T_{p,q}\\# \\overline{T}_{p,q}$, respectively. We\nalso show that the bridge index of $T_{p,q}$ is minimal within its concordance\nclass.\n  The torsion order bounds a refinement of the cobordism distance on knots,\nwhich is a metric. As a special case, we can bound the number of band moves\nrequired to get from one knot to the other. We show knot Floer homology also\ngives a lower bound on Sarkar's ribbon distance, and exhibit examples of ribbon\nknots with arbitrarily large ribbon distance from the unknot.\n"", 'The $CFK^\\infty$ Type of Almost L-space Knots   Heegaard Floer homology and knot Floer homology are powerful invariants of\n3-manifolds and links respectively. L-space knots are knots which admit Dehn\nsurgeries to 3-manifolds with Heegaard Floer homology of minimal rank. In this\npaper we study almost L-space knots, which are knots admitting large Dehn\nsurgeries to 3-manifolds with Heegaard Floer homology of next-to-minimal rank.\nOur main result is a classification of the $CFK^\\infty$ type of almost L-space\nknots. As corollaries we show that almost L-space knots satisfy various\ntopological properties, including some given by Baldwin-Sivek. We also give\nsome new cable link detection results.\n']","[('knot floer homology', 0.75910484790802), ('classical knots', 0.6912286877632141), ('knots links', 0.6890235543251038), ('space knots', 0.6854243874549866), ('alternating knots', 0.672646164894104), ('ribbon knots', 0.6645262241363525), ('knots', 0.6641207337379456), ('knot diagrams', 0.647487223148346), ('torus knots', 0.6406930685043335), ('bridge knots', 0.6242289543151855)]"
24,24,603,24_weighted bergman spaces_bergman spaces_bergman space_weighted bergman,"['weighted bergman spaces', 'bergman spaces', 'bergman space', 'weighted bergman', 'toeplitz operators', 'operators hardy space', 'toeplitz operator', 'bergman', 'toeplitz algebra', 'hankel operators']","['Difference of weighted composition operators on weighted Bergman spaces\n  over the unit Ball   In this paper, we characterize the boundedness and compactness of differences\nof weighted composition operators from weighted Bergman spaces $A^p_\\omega$\ninduced by a doubling weight $\\omega$ to Lebesgue spaces $L^q_\\mu$ on the unit\nball for full $0<p,q<\\infty$, which extend many results on the unit disk. As a\nbyproduct, a new characterization of $q$-Carleson the measure for $A^p_\\omega$\nin terms of the Bergman metric ball is also presented.\n', 'Numerical range of Toeplitz and Composition operators on weighted\n  Bergman spaces   In this paper we completely describe the numerical range of Toeplitz\noperators on weighted Bergman spaces with harmonic symbol. We also characterize\nthe numerical range of weighted composition operators on weighted Bergman\nspaces and classify some sets which are the numerical range of composition\noperators. We investigate the inclusion of zero in the numerical range, and\ncompute the radius of circle and ellipse contained in the numerical range of\nweighted composition operators on weighted Bergman spaces.\n', ""Toeplitz operators on the weighted Bergman spaces of quotient domains   Let $G$ be a finite pseudoreflection group and $\\Omega\\subseteq \\mathbb C^d$\nbe a bounded domain which is a $G$-space. We establish identities involving\nToeplitz operators on the weighted Bergman spaces of $\\Omega$ and $\\Omega/G$\nusing invariant theory and representation theory of $G.$ This, in turn,\nprovides techniques to study algebraic properties of Toeplitz operators on the\nweighted Bergman space on $\\Omega/G.$ We specialize on the generalized\nzero-product problem and characterization of commuting pairs of Toeplitz\noperators. As a consequence, more intricate results on Toeplitz operators on\nthe weighted Bergman spaces on some specific quotient domains (namely\nsymmetrized polydisc, monomial polyhedron, Rudin's domain) have been obtained.\n""]","[('weighted bergman spaces', 0.7725027799606323), ('bergman spaces', 0.7209747433662415), ('bergman space', 0.6617593765258789), ('weighted bergman', 0.6196345090866089), ('toeplitz operators', 0.6061697006225586), ('operators hardy space', 0.5644598007202148), ('toeplitz operator', 0.5534411668777466), ('bergman', 0.5288882255554199), ('toeplitz algebra', 0.5063109993934631), ('hankel operators', 0.5041927099227905)]"
25,25,582,25_compressible navier stokes_compressible viscous_incompressible navier stokes_solutions navier stokes,"['compressible navier stokes', 'compressible viscous', 'incompressible navier stokes', 'solutions navier stokes', 'solutions compressible navier', 'navier stokes equations', 'compressible navier', 'full compressible navier', 'incompressible navier', 'navier stokes system']","['On self-similar solutions to degenerate compressible Navier-Stokes\n  equations   We study cavitating self-similar solutions to compressible Navier-Stokes\nequations with degenerate density-dependent viscosity. We prove both existence\nof expanders and non-existence of small shrinkers.\n', 'Weak solutions of 3D compressible Navier-Stokes equations in critical\n  case   New estimates of the potentials of solutions to the compressible\nNavier-Stokes equations are derived. The result obtained are applied to\nboundary value problems for the compressible Navier-Stokes equations with the\ncritical adiabatic exponents. The cancelation of concentrations of the kinetic\nenergy density is proved\n', ""Refined blow up criteria for the full compressible Navier-Stokes\n  equations involving temperature   In this paper, inspired by the study of the energy flux in local energy\ninequality of the 3D incompressible Navier-Stokes equations, we improve almost\nall the blow up criteria involving temperature to allow the temperature in its\nscaling invariant space for the 3D full compressible Navier-Stokes equations.\nEnlightening regular criteria via pressure $\\Pi=\\frac{\\text\n{divdiv}}{-\\Delta}(u_{i}u_{j})$ of the 3D incompressible Navier-Stokes\nequations on bounded domain, we generalize Beirao da Veiga's result in [1] from\nthe incompressible Navier-Stokes equations to the isentropic compressible\nNavier-Stokes system in the case away from vacuum.\n""]","[('compressible navier stokes', 0.7995836138725281), ('compressible viscous', 0.7177016735076904), ('incompressible navier stokes', 0.7141798138618469), ('solutions navier stokes', 0.6990594267845154), ('solutions compressible navier', 0.6948102116584778), ('navier stokes equations', 0.6672114729881287), ('compressible navier', 0.6505613327026367), ('full compressible navier', 0.6397994756698608), ('incompressible navier', 0.6271966695785522), ('navier stokes system', 0.6144621968269348)]"
26,26,570,26_ahler ricci flow_ahler ricci solitons_ahler manifolds_ahler ricci soliton,"['ahler ricci flow', 'ahler ricci solitons', 'ahler manifolds', 'ahler ricci soliton', 'ahler manifold', 'ahler einstein metrics', 'compact ahler manifold', 'scalar curvature ahler', 'curvature ahler', 'ahler metrics']","['Uniformly strong convergence of K\\""ahler-Ricci flows on a Fano manifold   In this paper, we study the uniformly strong convergence of K\\""ahler-Ricci\nflow on a Fano manifold with varied initial metrics and smooth deformation\ncomplex structures. As an application, we prove the uniqueness of\nK\\""ahler-Ricci solitons in sense of diffeomorphism orbits. The result\ngeneralizes Tian-Zhu\'s theorem for the uniqueness of of K\\""ahler-Ricci solitons\non a compact complex manifold, and it is also a generalization of Chen-Sun\'s\nresult of for the uniqueness of of K\\""ahler-Einstein metric orbits.\n', 'K\\""ahler-Ricci shrinkers and Fano fibrations   In this paper, we build connections between K\\""ahler-Ricci shrinkers, i.e.,\ncomplete (possibly non-compact) shrinking gradient K\\""ahler-Ricci solitons, and\nalgebraic geometry. In particular, we (1). prove that a K\\""ahler-Ricci shrinker\nis naturally a quasi-projective variety, using birational algebraic geometry;\n(2). formulate a conjecture relating the existence of K\\""ahler-Ricci shrinkers\nand K-stability of polarized Fano fibrations, which unifies and extends the YTD\ntype conjectures for K\\""ahler-Einstein metrics, Ricci-flat K\\""ahler cone\nmetrics and compact K\\""ahler-Ricci shrinkers; (3). formulate conjectures\nconnecting tangent flows at singularities of K\\""ahler-Ricci flows and algebraic\ngeometry, via a 2-step degeneration for the weighted volume of a Fano\nfibration.\n', 'On the H\\""older estimate of K\\""ahler-Ricci flow   In this work, we study the H\\""\x7folder regularity of the K\x7f\\""ahler- Ricci flow\non compact K\x7f\\""ahler manifolds with semi-ample canonical line bundle. By\nadapting the method in the work of Hein-Tosatti on collapsing Calabi-Yau\nmetrics, we obtain a uniform spatial H\\""older estimate of the K\x7f\\""ahler-Ricci\nflow for all time.\n']","[('ahler ricci flow', 0.7726456522941589), ('ahler ricci solitons', 0.7069482803344727), ('ahler manifolds', 0.6937129497528076), ('ahler ricci soliton', 0.672961413860321), ('ahler manifold', 0.6693341135978699), ('ahler einstein metrics', 0.6682796478271484), ('compact ahler manifold', 0.6633768677711487), ('scalar curvature ahler', 0.6331312656402588), ('curvature ahler', 0.626040518283844), ('ahler metrics', 0.6242706775665283)]"
27,27,566,27_free massive mimo_massive mimo_massive mimo systems_mimo systems,"['free massive mimo', 'massive mimo', 'massive mimo systems', 'mimo systems', 'mimo detection', 'mimo networks', 'mimo system', 'output mimo systems', 'output mimo', 'mimo']","['Improving Cell-Free Massive MIMO by Local Per-Bit Soft Detection   In this letter, we consider the uplink of a cell-free Massive multiple-input\nmultiple-output (MIMO) network where each user is decoded by a subset of access\npoints (APs). An additional step is introduced in the cell-free Massive MIMO\nprocessing: each AP in the uplink locally implements soft MIMO detection and\nthen shares the resulting bit log-likelihoods on the front-haul link. The\ndecoding of the data is performed at the central processing unit (CPU),\ncollecting the data from the APs. The non-linear processing at the APs consists\nof the approximate computation of the posterior density for each received data\nbit, exploiting only local channel state information. The proposed method\noffers good performance in terms of frame-error-rate and considerably lower\ncomplexity than the optimal maximum-likelihood demodulator.\n', 'Performance Analysis of Cell-Free Massive MIMO Systems with Massive\n  Connectivity   In this paper, we investigate the performance of cell-free massive MIMO\nsystems with massive connectivity. With the generalized approximate message\npassing (GAMP) algorithm, we obtain the minimum mean-squared error (MMSE)\nestimate of the effective channel coefficients from all users to all access\npoints (APs) in order to perform joint user activity detection and channel\nestimation. Subsequently, using the decoupling properties of MMSE estimation\nfor large linear systems and state evolution equations of the GAMP algorithm,\nwe obtain the variances of both the estimated channel coefficients and the\ncorresponding channel estimation error. Finally, we study the achievable uplink\nrates with zero-forcing (ZF) detector at the central processing unit (CPU) of\nthe cell-free massive MIMO system. With numerical results, we analyze the\nimpact of the number of pilots used for joint activity detection and channel\nestimation, the number of APs, and signal-to-noise ratio (SNR) on the\nachievable rates.\n', 'Structured Massive Access for Scalable Cell-Free Massive MIMO Systems   How to meet the demand for increasing number of users, higher data rates, and\nstringent quality-of-service (QoS) in the beyond fifth-generation (B5G)\nnetworks? Cell-free massive multiple-input multiple-output (MIMO) is considered\nas a promising solution, in which many wireless access points cooperate to\njointly serve the users by exploiting coherent signal processing. However,\nthere are still many unsolved practical issues in cell-free massive MIMO\nsystems, whereof scalable massive access implementation is one of the most\nvital. In this paper, we propose a new framework for structured massive access\nin cell-free massive MIMO systems, which comprises one initial access\nalgorithm, a partial large-scale fading decoding (P-LSFD) strategy, two pilot\nassignment schemes, and one fractional power control policy. New closed-form\nspectral efficiency (SE) expressions with maximum ratio (MR) combining are\nderived. The simulation results show that our proposed framework provides high\nSE when using local partial minimum mean-square error (LP-MMSE) and MR\ncombining. Specifically, the proposed initial access algorithm and pilot\nassignment schemes outperform their corresponding benchmarks, P-LSFD achieves\nscalability with a negligible performance loss compared to the conventional\noptimal large-scale fading decoding (LSFD), and scalable fractional power\ncontrol provides a controllable trade-off between user fairness and the average\nSE.\n']","[('free massive mimo', 0.6997988820075989), ('massive mimo', 0.6936701536178589), ('massive mimo systems', 0.6906079649925232), ('mimo systems', 0.5598278045654297), ('mimo detection', 0.5579091906547546), ('mimo networks', 0.5439000129699707), ('mimo system', 0.5295196771621704), ('output mimo systems', 0.5268043279647827), ('output mimo', 0.5073457956314087), ('mimo', 0.5035322904586792)]"
28,28,505,28_regularized optimal transport_unbalanced optimal transport_classical optimal transport_optimal transport,"['regularized optimal transport', 'unbalanced optimal transport', 'classical optimal transport', 'optimal transport', 'optimal transport optimal', 'discrete optimal transport', 'entropic optimal transport', 'transport optimal', 'transport optimal transport', 'optimal transport problems']","[""Entropic Optimal Transport between Unbalanced Gaussian Measures has a\n  Closed Form   Although optimal transport (OT) problems admit closed form solutions in a\nvery few notable cases, e.g. in 1D or between Gaussians, these closed forms\nhave proved extremely fecund for practitioners to define tools inspired from\nthe OT geometry. On the other hand, the numerical resolution of OT problems\nusing entropic regularization has given rise to many applications, but because\nthere are no known closed-form solutions for entropic regularized OT problems,\nthese approaches are mostly algorithmic, not informed by elegant closed forms.\nIn this paper, we propose to fill the void at the intersection between these\ntwo schools of thought in OT by proving that the entropy-regularized optimal\ntransport problem between two Gaussian measures admits a closed form. Contrary\nto the unregularized case, for which the explicit form is given by the\nWasserstein-Bures distance, the closed form we obtain is differentiable\neverywhere, even for Gaussians with degenerate covariance matrices. We obtain\nthis closed form solution by solving the fixed-point equation behind Sinkhorn's\nalgorithm, the default method for computing entropic regularized OT.\nRemarkably, this approach extends to the generalized unbalanced case -- where\nGaussian measures are scaled by positive constants. This extension leads to a\nclosed form expression for unbalanced Gaussians as well, and highlights the\nmass transportation / destruction trade-off seen in unbalanced optimal\ntransport. Moreover, in both settings, we show that the optimal transportation\nplans are (scaled) Gaussians and provide analytical formulas of their\nparameters. These formulas constitute the first non-trivial closed forms for\nentropy-regularized optimal transport, thus providing a ground truth for the\nanalysis of entropic OT and Sinkhorn's algorithm.\n"", 'Unbalanced Multi-Marginal Optimal Transport   Entropy regularized optimal transport and its multi-marginal generalization\nhave attracted increasing attention in various applications, in particular due\nto efficient Sinkhorn-like algorithms for computing optimal transport plans.\nHowever, it is often desirable that the marginals of the optimal transport plan\ndo not match the given measures exactly, which led to the introduction of the\nso-called unbalanced optimal transport. Since unbalanced methods were not\nexamined for the multi-marginal setting so far, we address this topic in the\npresent paper. More precisely, we introduce the unbalanced multi-marginal\noptimal transport problem and its dual, and show that a unique optimal\ntransport plan exists under mild assumptions. Further, we generalize the\nSinkhorn algorithm for regularized unbalanced optimal transport to the\nmulti-marginal setting and prove its convergence. If the cost function\ndecouples according to a tree, the iterates can be computed efficiently. At the\nend, we discuss three applications of our framework, namely two barycenter\nproblems and a transfer operator approach, where we establish a relation\nbetween the barycenter problem and the multi-marginal optimal transport with an\nappropriate tree-structured cost function.\n', 'An Homogeneous Unbalanced Regularized Optimal Transport model with\n  applications to Optimal Transport with Boundary   This work studies how the introduction of the entropic regularization term in\nunbalanced Optimal Transport (OT) models may alter their homogeneity with\nrespect to the input measures. We observe that in common settings (including\nbalanced OT and unbalanced OT with Kullback-Leibler divergence to the\nmarginals), although the optimal transport cost itself is not homogeneous,\noptimal transport plans and the so-called Sinkhorn divergences are indeed\nhomogeneous. However, homogeneity does not hold in more general Unbalanced\nRegularized Optimal Transport (UROT) models, for instance those using the Total\nVariation as divergence to the marginals. We propose to modify the entropic\nregularization term to retrieve an UROT model that is homogeneous while\npreserving most properties of the standard UROT model. We showcase the\nimportance of using our Homogeneous UROT (HUROT) model when it comes to\nregularize Optimal Transport with Boundary, a transportation model involving a\nspatially varying divergence to the marginals for which the standard\n(inhomogeneous) UROT model would yield inappropriate behavior.\n']","[('regularized optimal transport', 0.787919819355011), ('unbalanced optimal transport', 0.7526130080223083), ('classical optimal transport', 0.6900536417961121), ('optimal transport', 0.6895579695701599), ('optimal transport optimal', 0.6885741949081421), ('discrete optimal transport', 0.6883962750434875), ('entropic optimal transport', 0.6835771203041077), ('transport optimal', 0.6824114322662354), ('transport optimal transport', 0.6749223470687866), ('optimal transport problems', 0.6746578812599182)]"
29,29,504,29_quantum affine algebras_quantum affine algebra_schur weyl duality_quantized enveloping algebra,"['quantum affine algebras', 'quantum affine algebra', 'schur weyl duality', 'quantized enveloping algebra', 'weyl duality', 'quantum toroidal algebra', 'algebra u_q', 'representations quantum', 'u_q mathfrak sl', 'modules quantum']","['Tensor K-matrices for quantum symmetric pairs   Let $\\mathfrak{g}$ be a symmetrizable Kac-Moody algebra, $U_q(\\mathfrak{g})$\nits quantum group, and $U_q(\\mathfrak{k}) \\subset U_q(\\mathfrak{g})$ a quantum\nsymmetric pair subalgebra determined by a Lie algebra automorphism $\\theta$. We\nintroduce a category $W_\\theta$ of weight $U_q(\\mathfrak{k})$-modules, which is\nacted upon by the category of weight $U_q(\\mathfrak{g})$-modules via tensor\nproducts. We construct a universal tensor K-matrix $\\mathbb{K}$ (that is, a\nsolution of a reflection equation) in a completion of $U_q(\\mathfrak{k})\n\\otimes U_q(\\mathfrak{g})$. This yields a natural operator on any tensor\nproduct $M \\otimes V$, where $M\\in W_\\theta$ and $V\\in \\mathcal{O}_\\theta$,\nthat is $V$ is a $U_q(\\mathfrak{g})$-module in category $\\mathcal{O}$\nsatisfying an integrability property determined by $\\theta$. $W_\\theta$ is\nequipped with a structure of a bimodule category over $\\mathcal{O}_\\theta$ and\nthe action of $\\mathbb{K}$ is encoded by a new categorical structure, which we\ncall a boundary structure on $W_\\theta$. This generalizes a result of Kolb\nwhich describes a braided module structure on finite-dimensional\n$U_q(\\mathfrak{k})$-modules when $\\mathfrak{g}$ is finite-dimensional. We apply\nour construction to the case of an affine Lie algebra, where it yields a formal\ntensor K-matrix valued in the endomorphisms of the tensor product of any module\nin $W_\\theta$ and any finite-dimensional module over the corresponding quantum\naffine algebra. This formal series is normalized to a trigonometric K-matrix if\nthe factors in the tensor product are both finite-dimensional irreducible\nmodules over the quantum affine algebra.\n', ""RTT presentation of coideal subalgebra of quantized enveloping algebra\n  of type CI   The pair consisting of a quantum group and its corresponding coideal\nsubalgebra, known as a quantum symmetric pair, was developed independently by\nM. Noumi and G. Letzter through different approaches. The purpose of this paper\nis threefold. First, for symmetric pairs\n$(\\mathfrak{sp}_{2n},\\mathfrak{gl}_n)$, we construct a coideal subalgebra\n$U_q^{tw}(\\mathfrak{gl}_n)$ of the quantized enveloping algebra of type CI\nusing the $R$-matrix presentation, based on the work of Noumi. Second, we\nderive a Poincar\\'e-Birkhoff-Witt(PBW) basis for $U_q^{tw}(\\mathfrak{gl}_n)$ by\nthe $\\mathbb{A}$-form approach. As a consequence of the isomorphism btween\n$U_q^{tw}(\\mathfrak{gl}_n)$ and the $\\imath$quantum group\n$\\mathcal{U}^{\\imath}$, our method also yields the PBW basis for the\n$\\imath$quantum group of type CI. Finally, as an application of the $R$-matrix\npresentation, we construct a Poisson algebra $\\mathcal{P}_n$ associated with\n$U_q^{tw}(\\mathfrak{gl}_n)$, and explicitly describe the action of the braid\ngroup $\\mathcal{B}_n$ on the elements of $\\mathcal{P}_n$.\n"", ""Quantum $SL(2,\\mathbb{R})$ and its irreducible representations   We define for real $q$ a unital $*$-algebra\n$U_q(\\mathfrak{sl}(2,\\mathbb{R}))$ quantizing the universal enveloping\n$*$-algebra of $\\mathfrak{sl}(2,\\mathbb{R})$. The $*$-algebra\n$U_q(\\mathfrak{sl}(2,\\mathbb{R}))$ is realized as a $*$-subalgebra of the\nDrinfeld double of $U_q(\\mathfrak{su}(2))$ and its dual Hopf $*$-algebra\n$\\mathcal{O}_q(SU(2))$, generated by the equatorial Podle\\'s sphere coideal\n$*$-subalgebra $\\mathcal{O}_q(K\\backslash SU(2))$ of $\\mathcal{O}_q(SU(2))$ and\nits associated orthogonal coideal $*$-subalgebra $U_q(\\mathfrak{k}) \\subseteq\nU_q(\\mathfrak{su}(2))$. We then classify all the irreducible\n$*$-representations of $U_q(\\mathfrak{sl}(2,\\mathbb{R}))$.\n""]","[('quantum affine algebras', 0.6064537167549133), ('quantum affine algebra', 0.5730258822441101), ('schur weyl duality', 0.5531201362609863), ('quantized enveloping algebra', 0.5484906435012817), ('weyl duality', 0.5183145999908447), ('quantum toroidal algebra', 0.5062848329544067), ('algebra u_q', 0.49043381214141846), ('representations quantum', 0.48499131202697754), ('u_q mathfrak sl', 0.472282737493515), ('modules quantum', 0.47171878814697266)]"
30,30,498,30_schubert varieties_schubert polynomials_partial flag varieties_schubert calculus,"['schubert varieties', 'schubert polynomials', 'partial flag varieties', 'schubert calculus', 'hessenberg varieties', 'grassmannians', 'grassmannian', 'flag varieties', 'affine grassmannian', 'schubert cells']","[""Conormal Varieties of covexillary Schubert Varieties   A permutation is called covexillary if it avoids the pattern $3412$. We\nconstruct an open embedding of a covexillary matrix Schubert variety into a\nGrassmannian Schubert variety. As applications of this embedding, we show that\nthe characteristic cycles of covexillary Schubert varieties are irreducible,\nand provide a new proof of Lascoux's model computing Kazhdan-Lusztig\npolynomials of vexillary permutations. Combining the above embedding with\nearlier work of the author on the conormal varieties of Grassmannian Schubert\nvarieties, we develop an algebraic criterion identifying the conormal varieties\nof covexillary Schubert and matrix Schubert varieties as subvarieties of the\nrespective cotangent bundles.\n"", 'Which Schubert Varieties are Hessenberg Varieties?   After proving that every Schubert variety in the full flag variety of a\ncomplex reductive group $G$ is a general Hessenberg variety, we show that not\nall such Schubert varieties are adjoint Hessenberg varieties. In fact, in types\nA and C, we provide pattern avoidance criteria implying that the proportion of\nSchubert varieties that are adjoint Hessenberg varieties approaches zero as the\nrank of $G$ increases. We show also that in type A, some Schubert varieties are\nnot isomorphic to any adjoint Hessenberg variety.\n', 'On the Classification of Schubert Varieties in Partial Flag Varieties   We generalize the classification of isomorphism classes of Schubert varieties\nfrom complete flag varieties G/B to a class of partial flag varieties G/P. In\nparticular, we classify all Schubert varieties in G/P where P is a minimal\nparabolic subgroup, and all Schubert surfaces which are two-dimensional\nSchubert varieties. We also obtain several classes of isomorphisms of Schubert\nvarieties in flag varieties G/P where P is a maximal parabolic subgroup. In\nparticular, we find an upper bound of the number of isomorphism classes of\nSchubert threefolds which are three-dimensional Schubert varieties.\n']","[('schubert varieties', 0.8194012641906738), ('schubert polynomials', 0.6827368140220642), ('partial flag varieties', 0.6807036399841309), ('schubert calculus', 0.6415657997131348), ('hessenberg varieties', 0.6400653719902039), ('grassmannians', 0.6347375512123108), ('grassmannian', 0.6238434910774231), ('flag varieties', 0.6228710412979126), ('affine grassmannian', 0.6078886389732361), ('schubert cells', 0.6071770787239075)]"
31,31,495,31_gradient descent sgd_stochastic gradient descent_gradient descent_stochastic gradient methods,"['gradient descent sgd', 'stochastic gradient descent', 'gradient descent', 'stochastic gradient methods', 'descent sgd', 'adaptive gradient methods', 'stochastic optimization', 'stochastic gradient', 'learning rates', 'adaptive learning rate']","['Towards Practical Adam: Non-Convexity, Convergence Theory, and\n  Mini-Batch Acceleration   Adam is one of the most influential adaptive stochastic algorithms for\ntraining deep neural networks, which has been pointed out to be divergent even\nin the simple convex setting via a few simple counterexamples. Many attempts,\nsuch as decreasing an adaptive learning rate, adopting a big batch size,\nincorporating a temporal decorrelation technique, seeking an analogous\nsurrogate, \\textit{etc.}, have been tried to promote Adam-type algorithms to\nconverge. In contrast with existing approaches, we introduce an alternative\neasy-to-check sufficient condition, which merely depends on the parameters of\nthe base learning rate and combinations of historical second-order moments, to\nguarantee the global convergence of generic Adam for solving large-scale\nnon-convex stochastic optimization. This observation, coupled with this\nsufficient condition, gives much deeper interpretations on the divergence of\nAdam. On the other hand, in practice, mini-Adam and distributed-Adam are widely\nused without any theoretical guarantee. We further give an analysis on how the\nbatch size or the number of nodes in the distributed system affects the\nconvergence of Adam, which theoretically shows that mini-batch and distributed\nAdam can be linearly accelerated by using a larger mini-batch size or a larger\nnumber of nodes.At last, we apply the generic Adam and mini-batch Adam with the\nsufficient condition for solving the counterexample and training several neural\nnetworks on various real-world datasets. Experimental results are exactly in\naccord with our theoretical analysis.\n', 'A Unified Analysis of AdaGrad with Weighted Aggregation and Momentum\n  Acceleration   Integrating adaptive learning rate and momentum techniques into SGD leads to\na large class of efficiently accelerated adaptive stochastic algorithms, such\nas AdaGrad, RMSProp, Adam, AccAdaGrad, \\textit{etc}. In spite of their\neffectiveness in practice, there is still a large gap in their theories of\nconvergences, especially in the difficult non-convex stochastic setting. To\nfill this gap, we propose \\emph{weighted AdaGrad with unified momentum}, dubbed\nAdaUSM, which has the main characteristics that (1) it incorporates a unified\nmomentum scheme which covers both the heavy ball momentum and the Nesterov\naccelerated gradient momentum; (2) it adopts a novel weighted adaptive learning\nrate that can unify the learning rates of AdaGrad, AccAdaGrad, Adam, and\nRMSProp. Moreover, when we take polynomially growing weights in AdaUSM, we\nobtain its $\\mathcal{O}(\\log(T)/\\sqrt{T})$ convergence rate in the non-convex\nstochastic setting. We also show that the adaptive learning rates of Adam and\nRMSProp correspond to taking exponentially growing weights in AdaUSM, thereby\nproviding a new perspective for understanding Adam and RMSProp. Lastly,\ncomparative experiments of AdaUSM against SGD with momentum, AdaGrad, AdaEMA,\nAdam, and AMSGrad on various deep learning models and datasets are also carried\nout.\n', 'Noise Is Not the Main Factor Behind the Gap Between SGD and Adam on\n  Transformers, but Sign Descent Might Be   The success of the Adam optimizer on a wide array of architectures has made\nit the default in settings where stochastic gradient descent (SGD) performs\npoorly. However, our theoretical understanding of this discrepancy is lagging,\npreventing the development of significant improvements on either algorithm.\nRecent work advances the hypothesis that Adam and other heuristics like\ngradient clipping outperform SGD on language tasks because the distribution of\nthe error induced by sampling has heavy tails. This suggests that Adam\noutperform SGD because it uses a more robust gradient estimate. We evaluate\nthis hypothesis by varying the batch size, up to the entire dataset, to control\nfor stochasticity. We present evidence that stochasticity and heavy-tailed\nnoise are not major factors in the performance gap between SGD and Adam.\nRather, Adam performs better as the batch size increases, while SGD is less\neffective at taking advantage of the reduction in noise. This raises the\nquestion as to why Adam outperforms SGD in the full-batch setting. Through\nfurther investigation of simpler variants of SGD, we find that the behavior of\nAdam with large batches is similar to sign descent with momentum.\n']","[('gradient descent sgd', 0.6716616153717041), ('stochastic gradient descent', 0.6709936261177063), ('gradient descent', 0.5893061757087708), ('stochastic gradient methods', 0.5638436079025269), ('descent sgd', 0.5596717000007629), ('adaptive gradient methods', 0.526193380355835), ('stochastic optimization', 0.5228100419044495), ('stochastic gradient', 0.5220006108283997), ('learning rates', 0.5054051280021667), ('adaptive learning rate', 0.495924174785614)]"
32,32,486,32_mckean vlasov stochastic_vlasov stochastic differential_stochastic differential equations_mckean vlasov equations,"['mckean vlasov stochastic', 'vlasov stochastic differential', 'stochastic differential equations', 'mckean vlasov equations', 'vlasov stochastic', 'mckean vlasov sdes', 'differential equations sdes', 'stochastic differential', 'solutions stochastic', 'equations stochastic']","['Polynomial McKean-Vlasov SDEs   We study a new class of McKean-Vlasov stochastic differential equations\n(SDEs), possibly with common noise, applying the theory of time-inhomogeneous\npolynomial processes. The drift and volatility coefficients of these SDEs\ndepend on the state variables themselves as well as their conditional moments\nin a way that mimics the standard polynomial structure. Our approach leads to\nnew results on the existence and uniqueness of solutions to such conditional\nMcKean-Vlasov SDEs which are, to the best of our knowledge, not obtainable\nusing standard methods. Moreover, we show in the case without common noise that\nthe moments of these McKean-Vlasov SDEs can be computed by non-linear ODEs. As\na by-product, this also yields new results on the existence and uniqueness of\nglobal solutions to certain ODEs.\n', ""Well-posedness and averaging principle for L\\'evy-type McKean-Vlasov\n  stochastic differential equations under local Lipschitz conditions   In this paper, we investigate a class of McKean-Vlasov stochastic\ndifferential equations under L\\'evy-type perturbations. We first establish the\nexistence and uniqueness theorem for solutions of the McKean-Vlasov stochastic\ndifferential equations by utilizing the Euler-like approximation. Then under\nsome suitable conditions, we show that the solutions of McKean-Vlasov\nstochastic differential equations can be approximated by the solutions of the\nassociated averaged McKean-Vlasov stochastic differential equations in the\nsense of mean square convergence. In contrast to the existing work, a novel\nfeature is the use of a much weaker condition -- local Lipschitzian in the\nstate variables, allowing for possibly super-linearly growing drift, but\nlinearly growing diffusion and jump coefficients. Therefore, our results are\nsuitable for a wider class of McKean-Vlasov stochastic differential equations.\n"", 'On modified Euler methods for McKean-Vlasov stochastic differential\n  equations with super-linear coefficients   We introduce a new class of numerical methods for solving McKean-Vlasov\nstochastic differential equations, which are relevant in the context of\ndistribution-dependent or mean-field models, under super-linear growth\nconditions for both the drift and diffusion coefficients. Under certain\nnon-globally Lipschitz conditions, the proposed numerical approaches have\nhalf-order convergence in the strong sense to the corresponding system of\ninteracting particles associated with McKean-Vlasov SDEs. By leveraging a\nresult on the propagation of chaos, we establish the full convergence rate of\nthe modified Euler approximations to the solution of the McKean-Vlasov SDEs.\nNumerical experiments are included to validate the theoretical results.\n']","[('mckean vlasov stochastic', 0.7313613295555115), ('vlasov stochastic differential', 0.7004668116569519), ('stochastic differential equations', 0.6758068203926086), ('mckean vlasov equations', 0.6701658368110657), ('vlasov stochastic', 0.6331220269203186), ('mckean vlasov sdes', 0.6156038045883179), ('differential equations sdes', 0.5982131958007812), ('stochastic differential', 0.5953264236450195), ('solutions stochastic', 0.5942031741142273), ('equations stochastic', 0.5811588764190674)]"
33,33,476,33_classical orthogonal polynomials_discrete orthogonal polynomials_orthogonal polynomials_orthogonal polynomials respect,"['classical orthogonal polynomials', 'discrete orthogonal polynomials', 'orthogonal polynomials', 'orthogonal polynomials respect', 'polynomials orthogonal', 'polynomials orthogonal respect', 'monic orthogonal polynomials', 'orthogonal polynomial', 'orthogonal polynomials unit', 'laguerre polynomials']","['Continuous $-1$ Hypergeometric Orthogonal Polynomials   The study of $-1$ orthogonal polynomials viewed as $q =-1$ limits of the\n$q$-orthogonal polynomials is pursued. This paper present the continuous\npolynomials part of the $-1$ analog of the $q$-Askey scheme. A compendium of\nthe properties of all the continuous $-1$ hypergeometric polynomials and their\nconnections is provided.\n', 'Combinatorics of generalized orthogonal polynomials of type $R_{II}$   In 1995, Ismail and Masson introduced orthogonal polynomials of types \\( R_I\n\\) and \\( R_{II} \\), which are defined by specific three-term recurrence\nrelations with additional conditions. Recently, Kim and Stanton found a\ncombinatorial interpretation for the moments of orthogonal polynomials of type\n\\( R_I \\) in the spirit of the combinatorial theory of orthogonal polynomials\ndue to Flajolet and Viennot. In this paper, we push this combinatorial model\nfurther to orthogonal polynomials of type \\( R_{II} \\). Moreover, we generalize\northogonal polynomials of type \\( R_{II} \\) by relaxing some of their\nconditions. We then prove a master theorem, which generalizes combinatorial\nmodels for moments of various types of orthogonal polynomials: classical\northogonal polynomials, Laurent biorthogonal polynomials, and orthogonal\npolynomials of types \\( R_I \\) and \\( R_{II} \\).\n', 'Connecting Exceptional Orthogonal Polynomials of Different Kind   The known asymptotic relations interconnecting Jacobi, Laguerre, and Hermite\nclassical orthogonal polynomials are generalized to the corresponding\nexceptional orthogonal polynomials of codimension $m$. It is proved that\n$X_m$-Laguerre exceptional orthogonal polynomials of type I, II, or III can be\nobtained as limits of $X_m$-Jacobi exceptional orthogonal polynomials of the\nsame type. Similarly, $X_m$-Hermite exceptional orthogonal polynomials of type\nIII can be derived from $X_m$-Jacobi or $X_m$-Laguerre ones. The quadratic\ntransformations expressing Hermite classical orthogonal polynomials in terms of\nLaguerre ones is also extended to even $X_{2m}$-Hermite exceptional orthogonal\npolynomials.\n']","[('classical orthogonal polynomials', 0.78812575340271), ('discrete orthogonal polynomials', 0.7632415890693665), ('orthogonal polynomials', 0.7611648440361023), ('orthogonal polynomials respect', 0.743488073348999), ('polynomials orthogonal', 0.7224392890930176), ('polynomials orthogonal respect', 0.7042608261108398), ('monic orthogonal polynomials', 0.6901621222496033), ('orthogonal polynomial', 0.6895113587379456), ('orthogonal polynomials unit', 0.6589742302894592), ('laguerre polynomials', 0.6204869747161865)]"
34,34,474,34_passage percolation_percolation models_first passage percolation_continuum percolation,"['passage percolation', 'percolation models', 'first passage percolation', 'continuum percolation', 'percolation threshold', 'last passage percolation', 'oriented percolation', 'bernoulli percolation', 'percolation mathbb', 'percolation random']","['Strict inequality between the time constants of first-passage\n  percolation and directed first-passage percolation   In the models of first-passage percolation and directed first-passage\npercolation on $\\mathbb{Z}^d$, we consider a family of i.i.d. random variables\nindexed by the set of edges of the graph, called passage times. For every\nvertex $x \\in \\mathbb{Z}^d$ with nonnegative coordinates, we denote by $t(0,x)$\nthe shortest passage time to go from $0$ to $x$ and by $\\vec t(0,x)$ the\nshortest passage time to go from $0$ to $x$ following a directed path. Under\nsome assumptions, it is known that for every $x \\in \\mathbb{R}^d$ with\nnonnegative coordinates, $t(0,\\lfloor nx \\rfloor)/n$ converges to a constant\n$\\mu(x)$ and that $\\vec t(0,\\lfloor nx \\rfloor)/n$ converges to a constant\n$\\vec\\mu(x)$. With these definitions, we immediately get that $\\mu(x) \\le\n\\vec{\\mu}(x)$. In this paper, we get the strict inequality $\\mu(x) <\n\\vec\\mu(x)$ as a consequence of a new exponential bound for the comparison of\n$t(0,x)$ and $\\vec{t}(0,x)$ when $\\|x\\|$ goes to $\\infty$. This exponential\nbound is itself based on a lower bound on the number of edges of geodesics in\nfirst-passage percolation (where geodesics are paths with minimal passage\ntime).\n', 'The height problem in first passage percolation   We consider the first passage percolation model in Z2 with a distribution F\nfor 0 < F (0) < pc. In this paper, we solve the height problem.\n', 'Analyticity of the percolation density $\\theta$ in all dimensions   We prove that for Bernoulli bond percolation on $\\mathbb{Z}^d$, $d\\geq 2$ the\npercolation density is an analytic function of the parameter in the\nsupercritical interval $(p_c,1]$. This answers a question of Kesten from 1981.\n']","[('passage percolation', 0.7090518474578857), ('percolation models', 0.7063374519348145), ('first passage percolation', 0.683531641960144), ('continuum percolation', 0.674985945224762), ('percolation threshold', 0.6730762124061584), ('last passage percolation', 0.6679263114929199), ('oriented percolation', 0.6513352990150452), ('bernoulli percolation', 0.6422107219696045), ('percolation mathbb', 0.6323584318161011), ('percolation random', 0.6269589066505432)]"
35,35,461,35_queueing_scheduling policies_scheduling policy_queue,"['queueing', 'scheduling policies', 'scheduling policy', 'queue', 'status updates', 'markov decision process', 'iot', 'service time', 'information freshness', 'markov decision']","['Age of Information in Slotted ALOHA With Energy Harvesting   We examine the age of information (AoI) of a status update system that\nincorporates energy harvesting and uses the slotted ALOHA protocol. We derive\nanalytically the average AoI and the probability that the AoI exceeds a given\nthreshold. Via numerical results, we investigate two strategies to minimize the\nage of information (AoI): transmitting a new update whenever possible to\nexploit every chance to reduce the AoI, and transmitting only when sufficient\nenergy is available to increase the chance of successful delivery. The two\nstrategies are beneficial for low and high update generation rates,\nrespectively. However, an optimized approach that balances the two strategies\noutperforms them significantly in terms of both AoI and throughput.\n', 'Minimum Age of Information in the Internet of Things with Non-uniform\n  Status Packet Sizes   In this paper, a real-time Internet of Things (IoT) monitoring system is\nconsidered in which the IoT devices are scheduled to sample underlying physical\nprocesses and send the status updates to a common destination. In a real-world\nIoT, due to the possibly different dynamics of each physical process, the sizes\nof the status updates for different devices are often different and each status\nupdate typically requires multiple transmission slots. By taking into account\nsuch multi-time slot transmissions with non-uniform sizes of the status updates\nunder noisy channels, the problem of joint device scheduling and status\nsampling is studied in order to minimize the average age of information (AoI)\nat the destination. This stochastic problem is formulated as an infinite\nhorizon average cost Markov decision process (MDP). The monotonicity of the\nvalue function of the MDP is characterized and then used to show that the\noptimal scheduling and sampling policy is threshold-based with respect to the\nAoI at each device. To overcome the curse of dimensionality, a low-complexity\nsuboptimal policy is proposed through a semi-randomized base policy and linear\napproximated value functions. The proposed suboptimal policy is shown to\nexhibit a similar structure to the optimal policy, which provides a structural\nbase for its effective performance. A structure-aware algorithm is then\ndeveloped to obtain the suboptimal policy. The analytical results are further\nextended to the IoT monitoring system with random status update arrivals, for\nwhich, the optimal scheduling and sampling policy is also shown to be\nthreshold-based with the AoI at each device. Simulation results illustrate the\nstructures of the optimal policy and show a near-optimal AoI performance\nresulting from the proposed suboptimal solution approach.\n', 'Age-Oriented Opportunistic Relaying in Cooperative Status Update Systems\n  with Stochastic Arrivals   This paper considers a cooperative status update system with a source aiming\nto send randomly generated status updates to a designated destination as timely\nas possible with the help of a relay. We adopt a recently proposed concept, Age\nof Information (AoI), to characterize the timeliness of the status updates. We\npropose an age-oriented opportunistic relaying (AoR) protocol to reduce the AoI\nof the considered system. Specifically, the relay opportunistically replaces\nthe source to retransmit the successfully received status updates that have not\nbeen correctly delivered to the destination, but the retransmission of the\nrelay can be preempted by the arrival of a new status update at the source. By\ncarefully analyzing the evolution of AoI, we derive a closed-form expression of\nthe average AoI for the proposed AoR protocol. We further minimize the average\nAoI by optimizing the generation probability of the status updates at the\nsource. Simulation results validate our theoretical analysis and demonstrate\nthat the average AoI performance of the proposed AoR protocol is superior to\nthat of the non-cooperative system.\n']","[('queueing', 0.3802734315395355), ('scheduling policies', 0.37853190302848816), ('scheduling policy', 0.3708801865577698), ('queue', 0.3627288341522217), ('status updates', 0.35517677664756775), ('markov decision process', 0.339444100856781), ('iot', 0.32924821972846985), ('service time', 0.32488247752189636), ('information freshness', 0.31521064043045044), ('markov decision', 0.31088992953300476)]"
36,36,457,36_tensor completion_low rank tensor_low rank tensors_rank tensors,"['tensor completion', 'low rank tensor', 'low rank tensors', 'rank tensors', 'tensor rank', 'rank tensor', 'tensor decomposition', 'tensor decompositions', 'tensor approximation', 'sparse tensor']","[""A generalizable framework for low-rank tensor completion with numerical\n  priors   Low-Rank Tensor Completion, a method which exploits the inherent structure of\ntensors, has been studied extensively as an effective approach to tensor\ncompletion. Whilst such methods attained great success, none have\nsystematically considered exploiting the numerical priors of tensor elements.\nIgnoring numerical priors causes loss of important information regarding the\ndata, and therefore prevents the algorithms from reaching optimal accuracy.\nDespite the existence of some individual works which consider ad hoc numerical\npriors for specific tasks, no generalizable frameworks for incorporating\nnumerical priors have appeared. We present the Generalized CP Decomposition\nTensor Completion (GCDTC) framework, the first generalizable framework for\nlow-rank tensor completion that takes numerical priors of the data into\naccount. We test GCDTC by further proposing the Smooth Poisson Tensor\nCompletion (SPTC) algorithm, an instantiation of the GCDTC framework, whose\nperformance exceeds current state-of-the-arts by considerable margins in the\ntask of non-negative tensor completion, exemplifying GCDTC's effectiveness. Our\ncode is open-source.\n"", 'Riemannian Conjugate Gradient Descent Method for Third-Order Tensor\n  Completion   The goal of tensor completion is to fill in missing entries of a partially\nknown tensor under a low-rank constraint. In this paper, we mainly study low\nrank third-order tensor completion problems by using Riemannian optimization\nmethods on the smooth manifold. Here the tensor rank is defined to be a set of\nmatrix ranks where the matrices are the slices of the transformed tensor\nobtained by applying the Fourier-related transformation onto the tubes of the\noriginal tensor. We show that with suitable incoherence conditions on the\nunderlying low rank tensor, the proposed Riemannian optimization method is\nguaranteed to converge and find such low rank tensor with a high probability.\nIn addition, numbers of sample entries required for solving low rank tensor\ncompletion problem under different initialized methods are studied and derived.\nNumerical examples for both synthetic and image data sets are reported to\ndemonstrate the proposed method is able to recover low rank tensors.\n', 'Multi-Tubal Rank of Third Order Tensor and Related Low Rank Tensor\n  Completion Problem   Recently, a tensor factorization based method for a low tubal rank tensor\ncompletion problem of a third order tensor was proposed, which performed better\nthan some existing methods. Tubal rank is only defined on one mode of third\norder tensor without low rank structure in the other two modes. That is, low\nrank structures on the other two modes are missing. Motivated by this, we first\nintroduce multi-tubal rank, and then establish a relationship between\nmulti-tubal rank and Tucker rank. Based on the multi-tubal rank, we propose a\nnovel low rank tensor completion model. For this model, a tensor factorization\nbased method is applied and the corresponding convergence anlysis is\nestablished. In addition, spatio-temporal characteristics are intrinsic\nfeatures in video and internet traffic tensor data. To get better performance,\nwe make full use of such features and improve the established tensor completion\nmodel. Then we apply tensor factorization based method for the improved model.\nFinally, numerical results are reported on the completion of image, video and\ninternet traffic data to show the efficiency of our proposed methods. From the\nreported numerical results, we can assert that our methods outperform the\nexisting methods.\n']","[('tensor completion', 0.7987100481987), ('low rank tensor', 0.7452057600021362), ('low rank tensors', 0.7388402819633484), ('rank tensors', 0.7200812101364136), ('tensor rank', 0.7175435423851013), ('rank tensor', 0.7154941558837891), ('tensor decomposition', 0.6793173551559448), ('tensor decompositions', 0.6787387132644653), ('tensor approximation', 0.67316734790802), ('sparse tensor', 0.6654742360115051)]"
37,37,450,37_stochastic gradient langevin_gradient langevin dynamics_langevin monte carlo_langevin dynamics,"['stochastic gradient langevin', 'gradient langevin dynamics', 'langevin monte carlo', 'langevin dynamics', 'gradient langevin', 'langevin diffusion', 'hamiltonian monte carlo', 'monte carlo mcmc', 'mcmc algorithms', 'mcmc methods']","['Metropolis Adjusted Langevin Trajectories: a robust alternative to\n  Hamiltonian Monte Carlo   We introduce MALT: a new Metropolis adjusted sampler built upon the (kinetic)\nLangevin diffusion. Compared to Generalized Hamiltonian Monte Carlo (GHMC), the\nMetropolis correction is applied to whole Langevin trajectories, which prevents\nmomentum flips, and allows for larger step-sizes. We argue that MALT yields a\nneater extension of HMC, preserving many desirable properties. We extend\noptimal scaling results of HMC to MALT for isotropic targets, and obtain the\nsame scaling with respect to the dimension without additional assumptions. We\nshow that MALT improves both the robustness to tuning and the sampling\nperformance of HMC on anisotropic targets. We compare our approach with\nRandomized HMC, recently praised for its robustness. We show that, in\ncontinuous time, the Langevin diffusion achieves the fastest mixing rate for\nstrongly log-concave targets. We then assess the accuracies of MALT, GHMC, HMC\nand RHMC when performing numerical integration on anisotropic targets, both on\ntoy models and real data experiments on a Bayesian logistic regression. We show\nthat MALT outperforms GHMC, standard HMC, and is competitive with RHMC.\n', 'Gradient-adjusted underdamped Langevin dynamics for sampling   Sampling from a target distribution is a fundamental problem. Traditional\nMarkov chain Monte Carlo (MCMC) algorithms, such as the unadjusted Langevin\nalgorithm (ULA), derived from the overdamped Langevin dynamics, have been\nextensively studied. From an optimization perspective, the Kolmogorov forward\nequation of the overdamped Langevin dynamics can be treated as the gradient\nflow of the relative entropy in the space of probability densities embedded\nwith Wassrstein-2 metrics. Several efforts have also been devoted to including\nmomentum-based methods, such as underdamped Langevin dynamics for faster\nconvergence of sampling algorithms. Recent advances in optimizations have\ndemonstrated the effectiveness of primal-dual damping and Hessian-driven\ndamping dynamics for achieving faster convergence in solving optimization\nproblems. Motivated by these developments, we introduce a class of stochastic\ndifferential equations (SDEs) called gradient-adjusted underdamped Langevin\ndynamics (GAUL), which add stochastic perturbations in primal-dual damping\ndynamics and Hessian-driven damping dynamics from optimization. We prove that\nGAUL admits the correct stationary distribution, whose marginal is the target\ndistribution. The proposed method outperforms overdamped and underdamped\nLangevin dynamics regarding convergence speed in the total variation distance\nfor Gaussian target distributions. Moreover, using the Euler-Maruyama\ndiscretization, we show that the mixing time towards a biased target\ndistribution only depends on the square root of the condition number of the\ntarget covariance matrix. Numerical experiments for non-Gaussian target\ndistributions, such as Bayesian regression problems and Bayesian neural\nnetworks, further illustrate the advantages of our approach.\n', 'Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysis   Langevin algorithms are popular Markov chain Monte Carlo methods that are\noften used to solve high-dimensional large-scale sampling problems in machine\nlearning. The most classical Langevin Monte Carlo algorithm is based on the\noverdamped Langevin dynamics. There are many variants of Langevin dynamics that\noften show superior performance in practice. In this paper, we provide a\nunified approach to study the acceleration of the variants of the overdamped\nLangevin dynamics through the lens of large deviations theory. Numerical\nexperiments using both synthetic and real data are provided to illustrate the\nefficiency of these variants.\n']","[('stochastic gradient langevin', 0.6903210878372192), ('gradient langevin dynamics', 0.6744442582130432), ('langevin monte carlo', 0.6626823544502258), ('langevin dynamics', 0.6376721858978271), ('gradient langevin', 0.6122373342514038), ('langevin diffusion', 0.603545069694519), ('hamiltonian monte carlo', 0.5993126630783081), ('monte carlo mcmc', 0.58617103099823), ('mcmc algorithms', 0.5819875597953796), ('mcmc methods', 0.5653160214424133)]"
38,38,431,38_finite volume schemes_hyperbolic conservation laws_hyperbolic conservation_numerical fluxes,"['finite volume schemes', 'hyperbolic conservation laws', 'hyperbolic conservation', 'numerical fluxes', 'shallow water equations', 'volume schemes', 'numerical', 'order schemes', 'finite difference', 'water equations']","['High-order accurate entropy stable finite difference schemes for the\n  shallow water magnetohydrodynamics   This paper develops the high-order accurate entropy stable (ES) finite\ndifference schemes for the shallow water magnetohydrodynamic (SWMHD)\nequations.They are built on the numerical approximation of the modified SWMHD\nequations with the Janhunen source term. First, the second-order accurate\nwell-balanced semi-discrete entropy conservative (EC) schemes are constructed,\nsatisfying the entropy identity for the given convex entropy function and\npreserving the steady states of the lake at rest (with zero magnetic field).\nThe key is to match both discretizations for the fluxes and the non-flat river\nbed bottom and Janhunen source terms, and to find the affordable EC fluxes of\nthe second-order EC schemes. Next, by using the second-order EC schemes as\nbuilding block, high-order accurate well-balanced semi-discrete EC schemes are\nproposed. Then, the high-order accurate well-balanced semi-discrete ES schemes\n%satisfying the entropy inequality are derived by adding a suitable dissipation\nterm to the EC scheme with the WENO reconstruction of the scaled entropy\nvariables in order to suppress the numerical oscillations of the EC schemes.\nAfter that, the semi-discrete schemes are integrated in time by using the\nhigh-order strong stability preserving explicit Runge-Kutta schemes to obtain\nthe fully-discrete high-order well-balanced schemes. The ES property of the\nLax-Friedrichs flux is also proved and then the positivity-preserving ES\nschemes are studied by using the positivity-preserving flux limiter. Finally,\nextensive numerical tests are conducted to validate the accuracy, the\nwell-balanced, ES and positivity-preserving properties, and the ability to\ncapture discontinuities of our schemes.\n', ""Well-balanced fifth-order finite volume WENO schemes with constant\n  subtraction technique for shallow water equations   In this paper, we propose a new well-balanced fifth-order finite volume WENO\nmethod for solving one- and two-dimensional shallow water equations with bottom\ntopography. The well-balanced property is crucial to the ability of a scheme to\nsimulate perturbation waves over the ``lake-at-rest'' steady state such as\nwaves on a lake or tsunami waves in the deep ocean. We adopt the constant\nsubtraction technique such that both the flux gradient and source term in the\nnew pre-balanced form vanish at the lake-at-rest steady state, while the\nwell-balanced WENO method by Xing and Shu [Commun. Comput. Phys., 2006] uses\nhigh-order accurate numerical discretization of the source term and makes the\nexact balance between the source term and the flux gradient, to achieve the\nwell-balanced property. The scaling positivity-preserving limiter is used for\nthe water height near the dry areas. The fifth-order WENO-AO reconstruction is\nused to construct the solution since it has better resolution than the WENO-ZQ\nand WENO-MR reconstructions for the perturbation of steady state flows.\nExtensive one- and two-dimensional numerical examples are presented to\ndemonstrate the well-balanced, fifth-order accuracy, non-oscillatory, and\npositivity-preserving properties of the proposed method.\n"", 'A spatial-temporal weight analysis and novel nonlinear weights of\n  weighted essentially non-oscillatory schemes for hyperbolic conservation laws   In this paper we analyze the weighted essentially non-oscillatory (WENO)\nschemes in the finite volume framework by examining the first step of the\nexplicit third-order total variation diminishing Runge-Kutta method. The\nrationale for the improved performance of the finite volume WENO-M, WENO-Z and\nWENO-ZR schemes over WENO-JS in the first time step is that the nonlinear\nweights corresponding to large errors are adjusted to increase the accuracy of\nnumerical solutions. Based on this analysis, we propose novel Z-type nonlinear\nweights of the finite volume WENO scheme for hyperbolic conservation laws.\nInstead of taking the difference of the smoothness indicators for the global\nsmoothness indicator, we employ the logarithmic function with tuners to ensure\nthat the numerical dissipation is reduced around discontinuities while the\nessentially non-oscillatory property is preserved. The proposed scheme does not\nnecessitate substantial extra computational expenses. Numerical examples are\npresented to demonstrate the capability of the proposed WENO scheme in shock\ncapturing.\n']","[('finite volume schemes', 0.49831217527389526), ('hyperbolic conservation laws', 0.45879754424095154), ('hyperbolic conservation', 0.4580504894256592), ('numerical fluxes', 0.445628821849823), ('shallow water equations', 0.41606998443603516), ('volume schemes', 0.41351190209388733), ('numerical', 0.3971529006958008), ('order schemes', 0.3441780209541321), ('finite difference', 0.33267083764076233), ('water equations', 0.3260359764099121)]"
39,39,428,39_hausdorff dimension_self affine measures_dimension self_fractal dimension,"['hausdorff dimension', 'self affine measures', 'dimension self', 'fractal dimension', 'dimension theory', 'fractal dimensions', 'dimensions self', 'assouad dimension', 'affine measures', 'fractal sets']","[""The Assouad dimension of self-affine measures on sponges   We derive upper and lower bounds for the Assouad and lower dimensions of\nself-affine measures in $\\mathbb{R}^d$ generated by diagonal matrices and\nsatisfying suitable separation conditions. The upper and lower bounds always\ncoincide for $d=2,3$ yielding precise explicit formulae for the dimensions.\nMoreover, there are easy to check conditions guaranteeing that the bounds\ncoincide for $d \\geq 4$.\n  An interesting consequence of our results is that there can be a `dimension\ngap' for such self-affine constructions, even in the plane. That is, we show\nthat for some self-affine carpets of `Bara\\'nski type' the Assouad dimension of\nall associated self-affine measures strictly exceeds the Assouad dimension of\nthe carpet by some fixed $\\delta>0$ depending only on the carpet. We also\nprovide examples of self-affine carpets of `Bara\\'nski type' where there is no\ndimension gap and in fact the Assouad dimension of the carpet is equal to the\nAssouad dimension of a carefully chosen self-affine measure.\n"", 'Assouad-type Dimensions of Overlapping Self-affine Sets   We study the Assouad and quasi-Assoaud dimensions of dominated rectangular\nself-affine sets in the plane. In contrast to previous work on the dimension\ntheory of self-affine sets, we assume that the sets satisfy certain separation\nconditions on the projection to the principal axis, but otherwise have\narbitrary overlaps in the plane. We introduce and study regularity properties\nof a certain symbolic non-autonomous iterated function system corresponding to\n""symbolic slices"" of the self-affine set. We then establish dimensional\nformulas for the self-affine sets in terms of the dimension of the projection\nalong with the maximal dimension of slices orthogonal to the projection. Our\nresults are new even in the case when the self-affine set satisfies the strong\nseparation condition: in fact, as an application, we show that self-affine sets\nsatisfying the strong separation condition can have distinct Assouad and\nquasi-Assouad dimensions, answering a question of the first named author.\n', ""Tangents and slices of self-affine carpets   We study the fine scaling properties of planar self-affine carpets. For\nGatzouras--Lalley carpets, we give a precise formula for maximal Hausdorff\ndimension of a tangent in terms of the Hausdorff dimension of the projection\nand the Assouad dimension of the corresponding vertical slice. Using regularity\nproperties for the Assouad dimension of non-autonomous self-similar sets, this\nimplies that the set of points with tangents that are as large as possible has\nfull Hausdorff measure, at the critical exponent. On the other hand, we give an\nexplicit example of a Bara\\'nski carpet for which the Hausdorff dimension of\nthe set of points for which there exists a maximal tangent has Hausdorff\ndimension strictly less than the Hausdorff dimension of the original carpet.\n""]","[('hausdorff dimension', 0.6743176579475403), ('self affine measures', 0.626956045627594), ('dimension self', 0.6207682490348816), ('fractal dimension', 0.607244610786438), ('dimension theory', 0.5570173263549805), ('fractal dimensions', 0.5543171763420105), ('dimensions self', 0.5542188286781311), ('assouad dimension', 0.5503014922142029), ('affine measures', 0.5351769924163818), ('fractal sets', 0.5139787197113037)]"
40,40,425,40_combinatorial games_combinatorial game_game theory_game played graph,"['combinatorial games', 'combinatorial game', 'game theory', 'game played graph', 'played graph', 'winning strategy', 'winning strategies', 'strategy game', 'two player game', 'can win']","['The Maker-Breaker percolation game on a random board   The $(m,b)$ Maker-Breaker percolation game on $(\\mathbb{Z}^2)_p$, introduced\nby Day and Falgas-Ravry, is played in the following way. Before the game\nstarts, each edge of $\\mathbb{Z}^2$ is removed independently with probability\n$1-p$. After that, Maker chooses a vertex $v_0$ to protect. Then, in each round\nMaker and Breaker claim respectively $m$ and $b$ unclaimed edges of $G$.\nBreaker wins if after the removal of the edges claimed by him the component of\n$v_0$ becomes finite, and Maker wins if she can indefinitely prevent Breaker\nfrom winning.\n  We show that for any $p < 1$, Breaker almost surely has a wining strategy for\nthe $(1,1)$ game on $(\\mathbb{Z}^2)_p$. This fully answers a question of Day\nand Falgas-Ravry, who showed that for $p = 1$ Maker has a winning strategy for\nthe $(1,1)$ game. Further, we show that in the $(2,1)$ game on\n$(\\mathbb{Z}^2)_p$ Maker almost surely has a winning strategy whenever $p >\n0.9402$, while Breaker almost surely has a winning strategy whenever $p <\n0.5278$. This shows that the threshold value of $p$ above which Maker has a\nwinning strategy for the $(2,1)$ game on $\\mathbb{Z}^2$ is non-trivial. In\nfact, we prove similar results in various settings, including other lattices\nand biases $(m,b)$.\n  These results extend also to the most general case, which we introduce, where\neach edge is given to Maker with probability $\\alpha$ and to Breaker with\nprobability $\\beta$ before the game starts.\n', 'A Constructive Winning Maker Strategy in the Maker-Breaker $C_4$-Game   Maker-Breaker subgraph games are among the most famous combinatorial games.\nFor given $n,q \\in \\mathbb{N}$ and a subgraph $C$ of the complete graph $K_n$,\nthe two players, called Maker and Breaker, alternately claim edges of $K_n$. In\neach round of the game Maker claims one edge and Breaker is allowed to claim up\nto $q$ edges. If Maker is able to claim all edges of a copy of $C$, he wins the\ngame. Otherwise Breaker wins. In this work we introduce the first constructive\nstrategy for Maker for the $C_4$-Maker-Breaker game and show that he can win\nthe game if $q < 0.16 n^{2/3}$. According to the theorem of Bednarska and\nLuczak (2000) $n^{2/3}$ is asymptotically optimal for this game, but the\nconstant given there for a random Maker strategy is magnitudes apart from our\nconstant 0.16.\n', 'Maker-Breaker Percolation Games I: Crossing Grids   Motivated by problems in percolation theory, we study the following 2-player\npositional game. Let $\\Lambda_{m \\times n}$ be a rectangular grid-graph with\n$m$ vertices in each row and $n$ vertices in each column. Two players, Maker\nand Breaker, play in alternating turns. On each of her turns, Maker claims $p$\n(as-yet unclaimed) edges of the board $\\Lambda_{m \\times n}$, while on each of\nhis turns Breaker claims $q$ (as-yet unclaimed) edges of the board and destroys\nthem. Maker wins the game if she manages to claim all the edges of a crossing\npath joining the left-hand side of the board to its right-hand side, otherwise\nBreaker wins. We call this game the $(p,q)$-crossing game on $\\Lambda_{m \\times\nn}$.\n  Given $m,n\\in \\mathbb{N}$, for which pairs $(p,q)$ does Maker have a winning\nstrategy for the $(p,q)$-crossing game on $\\Lambda_{m \\times n}$? The\n$(1,1)$-case corresponds exactly to the popular game of Bridg-it, which is well\nunderstood due to it being a special case of the older Shannon switching game.\nIn this paper, we study the general $(p,q)$-case. Our main result is to\nestablish the following transition:\n  $\\bullet$ If $p\\geqslant 2q$, then Maker wins the game on arbitrarily long\nversions of the narrowest board possible, i.e. Maker has a winning strategy for\nthe $(2q, q)$-crossing game on $\\Lambda_{m \\times(q+1)}$ for any $m\\in\n\\mathbb{N}$;\n  $\\bullet$ if $p\\leqslant 2q-1$, then for every width $n$ of the board,\nBreaker has a winning strategy for the $(p,q)$-crossing game on $\\Lambda_{m\n\\times n}$ for all sufficiently large board-lengths $m$.\n  Our winning strategies in both cases adapt more generally to other grids and\ncrossing games. In addition we pose many new questions and problems.\n']","[('combinatorial games', 0.56508469581604), ('combinatorial game', 0.549239456653595), ('game theory', 0.503360390663147), ('game played graph', 0.4994741678237915), ('played graph', 0.4409196972846985), ('winning strategy', 0.42470064759254456), ('winning strategies', 0.42316678166389465), ('strategy game', 0.3965260088443756), ('two player game', 0.3707963228225708), ('can win', 0.3680345416069031)]"
41,41,415,41_black holes_black hole_de sitter spacetimes_einstein vacuum equations,"['black holes', 'black hole', 'de sitter spacetimes', 'einstein vacuum equations', 'schwarzschild black', 'sitter spacetimes', 'einstein scalar', 'positive cosmological', 'einstein vacuum', 'general relativity']","['Spectral (in)stability of quasinormal modes and strong cosmic censorship   Recent studies have shown that quasinormal modes suffer from spectral\ninstabilities, a frailty of black holes that leads to disproportional migration\nof their spectra in the complex plane when black-hole effective potentials are\nmodified by minuscule perturbations. Similar results have been found with the\nmathematical notion of the pseudospectrum which was recently introduced in\ngravitational physics. Environmental effects, such as the addition of a thin\naccretion disk or a matter shell, lead to a secondary bump that appears in the\neffective potential of black hole perturbations. Regardless of the\nenvironment\'s small contribution to the effective potential, its presence can\ncompletely destabilize the fundamental quasinormal mode and may potentially\naffect black hole spectroscopy. Here, we perform a comprehensive analysis of\nsuch phenomenon for Schwarzschild, Reissner-Nordstr\\""om, Schwarzschild-de\nSitter, and Reissner-Nordstr\\""om-de Sitter black holes by considering the\npotential for a test scalar field with the addition of a tiny bump sufficiently\naway from the photon sphere. We find a qualitatively similar destabilization\npattern for photon sphere, complex, scalar quasinormal modes in all cases, and\na surprising spectral stability for dominant scalar, purely imaginary, de\nSitter and near-extremal modes that belong to different families of the\nspectrum. For Reissner-Nordstr\\""om-de Sitter black holes, we re-evaluate the\nvalidity of the strong cosmic censorship and find that the addition of a\nrealistic bump in the effective potential cannot prevent its violation due to a\ncombination of the spectral stability of dominant de Sitter and near-extremal\nmodes for small cosmological constants and an ineffective migration of the\nphoton sphere modes that dominate the late-time ringdown signal for\nsufficiently large cosmological constants.\n', 'Gravitational collapse to extremal black holes and the third law of\n  black hole thermodynamics   We construct examples of black hole formation from regular, one-ended\nasymptotically flat Cauchy data for the Einstein-Maxwell-charged scalar field\nsystem in spherical symmetry which are exactly isometric to extremal\nReissner-Nordstr\\""om after a finite advanced time along the event horizon.\nMoreover, in each of these examples the apparent horizon of the black hole\ncoincides with that of a Schwarzschild solution at earlier advanced times. In\nparticular, our result can be viewed as a definitive disproof of the ""third law\nof black hole thermodynamics.""\n  The main step in the construction is a novel $C^k$ characteristic gluing\nprocedure, which interpolates between a light cone in Minkowski space and a\nReissner-Nordstr\\""om event horizon with specified charge to mass ratio $e/M$.\nOur setup is inspired by the recent work of Aretakis-Czimek-Rodnianski on\nperturbative characteristic gluing for the Einstein vacuum equations. However,\nour construction is fundamentally nonperturbative and is based on a finite\ncollection of scalar field pulses which are modulated by the Borsuk-Ulam\ntheorem.\n', 'Uniqueness of extremal charged black holes in de Sitter   We prove a uniqueness theorem for the charged Nariai black holes and\nultracold black holes in four dimensions. In particular, we show that an\nanalytic solution to four-dimensional Einstein-Maxwell theory with a positive\ncosmological constant containing a static extremal Killing horizon with\nspherical cross-sections of large radius (compared to the cosmological scale),\nmust be locally isometric to the extremal Reissner-Nordstr\\""om-de Sitter black\nhole or its near-horizon geometry. The theorem generalises to extremal static\nhorizons with small radius, establishing uniqueness of cold black holes for\ngeneric values of the radius.\n']","[('black holes', 0.6131636500358582), ('black hole', 0.5596070289611816), ('de sitter spacetimes', 0.5466445684432983), ('einstein vacuum equations', 0.5440360307693481), ('schwarzschild black', 0.516690731048584), ('sitter spacetimes', 0.49376681447029114), ('einstein scalar', 0.4719286561012268), ('positive cosmological', 0.4569825232028961), ('einstein vacuum', 0.4507296085357666), ('general relativity', 0.4502578377723694)]"
42,42,412,42_estimating causal_average treatment effects_causal inference_average treatment effect,"['estimating causal', 'average treatment effects', 'causal inference', 'average treatment effect', 'effect estimation', 'estimators', 'causal effects', 'estimating', 'treatment effects', 'unobserved']","['The CATT SATT on the MATT: semiparametric inference for sample treatment\n  effects on the treated   We study variants of the average treatment effect on the treated with\npopulation parameters replaced by their sample counterparts. For each estimand,\nwe derive the limiting distribution with respect to a semiparametric efficient\nestimator of the population effect and provide guidance on variance estimation.\nIncluded in our analysis is the well-known sample average treatment effect on\nthe treated, for which we obtain some unexpected results. Unlike the ordinary\nsample average treatment effect, we find that the asymptotic variance for the\nsample average treatment effect on the treated is point-identified and\nconsistently estimable, but it potentially exceeds that of the population\nestimand. To address this shortcoming, we propose a modification that yields a\nnew estimand, the mixed average treatment effect on the treated, which is\nalways estimated more precisely than both the population and sample effects. We\nalso introduce a second new estimand that arises from an alternative\ninterpretation of the treatment effect on the treated with which all\nindividuals are weighted by the propensity score.\n', 'Regression-adjusted average treatment effect estimates in stratified\n  randomized experiments   Researchers often use linear regression to analyse randomized experiments to\nimprove treatment effect estimation by adjusting for imbalances of covariates\nin the treatment and control groups. Our work offers a randomization-based\ninference framework for regression adjustment in stratified randomized\nexperiments. Under mild conditions, we re-establish the finite population\ncentral limit theorem for a stratified experiment. We prove that both the\nstratified difference-in-means and the regression-adjusted average treatment\neffect estimators are consistent and asymptotically normal. The asymptotic\nvariance of the latter is no greater and is typically lesser than that of the\nformer. We also provide conservative variance estimators to construct\nlarge-sample confidence intervals for the average treatment effect.\n', ""Semiparametric proximal causal inference   Skepticism about the assumption of no unmeasured confounding, also known as\nexchangeability, is often warranted in making causal inferences from\nobservational data; because exchangeability hinges on an investigator's ability\nto accurately measure covariates that capture all potential sources of\nconfounding. In practice, the most one can hope for is that covariate\nmeasurements are at best proxies of the true underlying confounding mechanism\noperating in a given observational study. In this paper, we consider the\nframework of proximal causal inference introduced by Miao et al. (2018);\nTchetgen Tchetgen et al. (2020), which while explicitly acknowledging covariate\nmeasurements as imperfect proxies of confounding mechanisms, offers an\nopportunity to learn about causal effects in settings where exchangeability on\nthe basis of measured covariates fails. We make a number of contributions to\nproximal inference including (i) an alternative set of conditions for\nnonparametric proximal identification of the average treatment effect; (ii)\ngeneral semiparametric theory for proximal estimation of the average treatment\neffect including efficiency bounds for key semiparametric models of interest;\n(iii) a characterization of proximal doubly robust and locally efficient\nestimators of the average treatment effect. Moreover, we provide analogous\nidentification and efficiency results for the average treatment effect on the\ntreated. Our approach is illustrated via simulation studies and a data\napplication on evaluating the effectiveness of right heart catheterization in\nthe intensive care unit of critically ill patients.\n""]","[('estimating causal', 0.5282000303268433), ('average treatment effects', 0.4836682677268982), ('causal inference', 0.4829055368900299), ('average treatment effect', 0.46095171570777893), ('effect estimation', 0.4286339581012726), ('estimators', 0.4091922342777252), ('causal effects', 0.39889323711395264), ('estimating', 0.38157957792282104), ('treatment effects', 0.37819772958755493), ('unobserved', 0.3750286102294922)]"
43,43,411,43_schur functions_schur polynomials_macdonald polynomials_quasisymmetric functions,"['schur functions', 'schur polynomials', 'macdonald polynomials', 'quasisymmetric functions', 'quasi symmetric functions', 'symmetric functions', 'semistandard tableaux', 'standard young tableaux', 'hall littlewood polynomials', 'quasi symmetric']","['Expanding quasisymmetric Schur $Q$-functions into peak Young\n  quasisymmetric Schur functions   The dual immaculate and Young quasisymmetric Schur bases of quasisymmetric\nfunctions possess analogues in the peak algebra: respectively, the\nquasisymmetric Schur $Q$-functions and the peak Young quasisymmetric Schur\nfunctions. We show elements of the former basis expand into the latter basis\nwith nonnegative coefficients.\n', ""Skew row-strict quasisymmetric Schur functions   Mason and Remmel introduced a basis for quasisymmetric functions known as the\nrow-strict quasisymmetric Schur functions. This basis is generated\ncombinatorially by fillings of composition diagrams that are analogous to the\nrow-strict tableaux that generate Schur functions. We introduce a modification\nknown as Young row-strict quasisymmetric Schur functions, which are generated\nby row-strict Young composition fillings. After discussing basic combinatorial\nproperties of these functions, we define a skew Young row-strict quasisymmetric\nSchur function using the Hopf algebra of quasisymmetric functions and then\nprove this is equivalent to a combinatorial description. We also provide a\ndecomposition of the skew Young row-strict quasisymmetric Schur functions into\na sum of Gessel's fundamental quasisymmetric functions and prove a\nmultiplication rule for the product of a Young row-strict quasisymmetric Schur\nfunction and a Schur function.\n"", 'Compact formulas for Macdonald polynomials and quasisymmetric Macdonald\n  polynomials   We present several new and compact formulas for the modified and integral\nform of the Macdonald polynomials, building on the compact ""multiline queue""\nformula for Macdonald polynomials due to Corteel, Mandelshtam, and Williams. We\nalso introduce a new quasisymmetric analogue of Macdonald polynomials. These\n""quasisymmetric Macdonald polynomials"" refine the (symmetric) Macdonald\npolynomials and specialize to the quasisymmetric Schur polynomials defined by\nHaglund, Luoto, Mason, and van Willigenburg.\n']","[('schur functions', 0.6462730169296265), ('schur polynomials', 0.6429260969161987), ('macdonald polynomials', 0.589475691318512), ('quasisymmetric functions', 0.5751291513442993), ('quasi symmetric functions', 0.5725226402282715), ('symmetric functions', 0.507175624370575), ('semistandard tableaux', 0.4884788990020752), ('standard young tableaux', 0.46837306022644043), ('hall littlewood polynomials', 0.4663620591163635), ('quasi symmetric', 0.45985034108161926)]"
44,44,410,44_algebraic tropical_tropical geometry_theory tropical_tropical curves,"['algebraic tropical', 'tropical geometry', 'theory tropical', 'tropical curves', 'moduli spaces tropical', 'tropicalization', 'tropical linear', 'tropical curve', 'tropical analogue', 'terms tropical']","['Cohomologically tropical varieties   Given the tropicalization of a complex subvariety of the torus, we define a\nmorphism between the tropical cohomology and the rational cohomology of their\nrespective tropical compactifications. We say that the subvariety of the torus\nis cohomologically tropical if this map is an isomorphism for all closed strata\nof the tropical compactification.\n  We prove that a sch\\""on subvariety of the torus is cohomologically tropical\nif and only if it is wundersch\\""on and its tropicalization is a tropical\nhomology manifold. The former property means that the open strata in the\nboundary of a tropical compactification are all connected and the mixed Hodge\nstructures on their cohomology are pure of maximum possible weight; the latter\nproperty requires that, locally, the tropicalization verifies tropical\nPoincar\\\'e duality.\n  We study other properties of cohomologically tropical and wundersch\\""on\nvarieties, and show that in a semistable degeneration to an arrangement of\ncohomologically tropical varieties, the Hodge numbers of the smooth fibers are\ncaptured in the tropical cohomology of the tropicalization. This extends the\nresults of Itenberg, Katzarkov, Mikhalkin, and Zharkov.\n', 'Tropical Normal Functions -- Higher Abel-Jacobi Invariants of Tropical\n  cycles   We consider the variation of tropical Hodge structure (TVHS) associated to\nfamilies of tropical varieties. The family of the tropical intermediate\nJacobians of the associated tropical Hodge structure defines a bundle of\ntropical Jacobians, whose sections we call the tropical normal functions. We\ndefine formal sequential derivatives of these functions on the base with\nrespect to the natural Gauss-Manin connection as the Hodge theoretic invariants\ndetecting tropical cycles in the fibers. The associated invariants which are\ndefined inductively are the higher Abel-Jacobi invariants in the tropical\ncategory. They naturally identify the tropical Bloch-Beilinson filtration on\nthe tropical Chow group. We examine this construction on the moduli of tropical\ncurves with marked points, in order to study the tropical tautological classes\nin the tautological ring of $\\mathcal{M}_{g,n}^{\\text{trop}}$. The expectation\nis the nontriviality of these cycles could be examined with less complexity in\nthe tropical category. The construction is compatible with the tropicalization\nfunctor on the category of schemes, and the aforementioned procedure will also\nprovide an alternative way to examine the relations in the tautological ring of\n$\\mathcal{M}_{g,n}$ in the schemes category.\n', 'Maximum Inscribed and Minimum Enclosing Tropical Balls of Tropical\n  Polytopes and Applications to Volume Estimation and Uniform Sampling   We consider a minimum enclosing and maximum inscribed tropical balls for any\ngiven tropical polytope over the tropical projective torus in terms of the\ntropical metric with the max-plus algebra. We show that we can obtain such\ntropical balls via linear programming. Then we apply minimum enclosing and\nmaximum inscribed tropical balls of any given tropical polytope to estimate the\nvolume of and sample uniformly from the tropical polytope.\n']","[('algebraic tropical', 0.7248362898826599), ('tropical geometry', 0.6453468203544617), ('theory tropical', 0.6326200366020203), ('tropical curves', 0.6249240040779114), ('moduli spaces tropical', 0.602134644985199), ('tropicalization', 0.5858491063117981), ('tropical linear', 0.5706323385238647), ('tropical curve', 0.5653814673423767), ('tropical analogue', 0.5642475485801697), ('terms tropical', 0.5622387528419495)]"
45,45,409,45_gradient ricci soliton_ricci solitons_ricci soliton_ricci curvature,"['gradient ricci soliton', 'ricci solitons', 'ricci soliton', 'ricci curvature', 'dimensional ricci', 'ricci tensor', 'solutions ricci', 'gradient ricci', 'ricci flows', 'singular ricci']","['On Complete Gradient Steady Ricci Solitons with Vanishing D-tensor   In this paper, we extend the work of Cao-Chen [9] on Bach-flat gradient Ricci\nsolitons to classify $n$-dimensional ($n\\ge 5$) complete $D$-flat gradient\nsteady Ricci solitons. More precisely, we prove that any $n$-dimensional\ncomplete noncompact gradient steady Ricci soliton with vanishing $D$-tensor is\neither Ricci-flat, or isometric to the Bryant soliton. Furthermore, the proof\nextends to the shrinking case and the expanding case as well.\n', 'Almost $\\eta$-Ricci solitons on Kenmotsu manifolds   In this paper we characterize the Einstein metrics in such broader classes of\nmetrics as almost $\\eta$-Ricci solitons and $\\eta$-Ricci solitons on Kenmotsu\nmanifolds, and generalize some results of other authors. First, we prove that a\nKenmotsu metric as an $\\eta$-Ricci soliton is Einstein metric if either it is\n$\\eta$-Einstein or the potential vector field $V$ is an infinitesimal contact\ntransformation or $V$ is collinear to the Reeb vector field. Further, we prove\nthat if a Kenmotsu manifold admits a gradient almost $\\eta$-Ricci soliton with\na Reeb vector field leaving the scalar curvature invariant, then it is an\nEinstein manifold. Finally, we present new examples of $\\eta$-Ricci solitons\nand gradient $\\eta$-Ricci solitons, which illustrate our results.\n', 'Triviality Results and Conjugate Radius Estimation of Ricci Solitons   The investigation of Ricci solitons is the focus of this work. We have proved\ntriviality results for compact gradient Ricci soliton under certain\nrestriction. Later, a rigidity result is derived for a compact gradient\nshrinking Ricci soliton. Also, we have estimated the conjugate radius for\nnon-compact gradient shrinking Ricci solitons with superharmonic potential.\nMoreover, an upper bound for the conjugate radius of Ricci soliton with\nconcircular potential vector field is determined. Finally, it is proved that a\nnon-compact gradient Ricci soliton with a pole and non-negative Ricci curvature\nis non-shrinking.\n']","[('gradient ricci soliton', 0.8153871893882751), ('ricci solitons', 0.798119843006134), ('ricci soliton', 0.7690591216087341), ('ricci curvature', 0.717526912689209), ('dimensional ricci', 0.7008510231971741), ('ricci tensor', 0.664598822593689), ('solutions ricci', 0.6633076667785645), ('gradient ricci', 0.639927327632904), ('ricci flows', 0.6228723526000977), ('singular ricci', 0.6222289800643921)]"
46,46,407,46_permutation patterns_pattern avoiding permutations_avoiding permutations_permutations length,"['permutation patterns', 'pattern avoiding permutations', 'avoiding permutations', 'permutations length', 'permutations avoiding', 'permutations s_n', 'alternating permutations', 'permutations', 'number permutations', 'permutation sigma']","['A Complete Enumeration of Ballot Permutations Avoiding Sets of Small\n  Patterns   Permutations whose prefixes contain at least as many ascents as descents are\ncalled ballot permutations. Lin, Wang, and Zhao have previously enumerated\nballot permutations avoiding small patterns and have proposed the problem of\nenumerating ballot permutations avoiding a pair of permutations of length $3$.\nWe completely enumerate ballot permutations avoiding two patterns of length $3$\nand we relate these avoidance classes with their respective recurrence\nrelations and formulas, which leads to an interesting bijection between ballot\npermutations avoiding $132$ and $312$ with left factors of Dyck paths. In\naddition, we also conclude the Wilf-classification of ballot permutations\navoiding sets of two patterns of length $3$, and we then extend our results to\ncompletely enumerate ballot permutations avoiding three patterns of length $3$.\n', 'Pattern-avoiding shallow permutations   Shallow permutations were defined in 1977 to be those that satisfy the lower\nbound of the Diaconis-Graham inequality. Recently, there has been renewed\ninterest in these permutations. In particular, Berman and Tenner showed they\nsatisfy certain pattern avoidance conditions in their cycle form and Woo showed\nthey are exactly those whose cycle diagrams are unlinked. Shallow permutations\nthat avoid 321 have appeared in many contexts; they are those permutations for\nwhich depth equals the reflection length, they have unimodal cycles, and they\nhave been called Boolean permutations. Motivated by this interest in\n321-avoiding shallow permutations, we investigate $\\sigma$-avoiding shallow\npermutations for all $\\sigma \\in \\mathcal{S}_3$. To do this, we develop more\ngeneral structural results about shallow permutations, and apply them to\nenumerate shallow permutations avoiding any pattern of length 3.\n', ""Descent generating polynomials for ($n-3$)- and ($n-4$)-stack-sortable\n  (pattern-avoiding) permutations   In this paper, we find distribution of descents over $(n-3)$- and\n$(n-4)$-stack-sortable permutations in terms of Eulerian polynomials. Our\nresults generalize the enumeration results by Claesson, Dukes, and\nSteingr\\'{\\i}msson on $(n-3)$- and $(n-4)$-stack-sortable permutations.\nMoreover, we find distribution of descents on $(n-2)$-, $(n-3)$- and\n$(n-4)$-stack-sortable permutations that avoid any given pattern of length 3,\nwhich extends known results in the literature on distribution of descents over\npattern-avoiding 1- and 2-stack-sortable permutations. Our distribution results\nalso give enumeration of $(n-2)$-, $(n-3)$- and $(n-4)$-stack-sortable\npermutations avoiding any pattern of length 3. One of our conjectures links our\nwork to stack-sorting with restricted stacks, and the other conjecture states\nthat 213-avoiding permutations sortable with $t$ stacks are equinumerous with\n321-avoiding permutations sortable with $t$ stacks for any $t$.\n""]","[('permutation patterns', 0.6891365647315979), ('pattern avoiding permutations', 0.6754373908042908), ('avoiding permutations', 0.6469812393188477), ('permutations length', 0.6260338425636292), ('permutations avoiding', 0.6240009069442749), ('permutations s_n', 0.5928261876106262), ('alternating permutations', 0.5714940428733826), ('permutations', 0.5664812922477722), ('number permutations', 0.5579226016998291), ('permutation sigma', 0.5549122095108032)]"
47,47,405,47_policy gradient methods_policy optimization_reinforcement learning rl_policy gradient,"['policy gradient methods', 'policy optimization', 'reinforcement learning rl', 'policy gradient', 'optimal policy', 'discounted markov', 'optimal policies', 'reinforcement learning', 'constrained markov decision', 'markov decision processes']","['Provably Efficient Representation Selection in Low-rank Markov Decision\n  Processes: From Online to Offline RL   The success of deep reinforcement learning (DRL) lies in its ability to learn\na representation that is well-suited for the exploration and exploitation task.\nTo understand how the choice of representation can improve the efficiency of\nreinforcement learning (RL), we study representation selection for a class of\nlow-rank Markov Decision Processes (MDPs) where the transition kernel can be\nrepresented in a bilinear form. We propose an efficient algorithm, called\nReLEX, for representation learning in both online and offline RL. Specifically,\nwe show that the online version of ReLEX, called ReLEX-UCB, always performs no\nworse than the state-of-the-art algorithm without representation selection, and\nachieves a strictly better constant regret if the representation function class\nhas a ""coverage"" property over the entire state-action space. For the offline\ncounterpart, ReLEX-LCB, we show that the algorithm can find the optimal policy\nif the representation class can cover the state-action space and achieves\ngap-dependent sample complexity. This is the first result with constant sample\ncomplexity for representation learning in offline RL.\n', 'Reward-Free Model-Based Reinforcement Learning with Linear Function\n  Approximation   We study the model-based reward-free reinforcement learning with linear\nfunction approximation for episodic Markov decision processes (MDPs). In this\nsetting, the agent works in two phases. In the exploration phase, the agent\ninteracts with the environment and collects samples without the reward. In the\nplanning phase, the agent is given a specific reward function and uses samples\ncollected from the exploration phase to learn a good policy. We propose a new\nprovably efficient algorithm, called UCRL-RFE under the Linear Mixture MDP\nassumption, where the transition probability kernel of the MDP can be\nparameterized by a linear function over certain feature mappings defined on the\ntriplet of state, action, and next state. We show that to obtain an\n$\\epsilon$-optimal policy for arbitrary reward function, UCRL-RFE needs to\nsample at most $\\tilde{\\mathcal{O}}(H^5d^2\\epsilon^{-2})$ episodes during the\nexploration phase. Here, $H$ is the length of the episode, $d$ is the dimension\nof the feature mapping. We also propose a variant of UCRL-RFE using\nBernstein-type bonus and show that it needs to sample at most\n$\\tilde{\\mathcal{O}}(H^4d(H + d)\\epsilon^{-2})$ to achieve an\n$\\epsilon$-optimal policy. By constructing a special class of linear Mixture\nMDPs, we also prove that for any reward-free algorithm, it needs to sample at\nleast $\\tilde \\Omega(H^2d\\epsilon^{-2})$ episodes to obtain an\n$\\epsilon$-optimal policy. Our upper bound matches the lower bound in terms of\nthe dependence on $\\epsilon$ and the dependence on $d$ if $H \\ge d$.\n', 'Stochastic first-order methods for average-reward Markov decision\n  processes   We study average-reward Markov decision processes (AMDPs) and develop novel\nfirst-order methods with strong theoretical guarantees for both policy\noptimization and policy evaluation. Compared with intensive research efforts in\nfinite sample analysis of policy gradient methods for discounted MDPs, existing\nstudies on policy gradient methods for AMDPs mostly focus on regret bounds\nunder restrictive assumptions, and they often lack guarantees on the overall\nsample complexities. Towards this end, we develop an average-reward stochastic\npolicy mirror descent (SPMD) method for solving AMDPs with and without\nregularizers and provide convergence guarantees in terms of the long-term\naverage reward. For policy evaluation, existing on-policy methods suffer from\nsub-optimal convergence rates as well as failure in handling insufficiently\nrandom policies due to the lack of exploration in the action space. To remedy\nthese issues, we develop a variance-reduced temporal difference (VRTD) method\nwith linear function approximation for randomized policies along with optimal\nconvergence guarantees, and design an exploratory VRTD method that resolves the\nexploration issue and provides comparable convergence guarantees. By combining\nthe policy evaluation and policy optimization parts, we establish sample\ncomplexity results for solving AMDPs under both generative and Markovian noise\nmodels. It is worth noting that when linear function approximation is utilized,\nour algorithm only needs to update in the low-dimensional parameter space and\nthus can handle MDPs with large state and action spaces.\n']","[('policy gradient methods', 0.5961518883705139), ('policy optimization', 0.5866567492485046), ('reinforcement learning rl', 0.5787047147750854), ('policy gradient', 0.5472708940505981), ('optimal policy', 0.5217691659927368), ('discounted markov', 0.5185737013816833), ('optimal policies', 0.5170655250549316), ('reinforcement learning', 0.5112757086753845), ('constrained markov decision', 0.5041696429252625), ('markov decision processes', 0.479580819606781)]"
48,48,404,48_semilinear wave equations_damped wave equations_semilinear damped wave_solutions semilinear wave,"['semilinear wave equations', 'damped wave equations', 'semilinear damped wave', 'solutions semilinear wave', 'semilinear damped', 'semilinear wave', 'time dependent damping', 'nonlinear wave equations', 'damped wave', 'wave equations']","['The lifespan of solutions of semilinear wave equations with the\n  scale-invariant damping in two space dimensions   In this paper, we study the initial value problem for semilinear wave\nequations with the time-dependent and scale-invariant damping in two\ndimensions. Similarly to the one dimensional case by Kato, Takamura and Wakasa\nin 2019, we obtain the lifespan estimates of the solution for a special\nconstant in the damping term, which are classified by total integral of the sum\nof the initial position and speed. The key fact is that, only in two space\ndimensions, such a special constant in the damping term is a threshold between\n""wave-like"" domain and ""heat-like"" domain. As a result, we obtain a new type of\nestimate especially for the critical exponent.\n', 'Sharp lifespan estimates for the weakly coupled system of semilinear\n  damped wave equations in the critical case   The open question, which seems to be also the final part, in terms of\nstudying the Cauchy problem for the weakly coupled system of damped wave\nequations or reaction-diffusion equations, is so far known as the sharp\nlifespan estimates in the critical case. In this paper, we mainly investigate\nlifespan estimates for solutions to the weakly coupled system of semilinear\ndamped wave equations in the critical case. By using a suitable test function\nmethod associated with nonlinear differential inequalities, we catch upper\nbound estimates for the lifespan. Moreover, we establish polynomial-logarithmic\ntype time-weighted Sobolev spaces to obtain lower bound estimates for the\nlifespan in low spatial dimensions. Then, together with the derived lifespan\nestimates, new and sharp results on estimates for the lifespan in the critical\ncase are claimed. Finally, we give an application of our results to the\nsemilinear reaction-diffusion system in the critical case.\n', 'Heat-like and wave-like lifespan estimates for solutions of semilinear\n  damped wave equations via a Kato\'s type lemma   In this paper we study several semilinear damped wave equations with\n""subcritical"" nonlinearities, focusing on demonstrating lifespan estimates for\nenergy solutions. Our main concern is on equations with scale-invariant damping\nand mass. Under different assumptions imposed on the initial data, lifespan\nestimates from above are clearly showed. The key fact is that we find\n""transition surfaces"", which distinguish lifespan estimates between ""wave-like""\nand ""heat-like"" behaviours. Moreover we conjecture that the lifespan estimates\non the ""transition surfaces"" can be logarithmically improved. As direct\nconsequences, we reorganize the blow-up results and lifespan estimates for the\nmassless case in which the ""transition surfaces"" degenerate to ""transition\ncurves"". Furthermore, we obtain improved lifespan estimates in one space\ndimension, comparing to the known results. We also study semilinear wave\nequations with the scattering damping and negative mass term, and find that if\nthe decay rate of the mass term equals to 2, the lifespan estimate is the same\nas one special case of the equations with the scale-invariant damping and\npositive mass. The main strategy of the proof consists of a Kato\'s type lemma\nin integral form, which is established by iteration argument.\n']","[('semilinear wave equations', 0.6504999995231628), ('damped wave equations', 0.6388559937477112), ('semilinear damped wave', 0.6249153017997742), ('solutions semilinear wave', 0.623485267162323), ('semilinear damped', 0.5592295527458191), ('semilinear wave', 0.5351925492286682), ('time dependent damping', 0.5337944626808167), ('nonlinear wave equations', 0.5224816203117371), ('damped wave', 0.5209072828292847), ('wave equations', 0.499022513628006)]"
49,49,398,49_circular orbits_periodic orbits_orbits_periodic orbit,"['circular orbits', 'periodic orbits', 'orbits', 'periodic orbit', 'celestial mechanics', 'keplerian', 'orbit', 'circular restricted three', 'orbital', 'restricted three body']","['Branches and bifurcations of ejection-collision orbits in the planar\n  circular restricted three body problem   The goal of this paper it to prove existence theorems for one parameter\nfamilies (branches) of ejection-collision orbits in the planar circular\nrestricted three body problem (CRTBP), and to study some of their bifurcations.\nThe orbits considered are ejected from one primary body and collide with the\nother (as opposed to more local ejections-collision orbits which involve only a\nsingle body). We consider branches which are (i) parameterized by the Jacobi\nintegral (energy like quantity conserved by the CRTBP) and (ii) parameterized\nby the two body mass ratio when energy is fixed. The method of proof is\nconstructive and computer assisted, hence can be applied in non perturbative\nsettings and (potentially) to other conservative systems of differential\nequations. The main requirement is that the system should admit a change of\ncoordinates which regularizes the singularities (collisions). In the planar\nCRTBP the necessary regularization is provided by the classical Levi-Civita\ntransformation.\n', 'A dynamical study of Hilda asteroids in the Circular and Elliptic RTBP   The Hilda group is a set of asteroids whose mean motion is in a 3:2 orbital\nresonance with Jupiter. In this paper we use the planar Circular Restricted\nThree-Body Problem (CRTBP) as a dynamical model and we show that there exists a\nfamily of stable periodic orbits that are surrounded by islands of\nquasi-periodic motions. We have computed the frequencies of these\nquasi-periodic motions and we have shown how the Hilda family fits inside these\nislands. We have compared these results with the ones obtained using the\nElliptic Restricted Three-Body Problem and they are similar, showing the\nsuitability of the CRTBP model. It turns out that, to decide if a given\nasteroid belongs to the Hilda class, it is much better to look at its\nfrequencies in the planar CRTBP rather than to use two-body orbital elements as\nit is commonly done today.\n', ""Jacobi stability analysis of the classical restricted three body problem   The circular restricted three body problem, which considers the dynamics of\nan infinitesimal particle in the presence of the gravitational interaction with\ntwo massive bodies moving on circular orbits about their common center of mass,\nis a very useful model for investigating the behavior of real astronomical\nobjects in the Solar System. In such a system, there are five Lagrangian\nequilibrium points, and one important characteristic of the motion is the\nexistence of linearly stable equilibria at the two equilibrium points that form\nequilateral triangles with the primaries, in the plane of the primaries' orbit.\nWe analyze the stability of motion in the restricted three body problem by\nusing the concept of Jacobi stability, as introduced and developed in the\nKosambi-Cartan-Chern (KCC) theory. The KCC theory is a differential geometric\napproach to the variational equations describing the deviation of the whole\ntrajectory of a dynamical system with respect to the nearby ones. We obtain the\ngeneral result that, from the point of view of the KCC theory and of Jacobi\nstability, all five Lagrangian equilibrium points of the restricted three body\nproblem are unstable.\n""]","[('circular orbits', 0.6289022564888), ('periodic orbits', 0.5931240320205688), ('orbits', 0.5663216710090637), ('periodic orbit', 0.5516265630722046), ('celestial mechanics', 0.4694705009460449), ('keplerian', 0.44999873638153076), ('orbit', 0.4436573088169098), ('circular restricted three', 0.4273732900619507), ('orbital', 0.4184876084327698), ('restricted three body', 0.4081304967403412)]"
50,50,397,50_shallow water waves_water waves_water wave_shallow water equations,"['shallow water waves', 'water waves', 'water wave', 'shallow water equations', 'wave solutions', 'solitary wave solutions', 'water equations', 'surface waves', 'waves surface', 'solitary waves']","['On the capillary water waves with constant vorticity   This article is devoted to the study of local well-posedness for deep water\nwaves with constant vorticity in two space dimensions on the real line. The\nwater waves can be paralinearized and written as a quasilinear dispersive\nsystem of equations. By using the energy estimate and the Strichartz estimate,\nwe show that for $s> \\frac{5}{4}$, the gravity-capillary water wave system with\nconstant vorticity is locally well-posed in $\\mathcal{H}^{s}(\\mathbb{R})$.\n', 'Bifurcation of gravity-capillary Stokes waves with constant vorticity   We consider the gravity-capillary water waves equations of a 2D fluid with\nconstant vorticity. Using variational methods we prove the bifurcation of\nsteady periodic traveling water waves for {\\it all} the values of gravity,\nsurface tension, constant vorticity, depth and wavelenght, extending previous\nresults valid for restricted values of the parameters. We parametrize the\nbifurcating Stokes waves either with their speed or their momentum.\n', 'On the amplitude of steady water waves with positive constant vorticity   For two-dimensional steady pure-gravity water waves with a unidirectional\nflow of constant favourable vorticity, we prove an explicit bound on the\namplitude of the wave, which decays to zero as the vorticity tends to infinity.\nNotably, our result holds true for arbitrary water waves, that is, we do not\nhave to restrict ourselves to periodic or solitary or symmetric waves.\n']","[('shallow water waves', 0.6633684635162354), ('water waves', 0.6602864861488342), ('water wave', 0.6214060187339783), ('shallow water equations', 0.6138467192649841), ('wave solutions', 0.613305926322937), ('solitary wave solutions', 0.6016306281089783), ('water equations', 0.5905227661132812), ('surface waves', 0.5768841505050659), ('waves surface', 0.5724037289619446), ('solitary waves', 0.5521935820579529)]"
51,51,397,51_amenable groups_amenable group_measure preserving actions_actions countable,"['amenable groups', 'amenable group', 'measure preserving actions', 'actions countable', 'action countable', 'group actions', 'countable groups', 'compact groups', 'countable group', 'preserving action']","['Tail variational principle and asymptotic $h$-expansiveness for amenable\n  group actions   In this paper we prove the tail variational principle for actions of\ncountable amenable groups. This allows us to extend some characterizations of\nasymptotic $h$-expansiveness from $\\mathbb{Z}$-actions to actions of countable\namenable groups.\n', ""Multiorders in amenable group actions   The paper offers a thorough study of multiorders and their applications to\nmeasure-preserving actions of countable amenable groups. By a~{\\em multiorder}\non a~countable group we mean any probability measure $\\nu$ on the collection\n$\\tilde{\\mathcal{O}}$ of linear orders of type $\\mathbb Z$ on $G$, invariant\nunder the natural action of $G$ on such orders. Every free measure-preserving\n$G$-action $(X,\\mu,G)$ has a~multiorder $(\\tilde{\\mathcal{O}},\\nu,G)$ as a\nfactor and has the same orbits as the $\\mathbb Z$-action $(X,\\mu,S)$, where $S$\nis the \\emph{successor map} determined by the multiorder factor. Moreover, the\nsub-sigma-algebra $\\Sigma_{\\tilde{\\mathcal{O}}}$ associated with the multiorder\nfactor is invariant under $S$, which makes the corresponding $\\mathbb Z$-action\n$(\\tilde{\\mathcal{O}},\\nu,\\tilde S)$ a factor of $(X,\\mu,S)$. We prove that the\nentropy of any $G$-process generated by a finite partition of $X$, conditional\nwith respect to $\\Sigma_{\\tilde{\\mathcal{O}}}$, is preserved by the orbit\nequivalence with $(X,\\mu,S)$. Furthermore, this entropy can be computed in\nterms of the so-called random past, by a formula analogous to $\nh(\\mu,T,\\mathcal P)=H(\\mu,\\mathcal P|\\mathcal{P}^-)$ known for $\\mathbb\nZ$-actions. The above fact is then applied to prove a variant of a result by\nRudolph and Weiss. The original theorem states that orbit equivalence between\nfree actions of countable amenable groups preserves conditional entropy with\nrespect to a~sub-sigma-algebra $\\Sigma$, as soon as the ``orbit change'' is\nmeasurable with respect to $\\Sigma$. In our variant, we replace the\nmeasurability assumption by a~simpler one: $\\Sigma$ should be invariant under\nboth actions and the actions on the resulting factor should be free. In\nconclusion we provide a characterization of the Pinsker sigma-algebra of any\n$G$-process in terms of an appropriately defined remote past arising from a\nmultiorder.\n"", 'Folner tilings for actions of amenable groups   We show that every probability-measure-preserving action of a countable\namenable group G can be tiled, modulo a null set, using finitely many finite\nsubsets of G (""shapes"") with prescribed approximate invariance so that the\ncollection of tiling centers for each shape is Borel. This is a dynamical\nversion of the Downarowicz--Huczek--Zhang tiling theorem for countable amenable\ngroups and strengthens the Ornstein--Weiss Rokhlin lemma. As an application we\nprove that, for every countably infinite amenable group G, the crossed product\nof a generic free minimal action of G on the Cantor set is Z-stable.\n']","[('amenable groups', 0.6227824091911316), ('amenable group', 0.5867101550102234), ('measure preserving actions', 0.5484967231750488), ('actions countable', 0.5471590161323547), ('action countable', 0.5343608260154724), ('group actions', 0.5283998847007751), ('countable groups', 0.5121774077415466), ('compact groups', 0.49674147367477417), ('countable group', 0.4953179657459259), ('preserving action', 0.4733406901359558)]"
52,52,381,52_fractional brownian motion_fractional brownian motions_driven fractional brownian_fractional brownian,"['fractional brownian motion', 'fractional brownian motions', 'driven fractional brownian', 'fractional brownian', 'brownian motion hurst', 'fractional stochastic', 'dimensional fractional brownian', 'motion hurst parameter', 'hurst parameter', 'motion hurst']","['Stochastic differential equations driven by fractional Brownian motion   The aim of this paper is to analyse a WIS-stochastic differential equation\ndriven by fractional Brownian motion with H>0.5. For this, we summarise the\ntheory of fractional white noise and prove a fundamental L^2-estimate for\nWIS-integrals. We apply this to prove the existence and uniqueness of a\nsolution in L^2(P) of a WIS-stochastic differential equation driven fractional\nBrownian motion with H>0.5 under Lipschitz conditions on its coefficients.\n', 'Branching fractional Brownian motion: discrete approximations and\n  maximal displacement   We construct and study branching fractional Brownian motion with Hurst\nparameter $H\\in(1/2,1)$. The construction relies on a generalization of the\ndiscrete approximation of fractional Brownian motion (Hammond and Sheffield,\nProbability Theory and Related Fields, 2013) to power law P\\\'olya urns indexed\nby trees. We show that the first order of the speed of branching fractional\nBrownian motion with Hurst parameter $H$ is $ct^{H+1/2}$ where $c$ is explicit\nand only depends on the Hurst parameter. A notion of ""branching property"" for\nprocesses with memory emerges naturally from our construction.\n', 'A note on the continuity in the Hurst index of the solution of rough\n  differential equations driven by a fractional Brownian motion   Within the rough path framework we prove the continuity of the solution to\nrandom differential equations driven by fractional Brownian motion with respect\nto the Hurst parameter $H$ when $H \\in (1/3, 1/2]$.\n']","[('fractional brownian motion', 0.7912901639938354), ('fractional brownian motions', 0.7747256755828857), ('driven fractional brownian', 0.761769711971283), ('fractional brownian', 0.7424856424331665), ('brownian motion hurst', 0.7383249998092651), ('fractional stochastic', 0.718473494052887), ('dimensional fractional brownian', 0.6924065947532654), ('motion hurst parameter', 0.6250861883163452), ('hurst parameter', 0.5868803858757019), ('motion hurst', 0.5601426362991333)]"
53,53,375,53_zeros riemann zeta_riemann zeta critical_riemann zeta_zeta riemann,"['zeros riemann zeta', 'riemann zeta critical', 'riemann zeta', 'zeta riemann', 'zeros zeta', 'riemann zeta zeta', 'values riemann zeta', 'zeta zeros', 'zeta functions', 'riemann hypothesis']","[""Almost all of the nontrivial zeros of the Riemann zeta-function are on\n  the critical line   Applying Littlewood's lemma in connection to Riemann's Hypothesis and\nexploiting the symmetry of Riemann's $xi$ function we show that almost all\nnontrivial Riemann's Zeta zeros are on the critical line.\n"", 'A Proof of Riemann Hypothesis   The meromorphic function $W(s)$ introduced in the Riemann-Zeta function\n$\\zeta(s) = W(s) \\zeta(1-s)$ maps the line of $s = 1/2 + it$ onto the unit\ncircle in $W$-space. $|W(s)| = 0$ gives the trivial zeroes of the Riemann-Zeta\nfunction $\\zeta(s)$. In the range: $0 < |W(s)| \\neq 1$, $\\zeta(s)$ does not\nhave nontrivial zeroes. $|W(s)|=1$ is the necessary condition for the\nnontrivial zeros of the Riemann-Zeta function. Writing $s = \\sigma + it$, in\nthe range: $0 \\leq \\sigma \\leq 1$, but $\\sigma \\neq 1/2$, even if $|W(s)|=1$,\nthe Riemann-Zeta function $\\zeta(s)$ is non-zero. Based on these arguments, the\nnontrivial zeros of the Riemann-Zeta function $\\zeta(s)$ can only be on the $s\n= 1/2 + it$ critical line. Therefore a proof of the Riemann Hypothesis is\npresented.\n', 'All Zeros of the Riemann Zeta Function in the Critical Strip are Located\n  on the Critical Line and are Simple   In this paper we study the function G(z) :=\n  int{0,infinity} y^{z-1}(1 + \\exp(y))^{-1} dy,\n  for z in C. We derive a functional equation\n  that relates G(z) and G(1 - z) for all z in C,\n  and we prove:\n  -- That G and the Riemann Zeta function Zeta have\n  exactly the same zeros in the critical region\n  D := z in C: Re z in (0,1);\n  -- All the zeros of the Riemann Zeta function\n  located on the critical line are simple; and\n  -- The Riemann hypothesis, i.e., that all of the zeros\n  of G in D are located on the critical line L :=\n  {z in D : Re z = 1/2}.\n']","[('zeros riemann zeta', 0.8029151558876038), ('riemann zeta critical', 0.733368456363678), ('riemann zeta', 0.6899474859237671), ('zeta riemann', 0.6872190833091736), ('zeros zeta', 0.6745483875274658), ('riemann zeta zeta', 0.6742033362388611), ('values riemann zeta', 0.671841025352478), ('zeta zeros', 0.6690836548805237), ('zeta functions', 0.6660757064819336), ('riemann hypothesis', 0.6498871445655823)]"
54,54,370,54_random walks_random walk_random walks random_walks random,"['random walks', 'random walk', 'random walks random', 'walks random', 'symmetric random walk', 'reinforced random walk', 'reinforced random walks', 'simple random walk', 'random walk random', 'walk random']","['Limit theorems for a random walk with memory perturbed by a dynamical\n  system   We introduce a new random walk with unbounded memory obtained as a mixture of\nthe Elephant Random Walk and the Dynamic Random Walk which we call the Dynamic\nElephant Random Walk (DERW). As a consequence of this mixture the distribution\nof the increments of the resulting random process is time dependent. We prove a\nstrong law of large numbers for the DERW and, in a particular case, we provide\nan explicit expression for its speed. Finally, we give sufficient conditions\nfor the central limit theorem and the law of the iterated logarithm to hold.\n', 'Universal survival probability for a correlated random walk and\n  applications to records   We consider a model of space-continuous one-dimensional random walk with\nsimple correlation between the steps: the probability that two consecutive\nsteps have same sign is $q$ with $0\\leq q\\leq 1$. The parameter $q$ allows thus\nto control the persistence of the random walk. We compute analytically the\nsurvival probability of a walk of $n$ steps, showing that it is independent of\nthe jump distribution for any finite $n$. This universality is a consequence of\nthe Sparre-Andersen theorem for random walks with uncorrelated and symmetric\nsteps. We then apply this result to derive the distribution of the step at\nwhich the random walk reaches its maximum and the record statistics of the\nwalk, which show the same universality. In particular, we show that the\ndistribution of the number of records for a walk of $n\\gg 1$ steps is the same\nas for a random walk with $n_{\\rm eff}(q)=n/(2(1-q))$ uncorrelated and\nsymmetrically distributed steps. We also show that in the regime where $n\\to\n\\infty$ and $q\\to 1$ with $y=n(1-q)$, this model converges to the\nrun-and-tumble particle, a persistent random walk often used to model the\nmotion of bacteria. Our theoretical results are confirmed by numerical\nsimulations.\n', 'Asymptotic Analysis of the Elephant Random Walk   In this work we study asymptotic properties of a long range memory random\nwalk known as elephant random walk. First we prove recurrence and positive\nrecurrence for the elephant random walk. Then, we establish the transience\nregime of the model. Finally, under the Poisson Hypothesis, we study the\nreplica mean field limit for this random walk and we obtain an upper bound for\nthe expected distance of the walker from the origin.\n']","[('random walks', 0.7261306047439575), ('random walk', 0.6946095824241638), ('random walks random', 0.6918124556541443), ('walks random', 0.6813173890113831), ('symmetric random walk', 0.6783797740936279), ('reinforced random walk', 0.6666761636734009), ('reinforced random walks', 0.6620033979415894), ('simple random walk', 0.6591676473617554), ('random walk random', 0.6527147889137268), ('walk random', 0.6514910459518433)]"
55,55,365,55_local langlands correspondence_langlands correspondence_langlands conjecture_geometric langlands,"['local langlands correspondence', 'langlands correspondence', 'langlands conjecture', 'geometric langlands', 'langlands parameters', 'representations adic', 'langlands parameter', 'local langlands', 'supercuspidal representations', 'adic groups']","['Local Langlands Correspondence for Even Orthogonal Groups via Theta\n  Lifts   Using theta correspondence, we obtain a classification of irreducible\nrepresentations of an arbitrary even orthogonal group (i.e. the local Langlands\ncorrespondence) by deducing it from the local Langlands correspondence for\nsymplectic groups due to Arthur. Moreover,we show that our classifications\ncoincide with the local Langlands correspondence established by Arthur and\nformulated precisely by Atobe-Gan for quasi-split even orthogonal groups.\n', ""Functoriality for supercuspidal L-packets   Kaletha constructs $L$-packets for supercuspidal $L$-parameters of tame\n$p$-adic groups. These $L$-packets consist entirely of supercuspidal\nrepresentations, which are explicitly described. Using the explicit\ndescriptions, we show that Kaletha's $L$-packets satisfy a fundamental\nfunctoriality property desired for the Local Langlands Correspondence.\n"", ""Local Langlands correspondence for regular supercuspidal representations\n  of GL(n)   In this paper, we prove the coincidence of Kaletha's recent construction of\nthe local Langlands correspondence for regular supercuspidal representations\nwith Harris--Taylor's one in the case of general linear groups. The keys are\nBushnell--Henniart's essentially tame local Langlands correspondence and Tam's\nresult on Bushnell--Henniart's rectifiers. By combining them, our problem is\nreduced to an elementary root-theoretic computation on the difference between\nKaletha's and Tam's $\\chi$-data.\n""]","[('local langlands correspondence', 0.6997964978218079), ('langlands correspondence', 0.699392557144165), ('langlands conjecture', 0.5890706777572632), ('geometric langlands', 0.5528521537780762), ('langlands parameters', 0.533141016960144), ('representations adic', 0.5308319926261902), ('langlands parameter', 0.5164182782173157), ('local langlands', 0.5107206702232361), ('supercuspidal representations', 0.4911685883998871), ('adic groups', 0.48800602555274963)]"
56,56,362,56_server queue_single server queue_server queues_queueing systems,"['server queue', 'single server queue', 'server queues', 'queueing systems', 'queueing system', 'queueing', 'queue lengths', 'queueing networks', 'queue length', 'queue']","[""Randomized Routing to Remote Queues   We study load balancing for a queueing system where parallel stations are\ndistant from customers. In the presence of traveling delays, the\njoin-the-shortest-queue (JSQ) policy induces queue length oscillations and\nprolongs the mean waiting time. A variant of the JSQ policy, dubbed the\nrandomized join-the-shortest-queue (RJSQ) policy, is devised to mitigate the\noscillation phenomenon. By the RJSQ policy, customers are sent to each station\nwith a probability approximately proportional to its service capacity; only a\nsmall fraction of customers are purposely routed to the shortest queue. The\nadditional probability of routing a customer to the shortest queue, referred to\nas the balancing fraction, dictates the policy's performance. When the\nbalancing fraction is within a certain range, load imbalance between the\nstations is negligible in heavy traffic, so that complete resource pooling is\nachieved. We specify the optimal order of magnitude for the balancing fraction,\nby which heuristic formulas are proposed to fine-tune the RJSQ policy. A joint\nproblem of capacity planning and load balancing is considered for\ngeographically separated stations. With well planned service capacities, the\nRJSQ policy sends all but a small fraction of customers to the nearest\nstations, rendering the system asymptotically equivalent to an aggregated\nsingle-server system with all customers having minimum traveling delays. If\neach customer's service requirement does not depend on the station, the RJSQ\npolicy is asymptotically optimal for reducing workload.\n"", 'Zero Queueing for Multi-Server Jobs   Cloud computing today is dominated by multi-server jobs. These are jobs that\nrequest multiple servers simultaneously and hold onto all of these servers for\nthe duration of the job. Multi-server jobs add a lot of complexity to the\ntraditional one-job-per-server model: an arrival might not ""fit"" into the\navailable servers and might have to queue, blocking later arrivals and leaving\nservers idle. From a queueing perspective, almost nothing is understood about\nmulti-server job queueing systems; even understanding the exact stability\nregion is a very hard problem.\n  In this paper, we investigate a multi-server job queueing model under scaling\nregimes where the number of servers in the system grows. Specifically, we\nconsider a system with multiple classes of jobs, where jobs from different\nclasses can request different numbers of servers and have different service\ntime distributions, and jobs are served in first-come-first-served order. The\nmulti-server job model opens up new scaling regimes where both the number of\nservers that a job needs and the system load scale with the total number of\nservers. Within these scaling regimes, we derive the first results on\nstability, queueing probability, and the transient analysis of the number of\njobs in the system for each class. In particular we derive sufficient\nconditions for zero queueing. Our analysis introduces a novel way of extracting\ninformation from the Lyapunov drift, which can be applicable to a broader scope\nof problems in queueing systems.\n', 'On the SRPT Scheduling Discipline in Many-Server Queues with Impatient\n  Customers   The shortest-remaining-processing-time (SRPT) scheduling policy has been\nextensively studied, for more than 50 years, in single-server queues with\ninfinitely patient jobs. Yet, much less is known about its performance in\nmultiserver queues. In this paper, we present the first theoretical analysis of\nSRPT in multiserver queues with abandonment. In particular, we consider the\nM/GI/s+GI queue and demonstrate that, in the many-sever overloaded regime,\nperformance in the SRPT queue is equivalent, asymptotically in steady state, to\na preemptive two-class priority queue where customers with short service times\n(below a threshold) are served without wait, and customers with long service\ntimes (above a threshold) eventually abandon without service. We prove that the\nSRPT discipline maximizes, asymptotically, the system throughput, among all\nscheduling disciplines. We also compare the performance of the SRPT policy to\nblind policies and study the effects of the patience-time and service-time\ndistributions.\n']","[('server queue', 0.6747714281082153), ('single server queue', 0.6666238307952881), ('server queues', 0.663223922252655), ('queueing systems', 0.6590560078620911), ('queueing system', 0.6336919665336609), ('queueing', 0.6335346698760986), ('queue lengths', 0.6286018490791321), ('queueing networks', 0.6209797263145447), ('queue length', 0.6142797470092773), ('queue', 0.6024184823036194)]"
57,57,358,57_large cardinal_large cardinals_inaccessible cardinal_compact cardinal,"['large cardinal', 'large cardinals', 'inaccessible cardinal', 'compact cardinal', 'forcing notions', 'regular cardinals', 'cardinal characteristics', 'cardinal', 'forcings', 'proper forcing']","['Large cardinals need not be large in HOD   We prove that large cardinals need not generally exhibit their large cardinal\nnature in HOD. For example, a supercompact cardinal $\\kappa$ need not be weakly\ncompact in HOD, and there can be a proper class of supercompact cardinals in\n$V$, none of them weakly compact in HOD, with no supercompact cardinals in HOD.\nSimilar results hold for many other types of large cardinals, such as\nmeasurable and strong cardinals.\n', 'Large cardinals, structural reflection, and the HOD Conjecture   We introduce exacting cardinals and a strengthening of these, ultraexacting\ncardinals. These are natural large cardinals defined equivalently as weak forms\nof rank-Berkeley cardinals, strong forms of J\\\'onsson cardinals, or in terms of\nprinciples of structural reflection. However, they challenge commonly held\nintuition on strong axioms of infinity. We prove that ultraexacting cardinals\nare consistent with Zermelo-Fraenkel Set Theory with the Axiom of Choice (ZFC)\nrelative to the existence of an I0 embedding. However, the existence of an\nultraexacting cardinal below a measurable cardinal implies the consistency of\nZFC with a proper class of I0 embeddings, thus challenging the\nlinear-incremental picture of the large cardinal hierarchy. We show that the\nexistence of an exacting cardinal implies that V is not equal to HOD (G\\""odel\'s\nuniverse of Hereditarily Ordinal Definable sets), showing that these cardinals\nsurpass the current hierarchy of large cardinals consistent with ZFC. We prove\nthat the consistency of ZFC with an exacting cardinal above an extendible\ncardinal refutes Woodin\'s HOD Conjecture and Ultimate-L Conjecture. Finally, we\nestablish the consistency of ZFC with the existence of an exacting cardinal\nabove an extendible cardinal from the consistency of ZF with certain large\ncardinals beyond choice.\n', 'Forcing with overlapping supercompact extenders   We build a supercompact version of the forcing defined in \\cite{gitik2019}.\nFor each singular cardinal in the ground model with any fixed cofinality, which\nis a limit of supercompact cardinals, it is possible to force so that the size\nof the powerset of the singular cardinal is arbitrarily large, while preserving\nthe singular cardinal. An important feature of this forcing is that it is\npossible to define the forcing so that the successor of the singular cardinal\nis collapsed, but all the cardinals above it are preserved.\n']","[('large cardinal', 0.5831047296524048), ('large cardinals', 0.5718084573745728), ('inaccessible cardinal', 0.5606800317764282), ('compact cardinal', 0.5526294112205505), ('forcing notions', 0.5444687008857727), ('regular cardinals', 0.5443752408027649), ('cardinal characteristics', 0.5298759341239929), ('cardinal', 0.48094403743743896), ('forcings', 0.4761696457862854), ('proper forcing', 0.4759313762187958)]"
58,58,356,58_gromov witten invariants_witten invariants_gromov witten theory_vafa witten invariants,"['gromov witten invariants', 'witten invariants', 'gromov witten theory', 'vafa witten invariants', 'genus gromov witten', 'toric varieties', 'relative gromov witten', 'witten theory', 'calabi yau manifolds', 'gromov witten']","['Gromov--Witten invariants with naive tangency conditions   We introduce Gromov-Witten invariants with naive tangency conditions at the\nmarked points of the source curve. We then establish an explicit formula which\nexpresses Gromov-Witten invariants with naive tangency conditions in terms of\ndescendent Gromov-Witten invariants. Several examples of genus zero\nGromov-Witten invariants with naive tangencies are computed in the case of\ncurves and surfaces. In particular, the counts of rational curves naively\ntangent to an anticanonical divisor on a del Pezzo surface are studied, and via\nmirror symmetry, we obtain a relation to the local Gromov-Witten invariants.\n', 'Gromov-Witten Invariants and Mirror Symmetry For Non-Fano Varieties Via\n  Tropical Disks   Under mirror symmetry a non-Fano variety $X$ corresponds to an instanton\ncorrected Hori-Vafa potential $W$. The classical period of $W$ equals the\nregularized quantum period of $X$, which is a generating function for\ndescendant Gromov-Witten invariants. These periods define closed mirror maps\nrelating complex with symplectic parameters and open mirror maps relating\ncoordinates on the mirror curves.\n  We interpret the corrections to $W$ by broken lines in a scattering diagram,\nso that $W$ is the primitive theta function $\\vartheta_1$. We show that, after\nwall crossing to infinity and application of the closed mirror map,\n$W=\\vartheta_1$ is equal to the open mirror map. By tropical correspondence,\n$\\vartheta_1$ is a generating function for $2$-marked logarithmic Gromov-Witten\ninvariants, which are algebraic analogues of counts of Maslov index $2$ disks.\nThis generalizes the predictions of mirror symmetry to the non-Fano case.\n', 'Relative Gromov-Witten invariants and the enumerative meaning of mirror\n  maps for toric Calabi-Yau orbifolds   We provide an enumerative meaning of the mirror maps for toric Calabi-Yau\norbifolds in terms of relative Gromov-Witten invariants of the toric\ncompactifications. As a consequence, we obtain an equality between relative\nGromov-Witten invariants and open Gromov-Witten invariants. Therefore, the\ninstanton corrected mirrors for toric Calabi-Yau orbifolds can be constructed\nusing relative Gromov-Witten invariants.\n']","[('gromov witten invariants', 0.8194909691810608), ('witten invariants', 0.7346245050430298), ('gromov witten theory', 0.6893924474716187), ('vafa witten invariants', 0.6826517581939697), ('genus gromov witten', 0.6084805130958557), ('toric varieties', 0.5856683254241943), ('relative gromov witten', 0.5819631814956665), ('witten theory', 0.5595704913139343), ('calabi yau manifolds', 0.49897950887680054), ('gromov witten', 0.49778592586517334)]"
59,59,355,59_wright fisher diffusion_population dynamics_fisher diffusion_population genetics,"['wright fisher diffusion', 'population dynamics', 'fisher diffusion', 'population genetics', 'evolutionary dynamics', 'evolution population', 'natural selection', 'populations', 'evolutionary', 'structured population']","['Active information requirements for fixation on the Wright-Fisher model\n  of population genetics   In the context of population genetics, active information can be extended to\nmeasure the change of information of a given event (e.g., fixation of an\nallele) from a neutral model in which only genetic drift is taken into account\nto a non-neutral model that includes other sources of frequency variation\n(e.g., selection and mutation). In this paper we illustrate active information\nin population genetics through the Wright-Fisher model.\n', 'A dual process for the coupled Wright-Fisher diffusion   The coupled Wright-Fisher diffusion is a multi-dimensional Wright-Fisher\ndiffusion for multi-locus and multi-allelic genetic frequencies, expressed as\nthe strong solution to a system of stochastic differential equations that are\ncoupled in the drift, where the pairwise interaction among loci is modelled by\nan inter-locus selection. In this paper, an ancestral process, which is dual to\nthe coupled Wright-Fisher diffusion, is derived. The dual process corresponds\nto the block counting process of coupled ancestral selection graphs, one for\neach locus. Jumps of the dual process arise from coalescence, mutation,\nsingle-branching, which occur at one locus at the time, and double-branching,\nwhich occur simultaneously at two loci. The coalescence and mutation rates have\nthe typical structure of the transition rates of the Kingman coalescent\nprocess. The single-branching rate not only contains the one-locus selection\nparameters in a form that generalises the rates of an ancestral selection\ngraph, but it also contains the two-locus selection parameters to include the\neffect of the pairwise interaction on the single loci. The double-branching\nrate reflects the particular structure of pairwise selection interactions of\nthe coupled Wright-Fisher diffusion. Moreover, in the special case of two loci,\ntwo alleles, with selection and parent independent mutation, the stationary\ndensity for the coupled Wright-Fisher diffusion and the transition rates of the\ndual process are obtained in an explicit form.\n', 'The Wright-Fisher model with efficiency   In populations competing for resources, it is natural to ask whether\nconsuming fewer resources provides any selective advantage. To answer this\nquestion, we propose a Wright- Fisher model with two types of individuals: the\ninefficient individuals, those who need more resources to reproduce and can\nhave a higher growth rate, and the efficient individuals. In this model, the\ntotal amount of resource N, is fixed, and the population size varies randomly\ndepending on the number of efficient individuals. We show that, as N increases,\nthe frequency process of efficient individuals converges to a diffusion which\nis a generalisation of the Wright- Fisher diffusion with selection. The\ngenealogy of this model is given by a branching-coalescing process that we call\nthe Ancestral Selection/Efficiency Graph, and that is an extension of the\nAncestral Selection Graph (Krone and Neuhauser (1997a), Krone and Neuhauser\n(1997b)). The main contribution of this paper is that, in evolving populations,\ninefficiency can arise as a promoter of selective advantage and not necessarily\nas a trade-off.\n']","[('wright fisher diffusion', 0.6031842231750488), ('population dynamics', 0.5601502060890198), ('fisher diffusion', 0.5309566855430603), ('population genetics', 0.5290646553039551), ('evolutionary dynamics', 0.5201376676559448), ('evolution population', 0.514836847782135), ('natural selection', 0.463375061750412), ('populations', 0.4594831168651581), ('evolutionary', 0.43851935863494873), ('structured population', 0.4313550293445587)]"
60,60,344,60_mean field games_mean field game_mean field equilibrium_mean field control,"['mean field games', 'mean field game', 'mean field equilibrium', 'mean field control', 'games mean field', 'deterministic mean field', 'differential games', 'stationary mean field', 'state mean field', 'nash equilibria']","['Master equations for finite state mean field games with nonlinear\n  activations   We formulate a class of mean field games on a finite state space with\nvariational principles resembling those in continuous-state mean field games.\nWe construct a controlled continuity equation featuring a nonlinear activation\nfunction on graphs induced by finite-state reversible continuous time Markov\nchains. In these graphs, each edge is weighted by the transition probability\nand invariant measure of the original process. Using these controlled dynamics\non the graph and the dynamic programming principle for the value function, we\nderive several key components: the mean field game systems, the functional\nHamilton-Jacobi equations, and the master equations on a finite probability\nspace for potential mean field games. The existence and uniqueness of solutions\nto the potential mean field game system are ensured through a convex\noptimization reformulation in terms of the density-flux pair. We also derive\nvariational principles for the master equations of both non-potential games and\nmixed games on a continuous state space. Finally, we offer several concrete\nexamples of discrete mean field game dynamics on a two-point space, complete\nwith closed-formula solutions. These examples include discrete Wasserstein\ndistances, mean field planning, and potential mean field games.\n', 'Mean Field Games of Controls: Propagation of Monotonicities   The theory of Mean Field Game of Controls considers a class of mean field\ngames where the interaction is through the joint distribution of the state and\ncontrol. It is well known that, for standard mean field games, certain\nmonotonicity condition is crucial to guarantee the uniqueness of mean field\nequilibria and then the global wellposedness for master equations. In the\nliterature, the monotonicity condition could be the Lasry-Lions monotonicity,\nthe displacement monotonicity, or the anti-monotonicity conditions. In this\npaper, we investigate all these three types of monotonicity conditions for Mean\nField Games of Controls and show their propagation along the solutions to the\nmaster equations with common noises. In particular, we extend the displacement\nmonotonicity to semi-monotonicity, whose propagation result is new even for\nstandard mean field games. This is the first step towards the global\nwellposedness theory for master equations of Mean Field Games of Controls.\n', 'Linear-Quadratic Mean Field Games of Controls with Non-Monotone Data   In this paper, we study a class of linear-quadratic (LQ) mean field games of\ncontrols with common noises and their corresponding $N$-player games. The\ntheory of mean field game of controls considers a class of mean field games\nwhere the interaction is via the joint law of both the state and control. By\nthe stochastic maximum principle, we first analyze the limiting behavior of the\nrepresentative player and obtain his/her optimal control in a feedback form\nwith the given distributional flow of the population and its control. The mean\nfield equilibrium is determined by the Nash certainty equivalence (NCE) system.\nThanks to the common noise, we do not require any monotonicity conditions for\nthe solvability of the NCE system. We also study the master equation arising\nfrom LQ mean field games of controls, which is a finite-dimensional\nsecond-order parabolic equation. It can be shown that the master equation\nadmits a unique classical solution over an arbitrary time horizon without any\nmonotonicity conditions. Beyond that, we can solve the $N$-player games\ndirectly by further assuming the non-degeneracy of the idiosyncratic noises. As\nbyproducts, we prove the quantitative convergence results from the $N$-player\ngame to the mean field game and the propagation of chaos property for the\nrelated optimal trajectories.\n']","[('mean field games', 0.6479817628860474), ('mean field game', 0.6373040080070496), ('mean field equilibrium', 0.6156010031700134), ('mean field control', 0.5613215565681458), ('games mean field', 0.5479129552841187), ('deterministic mean field', 0.5356229543685913), ('differential games', 0.5031536817550659), ('stationary mean field', 0.495622456073761), ('state mean field', 0.47456467151641846), ('nash equilibria', 0.47352883219718933)]"
61,61,340,61_angled artin groups_angled artin group_artin groups_artin group,"['angled artin groups', 'angled artin group', 'artin groups', 'artin group', 'relatively hyperbolic groups', 'hyperbolic groups', 'groups hyperbolic', 'graphs groups', 'parabolic subgroups', 'hyperbolic group']","['Droms Theorems for twisted right-angled Artin groups   We characterize twisted right-angled Artin groups whose finitely generated\nsubgroups are also twisted right-angled Artin groups. Additionally, we give a\nclassification of coherence within this class of groups in terms of the\ndefining graph. Furthermore, we provide a solution to the isomorphism problem\nfor a notable subclass of these groups.\n', 'Uniqueness of quasi-roots in right-angled Artin Groups   We introduce the notion of quasi-roots and study their uniqueness in\nright-angled Artin groups.\n', 'Around subgroups of Artin groups: derived subgroups and acylindrical\n  hyperbolicity in the even FC-case   We generalize to (certain) Artin groups some results previously known for\nright-angled Artin groups (RAAGs). First, we generalize a result by Droms, B.\nServatius, and H. Servatius, and prove that the derived subgroup of an Artin\ngroup is free if and only if the group is coherent. Second, coherent Artin\ngroups over non complete graphs split as free amalgamated products along free\nabelian subgroups, and we extend to arbitrary Artin groups admitting such a\nsplitting a recent result by Casals-Ruiz and the first author on finitely\ngenerated normal subgroups of RAAGs. Finally, we use splittings of even Artin\ngroups of FC-type to generalize results of Minasyan and Osin on acylindrical\nhyperbolicity of their subgroups.\n']","[('angled artin groups', 0.7894687056541443), ('angled artin group', 0.7589459419250488), ('artin groups', 0.7222594618797302), ('artin group', 0.633009672164917), ('relatively hyperbolic groups', 0.5826070308685303), ('hyperbolic groups', 0.5629180669784546), ('groups hyperbolic', 0.5590132474899292), ('graphs groups', 0.5315252542495728), ('parabolic subgroups', 0.5139179229736328), ('hyperbolic group', 0.5001447200775146)]"
62,62,338,62_gradient descent training_gradient descent_stochastic gradient descent_relu neural networks,"['gradient descent training', 'gradient descent', 'stochastic gradient descent', 'relu neural networks', 'relu networks', 'shallow neural networks', 'gradient flow', 'layer neural networks', 'linear neural networks', 'layer neural']","['Implicit Bias of Gradient Descent for Two-layer ReLU and Leaky ReLU\n  Networks on Nearly-orthogonal Data   The implicit bias towards solutions with favorable properties is believed to\nbe a key reason why neural networks trained by gradient-based optimization can\ngeneralize well. While the implicit bias of gradient flow has been widely\nstudied for homogeneous neural networks (including ReLU and leaky ReLU\nnetworks), the implicit bias of gradient descent is currently only understood\nfor smooth neural networks. Therefore, implicit bias in non-smooth neural\nnetworks trained by gradient descent remains an open question. In this paper,\nwe aim to answer this question by studying the implicit bias of gradient\ndescent for training two-layer fully connected (leaky) ReLU neural networks. We\nshowed that when the training data are nearly-orthogonal, for leaky ReLU\nactivation function, gradient descent will find a network with a stable rank\nthat converges to $1$, whereas for ReLU activation function, gradient descent\nwill find a neural network with a stable rank that is upper bounded by a\nconstant. Additionally, we show that gradient descent will find a neural\nnetwork such that all the training data points have the same normalized margin\nasymptotically. Experiments on both synthetic and real data backup our\ntheoretical findings.\n', 'On the existence of infinitely many realization functions of non-global\n  local minima in the training of artificial neural networks with ReLU\n  activation   Gradient descent (GD) type optimization schemes are the standard instruments\nto train fully connected feedforward artificial neural networks (ANNs) with\nrectified linear unit (ReLU) activation and can be considered as temporal\ndiscretizations of solutions of gradient flow (GF) differential equations. It\nhas recently been proved that the risk of every bounded GF trajectory converges\nin the training of ANNs with one hidden layer and ReLU activation to the risk\nof a critical point. Taking this into account it is one of the key research\nissues in the mathematical convergence analysis of GF trajectories and GD type\noptimization schemes, respectively, to study sufficient and necessary\nconditions for critical points of the risk function and, thereby, to obtain an\nunderstanding about the appearance of critical points in dependence of the\nproblem parameters such as the target function. In the first main result of\nthis work we prove in the training of ANNs with one hidden layer and ReLU\nactivation that for every $ a, b \\in \\mathbb{R} $ with $ a < b $ and every\narbitrarily large $ \\delta > 0 $ we have that there exists a Lipschitz\ncontinuous target function $ f \\colon [a,b] \\to \\mathbb{R} $ such that for\nevery number $ H > 1 $ of neurons on the hidden layer we have that the risk\nfunction has uncountably many different realization functions of non-global\nlocal minimum points whose risks are strictly larger than the sum of the risk\nof the global minimum points and the arbitrarily large $ \\delta $. In the\nsecond main result of this work we show in the training of ANNs with one hidden\nlayer and ReLU activation in the special situation where there is only one\nneuron on the hidden layer and where the target function is continuous and\npiecewise polynomial that there exist at most finitely many different\nrealization functions of critical points.\n', 'A Generalized Neural Tangent Kernel Analysis for Two-layer Neural\n  Networks   A recent breakthrough in deep learning theory shows that the training of\nover-parameterized deep neural networks can be characterized by a kernel\nfunction called \\textit{neural tangent kernel} (NTK). However, it is known that\nthis type of results does not perfectly match the practice, as NTK-based\nanalysis requires the network weights to stay very close to their\ninitialization throughout training, and cannot handle regularizers or gradient\nnoises. In this paper, we provide a generalized neural tangent kernel analysis\nand show that noisy gradient descent with weight decay can still exhibit a\n""kernel-like"" behavior. This implies that the training loss converges linearly\nup to a certain accuracy. We also establish a novel generalization error bound\nfor two-layer neural networks trained by noisy gradient descent with weight\ndecay.\n']","[('gradient descent training', 0.6504259705543518), ('gradient descent', 0.6143527626991272), ('stochastic gradient descent', 0.5933504104614258), ('relu neural networks', 0.5583204030990601), ('relu networks', 0.5495492219924927), ('shallow neural networks', 0.5378432869911194), ('gradient flow', 0.5105582475662231), ('layer neural networks', 0.5077417492866516), ('linear neural networks', 0.5045082569122314), ('layer neural', 0.49329453706741333)]"
63,63,337,63_vertex operator algebras_vertex operator algebra_vertex algebras_affine vertex algebras,"['vertex operator algebras', 'vertex operator algebra', 'vertex algebras', 'affine vertex algebras', 'vertex algebra', 'vertex operator', 'operator algebras', 'lattice vertex', 'affine algebras', 'operator algebra']","['Representations of the orbifold of parafermion vertex operator algebra\n  $K(osp(1|2),k)$   This paper is about the orbifold theory of parafermion vertex operator\nalgebras $K(osp(1|2),k)$ associated to the affine vertex operator superalgebra\n$L_{\\widehat{osp(1|2)}}(k,0)$ with any positive integer $k$. Among the main\nresults, we classify the irreducible modules for the orbifold of parafermion\nvertex operator algebra $K(osp(1|2),k)$.\n', '$\\mathbb{Z}_k$-code vertex operator algebras   We introduce a simple, self-dual, rational, and $C_2$-cofinite vertex\noperator algebra of CFT-type associated with a $\\mathbb{Z}_k$-code for $k \\ge\n2$ based on the $\\mathbb{Z}_k$-symmetry among the simple current modules for\nthe parafermion vertex operator algebra $K(\\mathfrak{sl}_2,k)$. We show that it\nis naturally realized as the commutant of a certain subalgebra in a lattice\nvertex operator algebra. Furthermore, we construct all the irreducible modules\ninside a module for the lattice vertex operator algebra.\n', 'Cliffold algebras, modular Virasoro vertex operator algebras and\n  Z[1/2]-forms   This paper consists of two parts: (1) Using a Z[1/2]-form of Virasoro vertex\noperator algebra L(1/2,0) with central charge 1/2, we obtain a modular vertex\noperator algebra over any field F of finite characteristic different from 2. We\ndetermine the generators and classify the irreducible modules for this vertex\noperator algebra. (2) We investigate modular framed vertex operator algebras.\nIn particular, the rationality of modular framed vertex operator algebras is\nestablished. For a modular code vertex operator algebra, the irreducible\nmodules are constructed and classified. Moreover, a Z[1/2]-form for any framed\nvertex operator algebra over complex field C is constructed. As a result, one\ncan obtain a modular framed vertex operator algebra from any framed vertex\noperator algebra over C.\n']","[('vertex operator algebras', 0.7292448282241821), ('vertex operator algebra', 0.695993959903717), ('vertex algebras', 0.653117299079895), ('affine vertex algebras', 0.6198201179504395), ('vertex algebra', 0.596803605556488), ('vertex operator', 0.5420979857444763), ('operator algebras', 0.4913882613182068), ('lattice vertex', 0.4626636803150177), ('affine algebras', 0.44809532165527344), ('operator algebra', 0.4354516565799713)]"
64,64,333,64_topological phases matter_symmetry topological_symmetry protected topological_topological phases,"['topological phases matter', 'symmetry topological', 'symmetry protected topological', 'topological phases', 'generalized symmetries', 'global symmetry', 'topological field theory', 'protected topological phases', 'topological defects', 'topological quantum field']","['ICTP Lectures on (Non-)Invertible Generalized Symmetries   What comprises a global symmetry of a Quantum Field Theory (QFT) has been\nvastly expanded in the past 10 years to include not only symmetries acting on\nhigher-dimensional defects, but also most recently symmetries which do not have\nan inverse. The principle that enables this generalization is the\nidentification of symmetries with topological defects in the QFT. In these\nlectures, we provide an introduction to generalized symmetries, with a focus on\nnon-invertible symmetries. We begin with a brief overview of invertible\ngeneralized symmetries, including higher-form and higher-group symmetries, and\nthen move on to non-invertible symmetries. The main idea that underlies many\nconstructions of non-invertible symmetries is that of stacking a QFT with\ntopological QFTs (TQFTs) and then gauging a diagonal non-anomalous global\nsymmetry. The TQFTs become topological defects in the gauged theory called\n(twisted) theta defects and comprise a large class of non-invertible symmetries\nincluding condensation defects, self-duality defects, and non-invertible\nsymmetries of gauge theories with disconnected gauge groups. We will explain\nthe general principle and provide numerous concrete examples. Following this\nextensive characterization of symmetry generators, we then discuss their action\non higher-charges, i.e. extended physical operators. As we will explain, even\nfor invertible higher-form symmetries these are not only representations of the\n$p$-form symmetry group, but more generally what are called\nhigher-representations. Finally, we give an introduction to the Symmetry\nTopological Field Theory (SymTFT) and its utility in characterizing symmetries,\ntheir gauging and generalized charges.\n  Lectures prepared for the ICTP Trieste Spring School, April 2023.\n', 'Gapped Phases with Non-Invertible Symmetries: (1+1)d   We propose a general framework to characterize gapped infra-red (IR) phases\nof theories with non-invertible (or categorical) symmetries. In this paper we\nfocus on (1+1)d gapped phases with fusion category symmetries. The approach\nthat we propose uses the Symmetry Topological Field Theory (SymTFT) as a key\ninput: associated to a field theory in d spacetime dimensions, the SymTFT lives\nin one dimension higher and admits a gapped boundary, which realizes the\ncategorical symmetries. It also admits a second, physical, boundary, which is\ngenerically not gapped. Upon interval compactification of the SymTFT by\ncolliding the gapped and physical boundaries, we regain the original theory. In\nthis paper, we realize gapped symmetric phases by choosing the physical\nboundary to be a gapped boundary condition as well. This set-up provides\ncomputational power to determine the number of vacua, the symmetry breaking\npattern, and the action of the symmetry on the vacua. The SymTFT also\nmanifestly encodes the order parameters for these gapped phases, thus providing\na generalized, categorical Landau paradigm for (1+1)d gapped phases. We find\nthat for non-invertible symmetries the order parameters involve multiplets\ncontaining both untwisted and twisted sector local operators, and hence can be\ninterpreted as mixtures of conventional and string order parameters. We also\nobserve that spontaneous breaking of non-invertible symmetries can lead to\nvacua that are physically distinguishable: unlike the standard symmetries\ndescribed by groups, non-invertible symmetries can have different actions on\ndifferent vacua of an irreducible gapped phase. This leads to the presence of\nrelative Euler terms between physically distinct vacua. We also provide a\nmathematical description of symmetric gapped phases as 2-functors from\ndelooping of fusion category characterizing the symmetry to Euler completion of\n2-vector spaces.\n', 'Higher Gauging and Non-invertible Condensation Defects   We discuss invertible and non-invertible topological condensation defects\narising from gauging a discrete higher-form symmetry on a higher codimensional\nmanifold in spacetime, which we define as higher gauging. A $q$-form symmetry\nis called $p$-gaugeable if it can be gauged on a codimension-$p$ manifold in\nspacetime. We focus on 1-gaugeable 1-form symmetries in general 2+1d QFT, and\ngauge them on a surface in spacetime. The universal fusion rules of the\nresulting invertible and non-invertible condensation surfaces are determined.\nIn the special case of 2+1d TQFT, every (invertible and non-invertible) 0-form\nglobal symmetry, including the $\\mathbb{Z}_2$ electromagnetic symmetry of the\n$\\mathbb{Z}_2$ gauge theory, is realized from higher gauging. We further\ncompute the fusion rules between the surfaces, the bulk lines, and lines that\nonly live on the surfaces, determining some of the most basic data for the\nunderlying fusion 2-category. We emphasize that the fusion ""coefficients"" in\nthese non-invertible fusion rules are generally not numbers, but rather 1+1d\nTQFTs. Finally, we discuss examples of non-invertible symmetries in\nnon-topological 2+1d QFTs such as the free $U(1)$ Maxwell theory and QED.\n']","[('topological phases matter', 0.6067975163459778), ('symmetry topological', 0.5943744778633118), ('symmetry protected topological', 0.5859113931655884), ('topological phases', 0.5685414671897888), ('generalized symmetries', 0.563668966293335), ('global symmetry', 0.5357531905174255), ('topological field theory', 0.5302693843841553), ('protected topological phases', 0.5172156691551208), ('topological defects', 0.5170701742172241), ('topological quantum field', 0.5120477676391602)]"
65,65,328,65_finite element methods_elliptic interface problems_virtual element methods_elliptic interface,"['finite element methods', 'elliptic interface problems', 'virtual element methods', 'elliptic interface', 'immersed finite element', 'galerkin finite element', 'element methods', 'discontinuous galerkin', 'galerkin finite', 'adaptive finite element']","['An immersed Raviart-Thomas mixed finite element method for elliptic\n  interface problems on unfitted meshes   This paper presents a lowest-order immersed Raviart-Thomas mixed triangular\nfinite element method for solving elliptic interface problems on unfitted\nmeshes independent of the interface. In order to achieve the optimal\nconvergence rates on unfitted meshes, an immersed finite element finite (IFE)\nis constructed by modifying the traditional Raviart-Thomas element. Some\nimportant properties are derived including the unisolvence of IFE basis\nfunctions, the optimal approximation capabilities of the IFE space and the\ncorresponding commuting digram. Optimal error estimates are rigorously proved\nfor the mixed IFE method and some numerical examples are also provided to\nvalidate the theoretical analysis.\n', 'Virtual Element Methods Without Extrinsic Stabilization   Virtual element methods (VEMs) without extrinsic stabilization in arbitrary\ndegree of polynomial are developed for second order elliptic problems,\nincluding a nonconforming VEM and a conforming VEM in arbitrary dimension. The\nkey is to construct local $H(\\textrm{div})$-conforming macro finite element\nspaces such that the associated $L^2$ projection of the gradient of virtual\nelement functions is computable, and the $L^2$ projector has a uniform lower\nbound on the gradient of virtual element function spaces in $L^2$ norm. Optimal\nerror estimates are derived for these VEMs. Numerical experiments are provided\nto test the VEMs without extrinsic stabilization.\n', 'Nonconforming virtual elements for the biharmonic equation with Morley\n  degrees of freedom on polygonal meshes   The lowest-order nonconforming virtual element extends the Morley triangular\nelement to polygons for the approximation of the weak solution $u\\in\nV:=H^2_0(\\Omega)$ to the biharmonic equation. The abstract framework allows\n(even a mixture of) two examples of the local discrete spaces $V_h(P)$ and a\nsmoother allows rough source terms $F\\in V^*=H^{-2}(\\Omega)$. The a priori and\na posteriori error analysis in this paper circumvents any trace of second\nderivatives by some computable conforming companion operator $J:V_h\\to V$ from\nthe nonconforming virtual element space $V_h$. The operator $J$ is a\nright-inverse of the interpolation operator and leads to optimal error\nestimates in piecewise Sobolev norms without any additional regularity\nassumptions on $u\\in V$. As a smoother the companion operator modifies the\ndiscrete right-hand side and then allows a quasi-best approximation. An\nexplicit residual-based a posteriori error estimator is reliable and efficient\nup to data oscillations. Numerical examples display the predicted empirical\nconvergence rates for uniform and optimal convergence rates for adaptive\nmesh-refinement.\n']","[('finite element methods', 0.681123673915863), ('elliptic interface problems', 0.6197921633720398), ('virtual element methods', 0.5843571424484253), ('elliptic interface', 0.5816698670387268), ('immersed finite element', 0.5724597573280334), ('galerkin finite element', 0.570099949836731), ('element methods', 0.5088618993759155), ('discontinuous galerkin', 0.4943977892398834), ('galerkin finite', 0.4883657395839691), ('adaptive finite element', 0.47028234601020813)]"
66,66,328,66_cohen macaulay modules_macaulay modules_maximal cohen macaulay_cohen macaulay ring,"['cohen macaulay modules', 'macaulay modules', 'maximal cohen macaulay', 'cohen macaulay ring', 'macaulay rings', 'gorenstein rings', 'macaulay ring', 'local rings', 'associated graded ring', 'noetherian local ring']","['Remarks on the Small Cohen-Macaulay conjecture and new instances of\n  maximal Cohen-Macaulay modules   We show that any quasi-Gorenstein deformation of a $3$-dimensional\nquasi-Gorenstein Buchsbaum local ring with $I$-invariant $1$ admits a maximal\nCohen-Macaulay module, provided it is a quotient of a Gorenstein ring. Such a\nclass of rings includes two instances of unique factorization domains\nconstructed by Marcel-Schenzel and by Imtiaz-Schenzel, respectively. Apart from\nthis result, motivated by the small Cohen-Macaulay conjecture in prime\ncharacteristic, we examine a question about when the Frobenius pushforward\n$F^e_*(M)$ of an $R$-module $M$ comprises a maximal Cohen-Macaulay direct\nsummand in both local and graded cases.\n', 'Some properties of ideals in Cohen-Macaulay local rings   For a Cohen-Macaulay local ring $(R,\\mathfrak{m})$ with canonical module, we\nstudy how relations between $\\text{index}(R)$ and $\\text{g}\\ell\\ell(R)$ and\nbetween $\\text{index}(R)$ and $e(R)$ are preserved when factoring out regular\nsequences and localizing at prime ideals. We then give conditions for when\nideals in a one-dimensional Cohen-Macaulay local ring are Elias and Burch, and\nuse these conditions to study the relationship between Elias, Burch, and Ulrich\nideals.\n', 'Representation-theoretic properties of balanced big Cohen-Macaulay\n  modules   Let $(R, \\m, k)$ be a complete Cohen-Macaulay local ring. In this paper, we\nassign a numerical invariant, for any balanced big Cohen-Macaulay module,\ncalled $\\uh$-length. Among other results, it is proved that, for a given\nbalanced big Cohen-Macaulay $R$-module $M$ with an $\\m$-primary cohomological\nannihilator, if there is a bound on the $\\uh$-length of all modules appearing\nin $\\CM$-support of $M$, then it is fully decomposable, i.e. it is a direct sum\nof finitely generated modules. While the first Brauer-Thrall conjecture fails\nin general by a counterexample of Dieterich dealing with multiplicities to\nmeasure the size of maximal Cohen-Macaulay modules, our formalism establishes\nthe validity of the conjecture for complete Cohen-Macaulay local rings. In\naddition, the pure-semisimplicity of a subcategory of balanced big\nCohen-Macaulay modules is settled. Namely, it is shown that $R$ is of finite\n$\\CM$-type if and only if the category of all fully decomposable balanced big\nCohen-Macaulay modules is closed under kernels of epimorphisms. Finally, we\nexamine the mentioned results in the context of Cohen-Macaulay artin algebras\nadmitting a dualizing bimodule $\\omega$, as defined by Auslander and Reiten. It\nwill turn out that, $\\omega$-Gorenstein projective modules with bounded\n$\\CM$-support are fully decomposable. In particular, a Cohen-Macaulay algebra\n$\\Lambda$ is of finite $\\CM$-type if and only if every $\\omega$-Gorenstein\nprojective module is of finite $\\CM$-type, which generalizes a result of Chen\nfor Gorenstein algebras. Our main tool in the proof of results is\nGabriel-Roiter (co)measure, an invariant assigned to modules of finite length,\nand defined by Gabriel and Ringel. This, in fact, provides an application of\nthe Gabriel-Roiter (co)measure in the category of maximal Cohen-Macaulay\nmodules.\n']","[('cohen macaulay modules', 0.7622952461242676), ('macaulay modules', 0.7202548384666443), ('maximal cohen macaulay', 0.7034443616867065), ('cohen macaulay ring', 0.6679750084877014), ('macaulay rings', 0.6548298001289368), ('gorenstein rings', 0.6321535706520081), ('macaulay ring', 0.6214548945426941), ('local rings', 0.5760817527770996), ('associated graded ring', 0.573706865310669), ('noetherian local ring', 0.548713207244873)]"
67,67,328,67_solutions reaction diffusion_reaction diffusion equations_reaction diffusion systems_reaction diffusion advection,"['solutions reaction diffusion', 'reaction diffusion equations', 'reaction diffusion systems', 'reaction diffusion advection', 'reaction diffusion', 'diffusion equations', 'reaction diffusion system', 'bistable reaction diffusion', 'nonlocal diffusion', 'nonlinear diffusion']","[""Front location determines convergence rate to traveling waves   We propose a novel method for establishing the convergence rates of solutions\nto reaction-diffusion equations to traveling waves. The analysis is based on\nthe study of the traveling wave shape defect function introduced in [2]. It\nturns out that the convergence rate is controlled by the distance between the\n``phantom front location'' for the shape defect function and the true front\nlocation of the solution. Curiously, the convergence to a traveling wave itself\nhas a pulled nature, regardless of whether the traveling wave is of pushed,\npulled, or pushmi-pullyu type. In addition to providing new results, this\napproach simplifies dramatically the proof in the Fisher-KPP case and gives a\nunified, succinct explanation for the known algebraic rates of convergence in\nthe Fisher-KPP case and the exponential rates in the pushed case.\n"", 'Asymptotic spreading for Fisher-KPP reaction-diffusion equations with\n  heterogeneous shifting diffusivity   We determine the asymptotic spreading speed of the solutions of a Fisher-KPP\nreaction-diffusion equation, starting from compactly supported initial data,\nwhen the diffusion coefficient is a fixed bounded monotone profile that is\nshifted at a given forcing speed and satisfies a general uniform ellipticity\ncondition. Depending on the monotony of the profile, we are able to\ncharacterize this spreading speed as a function of the forcing speed and the\ntwo linear spreading speeds associated to the asymptotic problems. Most\nnotably, when the profile of the coefficient diffusion is increasing we show\nthat there is an intermediate range for the forcing speed where spreading\nactually occurs at a speed which is larger than the linear speed associated\nwith the homogeneous state around the position of the front. We complement our\nstudy with the construction of strictly monotone traveling front solutions with\nstrong exponential decay near the unstable state when the profile of the\ncoefficient diffusion is decreasing and in the regime where the forcing speed\nis precisely the selected spreading speed.\n', 'Curved fronts of bistable reaction-diffusion equations in spatially\n  periodic media   In this paper, curved fronts are constructed for spatially periodic bistable\nreaction-diffusion equations under the a priori assumption that there exist\npulsating fronts in every direction. Some sufficient and some necessary\nconditions of the existence of curved fronts are given. Furthermore, the curved\nfront is proved to be unique and stable. Finally, a curved front with varying\ninterfaces is also constructed. Despite the effect of the spatial\nheterogeneity, the result shows the existence of curved fronts for spatially\nperiodic bistable reaction-diffusion equations which is known for the\nhomogeneous case.\n']","[('solutions reaction diffusion', 0.6905477643013), ('reaction diffusion equations', 0.6872763633728027), ('reaction diffusion systems', 0.6498636603355408), ('reaction diffusion advection', 0.6437410712242126), ('reaction diffusion', 0.6425260305404663), ('diffusion equations', 0.6250498294830322), ('reaction diffusion system', 0.6106491088867188), ('bistable reaction diffusion', 0.6090099811553955), ('nonlocal diffusion', 0.5994901061058044), ('nonlinear diffusion', 0.5994324088096619)]"
68,68,321,68_theory matroids_oriented matroids_matroid theory_matroids matroids,"['theory matroids', 'oriented matroids', 'matroid theory', 'matroids matroids', 'oriented matroid', 'regular matroids', 'valuated matroids', 'class matroids', 'matroids', 'matroidal']","['On the circuits of splitting matroids representable over GF(p)   We extend the splitting operation from binary matroids (Raghunathan et al.,\n1998) to $p$- matroids, where $p$-matroids refer to matroids representable over\n$GF(p).$ We also characterize circuits, bases, and independent sets of the\nresulting matroid. Sufficient conditions to yield Eulerian $p$-matroids from\nEulerian and non-Eulerian $p$-matroids by applying the splitting operation are\nobtained. A class of connected $p$-matroids that gives connected $p$-matroids\nunder the splitting operation is characterized.\n', 'Orientable arithmetic matroids   The theory of matroids has been generalized to oriented matroids and,\nrecently, to arithmetic matroids. We want to give a definition of ""oriented\narithmetic matroid"" and prove some properties like the ""uniqueness of\norientation"".\n', 'Generalized Splitting and element splitting operations on $p$-matroids   In this paper, we define generalized splitting and element splitting\noperations on $p$-matroids. $p$-matroids are the matroids representable over\n$GF(p).$ The circuits and the bases of the new matroid are characterized in\nterms of circuits and bases of the original matroid, respectively. A class of\n$n$-connected $p$-matroids which gives n-connected $p$- matroids using the\ngeneralized splitting operation is also characterized. We also prove that\nconnectivity of $p$-matroid is preserved under element splitting operation.\nSufficient conditions to obtain Eulerian $p$-matroid from Eulerian $p$-matroid\nunder splitting and element splitting operations are provided.\n']","[('theory matroids', 0.7655490636825562), ('oriented matroids', 0.7105458378791809), ('matroid theory', 0.7103597521781921), ('matroids matroids', 0.6962224245071411), ('oriented matroid', 0.6881923079490662), ('regular matroids', 0.6753185391426086), ('valuated matroids', 0.658841073513031), ('class matroids', 0.6515287756919861), ('matroids', 0.6335408091545105), ('matroidal', 0.6334044933319092)]"
69,69,318,69_lasso estimator_lasso_group lasso_sparse linear regression,"['lasso estimator', 'lasso', 'group lasso', 'sparse linear regression', 'high dimensional regression', 'generalized linear models', 'sparse linear', 'inference high dimensional', 'dimensional linear regression', 'least squares estimator']","['A Comparison of Hamming Errors of Representative Variable Selection\n  Methods   Lasso is a celebrated method for variable selection in linear models, but it\nfaces challenges when the variables are moderately or strongly correlated. This\nmotivates alternative approaches such as using a non-convex penalty, adding a\nridge regularization, or conducting a post-Lasso thresholding. In this paper,\nwe compare Lasso with 5 other methods: Elastic net, SCAD, forward selection,\nthresholded Lasso, and forward backward selection. We measure their\nperformances theoretically by the expected Hamming error, assuming that the\nregression coefficients are iid drawn from a two-point mixture and that the\nGram matrix is block-wise diagonal. By deriving the rates of convergence of\nHamming errors and the phase diagrams, we obtain useful conclusions about the\npros and cons of different methods.\n', 'High-dimensional Linear Regression for Dependent Data with Applications\n  to Nowcasting   Recent research has focused on $\\ell_1$ penalized least squares (Lasso)\nestimators for high-dimensional linear regressions in which the number of\ncovariates $p$ is considerably larger than the sample size $n$. However, few\nstudies have examined the properties of the estimators when the errors and/or\nthe covariates are serially dependent. In this study, we investigate the\ntheoretical properties of the Lasso estimator for a linear regression with a\nrandom design and weak sparsity under serially dependent and/or nonsubGaussian\nerrors and covariates. In contrast to the traditional case, in which the errors\nare independent and identically distributed and have finite exponential\nmoments, we show that $p$ can be at most a power of $n$ if the errors have only\nfinite polynomial moments. In addition, the rate of convergence becomes slower\nowing to the serial dependence in the errors and the covariates. We also\nconsider the sign consistency of the model selection using the Lasso estimator\nwhen there are serial correlations in the errors or the covariates, or both.\nAdopting the framework of a functional dependence measure, we describe how the\nrates of convergence and the selection consistency of the estimators depend on\nthe dependence measures and moment conditions of the errors and the covariates.\nSimulation results show that a Lasso regression can be significantly more\npowerful than a mixed-frequency data sampling regression (MIDAS) and a Dantzig\nselector in the presence of irrelevant variables. We apply the results obtained\nfor the Lasso method to nowcasting with mixed-frequency data, in which serially\ncorrelated errors and a large number of covariates are common. The empirical\nresults show that the Lasso procedure outperforms the MIDAS regression and the\nautoregressive model with exogenous variables in terms of both forecasting and\nnowcasting.\n', 'Adaptive Lasso, Transfer Lasso, and Beyond: An Asymptotic Perspective   This paper presents a comprehensive exploration of the theoretical properties\ninherent in the Adaptive Lasso and the Transfer Lasso. The Adaptive Lasso, a\nwell-established method, employs regularization divided by initial estimators\nand is characterized by asymptotic normality and variable selection\nconsistency. In contrast, the recently proposed Transfer Lasso employs\nregularization subtracted by initial estimators with the demonstrated capacity\nto curtail non-asymptotic estimation errors. A pivotal question thus emerges:\nGiven the distinct ways the Adaptive Lasso and the Transfer Lasso employ\ninitial estimators, what benefits or drawbacks does this disparity confer upon\neach method? This paper conducts a theoretical examination of the asymptotic\nproperties of the Transfer Lasso, thereby elucidating its differentiation from\nthe Adaptive Lasso. Informed by the findings of this analysis, we introduce a\nnovel method, one that amalgamates the strengths and compensates for the\nweaknesses of both methods. The paper concludes with validations of our theory\nand comparisons of the methods via simulation experiments.\n']","[('lasso estimator', 0.7003738284111023), ('lasso', 0.6722121834754944), ('group lasso', 0.5882463455200195), ('sparse linear regression', 0.4979754090309143), ('high dimensional regression', 0.41421636939048767), ('generalized linear models', 0.4057607650756836), ('sparse linear', 0.4018625020980835), ('inference high dimensional', 0.38101375102996826), ('dimensional linear regression', 0.3553524315357208), ('least squares estimator', 0.35059869289398193)]"
70,70,311,70_binary optimization qubo_optimization quantum_optimization qubo_quantum algorithms,"['binary optimization qubo', 'optimization quantum', 'optimization qubo', 'quantum algorithms', 'quantum computing', 'variational quantum algorithms', 'quantum computers', 'quantum computation', 'unconstrained binary optimization', 'quantum computer']","['Five Starter Problems: Solving Quadratic Unconstrained Binary\n  Optimization Models on Quantum Computers   This tutorial offers a quick hands-on introduction to solving Quadratic\nUnconstrained Binary Optimization (QUBO) problems on currently available\nquantum computers. We cover both IBM and D-Wave machines: IBM utilizes a\ngate/circuit architecture, and D-Wave is a quantum annealer. We provide\nexamples of three canonical problems and two models from practical\napplications. An associated GitHub repository provides the implementations in\nfive companion notebooks. In addition to undergraduate and graduate students in\ncomputationally intensive disciplines, this article aims to reach working\nindustry professionals seeking to explore the potential of near-term quantum\napplications.\n', 'QUBO.jl: A Julia Ecosystem for Quadratic Unconstrained Binary\n  Optimization   We present QUBO.jl, an end-to-end Julia package for working with QUBO\n(Quadratic Unconstrained Binary Optimization) instances. This tool aims to\nconvert a broad range of JuMP problems for straightforward application in many\nphysics and physics-inspired solution methods whose standard optimization form\nis equivalent to the QUBO. These methods include quantum annealing, quantum\ngate-circuit optimization algorithms (Quantum Optimization Alternating Ansatz,\nVariational Quantum Eigensolver), other hardware-accelerated platforms, such as\nCoherent Ising Machines and Simulated Bifurcation Machines, and more\ntraditional methods such as simulated annealing. Besides working with\nreformulations, QUBO.jl allows its users to interface with the aforementioned\nhardware, sending QUBO models in various file formats and retrieving results\nfor subsequent analysis. QUBO.jl was written as a JuMP / MathOptInterface (MOI)\nlayer that automatically maps between the input and output frames, thus\nproviding a smooth modeling experience.\n', 'Constraint Programming to Discover One-Flip Local Optima of Quadratic\n  Unconstrained Binary Optimization Problems   The broad applicability of Quadratic Unconstrained Binary Optimization (QUBO)\nconstitutes a general-purpose modeling framework for combinatorial optimization\nproblems and are a required format for gate array and quantum annealing\ncomputers. QUBO annealers as well as other solution approaches benefit from\nstarting with a diverse set of solutions with local optimality an additional\nbenefit. This paper presents a new method for generating a set of one-flip\nlocal optima leveraging constraint programming. Further, as demonstrated in\nexperimental testing, analysis of the solution set allows the generation of\nsoft constraints to help guide the optimization process.\n']","[('binary optimization qubo', 0.7562940716743469), ('optimization quantum', 0.7056757211685181), ('optimization qubo', 0.6867221593856812), ('quantum algorithms', 0.6568174958229065), ('quantum computing', 0.6185250878334045), ('variational quantum algorithms', 0.6060352325439453), ('quantum computers', 0.6008895635604858), ('quantum computation', 0.5920795202255249), ('unconstrained binary optimization', 0.5917913317680359), ('quantum computer', 0.583516001701355)]"
71,71,302,71_sensing communications isac_sensing communication isac_transmit beamforming_radar communication,"['sensing communications isac', 'sensing communication isac', 'transmit beamforming', 'radar communication', 'integrated sensing communications', 'communication radar', 'radar sensing', 'integrated sensing communication', 'sensing communications', 'mimo radar']","[""Cram\\'er-Rao Bound Minimization for IRS-Enabled Multiuser Integrated\n  Sensing and Communications   This paper investigates an intelligent reflecting surface (IRS) enabled\nmultiuser integrated sensing and communications (ISAC) system, which consists\nof one multi-antenna base station (BS), one IRS, multiple single-antenna\ncommunication users (CUs), and one target at the non-line-of-sight (NLoS)\nregion of the BS. The IRS is deployed to not only assist the communication from\nthe BS to the CUs, but also enable the BS's NLoS target sensing based on the\necho signals from the BS-IRS-target-IRS-BS link. We consider two types of\ntargets, namely the extended and point targets, for which the BS aims to\nestimate the complete target response matrix and the target\ndirection-of-arrival (DoA) with respect to the IRS, respectively. To provide\nfull degrees of freedom for sensing, we consider that the BS sends dedicated\nsensing signals in addition to the communication signals. Accordingly, we model\ntwo types of CU receivers, namely Type-I and Type-II CU receivers, which do not\nhave and have the capability of canceling the interference from the sensing\nsignals, respectively. Under each setup, we jointly optimize the transmit\nbeamforming at the BS and the reflective beamforming at the IRS to minimize the\nCram\\'er-Rao bound (CRB) for target estimation, subject to the minimum\nsignal-to-interference-plus-noise ratio (SINR) constraints at the CUs and the\nmaximum transmit power constraint at the BS. We present efficient algorithms to\nsolve the highly non-convex SINR-constrained CRB minimization problems, by\nusing the techniques of alternating optimization, semi-definite relaxation, and\nsuccessive convex approximation. Numerical results show that the proposed\ndesign achieves lower estimation CRB than other benchmark schemes, and the\nsensing signal interference cancellation at Type-II CU receivers is beneficial\nwhen the number of CUs is greater than one.\n"", ""Cram\\'er-Rao Bound Minimization for IRS-Enabled Multiuser Integrated\n  Sensing and Communication with Extended Target   This paper investigates an intelligent reflecting surface (IRS) enabled\nmultiuser integrated sensing and communication (ISAC) system, which consists of\none multi-antenna base station (BS), one IRS, multiple single-antenna\ncommunication users (CUs), and one extended target at the non-line-of-sight\n(NLoS) region of the BS. The IRS is deployed to not only assist the\ncommunication from the BS to the CUs, but also enable the BS's NLoS target\nsensing based on the echo signals from the BS-IRS-target-IRS-BS link. To\nprovide full degrees of freedom for sensing, we suppose that the BS sends\nadditional dedicated sensing signals combined with the information signals.\nAccordingly, we consider two types of CU receivers, namely Type-I and Type-II\nreceivers, which do not have and have the capability of cancelling the\ninterference from the sensing signals, respectively. Under this setup, we\njointly optimize the transmit beamforming at the BS and the reflective\nbeamforming at the IRS to minimize the Cram\\'er-Rao bound (CRB) for estimating\nthe target response matrix with respect to the IRS, subject to the minimum\nsignal-to-interference-plus-noise ratio (SINR) constraints at the CUs and the\nmaximum transmit power constraint at the BS. We present efficient algorithms to\nsolve the highly non-convex SINR-constrained CRB minimization problems, by\nusing the techniques of alternating optimization and semi-definite relaxation.\nNumerical results show that the proposed design achieves lower estimation CRB\nthan other benchmark schemes, and the sensing signal interference\npre-cancellation is beneficial when the number of CUs is greater than one.\n"", ""Integrated Sensing and Communication with Millimeter Wave Full Duplex\n  Hybrid Beamforming   Integrated Sensing and Communication (ISAC) has attracted substantial\nattraction in recent years for spectral efficiency improvement, enabling\nhardware and spectrum sharing for simultaneous sensing and signaling\noperations. In-band Full Duplex (FD) is being considered as a key enabling\ntechnology for ISAC applications due to its simultaneous transmission and\nreception capability. In this paper, we present an FD-based ISAC system\noperating at millimeter Wave (mmWave) frequencies, where a massive\nMultiple-Input Multiple-Output (MIMO) Base Station (BS) node employing hybrid\nAnalog and Digital (A/D) beamforming is communicating with a DownLink (DL)\nmulti-antenna user and the same waveform is utilized at the BS receiver for\nsensing the radar targets in its coverage environment. We develop a sensing\nalgorithm that is capable of estimating Direction of Arrival (DoA), range, and\nrelative velocity of the radar targets. A joint optimization framework for\ndesigning the A/D transmit and receive beamformers as well as the\nSelf-Interference (SI) cancellation is presented with the objective to maximize\nthe achievable DL rate and the accuracy of the radar target sensing\nperformance. Our simulation results, considering fifth Generation (5G)\nOrthogonal Frequency Division Multiplexing (OFDM) waveforms, verify our\napproach's high precision in estimating DoA, range, and velocity of multiple\nradar targets, while maximizing the DL communication rate.\n""]","[('sensing communications isac', 0.5745238661766052), ('sensing communication isac', 0.5547556281089783), ('transmit beamforming', 0.5161911845207214), ('radar communication', 0.5016705989837646), ('integrated sensing communications', 0.5016067624092102), ('communication radar', 0.497994989156723), ('radar sensing', 0.49150776863098145), ('integrated sensing communication', 0.477567583322525), ('sensing communications', 0.47511205077171326), ('mimo radar', 0.4638367295265198)]"
72,72,302,72_secrecy capacity_secrecy outage probability_secrecy performance_secrecy rate,"['secrecy capacity', 'secrecy outage probability', 'secrecy performance', 'secrecy rate', 'achievable secrecy', 'secrecy outage', 'secrecy', 'secure communication', 'secure transmission', 'physical layer security']","['Massive MIMO-NOMA Systems Secrecy in the Presence of Active\n  Eavesdroppers   Non-orthogonal multiple access (NOMA) and massive multiple-input\nmultiple-output (MIMO) systems are highly efficient. Massive MIMO systems are\ninherently resistant to passive attackers (eavesdroppers), thanks to\ntransmissions directed to the desired users. However, active attackers can\ntransmit a combination of legitimate user pilot signals during the channel\nestimation phase. This way they can mislead the base station (BS) to rotate the\ntransmission in their direction, and allow them to eavesdrop during the\ndownlink data transmission phase. In this paper, we analyse this vulnerability\nin an improved system model and stronger adversary assumptions, and investigate\nhow physical layer security can mitigate such attacks and ensure secure\n(confidential) communication. We derive the secrecy outage probability (SOP)\nand a lower bound on the ergodic secrecy capacity, using stochastic geometry\ntools when the number of antennas in the BSs tends to infinity. We adapt the\nresult to evaluate the secrecy performance in massive orthogonal multiple\naccess (OMA). We find that appropriate power allocation allows NOMA to\noutperform OMA in terms of ergodic secrecy rate and SOP.\n', ""Minimization of Secrecy Outage Probability in Reconfigurable Intelligent\n  Surface-Assisted MIMOME System   This article investigates physical layer security (PLS) in reconfigurable\nintelligent surface (RIS)-assisted multiple-input multiple-output\nmultiple-antenna-eavesdropper (MIMOME) channels. Existing researches ignore the\nproblem that secrecy rate can not be calculated if the eavesdropper's\ninstantaneous channel state information (CSI) is unknown. Furthermore, without\nthe secrecy rate expression, beamforming and phase shifter optimization with\nthe purpose of PLS enhancement is not available. To address these problems, we\nfirst give the expression of secrecy outage probability for any beamforming\nvector and phase shifter matrix as the RIS-assisted PLS metric, which is\nmeasured based on the eavesdropper's statistical CSI. Then, with the aid of the\nexpression, we formulate the minimization problem of secrecy outage probability\nthat is solved via alternately optimizing beamforming vectors and phase shift\nmatrices. In the case of single-antenna transmitter or single-antenna\nlegitimate receiver, the proposed alternating optimization (AO) scheme can be\nsimplified to reduce computational complexity. Finally, it is demonstrated that\nthe secrecy outage probability is significantly reduced with the proposed\nmethods compared to current RIS-assisted PLS systems.\n"", 'Secrecy Performance Analysis of Multi-Functional RIS-Assisted NOMA\n  Networks   Although reconfigurable intelligent surface (RIS) can improve the secrecy\ncommunication performance of wireless users, it still faces challenges such as\nlimited coverage and double-fading effect. To address these issues, in this\npaper, we utilize a novel multi-functional RIS (MF-RIS) to enhance the secrecy\nperformance of wireless users, and investigate the physical layer secrecy\nproblem in non-orthogonal multiple access (NOMA) networks. Specifically, we\nderive the secrecy outage probability (SOP) and secrecy throughput expressions\nof users in MF-RIS-assisted NOMA networks with external and internal\neavesdroppers. The asymptotic expressions for SOP and secrecy diversity order\nare also analyzed under high signal-to-noise ratio (SNR) conditions.\nAdditionally, we examine the impact of receiver hardware limitations and error\ntransmission-induced imperfect successive interference cancellation (SIC) on\nthe secrecy performance. Numerical results indicate that: i) under the same\npower budget, the secrecy performance achieved by MF-RIS significantly\noutperforms active RIS and simultaneously transmitting and reflecting RIS; ii)\nwith increasing power budget, residual interference caused by imperfect SIC\nsurpasses thermal noise as the primary factor affecting secrecy capacity; and\niii) deploying additional elements at the MF-RIS brings significant secrecy\nenhancements for the external eavesdropping scenario, in contrast to the\ninternal eavesdropping case.\n']","[('secrecy capacity', 0.6166078448295593), ('secrecy outage probability', 0.6094948053359985), ('secrecy performance', 0.6071178913116455), ('secrecy rate', 0.5950509309768677), ('achievable secrecy', 0.5493327379226685), ('secrecy outage', 0.539665162563324), ('secrecy', 0.5194307565689087), ('secure communication', 0.5036075115203857), ('secure transmission', 0.4942816197872162), ('physical layer security', 0.44134849309921265)]"
73,73,299,73_topological insulators_topological phases_topological phase_fractional quantum hall,"['topological insulators', 'topological phases', 'topological phase', 'fractional quantum hall', 'quantum hall', 'quantum hall effect', 'topological invariants', 'boundary states', 'insulators', 'hyperbolic lattices']","['Bulk-Boundary Correspondence for Topological Insulators with Quantized\n  Magneto-Electric Effect   We study bulk-boundary correspondences and related surface phenomena\nstabilized by the second Chern number in three-dimensional insulators driven in\nadiabatic cycles. Magnetic fields and disorder effects are incorporated in our\nanalysis using operator algebraic methods. We use the connecting maps between\nthe $K$-theories of bulk and boundary algebras as engines for the bulk-boundary\ncorrespondences. We discovered that both the exponential and the index\nconnecting maps are relevant for the context considered here as they lead to\ndistinct experimentally observable surface phenomena, such as pumping and\ntransfer of quantum surface Hall states or proximity induced Hall effect. The\nsurface Hall physics of time-reversal symmetric topological insulators is also\ninvestigated using the new tools, which can model irrational magnetic fluxes\nand arbitrary large surface disorder.\n', 'Non-Hermitian Hopf insulators   Hopf insulators represent a unique class of topological insulators that exist\nexclusively in two-band systems and are inherently unstable upon the inclusion\nof additional bands. Meanwhile, recent studies have shown that non-Hermiticity\ngives rise to distinctive complex-energy gap structures, known as point gaps,\nand associated topological phases with no analogs in Hermitian systems.\nHowever, non-Hermitian counterparts of Hopf insulators have remained largely\nelusive. Here, we generally classify topological phases of two-band\nnon-Hermitian systems based on the homotopy theory and uncover Hopf-type\npoint-gap topology present only for two bands. Specifically, we reveal such\nHopf-type point-gap topology for three-dimensional systems with chiral symmetry\n(class AIII) and four-dimensional systems with no symmetry (class A).\nExplicitly constructing prototypical models from the Hermitian Hopf insulator,\nwe further demonstrate that these non-Hermitian topological phases lead to\nanomalous point-gapless boundary states spectrally detachable from the bulk\nbands.\n', 'Multicellularity of delicate topological insulators   Being Wannierizable is not the end of the story for topological insulators.\nWe introduce a family of topological insulators that would be considered\ntrivial in the paradigm set by the tenfold way, topological quantum chemistry,\nand the method of symmetry-based indicators. Despite having a symmetric,\nexponentially-localized Wannier representation, each Wannier function cannot be\ncompletely localized to a single primitive unit cell in the bulk. Such\nmulticellular topology is shown to be neither stable, nor fragile, but\ndelicate, i.e., the topology can be nullified by adding trivial bands to either\nvalence or conduction band.\n']","[('topological insulators', 0.7248303294181824), ('topological phases', 0.5982376933097839), ('topological phase', 0.5543565154075623), ('fractional quantum hall', 0.5525529980659485), ('quantum hall', 0.5403799414634705), ('quantum hall effect', 0.5173443555831909), ('topological invariants', 0.4605960249900818), ('boundary states', 0.44470369815826416), ('insulators', 0.41901880502700806), ('hyperbolic lattices', 0.4069638252258301)]"
74,74,299,74_brunn minkowski inequality_symmetric convex bodies_convex bodies_symmetric convex body,"['brunn minkowski inequality', 'symmetric convex bodies', 'convex bodies', 'symmetric convex body', 'convex body', 'convex body mathbb', 'minkowski inequality', 'isoperimetric inequality', 'brunn minkowski theory', 'isoperimetric inequalities']","['Log-Brunn-Minkowski inequality under symmetry   We prove the log-Brunn-Minkowski conjecture for convex bodies with symmetries\nto $n$ independent hyperplanes, and discuss the equality case and the\nuniqueness of the solution of the related case of the logarithmic Minkowski\nproblem. We also clarify a small gap in the known argument classifying the\nequality case of the log-Brunn-Minkowski conjecture for unconditional convex\nbodies.\n', ""Dual Brunn-Minkowski inequality for C-star bodies   In this paper, we consider the concept of $C$-star body in a fixed pointed\nclosed convex cone $C$ and study the dual mixed volume for $C$-star bodies. For\n$C$-star bodies, we establish the corresponding dual Brunn-Minkowski\ninequality, the dual Minkowski inequality and the dual Aleksandrov-Fenchel\ninequality. Our dual Brunn-Minkowski inequality for $C$-star bodies strengthens\nSchneider's Brunn-Minkowski inequality for $C$-coconvex sets.\n"", ""Brunn-Minkowski and Reverse Isoperimetric Inequalities for Dual Quermassintegrals This paper establishes two new geometric inequalities in the dual Brunn-Minkowski theory. The first, originally conjectured by Lutwak, is the Brunn-Minkowski inequality for dual quermassintegrals of origin-symmetric convex bodies. The second, generalizing Ball's volume ratio inequality, is a reverse isoperimetric inequality: among all origin-symmetric convex bodies in John's position, the cube maximizes the dual quermassintegrals.""]","[('brunn minkowski inequality', 0.7012479305267334), ('symmetric convex bodies', 0.6867337822914124), ('convex bodies', 0.6772520542144775), ('symmetric convex body', 0.6428438425064087), ('convex body', 0.6295404434204102), ('convex body mathbb', 0.6184282898902893), ('minkowski inequality', 0.6006996035575867), ('isoperimetric inequality', 0.5860062837600708), ('brunn minkowski theory', 0.5859560966491699), ('isoperimetric inequalities', 0.5789101719856262)]"
75,75,299,75_edge ideals_ideals graphs_edge ideal_monomial ideals,"['edge ideals', 'ideals graphs', 'edge ideal', 'monomial ideals', 'monomial ideal', 'cohen macaulayness', 'ideal polynomial ring', 'ideals associated', 'chordal graphs', 'macaulayness']","['On the symbolic $F$-splitness of binomial edge ideals   We study the symbolic $F$-splitness of families of binomial edge ideals. We\nalso study the strong $F$-regularity of the symbolic blowup algebras of\nfamilies of binomial edge ideals. We make use of Fedder-like criteria and\ncombinatorial properties of the graphs associated to the binomial edge ideals\nin order to approach the aforementioned scenarios.\n', 'Regularity of parity binomial edge ideals   Let $G$ be a simple graph on $n$ vertices and $\\mathcal{I}_G$ denotes parity\nbinomial edge ideal of $G$ in the polynomial ring $S = \\mathbb{K}[x_1,\\ldots,\nx_n, y_1, \\ldots, y_n].$ We obtain a lower bound for the regularity of parity\nbinomial edge ideals of graphs. We then classify all graphs whose parity\nbinomial edge ideals have regularity $3$. We classify graphs whose parity\nbinomial edge ideals have pure resolution.\n', 'Generalized binomial edge ideals of bipartite graphs   Connected bipartite graphs whose binomial edge ideals are Cohen--Macaulay\nhave been classified by Bolognini et al. In this paper, we compute the depth,\nCastelnuovo--Mumford regularity, and dimension of the generalized binomial edge\nideals of these graphs.\n']","[('edge ideals', 0.7250354290008545), ('ideals graphs', 0.6963003873825073), ('edge ideal', 0.6602331399917603), ('monomial ideals', 0.586272120475769), ('monomial ideal', 0.5451591610908508), ('cohen macaulayness', 0.501245379447937), ('ideal polynomial ring', 0.4888550043106079), ('ideals associated', 0.48427021503448486), ('chordal graphs', 0.4578983187675476), ('macaulayness', 0.4464033842086792)]"
76,76,298,76_opinion dynamics_opinion formation_influence maximization_social network,"['opinion dynamics', 'opinion formation', 'influence maximization', 'social network', 'social networks', 'consensus formation', 'social influence', 'bounded confidence', 'dynamics networks', 'networks']","['A Bounded-Confidence Model of Opinion Dynamics with Heterogeneous\n  Node-Activity Levels   Agent-based models of opinion dynamics allow one to examine the spread of\nopinions between entities and to study phenomena such as consensus,\npolarization, and fragmentation. By studying a model of opinion dynamics on a\nsocial network, one can explore the effects of network structure on these\nphenomena. In social networks, some individuals share their ideas and opinions\nmore frequently than others. These disparities can arise from heterogeneous\nsociabilities, heterogeneous activity levels, different prevalences to share\nopinions when engaging in a social-media platform, or something else. To\nexamine the impact of such heterogeneities on opinion dynamics, we generalize\nthe Deffuant--Weisbuch (DW) bounded-confidence model (BCM) of opinion dynamics\nby incorporating node weights. The node weights allow us to model agents with\ndifferent probabilities of interacting. Using numerical simulations, we\nsystematically investigate (using a variety of network structures and\nnode-weight distributions) the effects of node weights, which we assign\nuniformly at random to the nodes. We demonstrate that introducing heterogeneous\nnode weights results in longer convergence times and more opinion fragmentation\nthan in a baseline DW model. The node weights in our BCM allow one to consider\na variety of sociological scenarios in which agents have heterogeneous\nprobabilities of interacting with other agents.\n', ""Bounded-Confidence Models of Multi-Dimensional Opinions with\n  Topic-Weighted Discordance   People's opinions on a wide range of topics often evolve over time through\ntheir interactions with others. Models of opinion dynamics primarily focus on\none-dimensional opinions which represent opinions on one topic. However,\nopinions on various topics are rarely isolated; instead, they can be\ninterdependent and exhibit correlations. In a bounded-confidence model (BCM) of\nopinion dynamics, agents influence each other's opinions only if their opinions\nare sufficiently similar. We extend classical agent-based BCMs -- namely, the\nHegeselmann--Krause BCM, which has synchronous interactions, and the\nDeffuant--Weisbuch BCM, which has asynchronous interactions -- to a\nmultidimensional setting, in which the opinions are multidimensional vectors\nrepresenting opinions of different topics and opinions on different topics are\ninterdependent. To measure opinion differences between agents, we introduce\ntopic-weighted discordance functions that account for opinion differences in\nall topics. We use the regions of receptiveness to characterize the\nsteady-state opinion clusters and provide an analytical approach to compute\nthese regions. In addition, we numerically simulate our models on various\nnetworks with initial opinions drawn from a variety of distributions. When\ninitial opinions are correlated across different topics, our topic-weighted\nBCMs yield significantly different results in both transient and steady states\ncompared to baseline models, where the dynamics of each opinion topic are\nindependent.\n"", 'A Weighted-Median Model of Opinion Dynamics on Networks   Social interactions influence people\'s opinions. In some situations, these\ninteractions result in a consensus opinion; in others, they result in opinion\nfragmentation and the formation of different opinion groups in the form of\n""echo chambers"". Consider a social network of individuals, who hold\ncontinuous-valued scalar opinions and change their opinions when they interact\nwith each other. In such an opinion model, it is common for an opinion-update\nrule to depend on the mean opinion of interacting individuals. However, we\nconsider an alternative update rule - which may be more realistic in some\nsituations - that instead depends on a weighted median opinion of interacting\nindividuals. Through numerical simulations of our opinion model, we investigate\nhow the limit opinion distribution depends on network structure. For\nconfiguration-model networks, we also derive a mean-field approximation for the\nasymptotic dynamics of the opinion distribution when there are infinitely many\nindividuals in a network.\n']","[('opinion dynamics', 0.6247344017028809), ('opinion formation', 0.5066361427307129), ('influence maximization', 0.4459257125854492), ('social network', 0.4257231652736664), ('social networks', 0.4053698182106018), ('consensus formation', 0.3966580629348755), ('social influence', 0.3954768776893616), ('bounded confidence', 0.3948301672935486), ('dynamics networks', 0.3888550102710724), ('networks', 0.3634338676929474)]"
77,77,292,77_number partitions_number partitions parts_integer partitions_partitions odd parts,"['number partitions', 'number partitions parts', 'integer partitions', 'partitions odd parts', 'integer partition', 'ramanujan like congruences', 'partitions odd', 'partitions distinct parts', 'partitions distinct', 'partitions']","['A conjecture of Baruah and Begum on the smallest parts function of\n  restricted overpartitions   In 2017, Andrews, Dixit, Schultz and Yee introduced the function\n$\\overline{\\textrm{spt}}_\\omega(n)$, which denotes the number of smallest parts\nin the overpartitions of $n$ in which the smallest part is always overlined and\nall odd parts are less than twice the smallest part. Recently, Baruah and Begum\nestablished several internal congruences and congruences modulo small powers of\n$5$ for $\\overline{\\textrm{spt}}_\\omega(n)$. Moreover, they conjectured a\nfamily of internal congruences modulo any powers of $5$ and two families of\ncongruences modulo any even powers of $5$. In this paper, we confirm three\nfamilies of congruences due to Baruah and Begum.\n', 'New congruences for partitions where the even parts are distinct   We denote the number of partitions of $n$ wherein the even parts are distinct\n(and the odd parts are unrestricted) by $ped(n)$. In this paper, we will use\ngenerating function manipulations to obtain new congruences for $ped(n)$ modulo\n$24$.\n', 'Congruences and density results for partitions into distinct even parts   In this paper, we consider the set of partitions $ped(n)$ which counts the\nnumber of partitions of $n$ wherein the even parts are distinct (and the odd\nparts are unrestricted). Using an algorithm developed by Radu, we prove\ncongruences modulo 192 which were conjectured by Nath. Further, we prove a few\ninfinite families of congruences modulo 24 by using a result of Newman. Also,\nwe prove that $ped(9n+7)$ is lacunary modulo $2^{k+2}\\cdot 3$ and $3^{k+1}\\cdot\n4$ for all positive integers $k\\geq0$. We further prove an infinite family of\ncongruences for $ped(n)$ modulo arbitrary powers of 2 by employing a result of\nOno and Taguchi on the nilpotency of Hecke operators.\n']","[('number partitions', 0.5987563133239746), ('number partitions parts', 0.5934842824935913), ('integer partitions', 0.5894445180892944), ('partitions odd parts', 0.5388807654380798), ('integer partition', 0.5296327471733093), ('ramanujan like congruences', 0.5196102857589722), ('partitions odd', 0.5112177729606628), ('partitions distinct parts', 0.4977954924106598), ('partitions distinct', 0.479521244764328), ('partitions', 0.4665648639202118)]"
78,78,290,78_eigenvalue laplacian_eigenvalues laplacian_dirichlet neumann eigenvalues_robin boundary conditions,"['eigenvalue laplacian', 'eigenvalues laplacian', 'dirichlet neumann eigenvalues', 'robin boundary conditions', 'neumann eigenvalues', 'neumann laplacian', 'laplacian bounded', 'eigenvalues neumann', 'neumann eigenvalue', 'dirichlet eigenvalues']","['Nodal sets of Robin and Neumann eigenfunctions   We investigate the measure of nodal sets for Robin and Neumann eigenfunctions\nin the domain and on the boundary of the domain. A polynomial upper bound for\nthe interior nodal sets is obtained for Robin eigenfunctions in the smooth\ndomain. For the analytic domain, the sharp upper bounds of the interior nodal\nsets was shown for Robin eigenfunctions. More importantly, we obtain the sharp\nupper bounds for the boundary nodal sets of Neumann eigenfunctions with new\nquantitative global Carleman estimates. Furthermore, the sharp doubling\ninequality and vanishing order of Robin eigenfunctions on the boundary of the\ndomain are obtained.\n', 'Geometric Optimization of the First Robin Eigenvalue in Exterior Domains   This paper addresses the geometric optimization problem of the first Robin\neigenvalue in exterior domains, specifically the lowest point of the spectrum\nof the Laplace operator under Robin boundary conditions in the complement of a\nbounded domain. In contrast to the Laplace operator on bounded domains, the\nspectrum of this operator is not purely discrete. The discrete nature of the\nfirst eigenvalue depends on the parameter of the Robin boundary condition. In\ntwo dimensions, D. Krejcirik and V. Lotoreichik show that the ball maximizes\nthe first Robin eigenvalue among all smooth, bounded, simply connected sets\nwith given perimeter or given area, provided the eigenvalue is discrete.\n  We extend these findings to higher dimensions. The discrete spectrum of the\nLaplace operator under Robin boundary conditions can be characterized through\nthe Steklov eigenvalue problem in exterior domains, a topic studied by G.\nAuchmuty and Q. Han. Assuming that the lowest point of the spectrum is a\ndiscrete eigenvalue, we show that the ball is a local maximizer among nearly\nspherical domains with prescribed measure. However, in general, the ball does\nnot emerge as the global maximizer for the first Robin eigenvalue under either\nprescribed measure or prescribed perimeter.\n', 'Bounds for higher Steklov and mixed Steklov Neumann eigenvalues on\n  domains with holes   In this article, we study Steklov eigenvalues and mixed Steklov Neumann\neigenvalues on a smooth bounded domain in $\\mathbb{R}^{n}$, $n \\geq 2$, having\na spherical hole. We focus on two main results related to Steklov eigenvalues.\nFirst, we obtain explicit expression for the second nonzero Steklov eigenvalue\non concentric annular domain. Secondly, we derive a sharp upper bound of the\nfirst $n$ nonzero Steklov eigenvalues on a domain $\\Omega \\subset\n\\mathbb{R}^{n}$ having symmetry of order $4$ and a ball removed from its\ncenter. This bound is given in terms of the corresponding Steklov eigenvalues\non a concentric annular domain of the same volume as $\\Omega$. Next, we\nconsider the mixed Steklov Neumann eigenvalue problem on $4^{\\text{th}}$ order\nsymmetric domains in $\\mathbb{R}^{n}$ having a spherical hole and obtain upper\nbound of the first $n$ nonzero eigenvalues. We also provide some examples to\nillustrate that symmetry assumption in our results is crucial. Finally, We make\nsome numerical observations about these eigenvalues using FreeFEM++ and state\nthem as conjectures.\n']","[('eigenvalue laplacian', 0.6139245629310608), ('eigenvalues laplacian', 0.6070164442062378), ('dirichlet neumann eigenvalues', 0.6057596802711487), ('robin boundary conditions', 0.5745633840560913), ('neumann eigenvalues', 0.5566800832748413), ('neumann laplacian', 0.5542556047439575), ('laplacian bounded', 0.5467641949653625), ('eigenvalues neumann', 0.5452121496200562), ('neumann eigenvalue', 0.5305745005607605), ('dirichlet eigenvalues', 0.519262969493866)]"
79,79,290,79_manifolds nonnegative ricci_ricci curvature bounds_ricci curvature bound_ricci curvature bounded,"['manifolds nonnegative ricci', 'ricci curvature bounds', 'ricci curvature bound', 'ricci curvature bounded', 'nonnegative ricci curvature', 'riemannian manifolds nonnegative', 'lower ricci curvature', 'curvature lower bounds', 'curvature lower bound', 'ricci curvature lower']","['Glued spaces and lower Ricci curvature bounds   We consider Riemannian manifolds $M_i$, ${i=0,1}$, with boundary and\n$\\Phi_i\\in C^{\\infty}(M_i)$ non-negative such that the pair $(M_i, \\Phi_i)$\nadmits Bakry-Emery $N$-Ricci curvature bounded from below by $K$. Let $Y_0$ and\n$Y_1$ be isometric, compact components of the boundary of $M_0$ and $M_1$\nrespectively and assume $\\Phi_0=\\Phi_1$ on $Y_0\\simeq Y_1$. We assume that\n$\\Pi_0+\\Pi_1=\\Pi \\geq 0$ (*), and $d\\Phi_0(\\nu_0)+ d\\Phi_1(\\nu_1)\\leq\n\\mbox{tr}\\Pi$ on $Y_0\\simeq Y_1$ (**) where $\\Pi_i$ is the second fundamental\nform and $\\nu_i$ is inner unit normal field along $\\partial M_i$. We show that\nthe metric glued space $M=M_0\\cup_{\\mathcal I}M_1$ together with the measure\n$\\Phi d\\mathcal H^n$ satisfies the curvature-dimension condition $CD(K,\\lceil N\n\\rceil)$ where $\\Phi: M\\rightarrow [0,\\infty)$ arises tautologically from\n$\\Phi_1$ and $\\Phi_2$. Moreover, $(M, \\Phi d\\mathcal H^n)$ is the collapsed\nGromov-Hausdorff limit of smooth, $\\lceil N \\rceil$-dimensional Riemannian\nmanifolds with Ricci curvature bounded from below by $K- \\epsilon$ and is also\nthe measured Gromov-Hausdorff limit of smooth, weighted Riemannian manifolds\nsuch that the Bakry-Emery $\\lceil N \\rceil$-Ricci curvature is bounded from\nbelow by $K-\\epsilon$. On the other hand we show that given a glued manifold as\ndescribed it satisfies the curvature-dimension condition $CD(K,N)$ only if the\ncondition (*) and (**) hold. The latter statement generalizes a theorem of\nKosovski\\u{\\i} for sectional lower curvature bounds and especially applies for\nthe unweighted case where a lower Ricci curvature bound and $\\dim_{M_i}\\leq N$\nreplaces a lower Bakry-Emery $N$-Ricci curvature bound.\n', 'On the existence of isoperimetric regions in manifolds with nonnegative\n  Ricci curvature and Euclidean volume growth   In this paper we provide new existence results for isoperimetric sets of\nlarge volume in Riemannian manifolds with nonnegative Ricci curvature and\nEuclidean volume growth. We find sufficient conditions for their existence in\nterms of the geometry at infinity of the manifold. As a byproduct we show that\nisoperimetric sets of big volume always exist on manifolds with nonnegative\nsectional curvature and Euclidean volume growth. Our method combines an\nasymptotic mass decomposition result for minimizing sequences, a sharp\nisoperimetric inequality on nonsmooth spaces, and the concavity property of the\nisoperimetric profile. The latter is new in the generality of noncollapsed\nmanifolds with Ricci curvature bounded below.\n', 'Optimal asymptotic volume ratio for noncompact 3-manifolds with\n  asymptotically nonnegative Ricci curvature and a uniformly positive scalar\n  curvature lower bound   In this paper, we study 3-dimensional complete non-compact Riemannian\nmanifolds with asymptotically nonnegative Ricci curvature and a uniformly\npositive scalar curvature lower bound. Our main result is that, if this\nmanifold has $k$ ends and finite first Betti number, then it has at most linear\nvolume growth, and furthermore, if the negative part of Ricci curvature decays\nsufficiently fast at infinity, then we have an optimal asymptotic volume ratio\n$\\limsup_{r\\rightarrow\\infty}\\frac{\\mathrm{Vol}(B(p, r))}{r}\\leq4k\\pi$. In\nparticular, our results apply to 3-dimensional complete non-compact Riemannian\nmanifolds with nonnegative Ricci curvature and a uniformly positive scalar\ncurvature lower bound.\n']","[('manifolds nonnegative ricci', 0.7157226800918579), ('ricci curvature bounds', 0.7110186815261841), ('ricci curvature bound', 0.7048435211181641), ('ricci curvature bounded', 0.7006486654281616), ('nonnegative ricci curvature', 0.693658173084259), ('riemannian manifolds nonnegative', 0.6675887107849121), ('lower ricci curvature', 0.6424309611320496), ('curvature lower bounds', 0.6341511607170105), ('curvature lower bound', 0.6302054524421692), ('ricci curvature lower', 0.6219433546066284)]"
80,80,286,80_billiard trajectories_billiards_billiard_convex bodies,"['billiard trajectories', 'billiards', 'billiard', 'convex bodies', 'hyperbolic plane', 'polygonal', 'conics', 'elliptic', 'periodic orbits', 'invariant curves']","[""On projective billiards with open subsets of triangular orbits   Ivrii's Conjecture states that in every billiard in Euclidean space the set\nof periodic orbits has measure zero. It implies that for every $k\\geq2$ there\nare no k-reflective billiards, i.e., billiards having an open set of k-periodic\norbits. This conjecture is open in Euclidean spaces, with just few partial\nresults. It is known that in the two-dimensional sphere there exist\n3-reflective billiards (Yu.M.Baryshnikov). All the 3-reflective spherical\nbilliards were classified in a paper by V.Blumen, K.Kim, J.Nance, V.Zharnitsky:\nthe boundary of each of them lies in three orthogonal big circles. In the\npresent paper we study the analogue of Ivrii's Conjecture for projective\nbilliards introduced by S.Tabachnikov. In two dimensions there exists a\n3-reflective projective billiard, the so-called right-spherical billiard, which\nis the projection of a spherical 3-reflective billiard. We show that the only\n3-reflective planar projective billiard with piecewise smooth boundary is the\nabove-mentioned right-spherical billiard. In higher dimensions, we prove the\nnon-existence of 3-reflective projective billiards with piecewise smooth\nboundary, and also the non-existence of projective billiards with piecewise\nsmooth boundary having a subset of triangular orbits of non-zero measure in the\nphase space.\n"", ""Isometric Billiards in Ellipses and Focal Billiards in Ellipsoids   Billiards in ellipses have a confocal ellipse or hyperbola as caustic. The\ngoal of this paper is to prove that for each billiard of one type there exists\nan isometric counterpart of the other type. Isometry means here that the\nlengths of corresponding sides are equal. The transition between these two\nisometric billiard can be carried out continuosly via isometric focal billiards\nin a fixed ellipsoid. The extended sides of these particular billiards in an\nellipsoid are focal axes, i.e., generators of confocal hyperboloids. This\ntransition enables to transfer properties of planar billiards to focal\nbilliards, in particular billiard motions and canonical parametrizations. A\nperiodic planar billiard and its associated Poncelet grid give rise to periodic\nfocal billiards and spatial Poncelet grids. If the sides of a focal billiard\nare materialized as thin rods with spherical joints at the vertices and other\ncrossing points between different sides, then we obtain Henrici's hyperboloid,\nwhich is flexible between the two planar limits.\n"", 'Back to Boundaries in Billiards   We prove Poisson limit laws for open billiards where the holes are on the\nboundaries of billiard tables (rather than some abstract holes in the phase\nspace of a billiard). Such holes are of the main interest for billiard systems,\nespecially for applications. Sinai billiards with or without a finite horizon,\ndiamond billiards, and semi-dispersing billiards, as well as focusing billiards\nwith slow decay of correlations, are considered.\n']","[('billiard trajectories', 0.733683705329895), ('billiards', 0.7180870771408081), ('billiard', 0.6883042454719543), ('convex bodies', 0.430026650428772), ('hyperbolic plane', 0.3771071434020996), ('polygonal', 0.36239156126976013), ('conics', 0.354881227016449), ('elliptic', 0.3504323959350586), ('periodic orbits', 0.34215378761291504), ('invariant curves', 0.340550035238266)]"
81,81,284,81_harmonic sums_multiple harmonic sums_zeta functions_harmonic numbers,"['harmonic sums', 'multiple harmonic sums', 'zeta functions', 'harmonic numbers', 'zeta values', 'harmonic number', 'multiple zeta values', 'values riemann zeta', 'riemann zeta', 'multiple zeta']","['On connection between values of Riemann zeta function at integers and\n  generalized harmonic numbers   Using Euler transformation of series we relate values of Hurwitz zeta\nfunction at integer and rational values of arguments to certain rapidly\nconverging series where some generalized harmonic numbers appear. The form of\nthese generalized harmonic numbers carries information about the values of the\narguments of Hurwitz function. In particular we prove: $\\forall k\\in\n\\mathbb{N}:$ $\\zeta (k,1)\\allowbreak =\\allowbreak \\frac{2^{k-1}}{2^{k-1}-1}%\n\\sum_{n=1}^{\\infty }\\frac{H_{n}^{(k-1)}}{n2^{n}},$ where $H_{n}^{(k)}$ are\ndefined below generalized harmonic numbers. Further we find generating function\nof the numbers $\\hat{\\zeta}(k)=\\sum_{j=1}^{\\infty }(-1)^{j-1}/j^{k}. $\n', 'Some identities on degenerate harmonic and degenerate higher-order\n  harmonic numbers   The harmonic numbers and higher-order harmonic numbers appear frequently in\nseveral areas which are related to combinatorial identities, many expressions\ninvolving special functions in analytic number theory, and analysis of\nalgorithms. The aim of this paper is to study the degenerate harmonic and\ndegenerate higher-order harmonic numbers, which are respectively degenerate\nversions of the harmonic and higher-order harmonic numbers, in connection with\nthe degenerate zeta and degenerate Hurwitz zeta function. Here the degenerate\nzeta and degenerate Hurwitz zeta function are respectively degenerate versions\nof the Riemann zeta and Hurwitz zeta function. We show that several infinite\nsums involving the degenerate higher-order harmonic numbers can be expressed in\nterms of the degenerate zeta function. Furthermore, we demonstrate that an\ninfinite sum involving finite sums of products of the degenerate harmonic\nnumbers can be represented by using the degenerate Hurwitz zeta function.\n', 'Some Evaluations of Parametric Euler Type Sums of Harmonic Numbers   We establish some identities of Euler related sums. By using these\nidentities, we discuss the closed form representations of sums of harmonic\nnumbers and reciprocal parametric binomial coefficients through parametric\nharmonic numbers, shifted harmonic numbers and Riemann zeta function with\npositive integer arguments. In particular we investigate products of quadratic\nand cubic harmonic numbers and reciprocal parametric binomial coefficients.\nSome illustrative special cases as well as immediate consequences of the main\nresults are also considered.\n']","[('harmonic sums', 0.631974995136261), ('multiple harmonic sums', 0.6304380297660828), ('zeta functions', 0.6047370433807373), ('harmonic numbers', 0.5844323039054871), ('zeta values', 0.5561501383781433), ('harmonic number', 0.5403225421905518), ('multiple zeta values', 0.5293399691581726), ('values riemann zeta', 0.52386075258255), ('riemann zeta', 0.5237631797790527), ('multiple zeta', 0.49006736278533936)]"
82,82,284,82_magnetohydrodynamic mhd equations_magnetohydrodynamics mhd equations_magnetohydrodynamics mhd_magnetohydrodynamic mhd,"['magnetohydrodynamic mhd equations', 'magnetohydrodynamics mhd equations', 'magnetohydrodynamics mhd', 'magnetohydrodynamic mhd', 'magnetohydrodynamics equations', 'magnetohydrodynamic equations', 'magnetohydrodynamics', 'ideal magnetohydrodynamics', 'magnetohydrodynamic', 'resistive mhd equations']","['On Magnetic Inhibition Theory in Non-resistive Magnetohydrodynamic\n  Fluids: Existence of Solutions in Some Classes of Large Data   This paper is concerned with existence of solutions to the incompressible\nnon-resistive viscous magnetohydrodynamic (MHD) equations with large initial\nperturbations in there-dimensional (3D) periodic domains (in Lagrangian\ncoordinates). Motivated by the Diophantine condition imposed by the approximate\ntheory of non-resistive MHD equations in \\cite{BCSCSPLL}, Chen--Zhang--Zhou in\n\\cite{chen2021} and the magnetic inhibition mechanism of Lagrangian coordinates\nversion in our previous paper \\cite{JFJSOMITIN}, we prove the existence of\nunique classical solutions under some class of large initial perturbations,\nwhere the intensity of impressive magnetic fields depends increasingly on the $\nH^{17}\\times H^{21}$-norm of the initial perturbation of both the velocity and\nmagnetic field. Our result not only mathematically verifies that magnetic\nfields prevent the singularity formation of solutions with large initial\nvelocity in the viscous case, but also provide a starting point for the\nexistence theory of large perturbation solutions of the 3D non-resistive\nviscous MHD equations. In addition, we further rigorously prove that, for large\ntime or strong magnetic field, the MHD equations reduce to the corresponding\nlinearized equations by providing the error estimates, which enjoy the types of\nalgebraic decay with respect to the both of time and field intensity, between\nthe solutions of both the nonlinear and linear equations.\n', 'On non-resistive limit of 1D MHD equations with no vacuum at infinity   In this paper, we consider the Cauchy problem for the one-dimensional\ncompressible isentropic magnetohydrodynamic (MHD) equations with no vacuum at\ninfinity, but the initial vacuum can be permitted inside the region. By\nderiving a priori $\\nu $ (resistivity coefficient)-independent estimates, we\nestablish the non-resistive limit of the global strong solutions with large\ninitial data. Moreover, as a by-product, the global well-posedness of strong\nsolutions for both the compressible resistive MHD equations and non-resistive\nMHD equations are also established, respectively.\n', 'On some Liouville type Theorems for the stationary MHD and Hall-MHD\n  equations   We prove several Liouville type results for the stationary MHD and Hall-MHD\nequations. In particular, we show that the velocity and magnetic field,\nbelonging to some Lorentz spaces or satisfying a priori decay assumption, must\nbe zero.\n']","[('magnetohydrodynamic mhd equations', 0.681038498878479), ('magnetohydrodynamics mhd equations', 0.6717129349708557), ('magnetohydrodynamics mhd', 0.6019619107246399), ('magnetohydrodynamic mhd', 0.5977572798728943), ('magnetohydrodynamics equations', 0.591821014881134), ('magnetohydrodynamic equations', 0.5869717001914978), ('magnetohydrodynamics', 0.535041093826294), ('ideal magnetohydrodynamics', 0.5342715978622437), ('magnetohydrodynamic', 0.5196254253387451), ('resistive mhd equations', 0.5176082849502563)]"
83,83,280,83_semidefinite programming_constrained optimization problems_constrained optimization_cone programming,"['semidefinite programming', 'constrained optimization problems', 'constrained optimization', 'cone programming', 'nonlinear programming', 'constraint qualification', 'optimality conditions', 'necessary optimality conditions', 'order optimality conditions', 'second order optimality']","['On second-order Karush--Kuhn--Tucker optimality conditions for $C^{1,1}$\n  vector optimization problems   This paper focuses on optimality conditions for $C^{1,1}$ vector optimization\nproblems with inequality constraints. By employing the limiting second-order\nsubdifferential and the second-order tangent set, we introduce a new type of\nsecond-order constraint qualification in the sense of Abadie. Then we establish\nsome second-order necessary optimality conditions of Karush--Kuhn--Tucker-type\nfor local (weak) efficient solutions of the considered problem. In addition, we\nprovide some sufficient conditions for a local efficient solution of the such\nproblem. The obtained results improve existing ones in the literature.\n', ""Sequential constant rank constraint qualifications for nonlinear\n  semidefinite programming with applications   We present new constraint qualification conditions for nonlinear semidefinite\nprogramming that extend some of the constant rank-type conditions from\nnonlinear programming. As an application of these conditions, we provide a\nunified global convergence proof of a class of algorithms to stationary points\nwithout assuming neither uniqueness of the Lagrange multiplier nor boundedness\nof the Lagrange multipliers set. This class of algorithm includes, for\ninstance, general forms of augmented Lagrangian, sequential quadratic\nprogramming, and interior point methods. We also compare these new conditions\nwith some of the existing ones, including the nondegeneracy condition,\nRobinson's constraint qualification, and the metric subregularity constraint\nqualification.\n"", ""Naive constant rank-type constraint qualifications for multifold\n  second-order cone programming and semidefinite programming   The constant rank constraint qualification, introduced by Janin in 1984 for\nnonlinear programming, has been extensively used for sensitivity analysis,\nglobal convergence of first- and second-order algorithms, and for computing the\nderivative of the value function. In this paper we discuss naive extensions of\nconstant rank-type constraint qualifications to second-order cone programming\nand semidefinite programming, which are based on the\nApproximate-Karush-Kuhn-Tucker necessary optimality condition and on the\napplication of the reduction approach. Our definitions are strictly weaker than\nRobinson's constraint qualification, and an application to the global\nconvergence of an augmented Lagrangian algorithm is obtained.\n""]","[('semidefinite programming', 0.6127392649650574), ('constrained optimization problems', 0.5555292367935181), ('constrained optimization', 0.5464184284210205), ('cone programming', 0.5039575695991516), ('nonlinear programming', 0.5007531046867371), ('constraint qualification', 0.49323174357414246), ('optimality conditions', 0.4926885664463043), ('necessary optimality conditions', 0.4917795956134796), ('order optimality conditions', 0.4893471896648407), ('second order optimality', 0.48871850967407227)]"
84,84,279,84_quadratic number fields_galois groups_fields galois_galois extensions,"['quadratic number fields', 'galois groups', 'fields galois', 'galois extensions', 'mathbb _p extensions', 'extensions number fields', 'galois group', 'galois group maximal', 'quadratic fields', 'galois']","[""Stabilization on ideal class groups in potential cyclic towers Let $p$ be a prime and let $F$ be a number field. Consider a Galois extension $K/F$ with Galois group $H\\rtimes \\Delta$ where $H\\cong \\mathbb{Z}_p$ or $\\mathbb{Z}/p^d\\mathbb{Z}$, and $\\Delta$ is an arbitrary Galois group. The subfields fixed\n  by $H^{p^n} \\rtimes \\Delta$ $(n=0,1,\\cdots)$ form a tower which we call it a potential cyclic $p$-tower in this paper. A radical $p$-tower is a typical example, say $\\mathbb{Z}\\subset \\mathbb{Z}(\\sqrt[p]{a})\\subset \\mathbb{Z}(\\sqrt[p^2]{a})\\subset \\cdots$ where $a\\in \\mathbb{Z}$.\n  We extend the stabilization result of Fukuda in Iwasawa theory on $p$-class groups in cyclic $p$-towers to potential cyclic $p$-towers. We also extend Iwasawa's class number formula in $\\mathbb{Z}_p$-extensions to potential $\\mathbb{Z}_p$-extensions."", ""On the $p$-rationality of consecutive quadratic fields   In 2016, in the work related to Galois representations, Greenberg conjectured\nthe existence of multi-quadratic $p$-rational number fields of degree $2^{t}$\nfor any odd prime number $p$ and any integer $t \\geq 1$. Using the criteria\nprovided by him to check $p$-rationality for abelian number fields, certain\ninfinite families of quadratic, biquadratic and triquadratic $p$-rational\nfields have been shown to exist in recent years. In this article, for any\ninteger $k \\geq 1$, we build upon the existing work and prove the existence of\ninfinitely many prime numbers $p$ for which the imaginary quadratic fields\n$\\mathbb{Q}(\\sqrt{-(p - 1)}),\\ldots,\\mathbb{Q}(\\sqrt{-(p - k)})$ and\n$\\mathbb{Q}(\\sqrt{-p(p - 1)}),\\ldots, \\mathbb{Q}(\\sqrt{-p(p - k)})$ are all\n$p$-rational. This can be construed as analogous results in the spirit of\nIizuka's conjecture on the divisibility of class numbers of consecutive\nquadratic fields. We also address a similar question of $p$-rationality for two\nconsecutive real quadratic fields by proving the existence of infinitely many\n$p$-rational fields of the form $\\mathbb{Q}(\\sqrt{p^{2} + 1})$ and\n$\\mathbb{Q}(\\sqrt{p^{2} + 2})$. The result for imaginary quadratic fields is\naccomplished by producing infinitely many primes for which the corresponding\nconsecutive discriminants have large square divisors and the same for real\nquadratic fields is proven using a result of Heath-Brown on the density of\nsquare-free values of polynomials at prime arguments.\n"", 'Theoretical and Experimental Approach to p-Class Field Towers of Cyclic\n  Cubic Number Fields   Cyclic number fields of odd prime degree are constructed as ray class fields\nover the rational number field. They are collected in multiplets sharing a\ncommon conductor and discriminant. The algorithms are implemented in Magma and\napplied to all cyclic quintic and cyclic cubic fields with conductors below\n100000. Our primary attention is devoted to the theory of cyclic cubic fields\nwith two or three prime divisors of the conductor. These fields form doublets\nand quartets. Theoretical techniques comprise cubic residue conditions between\nthe primes dividing the conductor, the structure of 3-class groups of all\ncomponents of doublets and quartets, Galois cohomology of unit groups and\nambiguous principal ideals, absolute genus fields and their bicyclic bicubic\nsubfields, class number relations, transfer kernels and abelian quotient\ninvariants of unramified cyclic cubic extensions and their impact on the class\nfield tower, pattern recognition via Artin transfers on descendant trees of\nfinite groups with order a power of 3, the Shafarevich Theorem on the relation\nrank of the 3-class field tower group, and the Galois action on the tower group\nand on its metabelianization. Rigorous proofs are given for the first\noccurrences of three-stage towers over cyclic cubic fields with elementary\nbicyclic or tricyclic or non-elementary bicyclic 3-class group. Experimentally,\nthe second p-class groups and the length of the p-class tower are determined\nfor all conductors below 100000 and for p=2,3,5, with the exception of the few\nintricate octets. An interesting application is able to identify and realize\nthe closed groups by Andozhskii and Tsvetkov.\n']","[('quadratic number fields', 0.565743088722229), ('galois groups', 0.5442380905151367), ('fields galois', 0.531828761100769), ('galois extensions', 0.5162577629089355), ('mathbb _p extensions', 0.5123005509376526), ('extensions number fields', 0.5075085759162903), ('galois group', 0.5030907392501831), ('galois group maximal', 0.4814697206020355), ('quadratic fields', 0.4791232645511627), ('galois', 0.47225701808929443)]"
85,85,276,85_mean curvature flows_mean curvature flow_curvature flows_solutions mean curvature,"['mean curvature flows', 'mean curvature flow', 'curvature flows', 'solutions mean curvature', 'curvature flow', 'mean curvature', 'curvature flow closed', 'inverse mean curvature', 'curvatures', 'principal curvatures']","['Singularity of mean curvature flow with bounded mean curvature and Morse\n  index   We study the multiplicity of the singularity of mean curvature flow with\nbounded mean curvature and Morse index. For $3\\leq n\\leq 6$, we show that\neither the mean curvature or the Morse index blows up at the first singular\ntime for a closed smooth embedded mean curvature flow in $\\mathbb{R}^{n+1}$.\n', 'Rotational symmetry of uniformly 3-convex translating solitons of mean\n  curvature flow in higher dimensions   In this paper, we generalize a previous result to higher dimension. We prove\nthat uniformly 3-convex translating solitons of mean curvature flow in\n$\\mathbb{R}^{n+1}$ which arise as blow up limit of embedded, mean convex mean\ncurvature flow must have $SO(n-1)$ symmetry.\n', '$SO(2)$ symmetry of the translating solitons of the mean curvature flow\n  in $\\mathbb{R}^4$   In this paper, we prove that the translating solitons of the mean curvature\nflow in $\\mathbb{R}^4$ which arise as blow up limit of embedded, mean convex\nmean curvature flow must have $SO(2)$ symmetry.\n']","[('mean curvature flows', 0.7938017845153809), ('mean curvature flow', 0.7516584396362305), ('curvature flows', 0.7194390892982483), ('solutions mean curvature', 0.68611079454422), ('curvature flow', 0.673192024230957), ('mean curvature', 0.6568965315818787), ('curvature flow closed', 0.6525897979736328), ('inverse mean curvature', 0.6291971206665039), ('curvatures', 0.5913762450218201), ('principal curvatures', 0.5739877223968506)]"
86,86,272,86_vortex dynamics_euler flows_vortex sheets_incompressible euler equations,"['vortex dynamics', 'euler flows', 'vortex sheets', 'incompressible euler equations', 'vortex sheet', '2d euler equations', 'vortex system', '3d euler equations', 'dimensional euler equations', 'dimensional incompressible euler']","[""On concentrated vortices of 3D incompressible Euler equations under\n  helical symmetry: with swirl   In this paper, we consider the existence of concentrated helical vortices of\n3D incompressible Euler equations with swirl. First, without the assumption of\nthe orthogonality condition, we derive a 2D vorticity-stream formulation of 3D\nincompressible Euler equations under helical symmetry. Then based on this\nsystem, we deduce a non-autonomous second order semilinear elliptic equations\nin divergence form, whose solutions correspond to traveling-rotating invariant\nhelical vortices with non-zero helical swirl. Finally, by using Arnold's\nvariational method, that is, finding maximizers of a properly defined energy\nfunctional over a certain function space and proving the asymptotic behavior of\nmaximizers, we construct families of concentrated traveling-rotating helical\nvortices of 3D incompressible Euler equations with non-zero helical swirl in\ninfinite cylinders. As parameter $ \\varepsilon\\to0 $, the associated vorticity\nfields tend asymptotically to a singular helical vortex filament evolved by the\nbinormal curvature flow.\n"", 'Contour dynamics and global regularity for periodic vortex patches and\n  layers   We study vortex patches for the 2D incompressible Euler equations. Prior\nworks on this problem take the support of the vorticity (i.e., the vortex\npatch) to be a bounded region. We instead consider the horizontally periodic\nsetting. This includes both the case of a periodic array of bounded vortex\npatches and the case of vertically bounded vortex layers. We develop the\ncontour dynamics equation for the boundary of the patch in this horizontally\nperiodic setting, and demonstrate global $C^{1,\\epsilon}$ regularity of this\npatch boundary. In the process of formulating the problem, we consider\ndifferent notions of periodic solutions of the 2D incompressible Euler\nequations, and demonstrate equivalence of these.\n', 'Convergence of filtered weak solutions to the 2D Euler equations with\n  vortex sheet initial data   We study weak solutions of the two-dimensional (2D) filtered Euler equations\nwhose vorticity is a finite Radon measure and velocity has locally finite\nkinetic energy, which is called the vortex sheet solution. The filtered Euler\nequations are a regularized model based on a spatial filtering to the Euler\nequations. The 2D filtered Euler equations have a unique global weak solution\nfor measure valued initial vorticity, while the 2D Euler equations require\ninitial vorticity to be in the vortex sheet class with a distinguished sign for\nthe existence of global solutions. In this paper, we prove that vortex sheet\nsolutions of the 2D filtered Euler equations converge to those of the 2D Euler\nequations in the limit of the filtering parameter provided that initial vortex\nsheet has a distinguished sign. We also show that a simple application of our\nproof yields the convergence of the vortex blob method for vortex sheet\nsolutions. Moreover, we make it clear what kind of condition should be imposed\non the spatial filter to show the convergence results and, according to the\ncondition, these results are applicable to well-known regularized models like\nthe Euler-$\\alpha$ model and the vortex blob model.\n']","[('vortex dynamics', 0.6414027214050293), ('euler flows', 0.5929661989212036), ('vortex sheets', 0.5679395198822021), ('incompressible euler equations', 0.5597637295722961), ('vortex sheet', 0.5404634475708008), ('2d euler equations', 0.5338709950447083), ('vortex system', 0.5298762321472168), ('3d euler equations', 0.5253154635429382), ('dimensional euler equations', 0.5214244723320007), ('dimensional incompressible euler', 0.5210809111595154)]"
87,87,267,87_metrizable spaces_tychonoff space_separable metrizable_metrizable space,"['metrizable spaces', 'tychonoff space', 'separable metrizable', 'metrizable space', 'countable space', 'countably compact', 'hausdorff spaces', 'compact spaces', 'hausdorff space', 'generalized topological']","[""Topological properties of some function spaces   Let $Y$ be a metrizable space containing at least two points, and let $X$ be\na $Y_{\\mathcal{I}}$-Tychonoff space for some ideal $\\mathcal{I}$ of compact\nsets of $X$. Denote by $C_{\\mathcal{I}}(X,Y)$ the space of continuous functions\nfrom $X$ to $Y$ endowed with the $\\mathcal{I}$-open topology. We prove that\n$C_{\\mathcal{I}}(X,Y)$ is Fr\\'{e}chet - Urysohn iff $X$ has the property\n$\\gamma_{\\mathcal{I}}$. We characterize zero - dimensional Tychonoff spaces $X$\nfor which the space $C_{\\mathcal{I}}(X,{\\bf 2})$ is sequential. Extending the\nclassical theorems of Gerlits, Nagy and Pytkeev we show that if $Y$ is not\ncompact, then $C_{p}(X,Y)$ is Fr\\'{e}chet - Urysohn iff it is sequential iff it\nis a $k$-space iff $X$ has the property $\\gamma$. An analogous result is\nobtained for the space of bounded continuous functions taking values in a\nmetrizable locally convex space. Denote by $B_{1}(X,Y)$ and $B(X,Y)$ the space\nof Baire one functions and the space of all Baire functions from $X$ to $Y$,\nrespectively. If $H$ is a subspace of $B(X,Y)$ containing $B_{1}(X,Y)$, then\n$H$ is metrizable iff it is a $\\sigma$ - space iff it has countable $cs^*$ -\ncharacter iff $X$ is countable. If additionally $Y$ is not compact, then $H$ is\nFr\\'{e}chet - Urysohn iff it is sequential iff it is a $k$ - space iff it has\ncountable tightness iff $X_{\\aleph_0}$ has the property $\\gamma$, where\n$X_{\\aleph_0}$ is the space $X$ with the Baire topology. We show that if $X$ is\na Polish space, then the space $B_{1}(X,\\mathbb{R})$ is normal iff $X$ is\ncountable.\n"", 'Baire property of some function spaces   A compact space $X$ is called $\\pi$-monolithic if for any surjective\ncontinuous mapping $f:X\\rightarrow K$ where $K$ is a metrizable compact space\nthere exists a metrizable compact space $T\\subseteq X$ such that $f(T)=K$. A\ntopological space $X$ is Baire if the intersection of any sequence of open\ndense subsets of $X$ is dense in $X$. Let $C_p(X,Y)$ denote the space of all\ncontinuous $Y$- valued functions $C(X,Y)$ on a Tychonoff space $X$ with the\ntopology of pointwise convergence. In this paper we have proved that for a\ntotally disconnected space $X$ the space $C_p(X,\\{0,1\\})$ is Baire if, and only\nif, $C_p(X,K)$ is Baire for every $\\pi$-monolithic compact space $K$. For a\nTychonoff space $X$ the space $C_p(X)$ is Baire if, and only if, $C_p(X,L)$ is\nBaire for each Frechet space $L$. We construct a totally disconnected Tychonoff\nspace $T$ such that $C_p(T,M)$ is Baire for a separable metric space $M$ if,\nand only if, $M$ is a Peano continuum. Moreover, $C_p(T,[0,1])$ is Baire but\n$Cp(T,\\{0,1\\})$ is not.\n', 'Baire property of space of Baire-one functions   A topological space $X$ is Baire if the Baire Category Theorem holds for $X$,\ni.e., the intersection of any sequence of open dense subsets of $X$ is dense in\n$X$. One of the interesting problems for the space $B_1(X)$ of all Baire-one\nreal-valued functions is characterization topological space $X$ for which the\nfunction space $B_1(X)$ is Baire. In this paper, we solve this problem, namely,\nwe have obtained a characterization when a function space $B_1(X)$ has the\nBaire property for any Tychonoff space $X$. Also we proved that $B_1(X)$ is\nBaire for any $\\gamma$-space $X$. This answers a question posed recently by T.\nBanakh and S. Gabriyelyan. We also conclude that, it is consistent there are no\nuncountable separable metrizable space $X$ such that $B_1(X)$ is countable\ndense homogeneous.\n']","[('metrizable spaces', 0.6194747090339661), ('tychonoff space', 0.5485701560974121), ('separable metrizable', 0.5417811274528503), ('metrizable space', 0.5363223552703857), ('countable space', 0.528065025806427), ('countably compact', 0.5270681977272034), ('hausdorff spaces', 0.5106580257415771), ('compact spaces', 0.5068575143814087), ('hausdorff space', 0.5045709609985352), ('generalized topological', 0.4913943409919739)]"
88,88,266,88_extriangulated category_triangulated categories_categories triangulated_triangulated category,"['extriangulated category', 'triangulated categories', 'categories triangulated', 'triangulated category', 'triangulated category mathcal', 'exact categories', 'angulated category', 'abelian categories', 'categories', 'additive category']","['Hearts of twin Cotorsion pairs on extriangulated categories   In this article, we study the heart of a cotorsion pairs on an exact category\nand a triangulated category in a unified meathod, by means of the notion of an\nextriangulated category. We prove that the heart is abelian, and construct a\ncohomological functor to the heart. If the extriangulated category has enough\nprojectives, this functor gives an equivalence between the heart and the\ncategory of coherent functors over the coheart modulo projectives. We also show\nhow an n-cluster tilting subcategory of an extriangulated category gives rise\nto a family of cotorsion pairs with equivalent hearts.\n', 'Recollements of extriangulated categories   We give a simultaneous generalization of recollements of abelian categories\nand triangulated categories, which we call recollements of extriangulated\ncategories. For a recollement $(\\mathcal{A}$, $\\mathcal{B}$, $\\mathcal{C})$ of\nextriangulated categories, we show that cotorsion pairs in $\\mathcal{A}$ and\n$\\mathcal{C}$ induce cotorsion pairs in $\\mathcal{B}$ under certain conditions.\nAs an application, our main result recovers a result given by Chen for\nrecollements of triangulated categories, and it also shows a new phenomena when\nit is applied to abelian categories.\n', 'Auslander-Buchweitz Approximation Theory for Extriangulated Categories   Extriangulated categories were introduced by Nakaoka and Palu as a\nsimultaneous generalization of exact categories and triangulated categories. In\nthis paper, we introduce and develop an analogous theory of Auslander-Buchweitz\napproximations for extriangulated categories. We establish the existence of\nprecovers pand preenvelopesq and obtain characterizations of relative\nhomological dimensions, which are based on certain subcategories under\nfiniteness of resolutions. Finally, we give a description of cotorsion pairs on\nextriangulated categories under some conditions, and provide a characterization\nof silting subcategories on stable categories. Keywords: Extriangulated\ncategory; Homological dimension; Cogenerator; Cotorsion pair.\n']","[('extriangulated category', 0.7464921474456787), ('triangulated categories', 0.7418402433395386), ('categories triangulated', 0.720866858959198), ('triangulated category', 0.6953268051147461), ('triangulated category mathcal', 0.6687672138214111), ('exact categories', 0.6244263052940369), ('angulated category', 0.6020929217338562), ('abelian categories', 0.5959756970405579), ('categories', 0.5676780939102173), ('additive category', 0.5550919771194458)]"
89,89,263,89_siegel modular forms_hilbert modular forms_eisenstein series_holomorphic modular forms,"['siegel modular forms', 'hilbert modular forms', 'eisenstein series', 'holomorphic modular forms', 'modular forms', 'valued modular forms', 'siegel modular', 'weight modular forms', 'modular forms weight', 'quasi modular forms']","['Harmonic weak Maass forms and periods II   In this paper we investigate the Fourier coefficients of harmonic Maass forms\nof negative half-integral weight. We relate the algebraicity of these\ncoefficients to the algebraicity of the coefficients of certain canonical\nmeromorphic modular forms of positive even weight with poles at Heegner\ndivisors. Moreover, we give an explicit formula for the coefficients of\nharmonic Maass forms in terms of periods of certain meromorphic modular forms\nwith algebraic coefficients.\n', 'Maass lifts of half-integral weight Eisenstein series and theta powers   In this paper, we explicitly construct mock modular forms whose shadows are\nEisenstein series of arbitrary integral and half-integral weight, level and\ncharacter at the cusps $\\infty$ and $0$. As an application, we give explicit\nconstruction of harmonic weak Maass forms which are Hecke eigenforms and are\nthe preimages of $\\Theta^k, k \\in \\{ 3, 5, 7\\}$ under the shadow operator,\nwhere $\\Theta$ is the classical Jacobi theta function.\n', ""A remark on $p$-adic Siegel Eisenstein series   A generalization of Serre's $p$-adic Eisenstein series in the case of Siegel\nmodular forms is studied and a coincidence between a $p$-adic Siegel Eisenstein\nseries and a genus theta series associated with a quaternary quadratic form is\nproved.\n""]","[('siegel modular forms', 0.7476714253425598), ('hilbert modular forms', 0.6601201891899109), ('eisenstein series', 0.6585590839385986), ('holomorphic modular forms', 0.6557342410087585), ('modular forms', 0.645485520362854), ('valued modular forms', 0.6452688574790955), ('siegel modular', 0.6184440851211548), ('weight modular forms', 0.6157535910606384), ('modular forms weight', 0.6040919423103333), ('quasi modular forms', 0.602994978427887)]"
90,90,262,90_bethe ansatz equations_bethe equations_bethe ansatz_quantum spin chains,"['bethe ansatz equations', 'bethe equations', 'bethe ansatz', 'quantum spin chains', 'quantum spin chain', 'quantum chains', 'spin chains', 'xxz spin chain', 'heisenberg spin', 'bethe']","['Phantom Bethe roots in the integrable open spin $1/2$ $XXZ$ chain   We investigate special solutions to the Bethe Ansatz equations (BAE) for open\nintegrable $XXZ$ Heisenberg spin chains containing phantom (infinite) Bethe\nroots. The phantom Bethe roots do not contribute to the energy of the Bethe\nstate, so the energy is determined exclusively by the remaining regular\nexcitations. We rederive the phantom Bethe roots criterion and focus on BAE\nsolutions for mixtures of phantom roots and regular (finite) Bethe roots. We\nprove that in the presence of phantom Bethe roots, all eigenstates are split\nbetween two invariant subspaces, spanned by chiral shock states. Bethe\neigenstates are described by two complementary sets of Bethe Ansatz equations\nfor regular roots, one for each invariant subspace. The respective\n""semi-phantom"" Bethe vectors are states of chiral nature, with chirality\nproperties getting less pronounced when more regular Bethe roots are added. For\nthe easy plane case ""semi-phantom"" Bethe states carry nonzero magnetic current,\nand are characterized by quasi-periodic modulation of the magnetization\nprofile, the most prominent example being the spin helix states (SHS). We\nillustrate our results investigating ""semi-phantom"" Bethe states generated by\none regular Bethe root (the other Bethe roots being phantom), with simple\nstructure of the invariant subspace, in all details. We obtain the explicit\nexpressions for Bethe vectors, and calculate the simplest correlation\nfunctions, including the spin-current for all the states in the single particle\nmultiplet.\n', 'Bethe Ansatz, Quantum Circuits, and the F-basis The Bethe Ansatz is a method for constructing exact eigenstates of quantum-integrable spin chains. Recently, deterministic quantum algorithms, referred to as ""algebraic Bethe circuits"", have been developed to prepare Bethe states for the spin-1/2 XXZ model. These circuits represent a unitary formulation of the standard algebraic Bethe Ansatz, expressed using matrix-product states that act on both the spin chain and an auxiliary space. In this work, we systematize these previous results, and show that algebraic Bethe circuits can be derived by a change of basis in the auxiliary space. The new basis, identical to the ""F-basis"" known from the theory of quantum-integrable models, generates the linear superposition of plane waves that is characteristic of the coordinate Bethe Ansatz. We explain this connection, highlighting that certain properties of the F-basis (namely, the exchange symmetry of the spins) are crucial for the construction of algebraic Bethe circuits. We demonstrate our approach by presenting new quantum circuits for the inhomogeneous spin-1/2 XXZ model.', 'Nested algebraic Bethe ansatz for orthogonal and symplectic open spin\n  chains   We present a nested algebraic Bethe ansatz for one-dimensional open so(2n)-\nand sp(2n)-symmetric spin chains with diagonal boundary conditions and\ndescribed by the extended twisted Yangian. We use a generalization of the Bethe\nansatz introduced by De Vega and Karowski which allows us to relate the\nspectral problem of a so(2n)- or sp(2n)-symmetric open spin chain to that of a\ngl(n)-symmetric open spin chain. We explicitly derive the structure of Bethe\nvectors and the nested Bethe equations.\n']","[('bethe ansatz equations', 0.7015261650085449), ('bethe equations', 0.6371603608131409), ('bethe ansatz', 0.5803810358047485), ('quantum spin chains', 0.5750341415405273), ('quantum spin chain', 0.5360403656959534), ('quantum chains', 0.5173208117485046), ('spin chains', 0.5068432092666626), ('xxz spin chain', 0.47932904958724976), ('heisenberg spin', 0.4690430462360382), ('bethe', 0.46574804186820984)]"
91,91,261,91_coded caching_caching_cache_caches,"['coded caching', 'caching', 'cache', 'caches', 'local cache', 'cache enabled', 'cached', 'scheme proposed', 'index coding', 'proposed scheme']","['Three-user D2D Coded Caching with Two Random Requesters and One Sender   In device-to-device (D2D) coded caching problems, it is possible that not all\nusers will make file requests in the delivery phase. Hence, we propose a new\nD2D centralized coded caching problem, named the 3-user D2D coded caching with\ntwo random requesters and one sender (2RR1S), where in the delivery phase, any\ntwo of the three users will make file requests, and the user that does not make\nany file request is the designated sender. We find the optimal caching and\ndelivery scheme, denoted as the 2RRIS scheme, for any number of files N by\nproving matching converse and achievability results. It is shown that coded\ncache placement is needed to achieve the optimal performance. Furthermore, the\noptimal rate-memory tradeoff has a uniform expression for N>=4 and different\nexpressions for N=2 and 3.\n  To examine the usefulness of the proposed model and scheme, we adapt the\n2RR1S scheme to three scenarios. The first one is the 3-user D2D coded caching\nmodel proposed by Ji et al. By characterizing the optimal rate-memory tradeoff\nfor the 3-user D2D coded caching when N=2, which was previously unknown, we\nshow that the adapted 2RR1S scheme is in fact optimal for the 3-user D2D coded\ncaching problem when N=2 and the cache size is medium. The benefit comes from\ncoded cache placement which is missing from existing D2D coded caching schemes.\nThe second scenario is where in the delivery phase, each user makes a file\nrequest randomly and independently with the same probability p. We call this\nmodel the request-random D2D coded caching problem. Adapting the 2RR1S scheme\nto this scenario, we show the superiority of our adapted scheme over other\nexisting D2D coded caching schemes for medium to large cache size. The third\nscenario is the K-user D2D coded caching with K-s random requesters and s\nsenders problem, for which an achievability result is obtained by generalizing\nthe 2RR1S scheme.\n', 'Improved Hotplug Caching Schemes Using PDAs and t-Designs   We consider a coded caching system in which some users are offline at the\ntime of delivery. Such systems are called hotplug coded caching systems. A\nplacement delivery array (PDA) is a well-known tool for constructing a coded\ncaching scheme for dedicated caches. In this paper, we introduce the concept of\nPDAs for hotplug coded caching schemes and refer to it as a hotplug placement\ndelivery array (HpPDA). We give an algorithm to describe the placement and the\ndelivery phase of a hotplug coded caching scheme using HpPDA. We show that an\nexisting hotplug coded caching scheme given by Y. Ma and D. Tuninetti in 2022\ncorresponds to a class of HpPDAs and then propose a method to further improve\nthe rate of that scheme. Additionally, we construct a class of HpPDAs using\n$t$-designs, which corresponds to a scheme for hotplug coded caching systems.\nWe further improve the rate of this scheme and prove that the cut-set bound is\nachieved in some higher memory range for a hotplug coded caching system with\nthree active users.\n', 'A Novel Transformation Approach of Shared-link Coded Caching Schemes for\n  Multiaccess Networks   This paper considers the multiaccess coded caching systems formulated by\nHachem et al., including a central server containing $N$ files connected to $K$\ncache-less users through an error-free shared link, and $K$ cache-nodes, each\nequipped with a cache memory size of $M$ files. Each user has access to $L$\nneighbouring cache-nodes with a cyclic wrap-around topology. The coded caching\nscheme proposed by Hachem et al. suffers from the case that $L$ does not divide\n$K$, where the needed number of transmissions (a.k.a. load) is at most four\ntimes the load expression for the case where $L$ divides $K$.\n  Our main contribution is to propose a novel {\\it transformation} approach to\nsmartly extend the schemes satisfying some conditions for the well known\nshared-link caching systems to the multiaccess caching systems. Then we can get\nmany coded caching schemes with different subpacketizations for multiaccess\ncoded caching system. These resulting schemes have the maximum local caching\ngain (i.e., the cached contents stored at any $L$ neighbouring cache-nodes are\ndifferent such that the number of retrieval packets by each user from the\nconnected cache-nodes is maximal) and the same coded caching gain as the\noriginal schemes. Applying the transformation approach to the well-known\nshared-link coded caching scheme proposed by Maddah-Ali and Niesen, we obtain a\nnew multiaccess coded caching scheme that achieves the same load as the scheme\nof Hachem et al. but for any system parameters. Under the constraint of the\ncache placement used in this new multiaccess coded caching scheme, our delivery\nstrategy is approximately optimal when $K$ is sufficiently large. Finally, we\nalso show that the transmission load of the proposed scheme can be further\nreduced by compressing the multicast message.\n']","[('coded caching', 0.7535286545753479), ('caching', 0.6457014083862305), ('cache', 0.6210858225822449), ('caches', 0.5804551839828491), ('local cache', 0.5669061541557312), ('cache enabled', 0.49716800451278687), ('cached', 0.42262202501296997), ('scheme proposed', 0.31702783703804016), ('index coding', 0.3131149411201477), ('proposed scheme', 0.31181076169013977)]"
92,92,256,92_pressure formulation_fluid structure interaction_flow porous media_mixed finite element,"['pressure formulation', 'fluid structure interaction', 'flow porous media', 'mixed finite element', 'poroelasticity', 'fluid structure', 'poroelastic', 'flow porous', 'field formulation', 'multiscale finite element']","['A mixed elasticity formulation for fluid-poroelastic structure\n  interaction   We develop a mixed finite element method for the coupled problem arising in\nthe interaction between a free fluid governed by the Stokes equations and flow\nin deformable porous medium modeled by the Biot system of poroelasticity. Mass\nconservation, balance of stress, and the Beavers--Joseph--Saffman condition are\nimposed on the interface. We consider a fully mixed Biot formulation based on a\nweakly symmetric stress-displacement-rotation elasticity system and Darcy\nvelocity-pressure flow formulation. A velocity-pressure formulation is used for\nthe Stokes equations. The interface conditions are incorporated through the\nintroduction of the traces of the structure velocity and the Darcy pressure as\nLagrange multipliers. Existence and uniqueness of a solution are established\nfor the continuous weak formulation. Stability and error estimates are derived\nfor the semi-discrete continuous-in-time mixed finite element approximation.\nNumerical experiments are presented to verify the theoretical results and\nillustrate the robustness of the method with respect to the physical\nparameters.\n', 'Domain decomposition and partitioning methods for mixed finite element\n  discretizations of the Biot system of poroelasticity   We develop non-overlapping domain decomposition methods for the Biot system\nof poroelasticity in a mixed form. The solid deformation is modeled with a\nmixed three-field formulation with weak stress symmetry. The fluid flow is\nmodeled with a mixed Darcy formulation. We introduce displacement and pressure\nLagrange multipliers on the subdomain interfaces to impose weakly continuity of\nnormal stress and normal velocity, respectively. The global problem is reduced\nto an interface problem for the Lagrange multipliers, which is solved by a\nKrylov space iterative method. We study both monolithic and split methods. In\nthe monolithic method, a coupled displacement-pressure interface problem is\nsolved, with each iteration requiring the solution of local Biot problems. We\nshow that the resulting interface operator is positive definite and analyze the\nconvergence of the iteration. We further study drained split and fixed stress\nBiot splittings, in which case we solve separate interface problems requiring\nelasticity and Darcy solves. We analyze the stability of the split\nformulations. Numerical experiments are presented to illustrate the convergence\nof the domain decomposition methods and compare their accuracy and efficiency.\n', 'A coupled multipoint stress -- multipoint flux mixed finite element\n  method for the Biot system of poroelasticity   We present a mixed finite element method for a five-field formulation of the\nBiot system of poroelasticity that reduces to a cell-centered\npressure-displacement system on simplicial and quadrilateral grids. A mixed\nstress-displacement-rotation formulation for elasticity with weak stress\nsymmetry is coupled with a mixed velocity-pressure Darcy formulation. The\nspatial discretization is based on combining the multipoint stress mixed finite\nelement (MSMFE) method for elasticity and the multipoint flux mixed finite\nelement (MFMFE) method for Darcy flow. It uses the lowest order\nBrezzi-Douglas-Marini mixed finite element spaces for the poroelastic stress\nand Darcy velocity, piecewise constant displacement and pressure, and\ncontinuous piecewise linear or bilinear rotation. A vertex quadrature rule is\napplied to the velocity, stress, and stress-rotation bilinear forms, which\nblock-diagonalizes the corresponding matrices and allows for local velocity,\nstress, and rotation elimination. This leads to a cell-centered\npositive-definite system for pressure and displacement at each time step. We\nperform error analysis for the semidiscrete and fully discrete formulations,\nestablishing first order convergence for all variables in their natural norms.\nThe numerical tests confirm the theoretical convergence rates and illustrate\nthe locking-free property of the method.\n']","[('pressure formulation', 0.42695096135139465), ('fluid structure interaction', 0.3812106251716614), ('flow porous media', 0.3785087764263153), ('mixed finite element', 0.3664292097091675), ('poroelasticity', 0.36236104369163513), ('fluid structure', 0.3464917838573456), ('poroelastic', 0.33886784315109253), ('flow porous', 0.33303532004356384), ('field formulation', 0.32862433791160583), ('multiscale finite element', 0.32195764780044556)]"
93,93,256,93_intersecting families_intersecting family_intersecting every_family mathcal subsets,"['intersecting families', 'intersecting family', 'intersecting every', 'family mathcal subsets', 'extremal families', 'families subsets', 'family sets', 'family subsets', 'intersections', 'intersecting']","['On a conjecture of Tokushige for cross-$t$-intersecting families   Two families of sets $\\mathcal{A}$ and $\\mathcal{B}$ are called\ncross-$t$-intersecting if $|A\\cap B|\\ge t$ for all $A\\in \\mathcal{A}$, $B\\in\n\\mathcal{B}$. An active problem in extremal set theory is to determine the\nmaximum product of sizes of cross-$t$-intersecting families. This incorporates\nthe classical Erd\\H{o}s--Ko--Rado (EKR) problem. In the present paper, we prove\nthat if $\\mathcal{A}$ and $\\mathcal{B}$ are cross-$t$-intersecting families of\n$\\binom {[n]}k$ with $k\\ge t\\ge 3$ and $n\\ge (t+1)(k-t+1)$, then\n$|\\mathcal{A}||\\mathcal{B}|\\le {\\binom{n-t}{k-t}}^2$; moreover, if\n$n>(t+1)(k-t+1)$, then equality holds if and only if $\\mathcal{A}=\\mathcal{B}$\nis a maximum $t$-intersecting subfamily of $\\binom{[n]}{k}$. This confirms a\nconjecture of Tokushige for $t\\ge 3$.\n', 'A note on distinct differences in $t$-intersecting families   For a family $\\mathcal{F}$ of subsets of $\\{1,2,\\ldots,n\\}$, let\n$\\mathcal{D}(\\mathcal{F}) = \\{F\\setminus G: F, G \\in \\mathcal{F}\\}$ be the\ncollection of all (setwise) differences of $\\mathcal{F}$. The family\n$\\mathcal{F}$ is called a $t$-intersecting family, if for some positive integer\n$t$ and any two members $F, G \\in \\mathcal{F}$ we have $|F\\cap G| \\geq t$. The\nfamily $\\mathcal{F}$ is simply called intersecting if $t=1$. Recently, Frankl\nproved an upper bound on the size of $\\mathcal{D}(\\mathcal{F})$ for the\nintersecting families $\\mathcal{F}$. In this note we extend the result of\nFrankl to $t$-intersecting families.\n', ""Stabilities of intersecting families revisited   The well-known Erd\\H{o}s--Ko--Rado theorem states that for $n> 2k$, every\nintersecting family of $k$-sets of $[n]:=\\{1,\\ldots ,n\\}$ has at most $ {n-1\n\\choose k-1}$ sets, and the extremal family consists of all $k$-sets containing\na fixed element (called a full star). The Hilton--Milner theorem provides a\nstability result by determining the maximum size of a uniform intersecting\nfamily that is not a subfamily of a full star. The further stabilities were\nstudied by Han and Kohayakawa (2017) and Huang and Peng (2024). Two families\n$\\mathcal{F}$ and $\\mathcal{G}$ are called cross-intersecting if for every\n$F\\in \\mathcal{F}$ and $G\\in \\mathcal{G}$, the intersection $F\\cap G$ is\nnon-empty. Let $k \\geq 1, t\\ge 0$ and $n \\geq 2 k+t$ be integers. Frankl (2016)\nproved that if $\\mathcal{F} \\subseteq\\binom{[n]}{k+t}$ and $\\mathcal{G}\n\\subseteq\\binom{[n]}{k}$ are cross-intersecting families, and $\\mathcal{F}$ is\nnon-empty and $(t+1)$-intersecting, then $|\\mathcal{F}|+|\\mathcal{G}|\n\\leq\\binom{n}{k}-\\binom{n-k-t}{k}+1$. Recently, Wu (2023) sharpened Frankl's\nresult by establishing a stability variant. The aim of this paper is two-fold.\nInspired by the above results, we first prove a further stability variant that\ngeneralizes both Frankl's result and Wu's result. Secondly, as an interesting\napplication, we illustrate that the aforementioned results on\ncross-intersecting families could be used to establish the stability results of\nthe Erd\\H{o}s--Ko--Rado theorem. More precisely, we present new short proofs of\nthe Hilton--Milner theorem, the Han--Kohayakawa theorem and the Huang--Peng\ntheorem. Our arguments are more straightforward, and it may be of independent\ninterest.\n""]","[('intersecting families', 0.6255097389221191), ('intersecting family', 0.5681121349334717), ('intersecting every', 0.4647175371646881), ('family mathcal subsets', 0.45719388127326965), ('extremal families', 0.44907423853874207), ('families subsets', 0.44405701756477356), ('family sets', 0.4158506691455841), ('family subsets', 0.4139929711818695), ('intersections', 0.4130651652812958), ('intersecting', 0.39788901805877686)]"
94,94,254,94_ensemble kalman filter_ensemble kalman_kalman filtering_kalman filters,"['ensemble kalman filter', 'ensemble kalman', 'kalman filtering', 'kalman filters', 'kalman filter', 'ensemble gaussian', 'state estimation', 'ensemble particles', 'ensemble based', 'kalman']","['Balanced data assimilation for highly-oscillatory mechanical systems   Data assimilation algorithms are used to estimate the states of a dynamical\nsystem using partial and noisy observations. The ensemble Kalman filter has\nbecome a popular data assimilation scheme due to its simplicity and robustness\nfor a wide range of application areas. Nevertheless, the ensemble Kalman filter\nalso has limitations due to its inherent Gaussian and linearity assumptions.\nThese limitations can manifest themselves in dynamically inconsistent state\nestimates. We investigate this issue in this paper for highly oscillatory\nHamiltonian systems with a dynamical behavior which satisfies certain balance\nrelations. We first demonstrate that the standard ensemble Kalman filter can\nlead to estimates which do not satisfy those balance relations, ultimately\nleading to filter divergence. We also propose two remedies for this phenomenon\nin terms of blended time-stepping schemes and ensemble-based penalty methods.\nThe effect of these modifications to the standard ensemble Kalman filter are\ndiscussed and demonstrated numerically for two model scenarios. First, we\nconsider balanced motion for highly oscillatory Hamiltonian systems and,\nsecond, we investigate thermally embedded highly oscillatory Hamiltonian\nsystems. The first scenario is relevant for applications from meteorology while\nthe second scenario is relevant for applications of data assimilation to\nmolecular dynamics.\n', 'The Mean Field Ensemble Kalman Filter: Near-Gaussian Setting   The ensemble Kalman filter is widely used in applications because, for high\ndimensional filtering problems, it has a robustness that is not shared for\nexample by the particle filter; in particular it does not suffer from weight\ncollapse. However, there is no theory which quantifies its accuracy as an\napproximation of the true filtering distribution, except in the Gaussian\nsetting. To address this issue we provide the first analysis of the accuracy of\nthe ensemble Kalman filter beyond the Gaussian setting. We prove two types of\nresults: the first type comprise a stability estimate controlling the error\nmade by the ensemble Kalman filter in terms of the difference between the true\nfiltering distribution and a nearby Gaussian; and the second type use this\nstability result to show that, in a neighbourhood of Gaussian problems, the\nensemble Kalman filter makes a small error, in comparison with the true\nfiltering distribution. Our analysis is developed for the mean field ensemble\nKalman filter. We rewrite the update equations for this filter, and for the\ntrue filtering distribution, in terms of maps on probability measures. We\nintroduce a weighted total variation metric to estimate the distance between\nthe two filters and we prove various stability estimates for the maps defining\nthe evolution of the two filters, in this metric. Using these stability\nestimates we prove results of the first and second types, in the weighted total\nvariation metric. We also provide a generalization of these results to the\nGaussian projected filter, which can be viewed as a mean field description of\nthe unscented Kalman filter.\n', 'An Explicit Probabilistic Derivation of Inflation in a Scalar Ensemble\n  Kalman Filter for Finite Step, Finite Ensemble Convergence   This paper uses a probabilistic approach to analyze the converge of an\nensemble Kalman filter solution to an exact Kalman filter solution in the\nsimplest possible setting, the scalar case, as it allows us to build upon a\nrich literature of scalar probability distributions and non-elementary\nfunctions. To this end we introduce the bare-bones Scalar Pedagogical Ensemble\nKalman Filter (SPEnKF). We show that in the asymptotic case of ensemble size,\nthe expected value of both the analysis mean and variance estimate of the\nSPEnKF converges to that of the true Kalman filter, and that the variances of\nboth tend towards zero, at each time moment. We also show that the ensemble\nconverges in probability in the complementary case, when the ensemble is\nfinite, and time is taken to infinity. Moreover, we show that in the\nfinite-ensemble, finite-time case, variance inflation and mean correction can\nbe leveraged to coerce the SPEnKF converge to its scalar Kalman filter\ncounterpart. We then apply this framework to analyze perturbed observations and\nexplain why perturbed observations ensemble Kalman filters underperform their\ndeterministic counterparts.\n']","[('ensemble kalman filter', 0.797838568687439), ('ensemble kalman', 0.749117374420166), ('kalman filtering', 0.6704036593437195), ('kalman filters', 0.6418724060058594), ('kalman filter', 0.6280379891395569), ('ensemble gaussian', 0.5951093435287476), ('state estimation', 0.5144817233085632), ('ensemble particles', 0.48629873991012573), ('ensemble based', 0.4655638635158539), ('kalman', 0.46028628945350647)]"
95,95,252,95_julia sets_filled julia_meromorphic functions_julia,"['julia sets', 'filled julia', 'meromorphic functions', 'julia', 'rational maps', 'finite rational maps', 'meromorphic', 'rational map', 'hausdorff dimension', 'entire functions']","['Local connectivity of Julia sets of some transcendental entire functions\n  with Siegel disks   Based on the weak expansion property of a long iteration of a family of\nquasi-Blaschke products near the unit circle established recently, we prove\nthat the Julia sets of a number of transcendental entire functions with bounded\ntype Siegel disks are locally connected. In particular, if $\\theta$ is of\nbounded type, then the Julia set of the sine function $S_\\theta(z)=e^{2\\pi\ni\\theta}\\sin(z)$ is locally connected. Moreover, we prove the existence of\ntranscendental entire functions having Siegel disks and locally connected Julia\nsets with asymptotic values.\n', 'The Hausdorff dimension of Julia sets of meromorphic functions in the\n  Speiser class   We show that for each $d\\in (0,2]$ there exists a meromorphic function $f$\nsuch that the inverse function of $f$ has three singularities and the Julia set\nof $f$ has Hausdorff dimension $d$.\n', ""Rational maps whose Julia sets are generalized Sierpi\\'{n}ski gaskets   It has been shown that the Sierpi\\'nski gasket-like sets can appear as the\nJulia sets of some geometrically finite rational maps. In this paper we prove\nthat such type of Julia sets can also appear in the rational maps containing\nSiegel disks, Cremer points or which are infinitely renormalizable. Based on\nthis, we prove the existence of gasket Julia sets with positive area. Moreover,\nwe present a criterion which guarantees the existence of gasket Julia sets in\nsome rational maps having exactly one fixed attracting or parabolic basin.\n""]","[('julia sets', 0.688570499420166), ('filled julia', 0.4997982978820801), ('meromorphic functions', 0.4935820996761322), ('julia', 0.47910454869270325), ('rational maps', 0.453568696975708), ('finite rational maps', 0.44018736481666565), ('meromorphic', 0.4392971098423004), ('rational map', 0.40769538283348083), ('hausdorff dimension', 0.39689067006111145), ('entire functions', 0.3946845233440399)]"
96,96,252,96_aerial vehicles uavs_aerial vehicle uav_multi uav_uav based,"['aerial vehicles uavs', 'aerial vehicle uav', 'multi uav', 'uav based', 'design uav', 'uav aided', 'unmanned aerial', 'uav', 'vehicles uavs', 'unmanned aerial vehicles']","['UAV-Sensing-Assisted Cellular Interference Coordination: A Cognitive\n  Radio Approach   Aerial-ground interference mitigation has been deemed as the main challenge\nin realizing cellular-connected unmanned aerial vehicle (UAV) communications.\nDue to the line-of-sight (LoS)-dominant air-ground channels, the UAV\ngenerates/suffers much stronger interference to/from cellular base stations\n(BSs) over a much larger region in its uplink/downlink communication, as\ncompared to the terrestrial users. As a result, conventional inter-cell\ninterference coordination (ICIC) techniques catered for terrestrial networks\nbecome ineffective in mitigating the more severe UAV-induced interference. To\ndeal with this new challenge, this letter introduces a cognitive radio based\nsolution by treating the UAV and terrestrial users as secondary and primary\nusers in the network, respectively. In particular, the LoS channels with\nterrestrial BSs/users endow the UAV with a powerful spectrum sensing capability\nfor detecting the terrestrial signals over a much larger region than its\nserving BS. By exploiting this unique feature, we propose a new\nUAV-sensing-assisted ICIC design for both the UAV downlink and uplink\ncommunications. Specifically, the UAV senses its received interference and the\ntransmissions of terrestrial users in the downlink and uplink, respectively,\nover the resource blocks (RBs) available at its serving BS to assist its RB\nallocation to the UAV for avoiding the interference with co-channel terrestrial\ncommunications. Numerical results demonstrate that the proposed UAV-assisted\nICIC outperforms the conventional terrestrial ICIC by engaging the neighboring\nBSs for cooperation only.\n', 'Access Points in the Air: Modeling and Optimization of Fixed-Wing UAV\n  Network   Fixed-wing unmanned aerial vehicles (UAVs) are of great potential to serve as\naerial access points (APs) owing to better aerodynamic performance and longer\nflight endurance. However, the inherent hovering feature of fixed-wing UAVs may\nresult in discontinuity of connections and frequent handover of ground users\n(GUs). In this work, we model and evaluate the performance of a fixed-wing UAV\nnetwork, where UAV APs provide coverage to GUs with millimeter wave backhaul.\nFirstly, it reveals that network spatial throughput (ST) is independent of the\nhover radius under real-time closest-UAV association, while linearly decreases\nwith the hover radius if GUs are associated with the UAVs, whose hover center\nis the closest. Secondly, network ST is shown to be greatly degraded with the\nover-deployment of UAV APs due to the growing air-to-ground interference under\nexcessive overlap of UAV cells. Finally, aiming to alleviate the interference,\na projection area equivalence (PAE) rule is designed to tune the UAV beamwidth.\nEspecially, network ST can be sustainably increased with growing UAV density\nand independent of UAV flight altitude if UAV beamwidth inversely grows with\nthe square of UAV density under PAE.\n', 'A Survey of Prototype and Experiment for UAV Communications   Unmanned aerial vehicle (UAV) communications have attracted significant\nattention from both academia and industry. To facilitate the large-scale usage\nof UAVs for various applications in practice, we provide a comprehensive survey\non the prototype and experiment for UAV communications. To this end, we first\nprovide an overview on the general architecture of the prototype and experiment\nfor UAV communications, and then present experimental verification for\nair-to-ground channel models and UAV energy consumption models. Next, we\ndiscuss measurement experiments on two promising paradigms of UAV\ncommunications, namely cellular-connected UAVs and UAV-enabled aerial\ncommunication platforms. For the former, we focus on the feasibility study and\naddress the interference mitigation issue. For UAV-enabled aerial communication\nplatforms, we present three scenarios, namely UAV-enabled aerial base stations,\nUAV-enabled aerial relays and UAV-enabled aerial data collection/dissemination.\nFinally, we point out some promising future directions for prototype and\nexperimental measurements for UAV communications.\n']","[('aerial vehicles uavs', 0.6711192727088928), ('aerial vehicle uav', 0.6530693173408508), ('multi uav', 0.6187604665756226), ('uav based', 0.6082590222358704), ('design uav', 0.6052718162536621), ('uav aided', 0.6043688654899597), ('unmanned aerial', 0.5971550345420837), ('uav', 0.5941479802131653), ('vehicles uavs', 0.5926380753517151), ('unmanned aerial vehicles', 0.5906161665916443)]"
97,97,252,97_sparse signal recovery_sparse recovery_compressed sensing_bit compressed sensing,"['sparse signal recovery', 'sparse recovery', 'compressed sensing', 'bit compressed sensing', 'recovering sparse', 'compressive sensing', 'recovery sparse', 'sparse signal', 'sparse signals', 'signals sparse']","['Improved Support Recovery in Universal One-bit Compressed Sensing   One-bit compressed sensing (1bCS) is an extremely quantized signal\nacquisition method that has been proposed and studied rigorously in the past\ndecade. In 1bCS, linear samples of a high dimensional signal are quantized to\nonly one bit per sample (sign of the measurement). Assuming the original signal\nvector to be sparse, existing results in 1bCS either aim to find the support of\nthe vector, or approximate the signal allowing a small error. The focus of this\npaper is support recovery, which often also computationally facilitate\napproximate signal recovery. A {\\em universal} measurement matrix for 1bCS\nrefers to one set of measurements that work for all sparse signals. With\nuniversality, it is known that $\\tilde{\\Theta}(k^2)$ 1bCS measurements are\nnecessary and sufficient for support recovery (where $k$ denotes the sparsity).\nTo improve the dependence on sparsity from quadratic to linear, in this work we\npropose approximate support recovery (allowing $\\epsilon>0$ proportion of\nerrors), and superset recovery (allowing $\\epsilon$ proportion of false\npositives). We show that the first type of recovery is possible with\n$\\tilde{O}(k/\\epsilon)$ measurements, while the later type of recovery, more\nchallenging, is possible with $\\tilde{O}(\\max\\{k/\\epsilon,k^{3/2}\\})$\nmeasurements. We also show that in both cases $\\Omega(k/\\epsilon)$ measurements\nwould be necessary for universal recovery.\n  Improved results are possible if we consider universal recovery within a\nrestricted class of signals, such as rational signals, or signals with bounded\ndynamic range. In both cases superset recovery is possible with only\n$\\tilde{O}(k/\\epsilon)$ measurements. Other results on universal but\napproximate support recovery are also provided in this paper. All of our main\nrecovery algorithms are simple and polynomial-time.\n', 'Binary Iterative Hard Thresholding Converges with Optimal Number of\n  Measurements for 1-Bit Compressed Sensing   Compressed sensing has been a very successful high-dimensional signal\nacquisition and recovery technique that relies on linear operations. However,\nthe actual measurements of signals have to be quantized before storing or\nprocessing. 1(One)-bit compressed sensing is a heavily quantized version of\ncompressed sensing, where each linear measurement of a signal is reduced to\njust one bit: the sign of the measurement. Once enough of such measurements are\ncollected, the recovery problem in 1-bit compressed sensing aims to find the\noriginal signal with as much accuracy as possible. The recovery problem is\nrelated to the traditional ""halfspace-learning"" problem in learning theory.\n  For recovery of sparse vectors, a popular reconstruction method from 1-bit\nmeasurements is the binary iterative hard thresholding (BIHT) algorithm. The\nalgorithm is a simple projected sub-gradient descent method, and is known to\nconverge well empirically, despite the nonconvexity of the problem. The\nconvergence property of BIHT was not theoretically justified, except with an\nexorbitantly large number of measurements (i.e., a number of measurement\ngreater than $\\max\\{k^{10}, 24^{48}, k^{3.5}/\\epsilon\\}$, where $k$ is the\nsparsity, $\\epsilon$ denotes the approximation error, and even this expression\nhides other factors). In this paper we show that the BIHT algorithm converges\nwith only $\\tilde{O}(\\frac{k}{\\epsilon})$ measurements. Note that, this\ndependence on $k$ and $\\epsilon$ is optimal for any recovery method in 1-bit\ncompressed sensing. With this result, to the best of our knowledge, BIHT is the\nonly practical and efficient (polynomial time) algorithm that requires the\noptimal number of measurements in all parameters (both $k$ and $\\epsilon$).\nThis is also an example of a gradient descent algorithm converging to the\ncorrect solution for a nonconvex problem, under suitable structural conditions.\n', 'Newton-Step-Based Hard Thresholding Algorithms for Sparse Signal\n  Recovery   Sparse signal recovery or compressed sensing can be formulated as certain\nsparse optimization problems. The classic optimization theory indicates that\nthe Newton-like method often has a numerical advantage over the gradient method\nfor nonlinear optimization problems. In this paper, we propose the so-called\nNewton-step-based iterative hard thresholding (NSIHT) and the Newton-step-based\nhard thresholding pursuit (NSHTP) algorithms for sparse signal recovery and\nsignal approximation. Different from the traditional iterative hard\nthresholding (IHT) and hard thresholding pursuit (HTP), the proposed algorithms\nadopts the Newton-like search direction instead of the steepest descent\ndirection.\n  A theoretical analysis for the proposed algorithms is carried out, and some\nsufficient conditions for the guaranteed success of sparse signal recovery via\nthese algorithms are established. Our results are shown under the restricted\nisometry property which is one of the standard assumptions widely used in the\nfield of compressed sensing and signal approximation. The empirical results\nobtained from synthetic data recovery indicate that the proposed algorithms are\nefficient signal recovery methods. The numerical stability of our algorithms in\nterms of the residual reduction is also investigated through simulations.\n']","[('sparse signal recovery', 0.8079383969306946), ('sparse recovery', 0.7543007731437683), ('compressed sensing', 0.7517628073692322), ('bit compressed sensing', 0.7241107821464539), ('recovering sparse', 0.7069054245948792), ('compressive sensing', 0.7041333913803101), ('recovery sparse', 0.6957337856292725), ('sparse signal', 0.6519076824188232), ('sparse signals', 0.6486606001853943), ('signals sparse', 0.6414875388145447)]"
98,98,251,98_boundary controllability_exact boundary controllability_controllability nonlinear_global approximate controllability,"['boundary controllability', 'exact boundary controllability', 'controllability nonlinear', 'global approximate controllability', 'approximate controllability', 'controllability linear', 'controllability properties', 'local controllability', 'controllability semilinear', 'null controllability']","['Local null controllability of a cubic Ginzburg-Landau equation with\n  dynamic boundary conditions   This paper deals with controllability properties of a cubic Ginzburg-Landau\nequation with dynamic boundary conditions. More precisely, we prove a local\nnull controllability result by using a single control supported in a small\nsubset of the domain. In order to achieve this result, we firstly linearize the\nsystem around the origin and we analyze it by the duality approach and an\nappropriate Carleman estimate. Then, by using an inverse function theorem, the\nlocal null controllability of the nonlinear system is proven.\n', ""Null controllability for degenerate parabolic equations with a nonlocal\n  space term   We consider two degenerate heat equations with a nonlocal space term,\nstudying, in particular, their null controllability property. To this aim, we\nfirst consider the associated nonhomogeneous degenerate heat equations: we\nstudy their well posedness, the Carleman estimates for the associated adjoint\nproblems and, finally, the null controllability. Then, as a consequence, using\nthe Kakutani's fixed point Theorem, we deduce the null controllability property\nfor the initial nonlocal problems.\n"", ""Null controllability for the singular heat equation with a memory term   In this paper we focus on the null controllability problem for the heat\nequation with the so-called inverse square potential and a memory term. To this\naim, we first establish the null controllability for a nonhomogeneous singular\nheat equation by a new Carleman inequality with weights which do not blow up at\nt=0. Then the null controllability property is proved for the singular heat\nequation with memory under a condition on the kernel, by means of Kakutani's\nfixed-point Theorem.\n""]","[('boundary controllability', 0.6627573370933533), ('exact boundary controllability', 0.6605948209762573), ('controllability nonlinear', 0.6540324687957764), ('global approximate controllability', 0.6318470239639282), ('approximate controllability', 0.6277977824211121), ('controllability linear', 0.6189098954200745), ('controllability properties', 0.6183149814605713), ('local controllability', 0.6151559352874756), ('controllability semilinear', 0.6101210117340088), ('null controllability', 0.5835803151130676)]"
99,99,250,99_theory continued fractions_continued fraction algorithms_continued fractions_continued fraction expansions,"['theory continued fractions', 'continued fraction algorithms', 'continued fractions', 'continued fraction expansions', 'regular continued fraction', 'continued fraction', 'continued fraction expansion', 'generalized continued', 'regular continued', 'fraction algorithms']","['Finiteness and periodicity of continued fractions over quadratic number\n  fields   We consider continued fractions with partial quotients in the ring of\nintegers of a quadratic number field $K$ and we prove a generalization to such\ncontinued fractions of the classical theorem of Lagrange. A particular example\nof these continued fractions is the $\\beta$-continued fraction introduced by\nBernat. As a corollary of our theorem we show that for any quadratic Perron\nnumber $\\beta$, the $\\beta$-continued fraction expansion of elements in\n$\\mathbb Q(\\beta)$ is either finite of eventually periodic. The same holds for\n$\\beta$ being a square root of an integer. We also show that for certain 4\nquadratic Perron numbers $\\beta$, the $\\beta$-continued fraction represents\nfinitely all elements of the quadratic field $\\mathbb Q(\\beta)$, thus answering\nquestions of Rosen and Bernat. Based on the validity of a conjecture of Mercat,\nthese are all quadratic Perron numbers with this feature.\n', 'On Euler polynomial continued fractions   In this paper, we introduce the polynomial continued fraction, a close\nrelative of the well-known simple continued fraction expansions which are\nwidely used in number theory and in general. While they may not possess all the\nintriguing properties of simple continued fractions, polynomial continued\nfractions have many interesting patterns which can be exploited. Specifically,\nwe explore the Euler continued fractions within this framework and present an\nalgorithm for their identification\n', 'Necessary and sufficient conditions for convergence of integer continued\n  fractions   Fundamental to the theory of continued fractions is the fact that every\ninfinite continued fraction with positive integer coefficients converges;\nhowever, it is unknown precisely which continued fractions with integer\ncoefficients (not necessarily positive) converge. Here we present a simple test\nthat determines whether an integer continued fraction converges or diverges. In\naddition, for convergent continued fractions the test specifies whether the\nlimit is rational or irrational.\n  An attractive way to visualise integer continued fractions is to model them\nas paths on the Farey graph, which is a graph embedded in the hyperbolic plane\nthat induces a tessellation of the hyperbolic plane by ideal triangles. With\nthis geometric representation of continued fractions our test for convergence\ncan be interpreted in a particularly elegant manner, giving deeper insight into\nthe nature of continued fraction convergence.\n']","[('theory continued fractions', 0.7622321248054504), ('continued fraction algorithms', 0.7606253027915955), ('continued fractions', 0.708773136138916), ('continued fraction expansions', 0.6918637752532959), ('regular continued fraction', 0.6836463809013367), ('continued fraction', 0.6663771271705627), ('continued fraction expansion', 0.6571727395057678), ('generalized continued', 0.5299197435379028), ('regular continued', 0.5029188394546509), ('fraction algorithms', 0.501265287399292)]"
100,100,247,100_domination graphs_graph dominating_dominating graph_domination number graph,"['domination graphs', 'graph dominating', 'dominating graph', 'domination number graph', 'dominating every vertex', 'dominating sets', 'total domination number', 'domination numbers', 'minimum dominating', 'connected domination number']","['Some results on the super domination number of a graph II   Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset\n$S\\subseteq V$ such that every vertex not in $S$ is adjacent to at least one\nvertex in $S$. The cardinality of a smallest dominating set of $G$, denoted by\n$\\gamma(G)$, is the domination number of $G$. A dominating set $S$ is called a\nsuper dominating set of $G$, if for every vertex $u\\in \\overline{S}=V-S$, there\nexists $v\\in S$ such that $N(v)\\cap \\overline{S}=\\{u\\}$. The cardinality of a\nsmallest super dominating set of $G$, denoted by $\\gamma_{sp}(G)$, is the super\ndomination number of $G$. In this paper, we obtain more results on the super\ndomination number of graphs which is modified by an operation on vertices.\nAlso, we present some sharp bounds for super domination number of chain and\nbouquet of pairwise disjoint connected graphs.\n', 'Semitotal domination in trees   In this paper, we study a parameter that is squeezed between arguably the two\nimportant domination parameters, namely the domination number, $\\gamma(G)$, and\nthe total domination number, $\\gamma_t(G)$. A set $S$ of vertices in $G$ is a\nsemitotal dominating set of $G$ if it is a dominating set of $G$ and every\nvertex in S is within distance $2$ of another vertex of $S$. The semitotal\ndomination number, $\\gamma_{t2}(G)$, is the minimum cardinality of a semitotal\ndominating set of $G$. We observe that $\\gamma(G)\\leq \\gamma_{t2}(G)\\leq\n\\gamma_t(G)$. In this paper, we give a lower bound for the semitotal domination\nnumber of trees and we characterize the extremal trees. In addition, we\ncharacterize trees with equal domination and semitotal domination numbers.\n', 'On accurate domination in graphs   A dominating set of a graph $G$ is a subset $D \\subseteq V_G$ such that every\nvertex not in $D$ is adjacent to at least one vertex in $D$. The cardinality of\na smallest dominating set of $G$, denoted by $\\gamma(G)$, is the domination\nnumber of $G$. The accurate domination number of $G$, denoted by $\\gamma_{\\rm\na}(G)$, is the cardinality of a smallest set $D$ that is a dominating set of\n$G$ and no $|D|$-element subset of $V_G \\setminus D$ is a dominating set of\n$G$. We study graphs for which the accurate domination number is equal to the\ndomination number. In particular, all trees $G$ for which $\\gamma_{\\rm a}(G) =\n\\gamma(G)$ are characterized. Furthermore, we compare the accurate domination\nnumber with the domination number of different coronas of a graph.\n']","[('domination graphs', 0.6942005753517151), ('graph dominating', 0.6576057076454163), ('dominating graph', 0.6521196365356445), ('domination number graph', 0.6513927578926086), ('dominating every vertex', 0.6432438492774963), ('dominating sets', 0.5506104826927185), ('total domination number', 0.5395416617393494), ('domination numbers', 0.5363888740539551), ('minimum dominating', 0.532594621181488), ('connected domination number', 0.5284194946289062)]"
101,101,246,101_schr odinger operators_schr odinger operator_eigenvalues schr odinger_odinger operators,"['schr odinger operators', 'schr odinger operator', 'eigenvalues schr odinger', 'odinger operators', 'odinger operator', 'schrodinger operators', 'dimensional schr odinger', 'schroedinger operators', 'odinger operators delta', 'discrete schr odinger']","['Perturbation determinant and Levinson\'s formula for Schr\\""odinger\n  operators with generalized point interaction   We consider the one dimensional Schr\\""odinger operator with properly\nconnecting generalized point interaction at the origin. We derive a trace\nformula for trace of difference of resolvents of perturbed and unperturbed\nSchr\\""odinger operators in terms of a Wronskian which results into an explicit\nexpression for perturbation determinant. Using the estimate for large time real\nargument on the trace norm of the resolvent difference of the perturbed and\nunperturbed Schr\\""odinger operators we express the spectral shift function in\nterms of perturbation determinant. Under certain integrability condition on the\npotential function, we calculate low energy asymptotics for the perturbation\ndeterminant and prove an analog of Levinson\'s formula.\n', 'Exactly solvable Schr\\""odinger operators related to the confluent\n  equation   Our paper investigates one-dimensional Schr\\""odinger operators defined as\nclosed operators on $L^2(\\mathbb{R})$ or $L^2(\\mathbb{R}_+)$ that are exactly\nsolvable in terms of confluent functions (or, equivalently, Whittaker\nfunctions). We allow the potentials to be complex. They fall into three\nfamilies: Whittaker operators (or radial Coulomb Hamiltonians), Schr\\""odinger\noperators with Morse potentials and isotonic oscillators. For each of them, we\ndiscuss the corresponding basic holomorphic family of closed operators and the\nintegral kernel of their resolvents. We also describe transmutation identities\nthat relate these resolvents. These identities interchange spectral parameters\nwith coupling constants across different operator families.\n  A similar analysis is performed for one-dimensional Schr\\""odinger operators\nsolvable in terms of Bessel functions (which are reducible to special cases of\nWhittaker functions). They fall into two families: Bessel operators and\nSchr\\""odinger operators with exponential potentials.\n  To make our presentation self-contained, we include a short summary of the\ntheory of closed one-dimensional Schr\\""odinger operators with singular boundary\nconditions. We also provide a concise review of special functions that we use.\n', 'One dimensional discrete Schr\\""odinger operators with resonant embedded\n  eigenvalues   In this paper, we introduce a new family of functions to construct\nSchr\\""odinger operators with embedded eigenvalues. This particularly allows us\nto construct discrete Schr\\""odinger operators with arbitrary prescribed sets of\neigenvalues.\n']","[('schr odinger operators', 0.7784305810928345), ('schr odinger operator', 0.7468805313110352), ('eigenvalues schr odinger', 0.7370734214782715), ('odinger operators', 0.6960021257400513), ('odinger operator', 0.6587184071540833), ('schrodinger operators', 0.6413707733154297), ('dimensional schr odinger', 0.6390368342399597), ('schroedinger operators', 0.6369979977607727), ('odinger operators delta', 0.6176550984382629), ('discrete schr odinger', 0.6119822263717651)]"
102,102,243,102_bandit algorithms_multi armed bandits_bandit problems_armed bandit problems,"['bandit algorithms', 'multi armed bandits', 'bandit problems', 'armed bandit problems', 'linear bandits', 'contextual bandits', 'multi armed bandit', 'contextual bandit', 'bandit feedback', 'armed bandits']","[""Optimal Best Arm Identification with Fixed Confidence in Restless\n  Bandits   We study best arm identification in a restless multi-armed bandit setting\nwith finitely many arms. The discrete-time data generated by each arm forms a\nhomogeneous Markov chain taking values in a common, finite state space. The\nstate transitions in each arm are captured by an ergodic transition probability\nmatrix (TPM) that is a member of a single-parameter exponential family of TPMs.\nThe real-valued parameters of the arm TPMs are unknown and belong to a given\nspace. Given a function $f$ defined on the common state space of the arms, the\ngoal is to identify the best arm -- the arm with the largest average value of\n$f$ evaluated under the arm's stationary distribution -- with the fewest number\nof samples, subject to an upper bound on the decision's error probability\n(i.e., the fixed-confidence regime). A lower bound on the growth rate of the\nexpected stopping time is established in the asymptote of a vanishing error\nprobability. Furthermore, a policy for best arm identification is proposed, and\nits expected stopping time is proved to have an asymptotic growth rate that\nmatches the lower bound. It is demonstrated that tracking the long-term\nbehavior of a certain Markov decision process and its state-action visitation\nproportions are the key ingredients in analyzing the converse and achievability\nbounds. It is shown that under every policy, the state-action visitation\nproportions satisfy a specific approximate flow conservation constraint and\nthat these proportions match the optimal proportions dictated by the lower\nbound under any asymptotically optimal policy. The prior studies on best arm\nidentification in restless bandits focus on independent observations from the\narms, rested Markov arms, and restless Markov arms with known arm TPMs. In\ncontrast, this work is the first to study best arm identification in restless\nbandits with unknown arm TPMs.\n"", ""Best Arm Identification in Restless Markov Multi-Armed Bandits   We study the problem of identifying the best arm in a multi-armed bandit\nenvironment when each arm is a time-homogeneous and ergodic discrete-time\nMarkov process on a common, finite state space. The state evolution on each arm\nis governed by the arm's transition probability matrix (TPM). A decision entity\nthat knows the set of arm TPMs but not the exact mapping of the TPMs to the\narms, wishes to find the index of the best arm as quickly as possible, subject\nto an upper bound on the error probability. The decision entity selects one arm\nat a time sequentially, and all the unselected arms continue to undergo state\nevolution ({\\em restless} arms). For this problem, we derive the first-known\nproblem instance-dependent asymptotic lower bound on the growth rate of the\nexpected time required to find the index of the best arm, where the asymptotics\nis as the error probability vanishes. Further, we propose a sequential policy\nthat, for an input parameter $R$, forcibly selects an arm that has not been\nselected for $R$ consecutive time instants. We show that this policy achieves\nan upper bound that depends on $R$ and is monotonically non-increasing as\n$R\\to\\infty$. The question of whether, in general, the limiting value of the\nupper bound as $R\\to\\infty$ matches with the lower bound, remains open. We\nidentify a special case in which the upper and the lower bounds match. Prior\nworks on best arm identification have dealt with (a) independent and\nidentically distributed observations from the arms, and (b) rested Markov arms,\nwhereas our work deals with the more difficult setting of restless Markov arms.\n"", 'Streaming Algorithms for Stochastic Multi-armed Bandits   We study the Stochastic Multi-armed Bandit problem under bounded arm-memory.\nIn this setting, the arms arrive in a stream, and the number of arms that can\nbe stored in the memory at any time, is bounded. The decision-maker can only\npull arms that are present in the memory. We address the problem from the\nperspective of two standard objectives: 1) regret minimization, and 2) best-arm\nidentification. For regret minimization, we settle an important open question\nby showing an almost tight hardness. We show {\\Omega}(T^{2/3}) cumulative\nregret in expectation for arm-memory size of (n-1), where n is the number of\narms. For best-arm identification, we study two algorithms. First, we present\nan O(r) arm-memory r-round adaptive streaming algorithm to find an\n{\\epsilon}-best arm. In r-round adaptive streaming algorithm for best-arm\nidentification, the arm pulls in each round are decided based on the observed\noutcomes in the earlier rounds. The best-arm is the output at the end of r\nrounds. The upper bound on the sample complexity of our algorithm matches with\nthe lower bound for any r-round adaptive streaming algorithm. Secondly, we\npresent a heuristic to find the {\\epsilon}-best arm with optimal sample\ncomplexity, by storing only one extra arm in the memory.\n']","[('bandit algorithms', 0.6933765411376953), ('multi armed bandits', 0.6537439823150635), ('bandit problems', 0.6371288895606995), ('armed bandit problems', 0.6269973516464233), ('linear bandits', 0.6118636131286621), ('contextual bandits', 0.6000877618789673), ('multi armed bandit', 0.5957125425338745), ('contextual bandit', 0.5884591937065125), ('bandit feedback', 0.5670821666717529), ('armed bandits', 0.5449606776237488)]"
103,103,241,103_phylogenetic trees_phylogenetics_phylogenetic_binary trees,"['phylogenetic trees', 'phylogenetics', 'phylogenetic', 'binary trees', 'networks tree', 'trees', 'tree topology', 'rooted trees', 'binary tree', 'two trees']","['Phylogenetic diversity indices from an affine and projective viewpoint   Phylogenetic diversity indices are commonly used to rank the elements in a\ncollection of species or populations for conservation purposes. The derivation\nof these indices is typically based on some quantitative description of the\nevolutionary history of the species in question, which is often given in terms\nof a phylogenetic tree. Both rooted and unrooted phylogenetic trees can be\nemployed, and there are close connections between the indices that are derived\nin these two different ways. In this paper, we introduce more general\nphylogenetic diversity indices that can be derived from collections of subsets\n(clusters) and collections of bipartitions (splits) of the given set of\nspecies. Such indices could be useful, for example, in case there is some\nuncertainty in the topology of the tree being used to derive a phylogenetic\ndiversity index. As well as characterizing some of the indices that we\nintroduce in terms of their special properties, we provide a link between\ncluster-based and split-based phylogenetic diversity indices that uses a\ndiscrete analogue of the classical link between affine and projective geometry.\nThis provides a unified framework for many of the various phylogenetic\ndiversity indices used in the literature based on rooted and unrooted\nphylogenetic trees, generalizations and new proofs for previous results\nconcerning tree-based indices, and a way to define some new phylogenetic\ndiversity indices that naturally arise as affine or projective variants of each\nother.\n', 'Displaying trees across two phylogenetic networks   Phylogenetic networks are a generalization of phylogenetic trees to\nleaf-labeled directed acyclic graphs that represent ancestral relationships\nbetween species whose past includes non-tree-like events such as hybridization\nand horizontal gene transfer. Indeed, each phylogenetic network embeds a\ncollection of phylogenetic trees. Referring to the collection of trees that a\ngiven phylogenetic network $N$ embeds as the display set of $N$, several\nquestions in the context of the display set of $N$ have recently been analyzed.\nFor example, the widely studied Tree-Containment problem asks if a given\nphylogenetic tree is contained in the display set of a given network. The focus\nof this paper are two questions that naturally arise in comparing the display\nsets of two phylogenetic networks. First, we analyze the problem of deciding if\nthe display sets of two phylogenetic networks have a tree in common.\nSurprisingly, this problem turns out to be NP-complete even for two temporal\nnormal networks. Second, we investigate the question of whether or not the\ndisplay sets of two phylogenetic networks are equal. While we recently showed\nthat this problem is polynomial-time solvable for a normal and a tree-child\nnetwork, it is computationally hard in the general case. In establishing\nhardness, we show that the problem is contained in the second level of the\npolynomial-time hierarchy. Specifically, it is $\\Pi_2^P$-complete. Along the\nway, we show that two other problems are also $\\Pi_2^P$-complete, one of which\nbeing a generalization of Tree-Containment.\n', 'Hypercubes and Hamilton cycles of display sets of rooted phylogenetic\n  networks   In the context of reconstructing phylogenetic networks from a collection of\nphylogenetic trees, several characterisations and subsequently algorithms have\nbeen established to reconstruct a phylogenetic network that collectively embeds\nall trees in the input in some minimum way. For many instances however, the\nresulting network also embeds additional phylogenetic trees that are not part\nof the input. However, little is known about these inferred trees. In this\npaper, we explore the relationships among all phylogenetic trees that are\nembedded in a given phylogenetic network. First, we investigate some\ncombinatorial properties of the collection P of all rooted binary phylogenetic\ntrees that are embedded in a rooted binary phylogenetic network N. To this end,\nwe associated a particular graph G, which we call rSPR graph, with the elements\nin P and show that, if |P|=2^k, where k is the number of vertices with\nin-degree two in N, then G has a Hamiltonian cycle. Second, by exploiting rSPR\ngraphs and properties of hypercubes, we turn to the well-studied class of\nrooted binary level-1 networks and give necessary and sufficient conditions for\nwhen a set of rooted binary phylogenetic trees can be embedded in a level-1\nnetwork without inferring any additional trees. Lastly, we show how these\nconditions translate into a polynomial-time algorithm to reconstruct such a\nnetwork if it exists.\n']","[('phylogenetic trees', 0.7501494288444519), ('phylogenetics', 0.6470094919204712), ('phylogenetic', 0.6377353072166443), ('binary trees', 0.5735158324241638), ('networks tree', 0.5174415111541748), ('trees', 0.5110283493995667), ('tree topology', 0.510705828666687), ('rooted trees', 0.4889962077140808), ('binary tree', 0.4882143437862396), ('two trees', 0.45909789204597473)]"
104,104,239,104_predictive control mpc_robust predictive control_stochastic predictive control_robust mpc,"['predictive control mpc', 'robust predictive control', 'stochastic predictive control', 'robust mpc', 'predictive control', 'nonlinear predictive control', 'control mpc', 'economic predictive control', 'based predictive control', 'linear mpc']","['Configuration-Constrained Tube MPC   This paper is about robust Model Predictive Control (MPC) for linear systems\nwith additive and multiplicative uncertainty. A novel class of\nconfiguration-constrained polytopic robust forward invariant tubes is\nintroduced, which admit a joint parameterization of their facets and vertices.\nThey are the foundation for the development of novel Configuration-Constrained\nTube MPC (CCTMPC) controllers that freely optimize the shape of their polytopic\ntube, subject to conic vertex configuration constraints, as well as associated\nvertex control laws by solving convex optimization problems online. It is shown\nthat CCTMPC is -- under appropriate assumptions -- systematically less\nconservative than Rigid- and Homothetic- Tube MPC. Additionally, it is proven\nthat there exist control systems for which CCTMPC is less conservative than\nElastic Tube MPC, Disturbance Affine Feedback MPC, and Fully Parameterized Tube\nMPC.\n', 'Transient Performance of MPC for Tracking   We analyse the closed-loop performance of a model predictive control (MPC)\nfor tracking formulation with artificial references. It has been shown that\nsuch a scheme guarantees closed-loop stability and recursive feasibility for\nany externally supplied reference, even if it is unreachable or time-varying.\nThe basic idea is to consider an artificial reference as an additional decision\nvariable and to formulate generalised terminal ingredients with respect to it.\nIn addition, its offset is penalised in the MPC optimisation problem, leading\nto closed-loop convergence to the best reachable reference. In this paper, we\nprovide a transient performance bound on the closed loop using MPC for\ntracking. We employ mild assumptions on the offset cost and scale it with the\nprediction horizon. In this case, an increasing horizon in MPC for tracking\nrecovers the infinite horizon optimal solution.\n', 'Computationally efficient robust MPC using optimized constraint\n  tightening   A robust model predictive control (MPC) method is presented for linear,\ntime-invariant systems affected by bounded additive disturbances. The main\ncontribution is the offline design of a disturbance-affine feedback gain\nwhereby the resulting constraint tightening is minimized. This is achieved by\nformulating the constraint tightening problem as a convex optimization problem\nwith the feedback term as a variable. The resulting MPC controller has the\ncomputational complexity of nominal MPC, and guarantees recursive feasibility,\nstability and constraint satisfaction. The advantages of the proposed approach\ncompared to existing robust MPC methods are demonstrated using numerical\nexamples.\n']","[('predictive control mpc', 0.7419878244400024), ('robust predictive control', 0.6509373188018799), ('stochastic predictive control', 0.5895362496376038), ('robust mpc', 0.5874357223510742), ('predictive control', 0.5856538414955139), ('nonlinear predictive control', 0.5827414393424988), ('control mpc', 0.5576879978179932), ('economic predictive control', 0.5525022149085999), ('based predictive control', 0.5489959120750427), ('linear mpc', 0.5372750163078308)]"
105,105,236,105_unitary dilation_pairs commuting_contractions_mathbb contraction,"['unitary dilation', 'pairs commuting', 'contractions', 'mathbb contraction', 'commutant', 'isometries', 'partial isometry', 'space operators', 'isometry', 'hilbert space operators']","['Minimal isometric dilations and operator models for the polydisc   For commuting contractions $T_1,\\dots ,T_n$ acting on a Hilbert space\n$\\mathcal H$ with $T=\\prod_{i=1}^n T_i$, we find a necessary and sufficient\ncondition under which $(T_1,\\dots ,T_n)$ dilates to commuting isometries\n$(V_1,\\dots ,V_n)$ on the minimal isometric dilation space $T$, where\n$V=\\prod_{i=1}^nV_i$ is the minimal isometric dilation of $T$. We construct\nboth Sch$\\ddot{a}$ffer and Sz. Nagy-Foias type isometric dilations for\n$(T_1,\\dots ,T_n)$ on the minimal dilation spaces of $T$. Also, a different\ndilation is constructed when the product $T$ is a $C._0$ contraction, that is\n${T^*}^n \\rightarrow 0$ as $n \\rightarrow \\infty$. As a consequence of these\ndilation theorems we obtain different functional models for $(T_1,\\dots ,T_n)$\nin terms of multiplication operators on vectorial Hardy spaces. One notable\nfact about our models is that the multipliers are analytic functions in one\nvariable. The dilation, when $T$ is a $C._0$ contraction, leads to a\nconditional factorization of a $T$. Several examples have been constructed.\n', ""Theory of $q$-commuting contractions-II: Regular $q$-unitary dilation\n  and Brehmer's positivity   We generalize regular unitary dilation and Brehmer's positivity condition to\n$q$-commuting tuples of contractions.\n"", ""A generalization of Ando's dilation, and isometric dilations for a class\n  of tuples of $q$-commuting contractions   Given a bounded operator $Q$ on a Hilbert space $\\mathcal{H}$, a pair of\nbounded operators $(T_1, T_2)$ on $\\mathcal{H}$ is said to be $Q$-commuting if\none of the following holds:\n  \\[\n  T_1T_2=QT_2T_1 \\text{ or }T_1T_2=T_2QT_1 \\text{ or }T_1T_2=T_2T_1Q. \\] We\ngive an explicit construction of isometric dilations for pairs of $Q$-commuting\ncontractions for unitary $Q$, which generalizes the isometric dilation of Ando\n[2] for pairs of commuting contractions. In particular, for\n$Q=qI_{\\mathcal{H}}$, where $q$ is a complex number of modulus $1$, this gives,\nas a corollary, an explicit construction of isometric dilations for pairs of\n$q$-commuting contractions which are well studied. There is an extended notion\nof $q$-commutativity for general tuples of operators and it is known that\nisometric dilation does not hold, in general, for an $n$-tuple of $q$-commuting\ncontractions, where $n\\geq 3$. Generalizing the class of commuting contractions\nconsidered by Brehmer [8], we construct a class of $n$-tuples of $q$-commuting\ncontractions and find isometric dilations explicitly for the class.\n""]","[('unitary dilation', 0.469603031873703), ('pairs commuting', 0.4510009288787842), ('contractions', 0.44442424178123474), ('mathbb contraction', 0.442218542098999), ('commutant', 0.4261814057826996), ('isometries', 0.41689208149909973), ('partial isometry', 0.416047066450119), ('space operators', 0.4130862057209015), ('isometry', 0.406267374753952), ('hilbert space operators', 0.40623214840888977)]"
106,106,235,106_massive mimo_mimo channel_massive mimo systems_mimo csi,"['massive mimo', 'mimo channel', 'massive mimo systems', 'mimo csi', 'output mimo', 'output mimo systems', 'deep learning dl', 'channel prediction', 'mimo systems', 'multiple output mimo']","['CNN-based Analog CSI Feedback in FDD MIMO-OFDM Systems   Massive multiple-input multiple-output (MIMO) systems require downlink\nchannel state information (CSI) at the base station (BS) to better utilize the\navailable spatial diversity and multiplexing gains. However, in a frequency\ndivision duplex (FDD) massive MIMO system, CSI feedback overhead degrades the\noverall spectral efficiency. Convolutional neural network (CNN)-based CSI\nfeedback compression schemes has received a lot of attention recently due to\nsignificant improvements in compression efficiency; however, they still require\nreliable feedback links to convey the compressed CSI information to the BS.\nInstead, we propose here a CNN-based analog feedback scheme, called\nAnalogDeepCMC, which directly maps the downlink CSI to uplink channel input.\nCorresponding noisy channel outputs are used by another CNN to reconstruct the\nDL channel estimate. Not only the proposed outperforms existing digital CSI\nfeedback schemes in terms of the achievable downlink rate, but also simplifies\nthe operation as it does not require explicit quantization, coding and\nmodulation, and provides a low-latency alternative particularly in rapidly\nchanging MIMO channels, where the CSI needs to be estimated and fed back\nperiodically.\n', 'Overview of Deep Learning-based CSI Feedback in Massive MIMO Systems   Many performance gains achieved by massive multiple-input and multiple-output\ndepend on the accuracy of the downlink channel state information (CSI) at the\ntransmitter (base station), which is usually obtained by estimating at the\nreceiver (user terminal) and feeding back to the transmitter. The overhead of\nCSI feedback occupies substantial uplink bandwidth resources, especially when\nthe number of the transmit antennas is large. Deep learning (DL)-based CSI\nfeedback refers to CSI compression and reconstruction by a DL-based autoencoder\nand can greatly reduce feedback overhead. In this paper, a comprehensive\noverview of state-of-the-art research on this topic is provided, beginning with\nbasic DL concepts widely used in CSI feedback and then categorizing and\ndescribing some existing DL-based feedback works. The focus is on novel neural\nnetwork architectures and utilization of communication expert knowledge to\nimprove CSI feedback accuracy. Works on bit-level CSI feedback and joint design\nof CSI feedback with other communication modules are also introduced, and some\npractical issues, including training dataset collection, online training,\ncomplexity, generalization, and standardization effect, are discussed. At the\nend of the paper, some challenges and potential research directions associated\nwith DL-based CSI feedback in future wireless communication systems are\nidentified.\n', 'Deep Learning-Based CSI Feedback for Beamforming in Single- and\n  Multi-cell Massive MIMO Systems   The potentials of massive multiple-input multiple-output (MIMO) are all based\non the available instantaneous channel state information (CSI) at the base\nstation (BS). Therefore, the user in frequency-division duplexing (FDD) systems\nhas to keep on feeding back the CSI to the BS, thereby occupying large uplink\ntransmission resources. Recently, deep learning (DL) has achieved great success\nin the CSI feedback. However, the existing works just focus on improving the\nfeedback accuracy and ignore the effects on the following modules, e.g.,\nbeamforming (BF). In this paper, we propose a DL-based CSI feedback framework\nfor BF design, called CsiFBnet. The key idea of the CsiFBnet is to maximize the\nBF performance gain rather than the feedback accuracy. We apply it to two\nrepresentative scenarios: single- and multi-cell systems. The CsiFBnet-s in the\nsingle-cell system is based on the autoencoder architecture, where the encoder\nat the user compresses the CSI and the decoder at the BS generates the BF\nvector. The CsiFBnet-m in the multicell system has to feed back two kinds of\nCSI: the desired and the interfering CSI. The entire neural networks are\ntrained by an unsupervised learning strategy. Simulation results show the great\nperformance improvement and complexity reduction of the CsiFBnet compared with\nthe conventional DL-based CSI feedback methods.\n']","[('massive mimo', 0.5400211215019226), ('mimo channel', 0.5200569033622742), ('massive mimo systems', 0.5072139501571655), ('mimo csi', 0.48126113414764404), ('output mimo', 0.47141727805137634), ('output mimo systems', 0.4709135890007019), ('deep learning dl', 0.4434564411640167), ('channel prediction', 0.4392489194869995), ('mimo systems', 0.42581674456596375), ('multiple output mimo', 0.4254796504974365)]"
107,107,235,107_characters finite group_irreducible characters finite_irreducible characters_irreducible character,"['characters finite group', 'irreducible characters finite', 'irreducible characters', 'irreducible character', 'finite simple groups', 'characters finite', 'character theory', 'character table', 'finite groups', 'character chi']","[""Normal $p$-complements and irreducible character codegrees   Let $G$ be a finite group and $p\\in \\pi(G)$, and let Irr$(G)$ be the set of\nall irreducible complex characters of $G$. Let $\\chi \\in {\\rm Irr}(G)$, we\nwrite ${\\rm cod}(\\chi)=|G:{\\rm ker} \\chi|/\\chi(1)$, and called it the codegree\nof the irreducible character $\\chi$. Let $N\\unlhd G$, write ${\\rm\nIrr}(G|N)=\\{\\chi \\in {\\rm Irr}(G)~|~N\\nsubseteq {\\rm ker}\\chi\\}$, and ${\\rm\ncod}(G|N)=\\{ {\\rm cod}(\\chi) ~|~\\chi\\in{\\rm Irr}(G|N)\\}.$ In this Ipaper, we\nprove that if $N\\unlhd G$ and every member of ${\\rm cod}(G|N')$ is not\ndivisible by some fixed prime $p\\in \\pi(G)$, then $N$ has a normal\n$p$-complement and $N$ is solvable.\n"", 'Groups in which the co-degrees of the irreducible characters are\n  distinct   Let $G$ be a finite group and let $\\rm{Irr}(G)$ be the set of all irreducible\ncomplex characters of $G$. For a character $\\chi \\in \\rm{Irr}(G)$, the number\n$\\rm{cod}(\\chi):=|G:\\rm{ker}\\chi|/\\chi(1)$ is called the co-degree of $\\chi$.\nThe set of co-degrees of all irreducible characters of $G$ is denoted by\n$\\rm{cod}(G)$. In this paper, we show that for a non-trivial finite group $G$,\n$|\\rm{Irr}(G)|=|\\rm{cod}(G)|$ if and only if $G$ is isomorphic to the cyclic\ngroup $\\mathbb{Z}_2$ or the symmetric group $S_3$.\n', ""On the multiplicities of the character codegrees   Let G be a finite group and ? be an irreducible character of G, the number\ncod(?) = jG :\n  Let $ G $ be a finite group and $ \\chi $ be an irreducible character of $ G\n$, the number $ \\cod(\\chi) = |G: \\kernel(\\chi)|/\\chi(1) $ is called the\ncodegree of $ \\chi $. Also, $ \\cod(G) = \\{ \\cod(\\chi) \\ | \\ \\chi \\in \\Irr(G) \\}\n$. For $d\\in\\cod(G)$, the multiplicity of $d$ in $G$, denoted by $m'_G(d)$, is\nthe number of irreducible characters of $G$ having codegree $d$. A finite group\n$G$ is called a $T'_k$-group for some integer $k\\geq 1$, if there exists\n$d_0\\in\\cod(G)$ such that $m'_G(d_0)=k$ and for every $d\\in\\cod(G)-\\{d_0\\}$, we\nhave $m'_G(d)=1$. In this note we characterize finite $T'_k$-groups completely,\nwhere $k\\geq 1$ is an integer.\n""]","[('characters finite group', 0.6607100963592529), ('irreducible characters finite', 0.6255673170089722), ('irreducible characters', 0.5768141150474548), ('irreducible character', 0.5388258695602417), ('finite simple groups', 0.4547386169433594), ('characters finite', 0.44616803526878357), ('character theory', 0.4254554212093353), ('character table', 0.42518365383148193), ('finite groups', 0.41769105195999146), ('character chi', 0.41445767879486084)]"
108,108,235,108_lie superalgebras_lie super algebras_nilpotent lie algebras_lie superalgebra,"['lie superalgebras', 'lie super algebras', 'nilpotent lie algebras', 'lie superalgebra', 'nilpotent lie algebra', 'lie algebras dimension', 'dimensional nilpotent lie', 'superalgebras', 'dimensional lie algebras', 'lie algebras']","['On the Schur multiplier of nilpotent Lie superalgebra   Let $L$ be an $(m\\vert n)$-dimensional nilpotent Lie superalgebra where $m +\nn \\geq 4$ and $n \\geq 1$. This paper classifies such nilpotent Lie\nsuperalgebras $L$ with a derived subsuperalgebra of dimension $m+n-2$ such that\n$\\gamma(L) = m + 2n - 2 - \\dim \\mathcal{M}(L)$, where $\\gamma(L) \\in \\{0, 1,\n2\\}$ and $\\mathcal{M}(L)$ denotes the Schur multiplier of $L$. Furthermore, we\nshow that all these superalgebras are capable.\n', 'On $2$-Nilpotent Multiplier of Lie Superalgebras   In this article we define the $c$-nilpotent multiplier of a finite\ndimensional Lie suepralgebra. We characterize the structure of $2$-nilpotent\nmultiplier of finite dimensional nilpotent Lie superalgebras whose derived\nsubalgebras have dimension at most one. Then we give an upper bound on the\ndimension of $2$-nilpotent multiplier of any finite dimensional nilpotent Lie\nsuperalgebra. Moreover, we discuses the $2$-capability of special as well as\nodd Heisenberg Lie superalgebras and abelian Lie superalgebras.\n', 'On the nilpotent Lie superalgebras of small superbreadth   In this paper, we classify finite-dimensional nilpotent Lie superalgebras of\nsuperbreadth at most two.\n']","[('lie superalgebras', 0.7531046867370605), ('lie super algebras', 0.7350338101387024), ('nilpotent lie algebras', 0.7072482109069824), ('lie superalgebra', 0.7032214999198914), ('nilpotent lie algebra', 0.6762458086013794), ('lie algebras dimension', 0.6334843039512634), ('dimensional nilpotent lie', 0.6322513818740845), ('superalgebras', 0.6297616958618164), ('dimensional lie algebras', 0.6275506019592285), ('lie algebras', 0.6092092990875244)]"
109,109,234,109_shimura varieties_shimura variety_unitary shimura varieties_shimura curves,"['shimura varieties', 'shimura variety', 'unitary shimura varieties', 'shimura curves', 'cohomology shimura', 'shimura curve', 'shimura', 'unitary shimura', 'eichler shimura', 'modular varieties']","['Igusa Stacks and the Cohomology of Shimura Varieties   We construct functorial Igusa stacks for all Hodge-type Shimura varieties,\nproving a conjecture of Scholze and extending earlier results of the\nfourth-named author for PEL-type Shimura varieties. Using the Igusa stack, we\nconstruct a sheaf on $\\mathrm{Bun}_G$ that controls the cohomology of the\ncorresponding Shimura variety. We use this sheaf and the spectral action of\nFargues-Scholze to prove a compatibility between the cohomology of Shimura\nvarieties of Hodge type and the semisimple local Langlands correspondence of\nFargues-Scholze, generalizing the Eichler-Shimura relation of Blasius-Rogawski\nto arbitrary level at $p$. When the given Shimura variety is proper, we show\nmoreover that the sheaf is perverse, which allows us to prove new torsion\nvanishing results for the cohomology of Shimura varieties.\n', 'On the Piatetski-Shapiro construction for integral models of Shimura\n  varieties   We study the Piatetski-Shapiro construction, which takes a totally real field\nF and a Shimura datum (G,X) and produces a new Shimura datum (H,Y). If F is\nGalois, then the Galois group Gamma of F acts on (H,Y), and we show that the\nGamma-fixed points of the Shimura varieties for (H,Y) recover the Shimura\nvarieties for (G,X) under some hypotheses. For Shimura varieties of Hodge type\nwith parahoric level, we show that the same is true for the p-adic integral\nmodels constructed by Pappas--Rapoport. We also study the Gamma-fixed points of\nthe Igusa stacks of Zhang for (H,Y) and prove optimal results.\n', 'Boundary structures of integral models of Hodge-type Shimura Varieties   We compute the level groups associated with mixed Shimura varieties that\nappear at the boundaries of compactifications of Shimura varieties and show\nthat the boundaries of minimal compactifications of Pappas-Rapoport integral\nmodels are finite quotients of smaller Pappas-Rapoport integral models.\nAdditionally, we prove that the compactifications of integral models of\nHodge-type Shimura varieties with quasi-parahoric level structures are\nindependent of the choice of Siegel embedding, and use this to construct and\nanalyze the change-of-parahoric morphisms on these compactifications.\n']","[('shimura varieties', 0.8054560422897339), ('shimura variety', 0.7662268280982971), ('unitary shimura varieties', 0.7515984773635864), ('shimura curves', 0.7417166829109192), ('cohomology shimura', 0.7148319482803345), ('shimura curve', 0.6808704137802124), ('shimura', 0.6086057424545288), ('unitary shimura', 0.5880695581436157), ('eichler shimura', 0.5677005648612976), ('modular varieties', 0.5394902229309082)]"
110,110,231,110_groups elliptic curves_elliptic curves_elliptic curves mathbb_families elliptic curves,"['groups elliptic curves', 'elliptic curves', 'elliptic curves mathbb', 'families elliptic curves', 'family elliptic curves', 'elliptic curves let', 'elliptic curves defined', 'cm elliptic curves', 'elliptic curve mathbb', 'elliptic curve']","['On the quadratic twist of elliptic curves with full $2$-torsion   Let $E: y^2=x(x-a^2)(x+b^2)$ be an elliptic curve with full $2$-torsion\ngroup, where $a$ and $b$ are coprime integers and $2(a^2+b^2)$ is a square.\nAssume that the $2$-Selmer group of $E$ has rank two. We characterize all\nquadratic twists of $E$ with Mordell-Weil rank zero and $2$-primary\nShafarevich-Tate groups $(\\mathbb Z/2\\mathbb Z)^2$, under certain conditions.\nWe also obtain a distribution result of these elliptic curves.\n', 'Uniform polynomial bounds on torsion from rational geometric isogeny\n  classes   In 1996, Merel showed there exists a function $B\\colon\n\\mathbb{Z}^+\\rightarrow \\mathbb{Z}^+$ such that for any elliptic curve $E/F$\ndefined over a number field of degree $d$, one has the torsion group bound $\\#\nE(F)[\\textrm{tors}]\\leq B(d)$. Based on subsequent work, it is conjectured that\none can choose $B$ to be polynomial in the degree $d$. In this paper, we show\nthat such bounds exist for torsion from the family $\\mathcal{I}_{\\mathbb{Q}}$\nof elliptic curves which are geometrically isogenous to at least one rational\nelliptic curve. More precisely, we show that for each $\\epsilon>0$, there\nexists $c_\\epsilon>0$ such that for any elliptic curve $E/F\\in\n\\mathcal{I}_{\\mathbb{Q}}$, one has \\[ E(F)[\\textrm{tors}]\\leq c_\\epsilon\\cdot\n[F:\\mathbb{Q}]^{3+\\epsilon}. \\] This generalizes work of the second author for\nelliptic curves within a fixed rational geometric isogeny class. For the family\nof elliptic curves with rational $j$-invariant, we also obtain bounds which\nimprove those of Clark and Pollack. In this case, our bounds on the exponent of\n$E(F)[\\textrm{tors}]$ are optimal if one does not exclude elliptic curves with\ncomplex multiplication.\n', 'Growth of torsion groups of elliptic curves upon base change   We study how the torsion of elliptic curves over number fields grows upon\nbase change, and in particular prove various necessary conditions for torsion\ngrowth. For a number field $F$, we show that for a large set of number fields\n$L$, whose Galois group of their normal closure over $F$ has certain\nproperties, it will hold that $E(L)_{tors}=E(F)_{tors}$ for all elliptic curves\n$E$ defined over $F$.\n  Our methods turn out to be particularly useful in studying the possible\ntorsion groups $E(K)_{tors}$, where $K$ is a number field and $E$ is a base\nchange of an elliptic curve defined over $\\mathbb Q$. Suppose that $E$ is a\nbase change of an elliptic curve over $\\mathbb Q$ for the remainder of the\nabstract. We prove that $E(K)_{tors}=E(\\mathbb Q)_{tors}$ for all elliptic\ncurves $E$ defined over $\\mathbb Q$ and all number fields $K$ of degree $d$,\nwhere $d$ is not divisible by a prime $\\leq 7$. Using this fact, we determine\nall the possible torsion groups $E(K)_{tors}$ over number fields $K$ of prime\ndegree $p\\geq 7$. We determine all the possible degrees of $[\\mathbb\nQ(P):\\mathbb Q]$, where $P$ is a point of prime order $p$ for all $p$ such that\n$p\\not\\equiv 8 \\pmod 9$ or $\\left( \\frac{-D}{p}\\right)=1$ for any $D\\in\n\\{1,2,7,11,19,43,67,163\\}$; this is true for a set of density\n$\\frac{1535}{1536}$ of all primes and in particular for all $p<3167$. Using\nthis result, we determine all the possible prime orders of a point $P\\in\nE(K)_{tors}$, where $[K:\\mathbb Q]=d$, for all $d\\leq 3342296$. Finally, we\ndetermine all the possible groups $E(K)_{tors}$, where $K$ is a quartic number\nfield and $E$ is an elliptic curve defined over $\\mathbb Q$ and show that no\nquartic sporadic point on a modular curves $X_1(m,n)$ comes from an elliptic\ncurve defined over $\\mathbb Q$.\n']","[('groups elliptic curves', 0.6767468452453613), ('elliptic curves', 0.6578449606895447), ('elliptic curves mathbb', 0.6440052390098572), ('families elliptic curves', 0.6410247683525085), ('family elliptic curves', 0.6248683929443359), ('elliptic curves let', 0.6100578308105469), ('elliptic curves defined', 0.6060531139373779), ('cm elliptic curves', 0.5993465185165405), ('elliptic curve mathbb', 0.586340606212616), ('elliptic curve', 0.5679534673690796)]"
111,111,230,111_meromorphic functions_meromorphic solutions_two meromorphic_meromorphic,"['meromorphic functions', 'meromorphic solutions', 'two meromorphic', 'meromorphic', 'entire functions', 'differential polynomials', 'differential difference equations', 'difference equations', 'solutions difference equations', 'transcendental entire']","['Value distribution and uniqueness for q-difference of meromorphic\n  functions Sharing Two Sets   In this paper, we investigate the value distribution for linear q-difference\npolynomials of transcendental meromorphic functions of zero order which\nimproves the results of Xu, Liu and Cao (\\cite{Xu & Liu & Cao & 2015}). We also\ninvestigate the uniqueness of zero order meromorphic function with its\nq-difference operator sharing two sets with finite weight. Some examples have\nbeen exhibited which are relevant to the content of the paper.\n', 'Meromorphic functions of finite $\\varphi$-order and linear\n  $q$-difference equations   The $\\varphi$-order was introduced in 2009 for meromorphic functions in the\nunit disc, and was used as a growth indicator for solutions of linear\ndifferential equations. In this paper, the properties of meromorphic functions\nin the complex plane are investigated in terms of the $\\varphi$-order, which\nmeasures the growth of functions between the classical order and the\nlogarithmic order. Several results on value distribution of meromorphic\nfunctions are discussed by using the $\\varphi$-order and the $\\varphi$-exponent\nof convergence. Instead of linear differential equations, the applications in\nthe complex plane lie in linear $q$-difference equations.\n', 'Meromorphic Solutions of Homogeneous and Non-homogeneous Higher Order\n  Linear Difference Equations in Terms of (p,q)-Order   In this paper we investigate the growth of meromorphic solutions of\nhomogeneous and non-homogeneous linear difference equations with entire or\nmeromorphic coefficients. We further extend and improve few results on the\norder of meromorphic solutions by using (p,q)-lower order and (p,q)-lower type\nfollowed by the investigation of Luo and Zheng (2016), Belaidi and Bellaama\n(2020).\n']","[('meromorphic functions', 0.6682156324386597), ('meromorphic solutions', 0.6157504320144653), ('two meromorphic', 0.542455792427063), ('meromorphic', 0.5040169954299927), ('entire functions', 0.44583216309547424), ('differential polynomials', 0.39659708738327026), ('differential difference equations', 0.38511979579925537), ('difference equations', 0.3720577657222748), ('solutions difference equations', 0.36563530564308167), ('transcendental entire', 0.3623711168766022)]"
112,112,226,112_quiver gauge theories_supersymmetric gauge theories_quiver gauge theory_mathcal gauge theories,"['quiver gauge theories', 'supersymmetric gauge theories', 'quiver gauge theory', 'mathcal gauge theories', 'gauge theories', 'superconformal field theories', 'supersymmetric gauge', 'gauge theory', 'quiver gauge', 'mathcal supersymmetric']","['Argyres-Douglas Theories, IR N-ality and Complete Graphs   We show that for a large subclass of Argyres-Douglas-type theories, the Higgs\nbranch admits multiple hyperkahler quotient realizations as Higgs branches of\nthree dimensional $\\mathcal{N}=4$ quiver gauge theories, which are related by a\nsequence of Seiberg-like IR dualities. We refer to this phenomenon as the\nHyperkahler Quotient N-ality of the four dimensional Higgs branch. The\nassociated set of 3d theories contains a special subset of maximal unitary\nquivers: quiver gauge theories for which the resolution/deformation parameters\nof the Higgs branch are manifest in the Lagrangian as Fayet-Iliopoulas\nparameters. Starting from the Type IIB description for a given SCFT, we present\nan explicit construction to determine the aforementioned set of 3d quivers,\nincluding the subset of maximal unitary quivers. As a byproduct, we find a\nsimple method for constructing the three dimensional mirror associated with the\nSCFT. We demonstrate the construction for the $(A_k, A_k)$ theories of Cecotti,\nNeitzke and Vafa, focusing on the cases $k=3$ and $k=4$. The associated maximal\nunitary quiver is unique up to field redefinitions and turns out to be an\nAbelian quiver gauge theory. The three dimensional mirror obtained in this\nfashion reproduces the well-known complete graph. In the appendices to the main\npaper, we study the quotient N-ality in the closely related family of $D^b_p\n(SU(N))$ SCFTs, for which both the maximal unitary quiver as well as the 3d\nmirror turn out to be non-Abelian gauge theories generically\n', '5d SCFTs from Isolated Complete Intersection Singularities   In this paper, we explore the zoo of 5d superconformal field theories (SCFTs)\nconstructed from M-theory on Isolated Complete Intersection Singularities\n(ICIS). We systematically investigate the crepant resolution of such\nsingularities, and obtain a classification of rank $\\leqslant 10$ models with a\nsmooth crepant resolution and smooth exceptional divisors, as well as a number\nof infinite sequences with the same smoothness properties. For these models, we\nstudy their Coulomb branch properties and compute the flavor symmetry algebra\nfrom the resolved CY3 and/or the magnetic quiver. We check the validity of the\nconjectures relating the properties of the 5d SCFT and the 4d $\\mathcal{N}=2$\nSCFT from IIB superstring on the same singularity. When the 4d $\\mathcal{N}=2$\nSCFT has a Lagrangian quiver gauge theory description, one can obtain the\nmagnetic quiver of the 5d theory by gauging flavor symmetry, which encodes the\n5d Higgs branch information. Regarding the smoothness of the crepant resolution\nand integrality of 4d Coulomb branch spectrum, we find examples with a smooth\nresolved CY3 and smooth exceptional divisors, but fractional 4d Coulomb branch\nspectrum. Moreover, we compute the discrete (higher)-symmetries of the 5d/4d\nSCFTs from the link topology for a few examples.\n', ""Mirror symmetry for circle compactified 4d $\\mathcal{N}=2$ SCFTs   We propose a mirror symmetry for 4d $\\mathcal{N}=2$ superconformal field\ntheories (SCFTs) compactified on a circle with finite size. The mirror symmetry\ninvolves vertex operator algebra (VOA) describing the Schur sector (containing\nHiggs branch) of 4d theory, and the Coulomb branch of the effective 3d theory.\nThe basic feature of the mirror symmetry is that many representational\nproperties of VOA are matched with geometric properties of the Coulomb branch\nmoduli space. Our proposal is verified for a large class of Argyres-Douglas\n(AD) theories engineered from M5 branes, whose VOAs are W-algebras, and Coulomb\nbranches are the Hitchin moduli spaces. VOA data such as simple modules, Zhu's\nalgebra, and modular properties are matched with geometric properties like\n$\\mathbb{C}^*$-fixed varieties in Hitchin fibers, cohomologies, and some DAHA\nrepresentations. We also mention relationships to 3d symplectic duality.\n""]","[('quiver gauge theories', 0.6717501282691956), ('supersymmetric gauge theories', 0.6455905437469482), ('quiver gauge theory', 0.6209503412246704), ('mathcal gauge theories', 0.5910360217094421), ('gauge theories', 0.5909909009933472), ('superconformal field theories', 0.5742486119270325), ('supersymmetric gauge', 0.5332513451576233), ('gauge theory', 0.5082007646560669), ('quiver gauge', 0.49770402908325195), ('mathcal supersymmetric', 0.47452282905578613)]"
113,113,225,113_quadrilaterals_polygons inscribed_convex polyhedra_quadrilateral,"['quadrilaterals', 'polygons inscribed', 'convex polyhedra', 'quadrilateral', 'convex polyhedron', 'polyhedral', 'polyhedral surfaces', 'diagonals', 'polyhedron', 'polygons']","['A generalization of parallelograms involving inscribed ellipses,\n  conjugate diameters, and tangency chords   A convex quadrilateral, $Q$, is called a midpoint diagonal quadrilateral if\nthe intersection point of the diagonals of $Q$ coincides with the midpoint of\nat least one of the diagonals of $Q$. A parallelogram, P, is a special case of\na midpoint diagonal quadrilateral since the diagonals of P bisect one another.\nWe prove two results about ellipses inscribed in midpoint diagonal\nquadrilaterals, which generalize properties of ellipses inscribed in\nparallelograms involving convex quadrilaterals. First, $Q$ is a midpoint\ndiagonal quadrilateral if and only if each ellipse inscribed in $Q$ has\ntangency chords which are parallel to one of the diagonals of $Q$. Second, $Q$\nis a midpoint diagonal quadrilateral if and only if each ellipse inscribed in\n$Q$ has a pair of conjugate diameters parallel to the diagonals of $Q$.\nFinally, we show that there is a unique ellipse, $E_I$, of minimal eccentricity\nincribed in a midpoint diagonal quadrilateral, $Q$, and we show that the equal\nconjugate diameters of $E_I$ are parallel to the diagonals of $Q$.\n', 'On the Coherent Labelling Conjecture of a Polyhedron in Three Dimensions   In this article we consider an open conjecture about coherently labelling a\npolyhedron in three dimensions. We exhibit all the forty eight possible\ncoherent labellings of a tetrahedron. We also exhibit that some simplicial\npolyhedra like bipyramids, Kleetopes, gyroelongated bipyramids are coherently\nlabellable. Also we prove that pyramids over $n$-gons for $n\\geq 4$, which are\nnot simplicial polyhedra, are coherently labellable. We prove that among\nplatonic solids, the cube and the dodecahedron are not coherently labellable,\neven though, the tetrahedron, the octahedron and the icosahedron are coherently\nlabellable. Unlike the case of a tetrahedron, in general for a polyhedron, we\nshow that a coherent labelling need not induce a coherent labelling at a\nvertex. We prove the main conjecture in the affirmative for a certain class of\npolyhedra which are constructible from tetrahedra through certain types of edge\nand face vanishing tetrahedron attachments. As a consequence we conclude that a\ncube cannot be obtained from only these type of tetrahedron attachments. We\nalso give an obstruction criterion for a polyhedron to be not coherently\nlabellable and consequentially show that any polyhedron obtained from a pyramid\nwith its apex chopped off is not coherently labellable. Finally with the\nsuggestion of the affirmative results we prove the main theorem that any\nsimplicial polyhedron is coherently labellable.\n', ""Non-simplicial Delaunay meshing via approximation by radical partitions   We consider the construction of a polyhedral Delaunay partition as a limit of\nthe sequence of power diagrams (radical partitions). The dual Voronoi diagram\nis obtained as a limit of the sequence of weighted Delaunay partitions. The\nproblem is reduced to the construction of two dual convex polyhedra, inscribed\nand superscribed around a circular paraboloid, as a limit of the sequence of\npairs of general dual convex polyhedra. The sequence of primal polyhedra should\nconverge to the superscribed polyhedron and the sequence of the dual polyhedra\nconverges to the inscribed polyhedron.\n  We are interested in the case when the vertices of primal polyhedra can move\nor merge together, i.e., no new faces are allowed for dual polyhedra. These\nrules define the transformation of the set of initial spheres into the set of\nDelaunay spheres using radius variation and sphere movement and elimination.\nExistence theorems are still unavailable but we suggest a functional measuring\nthe deviation of the convex polyhedron from the one inscribed into the\nparaboloid. It is the discrete Dirichlet functional for the power function\nwhich is a linear interpolant of the vertical distance of the dual vertices\nfrom the paraboloid. The functional's absolute minimizer is attained on the\nconstant power field, meaning that the inscribed polyhedron can be obtained by\na simple translation. This formulation of the functional for the dual surface\nis not quadratic since the unknowns are the vertices of the primal polyhedron,\nhence, the transformation of the set of spheres into Delaunay spheres is not\nunique.\n  We concentrate on the experimental confirmation of the approach viability and\nput aside mesh quality problems. The zero value of the gradient of the proposed\nfunctional defines a manifold describing the evolution of Delaunay spheres.\nHence, Delaunay-Voronoi meshes can be optimized using the manifold as a\nconstraint.\n""]","[('quadrilaterals', 0.5720642805099487), ('polygons inscribed', 0.5525200366973877), ('convex polyhedra', 0.5356132388114929), ('quadrilateral', 0.5281274914741516), ('convex polyhedron', 0.4961888790130615), ('polyhedral', 0.48507317900657654), ('polyhedral surfaces', 0.4839359521865845), ('diagonals', 0.4649105966091156), ('polyhedron', 0.4578579366207123), ('polygons', 0.45581182837486267)]"
114,114,225,114_semantic communications_semantic communication_semantic aware_encoder,"['semantic communications', 'semantic communication', 'semantic aware', 'encoder', 'autoencoder', 'decoder', 'encoder decoder', 'channel coding', 'source channel coding', 'semantic features']","['Wireless Image Transmission with Semantic and Security Awareness   Semantic communication is an increasingly popular framework for wireless\nimage transmission due to its high communication efficiency. With the aid of\nthe joint-source-and-channel (JSC) encoder implemented by neural network,\nsemantic communication directly maps original images into symbol sequences\ncontaining semantic information. Compared with the traditional separate source\nand channel coding design used in bitlevel communication systems, semantic\ncommunication systems are known to be more efficient and accurate especially in\nthe low signal-to-the-noise ratio (SNR) regime. This thus prompts an critical\nwhile yet to be tackled issue of security in semantic communication: it makes\nthe eavesdropper more easier to crack the semantic information as it can be\ndecoded even in a quite noisy channel. In this letter, we develop a semantic\ncommunication framework that accounts for both semantic meaning decoding\nefficiency and its risk of privacy leakage. To achieve this, targeting wireless\nimage transmission, we on the one hand propose an JSC autoencoder featuring\nresidual for efficient semantic meaning extraction and transmission, and on the\nother hand, propose a data-driven scheme that balances the efficiency-privacy\ntradeoff. Extensive experimental results are provided to show the effectiveness\nand robustness of the proposed scheme.\n', 'Variational Source-Channel Coding for Semantic Communication Semantic communication technology emerges as a pivotal bridge connecting AI with classical communication. The current semantic communication systems are generally modeled as an Auto-Encoder (AE). AE lacks a deep integration of AI principles with communication strategies due to its inability to effectively capture channel dynamics. This gap makes it difficult to justify the need for joint source-channel coding (JSCC) and to explain why performance improves. This paper begins by exploring lossless and lossy communication, highlighting that the inclusion of data distortion distinguishes semantic communication from classical communication. It breaks the conditions for the separation theorem to hold and explains why the amount of data transferred by semantic communication is less. Therefore, employing JSCC becomes imperative for achieving optimal semantic communication. Moreover, a Variational Source-Channel Coding (VSCC) method is proposed for constructing semantic communication systems based on data distortion theory, integrating variational inference and channel characteristics. Using a deep learning network, we develop a semantic communication system employing the VSCC method and demonstrate its capability for semantic transmission. We also establish semantic communication systems of equivalent complexity employing the AE method and the VAE method. Experimental results reveal that the VSCC model offers superior interpretability compared to AE model, as it clearly captures the semantic features of the transmitted data, represented as the variance of latent variables in our experiments. In addition, VSCC model exhibits superior semantic transmission capabilities compared to VAE model. At the same level of data distortion evaluated by PSNR, VSCC model exhibits stronger human interpretability, which can be partially assessed by SSIM.', 'Robust Semantic Communications Against Semantic Noise   Although the semantic communications have exhibited satisfactory performance\nin a large number of tasks, the impact of semantic noise and the robustness of\nthe systems have not been well investigated. Semantic noise is a particular\nkind of noise in semantic communication systems, which refers to the misleading\nbetween the intended semantic symbols and received ones. In this paper, we\nfirst propose a framework for the robust end-to-end semantic communication\nsystems to combat the semantic noise. Particularly, we analyze the causes of\nsemantic noise and propose a practical method to generate it. To remove the\neffect of semantic noise, adversarial training is proposed to incorporate the\nsamples with semantic noise in the training dataset. Then, the masked\nautoencoder (MAE) is designed as the architecture of a robust semantic\ncommunication system, where a portion of the input is masked. To further\nimprove the robustness of semantic communication systems, we firstly employ the\nvector quantization-variational autoencoder (VQ-VAE) to design a discrete\ncodebook shared by the transmitter and the receiver for encoded feature\nrepresentation. Thus, the transmitter simply needs to transmit the indices of\nthese features in the codebook. Simulation results show that our proposed\nmethod significantly improves the robustness of semantic communication systems\nagainst semantic noise with significant reduction on the transmission overhead.\n']","[('semantic communications', 0.543390691280365), ('semantic communication', 0.4892060160636902), ('semantic aware', 0.4582371413707733), ('encoder', 0.43819570541381836), ('autoencoder', 0.4337078928947449), ('decoder', 0.43122735619544983), ('encoder decoder', 0.42921188473701477), ('channel coding', 0.42287570238113403), ('source channel coding', 0.4122207462787628), ('semantic features', 0.3979778587818146)]"
115,115,225,115_closed hyperbolic surfaces_hyperbolic surfaces_hyperbolic manifolds_geodesics hyperbolic,"['closed hyperbolic surfaces', 'hyperbolic surfaces', 'hyperbolic manifolds', 'geodesics hyperbolic', 'closed hyperbolic surface', 'hyperbolic manifold', 'compact hyperbolic', 'hyperbolic surface', 'closed geodesics', 'hyperbolic metric']","['Effective mapping class group dynamics II: Geometric intersection\n  numbers   We show that the action of the mapping class group on the space of closed\ncurves of a closed surface effectively tracks the corresponding action on\nTeichm\\""uller space in the following sense: for all but quantitatively few\nmapping classes, the information of how a mapping class moves a given point of\nTeichm\\""uller space determines, up to a power saving error term, how it changes\nthe geometric intersection numbers of a given closed curve with respect to\narbitrary geodesic currents. Applications include an effective estimate\ndescribing the speed of convergence of Teichm\\""uller geodesic rays to the\nboundary at infinity of Teichm\\""uller space, an effective estimate comparing\nthe Teichm\\""uller and Thurston metrics along mapping class group orbits of\nTeichm\\""uller space, and, in the sequel, effective estimates for countings of\nfilling closed geodesics on closed, negatively curved surfaces.\n', 'Local Rigidity of Teichm\\""uller space with Thurston metric   We show that every $\\mathbb R$-linear surjective isometry between the\ncotangent spaces to the Teichm\\""uller space equipped with the Thurston norm is\ninduced by some isometry between the underlying hyperbolic surfaces, which is\nan analogue of Royden\'s theorem concerning the Teichm\\""uller metric.\n', 'Ray structures on Teichm\\""uller Space   While there may be many Thurston metric geodesics between a pair of points in\nTeichm\\""uller space, we find that by imposing an additional energy minimization\nconstraint on the geodesics, thought of as limits of harmonic map rays, we\nselect a unique Thurston geodesic through those points. Extending the target\nsurface to the Thurston boundary yields, for each point $Y$ in Teichm\\""uller\nspace, an ""exponential map"" of rays from that point $Y$ onto Teichm\\""uller\nspace with visual boundary the Thurston boundary of Teichm\\""uller space.\n  We first depict harmonic map ray structures on Teichm\\""uller space as a\ngeometric transition between Teichm\\""uller ray structures and Thurston geodesic\nray structures. In particular, by appropriately degenerating the source of a\nharmonic map between hyperbolic surfaces (along ""harmonic map dual rays""), the\nharmonic map rays through the target converge to a Thurston geodesic; by\nappropriately degenerating the target of the harmonic map, those harmonic map\ndual rays through the domain converge to Teichm\\""uller geodesics. We then\nextend this transition to one from Teichm\\""uller disks through Hopf\ndifferential disks to stretch-earthquake disks. These results apply to surfaces\nwith boundary, resolving a question on stretch maps between such surfaces.\n']","[('closed hyperbolic surfaces', 0.7042256593704224), ('hyperbolic surfaces', 0.6744956970214844), ('hyperbolic manifolds', 0.6548596620559692), ('geodesics hyperbolic', 0.6515372395515442), ('closed hyperbolic surface', 0.6494942903518677), ('hyperbolic manifold', 0.6227726936340332), ('compact hyperbolic', 0.6185656785964966), ('hyperbolic surface', 0.6084424257278442), ('closed geodesics', 0.5993683934211731), ('hyperbolic metric', 0.5958948731422424)]"
116,116,225,116_bounded pseudoconvex domains_bounded pseudoconvex domain_bergman metrics_strictly pseudoconvex domains,"['bounded pseudoconvex domains', 'bounded pseudoconvex domain', 'bergman metrics', 'strictly pseudoconvex domains', 'pseudoconvex domains', 'strongly pseudoconvex domain', 'pseudoconvex domains mathbb', 'bergman metric', 'strictly pseudoconvex domain', 'kobayashi metric']","['Some remarks on the Kobayashi--Fuks metric on strongly pseudoconvex\n  domains   The Ricci curvature of the Bergman metric on a bounded domain $D\\subset\n\\mathbb{C}^n$ is strictly bounded above by $n+1$ and consequently $\\log\n(K_D^{n+1}g_{B,D})$, where $K_D$ is the Bergman kernel for $D$ on the diagonal\nand $g_{B, D}$ is the Riemannian volume element of the Bergman metric on $D$,\nis the potential for a K\\""ahler metric on $D$ known as the Kobayashi--Fuks\nmetric. In this note we study the localization of this metric near holomorphic\npeak points and also show that this metric shares several properties with the\nBergman metric on strongly pseudoconvex domains.\n', 'Visibility domains that are not pseudoconvex The earliest examples of visibility domains, given by Bharali--Zimmer, are pseudoconvex. In fact, all known examples of visibility domains are pseudoconvex. We show that there exist non-pseudoconvex visibility domains. We supplement this proof by a general method to construct a wide range of non-pseudoconvex, hence non-Kobayashi-complete, visibility domains.', ""The Bergman-Fridman invariant on some classes of pseudoconvex domains   We study the boundary behaviour of a variant of the Fridman's invariant\nfunction (defined in terms of the Bergman metric) on Levi corank one domains,\nstrongly pseudoconvex domains, smoothly bounded convex domains in $\n\\mathbb{C}^n $ and polyhedral domains in $ \\mathbb{C}^2 $.\n""]","[('bounded pseudoconvex domains', 0.6928473114967346), ('bounded pseudoconvex domain', 0.6547444462776184), ('bergman metrics', 0.6406670212745667), ('strictly pseudoconvex domains', 0.6333358287811279), ('pseudoconvex domains', 0.6199033856391907), ('strongly pseudoconvex domain', 0.5979572534561157), ('pseudoconvex domains mathbb', 0.5964627861976624), ('bergman metric', 0.5926737785339355), ('strictly pseudoconvex domain', 0.5914952158927917), ('kobayashi metric', 0.5796822905540466)]"
117,117,224,117_change point detection_change point estimation_change detection_detecting change,"['change point detection', 'change point estimation', 'change detection', 'detecting change', 'detection change', 'detecting changes', 'changepoints', 'changepoint', 'change point', 'change points']","['Adversarially robust change point detection   Change point detection is becoming increasingly popular in many application\nareas. On one hand, most of the theoretically-justified methods are\ninvestigated in an ideal setting without model violations, or merely robust\nagainst identical heavy-tailed noise distribution across time and/or against\nisolate outliers; on the other hand, we are aware that there have been\nexponentially growing attacks from adversaries, who may pose systematic\ncontamination on data to purposely create spurious change points or disguise\ntrue change points. In light of the timely need for a change point detection\nmethod that is robust against adversaries, we start with, arguably, the\nsimplest univariate mean change point detection problem. The adversarial\nattacks are formulated through the Huber $\\varepsilon$-contamination framework,\nwhich in particular allows the contamination distributions to be different at\neach time point. In this paper, we demonstrate a phase transition phenomenon in\nchange point detection. This detection boundary is a function of the\ncontamination proportion $\\varepsilon$ and is the first time shown in the\nliterature. In addition, we derive the minimax-rate optimal localisation error\nrate, quantifying the cost of accuracy in terms of the contamination\nproportion. We propose a computationally feasible method, matching the minimax\nlower bound under certain conditions, saving for logarithmic factors. Extensive\nnumerical experiments are conducted with comparisons to robust change point\ndetection methods in the existing literature.\n', 'Optimal Change-Point Detection and Localization   Given a times series ${\\bf Y}$ in $\\mathbb{R}^n$, with a piece-wise contant\nmean and independent components, the twin problems of change-point detection\nand change-point localization respectively amount to detecting the existence of\ntimes where the mean varies and estimating the positions of those\nchange-points. In this work, we tightly characterize optimal rates for both\nproblems and uncover the phase transition phenomenon from a global testing\nproblem to a local estimation problem. Introducing a suitable definition of the\nenergy of a change-point, we first establish in the single change-point setting\nthat the optimal detection threshold is $\\sqrt{2\\log\\log(n)}$. When the energy\nis just above the detection threshold, then the problem of localizing the\nchange-point becomes purely parametric: it only depends on the difference in\nmeans and not on the position of the change-point anymore. Interestingly, for\nmost change-point positions, it is possible to detect and localize them at a\nmuch smaller energy level. In the multiple change-point setting, we establish\nthe energy detection threshold and show similarly that the optimal localization\nerror of a specific change-point becomes purely parametric. Along the way,\ntight optimal rates for Hausdorff and $l_1$ estimation losses of the vector of\nall change-points positions are also established. Two procedures achieving\nthese optimal rates are introduced. The first one is a least-squares estimator\nwith a new multiscale penalty that favours well spread change-points. The\nsecond one is a two-step multiscale post-processing procedure whose\ncomputational complexity can be as low as $O(n\\log(n))$. Notably, these two\nprocedures accommodate with the presence of possibly many low-energy and\ntherefore undetectable change-points and are still able to detect and localize\nhigh-energy change-points even with the presence of those nuisance parameters.\n', 'Online change-point detection for a transient change   We consider a popular online change-point problem of detecting a transient\nchange in distributions of i.i.d. random variables. For this change-point\nproblem, several change-point procedures are formulated and some advanced\nresults for a particular procedure are surveyed. Some new approximations for\nthe average run length to false alarm are offered and the power of these\nprocedures for detecting a transient change in mean of a sequence of normal\nrandom variables is compared.\n']","[('change point detection', 0.6986865997314453), ('change point estimation', 0.6946261525154114), ('change detection', 0.6465256810188293), ('detecting change', 0.6258073449134827), ('detection change', 0.6098940372467041), ('detecting changes', 0.5856846570968628), ('changepoints', 0.5252472162246704), ('changepoint', 0.4407447278499603), ('change point', 0.4350447952747345), ('change points', 0.42594078183174133)]"
118,118,222,118_smooth convex optimization_proximal gradient methods_convex optimization_nonsmooth optimization,"['smooth convex optimization', 'proximal gradient methods', 'convex optimization', 'nonsmooth optimization', 'convex optimization problems', 'gradient descent', 'proximal gradient', 'composite optimization', 'gradient methods', 'nonsmooth convex']","['Convergence of Nonmonotone Proximal Gradient Methods under the\n  Kurdyka-Lojasiewicz Property without a Global Lipschitz Assumption   We consider the composite minimization problem with the objective function\nbeing the sum of a continuously differentiable and a merely lower\nsemicontinuous and extended-valued function. The proximal gradient method is\nprobably the most popular solver for this class of problems. Its convergence\ntheory typically requires that either the gradient of the smooth part of the\nobjective function is globally Lipschitz continuous or the (implicit or\nexplicit) a priori assumption that the iterates generated by this method are\nbounded. Some recent results show that, without these assumptions, the proximal\ngradient method, combined with a monotone stepsize strategy, is still globally\nconvergent with a suitable rate-of-convergence under the Kurdyka-Lojasiewicz\nproperty. For a nonmonotone stepsize strategy, there exist some attempts to\nverify similar convergence results, but, so far, they need stronger\nassumptions. This paper is the first which shows that nonmonotone proximal\ngradient methods for composite optimization problems share essentially the same\nnice global and rate-of-convergence properties as its monotone counterparts,\nstill without assuming a global Lipschitz assumption and without an a priori\nknowledge of the boundedness of the iterates.\n', 'Inexact proximal methods for weakly convex functions   This paper proposes and develops inexact proximal methods for finding\nstationary points of the sum of a smooth function and a nonsmooth weakly convex\none, where an error is present in the calculation of the proximal mapping of\nthe nonsmooth term. A general framework for finding zeros of a continuous\nmapping is derived from our previous paper on this subject to establish\nconvergence properties of the inexact proximal point method when the smooth\nterm is vanished and of the inexact proximal gradient method when the smooth\nterm satisfies a descent condition. The inexact proximal point method achieves\nglobal convergence with constructive convergence rates when the Moreau envelope\nof the objective function satisfies the Kurdyka-Lojasiewicz (KL) property.\nMeanwhile, when the smooth term is twice continuously differentiable with a\nLipschitz continuous gradient and a differentiable approximation of the\nobjective function satisfies the KL property, the inexact proximal gradient\nmethod achieves the global convergence of iterates with constructive\nconvergence rates.\n', 'Accelerated Primal-Dual Gradient Method for Smooth and Convex-Concave\n  Saddle-Point Problems with Bilinear Coupling   In this paper we study the convex-concave saddle-point problem $\\min_x \\max_y\nf(x) + y^T \\mathbf{A} x - g(y)$, where $f(x)$ and $g(y)$ are smooth and convex\nfunctions. We propose an Accelerated Primal-Dual Gradient Method (APDG) for\nsolving this problem, achieving (i) an optimal linear convergence rate in the\nstrongly-convex-strongly-concave regime, matching the lower complexity bound\n(Zhang et al., 2021), and (ii) an accelerated linear convergence rate in the\ncase when only one of the functions $f(x)$ and $g(y)$ is strongly convex or\neven none of them are. Finally, we obtain a linearly convergent algorithm for\nthe general smooth and convex-concave saddle point problem $\\min_x \\max_y\nF(x,y)$ without the requirement of strong convexity or strong concavity.\n']","[('smooth convex optimization', 0.6436753273010254), ('proximal gradient methods', 0.6288390159606934), ('convex optimization', 0.5975933074951172), ('nonsmooth optimization', 0.579609215259552), ('convex optimization problems', 0.5776558518409729), ('gradient descent', 0.5215204954147339), ('proximal gradient', 0.5082480311393738), ('composite optimization', 0.4998741149902344), ('gradient methods', 0.49756118655204773), ('nonsmooth convex', 0.4854936897754669)]"
119,119,221,119_schr odinger operators_schr odinger operator_quasiperiodic schr odinger_discrete schr odinger,"['schr odinger operators', 'schr odinger operator', 'quasiperiodic schr odinger', 'discrete schr odinger', 'odinger operators', 'periodic schr odinger', 'quasiperiodic schr', 'odinger operator', 'odinger operators mathbb', 'anderson localization']","['Random Schr\\""odinger Operators and Anderson localization in aperiodic\n  media   In this note we review some results on localization and related properties\nfor random Schr\\""odinger operators arising in aperiodic media. These include\nthe Anderson model associated to disordered quasycrystals and also the\nso-called Delone operators, operators associated to deterministic aperiodic\nstructures.\n', 'Arithmetic version of anderson localization for quasiperiodic\n  Schr\\""odinger operators with even cosine type potentials   We propose a new method to prove Anderson localization for quasiperiodic\nSchr\\""odinger operators and apply it to the quasiperiodic model considered by\nSinai and Fr\\""ohlich-Spencer-Wittwer. More concretely, we prove Anderson\nlocalization for even $C^2$ cosine type quasiperiodic Schr\\""odinger operators\nwith large coupling constants, Diophantine frequencies and Diophantine phases.\n', 'On the spectrum of quasi-periodic Schr\\""odinger operators on\n  $\\mathbb{Z}^d$ with $C^2$-cosine type potentials   In this paper, we establish the Anderson localization, strong dynamical\nlocalization and the $(\\frac 12-)$-H\\""older continuity of the integrated\ndensity of states (IDS) for some multi-dimensional discrete quasi-periodic (QP)\nSchr\\""odinger operators with asymmetric $C^2$-cosine type potentials. We extend\nboth the iteration scheme of \\cite{CSZ23a} and the interlacing method of\n\\cite{FV21} to handle asymmetric Rellich functions with collapsed gaps.\n']","[('schr odinger operators', 0.6872833967208862), ('schr odinger operator', 0.6612794399261475), ('quasiperiodic schr odinger', 0.6471320986747742), ('discrete schr odinger', 0.6112416386604309), ('odinger operators', 0.6072113513946533), ('periodic schr odinger', 0.5967509150505066), ('quasiperiodic schr', 0.576072633266449), ('odinger operator', 0.5705596208572388), ('odinger operators mathbb', 0.5404006838798523), ('anderson localization', 0.5215941667556763)]"
120,120,219,120_chemotaxis system_navier stokes system_keller segel type_keller segel,"['chemotaxis system', 'navier stokes system', 'keller segel type', 'keller segel', 'chemotaxis', 'nonlinear diffusion', 'elliptic parabolic', 'segel', 'solutions parabolic', 'boundedness classical solutions']","['On the parabolic-elliptic Keller-Segel system with signal-dependent\n  motilities: a paradigm for global boundedness and steady states   This paper is concerned with a parabolic-elliptic Keller-Segel system where\nboth diffusive and chemotactic coefficients (motility functions) depend on the\nchemical signal density. This system was originally proposed by Keller and\nSegel in \\cite{KS-1971-JTB2} to describe the aggregation phase of {\\it\nDictyostelium discoideum} cells in response to the secreted chemical signal\ncyclic adenosine monophosphate (cAMP), but the available analytical results are\nvery limited by far. Considering system in a bounded smooth domain with Neumann\nboundary conditions, we establish the global boundedness of solutions in any\ndimensions with suitable general conditions on the signal-dependent motility\nfunctions, which are applicable to a wide class of motility functions. The\nexistence/nonexistence of non-constant steady states is studied and abundant\nstationary profiles are found. Some open questions are outlined for further\npursues. Our results demonstrate that the global boundedness and profile of\nstationary solutions to the Keller-Segel system with signal-dependent\nmotilities depend on the decay rates of motility functions, space dimensions\nand the relation between the diffusive and chemotactic motilities, which makes\nthe dynamics immensely wealthy.\n', 'A decoupled linear, mass-conservative block-centered finite difference\n  method for the Keller-Segel chemotaxis system   As a class of nonlinear partial differential equations, the Keller-Segel\nsystem is widely used to model chemotaxis in biology. In this paper, we present\nthe construction and analysis of a decoupled linear, mass-conservative,\nblock-centered finite difference method for the classical Keller-Segel\nchemotaxis system. We show that the scheme is mass conservative for the cell\ndensity at the discrete level. In addition, second-order temporal and spatial\nconvergence for both the cell density and the chemoattractant concentration are\nrigorously discussed, using the mathematical induction method, the discrete\nenergy method and detailed analysis of the truncation errors. Our scheme is\nproposed and analyzed on non-uniform spatial grids, which leads to more\naccurate and efficient modeling results for the chemotaxis system with rapid\nblow-up phenomenon. Furthermore, the existence and uniqueness of solutions to\nthe Keller-Segel chemotaxis system are also discussed. Numerical experiments\nare presented to verify the theoretical results and to show the robustness and\naccuracy of the scheme.\n', 'On the space-time analyticity of the Keller-Segel-Navier-Stokes system   In this paper, we study the coupled Keller-Segel-Navier-Stokes system, which\nmodels chemotaxis occuring in ambient viscous fluid. We consider this\nnonlinear, nonlocal system on a periodic strip, equipped with homogeneous\nNeumann boundary conditions for the Keller-Segel part and no-slip boundary\ncondition for the fluid part. We prove the simultaneous space-time analyticity\nof the solution up to the boundary based on energy methods.\n']","[('chemotaxis system', 0.5155515670776367), ('navier stokes system', 0.42684420943260193), ('keller segel type', 0.4255433678627014), ('keller segel', 0.418174147605896), ('chemotaxis', 0.39214301109313965), ('nonlinear diffusion', 0.35780829191207886), ('elliptic parabolic', 0.3562508225440979), ('segel', 0.35502198338508606), ('solutions parabolic', 0.3528815805912018), ('boundedness classical solutions', 0.35235437750816345)]"
121,121,215,121_autoregressive models_autoregressive time series_autoregressive_vector autoregressive,"['autoregressive models', 'autoregressive time series', 'autoregressive', 'vector autoregressive', 'autoregressive time', 'autoregressive processes', 'first order autoregressive', 'autoregressive conditional', 'time series models', 'autoregressive moving']","['Diagnostic checking of periodic vector autoregressive time series models\n  with dependent errors   In this article, we study the asymptotic behaviour of the residual\nautocorrelations for periodic vector autoregressive time series models (PVAR\nhenceforth) with uncorrelated but dependent innovations (i.e., weak PVAR). We\nthen deduce the asymptotic distribution of the Ljung-Box-McLeod modified\nPortmanteau statistics for weak PVAR models. In Monte Carlo experiments, we\nillustrate that the proposed test statistics have reasonable finite sample\nperformance. When the innovations exhibit conditional heteroscedasticity or\nother forms of dependence, it appears that the standard test statistics (under\nindependent and identically distributed innovations) are generally nonreliable,\noverrejecting, or underrejecting severely, while the proposed test statistics\noffer satisfactory levels. An illustrative application on real data is also\nproposed.\n', ""On the partial autocorrelation function for locally stationary time\n  series: characterization, estimation and inference   For stationary time series, it is common to use the plots of partial\nautocorrelation function (PACF) or PACF-based tests to explore the temporal\ndependence structure of such processes. To our best knowledge, such analogs for\nnon-stationary time series have not been fully established yet. In this paper,\nwe fill this gap for locally stationary time series with short-range\ndependence. First, we characterize the PACF locally in the time domain and show\nthat the $j$th PACF, denoted as $\\rho_{j}(t),$ decays with $j$ whose rate is\nadaptive to the temporal dependence of the time series $\\{x_{i,n}\\}$. Second,\nat time $i,$ we justify that the PACF $\\rho_j(i/n)$ can be efficiently\napproximated by the best linear prediction coefficients via the Yule-Walker's\nequations. This allows us to study the PACF via ordinary least squares (OLS)\nlocally. Third, we show that the PACF is smooth in time for locally stationary\ntime series. We use the sieve method with OLS to estimate $\\rho_j(\\cdot)$ and\nconstruct some statistics to test the PACFs and infer the structures of the\ntime series. These tests generalize and modify those used for stationary time\nseries. Finally, a multiplier bootstrap algorithm is proposed for practical\nimplementation and an $\\mathtt R$ package $\\mathtt {Sie2nts}$ is provided to\nimplement our algorithm. Numerical simulations and real data analysis also\nconfirm usefulness of our results.\n"", 'Statistical inference of high-dimensional vector autoregressive time\n  series with non-i.i.d. innovations   Independent or i.i.d. innovations is an essential assumption in the\nliterature for analyzing a vector time series. However, this assumption is\neither too restrictive for a real-life time series to satisfy or is hard to\nverify through a hypothesis test. This paper performs statistical inference on\na sparse high-dimensional vector autoregressive time series, allowing its white\nnoise innovations to be dependent, even non-stationary. To achieve this goal,\nit adopts a post-selection estimator to fit the vector autoregressive model and\nderives the asymptotic distribution of the post-selection estimator. The\ninnovations in the autoregressive time series are not assumed to be\nindependent, thus making the covariance matrices of the autoregressive\ncoefficient estimators complex and difficult to estimate. Our work develops a\nbootstrap algorithm to facilitate practitioners in performing statistical\ninference without having to engage in sophisticated calculations. Simulations\nand real-life data experiments reveal the validity of the proposed methods and\ntheoretical results.\n  Real-life data is rarely considered to exactly satisfy an autoregressive\nmodel with independent or i.i.d. innovations, so our work should better reflect\nthe reality compared to the literature that assumes i.i.d. innovations.\n']","[('autoregressive models', 0.6642975807189941), ('autoregressive time series', 0.6537430286407471), ('autoregressive', 0.6127533316612244), ('vector autoregressive', 0.599174976348877), ('autoregressive time', 0.5891879200935364), ('autoregressive processes', 0.5868762731552124), ('first order autoregressive', 0.5785619616508484), ('autoregressive conditional', 0.5709941983222961), ('time series models', 0.5549508333206177), ('autoregressive moving', 0.531025767326355)]"
122,122,215,122_index graphs_indices graphs_index graph_index trees,"['index graphs', 'indices graphs', 'index graph', 'index trees', 'topological index', 'topological indices', 'wiener index', 'extremal graphs', 'index introduced', 'vertex degree']","['Extremal problems on Sombor indices of unicyclic graphs with a given\n  diameter   Sombor index is a novel topological index, which was introduced by Gutman and\ndefined for a graph $G$ as $SO(G)=\\sum\\limits_{uv\\in\nE(G)}\\sqrt{d_{u}^{2}+d_{v}^{2}}$, where $d_{u}=d_{G}(u)$ denotes the degree of\nvertex $u$ in graph $G$.\n  Extremal problems on the Sombor index for trees with a given diameter has\nbeen considered by Chen et al. [H. Chen, W. Li, J. Wang, Extremal values on the\nSombor index of trees, MATCH Commun. Math. Comput. Chem. 87 (2022) 23--49] and\nLi et al. [S. Li, Z. Wang, M. Zhang, On the extremal Sombor index of trees with\na given diameter, Appl. Math. Comput. 416 (2022) 126731]. As an extension of\nresults introduces above, we determine the maximum Sombor indices for unicyclic\ngraphs with a fixed order and given diameter.\n', 'On the first Banhatti-Sombor index   Let $d_v$ be the degree of the vertex $v$ in a connected graph $G$. The first\nBanhatti-Sombor index of $G$ is defined as $BSO(G) =\\sum_{uv\\in\nE(G)}\\sqrt{\\frac{1}{d^2_u}+\\frac{1}{d^2_v}}$, which is a new\nvertex-degree-based topological index introduced by Kulli. In this paper, the\nmathematical relations between the first Banhatti-Sombor index and some other\nwell-known vertex-degree-based topological indices are established. In\naddition, the trees extremal with respect to the first Banhatti-Sombor index on\ntrees and chemical trees are characterized, respectively.\n', 'Bounding the $k$-Steiner Wiener and Wiener-type indices of trees in\n  terms of eccentric sequence   The eccentric sequence of a connected graph $G$ is the nondecreasing sequence\nof the eccentricities of its vertices. The Wiener index of $G$ is the sum of\nthe distances between all unordered pairs of vertices of $G$. The unique trees\nthat minimise the Wiener index among all trees with a given eccentric sequence\nwere recently determined by the present authors. In this paper we show that\nthese results hold not only for the Wiener index, but for a large class of\ndistance-based topological indices which we term Wiener-type indices.\nParticular cases of this class include the hyper-Wiener index, the Harary\nindex, the generalised Wiener index $W^{\\lambda}$ for $\\lambda>0$ and $\\lambda\n<0$, and the reciprocal complementary Wiener index. Our results imply and unify\nknown bounds on these Wiener-type indices for trees of given order and\ndiameter.\n  We also present similar results for the $k$-Steiner Wiener index of trees\nwith a given eccentric sequence. The Steiner distance of a set $A\\subseteq\nV(G)$ is theminimum number of edges in a subtree of $G$ whose vertex set\ncontains $A$, and the $k$-Steiner Wiener index is the sum of distances of all\n$k$-element subsets of $V(G)$. As a corollary, we obtain a sharp lower bound on\nthe $k$-Steiner Wiener index of trees with given order and diameter, and\ndetermine in which cases the extremal tree is unique, thereby correcting an\nerror in the literature.\n']","[('index graphs', 0.5883747339248657), ('indices graphs', 0.566207230091095), ('index graph', 0.5447283983230591), ('index trees', 0.523859977722168), ('topological index', 0.49064576625823975), ('topological indices', 0.4878237545490265), ('wiener index', 0.46490350365638733), ('extremal graphs', 0.4599975645542145), ('index introduced', 0.43618759512901306), ('vertex degree', 0.42984816431999207)]"
123,123,212,123_networks coupled oscillators_phase synchronization_frequency synchronization_synchronization coupled,"['networks coupled oscillators', 'phase synchronization', 'frequency synchronization', 'synchronization coupled', 'coupled oscillators', 'oscillator networks', 'kuramoto models', 'coupled oscillator', 'global synchronization', 'phase oscillators']","['Model Reduction for the Kuramoto-Sakaguchi Model: The Importance of\n  Non-entrained Rogue Oscillators   The Kuramoto-Sakaguchi model for coupled phase oscillators with\nphase-frustration is often studied in the thermodynamic limit of infinitely\nmany oscillators. Here we extend a model reduction method based on collective\ncoordinates to capture the collective dynamics of finite size\nKuramoto-Sakaguchi models. We find that the inclusion of the effects of rogue\noscillators is essential to obtain an accurate description, in contrast to the\noriginal Kuramoto model where we show that their effects can be ignored. We\nfurther introduce a more accurate ansatz function to describe the shape of\nsynchronized oscillators. Our results from this extended collective coordinate\napproach reduce in the thermodynamic limit to the well-known mean-field\nconsistency relations. For finite networks we show that our model reduction\ndescribes the collective behavior accurately, reproducing the order parameter,\nthe mean frequency of the synchronized cluster, and the size of the cluster at\ngiven coupling strength, as well as the critical coupling strength for partial\nand for global synchronization.\n', 'On the Synchronization Analysis of a Strong Competition Kuramoto Model   When modeling the classical Kuramoto model, one of the key features is the\ntendency to synchronize. Accordingly, the most well-adopted choice of the\ncoupling function is the sine function. Due to the oddness of the sine\nfunction, the synchronized frequency would be the average of all the natural\nfrequencies. In this article, we study the synchronization behaviors of the\nKuramoto model with a pure competition coupling function. Namely, instead of\nthe sine function, we choose $\\max \\{0, \\sin \\theta \\}$ to be the coupling\nfunction. This indicates the relation of pure competition between oscillators.\nWe prove asymptotical phase synchronization for identical oscillators and\nasymptotical frequency synchronization for non-identical oscillators under\nreasonable sufficient conditions. In particular, under our sufficient\nconditions, the synchronized frequency is the maximal frequency of all the\nnatural frequencies. On the other hand, in the parameter regime which is out of\nthe scope of the analysis of our theorems, it is possible that the synchronized\nfrequency could be larger than the maximal frequency of the natural frequencies\nof all the oscillators. In this article, we also provide numerical experiments\nto support the analysis of our theorem and to demonstrate the aforementioned\nphenomenon.\n', ""Stability and Synchronization of Kuramoto Oscillators   Imagine a group of oscillators, each endowed with their own rhythm or\nfrequency, be it the ticking of a biological clock, the swing of a pendulum, or\nthe glowing of fireflies. While these individual oscillators may seem\nindependent of one another at first glance, the true magic lies in their\nability to influence and synchronize with one another, like a group of\nfireflies glowing in unison.\n  The Kuramoto model was motivated by this phenomenon of collective\nsynchronization, when a group of a large number of oscillators spontaneously\nlock to a common frequency, despite vast differences in their individual\nfrequencies. Inspired by Kuramoto's groundbreaking work in the 1970s, this\nmodel captures the essence of how interconnected systems, ranging from\nbiological networks to power grids, can achieve a state of synchronization.\n  This work aims to study the stability and synchronization of Kuramoto\noscillators, starting off with an introduction to Kuramoto Oscillators and it's\nbroader applications. We then at a graph theoretic formulation for the same and\nestablish various criterion for the stability, synchronization of Kuramoto\nOscillators. Finally, we broadly analyze and experiment with various physical\nsystems that tend to behave like Kuramoto oscillators followed by further\nsimulations.\n""]","[('networks coupled oscillators', 0.6169372797012329), ('phase synchronization', 0.6034865379333496), ('frequency synchronization', 0.5786298513412476), ('synchronization coupled', 0.5749124884605408), ('coupled oscillators', 0.5747511386871338), ('oscillator networks', 0.5597873330116272), ('kuramoto models', 0.5471497178077698), ('coupled oscillator', 0.5162031054496765), ('global synchronization', 0.5039744973182678), ('phase oscillators', 0.4970850646495819)]"
124,124,209,124_bounded treewidth_graph treewidth_treewidth graph_free graphs bounded,"['bounded treewidth', 'graph treewidth', 'treewidth graph', 'free graphs bounded', 'hereditary graph classes', 'minor free graphs', 'induced subgraphs', 'graphs bounded', 'forbidden induced subgraphs', 'bounded tree']","['Induced subgraphs and tree decompositions VI. Graphs with 2-cutsets   This paper continues a series of papers investigating the following question:\nwhich hereditary graph classes have bounded treewidth? We call a graph\n$t$-clean if it does not contain as an induced subgraph the complete graph\n$K_t$, the complete bipartite graph $K_{t, t}$, subdivisions of a $(t \\times\nt)$-wall, and line graphs of subdivisions of a $(t \\times t)$-wall. It is known\nthat graphs with bounded treewidth must be $t$-clean for some $t$; however, it\nis not true that every $t$-clean graph has bounded treewidth. In this paper, we\nshow that three types of cutsets, namely clique cutsets, 2-cutsets, and\n1-joins, interact well with treewidth and with each other, so graphs that are\ndecomposable by these cutsets into basic classes of bounded treewidth have\nbounded treewidth. We apply this result to two hereditary graph classes, the\nclass of ($ISK_4$, wheel)-free graphs and the class of graphs with no cycle\nwith a unique chord. These classes were previously studied and decomposition\ntheorems were obtained for both classes. Our main results are that $t$-clean\n($ISK_4$, wheel)-free graphs have bounded treewidth and that $t$-clean graphs\nwith no cycle with a unique chord have bounded treewidth.\n', 'Induced subgraphs and tree decompositions V. One neighbor in a hole   What are the unavoidable induced subgraphs of graphs with large treewidth? It\nis well-known that the answer must include a complete graph, a complete\nbipartite graph, all subdivisions of a wall and line graphs of all subdivisions\nof a wall (we refer to these graphs as the ""basic treewidth obstructions""). So\nit is natural to ask whether graphs excluding the basic treewidth obstructions\nas induced subgraphs have bounded treewidth. Sintiari and Trotignon answered\nthis question in the negative. Their counterexamples, the so-called ""layered\nwheels,"" contain wheels, where a wheel consists of a hole (i.e., an induced\ncycle of length at least four) along with a vertex with at least three\nneighbors in the hole. This leads one to ask whether graphs excluding wheels\nand the basic treewidth obstructions as induced subgraphs have bounded\ntreewidth. This also turns out to be false due to Davies\' recent example of\ngraphs with large treewidth, no wheels and and no basic treewidth obstructions\nas induced subgraphs. However, in Davies\' example there exist holes and\nvertices (outside of the hole) with two neighbors in them. Here we prove that a\nhole with a vertex with at least two neighbors in it is inevitable in graphs\nwith large treewidth and no basic obstruction. Our main result is that graphs\nin which every vertex has at most one neighbor in every hole (that does not\ncontain it) and with the basic treewidth obstructions excluded as induced\nsubgraphs have bounded treewidth.\n', 'Product structure of graph classes with bounded treewidth   We show that many graphs with bounded treewidth can be described as subgraphs\nof the strong product of a graph with smaller treewidth and a bounded-size\ncomplete graph. To this end, define the ""underlying treewidth"" of a graph class\n$\\mathcal{G}$ to be the minimum non-negative integer $c$ such that, for some\nfunction $f$, for every graph ${G \\in \\mathcal{G}}$ there is a graph $H$ with\n${\\text{tw}(H) \\leq c}$ such that $G$ is isomorphic to a subgraph of ${H\n\\boxtimes K_{f(\\text{tw}(G))}}$. We introduce disjointed coverings of graphs\nand show they determine the underlying treewidth of any graph class. Using this\nresult, we prove that the class of planar graphs has underlying treewidth 3;\nthe class of $K_{s,t}$-minor-free graphs has underlying treewidth $s$ (for ${t\n\\geq \\max\\{s,3\\}}$); and the class of $K_t$-minor-free graphs has underlying\ntreewidth ${t-2}$. In general, we prove that a monotone class has bounded\nunderlying treewidth if and only if it excludes some fixed topological minor.\nWe also study the underlying treewidth of graph classes defined by an excluded\nsubgraph or excluded induced subgraph. We show that the class of graphs with no\n$H$ subgraph has bounded underlying treewidth if and only if every component of\n$H$ is a subdivided star, and that the class of graphs with no induced $H$\nsubgraph has bounded underlying treewidth if and only if every component of $H$\nis a star.\n']","[('bounded treewidth', 0.6229264140129089), ('graph treewidth', 0.6192233562469482), ('treewidth graph', 0.5963194966316223), ('free graphs bounded', 0.5815856456756592), ('hereditary graph classes', 0.5745610594749451), ('minor free graphs', 0.5729621648788452), ('induced subgraphs', 0.5656404495239258), ('graphs bounded', 0.5631838440895081), ('forbidden induced subgraphs', 0.5583187341690063), ('bounded tree', 0.5488495826721191)]"
125,125,208,125_stochastic navier stokes_stochastic navier_navier stokes equations_navier stokes,"['stochastic navier stokes', 'stochastic navier', 'navier stokes equations', 'navier stokes', '3d navier stokes', 'solutions stochastic', 'navier stokes system', '2d navier stokes', 'three dimensional stochastic', 'stochastic forcing']","['Three-Dimensional stochastic Navier-Stokes equations with Markov\n  switching   A finite-state Markov chain is introduced in the noise terms of the\nthree-dimensional stochastic Navier-Stokes equations in order to allow for\ntransitions between two types of multiplicative noises. We call such systems as\nstochastic Navier-Stokes equations with Markov switching. To solve such a\nsystem, a family of regularized stochastic systems is introduced. For each such\nregularized system, the existence of a unique strong solution (in the sense of\nstochastic analysis) is established by the method of martingale problems and\npathwise uniqueness. The regularization is removed in the limit by obtaining a\nweakly convergent sequence from the family of regularized solutions, and\nidentifying the limit as a solution of the three-dimensional stochastic\nNavier-Stokes equation with Markov switching.\n', ""Convergence of the stochastic Navier-Stokes-$\\alpha$ solutions toward\n  the stochastic Navier-Stokes solutions   Loosely speaking, the Navier-Stokes-$\\alpha$ model and the Navier-Stokes\nequations differ by a spatial filtration parametrized by a scale denoted\n$\\alpha$. Starting from a strong two-dimensional solution to the\nNavier-Stokes-$\\alpha$ model driven by a multiplicative noise, we demonstrate\nthat it generates a strong solution to the stochastic Navier-Stokes equations\nunder the condition $\\alpha$ goes to 0. The initially introduced probability\nspace and the Wiener process are maintained throughout the investigation,\nthanks to a local monotonicity property that abolishes the use of Skorokhod's\ntheorem. High spatial regularity a priori estimates for the fluid velocity\nvector field are carried out within periodic boundary conditions.\n"", 'Enhanced dissipation for stochastic Navier-Stokes equations with\n  transport noise   The phenomenon of dissipation enhancement by transport noise is shown for\nstochastic 2D Navier-Stokes equations in velocity form. In the 3D case,\nsuppression of blow-up is proved for stochastic Navier-Stokes equations in\nvorticity form; in particular, quantitative estimate allows us to choose the\nparameters of noise, uniformly in initial vorticity bounded in $L^2$-norm, so\nthat global solutions exist with a large probability sufficiently close to 1.\n']","[('stochastic navier stokes', 0.7832273244857788), ('stochastic navier', 0.6682472825050354), ('navier stokes equations', 0.6008821129798889), ('navier stokes', 0.561150074005127), ('3d navier stokes', 0.553706705570221), ('solutions stochastic', 0.5391770005226135), ('navier stokes system', 0.5376842617988586), ('2d navier stokes', 0.5352694392204285), ('three dimensional stochastic', 0.49258241057395935), ('stochastic forcing', 0.4820088744163513)]"
126,126,208,126_semigroups_semigroups finite_ordered semigroups_inverse semigroups,"['semigroups', 'semigroups finite', 'ordered semigroups', 'inverse semigroups', 'semigroup', 'semigroup mathcal', 'inverse semigroup', 'semigroup partial', 'inverse monoids', 'matrix semigroups']","['On the semigroup of injective monoid endomorphisms of the monoid\n  $\\boldsymbol{B}_{\\omega}^{\\mathscr{F}^3}$ with a three element family\n  $\\mathscr{F}^3$ of inductive nonempty subsets of $\\omega$   We describe injective monoid endomorphisms of the semigroup\n$\\boldsymbol{B}_{\\omega}^{\\mathscr{F}^3}$ with a three element family\n$\\mathscr{F}^3$ of inductive nonempty subsets of $\\omega$. Also, we show that\nthe monoid $\\boldsymbol{End}_*^1(\\boldsymbol{B}_{\\omega}^{\\mathscr{F}})$ of all\ninjective endomorphisms of the semigroup\n$\\boldsymbol{B}_{\\omega}^{\\mathscr{F}^3}$ is isomorphic to the multiplicative\nsemigroup of positive integers.\n', ""On the semigroup of monoid endomorphisms of the semigroup\n  $\\boldsymbol{B}_{\\omega}^{\\mathscr{F}}$ with a two-element family\n  $\\mathscr{F}$ of inductive nonempty subsets of $\\omega$   We study the semigroup of non-injective monoid endomorphisms of the semigroup\n$\\boldsymbol{B}_{\\omega}^{\\mathscr{F}}$ with a two-elements family\n$\\mathscr{F}$ of inductive nonempty subsets of $\\omega$. We describe the\nstructure of elements of the semigroup\n$\\boldsymbol{End}^*_0(\\boldsymbol{B}_{\\omega}^{\\mathscr{F}})$ of non-injective\nmonoid endomorphisms of the semigroup $\\boldsymbol{B}_{\\omega}^{\\mathscr{F}}$.\nIn particular we show that its subsemigroup\n$\\boldsymbol{End}^*(\\boldsymbol{B}_{\\omega}^{\\mathscr{F}})$ of non-injective\nnon-annihilating monoid endomorphisms of the semigroup\n$\\boldsymbol{B}_{\\omega}^{\\mathscr{F}}$ is isomorphic to the direct product of\nthe two-element left-zero semigroup and the multiplicative semigroup of\npositive integers and describe Green's relations on\n$\\boldsymbol{End}^*(\\boldsymbol{B}_{\\omega}^{\\mathscr{F}})$.\n"", ""On some generalization of the bicyclic monoid   We introduce an algebraic extension $\\boldsymbol{B}_{\\omega}^{\\mathscr{F}}$\nof the bicyclic monoid for an arbitrary $\\omega$-closed family $\\mathscr{F}$\nsubsets of $\\omega$ which generalizes the bicyclic monoid, the countable\nsemigroup of matrix units and some other combinatorial inverse semigroups. It\nis proved that $\\boldsymbol{B}_{\\omega}^{\\mathscr{F}}$ is a combinatorial\ninverse semigroup and Green's relations, the natural partial order on\n$\\boldsymbol{B}_{\\omega}^{\\mathscr{F}}$, and its set of idempotents are\ndescribed. We provide criteria of simplicity, $0$-simplicity, bisimplicity,\n$0$-bisimplicity of the semigroup $\\boldsymbol{B}_{\\omega}^{\\mathscr{F}}$ and\nwhen $\\boldsymbol{B}_{\\omega}^{\\mathscr{F}}$ has the identity, is isomorphic to\nthe bicyclic semigroup or the countable semigroup of matrix units.\n""]","[('semigroups', 0.5910272598266602), ('semigroups finite', 0.5616601705551147), ('ordered semigroups', 0.5550350546836853), ('inverse semigroups', 0.5534030199050903), ('semigroup', 0.5461874604225159), ('semigroup mathcal', 0.534157395362854), ('inverse semigroup', 0.509874165058136), ('semigroup partial', 0.5094262361526489), ('inverse monoids', 0.4837305247783661), ('matrix semigroups', 0.4748711884021759)]"
127,127,208,127_finite words_words length_binary words_word length,"['finite words', 'words length', 'binary words', 'word length', 'words binary', 'infinite words', 'palindromes', 'infinite word', 'palindrome', 'combinatorics words']","['Extensions and reductions of square-free words   A word is square-free if it does not contain a nonempty word of the form $XX$\nas a factor. A famous 1906 result of Thue asserts that there exist arbitrarily\nlong square-free words over a $3$-letter alphabet. We study square-free words\nwith additional properties involving single-letter deletions and extensions of\nwords.\n  A square-free word is steady if it remains square-free after deletion of any\nsingle letter. We prove that there exist infinitely many steady words over a\n$4$-letter alphabet. We also demonstrate that one may construct steady words of\nany length by picking letters from arbitrary alphabets of size $7$ assigned to\nthe positions of the constructed word. We conjecture that both bounds can be\nlowered to $4$, which is best possible.\n  In the opposite direction, we consider square-free words that remain\nsquare-free after insertion of a single (suitably chosen) letter at every\npossible position in the word. We call them bifurcate. We prove a somewhat\nsurprising fact, that over a fixed alphabet with at least three letters, every\nsteady word is bifurcate. We also consider families of bifurcate words\npossessing a natural tree structure. In particular, we prove that there exists\nan infinite tree of doubly infinite bifurcate words over alphabet of size $12$.\n', 'Some Remarks on Palindromic Periodicities   We say a finite word $x$ is a palindromic periodicity if there exist two\npalindromes $p$ and $s$ such that $|x| \\geq |ps|$ and $x$ is a prefix of the\nword $(ps)^\\omega = pspsps\\cdots$. In this paper we examine the palindromic\nperiodicities occurring in some classical infinite words, such as Sturmian\nwords, episturmian words, the Thue-Morse word, the period-doubling word, the\nRudin-Shapiro word, the paperfolding word, and the Tribonacci word, and prove a\nnumber of results about them. We also prove results about words with the\nsmallest number of palindromic periodicities.\n', 'On prefix palindromic length of automatic words   The prefix palindromic length $\\mathrm{PPL}_{\\mathbf{u}}(n)$ of an infinite\nword $\\mathbf{u}$ is the minimal number of concatenated palindromes needed to\nexpress the prefix of length $n$ of $\\mathbf{u}$. Since 2013, it is still\nunknown if $\\mathrm{PPL}_{\\mathbf{u}}(n)$ is unbounded for every aperiodic\ninfinite word $\\mathbf{u}$, even though this has been proven for almost all\naperiodic words. At the same time, the only well-known nontrivial infinite word\nfor which the function $\\mathrm{PPL}_{\\mathbf{u}}(n)$ has been precisely\ncomputed is the Thue-Morse word $\\mathbf{t}$. This word is $2$-automatic and,\npredictably, its function $\\mathrm{PPL}_{\\mathbf{t}}(n)$ is $2$-regular, but is\nthis the case for all automatic words?\n  In this paper, we prove that this function is $k$-regular for every\n$k$-automatic word containing only a finite number of palindromes. For two such\nwords, namely the paperfolding word and the Rudin-Shapiro word, we derive a\nformula for this function. Our computational experiments suggest that generally\nthis is not true: for the period-doubling word, the prefix palindromic length\ndoes not look $2$-regular, and for the Fibonacci word, it does not look\nFibonacci-regular. If proven, these results would give rare (if not first)\nexamples of a natural function of an automatic word which is not regular.\n']","[('finite words', 0.6182998418807983), ('words length', 0.5667690634727478), ('binary words', 0.5614867210388184), ('word length', 0.5305070281028748), ('words binary', 0.5266027450561523), ('infinite words', 0.5223904848098755), ('palindromes', 0.5020810961723328), ('infinite word', 0.4776669442653656), ('palindrome', 0.4766272306442261), ('combinatorics words', 0.47649142146110535)]"
128,128,207,128_efficient federated learning_learning federated learning_federated learning algorithms_optimization federated learning,"['efficient federated learning', 'learning federated learning', 'federated learning algorithms', 'optimization federated learning', 'federated learning via', 'federated learning', 'personalized federated learning', 'learning federated', 'federated learning framework', 'federated learning federated']","['Exploiting Shared Representations for Personalized Federated Learning   Deep neural networks have shown the ability to extract universal feature\nrepresentations from data such as images and text that have been useful for a\nvariety of learning tasks. However, the fruits of representation learning have\nyet to be fully-realized in federated settings. Although data in federated\nsettings is often non-i.i.d. across clients, the success of centralized deep\nlearning suggests that data often shares a global feature representation, while\nthe statistical heterogeneity across clients or tasks is concentrated in the\nlabels. Based on this intuition, we propose a novel federated learning\nframework and algorithm for learning a shared data representation across\nclients and unique local heads for each client. Our algorithm harnesses the\ndistributed computational power across clients to perform many local-updates\nwith respect to the low-dimensional local parameters for every update of the\nrepresentation. We prove that this method obtains linear convergence to the\nground-truth representation with near-optimal sample complexity in a linear\nsetting, demonstrating that it can efficiently reduce the problem dimension for\neach client. This result is of interest beyond federated learning to a broad\nclass of problems in which we aim to learn a shared low-dimensional\nrepresentation among data distributions, for example in meta-learning and\nmulti-task learning. Further, extensive experimental results show the empirical\nimprovement of our method over alternative personalized federated learning\napproaches in federated environments with heterogeneous data.\n', ""Efficient Distribution Similarity Identification in Clustered Federated\n  Learning via Principal Angles Between Client Data Subspaces   Clustered federated learning (FL) has been shown to produce promising results\nby grouping clients into clusters. This is especially effective in scenarios\nwhere separate groups of clients have significant differences in the\ndistributions of their local data. Existing clustered FL algorithms are\nessentially trying to group together clients with similar distributions so that\nclients in the same cluster can leverage each other's data to better perform\nfederated learning. However, prior clustered FL algorithms attempt to learn\nthese distribution similarities indirectly during training, which can be quite\ntime consuming as many rounds of federated learning may be required until the\nformation of clusters is stabilized. In this paper, we propose a new approach\nto federated learning that directly aims to efficiently identify distribution\nsimilarities among clients by analyzing the principal angles between the client\ndata subspaces. Each client applies a truncated singular value decomposition\n(SVD) step on its local data in a single-shot manner to derive a small set of\nprincipal vectors, which provides a signature that succinctly captures the main\ncharacteristics of the underlying distribution. This small set of principal\nvectors is provided to the server so that the server can directly identify\ndistribution similarities among the clients to form clusters. This is achieved\nby comparing the similarities of the principal angles between the client data\nsubspaces spanned by those principal vectors. The approach provides a simple,\nyet effective clustered FL framework that addresses a broad range of data\nheterogeneity issues beyond simpler forms of Non-IIDness like label skews. Our\nclustered FL approach also enables convergence guarantees for non-convex\nobjectives. Our code is available at https://github.com/MMorafah/PACFL.\n"", ""Federated Asymptotics: a model to compare federated learning algorithms   We propose an asymptotic framework to analyze the performance of\n(personalized) federated learning algorithms. In this new framework, we\nformulate federated learning as a multi-criterion objective, where the goal is\nto minimize each client's loss using information from all of the clients. We\nanalyze a linear regression model where, for a given client, we may\ntheoretically compare the performance of various algorithms in the\nhigh-dimensional asymptotic limit. This asymptotic multi-criterion approach\nnaturally models the high-dimensional, many-device nature of federated\nlearning. These tools make fairly precise predictions about the benefits of\npersonalization and information sharing in federated scenarios -- at least in\nour (stylized) model -- including that Federated Averaging with simple client\nfine-tuning achieves the same asymptotic risk as the more intricate\nmeta-learning and proximal-regularized approaches and outperforming Federated\nAveraging without personalization. We evaluate these predictions on federated\nversions of the EMNIST, CIFAR-100, Shakespeare, and Stack Overflow datasets,\nwhere the experiments corroborate the theoretical predictions, suggesting such\nframeworks may provide a useful guide to practical algorithmic development.\n""]","[('efficient federated learning', 0.8329651355743408), ('learning federated learning', 0.8149574995040894), ('federated learning algorithms', 0.8148489594459534), ('optimization federated learning', 0.8112525343894958), ('federated learning via', 0.78867506980896), ('federated learning', 0.7740342617034912), ('personalized federated learning', 0.7563639879226685), ('learning federated', 0.7470946311950684), ('federated learning framework', 0.746263861656189), ('federated learning federated', 0.7355530261993408)]"
129,129,202,129_finitely generated groups_finitely presented groups_free groups_products free groups,"['finitely generated groups', 'finitely presented groups', 'free groups', 'products free groups', 'groups free', 'generated groups', 'groups finitely', 'finitely generated group', 'solvable groups', 'finitely presented group']","['Groups with ET0L co-word problem   We study groups whose co-word problems are ET0L languages, which we call\ncoET0L groups, using an automaton based model due to van Leeuwen, and recently\nstudied by Bishop and Elder. In particular we prove a number of closure results\nfor the class of groups with co-word problems in a subclass of `special\' ET0L\nlanguages; that class of groups contains all groups that we know at the time of\nwriting to be co-ET0L, including all groups that were proved by Holt and\nR\\""over to be stack groups, and hence co-indexed. It includes virtually free\ngroups, bounded automata groups, and the Higman-Thompson groups, together with\ngroups constructed from those using finitely generated subgroups, finite\nextension, free and direct products, and by taking the restricted standard\nwreath product of a co-\\E group by a finitely generated virtually free top\ngroup.\n', ""Streaming word problems   We study deterministic and randomized streaming algorithms for word problems\nof finitely generated groups. For finitely generated linear groups, metabelian\ngroups and free solvable groups we show the existence of randomized streaming\nalgorithms with logarithmic space complexity for their word problems. We also\nshow that the class of finitely generated groups with a logspace randomized\nstreaming algorithm for the word problem is closed under several group\ntheoretical constructions: finite extensions, graph products and wreath\nproducts by free abelian groups. We contrast these results with several lower\nbound. An example of a finitely presented group, where the word problem has\nonly a linear space randomized streaming algorithm, is Thompson's group $F$.\nFinally, randomized streaming algorithms for subgroup membership problems in\nfree groups and direct products of free groups are studied.\n"", 'Dehn functions of subgroups of products of free groups. Part I: Uniform\n  upper bounds   Subgroups of direct products of finitely many finitely generated free groups\nform a natural class that plays an important role in geometric group theory.\nIts members include fundamental examples, such as the Stallings-Bieri groups.\nThis raises the problem of understanding their geometric invariants. We prove\nthat finitely presented subgroups of direct products of three free groups, as\nwell as subgroups of finiteness type $\\mathcal{F}_{n-1}$ in a direct product of\n$n$ free groups, have Dehn function bounded above by $N^9$. This gives a\npositive answer to a question of Dison within these important subclasses and\nprovides new insights in the context of Bridson\'s conjecture stating that\nfinitely presented subgroups of direct products of free groups have\npolynomially bounded Dehn function. To prove our results we generalise\ntechniques for ""pushing fillings"" into normal subgroups.\n']","[('finitely generated groups', 0.6426085829734802), ('finitely presented groups', 0.6334677934646606), ('free groups', 0.6194603443145752), ('products free groups', 0.6130813360214233), ('groups free', 0.6104738712310791), ('generated groups', 0.6072888374328613), ('groups finitely', 0.5955377221107483), ('finitely generated group', 0.5910731554031372), ('solvable groups', 0.5883920192718506), ('finitely presented group', 0.577272891998291)]"
130,130,201,130_fully nonlinear elliptic_regularity solutions_regularity fully nonlinear_nonlinear elliptic equations,"['fully nonlinear elliptic', 'regularity solutions', 'regularity fully nonlinear', 'nonlinear elliptic equations', 'degenerate elliptic equations', 'boundary regularity', 'nonlinear elliptic', 'regularity estimates', 'degenerate elliptic', 'elliptic problems']","['Sharp boundary and global regularity for degenerate fully nonlinear\n  elliptic equations   We obtain optimal boundary and global regularity estimates for viscosity\nsolutions of fully nonlinear elliptic equations whose ellipticity degenerates\nat the critical points of a given solution. We show that any solution is\n$C^{1,\\alpha}$ on the boundary of the domain, for an optimal and explicit\n$\\alpha$ given only in terms of the regularity of the boundary datum and the\nelliptic degeneracy degree, no matter how possibly low is the interior\nregularity for that class of equations. We also obtain sharp global estimates.\nOur findings are new even for model equations, involving only a degenerate\nLaplacian; all previous results of global nature give $C^{1,\\alpha}$ regularity\nonly for some small $\\alpha>0$.\n', 'C^{1,\\alpha}-regularity for a class of degenerate/singular fully\n  nonlinear elliptic equations   We establish an optimal C^{1,\\alpha}-regularity for viscosity solutions of\ndegenerate/singular fully nonlinear elliptic equations by finding minimal\nregularity requirements on the associated operator.\n', 'Regularity for solutions of fully nonlinear elliptic equations with\n  non-homogeneous degeneracy   We prove that viscosity solutions to fully nonlinear elliptic equations with\ndegeneracy of double phase type are locally $C^{1,\\gamma}$-regular.\n']","[('fully nonlinear elliptic', 0.6434824466705322), ('regularity solutions', 0.6411079168319702), ('regularity fully nonlinear', 0.6170555949211121), ('nonlinear elliptic equations', 0.6083025336265564), ('degenerate elliptic equations', 0.6061803102493286), ('boundary regularity', 0.6044937372207642), ('nonlinear elliptic', 0.5754162073135376), ('regularity estimates', 0.5587533712387085), ('degenerate elliptic', 0.5572906136512756), ('elliptic problems', 0.555152952671051)]"
131,131,200,131_fault tolerant quantum_codes quantum_quantum error correcting_quantum error correction,"['fault tolerant quantum', 'codes quantum', 'quantum error correcting', 'quantum error correction', 'quantum code', 'quantum codes', 'quantum computation', 'quantum computing', 'quantum error', 'tolerant quantum']","['Short Shor-style syndrome sequences   We optimize fault-tolerant quantum error correction to reduce the number of\nsyndrome bit measurements. Speeding up error correction will also speed up an\nencoded quantum computation, and should reduce its effective error rate. We\ngive both code-specific and general methods, using a variety of techniques and\nin a variety of settings. We design new quantum error-correcting codes\nspecifically for efficient error correction, e.g., allowing single-shot error\ncorrection. For codes with multiple logical qubits, we give methods for\ncombining error correction with partial logical measurements. There are\ntradeoffs in choosing a code and error-correction technique. While to date most\nwork has concentrated on optimizing the syndrome-extraction procedure, we show\nthat there are also substantial benefits to optimizing how the measured\nsyndromes are chosen and used. As an example, we design single-shot measurement\nsequences for fault-tolerant quantum error correction with the 16-qubit\nextended Hamming code. Our scheme uses 10 syndrome bit measurements, compared\nto 40 measurements with the Shor scheme. We design single-shot logical\nmeasurements as well: any logical Z measurement can be made together with\nfault-tolerant error correction using only 11 measurements. For comparison,\nusing the Shor scheme a basic implementation of such a non-destructive logical\nmeasurement uses 63 measurements. We also offer ten open problems, the\nsolutions of which could lead to substantial improvements of fault-tolerant\nerror correction.\n', 'Quantum Error Correction near the Coding Theoretical Bound   Recent advancements in quantum computing have led to the realization of\nsystems comprising tens of reliable logical qubits, constructed from thousands\nof noisy physical qubits. However, many of the critical applications that\nquantum computers aim to solve require quantum computations involving millions\nor more logical qubits. This necessitates highly efficient quantum error\ncorrection capable of handling large numbers of logical qubits. Classical error\ncorrection theory is well-developed, with low-density parity-check (LDPC) codes\nachieving performance limits by encoding large classical bits. Despite more\nthan two decades of effort, no efficiently decodable quantum error-correcting\ncode that approaches the hashing bound, which is a fundamental lower bound on\nquantum capacity, had been discovered. Here, we present quantum\nerror-correcting codes constructed from classical LDPC codes that approach the\nhashing bound while maintaining linear computational complexity in the number\nof physical qubits. This result establishes a pathway toward realizing\nlarge-scale, fault-tolerant quantum computers. By integrating our quantum error\ncorrection scheme with devices capable of managing vast numbers of qubits, the\nprospect of solving critical real-world problems through quantum computation is\nbrought significantly closer.\n', 'Beyond single-shot fault-tolerant quantum error correction   Extensive quantum error correction is necessary in order to perform a useful\ncomputation on a noisy quantum computer. Moreover, quantum error correction\nmust be implemented based on imperfect parity check measurements that may\nreturn incorrect outcomes or inject additional faults into the qubits. To\nachieve fault-tolerant error correction, Shor proposed to repeat the sequence\nof parity check measurements until the same outcome is observed sufficiently\nmany times. Then, one can use this information to perform error correction. A\nbasic implementation of this fault tolerance strategy requires $\\Omega(r d^2)$\nparity check measurements for a distance-d code defined by r parity checks. For\nsome specific highly structured quantum codes, Bombin has shown that\nsingle-shot fault-tolerant quantum error correction is possible using only r\nmeasurements. In this work, we demonstrate that fault-tolerant quantum error\ncorrection can be achieved using $O(d \\log(d))$ measurements for any code with\ndistance $d \\geq \\Omega(n^\\alpha)$ for some constant $\\alpha > 0$. Moreover, we\nprove the existence of a sub-single-shot fault-tolerant quantum error\ncorrection scheme using fewer than r measurements. In some cases, the number of\nparity check measurements required for fault-tolerant quantum error correction\nis exponentially smaller than the number of parity checks defining the code.\n']","[('fault tolerant quantum', 0.6858571171760559), ('codes quantum', 0.6765713095664978), ('quantum error correcting', 0.6735944747924805), ('quantum error correction', 0.668530285358429), ('quantum code', 0.6678707599639893), ('quantum codes', 0.6531369090080261), ('quantum computation', 0.5817036032676697), ('quantum computing', 0.5807619094848633), ('quantum error', 0.5743989944458008), ('tolerant quantum', 0.5722541213035583)]"
132,132,200,132_teaching mathematics_mathematics education_undergraduate mathematics_mathematics,"['teaching mathematics', 'mathematics education', 'undergraduate mathematics', 'mathematics', 'mathematics science', 'teaching learning', 'mathematicians', 'teaching', 'mathematical', 'mathematical sciences']","[""Evaluating the Effect of Activity Based Method of Teaching Mathematics\n  on Nigerian Secondary School Students Achievement in Mathematics   Mathematics is a compulsory subject in Nigerian secondary schools, and the\nsubject plays an important role in the scientific and technological growth and\ndevelopment of the nation. A shortfall in the knowledge of the students in\nMathematics means that the goal may not be realized, hence the need to improve\nteaching methods for solving the problem of poor performance in the subject.\nThis study evaluated the effect of the activity-based teaching method on the\nstudents' achievement in secondary school Mathematics. The design of the study\nwas a quasi-experimental pretest-posttest research design using intact classes.\nFinding revealed that there was a significant difference in the Mathematics\nperformance between the posttest mean scores of the students who were exposed\nto activity-based teaching methods (experimental) and those that were taught\nwith lecture method (control) groups after controlling for the effect of the\npre-test on Mathematics scores. The paper recommends among others that\nsecondary school Mathematics teachers should be trained and retrained to update\ntheir knowledge in the use of activity-based teaching for making the teaching\nand learning of Mathematics more interesting and rewarding.\n"", ""Challenges in teaching Real Analysis classes at the University of PGRI,\n  South Sumatra, Indonesia   This paper discusses our experiences and challenges in teaching advanced\nundergraduate Real Analysis classes for Mathematics Education students at the\nUniversity of PGRI (Persatuan Guru Republik Indonesia, Indonesian Teachers\nAssociation) Palembang, South Sumatra, Indonesia. We observe that the syllabus\ncontains topics with a high level of difficulty for the students who are\nspecialized in education and intend to teach mathematics at the secondary\nlevel. The conventional lecturing method is mainly implemented during the\nclass, with some possible variations of the method, including the Texas method\n(also known as Moore's method) and the small group guided discovery method. In\nparticular, the latter method has been implemented successfully for a Real\nAnalysis class at Dartmouth College, New Hampshire by Dumitra\\c{s}cu in 2006.\nAlthough it is a real challenge to apply a specific teaching method that will\nbe able to accommodate a large number of students, the existing teaching\nactivities can still be improved and a more effective method could be\nimplemented in the future. Furthermore, the curriculum contents should be\nadapted for an audience in Mathematics Education to equip them for their future\ncareer as mathematics teachers. Any constructive suggestions are welcome for\nthe improvement of our mathematics education system at the university as well\nas on the national scale.\n"", 'Applications of Teaching Secondary Mathematics in Undergraduate\n  Mathematics Courses   Robust preparation of future secondary mathematics teachers requires\nattention to the acquisition of mathematical knowledge for teaching. Many\nfuture teachers learn mathematics content primarily through mathematics major\ncourses that are taught by mathematicians who do not specialize in teacher\npreparation. How can mathematics education researchers assist mathematicians in\nmaking explicit connections between the content of undergraduate mathematics\ncourses and the content of secondary mathematics? We present an articulation of\nfive types of connections that can be used in secondary mathematics teacher\npreparation and give examples of question prompts that mathematicians can use\nas applications of teaching secondary mathematics in undergraduate mathematics\ncourses.\n']","[('teaching mathematics', 0.786462128162384), ('mathematics education', 0.7539025545120239), ('undergraduate mathematics', 0.6323861479759216), ('mathematics', 0.5946608781814575), ('mathematics science', 0.5770773887634277), ('teaching learning', 0.5614216327667236), ('mathematicians', 0.5309132933616638), ('teaching', 0.5085413455963135), ('mathematical', 0.5012674927711487), ('mathematical sciences', 0.4960803687572479)]"
133,133,198,133_finsler manifolds_finsler metrics_finsler manifold_finsler metric,"['finsler manifolds', 'finsler metrics', 'finsler manifold', 'finsler metric', 'finsler geometry', 'finsler structure', 'finslerian', 'lorentz finsler', 'reversible finsler', 'finsler']","[""Finsler Geometry, Spacetime & Gravity -- From Metrizability of Berwald\n  Spaces to Exact Vacuum Solutions in Finsler Gravity   This PhD dissertation covers a range of topics in Finsler geometry and\nFinsler gravity, most notably: (i) the characterization of Berwald spaces, (ii)\npseudo-Riemann (non-)metrizability of Berwald spaces, (iii)\n$(\\alpha,\\beta)$-metrics, (iv) exact solutions to Pfeifer and Wohlfarth's\nvacuum field equation in Finsler gravity, and (v) Finsler gravitational waves\nand their observational signature. An extended abstract can be found in the\ndissertation itself.\n"", 'Special Finsler spaces admitting a semi-concurrent vector field   The main objective of this paper is to study semi-concurrent vector fields on\na Finsler manifold. We show that the quasi-$C$-reducible Finsler space,\n$C3$-like Finsler space, $C^{h}$-recurrent Finsler space, and $P2$-like Finsler\nspace are equivalent to Riemannian if they admit a semi-concurrent vector\nfield. Further, we prove the necessary and sufficient condition for a Finsler\nspace satisfying $C$-conformal condition to become Riemannian.\n', 'On almost rational Finsler metrics   We study a special class of Finsler metrics which we refer to as Almost\nRational Finsler metrics (shortly, AR-Finsler metrics). We give necessary and\nsufficient conditions for an AR-Finsler manifold $(M,F)$ to be Riemannian. The\nrationality of the associated geometric objects such as Cartan torsion,\ngeodesic spray, Landsberg curvature, $S$-curvature, etc is investigated. We\nprove for a particular subset of AR-Finsler metrics that if $F$ has isotropic\n$S$-curvature, then its $S$-curvature identically vanishes. Further, if $F$ has\nisotropic mean Landsberg curvature, then it is weakly Landsberg. Also, if $F$\nis an Einstein metric, then it is Ricci-flat. Moreover, we show that Randers\nmetric can not be AR-Finsler metric. Finally, we provide some examples of\nAR-Finsler metrics and introduce a new Finsler metric which is called an\nextended $m$-th root metric. We show under what conditions an extended $m$-th\nroot metric is AR-Finsler metric and study its generalized Kropina change.\n']","[('finsler manifolds', 0.7738720178604126), ('finsler metrics', 0.7692248225212097), ('finsler manifold', 0.7523678541183472), ('finsler metric', 0.7421084642410278), ('finsler geometry', 0.7180613279342651), ('finsler structure', 0.6840816736221313), ('finslerian', 0.6136991381645203), ('lorentz finsler', 0.6048964262008667), ('reversible finsler', 0.5446584224700928), ('finsler', 0.5188799500465393)]"
134,134,197,134_isolated singularities_non isolated singularities_hypersurface singularities_isolated singularity,"['isolated singularities', 'non isolated singularities', 'hypersurface singularities', 'isolated singularity', 'intersection singularities', 'complete intersection singularities', 'hypersurface singularity', 'normal surface singularities', 'surface singularities', 'singularities']","['Morse numbers of function germs with isolated singularities   A set of Morse numbers is associated to a holomorphic function germ with\nstratified isolated singularity, extending the classical Milnor number to the\nsetting of a singular base space.\n', 'Milnor-Hamm sphere fibrations and the equivalence problem   We introduce the sphere fibration for real map germs with radial discriminant\nand we address the problem of its equivalence with the Milnor-Hamm tube\nfibration. Under natural conditions, we prove the existence of open book\nstructures with singularities and solve the equivalence problem.\n', 'Uniform stable radius and Milnor number for non-degenerate isolated\n  complete intersection singularities   We prove that for two germs of analytic mappings $f,g\\colon (\\mathbb{C}^n,0)\n\\rightarrow (\\mathbb{C}^p,0)$ with the same Newton polyhedra which are\n(Khovanskii) non-degenerate and their zero sets are complete intersections with\nisolated singularity at the origin, there is a piecewise analytic family\n$\\{f_t\\}$ of analytic maps with $f_0=f, f_1=g$ which has a so-called {\\it\nuniform stable radius for the Milnor fibration}. As a corollary, we show that\ntheir Milnor numbers are equal. Also, a formula for the Milnor number is given\nin terms of the Newton polyhedra of the component functions. This is a\ngeneralization of the result by C. Bivia-Ausina. Consequently, we obtain that\nthe Milnor number of a non-degenerate isolated complete intersection\nsingularity is an invariance of Newton boundaries.\n']","[('isolated singularities', 0.6224828958511353), ('non isolated singularities', 0.6172122955322266), ('hypersurface singularities', 0.5828645825386047), ('isolated singularity', 0.5769202709197998), ('intersection singularities', 0.5704389810562134), ('complete intersection singularities', 0.5702103972434998), ('hypersurface singularity', 0.5586485862731934), ('normal surface singularities', 0.5556958317756653), ('surface singularities', 0.540940523147583), ('singularities', 0.524422287940979)]"
135,135,194,135_numerical methods stochastic_stochastic differential equations_euler maruyama scheme_drift diffusion coefficients,"['numerical methods stochastic', 'stochastic differential equations', 'euler maruyama scheme', 'drift diffusion coefficients', 'approximation stochastic', 'nonlinear stochastic differential', 'stochastic differential', 'differential equations sdes', 'drift diffusion', 'discontinuous drift']","['Tamed Euler-Maruyama method for SDEs with non-globally Lipschitz drift\n  and multiplicative noise   Consider the following stochastic differential equation driven by\nmultiplicative noise on $\\mathbb{R}^d$ with a superlinearly growing drift\ncoefficient, \\begin{align*}\n  \\mathrm{d} X_t = b (X_t) \\, \\mathrm{d} t + \\sigma (X_t) \\, \\mathrm{d} B_t.\n\\end{align*} It is known that the corresponding explicit Euler schemes may not\nconverge. In this article, we analyze an explicit and easily implementable\nnumerical method for approximating such a stochastic differential equation,\ni.e. its tamed Euler-Maruyama approximation. Under partial dissipation\nconditions ensuring the ergodicity, we obtain the uniform-in-time convergence\nrates of the tamed Euler-Maruyama process under $L^{1}$-Wasserstein distance\nand total variation distance.\n', ""On the performance of the Euler-Maruyama scheme for multidimensional\n  SDEs with discontinuous drift coefficient   We study strong approximation of $d$-dimensional stochastic differential\nequations (SDEs) with a discontinuous drift coefficient. More precisely, we\nessentially assume that the drift coefficient is piecewise Lipschitz continuous\nwith an exceptional set $\\Theta\\subset \\mathbb{R}^d$ that is an orientable\n$C^4$-hypersurface of positive reach, the diffusion coefficient is assumed to\nbe Lipschitz continuous and, in a neighborhood of $\\Theta$, both coefficients\nare bounded and the diffusion coefficient has a non-degenerate portion\northogonal to $\\Theta$.\n  In recent years, a number of results have been proven in the literature for\nstrong approximation of such SDEs and, in particular, the performance of the\nEuler-Maruyama scheme was studied. For $d=1$ and finite $\\Theta$ it was shown\nthat the Euler-Maruyama scheme achieves an $L_p$-error rate of at least $1/2$\nfor all $p\\geq 1$ as in the classical case of Lipschitz continuous\ncoefficients. For $d>1$, it was only known so far, that the Euler-Maruyama\nscheme achieves an $L_2$-error rate of at least $1/4-$ if, additionally, the\ncoefficients $\\mu$ and $\\sigma$ are globally bounded.\n  In this article, we prove that in the above setting the Euler-Maruyama scheme\nin fact achieves an $L_{p}$-error rate of at least $1/2-$ for all\n$d\\in\\mathbb{N}$ and all $p\\geq 1$. The proof of this result is based on the\nwell-known approach of transforming such an SDE into an SDE with globally\nLipschitz continuous coefficients, a new It\\^{o} formula for a class of\nfunctions which are not globally $C^2$ and a detailed analysis of the expected\ntotal time that the actual position of the time-continuous Euler-Maruyama\nscheme and its position at the preceding time point on the underlying grid are\non 'different sides' of the hypersurface $\\Theta$.\n"", 'The Euler-Maruyama Scheme for SDEs with Irregular Drift: Convergence\n  Rates via Reduction to a Quadrature Problem   We study the strong convergence order of the Euler-Maruyama scheme for scalar\nstochastic differential equations with additive noise and irregular drift. We\nprovide a general framework for the error analysis by reducing it to a weighted\nquadrature problem for irregular functions of Brownian motion. Assuming\nSobolev-Slobodeckij-type regularity of order $\\kappa \\in (0,1)$ for the\nnon-smooth part of the drift, our analysis of the quadrature problem yields the\nconvergence order $\\min\\{3/4,(1+\\kappa)/2\\}-\\epsilon$ for the equidistant\nEuler-Maruyama scheme (for arbitrarily small $\\epsilon>0$). The cut-off of the\nconvergence order at $3/4$ can be overcome by using a suitable non-equidistant\ndiscretization, which yields the strong convergence order of\n$(1+\\kappa)/2-\\epsilon$ for the corresponding Euler-Maruyama scheme.\n']","[('numerical methods stochastic', 0.6422250866889954), ('stochastic differential equations', 0.6101545691490173), ('euler maruyama scheme', 0.5575408339500427), ('drift diffusion coefficients', 0.5565283298492432), ('approximation stochastic', 0.5551060438156128), ('nonlinear stochastic differential', 0.5526400208473206), ('stochastic differential', 0.5493524074554443), ('differential equations sdes', 0.5492722988128662), ('drift diffusion', 0.5234386324882507), ('discontinuous drift', 0.48455876111984253)]"
136,136,194,136_iwasawa theory_iwasawa invariants_hilbert modular forms_modular forms,"['iwasawa theory', 'iwasawa invariants', 'hilbert modular forms', 'modular forms', 'conjecture adic', 'conjecture modular', 'bloch kato conjecture', 'modular form', 'rankin selberg', 'hilbert modular']","['Asai-Flach classes, p-adic L-functions and the Bloch-Kato conjecture for\n  GO(4)   We prove the Bloch-Kato conjecture for critical values of Asai L-functions of\np-ordinary Hilbert modular forms over quadratic fields (with p split); and one\ninclusion in the Iwasawa main conjecture for these L-functions (up to a power\nof p). Along the way, we also prove a version of the p-adic Eichler-Shimura\ncomparison isomorphism for Hida families of Hilbert modular forms.\n', 'Iwasawa theory of twists of elliptic modular forms over imaginary\n  quadratic fields at inert primes   Our primary goal in this article is to study the Iwasawa theory for\nsemi-ordinary families of automorphic forms on\n$\\mathrm{GL}_2\\times\\mathrm{Res}_{K/\\mathbb{Q}}\\mathrm{GL}_1$, where $K$ is an\nimaginary quadratic field where the prime $p$ is inert. We prove divisibility\nresults towards Iwasawa main conjectures in this context, utilizing the\noptimized signed factorization procedure for Perrin-Riou functionals and\nBeilinson--Flach elements for a family of Rankin--Selberg products of\n$p$-ordinary forms with a fixed $p$-non-ordinary modular form. The optimality\nenables an effective control on the $\\mu$-invariants of Selmer groups and\n$p$-adic $L$-functions as the modular forms vary in families, which is crucial\nfor our patching argument to establish one divisibility in an Iwasawa main\nconjecture in three variables.\n', 'Iwasawa Main Conjecture for Rankin-Selberg $p$-adic $L$-functions:\n  Non-Ordinary Case   In this paper we prove that the $p$-adic $L$-function that interpolates the\nRankin-Selberg product of a general weight two modular form which is unramified\nand non-ordinary at $p$, and an ordinary CM form of higher weight contains the\ncharacteristic ideal of the corresponding Selmer group. This is one\ndivisibility of the Iwasawa-Greenberg main conjecture for the $p$-adic\n$L$-function. This generalizes an earlier work of the author to the\nnon-ordinary case. The result of this paper plays a crucial role in the proof\nof Iwasawa main conjecture and refined Birch-Swinnerton-Dyer formula for\nsupersingular elliptic curves.\n']","[('iwasawa theory', 0.5831080079078674), ('iwasawa invariants', 0.5651700496673584), ('hilbert modular forms', 0.564480721950531), ('modular forms', 0.5546868443489075), ('conjecture adic', 0.5244753360748291), ('conjecture modular', 0.5106748938560486), ('bloch kato conjecture', 0.4927351474761963), ('modular form', 0.48735758662223816), ('rankin selberg', 0.4683551788330078), ('hilbert modular', 0.4583769142627716)]"
137,137,193,137_graphs finite groups_graph finite group_graphs groups_graph group,"['graphs finite groups', 'graph finite group', 'graphs groups', 'graph group', 'power graphs', 'group graph', 'power graph', 'graphs finite', 'finite nilpotent groups', 'nilpotent groups']","['On connectivity, domination number and spectral radius of the proper\n  enhanced power graphs of finite nilpotent groups   For a group $G,$ the enhanced power graph of $G$ is a graph with vertex set\n$G$ in which two distinct elements $x, y$ are adjacent if and only if there\nexists an element $w$ in $G$ such that both $x$ and $y$ are powers of $w.$ The\nproper enhanced power graph is the induced subgraph of the enhanced power graph\non the set $G \\setminus S,$ where $S$ is the set of dominating vertices of the\nenhanced power graph. In this paper, we first characterize the dominating\nvertices of enhanced power graph of any finite nilpotent group. Thereafter, we\nclassify all nilpotent groups $G$ such that the proper enhanced power graphs\nare connected and find out their diameter. We also explicitly find out the\ndomination number of proper enhanced power graphs of finite nilpotent groups.\nFinally, we determine the multiplicity of the Laplacian spectral radius of the\nenhanced power graphs of nilpotent groups.\n', 'Nilpotent groups whose Difference graphs have positive genus   The power graph of a finite group $G$ is a simple undirected graph with\nvertex set $G$ and two vertices are adjacent if one is a power of the other.\nThe enhanced power graph of a finite group $G$ is a simple undirected graph\nwhose vertex set is the group $G$ and two vertices $a$ and $b$ are adjacent if\nthere exists $c \\in G$ such that both $a$ and $b$ are powers of $c$. In this\npaper, we study the difference graph $\\mathcal{D}(G)$ of a finite group $G$\nwhich is the difference of the enhanced power graph and the power graph of $G$\nwith all isolated vertices removed. We characterize all the finite nilpotent\ngroups $G$ such that the genus (or cross-cap) of the difference graph\n$\\mathcal{D}(G)$ is at most $2$.\n', 'An exact enumeration of vertex connectivity of the enhanced power graphs\n  of finite nilpotent groups   The enhanced power graph of a group $G$ is a graph with vertex set $G,$ where\ntwo distinct vertices $x$ and $y$ are adjacent if and only if there exists an\nelement $w$ in $G$ such that both $x$ and $y$ are powers of $w.$ In this paper,\nwe determine the vertex connectivity of the enhanced power graph of any finite\nnilpotent group.\n']","[('graphs finite groups', 0.715557336807251), ('graph finite group', 0.6863375306129456), ('graphs groups', 0.6746506094932556), ('graph group', 0.6218200922012329), ('power graphs', 0.6159515976905823), ('group graph', 0.5747502446174622), ('power graph', 0.56300950050354), ('graphs finite', 0.5402467846870422), ('finite nilpotent groups', 0.5311326384544373), ('nilpotent groups', 0.5154989957809448)]"
138,138,192,138_holomorphic foliations_singular foliation_foliations mathcal_foliations,"['holomorphic foliations', 'singular foliation', 'foliations mathcal', 'foliations', 'foliation mathcal', 'dimensional foliation', 'foliation mathbb', 'foliation', 'one holomorphic', 'singularities holomorphic']","['Unlikely intersections of codimension one foliations We study families of singular holomorphic foliations on complex projective manifolds whose total intersection defines a foliation of unexpectedly low codimension.', ""A brief introduction on residue theory of holomorphic foliations   This is a survey paper dealing with holomorphic foliations, with emphasis on\nresidue theory and its applications. We start recalling the definition of\nholomorphic foliations as a subsheaf of the tangent sheaf of a manifold. The\ntheory of Characteristic Classes of vector bundles is approached from this\nperspective. We define Chern classes of holomorphic foliations using the\nChern-Weil theory and we remark that the Baum-Bott residue is a great tool that\nhelp us to classify some foliations. We present throughout the survey several\nrecent results and advances in residue theory. We finish by presenting some\napplications of residues to solve for example the Poincar\\'e problem and the\nexistence of minimal sets for foliations.\n"", 'Extensions and restrictions of holomorphic foliations   We prove an extension criterion for codimension one foliations on projective\nhypersurfaces based on the degree of the foliation and the degree of the\nhypersurface, and we ensure, in some instances, an isomorphism between the\ncorresponding spaces of foliations. We also present some examples of foliations\nthat do not satisfy the extension criterion and do not extend.\n']","[('holomorphic foliations', 0.8408181071281433), ('singular foliation', 0.6878252029418945), ('foliations mathcal', 0.6488990187644958), ('foliations', 0.6362702250480652), ('foliation mathcal', 0.6199266314506531), ('dimensional foliation', 0.6166741251945496), ('foliation mathbb', 0.6048486232757568), ('foliation', 0.5876506567001343), ('one holomorphic', 0.5231415033340454), ('singularities holomorphic', 0.5182881951332092)]"
139,139,191,139_community detection_community structures_community structure_communities,"['community detection', 'community structures', 'community structure', 'communities', 'sparse networks', 'spectral clustering', 'stochastic block models', 'random graphs', 'information theoretic threshold', 'network analysis']","[""Robust recovery for stochastic block models, simplified and generalized   We study the problem of $\\textit{robust community recovery}$: efficiently\nrecovering communities in sparse stochastic block models in the presence of\nadversarial corruptions. In the absence of adversarial corruptions, there are\nefficient algorithms when the $\\textit{signal-to-noise ratio}$ exceeds the\n$\\textit{Kesten--Stigum (KS) threshold}$, widely believed to be the\ncomputational threshold for this problem. The question we study is: does the\ncomputational threshold for robust community recovery also lie at the KS\nthreshold? We answer this question affirmatively, providing an algorithm for\nrobust community recovery for arbitrary stochastic block models on any constant\nnumber of communities, generalizing the work of Ding, d'Orsi, Nasser & Steurer\non an efficient algorithm above the KS threshold in the case of $2$-community\nblock models.\n  There are three main ingredients to our work:\n  (i) The Bethe Hessian of the graph is defined as $H_G(t) \\triangleq\n(D_G-I)t^2 - A_Gt + I$ where $D_G$ is the diagonal matrix of degrees and $A_G$\nis the adjacency matrix. Empirical work suggested that the Bethe Hessian for\nthe stochastic block model has outlier eigenvectors corresponding to the\ncommunities right above the Kesten-Stigum threshold. We formally confirm the\nexistence of outlier eigenvalues for the Bethe Hessian, by explicitly\nconstructing outlier eigenvectors from the community vectors.\n  (ii) We develop an algorithm for a variant of robust PCA on sparse matrices.\nSpecifically, an algorithm to partially recover top eigenspaces from\nadversarially corrupted sparse matrices under mild delocalization constraints.\n  (iii) A rounding algorithm to turn vector assignments of vertices into a\ncommunity assignment, inspired by the algorithm of Charikar \\& Wirth\n\\cite{CW04} for $2$XOR.\n"", 'Exact Recovery of Community Detection in k-Community Gaussian Mixture\n  Model   We study the community detection problem on a Gaussian mixture model, in\nwhich vertices are divided into $k\\geq 2$ distinct communities. The major\ndifference in our model is that the intensities for Gaussian perturbations are\ndifferent for different entries in the observation matrix, and we do not assume\nthat every community has the same number of vertices. We explicitly find the\nthreshold for the exact recovery of the maximum likelihood estimation.\nApplications include the community detection on hypergraphs.\n', 'Pairwise Covariates-adjusted Block Model for Community Detection   One of the most fundamental problems in network study is community detection.\nThe stochastic block model (SBM) is a widely used model, for which various\nestimation methods have been developed with their community detection\nconsistency results unveiled. However, the SBM is restricted by the strong\nassumption that all nodes in the same community are stochastically equivalent,\nwhich may not be suitable for practical applications. We introduce a pairwise\ncovariates-adjusted stochastic block model (PCABM), a generalization of SBM\nthat incorporates pairwise covariate information. We study the maximum\nlikelihood estimates of the coefficients for the covariates as well as the\ncommunity assignments. It is shown that both the coefficient estimates of the\ncovariates and the community assignments are consistent under suitable sparsity\nconditions. Spectral clustering with adjustment (SCWA) is introduced to\nefficiently solve PCABM. Under certain conditions, we derive the error bound of\ncommunity detection under SCWA and show that it is community detection\nconsistent. In addition, we investigate model selection in terms of the number\nof communities and feature selection for the pairwise covariates, and propose\ntwo corresponding algorithms. PCABM compares favorably with the SBM or\ndegree-corrected stochastic block model (DCBM) under a wide range of simulated\nand real networks when covariate information is accessible.\n']","[('community detection', 0.7060063481330872), ('community structures', 0.5245562791824341), ('community structure', 0.517717719078064), ('communities', 0.4970037043094635), ('sparse networks', 0.4880691170692444), ('spectral clustering', 0.47725021839141846), ('stochastic block models', 0.4557701647281647), ('random graphs', 0.442865788936615), ('information theoretic threshold', 0.44198745489120483), ('network analysis', 0.44177329540252686)]"
140,140,189,140_multigrid solvers_algebraic multigrid methods_multigrid solver_multigrid methods,"['multigrid solvers', 'algebraic multigrid methods', 'multigrid solver', 'multigrid methods', 'multigrid preconditioner', 'grid methods', 'geometric multigrid', 'finite element discretizations', 'multigrid based', 'algebraic multigrid']","['Surface Multigrid via Intrinsic Prolongation   This paper introduces a novel geometric multigrid solver for unstructured\ncurved surfaces. Multigrid methods are highly efficient iterative methods for\nsolving systems of linear equations. Despite the success in solving problems\ndefined on structured domains, generalizing multigrid to unstructured curved\ndomains remains a challenging problem. The critical missing ingredient is a\nprolongation operator to transfer functions across different multigrid levels.\nWe propose a novel method for computing the prolongation for triangulated\nsurfaces based on intrinsic geometry, enabling an efficient geometric multigrid\nsolver for curved surfaces. Our surface multigrid solver achieves better\nconvergence than existing multigrid methods. Compared to direct solvers, our\nsolver is orders of magnitude faster. We evaluate our method on many geometry\nprocessing applications and a wide variety of complex shapes with and without\nboundaries. By simply replacing the direct solver, we upgrade existing\nalgorithms to interactive frame rates, and shift the computational bottleneck\naway from solving linear systems.\n', 'A Multigrid Preconditioner for Jacobian-free Newton-Krylov Methods   In this work, we propose a multigrid preconditioner for Jacobian-free\nNewton-Krylov (JFNK) methods. Our multigrid method does not require knowledge\nof the Jacobian at any level of the multigrid hierarchy. As it is common in\nstandard multigrid methods, the proposed method also relies on three building\nblocks: transfer operators, smoothers, and a coarse level solver. In addition\nto the restriction and prolongation operator, we also use a projection operator\nto transfer the current Newton iterate to a coarser level. The three-level\nChebyshev semi-iterative method is employed as a smoother, as it has good\nsmoothing properties and does not require the representation of the Jacobian\nmatrix. We replace the direct solver on the coarsest level with a matrix-free\nKrylov subspace method, thus giving rise to a truly Jacobian-free multigrid\npreconditioner. We will discuss all building blocks of our multigrid\npreconditioner in detail and demonstrate the robustness and the efficiency of\nthe proposed method using several numerical examples.\n', 'Hybrid multigrid methods for high-order discontinuous Galerkin\n  discretizations   The present work develops hybrid multigrid methods for high-order\ndiscontinuous Galerkin discretizations of elliptic problems. Fast matrix-free\noperator evaluation on tensor product elements is used to devise a\ncomputationally efficient PDE solver. The multigrid hierarchy exploits all\npossibilities of geometric, polynomial, and algebraic coarsening, targeting\nengineering applications on complex geometries. Additionally, a transfer from\ndiscontinuous to continuous function spaces is performed within the multigrid\nhierarchy. This does not only further reduce the problem size of the\ncoarse-grid problem, but also leads to a discretization most suitable for\nstate-of-the-art algebraic multigrid methods applied as coarse-grid solver. The\nrelevant design choices regarding the selection of optimal multigrid coarsening\nstrategies among the various possibilities are discussed with the metric of\ncomputational costs as the driving force for algorithmic selections. We find\nthat a transfer to a continuous function space at highest polynomial degree (or\non the finest mesh), followed by polynomial and geometric coarsening, shows the\nbest overall performance. The success of this particular multigrid strategy is\ndue to a significant reduction in iteration counts as compared to a transfer\nfrom discontinuous to continuous function spaces at lowest polynomial degree\n(or on the coarsest mesh). The coarsening strategy with transfer to a\ncontinuous function space on the finest level leads to a multigrid algorithm\nthat is robust with respect to the penalty parameter of the SIPG method.\nDetailed numerical investigations are conducted for a series of examples\nranging from academic test cases to more complex, practically relevant\ngeometries. Performance comparisons to state-of-the-art methods from the\nliterature demonstrate the versatility and computational efficiency of the\nproposed multigrid algorithms.\n']","[('multigrid solvers', 0.701389729976654), ('algebraic multigrid methods', 0.6846473217010498), ('multigrid solver', 0.662347137928009), ('multigrid methods', 0.6592667102813721), ('multigrid preconditioner', 0.6557677388191223), ('grid methods', 0.5651882290840149), ('geometric multigrid', 0.5601651668548584), ('finite element discretizations', 0.517833948135376), ('multigrid based', 0.5174821019172668), ('algebraic multigrid', 0.5127667784690857)]"
141,141,188,141_spin models_spin glass_spin interactions_step replica symmetry,"['spin models', 'spin glass', 'spin interactions', 'step replica symmetry', 'replica symmetry breaking', 'energy spin', 'spin glasses', 'replica symmetry', 'mean field spin', 'field spin']","['TAP variational principle for the constrained overlap multiple spherical\n  Sherrington-Kirkpatrick model   Spin glass models involving multiple replicas with constrained overlaps have\nbeen studied in [FPV92; PT07; Pan18a]. For the spherical versions of these\nmodels [Ko19; Ko20] showed that the limiting free energy is given by a Parisi\ntype minimization. In this work we show that for Sherrington-Kirkpatrick (i.e.\n2-spin) interactions, it can also be expressed in terms of a\nThouless-Andersson-Palmer (TAP) variational principle. This is only the second\nspin glass model where a mathematically rigorous TAP computation of the free\nenergy at all temperatures and external fields has been achieved. The\nvariational formula we derive here also confirms that the model is replica\nsymmetric, a fact which is natural but not obviously deducible from its Parisi\nformula.\n', 'On the Almeida-Thouless transition line in the Sherrington-Kirkpatrick\n  model with centered Gaussian external field   We study the phase transition of the free energy in the\nSherrington-Kirkpatrick mean-field spin glass model with centered Gaussian\nexternal field. We show that the corresponding Almeida-Thouless line is the\ncorrect transition curve that distinguishes between the replica symmetric and\nreplica symmetry breaking solutions in the Parisi formula.\n', 'Free Energy of the Quantum Sherrington-Kirkpatrick Spin-Glass Model with\n  Transverse Field   We consider the quantum Sherrington-Kirkpatrick (SK) spin-glass model with\ntransverse field and provide a formula for its free energy in the thermodynamic\nlimit, valid for all inverse temperatures $\\beta>0$. To characterize the free\nenergy, we use the path integral representation of the partition function and\napproximate the model by a sequence of finite-dimensional vector-spin glasses\nwith $\\mathbb{R}^d$-valued spins. This enables us to use results of Panchenko\nwho generalized in \\cite{Pan2,Pan3} the Parisi formula to classical vector-spin\nglasses. As a consequence, we can express the thermodynamic limit of the free\nenergy of the quantum SK model as the $d\\to\\infty$ limit of the free energies\nof the $d$-dimensional approximations of the model.\n']","[('spin models', 0.5612342953681946), ('spin glass', 0.5077273845672607), ('spin interactions', 0.47523075342178345), ('step replica symmetry', 0.46383532881736755), ('replica symmetry breaking', 0.4574061930179596), ('energy spin', 0.45054689049720764), ('spin glasses', 0.4433361887931824), ('replica symmetry', 0.4344150125980377), ('mean field spin', 0.4253738820552826), ('field spin', 0.4030223488807678)]"
142,142,187,142_class analytic functions_starlike functions_analytic functions_analytic functions unit,"['class analytic functions', 'starlike functions', 'analytic functions', 'analytic functions unit', 'univalent functions', 'class analytic', 'classes analytic', 'analytic', 'functions unit disk', 'functions associated']","['Coefficient bounds for starlike functions associated with Gregory\n  coefficients   It is of interest to know the sharp bounds of the Hankel determinant, Zalcman\nfunctionals, Fekete-Szeg$ \\ddot{o} $ inequality as a part of coefficient\nproblems for different classes of functions. Let $\\mathcal{H}$ be the class of\nfunctions $ f $ which are holomorphic in the open unit disk\n$\\mathbb{D}=\\{z\\in\\mathbb{C}: |z|<1\\}$ of the form\n  \\begin{align*}\n  f(z)=z+\\sum_{n=2}^{\\infty}a_nz^n\\; \\mbox{for}\\; z\\in\\mathbb{D}\n  \\end{align*}\n  and suppose that\n  \\begin{align*}\n  F_{f}(z):=\\log\\dfrac{f(z)}{z}=2\\sum_{n=1}^{\\infty}\\gamma_{n}(f)z^n, \\;\\;\nz\\in\\mathbb{D},\\;\\;\\log 1:=0,\n  \\end{align*}\n  where $ \\gamma_{n}(f) $ is the logarithmic coefficients. The second Hankel\ndeterminant of logarithmic coefficients $H_{2,1}(F_{f}/2)$ is defined as:\n$H_{2,1}(F_{f}/2) :=\\gamma_{1}\\gamma_{3} -\\gamma^2_{2}$, where $\\gamma_1,\n\\gamma_2,$ and $\\gamma_3$ are the first, second and third logarithmic\ncoefficients of functions belonging to the class $\\mathcal{S}$ of normalized\nunivalent functions. In this article, we first establish sharp inequalities\n$|H_{2,1}(F_{f}/2)|\\leq 1/64$ with logarithmic coefficients for the classes of\nstarlike functions associated with Gregory coefficients. In addition, we\nestablish the sharpness of Fekete-Szeg$ \\ddot{o} $ inequality, Zalcman\nfunctional and generalized Zalcman functional for the class starlike functions\nassociated with Gregory coefficients.\n', ""Theory of certain Non-Univalent Analytic functions   We investigate the non-univalent function's properties reminiscent of the\ntheory of univalent starlike functions. Let the analytic function\n$\\psi(z)=\\sum_{i=1}^{\\infty}A_i z^i$, $A_1\\neq0$ be univalent in the unit disk.\nNon-univalent functions may be found in the class $\\mathcal{F}(\\psi)$ of\nanalytic functions $f$ of the form $f(z)=z+\\sum_{k=2}^{\\infty}a_k z^k$\nsatisfying $({zf'(z)}/{f(z)}-1) \\prec \\psi(z)$. Such functions, like the Ma and\nMinda classes of starlike functions, also have nice geometric properties. For\nthese functions, growth and distortion theorems have been established. Further,\nwe obtain bounds for some sharp coefficient functionals and establish the Bohr\nand Rogosinki phenomenon for the class $\\mathcal{F}(\\psi)$. Non-analytic\nfunctions that share properties of analytic functions are known as\nPoly-analytic functions. Moreover, we compute Bohr and Rogosinski's radius for\nPoly-analytic functions with analytic counterparts in the class\n$\\mathcal{F}(\\psi)$ or classes of Ma-Minda starlike and convex functions.\n"", 'Starlikeness of Certain Non-Univalent Functions   We consider three classes of functions defined using the class $\\mathcal{P}$\nof all analytic functions $p(z)=1+cz+\\dotsb$ on the open unit disk having\npositive real part and study several radius problems for these classes. The\nfirst class consists of all normalized analytic functions $f$ with\n$f/g\\in\\mathcal{P}$ and $g/(zp)\\in\\mathcal{P}$ for some normalized analytic\nfunction $g$ and $p\\in \\mathcal{P}$. The second class is defined by replacing\nthe condition $f/g\\in\\mathcal{P}$ by $|(f/g)-1|<1$ while the other class\nconsists of normalized analytic functions $f$ with $f/(zp)\\in\\mathcal{P}$ for\nsome $p\\in \\mathcal{P}$. We have determined radii so that the functions in\nthese classes to belong to various subclasses of starlike functions. These\nsubclasses includes the classes of starlike functions of order $\\alpha$,\nparabolic starlike functions, as well as the classes of starlike functions\nassociated with lemniscate of Bernoulli, reverse lemniscate, sine function, a\nrational function, cardioid, lune, nephroid and modified sigmoid function.\n']","[('class analytic functions', 0.5706979632377625), ('starlike functions', 0.5496580004692078), ('analytic functions', 0.5114170908927917), ('analytic functions unit', 0.48569658398628235), ('univalent functions', 0.4773637652397156), ('class analytic', 0.4757828712463379), ('classes analytic', 0.41657498478889465), ('analytic', 0.38839611411094666), ('functions unit disk', 0.3600701689720154), ('functions associated', 0.31928524374961853)]"
143,143,186,143_sumsets_sum free sets_fold sumset_subset sums,"['sumsets', 'sum free sets', 'fold sumset', 'subset sums', 'additive number theory', 'sum elements', 'sumset', 'additive combinatorics', 'sums', 'a_1 a_2 ldots']","['Direct and Inverse Problems for Restricted Signed Sumsets -- I   Let $A=\\{a_{1},\\ldots,a_{k}\\}$ be a nonempty finite subset of an additive\nabelian group $G$. For a positive integer $h$, the $h$-fold signed sumset of\n$A$, denoted by $h_{\\pm}A$, is defined as $$h_{\\pm}A=\\left\\lbrace\n\\sum_{i=1}^{k} \\lambda_{i} a_{i}: \\lambda_{i} \\in \\{-h, \\ldots, 0, \\ldots, h\\}\n\\ \\text{for} \\ i= 1, 2, \\ldots, k \\ \\text{and} \\ \\sum_{i=1}^{k}\n\\left|\\lambda_{i} \\right| =h\\right\\rbrace,$$ and the restricted $h$-fold signed\nsumset of $A$, denoted by $h^{\\wedge}_{\\pm}A$, is defined as\n$$h^{\\wedge}_{\\pm}A=\\left\\lbrace \\sum_{i=1}^{k} \\lambda_{i} a_{i}: \\lambda_{i}\n\\in \\left\\lbrace -1, 0, 1\\right\\rbrace \\ \\text{for} \\ i= 1, 2, \\ldots, k \\\n\\text{and} \\ \\sum_{i=1}^{k} \\left|\\lambda_{i} \\right| = h\\right\\rbrace. $$ A\ndirect problem for the sumset $h^{\\wedge}_{\\pm}A$ is to find the optimal size\nof $h^{\\wedge}_{\\pm}A$ in terms of $h$ and $|A|$. An inverse problem for this\nsumset is to determine the structure of the underlying set $A$ when the sumset\n$h^{\\wedge}_{\\pm}A$ has optimal size. While some results are known for the\nsigned sumsets in finite abelian groups due to Bajnok and Matzke, not much is\nknown for the restricted $h$-fold signed sumset $h^{\\wedge}_{\\pm}A$ even in the\nadditive group of integers $\\Bbb Z$. In case of $G = \\Bbb Z$, Bhanja, Komatsu\nand Pandey studied these problems for the sumset $h^{\\wedge}_{\\pm}A$ for $h=2,\n3$, and $k$, and conjectured the direct and inverse results for $h \\geq 4$. In\nthis paper, we prove these conjectures completely for the sets of positive\nintegers. In a subsequent paper, we prove these conjectures for the sets of\nnonnegative integers.\n', 'Inverse problems for sumset sizes of finite sets of integers   Let $A$ be a finite set of integers and let $hA$ be its $h$-fold sumset. This\npaper investigates the sequence of sumset sizes $( |hA| )_{h=1}^{\\infty}$, the\nrelations between these sequences for affinely inequivalent sets $A$ and $B$,\nand the comparative growth rates and configurations of the sumset size\nsequences $( |hA| )_{h=1}^{\\infty}$ and $( |hA| )_{h=1}^{\\infty}$.\n', 'Direct and Inverse Problems for Restricted Signed Sumsets -- II   Let $A=\\{a_{1},\\ldots,a_{k}\\}$ be a nonempty finite subset of an additive\nabelian group $G$. For a positive integer $h$, the restricted $h$-fold signed\nsumset of $A$, denoted by $h^{\\wedge}_{\\pm}A$, is defined as\n$$h^{\\wedge}_{\\pm}A = \\left\\lbrace \\sum_{i=1}^{k} \\lambda_{i} a_{i}:\n\\lambda_{i} \\in \\left\\lbrace -1, 0, 1\\right\\rbrace \\ \\text{for} \\ i= 1, 2,\n\\ldots, k \\ \\text{and} \\ \\sum_{i=1}^{k} \\left|\\lambda_{i} \\right|\n=h\\right\\rbrace. $$ A direct problem for the restricted $h$-fold signed sumset\nis to find the optimal size of $h^{\\wedge}_{\\pm}A$ in terms of $h$ and $|A|$.\nAn inverse problem for this sumset is to determine the structure of the\nunderlying set $A$ when the sumset has optimal size. While the signed sumsets\n(which is defined differently compared to the restricted signed sumset) in\nfinite abelian groups has been investigated by Bajnok and Matzke, the\nrestricted $h$-fold signed sumset $h^{\\wedge}_{\\pm}A$ is not well studied even\nin the additive group of integers $\\Bbb Z$. Bhanja, Komatsu and Pandey studied\nthese problems for the restricted $h$-fold signed sumset for $h=2, 3$, and $k$,\nand conjectured some direct and inverse results for $h \\geq 4$. In a recent\npaper, Mistri and Prajapati proved these conjectures completely for the set of\npositive integers. In this paper, we prove these conjectures for the set of\nnonnegative integers, which settles all the conjectures completely.\n']","[('sumsets', 0.5231282711029053), ('sum free sets', 0.4712705612182617), ('fold sumset', 0.4705011248588562), ('subset sums', 0.4346328675746918), ('additive number theory', 0.38582274317741394), ('sum elements', 0.38224077224731445), ('sumset', 0.38025644421577454), ('additive combinatorics', 0.3689763844013214), ('sums', 0.3664957880973816), ('a_1 a_2 ldots', 0.34434762597084045)]"
144,144,186,144_otfs modulation_space otfs modulation_multiplexing ofdm_division multiplexing ofdm,"['otfs modulation', 'space otfs modulation', 'multiplexing ofdm', 'division multiplexing ofdm', 'delay doppler dd', 'frequency division multiplexing', 'ofdm', 'orthogonal frequency division', 'frequency space otfs', 'delay doppler']","[""Orthogonal Delay-Doppler Division Multiplexing Modulation   Inspired by the orthogonal time frequency space (OTFS) modulation, in this\npaper, we consider designing a multicarrier (MC) modulation on delay-Doppler\n(DD) plane, to couple the modulated signal with a doubly-selective channel\nhaving DD resolutions. A key challenge for the design of DD plane MC modulation\nis to investigate whether a realizable pulse orthogonal with respect to the DD\nplane's fine resolutions exists or not. To this end, we first indicate that a\nfeasible DD plane MC modulation is essentially a type of staggered multitone\nmodulation. Then, analogous to orthogonal frequency division multiplexing, we\npropose an orthogonal delay-Doppler division multiplexing (ODDM) modulation,\nand design the corresponding transmit pulse. Furthermore, we prove that the\nproposed transmit pulse is orthogonal with respect to the DD plane's\nresolutions and therefore a realizable DD plane orthogonal pulse does exist.\nThe orthogonality of this particular pulse significantly eases the derivation\nof the ODDM's DD domain channel input-output relation, and yields a channel\nmatrix with an elegant block-circulant-like structure. We demonstrate that the\nODDM outperforms the OTFS in terms of out-of-band emission and bit error rate,\nby achieving perfect coupling between the modulated signal and the DD channel.\n"", 'Orthogonal Time Frequency Space (OTFS) Modulation for Wireless\n  Communications   Orthogonal time frequency space (OTFS) modulation is a recently proposed\nmulti-carrier transmission scheme, which innovatively multiplexes the\ninformation symbols in the delay-Doppler (DD) domain instead of the\nconventional time-frequency (TF) domain. The DD domain symbol multiplexing\ngives rise to a direct interaction between the DD domain information symbols\nand DD domain channel responses, which are usually quasi-static, compact,\nseparable, and potentially sparse. Therefore, OTFS modulation enjoys appealing\nadvantages over the conventional orthogonal frequency-division multiplexing\n(OFDM) modulation for wireless communications. In this thesis, we investigate\nthe related subjects of OTFS modulation for wireless communications,\nspecifically focusing on its signal detection, performance analysis, and\napplications. These important aspects are discussed based on the review of the\nstate-of-the-art and a detailed derivation of OTFS modulation from the discrete\nZak transform (DZT). Finally, a summary of future research directions on OTFS\nmodulation are also provided.\n', 'On the Characterizations of OTFS Modulation over multipath Rapid Fading\n  Channel   Orthogonal time frequency space (OTFS) modulation has been confirmed to\nprovide significant performance advantages against Doppler in high-mobility\nscenarios. The core feature of OTFS is that the time-variant channel is\nconverted into a non-fading 2D channel in the delay-Doppler (DD) domain so that\nall symbols experience the same channel gain. In now available literature, the\nchannel is assumed to be quasi-static over an OTFS frame. As for more practical\nchannels, the input-output relation will be time-variant as the environment or\nmedium changes. In this paper, we analyze the characterizations of OTFS\nmodulation over a more general multipath channel, where the signal of each path\nhas experienced a unique rapid fading. First, we derive the explicit\ninput-output relationship of OTFS in the DD domain for the case of ideal pulse\nand rectangular pulse. It is shown that the rapid fading will produce extra\nDoppler dispersion without impacting on delay domain. We next demonstrate that\nOTFS can be interpreted as an efficient time diversity technology that combines\nspace-time encoding and interleaving. Simulation results reveal that OTFS is\ninsensitive to rapid fading and still outperforms orthogonal frequency-division\nmultiplexing (OFDM) in these types of channels.\n']","[('otfs modulation', 0.5485365390777588), ('space otfs modulation', 0.5277403593063354), ('multiplexing ofdm', 0.5268808603286743), ('division multiplexing ofdm', 0.5020744204521179), ('delay doppler dd', 0.49254339933395386), ('frequency division multiplexing', 0.4854007661342621), ('ofdm', 0.44697579741477966), ('orthogonal frequency division', 0.44512271881103516), ('frequency space otfs', 0.44168606400489807), ('delay doppler', 0.4396515190601349)]"
145,145,184,145_bose einstein condensation_bose einstein condensates_bose einstein condensate_bose gases,"['bose einstein condensation', 'bose einstein condensates', 'bose einstein condensate', 'bose gases', 'einstein condensates', 'einstein condensation', 'interacting bosons', 'einstein condensate', 'bose einstein', 'bose gas']","['Bose-Einstein Condensation for Lattice Bosons   We present a class of models of interacting lattice bosons which show\ncomplete Bose-Einstein condensation for the ground state.\n', 'Length scales for BEC in the dilute Bose gas   We give a short proof of Bose Einstein Condensation of dilute Bose gases on\nlength scales much longer than the Gross-Pitaevskii scale.\n', 'The Bose gas in a box with Neumann boundary conditions   We consider a gas of bosonic particles confined in a box with Neumann\nboundary conditions. We prove Bose-Einstein condensation in the\nGross-Pitaevskii regime, with an optimal bound on the condensate depletion. Our\nlower bound for the ground state energy in the box implies (via Neumann\nbracketing) a lower bound for the ground state energy of the Bose gas in the\nthermodynamic limit.\n']","[('bose einstein condensation', 0.8010678291320801), ('bose einstein condensates', 0.781952440738678), ('bose einstein condensate', 0.756225049495697), ('bose gases', 0.6343837976455688), ('einstein condensates', 0.5895387530326843), ('einstein condensation', 0.5850558280944824), ('interacting bosons', 0.5543807148933411), ('einstein condensate', 0.5538434386253357), ('bose einstein', 0.5402318239212036), ('bose gas', 0.46974286437034607)]"
146,146,184,146_reconfigurable intelligent surface_reconfigurable intelligent surfaces_intelligent surface ris_ris assisted wireless,"['reconfigurable intelligent surface', 'reconfigurable intelligent surfaces', 'intelligent surface ris', 'ris assisted wireless', 'intelligent surface bd', 'surface bd ris', 'intelligent surfaces riss', 'intelligent surfaces ris', 'diagonal reconfigurable intelligent', 'beyond diagonal reconfigurable']","['Reconfigurable Intelligent Surfaces 2.0: Beyond Diagonal Phase Shift\n  Matrices   Reconfigurable intelligent surface (RIS) has been envisioned as a promising\ntechnique to enable and enhance future wireless communications due to its\npotential to engineer the wireless channels in a cost-effective manner.\nExtensive research attention has been drawn to the use of conventional RIS 1.0\nwith diagonal phase shift matrices, where each RIS element is connected to its\nown load to ground but not connected to other elements. However, the simple\narchitecture of RIS 1.0 limits its flexibility of manipulating passive\nbeamforming. To fully exploit the benefits of RIS, in this paper, we introduce\nRIS 2.0 beyond diagonal phase shift matrices, namely beyond diagonal RIS\n(BD-RIS). We first explain the modeling of BD-RIS based on the scattering\nparameter network analysis and classify BD-RIS by the mathematical\ncharacteristics of the scattering matrix, supported modes, and architectures.\nThen, we provide simulations to evaluate the sum-rate performance with\ndifferent modes/architectures of BD-RIS. We summarize the benefits of BD-RIS in\nproviding high flexibility in wave manipulation, enlarging coverage,\nfacilitating the deployment, and requiring low complexity in resolution bit and\nelement numbers. Inspired by the benefits of BD-RIS, we also discuss potential\napplications of BD-RIS in various wireless systems. Finally, we list key\nchallenges in modeling, designing, and implementing BD-RIS in practice and\npoint to possible future research directions for BD-RIS.\n', 'Localized and Distributed Beyond Diagonal Reconfigurable Intelligent\n  Surfaces with Lossy Interconnections: Modeling and Optimization   Reconfigurable intelligent surface (RIS) is a key technology to control the\ncommunication environment in future wireless networks. Recently, beyond\ndiagonal RIS (BD-RIS) emerged as a generalization of RIS achieving larger\ncoverage through additional tunable impedance components interconnecting the\nRIS elements. However, conventional RIS and BD-RIS can effectively serve only\nusers in their proximity, resulting in limited coverage. To overcome this\nlimitation, in this paper, we investigate distributed RIS, whose elements are\ndistributed over a wide region, in opposition to localized RIS commonly\nconsidered in the literature. The scaling laws of distributed BD-RIS reveal\nthat it offers significant gains over distributed conventional RIS and\nlocalized BD-RIS, enabled by its interconnections allowing signal propagation\nwithin the BD-RIS. To assess the practical performance of distributed BD-RIS,\nwe model and optimize BD-RIS with lossy interconnections through transmission\nline theory. Our model accounts for phase changes and losses over the BD-RIS\ninterconnections arising when the interconnection lengths are not much smaller\nthan the wavelength. Numerical results show that the performance of localized\nBD-RIS is only slightly impacted by losses, given the short interconnection\nlengths. Besides, distributed BD-RIS can achieve orders of magnitude of gains\nover conventional RIS, even in the presence of low losses.\n', ""A Tutorial on Beyond-Diagonal Reconfigurable Intelligent Surfaces: Modeling, Architectures, System Design and Optimization, and Applications Written by its inventors, this first tutorial on Beyond-Diagonal Reconfigurable Intelligent Surfaces (BD-RISs) provides the readers with the basics and fundamental tools necessary to appreciate, understand, and contribute to this emerging and disruptive technology. Conventional (Diagonal) RISs (D-RISs) are characterized by a diagonal scattering matrix $\\mathbf{\\Theta}$ such that the wave manipulation flexibility of D-RIS is extremely limited. In contrast, BD-RIS refers to a novel and general framework for RIS where its scattering matrix is not limited to be diagonal (hence, the ``beyond-diagonal'' terminology) and consequently, all entries of $\\mathbf{\\Theta}$ can potentially help shaping waves for much higher manipulation flexibility. This physically means that BD-RIS can artificially engineer and reconfigure coupling across elements of the surface thanks to inter-element reconfigurable components which allow waves absorbed by one element to flow through other elements. Consequently, BD-RIS opens the door to more general and versatile intelligent surfaces that subsumes existing RIS architectures as special cases. In this tutorial, we share all the secret sauce to model, design, and optimize BD-RIS and make BD-RIS transformative in many different applications. Topics discussed include physics-consistent and multi-port network-aided modeling; transmitting, reflecting, hybrid, and multi-sector mode analysis; reciprocal and non-reciprocal architecture designs and optimal performance-complexity Pareto frontier of BD-RIS; signal processing, optimization, and channel estimation for BD-RIS; hardware impairments (discrete-value impedance and admittance, lossy interconnections and components, wideband effects, mutual coupling) of BD-RIS; benefits and applications of BD-RIS in communications, sensing, power transfer.""]","[('reconfigurable intelligent surface', 0.48249122500419617), ('reconfigurable intelligent surfaces', 0.4746350944042206), ('intelligent surface ris', 0.4567756652832031), ('ris assisted wireless', 0.45558246970176697), ('intelligent surface bd', 0.4455392360687256), ('surface bd ris', 0.42086902260780334), ('intelligent surfaces riss', 0.4130071699619293), ('intelligent surfaces ris', 0.41044390201568604), ('diagonal reconfigurable intelligent', 0.38818567991256714), ('beyond diagonal reconfigurable', 0.38127318024635315)]"
147,147,182,147_finite element stokes_finite element methods_galerkin methods_incompressible navier stokes,"['finite element stokes', 'finite element methods', 'galerkin methods', 'incompressible navier stokes', 'incompressible stokes', 'element stokes', 'discontinuous galerkin', 'navier stokes equations', 'hybridized discontinuous galerkin', 'navier stokes']","['Pressure robust SUPG-stabilized finite elements for the unsteady\n  Navier-Stokes equation   In the present contribution we propose a novel conforming Finite Element\nscheme for the time-dependent Navier-Stokes equation, which is proven to be\nboth convection quasi-robust and pressure robust. The method is built combining\na ""divergence-free"" velocity/pressure couple (such as the Scott-Vogelius\nelement), a Discontinuous Galerkin in time approximation, and a suitable\nSUPG-curl stabilization. A set of numerical tests, in accordance with the\ntheoretical results, is included.\n', 'A nonconforming pressure-robust finite element method for the Stokes\n  equations on anisotropic meshes   Most classical finite element schemes for the (Navier-)Stokes equations are\nneither pressure-robust, nor are they inf-sup stable on general anisotropic\ntriangulations. A lack of pressure-robustness may lead to large velocity\nerrors, whenever the Stokes momentum balance is dominated by a strong and\ncomplicated pressure gradient. It is a consequence of a method, which does not\nexactly satisfy the divergence constraint. However, inf-sup stable schemes can\noften be made pressure-robust just by a recent, modified discretization of the\nexterior forcing term, using $\\mathbf{H}(\\operatorname{div})$-conforming\nvelocity reconstruction operators. This approach has so far only been analyzed\non shape-regular triangulations. The novelty of the present contribution is\nthat the reconstruction approach for the Crouzeix-Raviart method, which has a\nstable Fortin operator on arbitrary meshes, is combined with results on the\ninterpolation error on anisotropic elements for reconstruction operators of\nRaviart-Thomas and Brezzi-Douglas-Marini type, generalizing the method to a\nlarge class of anisotropic triangulations. Numerical examples confirm the\ntheoretical results in a 2D and a 3D test case.\n', 'A pressure-robust embedded discontinuous Galerkin method for the Stokes\n  problem by reconstruction operators   The embedded discontinuous Galerkin (EDG) finite element method for the\nStokes problem results in a point-wise divergence-free approximate velocity on\ncells. However, the approximate velocity is not H(div)-conforming and it can be\nshown that this is the reason that the EDG method is not pressure-robust, i.e.,\nthe error in the velocity depends on the continuous pressure. In this paper we\npresent a local reconstruction operator that maps discretely divergence-free\ntest functions to exactly divergence-free test functions. This local\nreconstruction operator restores pressure-robustness by only changing the right\nhand side of the discretization, similar to the reconstruction operator\nrecently introduced for the Taylor--Hood and mini elements by Lederer et al.\n(SIAM J. Numer. Anal., 55 (2017), pp. 1291--1314). We present an a priori error\nanalysis of the discretization showing optimal convergence rates and\npressure-robustness of the velocity error. These results are verified by\nnumerical examples. The motivation for this research is that the resulting EDG\nmethod combines the versatility of discontinuous Galerkin methods with the\ncomputational efficiency of continuous Galerkin methods and accuracy of\npressure-robust finite element methods.\n']","[('finite element stokes', 0.642822802066803), ('finite element methods', 0.5738146305084229), ('galerkin methods', 0.56498122215271), ('incompressible navier stokes', 0.5463944673538208), ('incompressible stokes', 0.5272274017333984), ('element stokes', 0.5221638679504395), ('discontinuous galerkin', 0.5201390385627747), ('navier stokes equations', 0.5165606737136841), ('hybridized discontinuous galerkin', 0.486908882856369), ('navier stokes', 0.4720262885093689)]"
148,148,182,148_fusion frames_fusion frame_frames hilbert_dual frames,"['fusion frames', 'fusion frame', 'frames hilbert', 'dual frames', 'frame operator', 'frame dual', 'fusion', 'continuous frames', 'dual frame', 'frame theory']","['Fusion frames for operators and atomic systems   Recently, fusion frames and frames for operators were considered as\ngeneralizations of frames in Hilbert spaces. In this paper, we generalize some\nof the known results in frame theory to fusion frames related to a linear\nbounded operator K which we call K-fusion frames. We obtain new K-fusion frames\nby considering K-fusion frames with a class of bounded linear operators. We\nalso study the stability of K-fusion frames under small perturbations. We\nfurther give some characterizations of atomic systems with subspace sequences.\n', 'Controlled $K$-Fusion Frame for Hilbert Spaces   $K$-fusion frames are a generalization of fusion frames in frame theory. In\nthis paper, we extend the concept of controlled fusion frames to controlled\n$K$-fusion frames, and we develop some results on the controlled $K$-fusion\nframes for Hilbert spaces, which generalized some well known of controlled\nfusion frames case. also we discuss some characterizations of controlled Bessel\n$K$-fusion sequences and of controlled Bessel $K$-fusion. Further, we analyse\nstability conditions of controlled $K$-fusion frames under perturbation.\n', 'Robustness of controlled $K$-Fusion Frame in Hilbert C$^*$-modules under\n  erasures of submodules   Controlled $\\ast$-K-fusion frames are generalization of controlled fusion\nframes in frame theory. In this paper, we propose the notion of controlled\n$\\ast$-k-fusions frames on Hilbert $C^{\\ast}$-modules. We give some\ncaraterizations and some of their properties are obtained. Then we study the\nerasures of submodules of a controlled $k$-fusion frame in Hilbert\n$C^{\\ast}$-modules and we present some sufficient conditions under which a\nsequence remains a standart controlled k-fusion frame after deletion of some\nsubmodules. Finally, we introduce a perturbation for controlled $K$-fusion\nframes in Hilbert $C^{\\ast}$-modules and it is shown that under some conditions\ncontrolled $K$-fusion frames are stable under this perturbation, and we\ngeneralize some of the results obtained for perturbations of controlled\n$K$-fusion frames.\n']","[('fusion frames', 0.6473575234413147), ('fusion frame', 0.6102688908576965), ('frames hilbert', 0.5619090795516968), ('dual frames', 0.5269407629966736), ('frame operator', 0.5200565457344055), ('frame dual', 0.48538559675216675), ('fusion', 0.4724371135234833), ('continuous frames', 0.47070321440696716), ('dual frame', 0.4655287265777588), ('frame theory', 0.4425722658634186)]"
149,149,182,149_learning federated learning_federated learning_learning wireless_federated learning fl,"['learning federated learning', 'federated learning', 'learning wireless', 'federated learning fl', 'wireless federated', 'learning federated', 'distributed learning', 'edge learning', 'wireless networks', 'wireless channels']","['Reconfigurable Intelligent Surface Enabled Federated Learning: A Unified\n  Communication-Learning Design Approach   To exploit massive amounts of data generated at mobile edge networks,\nfederated learning (FL) has been proposed as an attractive substitute for\ncentralized machine learning (ML). By collaboratively training a shared\nlearning model at edge devices, FL avoids direct data transmission and thus\novercomes high communication latency and privacy issues as compared to\ncentralized ML. To improve the communication efficiency in FL model\naggregation, over-the-air computation has been introduced to support a large\nnumber of simultaneous local model uploading by exploiting the inherent\nsuperposition property of wireless channels. However, due to the heterogeneity\nof communication capacities among edge devices, over-the-air FL suffers from\nthe straggler issue in which the device with the weakest channel acts as a\nbottleneck of the model aggregation performance. This issue can be alleviated\nby device selection to some extent, but the latter still suffers from a\ntradeoff between data exploitation and model communication. In this paper, we\nleverage the reconfigurable intelligent surface (RIS) technology to relieve the\nstraggler issue in over-the-air FL. Specifically, we develop a learning\nanalysis framework to quantitatively characterize the impact of device\nselection and model aggregation error on the convergence of over-the-air FL.\nThen, we formulate a unified communication-learning optimization problem to\njointly optimize device selection, over-the-air transceiver design, and RIS\nconfiguration. Numerical experiments show that the proposed design achieves\nsubstantial learning accuracy improvement compared with the state-of-the-art\napproaches, especially when channel conditions vary dramatically across edge\ndevices.\n', 'CFLIT: Coexisting Federated Learning and Information Transfer   Future wireless networks are expected to support diverse mobile services,\nincluding artificial intelligence (AI) services and ubiquitous data\ntransmissions. Federated learning (FL), as a revolutionary learning approach,\nenables collaborative AI model training across distributed mobile edge devices.\nBy exploiting the superposition property of multiple-access channels,\nover-the-air computation allows concurrent model uploading from massive devices\nover the same radio resources, and thus significantly reduces the communication\ncost of FL. In this paper, we study the coexistence of over-the-air FL and\ntraditional information transfer (IT) in a mobile edge network. We propose a\ncoexisting federated learning and information transfer (CFLIT) communication\nframework, where the FL and IT devices share the wireless spectrum in an OFDM\nsystem. Under this framework, we aim to maximize the IT data rate and guarantee\na given FL convergence performance by optimizing the long-term radio resource\nallocation. A key challenge that limits the spectrum efficiency of the\ncoexisting system lies in the large overhead incurred by frequent communication\nbetween the server and edge devices for FL model aggregation. To address the\nchallenge, we rigorously analyze the impact of the computation-to-communication\nratio on the convergence of over-the-air FL in wireless fading channels. The\nanalysis reveals the existence of an optimal computation-to-communication ratio\nthat minimizes the amount of radio resources needed for over-the-air FL to\nconverge to a given error tolerance. Based on the analysis, we propose a\nlow-complexity online algorithm to jointly optimize the radio resource\nallocation for both the FL devices and IT devices. Extensive numerical\nsimulations verify the superior performance of the proposed design for the\ncoexistence of FL and IT devices in wireless cellular systems.\n', 'Digital Over-the-Air Federated Learning in Multi-Antenna Systems   In this paper, the performance optimization of federated learning (FL), when\ndeployed over a realistic wireless multiple-input multiple-output (MIMO)\ncommunication system with digital modulation and over-the-air computation\n(AirComp) is studied. In particular, a MIMO system is considered in which edge\ndevices transmit their local FL models (trained using their locally collected\ndata) to a parameter server (PS) using beamforming to maximize the number of\ndevices scheduled for transmission. The PS, acting as a central controller,\ngenerates a global FL model using the received local FL models and broadcasts\nit back to all devices. Due to the limited bandwidth in a wireless network,\nAirComp is adopted to enable efficient wireless data aggregation. However,\nfading of wireless channels can produce aggregate distortions in an\nAirComp-based FL scheme. To tackle this challenge, we propose a modified\nfederated averaging (FedAvg) algorithm that combines digital modulation with\nAirComp to mitigate wireless fading while ensuring the communication\nefficiency. This is achieved by a joint transmit and receive beamforming\ndesign, which is formulated as an optimization problem to dynamically adjust\nthe beamforming matrices based on current FL model parameters so as to minimize\nthe transmitting error and ensure the FL performance. To achieve this goal, we\nfirst analytically characterize how the beamforming matrices affect the\nperformance of the FedAvg in different iterations. Based on this relationship,\nan artificial neural network (ANN) is used to estimate the local FL models of\nall devices and adjust the beamforming matrices at the PS for future model\ntransmission. The algorithmic advantages and improved performance of the\nproposed methodologies are demonstrated through extensive numerical\nexperiments.\n']","[('learning federated learning', 0.544837236404419), ('federated learning', 0.5397226214408875), ('learning wireless', 0.5259676575660706), ('federated learning fl', 0.5190533399581909), ('wireless federated', 0.5016071796417236), ('learning federated', 0.49636536836624146), ('distributed learning', 0.4323342740535736), ('edge learning', 0.4009435772895813), ('wireless networks', 0.3980078399181366), ('wireless channels', 0.3705924153327942)]"
150,150,180,150_solutions vlasov poisson_vlasov poisson system_vlasov poisson_solutions vlasov,"['solutions vlasov poisson', 'vlasov poisson system', 'vlasov poisson', 'solutions vlasov', 'poisson equations', 'euler poisson system', 'limit vlasov', 'dimensional vlasov', 'poisson system', 'poisson systems']","['A Probabilistic Mean Field Limit for the Vlasov-Poisson System for Ions   The Vlasov-Poisson system for ions is a kinetic equation for dilute,\nunmagnetised plasma. It describes the evolution of the ions in a plasma under\nthe assumption that the electrons are thermalized. Consequently, the Poisson\ncoupling for the electrostatic potential contains an additional exponential\nnonlinearity not present in the electron Vlasov-Poisson system.\n  The system can be formally derived through a mean field limit from a\nmicroscopic system of ions interacting with a thermalized electron\ndistribution. However, it is an open problem to justify this limit rigorously\nfor ions modelled as point charges. Existing results on the derivation of the\nthree-dimensional ionic Vlasov-Poisson system require a truncation of the\nsingularity in the Coulomb interaction at spatial scales of order $N^{- \\beta}$\nwith $\\beta < 1/15$, which is more restrictive than the available results for\nthe electron Vlasov-Poisson system.\n  In this article, we prove that the Vlasov-Poisson system for ions can be\nderived from a microscopic system of ions and thermalized electrons with\ninteraction truncated at scale $N^{- \\beta}$ with $\\beta < 1/3$. We develop a\ngeneralisation of the probabilistic approach to mean field limits that is\napplicable to interaction forces defined through a nonlinear coupling with the\nparticle density. The proof is based on a quantitative uniform law of large\nnumbers for convolutions between empirical measures of independent, identically\ndistributed random variables and locally Lipschitz functions.\n', 'On the asymptotic behavior of solutions to the Vlasov-Poisson system   We prove small data modified scattering for the Vlasov-Poisson system in\ndimension $d=3$ using a method inspired from dispersive analysis. In\nparticular, we identify a simple asymptotic dynamic related to the scattering\nmass.\n', 'Backward problem for the 1D ionic Vlasov-Poisson equation   In this paper, we study the backward problem for the one-dimensional\nVlasov-Poisson system with massless electrons, and we show the Landau damping\nby fixing the asymptotic behaviour of our solution.\n']","[('solutions vlasov poisson', 0.7938392758369446), ('vlasov poisson system', 0.7756565809249878), ('vlasov poisson', 0.6863333582878113), ('solutions vlasov', 0.6118466258049011), ('poisson equations', 0.5624814033508301), ('euler poisson system', 0.5492361187934875), ('limit vlasov', 0.5166463851928711), ('dimensional vlasov', 0.5004605650901794), ('poisson system', 0.4864158034324646), ('poisson systems', 0.4676009714603424)]"
151,151,179,151_randomization tests_permutation tests_independence tests_independence testing,"['randomization tests', 'permutation tests', 'independence tests', 'independence testing', 'testing independence', 'test independence', 'conditional independence testing', 'test statistics', 'sample tests', 'proposed tests']","['Boosting the Power of Kernel Two-Sample Tests   The kernel two-sample test based on the maximum mean discrepancy (MMD) is one\nof the most popular methods for detecting differences between two distributions\nover general metric spaces. In this paper we propose a method to boost the\npower of the kernel test by combining MMD estimates over multiple kernels using\ntheir Mahalanobis distance. We derive the asymptotic null distribution of the\nproposed test statistic and use a multiplier bootstrap approach to efficiently\ncompute the rejection region. The resulting test is universally consistent and,\nsince it is obtained by aggregating over a collection of kernels/bandwidths, is\nmore powerful in detecting a wide range of alternatives in finite samples. We\nalso derive the distribution of the test statistic for both fixed and local\ncontiguous alternatives. The latter, in particular, implies that the proposed\ntest is statistically efficient, that is, it has non-trivial asymptotic\n(Pitman) efficiency. The consistency properties of the Mahalanobis and other\nnatural aggregation methods are also explored when the number of kernels is\nallowed to grow with the sample size. Extensive numerical experiments are\nperformed on both synthetic and real-world datasets to illustrate the efficacy\nof the proposed method over single kernel tests. The computational complexity\nof the proposed method is also studied, both theoretically and in simulations.\nOur asymptotic results rely on deriving the joint distribution of MMD estimates\nusing the framework of multiple stochastic integrals, which is more broadly\nuseful, specifically, in understanding the efficiency properties of recently\nproposed adaptive MMD tests based on kernel aggregation and also in developing\nmore computationally efficient (linear time) tests that combine multiple\nkernels. We conclude with an application of the Mahalanobis aggregation method\nfor kernels with diverging scaling parameters.\n', 'Cheap Permutation Testing   Permutation tests are a popular choice for distinguishing distributions and\ntesting independence, due to their exact, finite-sample control of false\npositives and their minimax optimality when paired with U-statistics. However,\nstandard permutation tests are also expensive, requiring a test statistic to be\ncomputed hundreds or thousands of times to detect a separation between\ndistributions. In this work, we offer a simple approach to accelerate testing:\ngroup your datapoints into bins and permute only those bins. For U and\nV-statistics, we prove that these cheap permutation tests have two remarkable\nproperties. First, by storing appropriate sufficient statistics, a cheap test\ncan be run in time comparable to evaluating a single test statistic. Second,\ncheap permutation power closely approximates standard permutation power. As a\nresult, cheap tests inherit the exact false positive control and minimax\noptimality of standard permutation tests while running in a fraction of the\ntime. We complement these findings with improved power guarantees for standard\npermutation testing and experiments demonstrating the benefits of cheap\npermutations over standard maximum mean discrepancy (MMD), Hilbert-Schmidt\nindependence criterion (HSIC), random Fourier feature, Wilcoxon-Mann-Whitney,\ncross-MMD, and cross-HSIC tests.\n', 'A Permutation-free Kernel Two-Sample Test   The kernel Maximum Mean Discrepancy~(MMD) is a popular multivariate distance\nmetric between distributions that has found utility in two-sample testing. The\nusual kernel-MMD test statistic is a degenerate U-statistic under the null, and\nthus it has an intractable limiting distribution. Hence, to design a\nlevel-$\\alpha$ test, one usually selects the rejection threshold as the\n$(1-\\alpha)$-quantile of the permutation distribution. The resulting\nnonparametric test has finite-sample validity but suffers from large\ncomputational cost, since every permutation takes quadratic time. We propose\nthe cross-MMD, a new quadratic-time MMD test statistic based on\nsample-splitting and studentization. We prove that under mild assumptions, the\ncross-MMD has a limiting standard Gaussian distribution under the null.\nImportantly, we also show that the resulting test is consistent against any\nfixed alternative, and when using the Gaussian kernel, it has minimax\nrate-optimal power against local alternatives. For large sample sizes, our new\ncross-MMD provides a significant speedup over the MMD, for only a slight loss\nin power.\n']","[('randomization tests', 0.5825642943382263), ('permutation tests', 0.5244858860969543), ('independence tests', 0.5157424211502075), ('independence testing', 0.5002722144126892), ('testing independence', 0.488186776638031), ('test independence', 0.4808075428009033), ('conditional independence testing', 0.47678306698799133), ('test statistics', 0.4355618953704834), ('sample tests', 0.39941760897636414), ('proposed tests', 0.39331960678100586)]"
152,152,179,152_renormalization group_renormalization_renormalizability_renormalizable,"['renormalization group', 'renormalization', 'renormalizability', 'renormalizable', 'renormalization group flow', 'renormalisation', 'renormalisation group', 'renormalization group rg', 'renormalized', 'quantum field theories']","['Semiclassical Trans-Series from the Perturbative Hopf-Algebraic\n  Dyson-Schwinger Equations: $\\phi^3$ QFT in 6 Dimensions   We analyze the asymptotically free massless scalar $\\phi^3$ quantum field\ntheory in 6 dimensions, using resurgent asymptotic analysis to find the\ntrans-series solutions which yield the non-perturbative completion of the\ndivergent perturbative solutions to the Kreimer-Connes Hopf-algebraic\nDyson-Schwinger equations for the anomalous dimension. This scalar conformal\nfield theory is asymptotically free and has a real Lipatov instanton. In the\nHopf-algebraic approach we find a trans-series having an intricate Borel\nsingularity structure, with three distinct but resonant non-perturbative terms,\neach repeated in an infinite series. These expansions are in terms of the\nrenormalized coupling. The resonant structure leads to powers of logarithmic\nterms at higher levels of the trans-series, analogous to logarithmic terms\narising from interactions between instantons and anti-instantons, but arising\nfrom a purely perturbative formalism rather than from a semi-classical\nanalysis.\n', ""On Haag's theorem and renormalization ambiguities   We revisit the implications of Haag's theorem in the light of the\nrenormalization group. There is still some lack of discussion in the literature\nabout the possible impact of the theorem on the standard (as opposite of\naxiomatic) quantum field theory, and we try to shed light in this direction.\nOur discussion then deals with the interplay between Haag's theorem and\nrenormalization. While we clarify how perturbative renormalization (for the\nsub-class of interactions that are renormalizable) marginalizes the its impact\nwhen the coupling is formally small, we argue that a non-perturbative and\nnon-ambiguous renormalization cannot be built if there is any reference to the\ninteraction picture with free fields. In other words, Haag's theorem should be\nregarded as a no-go theorem for the existence of a non-ambiguous analytic\ncontinuation from perturbative to non-perturbative QFT.\n"", 'Linearized renormalization Using an infinitesimal approach, this work addresses the renormalization problem to deal with the ultraviolet divergences arising in quantum field theory. Under the assumption that the action has already been renormalized to yield an ultraviolet-finite effective action that satisfies a certain set of renormalization conditions, we analyze how the action must be adjusted to reproduce a first-order change in these renormalization conditions. The analysis then provides the change that is induced on the correlation functions of the theory. This program is successfully carried out in the case of super-renormalizable theories, namely, a scalar field with cubic interaction in four space-time dimensions and with quartic interaction in three space-time dimensions. Relying on existing results in the theory of perturbative renormalization, we derive explicit renormalized expressions for these theories, each of which involves only a finite number of graphs constructed with full propagators and full $n$-point vertices. The renormalizable case is analyzed as well; the derived expressions are ultraviolet finite as the regulator is removed but cannot be written without a regulator. In this sense, the renormalization is not fully explicit in the renormalizable case. Nevertheless, a perturbative solution of the equations starting from the free theory provides the renormalized Feynman graphs, similar to the BPHZ program. For compatibility with the preservation of the renormalization conditions, a projective renormalization scheme, as opposed to a minimal one, is also introduced. The ideas developed are extended to the study of the renormalization of composite operators and the Schwinger-Dyson equations.']","[('renormalization group', 0.671108067035675), ('renormalization', 0.6598987579345703), ('renormalizability', 0.6451960206031799), ('renormalizable', 0.6420077681541443), ('renormalization group flow', 0.6217562556266785), ('renormalisation', 0.6151000261306763), ('renormalisation group', 0.6130029559135437), ('renormalization group rg', 0.6047101020812988), ('renormalized', 0.5776699781417847), ('quantum field theories', 0.5413388609886169)]"
153,153,178,153_lie symmetry analysis_lie symmetries_lie point symmetries_lie symmetry,"['lie symmetry analysis', 'lie symmetries', 'lie point symmetries', 'lie symmetry', 'generalized symmetries', 'approximate symmetries', 'variational symmetries', 'symmetries', 'invariant solutions', 'dimensional lie algebra']","['Lie symmetry analysis and similarity solutions for the Camassa-Choi\n  equations   The method of Lie symmetry analysis of differential equations is applied to\ndetermine exact solutions for the Camassa-Choi equation and its generalization.\nWe prove that the Camassa-Choi equation is invariant under an\ninfinite-dimensional Lie algebra, with an essential five-dimensional Lie\nalgebra. The application of the Lie point symmetries leads to the construction\nof exact similarity solutions.\n', 'Similarity solutions and Conservation laws for the\n  Bogoyavlensky-Konopelchenko Equation by Lie point symmetries   The 1 + 2 dimensional Bogoyavlensky-Konopelchenko Equation is investigated\nfor its solution and conservation laws using the Lie point symmetry analysis.\nIn the recent past, certain work has been done describing the Lie point\nsymmetries for the equation and this work seems to be incomplete (Ray S (2017)\nCompt. Math. Appl. 74, 1157). We obtained certain new symmetries and\ncorresponding conservation laws. The travelling-wave solution and some other\nsimilarity solutions are studied.\n', 'Symmetries of nonlinear ordinary differential equations: the modified\n  Emden equation as a case study   Lie symmetry analysis is one of the powerful tools to analyze nonlinear\nordinary differential equations. We review the effectiveness of this method in\nterms of various symmetries. We present the method of deriving Lie point\nsymmetries, contact symmetries, hidden symmetries, nonlocal symmetries,\n$\\lambda$-symmetries, adjoint symmetries and telescopic vector fields of a\nsecond-order ordinary differential equation. We also illustrate the algorithm\ninvolved in each method by considering a nonlinear oscillator equation as an\nexample. The connections between (i) symmetries and integrating factors and\n(ii) symmetries and integrals are also discussed and illustrated through the\nsame example. The interconnections between some of the above symmetries, that\nis (i) Lie point symmetries and $\\lambda$-symmetries and (ii) exponential\nnonlocal symmetries and $\\lambda$-symmetries are also discussed. The order\nreduction procedure is invoked to derive the general solution of the\nsecond-order equation.\n']","[('lie symmetry analysis', 0.7241292595863342), ('lie symmetries', 0.7200035452842712), ('lie point symmetries', 0.699038028717041), ('lie symmetry', 0.6702678799629211), ('generalized symmetries', 0.6600404381752014), ('approximate symmetries', 0.6050596237182617), ('variational symmetries', 0.5893681645393372), ('symmetries', 0.5802092552185059), ('invariant solutions', 0.5707628726959229), ('dimensional lie algebra', 0.5644188523292542)]"
154,154,178,154_reaction network theory_reaction networks_chemical reaction networks_reaction network,"['reaction network theory', 'reaction networks', 'chemical reaction networks', 'reaction network', 'chemical reaction network', 'biochemical reaction networks', 'reaction systems', 'kinetic systems', 'mass action kinetics', 'action kinetics']","['Analysis of Mass-Action Systems by Split Network Translation   We introduce the notion of corresponding a chemical reaction network to a\nsplit network translation, and use this novel process to extend the scope of\nexisting network-based theory for characterizing the steady state set of\nmass-action systems. In the process of network splitting, the reactions of a\nnetwork are divided into subnetworks, called slices, in such a way that, when\nsummed across the slices, the stoichiometry of each reaction sums to that of\nthe original network. This can produce a network with more desirable structural\nproperties, such as weak reversibility and a lower deficiency, which can then\nbe used to establish steady state properties of the original mass-action system\nsuch as multistationarity and absolute concentration robustness. We also\npresent a computational implementation utilizing mixed-integer linear\nprogramming for determining whether a given chemical reaction network has a\nweakly reversible split network translation.\n', 'A decomposition-based approach for deriving positive steady states of a\n  class of chemical reaction networks with non-mass-action kinetics   Steady states are frequently used to investigate the long-term behaviors of\n(bio)-chemical systems. Recently, there has been a growing interest in\nnetwork-based approaches due to their efficiency in deriving parametrizations\nof positive steady states in systems with mass-action kinetics. In this study,\nwe extend this approach to derive positive steady states in networks under\nnon-mass-action kinetics, specifically mixed kinetics. In a system with mixed\nkinetics, some reactions {may follow} mass-action kinetics, while others in the\nsame network follow different rate laws, such as quotient rate laws. An example\nof such complexity is evident in a mathematical model of the insulin signaling\npathway in type 2 diabetes. To compute its positive {steady states}, we adapt\nour existing network decomposition approach, originally designed for\nmass-action kinetics, to handle networks with non-mass-action kinetics. This\napproach involves breaking down a given network into smaller, independent\nsubnetworks to derive the positive steady states of each subnetwork separately.\nThese individual steady states are then combined to obtain the positive steady\nstates of the entire network. This strategy makes computations more manageable\nfor complex and large networks. More importantly, this method could separate\nreactions with purely mass-action kinetics into certain subnetworks from those\nthat follow different rate laws. We also present an illustrative example that\nprovides insights into methods for transforming networks with mixed kinetics\ninto their associated mass-action systems.\n', 'Global stability of first order endotactic reaction systems   Reaction networks are a general framework widely used in modelling diverse\nphenomena in different science disciplines. The dynamical process of a reaction\nnetwork endowed with mass-action kinetics is a mass-action system. In this\npaper we study dynamics of first order mass-action systems. We prove that every\nfirst order endotactic mass-action system has a weakly reversible deficiency\nzero realization, and has a unique equilibrium which is exponentially globally\nasymptotically stable (and is positive) in each (positive) stoichiometric\ncompatibility class. In particular, we prove that global attractivity\nconjecture holds for every linear complex balanced mass-action system. In this\nway, we exclude the possibility of first order endotactic mass-action systems\nto admit multistationarity or multistability. The result indicates that the\nimportance of binding molecules in reactants is crucial for (endotactic)\nreaction networks to have complicated dynamics like limit cycles. The proof\nrelies on the fact that $\\mathcal{A}$-endotacticity of first order reaction\nnetworks implies endotacticity for a finite set $\\mathcal{A}$, which is also\nproved in this paper.\n  Out of independent interest, we provide a sufficient condition for\nendotacticity of reaction networks which are not necessarily of first order.\n']","[('reaction network theory', 0.6770608425140381), ('reaction networks', 0.6225848197937012), ('chemical reaction networks', 0.619091808795929), ('reaction network', 0.6124193072319031), ('chemical reaction network', 0.6109707951545715), ('biochemical reaction networks', 0.6011883616447449), ('reaction systems', 0.542107343673706), ('kinetic systems', 0.5287255644798279), ('mass action kinetics', 0.5111426711082458), ('action kinetics', 0.47961410880088806)]"
155,155,178,155_bayesian inverse problems_bayesian inverse_bayesian inversion_statistical inverse problems,"['bayesian inverse problems', 'bayesian inverse', 'bayesian inversion', 'statistical inverse problems', 'nonlinear bayesian', 'nonlinear inverse problems', 'statistical inverse', 'large scale bayesian', 'nonlinear inverse', 'inverse problems partial']","['Optimal design of large-scale nonlinear Bayesian inverse problems under\n  model uncertainty   We consider optimal experimental design (OED) for Bayesian nonlinear inverse\nproblems governed by partial differential equations (PDEs) under model\nuncertainty. Specifically, we consider inverse problems in which, in addition\nto the inversion parameters, the governing PDEs include secondary uncertain\nparameters. We focus on problems with infinite-dimensional inversion and\nsecondary parameters and present a scalable computational framework for optimal\ndesign of such problems. The proposed approach enables Bayesian inversion and\nOED under uncertainty within a unified framework. We build on the Bayesian\napproximation error (BAE) approach, to incorporate modeling uncertainties in\nthe Bayesian inverse problem, and methods for A-optimal design of\ninfinite-dimensional Bayesian nonlinear inverse problems. Specifically, a\nGaussian approximation to the posterior at the maximum a posteriori probability\npoint is used to define an uncertainty aware OED objective that is tractable to\nevaluate and optimize. In particular, the OED objective can be computed at a\ncost, in the number of PDE solves, that does not grow with the dimension of the\ndiscretized inversion and secondary parameters. The OED problem is formulated\nas a binary bilevel PDE constrained optimization problem and a greedy\nalgorithm, which provides a pragmatic approach, is used to find optimal\ndesigns. We demonstrate the effectiveness of the proposed approach for a model\ninverse problem governed by an elliptic PDE on a three-dimensional domain. Our\ncomputational results also highlight the pitfalls of ignoring modeling\nuncertainties in the OED and/or inference stages.\n', 'Hyper-differential sensitivity analysis for nonlinear Bayesian inverse\n  problems   We consider hyper-differential sensitivity analysis (HDSA) of nonlinear\nBayesian inverse problems governed by PDEs with infinite-dimensional\nparameters. In previous works, HDSA has been used to assess the sensitivity of\nthe solution of deterministic inverse problems to additional model\nuncertainties and also different types of measurement data. In the present\nwork, we extend HDSA to the class of Bayesian inverse problems governed by\nPDEs. The focus is on assessing the sensitivity of certain key quantities\nderived from the posterior distribution. Specifically, we focus on analyzing\nthe sensitivity of the MAP point and the Bayes risk and make full use of the\ninformation embedded in the Bayesian inverse problem. After establishing our\nmathematical framework for HDSA of Bayesian inverse problems, we present a\ndetailed computational approach for computing the proposed HDSA indices. We\nexamine the effectiveness of the proposed approach on a model inverse problem\ngoverned by a PDE for heat conduction.\n', 'Non-intrusive optimal experimental design for large-scale nonlinear\n  Bayesian inverse problems using a Bayesian approximation error approach   We consider optimal experimental design (OED) for nonlinear inverse problems\nwithin the Bayesian framework. Optimizing the data acquisition process for\nlarge-scale nonlinear Bayesian inverse problems is a computationally\nchallenging task since the posterior is typically intractable and\ncommonly-encountered optimality criteria depend on the observed data. Since\nthese challenges are not present in OED for linear Bayesian inverse problems,\nwe propose an approach based on first linearizing the associated forward\nproblem and then optimizing the experimental design. Replacing an accurate but\ncostly model with some linear surrogate, while justified for certain problems,\ncan lead to incorrect posteriors and sub-optimal designs if model discrepancy\nis ignored. To avoid this, we use the Bayesian approximation error (BAE)\napproach to formulate an A-optimal design objective for sensor selection that\nis aware of the model error. In line with recent developments, we prove that\nthis uncertainty-aware objective is independent of the exact choice of\nlinearization. This key observation facilitates the formulation of an\nuncertainty-aware OED objective function using a completely trivial linear map,\nthe zero map, as a surrogate to the forward dynamics. The base methodology is\nalso extended to marginalized OED problems, accommodating uncertainties arising\nfrom both linear approximations and unknown auxiliary parameters. Our approach\nonly requires parameter and data sample pairs, hence it is particularly\nwell-suited for black box forward models. We demonstrate the effectiveness of\nour method for finding optimal designs in an idealized subsurface flow inverse\nproblem and for tsunami detection.\n']","[('bayesian inverse problems', 0.7436306476593018), ('bayesian inverse', 0.6929126977920532), ('bayesian inversion', 0.6380840539932251), ('statistical inverse problems', 0.5587443113327026), ('nonlinear bayesian', 0.5294186472892761), ('nonlinear inverse problems', 0.5147368311882019), ('statistical inverse', 0.5096768736839294), ('large scale bayesian', 0.47619983553886414), ('nonlinear inverse', 0.46806690096855164), ('inverse problems partial', 0.45156756043434143)]"
156,156,176,156_abelian varieties_abelian varieties mathbb_ordinary abelian varieties_polarized abelian varieties,"['abelian varieties', 'abelian varieties mathbb', 'ordinary abelian varieties', 'polarized abelian varieties', 'abelian varieties defined', 'groups abelian varieties', 'abelian variety', 'dimensional abelian varieties', 'ordinary abelian variety', 'varieties finite fields']","[""The Tate Conjecture for Certain Abelian Varieties over Finite Fields   Tate's theorem (Invent. Math. 1966)implies that the Tate conjecture holds for\nany abelian variety over a finite field whose Q_l-algebra of Tate classes is\ngenerated by those of degree 1. We construct families of abelian varieties over\nfinite fields for which this condition fails, but for which we are nevertheless\nable to prove the Tate conjecture.\n"", 'Categories of abelian varieties over finite fields II: Abelian varieties\n  over finite fields and Morita equivalence   The category of abelian varieties over $\\mathbb{F}_q$ is shown to be\nanti-equivalent to a category of $\\mathbb{Z}$-lattices that are modules for a\nnon-commutative pro-ring of endomorphisms of a suitably chosen direct system of\nabelian varieties over $\\mathbb{F}_q$. On full subcategories cut out by a\nfinite set $w$ of conjugacy classes of Weil $q$-numbers, the anti-equivalence\nis represented by what we call $w$-locally projective abelian varieties.\n', 'Isogenies of certain abelian varieties over finite fields with p-ranks\n  zero   We study the isogenies of certain abelian varieties over finite fields with\nnon-commutative endomorphism algebras with a view to potential use in\nisogeny-based cryptography. In particular, we show that any two such abelian\nvarieties with endomorphism rings maximal orders in the endomorphism algebra\nare linked by a cyclic isogeny of prime degree.\n']","[('abelian varieties', 0.7702721953392029), ('abelian varieties mathbb', 0.7372089624404907), ('ordinary abelian varieties', 0.7321255803108215), ('polarized abelian varieties', 0.7221680879592896), ('abelian varieties defined', 0.7199863791465759), ('groups abelian varieties', 0.7187954783439636), ('abelian variety', 0.7098590135574341), ('dimensional abelian varieties', 0.7000895738601685), ('ordinary abelian variety', 0.677660346031189), ('varieties finite fields', 0.6710683703422546)]"
157,157,175,157_liouville quantum gravity_quantum gravity lqg_liouville conformal_liouville conformal field,"['liouville quantum gravity', 'quantum gravity lqg', 'liouville conformal', 'liouville conformal field', 'liouville quantum', 'quantum gravity', 'random surfaces', 'sle curves', 'conformal', 'via conformal']","['Uniqueness of the welding problem for SLE and Liouville quantum gravity   We give a simple set of geometric conditions on curves $\\eta$, $\\tilde{\\eta}$\nin ${\\mathbf H}$ from $0$ to $\\infty$ so that if $\\varphi \\colon {\\mathbf H}\n\\to {\\mathbf H}$ is a homeomorphism which is conformal off $\\eta$ with\n$\\varphi(\\eta) = \\tilde{\\eta}$ then $\\varphi$ is a conformal automorphism of\n${\\mathbf H}$. Our motivation comes from the fact that it is possible to apply\nour result to random conformal welding problems related to the Schramm-Loewner\nevolution (SLE) and Liouville quantum gravity (LQG). In particular, we show\nthat if $\\eta$ is a non-space-filling SLE$_\\kappa$ curve in ${\\mathbf H}$ from\n$0$ to $\\infty$ and $\\varphi$ is a homeomorphism which is conformal on\n${\\mathbf H} \\setminus \\eta$ and $\\varphi(\\eta)$, $\\eta$ are equal in\ndistribution then $\\varphi$ is a conformal automorphism of ${\\mathbf H}$.\nApplying this result for $\\kappa=4$ establishes that the welding operation for\ncritical ($\\gamma=2$) Liouville quantum gravity (LQG) is well-defined. Applying\nit for $\\kappa \\in (4,8)$ gives a new proof that the welding of two independent\n$\\kappa/4$-stable looptrees of quantum disks to produce an SLE$_\\kappa$ on top\nof an independent $4/\\sqrt{\\kappa}$-LQG surface is well-defined.\n', 'Radial conformal welding in Liouville quantum gravity   The seminal work of Sheffield showed that when random surfaces called\nLiouville quantum gravity (LQG) are conformally welded, the resulting interface\nis Schramm-Loewner evolution (SLE). This has been proved for a variety of\nconfigurations, and has applications to the scaling limits of random planar\nmaps and the solvability of SLE and Liouville conformal field theory. We extend\nthe theory to the setting where two sides of a canonical three-pointed LQG\nsurface are conformally welded together, resulting in a radial SLE curve which\ncan be described by imaginary geometry.\n', 'Cutting $\\gamma$-Liouville quantum gravity by Schramm-Loewner evolution\n  for $\\kappa \\not\\in \\{\\gamma^2, 16/\\gamma^2\\}$   There are many deep and useful theorems relating Schramm-Loewner evolution\n(SLE$_\\kappa$) and Liouville quantum gravity ($\\gamma$-LQG) in the case when\nthe parameters satisfy $\\kappa \\in \\{\\gamma^2, 16/\\gamma^2\\}$. Roughly\nspeaking, these theorems say that the SLE$_\\kappa$ curve cuts the $\\gamma$-LQG\nsurface into two or more independent $\\gamma$-LQG surfaces. We extend these\ntheorems to the case when $\\kappa \\not\\in \\{\\gamma^2, 16/\\gamma^2\\}$. Roughly\nspeaking we show that if we have an appropriate variant of SLE$_\\kappa$ and an\nindependent $\\gamma$-LQG disk, then the SLE curve cuts the LQG disk into two or\nmore $\\gamma$-LQG surfaces which are conditionally independent given the values\nalong the SLE curve of a certain collection of auxiliary imaginary geometry\nfields, viewed modulo conformal coordinate change. These fields are sampled\nindependently from the SLE and the LQG and have the property that that the sum\nof the central charges associated with the SLE$_\\kappa$ curve, the $\\gamma$-LQG\nsurface, and the auxiliary fields is 26. This condition on the central charge\nis natural from the perspective of bosonic string theory. We also prove\nanalogous statements when the SLE curve is replaced by, e.g., an LQG metric\nball or a Brownian motion path. Statements of this type were conjectured by\nSheffield and are continuum analogs of certain Markov properties of random\nplanar maps decorated by two or more statistical physics models. We include a\nsubstantial list of open problems.\n']","[('liouville quantum gravity', 0.5535640120506287), ('quantum gravity lqg', 0.5311325788497925), ('liouville conformal', 0.5048843026161194), ('liouville conformal field', 0.4766657054424286), ('liouville quantum', 0.4733099639415741), ('quantum gravity', 0.43915680050849915), ('random surfaces', 0.4072670340538025), ('sle curves', 0.40712010860443115), ('conformal', 0.4028014540672302), ('via conformal', 0.400940477848053)]"
158,158,174,158_bifurcation limit_limit cycles_bifurcations_bifurcation,"['bifurcation limit', 'limit cycles', 'bifurcations', 'bifurcation', 'limit cycle', 'zero hopf bifurcation', 'hopf bifurcation', 'systems limit', 'bifurcate', 'polynomial systems']","['Limit cycles of piecewise smooth differential systems with nilpotent\n  center and linear saddle   In this paper, we study the number of limit cycles of a piecewise smooth\ndifferential system separated by one or two parallel straight lines or rays\nformed by a nilpotent center or degenerate center and linear saddle. Piecewise\nlinear differential systems separated by one or two parallel straight lines\nwith one of the subsystems of type nilpotent center and other subsystems of\ntype linear saddle can have at most two limit cycles and there are systems in\nthese classes having one limit cycle. The limit cycle in particular consists of\nsaddle separatrices of the subsystem.\n', 'Limit cycles appearing from the perturbation of differential systems\n  with multiple switching curves   This paper deals with the problem of limit cycle bifurcations for a piecewise\nnear-Hamilton system with four regions separated by algebraic curves $y=\\pm\nx^2$. By analyzing the obtained first order Melnikov function, we give an upper\nbound of the number of limit cycles which bifurcate from the period annulus\naround the origin under $n$-th degree polynomial perturbations. In the case\n$n=1$, we obtain that at least 4 (resp. 3) limit cycles can bifurcate from the\nperiod annulus if the switching curves are $y=\\pm x^2$ (resp. $y=x^2$ or\n$y=-x^2$). The results also show that the number of switching curves affects\nthe number of limit cycles.\n', 'On the number of limit cycles for Bogdanov-Takens system under\n  perturbations of piecewise smooth polynomials   In this paper, we study the bifurcate of limit cycles for Bogdanov-Takens\nsystem($\\dot{x}=y$, $\\dot{y}=-x+x^{2}$) under perturbations of piecewise smooth\npolynomials of degree $2$ and $n$ respectively. We bound the number of zeros of\nfirst order Melnikov function which controls the number of limit cycles\nbifurcating from the center. It is proved that the upper bounds of the number\nof limit cycles with switching curve $x=y^{2m}$($m$ is a positive integral) are\n$(39m+36)n+77m+21(m\\geq 2)$ and $50n+52(m=1)$ (taking into account the\nmultiplicity). The upper bounds number of limit cycles with switching lines\n$x=0$ and $y=0$ are 11 (taking into account the multiplicity) and it can be\nreached.\n']","[('bifurcation limit', 0.6433734893798828), ('limit cycles', 0.5862330794334412), ('bifurcations', 0.5670191049575806), ('bifurcation', 0.5374869108200073), ('limit cycle', 0.5305013656616211), ('zero hopf bifurcation', 0.4931919574737549), ('hopf bifurcation', 0.4757435619831085), ('systems limit', 0.4076173007488251), ('bifurcate', 0.40718457102775574), ('polynomial systems', 0.4000158905982971)]"
159,159,173,159_galton watson branching_branching processes_galton watson processes_watson branching process,"['galton watson branching', 'branching processes', 'galton watson processes', 'watson branching process', 'state branching processes', 'branching processes immigration', 'branching processes random', 'galton watson process', 'branching process', 'watson branching']","['Asymptotic behaviour of critical decomposable 2-type Galton-Watson\n  processes with immigration   In this paper the asymptotic behaviour of a critical 2-type Galton-Watson\nprocess with immigration is described when its offspring mean matrix is\nreducible, in other words, when the process is decomposable. It is proved that,\nunder second or fourth order moment assumptions on the offspring and\nimmigration distributions, a sequence of appropriately scaled random step\nprocesses formed from a critical decomposable 2-type Galton-Watson process with\nimmigration converges weakly. The limit process can be described using one or\ntwo independent squared Bessel processes and possibly the unique stationary\ndistribution of an appropriate single-type subcritical Galton-Watson process\nwith immigration. Our results complete and extend the results of Foster and Ney\n(1978) for some strongly critical decomposable 2-type Galton-Watson processes\nwith immigration.\n', ""Galton-Watson processes and their role as building blocks for branching\n  processes   This article is an essay, both expository and argumentative, on the\nGalton-Watson process as a tool in the domain of Branching Processes. It is at\nthe same time the author's ways to honour two distinguished scientists in this\ndomain, both from the Russian Academy of Science, and to congratulate them for\ntheir special birthdays coming up very soon. The thread of the article is the\nrole, which the Galton-Watson process had played in the author's own research.\nWe start with an article on a controlled Galton-Watson process. Then we pass to\nrandom absorbing processes, and also recall and discuss a problem in medicine.\nFurther questions will bring us via the Borel-Cantelli Lemma to\n$\\varphi$-branching processes and extensions. To gain more generality, we then\nlook at bisexual Galton-Watson processes. Finally we briefly discuss relatively\ncomplicated resource dependent branching processes to show that, here again,\nusing Galton-Watson reproduction schemes (whenever reasonable) can be a\nconvincing approach to new processes which are then sufficiently tractable to\nobtain results of interest.\n  Keywords: Controlled branching process; $\\varphi$-branching process, Bisexual\nreproduction, Borel-Cantelli Lemma; Resource dependence; Society forms,\nStopping times, Theorem of envelopment, BRS-inequality.\n"", 'On tail behaviour of stationary second-order Galton-Watson processes\n  with immigration   A second-order Galton-Watson process with immigration can be represented as a\ncoordinate process of a 2-type Galton-Watson process with immigration.\nSufficient conditions are derived on the offspring and immigration\ndistributions of a second-order Galton-Watson process with immigration under\nwhich the corresponding 2-type Galton-Watson process with immigration has a\nunique stationary distribution such that its common marginals are regularly\nvarying. In the course of the proof sufficient conditions are given under which\nthe distribution of a second-order Galton-Watson process (without immigration)\nat any fixed time is regularly varying provided that the initial sizes of the\npopulation are independent and regularly varying.\n']","[('galton watson branching', 0.6675693988800049), ('branching processes', 0.6585055589675903), ('galton watson processes', 0.6525123715400696), ('watson branching process', 0.6416667699813843), ('state branching processes', 0.6255120038986206), ('branching processes immigration', 0.6235400438308716), ('branching processes random', 0.6163804531097412), ('galton watson process', 0.6100903749465942), ('branching process', 0.5937008857727051), ('watson branching', 0.586607038974762)]"
160,160,172,160_braid groups_braid group_artin braid group_strand braid,"['braid groups', 'braid group', 'artin braid group', 'strand braid', 'braids', 'braid', 'pure braid', 'braid monoid', 'knot groups', 'artin braid']","['Homomorphisms between braid groups   We give a complete classification of homomorphisms from the braid group on\n$n$ strands to the braid group on $2n$ strands when $n$ is at least 5. We also\nclassify endomorphisms of the braid group on 4 strands, as well as\nhomomorphisms from the commutator subgroup of the braid group on $n$ strands to\nthe braid group on $2n-5$ strands. Our classifications suggest a recursive\nclassification of homomorphisms between any braid groups. We also give a\nsimple, geometric proof of a theorem of Lin that highly constrains the\nholomorphic maps that may exist between spaces of monic, square-free\npolynomials of two given degrees.\n', 'Characteristic subgroups and the R$_\\infty$-property for virtual braid\n  groups   Let $n\\geq 2$. Let $VB_n$ (resp. $VP_n$) denote the virtual braid group\n(resp. virtual pure braid group), let $WB_n$ (resp. $WP_n$) denote the welded\nbraid group (resp. welded pure braid group) and let $UVB_n$ (resp. $UVP_n$)\ndenote the unrestricted virtual braid group (resp. unrestricted virtual pure\nbraid group). In the first part of this paper we prove that, for $n\\geq 4$, the\ngroup $VP_n$ and for $n\\geq 3$ the groups $WP_n$ and $UVP_n$ are characteristic\nsubgroups of $VB_n$, $WB_n$ and $UVB_n$, respectively. In the second part of\nthe paper we show that, for $n\\geq 2$, the virtual braid group $VB_n$, the\nunrestricted virtual pure braid group $UVP_n$, and the unrestricted virtual\nbraid group $UVB_n$ have the R$_\\infty$-property. As a consequence of the\ntechnique used for few strings we also prove that, for $n=2,3,4$, the welded\nbraid group $WB_n$ has the R$_\\infty$-property and that for $n=2$ the\ncorresponding pure braid groups have the R$_\\infty$-property. On the other hand\nfor $n\\geq 3$ it is unknown if the R$_\\infty$-property holds or not for the\nvirtual pure braid group $VP_n$ and the welded pure braid group $WP_n$.\n', 'The braid group injects in the virtual braid group   The virtual braid groups are generalizations of the classical braid groups.\nThis paper gives an elementary proof that the classical braid group injects\ninto the virtual braid group over the same number of strands.\n']","[('braid groups', 0.7950873970985413), ('braid group', 0.7405962347984314), ('artin braid group', 0.6794162392616272), ('strand braid', 0.5906113982200623), ('braids', 0.589880108833313), ('braid', 0.5736347436904907), ('pure braid', 0.563644289970398), ('braid monoid', 0.538232147693634), ('knot groups', 0.5322605967521667), ('artin braid', 0.526665210723877)]"
161,161,172,161_mappings metric spaces_fixed point theorems_fixed point generalized_existence fixed points,"['mappings metric spaces', 'fixed point theorems', 'fixed point generalized', 'existence fixed points', 'spaces fixed point', 'contraction mappings', 'mappings metric', 'contractive mappings', 'mapping metric', 'fixed point theory']","['New directions in fixed point theory in $G$-metric spaces and\n  applications to mappings contracting perimeters of triangles   We are concerned with the study of fixed points for mappings $T: X\\to X$,\nwhere $(X,G)$ is a $G$-metric space in the sense of Mustafa and Sims. After the\npublication of the paper [Journal of Nonlinear and Convex Analysis. 7(2) (2006)\n289--297] by Mustafa and Sims, a great interest was devoted to the study of\nfixed points in $G$-metric spaces. In 2012, the first and third authors\nobserved that several fixed point theorems established in $G$-metric spaces are\nimmediate consequences of known fixed point theorems in standard metric spaces.\nThis observation demotivated the investigation of fixed points in $G$-metric\nspaces. In this paper, we open new directions in fixed point theory in\n$G$-metric spaces. Namely, we establish new versions of the Banach, Kannan and\nReich fixed point theorems in $G$-metric spaces. We point out that the approach\nused by the first and third authors [Fixed Point Theory Appl. 2012 (2012) 1--7]\nis inapplicable in the present study. We also provide some interesting\napplications related to mappings contracting perimeters of triangles.\n', 'Fixed point results for multipoint Kannan-type mappings   We introduce and study a new type of mappings in metric spaces termed\n$n$-point Kannan-type mappings. A fixed-point theorem is proved for these\nmappings. In general case such mappings are discontinuous in the domain but\nnecessarily continuous at fixed points. Conditions under which usual Kannan\nmappings and mapping contracting the total pairwise distances between $n$\npoints are $n$-point Kannan-type mappings are found. It is shown that\nadditional conditions of asymptotic regularity and continuity allow to extend\nthe value of the contraction coefficient in fixed-point theorems for $n$-point\nKannan-type mappings.\n', 'Fixed point theorem for generalized Kannan type mappings   We introduce a new type of mappings in metric spaces which are three-point\nanalogue of the well-known Kannan type mappings and call them generalized\nKannan type mappings. It is shown that in general case such mappings are\ndiscontinuous but continuous at fixed points as well as Kannan type mappings\nand that these two classes of mappings are independent. The fixed-point theorem\nfor generalized Kannan type mappings is proved. Additional conditions of\nasymptotic regularity and continuity allow us to extent the class of mappings\nfor which the fixed-point theorems hold. Following Kannan, we also obtain two\nother fixed-point theorems for generalized Kannan type mappings in metric\nspaces which are not obligatory complete.\n']","[('mappings metric spaces', 0.6647870540618896), ('fixed point theorems', 0.6355462074279785), ('fixed point generalized', 0.6272403001785278), ('existence fixed points', 0.6262998580932617), ('spaces fixed point', 0.6194776892662048), ('contraction mappings', 0.6144412755966187), ('mappings metric', 0.608924150466919), ('contractive mappings', 0.5776727199554443), ('mapping metric', 0.5740983486175537), ('fixed point theory', 0.5725624561309814)]"
162,162,171,162_dynamic mode decomposition_koopman operator based_based koopman operator_mode decomposition,"['dynamic mode decomposition', 'koopman operator based', 'based koopman operator', 'mode decomposition', 'koopman operator theory', 'systems koopman operator', 'mode decomposition dmd', 'koopman operators', 'koopman operator', 'koopman eigenfunctions']","[""Invariant Consistent Dynamic Mode Decomposition   Any deterministic autonomous dynamical system may be globally linearized by\nits' Koopman operator. This object is typically infinite-dimensional and can be\napproximated by the so-called Dynamic Mode Decomposition (DMD). In DMD, the\ncentral idea is to preserve a fundamental property of the Koopman operator:\nlinearity. This work augments DMD by preserving additional properties like\nfunctional relationships between observables and consistency along geometric\ninvariants. The first set of constraints provides a framework for understanding\nDMD variants like Higher-order DMD and Affine DMD. The latter set guarantees\nthe estimation of Koopman eigen-functions with eigen-value 1, whose level sets\nare known to delineate invariant sets. These benefits are realized with only a\nminimal increase in computational cost, primarily due to the linearity of\nconstraints.\n"", 'The kernel perspective on dynamic mode decomposition   This manuscript revisits theoretical assumptions concerning dynamic mode\ndecomposition (DMD) of Koopman operators, including the existence of lattices\nof eigenfunctions, common eigenfunctions between Koopman operators, and\nboundedness and compactness of Koopman operators. Counterexamples that\nillustrate restrictiveness of the assumptions are provided for each of the\nassumptions. In particular, this manuscript proves that the native reproducing\nkernel Hilbert space (RKHS) of the Gaussian RBF kernel function only supports\nbounded Koopman operators if the dynamics are affine. In addition, a new\nframework for DMD, that requires only densely defined Koopman operators over\nRKHSs is introduced, and its effectiveness is demonstrated through numerical\nexamples.\n', 'A concise introduction to Koopman operator theory and the Extended\n  Dynamic Mode Decomposition   The framework of Koopman operator theory is discussed along with its\nconnections to Dynamic Mode Decomposition (DMD) and (Kernel) Extended Dynamic\nMode Decomposition (EDMD). This paper provides a succinct overview with\nconsistent notation. The authors hope to provide an exposition that more\nnaturally emphasizes the connections between theory and algorithms which may\nresult in a sense of clarity on the subject.\n']","[('dynamic mode decomposition', 0.7435837984085083), ('koopman operator based', 0.658954918384552), ('based koopman operator', 0.6513270735740662), ('mode decomposition', 0.6494140625), ('koopman operator theory', 0.6374648213386536), ('systems koopman operator', 0.6280875205993652), ('mode decomposition dmd', 0.6209798455238342), ('koopman operators', 0.6200594305992126), ('koopman operator', 0.6058586239814758), ('koopman eigenfunctions', 0.5293915867805481)]"
163,163,169,163_decoder polar codes_polar code construction_polar codes based_decoder polar,"['decoder polar codes', 'polar code construction', 'polar codes based', 'decoder polar', 'codes polar codes', 'polar codes', 'polar code', 'codes polar', 'successive cancellation decoding', 'scl decoding']","['Row-Merged Polar Codes: Analysis, Design and Decoder Implementation   Row-merged polar codes are a family of pre-transformed polar codes (PTPCs)\nwith little precoding overhead. Providing an improved distance spectrum over\nplain polar codes, they are capable to perform close to the finite-length\ncapacity bounds. However, there is still a lack of efficient design procedures\nfor row-merged polar codes. Using novel weight enumeration algorithms with low\ncomputational complexity, we propose a design methodology for row-merged polar\ncodes that directly considers their minimum distance properties. The codes\nsignificantly outperform state-of-the-art cyclic redundancy check (CRC)-aided\npolar codes under successive cancellation list (SCL) decoding in\nerror-correction performance. Furthermore, we present fast simplified\nsuccessive cancellation list (Fast-SSCL) decoding of PTPCs, based on which we\nderive a high-throughput, unrolled architecture template for fully pipelined\ndecoders. Implementation results of SCL decoders for row-merged polar codes in\na 12 nm technology additionally demonstrate the superiority of these codes with\nrespect to the implementation costs, compared to state-of-the-art reference\ndecoder implementations.\n', 'Simplified Successive Cancellation List Decoding of PAC Codes   Polar codes are the first class of structured channel codes that achieve the\nsymmetric capacity of binary channels with efficient encoding and decoding. In\n2019, Arikan proposed a new polar coding scheme referred to as\npolarization-adjusted convolutional (PAC)} codes. In contrast to polar codes,\nPAC codes precode the information word using a convolutional code prior to\npolar encoding. This results in material coding gain over polar code under Fano\nsequential decoding as well as successive cancellation list (SCL) decoding.\nGiven the advantages of SCL decoding over Fano decoding in certain scenarios\nsuch as low-SNR regime or where a constraint on the worst case decoding latency\nexists, in this paper, we focus on SCL decoding and present a simplified SCL\n(SSCL) decoding algorithm for PAC codes. SSCL decoding of PAC codes reduces the\ndecoding latency by identifying special nodes in the decoding tree and\nprocessing them at the intermediate stages of the graph. Our simulation results\nshow that the performance of PAC codes under SSCL decoding is almost similar to\nthe SCL decoding while having lower decoding latency.\n', 'Successive Cancellation Automorphism List Decoding of Polar Codes   The discovery of suitable automorphisms of polar codes gained a lot of\nattention by applying them in Automorphism Ensemble Decoding (AED) to improve\nthe error-correction performance, especially for short block lengths. This\npaper introduces Successive Cancellation Automorphism List (SCAL) decoding of\npolar codes as a novel application of automorphisms in advanced Successive\nCancellation List (SCL) decoding. Initialized with L permutations sampled from\nthe automorphism group, a superposition of different noise realizations and\npath splitting takes place inside the decoder. In this way, the SCAL decoder\nautomatically adapts to the channel conditions and outperforms the\nerror-correction performance of conventional SCL decoding and AED. For a polar\ncode of length 128, SCAL performs near Maximum Likelihood (ML) decoding with\nL=8, in contrast to M=16 needed decoder cores in AED. Application-Specific\nIntegrated Circuit (ASIC) implementations in a 12 nm technology show that\nhigh-throughput, pipelined SCAL decoders outperform AED in terms of energy\nefficiency and power density, and SCL decoders additionally in area efficiency.\n']","[('decoder polar codes', 0.6968479156494141), ('polar code construction', 0.6283882260322571), ('polar codes based', 0.6228757500648499), ('decoder polar', 0.617719829082489), ('codes polar codes', 0.6092422008514404), ('polar codes', 0.6077226996421814), ('polar code', 0.5921953320503235), ('codes polar', 0.5817708969116211), ('successive cancellation decoding', 0.5515181422233582), ('scl decoding', 0.5430305004119873)]"
164,164,169,164_monomial ideals_monomial ideals let_monomial ideal_graded ideals,"['monomial ideals', 'monomial ideals let', 'monomial ideal', 'graded ideals', 'graded ideal', 'type ideals', 'ideals polynomial', 'ideals generated', 'ideal polynomial ring', 'ideals whose']","['On the copersistence property and nearly copersistence property of\n  monomial ideals   In this paper we investigate the monomial ideals which satisfy the\ncopersistence property or nearly copersistence property.\n', 'Simplicial Resolutions of Powers of Square-free Monomial Ideals   The Taylor resolution is almost never minimal for powers of monomial ideals,\neven in the square-free case. In this paper we introduce a smaller resolution\nfor each power of any square-free monomial ideal, which depends only on the\nnumber of generators of the ideal. More precisely, for every pair of fixed\nintegers $r$ and $q$, we construct a simplicial complex that supports a free\nresolution of the $r$-th power of any square-free monomial ideal with $q$\ngenerators. The resulting resolution is significantly smaller than the Taylor\nresolution, and is minimal for special cases. Considering the relations on the\ngenerators of a fixed ideal allows us to further shrink these resolutions. We\nalso introduce a class of ideals called ""extremal ideals"", and show that the\nBetti numbers of powers of all square-free monomial ideals are bounded by Betti\nnumbers of powers of extremal ideals. Our results lead to upper bounds on Betti\nnumbers of powers of any square-free monomial ideal that greatly improve the\nbinomial bounds offered by the Taylor resolution.\n', 'Powers of Principal $Q$-Borel ideals   Fix a poset $Q$ on $\\{x_1,\\ldots,x_n\\}$. A $Q$-Borel monomial ideal $I\n\\subseteq \\mathbb{K}[x_1,\\ldots,x_n]$ is a monomial ideal whose monomials are\nclosed under the Borel-like moves induced by $Q$. A monomial ideal $I$ is a\nprincipal $Q$-Borel ideal, denoted $I=Q(m)$, if there is a monomial $m$ such\nthat all the minimal generators of $I$ can be obtained via $Q$-Borel moves from\n$m$. In this paper we study powers of principal $Q$-Borel ideals. Among our\nresults, we show that all powers of $Q(m)$ agree with their symbolic powers,\nand that the ideal $Q(m)$ satisfies the persistence property for associated\nprimes. We also compute the analytic spread of $Q(m)$ in terms of the poset\n$Q$.\n']","[('monomial ideals', 0.7982827425003052), ('monomial ideals let', 0.7503976225852966), ('monomial ideal', 0.7490582466125488), ('graded ideals', 0.6292816400527954), ('graded ideal', 0.5613270401954651), ('type ideals', 0.5608906149864197), ('ideals polynomial', 0.5596798658370972), ('ideals generated', 0.5499230623245239), ('ideal polynomial ring', 0.5393364429473877), ('ideals whose', 0.5311498045921326)]"
165,165,167,165_constellation shaping_optical communications_coded modulation_optical communication,"['constellation shaping', 'optical communications', 'coded modulation', 'optical communication', 'modulation formats', 'probabilistic shaping', 'optical wireless communication', 'intensity modulation', 'modulation direct detection', 'intensity modulation direct']","['On the Performance of Multidimensional Constellation Shaping for Linear\n  and Nonlinear Optical Fiber Channel   Multidimensional constellation shaping of up to 32 dimensions with different\nspectral efficiencies are compared through AWGN and fiber-optic simulations.\nThe results show that no constellation is universal and the balance of required\nand effective SNRs should be jointly considered for the specific optical\ntransmission scenario.\n', 'Sequence-Selection-Based Constellation Shaping for Nonlinear Channels   Probabilistic shaping is a pragmatic approach to improve the performance of\ncoherent optical fiber communication systems. In the nonlinear regime, the\nadvantages offered by probabilistic shaping might increase thanks to the\nopportunity to obtain an additional nonlinear shaping gain. Unfortunately, the\noptimization of conventional shaping techniques, such as probabilistic\namplitude shaping (PAS), yields a relevant nonlinear shaping gain only in\nscenarios of limited practical interest. In this manuscript we use sequence\nselection to investigate the potential, opportunities, and challenges offered\nby probabilistic shaping for nonlinear channels. First, we show that ideal\nsequence selection is able to provide up to 0.13 bit/s/Hz gain with respect to\nPAS with an optimized blocklength. However, this additional gain is obtained\nonly if the selection metric accounts for the signs of the symbols: they must\nbe known to compute the selection metric, but there is no need to shape them.\nFurthermore, we show that the selection depends in a non-critical way on the\nsymbol rate and link length: the sequences selected for a certain scenario\nstill provide a relevant gain if these are modified. Then, we analyze and\ncompare several practical implementations of sequence selection by taking into\naccount interaction with forward error correction (FEC) and complexity.\nOverall, the single block and the multi block FEC-independent bit scrambling\nare the best options, with a gain up to 0.08 bit/s/Hz. The main challenge and\nlimitation to their practical implementation remains the evaluation of the\nmetric, whose complexity is currently too high. Finally, we show that the\nnonlinear shaping gain provided by sequence selection persists when carrier\nphase recovery is included.\n', 'Probabilistically Shaped 4-PAM for Short-Reach IM/DD Links with a Peak\n  Power Constraint   Probabilistic shaping for intensity modulation and direct detection (IM/DD)\nlinks is discussed and a peak power constraint determined by the limited\nmodulation extinction ratio (ER) of optical modulators is introduced. The input\ndistribution of 4-ary unipolar pulse amplitude modulation (PAM) symbols is\noptimized for short-reach transmission links without optical amplification nor\nin-line dispersion compensation. The resulting distribution is symmetric around\nits mean allowing to use probabilistic amplitude shaping (PAS) to generate\nsymbols that are protected by forward error correction (FEC) and that have the\noptimal input distribution. The numerical analysis is confirmed experimentally\nfor both an additive white Gaussian noise (AWGN) channel and a fiber channel,\nshowing gains in transmission reach and transmission rate, as well as rate\nadaptability.\n']","[('constellation shaping', 0.5586516261100769), ('optical communications', 0.5421646237373352), ('coded modulation', 0.4977280795574188), ('optical communication', 0.4918655455112457), ('modulation formats', 0.4917620122432709), ('probabilistic shaping', 0.48004239797592163), ('optical wireless communication', 0.4678390920162201), ('intensity modulation', 0.45748427510261536), ('modulation direct detection', 0.45307156443595886), ('intensity modulation direct', 0.4513396918773651)]"
166,166,165,166_deep reinforcement learning_reinforcement learning drl_deep network dqn_multi agent deep,"['deep reinforcement learning', 'reinforcement learning drl', 'deep network dqn', 'multi agent deep', 'radio resource management', 'agent reinforcement learning', 'network dqn', 'deep reinforcement', 'reinforcement learning', 'resource allocation']","['Deep Reinforcement Learning Based Multidimensional Resource Management\n  for Energy Harvesting Cognitive NOMA Communications   The combination of energy harvesting (EH), cognitive radio (CR), and\nnon-orthogonal multiple access (NOMA) is a promising solution to improve energy\nefficiency and spectral efficiency of the upcoming beyond fifth generation\nnetwork (B5G), especially for support the wireless sensor communications in\nInternet of things (IoT) system. However, how to realize intelligent frequency,\ntime, and energy resource allocation to support better performances is an\nimportant problem to be solved. In this paper, we study joint spectrum, energy,\nand time resource management for the EH-CR-NOMA IoT systems. Our goal is to\nminimize the number of data packets losses for all secondary sensing users\n(SSU), while satisfying the constraints on the maximum charging battery\ncapacity, maximum transmitting power, maximum buffer capacity, and minimum data\nrate of primary users (PU) and SSUs. Due to the non-convexity of this\noptimization problem and the stochastic nature of the wireless environment, we\npropose a distributed multidimensional resource management algorithm based on\ndeep reinforcement learning (DRL). Considering the continuity of the resources\nto be managed, the deep deterministic policy gradient (DDPG) algorithm is\nadopted, based on which each agent (SSU) can manage its own multidimensional\nresources without collaboration. In addition, a simplified but practical action\nadjuster (AA) is introduced for improving the training efficiency and battery\nperformance protection. The provided results show that the convergence speed of\nthe proposed algorithm is about 4 times faster than that of DDPG, and the\naverage number of packet losses (ANPL) is about 8 times lower than that of the\ngreedy algorithm.\n', 'Dynamic Channel Access and Power Control in Wireless Interference\n  Networks via Multi-Agent Deep Reinforcement Learning   Due to the scarcity in the wireless spectrum and limited energy resources\nespecially in mobile applications, efficient resource allocation strategies are\ncritical in wireless networks. Motivated by the recent advances in deep\nreinforcement learning (DRL), we address multi-agent DRL-based joint dynamic\nchannel access and power control in a wireless interference network. We first\npropose a multi-agent DRL algorithm with centralized training (DRL-CT) to\ntackle the joint resource allocation problem. In this case, the training is\nperformed at the central unit (CU) and after training, the users make\nautonomous decisions on their transmission strategies with only local\ninformation. We demonstrate that with limited information exchange and faster\nconvergence, DRL-CT algorithm can achieve 90% of the performance achieved by\nthe combination of weighted minimum mean square error (WMMSE) algorithm for\npower control and exhaustive search for dynamic channel access. In the second\npart of this paper, we consider distributed multi-agent DRL scenario in which\neach user conducts its own training and makes its decisions individually,\nacting as a DRL agent. Finally, as a compromise between centralized and fully\ndistributed scenarios, we consider federated DRL (FDRL) to approach the\nperformance of DRL-CT with the use of a central unit in training while limiting\nthe information exchange and preserving privacy of the users in the wireless\nsystem. Via simulation results, we show that proposed learning frameworks lead\nto efficient adaptive channel access and power control policies in dynamic\nenvironments.\n', 'Meta-Reinforcement Learning Based Resource Allocation for Dynamic V2X\n  Communications   This paper studies the allocation of shared resources between\nvehicle-to-infrastructure (V2I) and vehicle-to-vehicle (V2V) links in\nvehicle-to-everything (V2X) communications. In existing algorithms, dynamic\nvehicular environments and quantization of continuous power become the\nbottlenecks for providing an effective and timely resource allocation policy.\nIn this paper, we develop two algorithms to deal with these difficulties.\nFirst, we propose a deep reinforcement learning (DRL)-based resource allocation\nalgorithm to improve the performance of both V2I and V2V links. Specifically,\nthe algorithm uses deep Q-network (DQN) to solve the sub-band assignment and\ndeep deterministic policy-gradient (DDPG) to solve the continuous power\nallocation problem. Second, we propose a meta-based DRL algorithm to enhance\nthe fast adaptability of the resource allocation policy in the dynamic\nenvironment. Numerical results demonstrate that the proposed DRL-based\nalgorithm can significantly improve the performance compared to the DQN-based\nalgorithm that quantizes continuous power. In addition, the proposed meta-based\nDRL algorithm can achieve the required fast adaptation in the new environment\nwith limited experiences.\n']","[('deep reinforcement learning', 0.546940267086029), ('reinforcement learning drl', 0.5117605328559875), ('deep network dqn', 0.483656644821167), ('multi agent deep', 0.44250497221946716), ('radio resource management', 0.4358658790588379), ('agent reinforcement learning', 0.4342656135559082), ('network dqn', 0.43169939517974854), ('deep reinforcement', 0.4256437122821808), ('reinforcement learning', 0.422063410282135), ('resource allocation', 0.40901046991348267)]"
167,167,165,167_superintegrable systems_superintegrability_superintegrable_integrable systems,"['superintegrable systems', 'superintegrability', 'superintegrable', 'integrable systems', 'integrable hamiltonian', 'system integrable', 'hamiltonian systems', 'degenerate second order', 'lagrangian form', 'hamiltonian system']","['Classical Superintegrable Systems in a Magnetic Field that Separate in\n  Cartesian Coordinates   We consider superintegrability in classical mechanics in the presence of\nmagnetic fields. We focus on three-dimensional systems which are separable in\nCartesian coordinates. We construct all possible minimally and maximally\nsuperintegrable systems in this class with additional integrals quadratic in\nthe momenta. Together with the results of our previous paper [J. Phys. A: Math.\nTheor. 50 (2017), 245202, 24 pages], where one of the additional integrals was\nby assumption linear, we conclude the classification of three-dimensional\nquadratically minimally and maximally superintegrable systems separable in\nCartesian coordinates. We also describe two particular methods for constructing\nsuperintegrable systems with higher-order integrals.\n', 'Abundant Superintegrable Systems and Hessian Structures   We show that a large class of non-degenerate second-order (maximally)\nsuperintegrable systems gives rise to Hessian structures, which admit natural\n(Hessian) coordinates adapted to the superintegrable system. In particular,\nabundant superintegrable systems on Riemannian manifolds of constant sectional\ncurvature fall into this class. We explicitly compute the natural Hessian\ncoordinates for examples of non-degenerate second-order superintegrable systems\nin dimensions two and three.\n', 'Algebraic Conditions for Conformal Superintegrability in Arbitrary\n  Dimension   We show that the definition of a second order superintegrable system on a\n(pseudo-)Riemannian manifold gives rise to a conformally invariant notion of\nsuperintegrability. Conformal equivalence is the natural extension of the\nwell-known St\\""ackel transform, which in turn originates from the classical\nMaupertuis-Jacobi principle. We extend our recently developed algebraic\ngeometric approach for the classification of second order superintegrable\nsystems in arbitrarily high dimension to conformally superintegrable systems,\nwhich are presented via conformal scale choices of second order superintegrable\nsystems defined within a conformal geometry.\n  For superintegrable systems on constant curvature spaces, we find that the\nconformal scales of St\\""ackel equivalent systems arise from eigenfunctions of\nthe Laplacian and that their equivalence is characterised by a conformal\ndensity of weight two.\n  Our approach yields an algebraic equation that governs the classification\nunder conformal equivalence for a prolific class of second order conformally\nsuperintegrable systems. This class contains all non-degenerate examples known\nto date, and is given by a simple algebraic constraint of degree two on a\ngeneral harmonic cubic form. In this way the yet unsolved classification\nproblem is put into the reach of algebraic geometry and geometric invariant\ntheory. In particular, no obstruction exists in dimension three, and thus the\nknown classification of conformally superintegrable systems is reobtained in\nthe guise of an unrestricted univariate sextic. In higher dimensions, the\nobstruction is new and has never been revealed by traditional approaches.\n']","[('superintegrable systems', 0.7914242148399353), ('superintegrability', 0.612334668636322), ('superintegrable', 0.596089243888855), ('integrable systems', 0.5664674639701843), ('integrable hamiltonian', 0.44306033849716187), ('system integrable', 0.4345724284648895), ('hamiltonian systems', 0.41521817445755005), ('degenerate second order', 0.4059016704559326), ('lagrangian form', 0.35218384861946106), ('hamiltonian system', 0.3466879427433014)]"
168,168,162,168_irs assisted wireless_aided wireless communication_reflecting surface irs_aided wireless,"['irs assisted wireless', 'aided wireless communication', 'reflecting surface irs', 'aided wireless', 'passive beamforming', 'wireless communication', 'passive irs', 'irs reflection', 'intelligent reflecting surface', 'reflecting surface aided']","['Multi-Hop Beam Routing for Hybrid Active/Passive IRS Aided Wireless\n  Communications   Prior studies on intelligent reflecting surface (IRS) have mostly considered\nwireless communication systems aided by a single passive IRS, which, however,\nhas limited control over wireless propagation environment and suffers from\nproduct-distance path-loss. To address these issues, we propose in this paper a\nnew hybrid active/passive IRS aided wireless communication system, where an\nactive IRS and multiple passive IRSs are deployed to assist the communication\nbetween a base station (BS) and a remote user in complex environment, by\nestablishing a multihop reflection path across active/passive IRSs. In\nparticular, the active IRS enables signal reflection with power amplification,\nthus effectively compensating the severe path-loss in the multi-reflection\npath. To maximize the achievable rate at the user, we first design the optimal\nbeamforming of the BS and selected (active/passive) IRSs for a given\nmulti-reflection path, and then propose an efficient algorithm to obtain the\noptimal multi-reflection path by using the path decomposition method and graph\ntheory. We show that the active IRS should be selected to establish the beam\nrouting path when its amplification power and/or number of active reflecting\nelements are sufficiently large. Last, numerical results demonstrate the\neffectiveness of the proposed hybrid active/passive IRS beam routing design as\ncompared to the benchmark scheme with passive IRSs only.\n', ""Simultaneous Transmit Diversity and Passive Beamforming with Large-Scale\n  Intelligent Reflecting Surface: Far-Field or Near-Field?   Intelligent reflecting surface (IRS) has emerged as a cost-effective solution\nto enhance wireless communication performance via passive signal reflection.\nExisting works on IRS have mainly focused on investigating IRS's passive\nbeamforming/reflection design to boost the communication rate for users\nassuming that their channel state information (CSI) is fully or partially\nknown. However, how to exploit IRS to improve the wireless transmission\nreliability without any CSI, which is typical in high-mobility/delay-sensitive\ncommunication scenarios, remains largely open. In this paper, we study a new\nIRS-aided communication system with the IRS integrated to its aided access\npoint (AP) to achieve both functions of transmit diversity and passive\nbeamforming simultaneously. Specifically, we first show an interesting result\nthat the IRS's passive beamforming gain in any direction is invariant to the\ncommon phase-shift applied to all of its reflecting elements. Accordingly, we\ndesign the common phase-shift of IRS elements to achieve transmit diversity at\nthe AP side without the need of any CSI of the users. In addition, we propose a\npractical method for the users to estimate the CSI at the receiver side for\ninformation decoding. Meanwhile, we show that the conventional passive\nbeamforming gain of IRS can be retained for the other users with their CSI\nknown at the AP. Furthermore, we derive the asymptotic performance of both\nIRS-aided transmit diversity and passive beamforming in closed-form, by\nconsidering the large-scale IRS with an infinite number of elements. Numerical\nresults validate our analysis and show the performance gains of the proposed\nIRS-aided simultaneous transmit diversity and passive beamforming scheme over\nother benchmark schemes.\n"", ""Wireless Communication Aided by Intelligent Reflecting Surface: Active\n  or Passive?   In this letter, we consider an intelligent reflecting surface (IRS)-aided\nwireless communication system, where an active or passive IRS is employed to\nassist the communication between an access point and a user. First, we consider\nthe downlink/uplink communication separately and optimize the IRS placement for\nrate maximization with an active or passive IRS. We show that the active IRS\nshould be deployed closer to the receiver with the IRS's decreasing\namplification power; while in contrast, the passive IRS should be deployed near\neither the transmitter or receiver. Moreover, with optimized IRS placement, the\npassive IRS is shown to outperform its active counterpart when the number of\nreflecting elements is sufficiently large and/or the active-IRS amplification\npower is too small. Next, we optimize the IRS placement for both active and\npassive IRSs to maximize the weighted sum-rate of uplink and downlink\ncommunications. We show that in this case, the passive IRS is more likely to\nachieve superior rate performance. This is because the optimal active-IRS\nplacement needs to balance the rate performance in the uplink and downlink,\nwhile deploying the passive IRS near the transmitter or receiver is optimal\nregardless of the uplink or downlink.\n""]","[('irs assisted wireless', 0.5621314644813538), ('aided wireless communication', 0.5074683427810669), ('reflecting surface irs', 0.4987248480319977), ('aided wireless', 0.47848302125930786), ('passive beamforming', 0.4616667330265045), ('wireless communication', 0.4525820314884186), ('passive irs', 0.4507982134819031), ('irs reflection', 0.4244692325592041), ('intelligent reflecting surface', 0.3988785147666931), ('reflecting surface aided', 0.3979097306728363)]"
169,169,161,169_fractional sobolev spaces_fractional sobolev space_orlicz sobolev spaces_fractional sobolev,"['fractional sobolev spaces', 'fractional sobolev space', 'orlicz sobolev spaces', 'fractional sobolev', 'sobolev embeddings', 'orlicz sobolev', 'sobolev type inequalities', 'sobolev spaces', 'sobolev space', 'sobolev inequalities']","[""Asymptotic behaviours in Fractional Orlicz-Sobolev spaces on Carnot\n  groups   In this article we define a class of fractional Orlicz-Sobolev spaces on\nCarnot groups and, in the spirit of the celebrated results of\nBourgain-Brezis-Mironescu and of Maz'ya-Shaposhnikova, we study the asymptotic\nbehavior of the Orlicz functionals when the fractional parameter goes to $1$\nand $0$.\n"", ""Sobolev embeddings in Musielak-Orlicz space   An embedding theorem for Sobolev spaces built upon general Musielak-Orlicz\nnorms is offered. These norms are defined in terms of generalized Young\nfunctions which also depend on the $x$ variable. Under minimal conditions on\nthe latter dependence, a Sobolev conjugate is associated with any function of\nthis type. Such a conjugate is sharp, in the sense that, for each fixed $x$, it\nagrees with the sharp Sobolev conjugate in classical Orlicz spaces. Both\nSobolev inequalities in the whole $\\mathbb{R}^n$ and Sobolev-Poincar\\'e\ninequalities in domains are established. Compact Sobolev embeddings are also\npresented. In particular, optimal embeddings for standard Orlicz-Sobolev\nspaces, variable exponent Sobolev spaces, and double-phase Sobolev spaces are\nrecovered and complemented in borderline cases. A key tool, of independent\ninterest, in our approach is a new weak type inequality for Riesz potentials in\nMusielak-Orlicz spaces involving a sharp fractional-order Sobolev conjugate.\n"", ""Asymptotics of weighted Gagliardo seminorms   In this paper we consider fractional Sobolev spaces equipped with weights\nbeing powers of the distance to the boundary of the domain. We prove the\nversions of Bourgain--Brezis--Mironescu and Maz'ya--Shaposhnikova asymptotic\nformulae for weighted fractional Gagliardo seminorms. For $p>1$ we also provide\na nonlocal characterization of classical weighted Sobolev spaces with power\nweights.\n""]","[('fractional sobolev spaces', 0.7633336782455444), ('fractional sobolev space', 0.7372028827667236), ('orlicz sobolev spaces', 0.6994900107383728), ('fractional sobolev', 0.6820287704467773), ('sobolev embeddings', 0.630621075630188), ('orlicz sobolev', 0.6274746060371399), ('sobolev type inequalities', 0.6174506545066833), ('sobolev spaces', 0.6162246465682983), ('sobolev space', 0.597863495349884), ('sobolev inequalities', 0.5885314345359802)]"
170,170,160,170_klt singularities_semi ample_divisor k_x_kodaira dimension,"['klt singularities', 'semi ample', 'divisor k_x', 'kodaira dimension', 'calabi yau varieties', 'klt pairs', 'canonical bundle', 'log canonical pairs', 'canonical divisor', 'log canonical pair']","['An inductive approach to generalized abundance using nef reduction   We use the canonical bundle formula for parabolic fibrations to give an\ninductive approach to the generalized abundance conjecture using nef reduction.\nIn particular, we observe that generalized abundance holds for a klt pair\n$(X,B)$ if the nef dimension $n(K_X+B+L)=2$ and $K_X+B \\geq 0$ or\n$n(K_X+B+L)=3$ and $\\kappa(K_X+B )>0$.\n', ""Nef and abundant divisors, semiampleness and canonical bundle formula   In this paper, we use canonical bundle formulas to prove some generalizations\nof an old theorem of Kawamata on the semiampleness of nef and abundant log\ncanonical divisors. In particular, we show that for klt pairs $(X,B)$ with\n$K_X+B$ effective, $L \\in Pic (X)$ nef, nefness and abundance of $K_X+B+L$\nimplies semiampleness. This essentially generalizes Kawamata's theorem to the\nsetting of generalized abundance.\n"", 'Boundedness and volume of generalised pairs   In this paper we investigate boundedness and volumes of generalised pairs,\nand give applications to usual pairs especially to a class of pairs that we\ncall stable log minimal models.\n  Fixing the dimension and a DCC set controlling coefficients, we will show\nthat the set of volumes of all projective generalised lc pairs $(X,B+M)$ under\nthe given data, satisfies the DCC. Futhermore, we will show that in the klt\ncase, the set of such pairs with ample $K_X+B+M$ and fixed volume, forms a\nbounded family.\n  We prove a result about descent of nef divisors to bounded families. This is\nthe key to proving the above and various other results.\n  We will then apply the above to study projective lc pairs $(X,B)$ with\nabundant $K_X+B$ of arbitrary Kodaira dimension. In particular, we show that\nthe set of Iitaka volumes of such pairs satisfies DCC under some natural\nboundedness assumptions on the fibres of the Iitaka fibration.\n  We define stable log minimal models which consist of a projective lc pair\n$(X,B)$ with semi-ample $K_X+B$ together with a divisor $A\\ge 0$ so that\n$K_X+B+A$ is ample and $A$ does not contain any non-klt centre of $(X,B)$. This\nis a generalisation of both usual stable pairs of general type and stable log\nCalabi-Yau pairs. Fixing appropriate invariants we show that stable log minimal\nmodels form a bounded family. Then we discuss connection with moduli spaces.\n']","[('klt singularities', 0.541581928730011), ('semi ample', 0.4949767589569092), ('divisor k_x', 0.47101110219955444), ('kodaira dimension', 0.4557146728038788), ('calabi yau varieties', 0.4531457722187042), ('klt pairs', 0.44905680418014526), ('canonical bundle', 0.4391011893749237), ('log canonical pairs', 0.42496469616889954), ('canonical divisor', 0.42253074049949646), ('log canonical pair', 0.4184620678424835)]"
171,171,160,171_affine hecke algebras_hecke algebras type_affine hecke algebra_hecke algebras,"['affine hecke algebras', 'hecke algebras type', 'affine hecke algebra', 'hecke algebras', 'hecke algebra type', 'hecke algebra', 'iwahori hecke algebra', 'klr algebras', 'double affine hecke', 'quiver hecke']","['Affine Hecke algebras and generalisations of quiver Hecke algebras for\n  type B   We define and study cyclotomic quotients of affine Hecke algebras of type B.\nWe establish an isomorphism between direct sums of blocks of these algebras and\na generalisation, for type B, of cyclotomic quiver Hecke algebras which are a\nfamily of graded algebras closely related to algebras introduced by Varagnolo\nand Vasserot. Inspired by the work of Brundan and Kleshchev we first give a\nfamily of isomorphisms for the corresponding result in type A which includes\ntheir original isomorphism. We then select a particular isomorphism from this\nfamily and use it to prove our result.\n', 'Morita equivalences for cyclotomic Hecke algebras of type B and D   We give a Morita equivalence theorem for so-called cyclotomic quotients of\naffine Hecke algebras of type B and D, in the spirit of a classical result of\nDipper-Mathas in type A for Ariki-Koike algebras. As a consequence, the\nrepresentation theory of affine Hecke algebras of type B and D reduces to the\nstudy of their cyclotomic quotients with eigenvalues in a single orbit under\nmultiplication by $q^2$ and inversion. The main step in the proof consists in a\ndecomposition theorem for generalisations of quiver Hecke algebras that\nappeared recently in the study of affine Hecke algebras of type B and D. This\ntheorem reduces the general situation of a disconnected quiver with involution\nto a simpler setting. To be able to treat types B and D at the same time we\nunify the different definitions of generalisations of quiver Hecke algebra for\ntype B that exist in the literature.\n', 'Affine Hecke algebras of type D and generalisations of quiver Hecke\n  algebras   We define and study cyclotomic quotients of affine Hecke algebras of type D.\nWe establish an isomorphism between (direct sums of blocks of) these cyclotomic\nquotients and a generalisation of cyclotomic quiver Hecke algebras which are a\nfamily of Z-graded algebras closely related to algebras introduced by Shan,\nVaragnolo and Vasserot. To achieve this, we first complete the study of\ncyclotomic quotients of affine Hecke algebras of type B by considering the\nsituation when a deformation parameter p squares to 1. We then relate the two\ngeneralisations of quiver Hecke algebras showing that the one for type D can be\nseen as fixed point subalgebras of their analogues for type B, and we carefully\nstudy how far this relation remains valid for cyclotomic quotients. This allows\nus to obtain the desired isomorphism. This isomorphism completes the family of\nisomorphisms relating affine Hecke algebras of classical types to\n(generalisations of) quiver Hecke algebras, originating in the famous result of\nBrundan and Kleshchev for the type A.\n']","[('affine hecke algebras', 0.7833150029182434), ('hecke algebras type', 0.7604078054428101), ('affine hecke algebra', 0.7373615503311157), ('hecke algebras', 0.7020856738090515), ('hecke algebra type', 0.6776257753372192), ('hecke algebra', 0.5876506567001343), ('iwahori hecke algebra', 0.5874727368354797), ('klr algebras', 0.5820763111114502), ('double affine hecke', 0.5439761877059937), ('quiver hecke', 0.512229859828949)]"
172,172,160,172_bayesian optimization_optimization bayesian_bayesian optimization bo_black box optimization,"['bayesian optimization', 'optimization bayesian', 'bayesian optimization bo', 'black box optimization', 'efficient global optimization', 'global optimization', 'objective optimization', 'optimization tasks', 'multi objective optimization', 'optimization methods']","['Parallel Predictive Entropy Search for Multi-objective Bayesian\n  Optimization with Constraints   Real-world problems often involve the optimization of several objectives\nunder multiple constraints. An example is the hyper-parameter tuning problem of\nmachine learning algorithms. In particular, the minimization of the estimation\nof the generalization error of a deep neural network and at the same time the\nminimization of its prediction time. We may also consider as a constraint that\nthe deep neural network must be implemented in a chip with an area below some\nsize. Here, both the objectives and the constraint are black boxes, i.e.,\nfunctions whose analytical expressions are unknown and are expensive to\nevaluate. Bayesian optimization (BO) methodologies have given state-of-the-art\nresults for the optimization of black-boxes. Nevertheless, most BO methods are\nsequential and evaluate the objectives and the constraints at just one input\nlocation, iteratively. Sometimes, however, we may have resources to evaluate\nseveral configurations in parallel. Notwithstanding, no parallel BO method has\nbeen proposed to deal with the optimization of multiple objectives under\nseveral constraints. If the expensive evaluations can be carried out in\nparallel (as when a cluster of computers is available), sequential evaluations\nresult in a waste of resources. This article introduces PPESMOC, Parallel\nPredictive Entropy Search for Multi-objective Bayesian Optimization with\nConstraints, an information-based batch method for the simultaneous\noptimization of multiple expensive-to-evaluate black-box functions under the\npresence of several constraints. Iteratively, PPESMOC selects a batch of input\nlocations at which to evaluate the black-boxes so as to maximally reduce the\nentropy of the Pareto set of the optimization problem. We present empirical\nevidence in the form of synthetic, benchmark and real-world experiments that\nillustrate the effectiveness of PPESMOC.\n', 'Deterministic Global Optimization of the Acquisition Function in\n  Bayesian Optimization: To Do or Not To Do?   Bayesian Optimization (BO) with Gaussian Processes relies on optimizing an\nacquisition function to determine sampling. We investigate the advantages and\ndisadvantages of using a deterministic global solver (MAiNGO) compared to\nconventional local and stochastic global solvers (L-BFGS-B and multi-start,\nrespectively) for the optimization of the acquisition function. For CPU\nefficiency, we set a time limit for MAiNGO, taking the best point as optimal.\nWe perform repeated numerical experiments, initially using the Muller-Brown\npotential as a benchmark function, utilizing the lower confidence bound\nacquisition function; we further validate our findings with three alternative\nbenchmark functions. Statistical analysis reveals that when the acquisition\nfunction is more exploitative (as opposed to exploratory), BO with MAiNGO\nconverges in fewer iterations than with the local solvers. However, when the\ndataset lacks diversity, or when the acquisition function is overly\nexploitative, BO with MAiNGO, compared to the local solvers, is more likely to\nconverge to a local rather than a global ly near-optimal solution of the\nblack-box function. L-BFGS-B and multi-start mitigate this risk in BO by\nintroducing stochasticity in the selection of the next sampling point, which\nenhances the exploration of uncharted regions in the search space and reduces\ndependence on acquisition function hyperparameters. Ultimately, suboptimal\noptimization of poorly chosen acquisition functions may be preferable to their\noptimal solution. When the acquisition function is more exploratory, BO with\nMAiNGO, multi-start, and L-BFGS-B achieve comparable probabilities of\nconvergence to a globally near-optimal solution (although BO with MAiNGO may\nrequire more iterations to converge under these conditions).\n', 'Bayesian Optimization for Function Compositions with Applications to\n  Dynamic Pricing   Bayesian Optimization (BO) is used to find the global optima of black box\nfunctions. In this work, we propose a practical BO method of function\ncompositions where the form of the composition is known but the constituent\nfunctions are expensive to evaluate. By assuming an independent Gaussian\nprocess (GP) model for each of the constituent black-box function, we propose\nExpected Improvement (EI) and Upper Confidence Bound (UCB) based BO algorithms\nand demonstrate their ability to outperform not just vanilla BO but also the\ncurrent state-of-art algorithms. We demonstrate a novel application of the\nproposed methods to dynamic pricing in revenue management when the underlying\ndemand function is expensive to evaluate.\n']","[('bayesian optimization', 0.7215151786804199), ('optimization bayesian', 0.707835853099823), ('bayesian optimization bo', 0.7075497508049011), ('black box optimization', 0.6775373220443726), ('efficient global optimization', 0.5766164660453796), ('global optimization', 0.5707074403762817), ('objective optimization', 0.5061849355697632), ('optimization tasks', 0.49889442324638367), ('multi objective optimization', 0.496522456407547), ('optimization methods', 0.49646633863449097)]"
173,173,159,173_elliptic k3 surfaces_k3 surfaces_singular k3 surfaces_surfaces k3,"['elliptic k3 surfaces', 'k3 surfaces', 'singular k3 surfaces', 'surfaces k3', 'polarized k3 surfaces', 'k3 surface', 'k3 surfaces picard', 'kummer surfaces', 'k3 surface picard', 'elliptic k3']","['Enriques involutions on singular K3 surfaces of small discriminants   We classify Enriques involutions on a K3 surface, up to conjugation in the\nautomorphism group, in terms of lattice theory. We enumerate such involutions\non singular K3 surfaces with transcendental lattice of discriminant smaller\nthan or equal to 36. For 11 of these K3 surfaces, we apply Borcherds method to\ncompute the automorphism group of the Enriques surfaces covered by them. In\nparticular, we investigate the structure of the two most algebraic Enriques\nsurfaces.\n', ""Lectures on Supersingular K3 Surfaces and the Crystalline Torelli\n  Theorem   We survey crystalline cohomology, crystals, and formal group laws with an\nemphasis on geometry. We apply these concepts to K3 surfaces, and especially to\nsupersingular K3 surfaces. In particular, we discuss stratifications of the\nmoduli space of polarized K3 surfaces in positive characteristic, Ogus'\ncrystalline Torelli theorem for supersingular K3 surfaces, the Tate conjecture,\nand the unirationality of K3 surfaces.\n"", ""Elliptic fibrations and involutions on K3 surfaces   We survey our contributions on the classification of elliptic fibrations on\nK3 surfaces with a non-symplectic involution. We place them in the more general\nframework of K3 surfaces with an involution without any hypothesis on its fixed\nlocus or on the action on the symplectic 2-form. We revisit the complete\nclassification of elliptic fibrations on K3 surfaces with a 2-elementary\nN\\'eron--Severi lattice, and give a complete classification of extremal\nelliptic fibrations on K3 surfaces that are quadratic covers of rational\nelliptic surfaces.\n""]","[('elliptic k3 surfaces', 0.8379067182540894), ('k3 surfaces', 0.8053971529006958), ('singular k3 surfaces', 0.7988689541816711), ('surfaces k3', 0.7717417478561401), ('polarized k3 surfaces', 0.7716220617294312), ('k3 surface', 0.7272739410400391), ('k3 surfaces picard', 0.7210930585861206), ('kummer surfaces', 0.685120165348053), ('k3 surface picard', 0.6356074810028076), ('elliptic k3', 0.6326216459274292)]"
174,174,157,174_inequalities hilbert_radius hilbert_operator norm_operators complex hilbert,"['inequalities hilbert', 'radius hilbert', 'operator norm', 'operators complex hilbert', 'hilbert space operators', 'inequalities operator', 'inequalities numerical', 'radius operator', 'operators hilbert', 'bounded linear operators']","['On inequalities for A-numerical radius of operators   Let $A$ be a positive operator on a complex Hilbert space $\\mathcal{H}.$ We\npresent inequalities concerning upper and lower bounds for $A$-numerical radius\nof operators, which improve on and generalize the existing ones, studied\nrecently in [A. Zamani, A-Numerical radius inequalities for semi-Hilbertian\nspace operators, Linear Algebra Appl. 578 (2019) 159-183]. We also obtain some\ninequalities for $B$-numerical radius of $2\\times 2$ operator matrices where\n$B$ is the $2\\times 2$ diagonal operator matrix whose diagonal entries are $A$.\nFurther we obtain upper bounds for $A$-numerical radius for product of\noperators which improve on the existing bounds.\n', 'Refined inequalities for the numerical radius of Hilbert space operators   We present some new upper and lower bounds for the numerical radius of\nbounded linear operators on a complex Hilbert space and show that these are\nstronger than the existing ones. In particular, we prove that if $A$ is a\nbounded linear operator on a complex Hilbert space $\\mathcal{H}$ and if\n$\\Re(A)$, $\\Im(A)$ are the real part, the imaginary part of $A$, respectively,\nthen $$ w(A)\\geq\\frac{\\|A\\|}{2} +\\frac{1}{2\\sqrt{2}} \\Big |\n\\|\\Re(A)+\\Im(A)\\|-\\|\\Re(A)-\\Im(A)\\| \\Big | $$ and $$\nw^2(A)\\geq\\frac{1}{4}\\|A^*A+AA^*\\|+\\frac{1}{4}\\Big|\n\\|\\Re(A)+\\Im(A)\\|^2-\\|\\Re(A)-\\Im(A)\\|^2\\Big|. $$ Here $w(.)$ and $\\|.\\|$ denote\nthe numerical radius and the operator norm, respectively. Further, we obtain\nrefinement of inequalities for the numerical radius of the product of two\noperators. Finally, as an application of the second inequality mentioned above,\nwe obtain an improvement of upper bound for the numerical radius of the\ncommutators of operators.\n', 'On A-numerical radius inequalities for $2 \\times 2$ operator matrices   Let ($\\mathcal{H}, \\langle . , .\\rangle )$ be a complex Hilbert space and $A$\nbe a positive bounded linear operator on it. Let $w_A(T)$ be the $A$-numerical\nradius and $\\|T\\|_A$ be the $A$-operator seminorm of an operator $T$ acting on\nthe semi-Hilbertian space $(\\mathcal{H}, \\langle .,.\\rangle_A),$ where $\\langle\nx, y\\rangle_A:=\\langle Ax, y\\rangle$ for all $x,y\\in \\mathcal{H}$. In this\narticle, we establish several upper and lower bounds for $B$-numerical radius\nof $2\\times 2$ operator matrices, where $B=\\begin{bmatrix}\n  A & 0\n  0 & A\n  \\end{bmatrix}$. Further, we prove some refinements of earlier $A$-numerical\nradius inequalities for operators.\n']","[('inequalities hilbert', 0.5717406272888184), ('radius hilbert', 0.5024877190589905), ('operator norm', 0.501291811466217), ('operators complex hilbert', 0.4966748058795929), ('hilbert space operators', 0.4964488446712494), ('inequalities operator', 0.4931049644947052), ('inequalities numerical', 0.4762263596057892), ('radius operator', 0.47316405177116394), ('operators hilbert', 0.47102972865104675), ('bounded linear operators', 0.4651585519313812)]"
175,175,157,175_central limit theorems_weak law large_strong law large_moment convergence,"['central limit theorems', 'weak law large', 'strong law large', 'moment convergence', 'sublinear expectation', 'law large numbers', 'classical central limit', 'weak law', 'sums independent random', 'sums random variables']","['Strong laws of large numbers for sequences of blockwise $m$-dependent\n  and orthogonal random variables under sublinear expectations   In this paper, we establish some strong laws of large numbers (SLLN) for\nnon-independent random variables under the framework of sublinear expectations.\nOne of our main results is for blockwise $m$-dependent random variables, and\nanother is for orthogonal random variables. Both are the generalizations of\nSLLN for independent random variables in sublinear expectation spaces.\n', 'The sufficient and necessary conditions of the strong law of large\n  numbers under the sub-linear expectations   In this paper, by establishing a Borel-Cantelli lemma for a capacity which is\nnot necessarily continuous, and a link between a sequence of independent random\nvariables under the sub-linear expectation and a sequence of independent random\nvariables on $\\mathbb R^{\\infty}$ under a probability, we give the sufficient\nand necessary conditions of the strong law of large numbers for independent and\nidentically distributed random variables under the sub-liner expectation, and\nthe sufficient and necessary conditions for the convergence of an infinite\nseries of independent random variables, without any assumption on the\ncontinuity of the capacities. A purely probabilistic proof of a weak law of\nlarge numbers is also given.\n  In the version 1, there are errors in the proof of Lemma 2.1 and 2.2. Version\n2 corrected the errors under additional conditions, but Corollaries 3.1-3.4 are\nonly shown for the copy of the random variables in a new sub-linear expectation\nspace. In this version, we show that Corollaries 3.1-3.4 remain true for the\noriginal random variables and the results for the copy are just special cases.\n', 'Strong law of large numbers for $m$-dependent and stationary random\n  variables under sub-linear expectations   The arm of this paper is to establish the strong law of large numbers (SLLN)\nof $m$-dependent random variables under the framework of sub-linear\nexpectations. We establish the SLLN for a sequence of independent, but not\nnecessarily identically distributed random variables. The study further extends\nthe SLLN to $m$-dependent and stationary sequence of random variables with the\ncondition $C_{\\mathbb V}(|X_1|)<\\infty$ which is the sufficient and necessary\ncondition of SLLN in the case of independent and identically distributed random\nvariables.\n']","[('central limit theorems', 0.5470211505889893), ('weak law large', 0.5349351763725281), ('strong law large', 0.5155588984489441), ('moment convergence', 0.5154272317886353), ('sublinear expectation', 0.5070456862449646), ('law large numbers', 0.49707290530204773), ('classical central limit', 0.4835074841976166), ('weak law', 0.4643941819667816), ('sums independent random', 0.4639679193496704), ('sums random variables', 0.4633893668651581)]"
176,176,156,176_lie algebroids_lie groupoids_algebroids lie_lie groupoid,"['lie algebroids', 'lie groupoids', 'algebroids lie', 'lie groupoid', 'lie algebroid', 'symplectic groupoids', 'poisson lie group', 'courant algebroids', 'algebroids', 'lie group']","[""Exploring the Structure of Higher Algebroids   The notion of a \\emph{higher-order algebroid}, as introduced by\nJ\\'o\\'zwikowski and Rotkiewicz in their work \\emph{Higher-order analogs of Lie\nalgebroids via vector bundle comorphisms} (SIGMA, 2018), generalizes the\nconcepts of a higher-order tangent bundle $\\tau^k_M: \\mathrm{T}^k M \\to M$ and\na (Lie) algebroid. This idea is based on a (vector bundle) comorphism approach\nto (Lie) algebroids and the reduction procedure of homotopies from the level of\nLie groupoids to that of Lie algebroids. In brief, an alternative description\nof a Lie algebroid $(A, [\\cdot, \\cdot], \\sharp)$ is a vector bundle comorphism\n$\\kappa$, defined as the dual of the Poisson map $\\varepsilon: \\mathrm{T}^\\ast\nA \\to \\mathrm{T} A^\\ast$ associated with the Lie algebroid $A$. The framework\nof comorphisms has proven to be a suitable language for describing higher-order\nanalogues of Lie algebroids from the perspective of the role played by (Lie)\nalgebroids in geometric mechanics. In this work, we uncover the classical\nalgebraic structures underlying the somewhat mysterious description of\nhigher-order algebroids through comorphisms. For the case $k=2$, we establish a\none-to-one correspondence between higher-order Lie algebroids and pairs\nconsisting of a two-term representation (up to homotopy) of a Lie algebroid and\na morphism to the adjoint representation of this algebroid.\n"", ""On the integrability of Lie algebroids by diffeological spaces   Lie's third theorem does not hold for Lie groupoids and Lie algebroids. In\nthis article, we show that Lie's third theorem is valid within a specific class\nof diffeological groupoids that we call `singular Lie groupoids.' To achieve\nthis, we introduce a subcategory of diffeological spaces which we call\n`quasi-etale.' Singular Lie groupoids are precisely the groupoid objects within\nthis category, where the unit space is a manifold.\n  Our approach involves the construction of a functor that maps singular Lie\ngroupoids to Lie algebroids, extending the classical functor from Lie groupoids\nto Lie algebroids. We prove that the \\v{S}evera-Weinstein groupoid of an\nalgebroid is an example of a singular Lie groupoid, thereby establishing Lie's\nthird theorem in this context.\n"", 'Lie Algebroids   This is an overview article on Lie algebroids, and their role as the\ninfinitesimal counterparts of Lie groupoids.\n']","[('lie algebroids', 0.746404767036438), ('lie groupoids', 0.7216359972953796), ('algebroids lie', 0.7029484510421753), ('lie groupoid', 0.6780493259429932), ('lie algebroid', 0.6562644839286804), ('symplectic groupoids', 0.5955762267112732), ('poisson lie group', 0.5777502655982971), ('courant algebroids', 0.5519641637802124), ('algebroids', 0.5506556034088135), ('lie group', 0.5488434433937073)]"
177,177,155,177_toda hierarchy_toda lattice_integrable hierarchy_kp hierarchy,"['toda hierarchy', 'toda lattice', 'integrable hierarchy', 'kp hierarchy', 'integrable hierarchies', 'discrete painlev equations', 'bkp hierarchy', 'kdv hierarchy', 'toda', 'tau functions']","['The Modified Toda Hierarchy   In this paper, modified Toda (mToda) equation is generalized to form an\nintegrable hierarchy in the framework of Sato theory, which is therefore called\nmToda hierarchy. Inspired by the fact that Toda hierarchy is 2-component\ngeneralization of usual KP hierarchy, mToda hierarchy is constructed from\nbilinear equations of 2-component first modified KP hierarchy, where we provide\nthe corresponding equivalence with Lax formulations. Then it is demonstrated\nthat there are Miura links between Toda and mToda hierarchies, which means the\ndefinition of mToda hierarchy here is reasonable. Finally, Darboux\ntransformations of the Toda and mToda hierarchies are also constructed by using\nthe aforementioned Miura links.\n', 'Tau-function of the B-Toda hierarchy   We continue the study of the B-Toda hierarchy (the Toda lattice with the\nconstraint of type B) which can be regarded as a discretization of the BKP\nhierarchy. We introduce the tau-function of the B-Toda hierarchy and obtain the\nbilinear equations for it. Examples of soliton tau-functions are presented in\nthe explicit form.\n', 'From Toda hierarchy to KP hierarchy   Using the matrix-resolvent method and a formula of the second-named author on\nthe $n$-point function for a KP tau-function, we show that the tau-function of\nan arbitrary solution to the Toda lattice hierarchy is a KP tau-function. We\nthen generalize this result to tau-functions for the extended Toda hierarchy\n(ETH) by developing the matrix-resolvent method for the ETH. As an example the\npartition function of Gromov--Witten invariants of the complex projective line\nis a KP tau-function, and an application on irreducible representations of the\nsymmetric group is obtained.\n']","[('toda hierarchy', 0.6192165017127991), ('toda lattice', 0.6073318719863892), ('integrable hierarchy', 0.4832990765571594), ('kp hierarchy', 0.47325044870376587), ('integrable hierarchies', 0.4549882113933563), ('discrete painlev equations', 0.4157293140888214), ('bkp hierarchy', 0.402058869600296), ('kdv hierarchy', 0.3894851505756378), ('toda', 0.387112021446228), ('tau functions', 0.3806837797164917)]"
178,178,154,178_electric vehicle charging_vehicle charging_ev charging_charging discharging,"['electric vehicle charging', 'vehicle charging', 'ev charging', 'charging discharging', 'charging station', 'charging stations', 'electric vehicle ev', 'fast charging', 'electric vehicles evs', 'electric vehicle']","[""Health-aware and user-involved battery charging management for electric\n  vehicles: linear quadratic strategies   This paper studies control-theory-enabled intelligent charging management for\nbattery systems in electric vehicles (EVs). Charging is crucial for the battery\nperformance and life as well as a contributory factor to a user's confidence in\nor anxiety about EVs. For the existing practices and methods, many run with a\nlack of battery health awareness during charging, and none includes the user\nneeds into the charging loop. To remedy such deficiencies, we propose to\nperform charging that, for the first time, allows the user to specify charging\nobjectives and accomplish them through dynamic control, in addition to\nsuppressing the charging-induced negative effects on battery health. Two\ncharging strategies are developed using the linear quadratic control theory.\nAmong them, one is based on control with fixed terminal charging state, and the\nother on tracking a reference charging path. They are computationally\ncompetitive, without requiring real-time constrained optimization as needed in\nmost charging techniques available in the literature. A simulation-based study\ndemonstrates their effectiveness and potential. It is anticipated that charging\nwith health awareness and user involvement guaranteed by the proposed\nstrategies will bring major improvements to not only the battery longevity but\nalso the EV user satisfaction.\n"", ""Coordinated vehicle dispatching and charging scheduling for an electric\n  ride-hailing fleet under charging congestion and dynamic prices   Effective utilization of charging station capacity plays an important role in\nenhancing the profitability of ride-hailing systems using electric vehicles.\nExisting studies assume constant energy prices and uncapacitated charging\nstations or do not explicitly consider vehicle queueing at charging stations,\nresulting in over-optimistic charging infrastructure utilization. In this\nstudy, we develop a dynamic charging scheduling method (named CongestionAware)\nthat anticipates vehicles' energy needs and coordinates their charging\noperations with real-time energy prices to avoid long waiting time at charging\nstations and increase the total profit of the system. A sequential mixed\ninteger linear programming model is proposed to devise vehicles' day-ahead\ncharging plans based on their experienced charging waiting times and energy\nconsumption. The obtained charging plans are adapted within the day in response\nto vehicles' energy needs and charging station congestion. The developed\ncharging policy is tested using NYC yellow taxi data in a Manhattan-like study\narea with a fleet size of 100 vehicles given the scenarios of 3000 and 4000\ncustomers per day. The computational results show that our CongestionAware\npolicy outperforms different benchmark policies with up to +15.06% profit and\n+19.16% service rate for 4000 customers per day. Sensitivity analysis is\nconducted with different system parameters and managerial insights are\ndiscussed.\n"", 'A Game-theoretic Approach for Dynamic Service Scheduling at Charging\n  Facilities   Electric vehicle (EV) charging patterns are highly uncertain in both\nlocation, time, and duration particularly in association with the predicted\nhigh demand for electric mobility in the future. An EV can be charged at home,\nat charging stations near highway ramps, or on parking lots next to office\nbuildings, shops, airports, among other locations. Charging time and duration\ncan be fixed and continuous or flexible and intermittent. EV user preferences\nof charging services depend on many factors (e.g., charging prices, choice of\ndestinations), causing EV charging patterns to shift in real-time. Hence, there\nis a need for a highly flexible EV charging network to support the rapid\nadoption of the technology. This study presents a dynamic scheduling scheme for\nEV charging facilities considering uncertainties in charging demand, charger\navailability, and charging rate. The problem is formulated as a dynamic\nprogramming model that minimizes the travel and waiting costs and charging\nexpenses while penalizing overcharging attempts. An integrated generalized Nash\nequilibrium technique is introduced to solve the problem that incorporates a\nMonte Carlo tree search algorithm to efficiently capture the uncertainties and\napproximate the value function of the dynamic program. Numerical experiments on\nhypothetical and real-world networks confirm the solution quality and\ncomputational efficiency of the proposed methodology. This study will promote\nEV adoption and support environmental sustainability by helping users lower the\ncharging spot search burden via a real-time, user-adaptive optimizer.\nStakeholders can retrieve charger utilization and pricing data and get feedback\non their charging network policies.\n']","[('electric vehicle charging', 0.6316206455230713), ('vehicle charging', 0.6028374433517456), ('ev charging', 0.5797463059425354), ('charging discharging', 0.5136127471923828), ('charging station', 0.4903143644332886), ('charging stations', 0.4850555658340454), ('electric vehicle ev', 0.483822226524353), ('fast charging', 0.4756144881248474), ('electric vehicles evs', 0.46432650089263916), ('electric vehicle', 0.45809245109558105)]"
179,179,153,179_discrete memoryless channel_discrete memoryless channels_memoryless channel_memoryless channels,"['discrete memoryless channel', 'discrete memoryless channels', 'memoryless channel', 'memoryless channels', 'binary symmetric channel', 'binary erasure channel', 'channel coding', 'channel capacity', 'shannon capacity', 'symmetric channel']","[""Variable-Length Codes with Bursty Feedback   We study variable-length codes for point-to-point discrete memoryless\nchannels with noiseless unlimited-rate feedback that occurs in $L$ bursts. We\nterm such codes variable-length bursty-feedback (VLBF) codes. Unlike classical\ncodes with feedback after each transmitted code symbol, bursty feedback fits\nbetter with protocols that employ sparse feedback after a packet is sent and\nalso with half-duplex end devices that cannot transmit and listen to the\nchannel at the same time. We present a novel non-asymptotic achievability bound\nfor VLBF codes with $L$ bursts of feedback over any discrete memoryless\nchannel. We numerically evaluate the bound over the binary symmetric channel\n(BSC). We perform optimization over the time instances at which feedback occurs\nfor both our own bound and Yavas et al.'s non-asymptotic achievability bound\nfor variable-length stop-feedback (VLSF) codes, where only a single bit is sent\nat each feedback instance. Our results demonstrate the advantages of richer\nfeedback: VLBF codes significantly outperform VLSF codes at short blocklengths,\nespecially as the error probability $\\epsilon$ decreases. Remarkably, for\nBSC(0.11) and error probability $10^{-10}$, our VLBF code with $L=5$ and\nexpected decoding time $N\\leq 400$ outperforms the achievability bound given by\nPolyanskiy et al. for VLSF codes with $L=\\infty$, and our VLBF code with $L=3$.\n"", ""Identification Over Binary Noisy Permutation Channels   We study message identification over the binary noisy permutation channel.\nFor discrete memoryless channels (DMCs), the number of identifiable messages\ngrows doubly exponentially, and the maximum second-order exponent is the\nShannon capacity of the DMC. We consider a binary noisy permutation channel\nwhere the transmitted vector is first permuted by a permutation chosen\nuniformly at random, and then passed through a binary symmetric channel with\ncrossover probability $p$. In an earlier work, it was shown that $2^{c_n n}$\nmessages can be identified over binary (noiseless) permutation channel if\n$c_n\\rightarrow 0$. For the binary noisy permutation channel, we show that\nmessage sizes growing as $2^{\\epsilon_n \\sqrt{\\frac{n}{\\log n}}}$ are\nidentifiable for any $\\epsilon_n\\rightarrow 0$. We also prove a strong converse\nresult showing that for any sequence of identification codes with message size\n$2^{R_n \\sqrt{n}\\log n}$, where $R_n \\rightarrow \\infty$, the sum of Type-I and\nType-II error probabilities approaches at least $1$ as $n\\rightarrow \\infty$.\nOur proof of the strong converse uses the idea of channel resolvability. The\nchannel of interest turns out to be the ``binary weight-to-weight (BWW)\nchannel'' which captures the effect on the Hamming weight of a vector, when the\nvector is passed through a binary symmetric channel. We propose a novel\ndeterministic quantization scheme for quantization of a distribution over\n$\\{0,1,\\cdots, n\\}$ by an $M$-type input distribution when the distortion is\nmeasured on the output distribution (over the BWW channel) in total variation\ndistance. This plays a key role in the converse proof.\n"", ""Sequential Transmission Over Binary Asymmetric Channels With Feedback   In this paper, we consider the problem of variable-length coding over the\nclass of memoryless binary asymmetric channels (BACs) with noiseless feedback,\nincluding the binary symmetric channel (BSC) as a special case. In 2012,\nNaghshvar et al. introduced an encoding scheme, which we refer to as the\nsmall-enough-difference (SED) encoder, which asymptotically achieves both\ncapacity and Burnashev's optimal error exponent for symmetric binary-input\nchannels. Building on the work of Naghshvar et al., this paper extends the SED\nencoding scheme to the class of BACs and develops a non-asymptotic upper bound\non the average blocklength that is shown to achieve both capacity and the\noptimal error exponent. For the specific case of the BSC, we develop an\nadditional non-asymptotic bound using a two-phase analysis that leverages both\na submartingale synthesis and a Markov chain time of first passage analysis.\nFor the BSC with capacity $1/2$, both new achievability bounds exceed the\nachievability bound of Polyanskiy et al. for a system limited to stop-feedback\ncodes.\n""]","[('discrete memoryless channel', 0.7355169057846069), ('discrete memoryless channels', 0.7326219081878662), ('memoryless channel', 0.6839974522590637), ('memoryless channels', 0.6730499267578125), ('binary symmetric channel', 0.6195023655891418), ('binary erasure channel', 0.6190193891525269), ('channel coding', 0.6124290227890015), ('channel capacity', 0.5902085900306702), ('shannon capacity', 0.5861333012580872), ('symmetric channel', 0.5662034153938293)]"
180,180,152,180_boltzmann collision operator_spatially homogeneous boltzmann_limit boltzmann_boltzmann collision,"['boltzmann collision operator', 'spatially homogeneous boltzmann', 'limit boltzmann', 'boltzmann collision', 'homogeneous boltzmann', 'boltzmann equations', 'solutions boltzmann', 'linear boltzmann', 'boltzmann operator', 'linearized boltzmann']","['$L^p$-norms for the homogeneous non-cutoff Boltzmann equation with soft\n  potentials   We establish a priori estimates showing the propagation and generation of\n$L^p$-norms for solutions to the non-cutoff spatially homogeneous Boltzmann\nequation with soft potentials. The singularity of the collision kernel is key\nto generate regularization and inhomogeneity in the energy estimates of the\n$L^p$-norms. Our result extends \\cite{Alo19} from the hard potential cases to\nthe soft ones.\n', 'Global existence for an isotropic modification of the Boltzmann equation   Motivated by the open problem of large-data global existence for the\nnon-cutoff Boltzmann equation, we introduce a model equation that in some sense\ndisregards the anisotropy of the Boltzmann collision kernel. We refer to this\nmodel equation as isotropic Boltzmann, by analogy with the isotropic Landau\nequation introduced by Krieger and Strain [Comm. Partial Differential Equations\n37(4), 2012, 647--689]. The collision operator of our isotropic Boltzmann model\nconverges to the isotropic Landau collision operator under a scaling limit that\nis analogous to the grazing collisions limit connecting (true) Boltzmann with\n(true) Landau.\n  Our main result is global existence for the isotropic Boltzmann equation in\nthe space homogeneous case, for certain parts of the ""very soft potentials""\nregime in which global existence is unknown for the space homogeneous Boltzmann\nequation. The proof strategy is inspired by the work of Gualdani-Guillen [J.\nFunct. Anal. 283(6), 2022, Paper No. 109559] on isotropic Landau, and makes use\nof recent progress on weighted fractional Hardy inequalities.\n', 'High-velocity tails of the inelastic and the multi-species mixture\n  Boltzmann equations   We study high-velocity tails of some homogeneous Boltzmann equations on $v\n\\in \\mathbb{R}_{v}^d$. First, we consider spatially homogeneous inelastic\nBoltzmann equation with noncutoff collision kernel, in the case of moderately\nsoft potentials. We also study spatially homogeneous mixture Boltzmann\nequations : for both noncutoff collision kernel with moderately soft potentials\nand cutoff collision kernel with hard potentials. In the case of noncutoff\ninelastic Boltzmann, we obtain\n  \\[\n  f(t,v) \\geq a(t) e^{-b(t)|v|^p}, \\quad 2 < p < 6.213\n  \\]\n  by extending Cancellation lemma and spreading lemma and assuming $f\\in\nC^{\\infty}$. For the Mixture type Boltzmann equations, we prove Maxwellian\n$p=2$.\n']","[('boltzmann collision operator', 0.6726526021957397), ('spatially homogeneous boltzmann', 0.655865490436554), ('limit boltzmann', 0.6461961269378662), ('boltzmann collision', 0.6296980977058411), ('homogeneous boltzmann', 0.6208404302597046), ('boltzmann equations', 0.6170396208763123), ('solutions boltzmann', 0.588249921798706), ('linear boltzmann', 0.5847154259681702), ('boltzmann operator', 0.5845261216163635), ('linearized boltzmann', 0.5811803340911865)]"
181,181,152,181_regularity minimizers_minimizers variational_variational problems_minimizers functionals,"['regularity minimizers', 'minimizers variational', 'variational problems', 'minimizers functionals', 'regularity theory', 'partial regularity', 'lipschitz regularity', 'local minimizers', 'minimizers non', 'regularity local']","['Higher differentiability results for solutions to a class of\n  non-autonomous obstacle problems with sub-quadratic growth conditions   We establish some higher differentiability results of integer and fractional\norder for solution to non-autonomous obstacle problems of the form\n  \\begin{equation*}\n  \\min \\left\\{\\int_{\\Omega}f(x, Dv(x))\\,:\\, v\\in\n  \\mathcal{K}_\\psi(\\Omega)\\right\\},\n  \\end{equation*} where the function $f$ satisfies $p-$growth conditions with\nrespect to the gradient variable, for $1<p<2$, and $\\mathcal{K}_\\psi(\\Omega)$\nis the class of admissible functions $v\\in u_0+W^{1, p}_0(\\Omega)$ such that\n$v\\ge\\psi$ a. e. in $\\Omega$, where $u_0\\in W^{1,p}(\\Omega)$ is a fixed\nboundary datum.\n  Here we show that a Sobolev or Besov-Lipschitz regularity assumption on the\ngradient of the obstacle $\\psi$ transfers to the gradient of the solution,\nprovided the partial map $x\\mapsto D_\\xi f(x,\\xi)$ belongs to a suitable\nSobolev or Besov space. The novelty here is that we deal with subquadratic\ngrowth conditions with respect to the gradient variable, i. e. $f(x,\n\\xi)\\approx a(x)|\\xi|^p$ with $1<p<2,$ and where the map $a$ belongs to a\nSobolev or Besov-Lipschitz space.\n', 'Regularity results for solutions to a class of non-autonomous obstacle\n  problems with sub-quadratic growth conditions   We establish some higher differentiability results for solution to\nnon-autonomous obstacle problems of the form\n  \\begin{equation*}\n  \\min \\left\\{\\int_{\\Omega}f\\left(x, Dv(x)\\right)dx\\,:\\, v\\in\n  \\mathcal{K}_\\psi(\\Omega)\\right\\},\n  \\end{equation*} where the function $f$ satisfies $p-$growth conditions with\nrespect to the gradient variable, for $1<p<2$, and $\\mathcal{K}_\\psi(\\Omega)$\nis the class of admissible functions. Here we show that, if the obstacle $\\psi$\nis bounded, then a Sobolev regularity assumption on the gradient of the\nobstacle $\\psi$ transfers to the gradient of the solution, provided the partial\nmap $x\\mapsto D_\\xi f(x,\\xi)$ belongs to a Sobolev space, $W^{1, p+2}$. The\nnovelty here is that we deal with subquadratic growth conditions with respect\nto the gradient variable, i.e. $f(x, \\xi)\\approx a(x)|\\xi|^p$ with $1<p<2,$ and\nwhere the map $a$ belongs to a Sobolev space.\n', 'Regularity for minimizers of scalar integral functionals   We prove the local Lipschitz regularity of the local minimizers of scalar\nintegral functionals of the form \\begin{equation*} \\mathcal{F}(v;\\Omega)=\n\\int_{\\Omega} f (x, Dv) dx \\end{equation*} under $(p,q)$-growth conditions. The\nmain novelty is that, beside a suitable regularity assumption on the partial\nmap $x\\mapsto f(x,\\xi)$, we do not assume any special structure for the energy\ndensity as a function of the $\\xi$-variable.\n']","[('regularity minimizers', 0.599331796169281), ('minimizers variational', 0.5421497821807861), ('variational problems', 0.5336799621582031), ('minimizers functionals', 0.5302592515945435), ('regularity theory', 0.5087460279464722), ('partial regularity', 0.48558881878852844), ('lipschitz regularity', 0.47651979327201843), ('local minimizers', 0.4587504267692566), ('minimizers non', 0.4392603635787964), ('regularity local', 0.4383421838283539)]"
182,182,151,182_henselian valued field_henselian valued_valued fields_valued field,"['henselian valued field', 'henselian valued', 'valued fields', 'valued field', 'minimal fields', 'fields characteristic', 'minimal field', 'fields equipped', 'fields', 'valuation ring']","['Residue field domination in some henselian valued fields   We generalize previous results about stable domination and residue field\ndomination to henselian valued fields of equicharacteristic 0 with bounded\nGalois group, and we provide an alternate characterization of stable domination\nin algebraically closed valued fields for types over parameters in the field\nsort.\n', ""Artin-Schreier extensions and combinatorial complexity in henselian\n  valued fields   We give explicit formulas witnessing IP, \\IPn or TP2 in fields with\nArtin-Schreier extensions. We use them to control $p$-extensions of mixed\ncharacteristic henselian valued fields, allowing us most notably to generalize\nto the \\NIPn context one way of Anscombe-Jahnke's classification of NIP\nhenselian valued fields. As a corollary, we obtain that \\NIPn henselian valued\nfields with NIP residue field are NIP. We also discuss tameness results for\nNTP2 henselian valued fields.\n"", 'Burden of henselian valued fields in the Denef-Pas language   Motivated by the Ax-Kochen/Ershov principle, a large number of questions\nabout henselian valued fields have been shown to reduce to analogous questions\nabout the value group and residue field. In this paper, we investigate the\nburden of henselian valued fields in the three-sorted Denef-Pas language. If\n$T$ is a theory of henselian valued fields admitting relative quantifier\nelimination (in any characteristic), we show that the burden of $T$ is equal to\nthe sum of the burdens of its value group and residue field. As a consequence,\n$T$ is NTP${}_2$ if and only if its residue field and value group are; the same\nis true for the statements ""$T$ is strong"" and ""$T$ has finite burden.""\n']","[('henselian valued field', 0.7689988017082214), ('henselian valued', 0.6339719891548157), ('valued fields', 0.6151056885719299), ('valued field', 0.548546552658081), ('minimal fields', 0.5276182889938354), ('fields characteristic', 0.5141218900680542), ('minimal field', 0.48927566409111023), ('fields equipped', 0.4880652129650116), ('fields', 0.4853709638118744), ('valuation ring', 0.4822298586368561)]"
183,183,149,183_regularity weak solutions_local weak solutions_regularity solutions_gradient weak solutions,"['regularity weak solutions', 'local weak solutions', 'regularity solutions', 'gradient weak solutions', 'weak solutions', 'parabolic laplacian', 'quasilinear parabolic equations', 'regularity estimates', 'regularity weak', 'degenerate parabolic equations']","['Regularity results for a class of widely degenerate parabolic equations   Motivated by applications to gas filtration problems, we study the regularity\nof weak solutions to the strongly degenerate parabolic PDE\n  $u_{t}-\\mathrm{div}\\left((\\vert Du\\vert-\\nu)_{+}^{p-1}\\frac{Du}{\\vert\nDu\\vert}\\right)=f$ in $\\Omega_{T}=\\Omega\\times(0,T)$,\n  where $\\Omega$ is a bounded domain in $\\mathbb{R}^{n}$ for $n\\geq2$,\n$p\\geq2$, $\\nu$ is a positive constant and $\\left(\\,\\cdot\\,\\right)_{+}$ stands\nfor the positive part. Assuming that the datum $f$ belongs to a suitable\nLebesgue-Sobolev parabolic space, we establish the Sobolev spatial regularity\nof a nonlinear function of the spatial gradient of the weak solutions, which in\nturn implies the existence of the weak time derivative $u_{t}$. The main\nnovelty here is that the structure function of the above equation satisfies\nstandard growth and ellipticity conditions only outside a ball with radius\n$\\nu$ centered at the origin. We would like to point out that the first result\nobtained here can be considered, on the one hand, as the parabolic counterpart\nof an elliptic result established in [5], and on the other hand as the\nextension to a strongly degenerate context of some known results for less\ndegenerate parabolic equations.\n', 'On the regularity theory for mixed local and nonlocal quasilinear\n  parabolic equations   We consider mixed local and nonlocal quasilinear parabolic equations of\n$p$-Laplace type and discuss several regularity properties of weak solutions\nfor such equations. More precisely, we establish local boundeness of weak\nsubsolutions, lower semicontinuity of weak supersolutions as well as upper\nsemicontinuity of weak subsolutions. We also discuss the pointwise behavior of\nthe semicontinuous representatives. Our main results are valid for sign\nchanging solutions. Our approach is purely analytic and is based on energy\nestimates and the De Giorgi theory.\n', 'Regularity of weak solutions for mixed local and nonlocal double phase\n  parabolic equations   We study the mixed local and nonlocal double phase parabolic equation\n\\begin{align*} \\partial_t u(x,t)-\\mathrm{div}(a(x,t)|\\nabla u|^{q-2}\\nabla u)\n+\\mathcal{L}u(x,t)=0 \\end{align*} in $Q_T=\\Omega\\times(0,T)$, where\n$\\mathcal{L}$ is the nonlocal $p$-Laplace type operator. The local boundedness\nof weak solutions is proved by means of the De Giorgi-Nash-Moser iteration with\nthe nonnegative coefficient function $a(x,t)$ being bounded. In addition, when\n$a(x,t)$ is H\\""{o}lder continuous, we discuss the pointwise behavior and lower\nsemicontinuity of weak supersolutions based on energy estimates and De Giorgi\ntype lemma. Analogously, the corresponding results are also valid for weak\nsubsolutions.\n']","[('regularity weak solutions', 0.650863528251648), ('local weak solutions', 0.6197177171707153), ('regularity solutions', 0.5982332825660706), ('gradient weak solutions', 0.5631168484687805), ('weak solutions', 0.5368032455444336), ('parabolic laplacian', 0.5299834609031677), ('quasilinear parabolic equations', 0.5262981057167053), ('regularity estimates', 0.5200533270835876), ('regularity weak', 0.4970753788948059), ('degenerate parabolic equations', 0.47958213090896606)]"
184,184,149,184_submodules_modules rings_rings modules_modules commutative,"['submodules', 'modules rings', 'rings modules', 'modules commutative', 'submodule', 'modules generalizations', 'module commutative', 'modules terms', 'modules', 'ring module']","['The dual of the notions r-submodules, n-submodules, and J-submodules   Let R be a commutative ring with identity and M be an R-module. The purpose\nof this paper is to introduce and investigate the dual notions of r-submodules,\nn-submodules, and J-submodules of M.\n', 'Weakly J-submodules of Modules over Commutative Rings   Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module.\nBy $J(R),$ we denote the Jacobson radical of $R$. The purpose of this paper is\nto introduce the concept of weakly $J$-submodules generalizing $J$-submodules.\nWe call a proper submodule $N$ of $M$ a weakly $J$-submodule if whenever $0\\neq\nrm\\in N$ for $r\\in R$ and $m\\in M$, then $r\\in(J(R)M:M)$ or $m\\in N.$ Various\nproperties and characterizations of weakly $J$-submodules are investigated\nespecially in the case of multiplication modules.\n', '$S$-2-absorbing submodules and $S$-2-absorbing second submodules   Let R be a commutative ring with identity, S be a multiplicatively closed\nsubset of R, and let M be an R-module. In this paper, we introduce the notion\nof S-2-absorbing second submodules of M as a generalization of S-second\nsubmodules and strongly 2-absorbing second submodules of M. We investigate some\nproperties of this class of submodules. Also, we obtain some results concerning\nS-2-absorbing submodules of M.\n']","[('submodules', 0.7157168984413147), ('modules rings', 0.6661609411239624), ('rings modules', 0.6626847386360168), ('modules commutative', 0.6564134955406189), ('submodule', 0.6516270637512207), ('modules generalizations', 0.6458584070205688), ('module commutative', 0.6312988996505737), ('modules terms', 0.6159712076187134), ('modules', 0.6009100675582886), ('ring module', 0.5815956592559814)]"
185,185,148,185_optimal investment_optimal investment strategy_utility maximization_optimal portfolio,"['optimal investment', 'optimal investment strategy', 'utility maximization', 'optimal portfolio', 'risk aversion', 'investment strategy', 'investment', 'semimartingale', 'consumption', 'expected utility']","[""Value-at-Risk constrained portfolios in incomplete markets: a dynamic programming approach to Heston's model We solve an expected utility-maximization problem with a Value-at-risk constraint on the terminal portfolio value in an incomplete financial market due to stochastic volatility. To derive the optimal investment strategy, we use the dynamic programming approach. We demonstrate that the value function in the constrained problem can be represented as the expected modified utility function of a vega-neutral financial derivative on the optimal terminal wealth in the unconstrained utility-maximization problem. Via the same financial derivative, the optimal wealth and the optimal investment strategy in the constrained problem are linked to the optimal wealth and the optimal investment strategy in the unconstrained problem. In numerical studies, we substantiate the impact of risk aversion levels and investment horizons on the optimal investment strategy. We observe a 20% relative difference between the constrained and unconstrained allocations for average parameters in a low-risk-aversion short-horizon setting."", 'Smoothness of the Value Function for Optimal Consumption Model with\n  Consumption-Wealth Utility and Borrowing Constraint   This paper studies an optimal consumption-investment problem for an investor\nwhose instantaneous utility depends on both consumption and wealth, and the\ninvestor faces a general borrowing constraint that the investment amount in the\nrisky asset does not exceed an exogenous function of the wealth. We show that\nthe value function is second-order smooth and present the optimal\nconsumption-investment policy in a feedback form. Moreover, when the risky\ninvestment amount is bounded above by a fixed constant, we show that under\ncertain conditions, the constraint is binding if and only if an endogenous\nthreshold bounds the portfolio wealth, and we determine the endogenous wealth\nthreshold with the smooth fit condition. Our results encompass several\nwell-developed portfolio choice models and imply new applications.\n', ""Robust optimal investment and consumption strategies with portfolio\n  constraints and stochastic environment   We investigate a continuous-time investment-consumption problem with model\nuncertainty in a general diffusion-based market with random model coefficients.\nWe assume that a power utility investor is ambiguity-averse, with the\npreference to robustness captured by the homothetic multiplier robust\nspecification, and the investor's investment and consumption strategies are\nconstrained to closed convex sets. To solve this constrained robust control\nproblem, we employ the stochastic Hamilton-Jacobi-Bellman-Isaacs equations,\nbackward stochastic differential equations, and bounded mean oscillation\nmartingale theory. Furthermore, we show the investor incurs (non-negative)\nutility loss, i.e. the loss in welfare, if model uncertainty is ignored. When\nthe model coefficients are deterministic, we establish formally the\nrelationship between the investor's robustness preference and the robust\noptimal investment-consumption strategy and the value function, and the impact\nof investment and consumption constraints on the investor's robust optimal\ninvestment-consumption strategy and value function. Extensive numerical\nexperiments highlight the significant impact of ambiguity aversion, consumption\nand investment constraints, on the investor's robust optimal\ninvestment-consumption strategy, utility loss, and value function. Key findings\ninclude: 1) short-selling restriction always reduces the investor's utility\nloss when model uncertainty is ignored; 2) the effect of consumption\nconstraints on utility loss is more delicate and relies on the investor's risk\naversion level.\n""]","[('optimal investment', 0.5854794979095459), ('optimal investment strategy', 0.5479139685630798), ('utility maximization', 0.5259596705436707), ('optimal portfolio', 0.5218998193740845), ('risk aversion', 0.49477431178092957), ('investment strategy', 0.4337094724178314), ('investment', 0.42981287837028503), ('semimartingale', 0.4166948199272156), ('consumption', 0.4019351601600647), ('expected utility', 0.3995110094547272)]"
186,186,148,186_numerical semigroups_numerical semigroup_semigroups generated_semigroups,"['numerical semigroups', 'numerical semigroup', 'semigroups generated', 'semigroups', 'semigroup generated', 'semigroup', 'families numerical', 'semigroups let', 'generalized numerical', 'fixed frobenius']","['On integer partitions corresponding to numerical semigroups   Numerical semigroups are cofinite additive submonoids of the natural numbers.\nIn 2011, Keith and Nath illustrated an injection from numerical semigroups to\ninteger partitions. We explore this connection between partitions and numerical\nsemigroups with a focus on classifying the partitions that appear in the image\nof the injection from numerical semigroups. In particular, we count the number\nof partitions that correspond to numerical semigroups in terms of genus,\nFrobenius number, and multiplicity, with some restrictions.\n', 'Numerical Semigroups of small and large type   A numerical semigroup is a sub-semigroup of the natural numbers that has a\nfinite complement. Some of the key properties of a numerical semigroup are its\nFrobenius number F, genus g and type t. It is known that for any numerical\nsemigroup $\\frac{g}{F+1-g}\\leq t\\leq 2g-F$. Numerical semigroups with $t=2g-F$\nare called almost symmetric, we introduce a new property that characterises\nthem. We give an explicit characterisation of numerical semigroups with\n$t=\\frac{g}{F+1-g}$. We show that for a fixed $\\alpha$ the number of numerical\nsemigroups with Frobenius number $F$ and type $F-\\alpha$ is eventually constant\nfor large $F$. Also the number of numerical semigroups with genus $g$ and type\n$g-\\alpha$ is also eventually constant for large $g$.\n', 'On the enumeration of the set of atomic numerical semigroups with fixed\n  Frobenius number   A numerical semigroup is irreducible if it cannot be obtained as intersection\nof two numerical semigroups containing it properly. If we only consider\nnumerical semigroups with the same Frobenius number, that concept is\ngeneralized to atomic numerical semigroup. Based on a previous one developed to\nobtain all irreducible numerical semigroups with a fixed Frobenius number, we\npresent an algorithm to compute all atomic numerical semigroups with a fixed\nFrobenius number.\n']","[('numerical semigroups', 0.7519791126251221), ('numerical semigroup', 0.7210885882377625), ('semigroups generated', 0.5557281374931335), ('semigroups', 0.5319920182228088), ('semigroup generated', 0.5258738398551941), ('semigroup', 0.49916425347328186), ('families numerical', 0.4886474907398224), ('semigroups let', 0.48605024814605713), ('generalized numerical', 0.47559675574302673), ('fixed frobenius', 0.46753665804862976)]"
187,187,148,187_gauge theories_gauge theory_gauge symmetry_gauge symmetries,"['gauge theories', 'gauge theory', 'gauge symmetry', 'gauge symmetries', 'gauge invariant', 'gauge transformations', 'gauge group', 'fields spin', 'spin field', 'bosonic fields']","[""BRST-BV Quantum Actions for Constrained Totally-Symmetric Integer HS\n  Fields   A constrained BRST-BV Lagrangian formulation for totally symmetric massless\nHS fields in a $d$-dimensional Minkowski space is extended to a non-minimal\nconstrained BRST-BV Lagrangian formulation by using a non-minimal BRST operator\n$Q_{c|\\mathrm{tot}}$ with non-minimal Hamiltonian BFV oscillators\n$\\overline{C}, \\overline{\\mathcal{P}}, \\lambda, \\pi$, as well as antighost and\nNakanishi-Lautrup tensor fields, in order to introduce an admissible\nself-consistent gauge condition. The gauge-fixing procedure involves an\noperator gauge-fixing BRST-BFV Fermion $\\Psi_H$ as a kernel of the gauge-fixing\nBRST-BV Fermion functional $\\Psi$, manifesting the concept of BFV-BV duality. A\nFock-space quantum action with non-minimal BRST-extended off-shell constraints\nis constructed as a shift of the total generalized field-antifield vector by a\nvariational derivative of the gauge-fixing Fermion $\\Psi$ in a total BRST-BV\naction $S^{\\Psi}_{0|s} = \\int d \\eta_0 \\langle \\chi^{\\Psi{} 0}_{\\mathrm{tot}|c}\n\\big| Q_{c|\\mathrm{tot}}\\big| \\chi^{\\Psi{} 0}_{\\mathrm{tot}|c}\\rangle$. We use\na gauge condition which depends on two gauge parameters, thereby extending the\ncase of $R_\\xi$-gauges. For triplet and duplet formulations we explored the\nrepresentations with only traceless field-antifield and source variables. For\nthe generating functionals of Green's functions, BRST symmetry transformations\nare suggested and Ward identities are obtained.\n"", ""Twisted BRST symmetry in gauge theories on $\\kappa$-Minkowski   Algebraic properties of the BRST symmetry associated to the twisted gauge\nsymmetry occurring in the $\\kappa$-Poincar\\'e invariant gauge theories on the\n$\\kappa$-Minkowski space are investigated. We find that the BRST operation\nassociated to the gauge invariance of the action functional can be continuously\ndeformed together with its corresponding Leibniz rule, into a nilpotent twisted\nBRST operation, leading to a twisted BRST symmetry algebra which may be viewed\nas a noncommutative analog of the usual Yang-Mills BRST algebra.\n"", 'BRST-BV approach for interacting higher spin fields   We develop the BRST-BV approach to construct the general off-shell Lorentz\ncovariant cubic, quartic, $e$-tic interaction vertices for irreducible higher\nspin fields on $d$-dimensional Minkowski space. We consider two different cases\nfor interacting integer higher spin fields both with massless and with massive\nfields. The deformation procedure to find minimal (determined with help of\ngeneralized Hilbert space) BRST-BV action for interacting higher spin fields is\nbased on the preservation of master equation validity in each power of coupling\nconstant $g$ starting from the Lagrangian formulation for free gauge theory. As\nexamples we consider the construction of local cubic vertices for $k$\nirreducible massless fields of integer helicities, and $k-1$ massless with one\nmassive fields of spins $s_1, ,..., s_{k-1}, s_k$. For triple of two massless\nscalars and tensor field of integer spin the BRST-BV action with cubic\ninteraction is explicitly found. Unlike the previous results on cubic vertices\nwe follow our result for BRST approach [arXiv:2105.12030[hep-th]] for massless\nfields, but for the unique BRST-BV action instead of classical action with\nreducible gauge transformations. The procedure is based on the complete BRST\noperator, including the trace constraints that is used to formulate an\nirreducible representation with definite integer spin.\n']","[('gauge theories', 0.5536081790924072), ('gauge theory', 0.5280138850212097), ('gauge symmetry', 0.5276015400886536), ('gauge symmetries', 0.5257627964019775), ('gauge invariant', 0.5180887579917908), ('gauge transformations', 0.49017319083213806), ('gauge group', 0.44707566499710083), ('fields spin', 0.41468897461891174), ('spin field', 0.411056786775589), ('bosonic fields', 0.39920273423194885)]"
188,188,148,188_hamiltonian graphs_hamiltonian graph_graph hamiltonian_chordal graphs,"['hamiltonian graphs', 'hamiltonian graph', 'graph hamiltonian', 'chordal graphs', 'hamilton cycle', 'cubic graphs', 'free graphs', 'hamiltonian cycles', 'connected graphs', 'free graph']","[""Chords of longest cycles passing through a specified small set   A long-standing conjecture of Thomassen says that every longest cycle of a\n$3$-connected graph has a chord. Thomassen (2018) proved that if $G$ is\n$2$-connected and cubic, then any longest cycle must have a chord. He also\nshowed that if $G$ is a $3$-connected graph with minimum degree at least $4$,\nthen some of the longest cycles in $G$ must have a chord. Zhang (1987) proved\nthat if $G$ is a $3$-connected simple planar graph which is 3-regular or has\nminimum degree at least $4$, then every longest cycle of $G$ must have a chord.\nRecently, Li and Liu showed that if $G$ is a $2$-connected cubic graph and $x,\ny$ are two distinct vertices of $G$, then every longest $(x,y)$-path of $G$\ncontains at least one internal vertex whose neighbors are all in the path. In\nthis paper, we study chords of longest cycles passing through a specified small\nset and generalize Thomassen's and Zhang's above results by proving the\nfollowing results. (i) Let $G$ be a $2$-connected cubic graph and $S$ be a\nspecified set consisting of an edge plus a vertex. Then every longest cycle of\n$G$ containing $S$ must have a chord. (ii) Let $G$ be a $3$-connected graph\nwith minimum degree at least $4$ and $e$ be a specified edge of $G$. Then some\nlongest cycle of $G$ containing $e$ must have a chord. (iii) Let $G$ be a\n$3$-connected planar graph with minimum degree at least $4$. Suppose $S$ is a\nspecified set consisting of either three vertices or an edge plus a vertex.\nThen every longest cycle of $G$ containing $S$ must have a chord. We also\nextend the above-mentioned result of Li and Liu for $2$-connected cubic graphs.\n"", 'A note on hamiltonian cycles in $4$-tough $(P_2\\cup kP_1)$-free graphs   Let $t>0$ be a real number and $G$ be a graph. We say $G$ is $t$-tough if for\nevery cutset $S$ of $G$, the ratio of $|S|$ to the number of components of\n$G-S$ is at least $t$. The Toughness Conjecture of Chv\\\'atal, stating that\nthere exists a constant $t_0$ such that every $t_0$-tough graph with at least\nthree vertices is hamiltonian, is still open in general. For any given integer\n$k\\ge 1$, a graph $G$ is $(P_2\\cup kP_1)$ free if $G$ does not contain the\ndisjoint union of $P_2$ and $k$ isolated vertices as an induced subgraph.\n  In this note, we show that every 4-tough and $2k$-connected $(P_2\\cup\nkP_1)$-free graph with at least three vertices is hamiltonian.\n  This result in some sense is an ""extension"" of the classical\nChv\\\'{a}tal-Erd\\H{o}s Theorem that every $\\max\\{2,k\\}$-connected\n  $(k+1)P_1$-free graph on at least three vertices is hamiltonian.\n', 'Hamiltonicity of $1$-tough $(P_2\\cup kP_1)$-free graphs   Given a graph $H$, a graph $G$ is $H$-free if $G$ does not contain $H$ as an\ninduced subgraph. For a positive real number $t$, a non-complete graph $G$ is\nsaid to be $t$-tough if for every vertex cut $S$ of $G$, the ratio of $|S|$ to\nthe number of components of $G-S$ is at least $t$. A complete graph is said to\nbe $t$-tough for any $t>0$. Chv\\\'{a}tal\'s toughness conjecture, stating that\nthere exists a constant $t_0$ such that every $t_0$-tough graph with at least\nthree vertices is Hamiltonian, is still open in general. Chv\\\'{a}tal and\nErd\\""{o}s \\cite{CE} proved that, for any integer $k\\ge 1$, every\n$\\max\\{2,k\\}$-connected $(k+1)P_1$-free graph on at least three vertices is\nHamiltonian. Along the Chv\\\'{a}tal-Erd\\""{o}s theorem, Shi and Shan \\cite{SS}\nproved that, for any integer $k\\ge 4$, every $4$-tough $2k$-connected $(P_2\\cup\nkP_1)$-free graph with at least three vertices is Hamiltonian, and furthermore,\nthey proposed a conjecture that for any integer $k\\ge 1$, any $1$-tough\n$2k$-connected $(P_2\\cup kP_1)$-free graph is Hamiltonian. In this paper, we\nconfirm the conjecture, and furthermore, we show that if $k\\ge 3$, then the\ncondition `$2k$-connected\' may be weakened to be `$2(k-1)$-connected\'. As an\nimmediate consequence, for any integer $k\\ge 3$, every $(k-1)$-tough $(P_2\\cup\nkP_1)$-free graph is Hamiltonian. This improves the result of Hatfield and\nGrimm \\cite{HG}, stating that every $3$-tough $(P_2\\cup 3P_1)$-free graph is\nHamiltonian.\n']","[('hamiltonian graphs', 0.5885749459266663), ('hamiltonian graph', 0.5437144041061401), ('graph hamiltonian', 0.5297220349311829), ('chordal graphs', 0.4890170693397522), ('hamilton cycle', 0.4888312816619873), ('cubic graphs', 0.48171934485435486), ('free graphs', 0.4736254811286926), ('hamiltonian cycles', 0.4723476767539978), ('connected graphs', 0.4621918201446533), ('free graph', 0.46211305260658264)]"
189,189,147,189_multiple access noma_orthogonal multiple access_access noma_noma systems,"['multiple access noma', 'orthogonal multiple access', 'access noma', 'noma systems', 'performance noma', 'uplink noma', 'downlink noma', 'multiple access rsma', 'noma system', 'noma scheme']","[""Resource Allocation and Performance Analysis of Hybrid RSMA-NOMA in the\n  Downlink   Rate splitting multiple access (RSMA) and non-orthogonal multiple access\n(NOMA) are the key enabling multiple access techniques to enable massive\nconnectivity. However, it is unclear whether RSMA would consistently outperform\nNOMA from a system sum-rate perspective, users' fairness, as well as\nconvergence and feasibility of the resource allocation solutions. This paper\ninvestigates the weighted sum-rate maximization problem to optimize power and\nrate allocations in a hybrid RSMA-NOMA network. In the hybrid RSMA-NOMA, by\noptimally allocating the maximum power budget to each scheme, the BS operates\non NOMA and RSMA in two orthogonal channels, allowing users to simultaneously\nreceive signals on both RSMA and NOMA. Based on the successive convex\napproximation (SCA) approach, we jointly optimize the power allocation of users\nin NOMA and RSMA, the rate allocation of users in RSMA, and the power budget\nallocation for NOMA and RSMA considering successive interference cancellation\n(SIC) constraints. Numerical results demonstrate the trade-offs that hybrid\nRSMA-NOMA access offers in terms of system sum rate, fairness, convergence, and\nfeasibility of the solutions.\n"", 'Performance Analysis of Uplink Adaptive NOMA Depending on Channel\n  Knowledge   Non Orthogonal Multiple Access (NOMA) is a key technique to satisfy large\nusers densities in future wireless networks. However, NOMA may provide poor\nperformance compared to Orthogonal Multiple Access (OMA) due to inter-user\ninterference. In this paper, we obtain closed-form expressions of the uplink\nNOMA and OMA throughputs when no Channel State Information at Transmitter\n(CSIT) is available, and of the average data rates assuming that instantaneous\nrates should be larger than a minimum threshold when full CSIT is available.\nAnalytical comparisons of OMA and NOMA prove that there is no global dominant\nstrategy valid in all situations. Based on this conclusion, we propose a new\nmultiple-access (MA) strategy called NOMA-Adaptive (NOMA-A) that selects the\nbest MA technique between OMA and NOMA. NOMA-A aims at maximizing the sum\nthroughput in the no CSIT case, and the probability that both users are active\nin the full CSIT case. NOMA-A is shown to outperform the other strategies in\nterms of sum throughput and rate.\n', 'Partial Non-Orthogonal Multiple Access (NOMA) in Downlink Poisson\n  Networks   Non-orthogonal multiple access (NOMA) allows users sharing a resource-block\nto efficiently reuse spectrum and improve cell sum rate $\\mathcal{R}_{\\rm tot}$\nat the expense of increased interference. Orthogonal multiple access (OMA), on\nthe other hand, guarantees higher coverage. We introduce partial-NOMA in a\nlarge two-user downlink network to provide both throughput and reliability. The\nassociated partial overlap controls interference while still offering spectrum\nreuse. The nature of the partial overlap also allows us to employ\nreceive-filtering to further suppress interference. For signal decoding in our\npartial-NOMA setup, we propose a new technique called flexible successive\ninterference cancellation (FSIC) decoding. We plot the rate region abstraction\nand compare with OMA and NOMA. We formulate a problem to maximize\n$\\mathcal{R}_{\\rm tot}$ constrained to a minimum throughput requirement for\neach user and propose an algorithm to find a feasible resource allocation\nefficiently. Our results show that partial-NOMA allows greater flexibility in\nterms of performance. Partial-NOMA can also serve users that NOMA cannot. We\nalso show that with appropriate parameter selection and resource allocation,\npartial-NOMA can outperform NOMA.\n']","[('multiple access noma', 0.6843768954277039), ('orthogonal multiple access', 0.6039155721664429), ('access noma', 0.5809214115142822), ('noma systems', 0.5716182589530945), ('performance noma', 0.5633791089057922), ('uplink noma', 0.5567799210548401), ('downlink noma', 0.5458943247795105), ('multiple access rsma', 0.5287384390830994), ('noma system', 0.5205540657043457), ('noma scheme', 0.5203250050544739)]"
190,190,146,190_inverse scattering problems_inverse scattering_acoustic scattering_obstacle scattering,"['inverse scattering problems', 'inverse scattering', 'acoustic scattering', 'obstacle scattering', 'inverse acoustic', 'elastic scattering', 'scattering problems', 'scattering', 'scattered field', 'scattered fields']","[""Direct sampling for recovering sound soft scatterers from point source\n  measurements   In this paper, we consider the inverse problem of recovering a sound soft\nscatterer from the measured scattered field. The scattered field is assumed to\nbe induced by a point source on a curve/surface that is known. Here we will\npropose and analyze new direct sampling methods for this problem. The first\nmethod we consider uses a far-field transformation of the near-field data which\nwill allow us to derive explicit bounds in the resolution analysis for the\ndirect sampling method's imaging functional. Two direct sampling methods will\nbe studied using the far-field transformation. For these imaging functionals,\nwe will use the Funk-Hecke identities to study the resolution analysis. We will\nalso study a direct sampling method for the case of the given Cauchy data.\nNumerical examples are given to show the applicability of the new imaging\nfunctionals for recovering a sound soft scatterer in 2D.\n"", 'Inverse elastic scattering problems with phaseless far field data   This paper is concerned with uniqueness, phase retrieval and shape\nreconstruction methods for inverse elastic scattering problems with phaseless\nfar field data. Systematically, we study two basic models, i.e., inverse\nscattering of plane waves by rigid bodies and inverse scattering of sources\nwith compact support. For both models, we show that the location of the objects\ncan not be uniquely recovered by the data. To solve this problem, we consider\nsimultaneously the incident point sources with one fixed source point and at\nmost three scattering strengths. We then establish some uniqueness results for\nsource scattering problem with multi-frequency phaseless far field data.\nFurthermore, a fast and stable phase retrieval approach is proposed based on a\nsimple geometric result which provides a stable reconstruction of a point in\nthe plane from three distances to given points. Difficulties arise for inverse\nscattering by rigid bodies due to the additional unknown far field pattern of\nthe point sources. To overcome this difficulty, we introduce an artificial\nrigid body into the system and show that the underlying rigid bodies can be\nuniquely determined by the corresponding phaseless far field data at a fixed\nfrequency. Noting that the far field pattern of the scattered field\ncorresponding to point sources is very small if the source point is far away\nfrom the scatterers, we propose an appropriate phase retrieval method for\nobstacle scattering problems, without using the artificial rigid body. Finally,\nwe propose several sampling methods for shape reconstruction with phaseless far\nfield data. Extended numerical examples in two dimensions are conducted with\nnoisy data, and the results further verify the effectiveness and robustness of\nthe proposed phase retrieval techniques and sampling methods.\n', 'Uniqueness in phaseless inverse scattering problems with superposition\n  of incident point sources   This paper is concerned with the uniqueness in inverse acoustic scattering\nproblems with the modulus of the far-field patterns co-produced by the obstacle\n(resp. medium) and the point sources. Based on the superposition of point\nsources as the incident waves, we overcome the difficulty of translation\ninvariance induced by a single incident plane wave, and rigorously prove that\nthe location and shape of the obstacle as well as its boundary condition or the\nrefractive index can be uniquely determined by the modulus of far-field\npatterns. This work is different from our previous work on phaseless inverse\nscattering problems [2018 Inverse Problems 34, 085002], in which the reference\nball technique and the superposition of incident waves were used, and the\nphaseless far-field data generated only by the the scatterer were considered.\nIn this paper, the phaseless far-field data co-produced by the scatterer and\nthe point sources are used, thus the configuration is practically more\nfeasible. Moreover, since the reference ball is not needed, the justification\nof uniqueness is much more clear and concise.\n']","[('inverse scattering problems', 0.6704345345497131), ('inverse scattering', 0.6469432711601257), ('acoustic scattering', 0.6152991056442261), ('obstacle scattering', 0.5765234231948853), ('inverse acoustic', 0.5524341464042664), ('elastic scattering', 0.5251167416572571), ('scattering problems', 0.5212149024009705), ('scattering', 0.5129374265670776), ('scattered field', 0.5120040774345398), ('scattered fields', 0.4765367805957794)]"
191,191,146,191_ramsey properties_ramsey theory_ramsey type_ramsey,"['ramsey properties', 'ramsey theory', 'ramsey type', 'ramsey', 'relational structures', 'infinite structures', 'structures finite', 'finite structures', 'structure finite', 'classes finite']","['A survey on big Ramsey structures   In recent years, there has been much progress in the field of structural\nRamsey theory, in particular in the study of big Ramsey degrees. In all known\nexamples of infinite structures with finite big Ramsey degrees, there is in\nfact a single expansion of the structure, called a big Ramsey structure, which\ncorrectly encodes the exact big Ramsey degrees of every finite substructure\nsimultaneously. The first half of the article collects facts about this\nphenomenon that have appeared in the literature into a single cohesive\nframework, thus offering a conceptual survey of big Ramsey structures. We\npresent some original results indicating that the standard methods of proving\nfinite big Ramsey degrees automatically yield big Ramsey structures, often with\ndesirable extra properties. The second half of the article is a survey in the\nmore traditional sense, discussing numerous examples from the literature and\nshowing how they fit into our framework. We also present some general results\non how big Ramsey degrees are affected by expanding structures with unary\nfunctions.\n', 'Big Ramsey Degrees and Infinite Languages   This paper investigates big Ramsey degrees of unrestricted relational\nstructures in (possibly) infinite languages. Despite significant progress in\nthe study of big Ramsey degrees, the big Ramsey degrees of many classes of\nstructures with finite small Ramsey degrees are still not well understood. We\nshow that if there are only finitely many relations of every arity greater than\none, then unrestricted relational structures have finite big Ramsey degrees,\nand give some evidence that this is tight. This is the first time finiteness of\nbig Ramsey degrees has been established for a random structure in an infinite\nlanguage. Our results represent an important step towards a better\nunderstanding of big Ramsey degrees for structures with relations of arity\ngreater than two.\n', 'On Ramsey degrees, compactness and approximability   One of the consequences of the Compactness Principle in structural Ramsey\ntheory is that the small Ramsey degrees cannot exceed the corresponding big\nRamsey degrees, thereby justifying the choice of adjectives. However, it is\nunclear what happens in the realm of dual Ramsey degrees due to the lack of the\ncompactness argument that applies to that setting. In this paper we present a\nframework within which both ""direct"" and dual Ramsey statements can be stated\nand reasoned about in a uniform fashion. We introduce the notion of\napproximability which yields a general compactness argument powerful enough to\nprove statements about both ""direct"" and dual Ramsey phenomena. We conclude the\npaper with an application of the new strategies by generalizing Voigt\'s\n$\\star$-version of the Infinite Ramsey Theorem to a large class of relational\nstructures and deriving a Ramsey statement for ""loose colorings"" of enumerated\nFra\\""{\\i}ss\\\'{e} limits.\n']","[('ramsey properties', 0.8016266226768494), ('ramsey theory', 0.7822386026382446), ('ramsey type', 0.685300350189209), ('ramsey', 0.5834973454475403), ('relational structures', 0.46328988671302795), ('infinite structures', 0.45922449231147766), ('structures finite', 0.4527060091495514), ('finite structures', 0.44656842947006226), ('structure finite', 0.4026438891887665), ('classes finite', 0.39793843030929565)]"
192,192,146,192_neumann boundary conditions_homogeneous neumann boundary_neumann boundary_homogeneous neumann,"['neumann boundary conditions', 'homogeneous neumann boundary', 'neumann boundary', 'homogeneous neumann', 'parabolic elliptic', 'u_t nabla', 'chemotaxis system', 'omega u_0', 'finite time blow', 'classical solutions']","['Blow-up phenomena in a parabolic-elliptic-elliptic attraction-repulsion\n  chemotaxis system with superlinear logistic degradation   This paper is concerned with the attraction-repulsion chemotaxis system with\nsuperlinear logistic degradation, \\begin{align*} \\begin{cases} u_t = \\Delta u -\n\\chi \\nabla\\cdot(u \\nabla v)\n  + \\xi \\nabla\\cdot (u \\nabla w) + \\lambda u - \\mu u^k, \\quad\n  &x \\in \\Omega,\\ t>0,\\\\[1.05mm] 0= \\Delta v + \\alpha u - \\beta v, \\quad\n  &x \\in \\Omega,\\ t>0,\\\\[1.05mm] 0= \\Delta w + \\gamma u - \\delta w, \\quad\n  &x \\in \\Omega,\\ t>0, \\end{cases} \\end{align*} under homogeneous Neumann\nboundary conditions, in a ball $\\Omega \\subset \\mathbb{R}^n$ ($n \\ge 3$), with\nconstant parameters $\\lambda \\in \\mathbb{R}$, $k>1$, $\\mu, \\chi, \\xi, \\alpha,\n\\beta, \\gamma, \\delta>0$. Blow-up phenomena in the system have been well\ninvestigated in the case $\\lambda=\\mu=0$, whereas the attraction-repulsion\nchemotaxis system with logistic degradation has been not studied. Under the\ncondition that $k>1$ is close to $1$, this paper ensures a solution which blows\nup in $L^\\infty$-norm and $L^\\sigma$-norm with some $\\sigma>1$ for some\nnonnegative initial data. Moreover, a lower bound of blow-up time is derived.\n', 'Prescribed signal concentration on the boundary: Weak solvability in a\n  chemotaxis-Stokes system with proliferation   We study a chemotaxis-Stokes system with signal consumption and logistic\nsource terms of the form \\noindent \\begin{align*} \\left\\{ \\begin{array}{r@{\\\n}l@{\\quad}l@{\\quad}l@{\\,}c} n_{t}+u\\cdot\\!\\nabla n&=\\Delta\nn-\\nabla\\!\\cdot(n\\nabla c)+\\kappa n-\\mu n^{2},\\ &x\\in\\Omega,& t>0,\\\\\nc_{t}+u\\cdot\\!\\nabla c&=\\Delta c-nc,\\ &x\\in\\Omega,& t>0,\\\\ u_{t}&=\\Delta\nu+\\nabla P+n\\nabla\\phi,\\ &x\\in\\Omega,& t>0,\\\\ \\nabla\\cdot u&=0,\\ &x\\in\\Omega,&\nt>0,\\\\ \\big(\\nabla n-n\\nabla c\\big)\\cdot\\nu&=0,\\quad c=c_{\\star}(x),\\quad u=0,\n&x\\in\\partial\\Omega,& t>0, \\end{array}\\right. \\end{align*} where $\\kappa\\geq0$,\n$\\mu>0$ and, in contrast to the commonly investigated variants of\nchemotaxis-fluid systems, the signal concentration on the boundary of the\ndomain $\\Omega\\subset\\mathbb{R}^N$ with $N\\in\\{2,3\\}$, is a prescribed\ntime-independent nonnegative function $c_{\\star}\\in\nC^{2}\\!\\big(\\overline{\\Omega}\\big)$. Making use of the boundedness information\nentailed by the quadratic decay term of the first equation, we will show that\nthe system above has at least one global weak solution for any suitably regular\ntriplet of initial data.\n', 'A new (and optimal) result for boundedness of solution of a quasilinear\n  chemotaxis--haptotaxis model (with logistic source)   This article deals with an initial-boundary value problem for the coupled\nchemotaxis-haptotaxis system with nonlinear diffusion\n$$\\left\\{\\begin{array}{ll} u_t=\\nabla\\cdot( D(u)\\nabla\nu)-\\chi\\nabla\\cdot(u\\nabla v)- \\xi\\nabla\\cdot(u\\nabla w)+\\mu u(1- u-w), x\\in\n\\Omega, t>0,\\\\ \\tau v_t=\\Delta v- v +u,\\quad x\\in \\Omega, t>0,\\\\ w_t=- vw,\\quad\nx\\in \\Omega, t>0, \\end{array}\\right.$$ under homogeneous Neumann boundary\nconditions in a smooth bounded domain $\\Omega\\subset\\mathbb{R}^N(N\\geq1)$,\nwhere $\\tau\\in\\{0,1\\}$ and $\\chi$, $\\xi$ and $\\mu$ are given nonnegative\nparameters. As far as we know, this situation provides the first {\\bf rigorous}\nresult which (precisely) gives the relationship between $m,\\xi,\\chi$ and $\\mu$\nthat yields to the boundedness of the solutions. Moreover, these results\nthereby significantly extending results of previous results of several authors\n(see Remarks 1.1 and 1.2) and some optimal results are obtained.\n']","[('neumann boundary conditions', 0.5254983305931091), ('homogeneous neumann boundary', 0.47823306918144226), ('neumann boundary', 0.47104471921920776), ('homogeneous neumann', 0.42646488547325134), ('parabolic elliptic', 0.41688480973243713), ('u_t nabla', 0.36006641387939453), ('chemotaxis system', 0.3492005169391632), ('omega u_0', 0.338458389043808), ('finite time blow', 0.33299005031585693), ('classical solutions', 0.32283464074134827)]"
193,193,146,193_consensus multi agent_consensus algorithms_consensus protocol_control multi agent,"['consensus multi agent', 'consensus algorithms', 'consensus protocol', 'control multi agent', 'distributed control', 'multi agent systems', 'consensus multi', 'multi agent system', 'linear multi agent', 'multiagent systems']","['Output Consensus of Heterogeneous Multi-Agent Systems with Mismatched\n  Uncertainties and Measurement Noises: An ADRC Approach   In this paper, the practical output consensus problem for heterogeneous\nhigh-order leader-follower multi-agent systems under directed communication\ntopology containing a directed spanning tree and subject to large-scale\nmismatched disturbances, mismatched uncertainties, and measurement noises is\naddressed. By introducing a reversible state transformation without changing\nthe output, the actual total disturbance affecting output performance of each\nagent and matched with the control input of the transformed system is extracted\nand estimated by extended state observers. Then, the control protocols based on\nestimates of extended state observers, are designed by combing the output\nfeedback control ones to obtain output consensus and feedforward compensators\nto attenuating the total disturbance of each agent actively. It is shown with a\nrigorous proof that the outputs of all followers can track practically the\noutput of the leader, and all the states of the leader-follower multi-agent\nsystems are bounded. Some numerical simulations are performed to verify the\nvalidity of the control protocols and theoretical result.\n', 'Observer-based Leader-following Consensus for Positive Multi-agent\n  Systems Over Time-varying Graphs   This paper addresses the leader-following consensus problem for discrete-time\npositive multi-agent systems over time-varying graphs. We assume that the\nfollowers may have mutually different positive dynamics which can also be\ndifferent from the leader. Compared with most existing positive consensus works\nfor homogeneous multi-agent systems, the formulated problem is more general and\nchallenging due to the interplay between the positivity requirement and\nhigh-order heterogeneous dynamics. To solve the problem, we present an extended\nversion of existing observer-based design for positive multi-agent systems. By\nvirtue of the common quadratic Lyapunov function technique, we show the\nfollowers will maintain their state variables in the positive orthant and\nfinally achieve an output consensus specified by the leader. A numerical\nexample is used to verify the efficacy of our algorithms.\n', 'Distributed Event-Triggered Leader-Follower Consensus of Nonlinear\n  Multi-Agent Systems   We consider the distributed leader-follower consensus problem with\nevent-triggered communications. The system under consideration is a non-linear\ninput-affine multi agent system. The agents are assumed to have identical\ndynamics structure with uncertain parameters and satisfying an incremental\nstabilisability condition. A distributed control law is proposed which achieves\nconsensus based on two novel Communication Triggering Conditions (CTCs): the\nfirst one to achieve an asymptotic consensus but without any guarantees on Zeno\nbehaviour and the second one to exclude Zeno behaviour but with practical\nconsensus.\n']","[('consensus multi agent', 0.7050110101699829), ('consensus algorithms', 0.618108332157135), ('consensus protocol', 0.5975180268287659), ('control multi agent', 0.5632423162460327), ('distributed control', 0.5554451942443848), ('multi agent systems', 0.5416117310523987), ('consensus multi', 0.5307525992393494), ('multi agent system', 0.5017889738082886), ('linear multi agent', 0.48507925868034363), ('multiagent systems', 0.4227755665779114)]"
194,194,145,194_copulas_copula based_copula_dependence measures,"['copulas', 'copula based', 'copula', 'dependence measures', 'dependence properties', 'dependence structure', 'multivariate distributions', 'marginals', 'marginal distributions', 'dependence functions']","['Right-truncated Archimedean and related copulas   The copulas of random vectors with standard uniform univariate margins\ntruncated from the right are considered and a general formula for such\nright-truncated conditional copulas is derived. This formula is analytical for\ncopulas that can be inverted analytically as functions of each single argument.\nThis is the case, for example, for Archimedean and related copulas. The\nresulting right-truncated Archimedean copulas are not only analytically\ntractable but can also be characterized as tilted Archimedean copulas. This\nfinding allows one, for example, to more easily derive analytical properties\nsuch as the coefficients of tail dependence or sampling procedures of\nright-truncated Archimedean copulas. As another result, one can easily obtain a\nlimiting Clayton copula for a general vector of truncation points converging to\nzero; this is an important property for (re)insurance and a fact already known\nin the special case of equal truncation points, but harder to prove without\naforementioned characterization. Furthermore, right-truncated Archimax copulas\nwith logistic stable tail dependence functions are characterized as tilted\nouter power Archimedean copulas and an analytical form of right-truncated\nnested Archimedean copulas is also derived.\n', ""Final solution to the problem of relating a true copula to an imprecise\n  copula   In this paper we solve in the negative the problem proposed in this journal\n(I. Montes et al., Sklar's theorem in an imprecise setting, Fuzzy Sets and\nSystems, 278 (2015), 48-66) whether an order interval defined by an imprecise\ncopula contains a copula. Namely, if $\\mathcal{C}$ is a nonempty set of\ncopulas, then $\\underline{C} = \\inf\\{C\\}_{C\\in\\mathcal{C}}$ and $\\overline{C}=\n\\sup\\{C\\}_{C\\in\\mathcal{C}}$ are quasi-copulas and the pair\n$(\\underline{C},\\overline{C})$ is an imprecise copula according to the\ndefinition introduced in the cited paper, following the ideas of $p$-boxes. We\nshow that there is an imprecise copula $(A,B)$ in this sense such that there is\nno copula $C$ whatsoever satisfying $A \\leqslant C\\leqslant B$. So, it is\nquestionable whether the proposed definition of the imprecise copula is in\naccordance with the intentions of the initiators. Our methods may be of\nindependent interest: We upgrade the ideas of Dibala et al. (Defects and\ntransformations of quasi-copulas, Kybernetika, 52 (2016), 848-865) where\npossibly negative volumes of quasi-copulas as defects from being copulas were\nstudied.\n"", 'New copulas and their applications to symmetrizations of bivariate\n  copulas   New copulas, based on perturbation theory, are introduced to clarify a\n\\emph{symmetrization} procedure for asymmetric copulas. We give also some\nproperties of the \\emph{symmetrized} copula. Finally, we examine families of\ncopulas with a prescribed symmetrized one. By the way, we study topologically,\nthe set of all symmetric copulas and give some of its classical and new\nproperties.\n']","[('copulas', 0.7245012521743774), ('copula based', 0.6973357200622559), ('copula', 0.6900383830070496), ('dependence measures', 0.3908790647983551), ('dependence properties', 0.35512977838516235), ('dependence structure', 0.3498140573501587), ('multivariate distributions', 0.34560227394104004), ('marginals', 0.3440547585487366), ('marginal distributions', 0.34275034070014954), ('dependence functions', 0.3343869149684906)]"
195,195,145,195_stochastic differential bsde_reflected stochastic differential_backward stochastic differential_stochastic differential equations,"['stochastic differential bsde', 'reflected stochastic differential', 'backward stochastic differential', 'stochastic differential equations', 'forward backward stochastic', 'backward stochastic', 'reflected stochastic', 'equations driven brownian', 'differential equations bsdes', 'backward sdes']","['Existence and uniqueness of solutions for multi-dimensional reflected\n  BSDEs with diagonally quadratic generators   In this paper, we study multi-dimensional reflected backward stochastic\ndifferential equations with diagonally quadratic generators. Using the\ncomparison theorem for diagonally quadratic BSDEs which is established recently\nin [14], we obtain the existence and uniqueness of a solution by a penalization\nmethod. Moreover, we provide a comparison theorem.\n', 'Multi-dimensional reflected BSDEs driven by $G$-Brownian motion with\n  diagonal generators   We consider the well-posedness problem of multi-dimensional reflected\nbackward stochastic differential equations driven by $G$-Brownian motion\n($G$-BSDEs) with diagonal generators. Two methods, i.e., the penalization\nmethod and the Picard iteration argument, are provided to prove the existence\nand uniqueness of solutions. We also study its connection with the obstacle\nproblem of a system of fully nonlinear PDEs.\n', '$G$-BSDEs with mean constraints in time-dependent intervals   In this paper, we study a collection of mean-reflected backward stochastic\ndifferential equations driven by $G$-Brownian motions ($G$-BSDEs), where\n$G$-expectations are constrained in some time-dependent intervals. To establish\nwell-posedness results, we firstly construct a backward Skorokhod problem with\nsublinear expectation, and then apply that in the study of doubly\nmean-reflected $G$-BSDEs involving Lipschitz and quadratic generators under\nbounded and unbounded terminal conditions. Also we utilize fixed-point\nargumentations and $\\theta$-methods while solving these equations. Finally, we\nextend the results to multi-dimensional doubly mean-reflected $G$-BSDEs with\ndiagonal generators.\n']","[('stochastic differential bsde', 0.639890193939209), ('reflected stochastic differential', 0.6121283173561096), ('backward stochastic differential', 0.591974139213562), ('stochastic differential equations', 0.5678649544715881), ('forward backward stochastic', 0.5599536299705505), ('backward stochastic', 0.555921733379364), ('reflected stochastic', 0.5365515947341919), ('equations driven brownian', 0.527848482131958), ('differential equations bsdes', 0.5183508396148682), ('backward sdes', 0.5043823719024658)]"
196,196,144,196_hamilton jacobi theory_hamilton jacobi equations_hamiltonian vector field_hamiltonian systems,"['hamilton jacobi theory', 'hamilton jacobi equations', 'hamiltonian vector field', 'hamiltonian systems', 'contact hamiltonian systems', 'hamiltonian dynamics', 'hamiltonian mechanics', 'hamiltonian system', 'hamiltonian', 'contact hamiltonian']","['Hamilton-Jacobi Equations of Nonholonomic Magnetic Hamiltonian Systems   In order to describe the impact of different geometric structures and\nconstraints for the dynamics of a Hamiltonian system, in this paper, for a\nmagnetic Hamiltonian system defined by a magnetic symplectic form, we first\ndrive precisely the geometric constraint conditions of magnetic symplectic form\nfor the magnetic Hamiltonian vector field.which are called the Type I and Type\nII of Hamilton-Jacobi equation. Secondly, for the magnetic Hamiltonian system\nwith nonholonomic constraint, we first define a distributional magnetic\nHamiltonian system, then derive its two types of Hamilton-Jacobi equation.\nMoreover, we generalize the above results to nonholonomic reducible magnetic\nHamiltonian system with symmetry. We define a nonholonomic reduced\ndistributional magnetic Hamiltonian system, and prove two types of\nHamilton-Jacobi theorem. These research work reveal the deeply internal\nrelationships of the magnetic symplectic structure, nonholonomic constraint,\nthe distributional two-form, and the dynamical vector field of the nonholonomic\nmagnetic Hamiltonian system.\n', 'The Hamilton--Jacobi theory for contact Hamiltonian systems   The aim of this paper is to develop a Hamilton--Jacobi theory for contact\nHamiltonian systems. We find several forms for a suitable Hamilton-Jacobi\nequation accordingly to the Hamiltonian and the evolution vector fields for a\ngiven Hamiltonian function. We also analyze the corresponding formulation on\nthe symplectification of the contact Hamiltonian system, and establish the\nrelations between these two approaches. In the last section, some examples are\ndiscussed.\n', 'A Discrete Hamilton--Jacobi Theory for Contact Hamiltonian Dynamics   In this paper, we propose a discrete Hamilton--Jacobi theory for (discrete)\nHamiltonian dynamics defined on a (discrete) contact manifold. To this end, we\nfirst provide a novel geometric Hamilton--Jacobi theory for continuous contact\nHamiltonian dynamics. Then, rooting on the discrete contact Lagrangian\nformulation, we obtain the discrete equations for Hamiltonian dynamics by the\ndiscrete Legendre transformation. Based on the discrete contact Hamilton\nequation, we construct a discrete Hamilton--Jacobi equation for contact\nHamiltonian dynamics. We show how the discrete Hamilton--Jacobi equation is\nrelated to the continuous Hamilton--Jacobi theory presented in this work. Then,\nwe propose geometric foundations of the discrete Hamilton--Jacobi equations on\ncontact manifolds in terms of discrete contact flows. At the end of the paper\nwe provide a numerical example to test the theory.\n']","[('hamilton jacobi theory', 0.694292426109314), ('hamilton jacobi equations', 0.6914938688278198), ('hamiltonian vector field', 0.6639248728752136), ('hamiltonian systems', 0.6595036387443542), ('contact hamiltonian systems', 0.6410999298095703), ('hamiltonian dynamics', 0.636786162853241), ('hamiltonian mechanics', 0.6345198750495911), ('hamiltonian system', 0.6290178298950195), ('hamiltonian', 0.613467812538147), ('contact hamiltonian', 0.6050981283187866)]"
197,197,142,197_electromagnetic scattering problems_electromagnetic scattering_wave scattering_scattering problems,"['electromagnetic scattering problems', 'electromagnetic scattering', 'wave scattering', 'scattering problems', 'elastic scattering', 'acoustic scattering', 'boundary integral equations', 'scattering', 'scattering time harmonic', 'boundary integral']","[""A highly accurate perfectly-matched-layer boundary integral equation\n  solver for acoustic layered-medium problems   Based on the perfectly matched layer (PML) technique, this paper develops a\nhigh-accuracy boundary integral equation (BIE) solver for acoustic scattering\nproblems in locally defected layered media in both two and three dimensions.\nThe original scattering problem is truncated onto a bounded domain by the PML.\nAssuming the vanishing of the scattered field on the PML boundary, we derive\nBIEs on local defects only in terms of using PML-transformed free-space Green's\nfunction, and the four standard integral operators: single-layer, double-layer,\ntranspose of double-layer, and hyper-singular boundary integral operators. The\nhyper-singular integral operator is transformed into a combination of\nweakly-singular integral operators and tangential derivatives. We develop a\nhigh-order Chebyshev-based rectangular-polar singular-integration solver to\ndiscretize all weakly-singular integrals. Numerical experiments for both two-\nand three-dimensional problems are carried out to demonstrate the accuracy and\nefficiency of the proposed solver.\n"", 'PML-based boundary integral equation method for electromagnetic\n  scattering problems in a layered-medium   This paper proposes a new boundary integral equation (BIE) methodology based\non the perfectly matched layer (PML) truncation technique for solving the\nelectromagnetic scattering problems in a multi-layered medium. Instead of using\nthe original PML stretched fields, artificial fields which are also equivalent\nto the solutions in the physical region are introduced. This significantly\nsimplifies the study of the proposed methodology to derive the PML problem.\nThen some PML transformed layer potentials and the associated boundary integral\noperators (BIOs) are defined and the corresponding jump relations are shown.\nUnder the assumption that the fields vanish on the PML boundary, the solution\nrepresentations, as well as the related BIEs and regularization of the\nhyper-singular operators, in terms of the current density functions on the\ntruncated interface, are derived. Numerical experiments are presented to\ndemonstrate the efficiency and accuracy of the method.\n', 'An adaptive finite element PML method for the open cavity scattering\n  problems   Consider the electromagnetic scattering of a time-harmonic plane wave by an\nopen cavity which is embedded in a perfectly electrically conducting infinite\nground plane. This paper is concerned with the numerical solutions of the\ntransverse electric and magnetic polarizations of the open cavity scattering\nproblems. In each polarization, the scattering problem is reduced equivalently\ninto a boundary value problem of the two-dimensional Helmholtz equation in a\nbounded domain by using the transparent boundary condition (TBC). An a\nposteriori estimate based adaptive finite element method with the perfectly\nmatched layer (PML) technique is developed to solve the reduced problem. The\nestimate takes account both of the finite element approximation error and the\nPML truncation error, where the latter is shown to decay exponentially with\nrespect to the PML medium parameter and the thickness of the PML layer.\nNumerical experiments are presented and compared with the adaptive finite\nelement TBC method for both polarizations to illustrate the competitive\nbehavior of the proposed method.\n']","[('electromagnetic scattering problems', 0.5893192291259766), ('electromagnetic scattering', 0.5568650960922241), ('wave scattering', 0.5562001466751099), ('scattering problems', 0.5477560758590698), ('elastic scattering', 0.533201277256012), ('acoustic scattering', 0.5224769115447998), ('boundary integral equations', 0.5158914923667908), ('scattering', 0.47872623801231384), ('scattering time harmonic', 0.45043209195137024), ('boundary integral', 0.4465225636959076)]"
198,198,141,198_cluster algebras_cluster algebra_upper cluster algebras_cluster algebra mathcal,"['cluster algebras', 'cluster algebra', 'upper cluster algebras', 'cluster algebra mathcal', 'rank cluster algebras', 'upper cluster algebra', 'algebra cluster', 'cluster categories', 'cluster theory', 'cluster structures']","['Cluster Algebras and Scattering Diagrams, Part I. Basics in Cluster\n  Algebras   This is a first step guide to the theory of cluster algebras. We especially\nfocus on basic notions, techniques, and results concerning seeds, cluster\npatterns, and cluster algebras.\n', 'Cluster algebras generated by projective cluster variables   We introduce the notion of a lower bound cluster algebra generated by\nprojective cluster variables as a polynomial ring over the initial cluster\nvariables and the so-called projective cluster variables. We show that under an\nacyclicity assumption, the cluster algebra and the lower bound cluster algebra\ngenerated by projective cluster variables coincide. In this case we use our\nresults to construct a basis for the cluster algebra. We also show that any\ncoefficient-free cluster algebra of types $A_n$ or $\\widetilde{A}_n$ is equal\nto the corresponding lower bound cluster algebra generated by projective\ncluster variables.\n', 'F-invariant in cluster algebras   In this paper, we introduce the $F$-invariant in cluster algebras using\ntropicalization. This is an analog of the $E$-invariant introduced by Derksen,\nWeyman and Zelevinsky in the additive categorification of cluster algebras and\nthe $\\mathfrak{d}$-invariant introduced by Kang, Kashiwara, Kim and Oh in the\nmonoidal categorification of (quantum) cluster algebras. We prove that the\nproduct of two cluster monomials is still a cluster monomial if and only if\ntheir $F$-invariant is zero. For cluster algebras with a compatible Poisson\nbracket, we prove that if two cluster variables are log-cannonical, then they\nare contained in the same cluster.\n  Inspired by $F$-invariant, we introduce the dominant sets for seeds of\ncluster algebras as an replacement of torsion classes for $\\tau$-tilting pairs\nin $\\tau$-tilting theory and as an replacement of inversion sets in the study\nof right weak order on Weyl groups. With the help of the dominant sets, we\nprove that the oriented exchange graphs of cluster algebras are acyclic. In\nparticular, this implies that green mutations induce a partial order on the set\nof seeds (up to seed equivalence) of cluster algebras. We prove that the\noriented exchange graphs of cluster algebras coincide with the Hasse quivers of\nthe above posets of seeds.\n']","[('cluster algebras', 0.847059428691864), ('cluster algebra', 0.7769380807876587), ('upper cluster algebras', 0.775303304195404), ('cluster algebra mathcal', 0.7392396926879883), ('rank cluster algebras', 0.7300757765769958), ('upper cluster algebra', 0.7275113463401794), ('algebra cluster', 0.6941986083984375), ('cluster categories', 0.5777347087860107), ('cluster theory', 0.5650089383125305), ('cluster structures', 0.5639484524726868)]"
199,199,141,199_rank matrix recovery_matrix recovery_rank matrix completion_rank minimization,"['rank matrix recovery', 'matrix recovery', 'rank matrix completion', 'rank minimization', 'sparse low rank', 'rank matrix estimation', 'low rank matrices', 'matrix completion', 'low rank matrix', 'robust low rank']","['Low-rank matrix recovery via regularized nuclear norm minimization   In this paper, we theoretically investigate the low-rank matrix recovery\nproblem in the context of the unconstrained regularized nuclear norm\nminimization (RNNM) framework. Our theoretical findings show that, the RNNM\nmethod is able to provide a robust recovery of any matrix $X$ (not necessary to\nbe exactly low-rank) from its few noisy measurements\n$\\textbf{b}=\\mathcal{A}(X)+\\textbf{n}$ with a bounded constraint\n$\\|\\textbf{n}\\|_{2}\\leq\\epsilon$, provided that the $tk$-order restricted\nisometry constant (RIC) of $\\mathcal{A}$ satisfies a certain constraint related\nto $t>0$. Specifically, the obtained recovery condition in the case of $t>4/3$\nis found to be same with the sharp condition established previously by Cai and\nZhang (2014) to guarantee the exact recovery of any rank-$k$ matrix via the\nconstrained nuclear norm minimization method. More importantly, to the best of\nour knowledge, we are the first to establish the $tk$-order RIC based\ncoefficient estimate of the robust null space property in the case of\n$0<t\\leq1$.\n', 'Global and Local Analyses of Nonlinear Low-Rank Matrix Recovery Problems   The restricted isometry property (RIP) is a well-known condition that\nguarantees the absence of spurious local minima in low-rank matrix recovery\nproblems with linear measurements. In this paper, we introduce a novel property\nnamed bound difference property (BDP) to study low-rank matrix recovery\nproblems with nonlinear measurements. Using RIP and BDP jointly, we first focus\non the rank-1 matrix recovery problem, for which we propose a new criterion to\ncertify the nonexistence of spurious local minima over the entire space. We\nthen analyze the general case with an arbitrary rank and derive a condition to\nrule out the possibility of having a spurious solution in a ball around the\ntrue solution. The developed conditions lead to much stronger theoretical\nguarantees than the existing bounds on RIP.\n', 'The perturbation analysis of nonconvex low-rank matrix robust recovery   In this paper, we bring forward a completely perturbed nonconvex Schatten\n$p$-minimization to address a model of completely perturbed low-rank matrix\nrecovery. The paper that based on the restricted isometry property generalizes\nthe investigation to a complete perturbation model thinking over not only noise\nbut also perturbation, gives the restricted isometry property condition that\nguarantees the recovery of low-rank matrix and the corresponding reconstruction\nerror bound. In particular, the analysis of the result reveals that in the case\nthat $p$ decreases $0$ and $a>1$ for the complete perturbation and low-rank\nmatrix, the condition is the optimal sufficient condition $\\delta_{2r}<1$\n\\cite{Recht et al 2010}. The numerical experiments are conducted to show better\nperformance, and provides outperformance of the nonconvex Schatten\n$p$-minimization method comparing with the convex nuclear norm minimization\napproach in the completely perturbed scenario.\n']","[('rank matrix recovery', 0.7234122157096863), ('matrix recovery', 0.66071617603302), ('rank matrix completion', 0.6258109211921692), ('rank minimization', 0.618076741695404), ('sparse low rank', 0.6007322072982788), ('rank matrix estimation', 0.5863980650901794), ('low rank matrices', 0.5834415555000305), ('matrix completion', 0.5831955671310425), ('low rank matrix', 0.567994236946106), ('robust low rank', 0.5649486780166626)]"
200,200,141,200_cayley graphs generalized_vertex transitive graphs_cayley graphs_transitive graphs,"['cayley graphs generalized', 'vertex transitive graphs', 'cayley graphs', 'transitive graphs', 'cayley graphs finite', 'cayley graphs abelian', 'normal cayley graphs', 'cayley graph', 'vertex transitive graph', 'vertex transitive']","['2-Arc-transitive Cayley graphs on alternating groups   An interesting fact is that most of the known connected $2$-arc-transitive\nnonnormal Cayley graphs of small valency on finite simple groups are\n$(\\mathrm{A}_{n+1},2)$-arc-transitive Cayley graphs on $\\mathrm{A}_n$. This\nmotivates the study of $2$-arc-transitive Cayley graphs on $\\mathrm{A}_n$ for\narbitrary valency. In this paper, we characterize the automorphism groups of\nsuch graphs. In particular, we show that for a non-complete\n$(G,2)$-arc-transitive Cayley graph on $\\mathrm{A}_n$ with $G$ almost simple,\nthe socle of $G$ is either $\\mathrm{A}_{n+1}$ or $\\mathrm{A}_{n+2}$. We also\nconstruct the first infinite family of $(\\mathrm{A}_{n+2},2)$-arc-transitive\nCayley graphs on $\\mathrm{A}_n$.\n', 'The classification of two-distance transitive dihedrants   A vertex transitive graph $\\Gamma$ is said to be $2$-distance transitive if\nfor each vertex $u$, the group of automorphisms of $\\Gamma$ fixing the vertex\n$u$ acts transitively on the set of vertices at distance $1$ and $2$ from $u$,\nwhile $\\Gamma$ is said to be $2$-arc transitive if its automorphism group is\ntransitive on the set of $2$-arcs. Then $2$-arc transitive graphs are\n$2$-distance transitive. The classification of $2$-arc transitive Cayley graphs\non dihedral groups was given by Du, Malni\\v{c} and Maru\\v{s}i\\v{c} in\n[Classification of 2-arc-transitive dihedrants, J. Combin. Theory Ser. B 98\n(2008), 1349--1372]. In this paper, it is shown that a connected 2-distance\ntransitive Cayley graph on the dihedral group of order $2n$ is either $2$-arc\ntransitive, or isomorphic to the complete multipartite graph $K_{m[b]}$ for\nsome $m\\geq3$ and $b\\geq2$ with $mb=2n$.\n', ""On basic $2$-arc-transitive graphs   A connected graph $\\Gamma=(V,E)$ of valency at least $3$ is called a basic\n$2$-arc-transitive graph if its full automorphism group has a subgroup $G$ with\nthe following properties: (i) $G$ acts transitively on the set of $2$-arcs of\n$\\Gamma$, and (ii) every minimal normal subgroup of $G$ has at most two orbits\non $V$.\n  In her papers [17,18], Praeger proved a connected $2$-arc-transitive graph of\nvalency at least $3$ is a normal cover of some basic $2$-arc-transitive graph,\nand characterized the group-theoretic structures for basic $2$-arc-transitive\ngraphs.\n  Based on Praeger's theorems on $2$-arc-transitive graphs, this paper presents\na further understanding on basic $2$-arc-transitive graphs.\n""]","[('cayley graphs generalized', 0.6913042664527893), ('vertex transitive graphs', 0.6665676236152649), ('cayley graphs', 0.6574633121490479), ('transitive graphs', 0.6484103202819824), ('cayley graphs finite', 0.6435918211936951), ('cayley graphs abelian', 0.6391462683677673), ('normal cayley graphs', 0.6176884174346924), ('cayley graph', 0.6050353050231934), ('vertex transitive graph', 0.5957822799682617), ('vertex transitive', 0.5901555418968201)]"
201,201,140,201_based topology optimization_topology optimization_topology optimization framework_topology optimization problems,"['based topology optimization', 'topology optimization', 'topology optimization framework', 'topology optimization problems', 'structural optimization', 'optimization design', 'design optimization', 'optimization based', 'optimization framework', 'optimization']","['A globally convergent method to accelerate topology optimization using\n  on-the-fly model reduction   We present a globally convergent method to accelerate density-based topology\noptimization using projection-based reduced-order models (ROMs) and\ntrust-region methods. To accelerate topology optimization, we replace the\nlarge-scale finite element simulation, which dominates the computational cost,\nwith ROMs that reduce the cost of objective function and gradient evaluations\nby orders of magnitude. To guarantee convergence, we first introduce a\ntrust-region method that employs generalized trust-region constraints and prove\nit is globally convergent. We then devise a class of globally convergent\nROM-accelerated topology optimization methods informed by two theories: the\naforementioned trust-region theory, which identifies the ROM accuracy\nconditions required to guarantee the method converges to a critical point of\nthe original topology optimization problem; a posteriori error estimation\ntheory for projection-based ROMs, which informs ROM construction procedure to\nmeet the accuracy conditions. This leads to trust-region methods that construct\nand update the ROM on-the-fly during optimization; the methods are guaranteed\nto converge to a critical point of the original, unreduced topology\noptimization problem, regardless of starting point. Numerical experiments on\nthree different structural topology optimization problems demonstrate the\nproposed reduced topology optimization methods accelerate convergence to the\noptimal design by up to an order of magnitude.\n', 'On smooth or 0/1 designs of the fixed-mesh element-based topology\n  optimization   The traditional element-based topology optimization based on material\npenalization typically aims at a 0/1 design. Our numerical experiments reveal\nthat the compliance of a smooth design is overestimated when material\nproperties of boundary intermediate elements under the fixed-mesh finite\nelement analysis are interpolated with a material penalization model. This\npaper proposes a floating projection topology optimization (FPTO) method for\nseeking a smooth design using the ersatz material model or a 0/1 design using a\nmaterial penalization model. The proposed floating projection constraint\ncombining with the upper and lower bounds heuristically simulates 0/1\nconstraints of design variables in the original discrete optimization problem.\nNumerical examples demonstrate the capability of the proposed element-based\ntopology optimization approach in obtaining 0/1 or smooth designs for 2D and 3D\ncompliance minimization problems. The proposed topology optimization approach\ncan be easily implemented under the framework of the fixed-mesh finite element\nanalysis and provides an alternative way to form explicit topologies of\nstructures, especially when the ersatz material model is adopted.\n', 'A Novel Deflation Approach for Topology Optimization and Application for\n  Optimization of Bipolar Plates of Electrolysis Cells   Topology optimization problems usually feature multiple local minimizers. To\nguarantee convergence to local minimizers that perform best globally or to find\nlocal solutions that are desirable for practical applications due to easy\nmanufacturability or aesthetic designs, it is important to compute multiple\nlocal minimizers of topology optimization problems. Existing methods typically\nrely on Newton-type solvers during the optimization process, which makes them\nunsuitable for sensitivity-based topology optimization. In this paper, we\nintroduce a novel deflation approach to systematically find multiple local\nminimizers of general topology optimization problems. The approach is based on\na penalization of previously found local solutions in the objective. We\nvalidate our approach on the so-called two-pipes five-holes example. Finally,\nwe introduce a model for the topology optimization of bipolar plates of\nhydrogen electrolysis cells and demonstrate that our deflation approach enables\nthe discovery of novel designs for such plates.\n']","[('based topology optimization', 0.7502126693725586), ('topology optimization', 0.7472184300422668), ('topology optimization framework', 0.7439637184143066), ('topology optimization problems', 0.7359484434127808), ('structural optimization', 0.5507319569587708), ('optimization design', 0.5383301377296448), ('design optimization', 0.5210357904434204), ('optimization based', 0.4850613474845886), ('optimization framework', 0.48438480496406555), ('optimization', 0.47165849804878235)]"
202,202,140,202_cr manifolds_cr manifold_hypersurfaces complex_complex manifold,"['cr manifolds', 'cr manifold', 'hypersurfaces complex', 'complex manifold', 'real hypersurfaces', 'hypersurface complex', 'degenerate hypersurfaces', 'stein manifolds', 'real submanifolds', 'homogeneous hypersurfaces']","['Homogeneous models for Levi-degenerate CR manifolds   We extend the notion of a fundamental negatively $\\mathbb Z$-graded Lie\nalgebra $\\mathfrak{m}_x=\\bigoplus_{p\\leq -1}\\mathfrak{m}_x^p$ associated to any\npoint of a Levi nondegenerate CR manifold to the class of $k$-nondegenerate CR\nmanifolds $(M,\\mathcal D,\\mathcal J)$ for all $k\\geq 2$ and call this invariant\nthe core at $x\\in M$. It consists of a $\\mathbb Z$-graded vector space\n$\\mathfrak{m}_x=\\bigoplus_{p\\leq k-2}\\mathfrak{m}_x^p$ of height $k-2$ endowed\nwith the natural algebraic structure induced by the Tanaka and Freeman\nsequences of $(M,\\mathcal D,\\mathcal J)$ and the Levi forms of higher order. In\nthe case of CR manifolds of hypersurface type we propose a definition of a\nhomogeneous model of type $\\mathfrak m$, that is, a homogeneous\n$k$-nondegenerate CR manifold $M=G/G_o$ with core $\\mathfrak m$ associated with\nan appropriate $\\mathbb Z$-graded Lie algebra $Lie(G)=\\mathfrak\ng=\\bigoplus\\mathfrak g^p$ and subalgebra $Lie(G_o)=\\mathfrak\ng_o=\\bigoplus\\mathfrak g_o^p$ of the nonnegative part $\\bigoplus_{p\\geq\n0}\\mathfrak g^p$. It generalizes the classical notion of Tanaka of homogeneous\nmodel for Levi nondegenerate CR manifolds and the tube over the future light\ncone, the unique (up to local CR diffeomorphisms) maximally homogeneous\n$5$-dimensional $2$-nondegenerate CR manifold. We investigate the basic\nproperties of cores and models and study the $7$-dimensional CR manifolds of\nhypersurface type from this perspective. We first classify cores of\n$7$-dimensional $2$-nondegenerate CR manifolds up to isomorphism and then\nconstruct homogeneous models for seven of these classes. We finally show that\nthere exists a unique core and homogeneous model in the $3$-nondegenerate\nclass.\n', ""On geometry of $2$-nondegenerate CR structures of hypersurface type and\n  flag structures on leaf spaces of Levi foliations   We construct canonical absolute parallelisms over real-analytic manifolds\nequipped with $2$-nondegenerate, hypersurface-type CR structures of arbitrary\nodd dimension not less than $7$ whose Levi kernel has constant rank belonging\nto a broad subclass of CR structures that we label as recoverable. For this we\ndevelop a new approach based on a reduction to a special flag structure, called\nthe dynamical Legendrian contact structure, on the leaf space of the CR\nstructure's associated Levi foliation. This extends the results of\nPorter-Zelenko [20] from the case of regular CR symbols constituting a discrete\nset in the set of all CR symbols to the case of the arbitrary CR symbols for\nwhich the original CR structure can be uniquely recovered from its\ncorresponding dynamical Legendrian contact structure. Our method clarifies the\nrelationship between the bigraded Tanaka prolongation of regular symbols\ndeveloped in Porter-Zelenko [20] and their usual Tanaka prolongation, providing\na geometric interpretation of conditions under which they are equal. Motivated\nby the search for homogeneous models with given nonregular symbol, we also\ndescribe a process of reduction from the original natural frame bundle, which\nis inevitable for structures with nonregular CR symbols. We demonstrate this\nreduction procedure for examples whose underlying manifolds have dimension $7$\nand $9$. We show that, for any fixed rank $r>1$, in the set of all CR symbols\nassociated with 2-nondegenerate, hypersurface-type CR manifolds of odd\ndimension greater than $4r+1$ with rank $r$ Levi kernel, the CR symbols not\nassociated with any homogeneous model are generic, and, for $r=1$, the same\nresult holds if the CR structure is pseudoconvex.\n"", 'On CR singular CR images   We say that a CR singular submanifold $M$ has a removable CR singularity if\nthe CR structure at the CR points of $M$ extends through the singularity as an\nabstract CR structure on $M$. We study such real-analytic submanifolds, in\nwhich case removability is equivalent to $M$ being the image of a generic\nreal-analytic submanifold $N$ under a holomorphic map that is a diffeomorphism\nof $N$ onto $M$, what we call a CR image. We study the stability of the CR\nsingularity under perturbation, the associated quadratic invariants, and\nconditions for removability of a CR singularity. A lemma is also proved about\nperturbing away the zeros of holomorphic functions on CR submanifolds, which\ncould be of independent interest.\n']","[('cr manifolds', 0.6530126333236694), ('cr manifold', 0.6242998838424683), ('hypersurfaces complex', 0.5302046537399292), ('complex manifold', 0.5191347599029541), ('real hypersurfaces', 0.5047154426574707), ('hypersurface complex', 0.5035046339035034), ('degenerate hypersurfaces', 0.5001834630966187), ('stein manifolds', 0.4883904755115509), ('real submanifolds', 0.48535609245300293), ('homogeneous hypersurfaces', 0.478778600692749)]"
203,203,139,203_runge kutta methods_implicit runge kutta_explicit runge kutta_runge kutta schemes,"['runge kutta methods', 'implicit runge kutta', 'explicit runge kutta', 'runge kutta schemes', 'kutta methods', 'exponential runge kutta', 'runge kutta', 'kutta schemes', 'runge kutta rk', 'stage runge kutta']","[""A New Class of Runge-Kutta Methods for Nonlinearly Partitioned Systems   This work introduces a new class of Runge-Kutta methods for solving\nnonlinearly partitioned initial value problems. These new methods, named\nnonlinearly partitioned Runge-Kutta (NPRK), generalize existing additive and\ncomponent-partitioned Runge-Kutta methods, and allow one to distribute\ndifferent types of implicitness within nonlinear terms. The paper introduces\nthe NPRK framework and discusses order conditions, linear stability, and the\nderivation of implicit-explicit and implicit-implicit NPRK integrators. The\npaper concludes with numerical experiments that demonstrate the utility of NPRK\nmethods for solving viscous Burger's and the gray thermal radiation transport\nequations.\n"", 'Projective Integration Methods in the Runge-Kutta Framework and the\n  Extension to Adaptivity in Time   Projective Integration methods are explicit time integration schemes for\nstiff ODEs with large spectral gaps. In this paper, we show that all existing\nProjective Integration methods can be written as Runge-Kutta methods with an\nextended Butcher tableau including many stages. We prove consistency and order\nconditions of the Projective Integration methods using the Runge-Kutta\nframework. Spatially adaptive Projective Integration methods are included via\npartitioned Runge-Kutta methods. New time adaptive Projective Integration\nschemes are derived via embedded Runge-Kutta methods and step size variation\nwhile their accuracy, stability, convergence, and error estimators are\ninvestigated analytically and numerically.\n', 'Isomeric trees and the order of Runge--Kutta methods   The conditions for a Runge--Kutta method to be of order $p$ with $p\\ge 5$ for\na scalar non-autonomous problem are a proper subset of the order conditions for\na vector problem. Nevertheless, Runge--Kutta methods that were derived\nhistorically only for scalar problems happened to be of the same order for\nvector problems. We relate the order conditions for scalar problems to\nfactorisations of the Runge--Kutta trees into ""atomic stumps"" and enumerate\nthose conditions up to $p=20$. Using a special search procedure over\nunsatisfied order conditions, new Runge--Kutta methods of ""ambiguous orders""\nfive and six are constructed. These are used to verify the validity of the\nresults.\n']","[('runge kutta methods', 0.7596908807754517), ('implicit runge kutta', 0.7253571152687073), ('explicit runge kutta', 0.7182224988937378), ('runge kutta schemes', 0.6665934324264526), ('kutta methods', 0.6515488028526306), ('exponential runge kutta', 0.5916427969932556), ('runge kutta', 0.5840024948120117), ('kutta schemes', 0.5380933880805969), ('runge kutta rk', 0.532291829586029), ('stage runge kutta', 0.5319293737411499)]"
204,204,139,204_stirling numbers kinds_terms stirling numbers_stirling numbers_polynomials stirling,"['stirling numbers kinds', 'terms stirling numbers', 'stirling numbers', 'polynomials stirling', 'numbers stirling', 'stirling numbers first', 'stirling numbers second', 'terms stirling', 'stirling', 'bernoulli numbers polynomials']","['Study on r-truncated degenerate stirling numbers of the second kind   The degenerate Stirling numbers of the second kind and of the first kind,\nwhich are respectively degenerate versions of the Stirling numbers of the\nsecond kind and of the first kind, appear frequently when we study various\ndegenerate versions of some special numbers and polynomials. The aim of this\npaper is to consider the r-truncated degenerate Stirling numbers of the second\nkind, which reduce to the degenerate Stirling numbers of the second for r = 1,\nand to investigate their explicit expressions, some properties and related\nidentities, in connection with several other degenerate special numbers and\npolynomials.\n', 'Some formulas for fully degenerate Bernoulli numbers and polynomials   The aim of this paper is to study the fully degenerate Bernoulli polynomials\nand numbers, which are a degenerate version of Bernoulli polynomials and\nnumbers and arise naturally from the Volkenborn integral of the degenerate\nexponential functions on Zp. We find some explicit expressions for the fully\ndegenerate Bernoulli polynomials and numbers in terms of the degenerate\nStirling numbers of the second kind, the degenerate r-Stirling numbers of the\nsecond kind and of the degenerate Stirling polynomials.\n  We also consider the degenerate poly-Bernoulli polynomials and derive\nexplicit representations for them in terms of the same degenerate Stirling\nnumbers and polynomials.\n', 'Multi-Stirling numbers of the second kind   The multi-Stirling numbers of the second kind, the unsigned multi-Stirling\nnumbers of the first kind, the multi-Lah numbers and the multi-Bernoulli\nnumbers are all defined with the help of the multiple logarithm, and generalize\nrespectively the Stirling numbers of the second kind, the unsigned Stirling\nnumbers of the first kind, the unsigned Lah numbers and the higher-order\nBernoulli numbers . The aim of this paper is to introduce the multi-Stirling\nnumbers of the second kind and to find several identities involving those four\nnumbers defined by means of the multiple logarithm and some other special\nnumbers.\n']","[('stirling numbers kinds', 0.7485108375549316), ('terms stirling numbers', 0.7479015588760376), ('stirling numbers', 0.7401047348976135), ('polynomials stirling', 0.6981662511825562), ('numbers stirling', 0.6916183829307556), ('stirling numbers first', 0.682701826095581), ('stirling numbers second', 0.6730840802192688), ('terms stirling', 0.6224032640457153), ('stirling', 0.5626400709152222), ('bernoulli numbers polynomials', 0.5191471576690674)]"
205,205,138,205_large language models_models large language_language models_language models llms,"['large language models', 'models large language', 'language models', 'language models llms', 'large language', 'natural language', 'semantic', 'language processing', 'natural language processing', 'question answering']","['Extending Context Window of Large Language Models via Semantic\n  Compression   Transformer-based Large Language Models (LLMs) often impose limitations on\nthe length of the text input to ensure the generation of fluent and relevant\nresponses. This constraint restricts their applicability in scenarios involving\nlong texts. We propose a novel semantic compression method that enables\ngeneralization to texts that are 6-8 times longer, without incurring\nsignificant computational costs or requiring fine-tuning. Our proposed\nframework draws inspiration from source coding in information theory and\nemploys a pre-trained model to reduce the semantic redundancy of long inputs\nbefore passing them to the LLMs for downstream tasks. Experimental results\ndemonstrate that our method effectively extends the context window of LLMs\nacross a range of tasks including question answering, summarization, few-shot\nlearning, and information retrieval. Furthermore, the proposed semantic\ncompression method exhibits consistent fluency in text generation while\nreducing the associated computational overhead.\n', 'LLMs4OL: Large Language Models for Ontology Learning   We propose the LLMs4OL approach, which utilizes Large Language Models (LLMs)\nfor Ontology Learning (OL). LLMs have shown significant advancements in natural\nlanguage processing, demonstrating their ability to capture complex language\npatterns in different knowledge domains. Our LLMs4OL paradigm investigates the\nfollowing hypothesis: \\textit{Can LLMs effectively apply their language pattern\ncapturing capability to OL, which involves automatically extracting and\nstructuring knowledge from natural language text?} To test this hypothesis, we\nconduct a comprehensive evaluation using the zero-shot prompting method. We\nevaluate nine different LLM model families for three main OL tasks: term\ntyping, taxonomy discovery, and extraction of non-taxonomic relations.\nAdditionally, the evaluations encompass diverse genres of ontological\nknowledge, including lexicosemantic knowledge in WordNet, geographical\nknowledge in GeoNames, and medical knowledge in UMLS.\n', 'The structure of the token space for large language models   Large language models encode the correlational structure present in natural\nlanguage by fitting segments of utterances (tokens) into a high dimensional\nambient latent space upon which the models then operate. We assert that in\norder to develop a foundational, first-principles understanding of the behavior\nand limitations of large language models, it is crucial to understand the\ntopological and geometric structure of this token subspace. In this article, we\npresent estimators for the dimension and Ricci scalar curvature of the token\nsubspace, and apply it to three open source large language models of moderate\nsize: GPT2, LLEMMA7B, and MISTRAL7B. In all three models, using these\nmeasurements, we find that the token subspace is not a manifold, but is instead\na stratified manifold, where on each of the individual strata, the Ricci\ncurvature is significantly negative. We additionally find that the dimension\nand curvature correlate with generative fluency of the models, which suggest\nthat these findings have implications for model behavior.\n']","[('large language models', 0.6745694279670715), ('models large language', 0.6613578200340271), ('language models', 0.6285194158554077), ('language models llms', 0.6220681071281433), ('large language', 0.5030139088630676), ('natural language', 0.48940861225128174), ('semantic', 0.4731389284133911), ('language processing', 0.4725210964679718), ('natural language processing', 0.4712941348552704), ('question answering', 0.4524381756782532)]"
206,206,137,206_fractional order_nonlinear fractional_order fractional_systems fractional,"['fractional order', 'nonlinear fractional', 'order fractional', 'systems fractional', 'fractional differential equations', 'system fractional', 'fractional differential', 'fractional linear', 'generalized fractional', 'linear fractional']","[""On fractional-order maps and their synchronization   We study the stability of linear fractional order maps. We show that in the\nstable region, the evolution is described by Mittag-Leffler functions and a\nwell defined effective Lyapunov exponent can be obtained in these cases. For\none-dimensional systems, this exponent can be related to the corresponding\nfractional differential equation. A fractional equivalent of map $f(x)=ax$ is\nstable for $a_c(\\alpha)<a<1$ where $\\alpha$ is a fractional order parameter and\n$a_c(\\alpha)\\approx -\\alpha$. For coupled linear fractional maps, we can obtain\n`normal modes' and reduce the evolution to effectively one-dimensional system.\nIf the eigenvalues are real the stability of the coupled system is dictated by\nthe stability of effectively one-dimensional normal modes. For complex\neigenvalues, we obtain a much richer picture. However, in the stable region,\nthe evolution of modulus is dictated by Mittag-Leffler function and the\neffective Lyapunov exponent is determined by modulus of eigenvalues. We extend\nthese studies to synchronized fixed points of fractional nonlinear maps.\n"", 'Optimal Control and Approximate controllability of fractional semilinear\n  differential inclusion involving $\\psi$- Hilfer fractional derivatives   The current paper initially studies the optimal control of linear\n$\\psi$-Hilfer fractional derivatives with state-dependent control constraints\nand optimal control for a particular type of cost functional. Then, we\ninvestigate the approximate controllability of the abstract fractional\nsemilinear differential inclusion involving $\\psi$-Hilfer fractional derivative\nin reflexive Banach spaces. It is known that the existence, uniqueness, optimal\ncontrol, and approximate controllability of fractional differential equations\nor inclusions have been demonstrated for a similar type of fractional\ndifferential equations or inclusions with different fractional order derivative\noperators. Hence it has to research fractional differential equations with more\ngeneral fractional operators which incorporate all the specific fractional\nderivative operators. This motivates us to consider the $\\psi$-Hilfer\nfractional differential inclusion. We assume the compactness of the\ncorresponding semigroup and the approximate controllability of the associated\nlinear control system and define the control with the help of duality mapping.\nWe observe that convexity is essential in determining the controllability\nproperty of semilinear differential inclusion. In the case of Hilbert spaces,\nthere is no issue of convexity as the duality map becomes simply the identity\nmap. In contrast to Hilbert spaces, if we consider reflexive Banach spaces,\nthere is an issue of convexity due to the nonlinear nature of duality mapping.\nThe novelty of this paper is that we overcome this convexity issue and\nestablish our main result. Finally, we test our outcomes through an example.\n', 'Symmetry-breaking and bifurcation diagrams of fractional-order maps   In this paper two important aspects related to Caputo fractional-order\ndiscrete variant of a class of maps defined on the complex plane, are\nanalytically and numerically revealed: attractors symmetry-broken induced by\nthe fractional-order and the sensible problem of determining the right\nbifurcation diagram of discrete systems of fractional-order. It is proved that\nmaps of integer order with dihedral symmetry or cycle symmetry loose their\nsymmetry once they are transformed in fractional-order maps. Also, it is\nconjectured that, contrarily to integer-order maps, determining the bifurcation\ndiagrams of fractional-order maps is far from being a clarified problem. Two\nexamples are considered: dihedral logistic map and cyclic logistic map.\n']","[('fractional order', 0.6259058117866516), ('nonlinear fractional', 0.6202216148376465), ('order fractional', 0.6201684474945068), ('systems fractional', 0.6199235916137695), ('fractional differential equations', 0.6190584301948547), ('system fractional', 0.6135616302490234), ('fractional differential', 0.5899176597595215), ('fractional linear', 0.5797802209854126), ('generalized fractional', 0.5797743797302246), ('linear fractional', 0.5777477622032166)]"
207,207,136,207_blood flow_computational fluid dynamics_fluid flow_blood vessels,"['blood flow', 'computational fluid dynamics', 'fluid flow', 'blood vessels', 'fluid dynamics', 'arterial', 'arteries', 'computational fluid', 'circulation', 'fluid structure']","[""A Coupled Diffusion Approximation for Spatiotemporal Hemodynamic\n  Response and Deoxygenated Blood Volume Fraction in Microcirculation   Background and Objective: This proof of concept study investigates\nmathematical modelling of blood flow and oxygen transport in cerebral\nmicrocirculation, focusing on understanding hemodynamic responses. By coupling\noxygen transport models and blood flow dynamics, the research aims to predict\nspatiotemporal hemodynamic responses and their impact on blood oxygenation\nlevels, particularly in the context of deoxygenated and total blood volume (DBV\nand TBV) fractions. Methods: A coupled spatiotemporal model is developed using\nFick's law for diffusion, combined with the hemodynamic response function\nderived from a damped wave equation. The diffusion coefficient in Fick's law is\nbased on Hagen-Poiseuille flow, and arterial blood flow is approximated\nnumerically through pressure-Poisson equation (PPE). The equations are then\nnumerically solved with the finite element method (FEM). Numerical experiments\nare performed on a high-resolution 7-Tesla Magnetic Resonance Imaging (MRI)\ndataset for head segmentation, which facilitates the differentiation of\narterial blood vessels and various brain tissue compartments. Results: The\napplicability of the model is further demonstrated through numerical\nexperiments utilizing a 7 Tesla magnetic resonance imaging (MRI) dataset for\nhead segmentation, which facilitates the differentiation of arterial blood\nvessels and various brain tissue compartments. By simulating hemodynamical\nresponses and analyzing their impact on volumetric DBV and TBV, this study\noffers valuable insights into spatiotemporal modelling of brain tissue and\nblood flow. Conclusions: This study utilizes spatiotemporal modelling with\nhigh-resolution 7 Tesla-MRI head data to explore cerebral blood flow, oxygen\ntransport, and brain dynamics. It enhances understanding of cardiovascular\nconditions, improves simulation accuracy, and offers potential clinical\napplications for targeted interventions.\n"", 'A geometric multiscale model for the numerical simulation of blood flow\n  in the human left heart   We present a new computational model for the numerical simulation of blood\nflow in the human left heart. To this aim, we use the Navier-Stokes equations\nin an Arbitrary Lagrangian Eulerian formulation to account for the endocardium\nmotion and we model the cardiac valves by means of the Resistive Immersed\nImplicit Surface method. To impose a physiological displacement of the domain\nboundary, we use a 3D cardiac electromechanical model of the left ventricle\ncoupled to a lumped-parameter (0D) closed-loop model of the remaining\ncirculation. We thus obtain a one-way coupled electromechanics-fluid dynamics\nmodel in the left ventricle. To extend the left ventricle motion to the\nendocardium of the left atrium and to that of the ascending aorta, we introduce\na preprocessing procedure according to which an harmonic extension of the left\nventricle displacement is combined with the motion of the left atrium based on\nthe 0D model. To better match the 3D cardiac fluid flow with the external blood\ncirculation, we couple the 3D Navier-Stokes equations to the 0D circulation\nmodel, obtaining a multiscale coupled 3D-0D fluid dynamics model that we solve\nvia a segregated numerical scheme. We carry out numerical simulations for a\nhealthy left heart and we validate our model by showing that meaningful\nhemodynamic indicators are correctly reproduced.\n', ""Navier-Stokes Modelling of Non-Newtonian Blood Flow in Cerebral Arterial\n  Circulation and its Dynamic Impact on Electrical Conductivity in a Realistic\n  Multi-Compartment Head Model   Background and Objective: This study aims to evaluate the dynamic effect of\nnon-Newtonian cerebral arterial circulation on electrical conductivity\ndistribution (ECD) in a realistic multi-compartment head model. It addresses\nthe importance and challenges associated with electrophysiological modalities,\nsuch as transcranial electrical stimulation, electro-magnetoencephalography,\nand electrical impedance tomography. Factors such as electrical conductivity's\nimpact on forward modeling accuracy, complex vessel networks, data acquisition\nlimitations (especially in MRI), and blood flow phenomena are considered.\nMethods: The Navier-Stokes equations (NSEs) govern the non-Newtonian flow model\nused in this study. The solver comprises two stages: the first solves the\npressure field using a dynamical pressure-Poisson equation derived from NSEs,\nand the second updates the velocity field using Leray regularization and the\npressure distribution from the first stage. The Carreau-Yasuda model\nestablishes the connection between blood velocity and viscosity. Blood\nconcentration in microvessels is approximated using Fick's law of diffusion,\nand conductivity mapping is obtained via Archie's law. The head model used\ncorresponds to an open 7 Tesla MRI dataset, differentiating arterial vessels\nfrom other structures. Results: The results suggest the establishment of a\ndynamic model of cerebral blood flow for arterial and microcirculation. Blood\npressure and conductivity distributions are obtained through numerically\nsimulated pulse sequences, enabling approximation of blood concentration and\nconductivity within the brain. Conclusions: This model provides an\napproximation of dynamic blood flow and corresponding ECD in different brain\nregions. The advantage lies in its applicability with limited a priori\ninformation about blood flow and compatibility with arbitrary head models that\ndistinguish arteries.\n""]","[('blood flow', 0.573611855506897), ('computational fluid dynamics', 0.5094221830368042), ('fluid flow', 0.4650284945964813), ('blood vessels', 0.45679962635040283), ('fluid dynamics', 0.4559327960014343), ('arterial', 0.4505775570869446), ('arteries', 0.41793230175971985), ('computational fluid', 0.4164928197860718), ('circulation', 0.40744367241859436), ('fluid structure', 0.40076982975006104)]"
208,208,136,208_topological hochschild homology_hochschild homology_topological hochschild_cyclic homology,"['topological hochschild homology', 'hochschild homology', 'topological hochschild', 'cyclic homology', 'ring spectra', 'adams spectral sequence', 'theory spectrum', 'thom spectra', 'homology', 'ring spectrum']","['Topological Hochschild homology of truncated Brown-Peterson spectra I   We compute topological Hochschild homology of sufficiently structured forms\nof truncated Brown--Peterson spectra with coefficients. In particular, we\ncompute $\\mathrm{THH}_*(B\\langle n\\rangle ;H\\mathbb{Z}_{(p)})$ for all $n$ and\n$\\mathrm{THH}_*(B\\langle 2\\rangle ;M)$ for $M\\in \\{ k(1),k(2)\\}$ where\n$B\\langle n\\rangle$ is an $E_3$ form of $BP\\langle n\\rangle$ for certain primes\n$p$. For example, this gives a computation of\n$\\mathrm{THH}(\\mathrm{taf}^{D};M)$ for $M\\in \\{H\\mathbb{Z}_{(3)},k(1),k(1))$\nwhere $\\mathrm{taf}^{D}$ is the $E_{\\infty}$ form of $BP\\langle 2\\rangle$\nconstructed by Hill--Lawson.\n', 'The May filtration on THH and faithfully flat descent   In this paper, we prove that both topological Hochschild homology and\ntopological cyclic homology are sheaves for the fpqc topology on connective\ncommutative ring spectra, by exploiting the May filtration on topological\nHochschild homology.\n', 'Whitehead Filtrations for Computations in Topological Hochschild\n  Homology   We discuss spectral sequences coming from Whitehead filtrations in the\ncomputation of topological Hochschild homology of ring spectra. Using cyclic\ninvariance, this makes for simple computations of $THH$ of connective rings $R$\nwith coefficients in discrete ring spectra. In particular, we show how to use\nthis to compute $THH(tmf,\\mathbb{F}_2)$, and $THH(tmf,\\mathbb{Z}_{(2)})$, where\n$tmf$ denotes the $\\mathbb{E}_\\infty$ ring spectrum of topological modular\nforms. Then, we obtain a description of $THH(\\ell/v_1^n)$ in terms of\n$THH(\\ell,\\ell/v_1^n)$, where the latter can be computed by results of\narXiv:0710.4368. We next explain how the methods of this computation generalize\nto give us information about $THH(cofib(x^k:\\Sigma^{k|x|}R\\to R))$ for $R$ and\n$cofib(x^k)$ suitably structured connective ring spectra, $k>1$, and $x\\in\n\\pi_{*}(R)$ an arbitrary element in positive degree. Finally, we examine the\ngeneral framework to describe the topological Hochschild homology of 2-local\nconnective self-conjugate K-theory, $ksc_2$.\n']","[('topological hochschild homology', 0.6562371253967285), ('hochschild homology', 0.6160762906074524), ('topological hochschild', 0.5628445744514465), ('cyclic homology', 0.4990852475166321), ('ring spectra', 0.46829837560653687), ('adams spectral sequence', 0.46244993805885315), ('theory spectrum', 0.4596623182296753), ('thom spectra', 0.443885862827301), ('homology', 0.433401495218277), ('ring spectrum', 0.43092745542526245)]"
209,209,135,209_blockchain_blockchains_cryptocurrencies_cryptocurrency,"['blockchain', 'blockchains', 'cryptocurrencies', 'cryptocurrency', 'bitcoin', 'cryptographic', 'decentralization', 'adversary', 'decentralized', 'consensus protocols']","['Instantaneous and limiting behavior of an n-node blockchain under cyber\n  attacks from a single hacker   We investigate the instantaneous and limiting behavior of an n-node\nblockchain which is under continuous monitoring of the IT department of a\ncompany but faces non-stop cyber attacks from a single hacker. The blockchain\nis functional as far as no data stored on it has been changed, deleted, or\nlocked. Once the IT department detects the attack from the hacker, it will\nimmediately re-set the blockchain, rendering all previous efforts of the hacker\nin vain. The hacker will not stop until the blockchain is dysfunctional. For\narbitrary distributions of the hacking times and detecting times, we derive the\nlimiting functional probability, instantaneous functional probability, and mean\nfunctional time of the blockchain. We also show that all these quantities are\nincreasing functions of the number of nodes, substantiating the intuition that\nthe more nodes a blockchain has, the harder it is for a hacker to succeed in a\ncyber attack.\n', 'SoK of Used Cryptography in Blockchain   The underlying fundaments of blockchain are cryptography and cryptographic\nconcepts that provide reliable and secure decentralized solutions. Although\nmany recent papers study the use-cases of blockchain in different industrial\nareas, such as finance, health care, legal relations, IoT, information\nsecurity, and consensus building systems, only few studies scrutinize the\ncryptographic concepts used in blockchain. To the best of our knowledge, there\nis no Systematization of Knowledge (SoK) that gives a complete picture of the\nexisting cryptographic concepts which have been deployed or have the potential\nto be deployed in blockchain. In this paper, we thoroughly review and\nsystematize all cryptographic concepts which are already used in blockchain.\nAdditionally, we give a list of cryptographic concepts which have not yet been\napplied but have big potentials to improve the current blockchain solutions. We\nalso include possible instantiations of these cryptographic concepts in the\nblockchain domain. Last but not least, we explicitly postulate 21 challenging\nproblems that cryptographers interested in blockchain can work on.\n', 'Sensitivity-Based Optimization for Blockchain Selfish Mining   In this paper, we provide a novel dynamic decision method of blockchain\nselfish mining by applying the sensitivity-based optimization theory. Our aim\nis to find the optimal dynamic blockchain-pegged policy of the dishonest mining\npool. To study the selfish mining attacks, two mining pools is designed by\nmeans of different competitive criterions, where the honest mining pool follows\na two-block leading competitive criterion, while the dishonest mining pool\nfollows a modification of two-block leading competitive criterion through using\na blockchain-pegged policy. To find the optimal blockchain-pegged policy, we\nset up a policy-based continuous-time Markov process and analyze some key\nfactors. Based on this, we discuss monotonicity and optimality of the long-run\naverage profit with respect to the blockchain-pegged reward and prove the\nstructure of the optimal blockchain-pegged policy. We hope the methodology and\nresults derived in this paper can shed light on the dynamic decision research\non the selfish mining attacks of blockchain selfish mining.\n']","[('blockchain', 0.6430567502975464), ('blockchains', 0.6253762245178223), ('cryptocurrencies', 0.5491183400154114), ('cryptocurrency', 0.5303803086280823), ('bitcoin', 0.43706247210502625), ('cryptographic', 0.41960352659225464), ('decentralization', 0.3910648822784424), ('adversary', 0.37378689646720886), ('decentralized', 0.35031116008758545), ('consensus protocols', 0.34958553314208984)]"
210,210,135,210_sasakian manifolds_sasakian manifold_sasakian structure_contact manifolds,"['sasakian manifolds', 'sasakian manifold', 'sasakian structure', 'contact manifolds', 'dimensional sasakian', 'contact manifold', 'manifolds generalized', 'manifolds', 'sasakian', 'metric manifolds']","[""Immersions into Sasakian space forms   We study immersions of Sasakian manifolds into finite and infinite\ndimensional Sasakian space forms. After proving Calabi's rigidity results in\nthe Sasakian setting, we characterise all homogeneous Sasakian manifolds which\nadmit a (local) Sasakian immersion into a nonelliptic Sasakian space form.\nMoreover, we give a characterisation of homogeneous Sasakian manifolds which\ncan be embedded into the standard sphere both in the compact and noncompact\ncase.\n"", 'Characterization of Sasakian manifolds   Weak contact metric manifolds, i.e., the linear complex structure on the\ncontact distribution is replaced by a nonsingular skew-symmetric tensor,\ndefined by the author and R. Wolak, allowed us to take a new look at the theory\nof contact manifolds. In this paper, we continue our study, see\narXiv:2312.11411, of a structure of this type, called a weak nearly Sasakian\nstructure, and prove two theorems characterizing Sasakian manifolds. Our main\nresult generalizes the theorem by A. Nicola - G. Dileo - I. Yudin (2018) and\nprovides a new criterion for a weak almost contact metric manifold to be\nSasakian.\n', 'Nearly Sasakian geometry and $SU(2)$-structures   We carry on a systematic study of nearly Sasakian manifolds. We prove that\nany nearly Sasakian manifold admits two types of integrable distributions with\ntotally geodesic leaves which are, respectively, Sasakian or $5$-dimensional\nnearly Sasakian manifolds. As a consequence, any nearly Sasakian manifold is a\ncontact manifold. Focusing on the $5$-dimensional case, we prove that there\nexists a one-to-one correspondence between nearly Sasakian structures and a\nspecial class of nearly hypo $SU(2)$-structures. By deforming such a\n$SU(2)$-structure one obtains in fact a Sasaki-Einstein structure. Further we\nprove that both nearly Sasakian and Sasaki-Einstein $5$-manifolds are endowed\nwith supplementary nearly cosymplectic structures. We show that there is a\none-to-one correspondence between nearly cosymplectic structures and a special\nclass of hypo $SU(2)$-structures which is again strictly related to\nSasaki-Einstein structures. Furthermore, we study the orientable hypersurfaces\nof a nearly K\\""{a}hler 6-manifold and, in the last part of the paper, we define\ncanonical connections for nearly Sasakian manifolds, which play a role similar\nto the Gray connection in the context of nearly K\\""{a}hler geometry. In\ndimension $5$ we determine a connection which parallelizes all the nearly\nSasakian $SU(2)$-structure as well as the torsion tensor field. An analogous\nresult holds also for Sasaki-Einstein structures.\n']","[('sasakian manifolds', 0.8546037077903748), ('sasakian manifold', 0.8408783078193665), ('sasakian structure', 0.7040027379989624), ('contact manifolds', 0.617522120475769), ('dimensional sasakian', 0.607700765132904), ('contact manifold', 0.5900172591209412), ('manifolds generalized', 0.5639322400093079), ('manifolds', 0.5558815598487854), ('sasakian', 0.5557929873466492), ('metric manifolds', 0.5501869916915894)]"
211,211,134,211_uniform hypergraphs_uniform hypergraph_vertex uniform hypergraph_uniform hypergraph vertices,"['uniform hypergraphs', 'uniform hypergraph', 'vertex uniform hypergraph', 'uniform hypergraph vertices', 'hypergraphs', 'hypergraph', 'hypergraph vertices', 'vertex uniform', 'hypergraph mathcal', 'edges uniform']","[""Hypergraphs with arbitrarily small codegree Tur\\'an density   Let $k\\geq 3$. Given a $k$-uniform hypergraph $H$, the minimum codegree\n$\\delta(H)$ is the largest $d\\in\\mathbb{N}$ such that every $(k-1)$-set of\n$V(H)$ is contained in at least $d$ edges. Given a $k$-uniform hypergraph $F$,\nthe codegree Tur\\'an density $\\gamma(F)$ of $F$ is the smallest $\\gamma \\in\n[0,1]$ such that every $k$-uniform hypergraph on $n$ vertices with\n$\\delta(H)\\geq (\\gamma + o(1))n$ contains a copy of $F$. Similarly as other\nvariants of the hypergraph Tur\\'an problem, determining the codegree Tur\\'an\ndensity of a hypergraph is in general notoriously difficult and only few\nresults are known.\n  In this work, we show that for every $\\varepsilon>0$, there is a $k$-uniform\nhypergraph $F$ with $0<\\gamma(F)<\\varepsilon$. This is in contrast to the\nclassical Tur\\'an density, which cannot take any value in the interval\n$(0,k!/k^k)$ due to a fundamental result by Erd\\H{o}s.\n"", ""Hypergraphs with a quarter uniform Tur\\'an density   The uniform Tur\\'an density $\\pi_{1}(F)$ of a $3$-uniform hypergraph $F$ is\nthe supremum over all $d$ for which there is an $F$-free hypergraph with the\nproperty that every linearly sized subhypergraph with density at least $d$.\nDetermining $\\pi_{1}(F)$ for given hypergraphs $F$ was suggested by Erd\\H{o}s\nand S\\'os in 1980s. In particular, they raised the questions of determining\n$\\pi_{1}(K_4^{(3)-})$ and $\\pi_{1}(K_4^{(3)})$. The former question was solved\nrecently in [Israel J. Math. 211 (2016), 349-366] and [J. Eur. Math. Soc. 20\n(2018), 1139-1159], while the latter is still a major open problem. In addition\nto $K_4^{(3)-}$, there are very few hypergraphs whose uniform Tur\\'an density\nhas been determined.\n  In this paper, we give a sufficient condition for $3$-uniform hypergraphs $F$\nsatisfying $\\pi_{1}(F)=1/4$. In particular, currently all known $3$-uniform\nhypergraphs whose uniform Tur\\'an density is $1/4$, such as $K_4^{(3)-}$ and\nthe $3$-uniform hypergraphs $F^{\\star}_5$ studied in [arXiv:2211.12747],\nsatisfy this condition. Moreover, we find some intriguing $3$-uniform\nhypergraphs whose uniform Tur\\'an density is also $1/4$.\n"", 'Uniform Tur\\\'an density of cycles   In the early 1980s, Erd\\H{o}s and S\\\'os initiated the study of the classical\nTur\\\'an problem with a uniformity condition: the uniform Tur\\\'an density of a\nhypergraph $H$ is the infimum over all $d$ for which any sufficiently large\nhypergraph with the property that all its linear-size subhyperghraphs have\ndensity at least $d$ contains $H$. In particular, they raise the questions of\ndetermining the uniform Tur\\\'an densities of $K_4^{(3)-}$ and $K_4^{(3)}$. The\nformer question was solved only recently in [Israel J. Math. 211 (2016),\n349-366] and [J. Eur. Math. Soc. 20 (2018), 1139-1159], while the latter still\nremains open for almost 40 years. In addition to $K_4^{(3)-}$, the only\n$3$-uniform hypergraphs whose uniform Tur\\\'an density is known are those with\nzero uniform Tur\\\'an density classified by Reiher, R\\""odl and Schacht [J.\nLondon Math. Soc. 97 (2018), 77-97] and a specific family with uniform Tur\\\'an\ndensity equal to $1/27$.\n  We develop new tools for embedding hypergraphs in host hypergraphs with\npositive uniform density and apply them to completely determine the uniform\nTur\\\'an density of a fundamental family of $3$-uniform hypergraphs, namely\ntight cycles $C_\\ell^{(3)}$. The uniform Tur\\\'an density of $C_\\ell^{(3)}$,\n$\\ell\\ge 5$, is equal to $4/27$ if $\\ell$ is not divisible by three, and is\nequal to zero otherwise. The case $\\ell=5$ resolves a problem suggested by\nReiher.\n']","[('uniform hypergraphs', 0.6745749711990356), ('uniform hypergraph', 0.6396881341934204), ('vertex uniform hypergraph', 0.6321499943733215), ('uniform hypergraph vertices', 0.6197741627693176), ('hypergraphs', 0.5528275370597839), ('hypergraph', 0.486235648393631), ('hypergraph vertices', 0.4686743915081024), ('vertex uniform', 0.4661359190940857), ('hypergraph mathcal', 0.4618501663208008), ('edges uniform', 0.3937348425388336)]"
212,212,133,212_transitive tournaments_transitive tournament_tournaments_regular tournaments,"['transitive tournaments', 'transitive tournament', 'tournaments', 'regular tournaments', 'tournament', 'vertex disjoint cycles', 'every vertex', 'free vertex', 'vertex disjoint', 'free digraphs']","[""Construction, Extension and Paths of Near-Homogeneous Tournaments   A homogeneous tournament is a tournament with $4t+3$ vertices such that every\narc is contained in exactly $t+1$ cycles of length $3$. Homogeneous tournaments\nare the first class of tournaments that are proved to be path extendable, which\nmeans that every nonhamiltonian path $P$ in such a tournament $T$ can be\nextended to a path $P'$ with the same initial and terminal vertex and\n$V(P')=V(P)\\cup \\{u\\}$ for a certain vertex $u\\in V(T)\\backslash V(P)$. In\norder to find more path extendable tournaments we study the generalization of\nhomogeneous tournaments called near-homogeneous tournaments, in which every arc\nis contained in $t$ or $t+1$ cycles of length $3$. Near-homogeneity has been\ndefined in tournaments with $4t+1$ vertices. In this paper, we raise a new\nmethod to construct near-homogeneous tournaments with $4t+1$ vertices. We then\nshow that the definition of near-homogeneous tournament can be extended to\ntournaments with an even number of vertices. Finally we verify path\nextendability of near-homogeneous tournaments, thus expand the class of path\nextendable tournaments.\n"", 'On unimodular tournaments   A tournament is unimodular if the determinant of its skew-adjacency matrix is\n$1$. In this paper, we give some properties and constructions of unimodular\ntournaments. A unimodular tournament $T$ with skew-adjacency matrix $S$ is\ninvertible if $S^{-1}$ is the skew-adjacency matrix of a tournament. A spectral\ncharacterization of invertible tournaments is given. Lastly, we show that every\n$n$-tournament can be embedded in a unimodular tournament by adding at most $n\n- \\lfloor\\log_2(n)\\rfloor$ vertices.\n', 'Walecki tournaments with an arc that lies in a unique directed triangle   A Walecki tournament is any tournament that can be formed by choosing an\norientation for each of the Hamilton cycles in the Walecki decomposition of a\ncomplete graph on an odd number of vertices. In this paper, we show that if\nsome arc in a Walecki tournament on at least $7$ vertices lies in exactly one\ndirected triangle, then there is a vertex of the tournament (the vertex\ntypically labelled $*$ in the decomposition) that is fixed under every\nautomorphism of the tournament. Furthermore, any isomorphism between such\nWalecki tournaments maps the vertex labelled $*$ in one to the vertex labelled\n$*$ in the other.\n  We also show that among Walecki tournaments with a signature of even length\n$2k$, of the $2^{2k}$ possible signatures, at least $2^k$ produce tournaments\nthat have an arc that lies in a unique directed triangle (and therefore to\nwhich our result applies).\n']","[('transitive tournaments', 0.678771436214447), ('transitive tournament', 0.6662575602531433), ('tournaments', 0.6263172626495361), ('regular tournaments', 0.6193611025810242), ('tournament', 0.5587193965911865), ('vertex disjoint cycles', 0.48571351170539856), ('every vertex', 0.48487257957458496), ('free vertex', 0.4404512345790863), ('vertex disjoint', 0.43131786584854126), ('free digraphs', 0.4126645028591156)]"
213,213,132,213_contact manifolds_contact manifold_contact manifold xi_embedded contact homology,"['contact manifolds', 'contact manifold', 'contact manifold xi', 'embedded contact homology', 'contact homology', 'tight contact structures', 'contact structures', 'dimensional contact', 'contact topology', 'contact invariant']","['Bourgeois contact structures: tightness, fillability and applications   Given a contact structure on a manifold $V$ together with a supporting open\nbook decomposition, Bourgeois gave an explicit construction of a contact\nstructure on $V \\times \\mathbb{T}^2$. We prove that all such structures are\nuniversally tight in dimension $5$, independent on whether the original contact\nmanifold is itself tight or overtwisted. In arbitrary dimensions, we provide\nobstructions to the existence of strong symplectic fillings of Bourgeois\nmanifolds. This gives a broad class of new examples of weakly but not strongly\nfillable contact $5$-manifolds, as well as the first examples of weakly but not\nstrongly fillable contact structures in all odd dimensions. These obstructions\nare particular instances of more general obstructions for $\\mathbb\nS^1$-invariant contact manifolds. We also obtain a classification result in\narbitrary dimensions, namely that the unit cotangent bundle of the $n$-torus\nhas a unique symplectically aspherical strong filling up to diffeomorphism.\n', 'Liouville hypersurfaces and connect sum cobordisms   The purpose of this paper is to introduce Liouville hypersurfaces in contact\nmanifolds, which generalize ribbons of Legendrian graphs and pages of\nsupporting open books. Liouville hypersurfaces are used to define a gluing\noperation for contact manifolds called the Liouville connect sum. Performing\nthis operation on a contact manifold $(M, \\xi)$ gives an exact -- and in many\ncases, Weinstein -- cobordism whose concave boundary is $(M, \\xi)$ and whose\nconvex boundary is the surgered manifold. These cobordisms are used to\nestablish the existence of ""fillability"" and ""non-vanishing contact homology""\nmonoids in symplectomorphism groups of Liouville domains, study the symplectic\nfillability of a family of contact manifolds which fiber over the circle,\nassociate cobordisms to certain branched coverings of contact manifolds, and\nconstruct exact symplectic cobordisms that do not admit Weinstein structures.\n  The Liouville connect sum generalizes the Weinstein handle attachment and is\nused to extend the definition of contact $(1/k)$-surgery along Legendrian knots\nin contact 3-manifolds to contact $(1/k)$-surgery along Legendrian spheres in\ncontact manifolds of arbitrary dimension. We use contact surgery to construct\nexotic contact structures on $5$- and $13$-dimensional spheres after\nestablishing that $S^{2}$ and $S^{6}$ are the only spheres along which\ngeneralized Dehn twists smoothly square to the identity mapping. The exoticity\nof these contact structures implies that Dehn twists along $S^{2}$ and $S^{6}$\ndo not symplectically square to the identity, generalizing a theorem of Seidel.\nA similar argument shows that the $(2n+1)$-dimensional contact manifold\ndetermined by an open book whose page is $(T^{*}S^{n}, -\\lambda_{can})$ and\nwhose monodromy is any negative power of a symplectic Dehn twist is not exactly\nfillable.\n', 'Tight contact structures without symplectic fillings are everywhere   We show that for all $n \\geq 3$, any $(2n+1)$-dimensional manifold that\nadmits a tight contact structure, also admits a tight but non-fillable contact\nstructure, in the same almost contact class. For $n=2$, we obtain the same\nresult, provided that the first Chern class vanishes. We further construct\nLiouville but not Weinstein fillable contact structures on any Weinstein\nfillable contact manifold of dimension at least $7$ with torsion first Chern\nclass.\n']","[('contact manifolds', 0.777507483959198), ('contact manifold', 0.7404698729515076), ('contact manifold xi', 0.7092123627662659), ('embedded contact homology', 0.6127116680145264), ('contact homology', 0.6088070869445801), ('tight contact structures', 0.6034203171730042), ('contact structures', 0.5913172364234924), ('dimensional contact', 0.5758581161499023), ('contact topology', 0.5757358074188232), ('contact invariant', 0.5666598081588745)]"
214,214,132,214_dyck paths_dyck path_dyck words_dyck,"['dyck paths', 'dyck path', 'dyck words', 'dyck', 'catalan numbers', 'lattice paths', 'paths bijection', 'catalan number', 'catalan', 'paths']","['Restricted Dyck Paths on Valleys Sequence   In this paper we study a subfamily of a classic lattice path, the \\emph{Dyck\npaths}, called \\emph{restricted $d$-Dyck} paths, in short $d$-Dyck. A valley of\na Dyck path $P$ is a local minimum of $P$; if the difference between the\nheights of two consecutive valleys (from left to right) is at least $d$, we say\nthat $P$ is a restricted $d$-Dyck path. The \\emph{area} of a Dyck path is the\nsum of the absolute values of $y$-components of all points in the path. We find\nthe number of peaks and the area of all paths of a given length in the set of\n$d$-Dyck paths. We give a bivariate generating function to count the number of\nthe $d$-Dyck paths with respect to the the semi-length and number of peaks.\nAfter that, we analyze in detail the case $d=-1$. Among other things, we give\nboth, the generating function and a recursive relation for the total area.\n', 'Bijections from Dyck and Motzkin meanders with catastrophes to pattern\n  avoiding Dyck paths   In this note, we present constructive bijections from Dyck and Motzkin\nmeanders with catastrophes to Dyck paths avoiding some patterns. As a\nbyproduct, we deduce correspondences from Dyck and Motzkin excursions to\nrestricted Dyck paths.\n', 'Rational Dyck paths and decompositions   We study combinatorial properties of a rational Dyck path by decomposing it\ninto a tuple of Dyck paths. The combinatorial models such as $b$-Stirling\npermutations, $(b+1)$-ary trees, parenthesis presentations, and binary trees\nplay central roles to establish a correspondence between the rational Dyck path\nand the tuple of Dyck paths. We reinterpret two orders, the Young and the\nrotation orders, on rational Dyck paths in terms of the tuple of Dyck paths by\nuse of the decomposition. As an application, we show a duality between\n$(a,b)$-Dyck paths and $(b,a)$-Dyck paths in terms of binary trees.\n']","[('dyck paths', 0.7597846388816833), ('dyck path', 0.6825806498527527), ('dyck words', 0.6171249151229858), ('dyck', 0.5409167408943176), ('catalan numbers', 0.5318599939346313), ('lattice paths', 0.5274518728256226), ('paths bijection', 0.49759259819984436), ('catalan number', 0.4700050354003906), ('catalan', 0.4491305351257324), ('paths', 0.44229578971862793)]"
215,215,131,215_proof fermat last_proof fermat_generalized fermat_fermat last,"['proof fermat last', 'proof fermat', 'generalized fermat', 'fermat last', 'number theory', 'fermat', 'solutions diophantine', 'diophantine equations', 'diophantine', 'number solutions']","[""Remark on Fermat's Last Theorem   In this short article we do not prove Fermat's last theorem. We show that the\nnumber 2 is an exceptional number in this theorem.\n"", ""On Fermat's Last Theorem for odd prime exponents   We show that the Fermat equation $x^p + y^p = z^p$ has no solutions in\ncoprime positive integers $x, y, z$ for any odd prime $p$.\n"", ""The Cartesian method and Fermat's Last Theorem   Fermat's Last Theorem is proved by using the philosophical and mathematical\nknowledge of 1637 when the French mathematician Pierre de Fermat claimed to\nhave a truly marvelous proof of his conjecture. Our approach consists of\nsetting three variables of Fermat's equation as integers and then evaluating\nwhether the remaining variable can be an integer as well. Pythagorean triples\nplay a fundamental role in claiming that at least an irrational number is\nneeded to satisfy Fermat's equation. As a result, we confirm that Fermat's Last\nTheorem is valid.\n""]","[('proof fermat last', 0.724285364151001), ('proof fermat', 0.689723551273346), ('generalized fermat', 0.6710357666015625), ('fermat last', 0.640187680721283), ('number theory', 0.600033700466156), ('fermat', 0.5913141965866089), ('solutions diophantine', 0.4790397584438324), ('diophantine equations', 0.4753640294075012), ('diophantine', 0.45193585753440857), ('number solutions', 0.45116502046585083)]"
216,216,130,216_generalized nash equilibrium_generalized nash_convergence nash equilibrium_nash equilibrium problems,"['generalized nash equilibrium', 'generalized nash', 'convergence nash equilibrium', 'nash equilibrium problems', 'nash equilibrium', 'nash equilibrium gne', 'computing nash', 'stochastic nash', 'nash equilibria', 'nash equilibrium ne']","[""Nash Equilibrium Seeking for Games in Second-order Systems without\n  Velocity Measurement   The design of Nash equilibrium seeking strategies for games in which the\ninvolved players are of second-order integrator-type dynamics is investigated\nin this paper. Noticing that velocity signals are usually noisy or not\navailable for feedback control in practical engineering systems, this paper\nsupposes that the velocity signals are not accessible for the players. To deal\nwith the absence of velocity measurements, two estimators are designed, based\non which Nash equilibrium seeking strategies are constructed. The first\nstrategy is established by employing an observer, which has the same order as\nthe players' dynamics, to estimate the unavailable system states (e.g., the\nplayers' velocities). The second strategy is designed based on a high-pass\nfilter and is motivated by the incentive to reduce the order of the closed-loop\nsystem which in turn reduces the computation costs of the seeking algorithm.\nExtensions to Nash equilibrium seeking for networked games are provided. Taking\nthe advantages of leader-following consensus protocols, it turns out that both\nthe observer-based method and the filter-based method can be adapted to deal\nwith games in distributed systems, which shows the extensibility of the\ndeveloped strategies. Through Lyapunov stability analysis, it is analytically\nproven that the players' actions can be regulated to the Nash equilibrium point\nand their velocities can be regulated to zero by utilizing the proposed\nvelocity-free Nash equilibrium seeking strategies. A numerical example is\nprovided for the verifications of the proposed algorithms.\n"", 'Stochastic generalized Nash equilibrium seeking under partial-decision\n  information   We consider for the first time a stochastic generalized Nash equilibrium\nproblem, i.e., with expected-value cost functions and joint feasibility\nconstraints, under partial-decision information, meaning that the agents\ncommunicate only with some trusted neighbours. We propose several distributed\nalgorithms for network games and aggregative games that we show being special\ninstances of a preconditioned forward-backward splitting method. We prove that\nthe algorithms converge to a generalized Nash equilibrium when the forward\noperator is restricted cocoercive by using the stochastic approximation scheme\nwith variance reduction to estimate the expected value of the pseudogradient.\n', ""A distributed generalized Nash equilibrium seeking algorithm based on\n  extremum seeking control   In this paper, a distributed non-model based seeking algorithm which combines\nthe extremum seeking control (ESC) jointly with learning algorithms is proposed\nto seek a generalized Nash equilibrium (GNE) for a class of noncooperative\ngames with coupled equality constraint. The strategy of each agent is\nrestricted by both the coupled inter-agent constraint and local inequality\nconstraints. Thanks to the ESC, it is unnecessary to know the specific\nexpressions of agents' cost functions and local constraints and to know the\nstrategies of other agents for the implementation of the proposed GNE seeking\nalgorithm. To deal with the coupled constraints, only the Lagrange multiplier\nis transmitted among agents with some prior information about the coupled\nconstraints. Moreover, a diminishing dither signal is designed in the seeking\nalgorithm to remove undesirable steady-state oscillations. The non-local\nconvergence of the designed seeking algorithm is analyzed via the singular\nperturbation theory, averaging analysis and Lyapunov stability theory.\nNumerical examples are given to verify the effectiveness of our proposed\nmethod.\n""]","[('generalized nash equilibrium', 0.6173748970031738), ('generalized nash', 0.6001880764961243), ('convergence nash equilibrium', 0.5711443424224854), ('nash equilibrium problems', 0.5536573529243469), ('nash equilibrium', 0.5495613217353821), ('nash equilibrium gne', 0.536931037902832), ('computing nash', 0.5316476821899414), ('stochastic nash', 0.5308985710144043), ('nash equilibria', 0.5159444808959961), ('nash equilibrium ne', 0.500607430934906)]"
217,217,129,217_neural networks approximation_neural network approximation_relu networks_neural networks relu,"['neural networks approximation', 'neural network approximation', 'relu networks', 'neural networks relu', 'approximation deep', 'shallow neural networks', 'relu neural networks', 'networks approximation', 'deep relu networks', 'shallow networks']","['High-Order Approximation Rates for Shallow Neural Networks with Cosine\n  and ReLU$^k$ Activation Functions   We study the approximation properties of shallow neural networks with an\nactivation function which is a power of the rectified linear unit.\nSpecifically, we consider the dependence of the approximation rate on the\ndimension and the smoothness in the spectral Barron space of the underlying\nfunction $f$ to be approximated. We show that as the smoothness index $s$ of\n$f$ increases, shallow neural networks with ReLU$^k$ activation function obtain\nan improved approximation rate up to a best possible rate of\n$O(n^{-(k+1)}\\log(n))$ in $L^2$, independent of the dimension $d$. The\nsignificance of this result is that the activation function ReLU$^k$ is fixed\nindependent of the dimension, while for classical methods the degree of\npolynomial approximation or the smoothness of the wavelets used would have to\nincrease in order to take advantage of the dimension dependent smoothness of\n$f$. In addition, we derive improved approximation rates for shallow neural\nnetworks with cosine activation function on the spectral Barron space. Finally,\nwe prove lower bounds showing that the approximation rates attained are optimal\nunder the given assumptions.\n', 'On the Expressive Power of Neural Networks   In 1989 George Cybenko proved in a landmark paper that wide shallow neural\nnetworks can approximate arbitrary continuous functions on a compact set. This\nuniversal approximation theorem sparked a lot of follow-up research.\n  Shen, Yang and Zhang determined optimal approximation rates for ReLU-networks\nin $L^p$-norms with $p \\in [1,\\infty)$. Kidger and Lyons proved a universal\napproximation theorem for deep narrow ReLU-networks. Telgarsky gave an example\nof a deep narrow ReLU-network that cannot be approximated by a wide shallow\nReLU-network unless it has exponentially many neurons.\n  However, there are even more questions that still remain unresolved. Are\nthere any wide shallow ReLU-networks that cannot be approximated well by deep\nnarrow ReLU-networks? Is the universal approximation theorem still true for\nother norms like the Sobolev norm $W^{1,1}$? Do these results hold for\nactivation functions other than ReLU?\n  We will answer all of those questions and more with a framework of two\nexpressive powers. The first one is well-known and counts the maximal number of\nlinear regions of a function calculated by a ReLU-network. We will improve the\nbest known bounds for this expressive power. The second one is entirely new.\n', 'Expressivity and Approximation Properties of Deep Neural Networks with\n  ReLU$^k$ Activation   In this paper, we investigate the expressivity and approximation properties\nof deep neural networks employing the ReLU$^k$ activation function for $k \\geq\n2$. Although deep ReLU networks can approximate polynomials effectively, deep\nReLU$^k$ networks have the capability to represent higher-degree polynomials\nprecisely. Our initial contribution is a comprehensive, constructive proof for\npolynomial representation using deep ReLU$^k$ networks. This allows us to\nestablish an upper bound on both the size and count of network parameters.\nConsequently, we are able to demonstrate a suboptimal approximation rate for\nfunctions from Sobolev spaces as well as for analytic functions. Additionally,\nthrough an exploration of the representation power of deep ReLU$^k$ networks\nfor shallow networks, we reveal that deep ReLU$^k$ networks can approximate\nfunctions from a range of variation spaces, extending beyond those generated\nsolely by the ReLU$^k$ activation function. This finding demonstrates the\nadaptability of deep ReLU$^k$ networks in approximating functions within\nvarious variation spaces.\n']","[('neural networks approximation', 0.6808028221130371), ('neural network approximation', 0.6448177695274353), ('relu networks', 0.6230483055114746), ('neural networks relu', 0.622962236404419), ('approximation deep', 0.6227438449859619), ('shallow neural networks', 0.6220395565032959), ('relu neural networks', 0.6065765619277954), ('networks approximation', 0.5805625915527344), ('deep relu networks', 0.5600453019142151), ('shallow networks', 0.5599812865257263)]"
218,218,129,218_affine springer fibers_springer correspondence_springer fibers_affine springer,"['affine springer fibers', 'springer correspondence', 'springer fibers', 'affine springer', 'springer fiber', 'springer resolution', 'grothendieck springer', 'affine grassmannian', 'character sheaves', 'equivariant perverse sheaves']","['Parabolic Multiplicative Affine Springer Fibers   We introduce parabolic multiplicative affine Springer fibers, which resemble\nthe admissible union of affine Deligne Lusztig varieties in the affine flag\nvariety. We also study their global counterparts called parabolic\nmultiplicative Hitchin fibers. Their associated fibration is a global analogue\nof the Grothendieck simultaneous resolution for monoids. Using this fibration,\nwe show that the parabolic multiplicative affine Springer fibers are\nequidimensional and find their dimension.\n', ""Geometric and combinatorial properties of extended Springer fibers   We consider a generalization of the Springer resolution studied in earlier\nwork of the authors, called the extended Springer resolution. In type $A$, this\nmap plays a role in Lusztig's generalized Springer correspondence comparable to\nthat of the Springer resolution in the Springer correspondence. The fibers of\nthe Springer resolution play a key part in the latter story, and connect the\ncombinatorics of tableaux to geometry. Our main results prove the same is true\nfor fibers of the extended Springer resolution -- their geometry is governed by\nthe combinatorics of tableaux. In particular, we prove that these fibers are\npaved by affines, up to the action of a finite group, and give combinatorial\nformulas for their Betti numbers. This yields, among other things, a simple\nformula for dimensions of stalks of the Lusztig sheaves arising in the study of\nthe generalized Springer correspondence, and shows that there is a close\nresemblance between each Lusztig sheaf and the Springer sheaf for a smaller\ngroup.\n"", ""A new approach to the generalized Springer correspondence   The Springer resolution of the nilpotent cone is used to give a geometric\nconstruction of the irreducible representations of Weyl groups. Borho and\nMacPherson obtain the Springer correspondence by applying the decomposition\ntheorem to the Springer resolution, establishing an injective map from the set\nof irreducible Weyl group representations to simple equivariant perverse\nsheaves on the nilpotent cone. In this manuscript, we consider a generalization\nof the Springer resolution using a variety defined by the first author. Our\nmain result shows that in the type A case, applying the decomposition theorem\nto this map yields all simple perverse sheaves on the nilpotent cone with\nmultiplicity as predicted by Lusztig's generalized Springer correspondence.\n""]","[('affine springer fibers', 0.7449814677238464), ('springer correspondence', 0.6732165813446045), ('springer fibers', 0.6547508835792542), ('affine springer', 0.6232429146766663), ('springer fiber', 0.6012454628944397), ('springer resolution', 0.5476800799369812), ('grothendieck springer', 0.5152629017829895), ('affine grassmannian', 0.49460986256599426), ('character sheaves', 0.48753902316093445), ('equivariant perverse sheaves', 0.4613591730594635)]"
219,219,128,219_cyber attacks_cyber security_cyber physical systems_cybersecurity,"['cyber attacks', 'cyber security', 'cyber physical systems', 'cybersecurity', 'cyber physical system', 'attacks', 'proposed attack', 'attack strategy', 'attacks can', 'attack']","['Mathematical Modeling of Cyber Resilience   We identify quantitative characteristics of responses to cyber compromises\nthat can be learned from repeatable, systematic experiments. We model a vehicle\nequipped with an autonomous cyber-defense system and which also has some\ninherent physical resilience features. When attacked by malware, this ensemble\nof cyber-physical features (i.e., ""bonware"") strives to resist and recover from\nthe performance degradation caused by the malware\'s attack. We propose\nparsimonious continuous models, and develop stochastic models to aid in\nquantifying systems\' resilience to cyber attacks.\n', 'Security of Distributed Parameter Cyber-Physical Systems: Cyber-Attack\n  Detection in Linear Parabolic PDEs   Security of Distributed Parameter Cyber-Physical Systems (DPCPSs) is of\ncritical importance in the face of cyber-attack threats. Although security\naspects of Cyber-Physical Systems (CPSs) modelled by Ordinary differential\nEquations (ODEs) have been extensively explored during the past decade,\nsecurity of DPCPSs has not received its due attention despite its\nsafety-critical nature. In this work, we explore the security aspects of DPCPSs\nfrom a system theoretic viewpoint. Specifically, we focus on DPCPSs modelled by\nlinear parabolic Partial Differential Equations (PDEs) subject to cyber-attacks\nin actuation channel. First, we explore the detectability of such attacks and\nderive conditions for stealthy attacks. Next, we develop a design framework for\ncyber-attack detection algorithms based on output injection observers. Such\nattack detection algorithms explicitly consider stability, robustness and\nattack sensitivity in their design. Finally, theoretical analysis and\nsimulation studies are performed to illustrate the effectiveness of the\nproposed approach.\n', 'Method for Extracting Patterns of Coordinated Network Attacks on\n  Electric Power CPS based on Temporal-Topological Correlation   In the analysis of coordinated network attacks on electric power\ncyber-physical system (CPS), it is difficult to restore the complete attack\npath, and the intent of the attack cannot be identified automatically. A method\nis therefore proposed for the extracting patterns of coordinated network\nattacks on electric power CPS based on temporal-topological correlation. First,\nthe attack events are aggregated according to the alarm log of the cyber space,\nand a temporal-causal Bayesian network-based cyber attack recognition algorithm\nis proposed to parse out the cyber attack sequences of the same attacker. Then,\naccording to the characteristic curves of different attack measurement data in\nphysical space, a combination of physical attack event criteria algorithm is\ndesigned to distinguish the types of physical attack events. Finally, physical\nattack events and cyber attack sequences are matched via temporal-topological\ncorrelation, frequent patterns of attack sequences are extracted, and hidden\nmulti-step attack patterns are found from scattered grid measurement data and\ninformation from alarm logs. The effectiveness and efficiency of the proposed\nmethod are verified by the testbed at Mississippi State University.\n']","[('cyber attacks', 0.5960811376571655), ('cyber security', 0.5716978311538696), ('cyber physical systems', 0.5150355100631714), ('cybersecurity', 0.5114412307739258), ('cyber physical system', 0.48084717988967896), ('attacks', 0.46749699115753174), ('proposed attack', 0.43667083978652954), ('attack strategy', 0.42761877179145813), ('attacks can', 0.41610726714134216), ('attack', 0.4049917757511139)]"
220,220,128,220_complex monge ampere_compact ahler manifold_generalized monge amp_complex monge amp,"['complex monge ampere', 'compact ahler manifold', 'generalized monge amp', 'complex monge amp', 'compact hermitian manifolds', 'plurisubharmonic functions', 'almost hermitian manifolds', 'complex hessian equations', 'compact hermitian manifold', 'complex monge']","['Quasi-plurisubharmonic envelopes 3: Solving Monge-Amp\\`ere equations on\n  hermitian manifolds   We develop a new approach to $L^{\\infty}$-a priori estimates for degenerate\ncomplex Monge-Amp\\`ere equations on complex manifolds. It only relies on\ncompactness and envelopes properties of quasi-plurisubharmonic functions. In a\nprequel \\cite{GL21a} we have shown how this method allows one to obtain new and\nefficient proofs of several fundamental results in K\\""ahler geometry. In\n\\cite{GL21b} we have studied the behavior of Monge-Amp\\`ere volumes on\nhermitian manifolds. We extend here the techniques of \\cite{GL21a} to the\nhermitian setting and use the bounds established in \\cite{GL21b}, producing new\nrelative a priori estimates, as well as several existence results for\ndegenerate complex Monge-Amp\\`ere equations on compact hermitian manifolds.\n', 'Weak convergence of complex Monge-Amp\\`ere operators on compact\n  Hermitian manifolds   Let $(X,\\omega)$ be a compact Hermitian manifold and let $\\{\\beta\\}\\in\nH^{1,1}(X,\\mathbb R)$ be a real $(1,1)$-class with a smooth representative\n$\\beta$, such that $\\int_X\\beta^n>0$. Assume that there is a bounded\n$\\beta$-plurisubharmonic function $\\rho$ on $X$. First, we provide a criterion\nfor the weak convergence of non-pluripolar complex Monge-Amp\\`ere measures\nassociated to a sequence of $\\beta$-plurisubharmonic functions. Second, this\ncriterion is utilized to solve a degenerate complex Monge-Amp\\`ere equation\nwith an $L^1$-density. Finally, an $L^\\infty$-estimate of the solution to the\ncomplex Monge-Amp\\`ere equation for a finite positive Radon measure is given.\n', 'The complex Monge-Amp\\`ere equation with a gradient term   We consider the complex Monge-Amp\\`ere equation with an additional linear\ngradient term inside the determinant. We prove existence and uniqueness of\nsolutions to this equation on compact Hermitian manifolds.\n']","[('complex monge ampere', 0.5533415079116821), ('compact ahler manifold', 0.531808078289032), ('generalized monge amp', 0.4770559072494507), ('complex monge amp', 0.47291868925094604), ('compact hermitian manifolds', 0.44717714190483093), ('plurisubharmonic functions', 0.4392988979816437), ('almost hermitian manifolds', 0.43361952900886536), ('complex hessian equations', 0.42786210775375366), ('compact hermitian manifold', 0.42713242769241333), ('complex monge', 0.4194831848144531)]"
221,221,127,221_blow solutions_blowup solutions_finite time blow_blow finite time,"['blow solutions', 'blowup solutions', 'finite time blow', 'blow finite time', 'solutions blow', 'solutions semilinear heat', 'blow finite', 'self similar blow', 'blow profiles', 'blow profile']","['Blow up profiles for a quasilinear reaction-diffusion equation with\n  weighted reaction   We perform a thorough study of the blow up profiles associated to the\nfollowing second order reaction-diffusion equation with non-homogeneous\nreaction: $$ \\partial_tu=\\partial_{xx}(u^m) + |x|^{\\sigma}u^p, $$ in the range\nof exponents $1<p<m$ and $\\sigma>0$. We classify blow up solutions in\nself-similar form, that are likely to represent typical blow up patterns for\ngeneral solutions. We thus show that the non-homogeneous coefficient\n$|x|^{\\sigma}$ has a strong influence on the qualitative aspects related to the\nfinite time blow up. More precisely, for $\\sigma\\sim0$, blow up profiles have\nsimilar behavior to the well-established profiles for the homogeneous case\n$\\sigma=0$, and typically \\emph{global blow up} occurs, while for $\\sigma>0$\nsufficiently large, there exist blow up profiles for which blow up \\emph{occurs\nonly at space infinity}, in strong contrast with the homogeneous case. This\nwork is a part of a larger program of understanding the influence of unbounded\nweights on the blow up behavior for reaction-diffusion equations.\n', 'Global solutions versus finite time blow-up for the supercritical fast\n  diffusion equation with inhomogeneous source   Solutions in self-similar form, either global in time or presenting finite\ntime blow-up, to the supercritical fast diffusion equation with spatially\ninhomogeneous source $$ \\partial_tu=\\Delta u^m+|x|^{\\sigma}u^p, \\quad\n(x,t)\\in\\mathbb{R}^N\\times(0,\\infty) $$ with $$ m_c=\\frac{(N-2)_+}{N}\\leq m<1,\n\\quad \\sigma\\in(\\max\\{-2,-N\\},\\infty), \\quad\np>\\max\\left\\{1+\\frac{\\sigma(1-m)}{2},1\\right\\} $$ are considered. It is proved\nthat global self-similar solutions with the specific tail behavior $$\nu(x,t)\\sim C(m)|x|^{-2/(1-m)}, \\qquad {\\rm as} \\ |x|\\to\\infty $$ exist exactly\nfor $p\\in(p_F(\\sigma),p_s(\\sigma))$, where $$ p_F(\\sigma)=m+\\frac{\\sigma+2}{N},\n\\qquad p_s(\\sigma)=\\left\\{\\begin{array}{ll}\\frac{m(N+2\\sigma+2)}{N-2}, &\nN\\geq3,\\\\\\infty, & N\\in\\{1,2\\}, \\end{array}\\right. $$ are the renowned Fujita\nand Sobolev critical exponents. In contrast, it is shown that self-similar\nsolutions presenting finite time blow-up exist for any $\\sigma\\in(-2,0)$ and\n$p$ as above, but do not exist for any $\\sigma\\geq0$ and\n$p\\in(p_F(\\sigma),p_s(\\sigma))$. We stress that all these results are \\emph{new\nalso in the homogeneous case $\\sigma=0$}.\n', 'Self-similar blow-up profiles for a reaction-diffusion equation with\n  strong weighted reaction   We study the self-similar blow-up profiles associated to the following second\norder reaction-diffusion equation with strong weighted reaction and unbounded\nweight: $$ \\partial_tu=\\partial_{xx}(u^m) + |x|^{\\sigma}u^p, $$ posed for\n$x\\in\\real$, $t\\geq0$, where $m>1$, $0<p<1$ and $\\sigma>2(1-p)/(m-1)$. As a\nfirst outcome, we show that finite time blow-up solutions in self-similar form\nexist for $m+p>2$ and $\\sigma$ in the considered range, a fact that is\ncompletely new: in the already studied reaction-diffusion equation without\nweights there is no finite time blow-up when $p<1$. We moreover prove that, if\nthe condition $m+p>2$ is fulfilled, all the self-similar blow-up profiles are\ncompactly supported and there exist \\emph{two different interface behaviors}\nfor solutions of the equation, corresponding to two different interface\nequations. We classify the self-similar blow-up profiles having both types of\ninterfaces and show that in some cases \\emph{global blow-up} occurs, and in\nsome other cases finite time blow-up occurs \\emph{only at space infinity}. We\nalso show that there is no self-similar solution if $m+p<2$, while the critical\nrange $m+p=2$ with $\\sigma>2$ is postponed to a different work due to\nsignificant technical differences.\n']","[('blow solutions', 0.5712755918502808), ('blowup solutions', 0.5168793201446533), ('finite time blow', 0.5124731063842773), ('blow finite time', 0.49699726700782776), ('solutions blow', 0.48689979314804077), ('solutions semilinear heat', 0.4618259370326996), ('blow finite', 0.44867733120918274), ('self similar blow', 0.4087491035461426), ('blow profiles', 0.40739157795906067), ('blow profile', 0.3804416060447693)]"
222,222,127,222_triangular matrix algebras_multilinear polynomials_multilinear polynomial_upper triangular matrices,"['triangular matrix algebras', 'multilinear polynomials', 'multilinear polynomial', 'upper triangular matrices', 'noncommutative polynomials', 'matrix algebras', 'noncommutative polynomial', 'triangular matrices', 'upper triangular matrix', 'matrix algebra']","['Images of multilinear graded polynomials on upper triangular matrix\n  algebras   In this paper we study the images of multilinear graded polynomials on the\ngraded algebra of upper triangular matrices UT_n. For positive integers q \\leq\nn, we classify these images on UT_n endowed with a particular elementary\nZ_q-grading. As a consequence, we obtain the images of multilinear graded\npolynomials on UT_n with the natural Z_n-grading. We apply this classification\nin order to give a new condition for a multilinear polynomial in terms of\ngraded identities so that to obtain the traceless matrices in its image on the\nfull matrix algebra. We also describe the images of multilinear polynomials on\nthe graded algebras UT_2 and UT_3, for arbitrary gradings. We finish the paper\nby proving a similar result for the graded Jordan algebra UJ_2, and also for\nUJ_3 endowed with the natural elementary Z_3-grading.\n', 'Images of multilinear polynomials on $n\\times n$ upper triangular\n  matrices over infinite fields   In this paper we prove that the image of multilinear polynomials evaluated on\nthe algebra $UT_n(K)$ of $n\\times n$ upper triangular matrices over an infinite\nfield $K$ equals $J^r$, a power of its Jacobson ideal $J=J(UT_n(K))$. In\nparticular, this shows that the analogue of the Lvov-Kaplansky conjecture for\n$UT_n(K)$ is true, solving a conjecture of Fagundes and de Mello. To prove that\nfact, we introduce the notion of commutator-degree of a polynomial and\ncharacterize the multilinear polynomials of commutator-degree $r$ in terms of\nits coefficients. It turns out that the image of a multilinear polynomial $f$\non $UT_n(K)$ is $J^r$ if and only if $f$ has commutator degree $r$.\n', 'The image of multilinear polynomials evaluated on $3\\times 3$ upper\n  triangular matrices   We describe the images of multilinear polynomials of arbitrary degree\nevaluated on the $3\\times 3$ upper triangular matrix algebra over an infinite\nfield.\n']","[('triangular matrix algebras', 0.664170503616333), ('multilinear polynomials', 0.6171737909317017), ('multilinear polynomial', 0.569348156452179), ('upper triangular matrices', 0.5537323951721191), ('noncommutative polynomials', 0.5518999099731445), ('matrix algebras', 0.5478558540344238), ('noncommutative polynomial', 0.537807822227478), ('triangular matrices', 0.5081294178962708), ('upper triangular matrix', 0.4811248183250427), ('matrix algebra', 0.46658605337142944)]"
223,223,126,223_moment dirichlet functions_bounds moments_quadratic dirichlet_moment dirichlet,"['moment dirichlet functions', 'bounds moments', 'quadratic dirichlet', 'moment dirichlet', 'dirichlet functions', 'dirichlet series', 'moments quadratic', 'primitive dirichlet', 'moments functions', 'dirichlet characters']","['Bounds for moments of quadratic Dirichlet $L$-functions of prime-related\n  moduli   In this paper, we study the $k$-th moment of central values of the family of\nquadratic Dirichlet $L$-functions of moduli $8p$, with $p$ ranging over odd\nprimes. Assuming the truth of the generlized Riemann hypothesis, we establish\nsharp upper and lower bounds for the $k$-th power moment of these $L$-values\nfor all real $k \\geq 0$.\n', 'Upper bounds for moments of Dirichlet $L$-functions to a fixed modulus   We study the $2k$-th moment of central values of the family of Dirichlet\n$L$-functions to a fixed prime modulus and establish sharp upper bounds for all\nreal $k \\in [0,2]$.\n', 'First moment of central values of quadratic Dirichlet $L$-functions   We evaluate the first moment of central values of the family of quadratic\nDirichlet $L$-functions using the method of double Dirichlet series. Under the\ngeneralized Riemann hypothesis, we prove an asymptotic formula with an error\nterm of size that is the fourth root of that of the primary main term.\n']","[('moment dirichlet functions', 0.6152303814888), ('bounds moments', 0.5331991910934448), ('quadratic dirichlet', 0.5296170711517334), ('moment dirichlet', 0.5251895785331726), ('dirichlet functions', 0.5054897665977478), ('dirichlet series', 0.49832046031951904), ('moments quadratic', 0.4675029516220093), ('primitive dirichlet', 0.450280100107193), ('moments functions', 0.44535931944847107), ('dirichlet characters', 0.44008544087409973)]"
224,224,126,224_mod galois representations_adic galois representations_galois representations_galois representation,"['mod galois representations', 'adic galois representations', 'galois representations', 'galois representation', 'representations absolute galois', 'mod galois', 'adic galois', 'dimensional galois', 'absolute galois group', 'galois group']","['Galois deformation spaces with a sparsity of automorphic points   Let $k/\\mathbb F_p$ denote a finite field. For any split connected reductive\ngroup $G/W(k)$ and certain CM number fields $F$, we deform certain Galois\nrepresentations $\\overline\\rho:Gal(\\overline F/F) \\to G(k)$ to continuous\nfamilies $X_{\\overline\\rho}$ of Galois representations $Gal(\\overline F/F) \\to\nG(\\overline{\\mathbb Q_p})$ lifting $\\overline\\rho$ such that the space of\npoints of $X_{\\overline\\rho}$ which are geometric (in the sense of the\nFontaine-Mazur conjecture) with parallel Hodge-Tate weights has positive\ncodimension in $X_{\\overline\\rho}$. Thus the set of points in\n$X_{\\overline\\rho}$ which could (conjecturally) be associated to automorphic\nforms is sparse. This generalizes a result of Calegari and Mazur for $F/\\mathbb\nQ$ quadratic imaginary and $G = GL_2$. The sparsity of automorphic points for\n$F$ a CM field contrasts with the situation when $F$ is a totally real field,\nwhere automorphic points are often provably dense.\n', ""Lifting and automorphy of reducible mod p Galois representations over\n  global fields   We extend the lifting methods of our previous paper to lift reducible odd\nrepresentations $\\bar{\\rho}:\\mathrm{Gal}(\\overline{F}/F) \\to G(k)$ of Galois\ngroups of global fields $F$ valued in Chevalley groups $G(k)$. Lifting results,\nwhen combined with automorphy lifting results pioneered by Wiles in the number\nfield case and the results on the global Langlands correspondence proved by\nDrinfeld and L. Lafforgue in the function field case, give the only known\nmethod to access modularity of mod $p$ Galois representations in both reducible\nand irreducible cases. In the reducible case this allows one to show that the\nactual representation, rather than just its semisimplification, arises from\nreduction of the geometric representation attached to a cuspidal automorphic\nrepresentation on the dual group of $G$. As a particularly concrete\napplication, we get a version of Serre's modularity conjecture for reducible,\nodd representations $\\bar{\\rho}: \\mathrm{Gal}(\\overline{\\mathbb{Q}}/\\mathbb{Q})\n\\to \\mathrm{GL}_2(k)$. This extends earlier results of Hamblen and Ramakrishna\nin this classical case and proves modularity of infinitely many extensions of\nfixed characters that are not covered by loc. cit.\n"", 'Relative deformation theory, relative Selmer groups, and lifting\n  irreducible Galois representations   We study irreducible odd mod $p$ Galois representations $\\bar{\\rho} \\colon\n\\mathrm{Gal}(\\overline{F}/F) \\to G(\\overline{\\mathbb{F}}_p)$, for $F$ a totally\nreal number field and $G$ a general reductive group. For $p \\gg_{G, F} 0$, we\nshow that any $\\bar{\\rho}$ that lifts locally, and at places above $p$ to de\nRham and Hodge-Tate regular representations, has a geometric $p$-adic lift. We\nalso prove non-geometric lifting results without any oddness assumption.\n']","[('mod galois representations', 0.6667165756225586), ('adic galois representations', 0.6515649557113647), ('galois representations', 0.5906094908714294), ('galois representation', 0.5586845874786377), ('representations absolute galois', 0.5374079942703247), ('mod galois', 0.5271451473236084), ('adic galois', 0.5196214318275452), ('dimensional galois', 0.44192758202552795), ('absolute galois group', 0.4343925416469574), ('galois group', 0.43356966972351074)]"
225,225,125,225_feynman integrals_feynman integral_mellin barnes integrals_barnes integrals,"['feynman integrals', 'feynman integral', 'mellin barnes integrals', 'barnes integrals', 'feynman', 'feynman diagrams', 'iterated integrals', 'feynman graphs', 'feynman diagram', 'integrals can']","['Yangian Bootstrap for Massive Feynman Integrals   We extend the study of the recently discovered Yangian symmetry of massive\nFeynman integrals and its relation to massive momentum space conformal\nsymmetry. After proving the symmetry statements in detail at one and two loop\norders, we employ the conformal and Yangian constraints to bootstrap various\none-loop examples of massive Feynman integrals. In particular, we explore the\ninterplay between Yangian symmetry and hypergeometric expressions of the\nconsidered integrals. Based on these examples we conjecture single series\nrepresentations for all dual conformal one-loop integrals in D spacetime\ndimensions with generic massive propagators.\n', 'On $\\varepsilon$-factorised bases and pure Feynman integrals   We investigate $\\varepsilon$-factorised differential equations, uniform\ntranscendental weight and purity for Feynman integrals. We are in particular\ninterested in Feynman integrals beyond the ones which evaluate to multiple\npolylogarithms. We show that a $\\varepsilon$-factorised differential equation\ndoes not necessarily lead to Feynman integrals of uniform transcendental\nweight. We also point out that a proposed definition of purity works locally,\nbut not globally.\n', 'Taming Calabi-Yau Feynman integrals: The four-loop equal-mass banana\n  integral   Certain Feynman integrals are associated to Calabi-Yau geometries. We\ndemonstrate how these integrals can be computed with the method of differential\nequations. The four-loop equal-mass banana integral is the simplest Feynman\nintegral whose geometry is a non-trivial Calabi-Yau manifold. We show that its\ndifferential equation can be cast into an $\\varepsilon$-factorised form. This\nallows us to obtain the solution to any desired order in the dimensional\nregularisation parameter $\\varepsilon$. The method generalises to other\nCalabi-Yau Feynman integrals. Our calculation also shows that the four-loop\nbanana integral is only minimally more complicated than the corresponding\nFeynman integrals at two or three loops.\n']","[('feynman integrals', 0.7403555512428284), ('feynman integral', 0.6683647036552429), ('mellin barnes integrals', 0.5219870805740356), ('barnes integrals', 0.4940842390060425), ('feynman', 0.4880666434764862), ('feynman diagrams', 0.45908239483833313), ('iterated integrals', 0.4505249559879303), ('feynman graphs', 0.4475223124027252), ('feynman diagram', 0.42262721061706543), ('integrals can', 0.3868654668331146)]"
226,226,125,226_cosmological models_cosmologies_cosmology_cosmological,"['cosmological models', 'cosmologies', 'cosmology', 'cosmological', 'cosmological constant', 'spacetimes', 'spacetime', 'generalized scalar', 'global dynamics', 'friedmann lema']","[""Global dynamics in Einstein-Gauss-Bonnet scalar field cosmology with\n  matter   We study the dynamics of the field equations in a four-dimensional isotropic\nand homogeneous spatially flat Friedmann--Lema\\^{\\i}tre--Robertson--Walker\ngeometry in the context of Einstein-Gauss-Bonnet theory with a matter source\nand a scalar field coupled to the Gauss-Bonnet scalar. In this theory, the\nGauss-Bonnet term contributes to the field equations. The mass of the scalar\nfield depends on the potential function and the Gauss-Bonnet term. For the\nscalar field potential, we consider the exponential function and the coupling\nfunction between the scalar field and the Gauss-Bonnet scalar is considered to\nbe the linear function. Moreover, the scalar field can have a phantom\nbehaviour. We consider a set of dimensionless variables and write the field\nequations into a system or algebraic-differential equations. For the latter, we\ninvestigate the equilibrium points and their stability properties. In order to\nperform a global analysis of the asymptotic dynamics, we use compactified\nvariables. This gravitational theory can explain the Universe's recent and past\nacceleration phases. Therefore, it can be used as a toy model for studying\ninflation or as a dark energy candidate.\n"", ""Dynamical system analysis in multiscalar-torsion cosmology   We explore the phase-space of a multiscalar-torsion gravitational theory\nwithin a cosmological framework characterized by a spatially flat\nFriedmann-Lema\\^{\\i}tre-Robertson-Walker model. Our investigation focuses on\nteleparallelism and involves a gravitational model featuring two scalar fields,\nwhere one scalar field is coupled to the torsion scalar. We consider coupling\nin the two scalar fields' kinetic and potential components. We employ\nexponential functions for the scalar field potentials and analyze the field\nequations' equilibrium points to reconstruct the cosmological evolution.\nRemarkably, we discover many equilibrium points in this multiscalar field\nmodel, capable of describing various eras of cosmological evolution. Hence,\nthis model can be used to describe the early and late time acceleration phases\nof the universe and as a unification model for the elements of the dark sector\nof the universe.\n"", 'Averaging Generalized Scalar Field Cosmologies I: Locally Rotationally\n  Symmetric Bianchi III and open Friedmann-Lema\\^itre-Robertson-Walker models   Scalar field cosmologies with a generalized harmonic potential and a matter\nfluid with a barotropic Equation of State (EoS) with barotropic index $\\gamma$\nfor Locally Rotationally Symmetric (LRS) Bianchi III metric and open\nFriedmann-Lema\\^itre-Robertson-Walker (FLRW) metric are investigated. Methods\nfrom the theory of averaging of nonlinear dynamical systems are used to prove\nthat time-dependent systems and their corresponding time-averaged versions have\nthe same late-time dynamics. Therefore, simple time-averaged systems determine\nthe future asymptotic behavior. Depending on values of barotropic index\n$\\gamma$ late-time attractors of physical interests for LRS Bianchi III metric\nare Bianchi III flat spacetime, matter dominated FLRW universe (mimicking de\nSitter, quintessence or zero acceleration solutions) and matter-curvature\nscaling solution. For open FLRW metric late-time attractors are a matter\ndominated FLRW universe and Milne solution. With this approach, oscillations\nentering nonlinear system through Klein-Gordon (KG) equation can be controlled\nand smoothed out as the Hubble factor $H$ - acting as a time-dependent\nperturbation parameter - tends monotonically to zero. Numerical simulations are\npresented as evidence of such behaviour.\n']","[('cosmological models', 0.6457900404930115), ('cosmologies', 0.5900131464004517), ('cosmology', 0.5771521329879761), ('cosmological', 0.5542184710502625), ('cosmological constant', 0.5383117198944092), ('spacetimes', 0.41688090562820435), ('spacetime', 0.4100401699542999), ('generalized scalar', 0.4018734395503998), ('global dynamics', 0.38388553261756897), ('friedmann lema', 0.3836749792098999)]"
227,227,124,227_finite posets_boolean lattices_finite poset_boolean lattice,"['finite posets', 'boolean lattices', 'finite poset', 'boolean lattice', 'ramsey number', 'lattices', 'two posets', 'lattice', 'fixed poset', 'posets poset']","['Poset Ramsey number $R(P,Q_n)$. III. Chain Compositions and Antichains   An induced subposet $(P_2,\\le_2)$ of a poset $(P_1,\\le_1)$ is a subset of\n$P_1$ such that for every two $X,Y\\in P_2$, $X\\le_2 Y$ if and only if $X\\le_1\nY$. The Boolean lattice $Q_n$ of dimension $n$ is the poset consisting of all\nsubsets of $\\{1,\\dots,n\\}$ ordered by inclusion. Given two posets $P_1$ and\n$P_2$ the poset Ramsey number $R(P_1,P_2)$ is the smallest integer $N$ such\nthat in any blue/red coloring of the elements of $Q_N$ there is either a\nmonochromatically blue induced subposet isomorphic to $P_1$ or a\nmonochromatically red induced subposet isomorphic to $P_2$.\n  We provide upper bounds on $R(P,Q_n)$ for two classes of $P$: parallel\ncompositions of chains, i.e.\\ posets consisting of disjoint chains which are\npairwise element-wise incomparable, as well as subdivided $Q_2$, which are\nposets obtained from two parallel chains by adding a common minimal and a\ncommon maximal element. This completes the determination of $R(P,Q_n)$ for\nposets $P$ with at most $4$ elements. If $P$ is an antichain $A_t$ on $t$\nelements, we show that $R(A_t,Q_n)=n+3$ for $3\\le t\\le \\log \\log n$.\nAdditionally, we briefly survey proof techniques in the poset Ramsey setting\n$P$ versus $Q_n$.\n', 'Erd\\H{o}s-Hajnal problems for posets   We say that a poset $(Q,\\le_{Q})$ contains an induced copy of a poset\n$(P,\\le_P)$ if there is an injective function $\\phi\\colon P\\to Q$ such that for\nevery two $X,Y\\in P$,\\;\\;$X\\le_P Y$ if and only if $\\phi(X)\\le_Q \\phi(Y)$. We\ndenote the Boolean lattice $(2^{[n]},\\subseteq)$ by $Q_n$. Given a fixed\n$2$-coloring $c$ of a poset $P$, the poset Erd\\H{o}s-Hajnal number of this\ncolored poset is the smallest integer $N$ such that every $2$-coloring of the\nBoolean lattice $Q_N$ contains an induced copy of $P$ colored as in $c$, or a\nmonochromatic induced copy of $Q_n$. We present bounds on the poset\nErd\\H{o}s-Hajnal number of general colored posets, antichains, chains, and\nsmall Boolean lattices. Let the poset Ramsey number $R(Q_n,Q_n)$ be the least\n$N$ such that every $2$-coloring of $Q_N$ contains a monochromatic induced copy\nof $Q_n$. As a corollary, we show that $R(Q_n,Q_n)> 2.02n$, improving on the\nbest known lower bound $2n+1$ by Cox and Stolee \\cite{CS}.\n', ""Poset Ramsey numbers: large Boolean lattice versus a fixed poset   Given partially ordered sets (posets) $(P, \\leq_P)$ and $(P', \\leq_{P'})$, we\nsay that $P'$ contains a copy of $P$ if for some injective function $f:\nP\\rightarrow P'$ and for any $X, Y\\in P$, $X\\leq _P Y$ if and only of\n$f(X)\\leq_{P'} f(Y)$. For any posets $P$ and $Q$, the poset Ramsey number\n$R(P,Q)$ is the least positive integer $N$ such that no matter how the elements\nof an $N$-dimensional Boolean lattice are colored in blue and red, there is\neither a copy of $P$ with all blue elements or a copy of $Q$ with all red\nelements. We focus on a poset Ramsey number $R(P, Q_n)$ for a fixed poset $P$\nand an $n$-dimensional Boolean lattice $Q_n$, as $n$ grows large. We show a\nsharp jump in behaviour of this number as a function of $n$ depending on\nwhether or not $P$ contains a copy of either a poset $V$, i.e. a poset on\nelements $A, B, C$ such that $B>C$, $A>C$, and $A$ and $B$ incomparable, or a\nposet $\\Lambda$, its symmetric counterpart. Specifically, we prove that if $P$\ncontains a copy of $V$ or $\\Lambda$ then $R(P, Q_n) \\geq n +\\frac{1}{15}\n\\frac{n}{\\log n}$. Otherwise $R(P, Q_n) \\leq n + c(P)$ for a constant $c(P)$.\nThis gives the first non-marginal improvement of a lower bound on poset Ramsey\nnumbers and as a consequence gives $R(Q_2, Q_n) = n + \\Theta (\\frac{n}{\\log\nn})$.\n""]","[('finite posets', 0.5902584791183472), ('boolean lattices', 0.5295491814613342), ('finite poset', 0.5266969799995422), ('boolean lattice', 0.5074249505996704), ('ramsey number', 0.47793805599212646), ('lattices', 0.44697749614715576), ('two posets', 0.43520626425743103), ('lattice', 0.4315113425254822), ('fixed poset', 0.4097329378128052), ('posets poset', 0.39669737219810486)]"
228,228,123,228_diophantine approximations_simultaneous diophantine approximation_diophantine approximation_multiplicative diophantine approximation,"['diophantine approximations', 'simultaneous diophantine approximation', 'diophantine approximation', 'multiplicative diophantine approximation', 'approximation points', 'diophantine properties', 'approximations', 'approximation systems', 'duffin schaeffer conjecture', 'theory diophantine']","[""Independence inheritance and Diophantine approximation for systems of\n  linear forms   The classical Khintchine-Groshev theorem is a generalization of Khintchine's\ntheorem on simultaneous Diophantine approximation, from approximation of points\nin $\\mathbb R^m$ to approximation of systems of linear forms in $\\mathbb\nR^{nm}$. In this paper, we present an inhomogeneous version of the\nKhintchine-Groshev theorem which does not carry a monotonicity assumption when\n$nm>2$. Our results bring the inhomogeneous theory almost in line with the\nhomogeneous theory, where it is known by a result of Beresnevich and Velani\n(2010) that monotonicity is not required when $nm>1$. That result resolved a\nconjecture of Beresnevich, Bernik, Dodson, and Velani (2009), and our work\nresolves almost every case of the natural inhomogeneous generalization of that\nconjecture. Regarding the two cases where $nm=2$, we are able to remove\nmonotonicity by assuming extra divergence of a measure sum, akin to a linear\nforms version of the Duffin-Schaeffer conjecture. When $nm=1$ it is known by\nwork of Duffin and Schaeffer (1941) that the monotonicity assumption cannot be\ndropped.\n  The key new result is an independence inheritance phenomenon; the underlying\nidea is that the sets involved in the $((n+k)\\times m)$-dimensional\nKhintchine-Groshev theorem ($k\\geq 0$) are always $k$-levels more\nprobabilistically independent than the sets involved the $(n\\times\nm)$-dimensional theorem. Hence, it is shown that Khintchine's theorem itself\nunderpins the Khintchine-Groshev theory.\n"", 'Geometry of Diophantine exponents   Diophantine exponents are ones of the simplest quantitative characteristics\nresponsible for the approximation properties of linear subspaces of a Euclidean\nspace. This survey is aimed at describing the current state of the area of\nDiophantine approximation which studies Diophantine exponents and relations\nthey satisfy. We discuss classical Diophantine exponents arising in the problem\nof approximating zero with the set of the values of several linear forms at\ninteger points, their analogues in Diophantine approximation with weights,\nmultiplicative Diophantine exponents, and Diophantine exponents of lattices. We\npay special attention to the transference principle.\n', ""Littlewood and Duffin--Schaeffer-type problems in diophantine\n  approximation   Gallagher's theorem describes the multiplicative diophantine approximation\nrate of a typical vector. We establish a fully-inhomogeneous version of\nGallagher's theorem, a diophantine fibre refinement, and a sharp and unexpected\nthreshold for Liouville fibres. Along the way, we prove an inhomogeneous\nversion of the Duffin--Schaeffer conjecture for a class of non-monotonic\napproximation functions.\n""]","[('diophantine approximations', 0.6262028813362122), ('simultaneous diophantine approximation', 0.597880482673645), ('diophantine approximation', 0.578723132610321), ('multiplicative diophantine approximation', 0.5503103137016296), ('approximation points', 0.45639529824256897), ('diophantine properties', 0.4476146101951599), ('approximations', 0.44029951095581055), ('approximation systems', 0.4380536377429962), ('duffin schaeffer conjecture', 0.4339927136898041), ('theory diophantine', 0.431474894285202)]"
229,229,122,229_theory operads_symmetric operad_operads_koszul dual,"['theory operads', 'symmetric operad', 'operads', 'koszul dual', 'algebra operad', 'operadic', 'koszul duality', 'operad mathcal', 'operad', 'colored operads']","['Koszul duality for operadic categories   The aim of this sequel to arXiv:1812.02935 is to set up the cornerstones of\nKoszul duality and Koszulity in the context of operads over a large class of\noperadic categories. In particular, for these operadic categories we will study\nconcrete examples of binary quadratic operads, describe their Koszul duals and\nprove that they are Koszul. This includes operads whose algebras are the most\nimportant operad- and PROP-like structures such as the classical operads, their\nvariants such as cyclic, modular or wheeled operads, and also diverse versions\nof PROPs such as properads, dioperads, 1/2PROPs, and still more exotic objects\nsuch as permutads and pre-permutads.\n', 'Cliff operads: a hierarchy of operads on words   A new hierarchy of operads over the linear spans of $\\delta$-cliffs, which\nare some words of integers, is introduced. These operads are intended to be\nanalogues of the operad of permutations, also known as the associative\nsymmetric operad. We obtain operads whose partial compositions can be described\nin terms of intervals of the lattice of $\\delta$-cliffs. These operads are very\npeculiar in the world of the combinatorial operads since, despite to the\nrelative simplicity for their construction, they are infinitely generated and\nthey have nonquadratic and nonhomogeneous nontrivial relations. We provide a\ngeneral construction for some of their quotients. We use it to endow the spaces\nof permutations, $m$-increasing trees, $c$-rectangular paths, and $m$-Dyck\npaths with operad structures. The operads on $c$-rectangular paths admit, as\nKoszul duals, operads generalizing the duplicial and triplicial operads.\n', 'Operads on graphs: extending the pre-Lie operad and general construction   The overall aim of this paper is to define a structure of graph operads, thus\ngeneralizing the celebrated pre-Lie operad on rooted trees. More precisely, we\ndefine two operads on multigraphs, and exhibit a non trivial link between them\nand the pre-Lie and Kontsevich- Willwacher operads. We study one of these\noperads in more detail. While its structure is too involved to exhibit a\ndescription by generators and relations, we show that it has interesting\nfinitely generated sub-operads, with links with the commutative and the\nmagmatic commutative operads. In particular, one of them is Koszul and this\nallows us to compute its Koszul dual. Finally, we introduce a new framework on\nspecies and operads and a general way to define operads on multigraphs.\n']","[('theory operads', 0.668623685836792), ('symmetric operad', 0.6179003119468689), ('operads', 0.5704854726791382), ('koszul dual', 0.5642994046211243), ('algebra operad', 0.5589103102684021), ('operadic', 0.5419183373451233), ('koszul duality', 0.5412489175796509), ('operad mathcal', 0.5288982391357422), ('operad', 0.48933860659599304), ('colored operads', 0.468279093503952)]"
230,230,121,230_adversarial training_adversarial robustness_adversarial attack_adversarial learning,"['adversarial training', 'adversarial robustness', 'adversarial attack', 'adversarial learning', 'adversarial perturbations', 'robustness adversarial', 'adversarially robust', 'adversarial', 'adversarial perturbation', 'models adversarial']","['On the existence of solutions to adversarial training in multiclass\n  classification   We study three models of the problem of adversarial training in multiclass\nclassification designed to construct robust classifiers against adversarial\nperturbations of data in the agnostic-classifier setting. We prove the\nexistence of Borel measurable robust classifiers in each model and provide a\nunified perspective of the adversarial training problem, expanding the\nconnections with optimal transport initiated by the authors in previous work\nand developing new connections between adversarial training in the multiclass\nsetting and total variation regularization. As a corollary of our results, we\nprove the existence of Borel measurable solutions to the agnostic adversarial\ntraining problem in the binary classification setting, a result that improves\nresults in the literature of adversarial training, where robust classifiers\nwere only known to exist within the enlarged universal $\\sigma$-algebra of the\nfeature space.\n', 'Asymptotic Behavior of Adversarial Training Estimator under\n  $\\ell_\\infty$-Perturbation   Adversarial training has been proposed to protect machine learning models\nagainst adversarial attacks. This paper focuses on adversarial training under\n$\\ell_\\infty$-perturbation, which has recently attracted much research\nattention. The asymptotic behavior of the adversarial training estimator is\ninvestigated in the generalized linear model. The results imply that the\nasymptotic distribution of the adversarial training estimator under\n$\\ell_\\infty$-perturbation could put a positive probability mass at $0$ when\nthe true parameter is $0$, providing a theoretical guarantee of the associated\nsparsity-recovery ability. Alternatively, a two-step procedure is proposed --\nadaptive adversarial training, which could further improve the performance of\nadversarial training under $\\ell_\\infty$-perturbation. Specifically, the\nproposed procedure could achieve asymptotic variable-selection consistency and\nunbiasedness. Numerical experiments are conducted to show the sparsity-recovery\nability of adversarial training under $\\ell_\\infty$-perturbation and to compare\nthe empirical performance between classic adversarial training and adaptive\nadversarial training.\n', 'Asymptotic Behavior of Adversarial Training in Binary Classification   It has been consistently reported that many machine learning models are\nsusceptible to adversarial attacks i.e., small additive adversarial\nperturbations applied to data points can cause misclassification. Adversarial\ntraining using empirical risk minimization is considered to be the\nstate-of-the-art method for defense against adversarial attacks. Despite being\nsuccessful in practice, several problems in understanding generalization\nperformance of adversarial training remain open. In this paper, we derive\nprecise theoretical predictions for the performance of adversarial training in\nbinary classification. We consider the high-dimensional regime where the\ndimension of data grows with the size of the training data-set at a constant\nratio. Our results provide exact asymptotics for standard and adversarial test\nerrors of the estimators obtained by adversarial training with $\\ell_q$-norm\nbounded perturbations ($q \\ge 1$) for both discriminative binary models and\ngenerative Gaussian-mixture models with correlated features. Furthermore, we\nuse these sharp predictions to uncover several intriguing observations on the\nrole of various parameters including the over-parameterization ratio, the data\nmodel, and the attack budget on the adversarial and standard errors.\n']","[('adversarial training', 0.7706649899482727), ('adversarial robustness', 0.7449741959571838), ('adversarial attack', 0.7358807921409607), ('adversarial learning', 0.7340698838233948), ('adversarial perturbations', 0.7311572432518005), ('robustness adversarial', 0.7292900085449219), ('adversarially robust', 0.7230783700942993), ('adversarial', 0.722339928150177), ('adversarial perturbation', 0.7183722257614136), ('models adversarial', 0.7179685831069946)]"
231,231,120,231_symplectic integrators_preserving integrators_explicit symplectic_numerical integrators,"['symplectic integrators', 'preserving integrators', 'explicit symplectic', 'numerical integrators', 'integrators based', 'symplectic geometric', 'integrators', 'construct symplectic', 'symplecticity', 'symplectic']","[""Variational integrators for non-autonomous systems with applications to\n  stabilization of multi-agent formations   Numerical methods that preserve geometric invariants of the system, such as\nenergy, momentum or the symplectic form, are called geometric integrators.\nVariational integrators are an important class of geometric integrators. The\ngeneral idea for those variational integrators is to discretize Hamilton's\nprinciple rather than the equations of motion in a way that preserves some of\nthe invariants of the original system. In this paper we construct variational\nintegrators with fixed time step for time-dependent Lagrangian systems\nmodelling an important class of autonomous dissipative systems. These\nintegrators are derived via a family of discrete Lagrangian functions each one\nfor a fixed time-step. This allows to recover at each step on the set of\ndiscrete sequences the preservation properties of variational integrators for\nautonomous Lagrangian systems, such as symplecticity or backward error analysis\nfor these systems. We also present a discrete Noether theorem for this class of\nsystems. Applications of the results are shown for the problem of formation\nstabilization of multi-agent systems.\n"", 'The existence of explicit symplectic integrators for general\n  nonseparable Hamiltonian systems   The existence of explicit symplectic integrators for general nonseparable\nHamiltonian systems is an open and important problem in both numerical analysis\nand computing in science and engineering, as explicit integrators are usually\nmore efficient than the implicit integrators of the same order of accuracy. Up\nto now, all responses to this problem are negative. That is, there exist\nexplicit symplectic integrators only for some special nonseparable Hamiltonian\nsystems, whereas the universal design involving explicit symplectic integrators\nfor general nonseparable Hamiltonian systems has not yet been studied\nsufficiently. In this paper, we present a constructive proof for the existence\nof explicit symplectic integrators for general nonseparable Hamiltonian systems\nvia finding explicit symplectic mappings under which the special submanifold of\nthe extended phase space is invariant. It turns out that the proposed explicit\nintegrators are symplectic in both the extended phase space and the original\nphase space. Moreover, on the basis of the global modified Hamiltonians of the\nproposed integrators, the backward error analysis is made via a parameter\nrelaxation and restriction technique to show the linear growth of global errors\nand the near-preservation of first integrals. In particular, the effective\nestimated time interval is nearly the same as classical implicit symplectic\nintegrators when applied to (near-) integrable Hamiltonian systems. Numerical\nexperiments with a completely integrable nonseparable Hamiltonian and a\nnonintegrable nonseparable Hamiltonian illustrate the good long-term behavior\nand high efficiency of the explicit symplectic integrators proposed and\nanalyzed in this paper.\n', ""Adaptive Hamiltonian Variational Integrators and Symplectic Accelerated\n  Optimization   It is well known that symplectic integrators lose their near energy\npreservation properties when variable step sizes are used. The most common\napproach to combine adaptive step sizes and symplectic integrators involves the\nPoincar\\'e transformation of the original Hamiltonian. In this article, we\nprovide a framework for the construction of variational integrators using the\nPoincar\\'e transformation. Since the transformed Hamiltonian is typically\ndegenerate, the use of Hamiltonian variational integrators based on Type II or\nType III generating functions is required instead of the more traditional\nLagrangian variational integrators based on Type I generating functions. Error\nanalysis is provided and numerical tests based on the Taylor variational\nintegrator approach of Schmitt, Shingel, Leok (2018) to time-adaptive\nvariational integration of Kepler's 2-Body problem are presented. Finally, we\nuse our adaptive framework together with the variational approach to\naccelerated optimization presented in Wibisono, Wilson, Jordan (2016) to design\nefficient variational and non-variational explicit integrators for symplectic\naccelerated optimization.\n""]","[('symplectic integrators', 0.7407421469688416), ('preserving integrators', 0.6379668712615967), ('explicit symplectic', 0.6196940541267395), ('numerical integrators', 0.6090173721313477), ('integrators based', 0.5934515595436096), ('symplectic geometric', 0.5702683329582214), ('integrators', 0.5688220262527466), ('construct symplectic', 0.5579388737678528), ('symplecticity', 0.5496183037757874), ('symplectic', 0.5482276082038879)]"
232,232,120,232_group testing_testing algorithms_testing group_testing,"['group testing', 'testing algorithms', 'testing group', 'testing', 'tests', 'tests can', 'testing can', 'screening', 'test results', 'test']","['Efficient pooling designs and screening performance in group testing for\n  two type defectives   Group testing is utilized in the case when we want to find a few defectives\namong large amount of items. Testing n items one by one requires n tests, but\nif the ratio of defectives is small, group testing is an efficient way to\nreduce the number of tests. Many research have been developed for group testing\nfor a single type of defectives. In this paper, we consider the case where two\ntypes of defective A and B exist. For two types of defectives, we develop a\nbelief propagation algorithm to compute marginal posterior probability of\ndefectives. Furthermore, we construct several kinds of collections of pools in\norder to test for A and B. And by utilizing our belief propagation algorithm,\nwe evaluate the performance of group testing by conducting simulations.\n', 'Improved non-adaptive algorithms for threshold group testing with a gap   The basic goal of threshold group testing is to identify up to $d$ defective\nitems among a population of $n$ items, where $d$ is usually much smaller than\n$n$. The outcome of a test on a subset of items is positive if the subset has\nat least $u$ defective items, negative if it has up to $\\ell$ defective items,\nwhere $0\\leq\\ell<u$, and arbitrary otherwise. This is called threshold group\ntesting. The parameter $g=u-\\ell-1$ is called \\textit{the gap}. In this paper,\nwe focus on the case $g>0$, i.e., threshold group testing with a gap. Note that\nthe results presented here are also applicable to the case $g = 0$; however,\nthe results are not as efficient as those in related work. Currently, a few\nreported studies have investigated test designs and decoding algorithms for\nidentifying defective items. Most of the previous studies have not been\nfeasible because there are numerous constraints on their problem settings or\nthe decoding complexities of their proposed schemes are relatively large.\nTherefore, it is compulsory to reduce the number of tests as well as the\ndecoding complexity, i.e., the time for identifying the defective items, for\nachieving practical schemes.\n  The work presented here makes five contributions. The first is a more\naccurate theorem for a non-adaptive algorithm for threshold group testing\nproposed by Chen and Fu. The second is an improvement in the construction of\ndisjunct matrices, which are the main tools for tackling (threshold) group\ntesting and other tasks such as constructing cover-free families or learning\nhidden graphs. The third and fourth contributions are a reduced exact upper\nbound on the number of tests and a reduced asymptotic bound on the decoding\ntime for identifying defective items in a noisy setting on test outcomes. The\nfifth contribution is a simulation on the number of tests of the resulting\nimprovements for previous work and the proposed theorems.\n', 'Noisy Group Testing with Side Information   Group testing has recently attracted significant attention from the research\ncommunity due to its applications in diagnostic virology. An instance of the\ngroup testing problem includes a ground set of individuals which includes a\nsmall subset of infected individuals. The group testing procedure consists of a\nnumber of tests, such that each test indicates whether or not a given subset of\nindividuals includes one or more infected individuals. The goal of the group\ntesting procedure is to identify the subset of infected individuals with the\nminimum number of tests. Motivated by practical scenarios, such as testing for\nviral diseases, this paper focuses on the following group testing settings: (i)\nthe group testing procedure is noisy, i.e., the outcome of the group testing\nprocedure can be flipped with a certain probability; (ii) there is a certain\namount of side information on the distribution of the infected individuals\navailable to the group testing algorithm. The paper makes the following\ncontributions. First, we propose a probabilistic model, referred to as an\ninteraction model, that captures the side information about the probability\ndistribution of the infected individuals. Next, we present a decoding scheme,\nbased on the belief propagation, that leverages the interaction model to\nimprove the decoding accuracy. Our results indicate that the proposed algorithm\nachieves higher success probability and lower false-negative and false-positive\nrates when compared to the traditional belief propagation especially in the\nhigh noise regime.\n']","[('group testing', 0.6833682656288147), ('testing algorithms', 0.6146312355995178), ('testing group', 0.6007912158966064), ('testing', 0.46701154112815857), ('tests', 0.44760212302207947), ('tests can', 0.4161634147167206), ('testing can', 0.40549060702323914), ('screening', 0.39370203018188477), ('test results', 0.3800652325153351), ('test', 0.37797024846076965)]"
233,233,120,233_supersolvable groups_sylow subgroups_soluble groups_maximal groups,"['supersolvable groups', 'sylow subgroups', 'soluble groups', 'maximal groups', 'subgroups prime', 'sylow subgroup', 'maximal subgroups', 'group maximal', 'subgroups finite groups', 'every maximal subgroup']","['Finite groups with some subgroups of prime power order satisfying the\n  partial $ \\Pi $-property   Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies\nthe partial $ \\Pi $-property in $ G $ if there exists a $G$-chief series $\n\\varGamma_{G}: 1 =G_{0} < G_{1} < \\cdot\\cdot\\cdot < G_{n}= G $ of $ G $ such\nthat $ | G / G_{i-1} : N_{G/G_{i-1}} (HG_{i-1}/G_{i-1}\\cap G_{i}/G_{i-1})| $ is\na $ \\pi (HG_{i-1}/G_{i-1}\\cap G_{i}/G_{i-1}) $-number for every $ G $-chief\nfactor $ G_{i}/G_{i-1} $ of $ \\varGamma_{G} $, $1\\leq i\\leq n$. In this paper,\nwe investigate the structure of a finite group $ G $ under the assumption that\nsome subgroups of prime power order satisfy the partial $ \\Pi $-property.\n', 'On the partial $ \\Pi $-property of some subgroups of prime power order\n  of finite groups   Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies\nthe partial $ \\Pi $-property in $ G $ if if there exists a chief series $\n\\varGamma_{G}: 1 =G_{0} < G_{1} < \\cdot\\cdot\\cdot < G_{n}= G $ of $ G $ such\nthat for every $ G $-chief factor $ G_{i}/G_{i-1} (1\\leq i\\leq n) $ of $\n\\varGamma_{G} $, $ | G / G_{i-1} : N_{G/G_{i-1}} (HG_{i-1}/G_{i-1}\\cap\nG_{i}/G_{i-1})| $ is a $ \\pi (HG_{i-1}/G_{i-1}\\cap G_{i}/G_{i-1}) $-number. In\nthis paper, we study the influence of some subgroups of prime power order\nsatisfying the partial $ \\Pi $-property on the structure of a finite group.\n', 'On the partial $\\Pi$-property of second minimal or second maximal\n  subgroups of Sylow subgroups of finite groups   Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies\nthe partial $ \\Pi $-property in $ G $ if if there exists a chief series $\n\\varGamma_{G}: 1 =G_{0} < G_{1} < \\cdot\\cdot\\cdot < G_{n}= G $ of $ G $ such\nthat for every $ G $-chief factor $ G_{i}/G_{i-1} $ $ (1\\leq i\\leq n) $ of $\n\\varGamma_{G} $, $ | G / G_{i-1} : N_{G/G_{i-1}} (HG_{i-1}/G_{i-1}\\cap\nG_{i}/G_{i-1})| $ is a $ \\pi (HG_{i-1}/G_{i-1}\\cap G_{i}/G_{i-1}) $-number. In\nthis paper, we study the influence of some second minimal or second maximal\nsubgroups of a Sylow subgroup satisfying the partial $ \\Pi $-property on the\nstructure of a finite group.\n']","[('supersolvable groups', 0.5386922359466553), ('sylow subgroups', 0.536287784576416), ('soluble groups', 0.5306892395019531), ('maximal groups', 0.5230377912521362), ('subgroups prime', 0.515872597694397), ('sylow subgroup', 0.5152130126953125), ('maximal subgroups', 0.5071394443511963), ('group maximal', 0.49213021993637085), ('subgroups finite groups', 0.49095532298088074), ('every maximal subgroup', 0.4833085536956787)]"
234,234,119,234_zero divisor graphs_zero divisor graph_divisor graphs_divisor graph,"['zero divisor graphs', 'zero divisor graph', 'divisor graphs', 'divisor graph', 'zero divisors', 'zero divisor', 'divisors', 'finite rings', 'artinian rings', 'graphs finite']","['Induced subgraphs of zero-divisor graphs   The zero-divisor graph of a finite commutative ring with unity is the graph\nwhose vertex set is the set of zero-divisors in the ring, with $a$ and $b$\nadjacent if $ab=0$. We show that the class of zero-divisor graphs is universal,\nin the sense that every finite graph is isomorphic to an induced subgraph of a\nzero-divisor graph. This remains true for various restricted classes of rings,\nincluding boolean rings, products of fields, and local rings. But in more\nrestricted classes, the zero-divisor graphs do not form a universal family. For\nexample, the zero-divisor graph of a local ring whose maximal ideal is\nprincipal is a threshold graph; and every threshold graph is embeddable in the\nzero-divisor graph of such a ring. More generally, we give necessary and\nsufficient conditions on a non-local ring for which its zero-divisor graph to\nbe a threshold graph. In addition, we show that there is a countable local ring\nwhose zero-divisor graph embeds the Rado graph, and hence every finite or\ncountable graph, as induced subgraph. Finally, we consider embeddings in\nrelated graphs such as the $2$-dimensional dot product graph.\n', 'Laplacian spectrum of weakly zero-divisor graph of the ring\n  $\\mathbb{Z}_{n}$   Let $R$ be a commutative ring with unity. The weakly zero-divisor graph\n$W\\Gamma(R)$ of the ring $R$ is the simple undirected graph whose vertices are\nnonzero zero-divisors of $R$ and two vertices $x$, $y$ are adjacent if and only\nif there exists $r\\in {\\rm ann}(x)$ and $s \\in {\\rm ann}(y)$ such that $rs =0$.\nThe zero-divisor graph of a ring is a spanning subgraph of the weakly\nzero-divisor graph. It is known that the zero-divisor graph of the ring\n$\\mathbb{Z}_{{p^t}}$, where $p$ is a prime, is the Laplacian integral. In this\npaper, we obtain the Laplacian spectrum of the weakly zero-divisor graph\n$W\\Gamma(\\mathbb{Z}_{n})$ of the ring $\\mathbb{Z}_{n}$ and show that\n$W\\Gamma(\\mathbb{Z}_{n})$ is Laplacian integral for arbitrary $n$.\n', 'The characteristic equation and Wiener index of a compressed zero\n  divisor graph   The Zero divisor Graph of a commutative ring $R$, denoted by $\\Gamma[R]$, is\na graph whose vertices are non-zero zero divisors of R and two vertices are\nadjacent if their product is zero. The compressed zero divisor graph\n$\\Gamma_E[R]$ is the (undirected) graph whose vertices are the equivalence\nclasses such that distinct vertices [r] and [s] are adjacent if and only if rs\n= 0. In this paper we derive the characteristic polynomial and Wiener index of\nthe Compressed zero divisor graph $\\Gamma_{E}[\\mathbb{Z}_m]$ where $m=p^n$ with\nprime $p$.\n']","[('zero divisor graphs', 0.7219559550285339), ('zero divisor graph', 0.6612548232078552), ('divisor graphs', 0.6396285891532898), ('divisor graph', 0.5746139883995056), ('zero divisors', 0.5641082525253296), ('zero divisor', 0.5036260485649109), ('divisors', 0.45058122277259827), ('finite rings', 0.4177694022655487), ('artinian rings', 0.4163259267807007), ('graphs finite', 0.4075069725513458)]"
235,235,118,235_rigid graphs_graphs rigid_global rigidity_globally rigid,"['rigid graphs', 'graphs rigid', 'global rigidity', 'globally rigid', 'combinatorial rigidity', 'locally rigid', 'rigidity theory', 'infinitesimal rigidity', 'infinitesimally rigid', 'rigidity']","['Characterizing Generic Global Rigidity   A d-dimensional framework is a graph and a map from its vertices to E^d. Such\na framework is globally rigid if it is the only framework in E^d with the same\ngraph and edge lengths, up to rigid motions. For which underlying graphs is a\ngeneric framework globally rigid? We answer this question by proving a\nconjecture by Connelly, that his sufficient condition is also necessary: a\ngeneric framework is globally rigid if and only if it has a stress matrix with\nkernel of dimension d+1, the minimum possible.\n  An alternate version of the condition comes from considering the geometry of\nthe length-squared mapping l: the graph is generically locally rigid iff the\nrank of l is maximal, and it is generically globally rigid iff the rank of the\nGauss map on the image of l is maximal.\n  We also show that this condition is efficiently checkable with a randomized\nalgorithm, and prove that if a graph is not generically globally rigid then it\nis flexible one dimension higher.\n', ""Uniquely realisable graphs in polyhedral normed spaces   A framework (a straight-line embedding of a graph into a normed space\nallowing edges to cross) is globally rigid if any other framework with the same\nedge lengths with respect to the chosen norm is an isometric copy. We\ninvestigate global rigidity in polyhedral normed spaces: normed spaces where\nthe unit ball is a polytope. We first provide a deterministic algorithm for\nchecking whether or not a framework in a polyhedral normed space is globally\nrigid. After showing that determining if a framework is globally rigid is\nNP-Hard, we then provide necessary conditions for global rigidity for generic\nframeworks. We obtain stronger results for generic frameworks in\n$\\ell_\\infty^d$ (the vector space $\\mathbb{R}^d$ equipped with the\n$\\ell_\\infty$ metric) including an exact characterisation of global rigidity\nwhen $d=2$, and an easily-computable sufficient condition for global rigidity\nusing edge colourings. Our 2-dimensional characterisation also has a surprising\nconsequence: Hendrickson's global rigidity condition fails for generic\nframeworks in $\\ell_\\infty^2$.\n"", 'Minimally globally rigid graphs   A graph $G = (V,E)$ is globally rigid in $\\mathbb{R}^d$ if for any generic\nplacement $p : V \\rightarrow \\mathbb{R}^d$ of the vertices, the edge lengths\n$||p(u) - p(v)||, uv \\in E$ uniquely determine $p$, up to congruence. In this\npaper we consider minimally globally rigid graphs, in which the deletion of an\narbitrary edge destroys global rigidity. We prove that if $G=(V,E)$ is\nminimally globally rigid in $\\mathbb{R}^d$ on at least $d+2$ vertices, then\n$|E|\\leq (d+1)|V|-\\binom{d+2}{2}$. This implies that the minimum degree of $G$\nis at most $2d+1$. We also show that the only graph in which the upper bound on\nthe number of edges is attained is the complete graph $K_{d+2}$. It follows\nthat every minimally globally rigid graph in $\\mathbb{R}^d$ on at least $d+3$\nvertices is flexible in $\\mathbb{R}^{d+1}$. As a counterpart to our main result\non the sparsity of minimally globally rigid graphs, we show that in two\ndimensions, dense graphs always contain nontrivial globally rigid subgraphs.\nMore precisely, if some graph $G=(V,E)$ satisfies $|E|\\geq 5|V|$, then $G$\ncontains a subgraph on at least seven vertices that is globally rigid in\n$\\mathbb{R}^2$. If the well-known ""sufficient connectivity conjecture"" is true,\nthen our methods also extend to higher dimensions. Finally, we discuss a\nconjectured strengthening of our main result, which states that if a pair of\nvertices $\\{u,v\\}$ is linked in $G$ in $\\mathbb{R}^{d+1}$, then $\\{u,v\\}$ is\nglobally linked in $G$ in $\\mathbb{R}^d$. We prove this conjecture in the\n$d=1,2$ cases, along with a variety of related results.\n']","[('rigid graphs', 0.6816964745521545), ('graphs rigid', 0.6437137126922607), ('global rigidity', 0.6178087592124939), ('globally rigid', 0.6158517003059387), ('combinatorial rigidity', 0.5606987476348877), ('locally rigid', 0.5557151436805725), ('rigidity theory', 0.5473677515983582), ('infinitesimal rigidity', 0.531781792640686), ('infinitesimally rigid', 0.5274031758308411), ('rigidity', 0.5153154730796814)]"
236,236,118,236_wrapped fukaya category_fukaya categories_fukaya category_wrapped fukaya,"['wrapped fukaya category', 'fukaya categories', 'fukaya category', 'wrapped fukaya', 'fukaya', 'weinstein manifold', 'lefschetz fibrations', 'category symplectic', 'symplectic cohomology', 'symplectic topology']","['Recollements of partially wrapped Fukaya categories and surface cuts   In this paper we use recollements to investigate partially wrapped Fukaya\ncategories of surfaces with marked points. In particular, we show that cutting\nsurfaces gives rise to recollements of the corresponding partially wrapped\nFukaya categories. Our approach is based on the fact that the partially wrapped\nFukaya category of a surface with marked points is triangle equivalent to the\nperfect derived category of a homologically smooth and proper graded gentle\nalgebra with zero differential as shown by Haiden, Katzarkov and Kontsevich.\nUsing this, we study particular generators of partially wrapped Fukaya\ncategories, namely full exceptional sequences, silting objects and\nsimple-minded collections. In particular, we fully characterise the existence\nof full exceptional sequences and we give an example of a partially wrapped\nFukaya category which does not admit a silting object, that is a generator with\nno positive self-extensions.\n', 'Prime-localized Weinstein subdomains   For any high-dimensional Weinstein domain and finite collection of primes, we\nconstruct a Weinstein subdomain whose wrapped Fukaya category is a localization\nof the original wrapped Fukaya category away from the given primes. When the\noriginal domain is a cotangent bundle, these subdomains form a decreasing\nlattice whose order cannot be reversed.\n  Furthermore, we classify the possible wrapped Fukaya categories of Weinstein\nsubdomains of a cotangent bundle of a simply connected, spin manifold, showing\nthat they all coincide with one of these prime localizations. In the process,\nwe describe which twisted complexes in the wrapped Fukaya category of a\ncotangent bundle of a sphere are isomorphic to genuine Lagrangians.\n', 'Sectorial descent for wrapped Fukaya categories   We develop a set of tools for doing computations in and of (partially)\nwrapped Fukaya categories. In particular, we prove (1) a descent (cosheaf)\nproperty for the wrapped Fukaya category with respect to so-called Weinstein\nsectorial coverings and (2) that the partially wrapped Fukaya category of a\nWeinstein manifold with respect to a mostly Legendrian stop is generated by the\ncocores of the critical handles and the linking disks to the stop. We also\nprove (3) a `stop removal equals localization\' result, and (4) that the\nFukaya--Seidel category of a Lefschetz fibration with Liouville fiber is\ngenerated by the Lefschetz thimbles. These results are derived from three main\ningredients, also of independent use: (5) a K\\""unneth formula (6) an exact\ntriangle in the Fukaya category associated to wrapping a Lagrangian through a\nLegendrian stop at infinity and (7) a geometric criterion for when a\npushforward functor between wrapped Fukaya categories of Liouville sectors is\nfully faithful.\n']","[('wrapped fukaya category', 0.8007586002349854), ('fukaya categories', 0.7849248647689819), ('fukaya category', 0.7511608600616455), ('wrapped fukaya', 0.6805127263069153), ('fukaya', 0.580398440361023), ('weinstein manifold', 0.5370914340019226), ('lefschetz fibrations', 0.48869144916534424), ('category symplectic', 0.46650996804237366), ('symplectic cohomology', 0.39568957686424255), ('symplectic topology', 0.3822401762008667)]"
237,237,117,237_field theory tqft_theory tqft_tqft_tqfts,"['field theory tqft', 'theory tqft', 'tqft', 'tqfts', 'topological field theories', 'quantum invariants', 'topological theories', 'topological quantum field', 'quantum field theories', 'topological field theory']","['3d TQFTs and 3-manifold invariants   This is an invited contribution to the 2nd edition of the Encyclopedia of\nMathematical Physics. We give an overview of 3-dimensional topological quantum\nfield theories (TQFTs) and the corresponding quantum invariants of 3-manifolds.\nWe recall the main algebraic concepts and constructions, such as modular and\nspherical fusion categories, the Witten-Reshetikhin-Turaev and Turaev-Viro\ntheories, and the relation between these two TQFTs. We also briefly discuss\ngeneralizations of these constructions by providing a (non-exhaustive) review\nof some recent works on 3-dimensional extended TQFTs, defect TQFTs, homotopy\nQFTs, and non-semisimple TQFTs.\n', 'Alterfold Topological Quantum Field Theory   We introduce the 3-alterfold topological quantum field theory (TQFT) by\nextending the quantum invariant of 3-alterfolds. The bases of the TQFT are\nexplicitly characterized and the Levin-Wen model is naturally interpreted in\n3-alterfold TQFT bases. By naturally considering the RT TQFT and TV TQFT as\nsub-TQFTs within the 3-alterfold TQFT, we establish their equivalence. The\n3-alterfold TQFT is unitary when the input fusion category is unitary.\nAdditionally, we extend the 3-alterfold TQFT to the Morita context and\ndemonstrate that Morita equivalent fusion categories yield equivalent TV TQFTs.\nWe also provide a simple pictorial proof of complete positivity criteria for\nunitary categorization when the 3-alterfold TQFT is unitary. Expanding our\nscope to high-genus surfaces by replacing the torus, we introduce the high\ngenus topological indicators and proving the equivariance under the mapping\nclass group actions.\n', ""Internal Reshetikhin-Turaev TQFT   A 3-dimensional topological quantum field theory (TQFT) is a symmetric\nmonoidal functor from the category of 3-cobordisms to the category of vector\nspaces. Such TQFTs provide in particular numerical invariants of closed\n3-manifolds such as the Reshetikhin-Turaev invariants and representations of\nthe mapping class group of closed surfaces. In 1994, using a modular category,\nTuraev explains how to construct a TQFT. In this article, we describe a\ngeneralization of this construction starting from a ribbon category\n$\\mathcal{C}$ with coend. We present a cobordism by a special kind of tangle\nand we associate to the latter a morphism defined between tensorial products of\nthe coend as described by Lyubashenko in 1994. Composing with an\n\\emph{admissible} color and using extension of Kirby calculus on 3-cobordisms,\nthis morphism gives rise to an \\emph{internal} TQFT which takes values in the\nsymmetric monoidal subcategory of transparent objects of $\\mathcal{C}$. When\nthe category $\\mathcal{C}$ is modular, this subcategory is equivalent to the\ncategory of vector spaces. When the category $\\mathcal{C}$ is premodular and\nnormalizable with invertible dimension, our TQFT is a lift of Turaev's one\nassociated to the modularization of $\\mathcal{C}$.\n""]","[('field theory tqft', 0.6776611804962158), ('theory tqft', 0.6675843596458435), ('tqft', 0.6016784310340881), ('tqfts', 0.5927795767784119), ('topological field theories', 0.5793330669403076), ('quantum invariants', 0.5318775773048401), ('topological theories', 0.5271878838539124), ('topological quantum field', 0.5161888003349304), ('quantum field theories', 0.49912288784980774), ('topological field theory', 0.4962679445743561)]"
238,238,117,238_pt symmetric quantum_mathcal pt symmetry_hermitian theories_pt symmetry,"['pt symmetric quantum', 'mathcal pt symmetry', 'hermitian theories', 'pt symmetry', 'mathcal pt symmetric', 'non hermitian physics', 'hermitian physics', 'hermitian systems', 'non hermitian systems', 'non hermitian hamiltonians']","['Energy levels for $\\mathcal{PT}$-symmetric deformation of the Mathieu\n  equation   We propose a non-Hermitian deformation of the Mathieu equation that preserves\n$\\mathcal{PT}$ symmetry and study its spectrum and the transition from\n$\\mathcal{PT}$-unbroken to $\\mathcal{PT}$-broken phases. We show that our model\nnot only reproduces behaviors expected by the literature but also indicates the\nexistence of a richer structure for the spectrum. We also discuss the influence\nof the boundary condition and the model parameters in the exceptional line that\nmarks the $\\mathcal{PT}$ breaking.\n', 'Distinguishability Transitions in Non-Unitary Boson Sampling Dynamics   We discover novel transitions characterized by distinguishability of bosons\nin non-unitary dynamics with parity-time ($\\mathcal{PT}$) symmetry. We show\nthat $\\mathcal{PT}$ symmetry breaking, a unique transition in non-Hermitian\nopen systems, enhances regions in which bosons can be regarded as\ndistinguishable. This means that classical computers can sample the boson\ndistributions efficiently in these regions by sampling the distribution of\ndistinguishable particles. In a $\\mathcal{PT}$-symmetric phase, we find one\ndynamical transition upon which the distribution of bosons deviates from that\nof distinguishable particles, when bosons are initially put at distant sites.\nIf the system enters a $\\mathcal{PT}$-broken phase, the threshold time for the\ntransition is suddenly prolonged, since dynamics of each boson is diffusive\n(ballistic) in the $\\mathcal{PT}$-broken ($\\mathcal{PT}$-symmetric) phase.\nFurthermore, the $\\mathcal{PT}$-broken phase also exhibits a notable dynamical\ntransition on a longer time scale, at which the bosons again become\ndistinguishable. This transition, and hence the classical easiness of sampling\nbosons in long times, are true for generic postselected non-unitary quantum\ndynamics, while it is absent in unitary dynamics of isolated quantum systems.\n$\\mathcal{PT}$ symmetry breaking can also be characterized by the efficiency of\na classical algorithm based on the rank of matrices, which can (cannot)\nefficiently compute the photon distribution in the long-time regime of the\n$\\mathcal{PT}$-broken ($\\mathcal{PT}$-symmetric) phase.\n', '$\\mathcal{PT}$-Symmetry in Hartree-Fock Theory   $\\mathcal{PT}$-symmetry --- invariance with respect to combined space\nreflection $\\mathcal{P}$ and time reversal $\\mathcal{T}$ --- provides a weaker\ncondition than (Dirac) Hermiticity for ensuring a real energy spectrum of a\ngeneral non-Hermitian Hamiltonian. $\\mathcal{PT}$-symmetric Hamiltonians\ntherefore form an intermediate class between Hermitian and non-Hermitian\nHamiltonians. In this work, we derive the conditions for\n$\\mathcal{PT}$-symmetry in the context of electronic structure theory, and\nspecifically, within the Hartree-Fock (HF) approximation. We show that the HF\norbitals are symmetric with respect to the $\\mathcal{PT}$ operator \\textit{if\nand only if} the effective Fock Hamiltonian is $\\mathcal{PT}$-symmetric, and\n\\textit{vice versa}. By extension, if an optimal self-consistent solution is\ninvariant under $\\mathcal{PT}$, then its eigenvalues and corresponding HF\nenergy must be real. Moreover, we demonstrate how one can construct explicitly\n$\\mathcal{PT}$-symmetric Slater determinants by forming $\\mathcal{PT}$ doublets\n(i.e. pairing each occupied orbital with its $\\mathcal{PT}$-transformed\nanalogue), allowing $\\mathcal{PT}$-symmetry to be conserved throughout the\nself-consistent process. Finally, considering the \\ce{H2} molecule as an\nillustrative example, we observe $\\mathcal{PT}$-symmetry in the HF energy\nlandscape and find that the symmetry-broken unrestricted HF wave functions\n(i.e. diradical configurations) are $\\mathcal{PT}$-symmetric, while the\nsymmetry-broken restricted HF wave functions (i.e. ionic configurations) break\n$\\mathcal{PT}$-symmetry.\n']","[('pt symmetric quantum', 0.6522996425628662), ('mathcal pt symmetry', 0.651544988155365), ('hermitian theories', 0.5931118726730347), ('pt symmetry', 0.5889074206352234), ('mathcal pt symmetric', 0.5683639645576477), ('non hermitian physics', 0.5647793412208557), ('hermitian physics', 0.5559107065200806), ('hermitian systems', 0.5536679029464722), ('non hermitian systems', 0.5474528670310974), ('non hermitian hamiltonians', 0.5457854270935059)]"
239,239,117,239_hawkes processes_hawkes process_hawkes_point processes,"['hawkes processes', 'hawkes process', 'hawkes', 'point processes', 'markovian', 'marked point processes', 'point process', 'counting processes', 'process exponential', 'processes self']","['Precise deviations for Hawkes processes   Hawkes process is a class of simple point processes with self-exciting and\nclustering properties. Hawkes process has been widely applied in finance,\nneuroscience, social networks, criminology, seismology, and many other fields.\nIn this paper, we study precise deviations for Hawkes processes for large time\nasymptotics, that strictly extends and improves the existing results in the\nliterature. Numerical illustrations will also be provided.\n', 'Spatiotemporal Hawkes processes with a graphon-induced connectivity\n  structure   We introduce a spatiotemporal self-exciting point process $(N_t(x))$,\nboundedly finite both over time $[0,\\infty)$ and space $\\mathscr X$, with\nexcitation structure determined by a graphon $W$ on $\\mathscr{X}^2$. This\ngraphon Hawkes process generalizes both the multivariate Hawkes process and the\nHawkes process on a countable network, and despite being infinite-dimensional,\nit is surprisingly tractable. After proving existence, uniqueness and stability\nresults, we show, both in the annealed and in the quenched case, that for\ncompact, Euclidean $\\mathscr X\\subset\\mathbb R^m$, any graphon Hawkes process\ncan be obtained as the suitable limit of $d$-dimensional Hawkes processes\n$\\tilde N^d$, as $d\\to\\infty$. Furthermore, in the stable regime, we establish\nan FLLN and an FCLT for our infinite-dimensional process on compact $\\mathscr\nX\\subset\\mathbb R^m$, while in the unstable regime we prove divergence of\n$N_T(\\mathscr X)/T$, as $T\\to\\infty$. Finally, we exploit a cluster\nrepresentation to derive fixed-point equations for the Laplace functional of\n$N$, for which we set up a recursive approximation procedure. We apply these\nresults to show that, starting with multivariate Hawkes processes $\\tilde\nN^d_t$ converging to stable graphon Hawkes processes, the limits $d\\to\\infty$\nand $t\\to\\infty$ commute.\n', ""The Malliavin-Stein method for Hawkes functionals   In this paper, following Nourdin-Peccati's methodology, we combine the\nMalliavin calculus and Stein's method to provide general bounds on the\nWasserstein distance between functionals of a compound Hawkes process and a\ngiven Gaussian density. To achieve this, we rely on the Poisson embedding\nrepresentation of an Hawkes process to provide a Malliavin calculus for the\nHawkes processes, and more generally for compound Hawkes processes. As an\napplication, we close a gap in the literature by providing the first\nBerry-Ess\\'een bounds associated to Central Limit Theorems for the compound\nHawkes process.\n""]","[('hawkes processes', 0.774686872959137), ('hawkes process', 0.7314311861991882), ('hawkes', 0.5601485371589661), ('point processes', 0.4460737407207489), ('markovian', 0.4298159182071686), ('marked point processes', 0.3798469007015228), ('point process', 0.3725115954875946), ('counting processes', 0.35615548491477966), ('process exponential', 0.34971559047698975), ('processes self', 0.33359622955322266)]"
240,240,117,240_macroscopic traffic flow_traffic flows_traffic models_traffic flow,"['macroscopic traffic flow', 'traffic flows', 'traffic models', 'traffic flow', 'vehicular traffic', 'macroscopic traffic', 'traffic density', 'mixed traffic', 'traffic', 'flow models']","[""Stabilizing Traffic via Autonomous Vehicles: A Continuum Mean Field Game\n  Approach   This paper presents scalable traffic stability analysis for both pure\nautonomous vehicle (AV) traffic and mixed traffic based on continuum traffic\nflow models. Human vehicles are modeled by a non-equilibrium traffic flow\nmodel, i.e., Aw-Rascle-Zhang (ARZ), which is unstable. AVs are modeled by the\nmean field game which assumes AVs are rational agents with anticipation\ncapacities. It is shown from linear stability analysis and numerical\nexperiments that AVs help stabilize the traffic. Further, we quantify the\nimpact of AV's penetration rate and controller design on the traffic stability.\nThe results may provide insights for AV manufacturers and city planners.\n"", 'Shock formation in traffic flow models with nonlocal look ahead and\n  behind flux   In this work, we study a Lighthill-Whitham-Richard (LWR) type traffic flow\nmodel with a non-local flux. We identify a threshold condition for shock\nformation for traffic flow models with Arrhenius look-ahead-behind (i.e.,\nnudging) dynamics with concave-convex flux.\n', 'A model for traffic flow on a road with variable widths   We propose a model describing the traffic flow on a road with variable widths\nin this paper. The model, which is modified the Aw-Rascle model, is not\nconservative because of the source term. We obtain the elementary waves of the\nnew traffic flow model, including rarefaction waves, shock waves, contact\ndiscontinuities and stationary waves. The Riemann problems of the system for\nthe traffic flow are solved and some numerical results are given, which are\nalmost the same as the theoretical ones.\n']","[('macroscopic traffic flow', 0.7126469016075134), ('traffic flows', 0.6992964744567871), ('traffic models', 0.6849449872970581), ('traffic flow', 0.6745254397392273), ('vehicular traffic', 0.5950113534927368), ('macroscopic traffic', 0.5467821955680847), ('traffic density', 0.5459271669387817), ('mixed traffic', 0.5351182818412781), ('traffic', 0.5244625210762024), ('flow models', 0.48833101987838745)]"
241,241,116,241_motivic cohomology_theory motives_motives_motivic galois groups,"['motivic cohomology', 'theory motives', 'motives', 'motivic galois groups', 'motivic galois', 'hodge modules', 'motive', 'cohomology theories', 'adic cohomology', 'etale cohomology']","['Mixed Motives   A mixed Weil cohomology with values in an abelian rigid tensor category is a\ncohomological functor on Voevodsky\'s category of motives which is satisfying\nK\\""unneth formula and such that its restriction to Chow motives is a Weil\ncohomology. We show that the universal mixed Weil cohomology exists. Nori\nmotives can be recovered as a universal enrichment of Betti cohomology via a\nlocalisation. This new picture is drawing some consequences with respect to the\ntheory of mixed motives in arbitrary characteristic.\n', ""On the Nori and Hodge realisations of Voevodsky motives   We show that the derived category of perverse Nori motives and mixed Hodge\nmodules are the derived categories of their constructible hearts. This enables\nus to construct $\\infty$-categorical lifts of the six operations and therefore\nto obtain realisation functors from the category of Voevodsky \\'etale motives\nto the derived categories of perverse Nori motives and mixed Hodge modules that\ncommute with the operations. We give a proof that the realisation induces an\nequivalence of categories between Artin motives in the category of \\'etale\nmotives and Artin motives in the derived category of Nori motives. We also\nprove that if a motivic $t$-structure exists then Voevodsky \\'etale motives and\nthe derived category of perverse Nori motives are equivalent. Finally we give a\npresentation of the indization of the derived category of perverse Nori motives\nas a category of modules in Voevodsky \\'etale motives that gives a continuity\nresult for perverse Nori motives.\n"", ""Artin motives in relative Nori and Voevodsky motives   Over a scheme of finite type over a field of characteristic zero, we prove\nthat Nori an Voevodsky categories of relative Artin motives, that is the full\nsubcategories generated by the motives of \\'etale morphisms in relative Nori\nand Voevodsky motives, are canonically equivalent. As an application, we show\nthat over a normal base of characteristic zero an Artin motive is dualisable if\nand only if it lies in the thick category spanned by the motives of finite\n\\'etale schemes. We finish with an application to motivic Galois groups and\nobtain an analogue of the classical exact sequence of \\'etale fundamental\ngroups relating a variety over a field and its base change to the algebraic\nclosure.\n""]","[('motivic cohomology', 0.6652988791465759), ('theory motives', 0.6034061312675476), ('motives', 0.5855648517608643), ('motivic galois groups', 0.550028383731842), ('motivic galois', 0.523547351360321), ('hodge modules', 0.4959140121936798), ('motive', 0.4810596704483032), ('cohomology theories', 0.4721367657184601), ('adic cohomology', 0.4556986689567566), ('etale cohomology', 0.4549354314804077)]"
242,242,115,242_minkowski theory_brunn minkowski theory_classical minkowski_minkowski case,"['minkowski theory', 'brunn minkowski theory', 'classical minkowski', 'minkowski case', 'minkowski type', 'minkowski inequality', 'curvature measures', 'curvature measure', 'minkowski', 'convex solutions']","['Nonuniqueness of solutions to the $L_p$ chord Minkowski problem   This paper explores the nonuniqueness of solutions to the $L_p$ chord\nMinkowski problem for negative $p.$ The $L_p$ chord Minkowski problem was\nrecently posed by Lutwak, Xi, Yang and Zhang, which seeks to determine the\nnecessary and sufficient conditions for a given finite Borel measure such that\nit is the $L_p$ chord measure of a convex body, and it includes the chord\nMinkowski problem and the $L_p$ Minkowski problem.\n', 'Uniqueness and continuity of the solution to $L_p$ dual Minkowski\n  problem   Lutwak, Yang and Zhang \\cite{LYZ2018} introduced the $L_p$ dual curvature\nmeasure that unifies several other geometric measures in dual Brunn-Minkowski\ntheory and Brunn- Minkowski theory. Motivated by works in \\cite{LYZ2018}, we\nconsider the uniqueness and continuity of the solution to the $L_p$ dual\nMinkowski problem. To extend the important work (Theorem \\ref{uniquepolytope})\nof LYZ to the case for general convex bodies, we establish some new\nMinkowski-type inequalities which are closely related to the optimization\nproblem associated with the $L_p$ dual Minkowski problem. When $q< p$, the\nuniqueness of the solution to the $L_p$ dual Minkowski problem for general\nconvex bodies is obtained. Moreover, we obtain the continuity of the solution\nto the $L_p$ dual Minkowski problem for convex bodies.\n', 'Orlicz-Minkowski flows   We study the long-time existence and behavior for a class of anisotropic\nnon-homogeneous Gauss curvature flows whose stationary solutions, if exist,\nsolve the regular Orlicz-Minkowski problems. As an application, we obtain old\nand new results for the regular even Orlicz-Minkowski problems; the\ncorresponding $L_p$ version is the even $L_p$-Minkowski problem for $p>-n-1$.\nMoreover, employing a parabolic approximation method, we give new proofs of\nsome of the existence results for the general Orlicz-Minkowski problems; the\n$L_p$ versions are the even $L_p$-Minkowski problem for $p>0$ and the\n$L_p$-Minkowski problem for $p>1$. In the final section, we use a curvature\nflow with no global term to solve a class of $L_p$-Christoffel-Minkowski type\nproblems.\n']","[('minkowski theory', 0.6209728121757507), ('brunn minkowski theory', 0.5855619311332703), ('classical minkowski', 0.5763428807258606), ('minkowski case', 0.5649783611297607), ('minkowski type', 0.5459316968917847), ('minkowski inequality', 0.5372933745384216), ('curvature measures', 0.523510754108429), ('curvature measure', 0.504081666469574), ('minkowski', 0.47424018383026123), ('convex solutions', 0.4647621512413025)]"
243,243,115,243_models tumor_tumor growth_tumour growth_diffusion equations,"['models tumor', 'tumor growth', 'tumour growth', 'diffusion equations', 'diffusion', 'cancer invasion', 'tumor cells', 'tumour cells', 'reaction diffusion equations', 'reaction diffusion']","['Interface Dynamics in a Two-phase Tumor Growth Model   We study a tumor growth model in two space dimensions, where proliferation of\nthe tumor cells leads to expansion of the tumor domain and migration of\nsurrounding normal tissues into the exterior vacuum. The model features two\nmoving interfaces separating the tumor, the normal tissue, and the exterior\nvacuum. We prove local-in-time existence and uniqueness of strong solutions for\ntheir evolution starting from a nearly radial initial configuration. It is\nassumed that the tumor has lower mobility than the normal tissue, which is in\nline with the well-known Saffman-Taylor condition in viscous fingering.\n', 'Tumor Growth with Nutrients: Regularity and Stability   In this paper we study a tumor growth model with nutrients. The model\npresents dynamic patch solutions due to the contact inhibition among the tumor\ncells. We show that when the nutrients do not diffuse and the cells do not die,\nthe tumor density exhibits regularizing dynamics. In particular, we provide\ncontraction estimates, exponential rate of asymptotic convergence, and boundary\nregularity of the tumor patch. These results are in sharp contrast to the\nmodels either with nutrient diffusion or with death rate in tumor cells.\n', ""Tumor growth with nutrients: stability of the tumor patches   In this paper, we study a tumor growth model with nutrients. The contact\ninhibition for the tumor cells, presented in the model, results in the\nevolution of a congested tumor patch. We study the regularity of the tumor\npatch as the nutrients' diffusion strength $D$ diminishes. In particular, we\nshow that for small $D>0$ the boundary of the tumor patch stays in a small\nneighborhood of the smooth tumor patch boundary obtained with $D=0$, uniformly\nwith respect to the Hausdorff distance.\n""]","[('models tumor', 0.5862960815429688), ('tumor growth', 0.5228114724159241), ('tumour growth', 0.4892469346523285), ('diffusion equations', 0.47837868332862854), ('diffusion', 0.47539329528808594), ('cancer invasion', 0.4587196111679077), ('tumor cells', 0.4544416666030884), ('tumour cells', 0.4396587610244751), ('reaction diffusion equations', 0.43511709570884705), ('reaction diffusion', 0.41377004981040955)]"
244,244,115,244_steklov eigenvalues_steklov eigenfunctions_steklov eigenvalue_lower bounds eigenvalues,"['steklov eigenvalues', 'steklov eigenfunctions', 'steklov eigenvalue', 'lower bounds eigenvalues', 'eigenvalues laplacian', 'eigenvalue laplacian', 'bounds eigenvalues', 'first eigenvalue laplacian', 'steklov problems', 'compact manifolds']","['Higher dimensional surgery and Steklov eigenvalues   We show that for compact Riemannian manifolds of dimension at least $3$ with\nnonempty boundary, we can modify the manifold by performing surgeries of\ncodimension $2$ or higher, while keeping the Steklov spectrum nearly unchanged.\nThis shows that certain changes in the topology of a domain do not have an\neffect when considering shape optimization questions for Steklov eigenvalues in\ndimensions $3$ and higher. Our result generalizes the 1-dimensional surgery in\n[FS2] to higher dimensional surgeries and to higher eigenvalues. It is proved\nin [FS2] that the unit ball does not maximize the first nonzero normalized\nSteklov eigenvalue among contractible domains in $\\mathbb{R}^n$, for $n \\geq\n3$. We show that this is also true for higher Steklov eigenvalues. Using\nsimilar ideas we show that in $\\mathbb{R}^n$, for $n\\geq 3$, the $j$-th\nnormalized Steklov eigenvalue is not maximized in the limit by a sequence of\ncontractible domains degenerating to the disjoint union of $j$ unit balls, in\ncontrast to the case in dimension $2$ [GP1].\n', ""Large Steklov eigenvalues via homogenisation on manifolds   Using methods in the spirit of deterministic homogenisation theory we obtain\nconvergence of the Steklov eigenvalues of a sequence of domains in a Riemannian\nmanifold to weighted Laplace eigenvalues of that manifold. The domains are\nobtained by removing small geodesic balls that are asymptotically densely\nuniformly distributed as their radius tends to zero. We use this relationship\nto construct manifolds that have large Steklov eigenvalues.\n  In dimension two, and with constant weight equal to 1, we prove that\nKokarev's upper bound of $8\\pi$ for the first nonzero normalised Steklov\neigenvalue on orientable surfaces of genus 0 is saturated. For other\ntopological types and eigenvalue indices, we also obtain lower bounds on the\nbest upper bound for the eigenvalue in terms of Laplace maximisers. For the\nfirst two eigenvalues, these lower bounds become equalities. A surprising\nconsequence is the existence of free boundary minimal surfaces immersed in the\nunit ball by first Steklov eigenfunctions and with area strictly larger than\n$2\\pi$. This was previously thought to be impossible. We provide numerical\nevidence that some of the already known examples of free boundary minimal\nsurfaces have these properties and also exhibit simulations of new free\nboundary minimal surfaces of genus 0 in the unit ball with even larger area.\nThe first nonzero Steklov eigenvalue of all these examples is equal to 1, as a\nconsequence of their symmetries and topology, so that they verify a general\nconjecture by Fraser and Li.\n  In dimension three and larger, we prove that the isoperimetric inequality of\nColbois--El Soufi--Girouard is sharp and implies an upper bound for weighted\nLaplace eigenvalues. We also show that in any manifold with a fixed metric, one\ncan construct by varying the weight a domain with connected boundary whose\nfirst nonzero normalised Steklov eigenvalue is arbitrarily large.\n"", 'Applications of possibly hidden symmetry to Steklov and mixed Steklov\n  problems on surfaces   We consider three different questions related to the Steklov and mixed\nSteklov problems on surfaces. These questions are connected by the techniques\nthat we use to study them, which exploit symmetry in various ways even though\nthe surfaces we study do not necessarily have inherent symmetry.\n  In the spirit of the celebrated Hersch-Payne-Schiffer and Weinstock\ninequalities for Steklov eigenvalues, we obtain a sharp isoperimetric\ninequality for the mixed Steklov eigenvalues considering the interplay between\nthe eigenvalues of the mixed Steklov-Neumann and Steklov-Dirichlet eigenvalues.\n  In 1980, Bandle showed that the unit disk maximizes the $k$th nonzero\nnormalized Steklov eigenvalue on simply connected domains with rotational\nsymmetry of order $p$ when $k\\le p-1$. We discuss whether the disk remains the\nmaximizer in the class of simply connected rotationally symmetric domains when\n$k\\geq p$. In particular, we show that for $k$ large enough, the upper bound\nconverges to the Hersch-Payne-Schiffer upper bound.\n  We give full asymptotics for mixed Steklov problems on arbitrary surfaces,\nassuming some conditions at the meeting points of the Steklov boundary with the\nDirichlet or Neumann boundary.\n']","[('steklov eigenvalues', 0.6988528966903687), ('steklov eigenfunctions', 0.6718385815620422), ('steklov eigenvalue', 0.6662712097167969), ('lower bounds eigenvalues', 0.5108889937400818), ('eigenvalues laplacian', 0.5057592988014221), ('eigenvalue laplacian', 0.4989107847213745), ('bounds eigenvalues', 0.4933505952358246), ('first eigenvalue laplacian', 0.4730517268180847), ('steklov problems', 0.44795340299606323), ('compact manifolds', 0.4373243451118469)]"
245,245,114,245_splitting algorithms_douglas rachford splitting_forward backward splitting_convex optimization problems,"['splitting algorithms', 'douglas rachford splitting', 'forward backward splitting', 'convex optimization problems', 'backward splitting', 'operator splitting', 'monotone inclusion problems', 'maximal monotone operators', 'maximally monotone operators', 'monotone operators']","['Forward-Reflected-Backward and Shadow-Douglas--Rachford with partial\n  inverse for Solving Monotone Inclusions   In this article, we study two methods for solving monotone inclusions in real\nHilbert spaces involving the sum of a maximally monotone operator, a\nmonotone-Lipschitzian operator, a cocoercive operator, and a normal cone to a\nvector subspace. Our algorithms split and exploits the intrinsic properties of\neach operator involved in the inclusion. We derive our methods by combining\npartial inverse techniques with the forward-reflected-backward algorithm and\nwith the shadow-Douglas--Rachford algorithm, respectively. Our methods inherit\nthe advantages of those methods, requiring only one activation of the\nLipschitzian operator, one activation of the cocoercive operator, two\nprojections onto the closed vector subspace, and one calculation of the\nresolvent of the maximally monotone operator. Additionally, to allow larger\nstep-sizes in one of the proposed methods, we revisit FSDR by extending its\nconvergence for larger step-sizes. Furthermore, we provide methods for solving\nmonotone inclusions involving a sum of maximally monotone operators and for\nsolving a system of primal-dual inclusions involving a mixture of sums, linear\ncompositions, parallel sums, Lipschitzian operators, cocoercive operators, and\nnormal cones. We apply our methods to constrained composite convex optimization\nproblems as a specific example. Finally, in order to compare our methods with\nexisting methods in the literature, we provide numerical experiments on\nconstrained total variation least-squares optimization problems and computed\ntomography inverse problems. We obtain promising numerical results.\n', 'An outer reflected forward-backward splitting algorithm for solving\n  monotone inclusions   Monotone inclusions have wide applications in solving various convex\noptimization problems arising in signal and image processing, machine learning,\nand medical image reconstruction. In this paper, we propose a new splitting\nalgorithm for finding a zero of the sum of a maximally monotone operator, a\nmonotone Lipschitzian operator, and a cocoercive operator, which is called\nouter reflected forward-backward splitting algorithm. Under mild conditions on\nthe iterative parameters, we prove the convergence of the proposed algorithm.\nAs applications, we employ the proposed algorithm to solve composite monotone\ninclusions involving monotone Lipschitzian operator, cocoercive operator, and\nthe parallel sum of operators. The advantage of the obtained algorithm is that\nit is a completely splitting algorithm, in which the Lipschitzian operator and\nthe cocoercive operator are processed via explicit steps and the maximally\nmonotone operators are processed via their resolvents.\n', 'Four-operator splitting algorithms for solving monotone inclusions   Monotone inclusions involving the sum of three maximally monotone operators\nor more have received much attention in recent years. In this paper, we propose\nthree splitting algorithms for finding a zero of the sum of four monotone\noperators, which are two maximally monotone operators, one monotone Lipschitz\noperator, and one cocoercive operator. These three splitting algorithms are\nbased on the forward-reflected-Douglas-Rachford splitting algorithm,\nbackward-forward-reflected-backward splitting algorithm, and\nbackward-reflected-forward-backward splitting algorithm, respectively. As\napplications, we apply the proposed algorithms to solve the monotone inclusions\nproblem involving a finite sum of maximally monotone operators. Numerical\nresults on the Projection on Minkowski sums of convex sets demonstrate the\neffectiveness of the proposed algorithms.\n']","[('splitting algorithms', 0.5318504571914673), ('douglas rachford splitting', 0.5208746194839478), ('forward backward splitting', 0.5129674673080444), ('convex optimization problems', 0.5128394961357117), ('backward splitting', 0.4967433214187622), ('operator splitting', 0.4952457547187805), ('monotone inclusion problems', 0.4916916787624359), ('maximal monotone operators', 0.4850763976573944), ('maximally monotone operators', 0.4774269461631775), ('monotone operators', 0.4671781659126282)]"
246,246,114,246_theoretical fusion categories_fusion categories_fusion category_braided tensor categories,"['theoretical fusion categories', 'fusion categories', 'fusion category', 'braided tensor categories', 'braided tensor category', 'group theoretical fusion', 'braided monoidal category', 'group fusion', 'fusion rings', 'modular categories']","['Fiber 2-Functors and Tambara-Yamagami Fusion 2-Categories   We introduce group-theoretical fusion 2-categories, a strong categorification\nof the notion of a group-theoretical fusion 1-category. Physically speaking,\nsuch fusion 2-categories arise by gauging subgroups of a global symmetry. We\nshow that group-theoretical fusion 2-categories are completely characterized by\nthe property that the braided fusion 1-category of endomorphisms of the\nmonoidal unit is Tannakian. Then, we describe the underlying finite semisimple\n2-category of group-theoretical fusion 2-categories, and, more generally, of\ncertain 2-categories of bimodules. We also partially describe the fusion rules\nof group-theoretical fusion 2-categories, and investigate the group gradings of\nsuch fusion 2-categories. Using our previous results, we classify fusion\n2-categories admitting a fiber 2-functor. Next, we study fusion 2-categories\nwith a Tambara-Yamagami defect, that is $\\mathbb{Z}/2$-graded fusion\n2-categories whose non-trivially graded factor is $\\mathbf{2Vect}$. We classify\nthese fusion 2-categories, and examine more closely the more restrictive notion\nof Tambara-Yamagami fusion 2-categories. Throughout, we give many examples to\nillustrate our various results.\n', 'Drinfeld Centers and Morita Equivalence Classes of Fusion 2-Categories   We prove that the Drinfeld center of a fusion 2-category is invariant under\nMorita equivalence. We go on to show that the concept of Morita equivalence\nbetween connected fusion 2-categories recovers exactly the notion of Witt\nequivalence between braided fusion 1-categories. A strongly fusion 2-category\nis a fusion 2-category whose braided fusion 1-category of endomorphisms of the\nmonoidal unit is $\\mathbf{Vect}$ or $\\mathbf{SVect}$. We prove that every\nfusion 2-category is Morita equivalent to the 2-Deligne tensor product of a\nstrongly fusion 2-category and an invertible fusion 2-category. We proceed to\nshow that every fusion 2-category is Morita equivalent to a connected fusion\n2-category. As a consequence, we find that every rigid algebra in a fusion\n2-category is separable. This implies in particular that every fusion\n2-category is separable. Conjecturally, separability ensures that a fusion\n2-category is 4-dualizable. We define the dimension of a fusion 2-category, and\nprove that it is always non-zero. Finally, we show that the Drinfeld center of\nany fusion 2-category is a finite semisimple 2-category.\n', 'Near-integral fusion   We abstract the study of irreducible characters of finite groups vanishing on\nall but two conjugacy classes, initiated by S. Gagola, to irreducible\ncharacters of fusion rings whose kernel has maximal rank. These near-integral\nfusion rings include the near-groups which are currently one of the most\nabundant sources of novel examples of fusion categories to date. We generalize\nmany of the known results on near-group fusion categories from the literature\nto near-integral fusion categories and characterize when such categories are\nbraided. In particular, braided near-integral fusion categories describe all\nbraided fusion categories which are almost symmetrically braided. This novel\nresult allows a digestible characterization of the over $300$ braided\nequivalence classes of premodular fusion categories of rank $6$ or less.\n']","[('theoretical fusion categories', 0.7476836442947388), ('fusion categories', 0.7262428998947144), ('fusion category', 0.675487220287323), ('braided tensor categories', 0.607650101184845), ('braided tensor category', 0.5879489183425903), ('group theoretical fusion', 0.5688756704330444), ('braided monoidal category', 0.5681727528572083), ('group fusion', 0.5354735851287842), ('fusion rings', 0.5155060291290283), ('modular categories', 0.511906623840332)]"
247,247,114,247_weighted shift operators_shift operators_hypercyclicity_hypercyclic,"['weighted shift operators', 'shift operators', 'hypercyclicity', 'hypercyclic', 'weighted shifts', 'backward shifts', 'shift operator', 'composition operators', 'weighted shift', 'composition operators spaces']","['Chaos and frequent hypercyclicity for composition operators   The notions of chaos and frequent hypercyclicity enjoy an intimate\nrelationship in linear dynamics. Indeed, after a series of partial results, it\nwas shown by Bayart and Rusza in 2015 that for backward weighted shifts on\n$\\ell_p(\\mathbb{Z})$, the notions chaos and frequent hypercyclicity coincide.\nIt is with some effort that one shows that these two notions are distinct.\nBayart and Grivaux in 2007 constructed a non-chaotic frequently hypercyclic\nweighted shift on $c_0$. It was only in 2017 that Menet settled negatively\nwhether every chaotic operator is frequently hypercylic. In this article, we\nshow that for a large class of composition operators on $L^p$-spaces the\nnotions of chaos and frequent hypercyclicity coincide. Moreover, in this\nparticular class an invertible operator is frequently hypercyclic if and only\nif its inverse is frequently hypercyclic. This is in contrast to a very recent\nresult of Menet where an invertible frequently hypercyclic operator on $\\ell_1$\nwhose inverse is not frequently hypercyclic is constructed.\n', 'Recurrence properties of hypercyclic operators   We generalize the notions of hypercyclic operators, $\\mathfrak{U}$-frequently\nhypercyclic operators and frequently hypercyclic operators by introducing a new\nnotion of hypercyclicity, called $\\mathcal{A}$-frequent hypercyclicity. We then\nstate an $\\mathcal{A}$-Frequent Hypercyclicity Criterion, inspired from the\nHypercyclicity Criterion and the Frequent Hypercyclicity Criterion, and we show\nthat this criterion characterizes the $\\mathcal{A}$-frequent hypercyclicity for\nweighted shifts. We finish by investigating which kind of properties of density\ncan have the sets ${N(x, U)=\\{n\\in \\mathbb{N}:T^nx\\in U\\}}$ for a given\nhypercyclic operator and study the new notion of reiteratively hypercyclic\noperators.\n', ""Hereditarily frequently hypercyclic operators and disjoint frequent\n  hypercyclicity   We introduce and study the notion of hereditary frequent hypercyclicity,\nwhich is a reinforcement of the well known concept of frequent hypercyclicity.\nThis notion is useful for the study of the dynamical properties of direct sums\nof operators; in particular, a basic observation is that the direct sum of a\nhereditarily frequently hypercyclic operator with any frequently hypercyclic\noperator is frequently hypercyclic. Among other results, we show that operators\nsatisfying the Frequent Hypercyclicity Criterion are hereditarily frequently\nhypercyclic, as well as a large class of operators whose unimodular\neigenvectors are spanning with respect to the Lebesgue measure. On the other\nhand, we exhibit two frequently hypercyclic weighted shifts $B_w,B_{w'}$ on\n$c_0(\\mathbb{Z}_+)$ whose direct sum $B_w\\oplus B_{w'}$ is not\n$\\mathcal{U}$-frequently hypercyclic (so that neither of them is hereditarily\nfrequently hypercyclic), and we construct a $C$-type operator on\n$\\ell_p(\\mathbb{Z}_+)$, $1\\le p<\\infty$ which is frequently hypercyclic but not\nhereditarily frequently hypercyclic. We also solve several problems concerning\ndisjoint frequent hypercyclicity: we show that for every $N\\in\\mathbb{N}$, any\ndisjoint frequently hypercyclic $N$-tuple of operators $(T_1,\\dots ,T_N)$ can\nbe extended to a disjoint frequently hypercyclic $(N+1)$-tuple $(T_1,\\dots\n,T_N, T_{N+1})$ as soon as the underlying space supports a hereditarily\nfrequently hypercyclic operator; we construct a disjoint frequently hypercyclic\npair which is not densely disjoint hypercyclic; and we show that the pair\n$(D,\\tau_a)$ is disjoint frequently hypercyclic, where $D$ is the derivation\noperator acting on the space of entire functions and $\\tau_a$ is the operator\nof translation by $a\\in\\mathbb{C}\\setminus\\{ 0\\}$. Part of our results are in\nfact obtained in the general setting of Furstenberg families.\n""]","[('weighted shift operators', 0.5368105173110962), ('shift operators', 0.5061630606651306), ('hypercyclicity', 0.4970144033432007), ('hypercyclic', 0.475775808095932), ('weighted shifts', 0.46123939752578735), ('backward shifts', 0.4205475151538849), ('shift operator', 0.413607120513916), ('composition operators', 0.4075131118297577), ('weighted shift', 0.3942015767097473), ('composition operators spaces', 0.3793664574623108)]"
248,248,114,248_fracture mechanics_crack propagation_phase field models_cracks,"['fracture mechanics', 'crack propagation', 'phase field models', 'cracks', 'phase field', 'fracture', 'phase field approximation', 'crack', 'brittle materials', 'phase field variable']","['Crack opening calculation in phase-field modeling of fluid-filled\n  fracture: A robust and efficient strain-based method   The phase-field method has become popular for the numerical modeling of\nfluid-filled fractures, thanks to its ability to represent complex fracture\ngeometry without algorithms. However, the algorithm-free representation of\nfracture geometry poses a significant challenge in calculating the crack\nopening (aperture) of phase-field fracture, which governs the fracture\npermeability and hence the overall hydromechanical behavior. Although several\napproaches have been devised to compute the crack opening of phase-field\nfracture, they require a sophisticated algorithm for post-processing the\nphase-field values or an additional parameter sensitive to the element size and\nalignment. Here, we develop a novel method for calculating the crack opening of\nfluid-filled phase-field fracture, which enables one to obtain the crack\nopening without additional algorithms or parameters. We transform the\ndisplacement-jump-based kinematics of a fracture into a continuous strain-based\nversion, insert it into a force balance equation on the fracture, and apply the\nphase-field approximation. Through this procedure, we obtain a simple equation\nfor the crack opening which can be calculated with quantities at individual\nmaterial points. We verify the proposed method with analytical and numerical\nsolutions obtained based on discrete representations of fractures,\ndemonstrating its capability to calculate the crack opening regardless of the\nelement size or alignment.\n', ""An assessment of phase field fracture: crack initiation and growth   The phase field paradigm, in combination with a suitable variational\nstructure, has opened a path for using Griffith's energy balance to predict the\nfracture of solids. These so-called phase field fracture methods have gained\nsignificant popularity over the past decade, and are now part of commercial\nfinite element packages and engineering fitness-for-service assessments. Crack\npaths can be predicted, in arbitrary geometries and dimensions, based on a\nglobal energy minimisation - without the need for \\textit{ad hoc} criteria. In\nthis work, we review the fundamentals of phase field fracture methods and\nexamine their capabilities in delivering predictions in agreement with the\nclassical fracture mechanics theory pioneered by Griffith. The two most widely\nused phase field fracture models are implemented in the context of the finite\nelement method, and several paradigmatic boundary value problems are addressed\nto gain insight into their predictive abilities across all cracking stages;\nboth the initiation of growth and stable crack propagation are investigated. In\naddition, we examine the effectiveness of phase field models with an internal\nmaterial length scale in capturing size effects and the transition flaw size\nconcept. Our results show that phase field fracture methods satisfactorily\napproximate classical fracture mechanics predictions and can also reconcile\nstress and toughness criteria for fracture. The accuracy of the approximation\nis however dependent on modelling and constitutive choices; we provide a\nrationale for these differences and identify suitable approaches for delivering\nphase field fracture predictions that are in good agreement with\nwell-established fracture mechanics paradigms.\n"", 'Phase-Field Modeling of Fracture under Compression and Confinement in\n  Anisotropic Geomaterials   Strongly anisotropic geomaterials undergo fracture under compressive loading.\nThis paper applies a phase-field fracture model to study this fracture process.\nWhile phase-field fracture models have several advantages, they provide\nunphysical predictions when the stress state is complex and includes\ncompression that can cause crack faces to contact.\n  Building on a phase-field model that accounts for compressive traction across\nthe crack face, this paper extends the model to anisotropic fracture. The key\nfeatures include: (1) a homogenized anisotropic elastic response and\nstrongly-anisotropic model for the work to fracture; (2) an effective damage\nresponse that accounts consistently for compressive traction across the crack\nface, that is derived from the anisotropic elastic response; (3) a regularized\ncrack normal field that overcomes the shortcomings of the isotropic setting,\nand enables the correct crack response, both across and transverse to the crack\nface.\n  To test the model, we first compare the predictions to phase-field fracture\nevolution calculations in a fully-resolved layered specimen with spatial\ninhomogeneity, and show that it captures the overall patterns of crack growth.\nWe then apply the model to previously-reported experimental observations of\nfracture evolution in laboratory specimens of shales under compression with\nconfinement, and find that it predicts well the observed crack patterns in a\nbroad range of loading conditions. We further apply the model to predict the\ngrowth of wing cracks under compression and confinement. The effective crack\nresponse model enables us to treat the initial crack simply as a non-singular\ndamaged zone within the computational domain, thereby allowing for easy and\ngeneral computations.\n']","[('fracture mechanics', 0.6148492097854614), ('crack propagation', 0.5927866101264954), ('phase field models', 0.48513129353523254), ('cracks', 0.4414796829223633), ('phase field', 0.42910003662109375), ('fracture', 0.4243416488170624), ('phase field approximation', 0.4207246005535126), ('crack', 0.3993440568447113), ('brittle materials', 0.3897194564342499), ('phase field variable', 0.38832569122314453)]"
249,249,114,249_nakajima quiver varieties_quiver varieties_quiver variety_nakajima quiver,"['nakajima quiver varieties', 'quiver varieties', 'quiver variety', 'nakajima quiver', 'type quiver', 'quiver representations', 'associated quiver', 'quivers', 'representations quiver', 'quiver']","[""Quiver description of Cherkis bow varieties and Nakajima quiver\n  varieties   We provide a quiver description for Cherkis bow varieties in arbitrary type.\nWe explain how this generalizes the construction of Nakajima quiver varieties.\nWe give criteria for stability, non-emptiness, smoothness and discuss\ndeformations. In the appendix, we discuss the relation between the quiver\ndescription and the original Cherkis' construction of bow varieties.\n"", 'Translation quiver varieties   We introduce a framework of translation quiver varieties which includes\nNakajima quiver varieties as well as their graded and cyclic versions. An\nimportant feature of translation quiver varieties is that the sets of their\nfixed points under toric actions can be again realized as translation quiver\nvarieties. This allows one to simplify quiver varieties in several steps. We\nprove that translation quiver varieties are smooth, pure and have Tate motivic\nclasses. We also describe an algorithm to compute those motivic classes.\n', 'Namikawa-Weyl groups of affinizations of smooth Nakajima quiver\n  varieties   We give a description of the Namikawa-Weyl group of affinizations of smooth\nNakajima quiver varieties using combinatorial data of the underlying quiver,\nand compute some explicit examples. This extends a result of McGerty and Nevins\nfor quiver varieties coming from Dynkin quivers.\n']","[('nakajima quiver varieties', 0.8527599573135376), ('quiver varieties', 0.8057842254638672), ('quiver variety', 0.7712709307670593), ('nakajima quiver', 0.7052549719810486), ('type quiver', 0.6929800510406494), ('quiver representations', 0.6717305183410645), ('associated quiver', 0.6604915261268616), ('quivers', 0.6315149068832397), ('representations quiver', 0.6116652488708496), ('quiver', 0.6109452247619629)]"
250,250,114,250_smooth fano threefolds_fano threefolds_fano threefold_fano manifolds,"['smooth fano threefolds', 'fano threefolds', 'fano threefold', 'fano manifolds', 'fano varieties', 'fano folds', 'fano fold', 'fano variety', 'threefolds picard rank', 'stability fano']","['K-stable Fano threefolds of rank 2 and degree 30   We find all K-stable smooth Fano threefolds in the family No. 2.22.\n', 'K-moduli of Fano threefolds in family 3.10   We find all K-polystable limits of smooth Fano threefolds in family 3.10.\n', 'On K-moduli of Fano threefolds with degree 28 and Picard rank 4   We analyse the local structure of the K-moduli space of Fano varieties at a\ntoric singular K-polystable Fano 3-fold, which deforms to smooth Fano 3-folds\nwith anticanonical volume 28 and Picard rank 4. In particular, by constructing\nan algebraic deformation of this toric singular Fano, we show that the\nirreducible component of K-moduli parametrising these smooth Fano 3-folds is a\nrational surface.\n']","[('smooth fano threefolds', 0.7833970189094543), ('fano threefolds', 0.6963886022567749), ('fano threefold', 0.6647604703903198), ('fano manifolds', 0.6531844735145569), ('fano varieties', 0.6394033432006836), ('fano folds', 0.5972851514816284), ('fano fold', 0.5794104933738708), ('fano variety', 0.5452010631561279), ('threefolds picard rank', 0.5448037385940552), ('stability fano', 0.5354028940200806)]"
251,251,114,251_camassa holm_camassa holm ch_holm_holm ch,"['camassa holm', 'camassa holm ch', 'holm', 'holm ch', 'weak solutions', 'solitary wave solutions', 'wave solutions', 'soliton solutions', 'dissipative solutions', 'conserved quantities']","['Global conservative solution for the periodic $\\mu$-Camassa-Holm\n  equation   In this paper we mainly investigate the periodic $\\mu$-Camassa-Holm equation.\nWe show the existence of global conservative solutions to the Cauchy problem of\nthe periodic $\\mu$-Camassa-Holm equation. The result is obtained by introducing\na coordinate transformation into Lagrangian coordinates. Our solutions depend\ncontinuously on the initial data and has a semigroup property.\n', 'The conservative Camassa-Holm flow with step-like irregular initial data We extend the inverse spectral transform for the conservative Camassa-Holm flow on the line to a class of initial data that requires strong decay at one endpoint but only mild boundedness-type conditions at the other endpoint. The latter condition appears to be close to optimal in a certain sense for the well-posedness of the conservative Camassa-Holm flow. As a byproduct of our approach, we also find a family of new (almost) conservation laws for the Camassa-Holm equation, which could not be deduced from its bi-Hamiltonian structure before and which are connected to certain Besov-type norms (however, in a rather involved way). These results appear to be new even under positivity assumptions on the corresponding momentum, in which case the conservative Camassa-Holm flow coincides with the classical Camassa-Holm flow and no blow-ups occur.', 'Orbital stability of periodic peakons for a new higher-order\n  $\\mu$-Camassa-Holm equation   Consideration here is a higher-order $\\mu$-Camassa-Holm equation, which is a\nhigher-order extension of the $\\mu$-Camassa-Holm equation and retains some\nproperties of the $\\mu$-Camassa-Holm equation and the modified\n$\\mu$-Camassa-Holm equation. By utilizing the inequalities with the maximum and\nminimum of the solution related to the first three conservation laws, we\nestablish that the periodic peakons of this equation are orbitally stable under\nsmall perturbations in the energy space.\n']","[('camassa holm', 0.5147959589958191), ('camassa holm ch', 0.506384015083313), ('holm', 0.49900007247924805), ('holm ch', 0.4753722548484802), ('weak solutions', 0.4382557272911072), ('solitary wave solutions', 0.4220978319644928), ('wave solutions', 0.4086909294128418), ('soliton solutions', 0.3728395104408264), ('dissipative solutions', 0.35266926884651184), ('conserved quantities', 0.3507448732852936)]"
252,252,113,252_solutions fractional laplacian_fractional laplacians_fractional laplacian equations_fractional laplacian,"['solutions fractional laplacian', 'fractional laplacians', 'fractional laplacian equations', 'fractional laplacian', 'involving fractional laplacian', 'fractional laplacian operator', 'fractional sobolev regularity', 'fractional laplace operator', 'fractional elliptic', 'fractional laplace']","[""Hopf's lemmas and boundary behaviour of solutions to the fractional\n  Laplacian in Orlicz-Sobolev spaces   In this article we study different extensions of the celebrated Hopf's\nboundary lemma within the context of a family of nonlocal, nonlinear and\nnonstandard growth operators. More precisely, we examine the behavior of\nsolutions of the fractional $a-$Laplacian operator near the boundary of a\ndomain satisfying the interior ball condition. Our approach addresses problems\ninvolving both constant-sign and sign-changing potentials.\n"", ""Boundary behavior of solutions to fractional $p$-Laplacian equation   In this work, a generalized Hopf's lemma and a global boundary Harnack\ninequality are proved for solutions to fractional $p$-Laplacian equations.\nThen, the isolation of the first $(s,p)$-eigenvalue is shown in bounded open\nsets satisfying the Wiener criterion.\n"", 'Critical concave convex Ambrosetti-Prodi type problem for fractional\n  $p$-Laplacian   In this paper we consider a class of critical concave convex Ambrosetti-Prodi\ntype problems for the fractional $p$-Laplacian operator. By applying the\nLinking Theorem and the Mountain Pass Theorem as well, the interaction of the\nnonlinearities with the first eigenvalue of fractional $p$-Laplacian will be\nused to prove existence and multiplicity of solutions.\n']","[('solutions fractional laplacian', 0.7772558927536011), ('fractional laplacians', 0.754524827003479), ('fractional laplacian equations', 0.740452766418457), ('fractional laplacian', 0.7299390435218811), ('involving fractional laplacian', 0.7298989295959473), ('fractional laplacian operator', 0.7229564189910889), ('fractional sobolev regularity', 0.638395369052887), ('fractional laplace operator', 0.6246540546417236), ('fractional elliptic', 0.6013185977935791), ('fractional laplace', 0.5937572717666626)]"
253,253,113,253_hom lie algebras_hom lie algebra_cohomology deformations_cohomology lie,"['hom lie algebras', 'hom lie algebra', 'cohomology deformations', 'cohomology lie', 'post lie algebras', 'algebra cohomology', 'lie algebras', 'cohomology theory', 'graded lie algebra', 'lie algebra also']","['Derivation Hom-Lie 2-algebras and non-abelian extensions of Hom-Lie\n  algebras   In this paper, we introduce the notion of a derivation of a Hom-Lie algebra\nand construct the corresponding strict Hom-Lie 2-algebra, which is called the\nderivation Hom-Lie 2-algebra. As applications, we study non-abelian extensions\nof Hom-Lie algebras. We show that iso- morphism classes of diagonal non-abelian\nextensions of a Hom-Lie algebra g by a Hom-Lie algebra h are in one-to-one\ncorrespondence with homotopy classes of morphisms from g to the derivation\nHom-Lie 2-algebra DER(h).\n', 'On compatible Hom-Lie triple systems   In this paper, we consider compatible Hom-Lie triple systems. Compatible\nHom-Lie triple systems are characterized as Maurer-Cartan elements in a\nsuitable bidifferential graded Lie algebra. We also define a cohomology theory\nfor compatible Hom-Lie triple systems. As applications of cohomology, we study\nabelian extensions and deformations of compatible Hom-Lie triple systems.\n', 'Cohomology and deformations of compatible Hom-Lie algebras   In this paper, we consider compatible Hom-Lie algebras as a twisted version\nof compatible Lie algebras. Compatible Hom-Lie algebras are characterized as\nMaurer-Cartan elements in a suitable bidifferential graded Lie algebra. We also\ndefine a cohomology theory for compatible Hom-Lie algebras generalizing the\nrecent work of Liu, Sheng and Bai. As applications of cohomology, we study\nabelian extensions and deformations of compatible Hom-Lie algebras.\n']","[('hom lie algebras', 0.7682440280914307), ('hom lie algebra', 0.7461919188499451), ('cohomology deformations', 0.6236709356307983), ('cohomology lie', 0.6023072600364685), ('post lie algebras', 0.5936297178268433), ('algebra cohomology', 0.5768364071846008), ('lie algebras', 0.5675768256187439), ('cohomology theory', 0.5641571879386902), ('graded lie algebra', 0.5518754720687866), ('lie algebra also', 0.5384639501571655)]"
254,254,113,254_ldpc decoding_ldpc codes_check ldpc codes_parity check ldpc,"['ldpc decoding', 'ldpc codes', 'check ldpc codes', 'parity check ldpc', 'ldpc code', 'parity check codes', 'binary ldpc', 'decoding performance', 'propagation bp decoding', 'check ldpc']","['Probabilistic Shaping for Asymmetric Channels and Low-Density\n  Parity-Check Codes   An algorithm is proposed to encode low-density parity-check (LDPC) codes into\ncodewords with a non-uniform distribution. This enables power-efficient\nsignalling for asymmetric channels. We show gains of 0.9 dB for additive white\nGaussian noise (AWGN) channels with on-off keying modulation using 5G LDPC\ncodes.\n', 'Low Density Parity Check Code (LDPC Codes) Overview   This paper basically expresses the core fundamentals and brief overview of\nthe research of R. G. GALLAGER [1] on Low-Density Parity-Check (LDPC) codes and\nvarious parameters related to LDPC codes like, encoding and decoding of LDPC\ncodes, code rate, parity check matrix, tanner graph. We also discuss advantages\nand applications as well as the usage of LDPC codes in 5G technology. We have\nsimulated encoding and decoding of LDPC codes and have acquired results in\nterms of BER vs SNR graph in MATLAB software. This report was submitted as an\nassignment in Nirma University\n', 'Finite-Length Scaling of Spatially Coupled LDPC Codes Under Window\n  Decoding Over the BEC   We analyze the finite-length performance of spatially coupled low-density\nparity-check (SC-LDPC) codes under window decoding over the binary erasure\nchannel. In particular, we propose a refinement of the scaling law by Olmos and\nUrbanke for the frame error rate (FER) of terminated SC-LDPC ensembles under\nfull belief propagation (BP) decoding. The refined scaling law models the\ndecoding process as two independent Ornstein-Uhlenbeck processes, in\ncorrespondence to the two decoding waves that propagate toward the center of\nthe coupled chain for terminated SC-LDPC codes. We then extend the proposed\nscaling law to predict the performance of (terminated) SC-LDPC code ensembles\nunder the more practical sliding window decoding. Finally, we extend this\nframework to predict the bit error rate (BER) and block error rate (BLER) of\nSC-LDPC code ensembles. The proposed scaling law yields very accurate\npredictions of the FER, BLER, and BER for both full BP and window decoding.\n']","[('ldpc decoding', 0.6862438917160034), ('ldpc codes', 0.6800639033317566), ('check ldpc codes', 0.6510904431343079), ('parity check ldpc', 0.6033275127410889), ('ldpc code', 0.592729389667511), ('parity check codes', 0.5911148190498352), ('binary ldpc', 0.583713710308075), ('decoding performance', 0.5176470875740051), ('propagation bp decoding', 0.5075864791870117), ('check ldpc', 0.5019153952598572)]"
255,255,113,255_stabilizing controllers_stabilizing controller_robust controller_control nonlinear systems,"['stabilizing controllers', 'stabilizing controller', 'robust controller', 'control nonlinear systems', 'state feedback controller', 'robust control', 'feedback controllers', 'robust stability', 'feedback controller', 'controller synthesis']","['Closed-Loop Identification of Stabilized Models Using Dual Input-Output\n  Parameterization   This paper introduces a dual input-output parameterization (dual IOP) for the\nidentification of linear time-invariant systems from closed-loop data. It draws\ninspiration from the recent input-output parameterization developed to\nsynthesize a stabilizing controller. The controller is parameterized in terms\nof closed-loop transfer functions, from the external disturbances to the input\nand output of the system, constrained to lie in a given subspace. Analogously,\nthe dual IOP method parameterizes the unknown plant with analogous closed-loop\ntransfer functions, also referred to as dual parameters. In this case, these\nclosed-loop transfer functions are constrained to lie in an affine subspace\nguaranteeing that the identified plant is \\emph{stabilized} by the known\ncontroller. Compared with existing closed-loop identification techniques\nguaranteeing closed-loop stability, such as the dual Youla parameterization,\nthe dual IOP neither requires a doubly-coprime factorization of the controller\nnor a nominal plant that is stabilized by the controller. The dual IOP does not\ndepend on the order and the state-space realization of the controller either,\nas in the dual system-level parameterization. Simulation shows that the dual\nIOP outperforms the existing benchmark methods.\n', 'Direct Data Driven Control Using Noisy Measurements This paper presents a novel direct data-driven control framework for solving the linear quadratic regulator (LQR) under disturbances and noisy state measurements. The system dynamics are assumed unknown, and the LQR solution is learned using only a single trajectory of noisy input-output data while bypassing system identification. Our approach guarantees mean-square stability (MSS) and optimal performance by leveraging convex optimization techniques that incorporate noise statistics directly into the controller synthesis. First, we establish a theoretical result showing that the MSS of an uncertain data-driven system implies the MSS of the true closed-loop system. Building on this, we develop a robust stability condition using linear matrix inequalities (LMIs) that yields a stabilizing controller gain from noisy measurements. Finally, we formulate a data-driven LQR problem as a semidefinite program (SDP) that computes an optimal gain, minimizing the steady-state covariance. Extensive simulations on benchmark systems -- including a rotary inverted pendulum and an active suspension system -- demonstrate the superior robustness and accuracy of our method compared to existing data-driven LQR approaches. The proposed framework offers a practical and theoretically grounded solution for controller design in noise-corrupted environments where system identification is infeasible.', 'Synthesis of Dissipative Systems Using Input-State Data   This paper deals with the data-driven synthesis of dissipative linear systems\nin discrete time. We collect finitely many noisy data samples with which we\nsynthesise a controller that makes all systems that explain the data\ndissipative with respect to a given quadratic supply rate. By adopting the\ninformativity approach, we introduce the notion of informativity for\nclosed-loop dissipativity. Under certain assumptions on the noise and the\nsystem, with the help of tools for quadratic matrix inequalities, we provide\nnecessary and sufficient conditions for informativity for closed-loop\ndissipativity. We also provide a recipe to design suitable controllers by means\nof data-based linear matrix inequalities. This main result comprises two parts,\nto account for both the cases that the output matrices are known or unknown.\nLastly, we illustrate our findings with an example, for which we want to design\na data-driven controller achieving (strict) passivity.\n']","[('stabilizing controllers', 0.5247434973716736), ('stabilizing controller', 0.5041810274124146), ('robust controller', 0.5025574564933777), ('control nonlinear systems', 0.4979483187198639), ('state feedback controller', 0.4814956486225128), ('robust control', 0.4755575954914093), ('feedback controllers', 0.47344040870666504), ('robust stability', 0.4728104770183563), ('feedback controller', 0.45167770981788635), ('controller synthesis', 0.4475046694278717)]"
256,256,112,256_motivic spectra_motivic homotopy_motivic cohomology_motivic analogue,"['motivic spectra', 'motivic homotopy', 'motivic cohomology', 'motivic analogue', 'equivariant motivic', 'etale motivic', 'theory motivic', 'cohomology theories', 'base schemes', 'motivic']","['Motivic infinite loop spaces   We prove a recognition principle for motivic infinite P1-loop spaces over a\nperfect field. This is achieved by developing a theory of framed motivic\nspaces, which is a motivic analogue of the theory of E-infinity-spaces. A\nframed motivic space is a motivic space equipped with transfers along finite\nsyntomic morphisms with trivialized cotangent complex in K-theory. Our main\nresult is that grouplike framed motivic spaces are equivalent to the full\nsubcategory of motivic spectra generated under colimits by suspension spectra.\nAs a consequence, we deduce some representability results for suspension\nspectra of smooth varieties, and in particular for the motivic sphere spectrum,\nin terms of Hilbert schemes of points in affine spaces.\n', 'Norms in motivic homotopy theory   If $f:S\' \\to S$ is a finite locally free morphism of schemes, we construct a\nsymmetric monoidal ""norm"" functor $f_\\otimes: \\mathcal H_*(S\') \\to\\mathcal\nH_*(S)$, where $\\mathcal H_*(S)$ is the pointed unstable motivic homotopy\ncategory over $S$. If $f$ is finite \\\'etale, we show that it stabilizes to a\nfunctor $f_\\otimes: \\mathcal{SH}(S\') \\to \\mathcal{SH}(S)$, where\n$\\mathcal{SH}(S)$ is the $\\mathbb P^1$-stable motivic homotopy category over\n$S$. Using these norm functors, we define the notion of a normed motivic\nspectrum, which is an enhancement of a motivic $E_\\infty$-ring spectrum. The\nmain content of this text is a detailed study of the norm functors and of\nnormed motivic spectra, and the construction of examples. In particular: we\ninvestigate the interaction of norms with Grothendieck\'s Galois theory, with\nBetti realization, and with Voevodsky\'s slice filtration; we prove that the\nnorm functors categorify Rost\'s multiplicative transfers on Grothendieck-Witt\nrings; and we construct normed spectrum structures on the motivic cohomology\nspectrum $H\\mathbb Z$, the homotopy K-theory spectrum $KGL$, and the algebraic\ncobordism spectrum $MGL$. The normed spectrum structure on $H\\mathbb Z$ is a\ncommon refinement of Fulton and MacPherson\'s mutliplicative transfers on Chow\ngroups and of Voevodsky\'s power operations in motivic cohomology.\n', 'The localization theorem for framed motivic spaces   We prove the analog of the Morel-Voevodsky localization theorem for framed\nmotivic spaces. We deduce that framed motivic spectra are equivalent to motivic\nspectra over arbitrary schemes, and we give a new construction of the motivic\ncohomology of arbitrary schemes.\n']","[('motivic spectra', 0.7046006917953491), ('motivic homotopy', 0.6923215389251709), ('motivic cohomology', 0.6898288726806641), ('motivic analogue', 0.5817579627037048), ('equivariant motivic', 0.5183833241462708), ('etale motivic', 0.5031164288520813), ('theory motivic', 0.5018592476844788), ('cohomology theories', 0.4726020395755768), ('base schemes', 0.449385404586792), ('motivic', 0.43356120586395264)]"
257,257,112,257_private information retrieval_private information_information leakage_information retrieval pir,"['private information retrieval', 'private information', 'information leakage', 'information retrieval pir', 'revealing information', 'retrieval pir', 'privacy', 'information theoretic', 'privately', 'private']","['The Capacity of Single-Server Weakly-Private Information Retrieval   A private information retrieval (PIR) protocol guarantees that a user can\nprivately retrieve files stored in a database without revealing any information\nabout the identity of the requested file. Existing information-theoretic PIR\nprotocols ensure perfect privacy, i.e., zero information leakage to the servers\nstoring the database, but at the cost of high download. In this work, we\npresent weakly-private information retrieval (WPIR) schemes that trade off\nperfect privacy to improve the download cost when the database is stored on a\nsingle server. We study the tradeoff between the download cost and information\nleakage in terms of mutual information (MI) and maximal leakage (MaxL) privacy\nmetrics. By relating the WPIR problem to rate-distortion theory, the\ndownload-leakage function, which is defined as the minimum required download\ncost of all single-server WPIR schemes for a given level of information leakage\nand a fixed file size, is introduced. By characterizing the download-leakage\nfunction for the MI and MaxL metrics, the capacity of single-server WPIR is\nfully described.\n', 'Pliable Private Information Retrieval   We formulate a new variant of the private information retrieval (PIR) problem\nwhere the user is pliable, i.e., interested in any message from a desired\nsubset of the available dataset, denoted as pliable private information\nretrieval (PPIR). We consider a setup where a dataset consisting of $f$\nmessages is replicated in $n$ noncolluding databases and classified into\n$\\Gamma$ classes. For this setup, the user wishes to retrieve any $\\lambda\\geq\n1$ messages from multiple desired classes, i.e., $\\eta\\geq 1$, while revealing\nno information about the identity of the desired classes to the databases. We\nterm this problem multi-message PPIR (M-PPIR) and introduce the single-message\nPPIR (PPIR) problem as an elementary special case of M-PPIR. We first derive\nconverse bounds on the M-PPIR rate, which is defined as the ratio of the\ndesired amount of information and the total amount of downloaded information,\nfollowed by the corresponding achievable schemes. As a result, we show that the\nPPIR capacity, i.e., the maximum achievable PPIR rate, for $n$ noncolluding\ndatabases matches the capacity of PIR with $n$ databases and $\\Gamma$ messages.\nThus, enabling flexibility, i.e., pliability, where privacy is only guaranteed\nfor classes, but not for messages as in classical PIR, allows to trade-off\nprivacy versus download rate. A similar insight is shown to hold for the\ngeneral case of M-PPIR.\n', 'Semantic Private Information Retrieval   We investigate the problem of semantic private information retrieval\n(semantic PIR). In semantic PIR, a user retrieves a message out of $K$\nindependent messages stored in $N$ replicated and non-colluding databases\nwithout revealing the identity of the desired message to any individual\ndatabase. The messages come with \\emph{different semantics}, i.e., the messages\nare allowed to have \\emph{non-uniform a priori probabilities} denoted by\n$(p_i>0,\\: i \\in [K])$, which are a proxy for their respective popularity of\nretrieval, and \\emph{arbitrary message sizes} $(L_i,\\: i \\in [K])$. This is a\ngeneralization of the classical private information retrieval (PIR) problem,\nwhere messages are assumed to have equal a priori probabilities and equal\nmessage sizes. We derive the semantic PIR capacity for general $K$, $N$. The\nresults show that the semantic PIR capacity depends on the number of databases\n$N$, the number of messages $K$, the a priori probability distribution of\nmessages $p_i$, and the message sizes $L_i$. We present two achievable semantic\nPIR schemes: The first one is a deterministic scheme which is based on message\nasymmetry. This scheme employs non-uniform subpacketization. The second scheme\nis probabilistic and is based on choosing one query set out of multiple options\nat random to retrieve the required message without the need for exponential\nsubpacketization. We derive necessary and sufficient conditions for the\nsemantic PIR capacity to exceed the classical PIR capacity with equal priors\nand sizes. Our results show that the semantic PIR capacity can be larger than\nthe classical PIR capacity when longer messages have higher popularities.\nHowever, when messages are equal-length, the non-uniform priors cannot be\nexploited to improve the retrieval rate over the classical PIR capacity.\n']","[('private information retrieval', 0.6929699182510376), ('private information', 0.5506483316421509), ('information leakage', 0.47718000411987305), ('information retrieval pir', 0.4686659276485443), ('revealing information', 0.4662775695323944), ('retrieval pir', 0.4616197347640991), ('privacy', 0.4530813992023468), ('information theoretic', 0.4067840278148651), ('privately', 0.37498316168785095), ('private', 0.3675479292869568)]"
258,258,112,258_levy processes_similar markov processes_markov processes_quasi stationary distributions,"['levy processes', 'similar markov processes', 'markov processes', 'quasi stationary distributions', 'spectrally negative evy', 'markov process', 'semi markov', 'spectrally positive evy', 'quasi stationary distribution', 'negative evy processes']","[""Exit problems for positive self-similar Markov processes with one-sided\n  jumps   A systematic exposition of scale functions is given for positive self-similar\nMarkov processes (pssMp) with one-sided jumps. The scale functions express as\nconvolution series of the usual scale functions associated with spectrally\none-sided L\\'evy processes that underly the pssMp through the Lamperti\ntransform. This theory is then brought to bear on solving the spatio-temporal:\n(i) two-sided exit problem; (ii) joint first passage problem upwards for the\nthe pssMp and its multiplicative drawdown (resp. drawup) in the spectrally\nnegative (resp. positive) case.\n"", ""Stable L\\'evy processes in a cone   Ba\\~nuelos and Bogdan (2004) and Bogdan, Palmowski and Wang (2016) analyse\nthe asymptotic tail distribution of the first time a stable (L\\'evy) process in\ndimension $d\\geq 2$ exists a cone. We use these results to develop the notion\nof a stable process conditioned to remain in a cone as well as the the notion\nof a stable process conditioned to absorb continuously at the apex of a cone\n(without leaving the cone). As self-similar Markov processes we examine some of\ntheir fundamental properties through the lens of its Lamperti-Kiu\ndecomposition. In particular we are interested to understand the underlying\nstructure of the Markov additive process that drives such processes. As a\nconsequence of our interrogation of the underlying MAP, we are able to provide\nan answer by example to the open question: If the modulator of a MAP has a\nstationary distribution, under what conditions does its ascending ladder MAP\nhave a stationary distribution?\n  We show how the two forms of conditioning are dual to one another. Moreover,\nwe construct the recurrent extension of the stable process killed on exiting a\ncone, showing that it again remains in the class of self-similar Markov\nprocesses.\n  In the spirit of several very recent works, the results presented here show\nthat many previously unknown results of stable processes, which have long since\nbeen understood for Brownian motion, or are easily proved for Brownian motion,\nbecome accessible by appealing to the notion of the stable process as a\nself-similar Markov process, in addition to its special status as a L\\'evy\nprocesses with a semi-tractable potential analysis.\n"", ""Existence of quasi-stationary distributions for spectrally positive\n  L\\'evy processes on the half-line   For spectrally positive L\\'evy processes killed on exiting the half-line,\nexistence of a quasi-stationary distribution is characterized by the\nexponential integrability of the exit time, the Laplace exponent and the\nnon-negativity of the scale functions. It is proven that if there is a\nquasi-stationary distribution, there are necessarily infinitely many ones and\nthe set of quasi-stationary distributions is characterized. A sufficient\ncondition for the minimal quasi-stationary distribution to be the Yaglom limit\nis given.\n""]","[('levy processes', 0.6097230315208435), ('similar markov processes', 0.5755704045295715), ('markov processes', 0.5668426156044006), ('quasi stationary distributions', 0.5549851059913635), ('spectrally negative evy', 0.5439596772193909), ('markov process', 0.532330334186554), ('semi markov', 0.5247262120246887), ('spectrally positive evy', 0.5192314386367798), ('quasi stationary distribution', 0.5141048431396484), ('negative evy processes', 0.5109459757804871)]"
259,259,111,259_path algebras_algebras graded_graded ideals_path algebra,"['path algebras', 'algebras graded', 'graded ideals', 'path algebra', 'algebra graded', 'leavitt', 'algebras finite', 'graded theory', 'graph algebras', 'graded ideal']","[""On the ideals of ultragraph Leavitt path algebras   In this article, we provide an explicit description of a set of generators\nfor any ideal of an ultragraph Leavitt path algebra. We provide several\nadditional consequences of this description, including information about\ngenerating sets for graded ideals, the graded uniqueness and Cuntz-Krieger\ntheorems, the semiprimeness, and the semiprimitivity of ultragraph Leavitt path\nalgebras, a complete characterization of the prime and primitive ideals of an\nultragraph Leavitt path algebra. We also show that every primitive ideal of an\nultragraph Leavitt path algebra is exactly the annihilator of a Chen simple\nmodule. Consequently, we prove Exel's Effros-Hahn conjecture on primitive\nideals in the ultragraph Leavitt path algebra setting (a conclusion that is\nalso new in the context of Leavitt path algebras of graphs).\n"", 'A Generic Quotient of a Leavitt Path Algebra is a Leavitt Path Algebra   We provide a complete answer to the question ""When is a quotient of a Leavitt\npath algebra isomorphic to a Leavitt path algebra?"" in terms of the interaction\nof the kernel of the quotient homomorphism with the cycles of the digraph. A\nkey ingredient is the characterization of finitely generated projective\n(Leavitt path algebra) modules whose endomorphism algebras are finite\ndimensional. We define a stratification and a parametrization of the ideal\nspace of a Leavitt path algebra and show that a generic quotient of a Leavitt\npath algebra is a Leavitt path algebra. Along the way we show that the lattice\nof graded ideals of a Leavitt path algebra is a Morita invariant, hence\nindependent of the grading. Contrary to most algebraic properties of Leavitt\npath algebras, our criterion for a quotient to be isomorphic to a Leavitt path\nalgebra is not independent of the field of coefficients. We end this article by\npointing out an intriguing connection with quantum spaces.\n', 'Realizing ultragraph Leavitt path algebras as Steinberg algebras   In this article, we realize ultragraph Leavitt path algebras as Steinberg\nalgebras. This realization allows us to use the groupoid approach to obtain\nstructural results about these algebras. Using skew product groupoid, we show\nthat ultragraph Leavitt path algebras are graded von Neumann regular rings. We\ncharacterize strongly graded ultragraph Leavitt path algebras and show that\nevery ultragraph Leavitt path algebra is semiprimitive. Moreover, we\ncharacterize irreducible representations of ultragraph Leavitt path algebras.\nWe also show that ultragraph Leavitt path algebras can be realized as\nCuntz-Pimsner rings.\n']","[('path algebras', 0.5984772443771362), ('algebras graded', 0.5896286368370056), ('graded ideals', 0.5194516777992249), ('path algebra', 0.5113569498062134), ('algebra graded', 0.5056569576263428), ('leavitt', 0.48732703924179077), ('algebras finite', 0.4813289940357208), ('graded theory', 0.47535547614097595), ('graph algebras', 0.47326353192329407), ('graded ideal', 0.4670443832874298)]"
260,260,111,260_random polytopes_random polytope_convex hulls_convex hull points,"['random polytopes', 'random polytope', 'convex hulls', 'convex hull points', 'polytopes', 'convex bodies', 'convex hull', 'polytope', 'convex body', 'stochastic geometry']","['Beta Polytopes and Beta Cones: An Exactly Solvable Model in Geometric\n  Probability   Let $X_1,\\ldots, X_n$ be independent random points in the unit ball of\n$\\mathbb R^d$ such that $X_i$ follows a beta distribution with the density\nproportional to $(1-\\|x\\|^2)^{\\beta_i}1_{\\{\\|x\\| <1\\}}$. Here, $\\beta_1,\\ldots,\n\\beta_n> -1$ are parameters. We study random polytopes of the form\n$[X_1,\\ldots,X_n]$, called beta polytopes. We determine explicitly expected\nvalues of several functionals of these polytopes including the number of\n$k$-dimensional faces, the volume, the intrinsic volumes, the total $k$-volume\nof the $k$-skeleton, various angle sums, and the $S$-functional which\ngeneralizes and unifies many of the above examples. We identify and study the\ncentral object needed to analyze beta polytopes: beta cones. For these, we\ndetermine explicitly expected values of several functionals including the solid\nangle, conic intrinsic volumes and the number of $k$-dimensional faces. We\nidentify expected conic intrinsic volumes of beta cones as a crucial quantity\nneeded to express all the functionals mentioned above. We obtain a formula for\nthese expected conic intrinsic volumes in terms of a function $\\Theta$ for\nwhich we provide an explicit integral representation. The proofs combine\nmethods from integral and stochastic geometry with the study of the analytic\nproperties of the function $\\Theta$.\n', ""Beta polytopes and Poisson polyhedra: $f$-vectors and angles   We study random polytopes of the form $[X_1,\\ldots,X_n]$ defined as convex\nhulls of independent and identically distributed random points $X_1,\\ldots,X_n$\nin $\\mathbb{R}^d$ with one of the following densities: $$ f_{d,\\beta} (x) =\nc_{d,\\beta} (1-\\|x\\|^2)^{\\beta}, \\qquad \\|x\\| < 1, \\quad \\text{(beta\ndistribution, $\\beta>-1$)} $$ or $$ \\tilde f_{d,\\beta} (x) =\n\\tilde{c}_{d,\\beta} (1+\\|x\\|^2)^{-\\beta}, \\qquad x\\in\\mathbb{R}^d, \\quad\n\\text{(beta' distribution, $\\beta>d/2$)}. $$ This setting also includes the\nuniform distribution on the unit sphere and the standard normal distribution as\nlimiting cases. We derive exact and asymptotic formulae for the expected number\nof $k$-faces of $[X_1,\\ldots,X_n]$ for arbitrary $k\\in\\{0,1,\\ldots,d-1\\}$. We\nprove that for any such $k$ this expected number is strictly monotonically\nincreasing with $n$. Also, we compute the expected internal and external angles\nof these polytopes at faces of every dimension and, more generally, the\nexpected conic intrinsic volumes of their tangent cones. By passing to the\nlarge $n$ limit in the beta' case, we compute the expected $f$-vector of the\nconvex hull of Poisson point processes with power-law intensity function. Using\nconvex duality, we derive exact formulae for the expected number of $k$-faces\nof the zero cell for a class of isotropic Poisson hyperplane tessellations in\n$\\mathbb R^d$. This family includes the zero cell of a classical stationary and\nisotropic Poisson hyperplane tessellation and the typical cell of a stationary\nPoisson--Voronoi tessellation as special cases. In addition, we prove precise\nlimit theorems for this $f$-vector in the high-dimensional regime, as\n$d\\to\\infty$. Finally, we relate the $d$-dimensional beta and beta'\ndistributions to the generalized Pareto distributions known in extreme-value\ntheory.\n"", ""Angles of Random Simplices and Face Numbers of Random Polytopes   Pick $d+1$ points uniformly at random on the unit sphere in $\\mathbb R^d$.\nWhat is the expected value of the angle sum of the simplex spanned by these\npoints? Choose $n$ points uniformly at random in the $d$-dimensional ball. What\nis the expected number of faces of their convex hull? We answer these and some\nrelated questions of stochastic geometry. To this end, we compute expected\ninternal angles of random simplices whose vertices are independent random\npoints sampled from one of the following $d$-dimensional distributions: (i) the\nbeta distribution with the density proportional to $(1-\\|x\\|^2)^{\\beta}$, where\n$x$ is belongs to the unit ball in $\\mathbb R^d$; (ii) the beta' distribution\nwith the density proportional to $(1+\\|x\\|^2)^{-\\beta}$, where\n$x\\in\\mathbb{R}^{d}$. These results imply explicit formulae for the expected\nface numbers of the following random polytopes: (a) the typical Poisson-Voronoi\ncell; (b) the zero cell of the Poisson hyperplane tessellation; (c) beta and\nbeta' polytopes defined as convex hulls of i.i.d. samples from the\ncorresponding distributions.\n""]","[('random polytopes', 0.6208714246749878), ('random polytope', 0.5794429183006287), ('convex hulls', 0.5036776065826416), ('convex hull points', 0.48666200041770935), ('polytopes', 0.47826090455055237), ('convex bodies', 0.47437044978141785), ('convex hull', 0.4537370502948761), ('polytope', 0.4377724826335907), ('convex body', 0.4335496723651886), ('stochastic geometry', 0.4201650321483612)]"
261,261,111,261_sturm liouville operators_sturm liouville operator_inverse spectral theory_inverse spectral,"['sturm liouville operators', 'sturm liouville operator', 'inverse spectral theory', 'inverse spectral', 'liouville operators', 'spectral problems', 'liouville operator', 'sturm liouville problems', 'spectral parameter', 'sturm liouville type']","['Spectrum completion and inverse Sturm-Liouville problems   Given a finite set of eigenvalues of a regular Sturm-Liouville problem for\nthe equation -y{\\prime}{\\prime}+q(x)y={\\lambda}y, the potential q(x) of which\nis unknown. We show the possibility to compute more eigenvalues without any\nadditional information on the potential q(x). Moreover, considering the\nSturm-Liouville problem with the boundary conditions y{\\prime}(0)-hy(0)=0 and\ny{\\prime}({\\pi})+Hy({\\pi})=0, where h, H are some constants, we complete its\nspectrum without additional information neither on the potential q(x) nor on\nthe constants h and H. The eigenvalues are computed with a uniform absolute\naccuracy. Based on this result we propose a new method for numerical solution\nof the inverse Sturm-Liouville problem of recovering the potential from two\nspectra. The method includes the completion of the spectra in the first step\nand reduction to a system of linear algebraic equations in the second. The\npotential q(x) is recovered from the first component of the solution vector.\nThe approach is based on special Neumann series of Bessel functions\nrepresentations for solutions of Sturm-Liouville equations possessing\nremarkable properties and leads to an efficient numerical algorithm for solving\ninverse Sturm-Liouville problems.\n', 'Local solvability and stability of the inverse problem for the\n  non-self-adjoint Sturm-Liouville operator   We consider the non-self-adjoint Sturm-Liouville operator on a finite\ninterval. The inverse spectral problem is studied, which consists in recovering\nthis operator from its eigenvalues and generalized weight numbers. We prove\nlocal solvability and stability of this inverse problem, relying on the method\nof spectral mappings. Possible splitting of multiple eigenvalues is taken into\naccount.\n', 'Inverse Sturm-Liouville problem with analytical functions in the\n  boundary condition   The inverse spectral problem is studied for the Sturm-Liouville operator with\na complex-valued potential and arbitrary entire functions in one of the\nboundary conditions. We obtain necessary and sufficient conditions for\nuniqueness, and develop a constructive algorithm for the inverse problem\nsolution. The main results are applied to the Hochstadt-Lieberman half-inverse\nproblem. As an auxiliary proposition, we prove local solvability and stability\nfor the inverse Sturm-Liouville problem by the Cauchy data in the\nnon-self-adjoint case.\n']","[('sturm liouville operators', 0.6767178177833557), ('sturm liouville operator', 0.6752378940582275), ('inverse spectral theory', 0.6518281698226929), ('inverse spectral', 0.6469900012016296), ('liouville operators', 0.597019612789154), ('spectral problems', 0.5961850881576538), ('liouville operator', 0.5951401591300964), ('sturm liouville problems', 0.5894889831542969), ('spectral parameter', 0.5239428877830505), ('sturm liouville type', 0.520825207233429)]"
262,262,111,262_public transit_transportation network_transit systems_mobility systems,"['public transit', 'transportation network', 'transit systems', 'mobility systems', 'public transport', 'traffic congestion', 'transportation', 'transit', 'ridesharing', 'buses']","[""An algorithm for integrating peer-to-peer ridesharing and schedule-based\n  transit system for first mile/last mile access   Due to limited transit network coverage and infrequent service, suburban\ncommuters often face the transit first mile/last mile (FMLM) problem. To deal\nwith this, they either drive to a park-and-ride location to take transit, use\ncarpooling, or drive directly to their destination to avoid inconvenience.\nRidesharing, an emerging mode of transportation, can solve the transit first\nmile/last mile problem. In this setup, a driver can drive a ride-seeker to a\ntransit station, from where the rider can take transit to her respective\ndestination. The problem requires solving a ridesharing matching problem with\nthe routing of riders in a multimodal transportation network. We develop a\ntransit-based ridesharing matching algorithm to solve this problem. The method\nleverages the schedule-based transit shortest path to generate feasible matches\nand then solves a matching optimization program to find an optimal match\nbetween riders and drivers. The proposed method not only assigns an optimal\ndriver to the rider but also assigns an optimal transit stop and a transit\nvehicle trip departing from that stop for the rest of the rider's itinerary. We\nalso introduce the application of space-time prism (STP) (the geographical area\nwhich can be reached by a traveler given the time constraints) in the context\nof ridesharing to reduce the computational time by reducing the network search.\nAn algorithm to solve this problem dynamically using a rolling horizon approach\nis also presented. We use simulated data obtained from the activity-based\ntravel demand model of Twin Cities, MN to show that the transit-based\nridesharing can solve the FMLM problem and save a significant number of\nvehicle-hours spent in the system.\n"", 'Revitalizing Public Transit in Low Ridership Areas: An Exploration of\n  On-Demand Multimodal Transit Systems   Public transit plays an essential role in mitigating traffic congestion,\nreducing emissions, and enhancing travel accessibility and equity. One of the\ncritical challenges in designing public transit systems is distributing finite\nservice supplies temporally and spatially to accommodate time-varying and\nspace-heterogeneous travel demands. Particularly, for regions with low or\nscattered ridership, there is a dilemma in designing traditional transit lines\nand corresponding service frequencies. Dense transit lines and high service\nfrequency increase operation costs, while sparse transit lines and low service\nfrequency result in poor accessibility and long passenger waiting time. In the\ncoming era of Mobility-as-a-Service, the aforementioned challenge is expected\nto be addressed by on-demand services. In this study, we design an On-Demand\nMultimodel Transit System (ODMTS) for regions with low or scattered travel\ndemands, in which some low-ridership bus lines are replaced with flexible\non-demand ride-sharing shuttles. In the proposed ODMTS, riders within service\nregions can request shuttles to finish their trips or to connect to fixed-route\nservices such as bus, metro, and light rail. Leveraging the integrated\ntransportation system modeling platform, POLARIS, a simulation-based case study\nis conducted to assess the effectiveness of this system in Austin, Texas.\n', 'Planning of integrated mobility-on-demand and urban transit networks   We envision a multimodal transportation system where Mobility-on-Demand (MoD)\nservice is used to serve the first mile and last mile of transit trips. For\nthis purpose, the current research formulates an optimization model for\ndesigning an integrated MoD and urban transit system. The proposed model is a\nmixed-integer non-linear programming model that captures the strategic behavior\nof passengers in a multimodal network through a passenger assignment model. It\ndetermines which transit routes to operate, the frequency of the operating\nroutes, the fleet size of vehicles required in each transportation analysis\nzone to serve the demand, and the passenger flow on both road and transit\nnetworks. A Benders decomposition approach with several enhancements is\nproposed to solve the given optimization program. Computational experiments are\npresented for the Sioux Falls multimodal network. The results show a\nsignificant improvement in the congestion in the city center with the\nintroduction and optimization of an integrated transportation system. The\nproposed design allocates more vehicles to the outskirt zones in the network\n(to serve the first mile and last mile of transit trips) and more frequency to\nthe transit routes in the city center. The integrated system significantly\nimproves the share of transit passengers and their level of service in\ncomparison to the base optimized transit system. The sensitivity analysis of\nthe bus and vehicle fleet shows that increasing the number of buses has more\nimpact on improving the level of service of passengers compared to increasing\nthe number of MoD vehicles. Finally, we provide managerial insights for\ndeploying such multimodal service.\n']","[('public transit', 0.5629184246063232), ('transportation network', 0.5568921566009521), ('transit systems', 0.5222118496894836), ('mobility systems', 0.49462637305259705), ('public transport', 0.482656329870224), ('traffic congestion', 0.46912428736686707), ('transportation', 0.46783247590065), ('transit', 0.46449121832847595), ('ridesharing', 0.4630991518497467), ('buses', 0.44608980417251587)]"
263,263,110,263_boltzmann based_boltzmann transport_boltzmann bgk_boltzmann,"['boltzmann based', 'boltzmann transport', 'boltzmann bgk', 'boltzmann', 'convection diffusion', 'finite difference scheme', 'based lattice', 'finite difference', 'time lattice', 'kinetic scheme']","['An automatic approach to develop the fourth-order and L^2-stable lattice\n  Boltzmann model for diagonal-anisotropic diffusion equations   This paper discusses how to develop a high-order multiple-relaxation-time\nlattice Boltzmann (MRT-LB) model for the general d(>=1)-dimensional\ndiagonal-anisotropic diffusion equation. Such an MRT-LB model considers the\ntransformation matrix constructed in a natural way and the DdQ(2d^2+1) lattice\nstructure. A key step in developing the high-order MRT-LB model is to determine\nthe adjustable relaxation parameters and weight coefficients, which are used to\neliminate the truncation errors at certain orders of the MRT-LB model, while\nensuring the stability of the MRT-LB model. In this work, we first present a\nunified MRT-LB model for the diagonal-anisotropic diffusion equation. Then,\nthrough the direct Taylor expansion, we analyze the macroscopic modified\nequations of the MRT-LB model up to fourth-order, and further derive the\nfourth-order consistent conditions of the MRT-LB model. Additionally, we also\nconstruct the fourth-order initialization scheme for the present LB method.\nAfter that, the condition which guarantees that the MRT-LB model can satisfy\nthe stability structure is explicitly given, and from a numerical perspective,\nonce the stability structure is satisfied, the MRT-LB model must be L^2 stable.\nIn combination with the fourth-order consistent and L^2 stability conditions,\nthe relaxation parameters and weight coefficients of the MRT-LB model can be\nautomatically given by a simple computer code. Finally, we perform numerical\nsimulations of several benchmark problems, and find that the numerical results\ncan achieve a fourth-order convergence rate, which is in agreement with our\ntheoretical analysis. In particular, for the isotropic diffusion equation, we\nalso make a comparison between the fourth-order MRT-LB models with the\nDdQ(2d^2+1) and DdQ(2d+1) lattice structures, and the numerical results show\nthat the MRT-LB model with the DdQ(2d^2+1) lattice structure is more general.\n', 'A general fourth-order mesoscopic multiple-relaxation-time lattice\n  Boltzmann model and equivalent macroscopic finite-difference scheme for\n  two-dimensional diffusion equations   In this work, we first develop a general mesoscopic multiple-relaxation-time\nlattice Boltzmann (MRT-LB) model for the two-dimensional diffusion equation\nwith the constant diffusion coefficient and source term, where the D2Q5 (five\ndiscrete velocities in two-dimensional space) lattice structure is considered.\nThen we exactly derive the equivalent macroscopic finite-difference scheme of\nthe MRT-LB model. Additionally, we also propose a proper MRT-LB model for the\ndiffusion equation with a linear source term, and obtain an equivalent\nmacroscopic six-level finite-difference scheme. After that, we conduct the\naccuracy and stability analysis of the finite-difference scheme and the\nmesoscopic MRT-LB model. It is found that at the diffusive scaling, both of\nthem can achieve a fourth-order accuracy in space based on the Taylor\nexpansion. The stability analysis also shows that they are both unconditionally\nstable. Finally, some numerical experiments are conducted, and the numerical\nresults are also consistent with our theoretical analysis.\n', 'An immersed interface-lattice Boltzmann method for fluid-structure\n  interaction   An immersed interface-lattice Boltzmann method (II-LBM) is developed for\nmodelling fluid-structure systems. The key element of this approach is the\ndetermination of the jump conditions that are satisfied by the distribution\nfunctions within the framework of the lattice Boltzmann method when forces are\nimposed along a surface immersed in an incompressible fluid. In this initial\nII-LBM, the discontinuity related to the normal portion of the interfacial\nforce is sharply resolved by imposing the relevant jump conditions using an\napproach that is analogous to imposing the corresponding pressure jump\ncondition in the incompressible Navier-Stokes equations. We show that the jump\nconditions for the distribution functions are the same in both\nsingle-relaxation-time and multi-relaxation-time LBM formulations. Tangential\nforces are treated using the immersed boundary-lattice Boltzmann method\n(IB-LBM). The performance of the II-LBM method is compared to both the direct\nforcing IB-LBM for rigid-body fluid-structure interaction, and the classical\nIB-LBM for elastic interfaces. Higher order accuracy is observed with the\nII-LBM as compared to the IB-LBM for selected benchmark problems. Because the\njump conditions of the distribution function also satisfy the continuity of the\nvelocity field across the interface, the error in the velocity field is much\nsmaller for the II-LBM than the IB-LBM. The II-LBM is also demonstrated to\nprovide superior volume conservation when simulating flexible boundaries.\n']","[('boltzmann based', 0.49423280358314514), ('boltzmann transport', 0.491838276386261), ('boltzmann bgk', 0.428296834230423), ('boltzmann', 0.4282011389732361), ('convection diffusion', 0.4184987246990204), ('finite difference scheme', 0.38644522428512573), ('based lattice', 0.3481917679309845), ('finite difference', 0.3034323751926422), ('time lattice', 0.2992453873157501), ('kinetic scheme', 0.298686146736145)]"
264,264,110,264_skewness kurtosis_weibull distributions_weibull distribution_distributions,"['skewness kurtosis', 'weibull distributions', 'weibull distribution', 'distributions', 'lifetime distribution', 'tailed distributions', 'distribution', 'generalized skew', 'family distributions', 'proposed distribution']","['A Novel Bivariate Generalized Weibull Distribution with Properties and\n  Applications   Univariate Weibull distribution is a well-known lifetime distribution and has\nbeen widely used in reliability and survival analysis. In this paper, we\nintroduce a new family of bivariate generalized Weibull (BGW) distributions,\nwhose univariate marginals are exponentiated Weibull distribution. Different\nstatistical quantiles like marginals, conditional distribution, conditional\nexpectation, product moments, correlation and a measure component reliability\nare derived. Various measures of dependence and statistical properties along\nwith ageing properties are examined. Further, the copula associated with BGW\ndistribution and its various important properties are also considered. The\nmethods of maximum likelihood and Bayesian estimation are employed to estimate\nunknown parameters of the model. A Monte Carlo simulation and real data study\nare carried out to demonstrate the performance of the estimators and results\nhave proven the effectiveness of the distribution in real-life situations\n', 'A Bimodal Weibull Distribution: Properties and Inference   Modeling is a challenging topic and using parametric models is an important\nstage to reach flexible function for modeling. Weibull distribution has two\nparameters which are shape $\\alpha$ and scale $\\beta$. In this study,\nbimodality parameter is added and so bimodal Weibull distribution is proposed\nby using a quadratic transformation technique used to generate bimodal\nfunctions produced due to using the quadratic expression. The analytical\nsimplicity of Weibull and quadratic form give an advantage to derive a bimodal\nWeibull via constructing normalizing constant. The characteristics and\nproperties of the proposed distribution are examined to show its usability in\nmodeling. After examination as first stage in modeling issue, it is appropriate\nto use bimodal Weibull for modeling data sets. Two estimation methods which are\nmaximum $\\log_q$ likelihood and its special form including objective functions\n$\\log_q(f)$ and $\\log(f)$ are used to estimate the parameters of shape, scale\nand bimodality parameters of the function. The second stage in modeling is\novercome by using heuristic algorithm for optimization of function according to\nparameters due to fact that converging to global point of objective function is\nperformed by heuristic algorithm based on the stochastic optimization. Real\ndata sets are provided to show the modeling competence of the proposed\ndistribution.\n', ""An analysis of multivariate measures of skewness and kurtosis of\n  skew-elliptical distributions   This paper examines eight measures of skewness and Mardia measure of kurtosis\nfor skew-elliptical distributions. Multivariate measures of skewness considered\ninclude Mardia, Malkovich-Afifi, Isogai, Song, Balakrishnan-Brito-Quiroz,\nM$\\acute{o}$ri, Rohatgi and Sz$\\acute{e}$kely, Kollo and Srivastava measures.\nWe first study the canonical form of skew-elliptical distributions, and then\nderive exact expressions of all measures of skewness and kurtosis for the\nfamily of skew-elliptical distributions, except for Song's measure.\nSpecifically, the formulas of these measures for skew normal, skew $t$, skew\nlogistic, skew Laplace, skew Pearson type II and skew Pearson type VII\ndistributions are obtained. Next, as in Malkovich and Afifi (1973), test\nstatistics based on a random sample are constructed for illustrating the\nusefulness of the established results. In a Monte Carlo simulation study,\ndifferent measures of skewness and kurtosis for $2$-dimensional skewed\ndistributions are calculated and compared. Finally, real data is analyzed to\ndemonstrate all the results.\n""]","[('skewness kurtosis', 0.5365507006645203), ('weibull distributions', 0.5158618092536926), ('weibull distribution', 0.4836932420730591), ('distributions', 0.46811673045158386), ('lifetime distribution', 0.44535964727401733), ('tailed distributions', 0.436953604221344), ('distribution', 0.42862996459007263), ('generalized skew', 0.4285890758037567), ('family distributions', 0.4246518909931183), ('proposed distribution', 0.4161659777164459)]"
265,265,109,265_finite coxeter groups_finite coxeter group_coxeter groups_irreducible coxeter group,"['finite coxeter groups', 'finite coxeter group', 'coxeter groups', 'irreducible coxeter group', 'coxeter group', 'reflection groups', 'complex reflection groups', 'group coxeter', 'finite coxeter', 'reflection subgroups']","['Interval groups related to finite Coxeter groups I   We derive presentations of the interval groups related to all quasi-Coxeter\nelements in the Coxeter group of type $D_n$. Type $D_n$ is the only infinite\nfamily of finite Coxeter groups that admits proper quasi-Coxeter elements. The\npresentations we obtain are over a set of generators in bijection with what we\ncall a Carter generating set, and the relations are those defined by the\nrelated Carter diagram together with a twisted or a cycle commutator relator,\ndepending on whether the quasi-Coxeter element is a Coxeter element or not. The\nproof is based on the description of two combinatorial techniques related to\nthe intervals of quasi-Coxeter elements.\n  In a subsequent work [4], we complete our analysis to cover all the\nexceptional cases of finite Coxeter groups, and establish that almost all the\ninterval groups related to proper quasi-Coxeter elements are not isomorphic to\nthe related Artin groups, hence establishing a new family of interval groups\nwith nice presentations. Alongside the proof of the main results, we establish\nimportant properties related to the dual approach to Coxeter and Artin groups.\n', 'Reflection factorizations and quasi-Coxeter elements   We investigate the so-called dual Matsumoto property or Hurwitz action in\nfinite, affine and arbitrary Coxeter groups. In particular, we want to\ninvestigate how to reduce reflection factorizations and how two reflection\nfactorizations of the same element are related to each other. We are motivated\nby the dual approach to Coxeter groups proposed by Bessis and the question\nwhether there is an anlogue of the well known Matsumoto property for reflection\nfactorizations. Our aim is a substantial understanding of the Hurwitz action.\nWe therefore reprove uniformly results of Lewis and Reiner as well as\nBaumeister, Gobet, Roberts and the first author on the Hurwitz in finite\nCoxeter groups. Further we show that in an arbitrary Coxeter group all reduced\nreflection factorizations of the same element appear in the same Hurwitz orbit\nafter a suitable extension by simple reflections. As parabolic quasi-Coxeter\nelements play an outstanding role in the study of the Hurwitz action, we aim to\ncharacterize these elements. We give characterizations of maximal parabolic\nquasi-Coxeter elements in arbitrary Coxeter groups as well as a\ncharacterization of all parabolic quasi-Coxeter elements in affine Coxeter\ngroups.\n', 'Powers of Coxeter elements with unbounded reflection length   For Coxeter groups with sufficiently large braid relations, we prove that the\nsequence of powers of a Coxeter element has unbounded reflection length. We\nestablish a connection between the reflection length functions on arbitrary\nCoxeter groups and the reflection length functions on universal Coxeter groups\nof the same rank through the solution to the word problem for Coxeter groups.\nFor Coxeter groups corresponding to a Coxeter matrix with the same entry\neverywhere except the diagonal, upper bounds for the reflection length of the\npowers of Coxeter elements are established.\n']","[('finite coxeter groups', 0.7919273376464844), ('finite coxeter group', 0.7656177282333374), ('coxeter groups', 0.7157371640205383), ('irreducible coxeter group', 0.683555006980896), ('coxeter group', 0.6669554114341736), ('reflection groups', 0.6397227048873901), ('complex reflection groups', 0.6234914064407349), ('group coxeter', 0.6234174370765686), ('finite coxeter', 0.6183428168296814), ('reflection subgroups', 0.6151999235153198)]"
266,266,109,266_quasi geostrophic equations_surface quasi geostrophic_geostrophic equations_quasi geostrophic sqg,"['quasi geostrophic equations', 'surface quasi geostrophic', 'geostrophic equations', 'quasi geostrophic sqg', 'quasi geostrophic', 'surface quasi', 'global well posedness', 'local well posedness', 'global smooth solutions', 'geostrophic sqg']","['Existence of asymmetric vortex patch for the generalized SQG equations   This paper aims to study the existence of asymmetric solutions for the\ntwo-dimensional generalized surface quasi-geostrophic (gSQG) equations of\nsimply connected patches for $\\alpha\\in[1,2)$ in the whole plane, where\n$\\alpha=1$ corresponds to the surface quasi-geostrophic equations (SQG). More\nprecisely, we construct non-trivial simply connected co-rotating and traveling\npatches with unequal vorticity magnitudes. The proof is carried out by means of\na combination of a desingularization argument with the implicit function\ntheorem on the linearization of contour dynamics equation. Our results extend\nrecent ones in the range $\\alpha\\in[0,1)$ by Hassainia-Hmidi (DCDS-A, 2021) and\nHassainia-Wheeler (SIAM J. Math. Anal., 2022) to more singular velocities,\nfilling an open gap in the range of $\\alpha$.\n', 'Smooth traveling-wave solutions to the inviscid surface\n  quasi-geostrophic equations   In a recent article by Gravejat and Smets, it is built smooth solutions to\nthe inviscid surface quasi-geostrophic equation that have the form of a\ntraveling wave. In this article we work back on their construction to provide\nsolution to a more general class of quasi-geostrophic equation where the\nhalf-laplacian is replaced by any fractional laplacian.\n', 'Contour Dynamics for Surface Quasi-Geostrophic Fronts   We use contour dynamics to derive equations of motion for infinite planar\nsurface quasi-geostrophic (SQG) fronts, and show that it leads to the same\nresult as a regularization procedure introduced previously by Hunter and Shu\n(2018).\n']","[('quasi geostrophic equations', 0.7545023560523987), ('surface quasi geostrophic', 0.6546968817710876), ('geostrophic equations', 0.6217037439346313), ('quasi geostrophic sqg', 0.6136584281921387), ('quasi geostrophic', 0.594871997833252), ('surface quasi', 0.49794647097587585), ('global well posedness', 0.496463418006897), ('local well posedness', 0.484151691198349), ('global smooth solutions', 0.4638334810733795), ('geostrophic sqg', 0.45277267694473267)]"
267,267,108,267_vehicle routing_capacitated vehicle routing_vehicle routing problems_routes,"['vehicle routing', 'capacitated vehicle routing', 'vehicle routing problems', 'routes', 'routing', 'traveling salesman', 'routing time', 'routing problems', 'metaheuristics', 'route']","['Vehicle Routing for the Last-Mile Logistics Problem   Energy consumption is the major contributor associated with large and growing\ntransportation cost in logistics. Optimal vehicle routing approaches can\nprovide solutions to reduce their operating costs and address implications on\nenergy. This paper outlines a solution to the single-depot capacitated vehicle\nrouting problem with the objective of minimizing daily operation cost with a\nhomogeneous fleet of delivery vehicles. The problem is solved using Simulated\nAnnealing, to provide optimal routes for the vehicles traveling between the\ndepot and destinations. Simulation results demonstrate that the proposed\napproach is effective to recommend an optimal route and reduce operation cost.\nSupplementary information and video of our proposed approach can be found at:\nhttps://sites.google.com/view/ud-ids-lab/last-mile\n', ""An integrated selection and routing policy for urban waste collection   We study a daily urban waste collection problem arising in the municipality\nof Groningen, The Netherlands, where residents bring their waste to local\nunderground waste containers organised in clusters. The municipality plans\nroutes for waste collection vehicles to empty the container clusters. These\nroutes should be as short as possible to limit operational costs, but also long\nenough to visit sufficiently many clusters and ensure that containers do not\noverflow. A complicating factor is that the actual fill levels of the clusters'\ncontainers are not known, and only the number of deposits is observed.\nAdditionally, it is unclear whether the containers should be upgraded with\nexpensive fill level sensors so that the service level can be improved or\nrouting costs can be reduced. We propose an efficient integrated selection and\nrouting (ISR) policy that jointly optimises the daily cluster selection and\nrouting decisions. The integration is achieved by first estimating prizes that\nexpress the urgency of selecting a cluster to empty, and then solving a\nprize-collecting vehicle routing problem with time windows and driver breaks to\ncollect these prizes while minimising routing costs. We use a metaheuristic to\nsolve the prize-collecting vehicle routing problem inside a realistic\nsimulation environment that models the waste collection problem faced by the\nmunicipality. We show that solving the daily waste collection problem in this\nway is very effective, and can lead to substantial cost savings for the\nmunicipality in practice, with no reduction in service level. In particular, by\nintegrating the container selection and routing problems using our ISR policy,\nrouting costs can be reduced by more than 40% and the fleet size by 25%. We\nalso show that more advanced measuring techniques do not significantly reduce\nrouting costs, and the service level not at all.\n"", 'The Mobile Production Vehicle Routing Problem: Using 3D Printing in Last\n  Mile Distribution   We study a new variant of the vehicle routing problem, called the Mobile\nProduction Vehicle Routing Problem (MoP-VRP). In this problem, vehicles are\nequipped with 3D printers, and production takes place on the way to the\ncustomer. The objective is to minimize the weighted cost incurred by travel and\ndelay of service. We formulate a Mixed Integer Programming (MIP) model and\ndevelop an Adaptive Large Neighbourhood Search (ALNS) heuristic for this\nproblem. To show the advantage of mobile production, we compare the problem\nwith the Central Production Vehicle Routing Problem (CP-VRP), where production\ntakes place in a central depot. We also propose an efficient ALNS for the\nCP-VRP. We generate benchmark instances based on Vehicle Routing Problem with\nTime Windows (VRPTW) benchmark instances, and realistic instances based on\nreal-life data provided by the Danish Company 3D Printhuset. Overall, the\nproposed ALNS for both problems are efficient, and we solve instances up to 200\ncustomers within a short computational time. We test different scenarios with\nvarying numbers of machines in each vehicle, as well as different production\ntime. The results show that these are the key factors that influence travel and\ndelay costs. The key advantage of mobile production is flexibility: it can\nshorten the time span from the start of production to the delivery of products,\nand at the same time lower delivery costs. Moreover, long-term cost estimations\nshow that this technology has low operation costs and thus is feasible in real\nlife practice.\n']","[('vehicle routing', 0.708404004573822), ('capacitated vehicle routing', 0.7015138268470764), ('vehicle routing problems', 0.6300985813140869), ('routes', 0.4950123727321625), ('routing', 0.4940704107284546), ('traveling salesman', 0.44372880458831787), ('routing time', 0.44225990772247314), ('routing problems', 0.4267606735229492), ('metaheuristics', 0.4182952642440796), ('route', 0.4073580503463745)]"
268,268,108,268_hermite hadamard inequality_inequality convex functions_convex functions applications_hadamard inequality,"['hermite hadamard inequality', 'inequality convex functions', 'convex functions applications', 'hadamard inequality', 'jensen inequality', 'inequalities convex', 'inequality convex', 'convex functions', 'types convex', 'inequalities weighted']","[""On the equality problem of generalized Bajraktarevi\\'c means   The purpose of this paper is to investigate the equality problem of\ngeneralized Bajraktarevi\\'c means, i.e., to solve the functional equation\n\\begin{equation}\\label{E0}\\tag{*}\n  f^{(-1)}\\bigg(\\frac{p_1(x_1)f(x_1)+\\dots+p_n(x_n)f(x_n)}{p_1(x_1)+\\dots+p_n(x_n)}\\bigg)=g^{(-1)}\\bigg(\\frac{q_1(x_1)g(x_1)+\\dots+q_n(x_n)g(x_n)}{q_1(x_1)+\\dots+q_n(x_n)}\\bigg),\n\\end{equation} which holds for all $x=(x_1,\\dots,x_n)\\in I^n$, where $n\\geq 2$,\n$I$ is a nonempty open real interval, the unknown functions\n$f,g:I\\to\\mathbb{R}$ are strictly monotone, $f^{(-1)}$ and $g^{(-1)}$ denote\ntheir generalized left inverses, respectively, and\n$p=(p_1,\\dots,p_n):I\\to\\mathbb{R}_{+}^n$ and\n$q=(q_1,\\dots,q_n):I\\to\\mathbb{R}_{+}^n$ are also unknown functions. This\nequality problem in the symmetric two-variable (i.e., when $n=2$) case was\nalready investigated and solved under sixth-order regularity assumptions by\nLosonczi in 1999. In the nonsymmetric two-variable case, assuming three times\ndifferentiability of $f$, $g$ and the existence of $i\\in\\{1,2\\}$ such that\neither $p_i$ is twice continuously differentiable and $p_{3-i}$ is continuous\non $I$, or $p_i$ is twice differentiable and $p_{3-i}$ is once differentiable\non $I$, we prove that \\eqref{E0} holds if and only if there exist four\nconstants $a,b,c,d\\in\\mathbb{R}$ with $ad\\neq bc$ such that \\begin{equation*}\n  cf+d>0,\\qquad\n  g=\\frac{af+b}{cf+d},\\qquad\\mbox{and}\\qquad q_\\ell=(cf+d)p_\\ell\\qquad\n(\\ell\\in\\{1,\\dots,n\\}). \\end{equation*} In the case $n\\geq 3$, we obtain the\nsame conclusion with weaker regularity assumptions. Namely, we suppose that $f$\nand $g$ are three times differentiable, $p$ is continuous and there exist\n$i,j,k\\in\\{1,\\dots,n\\}$ with $i\\neq j\\neq k\\neq i$ such that $p_i,p_j,p_k$ are\ndifferentiable.\n"", 'On the equality of generalized Bajraktarevi\\\'c means under first-order\n  differentiability assumptions   In this paper we consider the equality problem of generalized Bajraktarevi\\\'c\nmeans, i.e., we are going to solve the functional equation\n\\begin{equation}\\label{E0}\\tag{*}\n  f^{(-1)}\\bigg(\\frac{p_1(x_1)f(x_1)+\\dots+p_n(x_n)f(x_n)}{p_1(x_1)+\\dots+p_n(x_n)}\\bigg)=g^{(-1)}\\bigg(\\frac{q_1(x_1)g(x_1)+\\dots+q_n(x_n)g(x_n)}{q_1(x_1)+\\dots+q_n(x_n)}\\bigg),\n\\end{equation} which holds for all $x=(x_1,\\dots,x_n)\\in I^n$, where $n\\geq 2$,\n$I$ is a nonempty open real interval, the unknown functions\n$f,g:I\\to\\mathbb{R}$ are strictly monotone, $f^{(-1)}$ and $g^{(-1)}$ denote\ntheir generalized left inverses, respectively, and the vector-valued weight\nfunctions $p=(p_1,\\dots,p_n):I\\to\\mathbb{R}_{+}^n$ and\n$q=(q_1,\\dots,q_n):I\\to\\mathbb{R}_{+}^n$ are also unknown. This equality\nproblem in the symmetric two-variable case (i.e., when $n=2$ and $p_1=p_2$,\n$q_1=q_2$) was solved under sixth-order regularity assumptions by Losonczi in\n1999. The authors of this paper improved this result in 2023 by reaching the\nsame conclusion assuming only first-order differentiability. In the\nnonsymmetric case, assuming third-order differentiability of $f$, $g$ and the\nfirst-order differentiability of at least three of the functions\n$p_1,\\dots,p_n$, Gr\\""unwald and P\\\'ales proved that \\eq{0} holds if and only if\nthere exist four constants $a,b,c,d\\in\\mathbb{R}$ with $ad\\neq bc$ such that $$\n  cf+d>0,\\qquad\n  g=\\frac{af+b}{cf+d},\\qquad\\mbox{and}\\qquad q_\\ell=(cf+d)p_\\ell\\qquad\n(\\ell\\in\\{1,\\dots,n\\}). $$ The main goal of this paper is to establish the same\nconclusion under first-order differentiability.\n', ""A tight Hermite-Hadamard's inequality and a generic method for\n  comparison between residuals of inequalities with convex functions   We present a tight parametrical Hermite-Hadamard type inequality with\nprobability measure, which yields a considerably closer upper bound for the\nmean value of convex function than the classical one. Our inequality becomes\nequality not only with affine functions, but also with a family of V-shaped\ncurves determined by the parameter. The residual (error) of this inequality is\nstrictly smaller than in the classical Hermite-Hadamard inequality under any\nprobability measure and with all non-affine convex functions. In the framework\nof Karamata's theorem on the inequalities with convex functions, we propose a\nmethod of measuring a global performance of inequalities in terms of average\nresiduals over functions of the type $x\\mapsto |x-u|$. Using average residuals\nenables comparing two or more inequalities as themselves, with same or\ndifferent measures and without referring to a particular function. Our method\nis applicable to all Karamata's type inequalities, with integrals or sums. A\nnumerical experiment with three different measures indicates that the average\nresidual in our inequality is about 4 times smaller than in classical right\nHermite-Hadamard, and also is smaller than in Jensen's inequality, with all\nthree measures.\n""]","[('hermite hadamard inequality', 0.649143636226654), ('inequality convex functions', 0.5810491442680359), ('convex functions applications', 0.5509800314903259), ('hadamard inequality', 0.5429782271385193), ('jensen inequality', 0.5213128328323364), ('inequalities convex', 0.5146775841712952), ('inequality convex', 0.5096773505210876), ('convex functions', 0.5084303617477417), ('types convex', 0.4825379252433777), ('inequalities weighted', 0.478243350982666)]"
269,269,108,269_equivariant spectral_atiyah singer index_index theorems_elliptic operators,"['equivariant spectral', 'atiyah singer index', 'index theorems', 'elliptic operators', 'index theory', 'singer index', 'eta invariants', 'elliptic operator', 'equivariant', 'compact manifolds']","['The index of families of projective operators   Let $1 \\to \\Gamma \\to \\tilde{G} \\to G \\to 1$ be a central extension by an\nabelian finite group. In this paper, we compute the index of families of\n$\\tilde{G}$-transversally elliptic operators on a $G$-principal bundle $P$. We\nthen introduce the notion of families of projective operators on fibrations\nequipped with an Azumaya bundle $\\mathcal{A}$. We define and compute the index\nof such families using the cohomological index formula for families of\n$SU(N)$-transversally elliptic operators. More precisely, a family $A$ of\nprojective operators can be pulled back in a family $\\tilde{A}$ of\n$SU(N)$-transversally elliptic operators on the $PU(N)$-principal bundle of\ntrivialisations of $\\mathcal{A}$. Through the distributional index of\n$\\tilde{A}$, we can define an index for the family $A$ of projective operators\nand using the index formula in equivariant cohomology for families of\n$SU(N)$-transversally elliptic operators, we derive an explicit cohomological\nindex formula in de Rham cohomology. Once this is done, we define and compute\nthe index of families of projective Dirac operators. As a second application of\nour computation of the index of families of $\\tilde{G}$-transversally elliptic\noperators on a $G$-principal bundle $P$, we consider the special case of a\nfamily of $Spin(2n)$-transversally elliptic Dirac operators over the bundle of\noriented orthonormal frames of an oriented fibration and we relate its\ndistributional index with the index of the corresponding family of projective\nDirac operators.\n', 'An equivariant Atiyah-Patodi-Singer index theorem for proper actions I:\n  the index formula   Consider a proper, isometric action by a unimodular locally compact group $G$\non a Riemannian manifold $M$ with boundary, such that $M/G$ is compact. For an\nequivariant, elliptic operator $D$ on $M$, and an element $g \\in G$, we define\na numerical index $\\operatorname{index}_g(D)$, in terms of a parametrix for $D$\nand a trace associated to $g$. We prove an equivariant Atiyah-Patodi-Singer\nindex theorem for this index. We first state general analytic conditions under\nwhich this theorem holds, and then show that these conditions are satisfied if\n$g=e$ is the identity element; if $G$ is a finitely generated, discrete group,\nand the conjugacy class of $g$ has polynomial growth; and if $G$ is a\nconnected, linear, real semisimple Lie group, and $g$ is a semisimple element.\nIn the classical case, where $M$ is compact and $G$ is trivial, our arguments\nreduce to a relatively short and simple proof of the original\nAtiyah-Patodi-Singer index theorem. In part II of this series, we prove that,\nunder certain conditions, $\\operatorname{index}_g(D)$ can be recovered from a\n$K$-theoretic index of $D$ via a trace defined by the orbital integral over the\nconjugacy class of $g$.\n', 'An equivariant Atiyah-Patodi-Singer index theorem for proper actions II:\n  the $K$-theoretic index   Consider a proper, isometric action by a unimodular locally compact group $G$\non a Riemannian manifold $M$ with boundary, such that $M/G$ is compact. Then an\nequivariant Dirac-type operator $D$ on $M$ under a suitable boundary condition\nhas an equivariant index $\\operatorname{index}_G(D)$ in the $K$-theory of the\nreduced group $C^*$-algebra $C^*_rG$ of $G$. This is a common generalisation of\nthe Baum-Connes analytic assembly map and the (equivariant)\nAtiyah-Patodi-Singer index. In part I of this series, a numerical index\n$\\operatorname{index}_g(D)$ was defined for an element $g \\in G$, in terms of a\nparametrix of $D$ and a trace associated to $g$. An Atiyah-Patodi-Singer type\nindex formula was obtained for this index. In this paper, we show that, under\ncertain conditions, $\\tau_g(\\operatorname{index}_G(D)) =\n\\operatorname{index}_g(D)$, for a trace $\\tau_g$ defined by the orbital\nintegral over the conjugacy class of $g$. This implies that the index theorem\nfrom part I yields information about the $K$-theoretic index\n$\\operatorname{index}_G(D)$. It also shows that $\\operatorname{index}_g(D)$ is\na homotopy-invariant quantity.\n']","[('equivariant spectral', 0.5085148215293884), ('atiyah singer index', 0.4942115247249603), ('index theorems', 0.4617134630680084), ('elliptic operators', 0.44478148221969604), ('index theory', 0.4319602847099304), ('singer index', 0.4240945875644684), ('eta invariants', 0.39385557174682617), ('elliptic operator', 0.38805079460144043), ('equivariant', 0.38106366991996765), ('compact manifolds', 0.3753744661808014)]"
270,270,108,270_generalized fibonacci numbers_generalized fibonacci_fibonacci sequences_fibonacci numbers,"['generalized fibonacci numbers', 'generalized fibonacci', 'fibonacci sequences', 'fibonacci numbers', 'fibonacci number', 'fibonacci sequence', 'fibonacci', 'sequence fibonacci', 'encyclopedia integer sequences', 'tribonacci']","['On the problem of Pillai with $k$--generalized Fibonacci numbers and\n  powers of $3$   For an integer $k\\ge 2$, let $\\{F^{(k)}_{n}\\}_{n\\ge 2-k}$ be the $\nk$--generalized Fibonacci sequence which starts with $0, \\ldots, 0,1$ (a total\nof $k$ terms) and for which each term afterwards is the sum of the $k$\npreceding terms. In this paper, we find all integers $ c $ with at least two\nrepresentations as a difference between a $ k $-generalized Fibonacci number\nand a power of $ 3 $. This paper continues the previous work of the first\nauthor for the Fibonacci numbers, and the Tribonacci numbers.\n', 'Fibonacci Numbers as Sums of Consecutive Terms in $k$-Generalized\n  Fibonacci Sequence   Let (F_n^{(k)})_{n\\geq -(k-2)} be the k-generalized Fibonacci sequence,\ndefined as the linear recurrence sequence whose first k terms are \\(0, 0,\n\\ldots, 0, 1\\), and whose subsequent terms are determined by the sum of the\npreceding k terms. This article is devoted to investigating when the sum of\nconsecutive numbers in the k-generalized Fibonacci sequence belongs to the\nFibonacci sequence. Namely, given d,k \\in \\N, with k \\geq 3, our main theorem\nstates that there are at most finitely many n \\in \\N such that F_n^{(k)} +\n\\cdots + F_{n+d}^{(k)} is a Fibonacci number. In particular, the intersection\nbetween the Fibonacci sequence and the k-generalized Fibonacci sequence is\nfinite.\n', 'On Concatenations of Two $ k $-Generalized Fibonacci Numbers   Let $ k \\geq 2 $ be an integer. The $ k- $generalized Fibonacci sequence is a\nsequence defined by the recurrence relation $ F_{n}^{(k)}=F_{n-1}^{(k)} +\n\\cdots + F_{n-k}^{(k)}$ for all $ n \\geq 2$ with the initial values $\nF_{i}^{(k)}=0 $ for $ i=2-k, \\ldots, 0 $ and $ F_{1}^{(k)}=1.$ In 2020, Banks\nand Luca, among other things, determined all Fibonacci numbers which are\nconcatenations of two Fibonacci numbers. In this paper, we consider the\nanalogue of this problem by taking into account $ k-$generalized Fibonacci\nnumbers as concatenations of two terms of the same sequence. We completely\nsolve this problem for all $ k \\geq 3.\n']","[('generalized fibonacci numbers', 0.8181111812591553), ('generalized fibonacci', 0.7561076283454895), ('fibonacci sequences', 0.720858633518219), ('fibonacci numbers', 0.7057169079780579), ('fibonacci number', 0.6661389470100403), ('fibonacci sequence', 0.6591576337814331), ('fibonacci', 0.6487018465995789), ('sequence fibonacci', 0.6411961913108826), ('encyclopedia integer sequences', 0.48553210496902466), ('tribonacci', 0.4707559049129486)]"
271,271,108,271_linearized elasticity_nonlinear elasticity_linear elasticity_linearly elastic,"['linearized elasticity', 'nonlinear elasticity', 'linear elasticity', 'linearly elastic', 'finite elasticity', 'linear elastic', 'elasticity', 'elastic energy', 'elastic plates', 'elastic']","['Pressure live loads and the variational derivation of linear elasticity   The rigorous derivation of linear elasticity from finite elasticity by means\nof Gamma-convergence is a well-known result, which has been extended to\ndifferent models also beyond the elastic regime. However, in these results the\napplied forces are usually assumed to be dead loads, that is, their density in\nthe reference configuration is independent of the actual deformation. In this\npaper we begin a study of the variational derivation of linear elasticity in\nthe presence of live loads. We consider a pure traction problem for a\nnonlinearly elastic body subject to a pressure live load and we compute its\nlinearization for small pressure by Gamma-convergence. We allow for a weakly\ncoercive elastic energy density and we prove strong convergence of minimizers.\n', 'A homogenized bending theory for prestrained plates   The presence of prestrain can have a tremendous effect on the mechanical\nbehavior of slender structures. Prestrained elastic plates show spontaneous\nbending in equilibrium -- a property that makes such objects relevant for the\nfabrication of active and functional materials. In this paper we study\nmicroheterogeneous, prestrained plates that feature nonflat equilibrium shapes.\nOur goal is to understand the relation between the properties of the\nprestrained microstructure and the global shape of the plate in mechanical\nequilibrium. To this end, we consider a three-dimensional, nonlinear elasticity\nmodel that describes a periodic material that occupies a domain with small\nthickness. We consider a spatially periodic prestrain described in the form of\na multiplicative decomposition of the deformation gradient. By simultaneous\nhomogenization and dimension reduction, we rigorously derive an effective plate\nmodel as a {\\Gamma}-limit for vanishing thickness and period. That limit has\nthe form of a nonlinear bending energy with an emergent spontaneous curvature\nterm. The homogenized properties of the bending model (bending stiffness and\nspontaneous curvature) are characterized by corrector problems. For a model\ncomposite -- a prestrained laminate composed of isotropic materials -- we\ninvestigate the dependence of the homogenized properties on the parameters of\nthe model composite. Secondly, we investigate the relation between the\nparameters of the model composite and the set of shapes with minimal bending\nenergy. Our study reveals a rather complex dependence of these shapes on the\ncomposite parameters.\n', 'Linearization of quasistatic fracture evolution in brittle materials   We prove a linearization result for quasistatic fracture evolution in\nnonlinear elasticity. As the stiffness of the material tends to infinity, we\nshow that rescaled displacement fields and their associated crack sets converge\nto a solution of quasistatic crack growth in linear elasticity without any a\npriori assumptions on the geometry of the crack set. This result corresponds to\nthe evolutionary counterpart of the static linearization result by the first\nauthor, where a Griffith model for nonsimple brittle materials has been\nconsidered featuring an elastic energy which also depends suitably on the\nsecond gradient of the deformations. The proof relies on a careful study of\nunilateral global minimality, as determined by the nonlinear evolutionary\nproblem, and its linearization together with a variant of the jump transfer\nlemma in GSBD.\n']","[('linearized elasticity', 0.743719756603241), ('nonlinear elasticity', 0.7212222814559937), ('linear elasticity', 0.7199895977973938), ('linearly elastic', 0.7017817497253418), ('finite elasticity', 0.6923862099647522), ('linear elastic', 0.661594033241272), ('elasticity', 0.6604415774345398), ('elastic energy', 0.5969340205192566), ('elastic plates', 0.5808668732643127), ('elastic', 0.5480794906616211)]"
272,272,107,272_multiple zeta values_multiple zeta functions_multiple zeta_zeta values,"['multiple zeta values', 'multiple zeta functions', 'multiple zeta', 'zeta values', 'among multiple zeta', 'zeta values level', 'zeta functions', 'zeta value', 'double zeta', 'multiple zeta star']","[""Truncated $t$-adic symmetric multiple zeta values and double shuffle\n  relations   We study a refinement of the symmetric multiple zeta value, called the\n$t$-adic symmetric multiple zeta value, by considering its finite truncation.\nMore precisely, two kinds of regularizations (harmonic and shuffle) give two\nkinds of the $t$-adic symmetric multiple zeta values, thus we introduce two\nkinds of truncations correspondingly. Then we show that our truncations tend to\nthe corresponding $t$-adic symmetric multiple zeta values, and satisfy the\nharmonic and shuffle relations, respectively. This gives a new proof of the\ndouble shuffle relations for $t$-adic symmetric multiple zeta values, first\nproved by Jarossay. In order to prove the shuffle relation, we develop the\ntheory of truncated $t$-adic symmetric multiple zeta values associated with\n$2$-colored rooted trees. Finally, we discuss a refinement of Kaneko-Zagier's\nconjecture and the $t$-adic symmetric multiple zeta values of Mordell-Tornheim\ntype.\n"", 'Interpolated polynomial multiple zeta values of fixed weight, depth, and\n  height   We define the interpolated polynomial multiple zeta values as a\ngeneralization of all of multiple zeta values, multiple zeta-star values,\ninterpolated multiple zeta values, symmetric multiple zeta values, and\npolynomial multiple zeta values. We then compute the generating function of the\nsum of interpolated polynomial multiple zeta values of fixed weight, depth, and\nheight.\n', ""Weighted sum formula for variants of half multiple zeta values   We prove some weighted sum formulas for half multiple zeta values, half\nfinite multiple zeta values, and half symmetric multiple zeta values. The key\npoint of our proof is Dougall's identity for the generalized hypergeometric\nfunction ${}_{5}F_{4}$. Similar results for interpolated refined symmetric\nmultiple zeta values and half refined symmetric multiple zeta values are also\ndiscussed.\n""]","[('multiple zeta values', 0.7035181522369385), ('multiple zeta functions', 0.6638880968093872), ('multiple zeta', 0.6520174741744995), ('zeta values', 0.6457189321517944), ('among multiple zeta', 0.6331401467323303), ('zeta values level', 0.571370005607605), ('zeta functions', 0.5636926293373108), ('zeta value', 0.5568626523017883), ('double zeta', 0.5564136505126953), ('multiple zeta star', 0.5563750267028809)]"
273,273,107,273_nonlinear schr_nonlinear schr odinger_cubic nonlinear schr_nonlinear klein gordon,"['nonlinear schr', 'nonlinear schr odinger', 'cubic nonlinear schr', 'nonlinear klein gordon', 'uniform error bound', 'methods nonlinear', 'optimal error bounds', 'splitting methods', 'nonlinear klein', 'uniform error bounds']","['Uniform error bounds of a time-splitting spectral method for the\n  long-time dynamics of the nonlinear Klein-Gordon equation with weak\n  nonlinearity   We establish uniform error bounds of time-splitting Fourier pseudospectral\n(TSFP) methods for the nonlinear Klein--Gordon equation (NKGE) with weak\npower-type nonlinearity and $O(1)$ initial data, while the nonlinearity\nstrength is characterized by $\\varepsilon^{p}$ with a constant $p \\in\n\\mathbb{N}^+$ and a dimensionless parameter $\\varepsilon \\in (0, 1]$, for the\nlong-time dynamics up to the time at $O(\\varepsilon^{-\\beta})$ with $0 \\leq\n\\beta \\leq p$. In fact, when $0 < \\varepsilon \\ll 1$, the problem is equivalent\nto the long-time dynamics of NKGE with small initial data and $O(1)$\nnonlinearity strength, while the amplitude of the initial data (and the\nsolution) is at $O(\\varepsilon)$. By reformulating the NKGE into a relativistic\nnonlinear Schr\\""{o}dinger equation, we adapt the TSFP method to discretize it\nnumerically. By using the method of mathematical induction to bound the\nnumerical solution, we prove uniform error bounds at\n$O(h^{m}+\\varepsilon^{p-\\beta}\\tau^2)$ of the TSFP method with $h$ mesh size,\n$\\tau$ time step and $m\\ge2$ depending on the regularity of the solution. The\nerror bounds are uniformly accurate for the long-time simulation up to the time\nat $O(\\varepsilon^{-\\beta})$ and uniformly valid for $\\varepsilon\\in(0,1]$.\nEspecially, the error bounds are uniformly at the second order rate for the\nlarge time step $\\tau = O(\\varepsilon^{-(p-\\beta)/2})$ in the parameter regime\n$0\\le\\beta <p$. Numerical results are reported to confirm our error bounds in\nthe long-time regime. Finally, the TSFP method and its error bounds are\nextended to a highly oscillatory complex NKGE which propagates waves with\nwavelength at $O(1)$ in space and $O(\\varepsilon^{\\beta})$ in time and wave\nvelocity at $O(\\varepsilon^{-\\beta})$.\n', 'Improved uniform error bounds of the time-splitting methods for the\n  long-time (nonlinear) Schr\\""odinger equation   We establish improved uniform error bounds for the time-splitting methods for\nthe long-time dynamics of the Schr\\""odinger equation with small potential and\nthe nonlinear Schr\\""odinger equation (NLSE) with weak nonlinearity. For the\nSchr\\""odinger equation with small potential characterized by a dimensionless\nparameter $\\varepsilon \\in (0, 1]$ representing the amplitude of the potential,\nwe employ the unitary flow property of the (second-order) time-splitting\nFourier pseudospectral (TSFP) method in $L^2$-norm to prove a uniform error\nbound at $C(T)(h^m +\\tau^2)$ up to the long time $T_\\varepsilon= T/\\varepsilon$\nfor any $T>0$ and uniformly for $0<\\varepsilon\\le1$, while $h$ is the mesh\nsize, $\\tau$ is the time step, $m \\ge 2$ depends on the regularity of the exact\nsolution, and $C(T) =C_0+C_1T$ grows at most linearly with respect to $T$ with\n$C_0$ and $C_1$ two positive constants independent of $T$, $\\varepsilon$, $h$\nand $\\tau$. Then by introducing a new technique of {\\sl regularity compensation\noscillation} (RCO) in which the high frequency modes are controlled by\nregularity and the low frequency modes are analyzed by phase cancellation and\nenergy method, an improved uniform error bound at $O(h^{m-1} + \\varepsilon\n\\tau^2)$ is established in $H^1$-norm for the long-time dynamics up to the time\nat $O(1/\\varepsilon)$ of the Schr\\""odinger equation with\n$O(\\varepsilon)$-potential with $m \\geq 3$, which is uniformly for\n$\\varepsilon\\in(0,1]$. Moreover, the RCO technique is extended to prove an\nimproved uniform error bound at $O(h^{m-1} + \\varepsilon^2\\tau^2)$ in\n$H^1$-norm for the long-time dynamics up to the time at $O(1/\\varepsilon^2)$ of\nthe cubic NLSE with $O(\\varepsilon^2)$-nonlinearity strength, uniformly for\n$\\varepsilon \\in (0, 1]$. Extensions to the first-order and fourth-order\ntime-splitting methods are discussed.\n', 'Improved uniform error bounds on time-splitting methods for long-time\n  dynamics of the nonlinear Klein--Gordon equation with weak nonlinearity   We establish improved uniform error bounds on time-splitting methods for the\nlong-time dynamics of the nonlinear Klein--Gordon equation (NKGE) with weak\ncubic nonlinearity, whose strength is characterized by $\\varepsilon^2$ with $0\n< \\varepsilon \\leq 1$ a dimensionless parameter. Actually, when $0 <\n\\varepsilon \\ll 1$, the NKGE with $O(\\varepsilon^2)$ nonlinearity and $O(1)$\ninitial data is equivalent to that with $O(1)$ nonlinearity and small initial\ndata of which the amplitude is at $O(\\varepsilon)$. We begin with a\nsemi-discretization of the NKGE by the second-order time-splitting method, and\nfollowed by a full-discretization via the Fourier spectral method in space.\nEmploying the regularity compensation oscillation (RCO) technique which\ncontrols the high frequency modes by the regularity of the exact solution and\nanalyzes the low frequency modes by phase cancellation and energy method, we\ncarry out the improved uniform error bounds at $O(\\varepsilon^2\\tau^2)$ and\n$O(h^m+\\varepsilon^2\\tau^2)$ for the second-order semi-discretization and\nfull-discretization up to the long time $T_\\varepsilon = T/\\varepsilon^2$ with\n$T$ fixed, respectively. Extensions to higher order time-splitting methods and\nthe case of an oscillatory complex NKGE are also discussed. Finally, numerical\nresults are provided to confirm the improved error bounds and to demonstrate\nthat they are sharp.\n']","[('nonlinear schr', 0.4185221493244171), ('nonlinear schr odinger', 0.4145113229751587), ('cubic nonlinear schr', 0.41397660970687866), ('nonlinear klein gordon', 0.4129919409751892), ('uniform error bound', 0.38310864567756653), ('methods nonlinear', 0.3804851174354553), ('optimal error bounds', 0.37817415595054626), ('splitting methods', 0.3720807433128357), ('nonlinear klein', 0.36489370465278625), ('uniform error bounds', 0.3624621331691742)]"
274,274,107,274_classical quantum channels_quantum channels_classical quantum channel_quantum channel,"['classical quantum channels', 'quantum channels', 'classical quantum channel', 'quantum channel', 'quantum information theory', 'channel discrimination', 'quantum information', 'quantum communication', 'classical channels', 'classical channel']","[""Query Complexity of Classical and Quantum Channel Discrimination   Quantum channel discrimination has been studied from an information-theoretic\nperspective, wherein one is interested in the optimal decay rate of error\nprobabilities as a function of the number of unknown channel accesses. In this\npaper, we study the query complexity of quantum channel discrimination, wherein\nthe goal is to determine the minimum number of channel uses needed to reach a\ndesired error probability. To this end, we show that the query complexity of\nbinary channel discrimination depends logarithmically on the inverse error\nprobability and inversely on the negative logarithm of the (geometric and\nHolevo) channel fidelity. As a special case of these findings, we precisely\ncharacterize the query complexity of discriminating between two classical\nchannels. We also provide lower and upper bounds on the query complexity of\nbinary asymmetric channel discrimination and multiple quantum channel\ndiscrimination. For the former, the query complexity depends on the geometric\nR\\'enyi and Petz R\\'enyi channel divergences, while for the latter, it depends\non the negative logarithm of (geometric and Uhlmann) channel fidelity. For\nmultiple channel discrimination, the upper bound scales as the logarithm of the\nnumber of channels.\n"", ""Towards the ultimate limits of quantum channel discrimination   This note studies the difficulty of discriminating quantum channels under\noperational regimes. First, we make a conjecture on the exponentially strong\nconverse of quantum channel hypothesis testing under coherent strategies,\nmeaning that any strategy to make the Type II error decays with an exponent\nlarger than the regularized channel relative entropy will unavoidably result in\nthe Type I error converging to one exponentially fast in the asymptotic limit.\nThis conjecture will imply the desirable quantum channel Stein's Lemma and the\ncontinuity of the regularized (amortized) Sandwiched R\\'{e}nyi channel\ndivergence at $\\alpha=1$. We also remark that there was a gap in the proof of\nthe above conjecture in our previous arXiv version. Such gap exists since a\nlemma basically comes from [Brandao and Plenio, 2010] was found to be false.\nSecond, we develop a framework to show the interplay between the strategies of\nchannel discrimination, the operational regimes, and variants of channel\ndivergences. This framework systematically underlies the operational meaning of\nquantum channel divergences in quantum channel discrimination. Our work makes\nan attempt towards understanding the ultimate limit of quantum channel\ndiscrimination, as well as its connection to quantum channel divergences in the\nasymptotic regime.\n"", ""Amortized Channel Divergence for Asymptotic Quantum Channel\n  Discrimination   It is well known that for the discrimination of classical and quantum\nchannels in the finite, non-asymptotic regime, adaptive strategies can give an\nadvantage over non-adaptive strategies. However, Hayashi [IEEE Trans. Inf.\nTheory 55(8), 3807 (2009)] showed that in the asymptotic regime, the\nexponential error rate for the discrimination of classical channels is not\nimproved in the adaptive setting. We extend this result in several ways. First,\nwe establish the strong Stein's lemma for classical-quantum channels by showing\nthat asymptotically the exponential error rate for classical-quantum channel\ndiscrimination is not improved by adaptive strategies. Second, we recover many\nother classes of channels for which adaptive strategies do not lead to an\nasymptotic advantage. Third, we give various converse bounds on the power of\nadaptive protocols for general asymptotic quantum channel discrimination.\nIntriguingly, it remains open whether adaptive protocols can improve the\nexponential error rate for quantum channel discrimination in the asymmetric\nStein setting. Our proofs are based on the concept of amortized\ndistinguishability of quantum channels, which we analyse using data-processing\ninequalities.\n""]","[('classical quantum channels', 0.6483159065246582), ('quantum channels', 0.6480512022972107), ('classical quantum channel', 0.643172025680542), ('quantum channel', 0.6420283913612366), ('quantum information theory', 0.5803766250610352), ('channel discrimination', 0.5701236724853516), ('quantum information', 0.5621207356452942), ('quantum communication', 0.5459775328636169), ('classical channels', 0.5220924019813538), ('classical channel', 0.5171129703521729)]"
275,275,106,275_chromatic symmetric_chromatic polynomials_chromatic polynomial_conjecture chromatic,"['chromatic symmetric', 'chromatic polynomials', 'chromatic polynomial', 'conjecture chromatic', 'symmetric functions', 'elementary symmetric functions', 'graphs chromatic', 'chromatic', 'symmetric graph', 'symmetric']","[""H-chromatic symmetric functions   We introduce $H$-chromatic symmetric functions, $X_{G}^{H}$, which use the\n$H$-coloring of a graph $G$ to define a generalization of Stanley's chromatic\nsymmetric functions. We say two graphs $G_1$ and $G_2$ are $H$-chromatically\nequivalent if $X_{G_1}^{H} = X_{G_2}^{H}$, and use this idea to study\nuniqueness results for $H$-chromatic symmetric functions, with a particular\nemphasis on the case $H$ is a complete bipartite graph. We also show that\nseveral of the classical bases of the space of symmetric functions, i.e. the\nmonomial symmetric functions, power sum symmetric functions, and elementary\nsymmetric functions, can be realized as $H$-chromatic symmetric functions. We\nend with some conjectures and open problems.\n"", 'A composition method for neat formulas of chromatic symmetric functions   We develop a composition method to unearth positive $e_I$-expansions of\nchromatic symmetric functions $X_G$, where the subscript $I$ stands for\ncompositions rather than integer partitions. Using this method, we derive\npositive and neat $e_I$-expansions for the chromatic symmetric functions of\ntadpoles, barbells and generalized bulls, and establish the $e$-positivity of\nhats. We also obtain a compact ribbon Schur analog for the chromatic symmetric\nfunction of cycles.\n', ""$(q,t)$-chromatic symmetric functions   By using level one polynomial representations of affine Hecke algebras of\ntype $A$, we obtain a $(q,t)$-analogue of the chromatic symmetric functions of\nunit interval graphs which generalizes Syu Kato's formula for the chromatic\nsymmetric functions of unit interval graphs. We show that at $q=1$, the\n$(q,t)$-chromatic symmetric functions essentially reduce to the chromatic\nquasisymmetric functions defined by Shareshian-Wachs, which in particular gives\nan algebraic proof of Kato's formula. We also give an explicit formula of the\n$(q,t)$-chromatic symmetric functions at $q=\\infty$, which leads to a\nprobability theoretic interpretation of $e$-expansion coefficients of chromatic\nquasisymmetric functions used in our proof of the Stanley-Stembridge\nconjecture.\n  Moreover, we observe that the $(q,t)$-chromatic symmetric functions are\nmultiplicative with respect to certain deformed multiplication on the ring of\nsymmetric functions. We give a simple description of such multiplication in\nterms of the affine Hecke algebras of type $A$. We also obtain a recipe to\nproduce $(q,t)$-chromatic symmetric functions from chromatic quasisymmetric\nfunctions, which actually makes sense for any oriented graphs.\n""]","[('chromatic symmetric', 0.6756919622421265), ('chromatic polynomials', 0.6665237545967102), ('chromatic polynomial', 0.610592782497406), ('conjecture chromatic', 0.6059914827346802), ('symmetric functions', 0.5925593972206116), ('elementary symmetric functions', 0.5826101303100586), ('graphs chromatic', 0.555230438709259), ('chromatic', 0.5063638687133789), ('symmetric graph', 0.4422476887702942), ('symmetric', 0.4056134521961212)]"
276,276,106,276_truncated hypergeometric series_congruences involving_pmod prime_sums involving,"['truncated hypergeometric series', 'congruences involving', 'pmod prime', 'sums involving', 'central binomial coefficients', 'involving binomial coefficients', 'frac binom 2k', 'bernoulli numbers', 'binom 2k', 'odd prime']","['Proof of some conjectural congruences involving Domb numbers   In this paper, we mainly prove the following conjectures of Z.-H. Sun\n\\cite{SH2}:\n  Let $p>3$ be a prime. If $p\\equiv1\\pmod3$ and $p=x^2+3y^2$, then we have $$\n\\sum_{k=0}^{p-1}\\frac{D_k}{4^k}\\equiv\\sum_{k=0}^{p-1}\\frac{D_k}{16^k}\\equiv4x^2-2p-\\frac{p^2}{4x^2}\\pmod{p^3},\n$$ and if $p\\equiv2\\pmod3$, then $$\n\\sum_{k=0}^{p-1}\\frac{D_k}{4^k}\\equiv-2\\sum_{k=0}^{p-1}\\frac{D_k}{16^k}\\equiv\\frac{p^2}2\\binom{\\frac{p-1}2}{\\frac{p-5}6}^{-2}\n\\pmod{p^3}, $$ where\n$D_n=\\sum_{k=0}^n\\binom{n}k^2\\binom{2k}k\\binom{2n-2k}{n-k}$ stands for the\n$n$th Domb number.\n', 'Proof of some conjectural hypergeometric supercongruences via curious\n  identities   In this paper, we prove several supercongruences conjectured by Z.-W. Sun ten\nyears ago via certain strange hypergeometric identities. For example, for any\nprime $p>3$, we show that\n$$\\sum_{k=0}^{p-1}\\frac{\\binom{4k}{2k+1}\\binom{2k}k}{48^k}\\equiv0\\pmod{p^2},$$\nand $$\n\\sum_{k=0}^{p-1}\\frac{\\binom{2k}{k}\\binom{3k}{k}}{24^k}\\equiv\\begin{cases}\\binom{(2p-2)/3}{(p-1)/3}\\pmod{p^2}\\\n&\\mbox{if}\\ p\\equiv1\\pmod{3},\\\\ p/\\binom{(2p+2)/3}{(p+1)/3}\\pmod{p^2}\\\n&\\mbox{if}\\ p\\equiv2\\pmod{3}.\\end{cases} $$ We also obtain some other results\nof such types.\n', ""Supercongruences via Beukers' method   Recently, using modular forms F. Beukers posed a unified method that can deal\nwith a large number of supercongruences involving binomial coefficients and\nAp\\'ery-like numbers. In this paper, we use Beukers' method to prove some\nconjectures of the first author concerning the congruences for\n$$\\sum_{k=0}^{(p-1)/2}\\frac{\\binom{2k}k^3}{m^k}, \\\n\\sum_{k=0}^{p-1}\\frac{\\binom{2k}k^2\\binom{4k}{2k}}{m^k}, \\\n\\sum_{k=0}^{p-1}\\frac{\\binom{2k}k\\binom{3k}k\\binom{6k}{3k}}{m^k}, \\\n\\sum_{n=0}^{p-1}\\frac{V_n}{m^n},\\ \\sum_{n=0}^{p-1}\\frac{T_n}{m^n},\\\n\\sum_{n=0}^{p-1}\\frac{D_n}{m^n} $$ and $\\sum_{n=0}^{p-1}(-1)^nA_n$ modulo\n$p^3$, where $p$ is an odd prime representable by some suitable binary\nquadratic form, $m$ is an integer not divisible by $p$,\n$V_n=\\sum_{k=0}^n\\binom{2k}k^2\\binom{2n-2k}{n-k}^2$, $T_n=\\sum_{k=0}^n\\binom\nnk^2\\binom{2k}n^2$, $D_n=\\sum_{k=0}^n\\binom nk^2\\binom{2k}k\\binom{2n-2k}{n-k}$\nand $A_n$ is the Ap\\'ery number given by $A_n=\\sum_{k=0}^n\\binom\nnk^2\\binom{n+k}k^2$.\n""]","[('truncated hypergeometric series', 0.43578290939331055), ('congruences involving', 0.37722277641296387), ('pmod prime', 0.3708067536354065), ('sums involving', 0.370731920003891), ('central binomial coefficients', 0.36701473593711853), ('involving binomial coefficients', 0.36404189467430115), ('frac binom 2k', 0.35041847825050354), ('bernoulli numbers', 0.3482406735420227), ('binom 2k', 0.3394494354724884), ('odd prime', 0.3375721573829651)]"
277,277,105,277_jump diffusion processes_jump diffusion_nonparametric estimation_adaptive estimators,"['jump diffusion processes', 'jump diffusion', 'nonparametric estimation', 'adaptive estimators', 'consistent estimator', 'adaptive estimator', 'proposed estimators', 'estimators', 'observed diffusion', 'drift diffusion']","[""Volatility of Volatility and Leverage Effect from Options   We propose model-free (nonparametric) estimators of the volatility of\nvolatility and leverage effect using high-frequency observations of short-dated\noptions. At each point in time, we integrate available options into estimates\nof the conditional characteristic function of the price increment until the\noptions' expiration and we use these estimates to recover spot volatility. Our\nvolatility of volatility estimator is then formed from the sample variance and\nfirst-order autocovariance of the spot volatility increments, with the latter\ncorrecting for the bias in the former due to option observation errors. The\nleverage effect estimator is the sample covariance between price increments and\nthe estimated volatility increments. The rate of convergence of the estimators\ndepends on the diffusive innovations in the latent volatility process as well\nas on the observation error in the options with strikes in the vicinity of the\ncurrent spot price. Feasible inference is developed in a way that does not\nrequire prior knowledge of the source of estimation error that is\nasymptotically dominating.\n"", ""Unbiased truncated quadratic variation for volatility estimation in jump\n  diffusion processes   The problem of integrated volatility estimation for the solution X of a\nstochastic differential equation with L{\\'e}vy-type jumps is considered under\ndiscrete high-frequency observations in both short and long time horizon. We\nprovide an asymptotic expansion for the integrated volatility that gives us, in\ndetail, the contribution deriving from the jump part. The knowledge of such a\ncontribution allows us to build an unbiased version of the truncated quadratic\nvariation, in which the bias is visibly reduced. In earlier results the\ncondition $\\beta$ > 1 2(2--$\\alpha$) on $\\beta$ (that is such that (1/n)\n$\\beta$ is the threshold of the truncated quadratic variation) and on the\ndegree of jump activity $\\alpha$ was needed to have the original truncated\nrealized volatility well-performed (see [22], [13]). In this paper we\ntheoretically relax this condition and we show that our unbiased estimator\nachieves excellent numerical results for any couple ($\\alpha$, $\\beta$).\nL{\\'e}vy-driven SDE, integrated variance, threshold estimator, convergence\nspeed, high frequency data.\n"", ""Volatility and jump activity estimation in a stable Cox-Ingersoll-Ross\n  model   We consider the parametric estimation of the volatility and jump activity in\na stable Cox-Ingersoll-Ross ($\\alpha$-stable CIR) model driven by a standard\nBrownian Motion and a non-symmetric stable L\\'evy process with jump activity\n$\\alpha \\in (1,2)$. The main difficulties to obtain rate efficiency in\nestimating these quantities arise from the superposition of the diffusion\ncomponent with jumps of infinite variation. Extending the approach proposed in\nMies (2020), we address the joint estimation of the volatility, scaling and\njump activity parameters from high-frequency observations of the process and\nprove that the proposed estimators are rate optimal up to a logarithmic factor.\n""]","[('jump diffusion processes', 0.554286539554596), ('jump diffusion', 0.5119404792785645), ('nonparametric estimation', 0.46253716945648193), ('adaptive estimators', 0.4599752724170685), ('consistent estimator', 0.4571860134601593), ('adaptive estimator', 0.44850507378578186), ('proposed estimators', 0.4428943991661072), ('estimators', 0.41377487778663635), ('observed diffusion', 0.39688366651535034), ('drift diffusion', 0.3943864703178406)]"
278,278,105,278_learning combinatorial optimization_constraint learning_graph neural networks_integer linear programs,"['learning combinatorial optimization', 'constraint learning', 'graph neural networks', 'integer linear programs', 'integer linear programming', 'linear programming milp', 'mixed integer programming', 'graph neural', 'integer programming mip', 'mixed integer programs']","['Modern graph neural networks do worse than classical greedy algorithms\n  in solving combinatorial optimization problems like maximum independent set   The recent work ``Combinatorial Optimization with Physics-Inspired Graph\nNeural Networks\'\' [Nat Mach Intell 4 (2022) 367] introduces a physics-inspired\nunsupervised Graph Neural Network (GNN) to solve combinatorial optimization\nproblems on sparse graphs. To test the performances of these GNNs, the authors\nof the work show numerical results for two fundamental problems: maximum cut\nand maximum independent set (MIS). They conclude that ""the graph neural network\noptimizer performs on par or outperforms existing solvers, with the ability to\nscale beyond the state of the art to problems with millions of variables.""\n  In this comment, we show that a simple greedy algorithm, running in almost\nlinear time, can find solutions for the MIS problem of much better quality than\nthe GNN. The greedy algorithm is faster by a factor of $10^4$ with respect to\nthe GNN for problems with a million variables. We do not see any good reason\nfor solving the MIS with these GNN, as well as for using a sledgehammer to\ncrack nuts.\n  In general, many claims of superiority of neural networks in solving\ncombinatorial problems are at risk of being not solid enough, since we lack\nstandard benchmarks based on really hard problems. We propose one of such hard\nbenchmarks, and we hope to see future neural network optimizers tested on these\nproblems before any claim of superiority is made.\n', 'MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers   Mixed-integer programming (MIP) technology offers a generic way of\nformulating and solving combinatorial optimization problems. While generally\nreliable, state-of-the-art MIP solvers base many crucial decisions on\nhand-crafted heuristics, largely ignoring common patterns within a given\ninstance distribution of the problem of interest. Here, we propose MIP-GNN, a\ngeneral framework for enhancing such solvers with data-driven insights. By\nencoding the variable-constraint interactions of a given mixed-integer linear\nprogram (MILP) as a bipartite graph, we leverage state-of-the-art graph neural\nnetwork architectures to predict variable biases, i.e., component-wise averages\nof (near) optimal solutions, indicating how likely a variable will be set to 0\nor 1 in (near) optimal solutions of binary MILPs. In turn, the predicted biases\nstemming from a single, once-trained model are used to guide the solver,\nreplacing heuristic components. We integrate MIP-GNN into a state-of-the-art\nMIP solver, applying it to tasks such as node selection and warm-starting,\nshowing significant improvements compared to the default setting of the solver\non two classes of challenging binary MILPs.\n', 'A GNN-Guided Predict-and-Search Framework for Mixed-Integer Linear\n  Programming   Mixed-integer linear programming (MILP) is widely employed for modeling\ncombinatorial optimization problems. In practice, similar MILP instances with\nonly coefficient variations are routinely solved, and machine learning (ML)\nalgorithms are capable of capturing common patterns across these MILP\ninstances. In this work, we combine ML with optimization and propose a novel\npredict-and-search framework for efficiently identifying high-quality feasible\nsolutions. Specifically, we first utilize graph neural networks to predict the\nmarginal probability of each variable, and then search for the best feasible\nsolution within a properly defined ball around the predicted solution. We\nconduct extensive experiments on public datasets, and computational results\ndemonstrate that our proposed framework achieves 51.1% and 9.9% performance\nimprovements to MILP solvers SCIP and Gurobi on primal gaps, respectively.\n']","[('learning combinatorial optimization', 0.5137065052986145), ('constraint learning', 0.5132868885993958), ('graph neural networks', 0.49848300218582153), ('integer linear programs', 0.4966943562030792), ('integer linear programming', 0.4931817054748535), ('linear programming milp', 0.4865953326225281), ('mixed integer programming', 0.47600120306015015), ('graph neural', 0.472699910402298), ('integer programming mip', 0.47221243381500244), ('mixed integer programs', 0.4643625020980835)]"
279,279,105,279_multiple access noma_noma networks_orthogonal multiple access_wireless information power,"['multiple access noma', 'noma networks', 'orthogonal multiple access', 'wireless information power', 'access noma', 'simultaneous wireless information', 'irs beamforming', 'wireless energy', 'simultaneous wireless', 'transmit power']","['Performance Analysis of Intelligent Reflecting Surface Assisted NOMA\n  Networks   Intelligent reflecting surface (IRS) is a promising technology to enhance the\ncoverage and performance of wireless networks. We consider the application of\nIRS to non-orthogonal multiple access (NOMA), where a base station transmits\nsuperposed signals to multiple users by the virtue of an IRS. The performance\nof an IRS-assisted NOMA networks with imperfect successive interference\ncancellation (ipSIC) and perfect successive interference cancellation (pSIC) is\ninvestigated by invoking 1-bit coding scheme. In particular, we derive new\nexact and asymptotic expressions for both outage probability and ergodic rate\nof the m-th user with ipSIC/pSIC. Based on analytical results, the diversity\norder of the m-th user with pSIC is in connection with the number of reflecting\nelements and channel ordering. The high signal-to-noise radio (SNR) slope of\nergodic rate for the $m$-th user is obtained. The throughput and energy\nefficiency of non-orthogonal users for IRS-NOMA are discussed both in\ndelay-limited and delay-tolerant transmission modes. Additionally, we derive\nnew exact expressions of outage probability and ergodic rate for IRS-assisted\northogonal multiple access (IRS-OMA). Numerical results are presented to\nsubstantiate our analyses and demonstrate that: i) The outage behaviors of\nIRS-NOMA are superior to that of IRS-OMA and relaying schemes; ii) With\nincreasing the number of reflecting elements, IRS-NOMA is capable of achieving\nenhanced outage performance; and iii) The M-th user has a larger ergodic rate\ncompared to IRS-OMA and benchmarks. However, the ergodic performance of the\n$m$-th user exceeds relaying schemes in the low SNR regime.\n', 'Joint Beamforming Design and Power Splitting Optimization in\n  IRS-Assisted SWIPT NOMA Networks   This paper proposes a novel network framework of intelligent reflecting\nsurface (IRS)-assisted simultaneous wireless information and power transfer\n(SWIPT) non-orthogonal multiple access (NOMA) networks, where IRS is used to\nenhance the NOMA performance and the wireless power transfer (WPT) efficiency\nof SWIPT. We formulate a problem of minimizing base station (BS) transmit power\nby jointly optimizing successive interference cancellation (SIC) decoding\norder, BS transmit beamforming vector, power splitting (PS) ratio and IRS phase\nshift while taking into account the quality-of-service (QoS) requirement and\nenergy harvested threshold of each user. The formulated problem is non-convex\noptimization problem, which is difficult to solve it directly. Hence, a\ntwo-stage algorithm is proposed to solve the above-mentioned problem by\napplying semidefinite relaxation (SDR), Gaussian randomization and successive\nconvex approximation (SCA). Specifically, after determining SIC decoding order\nby designing IRS phase shift in the first stage, we alternately optimize BS\ntransmit beamforming vector, PS ratio, and IRS phase shift to minimize the BS\ntransmit power. Numerical results validate the effectiveness of our proposed\noptimization algorithm in reducing BS transmit power compared to other baseline\nalgorithms. Meanwhile, compared with non-IRS-assisted network, the IRS-assisted\nSWIPT NOMA network can decrease BS transmit power by 51.13\\%.\n', 'IRS-Assisted Wireless Powered NOMA: Do We Really Need Different Phase\n  Shifts in DL and UL?   Intelligent reflecting surface (IRS) is a promising technology to improve the\nperformance of wireless powered communication networks (WPCNs) due to its\ncapability to reconfigure signal propagation environments via smart reflection.\nIn particular, the high passive beamforming gain promised by IRS can\nsignificantly enhance the efficiency of both downlink wireless power transfer\n(DL WPT) and uplink wireless information transmission (UL WIT) in WPCNs.\nAlthough adopting different IRS phase shifts for DL WPT and UL WIT, i.e.,\ndynamic IRS beamforming, is in principle possible but incurs additional\nsignaling overhead and computational complexity, it is an open problem whether\nit is actually beneficial. To answer this question, we consider an IRS-assisted\nWPCN where multiple devices employ a hybrid access point (HAP) to first harvest\nenergy and then transmit information using non-orthogonal multiple access\n(NOMA). Specifically, we aim to maximize the sum throughput of all devices by\njointly optimizing the IRS phase shifts and the resource allocation. To this\nend, we first prove that dynamic IRS beamforming is not needed for the\nconsidered system, which helps reduce the number of IRS phase shifts to be\noptimized. Then, we propose both joint and alternating optimization based\nalgorithms to solve the resulting problem. Simulation results demonstrate the\neffectiveness of our proposed designs over benchmark schemes and also provide\nuseful insights into the importance of IRS for realizing spectrally and energy\nefficient WPCNs.\n']","[('multiple access noma', 0.5296099781990051), ('noma networks', 0.5275352597236633), ('orthogonal multiple access', 0.5153922438621521), ('wireless information power', 0.456255167722702), ('access noma', 0.4482444226741791), ('simultaneous wireless information', 0.41845211386680603), ('irs beamforming', 0.4087236821651459), ('wireless energy', 0.4024522304534912), ('simultaneous wireless', 0.39122167229652405), ('transmit power', 0.3855009377002716)]"
280,280,105,280_modified bessel functions_bessel functions_bessel functions first_bessel series,"['modified bessel functions', 'bessel functions', 'bessel functions first', 'bessel series', 'zeros bessel', 'bessel differential', 'modified bessel', 'involving bessel', 'series bessel', 'asymptotic expansions']","['Discrete index transforms with Bessel and modified Bessel functions   Discrete analogs of the index transforms, involving Bessel and the modified\nBessel functions are introduced and investigated. The corresponding inversion\ntheorems for suitable classes of functions and sequences are established.\n', ""Asymptotics of some integrals involving modified Bessel and hyper-Bessel\n  functions   We investigate the asymptotic expansion of integrals analogous to Ball's\nintegral \\[\\int_0^\\infty\n\\left(\\frac{\\Gamma(1+\\nu)|J_\\nu(x)|}{(x/2)^\\nu}\\right)^{\\!n}dx\\] for large $n$\nin which the Bessel function $J_\\nu(x)$ is replaced by the modified Bessel\nfunctions $I_\\nu(x)$ and $K_\\nu(x)$ together with appropriate exponential\nfactors $e^{\\mp x}$, respectively.\n  The above integral with $J_\\nu(x)$ replaced by a hyper-Bessel function of the\ntype recently discussed in Aktas {\\it et al.} [The Ramanujan J., 2019] and\ntaken over a finite interval determined by the first positive zero of the\nfunction is also considered for $n\\to\\infty$. We give the leading asymptotic\nbehaviour of the hyper-Bessel function for $x\\to+\\infty$ in an appendix.\nNumerical examples are given to illustrate the accuracy of the various\nexpansions obtained.\n"", 'On the $\\nu$-zeros of the Bessel functions of purely imaginary order   The $\\nu$-zeros of the Bessel functions of purely imaginary order are\nexamined for fixed argument $x>0$. In the case of the modified Bessel function\nof the second kind $K_{i\\nu}(x)$, it is known that it possesses a countably\ninfinite sequence of real $\\nu$-zeros described by $\\nu_n\\sim \\pi n/\\log\\,n$ as\n$n\\to\\infty$. Here we apply a unified approach to determine asymptotic\nestimates of the $\\nu$-zeros of the modified Bessel functions\n$L_{i\\nu}(x)\\equiv I_{i\\nu}(x)+I_{-i\\nu}(x)$ and $K_{i\\nu}(x)$ and the ordinary\nBessel functions $J_{i\\nu}(x)\\pm J_{-i\\nu}(x)$.\n']","[('modified bessel functions', 0.7533238530158997), ('bessel functions', 0.7423427104949951), ('bessel functions first', 0.7092441320419312), ('bessel series', 0.5916098356246948), ('zeros bessel', 0.5877074003219604), ('bessel differential', 0.579613447189331), ('modified bessel', 0.5725294947624207), ('involving bessel', 0.5586037635803223), ('series bessel', 0.5484028458595276), ('asymptotic expansions', 0.5098870992660522)]"
281,281,104,281_poisson algebras_poisson algebra_noncommutative poisson_post lie algebras,"['poisson algebras', 'poisson algebra', 'noncommutative poisson', 'post lie algebras', 'poisson brackets', 'lie algebras', 'poisson lie groups', 'poisson bracket', 'lie bialgebras', 'poisson structures']","['Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras and bialgebras   The notions of transposed Hom-Poisson and Hom-pre-Lie Poisson algebras are\nintroduced. Their bimodules and matched pairs are defined and the relevant\nproperties and theorems are given. The notion of Manin triple of transposed\nHom-Poisson algebras is introduced, and its equivalence to the transposed\nHom-Poisson bialgebras is investigated. The notion of $\\mathcal{O}$-operator is\nexploited to illustrate the relations existing between transposed Hom-Poisson\nand Hom-pre-Lie Poisson algebras.\n', 'Quantizations of transposed Poisson algebras by Novikov deformations   The notions of the Novikov deformation of a commutative associative algebra\nand the corresponding classical limit are introduced. We show such a classical\nlimit belongs to a subclass of transposed Poisson algebras, and hence the\nNovikov deformation is defined to be the quantization of the corresponding\ntransposed Poisson algebra. As a direct consequence, we revisit the\nrelationship between transposed Poisson algebras and Novikov-Poisson algebras\ndue to the fact that there is a natural Novikov deformation of the commutative\nassociative algebra in a Novikov-Poisson algebra. Hence all transposed Poisson\nalgebras of Novikov-Poisson type, including unital transposed Poisson algebras,\ncan be quantized. Finally, we classify the quantizations of $2$-dimensional\ncomplex transposed Poisson algebras in which the Lie brackets are non-abelian\nup to equivalence.\n', 'Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras   We introduce a dual notion of the Poisson algebra by exchanging the roles of\nthe two binary operations in the Leibniz rule defining the Poisson algebra. We\nshow that the transposed Poisson algebra thus defined not only shares common\nproperties of the Poisson algebra, including the closure under taking tensor\nproducts and the Koszul self-duality as an operad, but also admits a rich class\nof identities. More significantly, a transposed Poisson algebra naturally\narises from a Novikov-Poisson algebra by taking the commutator Lie algebra of\nthe Novikov algebra. Consequently, the classic construction of a Poisson\nalgebra from a commutative associative algebra with a pair of commuting\nderivations has a similar construction of a transposed Poisson algebra when\nthere is one derivation. More broadly, the transposed Poisson algebra also\ncaptures the algebraic structures when the commutator is taken in pre-Lie\nPoisson algebras and two other Poisson type algebras. Furthermore, the\ntransposed Poisson algebra improves two processes in~[17] that produce 3-Lie\nalgebras from Poisson algebras with a strongness condition. When transposed\nPoisson algebras are used in one process, the strongness condition is no longer\nneeded and the resulting 3-Lie algebra gives a transposed Poisson 3-Lie\nalgebra. In the other process, the resulting 3-Lie algebra is shown to again\ngive a transposed Poisson 3-Lie algebra.\n']","[('poisson algebras', 0.8220510482788086), ('poisson algebra', 0.7586371898651123), ('noncommutative poisson', 0.6338534355163574), ('post lie algebras', 0.5957896113395691), ('poisson brackets', 0.590569019317627), ('lie algebras', 0.5867496728897095), ('poisson lie groups', 0.5707277059555054), ('poisson bracket', 0.544962465763092), ('lie bialgebras', 0.5420737862586975), ('poisson structures', 0.5355996489524841)]"
282,282,104,282_reduced rings_reduced ring_regular rings_regular ring,"['reduced rings', 'reduced ring', 'regular rings', 'regular ring', 'group rings', 'commutative rings', 'commutative rings let', 'rings rings', 'rings let commutative', 'group ring']","['On $\\phi$-1-Absorbing Prime Ideals   In this paper, we introduce $\\phi$-1-absorbing prime ideals in commutative\nrings. Let $R$ be a commutative ring with a nonzero identity $1\\neq0$ and\n$\\phi:\\mathcal{I}(R)\\rightarrow\\mathcal{I}(R)\\cup\\{\\emptyset\\}$ be a function\nwhere $\\mathcal{I}(R)$ is the set of all ideals of $R$. A proper ideal $I$ of\n$R$ is called a $\\phi$-1-absorbing prime ideal if for each nonunits $x,y,z\\in\nR$ with $xyz\\in I-\\phi(I)$, then either $xy\\in I$ or $z\\in I$. In addition to\ngive many properties and characterizations of $\\phi$-1-absorbing prime ideals,\nwe also determine rings in which every proper ideal is $\\phi$-1-absorbing\nprime.\n', 'Nil-prime ideals of a commutative ring   Let R be a commutative ring with identity and N(R) be the set of all\nnilpotent elements of R. The aim of this paper is to introduce and study the\nnotion of nil-prime ideals as a generalization of prime ideals. We say that a\nproper ideal P of R is a nil-prime ideal if there exists x \\in N(R) and\nwhenever ab \\in P, then a \\in P or b \\in P or a+x \\in P or b+x \\in P for each\na,b \\in R. Also, we introduce nil versions of some algebraic concepts in ring\ntheory such as nil-maximal ideal, nil-minimal ideal, nil-principal ideal and\ninvestigate some nil-version of a well-known results about them.\n', 'Rings whose Nil-Clean and Clean Elements are Uniquely Nil-Clean   We consider and study those rings in which each nil-clean or clean element is\nuniquely nil-clean. We establish that, for abelian rings, these rings have a\nsatisfactory description and even it is shown that the classes of abelian rings\nand the rings in which nil-clean elements are uniquely nil-clean do coincide.\nMoreover, we prove that the rings in which clean elements are uniquely\nnil-clean coincide with the subclass of abelian rings consisting of only\nunipotent units and, in particular, that in the semipotent case we have a\ncomplete characterization only in terms of the former ring and its divisions.\nLikewise, some extension properties and group rings for such kinds of rings are\nalso considered.\n']","[('reduced rings', 0.6035078167915344), ('reduced ring', 0.5917436480522156), ('regular rings', 0.5811471939086914), ('regular ring', 0.569028913974762), ('group rings', 0.5468825101852417), ('commutative rings', 0.5282719731330872), ('commutative rings let', 0.5221405029296875), ('rings rings', 0.5154115557670593), ('rings let commutative', 0.5151662230491638), ('group ring', 0.5144043564796448)]"
283,283,104,283_reservoir computing_reservoir_reservoirs_chaotic systems,"['reservoir computing', 'reservoir', 'reservoirs', 'chaotic systems', 'recurrent neural', 'recurrent neural networks', 'chaotic dynamical systems', 'recurrent neural network', 'neural networks rnns', 'learning dynamical']","['Reservoir computing with the Kuramoto model   Reservoir computing aims to achieve high-performance and low-cost machine\nlearning with a dynamical system as a reservoir. However, in general, there are\nalmost no theoretical guidelines for its high-performance or optimality. This\npaper focuses on the reservoir computing with the Kuramoto model and\ntheoretically reveals its approximation ability. The main result provides an\nexplicit expression of the dynamics of the Kuramoto reservoir by using the\norder parameters. Thus, the output of the reservoir computing is expressed as a\nlinear combination of the order parameters. As a corollary, sufficient\nconditions on hyperparameters are obtained so that the set of the order\nparameters gives the complete basis of the Lebesgue space. This implies that\nthe Kuramoto reservoir has a universal approximation property. Furthermore, the\nconjecture on {\\it the edge of bifurcation}, which is a generalization of the\nfamous criterion {\\it the edge of chaos} for designing a high-performance\nreservoir, is also discussed from the viewpoint of its approximation ability.\nIt is numerically demonstrated by a prediction task and a transformation task.\n', 'Reservoir Computing with Generalized Readout based on Generalized\n  Synchronization   Reservoir computing is a machine learning framework that exploits nonlinear\ndynamics, exhibiting significant computational capabilities. One of the\ndefining characteristics of reservoir computing is its low cost and\nstraightforward training algorithm, i.e. only the readout, given by a linear\ncombination of reservoir variables, is trained. Inspired by recent mathematical\nstudies based on dynamical system theory, in particular generalized\nsynchronization, we propose a novel reservoir computing framework with\ngeneralized readout, including a nonlinear combination of reservoir variables.\nThe first crucial advantage of using the generalized readout is its\nmathematical basis for improving information processing capabilities. Secondly,\nit is still within a linear learning framework, which preserves the original\nstrength of reservoir computing. In summary, the generalized readout is\nnaturally derived from mathematical theory and allows the extraction of useful\nbasis functions from reservoir dynamics without sacrificing simplicity. In a\nnumerical study, we find that introducing the generalized readout leads to a\nsignificant improvement in accuracy and an unexpected enhancement in robustness\nfor the short- and long-term prediction of Lorenz chaos, with a particular\nfocus on how to harness low-dimensional reservoir dynamics. A novel way and its\nadvantages for physical implementations of reservoir computing with generalized\nreadout are briefly discussed.\n', ""(Thesis) Reservoir Computing With Dynamical Systems   A reservoir computer is a special type of neural network, where most of the\nweights are randomly fixed and only a subset are trained.\n  In this thesis we prove results about reservoir computers trained on\ndeterministic dynamical systems, and stochastic processes. We focus mostly on a\nspecial type of reservoir computer called an Echo State Network (ESN).\n  In the deterministic case, we prove (under some assumptions) that if a\nreservoir computer has the Echo State Property (ESP), then there is a C1\ngeneralised synchronisation between the input dynamical system and the dynamics\nin the reservoir space. Furthermore, we prove that a reservoir computer with\nthe local ESP in several disjoint subsets of the reservoir space will admit\nseveral distinct generalised synchronisations. In the special case that the\nreservoir map is linear, and has the ESP, we prove that the generalised\nsynchronisation is generically an embedding. This result admits Takens'\nembedding Theorem as a special case.\n  We go to show that ESNs trained on scalar observations of an ergodic\ndynamical system can approximate an arbitrary target function, including the\nnext step map used in time series forecasting. This universal approximation\nproperty holds despite the training process being entirely linear.\n  We prove analogous results for ESNs trained on observations of a stochastic\nprocess, which are not be Markovian in general. We use these results to develop\nsupervised learning, and reinforcement learning algorithms supported by an ESN.\n  In the penultimate chapter of this thesis, we use a reservoir computer to\nnumerically solve linear PDEs. In the final chapter, we conclude and discuss\ndirections for future work.\n""]","[('reservoir computing', 0.7780985236167908), ('reservoir', 0.5620204210281372), ('reservoirs', 0.5005218386650085), ('chaotic systems', 0.48326876759529114), ('recurrent neural', 0.4641245901584625), ('recurrent neural networks', 0.45513278245925903), ('chaotic dynamical systems', 0.45091643929481506), ('recurrent neural network', 0.43721655011177063), ('neural networks rnns', 0.4267544150352478), ('learning dynamical', 0.4160478711128235)]"
284,284,102,284_tilings_tilings plane_tilings two_domino tilings,"['tilings', 'tilings plane', 'tilings two', 'domino tilings', 'tiling plane', 'tiling', 'tiling mathbb', 'tiles', 'penrose tilings', 'tile']","['An aperiodic tiling of variable geometry made of two tiles, a triangle\n  and a rhombus of any angle   Aperiodic tiling is a well-know area of research. First developed by\nmathematicians for the mathematical challenge they represent and the beauty of\ntheir resulting patterns, they became a growing field of interest when their\npractical use started to emerge. This was mainly in the eighties when a link\nwas established with quasi-periodic materials. Several aperiodic tilings made\nof two tiles were discovered, the first one being by Penrose in the seventies.\nSince then, scientists discovered other aperiodic tilings including the\nsquare-triangle one, a tiling that has been particularly useful for the study\nof dodecagonal quasicrystals and soft matters. Based on this previous work, we\ndiscovered an infinite number of aperiodic tilings made of two tiles, a\ntriangle and a rhombus of any angle. As a result, a variable geometry, i.e.\ncontinuously transformable, aperiodic tiling is proposed, whose underlying\nstructure is dodecagonal. We discuss this limit case where the rhombus is so\nthin that it becomes invisible. At the boundary of this infinite space of\ntilings are two periodic ones; this represents a uniform view of periodic and\naperiodic tilings.\n', 'An aperiodic tiling made of one tile, a triangle   How many different tiles are needed at the minimum to create aperiodicity?\nSeveral tilings made of two tiles were discovered, the first one being by\nPenrose in the seventies. Since then, scientists discovered other aperiodic\ntilings made of two tiles, including the square-triangle one, a tiling that has\nbeen particularly useful for the study of dodecagonal quasicrystals and soft\nmatters. An open problem still exists: Can one tile be sufficient to create\naperiodicity? This is known as the ein stein problem. We present in this paper\nan aperiodic tiling made of one single tile: an isosceles right triangle. The\ntile itself is not aperiodic and therefore not a solution to the ein stein\nproblem but we present a set of substitution rules on the same tile that forces\nthe tiling to be aperiodic. This paper presents its construction rules that\nproves its aperiodicity. We also show that this tiling offers an underlying\ndodecagonal structure close to the one of square-triangle tiling.\n', 'Turtles, Hats and Spectres: Aperiodic structures on a Rhombic tiling   These notes derive aperiodic monotiles (arXiv:2303.10798) from a set of\nrhombuses with matching rules. This dual construction is used to simplify the\nproof of aperiodicity by considering the tiling as a colouring game on a\nRhombille tiling. A simple recursive substitution system is then introduced to\nshow the existence of a non-periodic tiling without the need for computer-aided\nverification.\n  A new cut-and-project style construction linking the Turtle tiling with\n1-dimensional Fibonacci words provides a second proof of non-periodicity, and\nan alternative demonstration that the Turtle can tile the plane.\n  Deforming the Turtle into the Hat tile then provides a third proof for\nnon-periodicity by considering the effect on the lattice underlying the\nRhombille tiling.\n  Finally, attention turns to the Spectre tile. In collaboration with Erhard\nK\\""unzel and Yoshiaki Araki, we present two new substitution rules for\ngenerating Spectre tilings. This pair of conjugate rules show that the\naperiodic monotile tilings can be considered as a 2-dimensional analog to\nSturmian words.\n']","[('tilings', 0.6646642088890076), ('tilings plane', 0.6447667479515076), ('tilings two', 0.6372033357620239), ('domino tilings', 0.6278189420700073), ('tiling plane', 0.6266873478889465), ('tiling', 0.6080910563468933), ('tiling mathbb', 0.5705314874649048), ('tiles', 0.5538137555122375), ('penrose tilings', 0.5502240061759949), ('tile', 0.5445057153701782)]"
285,285,102,285_public key cryptography_cryptographic schemes_cryptosystems_based cryptosystems,"['public key cryptography', 'cryptographic schemes', 'cryptosystems', 'based cryptosystems', 'encryption scheme', 'cryptosystem', 'key cryptography', 'cryptography', 'public key encryption', 'homomorphic encryption']","['Public key cryptography based on twisted dihedral group algebras   In this paper, we propose to use a twisted dihedral group algebra for\npublic-key cryptography. For this, we introduce a new $2$-cocycle\n$\\alpha_{\\lambda}$ to twist the dihedral group algebra. Using the ambient space\n$\\mathbb{F}^{\\alpha_{\\lambda}} D_{2n}$, we then introduce a key exchange\nprotocol and present an analysis of its security. Moreover, we explore the\nproperties of the resulting twisted algebra\n$\\mathbb{F}^{\\alpha_{\\lambda}}D_{2n}$, exploiting them to enhance our key\nexchange protocol. We also introduce a probabilistic public-key scheme derived\nfrom our key-exchange protocol and obtain a key encapsulation mechanism (KEM)\nby applying a well-known generic transformation to our public-key scheme.\nFinally, we present a proof-of-concept implementation of the resulting key\nencapsulation mechanism.\n', 'Public key cryptography based on skew dihedral group rings   In this paper, we propose to use a skew dihedral group ring given by the\ngroup $D_{2n}$ and the finite field $\\mathbb{F}_{q^2}$ for public-key\ncryptography. Using the ambient space $\\mathbb{F}_{q^{2}}^{\\theta} D_{2n}$ and\na group homomorphism $\\theta: D_{2n} \\rightarrow\n\\mathrm{Aut}(\\mathbb{F}_{q^2})$, we introduce a key exchange protocol and\npresent an analysis of its security. Moreover, we explore the properties of the\nresulting skew group ring $\\mathbb{F}_{q^{2}}^{\\theta} D_{2n}$, exploiting them\nto enhance our key exchange protocol. We also introduce a probabilistic\npublic-key scheme derived from our key exchange protocol and obtain a key\nencapsulation mechanism (KEM) by applying a well-known generic transformation\nto our public-key scheme. Finally, we present a proof-of-concept implementation\nof our cryptographic constructions. To the best of our knowledge, this is the\nfirst paper that proposes a skew dihedral group ring for public-key\ncryptography.\n', 'Group ring based public key cryptosystems   In this paper, we propose two cryptosystems based on group rings and existing\ncryptosystem. First one is Elliptic ElGamal type group ring public key\ncryptosystem whose security is greater than security of cryptosystems based on\nelliptic curves discrete logarithmic problem (ECDLP). Second is ElGamal type\ngroup ring public key cryptosystem, which is analogous to ElGamal public key\ncryptosystem but has comparatively greater security. Examples are also given\nfor both the proposed cryptosystems.\n']","[('public key cryptography', 0.6589359045028687), ('cryptographic schemes', 0.6450658440589905), ('cryptosystems', 0.6269952654838562), ('based cryptosystems', 0.6269928216934204), ('encryption scheme', 0.6220546364784241), ('cryptosystem', 0.6195288300514221), ('key cryptography', 0.6136669516563416), ('cryptography', 0.6067943572998047), ('public key encryption', 0.5836165547370911), ('homomorphic encryption', 0.5801579356193542)]"
286,286,101,286_semidefinite relaxations_sparse polynomial optimization_hierarchy polynomial optimization_semidefinite programs,"['semidefinite relaxations', 'sparse polynomial optimization', 'hierarchy polynomial optimization', 'semidefinite programs', 'semidefinite programming', 'polynomial optimization', 'polynomial optimization problems', 'sparse semidefinite', 'moment sos relaxations', 'sparse polynomial']","[""A note on the computational complexity of the moment-SOS hierarchy for\n  polynomial optimization   The moment-sum-of-squares (moment-SOS) hierarchy is one of the most\ncelebrated and widely applied methods for approximating the minimum of an\nn-variate polynomial over a feasible region defined by polynomial\n(in)equalities. A key feature of the hierarchy is that, at a fixed level, it\ncan be formulated as a semidefinite program of size polynomial in the number of\nvariables n. Although this suggests that it may therefore be computed in\npolynomial time, this is not necessarily the case. Indeed, as O'Donnell (2017)\nand later Raghavendra & Weitz (2017) show, there exist examples where the\nsos-representations used in the hierarchy have exponential bit-complexity. We\nstudy the computational complexity of the moment-SOS hierarchy, complementing\nand expanding upon earlier work of Raghavendra & Weitz (2017). In particular,\nwe establish algebraic and geometric conditions under which polynomial-time\ncomputation is guaranteed to be possible.\n"", 'A Characterization for Tightness of the Sparse Moment-SOS Hierarchy   This paper studies the sparse Moment-SOS hierarchy of relaxations for solving\nsparse polynomial optimization problems. We show that this sparse hierarchy is\ntight if and only if the objective can be written as a sum of sparse\nnonnegative polynomials, each of which belongs to the sum of the ideal and\nquadratic module generated by the corresponding sparse constraints. Based on\nthis characterization, we give several sufficient conditions for the sparse\nMoment-SOS hierarchy to be tight. In particular, we show that this sparse\nhierarchy is tight under some assumptions such as convexity, optimality\nconditions or finiteness of constraining sets.\n', 'Finite convergence of Moment-SOS relaxations with non-real radical\n  ideals   We consider the linear conic optimization problem with the cone of\nnonnegative polynomials. Its dual optimization problem is the generalized\nmoment problem. Moment-SOS relaxations are powerful for solving them. This\npaper studies finite convergence of the Moment-SOS hierarchy when the\nconstraining set is defined by equations whose ideal may not be real radical.\nUnder the archimedeanness, we show that the Moment-SOS hierarchy has finite\nconvergence if some classical optimality conditions hold at every minimizer of\nthe optimal nonnegative polynomial for the linear conic optimization problem.\nWhen the archimedeanness fails (this is the case for unbounded sets), we\npropose a homogenized Moment-SOS hierarchy and prove its finite convergence\nunder similar assumptions. Furthermore, we also prove the finite convergence of\nthe Moment-SOS hierarchy with denominators. In particular, this paper resolves\na conjecture posed in the earlier work.\n']","[('semidefinite relaxations', 0.5984951257705688), ('sparse polynomial optimization', 0.5886731743812561), ('hierarchy polynomial optimization', 0.5502914190292358), ('semidefinite programs', 0.5364893078804016), ('semidefinite programming', 0.5340586304664612), ('polynomial optimization', 0.5336309671401978), ('polynomial optimization problems', 0.5329394936561584), ('sparse semidefinite', 0.5015854835510254), ('moment sos relaxations', 0.4881120026111603), ('sparse polynomial', 0.46514689922332764)]"
287,287,101,287_random field ising_ferromagnetic ising_ising models_two dimensional ising,"['random field ising', 'ferromagnetic ising', 'ising models', 'two dimensional ising', 'field ising', 'dimensional ising', 'quantum ising', 'random field', 'ising random', 'renormalization']","[""Exponential decay of correlations in the 2D random field Ising model   An extension of the Ising spin configurations to continuous functions is used\nfor an exact representation of the Random Field Ising Model's order parameter\nin terms of disagreement percolation. This facilitates an extension of the\nrecent analyses of the decay of correlations to positive temperatures, at\nhomogeneous but arbitrarily weak disorder.\n"", ""Absence of replica symmetry breaking in disordered FKG-Ising models\n  under uniform field   We prove that the variance of spin overlap vanishes in disordered Ising\nmodels satisfying the Fortuin-Kasteleyn-Ginibre (FKG) inequality under a\nuniform field, such as generally distributed random field Ising model, site-\nand bond-diluted Ising models with the Bernoulli distribution. Chatterjee's\nproof for the Gaussian random field Ising model is generalized to other\nindependent identically distributed quenched disorder under a uniform field.\n"", 'On the Ultrametricity Property in Random Field Ising Models   In this paper we show that the ultrametricity property remains valid in\nrandom field Ising models with independent disorder whenever the field strength\nis a small perturbation.\n']","[('random field ising', 0.6435322761535645), ('ferromagnetic ising', 0.5203744173049927), ('ising models', 0.5128669738769531), ('two dimensional ising', 0.49245527386665344), ('field ising', 0.4760688543319702), ('dimensional ising', 0.4735790491104126), ('quantum ising', 0.46720612049102783), ('random field', 0.4478329122066498), ('ising random', 0.4421938955783844), ('renormalization', 0.405673623085022)]"
288,288,101,288_online convex optimization_online optimization_convex optimization oco_online gradient descent,"['online convex optimization', 'online optimization', 'convex optimization oco', 'online gradient descent', 'online convex', 'regret minimization', 'cost convex', 'convex optimization', 'constrained online', 'regret bounds']","['Optimal Algorithms for Online Convex Optimization with Adversarial\n  Constraints   A well-studied generalization of the standard online convex optimization\n(OCO) framework is constrained online convex optimization (COCO). In COCO, on\nevery round, a convex cost function and a convex constraint function are\nrevealed to the learner after it chooses the action for that round. The\nobjective is to design an online learning policy that simultaneously achieves a\nsmall regret while ensuring a small cumulative constraint violation (CCV)\nagainst an adaptive adversary interacting over a horizon of length $T$. A\nlong-standing open question in COCO is whether an online policy can\nsimultaneously achieve $O(\\sqrt{T})$ regret and $\\tilde{O}(\\sqrt{T})$ CCV\nwithout any restrictive assumptions. For the first time, we answer this in the\naffirmative and show that a simple first-order policy can simultaneously\nachieve these bounds. Furthermore, in the case of strongly convex cost and\nconvex constraint functions, the regret guarantee can be improved to $O(\\log\nT)$ while keeping the CCV bound the same as above. We establish these results\nby effectively combining adaptive OCO policies as a blackbox with Lyapunov\noptimization - a classic tool from control theory. Surprisingly, the analysis\nis short and elegant.\n', 'Optimal Bounds for Adversarial Constrained Online Convex Optimization Constrained Online Convex Optimization (COCO) can be seen as a generalization of the standard Online Convex Optimization (OCO) framework. At each round, a cost function and constraint function are revealed after a learner chooses an action. The goal is to minimize both the regret and cumulative constraint violation (CCV) against an adaptive adversary. We show for the first time that is possible to obtain the optimal $O(\\sqrt{T})$ bound on both regret and CCV, improving the best known bounds of $O \\left( \\sqrt{T} \\right)$ and $\\tilde{O} \\left( \\sqrt{T} \\right)$ for the regret and CCV, respectively. Based on a new surrogate loss function enforcing a minimum penalty on the constraint function, we demonstrate that both the Follow-the-Regularized-Leader and the Online Gradient Descent achieve the optimal bounds.', 'Tight Bounds for Online Convex Optimization with Adversarial Constraints   A well-studied generalization of the standard online convex optimization\n(OCO) is constrained online convex optimization (COCO). In COCO, on every\nround, a convex cost function and a convex constraint function are revealed to\nthe learner after the action for that round is chosen. The objective is to\ndesign an online policy that simultaneously achieves a small regret while\nensuring small cumulative constraint violation (CCV) against an adaptive\nadversary. A long-standing open question in COCO is whether an online policy\ncan simultaneously achieve $O(\\sqrt{T})$ regret and $O(\\sqrt{T})$ CCV without\nany restrictive assumptions. For the first time, we answer this in the\naffirmative and show that an online policy can simultaneously achieve\n$O(\\sqrt{T})$ regret and $\\tilde{O}(\\sqrt{T})$ CCV. We establish this result by\neffectively combining the adaptive regret bound of the AdaGrad algorithm with\nLyapunov optimization - a classic tool from control theory. Surprisingly, the\nanalysis is short and elegant.\n']","[('online convex optimization', 0.713070809841156), ('online optimization', 0.6125994324684143), ('convex optimization oco', 0.60982346534729), ('online gradient descent', 0.600878119468689), ('online convex', 0.5918715596199036), ('regret minimization', 0.5464288592338562), ('cost convex', 0.543549120426178), ('convex optimization', 0.5409886240959167), ('constrained online', 0.5038425922393799), ('regret bounds', 0.4922301471233368)]"
289,289,101,289_hopf algebras_dimensional hopf algebras_hopf algebras hopf_cocommutative hopf algebra,"['hopf algebras', 'dimensional hopf algebras', 'hopf algebras hopf', 'cocommutative hopf algebra', 'hopf algebra', 'dimensional hopf algebra', 'graded hopf algebra', 'hopf algebra mathcal', 'algebras hopf', 'hopf subalgebra']","['On Hopf algebras over basic Hopf algebras of dimension 24   We determine finite-dimensional Hopf algebras over an algebraically closed\nfield of characteristic zero, whose Hopf coradical is isomorphic to a\nnon-pointed basic Hopf algebra of dimension $24$ and the infinitesimal\nbraidings are indecomposable objects. In particular, we obtain families of new\nfinite-dimensional Hopf algebras without the dual Chevalley property.\n', ""Braided Hopf Crossed Modules Through Simplicial Structures   Any simplicial Hopf algebra involves $2n$ different projections between the\nHopf algebras $H_n,H_{n-1}$ for each $n \\geq 1$. The word projection, here\nmeaning a tuple $\\partial \\colon H_{n} \\to H_{n-1}$ and $i \\colon H_{n-1} \\to\nH_{n}$ of Hopf algebra morphisms, such that $\\partial \\, i = \\mathrm{id}$.\nGiven a Hopf algebra projection $(\\partial \\colon I \\to H,i)$ in a braided\nmonoidal category $\\mathfrak{C}$, one can obtain a new Hopf algebra structure\nliving in the category of Yetter-Drinfeld modules over $H$, due to Radford's\ntheorem. The underlying set of this Hopf algebra is obtained by an equalizer\nwhich only defines a sub-algebra (not a sub-coalgebra) of $I$ in\n$\\mathfrak{C}$. In fact, this is a braided Hopf algebra since the category of\nYetter-Drinfeld modules over a Hopf algebra with an invertible antipode is\nbraided monoidal. To apply Radford's theorem in a simplicial Hopf algebra\nsuccessively, we require some extra functorial properties of Yetter-Drinfeld\nmodules. Furthermore, this allows us to model Majid's braided Hopf crossed\nmodule notion from the perspective of a simplicial structure.\n"", 'A decomposition Theorem for pointed braided Hopf algebras   A known fundamental Theorem for braided pointed Hopf algebras states that for\neach coideal subalgebra, that fulfils a few properties, there is an associated\nquotient coalgebra right module such that the braided Hopf algebra can be\ndecomposed into a tensor product of these two. Often one considers braided Hopf\nalgebras in a Yetter-Drinfeld category of an ordinary Hopf algebra. In this\ncase the braided Hopf algebra is in particular a comodule, as well as many\ninteresting coideal subalgebras. We extend the mentioned Theorem by proving\nthat the decomposition is compatible with this comodule structure if the\nunderlying ordinary Hopf algebra is cosemisimple.\n']","[('hopf algebras', 0.8355023860931396), ('dimensional hopf algebras', 0.8168233036994934), ('hopf algebras hopf', 0.806178867816925), ('cocommutative hopf algebra', 0.7849347591400146), ('hopf algebra', 0.7723343372344971), ('dimensional hopf algebra', 0.7695274353027344), ('graded hopf algebra', 0.7435978651046753), ('hopf algebra mathcal', 0.7320660352706909), ('algebras hopf', 0.7171132564544678), ('hopf subalgebra', 0.6897382140159607)]"
290,290,101,290_microgrid_microgrids_inverter based resources_power grid,"['microgrid', 'microgrids', 'inverter based resources', 'power grid', 'power grids', 'inverter based', 'power systems', 'frequency control', 'synchronous machine', 'inverters']","['Flexible Control Strategy of DC Bus for AC-DC Hybrid Microgrid with\n  Electric Vehicle   As a new type of microgrid structure, AC-DC hybrid microgrid can efficiently\nconsume new energy distributed generator based on photovoltaics, which is very\nsuitable for microgrid systems with electric vehicles as the main load. Unlike\nthe AC microgrid, the DC bus of the AC-DC hybrid microgrid is a low-inertia\nsystem. How to improve the DC bus inertia of the AC-DC hybrid microgrid system\nand the stability of the DC bus voltage become particularly important. Based on\nthis, this paper presents a method for flexible control strategy of microgrid\nbus voltage based on multi-node droop. By considering the P / U droop\ncharacteristics of DC ports of power electronic equipment such as energy\nstorage and electric vehicle charging-discharging equipment, different types of\ndistributed generator are comprehensively considered. The power reserve rate\nand energy reserve rate, through curve shift and other adjustment methods,\nimprove the DC bus inertia, which effectively guarantees the stability of the\nmicrogrid system voltage. The validity of the proposed method is verified by\nbuilding a matlab / simulik simulation system.\n', 'Decentralized Droop-based Finite-Control-Set Model Predictive Control of\n  Inverter-based Resources in Islanded AC Microgrid   This paper presents an improved droop control method to ensure effective\npower sharing, voltage regulation, and frequency stabilization of\ninverter-based resources (IBRs) connected in parallel in an islanded AC\nmicrogrid. In the contemporary droop control algorithm, the distance between\nconnected inverters affects the effectiveness of the active power-frequency and\nthe reactive power-voltage droop characteristics which results in poor power\nsharing at the primary level of the microgrid. That is, high impedance\nemanating from long transmission lines results in instability, poor voltage\ntracking, and ineffective frequency regulation. Hence, in this work, we use a\nfinite-control-set model predictive controller (FCS-MPC) in the inner loop,\nwhich gives efficient voltage tracking, good frequency regulation, and faster\nperformance response. FCS-MPC is easy to implement in fast switching converters\nand does not suffer from computational burden unlike the continuous-set MPC and\nis also devoid of issues of multiple-loop, parameter variation, and slow\nresponse associated with conventional droop control methods. We derived the\ncondition for bounded stability for the FCS-MPC and the proposed method is\ntested via a numerical simulation on three IBRs. The results show effective\npower sharing, capacitor voltage tracking, and efficient frequency regulation\nwith reduced oscillations to changes in load.\n', 'Frequency Stability of Synchronous Machines and Grid-Forming Power\n  Converters   An inevitable consequence of the global power system transition towards\nnearly 100% renewable-based generation is the loss of conventional bulk\ngeneration by synchronous machines, their inertia, and accompanying frequency\nand voltage control mechanisms. This gradual transformation of the power system\nto a low-inertia system leads to critical challenges in maintaining system\nstability. Novel control techniques for converters, so-called grid-forming\nstrategies, are expected to address these challenges and replicate\nfunctionalities that so far have been provided by synchronous machines. This\narticle presents a low-inertia case study that includes synchronous machines\nand converters controlled under various grid-forming techniques. In this work\n1) the positive impact of the grid-forming converters on the frequency\nstability of synchronous machines is highlighted, 2) a qualitative analysis\nwhich provides insights into the frequency stability of the system is\npresented, 3) we explore the behavior of the grid-forming controls when\nimposing the converter dc and ac current limitations, 4) the importance of the\ndc dynamics in grid-forming control design as well as the critical need for an\neffective ac current limitation scheme are reported, and lastly 5) we analyze\nhow and when the interaction between the fast grid-forming converter and the\nslow synchronous machine dynamics can contribute to the system instability\n']","[('microgrid', 0.5391208529472351), ('microgrids', 0.5289328098297119), ('inverter based resources', 0.4125961363315582), ('power grid', 0.4029500484466553), ('power grids', 0.3757054805755615), ('inverter based', 0.3319069445133209), ('power systems', 0.3315112590789795), ('frequency control', 0.3019428849220276), ('synchronous machine', 0.2996561825275421), ('inverters', 0.2927307188510895)]"
291,291,100,291_prey dynamics_predator prey system_predator prey models_prey models,"['prey dynamics', 'predator prey system', 'predator prey models', 'prey models', 'prey system', 'prey population', 'prey predator', 'predator prey', 'hopf bifurcations', 'bifurcation analysis']","[""Dynamical behavior of Predator-Prey with Allee Effect on Both\n  Populations and Disease in Predator   In the current study, we took into account a model of nonlinear\n``predator-prey'' interactions including the ``Allee effect'' on both\npopulations and disease in the predator population. The population as a whole\nis split into three: the prey population, susceptible predator, and diseased\npredator. The ``Takagi-Sugeno (T-S) impulsive control model'' and the Fuzzy\nimpulsive control model have been used to test the stability of the\nthree-dimensional ``Lotka-Volterra predator-prey system'' model. Following the\nmodel's formulation, the global-stability and the fuzzy solution are examined\nusing numerical simulations and graphical displays, together with the necessary\nconsultation, to help comprehend the effectiveness of our suggested model.\n"", 'Complex dynamics of a predator-prey model with constant-yield prey\n  harvesting and Allee effect in predator   This paper investigates the dynamical behaviors of a Holling type I\nLeslie-Gower predator-prey model where the predator exhibits an Allee effect\nand is subjected to constant harvesting. The model demonstrates three types of\nequilibrium points under different parameter conditions, which could be either\nstable or unstable nodes (foci), saddle nodes, weak centers, or cusps. The\nsystem exhibits a saddle-node bifurcation near the saddle-node point and a Hopf\nbifurcation near the weak center. By calculating the first Lyapunov\ncoefficient, the conditions for the occurrence of both supercritical and\nsubcritical Hopf bifurcations are derived. Finally, it is proven that when the\npredator growth rate and the prey capture coefficient vary within a specific\nsmall neighborhood, the system undergoes a codimension-2 Bogdanov-Takens\nbifurcation near the cusp point.\n', 'Modelling and analysis of a modified May-Holling-Tanner predator-prey\n  model with Allee effect in the prey and an alternative food source for the\n  predator   In the present study, we have modified the traditional May-Holling-Tanner\npredator-prey model used to represent the interaction between least weasel and\nfield-vole population by adding an Allee effect (strong and weak) on the\nfield-vole population and alternative food source for the weasel population. It\nis shown that the dynamic is different from the original May-Holling-Tanner\npredator-prey interaction since new equilibrium points have appeared in the\nfirst quadrant. Moreover, the modified model allows the extinction of both\nspecies when the Allee effect (strong and weak) on the prey is included, while\nthe inclusion of the alternative food source for the predator shows that the\nsystem can support the coexistence of the populations, extinction of the prey\nand coexistence and oscillation of the populations at the same time.\nFurthermore, we use numerical simulations to illustrate the impact that\nchanging the predation rate and the predator intrinsic growth rate have on the\nbasin of attraction of the stable equilibrium point or stable limit cycle in\nthe first quadrant. These simulations show the stabilisation of predator and\nprey populations and/or the oscillation of these two species over time.\n']","[('prey dynamics', 0.7368687987327576), ('predator prey system', 0.6654950976371765), ('predator prey models', 0.6647133827209473), ('prey models', 0.662108838558197), ('prey system', 0.6201860308647156), ('prey population', 0.5596035718917847), ('prey predator', 0.5371400713920593), ('predator prey', 0.5163719058036804), ('hopf bifurcations', 0.4924505054950714), ('bifurcation analysis', 0.49015429615974426)]"
292,292,100,292_evolutionary game theory_evolutionary game dynamics_evolutionary games_evolutionary game,"['evolutionary game theory', 'evolutionary game dynamics', 'evolutionary games', 'evolutionary game', 'game theory', 'evolutionary dynamics', 'levels cooperation', 'cooperation', 'game dynamics', 'population games']","[""Impact of misinformation in the evolution of collective cooperation   Human societies are organized and developed through collective cooperative\nbehaviors, in which interactions between individuals are governed by the\nunderlying social connections. It is well known that, based on the information\nin their environment, individuals can form collective cooperation by\nstrategically imitating superior behaviors and changing unfavorable\nsurroundings in self-organizing ways. However, facing the tough situation that\nsome humans and social bots keep spreading misinformation, we still lack the\nsystematic investigation on the impact of such proliferation of misinformation\non the evolution of social cooperation. Here we study this problem by virtue of\nclassical evolutionary game theory. We find that misinformation generally\nimpedes the emergence of collective cooperation compared to scenarios with\ncompletely true information, although the level of cooperation is slightly\nhigher when the benefits provided by cooperators are reduced below a proven\nthreshold. We further show that this possible advantage shrinks as social\nconnections become denser, suggesting that misinformation is more detrimental\nto the formation of collective cooperation when 'social viscosity' is low. Our\nresults uncover the quantitative effect of misinformation on the social\ncooperative behavior in the complex networked society, and pave the way for\ndesigning possible interventions to improve collective cooperation.\n"", ""Convergence Analysis and Strategy Control of Evolutionary Games with\n  Imitation Rule on Toroidal Grid: A Full Version   This paper investigates discrete-time evolutionary games with a general\nstochastic imitation rule on the toroidal grid, which is a grid network with\nperiodic boundary conditions. The imitation rule has been considered as a\nfundamental rule to the field of evolutionary game theory, while the grid is\ntreated as the most basic network and has been widely used in the research of\nspatial (or networked) evolutionary games. However, currently the investigation\nof evolutionary games on grids mainly uses simulations or approximation\nmethods, while few strict analysis is carried out on one-dimensional grids.\nThis paper proves the convergence of evolutionary prisoner's dilemma,\nevolutionary snowdrift game, and evolutionary stag hunt game with the imitation\nrule on the two-dimensional grid, for the first time to our best knowledge.\nSimulations show that our results may almost reach the critical convergence\ncondition for the evolutionary snowdrift (or hawk-dove, chicken) game. Also,\nthis paper provides some theoretical results for the strategy control of\nevolutionary games, and solves the Minimum Agent Consensus Control (MACC)\nproblem under some parameter conditions. We show that for some evolutionary\ngames (like the evolutionary prisoner's dilemma) on the toroidal grid, one\nfixed defection node can drive all nodes almost surely converging to defection,\nwhile at least four fixed cooperation nodes are required to lead all nodes\nalmost surely converging to cooperation.\n"", 'Indirect exclusion can promote cooperation in repeated group\n  interactions   Social exclusion has been regarded as one of the most effective measures to\npromote the evolution of cooperation. In real society, the way in which social\nexclusion works can be direct or indirect. However, thus far there is no\nrelated work to explore how indirect exclusion influences the evolution of\ncooperation from a theoretical perspective. Here, we introduce indirect\nexclusion into the repeated public goods game where the game organizer\nprobabilistically selects cooperators after the first game round to participate\nin the following possible game interactions. We then investigate the\nevolutionary dynamics of cooperation both in infinite and finite well-mixed\npopulations. Through theoretical analysis and numerical calculations, we find\nthat the introduction of indirect exclusion can induce the stable coexistence\nof cooperators and defectors or the dominance of cooperators, which thus\neffectively promotes the evolution of cooperation. Besides, we show that the\nidentifying probability of the organizer has a nonlinear effect on public\ncooperation when its value is lower than an intermediate value, while the\nhigher identifying probability can maintain a high level of cooperation.\nFurthermore, our results show that increasing the average rounds of game\ninteractions can effectively promote the evolution of cooperation.\n']","[('evolutionary game theory', 0.6684067845344543), ('evolutionary game dynamics', 0.6546117067337036), ('evolutionary games', 0.6055818796157837), ('evolutionary game', 0.6001691222190857), ('game theory', 0.5616331696510315), ('evolutionary dynamics', 0.5356045365333557), ('levels cooperation', 0.5250875949859619), ('cooperation', 0.5219841599464417), ('game dynamics', 0.4971426725387573), ('population games', 0.48958903551101685)]"
293,293,100,293_ruin probability_ruin theory_risk theory_ruin,"['ruin probability', 'ruin theory', 'risk theory', 'ruin', 'risk models', 'risk processes', 'risk process', 'semi markov', 'insurance', 'markov models']","[""Confidence intervals of ruin probability under L\\'evy surplus   The aim of this paper is to construct the confidence interval of the ultimate\nruin probability under the insurance surplus driven by a L\\'evy process.\nAssuming a parametric family for the L\\'evy measures, we estimate the parameter\nfrom the surplus data and estimate the ruin probability via the delta method.\nHowever the asymptotic variance includes the derivative of the ruin probability\nwith respect to the parameter, which is not generally given explicitly, and the\nconfidence interval is not straightforward even if the ruin probability is well\nestimated. This paper gives the Cram\\'er-type approximation for the derivative\nand gives an asymptotic confidence interval of ruin probability.\n"", 'Ruin probabilities with investments: smoothness, IDE and ODE, asymptotic\n  behavior   The study deals with the ruin problem when an insurance company having two\nbusiness branches, life insurance and non-life insurance, invests its reserve\ninto a risky asset with the price dynamics given by a geometric Brownian\nmotion. We prove a result on smoothness of the ruin probability as a function\nof the initial capital and obtain for it an integro-differential equation\nunderstood in the classical sense. For the case of exponentially distributed\njumps we show that the survival probability is a solution of an ordinary\ndifferential equation of the 4th order. Asymptotic analysis of the latter leads\nto the conclusion that the ruin probability decays to zero in the same way as\nin the already studied cases of models with one-side jumps.\n', 'Approximation of ruin probability and ruin time in discrete Brownian\n  risk models   We analyze the classical Brownian risk models discussing the approximation of\nruin probabilities (classical, {\\gamma}-reflected, Parisian and cumulative\nParisian) for the case that ruin can occur only on specific discrete grids. A\npractical and natural grid of points is for instance G(1) = {0,1,2,...}, which\nallows us to study the probability of the ruin on the first day, second day,\nand so one. For such a discrete setting, there are no explicit formulas for the\nruin probabilities mentioned above. In this contribution we derive accurate\napproximations of ruin probabilities for uniform grids by letting the initial\ncapital to grow to infinity.\n']","[('ruin probability', 0.6408944725990295), ('ruin theory', 0.6068145036697388), ('risk theory', 0.4649607241153717), ('ruin', 0.44692742824554443), ('risk models', 0.4303797781467438), ('risk processes', 0.4168403148651123), ('risk process', 0.40789729356765747), ('semi markov', 0.3886312246322632), ('insurance', 0.36251991987228394), ('markov models', 0.3566552996635437)]"
294,294,100,294_symmetric designs_group divisible designs_transitive automorphism groups_symmetric design,"['symmetric designs', 'group divisible designs', 'transitive automorphism groups', 'symmetric design', 'designs constructed', 'transitive automorphism group', 'designs', 'symmetric configurations', 'divisible designs', 'transitive automorphism']","['Almost simple groups as flag-transitive automorphism groups of 2-designs\n  with {\\lambda} = 2   In this article, we study $2$-designs with $\\lambda=2$ admitting a\nflag-transitive almost simple automorphism group with socle a finite simple\nexceptional group of Lie type, and we prove that such a $2$-design does not\nexist. In conclusion, we present a classification of $2$-designs with\n$\\lambda=2$ admitting flag-transitive and point-primitive automorphism groups\nof almost simple type, which states that such a $2$-design belongs to an\ninfinite family of $2$-designs with parameter set $((3^n-1)/2,3,2)$ and\n$X=PSL_n(3)$ for some $n\\geq 3$, or it is isomorphic to the $2$-design with\nparameter set $(6,3,2)$, $(7,4,2)$, $(10,4,2)$, $(10,4,2)$, $(11,5,2)$,\n$(28,7,2)$, $(28,3,2)$, $(36,6,2)$, $(126,6,2)$ or $(176,8,2)$.\n', 'Sporadic simple groups as flag-transitive automorphism groups of\n  symmetric designs   In this article, we study symmetric designs admitting flag-transitive,\npoint-imprimitive almost simple automorphism groups with socle sporadic simple\ngroups. As a corollary, we present a classification of symmetric designs\nadmitting flag-transitive automorphism group whose socle is a sporadic simple\ngroup, and in conclusion, there are exactly seven such designs, one of which\nadmits a point-imprimitive automorphism group and the remaining are\npoint-primitive.\n', 'On symmetric 2-designs of prime order with almost simple flag-transitive\n  automorphism groups   In this article, we investigate symmetric 2-designs of prime order admitting\na flag-transitive automorphism group G. Recently, the authors proved that the\nautomorphism group G of this type of designs must be point-primitive, and is of\naffine or almost simple type. Here, we give the complete classification of\nsymmetric 2-designs of prime order, admitting a flag-transitive almost simple\nautomorphism group.\n']","[('symmetric designs', 0.6274985074996948), ('group divisible designs', 0.5553106069564819), ('transitive automorphism groups', 0.5206305384635925), ('symmetric design', 0.5188502669334412), ('designs constructed', 0.4952312111854553), ('transitive automorphism group', 0.49329033493995667), ('designs', 0.4788030982017517), ('symmetric configurations', 0.47668033838272095), ('divisible designs', 0.4657790958881378), ('transitive automorphism', 0.4607222378253937)]"
295,295,99,295_distributionally robust optimization_driven distributionally robust_robust chance constrained_distributionally robust,"['distributionally robust optimization', 'driven distributionally robust', 'robust chance constrained', 'distributionally robust', 'distributional robustness', 'robust optimization', 'based distributionally robust', 'robust optimization dro', 'robust optimization problems', 'chance constrained optimization']","['Data-driven Approximation of Distributionally Robust Chance Constraints\n  using Bayesian Credible Intervals   The non-convexity and intractability of distributionally robust chance\nconstraints make them challenging to cope with. From a data-driven perspective,\nwe propose formulating it as a robust optimization problem to ensure that the\ndistributionally robust chance constraint is satisfied with high probability.\nTo incorporate available data and prior distribution knowledge, we construct\nambiguity sets for the distributionally robust chance constraint using Bayesian\ncredible intervals. We establish the congruent relationship between the\nambiguity set in Bayesian distributionally robust chance constraints and the\nuncertainty set in a specific robust optimization. In contrast to most existent\nuncertainty set construction methods which are only applicable for particular\nsettings, our approach provides a unified framework for constructing\nuncertainty sets under different marginal distribution assumptions, thus making\nit more flexible and widely applicable. Additionally, under the concavity\nassumption, our method provides strong finite sample probability guarantees for\noptimal solutions. The practicality and effectiveness of our approach are\nillustrated with numerical experiments on portfolio management and queuing\nsystem problems. Overall, our approach offers a promising solution to\ndistributionally robust chance constrained problems and has potential\napplications in other fields.\n', 'Structured ambiguity sets for distributionally robust optimization   Distributionally robust optimization (DRO) incorporates robustness against\nuncertainty in the specification of probabilistic models. This paper focuses on\nmitigating the curse of dimensionality in data-driven DRO problems with optimal\ntransport ambiguity sets. By exploiting independence across lower-dimensional\ncomponents of the uncertainty, we construct structured ambiguity sets that\nexhibit a faster shrinkage as the number of collected samples increases. This\nnarrows down the plausible models of the data-generating distribution and\nmitigates the conservativeness that the decisions of DRO problems over such\nambiguity sets may face. We establish statistical guarantees for these\nstructured ambiguity sets and provide dual reformulations of their associated\nDRO problems for a wide range of objective functions. The benefits of the\napproach are demonstrated in a numerical example.\n', 'Residuals-based distributionally robust optimization with covariate\n  information   We consider data-driven approaches that integrate a machine learning\nprediction model within distributionally robust optimization (DRO) given\nlimited joint observations of uncertain parameters and covariates. Our\nframework is flexible in the sense that it can accommodate a variety of\nregression setups and DRO ambiguity sets. We investigate asymptotic and finite\nsample properties of solutions obtained using Wasserstein, sample robust\noptimization, and phi-divergence-based ambiguity sets within our DRO\nformulations, and explore cross-validation approaches for sizing these\nambiguity sets. Through numerical experiments, we validate our theoretical\nresults, study the effectiveness of our approaches for sizing ambiguity sets,\nand illustrate the benefits of our DRO formulations in the limited data regime\neven when the prediction model is misspecified.\n']","[('distributionally robust optimization', 0.7862428426742554), ('driven distributionally robust', 0.6592183113098145), ('robust chance constrained', 0.6478214263916016), ('distributionally robust', 0.6412978768348694), ('distributional robustness', 0.6326380372047424), ('robust optimization', 0.6316155195236206), ('based distributionally robust', 0.6304689049720764), ('robust optimization dro', 0.622837245464325), ('robust optimization problems', 0.6152534484863281), ('chance constrained optimization', 0.5934524536132812)]"
296,296,99,296_ergodic markov chains_markov chains general_ergodic markov_reversible markov chains,"['ergodic markov chains', 'markov chains general', 'ergodic markov', 'reversible markov chains', 'non reversible markov', 'limit markov', 'markov additive processes', 'markov chain finite', 'reversible markov', 'markov additive']","['Analysis of non-reversible Markov chains via similarity orbit   In this paper, we develop an in-depth analysis of non-reversible Markov\nchains on denumerable state space from a similarity orbit perspective. In\nparticular, we study the class of Markov chains whose transition kernel is in\nthe similarity orbit of a normal transition kernel, such as the one of\nbirth-death chains or reversible Markov chains. We start by identifying a set\nof sufficient conditions for a Markov chain to belong to the similarity orbit\nof a birth-death one. As by-products, we obtain a spectral representation in\nterms of non-self-adjoint resolutions of identity in the sense of Dunford [21]\nand offer a detailed analysis on the convergence rate, separation cutoff and\n${\\rm{L}}^2$-cutoff of this class of non-reversible Markov chains. We also look\ninto the problem of estimating the integral functionals from discrete\nobservations for this class. In the last part of this paper, we investigate a\nparticular similarity orbit of reversible Markov kernels, that we call the pure\nbirth orbit, and analyze various possibly non-reversible variants of classical\nbirth-death processes in this orbit.\n', ""Variational Formulas of Asymptotic Variance for General Discrete-time\n  Markov Chains   The asymptotic variance is an important criterion to evaluate the performance\nof Markov chains, especially for the central limit theorems. We give the\nvariational formulas for the asymptotic variance of discrete-time\n(non-reversible) Markov chains on general state space. The variational formulas\nprovide many applications, extending the classical Peskun's comparison theorem\nto non-reversible Markov chains, and obtaining several comparison theorems\nbetween Markov chains with various perturbations.\n"", ""On a boundary of the central limit theorem for strictly stationary,\n  reversible Markov chains   Consider the class of (functions of) strictly stationary Markov chains in\nwhich (i) the second moments are finite and (ii) absolute regularity\n(beta-mixing) is satisfied with exponential mixing rate. For (functions of)\nMarkov chains in that class that are also reversible, the central limit theorem\nholds, as a well known byproduct of results of Roberts, Rosenthal, and Tweedie\nin two papers in 1997 and 2001 involving reversible Markov chains. In contrast,\nfor (functions of) Markov chains in that class that are not reversible, the\ncentral limit theorem may fail to hold, as is known from counterexamples,\nincluding ones with arbitrarily fast mixing rate (for absolute regularity).\nHere it will be shown that for Markov chains in that class that are reversible,\nthe``borderline'' class of mixing rates (for absolute regularity) for the\ncentral limit theorem is in fact exponential. That will be shown here with a\nclass of counterexamples: strictly stationary, countable-state Markov chains\nthat are reversible, have finite second moments, and satisfy absolute\nregularity with mixing rates that can be arbitrarily close to (but not quite)\nexponential, but fail to satisfy the central limit theorem.\n""]","[('ergodic markov chains', 0.684191107749939), ('markov chains general', 0.6353650689125061), ('ergodic markov', 0.6214306950569153), ('reversible markov chains', 0.620637059211731), ('non reversible markov', 0.6057683825492859), ('limit markov', 0.5991434454917908), ('markov additive processes', 0.5934847593307495), ('markov chain finite', 0.5930190086364746), ('reversible markov', 0.570824146270752), ('markov additive', 0.5687114000320435)]"
297,297,99,297_survival analysis_survival functions_censoring_cox proportional hazards,"['survival analysis', 'survival functions', 'censoring', 'cox proportional hazards', 'survival time', 'censored', 'proportional hazards', 'survival times', 'proportional hazard', 'right censored']","['Proximal Survival Analysis to Handle Dependent Right Censoring   Many epidemiological and clinical studies aim at analyzing a time-to-event\nendpoint. A common complication is right censoring. In some cases, it arises\nbecause subjects are still surviving after the study terminates or move out of\nthe study area, in which case right censoring is typically treated as\nindependent or non-informative. Such an assumption can be further relaxed to\nconditional independent censoring by leveraging possibly time-varying covariate\ninformation, if available, assuming censoring and failure time are independent\namong covariate strata. In yet other instances, events may be censored by other\ncompeting events like death and are associated with censoring possibly through\nprognoses. Realistically, measured covariates can rarely capture all such\nassociations with certainty. For such dependent censoring, often covariate\nmeasurements are at best proxies of underlying prognoses. In this paper, we\nestablish a nonparametric identification framework by formally admitting that\nconditional independent censoring may fail in practice and accounting for\ncovariate measurements as imperfect proxies of underlying association. The\nframework suggests adaptive estimators which we give generic assumptions under\nwhich they are consistent, asymptotically normal, and doubly robust. We\nillustrate our framework with concrete settings, where we examine the\nfinite-sample performance of our proposed estimators via a Monte-Carlo\nsimulation and apply them to the SEER-Medicare dataset.\n', 'Doubly Robust and Efficient Calibration of Prediction Sets for Censored\n  Time-to-Event Outcomes   Our objective is to construct well-calibrated prediction sets for a\ntime-to-event outcome subject to right-censoring with guaranteed coverage. Our\napproach is inspired by modern conformal inference literature in that, unlike\nclassical frameworks, we obviate the need for a well-specified parametric or\nsemiparametric survival model to accomplish our goal. In contrast to existing\nconformal prediction methods for survival data, which restrict censoring to be\nof Type I, whereby potential censoring times are assumed to be fully observed\non all units in both training and validation samples, we consider the more\ncommon right-censoring setting in which either only the censoring time or only\nthe event time of primary interest is directly observed, whichever comes first.\nUnder a standard conditional independence assumption between the potential\nsurvival and censoring times given covariates, we propose and analyze two\nmethods to construct valid and efficient lower predictive bounds for the\nsurvival time of a future observation. The proposed methods build upon modern\nsemiparametric efficiency theory for censored data, in that the first approach\nincorporates inverse-probability-of-censoring weighting to account for\ncensoring, while the second approach is based on augmenting this method with an\nadditional correction term. For both methods, we formally establish asymptotic\ncoverage guarantees and demonstrate, both theoretically and through empirical\nexperiments, that the augmented approach substantially improves efficiency over\nthe inverse-probability-of-censoring weighting method. Specifically, its\ncoverage error bound is of second-order mixed bias type, that is doubly robust,\nand therefore guaranteed to be asymptotically negligible relative to the\ncoverage error of the non-augmented method.\n', 'Factorial survival analysis for treatment effects under dependent\n  censoring   Factorial analyses offer a powerful nonparametric means to detect main or\ninteraction effects among multiple treatments. For survival outcomes, e.g. from\nclinical trials, such techniques can be adopted for comparing reasonable\nquantifications of treatment effects. The key difficulty to solve in survival\nanalysis concerns the proper handling of censoring. So far, all existing\nfactorial analyses for survival data were developed under the independent\ncensoring assumption, which is too strong for many applications. As a solution,\nthe central aim of this article is to develop new methods in factorial survival\nanalyses under quite general dependent censoring regimes. This will be\naccomplished by combining existing results for factorial survival analyses with\ntechniques developed for survival copula models. As a result, we will present\nan appealing F-test that exhibits sound performance in our simulation study.\nThe new methods are illustrated in real data analysis. We implement the\nproposed method in an R function surv.factorial(.) in the R package\ncompound.Cox.\n']","[('survival analysis', 0.5500445365905762), ('survival functions', 0.46443426609039307), ('censoring', 0.44777026772499084), ('cox proportional hazards', 0.43008488416671753), ('survival time', 0.3863523006439209), ('censored', 0.36947694420814514), ('proportional hazards', 0.3679204285144806), ('survival times', 0.3608013987541199), ('proportional hazard', 0.3545358180999756), ('right censored', 0.3492422103881836)]"
298,298,99,298_strichartz type estimates_strichartz estimates_schr odinger equations_strichartz estimate,"['strichartz type estimates', 'strichartz estimates', 'schr odinger equations', 'strichartz estimate', 'estimate schr odinger', 'schr odinger operators', 'estimates schr odinger', 'schr odinger operator', 'sobolev estimates', 'odinger operators']","['Quasimode and Strichartz estimates for time-dependent Schr\\""odinger\n  equations with singular potentials   We generalize the Strichartz estimates for Schr\\""odinger operators on compact\nmanifolds of Burq, G\\\'erard and Tzvetkov [10] by allowing critically singular\npotentials $V$. Specifically, we show that their $1/p$--loss\n$L^p_tL^q_x(I\\times M)$-Strichartz estimates hold for $e^{-itH_V}$ when\n$H_V=-\\Delta_g+V(x)$ with $V\\in L^{n/2}(M)$ if $n\\ge3$ or $V\\in\nL^{1+\\delta}(M)$, $\\delta>0$, if $n=2$, with $(p,q)$ being as in the Keel-Tao\ntheorem and $I\\subset {\\mathbb R}$ a bounded interval. We do this by\nformulating and proving new ""quasimode"" estimates for scaled dyadic unperturbed\nSchr\\""odinger operators and taking advantage of the the fact that\n$1/q\'-1/q=2/n$ for the endpoint Strichartz estimates when $(p,q)=(2,2n/(n-2))$.\nWe also show that the universal quasimode estimates that we obtain are\nsaturated on {\\em any} compact manifolds; however, we suggest that they may\nlend themselves to improved Strichartz estimates in certain geometries using\nrecently developed ""Kakeya-Nikodym"" techniques developed to obtain improved\neigenfunction estimates assuming, say, negative curvatures.\n', 'Orthonormal Strichartz estimates for Schr\\""odinger operator and their\n  applications to infinitely many particle systems   We develop an abstract perturbation theory for the orthonormal Strichartz\nestimates, which were first studied by Frank-Lewin-Lieb-Seiringer. The method\nused in the proof is based on the duality principle and the smooth perturbation\ntheory by Kato. We also deduce the refined Strichartz estimates for the\nSchr\\""odinger operator in terms of the Besov space. Finally we prove the global\nexistence of a solution for the Hartree equation with electromagnetic\npotentials describing the dynamics of infinitely many fermions. This would be\nthe first result on the orthonormal Strichartz estimates for the Schr\\""odinger\noperator with general time-independent potentials including very short range\nand inverse square type potentials.\n', 'Uniform resolvent and orthonormal Strichartz estimates for repulsive\n  Hamiltonian   We consider the uniform resolvent and orthonormal Strichartz estimates for\nthe Schr\\""odinger operator. First we prove the Keel-Tao type theorem for the\northonormal Strichartz estimates, which means that the dispersive estimates\nyield the orthonormal Strichartz estimates for strongly continuous unitary\ngroups. This result applies to many Schr\\""odinger propagators which are\ndifficult to treat by the smooth perturbation theory, for example,\nlocal-in-time estimates for the Schr\\""odinger operator with unbounded\nelectromagnetic potentials, the $(k, a)$-generalized Laguerre operators and\nglobal-in-time estimates for the Schr\\""odinger operator with scaling critical\nmagnetic potentials including the Aharonov-Bohm potentials. Next we observe\nmapping properties of resolvents for the repulsive Hamiltonian and apply to the\northonormal Strichartz estimates. We prove the Kato-Yajima type uniform\nresolvent estimates with logarithmic decaying weight functions. This is new\neven when without perturbations. The proof is dependent on the microlocal\nanalysis and the Mourre theory. We also discuss mapping properties on the\nSchwartz class and the Lebesgue space.\n']","[('strichartz type estimates', 0.6809118986129761), ('strichartz estimates', 0.6539252996444702), ('schr odinger equations', 0.6419706344604492), ('strichartz estimate', 0.6305539011955261), ('estimate schr odinger', 0.624035656452179), ('schr odinger operators', 0.6230199337005615), ('estimates schr odinger', 0.6132360100746155), ('schr odinger operator', 0.608494222164154), ('sobolev estimates', 0.5763112902641296), ('odinger operators', 0.5646747350692749)]"
299,299,99,299_permutation polynomials_permutation polynomial_polynomials finite fields_functions finite fields,"['permutation polynomials', 'permutation polynomial', 'polynomials finite fields', 'functions finite fields', 'permutes', 'dickson polynomials', 'finite field odd', 'finite fields even', 'finite fields', 'irreducible polynomials']","['The compositional inverses of three classes of permutation polynomials\n  over finite fields   Recently, P. Yuan presented a local method to find permutation polynomials\nand their compositional inverses over finite fields. The work of P. Yuan\ninspires us to compute the compositional inverses of three classes of the\npermutation polynomials: (a) the permutation polynomials of the form\n$ax^q+bx+(x^q-x)^k$ over $\\mathbb{F}_{q^2},$ where $a+b \\in \\mathbb{F}_q^*$ or\n$a^q=b;$ (b) the permutation polynomials of the forms\n$f(x)=-x+x^{(q^2+1)/2}+x^{(q^3+q)/2} $ and $f(x)+x$ over $\\mathbb{F}_{q^3};$\n(c) the permutation polynomial of the form $A^{m}(x)+L(x)$ over\n$\\mathbb{F}_{q^n},$ where ${\\rm Im}(A(x))$ is a vector space with dimension $1$\nover $\\mathbb{F}_{q}$ and $L(x)$ is not a linearized permutation polynomial.\n', 'Permutation Polynomials of $\\mathbb{F}_{q^2}$ : A Linear Algebraic\n  Approach   In this paper, we present a linear algebraic approach to the study of\npermutation polynomials that arise from linear maps over a finite field\n$\\mathbb{F}_{q^2}$. We study a particular class of permutation polynomials over\n$\\mathbb{F}_{q^2}$, in the context of rank deficient and full rank linear maps\nover $\\mathbb{F}_{q^2}$. We derive necessary and sufficient conditions under\nwhich the given class of polynomials are permutation polynomials. We further\nshow that the number of such permutation polynomials can be easily enumerated.\nOnly a subset of these permutation polynomials have been reported in literature\nearlier. It turns out that this class of permutation polynomials have\ncompositional inverses of the same kind and we provide algorithms to evaluate\nthe compositional inverses of most of these permutation polynomials.\n', ""New classes of permutation polynomials with coefficients 1 over finite\n  fields   Permutation polynomials with coefficients 1 over finite fields attract\nresearchers' interests due to their simple algebraic form. In this paper, we\nfirst construct four classes of fractional permutation polynomials over the\ncyclic subgroup of $ \\mathbb{F}_{2^{2m}} $. From these permutation polynomials,\nthree new classes of permutation polynomials with coefficients 1 over $\n\\mathbb{F}_{2^{2m}} $ are constructed, and three more general new classes of\npermutation polynomials with coefficients 1 over $ \\mathbb{F}_{2^{2m}} $ are\nconstructed using a new method we presented recently. Some known permutation\npolynomials are the special cases of our new permutation polynomials.\nFurthermore, we prove that, in all new permutation polynomials, there exists a\npermutation polynomial which is EA-inequivalent to known permutation\npolynomials for all even positive integer $ m $. This proof shows that\nEA-inequivalent permutation polynomials over $ \\mathbb{F}_{q} $ can be\nconstructed from EA-equivalent permutation polynomials over the cyclic subgroup\nof $ \\mathbb{F}_{q} $. From this proof, it is obvious that, in all new\npermutation polynomials, there exists a permutation polynomial of which\nalgebraic degree is the maximum algebraic degree of permutation polynomials\nover $ \\mathbb{F}_{2^{2m}} $.\n""]","[('permutation polynomials', 0.7118240594863892), ('permutation polynomial', 0.6588146090507507), ('polynomials finite fields', 0.5783352255821228), ('functions finite fields', 0.49525555968284607), ('permutes', 0.49188750982284546), ('dickson polynomials', 0.4795876145362854), ('finite field odd', 0.4655281901359558), ('finite fields even', 0.46514827013015747), ('finite fields', 0.46247124671936035), ('irreducible polynomials', 0.453781396150589)]"
300,300,98,300_ergodic averages_ergodic theorems_ergodic theory_ergodic measure,"['ergodic averages', 'ergodic theorems', 'ergodic theory', 'ergodic measure', 'pointwise ergodic', 'convergence ergodic', 'ergodic measure preserving', 'ergodicity', 'ergodic', 'ergodic systems']","['Seminorm control for ergodic averages with commuting transformations and\n  pairwise dependent polynomial iterates   We examine multiple ergodic averages of commuting transformations with\npolynomial iterates in which the polynomials may be pairwise dependent. In\nparticular, we show that such averages are controlled by the Gowers-Host-Kra\nseminorms whenever the system satisfies some mild ergodicity assumptions.\nCombining this result with the general criteria for joint ergodicity\nestablished in our earlier work, we determine a necessary and sufficient\ncondition under which such averages are jointly ergodic, in the sense that they\nconverge in the mean to the product of integrals, or weakly jointly ergodic, in\nthat they converge to the product of conditional expectations. As a corollary,\nwe deduce a special case of a conjecture by Donoso, Koutsogiannis, and Sun in a\nstronger form.\n', ""Multiple ergodic averages along functions from a Hardy field:\n  convergence, recurrence and combinatorial applications   We obtain new results pertaining to convergence and recurrence of multiple\nergodic averages along functions from a Hardy field. Among other things, we\nconfirm some of the conjectures posed by Frantzikinakis in [Fra10; Fra16] and\nobtain combinatorial applications which contain, as rather special cases,\nseveral previously known (polynomial and non-polynomial) extensions of\nSzemeredi's theorem on arithmetic progressions [BL96; BLL08; FW09; Fra10;\nBMR17]. One of the novel features of our results, which is not present in\nprevious work, is that they allow for a mixture of polynomials and\nnon-polynomial functions. As an illustration, assume\n$f_i(t)=a_{i,1}t^{c_{i,1}}+\\cdots+a_{i,d}t^{c_{i,d}}$ for $c_{i,j}>0$ and\n$a_{i,j}\\in\\mathbb{R}$. Then\n  $\\bullet$ for any measure preserving system $(X,{\\mathcal B},\\mu,T)$ and\n$h_1,\\dots,h_k\\in L^\\infty(X)$, the limit\n$$\\lim_{N\\to\\infty}\\frac{1}{N}\\sum_{n=1}^N T^{[f_1(n)]}h_1\\cdots\nT^{[f_k(n)]}h_k$$ exists in $L^2$;\n  $\\bullet$ for any $E\\subset \\mathbb{N}$ with $\\overline{\\mathrm{d}}(E)>0$\nthere are $a,n\\in\\mathbb{N}$ such that $\\{a,\\,\na+[f_1(n)],\\ldots,a+[f_k(n)]\\}\\subset E$.\n  We also show that if $f_1,\\dots,f_k$ belong to a Hardy field, have polynomial\ngrowth, and are such that no linear combination of them is a polynomial, then\nfor any measure preserving system $(X,{\\mathcal B},\\mu,T)$ and any\n$A\\in{\\mathcal B}$, $$\\limsup_{N\\to\\infty}\\frac{1}{N}\\sum_{n=1}^N\\mu\\Big(A\\cap\nT^{-[ f_1(n) ]}A\\cap\\ldots\\cap T^{-[f_k(n)]}A\\Big)\\,\\geq\\,\\mu(A)^{k+1}.$$\n"", 'Pointwise convergence of ergodic averages with M\\""obius weight   Let $(X,\\nu,T)$ be a measure-preserving system, and let $P_1,\\ldots, P_k$ be\npolynomials with integer coefficients. We prove that, for any $f_1,\\ldots,\nf_k\\in L^{\\infty}(X)$, the M\\""obius-weighted polynomial multiple ergodic\naverages \\begin{align*}\\frac{1}{N}\\sum_{n\\leq N}\\mu(n)f_1(T^{P_1(n)}x)\\cdots\nf_k(T^{P_k(n)}x) \\end{align*} converge to $0$ pointwise almost everywhere.\nSpecialising to $P_1(y)=y, P_2(y)=2y$, this solves a problem of Frantzikinakis.\nWe also prove pointwise convergence for a more general class of multiplicative\nweights for multiple ergodic averages involving distinct degree polynomials.\nFor the proofs we establish some quantitative generalised von Neumann theorems\nfor polynomial configurations that are of independent interest.\n']","[('ergodic averages', 0.6918820142745972), ('ergodic theorems', 0.6551902890205383), ('ergodic theory', 0.6304371356964111), ('ergodic measure', 0.61395663022995), ('pointwise ergodic', 0.6079837679862976), ('convergence ergodic', 0.5968882441520691), ('ergodic measure preserving', 0.5720388293266296), ('ergodicity', 0.552375316619873), ('ergodic', 0.5447224378585815), ('ergodic systems', 0.5103983283042908)]"
301,301,98,301_generative diffusion models_score based diffusion_diffusion based generative_diffusion generative,"['generative diffusion models', 'score based diffusion', 'diffusion based generative', 'diffusion generative', 'generative diffusion', 'denoising diffusion probabilistic', 'diffusion probabilistic models', 'diffusion probabilistic', 'score based generative', 'generative models']","['Sampling is as easy as learning the score: theory for diffusion models\n  with minimal data assumptions   We provide theoretical convergence guarantees for score-based generative\nmodels (SGMs) such as denoising diffusion probabilistic models (DDPMs), which\nconstitute the backbone of large-scale real-world generative models such as\nDALL$\\cdot$E 2. Our main result is that, assuming accurate score estimates,\nsuch SGMs can efficiently sample from essentially any realistic data\ndistribution. In contrast to prior works, our results (1) hold for an\n$L^2$-accurate score estimate (rather than $L^\\infty$-accurate); (2) do not\nrequire restrictive functional inequality conditions that preclude substantial\nnon-log-concavity; (3) scale polynomially in all relevant problem parameters;\nand (4) match state-of-the-art complexity guarantees for discretization of the\nLangevin diffusion, provided that the score error is sufficiently small. We\nview this as strong theoretical justification for the empirical success of\nSGMs. We also examine SGMs based on the critically damped Langevin diffusion\n(CLD). Contrary to conventional wisdom, we provide evidence that the use of the\nCLD does not reduce the complexity of SGMs.\n', 'Analyzing Neural Network-Based Generative Diffusion Models through\n  Convex Optimization   Diffusion models are gaining widespread use in cutting-edge image, video, and\naudio generation. Score-based diffusion models stand out among these methods,\nnecessitating the estimation of score function of the input data distribution.\nIn this study, we present a theoretical framework to analyze two-layer neural\nnetwork-based diffusion models by reframing score matching and denoising score\nmatching as convex optimization. We prove that training shallow neural networks\nfor score prediction can be done by solving a single convex program. Although\nmost analyses of diffusion models operate in the asymptotic setting or rely on\napproximations, we characterize the exact predicted score function and\nestablish convergence results for neural network-based diffusion models with\nfinite data. Our results provide a precise characterization of what neural\nnetwork-based diffusion models learn in non-asymptotic settings.\n', 'Score-based Generative Modeling Secretly Minimizes the Wasserstein\n  Distance   Score-based generative models are shown to achieve remarkable empirical\nperformances in various applications such as image generation and audio\nsynthesis. However, a theoretical understanding of score-based diffusion models\nis still incomplete. Recently, Song et al. showed that the training objective\nof score-based generative models is equivalent to minimizing the\nKullback-Leibler divergence of the generated distribution from the data\ndistribution. In this work, we show that score-based models also minimize the\nWasserstein distance between them under suitable assumptions on the model.\nSpecifically, we prove that the Wasserstein distance is upper bounded by the\nsquare root of the objective function up to multiplicative constants and a\nfixed constant offset. Our proof is based on a novel application of the theory\nof optimal transport, which can be of independent interest to the society. Our\nnumerical experiments support our findings. By analyzing our upper bounds, we\nprovide a few techniques to obtain tighter upper bounds.\n']","[('generative diffusion models', 0.6171424984931946), ('score based diffusion', 0.6072118282318115), ('diffusion based generative', 0.5847808718681335), ('diffusion generative', 0.5750082731246948), ('generative diffusion', 0.5612032413482666), ('denoising diffusion probabilistic', 0.5228789448738098), ('diffusion probabilistic models', 0.519690752029419), ('diffusion probabilistic', 0.4994124472141266), ('score based generative', 0.4944779574871063), ('generative models', 0.4739978611469269)]"
302,302,98,302_quantum walks graphs_vertices quantum_quantum walks_unitary cayley graphs,"['quantum walks graphs', 'vertices quantum', 'quantum walks', 'unitary cayley graphs', 'quantum state transfer', 'quantum walk', 'perfect state transfer', 'transfer quantum', 'walks graphs', 'time quantum walks']","[""State transfer in discrete-time quantum walks via projected transition\n  matrices   In this paper, we analyze state transfer in quantum walks by using\ncombinatorial methods. We generalize perfect state transfer in two-reflection\ndiscrete-time quantum walks to a notion that we call 'peak state transfer'; we\ndefine peak state transfer as the highest state transfer that can be achieved\nbetween an initial and a target state under unitary evolution, even when\nperfect state transfer is unattainable. We give a spectral characterization of\npeak state transfer that allows us to fully characterize peak state transfer in\nthe arc-reversal (Grover) walk on various families of graphs, including\nstrongly regular graphs and incidence graphs of block designs (assuming that\nthe walk starts at a point of the design). In addition, we provide many\nexamples of peak state transfer, including an infinite family where the amount\nof peak state transfer tends to $1$ as the number of vertices grows. We further\ndemonstrate that peak state transfer properties extend to infinite families of\ngraphs generated by vertex blow-ups, and we characterize periodicity in the\nvertex-face walk on toroidal grids. In our analysis, we make extensive use of\nthe spectral decomposition of a matrix that is obtained by projecting the\ntransition matrix down onto a subspace. Though we are motivated by a problem in\nquantum computing, we identify several open problems that are purely\ncombinatorial, arising from the spectral conditions required for peak state\ntransfer in discrete-time quantum walks.\n"", ""State Transfer in Complex Quantum Walks   Given a graph with Hermitian adjacency matrix $H$, perfect state transfer\noccurs from vertex $a$ to vertex $b$ if the $(b,a)$-entry of the unitary matrix\n$\\exp(-iHt)$ has unit magnitude for some time $t$. This phenomenon is relevant\nfor information transmission in quantum spin networks and is known to be\nmonogamous under real symmetric matrices. We prove the following results:\n  1. For oriented graphs (whose nonzero weights are $\\pm i$), the oriented\n$3$-cycle and the oriented edge are the only graphs where perfect state\ntransfer occurs between every pair of vertices. This settles a conjecture of\nCameron et al. On the other hand, we construct an infinite family of oriented\ngraphs with perfect state transfer between any pair of vertices on a subset of\nsize four.\n  2. There are infinite families of Hermitian graphs with one-way perfect state\ntransfer, where perfect state transfer occurs without periodicity. In contrast,\nperfect state transfer implies periodicity whenever the adjacency matrix has\nalgebraic entries (as shown by Godsil).\n  3. There are infinite families with non-monogamous pretty good state transfer\nin rooted graph products. In particular, we generalize known results on double\nstars (due to Fan and Godsil) and on paths with loops (due to Kempton, Lippner\nand Yau). The latter extends the experimental observation of quantum transport\n(made by Zimbor\\'{a}s et al.) and shows non-monogamous pretty good state\ntransfer can occur amongst distant vertices.\n"", 'Fractional revival on non-cospectral vertices   Perfect state transfer and fractional revival can be used to move information\nbetween pairs of vertices in a quantum network. While perfect state transfer\nhas received a lot of attention, fractional revival is newer and less studied.\nOne problem is to determine the differences between perfect state transfer and\nfractional revival. If perfect state transfer occurs between two vertices in a\ngraph, the vertices must be cospectral. Further if there is perfect state\ntransfer between vertices $a$ and $b$ in a graph, there cannot be perfect state\ntransfer from $a$ to any other vertex. No examples of unweighted graphs with\nfractional revival between non-cospectral vertices were known; here we give an\ninfinite family of such graphs. No examples of unweighted graphs where the\npairs involved in fractional revival overlapped were known; we give examples of\nsuch graphs as well.\n']","[('quantum walks graphs', 0.6863824129104614), ('vertices quantum', 0.5901586413383484), ('quantum walks', 0.5730440616607666), ('unitary cayley graphs', 0.5433191061019897), ('quantum state transfer', 0.5362439751625061), ('quantum walk', 0.529325008392334), ('perfect state transfer', 0.5271399617195129), ('transfer quantum', 0.5135959386825562), ('walks graphs', 0.5093940496444702), ('time quantum walks', 0.4943068027496338)]"
303,303,98,303_scheduling_hospital_capacity planning_hospitals,"['scheduling', 'hospital', 'capacity planning', 'hospitals', 'mixed integer programming', 'integer programming', 'appointment', 'queueing', 'routing scheduling', 'schedules']","['Optimal Hospital Capacity Management During Demand Surges   Effective hospital capacity management is pivotal for enhancing patient care\nquality, operational efficiency, and healthcare system resilience, notably\nduring demand spikes like those seen in the COVID-19 pandemic. However,\ndevising optimal capacity strategies is complicated by fluctuating demand,\nconflicting objectives, and multifaceted practical constraints. This study\npresents a data-driven framework to optimize capacity management decisions\nwithin hospital systems during surge events. Two key decisions are optimized\nover a tactical planning horizon: allocating dedicated capacity to surge\npatients and transferring incoming patients between emergency departments (EDs)\nof hospitals to better distribute demand. The optimization models are\nformulated as robust mixed-integer linear programs, enabling efficient\ncomputation of optimal decisions that are robust against demand uncertainty.\nThe models incorporate practical constraints and costs, including setup times\nand costs for adding surge capacity, restrictions on ED patient transfers, and\nrelative costs of different decisions that reflect impacts on care quality and\noperational efficiency. The methodology is evaluated retrospectively in a\nhospital system during the height of the COVID-19 pandemic to demonstrate the\npotential impact of the recommended decisions. The results show that optimally\nallocating beds and transferring just 32 patients over a 63 day period around\nthe peak, about one transfer every two days, could have reduced the need for\nsurge capacity in the hospital system by nearly 90%. Overall, this work\nintroduces a practical tool to transform capacity management decision-making,\nenabling proactive planning and the use of data-driven recommendations to\nimprove outcomes.\n', 'Integrated patient-to-room and nurse-to-patient assignment in hospital\n  wards   Assigning patients to rooms and nurses to patients are critical tasks within\nhospitals that directly affect patient and staff satisfaction, quality of care,\nand hospital efficiency. Both patient-to-room assignments and nurse-to-patient\nassignments are typically agreed upon at the ward level, and they interact in\nseveral ways such as jointly determining the walking distances nurses must\ncover between different patient rooms. This motivates to consider both problems\njointly in an integrated fashion.\n  This paper presents the first optimization models and algorithms for the\nintegrated patient-to-room and nurse-to-patient assignment problem. We provide\na mixed integer programming formulation of the integrated problem that\nconsiders the typical objectives from the single problems as well as additional\nobjectives that can only be properly evaluated when integrating both problems.\nMoreover, motivated by the inherent complexity that results from integrating\nthese two NP-hard and already computationally challenging problems, we devise\nan efficient heuristic for the integrated patient-to-room and nurse-to-patient\nassignment problem. To evaluate the running time and quality of the solution\nobtained with the heuristic, we conduct extensive computational experiments on\nboth artificial and real-world instances. The artificial instances are\ngenerated by a parameterized instance generator for the integrated problem that\nis made freely available.\n', ""Data-Driven Inpatient Bed Assignment Using the P Model   Problem definition: Emergency department (ED) boarding refers to the practice\nof holding patients in the ED after they have been admitted to hospital wards,\nusually resulting from insufficient inpatient resources. Boarded patients may\ncompete with new patients for medical resources in the ED, compromising the\nquality of emergency care. A common expedient for mitigating boarding is\npatient overflowing, i.e., sending patients to beds in other specialties or\naccommodation classes, which may compromise the quality of inpatient care and\nbring on operational challenges. We study inpatient bed assignment to shorten\nboarding times without excessive patient overflowing.\n  Methodology: We use a queue with multiple customer classes and multiple\nserver pools to model hospital wards. Exploiting patient flow data from a\nhospital, we propose a computationally tractable approach to formulating the\nbed assignment problem, where the joint probability of all waiting patients\nmeeting their respective delay targets is maximized.\n  Results: By dynamically adjusting the overflow rate, the proposed approach is\ncapable not only of reducing patients' waiting times, but also of mitigating\nthe time-of-day effect on boarding times. In numerical experiments, our\napproach greatly outperforms both early discharge policies and threshold-based\noverflowing policies, which are commonly used in practice.\n  Managerial implications: We provide a practicable approach to solving the bed\nassignment problem. This data-driven approach captures critical features of\npatient flow management, while the resulting optimization problem is\npractically solvable. The proposed approach is a useful tool for the control of\nqueueing systems with time-sensitive service requirements.\n""]","[('scheduling', 0.466738224029541), ('hospital', 0.4311049282550812), ('capacity planning', 0.43044987320899963), ('hospitals', 0.41544780135154724), ('mixed integer programming', 0.39312225580215454), ('integer programming', 0.3897287845611572), ('appointment', 0.38649460673332214), ('queueing', 0.36756908893585205), ('routing scheduling', 0.35588592290878296), ('schedules', 0.3309378921985626)]"
304,304,96,304_fibonacci polynomials_generalized fibonacci_fibonacci numbers_fibonacci lucas,"['fibonacci polynomials', 'generalized fibonacci', 'fibonacci numbers', 'fibonacci lucas', 'fibonacci type', 'fibonacci number', 'lucas sequences', 'fibonacci', 'lucas numbers', 'chebyshev polynomials']","['Irreducibility of generalized Fibonacci polynomials   A second order polynomial sequence is of Fibonacci-type $\\mathcal{F}_{n}$\n(Lucas-type $\\mathcal{L}_{n}$) if its Binet formula has a structure similar to\nthat for Fibonacci (Lucas) numbers. Under certain conditions these polynomials\nare irreducible if and only if $n$ is a prime number. For example, the\nFibonacci polynomials, Pell polynomials, Fermat polynomials, Lucas polynomials,\nPell-Lucas polynomials, Fermat-Lucas polynomials are irreducible when $n$ is a\nprime number; and Chebyshev polynomials (second kind), Morgan-Voyce polynomials\n(Fibonacci type), and Vieta polynomials are reducible when $n$ is a prime\nnumber.\n  In this paper we give some theorems to determine whether the Fibonacci type\npolynomials and Lucas type polynomials are irreducible when $n$ is prime.\n', 'New binomial Fibonacci sums   We present some new linear, quadratic, cubic and quartic binomial Fibonacci,\nLucas and Fibonacci--Lucas summation identities.\n', 'Identities and Generating Functions of Products of Generalized Fibonacci\n  numbers, Catalan and Harmonic Numbers   We considered the properties of generalized Fibonacci and Lucas numbers\nclass. The analogues of well-known Fibonacci identities for generalized numbers\nare obtained. We gained a new identity of product convolution of generalized\nFibonacci and Lucas numbers. We wrote down generating functions of generalized\nFibonacci and Lucas numbers products, their multisections, harmonic numbers and\nCatalan numbers.\n']","[('fibonacci polynomials', 0.7284879684448242), ('generalized fibonacci', 0.6838634610176086), ('fibonacci numbers', 0.6587858200073242), ('fibonacci lucas', 0.6554457545280457), ('fibonacci type', 0.6426297426223755), ('fibonacci number', 0.6069853901863098), ('lucas sequences', 0.599733829498291), ('fibonacci', 0.5867537260055542), ('lucas numbers', 0.5669703483581543), ('chebyshev polynomials', 0.48506060242652893)]"
305,305,96,305_free sequences_sequences length_sequences maximal_mathbb z_n,"['free sequences', 'sequences length', 'sequences maximal', 'mathbb z_n', 'sequence elements', 'weighted zero', 'zero sum', 'a_1 ldots a_n', 'subsequence length', 'sequence length']","['Zero-sum constants related to the Jacobi symbol   For $A\\subseteq\\mathbb Z_n$, the $A$-weighted Gao constant $E_A(n)$ is\ndefined to be the smallest natural number $k$ such that any sequence of $k$\nelements in $\\mathbb Z_n$ has a subsequence of length $n$ whose $A$-weighted\nsum is zero. When $A$ is the set of all units in $\\mathbb Z_n$, we determine\nthe value of $E_A(n)$ and values of two related constants $C_A(n)$ and\n$D_A(n)$. We also characterize all sequences of length $E_A(n)-1$ in $\\mathbb\nZ_n$ which do not have any $A$-weighted zero-sum subsequence of length $n$ when\n$n$ is a power of 2.\n', 'Square-weighted zero-sum constants   Let $A\\subseteq \\mathbb Z_n$ be a subset. A sequence $S=(x_1,\\ldots,x_k)$ in\n$\\mathbb Z_n$ is said to be an $A$-weighted zero-sum sequence if there exist\n$a_1,\\ldots,a_k\\in A$ such that $a_1x_1+\\cdots+a_kx_k=0$. By a square, we shall\nmean a non-zero square in $\\mathbb Z_n$. We determine the smallest natural\nnumber $k$, such that every sequence in $\\mathbb Z_n$ whose length is $k$, has\na square-weighted zero-sum subsequence. We also determine the smallest natural\nnumber $k$, such that every sequence in $\\mathbb Z_n$ whose length is $k$, has\na square-weighted zero-sum subsequence whose terms are consecutive terms of the\ngiven sequence.\n', 'Smooth weighted zero-sum constants   Let $A\\subseteq\\mathbb Z_n$ be a weight-set and $S=(x_1,x_2,\\ldots, x_k)$ be\na sequence in $\\mathbb Z_n$. We say that $S$ is a smooth $A$-weighted zero-sum\nsequence if there exists $(a_1,\\ldots,a_k)\\in A^k$ such that we have\n$a_1x_1+\\cdots+a_kx_k=0$ and $a_1+\\cdots+a_k=0$. It is easy to see that if $S$\nis a smooth $A$-weighted zero-sum sequence, then for every $y\\in \\mathbb Z_n$\nthe sequence $S+y=(x_1+y,\\ldots,x_k+y)$ is also a smooth $A$-weighted zero-sum\nsequence. From the well known EGZ-theorem it follows that if $S$ has length at\nleast $2n-1$, then $S$ has a smooth $A$-weighted zero-sum subsequence of length\n$n$. The constant $\\bar E_A$ is defined to be the smallest positive integer $k$\nsuch that any sequence of length $k$ in $\\mathbb Z_n$ has a smooth $A$-weighted\nzero-sum subsequence of length $n$. A sequence in $\\mathbb Z_n$ of length $\\bar\nE_A-1$ which does not have any smooth $A$-weighted zero-sum subsequence of\nlength $n$ is called an $\\bar E$-extremal sequence for $A$. For every $n$ we\nconsider the weight-sets $\\{1\\}$ and $\\mathbb Z_n\\setminus\\{0\\}$. When $n$ is\nan odd prime $p$ we consider the weight-set $Q_p$ of all non-zero quadratic\nresidues. We also study the related constants $\\bar C_A$ and $\\bar D_A$.\n']","[('free sequences', 0.41678935289382935), ('sequences length', 0.39781123399734497), ('sequences maximal', 0.3959481716156006), ('mathbb z_n', 0.38152530789375305), ('sequence elements', 0.3752725422382355), ('weighted zero', 0.3751172125339508), ('zero sum', 0.3673713803291321), ('a_1 ldots a_n', 0.3669999837875366), ('subsequence length', 0.36319249868392944), ('sequence length', 0.3525412380695343)]"
306,306,96,306_gorenstein projective modules_gorenstein algebras_gorenstein algebra_modules gorenstein,"['gorenstein projective modules', 'gorenstein algebras', 'gorenstein algebra', 'modules gorenstein', 'gorenstein projective', 'gorenstein projective dimension', 'higher auslander algebras', 'auslander algebras', 'projective modules', 'nakayama algebras']","['From Gorenstein derived equivalences to stable functors of Gorenstein\n  projective modules   In the paper, we mainly connect the Gorenstein derived equivalence and stable\nfunctors of Gorenstein projective modules. Specially, we prove that a\nGorenstein derived equivalence between CM-finite algebras A and B can induce a\nstable functor between the factor categories A-mod/A-Gproj and B-mod\\B-Gproj.\nFurthermore, the above stable functor is an equivalence when A and B are\nGorenstein.\n', 'Monic modules and semi-Gorenstein-projective modules   The category ${\\rm gp}(\\Lambda)$ of Gorenstein-projective modules over tensor\nalgebra $\\Lambda = A\\otimes_kB$ can be described as the monomorphism category\n${\\rm mon}(B, {\\rm gp}(A))$ of $B$ over ${\\rm gp}(A)$. In particular,\nGorenstein-projective $\\Lambda$-modules are monic. In this paper, we find the\nsimilar relation between semi-Gorenstein-projective $\\Lambda$-modules and\n$A$-modules, via monic modules, namely, ${\\rm mon}(B, \\ ^\\perp A) = {\\rm\nmon}(B, A)\\cap \\ ^\\perp \\Lambda.$ Using this, it is proved that if $A$ is\nweakly Gorenstein, then $\\Lambda$ is weakly Gorenstein if and only each\nsemi-Gorenstein-projective $\\Lambda$-modules are monic; and that if $B = kQ$\nwith $Q$ a finite acyclic quiver, then $\\Lambda$ is weakly Gorenstein if and\nonly if $A$ is weakly Gorenstein. However, this relation itself does not answer\nthe question whether there exist double semi-Gorenstein-projective\n$\\Lambda$-modules which are not monic. Using the recent discovered examples of\ndouble semi-Gorenstein-projective $A$-modules which are not torsionless, we\npositively answer this question, by explicitly constructing a class of double\nsemi-Gorenstein-projective $T_2(A)$-modules with one parameter such that they\nare not monic, and hence not torsionless. The corresponding results are\nobtained also for the monic modules and semi-Gorenstein-projective modules over\nthe triangular matrix algebras given by bimodules.\n', 'Invariants and Gorenstein projective modules   Invariants with respect to recollements of the stable category of Gorenstein\nprojective A-modules over an algebra A and stable equivalences are\ninvestigated. Specifically, the Gorenstein rigidity dimension is introduced. It\nis shown that the Gorenstein rigidity dimension is invariant with respect to\nboth Morita equivalences and the stable equivalences of Gorenstein projective\nmodules. As a consequence, the Gorenstein rigidity dimension is shown the\ninvariant of derived equivalences. The Gorenstein rigidity dimension is\ncompared along the recollements of the stable category of Gorenstein projective\nmodules. Moreover, the bounds of Gorenstein rigidity dimension is given for\nseveral classes of algebras, respectively.\n']","[('gorenstein projective modules', 0.7890381217002869), ('gorenstein algebras', 0.7784405946731567), ('gorenstein algebra', 0.7400009632110596), ('modules gorenstein', 0.7106363773345947), ('gorenstein projective', 0.6988552212715149), ('gorenstein projective dimension', 0.696379542350769), ('higher auslander algebras', 0.6040723323822021), ('auslander algebras', 0.5966385006904602), ('projective modules', 0.5523259043693542), ('nakayama algebras', 0.5340820550918579)]"
307,307,96,307_quantum communication_entanglement assisted_communication quantum_entanglement assistance,"['quantum communication', 'entanglement assisted', 'communication quantum', 'entanglement assistance', 'quantum channel', 'quantum channels', 'shared entanglement', 'entanglement', 'quantum entanglement', 'entanglement can']","[""Permutation Enhances Classical Communication Assisted by Entangled\n  States   We give a capacity formula for the classical communication over a noisy\nquantum channel, when local operations and global permutations allowed in the\nencoding and bipartite states preshared between the sender and the receiver.\nThe two endpoints of this formula are the Holevo capacity (without entanglement\nassistance) and the entanglement-assisted capacity (with unlimited entanglement\nassistance). What's more, we show that the capacity satisfies the strong\nconverse property and thus the formula serves as a sharp dividing line between\nachievable and unachievable rates of communication. We prove that the\ndifference between the assisted capacity and the Holevo capacity is upper\nbounded by the discord of formation of the preshared state. As examples, we\nderive analytically the classical capacity of various quantum channels of\ninterests. Our result witnesses the power of random permutation in classical\ncommunication, whenever entanglement assistance is available.\n"", 'Entanglement-assisted capacity regions and protocol designs for quantum\n  multiple-access channels   We solve the entanglement-assisted (EA) classical capacity region of quantum\nmultiple-access channels with an arbitrary number of senders. As an example, we\nconsider the bosonic thermal-loss multiple-access channel and solve the\none-shot capacity region enabled by an entanglement source composed of\nsender-receiver pairwise two-mode squeezed vacuum states. The EA capacity\nregion is strictly larger than the capacity region without\nentanglement-assistance. With two-mode squeezed vacuum states as the source and\nphase modulation as the encoding, we also design practical receiver protocols\nto realize the entanglement advantages. Four practical receiver designs, based\non optical parametric amplifiers, are given and analyzed. In the parameter\nregion of a large noise background, the receivers can enable a simultaneous\nrate advantage of 82.0% for each sender. Due to teleportation and superdense\ncoding, our results for EA classical communication can be directly extended to\nEA quantum communication at half of the rates. Our work provides a unique and\npractical network communication scenario where entanglement can be beneficial.\n', 'Communication with Unreliable Entanglement Assistance   Entanglement resources can increase transmission rates substantially.\nUnfortunately, entanglement is a fragile resource that is quickly degraded by\ndecoherence effects. In order to generate entanglement for optical\ncommunication, the transmitter and the receiver first prepare entangled\nspin-photon pairs locally, and then the photon at the transmitter is sent to\nthe receiver through an optical fiber or free space. Without feedback, the\ntransmitter does not know whether the entangled photon has reached the\nreceiver. The present work introduces a new model of unreliable entanglement\nassistance, whereby the communication system operates whether entanglement\nassistance is present or not. While the sender is ignorant, the receiver knows\nwhether the entanglement generation was successful. In the case of a failure,\nthe receiver decodes less information. In this manner, the effective\ntransmission rate is adapted according to the assistance status. Regularized\nformulas are derived for the classical and quantum capacity regions with\nunreliable entanglement assistance, characterizing the tradeoff between the\nunassisted rate and the excess rate that can be obtained from entanglement\nassistance. It is further established that time division between\nentanglement-assisted and unassisted coding strategies is optimal for the\nnoiseless qubit channel, but can be strictly suboptimal for a noisy channel.\n']","[('quantum communication', 0.6435990929603577), ('entanglement assisted', 0.6413981318473816), ('communication quantum', 0.6365482211112976), ('entanglement assistance', 0.6326714158058167), ('quantum channel', 0.6262831091880798), ('quantum channels', 0.623734176158905), ('shared entanglement', 0.6053441762924194), ('entanglement', 0.5988942384719849), ('quantum entanglement', 0.5929568409919739), ('entanglement can', 0.5852760672569275)]"
308,308,96,308_fractional derivatives_riemann liouville fractional_caputo fractional derivatives_fractional derivative,"['fractional derivatives', 'riemann liouville fractional', 'caputo fractional derivatives', 'fractional derivative', 'fractional differential', 'fractional integrals', 'fractional operators', 'linear fractional differential', 'liouville fractional', 'fractional differential equations']","['Fractional derivatives and the fundamental theorem of Fractional\n  Calculus   In this paper, we address the one-parameter families of the fractional\nintegrals and derivatives defined on a finite interval. First we remind the\nreader of the known fact that under some reasonable conditions, there exists\nprecisely one unique family of the fractional integrals, namely, the well-known\nRiemann-Liouville fractional integrals. As to the fractional derivatives, their\nnatural definition follows from the fundamental theorem of the Fractional\nCalculus, i.e., they are introduced as the left-inverse operators to the\nRiemann-Liouville fractional integrals. Until now, three families of such\nderivatives were suggested in the literature: the Riemann-Liouville fractional\nderivatives, the Caputo fractional derivatives, and the Hilfer fractional\nderivatives. We clarify the interconnections between these derivatives on\ndifferent spaces of functions and provide some of their properties including\nthe formulas for their projectors and the Laplace transforms. However, it turns\nout that there exist infinitely many other families of the fractional\nderivatives that are the left-inverse operators to the Riemann-Liouville\nfractional integrals. In this paper, we focus on an important class of these\nfractional derivatives and discuss some of their properties.\n', 'The 1st Level General Fractional Derivatives and some of their\n  Properties   In this paper, we first provide a short summary of the main properties of the\nso-called general fractional derivatives with the Sonin kernels introduced so\nfar. These are integro-differential operators defined as compositions of the\nfirst order derivative and an integral operator of convolution type. Depending\non succession of these operators, the general fractional derivatives of the\nRiemann-Liouville and of the Caputo types were defined and studied. The main\nobjective of this paper is a construction of the 1st level general fractional\nderivatives that comprise both the general fractional derivative of the\nRiemann-Liouville type and the general fractional derivative of the Caputo\ntype. We also provide some of their properties including the 1st and the 2nd\nfundamental theorems of Fractional Calculus for these derivatives and the\nsuitably defined general fractional integrals.\n', 'Special Functions of Fractional Calculus in Form of Convolution Series\n  and their Applications   In this paper, we first discuss the convolution series that are generated by\nthe Sonine kernels from a class of functions continuous on the real positive\nsemi-axis that have an integrable singularity of power function type at the\npoint zero. These convolution series are closely related to the general\nfractional integrals and derivatives with the Sonine kernels and represent a\nnew class of the special functions of Fractional Calculus. The Mittag-Leffler\nfunctions as solutions to the fractional differential equations with the\nfractional derivatives of both Riemann-Liouville and Caputo types are\nparticular cases of the convolution series generated by the Sonine kernel\n$\\kappa(t) = t^{\\alpha -1}/\\Gamma(\\alpha),\\ 0<\\alpha <1$. The main result of\nthe paper is derivation of analytic solutions to the single- and multi-term\nfractional differential equations with the general fractional derivatives of\nthe Riemann-Liouville type that were not yet considered in the Fractional\nCalculus publications.\n']","[('fractional derivatives', 0.7290586233139038), ('riemann liouville fractional', 0.7158215641975403), ('caputo fractional derivatives', 0.7091243267059326), ('fractional derivative', 0.6943056583404541), ('fractional differential', 0.686689555644989), ('fractional integrals', 0.6744641661643982), ('fractional operators', 0.6554487943649292), ('linear fractional differential', 0.6494179368019104), ('liouville fractional', 0.6335816383361816), ('fractional differential equations', 0.6291098594665527)]"
309,309,96,309_collatz conjecture_collatz_conjecture also known_conjecture presented,"['collatz conjecture', 'collatz', 'conjecture also known', 'conjecture presented', 'conjecture', 'conjecture states', 'mathcal sequence', 'conjecture equivalent', 'sequences', 'conjecture true']","['A Collatz Conjecture Proof   We represent the generalized Collatz function with the recursive ruler\nfunction r(2n) = r(n) + 1 and r(2n + 1) = 1. We generate even-only and odd-only\nCollatz subsequences that contain significantly fewer elements term by term, to\n2 and 1, respectively, than are present in the original 3n + 1 and the\nTerras-modified Collatz sequences. We show that a nonlinear, coupled system of\ndifference equations yields a complete acyclic (except for the trivial cycle)\nCollatz tree in odds not divisible by 3 with root vertex 1. We construct a\ncomplete Collatz tree with the axiom of choice and prove the Collatz\nconjecture.\n', 'Collatz Conjecture: Patterns Within   Collatz Conjecture sequences increase and decrease in seemingly random\nfashion. By identifying and analyzing the forms of numbers, we discover that\nCollatz sequences are governed by very specific, well-defined rules, which we\ncall cascades.\n', 'Proof of the Collatz Conjecture by Collatz Graph   The 3n+1 problem, or Collatz problem, is an extremely simple to state,\nextremely hard to solve, problem. A number of Collatz graphs have been\npresented to visualize the Collatz sequences. The Collatz graph is grown by\nconsidering the bottom-up method with the inverse relation. If n is the Collatz\nfunctional value of m, then n is connected by m. The concept is simple, the\ntree-based graphs indeed provide a path starting from n down to the root, the\nnumber of 1, for a given seed n, and demonstrate the generated Collatz\nsequences eventually converges to 1. However, as a general case, due to the\nirregular structures, no one has yet proved the completeness of the Collatz\ngraphs. By completeness we mean that the Collatz graph contains all positive\nintegers n. This paper proves the Collatz conjecture by constructing a Collatz\ngraph with the regular structure. The developed Collatz graph consists of\nCollatz nodes located various levels of the graph. In the developed graph, each\nnode consists of all positive integers m which have the functional value n. A\nset of simple, yet efficient connection rules is also developed to construct\nthe graph. Results show that the developed Collatz graph generates the Collatz\ntrajectories for all positive integers and the sequences converge to 1. This\nproves the completeness of the developed Collatz graph and Collatz conjecture.\n']","[('collatz conjecture', 0.8326124548912048), ('collatz', 0.5569911003112793), ('conjecture also known', 0.49604108929634094), ('conjecture presented', 0.4850326478481293), ('conjecture', 0.48206865787506104), ('conjecture states', 0.45909860730171204), ('mathcal sequence', 0.44605714082717896), ('conjecture equivalent', 0.444582998752594), ('sequences', 0.4274364113807678), ('conjecture true', 0.41882064938545227)]"
310,310,96,310_cellular automata_linear cellular automata_cellular automata ca_cellular automaton,"['cellular automata', 'linear cellular automata', 'cellular automata ca', 'cellular automaton', 'automata', 'automata ca', 'dimensional cellular', 'construct cellular', 'linear cellular', 'automaton']","['One-dimensional cellular automata with a unique active transition   A one-dimensional cellular automaton $\\tau : A^\\mathbb{Z} \\to A^\\mathbb{Z}$\nis a transformation of the full shift defined via a finite neighborhood $S\n\\subset \\mathbb{Z}$ and a local function $\\mu : A^S \\to A$. We study the family\nof cellular automata whose finite neighborhood $S$ is an interval containing\n$0$, and there exists a pattern $p \\in A^S$ satisfying that $\\mu(z) = z(0)$ if\nand only if $z \\neq p$; this means that these cellular automata have a unique\n\\emph{active transition}. Despite its simplicity, this family presents\ninteresting and subtle problems, as the behavior of the cellular automaton\ncompletely depends on the structure of $p$. We show that every cellular\nautomaton $\\tau$ with a unique active transition $p \\in A^S$ is either\nidempotent or strictly almost equicontinuous, and we completely characterize\neach one of these situations in terms of $p$. In essence, the idempotence of\n$\\tau$ depends on the existence of a certain subpattern of $p$ with a\ntranslational symmetry.\n', 'On Cellular Automata   Cellular automata are a fundamental computational model with applications in\nmathematics, computer science, and physics. In this work, we explore the study\nof cellular automata to cases where the universe is a group, introducing the\nconcept of \\( \\phi \\)-cellular automata. We establish new theoretical results,\nincluding a generalized Uniform Curtis-Hedlund Theorem and linear \\( \\phi\n\\)-cellular automata. Additionally, we define the covering map for \\( \\phi\n\\)-cellular automata and investigate its properties. Specifically, we derive\nresults for quotient covers when the universe of the automaton is a circulant\ngraph. This work contributes to the algebraic and topological understanding of\ncellular automata, paving the way for future exploration of different types of\ncovers and their applications to broader classes of graphs and dynamical\nsystems.\n', 'Further results on generalized cellular automata   Given a finite set $A$ and a group homomorphism $\\phi : H \\to G$, a\n$\\phi$-cellular automaton is a function $\\mathcal{T} : A^G \\to A^H$ that is\ncontinuous with respect to the prodiscrete topologies and $\\phi$-equivariant in\nthe sense that $h \\cdot \\mathcal{T}(x) = \\mathcal{T}( \\phi(h) \\cdot x)$, for\nall $x \\in A^G, h \\in H$, where $\\cdot$ denotes the shift actions of $G$ and\n$H$ on $A^G$ and $A^H$, respectively. When $G=H$ and $\\phi = \\text{id}$, the\ndefinition of $\\text{id}$-cellular automata coincides with the classical\ndefinition of cellular automata. The purpose of this paper is to expand the\ntheory of $\\phi$-cellular automata by focusing on the differences and\nsimilarities with their classical counterparts. After discussing some basic\nresults, we introduce the following definition: a $\\phi$-cellular automaton\n$\\mathcal{T} : A^G \\to A^H$ has the unique homomorphism property (UHP) if\n$\\mathcal{T}$ is not $\\psi$-equivariant for any group homomorphism $\\psi : H\n\\to G$, $\\psi \\neq \\phi$. We show that if the difference set $\\Delta(\\phi,\n\\psi)$ is infinite, then $\\mathcal{T}$ is not $\\psi$-equivariant; it follows\nthat when $G$ is torsion-free abelian, every non-constant $\\mathcal{T}$ has the\nUHP. Furthermore, inspired by the theory of classical cellular automata, we\nstudy $\\phi$-cellular automata over quotient groups, as well as their\nrestriction and induction to subgroups and supergroups, respectively.\n']","[('cellular automata', 0.7478221654891968), ('linear cellular automata', 0.7425626516342163), ('cellular automata ca', 0.6909613013267517), ('cellular automaton', 0.6475185751914978), ('automata', 0.6195375919342041), ('automata ca', 0.5389252305030823), ('dimensional cellular', 0.4406640827655792), ('construct cellular', 0.44046923518180847), ('linear cellular', 0.4385699927806854), ('automaton', 0.41195911169052124)]"
311,311,95,311_training generative adversarial_generative adversarial networks_adversarial networks gans_networks gans,"['training generative adversarial', 'generative adversarial networks', 'adversarial networks gans', 'networks gans', 'generative adversarial', 'generative adversarial network', 'training generative', 'gans', 'gan', 'gan based']","['A game-theoretic approach for Generative Adversarial Networks   Generative adversarial networks (GANs) are a class of generative models,\nknown for producing accurate samples. The key feature of GANs is that there are\ntwo antagonistic neural networks: the generator and the discriminator. The main\nbottleneck for their implementation is that the neural networks are very hard\nto train. One way to improve their performance is to design reliable algorithms\nfor the adversarial process. Since the training can be cast as a stochastic\nNash equilibrium problem, we rewrite it as a variational inequality and\nintroduce an algorithm to compute an approximate solution. Specifically, we\npropose a stochastic relaxed forward-backward algorithm for GANs. We prove that\nwhen the pseudogradient mapping of the game is monotone, we have convergence to\nan exact solution or in a neighbourhood of it.\n', 'MIM-Based GAN: Information Metric to Amplify Small Probability Events\n  Importance in Generative Adversarial Networks   In terms of Generative Adversarial Networks (GANs), the information metric to\ndiscriminate the generative data from the real data, lies in the key point of\ngeneration efficiency, which plays an important role in GAN-based applications,\nespecially in anomaly detection. As for the original GAN, there exist drawbacks\nfor its hidden information measure based on KL divergence on rare events\ngeneration and training performance for adversarial networks. Therefore, it is\nsignificant to investigate the metrics used in GANs to improve the generation\nability as well as bring gains in the training process. In this paper, we adopt\nthe exponential form, referred from the information measure, i.e. MIM, to\nreplace the logarithm form of the original GAN. This approach is called\nMIM-based GAN, has better performance on networks training and rare events\ngeneration. Specifically, we first discuss the characteristics of training\nprocess in this approach. Moreover, we also analyze its advantages on\ngenerating rare events in theory. In addition, we do simulations on the\ndatasets of MNIST and ODDS to see that the MIM-based GAN achieves\nstate-of-the-art performance on anomaly detection compared with some classical\nGANs.\n', 'Dynamics of Fourier Modes in Torus Generative Adversarial Networks   Generative Adversarial Networks (GANs) are powerful Machine Learning models\ncapable of generating fully synthetic samples of a desired phenomenon with a\nhigh resolution. Despite their success, the training process of a GAN is highly\nunstable and typically it is necessary to implement several accessory\nheuristics to the networks to reach an acceptable convergence of the model. In\nthis paper, we introduce a novel method to analyze the convergence and\nstability in the training of Generative Adversarial Networks. For this purpose,\nwe propose to decompose the objective function of the adversary min-max game\ndefining a periodic GAN into its Fourier series. By studying the dynamics of\nthe truncated Fourier series for the continuous Alternating Gradient Descend\nalgorithm, we are able to approximate the real flow and to identify the main\nfeatures of the convergence of the GAN. This approach is confirmed empirically\nby studying the training flow in a $2$-parametric GAN aiming to generate an\nunknown exponential distribution. As byproduct, we show that convergent orbits\nin GANs are small perturbations of periodic orbits so the Nash equillibria are\nspiral attractors. This theoretically justifies the slow and unstable training\nobserved in GANs.\n']","[('training generative adversarial', 0.7054526209831238), ('generative adversarial networks', 0.674027144908905), ('adversarial networks gans', 0.6724812984466553), ('networks gans', 0.6627607941627502), ('generative adversarial', 0.6609774231910706), ('generative adversarial network', 0.6560516357421875), ('training generative', 0.6486801505088806), ('gans', 0.6381857991218567), ('gan', 0.6251876354217529), ('gan based', 0.6041010022163391)]"
312,312,95,312_molecular_based molecular_molecule_molecules,"['molecular', 'based molecular', 'molecule', 'molecules', 'transmitter receiver', 'communication systems', 'signaling', 'communications', 'communication via', 'transmitters']","[""Frequency-Domain Detection for Molecular Communications   Molecular Communications (MC) is a bio-inspired communication paradigm which\nuses molecules as information carriers, thereby requiring unconventional\ntransmitter/receiver architectures and modulation/detection techniques.\nPractical MC receivers (MC-Rxs) can be implemented based on field-effect\ntransistor biosensor (bioFET) architectures, where surface receptors reversibly\nreact with ligands, whose concentration encodes the information. The\ntime-varying concentration of ligand-bound receptors is then translated into\nelectrical signals via field-effect, which is used to decode the transmitted\ninformation. However, ligand-receptor interactions do not provide an ideal\nmolecular selectivity, as similar types of ligands, i.e., interferers,\nco-existing in the MC channel can interact with the same type of receptors,\nresulting in cross-talk. Overcoming this molecular cross-talk with time-domain\nsamples of the Rx's electrical output is not always attainable, especially when\nRx has no knowledge of the interferer statistics or it operates near\nsaturation. In this study, we propose a frequency-domain detection (FDD)\ntechnique for bioFET-based MC-Rxs, which exploits the difference in binding\nreaction rates of different types of ligands, reflected to the noise spectrum\nof the ligand-receptor binding fluctuations. We analytically derive the bit\nerror probability (BEP) of the FDD technique, and demonstrate its effectiveness\nin decoding transmitted concentration signals under stochastic molecular\ninterference, in comparison to a widely-used time-domain detection (TDD)\ntechnique. The proposed FDD method can be applied to any biosensor-based\nMC-Rxs, which employ receptor molecules as the channel-Rx interface.\n"", 'Molecular communication networks with general molecular circuit\n  receivers   In a molecular communication network, transmitters may encode information in\nconcentration or frequency of signalling molecules. When the signalling\nmolecules reach the receivers, they react, via a set of chemical reactions or a\nmolecular circuit, to produce output molecules. The counts of output molecules\nover time is the output signal of the receiver. The aim of this paper is to\ninvestigate the impact of different reaction types on the information\ntransmission capacity of molecular communication networks. We realise this aim\nby using a general molecular circuit model. We derive general expressions of\nmean receiver output, and signal and noise spectra. We use these expressions to\ninvestigate the information transmission capacities of a number of molecular\ncircuits.\n', 'Performance Analysis and ISI Mitigation with Imperfect Transmitter in\n  Molecular Communication   In molecular communication (MC), molecules are released from the transmitter\nto convey information. This paper considers a realistic molecule shift keying\n(MoSK) scenario with two species of molecule in two reservoirs, where the\nmolecules are harvested from the environment and placed into different\nreservoirs, which are purified by exchanging molecules between the reservoirs.\nThis process consumes energy, and for a reasonable energy cost, the reservoirs\ncannot be pure; thus, our MoSK transmitter is imperfect, releasing mixtures of\nboth molecules for every symbol, resulting in inter-symbol interference (ISI).\nTo mitigate ISI, the properties of the receiver are analyzed and a detection\nmethod based on the ratio of different molecules is proposed. Theoretical and\nsimulation results are provided, showing that with the increase of energy cost,\nthe system achieves better performance. The good performance of the proposed\ndetection scheme is also demonstrated.\n']","[('molecular', 0.41129299998283386), ('based molecular', 0.40879690647125244), ('molecule', 0.39918458461761475), ('molecules', 0.3844543993473053), ('transmitter receiver', 0.3353166878223419), ('communication systems', 0.3315960764884949), ('signaling', 0.33134230971336365), ('communications', 0.3169781565666199), ('communication via', 0.31548890471458435), ('transmitters', 0.31114456057548523)]"
313,313,94,313_virasoro algebras_tensor product modules_irreducible modules_virasoro algebra,"['virasoro algebras', 'tensor product modules', 'irreducible modules', 'virasoro algebra', 'modules irreducible', 'weight modules', 'verma modules', 'modules affine', 'highest weight modules', 'modules twisted']","['A new class of irreducible modules over the affine-Virasoro algebra of\n  type $A_1$   In this paper, we construct a class of non-weight modules over the\naffine-Virasoro algebra of type $A_1$ by taking tensor products of a finite\nnumber of irreducible modules $M(\\lambda, \\alpha, \\beta, \\gamma)$ with\nirreducible highest weight modules $V(\\eta, \\epsilon, \\theta)$. We obtain the\nnecessary and sufficient conditions for such tensor product modules to be\nirreducible, and determine the necessary and sufficient conditions for such two\nmodules to be isomorphic. We also compare these modules with other known\nnon-weight modules, showing that these irreducible modules are new.\n', 'Tensor product weight modules for the mirror-twisted Heisenberg-Virasoro\n  algebra   In this paper, we study irreducible weight modules with infinite dimensional\nweight spaces over the mirror-twisted Heisenberg-Virasoro algebra\n$\\mathcal{D}$. More precisely, the necessary and sufficient conditions for the\ntensor products of irreducible highest weight modules and irreducible modules\nof intermediates series over $\\mathcal{D}$ to be irreducible are determined by\nusing ""shifting technique"". This leads to a family of new irreducible weight\nmodules over $\\mathcal{D}$. Then we obtain that any two such tensor products\nare isomorphic if and only if the corresponding highest weight modules and\nmodules of intermediate series are isomorphic respectively. Also we discuss\nsubmodules of the tensor product module when it is not irreducible.\n', 'Tensor product weight modules over the affine-Virasoro algebra   In this paper, we study the tensor products of irreducible highest weight\nmodules with irreducible loop modules over the affine-Virasoro algebra with aid\nof the ``shifting technique"" established for the Virasoro algebra in [H. Chen,\nX. Guo, K. Zhao, Tensor product weight modules over the Virasoro algebra, J.\nLond. Math. Soc. 88(2013), 829-844.]. All such tensor product modules are\nindecomposable modules with infinite-dimensional weight spaces. Moreover, we\nobtain the necessary and sufficient conditions for such tensor product modules\nto be irreducible. Therefore, we obtain a class of new irreducible weight\nmodules over the affine-Virasoro algebra. Finally, the necessary and sufficient\nconditions for any two such tensor product modules to be isomorphic are also\ndetermined.\n']","[('virasoro algebras', 0.6546501517295837), ('tensor product modules', 0.6183584332466125), ('irreducible modules', 0.6020403504371643), ('virasoro algebra', 0.5959154367446899), ('modules irreducible', 0.589033842086792), ('weight modules', 0.5601736903190613), ('verma modules', 0.5566099882125854), ('modules affine', 0.554084062576294), ('highest weight modules', 0.5498604774475098), ('modules twisted', 0.5277564525604248)]"
314,314,94,314_graphs metric_graph metric_dimension graphs_dimension graph,"['graphs metric', 'graph metric', 'dimension graphs', 'dimension graph', 'dimension vertex', 'metric dimension', 'dimension edge', 'dimension metric', 'metric dimensions', 'edge metric']","['Fault tolerance for metric dimension and its variants   Hernando et al. (2008) introduced the fault-tolerant metric dimension\n$\\text{ftdim}(G)$, which is the size of the smallest resolving set $S$ of a\ngraph $G$ such that $S-\\left\\{s\\right\\}$ is also a resolving set of $G$ for\nevery $s \\in S$. They found an upper bound $\\text{ftdim}(G) \\le \\dim(G) (1+2\n\\cdot 5^{\\dim(G)-1})$, where $\\dim(G)$ denotes the standard metric dimension of\n$G$. It was unknown whether there exists a family of graphs where\n$\\text{ftdim}(G)$ grows exponentially in terms of $\\dim(G)$, until recently\nwhen Knor et al. (2024) found a family with $\\text{ftdim}(G) =\n\\dim(G)+2^{\\dim(G)-1}$ for any possible value of $\\dim(G)$. We improve the\nupper bound on fault-tolerant metric dimension by showing that $\\text{ftdim}(G)\n\\le \\dim(G)(1+3^{\\dim(G)-1})$ for every connected graph $G$. Moreover, we find\nan infinite family of connected graphs $J_k$ such that $\\dim(J_k) = k$ and\n$\\text{ftdim}(J_k) \\ge 3^{k-1}-k-1$ for each positive integer $k$. Together,\nour results show that \\[\\lim_{k \\rightarrow \\infty} \\left( \\max_{G: \\text{ }\n\\dim(G) = k} \\frac{\\log_3(\\text{ftdim}(G))}{k} \\right) = 1.\\] In addition, we\nconsider the fault-tolerant edge metric dimension $\\text{ftedim}(G)$ and bound\nit with respect to the edge metric dimension $\\text{edim}(G)$, showing that\n\\[\\lim_{k \\rightarrow \\infty} \\left( \\max_{G: \\text{ } \\text{edim}(G) = k}\n\\frac{\\log_2(\\text{ftedim}(G))}{k} \\right) = 1.\\] We also obtain sharp extremal\nbounds on fault-tolerance for adjacency dimension and $k$-truncated metric\ndimension. Furthermore, we obtain sharp bounds for some other extremal problems\nabout metric dimension and its variants. In particular, we prove an equivalence\nbetween an extremal problem about edge metric dimension and an open problem of\nErd\\H{o}s and Kleitman (1974) in extremal set theory.\n', 'Extremal results for graphs of bounded metric dimension   Metric dimension is a graph parameter motivated by problems in robot\nnavigation, drug design, and image processing. In this paper, we answer several\nopen extremal problems on metric dimension and pattern avoidance in graphs from\n(Geneson, Metric dimension and pattern avoidance, Discrete Appl. Math. 284,\n2020, 1-7). Specifically, we construct a new family of graphs that allows us to\ndetermine the maximum possible degree of a graph of metric dimension at most\n$k$, the maximum possible degeneracy of a graph of metric dimension at most\n$k$, the maximum possible chromatic number of a graph of metric dimension at\nmost $k$, and the maximum $n$ for which there exists a graph of metric\ndimension at most $k$ that contains $K_{n, n}$.\n  We also investigate a variant of metric dimension called edge metric\ndimension and solve another problem from the same paper for $n$ sufficiently\nlarge by showing that the edge metric dimension of $P_n^{d}$ is $d$ for $n \\geq\nd^{d-1}$. In addition, we use a probabilistic argument to make progress on\nanother open problem from the same paper by showing that the maximum possible\nclique number of a graph of edge metric dimension at most $k$ is\n$2^{\\Theta(k)}$. We also make progress on a problem from (N. Zubrilina, On the\nedge dimension of a graph, Discrete Math. 341, 2018, 2083-2088) by finding a\nfamily of new triples $(x, y, n)$ for which there exists a graph of metric\ndimension $x$, edge metric dimension $y$, and order $n$. In particular, we show\nthat for each integer $k > 0$, there exist graphs $G$ with metric dimension\n$k$, edge metric dimension $3^k(1-o(1))$, and order $3^k(1+o(1))$.\n', 'Graphs with the edge metric dimension smaller than the metric dimension   Given a connected graph $G$, the metric (resp. edge metric) dimension of $G$\nis the cardinality of the smallest ordered set of vertices that uniquely\nidentifies every pair of distinct vertices (resp. edges) of $G$ by means of\ndistance vectors to such a set. In this work, we settle three open problems on\n(edge) metric dimension of graphs. Specifically, we show that for every $r,t\\ge\n2$ with $r\\ne t$, there is $n_0$, such that for every $n\\ge n_0$ there exists a\ngraph $G$ of order $n$ with metric dimension $r$ and edge metric dimension $t$,\nwhich among other consequences, shows the existence of infinitely many graph\nwhose edge metric dimension is strictly smaller than its metric dimension. In\naddition, we also prove that it is not possible to bound the edge metric\ndimension of a graph $G$ by some constant factor of the metric dimension of\n$G$.\n']","[('graphs metric', 0.7215189933776855), ('graph metric', 0.6776668429374695), ('dimension graphs', 0.665395975112915), ('dimension graph', 0.6337288022041321), ('dimension vertex', 0.594786524772644), ('metric dimension', 0.5883110761642456), ('dimension edge', 0.5791905522346497), ('dimension metric', 0.577264666557312), ('metric dimensions', 0.5733900666236877), ('edge metric', 0.5605775713920593)]"
315,315,93,315_fairness metrics_fairness constraints_algorithmic fairness_fairness measures,"['fairness metrics', 'fairness constraints', 'algorithmic fairness', 'fairness measures', 'group fairness', 'ensuring fairness', 'fairness aware', 'optimal fair', 'discriminatory', 'discrimination']","['InfoFair: Information-Theoretic Intersectional Fairness   Algorithmic fairness is becoming increasingly important in data mining and\nmachine learning. Among others, a foundational notation is group fairness. The\nvast majority of the existing works on group fairness, with a few exceptions,\nprimarily focus on debiasing with respect to a single sensitive attribute,\ndespite the fact that the co-existence of multiple sensitive attributes (e.g.,\ngender, race, marital status, etc.) in the real-world is commonplace. As such,\nmethods that can ensure a fair learning outcome with respect to all sensitive\nattributes of concern simultaneously need to be developed. In this paper, we\nstudy the problem of information-theoretic intersectional fairness (InfoFair),\nwhere statistical parity, a representative group fairness measure, is\nguaranteed among demographic groups formed by multiple sensitive attributes of\ninterest. We formulate it as a mutual information minimization problem and\npropose a generic end-to-end algorithmic framework to solve it. The key idea is\nto leverage a variational representation of mutual information, which considers\nthe variational distribution between learning outcomes and sensitive\nattributes, as well as the density ratio between the variational and the\noriginal distributions. Our proposed framework is generalizable to many\ndifferent settings, including other statistical notions of fairness, and could\nhandle any type of learning task equipped with a gradient-based optimizer.\nEmpirical evaluations in the fair classification task on three real-world\ndatasets demonstrate that our proposed framework can effectively debias the\nclassification results with minimal impact to the classification accuracy.\n', ""Distributionally Fair Stochastic Optimization using Wasserstein Distance   A traditional stochastic program under a finite population typically seeks to\noptimize efficiency by maximizing the expected profits or minimizing the\nexpected costs, subject to a set of constraints. However, implementing such\noptimization-based decisions can have varying impacts on individuals, and when\nassessed using the individuals' utility functions, these impacts may differ\nsubstantially across demographic groups delineated by sensitive attributes,\nsuch as gender, race, age, and socioeconomic status. As each group comprises\nmultiple individuals, a common remedy is to enforce group fairness, which\nnecessitates the measurement of disparities in the distributions of utilities\nacross different groups. This paper introduces the concept of Distributionally\nFair Stochastic Optimization (DFSO) based on the Wasserstein fairness measure.\nThe DFSO aims to minimize distributional disparities among groups, quantified\nby the Wasserstein distance, while adhering to an acceptable level of\ninefficiency. Our analysis reveals that: (i) the Wasserstein fairness measure\nrecovers the demographic parity fairness prevalent in binary classification\nliterature; (ii) this measure can approximate the well-known Kolmogorov-Smirnov\nfairness measure with considerable accuracy; and (iii) despite DFSO's biconvex\nnature, the epigraph of the Wasserstein fairness measure is generally\nMixed-Integer Convex Programming Representable (MICP-R). Additionally, we\nintroduce two distinct lower bounds for the Wasserstein fairness measure: the\nJensen bound, applicable to the general Wasserstein fairness measure, and the\nGelbrich bound, specific to the type-2 Wasserstein fairness measure. We\nestablish the exactness of the Gelbrich bound and quantify the theoretical\ndifference between the Wasserstein fairness measure and the Gelbrich bound.\n"", 'On the (In)Compatibility between Group Fairness and Individual Fairness   We study the compatibility between the optimal statistical parity solutions\nand individual fairness. While individual fairness seeks to treat similar\nindividuals similarly, optimal statistical parity aims to provide similar\ntreatment to individuals who share relative similarity within their respective\nsensitive groups. The two fairness perspectives, while both desirable from a\nfairness perspective, often come into conflict in applications. Our goal in\nthis work is to analyze the existence of this conflict and its potential\nsolution. In particular, we establish sufficient (sharp) conditions for the\ncompatibility between the optimal (post-processing) statistical parity $L^2$\nlearning and the ($K$-Lipschitz or $(\\epsilon,\\delta)$) individual fairness\nrequirements. Furthermore, when there exists a conflict between the two, we\nfirst relax the former to the Pareto frontier (or equivalently the optimal\ntrade-off) between $L^2$ error and statistical disparity, and then analyze the\ncompatibility between the frontier and the individual fairness requirements.\nOur analysis identifies regions along the Pareto frontier that satisfy\nindividual fairness requirements. (Lastly, we provide individual fairness\nguarantees for the composition of a trained model and the optimal\npost-processing step so that one can determine the compatibility of the\npost-processed model.) This provides practitioners with a valuable approach to\nattain Pareto optimality for statistical parity while adhering to the\nconstraints of individual fairness.\n']","[('fairness metrics', 0.6895659565925598), ('fairness constraints', 0.6779206395149231), ('algorithmic fairness', 0.677497148513794), ('fairness measures', 0.6562469005584717), ('group fairness', 0.616180956363678), ('ensuring fairness', 0.6088709235191345), ('fairness aware', 0.6032359600067139), ('optimal fair', 0.5453528761863708), ('discriminatory', 0.5405285954475403), ('discrimination', 0.5177664756774902)]"
316,316,93,316_quadratic fields_real quadratic fields_binary quadratic forms_quadratic forms,"['quadratic fields', 'real quadratic fields', 'binary quadratic forms', 'quadratic forms', 'integral quadratic forms', 'quadratic field', 'imaginary quadratic fields', 'quartic fields', 'binary quadratic form', 'real number fields']","['Can we recover an integral quadratic form by representing all its\n  subforms?   Let $\\mathfrak o$ be the ring of integers of a totally real number field. If\n$f$ is a quadratic form over $\\mathfrak o$ and $g$ is another quadratic form\nover $\\mathfrak o$ which represents all proper subforms of $f$, does $g$\nrepresent $f$? We show that if $g$ is indefinite, then $g$ indeed represents\n$f$. However, when $f$ is positive definite and indecomposable, then there\nexists a $g$ which represents all proper subforms of $f$ but not $f$ itself.\nAlong the way we give a new characterization of positive definite decomposable\nquadratic forms over $\\mathfrak o$ and a number-field generalization of the\nfiniteness theorem of representations of quadratic forms by quadratic forms\nover $\\mathbb Z$ which asserts that given any infinite set $\\mathscr S$ of\nclasses of positive definite integral quadratic forms over $\\mathfrak o$ of a\nfixed rank, there exists a finite subset $\\mathscr S_0$ of $\\mathscr S$ with\nthe property that a positive definite quadratic form over $\\mathfrak o$\nrepresents all classes in $\\mathscr S$ if and only if it represents all classes\nin $\\mathscr S_0$.\n', ""On Kitaoka's conjecture and lifting problem for universal quadratic\n  forms   For a totally positive definite quadratic form over the ring of integers of a\ntotally real number field $K$, we show that there are only finitely many\ntotally real field extensions of $K$ of a fixed degree over which the form is\nuniversal (namely, those that have a short basis in a suitable sense). Along\nthe way we give a general construction of a universal form of rank bounded by\n$D(\\log D)^{d-1}$, where $d$ is the degree of $K$ over $\\mathbb Q$ and $D$ is\nits discriminant. Furthermore, for any fixed degree we prove (weak) Kitaoka's\nconjecture that there are only finitely many totally real number fields with a\nuniversal ternary quadratic form.\n"", 'Lifting problem for universal quadratic forms over totally real cubic\n  number fields   Lifting problem for universal quadratic forms asks for totally real number\nfields $K$ that admit a positive definite quadratic form with coefficients in\n$\\mathbb{Z}$ that is universal over the ring of integers of $K$. In this paper,\nwe show that $K=\\mathbb{Q}(\\zeta_7+\\zeta_7^{-1})$ is the only such totally real\ncubic field. Moreover, we show that there is no such biquadratic field.\n']","[('quadratic fields', 0.6533887386322021), ('real quadratic fields', 0.648636519908905), ('binary quadratic forms', 0.6357783079147339), ('quadratic forms', 0.6280044317245483), ('integral quadratic forms', 0.6122909784317017), ('quadratic field', 0.5608735084533691), ('imaginary quadratic fields', 0.5448789596557617), ('quartic fields', 0.5257765054702759), ('binary quadratic form', 0.5252548456192017), ('real number fields', 0.5107588171958923)]"
317,317,93,317_nonnegative polynomials_polynomials sums squares_cones symmetric_polynomials sums,"['nonnegative polynomials', 'polynomials sums squares', 'cones symmetric', 'polynomials sums', 'polynomial nonnegative', 'forms sums', 'cone nonnegative', 'squares polynomials', 'symmetric nonnegative', 'polynomial entries']","[""Geometrical Study of the Cone of Sums of Squares plus Sums of\n  Nonnegative Circuits   In this article, we combine sums of squares (SOS) and sums of nonnegative\ncircuit (SONC) forms, two independent nonnegativity certificates for real\nhomogeneous polynomials. We consider the convex cone SOS+SONC of forms that\ndecompose into a sum of an SOS and a SONC form and study it from a geometric\npoint of view. We show that the SOS+SONC cone is proper and neither closed\nunder multiplications nor under linear transformation of variables. Moreover,\nwe present an alternative proof of an analog of Hilbert's 1888 Theorem for the\nSOS+SONC cone and prove that in the non-Hilbert cases it provides a proper\nsuperset of both the SOS and the SONC cone. This follows by exploiting a new\nnecessary condition for membership in the SONC cone.\n"", 'Moments, Sums of Squares, and Tropicalization   We use tropicalization to study the duals to cones of nonnegative polynomials\nand sums of squares on a semialgebraic set $S$. The truncated cones of moments\nof measures supported on the set $S$ is dual to nonnegative polynomials on $S$,\nwhile ""pseudo-moments"" are dual to sums of squares approximations to\nnonnegative polynomials. We provide explicit combinatorial descriptions of\ntropicalizations of the moment and pseudo-moment cones, and demonstrate their\nusefulness in distinguishing between nonnegative polynomials and sums of\nsquares. We give examples that show new limitations of sums of squares\napproximations of nonnegative polynomials. When the semialgebraic set is\ndefined by binomial inequalites, its moment and pseuo-moment cones are closed\nunder Hadamard product. In this case, their tropicalizations are polyhedral\ncones that encode all binomial inequalities on the moment and pseudo-moment\ncones.\n', 'Power mean inequalities and sums of squares   For fixed degree and increasing number of variables the dimension of the\nvector space of $n$-variate real symmetric homogeneous polynomials (forms) of\ndegree $d$ stabilizes. We study the limits of the cones of symmetric\nnonnegative polynomials and symmetric sums of squares, when expressed in\npower-mean or monomial-mean basis. These limits correspond to forms with stable\nexpression in power-mean (or monomial-mean) polynomials that are globally\nnonnegative (resp. sums of squares) regardless of the number of variables. We\nintroduce partial symmetry reduction to describe the limit cone of symmetric\nsums of squares, and reprove a result of arXiv:1205.3102v4 that limits of\nsymmetric nonnegative polynomials and sums of squares agree in degree $4$. We\nuse tropicalization of the dual cones, which was first in the context of\ncomparing nonnegative polynomials and sums of squares in arXiv:2203.06291, to\nshow differences between cones of symmetric polynomials and sums of squares\nstarting in degree 6, which disproves a conjecture of arXiv:1205.3102v4. For\neven symmetric nonnegative forms and sums of squares we show that the cones\nagree for degree at most 8, and are different starting with degree 10. We also\nfind, via tropicalization, explicit examples of symmetric forms that are\nnonnegative but not sums of squares in the limit.\n']","[('nonnegative polynomials', 0.5641381144523621), ('polynomials sums squares', 0.5378097295761108), ('cones symmetric', 0.5063253045082092), ('polynomials sums', 0.4994160830974579), ('polynomial nonnegative', 0.4857032299041748), ('forms sums', 0.4834195077419281), ('cone nonnegative', 0.4797287583351135), ('squares polynomials', 0.47333401441574097), ('symmetric nonnegative', 0.44454386830329895), ('polynomial entries', 0.4259450435638428)]"
318,318,93,318_tensors rank_rank tensors_tensor rank_rank tensor,"['tensors rank', 'rank tensors', 'tensor rank', 'rank tensor', 'tensor decompositions', 'tensors', 'symmetric tensors', 'complex tensors', 'order tensors', 'tensors fixed']","[""Symmetrization maps and minimal border rank Comon's conjecture   One of the fundamental open problems in the field of tensors is the border\nComon's conjecture: given a symmetric tensor $F\\in(\\mathbb{C}^n)^{\\otimes d}$\nfor $d\\geq 3$, its border and symmetric border ranks are equal. In this paper,\nwe prove the conjecture for large classes of concise tensors in\n$(\\mathbb{C}^n)^{\\otimes d}$ of border rank $n$, i.e., tensors of minimal\nborder rank. These families include all tame tensors and all tensors whenever\n$n\\leq d+1$. Our technical tools are border apolarity and border varieties of\nsums of powers.\n"", 'Border rank bounds for $GL(V)$-invariant tensors arising from matrices\n  of constant rank   We prove border rank bounds for a class of $GL(V)$-invariant tensors in\n$V^*\\otimes U\\otimes W$, where $U$ and $W$ are $GL(V)$-modules. These tensors\ncorrespond to spaces of matrices of constant rank. In particular we prove lower\nbounds for tensors in $\\mathbb{C}^l\\otimes\\mathbb{C}^m\\otimes\\mathbb{C}^n$ that\nare not $1_A$-generic, where no nontrivial bounds were known, and also when\n$l,m\\ll n$, where previously only bounds for unbalanced matrix multiplication\ntensors were known. We give the first explicit use of Young flattenings for\ntensors beyond Koszul to obtain border rank lower bounds, and determine the\nborder rank of three tensors.\n', 'Rank and border rank of Kronecker powers of tensors and Strassen\'s laser\n  method   We prove that the border rank of the Kronecker square of the little\nCoppersmith-Winograd tensor $T_{cw,q}$ is the square of its border rank for $q\n> 2$ and that the border rank of its Kronecker cube is the cube of its border\nrank for $q > 4$. This answers questions raised implicitly in\n[Coppersmith-Winograd, 1990] and explicitly in [Bl\\""aser, 2013] and rules out\nthe possibility of proving new upper bounds on the exponent of matrix\nmultiplication using the square or cube of a little Coppersmith-Winograd tensor\nin this range.\n  In the positive direction, we enlarge the list of explicit tensors\npotentially useful for Strassen\'s laser method, introducing a skew-symmetric\nversion of the Coppersmith-Winograd tensor, $T_{skewcw,q}$. For $q = 2$, the\nKronecker square of this tensor coincides with the $3\\times 3$ determinant\npolynomial, $\\det_3 \\in \\mathbb{C}^9\\otimes \\mathbb{C}^9\\otimes \\mathbb{C}^9$,\nregarded as a tensor. We show that this tensor could potentially be used to\nshow that the exponent of matrix multiplication is two.\n  We determine new upper bounds for the (Waring) rank and the (Waring) border\nrank of $\\det_3$, exhibiting a strict submultiplicative behaviour for\n$T_{skewcw,2}$ which is promising for the laser method.\n  We establish general results regarding border ranks of Kronecker powers of\ntensors, and make a detailed study of Kronecker squares of tensors in\n$\\mathbb{C}^3\\otimes \\mathbb{C}^3\\otimes \\mathbb{C}^3$.\n']","[('tensors rank', 0.7055322527885437), ('rank tensors', 0.703319787979126), ('tensor rank', 0.6664263010025024), ('rank tensor', 0.6453588008880615), ('tensor decompositions', 0.6097320318222046), ('tensors', 0.5998878479003906), ('symmetric tensors', 0.593806266784668), ('complex tensors', 0.5879453420639038), ('order tensors', 0.5834587216377258), ('tensors fixed', 0.574429988861084)]"
319,319,93,319_linear network coding_network coding_relay channel_relay networks,"['linear network coding', 'network coding', 'relay channel', 'relay networks', 'relay network', 'relay destination', 'source relay', 'relaying', 'relay node', 'relay']","['Adaptive relaying for streaming erasure codes in a three node relay\n  network   This paper investigates adaptive streaming codes over a three-node relayed\nnetwork. In this setting, a source node transmits a sequence of message packets\nto a destination through a relay. The source-to-relay and relay-to-destination\nlinks are unreliable and introduce at most $N_1$ and $N_2$ packet erasures,\nrespectively. The destination node must recover each message packet within a\nstrict delay constraint $T$. The paper presents achievable streaming codes for\nall feasible parameters $\\{N_1, N_2, T\\}$ that exploit the fact that the relay\nnaturally observes the erasure pattern occurring in the link from source to\nrelay, thus it can adapt its relaying strategy based on these observations. In\na recent work, Fong et al. provide streaming codes featuring\nchannel-state-independent relaying strategies. The codes proposed in this paper\nachieve rates higher than the ones proposed by Fong et al. whenever $N_2 >\nN_1$, and achieve the same rate when $N_2 = N_1$. The paper also presents an\nupper bound on the achievable rate that takes into account erasures in both\nlinks in order to bound the rate in the second link. The upper bound is shown\nto be tighter than a trivial bound that considers only the erasures in the\nsecond link.\n', 'Rate-Optimal Streaming Codes Over the Three-Node Decode-And-Forward\n  Relay Network   In this paper, we study the three-node Decode-and-Forward (D&F) relay network\nsubject to random and burst packet erasures. The source wishes to transmit an\ninfinite stream of packets to the destination via the relay. The three-node D&F\nrelay network is constrained by a decoding delay of T packets, i.e., the packet\ntransmitted by the source at time i must be decoded by the destination by time\ni+T. For the individual channels from source to relay and relay to destination,\nwe assume a delay-constrained sliding-window (DCSW) based packet-erasure model\nthat can be viewed as a tractable approximation to the commonly-accepted\nGilbert-Elliot channel model. Under the model, any time-window of width w\ncontains either up to a random erasure or else erasure burst of length at most\nb (>= a). Thus the source-relay and relay-destination channels are modeled as\n(a_1, b_1, w_1, T_1) and (a_2, b_2, w_2, T_2) DCSW channels. We first derive an\nupper bound on the capacity of the three-node D&F relay network. We then show\nthat the upper bound is tight for the parameter regime: max{b_1,\nb_2}|(T-b_1-b_2-max{a_1, a_2}+1), a1=a2 OR b1=b2 by constructing streaming\ncodes achieving the bound. The code construction requires field size linear in\nT, and has decoding complexity equivalent to that of decoding an MDS code.\n', 'Optimal Streaming Erasure Codes over the Three-Node Relay Network   This paper investigates low-latency streaming codes for a three-node relay\nnetwork. The source transmits a sequence of messages (streaming messages) to\nthe destination through the relay between them, where the first-hop channel\nfrom the source to the relay and the second-hop channel from the relay to the\ndestination are subject to packet erasures. Every source message must be\nrecovered perfectly at the destination subject to a fixed decoding delay of $T$\ntime slots. In any sliding window of $T+1$ time slots, we assume no more than\n$N_1$ and $N_2$ erasures are introduced by the first-hop channel and second-hop\nchannel respectively. Under this channel loss assumption, we fully characterize\nthe maximum achievable rate in terms of $T$, $N_1$ and $N_2$. The achievability\nis proved by using a symbol-wise decode-forward strategy where the source\nsymbols within the same message are decoded by the relay with different delays.\nThe converse is proved by analyzing the maximum achievable rate for each\nchannel when the erasures in the other channel are consecutive (bursty). In\naddition, we show that traditional message-wise decode-forward strategies,\nwhich require the source symbols within the same message to be decoded by the\nrelay with the same delay, are sub-optimal in general.\n']","[('linear network coding', 0.6157442331314087), ('network coding', 0.6012657284736633), ('relay channel', 0.5795783400535583), ('relay networks', 0.5677434802055359), ('relay network', 0.49182695150375366), ('relay destination', 0.4896363317966461), ('source relay', 0.4849899411201477), ('relaying', 0.47077447175979614), ('relay node', 0.4636051058769226), ('relay', 0.46326473355293274)]"
320,320,92,320_transitive permutation group_primitive permutation group_transitive groups_permutation groups,"['transitive permutation group', 'primitive permutation group', 'transitive groups', 'permutation groups', 'transitive group', 'permutation group', 'primitive permutation', 'transitive permutation', 'primitive groups', 'almost simple groups']","['Fixers and derangements of finite permutation groups   Let $G\\leqslant\\mathrm{Sym}(\\Omega)$ be a finite transitive permutation group\nwith point stabiliser $H$. We say that a subgroup $K$ of $G$ is a fixer if\nevery element of $K$ has fixed points, and we say that $K$ is large if $|K|\n\\geqslant |H|$. There is a special interest in studying large fixers due to\nconnections with Erd\\H{o}s-Ko-Rado type problems. In this paper, we classify up\nto conjugacy the large fixers of the almost simple primitive groups with socle\n$\\mathrm{PSL}_2(q)$, and we use this result to verify a special case of a\nconjecture of Spiga on permutation characters. We also present some results on\nlarge fixers of almost simple primitive groups with socle an alternating or\nsporadic group.\n', 'Intersection density of transitive groups with cyclic point stabilizers   For a permutation group $G$ acting on a set $V$, a subset $\\mathcal{F}$ of\n$G$ is said to be an intersecting set if for every pair of elements $g,h\\in\n\\mathcal{F}$ there exists $v \\in V$ such that $g(v) = h(v)$. The intersection\ndensity $\\rho(G)$ of a transitive permutation group $G$ is the maximum value of\nthe quotient $|\\mathcal{F}|/|G_v|$ where $G_v$ is a stabilizer of a point $v\\in\nV$ and $\\mathcal{F}$ runs over all intersecting sets in $G$.\n  If $G_v$ is a largest intersecting set in $G$ then $G$ is said to have the\nErd\\H{o}s-Ko-Rado (EKR)-property. This paper is devoted to the study of\ntransitive permutation groups, with point stabilizers of prime order with a\nspecial emphasis given to orders 2 and 3, which do not have the EKR-property.\nAmong other, constructions of infinite family of transitive permutation groups\nhaving point stabilizer of order $3$ with intersection density $4/3$ and of\ninfinite families of transitive permutation groups having point stabilizer of\norder $3$ with arbitrarily large intersection density are given.\n', 'Erd\\H{o}s-Ko-Rado problems for permutation groups   In this paper, we study intersecting sets in primitive and quasiprimitive\npermutation groups. Let $G \\leqslant \\mathrm{Sym}(\\Omega)$ be a transitive\npermutation group, and ${S}$ an intersecting set. Previous results show that if\n$G$ is either 2-transitive or a Frobenius group, then\n$|{S}|\\leqslant|G_{\\omega}|$ (for some $\\omega \\in \\Omega$). Furthermore, for\nsome 2-transitive groups, $|{S}|=|G_{\\omega}|$ if and only if ${S}$ is a coset\nof a stabilizer. In this paper, we prove that these statements are far from the\ntruth for general transitive groups. In particular, we show that in the case of\nprimitive groups, there is even no absolute constant $c$ such that\n$|{S}|\\leqslant c|G_\\omega|$. In the case $G$ is a primitive permutation group\nisomorphic to $\\mathrm{PSL(2,p)}$, we characterize the subgroups of $G$ which\nare intersecting sets. We also show that if $G \\leqslant \\mathrm{Sym}(\\Omega)$\nis a permutation group of prime power degree, then for any intersecting set\n$S$, we have $|S|\\leq |G_{\\omega}|$ (for some $\\omega \\in \\Omega$). This proves\na part of a conjecture in \\cite{MRS}.\n']","[('transitive permutation group', 0.6227477192878723), ('primitive permutation group', 0.6165199875831604), ('transitive groups', 0.5797378420829773), ('permutation groups', 0.5757656097412109), ('transitive group', 0.5384686589241028), ('permutation group', 0.5195295214653015), ('primitive permutation', 0.50467449426651), ('transitive permutation', 0.48283058404922485), ('primitive groups', 0.4560961127281189), ('almost simple groups', 0.43128278851509094)]"
321,321,92,321_monoid algebras_cancellative monoids_monoids_commutative monoids,"['monoid algebras', 'cancellative monoids', 'monoids', 'commutative monoids', 'commutative monoid', 'cancellative monoid', 'monoid whose', 'monoid', 'free commutative', 'atomicity']","['Factorizations in reciprocal Puiseux monoids   A Puiseux monoid is an additive submonoid of the real line consisting of\nrationals. We say that a Puiseux monoid is reciprocal if it can be generated by\nthe reciprocals of the terms of a strictly increasing sequence of pairwise\nrelatively primes positive integers. We say that a commutative and cancellative\n(additive) monoid is atomic if every non-invertible element $x$ can be written\nas a sum of irreducibles. The number of irreducibles in this sum is called a\nlength of $x$. In this paper, we identify and investigate generalized classes\nof reciprocal Puiseux monoids that are atomic. Moreover, for the atomic monoids\nin the identified classes, we study the ascending chain condition on principal\nideals and also the sets of lengths of their elements.\n', 'On the atomicity of power monoids of Puiseux monoids   A submonoid of the additive group $\\mathbb{Q}$ is called a Puiseux monoid if\nit consists of nonnegative rationals. Given a monoid $M$, the set consisting of\nall nonempty finite subsets of $M$ is also a monoid under the Minkowski sum,\nand it is called the (finitary) power monoid of $M$. In this paper we study\natomicity and factorization properties in power monoids of Puiseux monoids. We\nspecially focus on the ascent of the property of being atomic and both the\nbounded and the finite factorization properties (the ascending chain on\nprincipal ideals and the length-finite factorization properties are also\nconsidered here). We prove that both the bounded and the finite factorization\nproperties ascend from any Puiseux monoid to its power monoid. On the other\nhand, we construct an atomic Puiseux monoid whose power monoid is not atomic.\nWe also prove that the existence of maximal common divisors for nonempty finite\nsubsets is a sufficient condition for the property of being atomic to ascend\nfrom a Puiseux monoid to its power monoid.\n', ""Atomicity and Factorization of Puiseux Monoids   A Puiseux monoid is an additive submonoid of the nonnegative cone of rational\nnumbers. Although Puiseux monoids are torsion-free rank-one monoids, their\natomic structure is rich and highly complex. For this reason, they have been\nimportant objects to construct crucial examples in commutative algebra and\nfactorization theory. In 1974 Anne Grams used a Puiseux monoid to construct the\nfirst example of an atomic domain not satisfying the ACCP, disproving Cohn's\nconjecture that every atomic domain satisfies the ACCP. Even recently, Jim\nCoykendall and Felix Gotti have used Puiseux monoids to construct the first\natomic monoids with monoid algebras (over a field) that are not atomic,\nanswering a question posed by Robert Gilmer back in the 1980s.\n  This dissertation is focused on the investigation of the atomic structure and\nfactorization theory of Puiseux monoids. Here we established various sufficient\nconditions for a Puiseux monoid to be atomic (or satisfy the ACCP). We do the\nsame for two of the most important atomic properties: the finite-factorization\nproperty and the bounded-factorization property. Then we compare these four\natomic properties in the context of Puiseux monoids. This leads us to construct\nand study several classes of Puiseux monoids with distinct atomic structure.\nOur investigation provides sufficient evidence to believe that the class of\nPuiseux monoids is the simplest class with enough complexity to find monoids\nsatisfying almost every fundamental atomic behavior.\n""]","[('monoid algebras', 0.5508178472518921), ('cancellative monoids', 0.5255594849586487), ('monoids', 0.5192021131515503), ('commutative monoids', 0.5047465562820435), ('commutative monoid', 0.4787691533565521), ('cancellative monoid', 0.45584478974342346), ('monoid whose', 0.45419105887413025), ('monoid', 0.44952458143234253), ('free commutative', 0.33469927310943604), ('atomicity', 0.32484814524650574)]"
322,322,92,322_mathematician_mathematicians_mathematics education_mathematics,"['mathematician', 'mathematicians', 'mathematics education', 'mathematics', 'mathematical society', 'mathematical works', 'mathematical knowledge', 'new mathematics', 'mathematical research', 'mathematical']","['Mathematics education policy as a high stakes political struggle: The\n  case of Soviet Russia of the 1930s   This paper is an introduction to our ongoing more comprehensive work on a\ncritically important period in the history of Russian mathematics education; it\nprovides a glimpse into the socio-political environment in which the famous\nSoviet tradition of mathematics education was born. The authors are\npractitioners of mathematics education in two very different countries, England\nand Russia. We have a chance to see that too many trends and debates in current\neducation policy resemble battles around mathematics education in the 1920s and\n1930s Soviet Russia. This is why this period should be revisited and\nre-analysed, despite quite a considerable amount of previous research. Our main\nconclusion: mathematicians, first of all, were fighting for control over\nselection, education, and career development, of young mathematicians. In the\nharshest possible political environment, they were taking potentially lethal\nrisks.\n', 'Blaschke, Osgood, Wiener, Hadamard and the Early Development of Modern\n  Mathematics in China   In ancient times, China made great contributions to world civilization and in\nparticular to mathematics. However, modern sciences including mathematics came\nto China rather too late. The first Chinese university was founded in 1895. The\nfirst mathematics department in China was formally opened at the university\nonly in 1913. At the beginning of the twentieth century, some Chinese went to\nEurope, the United States of America and Japan for higher education in modern\nmathematics and returned to China as the pioneer generation. They created\nmathematics departments at the Chinese universities and sowed the seeds of\nmodern mathematics in China. In 1930s, when a dozen of Chinese universities\nalready had mathematics departments, several leading mathematicians from Europe\nand USA visited China, including Wilhelm Blaschke, George D. Birkhoff, William\nF. Osgood, Norbert Wiener and Jacques Hadamard. Their visits not only had\nprofound impact on the mathematical development in China, but also became\nsocial events sometimes. This paper tells the history of their visits.\n', 'In Memoriam Cem Tezer (1955-2020)   Cem Tezer was a fastidious, meticulous, highly idiosyncratic and versatile\nscientist. Without him Turkish community of mathematics would be incomplete.\nOur sense of gratitude for his work in various areas of mathematics, history of\nsciences, literature, music and his encouragement to do mathematics for only\nits beauty was hardly unique and even unusual. After he passed away on 27\nFebruary 2020, while working actively at Middle East Technical University, the\nnumber of colleagues and former students described the ways in which their\nstudies and indeed their view towards mathematics had been transformed by\nhaving known him might have surprised only those who had never met him. In this\narticle not only, his contributions to mathematics will be classified and\nsummarized but also his unique and distinguished personality as a mathematician\nwill be emphasized.\n']","[('mathematician', 0.6674006581306458), ('mathematicians', 0.6458592414855957), ('mathematics education', 0.6125460863113403), ('mathematics', 0.5716867446899414), ('mathematical society', 0.5569125413894653), ('mathematical works', 0.5532761216163635), ('mathematical knowledge', 0.5275935530662537), ('new mathematics', 0.5107370018959045), ('mathematical research', 0.49701306223869324), ('mathematical', 0.47717300057411194)]"
323,323,90,323_graph signal processing_graph signals_graph signal_graph spectral,"['graph signal processing', 'graph signals', 'graph signal', 'graph spectral', 'sparse graph', 'graph sparsification', 'graph clustering', 'spectral graph', 'graph structures', 'graphs']","[""Graph Signal Processing Meets Blind Source Separation   In graph signal processing (GSP), prior information on the dependencies in\nthe signal is collected in a graph which is then used when processing or\nanalyzing the signal. Blind source separation (BSS) techniques have been\ndeveloped and analyzed in different domains, but for graph signals the research\non BSS is still in its infancy. In this paper, this gap is filled with two\ncontributions. First, a nonparametric BSS method, which is relevant to the GSP\nframework, is refined, the Cram\\'{e}r-Rao bound (CRB) for mixing and unmixing\nmatrix estimators in the case of Gaussian moving average graph signals is\nderived, and for studying the achievability of the CRB, a new parametric method\nfor BSS of Gaussian moving average graph signals is introduced. Second, we also\nconsider BSS of non-Gaussian graph signals and two methods are proposed.\nIdentifiability conditions show that utilizing both graph structure and\nnon-Gaussianity provides a more robust approach than methods which are based on\nonly either graph dependencies or non-Gaussianity. It is also demonstrated by\nnumerical study that the proposed methods are more efficient in separating\nnon-Gaussian graph signals.\n"", 'Graph signal processing with categorical perspective   In this paper, we propose a framework for graph signal processing using\ncategory theory. The aim is to generalize a few recent works on probabilistic\napproaches to graph signal processing, which handle signal and graph\nuncertainties.\n', 'Modelling Graph Errors: Towards Robust Graph Signal Processing   The first step for any graph signal processing (GSP) procedure is to learn\nthe graph signal representation, i.e., to capture the dependence structure of\nthe data into an adjacency matrix. Indeed, the adjacency matrix is typically\nnot known a priori and has to be learned. However, it is learned with errors. A\nlittle attention has been paid to modelling such errors in the adjacency\nmatrix, and studying their effects on GSP methods. However, modelling errors in\nthe adjacency matrix will enable both to study the graph error effects in GSP\nand to develop robust GSP algorithms. In this paper, we therefore introduce\npractically justifiable graph error models. We also study, both analytically\nwhen possible and numerically, the graph error effect on the performance of GSP\nmethods in different types of problems such as filtering of graph signals and\nindependent component analysis of graph signals (graph decorrelation).\n']","[('graph signal processing', 0.7926475405693054), ('graph signals', 0.7073143124580383), ('graph signal', 0.6748658418655396), ('graph spectral', 0.5767446160316467), ('sparse graph', 0.5684632062911987), ('graph sparsification', 0.5523306131362915), ('graph clustering', 0.533004105091095), ('spectral graph', 0.49229952692985535), ('graph structures', 0.48492196202278137), ('graphs', 0.4799664616584778)]"
324,324,89,324_bundles rank_stable vector bundles_vector bundles_bundles projective,"['bundles rank', 'stable vector bundles', 'vector bundles', 'bundles projective', 'bundles smooth projective', 'line bundles', 'stable bundles', 'bundles', 'bundles smooth', 'bundle rank']","['On some ""sporadic"" moduli spaces of Ulrich bundles on some 3-fold\n  scrolls over $\\mathbb{F}_0$   We investigate on the existence of some ""sporadic"", rank-$r \\geqslant 1$\nUlrich vector bundles on suitable $3$-fold scrolls $X$ over the Hirzebruch\nsurface $\\mathbb{F}_0$, which arise as tautological embeddings of\nprojectivization of very-ample vector bundles on $\\mathbb{F}_0$ that are\nuniform in the sense of Brosius and Aprodu--Brinzanescu. Such Ulrich bundles\narise as deformations of ``iterative"" extensions by means of ""sporadic"" Ulrich\nline bundles. We moreover explicitely describe irreducible components of the\ncorresponding ""sporadic"" moduli spaces of rank $r \\geqslant 1$ vector bundles\nwhich are Ulrich with respect to the tautological polarization on $X$. In some\ncases such irreducible components turn out to be a singleton, in some other\ncases such components are generically smooth, whose positive dimension has been\ncomputed and whose general point turns out to be a slope-stable vector bundle.\n', 'Ulrich bundles on a general blow--up of the plane   We prove that on $X_n$, the plane blown--up at $n$ general points, there are\nUlrich line bundles with respect to a line bundle corresponding to curves of\ndegree $m$ passing simply through the $n$ blown--up points, with $m\\leq\n2\\sqrt{n}$ and such that the line bundle in question is very ample on $X_n$. We\nprove that the number of these Ulrich line bundles tends to infinity with $n$.\n  We also prove the existence of slope--stable rank--$r$ Ulrich vector bundles\non $X_n$, for $n\\geq 2$ and any $r \\geq 1$ and we compute the dimensions of\ntheir moduli spaces. These computations imply that $X_n$ is {Ulrich wild}.\n', 'Characterization of Ulrich bundles on Hirzebruch surfaces   In this work we characterize Ulrich bundles of any rank on polarized rational\nruled surfaces over $\\mathbb{P}^1$. We show that every Ulrich bundle admits a\nresolution in terms of line bundles. Conversely, given an injective map between\nsuitable totally decomposed vector bundles, we show that its cokernel is Ulrich\nif it satisfies a vanishing in cohomology. As a consequence we obtain, once we\nfix a polarization, the existence of Ulrich bundles for any admissible rank and\nfirst Chern class. Moreover we show the existence of stable Ulrich bundles for\ncertain pairs $(\\textrm{rk}(E),c_1(E))$ and with respect to a family of\npolarizations. Finally we construct examples of indecomposable Ulrich bundles\nfor several different polarizations and ranks.\n']","[('bundles rank', 0.6277967691421509), ('stable vector bundles', 0.6179108619689941), ('vector bundles', 0.6116608381271362), ('bundles projective', 0.6110982298851013), ('bundles smooth projective', 0.5997965931892395), ('line bundles', 0.5919497013092041), ('stable bundles', 0.5889906287193298), ('bundles', 0.5856747031211853), ('bundles smooth', 0.5745508074760437), ('bundle rank', 0.573387086391449)]"
325,325,89,325_causal discovery_structural causal models_learning causal_causal structures,"['causal discovery', 'structural causal models', 'learning causal', 'causal structures', 'causal graphs', 'structural causal', 'causal structure', 'causal models', 'models causal', 'causal inference']","['Axiomatization of Interventional Probability Distributions   Causal intervention is an essential tool in causal inference. It is\naxiomatized under the rules of do-calculus in the case of structure causal\nmodels. We provide simple axiomatizations for families of probability\ndistributions to be different types of interventional distributions. Our\naxiomatizations neatly lead to a simple and clear theory of causality that has\nseveral advantages: it does not need to make use of any modeling assumptions\nsuch as those imposed by structural causal models; it only relies on\ninterventions on single variables; it includes most cases with latent variables\nand causal cycles; and more importantly, it does not assume the existence of an\nunderlying true causal graph as we do not take it as the primitive object--in\nfact, a causal graph is derived as a by-product of our theory. We show that,\nunder our axiomatizations, the intervened distributions are Markovian to the\ndefined intervened causal graphs, and an observed joint probability\ndistribution is Markovian to the obtained causal graph; these results are\nconsistent with the case of structural causal models, and as a result, the\nexisting theory of causal inference applies. We also show that a large class of\nnatural structural causal models satisfy the theory presented here. We note\nthat the aim of this paper is axiomatization of interventional families, which\nis subtly different from ""causal modeling.""\n', 'Causal Discovery in Linear Structural Causal Models with Deterministic\n  Relations   Linear structural causal models (SCMs) -- in which each observed variable is\ngenerated by a subset of the other observed variables as well as a subset of\nthe exogenous sources -- are pervasive in causal inference and casual\ndiscovery. However, for the task of causal discovery, existing work almost\nexclusively focus on the submodel where each observed variable is associated\nwith a distinct source with non-zero variance. This results in the restriction\nthat no observed variable can deterministically depend on other observed\nvariables or latent confounders. In this paper, we extend the results on\nstructure learning by focusing on a subclass of linear SCMs which do not have\nthis property, i.e., models in which observed variables can be causally\naffected by any subset of the sources, and are allowed to be a deterministic\nfunction of other observed variables or latent confounders. This allows for a\nmore realistic modeling of influence or information propagation in systems. We\nfocus on the task of causal discovery form observational data generated from a\nmember of this subclass. We derive a set of necessary and sufficient conditions\nfor unique identifiability of the causal structure. To the best of our\nknowledge, this is the first work that gives identifiability results for causal\ndiscovery under both latent confounding and deterministic relationships.\nFurther, we propose an algorithm for recovering the underlying causal structure\nwhen the aforementioned conditions are satisfied. We validate our theoretical\nresults both on synthetic and real datasets.\n', 'Confidence in Causal Inference under Structure Uncertainty in Linear\n  Causal Models with Equal Variances   Inferring the effect of interventions within complex systems is a fundamental\nproblem of statistics. A widely studied approach employs structural causal\nmodels that postulate noisy functional relations among a set of interacting\nvariables. The underlying causal structure is then naturally represented by a\ndirected graph whose edges indicate direct causal dependencies. In a recent\nline of work, additional assumptions on the causal models have been shown to\nrender this causal graph identifiable from observational data alone. One\nexample is the assumption of linear causal relations with equal error variances\nthat we will take up in this work. When the graph structure is known, classical\nmethods may be used for calculating estimates and confidence intervals for\ncausal effects. However, in many applications, expert knowledge that provides\nan a priori valid causal structure is not available. Lacking alternatives, a\ncommonly used two-step approach first learns a graph and then treats the graph\nas known in inference. This, however, yields confidence intervals that are\noverly optimistic and fail to account for the data-driven model choice. We\nargue that to draw reliable conclusions, it is necessary to incorporate the\nremaining uncertainty about the underlying causal structure in confidence\nstatements about causal effects. To address this issue, we present a framework\nbased on test inversion that allows us to give confidence regions for total\ncausal effects that capture both sources of uncertainty: causal structure and\nnumerical size of nonzero effects.\n']","[('causal discovery', 0.6841328144073486), ('structural causal models', 0.6640893816947937), ('learning causal', 0.6605302095413208), ('causal structures', 0.6483623385429382), ('causal graphs', 0.6455214023590088), ('structural causal', 0.6433388590812683), ('causal structure', 0.6386620402336121), ('causal models', 0.6342267990112305), ('models causal', 0.6336314082145691), ('causal inference', 0.6325345635414124)]"
326,326,89,326_lucas numbers_pell numbers_lucas sequences_generalized pell,"['lucas numbers', 'pell numbers', 'lucas sequences', 'generalized pell', 'fibonacci lucas', 'lucas sequence', 'two fibonacci numbers', 'fibonacci numbers', 'th fibonacci number', 'solutions diophantine']","['Pell or Pell-Lucas numbers as concatenations of two repdigits in base\n  $b$   Let $b$ be a positive integer such that $2 \\leq b \\leq 10$. In this study, we\nfind all Pell or Pell-Lucas numbers as concatenations of two repdigits in base\n$b$. As a corollary, it is show that the largest Pell or Pell-Lucas numbers\nwhich can be expressible as a concatenations of two repdigits in base $b$ are\n$P_{11} = 5741$ and $Q_5 = 82$, respectively.\n', 'On Mixed Concatenations of Fibonacci and Lucas Numbers Which are\n  Fibonacci Numbers   Let $(F_n)_{n\\geq 0}$ and $(L_n)_{n\\geq 0}$ be the Fibonacci and Lucas\nsequences, respectively. In this paper we determine all Fibonacci numbers which\nare mixed concatenations of a Fibonacci and a Lucas numbers. By mixed\nconcatenations of $ a $ and $ b $, we mean the both concatenations\n$\\overline{ab}$ and $\\overline{ba}$ together, where $ a $ and $ b $ are any two\nnon negative integers. So, the mathematical formulation of this problem leads\nus searching the solutions of two Diophantine equations $ F_n=10^d F_m +L_k $\nand $ F_n=10^d L_m+F_k $ in non-negative integers $ (n,m,k) ,$ where $ d $\ndenotes the number of digits of $ L_k $ and $ F_k $, respectively. We use lower\nbounds for linear forms in logarithms and reduction method in Diophantine\napproximation to get the results.\n', 'Pell and Pell-Lucas numbers as sums of three repdigits   In this study, we find all Pell and Pell-Lucas numbers which are sums of\nthree base 10 repdigits. The proof of our main theorem uses lower bounds for\nlinear forms in logarithms of algebraic numbers and a version of the\nBaker-Davenport reduction method.\n']","[('lucas numbers', 0.6012345552444458), ('pell numbers', 0.59117192029953), ('lucas sequences', 0.5876402258872986), ('generalized pell', 0.5538355112075806), ('fibonacci lucas', 0.5219541192054749), ('lucas sequence', 0.5087997317314148), ('two fibonacci numbers', 0.4902350902557373), ('fibonacci numbers', 0.47739115357398987), ('th fibonacci number', 0.46470844745635986), ('solutions diophantine', 0.4542323052883148)]"
327,327,88,327_directed polymers random_polymer models_random polymer_directed polymer,"['directed polymers random', 'polymer models', 'random polymer', 'directed polymer', 'directed polymers', 'polymers random', 'polymer measures', 'polymer', 'polymers', 'disorder phase']","['On the phase diagram of the polymer model   In dimensions 3 or larger, it is a classical fact that the directed polymer\nmodel has two phases: Brownian behavior at high temperature, and non-Brownian\nbehavior at low temperature. We consider the response of the polymer to an\nexternal field or tilt, and show that at fixed temperature, the polymer has\nBrownian behavior for some fields and non-Brownian behavior for others. In\nother words, the external field can induce the phase transition in the directed\npolymer model.\n', ""Borodin-P\\'ech\\'e fluctuations of the free energy in directed random\n  polymer models   We consider two directed polymer models in the Kardar-Parisi-Zhang (KPZ)\nuniversality class: the O'Connell-Yor semi-discrete directed polymer with\nboundary sources and the continuum directed random polymer with (m,n)-spiked\nboundary perturbations. The free energy of the continuum polymer is the\nHopf-Cole solution of the KPZ equation with the corresponding (m,n)-spiked\ninitial condition. This new initial condition is constructed using two\nsemi-discrete polymer models with independent bulk randomness and coupled\nboundary sources. We prove that the limiting fluctuations of the free energies\nrescaled by the 1/3rd power of time in both polymer models converge to the\nBorodin-Peche type deformations of the GUE Tracy-Widom distribution.\n"", 'Pinning, diffusive fluctuations, and Gaussian limits for half-space\n  directed polymer models   Half-space directed polymers in random environments are models of interface\ngrowth in the presence of an attractive hard wall. They arise naturally in the\nstudy of wetting and entropic repulsion phenomena. In 1985, Kardar predicted a\n""depinning"" phase transition as the attractive force of the wall is weakened.\nThis phase transition has been rigorously established for integrable models of\nhalf-space last passage percolation, i.e. half-space directed polymers at zero\ntemperature, in a line of study tracing back to work of Baik--Rains. On the\nother hand, for integrable positive temperature models, the first rigorous\nproof of this phase transition has only been obtained very recently through a\nseries of works of Barraquand--Wang, Imamura--Mucciconi--Sasamoto [IMS],\nBarraquand--Corwin--Das, and Das--Zhu [DZ] on the half-space log-Gamma polymer.\nIn this paper we study a broad class of half-space directed polymer models with\nminimal assumptions on the random environment. We prove that an attractive\nforce on the wall strong enough to macroscopically increase the free energy\ninduces phenomena characteristic of the subcritical ""bound phase,"" namely the\npinning of the polymer to the wall and the diffusive fluctuations and limiting\nGaussianity of the free energy. Our arguments are geometric in nature and allow\nus to analyze the positive temperature and zero temperature models\nsimultaneously. Moreover, given the macroscopic free energy increase proven in\n[IMS] for the half-space log-Gamma polymer, our arguments can be used to\nreprove the results of [IMS, DZ] on polymer geometry and free energy\nfluctuations in the bound phase.\n']","[('directed polymers random', 0.6765324473381042), ('polymer models', 0.6175298094749451), ('random polymer', 0.5882711410522461), ('directed polymer', 0.5862219929695129), ('directed polymers', 0.572493314743042), ('polymers random', 0.5718855857849121), ('polymer measures', 0.46606460213661194), ('polymer', 0.45150917768478394), ('polymers', 0.44433706998825073), ('disorder phase', 0.42157626152038574)]"
328,328,88,328_stochastic bilevel optimization_bilevel optimization_optimization bilevel_bilevel optimization problems,"['stochastic bilevel optimization', 'bilevel optimization', 'optimization bilevel', 'bilevel optimization problems', 'single level optimization', 'hyperparameter optimization', 'bi level optimization', 'optimization', 'level optimization', 'solving bilevel']","['Overcoming Lower-Level Constraints in Bilevel Optimization: A Novel\n  Approach with Regularized Gap Functions   Constrained bilevel optimization tackles nested structures present in\nconstrained learning tasks like constrained meta-learning, adversarial\nlearning, and distributed bilevel optimization. However, existing bilevel\noptimization methods mostly are typically restricted to specific constraint\nsettings, such as linear lower-level constraints. In this work, we overcome\nthis limitation and develop a new single-loop, Hessian-free constrained bilevel\nalgorithm capable of handling more general lower-level constraints. We achieve\nthis by employing a doubly regularized gap function tailored to the constrained\nlower-level problem, transforming constrained bilevel optimization into an\nequivalent single-level optimization problem with a single smooth constraint.\nWe rigorously establish the non-asymptotic convergence analysis of the proposed\nalgorithm under the convexity of lower-level problem, avoiding the need for\nstrong convexity assumptions on the lower-level objective or coupling convexity\nassumptions on lower-level constraints found in existing literature.\nAdditionally, the generality of our method allows for its extension to bilevel\noptimization with minimax lower-level problem. We evaluate the effectiveness\nand efficiency of our algorithm on various synthetic problems, typical\nhyperparameter learning tasks, and generative adversarial network.\n', 'Alternating Implicit Projected SGD and Its Efficient Variants for\n  Equality-constrained Bilevel Optimization   Stochastic bilevel optimization, which captures the inherent nested structure\nof machine learning problems, is gaining popularity in many recent\napplications. Existing works on bilevel optimization mostly consider either\nunconstrained problems or constrained upper-level problems. This paper\nconsiders the stochastic bilevel optimization problems with equality\nconstraints both in the upper and lower levels. By leveraging the special\nstructure of the equality constraints problem, the paper first presents an\nalternating implicit projected SGD approach and establishes the $\\tilde{\\cal\nO}(\\epsilon^{-2})$ sample complexity that matches the state-of-the-art\ncomplexity of ALSET \\citep{chen2021closing} for unconstrained bilevel problems.\nTo further save the cost of projection, the paper presents two alternating\nimplicit projection-efficient SGD approaches, where one algorithm enjoys the\n$\\tilde{\\cal O}(\\epsilon^{-2}/T)$ upper-level and $\\tilde{\\cal\nO}(\\epsilon^{-1.5}/T^{\\frac{3}{4}})$ lower-level projection complexity with\n${\\cal O}(T)$ lower-level batch size, and the other one enjoys $\\tilde{\\cal\nO}(\\epsilon^{-1.5})$ upper-level and lower-level projection complexity with\n${\\cal O}(1)$ batch size. Application to federated bilevel optimization has\nbeen presented to showcase the empirical performance of our algorithms. Our\nresults demonstrate that equality-constrained bilevel optimization with\nstrongly-convex lower-level problems can be solved as efficiently as stochastic\nsingle-level optimization problems.\n', 'On Momentum-Based Gradient Methods for Bilevel Optimization with\n  Nonconvex Lower-Level   Bilevel optimization is a popular two-level hierarchical optimization, which\nhas been widely applied to many machine learning tasks such as hyperparameter\nlearning, meta learning and continual learning. Although many bilevel\noptimization methods recently have been developed, the bilevel methods are not\nwell studied when the lower-level problem is nonconvex. To fill this gap, in\nthe paper, we study a class of nonconvex bilevel optimization problems, where\nboth upper-level and lower-level problems are nonconvex, and the lower-level\nproblem satisfies Polyak-{\\L}ojasiewicz (PL) condition. We propose an efficient\nmomentum-based gradient bilevel method (MGBiO) to solve these deterministic\nproblems. Meanwhile, we propose a class of efficient momentum-based stochastic\ngradient bilevel methods (MSGBiO and VR-MSGBiO) to solve these stochastic\nproblems. Moreover, we provide a useful convergence analysis framework for our\nmethods. Specifically, under some mild conditions, we prove that our MGBiO\nmethod has a sample (or gradient) complexity of $O(\\epsilon^{-2})$ for finding\nan $\\epsilon$-stationary solution of the deterministic bilevel problems (i.e.,\n$\\|\\nabla F(x)\\|\\leq \\epsilon$), which improves the existing best results by a\nfactor of $O(\\epsilon^{-1})$. Meanwhile, we prove that our MSGBiO and VR-MSGBiO\nmethods have sample complexities of $\\tilde{O}(\\epsilon^{-4})$ and\n$\\tilde{O}(\\epsilon^{-3})$, respectively, in finding an $\\epsilon$-stationary\nsolution of the stochastic bilevel problems (i.e., $\\mathbb{E}\\|\\nabla\nF(x)\\|\\leq \\epsilon$), which improves the existing best results by a factor of\n$\\tilde{O}(\\epsilon^{-3})$. Extensive experimental results on bilevel PL game\nand hyper-representation learning demonstrate the efficiency of our algorithms.\nThis paper commemorates the mathematician Boris Polyak (1935 -2023).\n']","[('stochastic bilevel optimization', 0.6981062889099121), ('bilevel optimization', 0.6705852150917053), ('optimization bilevel', 0.6516332626342773), ('bilevel optimization problems', 0.6320083141326904), ('single level optimization', 0.524623692035675), ('hyperparameter optimization', 0.512276828289032), ('bi level optimization', 0.512045681476593), ('optimization', 0.4754711389541626), ('level optimization', 0.46559035778045654), ('solving bilevel', 0.4550883173942566)]"
329,329,88,329_closed symplectic manifolds_symplectic homology_symplectic manifolds_hamiltonian diffeomorphisms,"['closed symplectic manifolds', 'symplectic homology', 'symplectic manifolds', 'hamiltonian diffeomorphisms', 'manifolds hamiltonian', 'closed symplectic manifold', 'symplectic topology', 'symplectic manifold', 'group hamiltonian diffeomorphisms', 'manifold hamiltonian']","['On the existence of infinitely many non-contractible periodic orbits of\n  Hamiltonian diffeomorphisms of closed symplectic manifolds   We show that the presence of a non-contractible one-periodic orbit of a\nHamiltonian diffeomorphism of a connected closed symplectic manifold\n$(M,\\omega)$ implies the existence of infinitely many non-contractible simple\nperiodic orbits, provided that the symplectic form $\\omega$ is aspherical and\nthe fundamental group $\\pi_1(M)$ is either a virtually abelian group or an\n$\\mathrm{R}$-group. We also show that a similar statement holds for Hamiltonian\ndiffeomorphisms of closed monotone or negative monotone symplectic manifolds\nunder the same conditions on their fundamental groups. These results generalize\nsome works by Ginzburg and G\\""urel. The proof uses the filtered Floer--Novikov\nhomology for non-contractible periodic orbits.\n', 'The action spectrum and C^0 symplectic topology   Our first main result states that the spectral norm on the group of\nHamiltonian diffeomorphisms, introduced in the works of Viterbo, Schwarz and\nOh, is continuous with respect to the C^0 topology, when M is symplectically\naspherical. This statement was previously proven only in the case of closed\nsurfaces. As a corollary, using a recent result of Kislev and Shelukhin, we\nobtain C^0 continuity of barcodes on aspherical symplectic manifolds, and\nfurthermore define barcodes for Hamiltonian homeomorphisms. We also present\nseveral applications to Hofer geometry and dynamics of Hamiltonian\nhomeomorphisms.\n  Our second main result is related to the Arnold conjecture about fixed points\nof Hamiltonian diffeomorphisms. The recent example of a Hamiltonian\nhomeomorphism, on any closed symplectic manifold of dimension greater than 2,\nhaving only one fixed point, shows that the conjecture does not admit a direct\ngeneralization to the C^0 setting. However, in this paper we demonstrate that a\nreformulation of the conjecture in terms of fixed points as well as spectral\ninvariants still holds for Hamiltonian homeomorphisms on symplectically\naspherical manifolds.\n', 'On the Hofer-Zehnder conjecture for non-contractible periodic orbits in\n  Hamiltonian dynamics   In this paper, we treat an open problem related to the number of periodic\norbits of Hamiltonian diffeomorphisms on closed symplectic manifolds.\nHofer-Zehnder conjecture states that a Hamiltonian diffeomorphisms has\ninfinitely many periodic orbits if it has ""homologically unnecessary periodic\norbits"""". For example, non-contractible periodic orbits are homologically\nunnecessary periodic orbits because Floer homology of non-contractible periodic\norbits is trivial. We prove Hofer-Zehnder conjecture for non-contractible\nperiodic orbits for very wide classes of symplectic manifolds.\n']","[('closed symplectic manifolds', 0.6713241338729858), ('symplectic homology', 0.6660773158073425), ('symplectic manifolds', 0.6654714941978455), ('hamiltonian diffeomorphisms', 0.6561568379402161), ('manifolds hamiltonian', 0.6475052237510681), ('closed symplectic manifold', 0.64234858751297), ('symplectic topology', 0.6389654278755188), ('symplectic manifold', 0.6373451948165894), ('group hamiltonian diffeomorphisms', 0.6334617733955383), ('manifold hamiltonian', 0.6241819262504578)]"
330,330,88,330_secrecy capacity_covert communications_secrecy rate_secrecy constraint,"['secrecy capacity', 'covert communications', 'secrecy rate', 'secrecy constraint', 'covert communication', 'wiretap channels', 'strong secrecy', 'secrecy', 'wiretap channel', 'wiretap coding']","['The Secrecy Capacity of The Gaussian Wiretap Channel with Rate-Limited\n  Help   The Gaussian wiretap channel with rate-limited help, available at the\nlegitimate receiver (Rx) or/and transmitter (Tx), is studied under various\nchannel configurations (degraded, reversely degraded and non-degraded). In the\ncase of Rx help and all channel configurations, the rate-limited help results\nin a secrecy capacity boost equal to the help rate irrespective of whether the\nhelp is secure or not, so that the secrecy of help does not provide any\ncapacity increase. The secrecy capacity is positive for the reversely-degraded\nchannel (where the no-help secrecy capacity is zero) and no wiretap coding is\nneeded to achieve it. More noise at the legitimate receiver can sometimes\nresult in higher secrecy capacity. The secrecy capacity with Rx help is not\nincreased even if the helper is aware of the message being transmitted. The\nsame secrecy capacity boost also holds if non-secure help is available to the\ntransmitter (encoder), in addition to or instead of the same Rx help, so that,\nin the case of the joint Tx/Rx help, one help link can be omitted without\naffecting the capacity. If Rx/Tx help links are independent of each other, then\nthe boost in the secrecy capacity is the sum of help rates and no link can be\nomitted without a loss in the capacity. Non-singular correlation of the\nreceiver and eavesdropper noises does not affect the secrecy capacity and\nnon-causal help does not bring in any capacity increase over the causal one.\n', 'Probabilistic Shaped Multilevel Polar Coding for Wiretap Channel   A wiretap channel is served as the fundamental model of physical layer\nsecurity techniques, where the secrecy capacity of the Gaussian wiretap channel\nis proven to be achieved by Gaussian input. However, there remains a gap\nbetween the Gaussian secrecy capacity and the secrecy rate with conventional\nuniformly distributed discrete constellation input, e.g. amplitude shift keying\n(ASK) and quadrature amplitude modulation (QAM). In this paper, we propose a\nprobabilistic shaped multilevel polar coding scheme to bridge the gap.\nSpecifically, the input distribution optimization problem for maximizing the\nsecrecy rate with ASK/QAM input is solved. Numerical results show that the\nresulting sub-optimal solution can still approach the Gaussian secrecy\ncapacity. Then, we investigate the polarization of multilevel polar codes for\nthe asymmetric discrete memoryless wiretap channel, and thus propose a\nmultilevel polar coding scheme integration with probabilistic shaping. It is\nproved that the scheme can achieve the secrecy capacity of the Gaussian wiretap\nchannel with discrete constellation input, and satisfies the reliability\ncondition and weak security condition. A security-oriented polar code\nconstruction method to natively satisfies the leakage-based security condition\nis also investigated. Simulation results show that the proposed scheme achieves\nmore efficient and secure transmission than the uniform constellation input\ncase over both the Gaussian wiretap channel and the Rayleigh fading wiretap\nchannel.\n', 'Finite-Length Analysis of Polar Secrecy Codes for Wiretap Channels   In a classical wiretap channel setting, Alice communicates with Bob through a\nmain communication channel, while her transmission also reaches an eavesdropper\nEve through a wiretap channel. In this paper, we consider a general class of\npolar secrecy codes for wiretap channels and study their finite-length\nperformance. In particular, bounds on the normalized mutual information\nsecurity (MIS) leakage, a fundamental measure of secrecy in\ninformation-theoretic security frameworks, are presented for polar secrecy\ncodes. The bounds are utilized to characterize the finite-length scaling\nbehavior of polar secrecy codes, where scaling here refers to the\nnon-asymptotic behavior of both the gap to the secrecy capacity as well as the\nMIS leakage. Furthermore, the bounds are shown to facilitate characterizing\nnumerical bounds on the secrecy guarantees of polar secrecy codes in finite\nblock lengths of practical relevance, where directly calculating the MIS\nleakage is in general infeasible.\n']","[('secrecy capacity', 0.6716724634170532), ('covert communications', 0.6125853657722473), ('secrecy rate', 0.5963102579116821), ('secrecy constraint', 0.5915680527687073), ('covert communication', 0.5891890525817871), ('wiretap channels', 0.5684724450111389), ('strong secrecy', 0.5661767721176147), ('secrecy', 0.5582508444786072), ('wiretap channel', 0.5511655211448669), ('wiretap coding', 0.545809805393219)]"
331,331,87,331_trajectory optimization_trajectory optimization problems_optimal trajectory_trajectory generation,"['trajectory optimization', 'trajectory optimization problems', 'optimal trajectory', 'trajectory generation', 'trajectory design', 'trajectory planning', 'optimal trajectories', 'low thrust', 'maneuvers', 'trajectory']","['Optimization, guidance, and control of low-thrust transfers from the\n  Lunar Gateway to low lunar orbit   The Gateway will represent a primary space system useful for the Artemis\nprogram, Earth-Moon transportation, and deep space exploration. It is expected\nto serve as a staging location on the way to the lunar surface. This study\nfocuses on low-thrust transfer dynamics, from the Near-Rectilinear Halo Orbit\ntraveled by Gateway to a specified Low-altitude Lunar Orbit (LLO). This\nresearch addresses: (i) determination of the minimum-time low-thrust trajectory\nand (ii) design, implementation, and testing of a guidance and control\narchitecture, for a space vehicle that travels from Gateway to LLO. Orbit\ndynamics is described in terms of modified equinoctial elements, in the context\nof a high-fidelity ephemeris model. The minimum-time trajectory from Gateway to\na specified lunar orbit is detected through an indirect heuristic approach,\nwhich uses the analytical conditions arising in optimal control theory in\nconjunction with a heuristic technique. However, future missions will pursue a\ngrowing level of autonomy, and this circumstance implies the mandatory design\nof an efficient feedback guidance scheme, capable of compensating for\nnonnominal flight conditions. This research proposes nonlinear orbit control as\na viable option for autonomous explicit guidance of low-thrust transfers from\nGateway to LLO. This approach allows defining a feedback law that enjoys\nquasi-global stability properties without requiring any offline reference\ntrajectory. The overall spacecraft dynamics is modeled including attitude\ncontrol and actuation. The latter is demanded to an array of reaction wheels,\narranged in a pyramidal configuration. Guidance, attitude control, and\nactuation are implemented in an iterative scheme. Monte Carlo simulations\ndemonstrate that the guidance and control architecture is effective with random\nstarting points from Gateway and the temporary unavailability of the propulsion\nsystem.\n', 'Low-Thrust Many-Revolution Trajectory Design Under Operational\n  Uncertainties for DESTINY+ Mission   DESTINY+ is a planned JAXA medium-class Epsilon mission from Earth to deep\nspace using a low-thrust, many-revolution orbit. Such a trajectory design is a\nchallenging problem not only for trajectory design but also for flight\noperations, and in particular, it is essential to evaluate the impact of\noperational uncertainties to ensure mission success. In this study, we design\nthe low-thrust trajectory from Earth orbit to a lunar transfer orbit by\ndifferential dynamic programming using the Sundman transformation. The results\nof Monte Carlo simulations with operational uncertainties confirm that the\nspacecraft can be successfully guided to the lunar transfer orbit by using the\nfeedback control law of differential dynamic programming in the angular domain.\n', 'Low Thrust Trajectory Design Using A Semi-Analytic Approach   Space missions that use low-thrust propulsion technology are becoming\nincreasingly popular since they utilize propellant more efficiently and thus\nreduce mission costs. However, optimizing continuous-thrust trajectories is\ncomplex, time-consuming, and extremely sensitive to initial guesses. Hence,\ngenerating approximate trajectories that can be used as reliable initial\nguesses in trajectory generators is essential. This paper presents a\nsemi-analytic approach for designing planar and three-dimensional trajectories\nusing Hills equations. The spacecraft is assumed to be acted upon by a constant\nthrust acceleration magnitude. The proposed equations are employed in a\nNonlinear Programming Problem (NLP) solver to obtain the thrust directions.\nTheir applicability is tested for various design scenarios like orbit raising,\norbit insertion, and rendezvous. The trajectory solutions are then validated as\ninitial guesses in high-fidelity optimal control tools. The usefulness of this\nmethod lies in the preliminary stages of low-thrust mission design, where speed\nand reliability are key.\n']","[('trajectory optimization', 0.6290619373321533), ('trajectory optimization problems', 0.6089245676994324), ('optimal trajectory', 0.5911309719085693), ('trajectory generation', 0.5574852228164673), ('trajectory design', 0.5508931279182434), ('trajectory planning', 0.5438511371612549), ('optimal trajectories', 0.5097714066505432), ('low thrust', 0.4813888669013977), ('maneuvers', 0.43571776151657104), ('trajectory', 0.43401089310646057)]"
332,332,86,332_mathbb f_q__q finite field__q finite_f_q,"['mathbb f_q', '_q finite field', '_q finite', 'f_q', 'mathbb _q finite', 'finite fields', 'finite fields let', 'arbitrary finite fields', 'distance finite', 'subset mathbb _q']","[""Distribution of similar configurations in subsets of $\\mathbb{F}_q^d$   Let $\\mathbb{F}_q$ be a finite field of order $q$ and $E$ be a set in\n$\\mathbb{F}_q^d$. The distance set of $E$ is defined by $\\Delta(E):=\\{\\lVert\nx-y \\rVert :x,y\\in E\\}$, where $\\lVert \\alpha\n\\rVert=\\alpha_1^2+\\dots+\\alpha_d^2$. Iosevich, Koh and Parshall (2018) proved\nthat if $d\\geq 2$ is even and $|E|\\geq 9q^{d/2}$, then $$\\mathbb{F}_q=\n\\frac{\\Delta(E)}{\\Delta(E)}=\\left\\{\\frac{a}{b}: a\\in \\Delta(E),\\ b\\in\n\\Delta(E)\\setminus\\{0\\} \\right\\}.$$ In other words, for each $r\\in\n\\mathbb{F}_q^*$ there exist $(x,y)\\in E^2$ and $(x',y')\\in E^2$ such that\n$\\lVert x-y\\rVert\\neq0$ and $\\lVert x'-y' \\rVert=r\\lVert x-y\\rVert$.\n  Geometrically, this means that if the size of $E$ is large, then for any\ngiven $r \\in \\mathbb{F}_q^*$ we can find a pair of edges in the complete graph\n$K_{|E|}$ with vertex set $E$ such that one of them is dilated by $r\\in\n\\mathbb{F}_q^*$ with respect to the other. A natural question arises whether it\nis possible to generalize this result to arbitrary subgraphs of $K_{|E|}$ with\nvertex set $E$ and this is the goal of this paper.\n  In this paper, we solve this problem for $k$-paths $(k\\geq 2)$, simplexes and\n4-cycles. We are using a mix of tools from different areas such as enumerative\ncombinatorics, group actions and Tur\\'an type theorems.\n"", 'Near optimal thresholds for existence of dilated configurations in\n  $\\mathbb{F}_q^d$   Let $E\\subset\\mathbb{F}_q^d$ and $\\lVert \\cdot \\rVert:\\mathbb{F}_q^d\\to\n\\mathbb{F}_q$ defined as $\\lVert \\alpha\\rVert:= \\alpha_1^2+\\dots+\\alpha_d^2$ if\n$\\alpha=(\\alpha_1,\\dots,\\alpha_d)\\in \\mathbb{F}_q^d$, where $\\mathbb{F}_q^d$ is\nthe $d$-dimensional vector space over the finite field $\\mathbb{F}_q$ with $q$\nelements. Let $k\\geq 1$ and $A$ is a nonempty subset of $\\{(i,j):1\\leq i<j\\leq\nk+1\\}$. In this paper, we prove that for any nonzero square element $r\\in\n\\mathbb{F}_q$ and $\\lvert E\\rvert\\gg_kq^{d/2}$ one can find two $(k+1)$-tuples\nin $E$ such that one of them is dilated by $r$ with respect to the other only\non $|A|$ edges. More precisely, there exist $(x_1,\\dots,x_{k+1})\\in E^{k+1}$\nand $(y_1,\\dots,y_{k+1})\\in E^{k+1}$ such that $\\lVert y_i-y_j\\rVert=r\\lVert\nx_i-x_j\\rVert$ if $(i,j)\\in A$ and $x_i\\neq x_j, y_i\\neq y_j$ if $1\\leq i<j\\leq\nk+1$. In particular, we present two proofs first of which utilizes the\nmachinery of group actions which is typically used to handle problems of this\nnature, whereas the second one is more combinatorial in nature and is based on\nthe averaging argument. Moreover, we show that in two dimensions the threshold\n$d/2$ is sharp when $q\\equiv 3 \\pmod 4$.\n  As a corollary of this result, varying the underlying set $A$ we obtain\nthresholds for existence of dilated $k$-paths, $k$-cycles, and $k$-stars\n$(k\\geq 3)$. These results partly generalize some results of the second author.\n', 'Group Action Approaches in Erdos Quotient Set Problem   Let $\\mathbb{F}_q$ denote the finite field of $q$ elements. For $E \\subset\n\\mathbb{F}_q^d$, denote the distance set $\\Delta(E)= \\{\\|x-y\\|^2:=(x_1-y_1)^2+\n\\cdots + (x_d-y_d)^2 : (x,y)\\in E^2 \\}$.\n  The Erdos quotient set problem was introduced in \\cite{Iosevich_2019} where\nit was shown that for even $d\\geq2$ that if $|E| \\subset \\mathbb{F}_q^2$ such\nthat $|E| >> q^{d/2}$, then $\\frac{\\Delta(E)}{\\Delta(E)}:= \\{\\frac{s}{t}:s,t\n\\in \\Delta(E), t\\not=0\\} =\\mathbb{F}_q^d$. The proof of the latter result is\nquite sophisticated and in \\cite{pham2023group}, a simple proof using a\ngroup-action approach was obtained for the case of $q \\equiv 3 \\mod 4$ when\n$d=2$. In the $q \\equiv 3 \\mod 4$ setting, for each $r \\in (\\mathbb{F}_q)^2$,\n\\cite{pham2023group} showed if $E \\subset \\mathbb{F}_q$, then $V(r):= \\#\n\\left\\{ (a,b,c,d) \\in E^2: \\frac{\\|a-b\\|^2}{\\|c-d\\|^2} = r \\right\\} >>\n\\frac{|E|^4}{q}$. In this work we use group action techniques in the $q \\equiv\n3 \\mod 4$ setting, for $d=2$ and improve the results of \\cite{pham2023group} by\nremoving the assumption on $r \\in (\\mathbb{F}_q)^2$. Specifically we show if\n$d=2$ and $q \\equiv 3 \\mod 4$, then for each $r \\in \\mathbb{F}_q^*$,$V(r)\\geq\n\\frac{|E|^4}{2q}$if $|E|\\geq \\sqrt{2}q$ for all $r \\in \\mathbb{F}_q$. Finally,\nwe improve the main result of \\cite{bhowmik2023near} using our proof techniques\nfrom our quotient set results.\n']","[('mathbb f_q', 0.48961204290390015), ('_q finite field', 0.471306174993515), ('_q finite', 0.40679532289505005), ('f_q', 0.3945041596889496), ('mathbb _q finite', 0.37346774339675903), ('finite fields', 0.3721294701099396), ('finite fields let', 0.3675437569618225), ('arbitrary finite fields', 0.36215081810951233), ('distance finite', 0.35219624638557434), ('subset mathbb _q', 0.3502488136291504)]"
333,333,86,333_painlev equations_equations painlev_painlev transcendents_painlev transcendent,"['painlev equations', 'equations painlev', 'painlev transcendents', 'painlev transcendent', 'solutions painlev', 'painlev type', 'associated painlev', 'discrete painlev', 'form painlev', 'painlev iii']","['Algebraic relations between solutions of Painlev\\\'e equations   In this manuscript we make major progress classifying algebraic relations\nbetween solutions of Painlev\\\'e equations. Our main contribution is to\nestablish the algebraic independence of solutions of various pairs of equations\nin the Painlev\\\'e families; for generic coefficients, we show all algebraic\nrelations between solutions of equations in the same Painlev\\\'e family come\nfrom classically studied B{\\""a}cklund transformations. We also apply our\nanalysis of ranks to establish some transcendence results for pairs of\nPainlev\\\'e equations from different families. In that area, we answer several\nopen questions of Nagloo (2016), and in the process answer a question of Boalch\n(2012).\n  We calculate model theoretic ranks of all Painlev\\\'e equations in this\narticle, extending results of Nagloo and Pillay (2017). We show that the type\nof the generic solution of any equation in the second Painlev\\\'e family is\ngeometrically trivial, extending a result of Nagloo (2015). We give the first\nmodel theoretic analysis of several special families of the third Painlev\\\'e\nequation, proving results analogous to Nagloo and Pillay (2017). We also give a\nnovel new proof of the irreducibility of the third, fifth and sixth Painlev\\\'e\nequations using recent work of Freitag, Jaoui, and Moosa (2022). Our proof is\nfundamentally different than the existing transcendence proofs of Watanabe\n(1998) or Cantat and Loray (2009).\n', ""On existence and properties of roots of third Painlev\\'e' transcendents   A closed proof of existence of solutions to third Painlev\\'e' equation\n(Painlev\\'e' transcendents) vanishing at arbitrary given point distinct from\nzero is presented. The structure of the set of Painlev\\'e' transcendents with\ncommon parameters vanishing at a given point is described. The approximate\nexplicit representation of a Painlev\\'e' transcendent in vicinity of its\nnon-zero root is given.\n"", 'The wild monodromy of the Fifth Painlev\\\'e equation and its action on\n  wild character variety: an approach of confluence   The article studies the Fifth Painlev\\\'e equation and of the nonlinear Stokes\nphenomenon at its irregular singularity at infinity from the point of view of\nconfluence from the Sixth Painlev\\\'e equation. This approach is developped\nseparately on both sides of the Riemann-Hilbert correspondance. On the side of\nthe nonlinear Painlev\\\'e-Okamoto foliation the relation between the nonlinear\nmonodromy group of Painlev\\\'e VI and the ""nonlinear wild monodromy pseudogroup""\nof Painlev\\\'e V (that is the pseudogroup generated by nonlinear monodromy,\nnonlinear Stokes operators and nonlinear exponential torus) is explained in\ndetail. On the side of the corresponding linear isomonodromic problem, the\n""wild"" character variety (the space of the linear monodromy and Stokes data)\nassociated to Painlev\\\'e V is constructed through a birational transformation\nfrom the character variety (the space of the linear monodromy data) associated\nto Painlev\\\'e VI. This allows to transport the known description of the action\nof the nonlinear monodromy of Painlev\\\'e VI on its character variety to that of\nPainlev\\\'e V, and to provide explicit formulas for the action of the ""nonlinear\nwild monodromy"" of Painlev\\\'e V on its character variety.\n']","[('painlev equations', 0.7022639513015747), ('equations painlev', 0.6645783185958862), ('painlev transcendents', 0.6579515337944031), ('painlev transcendent', 0.600229024887085), ('solutions painlev', 0.5781053900718689), ('painlev type', 0.5595130324363708), ('associated painlev', 0.5346900820732117), ('discrete painlev', 0.5261051058769226), ('form painlev', 0.5180874466896057), ('painlev iii', 0.5085399746894836)]"
334,334,86,334_nematic liquid crystals_nematic liquid crystal_liquid crystals_liquid crystal,"['nematic liquid crystals', 'nematic liquid crystal', 'liquid crystals', 'liquid crystal', 'nematic liquid', 'solutions landau', 'crystalline', 'crystals', 'nematic', 'crystal']","['Existence of minimizers and convergence of critical points for a new\n  Landau-de Gennes energy functional in nematic liquid crystals   The Landau-de Gennes energy in nematic liquid crystals depends on four\nelastic constants $L_1$, $L_2$, $L_3$, $L_4$. In the case of $L_4\\neq 0$, Ball\nand Majumdar (Mol. Cryst. Liq. Cryst., 2010) found an example that the original\nLandau-de Gennes energy functional in physics does not satisfy a coercivity\ncondition, which causes a problem in mathematics to establish existence of\nenergy minimizers. At first, we introduce a new Landau-de Gennes energy density\nwith $L_4\\neq 0$, which is equivalent to the original Landau-de Gennes density\nfor uniaxial tensors and satisfies the coercivity condition for all\n$Q$-tensors. Secondly, we prove that solutions of the Landau-de Gennes system\ncan approach a solution of the $Q$-tensor Oseen-Frank system without using\nenergy minimizers. Thirdly, we develop a new approach to generalize the Nguyen\nand Zarnescu (Calc. Var. PDEs, 2013) convergence result to the case of non-zero\nelastic constants $L_2$, $L_3$, $L_4$.\n', 'Bayesian Parameter Identification in the Landau-de Gennes Theory for\n  Nematic Liquid Crystals   This manuscript establishes a pathway to reconstruct material parameters from\nmeasurements within the Landau-de Gennes model for nematic liquid crystals. We\npresent a Bayesian approach to this inverse problem and analyse its properties\nusing given, simulated data for benchmark problems of a planar bistable nematic\ndevice. In particular, we discuss the accuracy of the Markov chain Monte Carlo\napproximations, confidence intervals and the limits of identifiability.\n', 'A new representation for the Landau-de Gennes energy of nematic liquid\n  crystals   In the Landau-de Gennes theory on nematic liquid crystals, the well-known\nLandau-de Gennes energy depends on four elastic constants; $L_1$, $L_2$, $L_3$,\n$L_4$. For the general case of $L_4\\neq 0$, Ball-Majumdar \\cite {BM} found an\nexample that the Landau-de Gennes energy functional from physics literature\n\\cite{MN} does not satisfy a coercivity condition, which causes a problem in\nmathematics to establish existence of energy minimizers. In order to solve this\nproblem, we observe that the original third order term on $L_4$, proposed by\nSchiele and Trimper \\cite{ST} in physics, is a linear combination of a fourth\norder term and a second order term. Therefore, we can propose a new Landau-de\nGennes energy, which is equal to the original for uniaxial nematic $Q$-tensors.\nThe new Landau-de Gennes energy with general elastic constants satisfies the\ncoercivity condition for all $Q$-tensors, which establishes a new link between\nmathematical and physical theory. Similarly to the work of Majumdar-Zarnescu\n\\cite{MZ}, we prove existence and convergence of minimizers of the new\nLandau-de Gennes energy. Moreover, we find a new way to study the limiting\nproblem of the Landau-de Gennes system since the cross product method\n\\cite{Chen} on the Ginzburg-Landau equation does not work for the Landau-de\nGennes system.\n']","[('nematic liquid crystals', 0.59190434217453), ('nematic liquid crystal', 0.5760822892189026), ('liquid crystals', 0.49979567527770996), ('liquid crystal', 0.4724924564361572), ('nematic liquid', 0.44954049587249756), ('solutions landau', 0.41055426001548767), ('crystalline', 0.37830814719200134), ('crystals', 0.37492871284484863), ('nematic', 0.3473326563835144), ('crystal', 0.34525105357170105)]"
335,335,86,335_resonant frequencies_resonant modes_wave scattering_resonators,"['resonant frequencies', 'resonant modes', 'wave scattering', 'resonators', 'electromagnetic waves', 'metamaterials', 'sub wavelength', 'resonant states', 'resonances', 'metamaterial']","[""Mathematical theory on multi-layer high contrast acoustic subwavelength\n  resonators   Subwavelength resonance is a vital acoustic phenomenon in contrasting media.\nThe narrow bandgap width of single-layer resonator has prompted the exploration\nof multi-layer metamaterials as an effective alternative, which consist of\nalternating nests of high-contrast materials, called ``resonators'', and a\nbackground media. In this paper, we develop a general mathematical framework\nfor studying acoustics within multi-layer high-contrast structures. Firstly, by\nusing layer potential techniques, we establish the representation formula in\nterms of a matrix type operator with a block tridiagonal form for multi-layer\nstructures within general geometry. Then we prove the existence of\nsubwavelength resonances via Gohberg-Sigal theory, which generalizes the\ncelebrated Minnaert resonances in single-layer structures. Intriguingly, we\nfind that the primary contribution to mode splitting lies in the fact that as\nthe number of nested resonators increases, the degree of the corresponding\ncharacteristic polynomial also increases, while the type of resonance (consists\nsolely of monopolar resonances) remains unchanged. Furthermore, we derive\noriginal formulas for the subwavelength resonance frequencies of concentric\ndual-resonator. Numerical results associated with different nested resonators\nare presented to corroborate the theoretical findings.\n"", 'From all-dieletric nanoresonators to extended quasi-static plasmonic\n  resonators   We derive the electromagnetic medium equivalent to a cluster of\nall-dielectric nanoparticles (i.e. enjoying high refractive indices),\ndistributed periodically in a smooth domain $\\Omega$, while excited at nearly\nresonating dielectric incident frequencies (i.e. subwavelength Mie-resonant\nfrequencies). This effective medium is an alteration of the permeability that\nkeeps the permittivity unchanged. We provide regimes under which the effective\npermeability can be positive or negative valued. In addition, if the incident\nfrequency is close to any of the subwavelength all-dielectric resonances, then\nthe distributed cluster behaves as an extended quasi-static plasmonic\nresonator. Therefore, exciting the cluster of all-dielectric nanoresonators\nwith nearly resonating incident frequencies, we can generate an extended\nquasi-static plasmonic resonator which creates giant electromagnetic fields in\nits surrounding.\n', 'The interaction between two close-to-touching convex acoustic\n  subwavelength resonators   The Minneart resonance is a low frequency resonance in which the wavelength\nis much larger than the size of the resonators. It is interesting to study the\ninteraction between two adjacent bubbles when they are brought close together.\nBecause the bubbles are usually compressible, in this paper we mainly\ninvestigate resonant modes of two general convex resonators with arbitrary\nshapes to extend the results of Ammari, Davies, Yu in [4], where a pair of\nspherical resonators are considered by using bispherical coordinates. We\ncombine the layer potential method for Helmholtz equation in [4,5] and the\nelliptic theory for gradient estimates in [26,30] to calculate the capacitance\ncoefficients for the coupled $C^{2,\\alpha}$ resonators, then show the\nleading-order asymptotic behaviors of two different resonant modes and reveal\nthe dependance of the resonant frequencies on their geometric properties, such\nas convexity, volumes and curvatures. By the way, the blow-up rates of gradient\nof the scattered pressure are also presented.\n']","[('resonant frequencies', 0.5760574340820312), ('resonant modes', 0.5578566789627075), ('wave scattering', 0.4727904498577118), ('resonators', 0.4530487060546875), ('electromagnetic waves', 0.445627361536026), ('metamaterials', 0.434452086687088), ('sub wavelength', 0.43205130100250244), ('resonant states', 0.42991235852241516), ('resonances', 0.4143017828464508), ('metamaterial', 0.40731197595596313)]"
336,336,86,336_gromov hyperbolic spaces_gromov hyperbolic space_hyperbolic spaces_gromov hyperbolicity,"['gromov hyperbolic spaces', 'gromov hyperbolic space', 'hyperbolic spaces', 'gromov hyperbolicity', 'hyperbolic metric', 'metric hyperbolic', 'hyperbolic space', 'gromov hyperbolic', 'gromov hausdorff distance', 'metric gromov']","['A Gromov Hyperbolic metric and M\\""obius transformations   We compare a Gromov hyperbolic metric with the hyperbolic metric in the unit\nball or in the upper half space, and prove sharp comparison inequalities\nbetween the Gromov hyperbolic metric and some hyperbolic type metrics. We also\nobtain several sharp distortion inequalities for the Gromov hyperbolic metric\nunder some families of M\\""{o}bius transformations.\n', 'Gromov-Hausdorff convergence of maximal Gromov hyperbolic spaces and\n  their boundaries   The relation between negatively curved spaces and their boundaries is\nimportant for various rigidity problems. In \\cite{biswas2024quasi}, the class\nof Gromov hyperbolic spaces called maximal Gromov hyperbolic spaces was\nintroduced, and the boundary functor $X \\mapsto \\partial X$ was shown to give\nan equivalence of categories between maximal Gromov hyperbolic spaces (with\nmorphisms being isometries) and a class of compact quasi-metric spaces called\nquasi-metric antipodal spaces (with morphisms being Moebius homeomorphisms).\nThe proof of this equivalence involved the construction of a filling functor $Z\n\\mapsto {\\mathcal M}(Z)$, associating to any quasi-metric antipodal space $Z$ a\nmaximal Gromov hyperbolic space ${\\mathcal M}(Z)$.\n  We study the ``continuity"" properties of the boundary and filling functors.\nWe show that convergence of a sequence of quasi-metric antipodal spaces (in a\ncertain sense called ``almost-isometric convergence"") implies convergence (in\nthe Gromov-Hausdorff sense) of the associated maximal Gromov hyperbolic spaces.\nConversely, we show that convergence of maximal Gromov hyperbolic spaces\ntogether with a natural hypothesis of ``equicontinuity"" on the boundaries\nimplies convergence of boundaries. We use this to show that Gromov-Hausdorff\nconvergence of a sequence of proper, geodesically complete CAT(-1) spaces\nimplies Gromov-Hausdorff convergence of their boundaries equipped with visual\nmetrics. We also show that convergence of maximal Gromov hyperbolic spaces to a\nmaximal Gromov hyperbolic space with finite boundary implies convergence of\nboundaries.\n', 'Sphericalization with its applications in Gromov hyperbolic spaces   In this paper, we study certain applications of sphericalization in Gromov\nhyperbolic metric spaces. We first show that the doubling property regarding\ntwo classes of metrics on the Gromov boundary of hyperbolic spaces are\ncoincided. Next, we obtain a characterization of unbounded Gromov hyperbolic\ndomains via metric spaces sphericalization. Finally, we investigate the\ntopological equivalence of Gromov hyperbolic $\\varphi$-uniform domains between\nthe Gromov boundary and the inner metric boundary.\n']","[('gromov hyperbolic spaces', 0.8211418986320496), ('gromov hyperbolic space', 0.7949934601783752), ('hyperbolic spaces', 0.7304816842079163), ('gromov hyperbolicity', 0.7281255125999451), ('hyperbolic metric', 0.7228191494941711), ('metric hyperbolic', 0.7121182084083557), ('hyperbolic space', 0.7011472582817078), ('gromov hyperbolic', 0.678946852684021), ('gromov hausdorff distance', 0.6280235052108765), ('metric gromov', 0.608828604221344)]"
337,337,86,337_zeros random polynomials_random polynomials_polynomials random_random polynomial,"['zeros random polynomials', 'random polynomials', 'polynomials random', 'random polynomial', 'roots polynomials', 'kac polynomials', 'distribution roots', 'polynomials gaussian', 'asymptotics', 'gaussian coefficients']","['Real roots of random polynomials with coefficients of polynomial growth:\n  a comparison principle and applications   This paper seeks to further explore the distribution of the real roots of\nrandom polynomials with non-centered coefficients. We focus on polynomials\nwhere the typical values of the coefficients have power growth and count the\naverage number of real zeros. Almost all previous results require coefficients\nwith zero mean, and it is non-trivial to extend these results to the general\ncase. Our approach is based on a novel comparison principle that reduces the\ngeneral situation to the mean-zero setting. As applications, we obtain new\nresults for the Kac polynomials, hyperbolic random polynomials, their\nderivatives, and generalizations of these polynomials. The proof features new\nlogarithmic integrability estimates for random polynomials (both local and\nglobal) and fairly sharp estimates for the local number of real zeros.\n', 'Real roots of random polynomials: asymptotics of the variance   We compute the precise leading asymptotics of the variance of the number of\nreal roots for a large class of random polynomials, where the random\ncoefficients have polynomial growth. Our results apply to many classical\nensembles, including the Kac polynomials, hyperbolic polynomials, their\nderivatives, and any linear combinations of these polynomials. Prior to this\npaper, such asymptotics was only established for the Kac polynomials in the\n1970s, with the seminal contribution of Maslova. The main ingredients of the\nproof are new asymptotic estimates for the two-point correlation function of\nthe real roots, revealing geometric structures in the distribution of the real\nroots of these random polynomials. As a corollary, we obtain asymptotic\nnormality for the real roots for these random polynomials, extending and\nstrengthening a related result of O. Nguyen and V. Vu.\n', ""Random polynomials: central limit theorems for the real roots   The number of real roots has been a central subject in the theory of random\npolynomials and random functions since the fundamental papers of\nLittlewood-Offord and Kac in the 1940s. The main task here is to determine the\nlimiting distribution of this random variable.\n  In 1974, Maslova famously proved a central limit theorem (CLT) for the number\nof real roots of Kac polynomials. It has remained the only limiting theorem\navailable for the number of real roots for more than four decades.\n  In this paper, using a new approach, we derive a general CLT for the number\nof real roots of a large class of random polynomials with coefficients growing\npolynomially. Our result both generalizes and strengthens Maslova's theorem.\n""]","[('zeros random polynomials', 0.6439638137817383), ('random polynomials', 0.6188182830810547), ('polynomials random', 0.5634115934371948), ('random polynomial', 0.5495743155479431), ('roots polynomials', 0.5032581686973572), ('kac polynomials', 0.49521946907043457), ('distribution roots', 0.48071083426475525), ('polynomials gaussian', 0.46819230914115906), ('asymptotics', 0.4247668981552124), ('gaussian coefficients', 0.4169030785560608)]"
338,338,86,338_quasilinear elliptic equations_sobolev orlicz_orlicz sobolev spaces_orlicz sobolev,"['quasilinear elliptic equations', 'sobolev orlicz', 'orlicz sobolev spaces', 'orlicz sobolev', 'quasilinear elliptic', 'semilinear elliptic', 'musielak orlicz sobolev', 'multiplicity positive solutions', 'double phase', 'singular solutions']","['Positive solutions for singular double phase problems   We study the existence of positive solutions for a class of double phase\nDirichlet equations which have the combined effects of a singular term and of a\nparametric superlinear term. The differential operator of the equation is the\nsum of a $p$-Laplacian and of a weighted $q$-Laplacian ($q<p$) with\ndiscontinuous weight. Using the Nehari method, we show that for all small\nvalues of the parameter $\\lambda>0$, the equation has at least two positive\nsolutions.\n', 'Parametric superlinear double phase problems with singular term and\n  critical growth on the boundary   In this paper we study quasilinear elliptic equations driven by the double\nphase operator along with a reaction that has a singular and a parametric\nsuperlinear term and with a nonlinear Neumann boundary condition of critical\ngrowth. Based on a new equivalent norm for Musielak-Orlicz Sobolev spaces and\nthe Nehari manifold along with the fibering method we prove the existence of at\nleast two weak solutions provided the parameter is sufficiently small.\n', 'A new class of anisotropic double phase problems: exponents depending on\n  solutions and their gradients   In this work, we introduce two novel classes of quasilinear elliptic\nequations, each driven by the double phase operator with variable exponents.\nThe first class features a new double phase equation where exponents depend on\nthe gradient of the solution. We delve into proving various properties of the\ncorresponding Musielak-Orlicz Sobolev spaces, including the $\\Delta_2$\nproperty, uniform convexity, density and compact embedding. Additionally, we\nexplore the characteristics of the new double phase operator, such as\ncontinuity, strict monotonicity, and the (S$_+$)-property. Employing both\nvariational and nonvariational methods, we establish the existence of solutions\nfor this inaugural class of double phase equations. In the second category, the\ntreatment of exponents is dependent on the solution itself. This class differs\nfrom the first one due to the unavailability of suitable Musielak-Orlicz\nSobolev spaces. For this reason, we employ a perturbation argument that leads\nto the classical double phase class. These two new classes highlight how\ndifferent physical processes like the movement of special fluids through porous\nmaterials, phase changes, and fluid dynamics interact with each other. Our\nresults are novel in this context and includes a self-contained techniques.\n']","[('quasilinear elliptic equations', 0.5306101441383362), ('sobolev orlicz', 0.5152391195297241), ('orlicz sobolev spaces', 0.5035319924354553), ('orlicz sobolev', 0.4958511292934418), ('quasilinear elliptic', 0.483857125043869), ('semilinear elliptic', 0.46725597977638245), ('musielak orlicz sobolev', 0.46237000823020935), ('multiplicity positive solutions', 0.45546966791152954), ('double phase', 0.4536304473876953), ('singular solutions', 0.4430954158306122)]"
339,339,86,339_optimized schwarz methods_helmholtz equations_schwarz methods_methods helmholtz,"['optimized schwarz methods', 'helmholtz equations', 'schwarz methods', 'methods helmholtz', 'helmholtz problems', 'schwarz preconditioners', 'heterogeneous helmholtz', 'high frequency helmholtz', 'finite element discretisations', 'domain decomposition methods']","['Convergence of overlapping domain decomposition methods with PML\n  transmission conditions applied to nontrapping Helmholtz problems   We study overlapping Schwarz methods for the Helmholtz equation posed in any\ndimension with large, real wavenumber and smooth variable wave speed. The\nradiation condition is approximated by a Cartesian perfectly-matched layer\n(PML). The domain-decomposition subdomains are overlapping hyperrectangles with\nCartesian PMLs at their boundaries. The overlaps of the subdomains and the\nwidths of the PMLs are all taken to be independent of the wavenumber.\n  For both parallel (i.e., additive) and sequential (i.e., multiplicative)\nmethods, we show that after a specified number of iterations -- depending on\nthe behaviour of the geometric-optic rays -- the error is smooth and smaller\nthan any negative power of the wavenumber. For the parallel method, the\nspecified number of iterations is less than the maximum number of subdomains,\ncounted with their multiplicity, that a geometric-optic ray can intersect.\n  These results, which are illustrated by numerical experiments, are the first\nwavenumber-explicit results about convergence of overlapping Schwarz methods\nfor the Helmholtz equation, and the first wavenumber-explicit results about\nconvergence of any domain-decomposition method for the Helmholtz equation with\na non-trivial scatterer (here a variable wave speed).\n', 'Two-level hybrid Schwarz Preconditioners for The Helmholtz Equation with\n  high wave number   In this work, we propose and analyze two two-level hybrid Schwarz\npreconditioners for solving the Helmholtz equation with high wave number in two\nand three dimensions. Both preconditioners are defined over a set of\noverlapping subdomains, with each preconditioner formed by a global coarse\nsolver and one local solver on each subdomain. The global coarse solver is\nbased on the localized orthogonal decomposition (LOD) technique, which was\nproposed in [30,31] originally for the discretization schemes for elliptic\nmultiscale problems with heterogeneous and highly oscillating coefficients and\nHelmholtz problems with high wave number to eliminate the pollution effect. The\nlocal subproblems are Helmholtz problems in subdomains with homogeneous\nboundary conditions (the first preconditioner) or impedance boundary conditions\n(the second preconditioner). Both preconditioners are shown to be optimal under\nsome reasonable conditions, that is, a uniform upper bound of the\npreconditioned operator norm and a uniform lower bound of the field of values\nare established in terms of all the key parameters, such as the fine mesh size,\nthe coarse mesh size, the subdomain size and the wave numbers. It is the first\ntime to show that the LOD solver can be a very effective coarse solver when it\nis used appropriately in the Schwarz method with multiple overlapping\nsubdomains. Numerical experiments are presented to confirm the optimality and\nefficiency of the two proposed preconditioners.\n', 'Convergence theory for two-level hybrid Schwarz preconditioners for\n  high-frequency Helmholtz problems   We give a novel convergence theory for two-level hybrid Schwarz\ndomain-decomposition (DD) methods for finite-element discretisations of the\nhigh-frequency Helmholtz equation. This theory gives sufficient conditions for\nthe preconditioned matrix to be close to the identity, and covers DD subdomains\nof arbitrary size, and arbitrary absorbing layers/boundary conditions on both\nthe global and local Helmholtz problems. The assumptions on the coarse space\nare satisfied by the approximation spaces using problem-adapted basis functions\nthat have been recently analysed as coarse spaces for the Helmholtz equation,\nas well as all spaces that are known to be quasi-optimal via a Schatz-type\nargument.\n  As an example, we apply this theory when the coarse space consists of\npiecewise polynomials; these are then the first rigorous convergence results\nabout a two-level Schwarz preconditioner applied to the high-frequency\nHelmholtz equation with a coarse space that does not consist of problem-adapted\nbasis functions.\n']","[('optimized schwarz methods', 0.6129418611526489), ('helmholtz equations', 0.5659035444259644), ('schwarz methods', 0.5560148358345032), ('methods helmholtz', 0.5517004728317261), ('helmholtz problems', 0.5374416708946228), ('schwarz preconditioners', 0.5252017378807068), ('heterogeneous helmholtz', 0.5033714771270752), ('high frequency helmholtz', 0.47463148832321167), ('finite element discretisations', 0.467978835105896), ('domain decomposition methods', 0.45804449915885925)]"
340,340,85,340_graph neural networks_graph neural_graph convolutional neural_graph convolutional networks,"['graph neural networks', 'graph neural', 'graph convolutional neural', 'graph convolutional networks', 'graph neural network', 'graph learning', 'neural networks graph', 'networks gnns', 'graph representation learning', 'learning graph']","[""Optimization of Graph Neural Networks: Implicit Acceleration by Skip\n  Connections and More Depth   Graph Neural Networks (GNNs) have been studied through the lens of expressive\npower and generalization. However, their optimization properties are less well\nunderstood. We take the first step towards analyzing GNN training by studying\nthe gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that\ndespite the non-convexity of training, convergence to a global minimum at a\nlinear rate is guaranteed under mild assumptions that we validate on real-world\ngraphs. Second, we study what may affect the GNNs' training speed. Our results\nshow that the training of GNNs is implicitly accelerated by skip connections,\nmore depth, and/or a good label distribution. Empirical results confirm that\nour theoretical results for linearized GNNs align with the training behavior of\nnonlinear GNNs. Our results provide the first theoretical support for the\nsuccess of GNNs with skip connections in terms of optimization, and suggest\nthat deep GNNs with skip connections would be promising in practice.\n"", 'GraphNorm: A Principled Approach to Accelerating Graph Neural Network\n  Training   Normalization is known to help the optimization of deep neural networks.\nCuriously, different architectures require specialized normalization methods.\nIn this paper, we study what normalization is effective for Graph Neural\nNetworks (GNNs). First, we adapt and evaluate the existing methods from other\ndomains to GNNs. Faster convergence is achieved with InstanceNorm compared to\nBatchNorm and LayerNorm. We provide an explanation by showing that InstanceNorm\nserves as a preconditioner for GNNs, but such preconditioning effect is weaker\nwith BatchNorm due to the heavy batch noise in graph datasets. Second, we show\nthat the shift operation in InstanceNorm results in an expressiveness\ndegradation of GNNs for highly regular graphs. We address this issue by\nproposing GraphNorm with a learnable shift. Empirically, GNNs with GraphNorm\nconverge faster compared to GNNs using other normalization. GraphNorm also\nimproves the generalization of GNNs, achieving better performance on graph\nclassification benchmarks.\n', ""On the Expressive Power of Geometric Graph Neural Networks   The expressive power of Graph Neural Networks (GNNs) has been studied\nextensively through the Weisfeiler-Leman (WL) graph isomorphism test. However,\nstandard GNNs and the WL framework are inapplicable for geometric graphs\nembedded in Euclidean space, such as biomolecules, materials, and other\nphysical systems. In this work, we propose a geometric version of the WL test\n(GWL) for discriminating geometric graphs while respecting the underlying\nphysical symmetries: permutations, rotation, reflection, and translation. We\nuse GWL to characterise the expressive power of geometric GNNs that are\ninvariant or equivariant to physical symmetries in terms of distinguishing\ngeometric graphs. GWL unpacks how key design choices influence geometric GNN\nexpressivity: (1) Invariant layers have limited expressivity as they cannot\ndistinguish one-hop identical geometric graphs; (2) Equivariant layers\ndistinguish a larger class of graphs by propagating geometric information\nbeyond local neighbourhoods; (3) Higher order tensors and scalarisation enable\nmaximally powerful geometric GNNs; and (4) GWL's discrimination-based\nperspective is equivalent to universal approximation. Synthetic experiments\nsupplementing our results are available at\n\\url{https://github.com/chaitjo/geometric-gnn-dojo}\n""]","[('graph neural networks', 0.718954861164093), ('graph neural', 0.6804763674736023), ('graph convolutional neural', 0.6569922566413879), ('graph convolutional networks', 0.6547192931175232), ('graph neural network', 0.6534029245376587), ('graph learning', 0.6505913138389587), ('neural networks graph', 0.6398795247077942), ('networks gnns', 0.6215394139289856), ('graph representation learning', 0.6060059666633606), ('learning graph', 0.5868319272994995)]"
341,341,85,341_fractional diffusion equations_fractional diffusion_time fractional diffusion_fractional diffusion wave,"['fractional diffusion equations', 'fractional diffusion', 'time fractional diffusion', 'fractional diffusion wave', 'fractional reaction diffusion', 'fractional pdes', 'time fractional derivative', 'fractional derivatives', 'fractional derivative', 'time fractional']","['Inverse source problem with a posteriori boundary measurement for\n  fractional diffusion equations   In this article we study inverse source problems for time-fractional\ndiffusion equations from \\textit{a posteriori} boundary measurement. Using the\nmemory effect of these class of equations, we solve these inverse problems for\nseveral class of space or time dependent source terms. We prove also the unique\ndetermination of a general class of space-time dependent separated variables\nsource terms from such measurement. Our approach is based on the study of\nsingularities of the Laplace transform in time of boundary traces of solutions\nof time-fractional diffusion equations.\n', 'Logarithmic stable recovery of the source and the initial state of time\n  fractional diffusion equations   In this paper we study the inverse problem of identifying a source or an\ninitial state in a time-fractional diffusion equation from the knowledge of a\nsingle boundary measurement. We derive logarithmic stability estimates for both\ninversions. These results show that the ill-posedness increases exponentially\nwhen the fractional derivative order tends to zero, while it exponentially\ndecreases when the regularity of the source or the initial state becomes\nlarger. The stability estimate concerning the problem of recovering the initial\nstate can be considered as a weak observability inequality in control theory.\nThe analysis is mainly based on Laplace inversion techniques and a precise\nquantification of the unique continuation property for the resolvent of the\ntime-fractional diffusion operator as a function of the frequency in the\ncomplex plane. We also determine a global time regularity for the\ntime-fractional diffusion equation which is of interest itself.\n', 'Simultaneous uniqueness for multiple parameters identification in a\n  fractional diffusion-wave equation   This article deals with the uniqueness in identifying multiple parameters\nsimultaneously in the one-dimensional time-fractional diffusion-wave equation\nof fractional time-derivative order $\\in (0,2)$ with the zero Robin boundary\ncondition. Using the Laplace transform and a transformation formula, we prove\nthe uniqueness in determining an order of the fractional derivative, a\nspatially varying potential, initial values and Robin coefficients\nsimultaneously by boundary measurement data, provided that all the eigenmodes\nof an initial value do not vanish. Furthermore, for another formulation of\ninverse problem with input source term in place of initial value, by the\nuniqueness in the case of non-zero initial value and a Duhamel principle, we\nprove the simultaneous uniqueness in determining multiple parameters for a\ntime-fractional diffusion-wave equation.\n']","[('fractional diffusion equations', 0.7531884908676147), ('fractional diffusion', 0.7412456274032593), ('time fractional diffusion', 0.7405505180358887), ('fractional diffusion wave', 0.7209903001785278), ('fractional reaction diffusion', 0.6577085852622986), ('fractional pdes', 0.6560023427009583), ('time fractional derivative', 0.5913410186767578), ('fractional derivatives', 0.5319929718971252), ('fractional derivative', 0.5246750712394714), ('time fractional', 0.5057593584060669)]"
342,342,85,342_ricci curvatures_ollivier ricci curvature_ricci curvature_ricci curvature bound,"['ricci curvatures', 'ollivier ricci curvature', 'ricci curvature', 'ricci curvature bound', 'coarse ricci curvature', 'lower ricci curvature', 'discrete curvature', 'curvature free', 'curvatures', 'ollivier ricci']","['The convergence and uniqueness of a discrete-time nonlinear Markov chain   In this paper, we prove the convergence and uniqueness of a general\ndiscrete-time nonlinear Markov chain with specific conditions. The results have\nimportant applications in discrete differential geometry. First, on a general\nfinite weighted graph, we prove the discrete-time Ollivier Ricci curvature flow\n$d_{n+1}\\coloneqq(1-\\alpha\\kappa_{d_{n}})d_{n}$ converges to a constant\ncurvature metric. Then the author in \\cite[Theorem 5.1]{M23} proved a Laplacian\nseparation principle on a locally finite graph with non-negative Ollivier\ncurvature. Here we prove the Laplacian separation flow converges to the\nconstant Laplacian solution and generalize the result to nonlinear $p$-Laplace\noperators. Moreover, our results can also be applied to study the long-time\nbehavior in the nonlinear Dirichlet forms theory and nonlinear\nPerron--Frobenius theory. At last, we define the Ollivier Ricci curvature of\nnonlinear Markov chain which is consistent with the classical Ollivier Ricci\ncurvature, sectional curvature \\cite{CMS24}, coarse Ricci curvature on\nhypergraphs \\cite{IKTU21} and the modified Ollivier Ricci curvature for\n$p$-Laplace. And we prove the convergence results for the nonlinear Markov\nchain with nonnegative Ollivier Ricci curvature.\n', 'Ollivier-Ricci curvature of regular graphs   We derive explicit formulas for the Lin-Lu-Yau curvature and the\nOllivier-Ricci curvature in terms of graph parameters and an optimal\nassignment. Utilizing these precise expressions, we examine the relationship\nbetween the Lin-Lu-Yau curvature and the 0-Ollivier-Ricci curvature, resulting\nin an equality condition on regular graphs. This condition allows us to\ncharacterize edges that are bone idle in regular graphs of girth four and to\nconstruct a family of bone idle graphs with this girth. We then use our\nformulas to provide an efficient implementation of the Ollivier-Ricci curvature\non regular graphs, enabling us to identify all bone idle, regular graphs with\nfewer than 15 vertices. Moreover, we establish a rigidity theorem for cocktail\nparty graphs, proving that a regular graph is a cocktail party graph if and\nonly if its Lin-Lu-Yau curvature is equal to one. Furthermore, we present a\ncondition on the degree of a regular graph that guarantees positive Ricci\ncurvature. We conclude this work by discussing the maximal number of vertices\nthat a regular graph of fixed degree with positive Lin-Lu-Yau curvature can\nhave.\n', 'Discrete Ollivier-Ricci curvature   We analyze both continuous and discrete-time Ollivier-Ricci curvatures of\nlocally-finite weighted graphs $\\G$ equipped with a given distance ""$\\dist$""\n(w.r.t. which $\\G$ is metrically complete) and for general random walks. We\nshow the continuous-time Ollivier-Ricci curvature is well-defined for a large\nclass of Markovian and non-Markovian random walks and provide a criterion for\nexistence of continuous-time Ollivier-Ricci curvature; the said results\ngeneralize the previous rather limited constructions in the literature. In\naddition, important properties of both discrete-time and continuous-time\nOllivier-Ricci curvatures are obtained including -- to name a few -- Lipschitz\ncontinuity, concavity properties, piece-wise regularity (piece-wise linearity\nin the case of linear walks) for the discrete-time Ollivier-Ricci as well as\nLipschitz continuity and limit-free formulation for the continuous-time\nOllivier-Ricci. these properties were previously known only for very specific\ndistances and very specific random walks. As an application of Lipschitz\ncontinuity, we obtain existence and uniqueness of generalized continuous-time\nOllivier-Ricci curvature flows. Along the way, we obtain -- by optimizing\nMcMullen\'s upper bounds -- a sharp upper bound estimate on the number of\nvertices of a convex polytope in terms of number of its facets and the ambient\ndimension, which might be of independent interest in convex geometry. The said\nupper bound allows us to bound the number of polynomial pieces of the\ndiscrete-time Ollivier-Ricci curvature as a function of time in the\ntime-polynomial random walk. The limit-free formulation we establish allows us\nto define an operator theoretic Ollivier-Ricci curvature which is a non-linear\nconcave functional on suitable operator spaces.\n']","[('ricci curvatures', 0.6258651614189148), ('ollivier ricci curvature', 0.6190553903579712), ('ricci curvature', 0.5951210260391235), ('ricci curvature bound', 0.5888552665710449), ('coarse ricci curvature', 0.5876798033714294), ('lower ricci curvature', 0.5697886347770691), ('discrete curvature', 0.548794150352478), ('curvature free', 0.5263609886169434), ('curvatures', 0.5157896280288696), ('ollivier ricci', 0.509640097618103)]"
343,343,85,343_rogers ramanujan identities_identities rogers ramanujan_ramanujan type identities_ramanujan identities,"['rogers ramanujan identities', 'identities rogers ramanujan', 'ramanujan type identities', 'ramanujan identities', 'identities ramanujan', 'rogers ramanujan type', 'series identities', 'ramanujan type', 'identities rogers', 'rogers ramanujan']","['Rogers-Ramanujan type identities and Chebyshev Polynomials of the third\n  kind   It is known that $q$-orthogonal polynomials play an important role in the\nfield of $q$-series and special functions. During studying Dyson\'s ""favorite""\nidentity of Rogers--Ramanujan type, Andrews pointed out that the classical\northogonal polynomials also have surprising applications in the world of $q$.\nBy inserting Chebyshev polynomials of the third and the fourth kinds into\nBailey pairs, Andrews derived a family of Rogers--Ramanujan type identities and\nalso results related to mock theta functions and Hecke--type series. In this\npaper, by constructing a new Bailey pair involving Chebyshev polynomials of the\nthird kind, we further extend Andrews\' way in the studying of Rogers--Ramanujan\ntype identities. By fitting this Bailey pair into different weak forms of\nBailey\'s lemma, we obtain a companion identity to Dyson\'s favorite one and also\nmany other Rogers--Ramanujan type identities. Furthermore, as immediate\nconsequences, we also obtain some results related to Appell--Lerch series and\nthe generalized Hecke--type series.\n', ""Bilateral Bailey pairs and Rogers-Ramanujan type identities   Rogers-Ramanujan type identities occur in various branches of mathematics and\nphysics. As a classic and powerful tool to deal with Rogers-Ramanujan type\nidentities, the theory of Bailey's lemma has been extensively studied and\ngeneralized. In this paper, we found a bilateral Bailey pair that naturally\narises from the q-binomial theorem. By applying the bilateral versions of\nBailey lemmas, Bailey chains and Bailey lattices, we derive a number of\nRogers-Ramanujan type identities, which unify many known identities as special\ncases. Further combined with the bilateral Bailey chains due to Berkovich,\nMcCoy and Schilling and the bilateral Bailey lattices due to Jouhet et al., we\nalso obtain identities on Appell-Lerch series and identities of Andrews-Gordon\ntype. Moreover, by applying Andrews and Warnaar's bilateral Bailey lemmas, we\nderive identities on Hecke-type series.\n"", 'Rogers-Ramanujan Type Identities Involving Double Sums   We prove four new Rogers-Ramanujan-type identities for double series. They\nfollow from the classical Rogers-Ramanujan identities using the constant term\nmethod and properties of Rogers-Szeg\\H{o} polynomials.\n']","[('rogers ramanujan identities', 0.8194177150726318), ('identities rogers ramanujan', 0.7887154221534729), ('ramanujan type identities', 0.7881442308425903), ('ramanujan identities', 0.7563080787658691), ('identities ramanujan', 0.7226468324661255), ('rogers ramanujan type', 0.5869064927101135), ('series identities', 0.5439280271530151), ('ramanujan type', 0.540023684501648), ('identities rogers', 0.5276141166687012), ('rogers ramanujan', 0.5022078156471252)]"
344,344,85,344_scalar curvature conformal_curvature conformal_conformal metrics_prescribed scalar curvature,"['scalar curvature conformal', 'curvature conformal', 'conformal metrics', 'prescribed scalar curvature', 'curvature metrics', 'positive scalar curvature', 'conformal metric', 'scalar curvatures', 'metrics constant curvature', 'metric conformal']","[""A generalization of Aubin's result for a Yamabe-type problem on smooth\n  metric measure spaces   The Yamabe problem in compact closed Riemannian manifolds is concerned with\nfinding a metric with constant scalar curvature in the conformal class of a\ngiven metric. This problem was solved by the combined work of Yamabe,\nTrudinger, Aubin, and Schoen. In particular, Aubin solved the case when the\nRiemannian manifold is compact, is nonlocally conformally flat and has a\ndimension equal to or greater than $6$. In $2015$, Case considered a\nYamabe-type problem in the setting of smooth measure space in manifolds and for\na parameter $m$, which generalizes the original Yamabe problem when $m=0$.\nAdditionally, Case solved this problem when the parameter $m$ is a natural\nnumber. In the context of the Yamabe-type problem, we generalize Aubin's result\nfor nonlocally conformally flat manifolds, with dimension equal and greater\nthan 6 and parameter $m$ close to nonnegative integers.\n"", 'A compactness theorem for conformal metrics with constant scalar\n  curvature and constant boundary mean curvature in dimension three   On a compact three-dimensional Riemannian manifold with boundary, we prove\nthe compactness of the full set of conformal metrics with positive constant\nscalar curvature and constant mean curvature on the boundary. This involves a\nblow-up analysis of a Yamabe equation with critical Sobolev exponents both in\nthe interior and on the boundary.\n', 'A priori estimates for negative constant scalar curvature conformal\n  metrics with positive constant boundary mean curvature   On a compact Riemannian manifold with boundary, we study the set of conformal\nmetrics of negative constant scalar curvature in the interior and positive\nconstant mean curvature on the boundary. Working in the case of positive Yamabe\nconformal invariant, we prove that this set is a priori bounded in the\nthree-dimensional case and in the locally conformally flat with umbilical\nboundary case in any dimension not less than three.\n']","[('scalar curvature conformal', 0.6955310702323914), ('curvature conformal', 0.668799102306366), ('conformal metrics', 0.642512857913971), ('prescribed scalar curvature', 0.6367846727371216), ('curvature metrics', 0.6339276432991028), ('positive scalar curvature', 0.6248174905776978), ('conformal metric', 0.6118388175964355), ('scalar curvatures', 0.6091641783714294), ('metrics constant curvature', 0.6082251667976379), ('metric conformal', 0.6070050001144409)]"
345,345,85,345_lorentzian metrics_minkowski spacetime_lorentzian metric_lorentzian manifolds,"['lorentzian metrics', 'minkowski spacetime', 'lorentzian metric', 'lorentzian manifolds', 'lorentzian geometry', 'lorentzian manifold', 'globally hyperbolic lorentzian', 'length spaces', 'hyperbolic spacetimes', 'globally hyperbolic spacetimes']","['Comparison theorems for Lorentzian length spaces with lower timelike\n  curvature bounds   In this article we introduce a notion of normalized angle for Lorentzian\npre-length spaces. This concept allows us to prove some equivalences to the\ndefinition of timelike curvature bounds from below for Lorentzian pre-length\nspaces. Specifically, we establish some comparison theorems known as the local\nLorentzian version of the Toponogov theorem and the Alexandrov convexity\nproperty. Finally, as an application we obtain a first variation Formula for\nnon-negatively curved globally hyperbolic Lorentzian length spaces.\n', ""Lorentzian metric spaces and their Gromov-Hausdorff convergence   We present an abstract approach to Lorentzian Gromov-Hausdorff distance and\nconvergence, and an alternative approach to Lorentzian length spaces that does\nnot use auxiliary ``positive signature'' metrics or other unobserved fields. We\nbegin by defining a notion of (abstract) bounded Lorentzian-metric space which\nis sufficiently general to comprise compact causally convex subsets of globally\nhyperbolic spacetimes and causets. We define the Gromov-Hausdorff distance and\nshow that two bounded Lorentzian-metric spaces at zero GH distance are indeed\nboth isometric and homeomorphic. Then we show how to define from the Lorentzian\ndistance, beside topology, the causal relation and the causal curves for these\nspaces, obtaining useful limit curve theorems. Next, we define Lorentzian\n(length) prelength spaces via suitable (maximal) chronal connectedness\nproperties. These definitions are proved to be stable under GH limits.\nFurthermore, we define bounds on sectional curvature for our Lorentzian length\nspaces and prove that they are also stable under GH limits. We conclude with a\n(pre)compactness theorem.\n"", 'Null distance and convergence of Lorentzian length spaces   The null distance of Sormani and Vega encodes the manifold topology as well\nas the causality structure of a (smooth) spacetime. We extend this concept to\nLorentzian length spaces, the analog of (metric) length spaces, which\ngeneralize Lorentzian causality theory beyond the manifold level. We then study\nGromov-Hausdorff convergence based on the null distance in warped product\nLorentzian length spaces and prove first results on its compatibility with\nsynthetic curvature bounds.\n']","[('lorentzian metrics', 0.6775479316711426), ('minkowski spacetime', 0.632887601852417), ('lorentzian metric', 0.6293992400169373), ('lorentzian manifolds', 0.6085663437843323), ('lorentzian geometry', 0.6019105911254883), ('lorentzian manifold', 0.5944165587425232), ('globally hyperbolic lorentzian', 0.5730610489845276), ('length spaces', 0.565985918045044), ('hyperbolic spacetimes', 0.550629198551178), ('globally hyperbolic spacetimes', 0.5438529849052429)]"
346,346,85,346_reduced order modeling_reduced order modelling_nonlinear reduction_reduced order models,"['reduced order modeling', 'reduced order modelling', 'nonlinear reduction', 'reduced order models', 'deep learning', 'reduced dynamics', 'parametrized pdes', 'deep learning based', 'dimensionality reduction', 'nonlinear time dependent']","[""Long-time prediction of nonlinear parametrized dynamical systems by deep\n  learning-based reduced order models   Deep learning-based reduced order models (DL-ROMs) have been recently\nproposed to overcome common limitations shared by conventional ROMs - built,\ne.g., exclusively through proper orthogonal decomposition (POD) - when applied\nto nonlinear time-dependent parametrized PDEs. In particular, POD-DL-ROMs can\nachieve extreme efficiency in the training stage and faster than real-time\nperformances at testing, thanks to a prior dimensionality reduction through POD\nand a DL-based prediction framework. Nonetheless, they share with conventional\nROMs poor performances regarding time extrapolation tasks. This work aims at\ntaking a further step towards the use of DL algorithms for the efficient\nnumerical approximation of parametrized PDEs by introducing the $\\mu\nt$-POD-LSTM-ROM framework. This novel technique extends the POD-DL-ROM\nframework by adding a two-fold architecture taking advantage of long short-term\nmemory (LSTM) cells, ultimately allowing long-term prediction of complex\nsystems' evolution, with respect to the training window, for unseen input\nparameter values. Numerical results show that this recurrent architecture\nenables the extrapolation for time windows up to 15 times larger than the\ntraining time domain, and achieves better testing time performances with\nrespect to the already lightning-fast POD-DL-ROMs.\n"", 'POD-DL-ROM: enhancing deep learning-based reduced order models for\n  nonlinear parametrized PDEs by proper orthogonal decomposition   Deep learning-based reduced order models (DL-ROMs) have been recently\nproposed to overcome common limitations shared by conventional reduced order\nmodels (ROMs) - built, e.g., through proper orthogonal decomposition (POD) -\nwhen applied to nonlinear time-dependent parametrized partial differential\nequations (PDEs). These might be related to (i) the need to deal with\nprojections onto high dimensional linear approximating trial manifolds, (ii)\nexpensive hyper-reduction strategies, or (iii) the intrinsic difficulty to\nhandle physical complexity with a linear superimposition of modes. All these\naspects are avoided when employing DL-ROMs, which learn in a non-intrusive way\nboth the nonlinear trial manifold and the reduced dynamics, by relying on deep\n(e.g., feedforward, convolutional, autoencoder) neural networks. Although\nextremely efficient at testing time, when evaluating the PDE solution for any\nnew testing-parameter instance, DL-ROMs require an expensive training stage,\nbecause of the extremely large number of network parameters to be estimated. In\nthis paper we propose a possible way to avoid an expensive training stage of\nDL-ROMs, by (i) performing a prior dimensionality reduction through POD, and\n(ii) relying on a multi-fidelity pretraining stage, where different physical\nmodels can be efficiently combined. The proposed POD-DL-ROM is tested on\nseveral (both scalar and vector, linear and nonlinear) time-dependent\nparametrized PDEs (such as, e.g., linear advection-diffusion-reaction,\nnonlinear diffusion-reaction, nonlinear elastodynamics, and Navier-Stokes\nequations) to show the generality of this approach and its remarkable\ncomputational savings.\n', 'A comprehensive deep learning-based approach to reduced order modeling\n  of nonlinear time-dependent parametrized PDEs   Traditional reduced order modeling techniques such as the reduced basis (RB)\nmethod (relying, e.g., on proper orthogonal decomposition (POD)) suffer from\nsevere limitations when dealing with nonlinear time-dependent parametrized\nPDEs, because of the fundamental assumption of linear superimposition of modes\nthey are based on. For this reason, in the case of problems featuring coherent\nstructures that propagate over time such as transport, wave, or\nconvection-dominated phenomena, the RB method usually yields inefficient\nreduced order models (ROMs) if one aims at obtaining reduced order\napproximations sufficiently accurate compared to the high-fidelity, full order\nmodel (FOM) solution. To overcome these limitations, in this work, we propose a\nnew nonlinear approach to set reduced order models by exploiting deep learning\n(DL) algorithms. In the resulting nonlinear ROM, which we refer to as DL-ROM,\nboth the nonlinear trial manifold (corresponding to the set of basis functions\nin a linear ROM) as well as the nonlinear reduced dynamics (corresponding to\nthe projection stage in a linear ROM) are learned in a non-intrusive way by\nrelying on DL algorithms; the latter are trained on a set of FOM solutions\nobtained for different parameter values. In this paper, we show how to\nconstruct a DL-ROM for both linear and nonlinear time-dependent parametrized\nPDEs; moreover, we assess its accuracy on test cases featuring different\nparametrized PDE problems. Numerical results indicate that DL-ROMs whose\ndimension is equal to the intrinsic dimensionality of the PDE solutions\nmanifold are able to approximate the solution of parametrized PDEs in\nsituations where a huge number of POD modes would be necessary to achieve the\nsame degree of accuracy.\n']","[('reduced order modeling', 0.5194048285484314), ('reduced order modelling', 0.5048559308052063), ('nonlinear reduction', 0.4615936577320099), ('reduced order models', 0.4418022036552429), ('deep learning', 0.4123944640159607), ('reduced dynamics', 0.3798721432685852), ('parametrized pdes', 0.3726089596748352), ('deep learning based', 0.37121137976646423), ('dimensionality reduction', 0.36696410179138184), ('nonlinear time dependent', 0.3648185431957245)]"
347,347,84,347_foliations manifolds_singular foliations_foliated manifolds_riemannian foliations,"['foliations manifolds', 'singular foliations', 'foliated manifolds', 'riemannian foliations', 'singular foliation', 'foliated manifold', 'riemannian foliation', 'dimensional foliations', 'foliations', 'foliations compact']","['A classification of neighborhoods around leaves of a singular foliation   We classify singular foliations admitting a given leaf and a given transverse\nsingular foliation.\n', ""Leaf closures of Riemannian foliations: a survey on topological and\n  geometric aspects of Killing foliations   A smooth foliation is Riemannian when its leaves are locally equidistant. The\nclosures of the leaves of a Riemannian foliation on a simply connected\nmanifold, or more generally of a Killing foliation, are described by flows of\ntransverse Killing vector fields. This offers significant technical advantages\nin the study of this class of foliations, which nonetheless includes other\nimportant classes, such as those given by the orbits of isometric Lie group\nactions. Aiming at a broad audience, in this survey we introduce Killing\nfoliations from the very basics, starting with a brief revision of the main\nobjects appearing in this theory, such as pseudogroups, sheaves, holonomy and\nbasic cohomology. We then review Molino's structural theory for Riemannian\nfoliations and present its transverse counterpart in the theory of complete\npseudogroups of isometries, emphasizing the connections between these topics.\nWe also survey some classical results and recent developments in the theory of\nKilling foliations. Finally, we review some topics in the theory of singular\nRiemannian foliations and discuss singular Killing foliations.\n"", ""Singular foliations through diffeology   A singular foliation is a partition of a manifold into leaves of perhaps\nvarying dimension. Stefan and Sussmann carried out fundamental work on singular\nfoliations in the 1970s. We survey their contributions, show how diffeological\nobjects and ideas arise naturally in this setting, and highlight some\nconsequences within diffeology. We then introduce a definition of transverse\nequivalence of singular foliations, following Molino's definition for regular\nfoliations. We show that, whereas transverse equivalent singular foliations\nalways have diffeologically diffeomorphic leaf spaces, the converse holds only\nfor certain classes of singular foliations. We finish by showing that the basic\ncohomology of a singular foliation is invariant under transverse equivalence.\n""]","[('foliations manifolds', 0.8084205985069275), ('singular foliations', 0.8074313998222351), ('foliated manifolds', 0.7747153043746948), ('riemannian foliations', 0.7691821455955505), ('singular foliation', 0.7579966187477112), ('foliated manifold', 0.7579653263092041), ('riemannian foliation', 0.7433251738548279), ('dimensional foliations', 0.7333378195762634), ('foliations', 0.7264592051506042), ('foliations compact', 0.7133316993713379)]"
348,348,84,348_finite element exterior_element exterior calculus_exterior calculus_finite element spaces,"['finite element exterior', 'element exterior calculus', 'exterior calculus', 'finite element spaces', 'differential forms', 'tetrahedral meshes', 'de rham complexes', 'geometric decompositions', 'finite element space', 'hilbert complexes']","[""Symmetry and Invariant Bases in Finite Element Exterior Calculus   We study symmetries of bases and spanning sets in finite element exterior\ncalculus, using representation theory. We want to know which vector-valued\nfinite element spaces have bases invariant under permutation of vertex indices.\nThe permutations of vertex indices correspond to the symmetry group of the\nsimplex. That symmetry group is represented on simplicial finite element spaces\nby the pullback action. We determine a natural notion of invariance and\nsufficient conditions on the dimension and polynomial degree for the existence\nof invariant bases. We conjecture that these conditions are necessary too. We\nutilize Djokovi\\'c and Malzan's classification of monomial irreducible\nrepresentations of the symmetric group, and show new symmetries of the\ngeometric decomposition and canonical isomorphisms of the finite element\nspaces. Explicit invariant bases with complex coefficients are constructed in\ndimensions two and three for different spaces of finite element differential\nforms.\n"", 'Finite Element de Rham and Stokes Complexes in Three Dimensions   Finite element de Rham complexes and finite element Stokes complexes with\nvarious smoothness in three dimensions are systematically constructed. First\nsmooth scalar finite elements in three dimensions are derived through a\nnon-overlapping decomposition of the simplicial lattice. Based on the smooth\nscalar finite elements, both H(div)-conforming finite elements and\nH(curl)-conforming finite elements with various smoothness are devised, which\ninduce the finite element de Rham complexes with various smoothness and the\nassociated commutative diagrams. The div stability is established for the\nH(div)-conforming finite elements, and the exactness of these finite element\ncomplexes.\n', 'Conforming Finite Element Function Spaces in Four Dimensions, Part II:\n  The Pentatope and Tetrahedral Prism   In this paper, we present explicit expressions for conforming finite element\nfunction spaces, basis functions, and degrees of freedom on the pentatope and\ntetrahedral prism elements. More generally, our objective is to construct\nfinite element function spaces that maintain conformity with\ninfinite-dimensional spaces of a carefully chosen de Rham complex. This paper\nis a natural extension of the companion paper entitled ""Conforming Finite\nElement Function Spaces in Four Dimensions, Part I: Foundational Principles and\nthe Tesseract"" by Nigam and Williams, (2023). In contrast to Part I, in this\npaper we focus on two of the most popular elements which do not possess a full\ntensor-product structure in all four coordinate directions. We note that these\nelements appear frequently in existing space-time finite element methods. In\norder to build our finite element spaces, we utilize powerful techniques from\nthe recently developed \'Finite Element Exterior Calculus\'. Subsequently, we\ntranslate our results into the well-known language of linear algebra (vectors\nand matrices) in order to facilitate implementation by scientists and\nengineers.\n']","[('finite element exterior', 0.5510908961296082), ('element exterior calculus', 0.5447045564651489), ('exterior calculus', 0.5252583622932434), ('finite element spaces', 0.49445343017578125), ('differential forms', 0.48843318223953247), ('tetrahedral meshes', 0.4767918288707733), ('de rham complexes', 0.47433748841285706), ('geometric decompositions', 0.4639429748058319), ('finite element space', 0.45623764395713806), ('hilbert complexes', 0.43423527479171753)]"
349,349,84,349_information decomposition_partial information decomposition_information theoretic_information theoretic quantities,"['information decomposition', 'partial information decomposition', 'information theoretic', 'information theoretic quantities', 'information theoretic approaches', 'information theoretic measures', 'higher order information', 'redundant information', 'mutual information', 'partial information']","['A scalable, synergy-first backbone decomposition of higher-order\n  structures in complex systems   Since its introduction in 2011, the partial information decomposition (PID)\nhas triggered an explosion of interest in the field of multivariate information\ntheory and the study of emergent, higher-order (""synergistic"") interactions in\ncomplex systems. Despite its power, however, the PID has a number of\nlimitations that restrict its general applicability: it scales poorly with\nsystem size and the standard approach to decomposition hinges on a definition\nof ""redundancy"", leaving synergy only vaguely defined as ""that information not\nredundant."" Other heuristic measures, such as the O-information, have been\nintroduced, although these measures typically only provided a summary statistic\nof redundancy/synergy dominance, rather than direct insight into the synergy\nitself. To address this issue, we present an alternative decomposition that is\nsynergy-first, scales much more gracefully than the PID, and has a\nstraightforward interpretation. Our approach defines synergy as that\ninformation in a set that would be lost following the minimally invasive\nperturbation on any single element. By generalizing this idea to sets of\nelements, we construct a totally ordered ""backbone"" of partial synergy atoms\nthat sweeps systems scales. Our approach starts with entropy, but can be\ngeneralized to the Kullback-Leibler divergence, and by extension, to the total\ncorrelation and the single-target mutual information. Finally, we show that\nthis approach can be used to decompose higher-order interactions beyond just\ninformation theory: we demonstrate this by showing how synergistic combinations\nof pairwise edges in a complex network supports signal communicability and\nglobal integration. We conclude by discussing how this perspective on\nsynergistic structure (information-based or otherwise) can deepen our\nunderstanding of part-whole relationships in complex systems.\n', 'A partial information decomposition for discrete and continuous\n  variables   Conceptually, partial information decomposition (PID) is concerned with\nseparating the information contributions several sources hold about a certain\ntarget by decomposing the corresponding joint mutual information into\ncontributions such as synergistic, redundant, or unique information. Despite\nPID conceptually being defined for any type of random variables, so far, PID\ncould only be quantified for the joint mutual information of discrete systems.\nRecently, a quantification for PID in continuous settings for two or three\nsource variables was introduced. Nonetheless, no ansatz has managed to both\nquantify PID for more than three variables and cover general measure-theoretic\nrandom variables, such as mixed discrete-continuous, or continuous random\nvariables yet. In this work we will propose an information quantity, defining\nthe terms of a PID, which is well-defined for any number or type of source or\ntarget random variable. This proposed quantity is tightly related to a recently\ndeveloped local shared information quantity for discrete random variables based\non the idea of shared exclusions. Further, we prove that this newly proposed\ninformation-measure fulfills various desirable properties, such as satisfying a\nset of local PID axioms, invariance under invertible transformations,\ndifferentiability with respect to the underlying probability density, and\nadmitting a target chain rule.\n', 'Bits and Pieces: Understanding Information Decomposition from Part-whole\n  Relationships and Formal Logic   Partial information decomposition (PID) seeks to decompose the multivariate\nmutual information that a set of source variables contains about a target\nvariable into basic pieces, the so called ""atoms of information"". Each atom\ndescribes a distinct way in which the sources may contain information about the\ntarget. In this paper we show, first, that the entire theory of partial\ninformation decomposition can be derived from considerations of elementary\nparthood relationships between information contributions. This way of\napproaching the problem has the advantage of directly characterizing the atoms\nof information, instead of taking an indirect approach via the concept of\nredundancy. Secondly, we describe several intriguing links between PID and\nformal logic. In particular, we show how to define a measure of PID based on\nthe information provided by certain statements about source realizations.\nFurthermore, we show how the mathematical lattice structure underlying PID\ntheory can be translated into an isomorphic structure of logical statements\nwith a particularly simple ordering relation: logical implication. The\nconclusion to be drawn from these considerations is that there are three\nisomorphic ""worlds"" of partial information decomposition, i.e. three equivalent\nways to mathematically describe the decomposition of the information carried by\na set of sources about a target: the world of parthood relationships, the world\nof logical statements, and the world of antichains that was utilized by\nWilliams and Beer in their original exposition of PID theory. We additionally\nshow how the parthood perspective provides a systematic way to answer a type of\nquestion that has been much discussed in the PID field: whether a partial\ninformation decomposition can be uniquely determined based on concepts other\nthan redundant information.\n']","[('information decomposition', 0.6980679035186768), ('partial information decomposition', 0.6973376870155334), ('information theoretic', 0.6343063712120056), ('information theoretic quantities', 0.6321653723716736), ('information theoretic approaches', 0.6078740954399109), ('information theoretic measures', 0.6070868968963623), ('higher order information', 0.6019494533538818), ('redundant information', 0.6017341613769531), ('mutual information', 0.5841729044914246), ('partial information', 0.5799974203109741)]"
350,350,84,350_klein gordon equations_nonlinear klein gordon_wave klein gordon_klein gordon system,"['klein gordon equations', 'nonlinear klein gordon', 'wave klein gordon', 'klein gordon system', 'gordon equations', 'nonlinear klein', 'linear klein gordon', 'wave klein', 'klein gordon', 'linear klein']","['Global Existence and Scattering of the Klein-Gordon-Zakharov System in\n  Two Space Dimensions   We are interested in the Klein-Gordon-Zakharov system in $\\mathbb{R}^{1+2}$,\nwhich is an important model in plasma physics with extensive mathematical\nstudies. The system can be regarded as semilinear coupled wave and Klein-Gordon\nequations with nonlinearities violating the null conditions. Without the\ncompactness assumptions on the initial data, we aim to establish the existence\nof small global solutions, and in addition, we want to illustrate the optimal\npointwise decay of the solutions. Furthermore, we show that the Klein-Gordon\npart of the system enjoys linear scattering while the wave part has uniformly\nbounded low-order energy. None of these goals is easy because of the slow\npointwise decay nature of the linear wave and Klein-Gordon components in\n$\\mathbb{R}^{1+2}$. We tackle the difficulties by carefully exploiting the\nproperties of the wave and the Klein-Gordon components, and by relying on the\nghost weight energy estimates to close higher-order energy estimates. This\nappears to be the first pointwise decay result and the first scattering result\nfor the Klein-Gordon-Zakharov system in $\\mathbb{R}^{1+2}$ without compactness\nassumptions.\n', ""Global solution to the wave and Klein-Gordon system under null condition\n  in dimension two   We are interested in studying the coupled wave and Klein-Gordon equations\nwith null quadratic nonlinearities in $\\mathbb{R}^{2+1}$. We want to establish\nthe small data global existence result, and in addition, we also demonstrate\nthe pointwise asymptotic behaviour of the solution to the coupled system. The\ninitial data are not required to have compact support, and this is achieved by\napplying the Alinhac's ghost weight method to both the wave and the\nKlein-Gordon equations.\n"", 'Asymptotic Behavior of the Solution to the Klein-Gordon-Zakharov Model\n  in Dimension Two   Consider the Klein-Gordon-Zakharov equations in $\\mathbb{R}^{1+2}$, and we\nare interested in establishing the small global solution to the equations and\nin investigating the pointwise asymptotic behavior of the solution. The\nKlein-Gordon-Zakharov equations can be regarded as a coupled semilinear wave\nand Klein-Gordon system with quadratic nonlinearities which do not satisfy the\nnull conditions, and the fact that wave components and Klein-Gordon components\ndo not decay sufficiently fast makes it harder to conduct the analysis. In\norder to conquer the difficulties, we will rely on the hyperboloidal foliation\nmethod and a minor variance of the ghost weight method. As a side result of the\nanalysis, we are also able to show the small data global existence result for a\nclass of quasilinear wave and Klein-Gordon system violating the null\nconditions.\n']","[('klein gordon equations', 0.7093415260314941), ('nonlinear klein gordon', 0.6906729340553284), ('wave klein gordon', 0.6314749121665955), ('klein gordon system', 0.6292123198509216), ('gordon equations', 0.5974247455596924), ('nonlinear klein', 0.5772050023078918), ('linear klein gordon', 0.5520870089530945), ('wave klein', 0.5281139612197876), ('klein gordon', 0.47577762603759766), ('linear klein', 0.45498722791671753)]"
351,351,83,351_thz frequencies_thz communications_thz wireless_millimeter wave,"['thz frequencies', 'thz communications', 'thz wireless', 'millimeter wave', '28 ghz', '100 ghz', 'thz channel', 'ghz', 'thz communication', 'channel characteristics']","['3-D Statistical Indoor Channel Model for Millimeter-Wave and\n  Sub-Terahertz Bands   Millimeter-wave (mmWave) and Terahertz (THz) will be used in the\nsixth-generation (6G) wireless systems, especially for indoor scenarios. This\npaper presents an indoor three-dimensional (3-D) statistical channel model for\nmmWave and sub-THz frequencies, which is developed from extensive channel\npropagation measurements conducted in an office building at 28 GHz and 140 GHz\nin 2014 and 2019. Over 15,000 power delay profiles (PDPs) were recorded to\nstudy channel statistics such as the number of time clusters, cluster delays,\nand cluster powers. All the parameters required in the channel generation\nprocedure are derived from empirical measurement data for 28 GHz and 140 GHz\nline-of-sight (LOS) and non-line-of-sight (NLOS) scenarios. The channel model\nis validated by showing that the simulated root mean square (RMS) delay spread\nand RMS angular spread yield good agreements with measured values. An indoor\nchannel simulation software is built upon the popular NYUSIM outdoor channel\nsimulator, which can generate realistic channel impulse response, PDP, and\npower angular spectrum.\n', '220 GHz Urban Microcell Channel Measurement and Characterization on a\n  University Campus   Owning abundant bandwidth resources, the Terahertz (THz) band (0.1-10~THz) is\nenvisioned as a key technology to realize ultra-high-speed communications in 6G\nand beyond wireless networks. To realize reliable THz communications in urban\nmicrocell (UMi) environments, propagation analysis and channel characterization\nare still insufficient. In this paper, channel measurement campaigns are\nconducted in a UMi scenario at 220~GHz, using a correlation-based time domain\nchannel sounder. 24 positions are measured along a road on the university\ncampus, with distances ranging from 34~m to 410~m. Based on the measurement\nresults, the spatial consistency and interaction of THz waves to the\nsurrounding environments are analyzed. Moreover, the additional loss due to\nfoliage blockage is calculated and an average value of 16.7~dB is observed.\nFurthermore, a full portrait of channel characteristics, including path loss,\nshadow fading, K-factor, delay and angular spreads, as well as cluster\nparameters, is calculated and analyzed. Specifically, an average K-factor value\nof 17.5 dB is measured in the line-of-sight (LoS) case, which is nearly two\ntimes larger than the extrapolated values from the 3GPP standard, revealing\nweak multipath effects in the THz band. Additionally, 2.5 clusters on average\nare observed in the LoS case, around one fifth of what is defined in the 3GPP\nmodel, which uncovers the strong sparsity in THz UMi. The results and analysis\nin this work can offer guidance for system design for future THz UMi networks.\n', 'Terahertz Channel Measurement and Analysis on a University Campus Street   Owning abundant bandwidth resource, the Terahertz (0.1-10 THz) band is a\npromising spectrum to support sixth-generation (6G) and beyond communications.\nAs the foundation of channel study in the spectrum, channel measurement is\nongoing in covering representative 6G communication scenarios and promising THz\nfrequency bands. In this paper, a wideband channel measurement in an L-shaped\nuniversity campus street is conducted at 306-321 GHz and 356-371 GHz. In\nparticular, ten line-of-sight (LoS) and eight non-line-of-sight (NLoS) points\nare measured at the two frequency bands, respectively. In total, 6480 channel\nimpulse responses (CIRs) are obtained from the measurement, based on which\nmulti-path propagation in the L-shaped roadway in the THz band is elaborated to\nidentify major scatterers of walls, vehicles, etc. in the environment and their\nimpact on multi-path components (MPCs). Furthermore, outdoor THz channel\ncharacteristics in the two frequency bands are analyzed, including path losses,\nshadow fading, cluster parameters, delay spread and angular spread. In contrast\nwith the counterparts in the similar outdoor scenario at lower frequencies, the\nresults verify the sparsity of MPCs at THz frequencies and indicate smaller\npower spreads in both temporal and spatial domains in the THz band.\n']","[('thz frequencies', 0.5388880968093872), ('thz communications', 0.5356906056404114), ('thz wireless', 0.5064778327941895), ('millimeter wave', 0.5044837594032288), ('28 ghz', 0.47853007912635803), ('100 ghz', 0.4726574122905731), ('thz channel', 0.46562644839286804), ('ghz', 0.45826268196105957), ('thz communication', 0.44302308559417725), ('channel characteristics', 0.4252130687236786)]"
352,352,83,352_mock theta functions_ramanujan theta_functions ramanujan_theta series,"['mock theta functions', 'ramanujan theta', 'functions ramanujan', 'theta series', 'theta functions', 'identities ramanujan', 'mock theta', 'analogues ramanujan', 'order mock theta', 'identities theta']","['A Comprehensive Study of Complete Generalized New Mock Theta Functions   The generalization of new mock theta functions of Andrews and Bringmann et al\nare given. Further we have given the expansion of these bilateral generalized\nnew mock theta functions as 2 phi 1 series by Slaters transformation. After\nthat we have given the continued fraction representation of these generalized\nmock theta functions.\n', ""On Ramanujan's lost notebook and new tenth-order like identities for\n  second-, sixth-, and eighth-order mock theta functions   Ramanujan's lost notebook contains many mock theta functions and mock theta\nfunction identities not mentioned in his last letter to Hardy. For example, we\nfind the four tenth-order mock theta functions and their six identities. The\nsix identities themselves are of a spectacular nature and were first proved by\nChoi. We also find eight sixth-order mock theta functions in the lost notebook,\nbut among their many identities there is only a single relationship like those\nof the tenth-orders. Using Appell function properties of Hickerson and\nMortenson, we discover and prove three new identities for the sixth-order mock\ntheta functions that are in the spirit of the six tenth-order identities. We\nalso include an additional nineteen tenth-order like identities for various\ncombinations of second-, sixth-, and eighth-order mock theta functions.\n"", ""Splitting Appell functions in terms of single quotients of theta\n  functions   Ramanujan's last letter to Hardy introduced the world to mock theta\nfunctions, and the mock theta function identities found in Ramanujan's lost\nnotebook added to their intriguing nature. For example, we find the four\ntenth-order mock theta functions and their six identities. The six identities\nthemselves are of a spectacular nature and were first proved by Choi. We also\nfind over eight sixth-order mock theta functions in the lost notebook, but\namong their many identities there is only one relationship like those of the\ntenth-orders. Recently, three new identities for the sixth-order mock theta\nfunctions that are in the spirit of the six tenth-order identities were\ndiscovered. Here we present several families of tenth-order like identities for\nAppell functions, which are the building blocks of Ramanujan's mock theta\nfunctions.\n""]","[('mock theta functions', 0.6545985341072083), ('ramanujan theta', 0.6295924186706543), ('functions ramanujan', 0.5943416357040405), ('theta series', 0.587457537651062), ('theta functions', 0.5813612937927246), ('identities ramanujan', 0.5551382899284363), ('mock theta', 0.5442083477973938), ('analogues ramanujan', 0.5418627858161926), ('order mock theta', 0.5290905237197876), ('identities theta', 0.5153177380561829)]"
353,353,83,353_game graphs_planar graphs graphs_cops robbers_p_5 free graphs,"['game graphs', 'planar graphs graphs', 'cops robbers', 'p_5 free graphs', 'planar graphs', 'free graphs', 'game graph', 'graphs graphs can', 'robbers', 'game played graphs']","['Cops and Attacking Robbers with Cycle Constraints   This paper considers the Cops and Attacking Robbers game, a variant of Cops\nand Robbers, where the robber is empowered to attack a cop in the same way a\ncop can capture the robber. In a graph $G$, the number of cops required to\ncapture a robber in the Cops and Attacking Robbers game is denoted by\n$\\attCop(G)$. We characterise the triangle-free graphs $G$ with $\\attCop(G)\n\\leq 2$ via a natural generalisation of the cop-win characterisation by\nNowakowski and Winkler \\cite{nowakowski1983vertex}. We also prove that all\nbipartite planar graphs $G$ have $\\attCop(G) \\leq 4$ and show this is tight by\nconstructing a bipartite planar graph $G$ with $\\attCop(G) = 4$. Finally we\nconstruct $17$ non-isomorphic graphs $H$ of order $58$ with $\\attCop(H) = 6$\nand $\\cop(H)=3$. This provides the first example of a graph $H$ with\n$\\attCop(H) - \\cop(H) \\geq 3$ extending work by Bonato, Finbow, Gordinowicz,\nHaidar, Kinnersley, Mitsche, Pra\\l{}at, and Stacho \\cite{bonato2014robber}. We\nconclude with a list of conjectures and open problems.\n', ""Cops and Robbers for Graphs on Surfaces with Crossings   Cops and Robbers is a game played on a graph where a set of cops attempt to\ncapture a single robber. The game proceeds in rounds, where each round first\nconsists of the cops' turn, followed by the robber's turn. In the cops' turn,\nevery cop can choose to either stay on the same vertex or move to an adjacent\nvertex, and likewise the robber in his turn. The robber is considered to be\ncaptured if, at any point in time, there is some cop on the same vertex as the\nrobber. A natural question in this game concerns the cop-number of a graph --\nthe minimum number of cops needed to capture the robber. It has long been known\nthat graphs embeddable (without crossings) on surfaces of bounded genus have\nbounded cop-number. In contrast, the class of 1-planar graphs -- graphs that\ncan be drawn on the plane with at most one crossing per edge -- does not have\nbounded cop-number. This paper initiates an investigation into how distance\nbetween crossing pairs of edges influences a graph's cop number. In particular,\nwe look at Distance $d$ Cops and Robbers, a variant of the classical game,\nwhere the robber is considered to be captured if there is a cop within distance\n$d$ of the robber. Let $c_d(G)$ denote the minimum number of cops required in\nthe graph $G$ to capture a robber within distance $d$. We look at various\nclasses of graphs, such as 1-plane graphs, $k$-plane graphs (graphs where each\nedge is crossed at most $k$ times), and even general graph drawings, and show\nthat if every crossing pair of edges can be connected by a path of small\nlength, then $c_d(G)$ is bounded, for small values of $d$.\n"", ""On 1-Planar Graphs with Bounded Cop-Number   Cops and Robbers is a type of pursuit-evasion game played on a graph where a\nset of cops try to capture a single robber. The cops first choose their initial\nvertex positions, and later the robber chooses a vertex. The cops and robbers\nmake their moves in alternate turns: in the cops' turn, every cop can either\nchoose to move to an adjacent vertex or stay on the same vertex, and likewise\nthe robber in his turn. If the cops can capture the robber in a finite number\nof rounds, the cops win, otherwise the robber wins. The cop-number of a graph\nis the minimum number of cops required to catch a robber in the graph. It has\nlong been known that graphs embedded on surfaces (such as planar graphs and\ntoroidal graphs) have a small cop-number. Recently, Durocher et al. [Graph\nDrawing, 2023] investigated the problem of cop-number for the class of\n$1$-planar graphs, which are graphs that can be embedded in the plane such that\neach edge is crossed at most once. They showed that unlike planar graphs which\nrequire just three cops, 1-planar graphs have an unbounded cop-number. On the\npositive side, they showed that maximal 1-planar graphs require only three cops\nby crucially using the fact that the endpoints of every crossing in an embedded\nmaximal 1-planar graph induce a $K_4$. In this paper, we show that the\ncop-number remains bounded even under the relaxed condition that the endpoints\ninduce at least three edges. More precisely, let an $\\times$-crossing of an\nembedded 1-planar graph be a crossing whose endpoints induce a matching; i.e.,\nthere is no edge connecting the endpoints apart from the crossing edges\nthemselves. We show that any 1-planar graph that can be embedded without\n$\\times$-crossings has cop-number at most 21. Moreover, any 1-planar graph that\ncan be embedded with at most $\\gamma$ $\\times$-crossings has cop-number at most\n$\\gamma + 21$.\n""]","[('game graphs', 0.5541633367538452), ('planar graphs graphs', 0.5490993857383728), ('cops robbers', 0.5303875207901001), ('p_5 free graphs', 0.5277249217033386), ('planar graphs', 0.5254729986190796), ('free graphs', 0.5139639377593994), ('game graph', 0.5112987160682678), ('graphs graphs can', 0.5092583894729614), ('robbers', 0.5053318738937378), ('game played graphs', 0.5026987195014954)]"
354,354,83,354_g_2 manifolds_g_2 manifold__2 manifolds_closed g_2 structure,"['g_2 manifolds', 'g_2 manifold', '_2 manifolds', 'closed g_2 structure', 'g_2 structures', 'g_2 structure', 'manifolds admitting', 'manifolds', 'compact manifolds', 'holonomy metrics']","['A new construction of compact torsion-free $G_2$-manifolds by gluing\n  families of Eguchi-Hanson spaces   We give a new construction of compact Riemannian 7-manifolds with holonomy\n$G_2$. Let $M$ be a torsion-free $G_2$-manifold (which can have holonomy a\nproper subgroup of $G_2$) such that $M$ admits an involution $\\iota$ preserving\nthe $G_2$-structure. Then $M/{\\langle \\iota \\rangle}$ is a $G_2$-orbifold, with\nsingular set $L$ an associative submanifold of $M$, where the singularities are\nlocally of the form $\\mathbb R^3 \\times (\\mathbb R^4 / \\{\\pm 1\\})$. We resolve\nthis orbifold by gluing in a family of Eguchi-Hanson spaces, parametrized by a\nnonvanishing closed and coclosed $1$-form $\\lambda$ on $L$. Much of the\nanalytic difficulty lies in constructing appropriate closed $G_2$-structures\nwith sufficiently small torsion to be able to apply the general existence\ntheorem of the first author. In particular, the construction involves solving a\nfamily of elliptic equations on the noncompact Eguchi-Hanson space,\nparametrized by the singular set $L$. We also present two generalizations of\nthe main theorem, and we discuss several methods of producing examples from\nthis construction.\n', 'Bryant-Salamon $\\mathrm{G}_2$ manifolds and coassociative fibrations   Bryant-Salamon constructed three 1-parameter families of complete manifolds\nwith holonomy $\\mathrm{G}_2$ which are asymptotically conical to a holonomy\n$\\mathrm{G}_2$ cone. For each of these families, including their asymptotic\ncone, we construct a fibration by asymptotically conical and conically singular\ncoassociative 4-folds. We show that these fibrations are natural\ngeneralizations of the following three well-known coassociative fibrations on\n$\\mathbb R^7$: the trivial fibration by 4-planes, the product of the standard\nLefschetz fibration of $\\mathbb C^3$ with a line, and the Harvey-Lawson\ncoassociative fibration. In particular, we describe coassociative fibrations of\nthe bundle of anti-self-dual 2-forms over the 4-sphere $\\mathcal{S}^4$, and the\ncone on $\\mathbb C \\mathbb P^3$, whose smooth fibres are $T^*\\mathcal{S}^2$,\nand whose singular fibres are $\\mathbb R^4/\\{\\pm 1\\}$. We relate these\nfibrations to hypersymplectic geometry, Donaldson\'s work on Kovalev-Lefschetz\nfibrations, harmonic 1-forms and the Joyce--Karigiannis construction of\nholonomy $\\mathrm{G}_2$ manifolds, and we construct vanishing cycles and\nassociative ""thimbles"" for these fibrations.\n', 'Infinitely many new families of complete cohomogeneity one\n  G_2-manifolds: G_2 analogues of the Taub-NUT and Eguchi-Hanson spaces   We construct infinitely many new 1-parameter families of simply connected\ncomplete noncompact G_2-manifolds with controlled geometry at infinity. The\ngeneric member of each family has so-called asymptotically locally conical\n(ALC) geometry. However, the nature of the asymptotic geometry changes at two\nspecial parameter values: at one special value we obtain a unique member of\neach family with asymptotically conical (AC) geometry; on approach to the other\nspecial parameter value the family of metrics collapses to an AC Calabi-Yau\n3-fold. Our infinitely many new diffeomorphism types of AC G_2-manifolds are\nparticularly noteworthy: previously the three examples constructed by Bryant\nand Salamon in 1989 furnished the only known simply connected AC G_2-manifolds.\n  We also construct a closely related conically singular G_2 holonomy space:\naway from a single isolated conical singularity, where the geometry becomes\nasymptotic to the G_2-cone over the standard nearly K\\""ahler structure on the\nproduct of a pair of 3-spheres, the metric is smooth and it has ALC geometry at\ninfinity. We argue that this conically singular ALC G_2-space is the natural\nG_2 analogue of the Taub-NUT metric in 4-dimensional hyperKaehler geometry and\nthat our new AC G_2-metrics are all analogues of the Eguchi-Hanson metric, the\nsimplest ALE hyperK\\""ahler manifold. Like the Taub-NUT and Eguchi-Hanson\nmetrics, all our examples are cohomogeneity one, i.e. they admit an isometric\nLie group action whose generic orbit has codimension one.\n']","[('g_2 manifolds', 0.6567509770393372), ('g_2 manifold', 0.6394803524017334), ('_2 manifolds', 0.6204916834831238), ('closed g_2 structure', 0.5776509046554565), ('g_2 structures', 0.5484468340873718), ('g_2 structure', 0.5306441187858582), ('manifolds admitting', 0.5083328485488892), ('manifolds', 0.5038849115371704), ('compact manifolds', 0.48590150475502014), ('holonomy metrics', 0.478613018989563)]"
355,355,82,355_trained transformers_trained transformer_transformer models_attention weights,"['trained transformers', 'trained transformer', 'transformer models', 'attention weights', 'large language models', 'transformer', 'transformers', 'transformer architectures', 'transformer architecture', 'softmax']","[""Clustering in pure-attention hardmax transformers and its role in\n  sentiment analysis   Transformers are extremely successful machine learning models whose\nmathematical properties remain poorly understood. Here, we rigorously\ncharacterize the behavior of transformers with hardmax self-attention and\nnormalization sublayers as the number of layers tends to infinity. By viewing\nsuch transformers as discrete-time dynamical systems describing the evolution\nof points in a Euclidean space, and thanks to a geometric interpretation of the\nself-attention mechanism based on hyperplane separation, we show that the\ntransformer inputs asymptotically converge to a clustered equilibrium\ndetermined by special points called leaders. We then leverage this theoretical\nunderstanding to solve sentiment analysis problems from language processing\nusing a fully interpretable transformer model, which effectively captures\n`context' by clustering meaningless words around leader words carrying the most\nmeaning. Finally, we outline remaining challenges to bridge the gap between the\nmathematical analysis of transformers and their real-life implementation.\n"", 'AlgoFormer: An Efficient Transformer Framework with Algorithmic\n  Structures   Besides natural language processing, transformers exhibit extraordinary\nperformance in solving broader applications, including scientific computing and\ncomputer vision. Previous works try to explain this from the expressive power\nand capability perspectives that standard transformers are capable of\nperforming some algorithms. To empower transformers with algorithmic\ncapabilities and motivated by the recently proposed looped transformer, we\ndesign a novel transformer framework, dubbed Algorithm Transformer (abbreviated\nas AlgoFormer). We provide an insight that efficient transformer architectures\ncan be designed by leveraging prior knowledge of tasks and the underlying\nstructure of potential algorithms. Compared with the standard transformer and\nvanilla looped transformer, the proposed AlgoFormer can perform efficiently in\nalgorithm representation in some specific tasks. In particular, inspired by the\nstructure of human-designed learning algorithms, our transformer framework\nconsists of a pre-transformer that is responsible for task preprocessing, a\nlooped transformer for iterative optimization algorithms, and a\npost-transformer for producing the desired results after post-processing. We\nprovide theoretical evidence of the expressive power of the AlgoFormer in\nsolving some challenging problems, mirroring human-designed algorithms.\nFurthermore, some theoretical and empirical results are presented to show that\nthe designed transformer has the potential to perform algorithm representation\nand learning. Experimental results demonstrate the empirical superiority of the\nproposed transformer in that it outperforms the standard transformer and\nvanilla looped transformer in some specific tasks. An extensive experiment on\nreal language tasks (e.g., neural machine translation of German and English,\nand text classification) further validates the expressiveness and effectiveness\nof AlgoFormer.\n', 'Transformers learn variable-order Markov chains in-context   Large language models have demonstrated impressive in-context learning (ICL)\ncapability. However, it is still unclear how the underlying transformers\naccomplish it, especially in more complex scenarios. Toward this goal, several\nrecent works studied how transformers learn fixed-order Markov chains (FOMC) in\ncontext, yet natural languages are more suitably modeled by variable-order\nMarkov chains (VOMC), i.e., context trees (CTs). In this work, we study the ICL\nof VOMC by viewing language modeling as a form of data compression and focus on\nsmall alphabets and low-order VOMCs. This perspective allows us to leverage\nmature compression algorithms, such as context-tree weighting (CTW) and\nprediction by partial matching (PPM) algorithms as baselines, the former of\nwhich is Bayesian optimal for a class of CTW priors. We empirically observe a\nfew phenomena: 1) Transformers can indeed learn to compress VOMC in-context,\nwhile PPM suffers significantly; 2) The performance of transformers is not very\nsensitive to the number of layers, and even a two-layer transformer can learn\nin-context quite well; and 3) Transformers trained and tested on non-CTW priors\ncan significantly outperform the CTW algorithm. To explain these phenomena, we\nanalyze the attention map of the transformers and extract two mechanisms, on\nwhich we provide two transformer constructions: 1) A construction with $D+2$\nlayers that can mimic the CTW algorithm accurately for CTs of maximum order\n$D$, 2) A 2-layer transformer that utilizes the feed-forward network for\nprobability blending. One distinction from the FOMC setting is that a counting\nmechanism appears to play an important role. We implement these synthetic\ntransformer layers and show that such hybrid transformers can match the ICL\nperformance of transformers, and more interestingly, some of them can perform\neven better despite the much-reduced parameter sets.\n']","[('trained transformers', 0.5952528715133667), ('trained transformer', 0.5869207382202148), ('transformer models', 0.5072760581970215), ('attention weights', 0.5011747479438782), ('large language models', 0.4823548197746277), ('transformer', 0.4761291742324829), ('transformers', 0.47298306226730347), ('transformer architectures', 0.4721764326095581), ('transformer architecture', 0.458271861076355), ('softmax', 0.44750717282295227)]"
356,356,82,356_control false discovery_false discovery rate_discovery rate fdr_discovery rate control,"['control false discovery', 'false discovery rate', 'discovery rate fdr', 'discovery rate control', 'false discovery', 'multiple hypothesis testing', 'discovery rate', 'multiple testing', 'rate fdr control', 'hypothesis testing']","['A New Procedure for Controlling False Discovery Rate in Large-Scale\n  t-tests   This paper is concerned with false discovery rate (FDR) control in\nlarge-scale multiple testing problems. We first propose a new data-driven\ntesting procedure for controlling the FDR in large-scale t-tests for one-sample\nmean problem. The proposed procedure achieves exact FDR control in finite\nsample settings when the populations are symmetric no matter the number of\ntests or sample sizes. Comparing with the existing bootstrap method for FDR\ncontrol, the proposed procedure is computationally efficient. We show that the\nproposed method can control the FDR asymptotically for asymmetric populations\neven when the test statistics are not independent. We further show that the\nproposed procedure with a simple correction is as accurate as the bootstrap\nmethod to the second-order degree, and could be much more effective than the\nexisting normal calibration. We extend the proposed procedure to two-sample\nmean problem. Empirical results show that the proposed procedures have better\nFDR control than existing ones when the proportion of true alternative\nhypotheses is not too low, while maintaining reasonably good detection ability.\n', 'Conditional calibration for false discovery rate control under\n  dependence   We introduce a new class of methods for finite-sample false discovery rate\n(FDR) control in multiple testing problems with dependent test statistics where\nthe dependence is fully or partially known. Our approach separately calibrates\na data-dependent p-value rejection threshold for each hypothesis, relaxing or\ntightening the threshold as appropriate to target exact FDR control. In\naddition to our general framework we propose a concrete algorithm, the\ndependence-adjusted Benjamini-Hochberg (dBH) procedure, which adaptively\nthresholds the q-value for each hypothesis. Under positive regression\ndependence the dBH procedure uniformly dominates the standard BH procedure, and\nin general it uniformly dominates the Benjamini-Yekutieli (BY) procedure (also\nknown as BH with log correction). Simulations and real data examples illustrate\npower gains over competing approaches to FDR control under dependence.\n', 'Large-scale Multiple Testing: Fundamental Limits of False Discovery Rate\n  Control and Compound Oracle   The false discovery rate (FDR) and the false non-discovery rate (FNR),\ndefined as the expected false discovery proportion (FDP) and the false\nnon-discovery proportion (FNP), are the most popular benchmarks for multiple\ntesting. Despite the theoretical and algorithmic advances in recent years, the\noptimal tradeoff between the FDR and the FNR has been largely unknown except\nfor certain restricted classes of decision rules, e.g., separable rules, or for\nother performance metrics, e.g., the marginal FDR and the marginal FNR (mFDR\nand mFNR). In this paper, we determine the asymptotically optimal FDR-FNR\ntradeoff under the two-group random mixture model when the number of hypotheses\ntends to infinity. Distinct from the optimal mFDR-mFNR tradeoff, which is\nachieved by separable decision rules, the optimal FDR-FNR tradeoff requires\ncompound rules even in the large-sample limit and for models as simple as the\nGaussian location model. This suboptimality of separable rules also holds for\nother objectives, such as maximizing the expected number of true discoveries.\nFinally, to address the limitation of the FDR which only controls the\nexpectation but not the fluctuation of the FDP, we also determine the optimal\ntradeoff when the FDP is controlled with high probability and show it coincides\nwith that of the mFDR and the mFNR. Extensions to models with a fixed non-null\nproportion are also obtained.\n']","[('control false discovery', 0.6075212955474854), ('false discovery rate', 0.5963813662528992), ('discovery rate fdr', 0.5503056645393372), ('discovery rate control', 0.5147057175636292), ('false discovery', 0.476547509431839), ('multiple hypothesis testing', 0.47511419653892517), ('discovery rate', 0.4400155246257782), ('multiple testing', 0.42730021476745605), ('rate fdr control', 0.4174032509326935), ('hypothesis testing', 0.40313130617141724)]"
357,357,82,357_quantum codes_new quantum codes_codes quantum_codes entanglement,"['quantum codes', 'new quantum codes', 'codes quantum', 'codes entanglement', 'quasi cyclic codes', 'linear codes', 'assisted quantum error', 'self dual codes', 'cyclic codes', 'binary quantum']","['New MDS Entanglement-Assisted Quantum Codes from MDS Hermitian\n  Self-Orthogonal Codes   The intersection ${\\bf C}\\bigcap {\\bf C}^{\\perp_H}$ of a linear code ${\\bf C}\n\\subset {\\bf F}_{q^2}$ and its Hermitian dual ${\\bf C}^{\\perp_H}$ is called the\nHermitian hull of this code. A linear code ${\\bf C} \\subset {\\bf F}_{q^2}$\nsatisfying ${\\bf C} \\subset {\\bf C}^{\\perp_H}$ is called Hermitian\nself-orthogonal. Many Hermitian self-orthogonal codes were given for the\nconstruction of MDS quantum error correction codes (QECCs). In this paper we\nprove that for a nonnegative integer $h$ satisfying $0 \\leq h \\leq k$, a linear\nHermitian self-orthogonal $[n, k]_{q^2}$ code is equivalent to a linear\n$h$-dimension Hermitian hull code. Therefore a lot of new MDS\nentanglement-assisted quantum error correction (EAQEC) codes can be constructed\nfrom previous known Hermitian self-orthogonal codes. Actually our method shows\nthat previous constructed quantum MDS codes from Hermitian self-orthogonal\ncodes can be transformed to MDS entanglement-assisted quantum codes with\nnonzero consumption parameter $c$ directly. We prove that MDS EAQEC $[[n, k, d,\nc]]_q$ codes with nonzero $c$ parameters and $d\\leq \\frac{n+2}{2}$ exist for\narbitrary length $n \\leq q^2+1$. Moreover any QECC constructed from\n$k$-dimensional Hermitian self-orthogonal codes can be transformed to $k$\ndifferent EAQEC codes.\n', 'Cyclic codes and some new entanglement-assisted quantum MDS codes   Entanglement-assisted quantum error correcting codes (EAQECCs) play a\nsignificant role in protecting quantum information from decoherence and quantum\nnoise. Recently, constructing entanglement-assisted quantum maximum distance\nseparable (EAQMDS) codes with flexible parameters has received much attention.\nIn this work, four families of EAQMDS codes with a more general length are\npresented. And the method of selecting defining set is different from others.\nCompared with all the previously known results, the EAQMDS codes we constructed\nhave larger minimum distance. All of these EAQMDS codes are new in the sense\nthat their parameters are not covered by the quantum codes available in the\nliterature.\n', 'Constructions of entanglement-assisted quantum MDS codes from\n  generalized Reed-Solomon codes   By generalizing the stabilizer quantum error-correcting codes,\nentanglement-assisted quantum error-correcting (EAQEC) codes were introduced,\nwhich could be derived from any classical linear codes via the relaxation of\nself-orthogonality conditions with the aid of pre-shared entanglement between\nthe sender and the receiver. In this paper, three classes of\nentanglement-assisted quantum error-correcting maximum-distance-separable\n(EAQMDS) codes are constructed through generalized Reed-Solomon codes. Under\nour constructions, the minimum distances of our EAQMDS codes are much larger\nthan those of the known EAQMDS codes of the same lengths that consume the same\nnumber of ebits. Furthermore, some of the lengths of the EAQMDS codes are not\ndivisors of $q^2-1$, which are completely new and unlike all those known\nlengths existed before.\n']","[('quantum codes', 0.7173324227333069), ('new quantum codes', 0.7068290114402771), ('codes quantum', 0.7065497040748596), ('codes entanglement', 0.6712090373039246), ('quasi cyclic codes', 0.5026440024375916), ('linear codes', 0.5006842613220215), ('assisted quantum error', 0.49590864777565), ('self dual codes', 0.4902454614639282), ('cyclic codes', 0.48366236686706543), ('binary quantum', 0.480954647064209)]"
358,358,82,358_sum stochastic games_stochastic games_stochastic game_games stochastic,"['sum stochastic games', 'stochastic games', 'stochastic game', 'games stochastic', 'pure nash equilibrium', 'games finite', 'zero sum games', 'nash equilibrium', 'pure nash equilibria', 'random games']","['Limit Value in Zero-Sum Stochastic Games with Vanishing Stage Duration\n  and Public Signals   We consider the behaviour of $\\lambda$-discounted zero-sum games as the\ndiscount factor $\\lambda$ approaches $0$ (that is, the players are more and\nmore patient), in the context of games with stage duration. In stochastic games\nwith stage duration $h$, players act at times $0, h, 2h,$ and so on. The payoff\nand leaving probabilities are proportional to $h$. When $h$ tends to $0$, such\ndiscrete-time games approximate games played in continuous time. The asymptotic\nbehavior of the values (when both $\\lambda$ and $h$ tend to $0$) was already\nstudied in the case of stochastic games with perfect observation of the state\nand in the state-blind case. We consider the same question for the case of\nstochastic games with imperfect observation of the state. More precisely, we\nconsider a particular case of such games, stochastic games with public signals,\nin which players are given at each stage a public signal that depends only on\nthe current state. Our main result states that there exists a stochastic game\nwith public signals, with no limit value (as the discount factor $\\lambda$ goes\nto $0$) if stage duration is $1$, but with a limit value when stage duration\n$h$ and discount factor $\\lambda$ both tend to $0$. Informally speaking, it\nmeans that the limit value in discrete time does not exist, but the limit value\nin continuous time (i.e. when $h$ approaches $0$) exists. Such a situation is\nimpossible in the case of stochastic games with perfect observation of the\nstate.\n', 'Limit Value in Zero-Sum Stochastic Games with Vanishing Stage Duration\n  and Public Signals   We consider the behaviour of $\\lambda$-discounted zero-sum games as the\ndiscount factor $\\lambda$ approaches 0 (that is, the players are more and more\npatient), in the context of games with stage duration. In stochastic games with\nstage duration h, players act at times 0, h, 2h, and so on. The payoff and\nleaving probabilities are proportional to h. When h tends to 0, such\ndiscrete-time games approximate games played in continuous time. The asymptotic\nbehavior of the values (when both $\\lambda$ and h tend to 0) was already\nstudied in the case of stochastic games with perfect observation of the state\nand in the state-blind case.We consider the same question for the case of\nstochastic games with imperfect observation of the state. More precisely, we\nconsider a particular case of such games, stochastic games with public signals,\nin which players are given at each stage a public signal that depends only on\nthe current state. Our main result states that there exists a stochastic game\nwith public signals, with no limit value (as the discount factor $\\lambda$ goes\nto 0) if stage duration is 1, but with a limit value when stage duration h and\ndiscount factor $\\lambda$ both tend to 0. Informally speaking, it means that\nthe limit value in discrete time does not exist, but the limit value in\ncontinuous time (i.e. when h approaches 0) exists. Such a situation is\nimpossible in the case of stochastic games with perfect observation of the\nstate.\n', ""Best-Response dynamics in two-person random games with correlated\n  payoffs   We consider finite two-player normal form games with random payoffs. Player\nA's payoffs are i.i.d. from a uniform distribution. Given p in [0, 1], for any\naction profile, player B's payoff coincides with player A's payoff with\nprobability p and is i.i.d. from the same uniform distribution with probability\n1-p. This model interpolates the model of i.i.d. random payoff used in most of\nthe literature and the model of random potential games. First we study the\nnumber of pure Nash equilibria in the above class of games. Then we show that,\nfor any positive p, asymptotically in the number of available actions, best\nresponse dynamics reaches a pure Nash equilibrium with high probability.\n""]","[('sum stochastic games', 0.6986882090568542), ('stochastic games', 0.6968392729759216), ('stochastic game', 0.6794417500495911), ('games stochastic', 0.6700209975242615), ('pure nash equilibrium', 0.6056612133979797), ('games finite', 0.5907350778579712), ('zero sum games', 0.582808256149292), ('nash equilibrium', 0.5689256191253662), ('pure nash equilibria', 0.5567223429679871), ('random games', 0.5148462653160095)]"
359,359,82,359_crossing number graph_crossing edges_number crossings_crossings,"['crossing number graph', 'crossing edges', 'number crossings', 'crossings', 'crossing number', 'number edges', 'edges cross', 'planar graphs', 'crossing', 'crossing critical']","[""An algorithm for estimating the crossing number of dense graphs, and\n  continuous analogs of the crossing and rectilinear crossing numbers   We present a deterministic $n^{2+o(1)}$-time algorithm that approximates the\ncrossing number of any graph $G$ of order $n$ up to an additive error of\n$o(n^4)$. We also provide a randomized polynomial-time algorithm that\nconstructs a drawing of $G$ with $\\text{cr}(G)+o(n^4)$ crossings. These results\nyield a $1+o(1)$ approximation algorithm for the crossing number of dense\ngraphs. Our work complements a paper of Fox, Pach and S\\'uk, who obtained\nsimilar results for the rectilinear crossing number.\n  The results of Fox, Pach and S\\'uk and in this paper imply that the\n(normalized) crossing and rectilinear crossing numbers are estimable\nparameters. Motivated by this, we introduce two graphon parameters, the\n\\textit{crossing density} and the \\textit{rectilinear crossing density}, and we\nprove that, in a precise sense, these are the correct continuous analogs of the\ncrossing and rectilinear crossing numbers of graphs.\n"", 'Rectilinear Crossing Number of Graphs Excluding Single-Crossing Graphs\n  as Minors   The crossing number of a graph $G$ is the minimum number of crossings in a\ndrawing of $G$ in the plane. A rectilinear drawing of a graph $G$ represents\nvertices of $G$ by a set of points in the plane and represents each edge of $G$\nby a straight-line segment connecting its two endpoints. The rectilinear\ncrossing number of $G$ is the minimum number of crossings in a rectilinear\ndrawing of $G$.\n  By the crossing lemma, the crossing number of an $n$-vertex graph $G$ can be\n$O(n)$ only if $|E(G)|\\in O(n)$. Graphs of bounded genus and bounded degree\n(B\\""{o}r\\""{o}czky, Pach and T\\\'{o}th, 2006) and in fact all bounded degree\nproper minor-closed families (Wood and Telle, 2007) have been shown to admit\nlinear crossing number, with tight $\\Theta(\\Delta n)$ bound shown by\nDujmovi\\\'c, Kawarabayashi, Mohar and Wood, 2008.\n  Much less is known about rectilinear crossing number. It is not bounded by\nany function of the crossing number. We prove that graphs that exclude a\nsingle-crossing graph as a minor have the rectilinear crossing number $O(\\Delta\nn)$. This dependence on $n$ and $\\Delta$ is best possible. A single-crossing\ngraph is a graph whose crossing number is at most one. Thus the result applies\nto $K_5$-minor-free graphs, for example. It also applies to bounded treewidth\ngraphs, since each family of bounded treewidth graphs excludes some fixed\nplanar graph as a minor. Prior to our work, the only bounded degree\nminor-closed families known to have linear rectilinear crossing number were\nbounded degree graphs of bounded treewidth (Wood and Telle, 2007), as well as,\nbounded degree $K_{3,3}$-minor-free graphs (Dujmovi\\\'c, Kawarabayashi, Mohar\nand Wood, 2008). In the case of bounded treewidth graphs, our $O(\\Delta n)$\nresult is again tight and improves on the previous best known bound of\n$O(\\Delta^2 n)$ by Wood and Telle, 2007 (obtained for convex geometric\ndrawings).\n', 'Improvement on the crossing number of crossing-critical graphs   The crossing number of a graph $G$ is the minimum number of edge crossings\nover all drawings of $G$ in the plane. A graph $G$ is $k$-crossing-critical if\nits crossing number is at least $k$, but if we remove any edge of $G$, its\ncrossing number drops below $k$. There are examples of $k$-crossing-critical\ngraphs that do not have drawings with exactly $k$ crossings. Richter and\nThomassen proved in 1993 that if $G$ is $k$-crossing-critical, then its\ncrossing number is at most $2.5k+16$. We improve this bound to\n$2k+6\\sqrt{k}+44$.\n']","[('crossing number graph', 0.6488727331161499), ('crossing edges', 0.6253199577331543), ('number crossings', 0.603298544883728), ('crossings', 0.55625319480896), ('crossing number', 0.5324494242668152), ('number edges', 0.515736997127533), ('edges cross', 0.507216215133667), ('planar graphs', 0.5050764679908752), ('crossing', 0.5036954879760742), ('crossing critical', 0.5019853711128235)]"
360,360,82,360_lipschitz stability inverse_stability inverse source_stability inverse_inverse boundary value,"['lipschitz stability inverse', 'stability inverse source', 'stability inverse', 'inverse boundary value', 'inverse boundary', 'stability estimates', 'inverse source problems', 'estimate inverse', 'lipschitz stability', 'stability estimate']","['Stability for inverse source problems by Carleman estimates   In this article, we provide a modified argument for proving conditional\nstability for inverse problems of determining spatially varying functions in\nevolution equations by Carleman estimates. Our method needs not any cut-off\nprocedures and can simplify the existing proofs. We establish the conditional\nstability for inverse source problems for a hyperbolic equation and a parabolic\nequation, and our method is widely applicable to various evolution equations.\n', 'Lipschitz stability for an inverse source problem in anisotropic\n  parabolic equations with dynamic boundary conditions   In this paper, we study an inverse problem for linear parabolic system with\nvariable diffusion coefficients subject to dynamic boundary conditions. We\nprove a global Lipschitz stability for the inverse problem involving a\nsimultaneous recovery of two source terms from a single measurement and\ninterior observations, based on a recent Carleman estimate for such problems.\n', 'Carleman estimate and an inverse source problem for the Kelvin-Voigt\n  model for viscoelasticity   We consider the Kelvin-Voigt model for the viscoelasticity, and prove a\nCarleman estimate for functions without compact supports. Then we apply the\nCarleman estimate to prove the Lipschitz stability in determining a spatial\nvarying function in an external source term of Kelvin-Voigt model by a single\nmeasurement. Finally as a related system, we consider an isothermal\ncompressible fluid system and apply the Carleman estimate to establish the\nLipschitz stability for an inverse source problem for the compressible fluid\nsystem.\n']","[('lipschitz stability inverse', 0.6540228724479675), ('stability inverse source', 0.6118014454841614), ('stability inverse', 0.5806444883346558), ('inverse boundary value', 0.5293729901313782), ('inverse boundary', 0.5090106725692749), ('stability estimates', 0.5011268258094788), ('inverse source problems', 0.4926595985889435), ('estimate inverse', 0.48376035690307617), ('lipschitz stability', 0.4674394130706787), ('stability estimate', 0.45525774359703064)]"
361,361,82,361_nonexpansive mappings_fixed point nonexpansive_nonexpansive operators_mappings banach,"['nonexpansive mappings', 'fixed point nonexpansive', 'nonexpansive operators', 'mappings banach', 'point nonexpansive', 'mappings banach spaces', 'nonexpansiveness', 'point mappings', 'existence fixed points', 'mappings uniformly']","['Convergence of modified Picard-Mann hybrid iteration process for nearly\n  nonexpansive mappings   In this paper, we prove the strong convergence theorems for nearly\nnonexpansive mappings, using the modified Picard-Mann hybrid iteration process\nin the context of uniformly convex Banach space.\n', 'On a useful lemma that relates quasi-nonexpansive and demicontractive\n  mappings in Hilbert spaces   We give a brief account on a basic result (Lemma \\ref{lem2}) which is a very\nuseful tool in proving various convergence theorems in the framework of the\niterative approximation of fixed points of demicontractive mappings in Hilbert\nspaces. This Lemma relates the class of quasi-nonexpansive mappings, by one\nhand, and the class of $k$-demicontractive mappings (quasi $k$-strict\npseudocontractions), on the other hand and essentially states that the class of\ndemicontractive mappings, which strictly includes the class of\nquasi-nonexpansive mappings, can be embedded in the later by means of an\naveraged perturbation. From the point of view of the fixed point problem, this\nmeans that any convergence result for Krasnoselskij-Mann iterative algorithms\nin the class of $k$-demicontractive mappings can be derived from its\ncorresponding counterpart from quasi-nonexpansive mappings.\n', 'Fixed points theorems for $b$-enriched multivalued nonexpansive mappings\n  and *-$b$-enriched nonexpansive mappings   The main purpose of this paper is to extend some fixed point results for\nsingle valued $b$-enriched nonexpansive mappings to the case of multivalued\nmappings. To this end, we introduce *-$b$-enriched nonexpansive mappings, as a\ngeneralization of *-nonexpansive mappings \\cite{Abdul Rahim Khan} for which we\nestablish an existence theorem in Hilbert space.\n  We proved weak and strong convergence results of Krasnoselskii iteration\nprocess for $b$-enriched multivalued nonexpasive mappings and *-$b$-enriched\nnonexpansive mappings.\n']","[('nonexpansive mappings', 0.7482295036315918), ('fixed point nonexpansive', 0.6364729404449463), ('nonexpansive operators', 0.5305425524711609), ('mappings banach', 0.5253399014472961), ('point nonexpansive', 0.49718889594078064), ('mappings banach spaces', 0.49029868841171265), ('nonexpansiveness', 0.4706607758998871), ('point mappings', 0.4569548964500427), ('existence fixed points', 0.4548880457878113), ('mappings uniformly', 0.4458502233028412)]"
362,362,81,362_monic polynomial mathbb_quartic polynomials_monic irreducible polynomial_monic polynomial,"['monic polynomial mathbb', 'quartic polynomials', 'monic irreducible polynomial', 'monic polynomial', 'cyclic galois group', 'quartic fields', 'galois groups', 'quadratic fields', 'algebraic number field', 'galois group mathbb']","['Monogenic trinomials and class numbers of related quadratic fields   We say that a monic polynomial $f(x)\\in {\\mathbb Z}[x]$ of degree $N\\ge 2$ is\nmonogenic if $f(x)$ is irreducible over ${\\mathbb Q}$ and\n$\\{1,\\theta,\\theta^2,\\ldots ,\\theta^{N-1}\\}$ is a basis for the ring of\nintegers of ${\\mathbb Q}(\\theta)$, where $f(\\theta)=0$. In this article, we\ninvestigate the divisibility of the class numbers of quadratic fields ${\\mathbb\nQ}(\\sqrt{\\delta})$ for certain families of monogenic trinomials\n$f(x)=x^N+Ax+B$, where $\\delta\\ne \\pm 1$ is a squarefree divisor of the\ndiscriminant of $f(x)$.\n', 'Monogenic Cyclic Quartic Trinomials   A monic polynomial $f(x)\\in {\\mathbb Z}[x]$ of degree $N$ is called monogenic\nif $f(x)$ is irreducible over ${\\mathbb Q}$ and $\\{1,\\theta,\\theta^2,\\ldots\n,\\theta^{N-1}\\}$ is a basis for the ring of integers of ${\\mathbb Q}(\\theta)$,\nwhere $f(\\theta)=0$. In this brief note, we prove that there exist exactly\nthree distinct monogenic trinomials of the form $x^4+bx^2+d$ whose Galois group\nis the cyclic group of order 4.\n', 'Monogenic Reciprocal Quartic Polynomials And Their Galois Groups   Suppose that $f(x)=x^4+Ax^3+Bx^2+Ax+1\\in {\\mathbb Z}[x]$. We say that $f(x)$\nis monogenic if $f(x)$ is irreducible over ${\\mathbb Q}$ and\n$\\{1,\\theta,\\theta^2,\\theta^3\\}$ is a basis for the ring of integers of\n${\\mathbb Q}(\\theta)$, where $f(\\theta)=0$. For each possible Galois group $G$\nthat can occur in the two cases of $A\\ne 0$ with $B=0$, and $AB\\ne 0$, we\ndetermine all monogenic polynomials $f(x)$ with Galois group $G$.\n']","[('monic polynomial mathbb', 0.5325750112533569), ('quartic polynomials', 0.5195972919464111), ('monic irreducible polynomial', 0.5091495513916016), ('monic polynomial', 0.47688817977905273), ('cyclic galois group', 0.46957871317863464), ('quartic fields', 0.4653441309928894), ('galois groups', 0.4612483084201813), ('quadratic fields', 0.4561796188354492), ('algebraic number field', 0.4532676935195923), ('galois group mathbb', 0.4448647201061249)]"
363,363,81,363_gabor frames_frame operator_gabor frame_frames mathbb,"['gabor frames', 'frame operator', 'gabor frame', 'frames mathbb', 'gabor transform', 'frames finite', 'wavelet frames', 'frames frames', 'frames', 'dual frames']","['On Gabor g-frames and Fourier series of operators   We show that Hilbert-Schmidt operators can be used to define frame-like\nstructures for $L^2(\\mathbb{R}^d)$ over lattices in $\\mathbb{R}^{2d}$ that\ninclude multi-window Gabor frames as a special case. These frame-like\nstructures are called Gabor g-frames, as they are examples of g-frames as\nintroduced by Sun. We show that Gabor g-frames share many properties of Gabor\nframes, including a Janssen representation and Wexler-Raz biorthogonality\nconditions. A central part of our analysis is a notion of Fourier series of\nperiodic operators based on earlier work by Feichtinger and Kozek, where we\nshow in particular a Poisson summation formula for trace class operators. By\nchoosing operators from certain Banach subspaces of the Hilbert Schmidt\noperators, Gabor g-frames give equivalent norms for modulation spaces in terms\nof weighted $\\ell^p$-norms of an associated sequence, as previously shown for\nlocalization operators by D\\""orfler, Feichtinger and Gr\\""ochenig.\n', 'Gabor Frames: Characterizations and Coarse Structure   This survey offers a systematic and streamlined exposition of the most\nimportant characterizations of Gabor frames over a lattice. The goal is to\ncollect the most important characterizations of Gabor frames and offer a\nsystematic exposition of these structures. In the center of these\ncharacterizations is the duality theorem for Gabor frames. Most\ncharacterizations within the $L^2$-theory follow directly from this fundamental\nduality. In particular, the celebrated characterizations of Janssen and\nRon-Shen are consequences of the duality theorem, and the characterization of\nZeevi and Zibulski for rational lattices also becomes a corollary. The novelty\nis the streamlined sequence of proofs, so that most of the structure theory of\nGabor frames fits into a single, short article. The only prerequisite is the\nthorough mastery of the Poisson summation formula and some basic facts about\nframes and Riesz sequences.\n', 'Matrix-Valued Gabor Frames over LCA Groups for Operators   G\\v avruta studied atomic systems in terms of frames for range of operators\n(that is, for subspaces), namely $K$-frames, where the lower frame condition is\ncontrolled by the Hilbert-adjoint of a bounded linear operator $K$. For a\nlocally compact abelian group G and a positive integer $n$, we study frames of\nmatrix-valued Gabor systems in the matrix-valued Lebesgue space $L^2(G,\n\\mathbb{C}^{n\\times n})$ , where a bounded linear operator $\\Theta$ on $L^2(G,\n\\mathbb{C}^{n\\times n})$ controls not only lower but also the upper frame\ncondition. We term such frames matrix-valued $(\\Theta, \\Theta^*)$-Gabor frames.\nFirstly, we discuss frame preserving mapping in terms of hyponormal operators.\nSecondly, we give necessary and sufficient conditions for the existence of\nmatrix-valued $(\\Theta, \\Theta^*)$- Gabor frames in terms of hyponormal\noperators. It is shown that if $\\Theta$ is adjointable hyponormal operator,\nthen $L^2(G, \\mathbb{C}^{n\\times n})$ admits a $\\lambda$-tight $(\\Theta,\n\\Theta^*)$-Gabor frame for every positive real number $\\lambda$. A\ncharacterization of matrix-valued $(\\Theta, \\Theta^*)$-Gabor frames is given.\nFinally, we show that matrix-valued $(\\Theta, \\Theta^*)$-Gabor frames are\nstable under small perturbation of window functions. Several examples are given\nto support our study.\n']","[('gabor frames', 0.6047268509864807), ('frame operator', 0.5672231316566467), ('gabor frame', 0.5481982231140137), ('frames mathbb', 0.5198169946670532), ('gabor transform', 0.5086774230003357), ('frames finite', 0.4911607801914215), ('wavelet frames', 0.47465020418167114), ('frames frames', 0.4694933295249939), ('frames', 0.44996631145477295), ('dual frames', 0.44576403498649597)]"
364,364,80,364_k_ free graphs_bounded clique number_k_ free graph_bounded clique,"['k_ free graphs', 'bounded clique number', 'k_ free graph', 'bounded clique', 'maximum cliques', 'subgraphs', 'induced subgraph', 'free graphs', 'cliques size', 'number cliques']","['Small subgraphs with large average degree   In this paper we study the fundamental problem of finding small dense\nsubgraphs in a given graph. For a real number $s>2$, we prove that every graph\non $n$ vertices with average degree at least $d$ contains a subgraph of average\ndegree at least $s$ on at most $nd^{-\\frac{s}{s-2}}(\\log d)^{O_s(1)}$ vertices.\nThis is optimal up to the polylogarithmic factor, and resolves a conjecture of\nFeige and Wagner. In addition, we show that every graph with $n$ vertices and\naverage degree at least $n^{1-\\frac{2}{s}+\\varepsilon}$ contains a subgraph of\naverage degree at least $s$ on $O_{\\varepsilon,s}(1)$ vertices, which is also\noptimal up to the constant hidden in the $O(.)$ notation, and resolves a\nconjecture of Verstra\\""ete.\n', 'Balanced subdivisions of cliques in graphs   Given a graph $H$, a balanced subdivision of $H$ is a graph obtained from $H$\nby subdividing every edge the same number of times. In 1984, Thomassen\nconjectured that for each integer $k\\ge 1$, high average degree is sufficient\nto guarantee a balanced subdivision of $K_k$. Recently, Liu and Montgomery\nresolved this conjecture. We give an optimal estimate up to an absolute\nconstant factor by showing that there exists $c>0$ such that for sufficiently\nlarge $d$, every graph with average degree at least $d$ contains a balanced\nsubdivision of a clique with at least $cd^{1/2}$ vertices. It also confirms a\nconjecture from Verstra{\\""e}te: every graph of average degree $cd^2$, for some\nabsolute constant $c>0$, contains a pair of disjoint isomorphic subdivisions of\nthe complete graph $K_d$. We also prove that there exists some absolute $c>0$\nsuch that for sufficiently large $d$, every $C_4$-free graph with average\ndegree at least $d$ contains a balanced subdivision of the complete graph\n$K_{cd}$, which extends a result of Balogh, Liu and Sharifzadeh.\n', ""Induced subdivisions in $K_{s,s}$-free graphs with polynomial average\n  degree   In this paper we prove that for every $s\\geq 2$ and every graph $H$ the\nfollowing holds. Let $G$ be a graph with average degree $\\Omega_H(s^{C|H|^2})$,\nfor some absolute constant $C>0$, then $G$ either contains a $K_{s,s}$ or an\ninduced subdivision of $H$. This is essentially tight and confirms a conjecture\nof Bonamy, Bousquet, Pilipczuk, Rz\\k{a}\\.zewski, Thomass\\'e, and Walczak. A\nslightly weaker form of this has been independently proved by Bourneuf,\nBuci\\'c, Cook, and Davies.\n  We actually prove a much more general result which implies the above (with\nworse dependence on $|H|$). We show that for every $ k\\geq 2$ there is $C_k>0$\nsuch that any graph $G$ with average degree $s^{C_k}$ either contains a\n$K_{s,s}$ or an induced subgraph $G'\\subseteq G$ without $C_4$'s and with\naverage degree at least $k$.\n  Finally, using similar methods we can prove the following. For every $k,t\\geq\n2$ every graph $G$ with average degree at least $C_tk^{\\Omega(t)}$ must contain\neither a $K_k$, an induced $K_{t,t}$ or an induced subdivision of $K_k$. This\nis again essentially tight up to the implied constants and answers in a strong\nform a question of Davies.\n""]","[('k_ free graphs', 0.5627554059028625), ('bounded clique number', 0.5537981986999512), ('k_ free graph', 0.5176203846931458), ('bounded clique', 0.5075780749320984), ('maximum cliques', 0.4916137754917145), ('subgraphs', 0.4840104281902313), ('induced subgraph', 0.47054368257522583), ('free graphs', 0.4500736892223358), ('cliques size', 0.42718854546546936), ('number cliques', 0.42507264018058777)]"
365,365,80,365_quasi newton methods_hessian approximations_superlinear convergence rate_hessian approximation,"['quasi newton methods', 'hessian approximations', 'superlinear convergence rate', 'hessian approximation', 'regularized newton', 'memory quasi newton', 'newton methods', 'quasi newton', 'superlinear convergence', 'cubic regularized newton']","['Sharpened Quasi-Newton Methods: Faster Superlinear Rate and Larger Local\n  Convergence Neighborhood   Non-asymptotic analysis of quasi-Newton methods have gained traction\nrecently. In particular, several works have established a non-asymptotic\nsuperlinear rate of $\\mathcal{O}((1/\\sqrt{t})^t)$ for the (classic) BFGS method\nby exploiting the fact that its error of Newton direction approximation\napproaches zero. Moreover, a greedy variant of BFGS was recently proposed which\naccelerates its convergence by directly approximating the Hessian, instead of\nthe Newton direction, and achieves a fast local quadratic convergence rate.\nAlas, the local quadratic convergence of Greedy-BFGS requires way more updates\ncompared to the number of iterations that BFGS requires for a local superlinear\nrate. This is due to the fact that in Greedy-BFGS the Hessian is directly\napproximated and the Newton direction approximation may not be as accurate as\nthe one for BFGS. In this paper, we close this gap and present a novel BFGS\nmethod that has the best of both worlds in that it leverages the approximation\nideas of both BFGS and Greedy-BFGS to properly approximate the Newton direction\nand the Hessian matrix simultaneously. Our theoretical results show that our\nmethod out-performs both BFGS and Greedy-BFGS in terms of convergence rate,\nwhile it reaches its quadratic convergence rate with fewer steps compared to\nGreedy-BFGS. Numerical experiments on various datasets also confirm our\ntheoretical findings.\n', 'Regularization of Limited Memory Quasi-Newton Methods for Large-Scale\n  Nonconvex Minimization   This paper deals with regularized Newton methods, a flexible class of\nunconstrained optimization algorithms that is competitive with line search and\ntrust region methods and potentially combines attractive elements of both. The\nparticular focus is on combining regularization with limited memory\nquasi-Newton methods by exploiting the special structure of limited memory\nalgorithms. Global convergence of regularization methods is shown under mild\nassumptions and the details of regularized limited memory quasi-Newton updates\nare discussed including their compact representations.\n  Numerical results using all large-scale test problems from the CUTEst\ncollection indicate that our regularized version of L-BFGS is competitive with\nstate-of-the-art line search and trust-region L-BFGS algorithms and previous\nattempts at combining L-BFGS with regularization, while potentially\noutperforming some of them, especially when nonmonotonicity is involved.\n', 'Limited-Memory Greedy Quasi-Newton Method with Non-asymptotic\n  Superlinear Convergence Rate   Non-asymptotic convergence analysis of quasi-Newton methods has gained\nattention with a landmark result establishing an explicit local superlinear\nrate of O$((1/\\sqrt{t})^t)$. The methods that obtain this rate, however,\nexhibit a well-known drawback: they require the storage of the previous Hessian\napproximation matrix or all past curvature information to form the current\nHessian inverse approximation. Limited-memory variants of quasi-Newton methods\nsuch as the celebrated L-BFGS alleviate this issue by leveraging a limited\nwindow of past curvature information to construct the Hessian inverse\napproximation. As a result, their per iteration complexity and storage\nrequirement is O$(\\tau d)$ where $\\tau\\le d$ is the size of the window and $d$\nis the problem dimension reducing the O$(d^2)$ computational cost and memory\nrequirement of standard quasi-Newton methods. However, to the best of our\nknowledge, there is no result showing a non-asymptotic superlinear convergence\nrate for any limited-memory quasi-Newton method. In this work, we close this\ngap by presenting a Limited-memory Greedy BFGS (LG-BFGS) method that can\nachieve an explicit non-asymptotic superlinear rate. We incorporate\ndisplacement aggregation, i.e., decorrelating projection, in post-processing\ngradient variations, together with a basis vector selection scheme on variable\nvariations, which greedily maximizes a progress measure of the Hessian estimate\nto the true Hessian. Their combination allows past curvature information to\nremain in a sparse subspace while yielding a valid representation of the full\nhistory. Interestingly, our established non-asymptotic superlinear convergence\nrate demonstrates an explicit trade-off between the convergence speed and\nmemory requirement, which to our knowledge, is the first of its kind. Numerical\nresults corroborate our theoretical findings and demonstrate the effectiveness\nof our method.\n']","[('quasi newton methods', 0.6801259517669678), ('hessian approximations', 0.5986191034317017), ('superlinear convergence rate', 0.5887972712516785), ('hessian approximation', 0.5826637148857117), ('regularized newton', 0.5527123212814331), ('memory quasi newton', 0.5460689067840576), ('newton methods', 0.5448038578033447), ('quasi newton', 0.5198156237602234), ('superlinear convergence', 0.5197476744651794), ('cubic regularized newton', 0.5082272291183472)]"
366,366,80,366_functions quaternionic_regular functions_functions slice_slice regular,"['functions quaternionic', 'regular functions', 'functions slice', 'slice regular', 'quaternionic analogues', 'axially symmetric domains', 'quaternion valued', 'quaternions', 'quaternionic', 'riemann operators']","['Quaternionic slice regular functions and quaternionic Laplace transforms   The functions studied in the paper are quaternion-valued functions of a\nquaternionic variable. It is show that the left slice regular functions and\nright slice regular functions are related by a particular involution. The\nrelation between left slice regular functions, right slice regular functions\nand intrinsic regular functions is revealed. The classical Laplace transform\ncan be naturally generalized to quaternions in two different ways, which\ntransform a quaternion-valued function of a real variable to a left or right\nslice regular quaternion-valued function of a quaternionic variable. The usual\nproperties of the classical Laplace transforms are generalized to quaternionic\nLaplace transforms.\n', ""Zeroes of weakly slice regular functions of several quaternionic\n  variables on non-axially symmetric domains   In this research, we study zeroes of weakly slice regular functions within\nthe framework of several quaternionic variables, specifically focusing on\nnon-axially symmetric domains. Our recent work introduces path-slice stem\nfunctions, along with a novel $*$-product, tailored for weakly slice regular\nfunctions. This innovation allows us to explore new techniques for conjugating\nand symmetrizing path-slice functions. A key finding of our study is the\ndiscovery that the zeroes of a path-slice function are comprehensively\nencapsulated within the zeroes of its symmetrized counterpart. This insight is\nparticularly significant in the context of path-slice stem functions. We\nestablish that for weakly slice regular functions, the processes of conjugation\nand symmetrization gain prominence once the function's slice regularity is\naffirmed. Furthermore, our investigation sheds light on the intricate nature of\nthe zeroes of a slice regular function. We ascertain that these zeroes\nconstitute a path-slice analytic set. This conclusion is drawn from the\nobserved phenomenon that the zeroes of the symmetrization of a slice regular\nfunction also form a path-slice analytic set. This finding marks an advancement\nin understanding the complex structure and properties of weakly slice regular\nfunctions in quaternionic analysis.\n"", 'Algebra of slice regular functions on non-symmetric domains in several\n  quaternionic variables   The primary objective of this paper is to establish an algebraic framework\nfor the space of weakly slice regular functions over several quaternionic\nvariables. We recently introduced a $*$-product that maintains the path-slice\nproperty within the class of path-slice functions. It is noteworthy that this\n$*$-product is directly applicable to weakly slice regular functions, as every\nslice regular function defined on a slice-open set inherently possesses\npath-slice properties. Building on this foundation, we propose a precise\ndefinition of an open neighborhood for a path $\\gamma$ in the path space\n$\\mathscr{P}(\\mathbb{C}^n)$. This definition is pivotal in establishing the\nholomorphism of stem functions. Consequently, we demonstrate that the\n$*$-product of two weakly slice regular functions retains its weakly slice\nregular nature. This retention is facilitated by holomorphy of stem functions\nand their relationship with weakly slice regular functions, providing a\ncomprehensive algebraic structure for this class of functions.\n']","[('functions quaternionic', 0.5740630626678467), ('regular functions', 0.5192071199417114), ('functions slice', 0.5058193206787109), ('slice regular', 0.4808725118637085), ('quaternionic analogues', 0.4705413281917572), ('axially symmetric domains', 0.46582043170928955), ('quaternion valued', 0.4533429443836212), ('quaternions', 0.4433773458003998), ('quaternionic', 0.40399011969566345), ('riemann operators', 0.40103036165237427)]"
367,367,80,367_random permutation_random permutations_permutons_mallows permutations,"['random permutation', 'random permutations', 'permutons', 'mallows permutations', 'mallows permutation', 'uniform permutations', 'permutations size', 'baxter permutations', 'avoiding permutations', 'permutations also']","['High-dimensional permutons: theory and applications   Permutons, which are probability measures on the unit square $[0, 1]^2$ with\nuniform marginals, are the natural scaling limits for sequences of (random)\npermutations.\n  We introduce a $d$-dimensional generalization of these measures for all $d\n\\ge 2$, which we call $d$-dimensional permutons, and extend -- from the\ntwo-dimensional setting -- the theory to prove convergence of sequences of\n(random) $d$-dimensional permutations to (random) $d$-dimensional permutons.\n  Building on this new theory, we determine the random high-dimensional\npermuton limits for two natural families of high-dimensional permutations.\nFirst, we determine the $3$-dimensional permuton limit for Schnyder wood\npermutations, which bijectively encode planar triangulations decorated by\ntriples of spanning trees known as Schnyder woods. Second, we identify the\n$d$-dimensional permuton limit for $d$-separable permutations, a\npattern-avoiding class of $d$-dimensional permutations generalizing ordinary\nseparable permutations.\n  Both high-dimensional permuton limits are random and connected to previously\nstudied universal 2-dimensional permutons, such as the Brownian separable\npermutons and the skew Brownian permutons, and share interesting connections\nwith objects arising from random geometry, including the continuum random tree,\nSchramm--Loewner evolutions, and Liouville quantum gravity surfaces.\n', 'Random Permutations -- A geometric point of view   We look at geometric limits of large random non-uniform permutations. We\nmainly consider two theories for limits of permutations: permuton limits,\nintroduced by Hoppen, Kohayakawa, Moreira, Rath, and Sampaio to define a notion\nof scaling limits for permutations; and Benjamini-Schramm limits, introduced by\nthe author to define a notion of local limits for permutations. The models of\nrandom permutations that we consider are mainly constrained models, that is,\nuniform permutations belonging to a given subset of the set of all\npermutations. We often identify this subset using pattern-avoidance, focusing\non: permutations avoiding a pattern of length three, substitution-closed\nclasses, (almost) square permutations, permutation families encoded by\ngenerating trees, and Baxter permutations. We explore some universal phenomena\nfor the models mentioned above. For Benjamini-Schramm limits we explore a\nconcentration phenomenon for the limiting objects. For permuton limits we\ndeepen the study of some known universal permutons, called biased Brownian\nseparable permutons, and we introduce some new ones, called Baxter permuton and\nskew Brownian permutons. In addition, for (almost) square permutations, we\ninvestigate the occurrence of a phase transition for the limiting permutons. On\nthe way, we establish various combinatorial results both for permutations and\nother related objects. Among others, we give a complete description of the\nfeasible region for consecutive patterns as the cycle polytope of a specific\ngraph; and we find new bijections relating Baxter permutations, bipolar\norientations, walks in cones, and a new family of discrete objects called\ncoalescent-walk processes.\n', 'Large deviation principle for random permutations   We derive a large deviation principle for random permutations induced by\nprobability measures of the unit square, called permutons. These permutations\nare called $\\mu$-random permutations. We also introduce and study a new general\nclass of models of random permutations, called Gibbs permutation models, which\ncombines and generalizes $\\mu$-random permutations and the celebrated Mallows\nmodel for permutations. Most of our results hold in the general setting of\nGibbs permutation models.\n  We apply the tools that we develop to the case of $\\mu$-random permutations\nconditioned to have an atypical proportion of patterns. Several results are\nmade more concrete in the specific case of inversions. For instance, we prove\nthe existence of at least one phase transition for a generalized version of the\nMallows model where the base measure is non-uniform. This is in contrast with\nthe results of Starr (2009, 2018) on the (standard) Mallows model, where the\nabsence of phase transition, i.e., phase uniqueness, was proven.\n  Our results naturally lead us to investigate a new notion of permutons,\ncalled conditionally constant permutons, which generalizes both\npattern-avoiding and pattern-packing permutons. We describe some properties of\nconditionally constant permutons with respect to inversions. The study of\nconditionally constant permutons for general patterns seems to be a challenging\nproblem.\n']","[('random permutation', 0.5658107995986938), ('random permutations', 0.5631712675094604), ('permutons', 0.5559492707252502), ('mallows permutations', 0.5422400832176208), ('mallows permutation', 0.5403287410736084), ('uniform permutations', 0.5309769511222839), ('permutations size', 0.5104572772979736), ('baxter permutations', 0.4800531566143036), ('avoiding permutations', 0.474301278591156), ('permutations also', 0.4519740343093872)]"
368,368,79,368_rough path theory_rough paths_geometric rough path_rough path,"['rough path theory', 'rough paths', 'geometric rough path', 'rough path', 'rough differential', 'rough differential equations', 'driven rough', 'geometric rough', 'unbounded rough', 'rough stochastic']","['A combinatorial approach to geometric rough paths and their controlled\n  paths   We develop the structure theory for transformations of weakly geometric rough\npaths of bounded $1 < p$-variation and their controlled paths. Our approach\ndiffers from existing approaches as it does not rely on smooth approximations.\nWe derive an explicit combinatorial expression for the rough path lift of a\ncontrolled path, and use it to obtain fundamental identities such as the\nassociativity of the rough integral, the adjunction between pushforwards and\npullbacks, and a change of variables formula for rough differential equations\n(RDEs). As applications we define rough paths, rough integration and RDEs on\nmanifolds, extending the results of [CDL15] to the case of arbitrary $p$.\n', 'Rough differential equations and planarly branched universal limit\n  theorem   The universal limit theorem is a central result in rough path theory, which\nhas been proved for: (i) rough paths with roughness $\\frac{1}{3}< \\alpha \\leq\n\\frac{1}{2}$; (ii) geometric rough paths with roughness $0< \\alpha \\leq 1$;\n(iii) branched rough paths with roughness $0< \\alpha \\leq 1$. Planarly branched\nrough paths are natural generalizations of both rough paths and branched rough\npaths, in the sense that post-Lie algebras are generalizations of both Lie\nalgebras and pre-Lie algebras. Here the primitive elements of the graded dual\nHopf algebra of the Hopf algebra corresponding to the planarly branched rough\npaths (resp. rough paths, resp. branched rough paths) form a post-Lie (resp.\nLie, resp. pre-Lie algebra). In this paper, we prove the universal limit\ntheorem for planarly branched rough paths with roughness $\\frac{1}{4}< \\alpha\n\\leq \\frac{1}{3}$, via the method of Banach fixed point theorem.\n', ""A Transfer Principle for Branched Rough Paths   A branched rough path $X$ consists of a rough integral calculus for $X \\colon\n[0, T] \\to \\mathbb R^d$ which may fail to satisfy integration by parts. Using\nKelly's bracket extension [Kel12], we define a notion of pushforward of\nbranched rough paths through smooth maps, which leads naturally to a definition\nof branched rough path on a smooth manifold. Once a covariant derivative is\nfixed, we are able to give a canonical, coordinate-free definition of integral\nagainst such rough paths. After characterising quasi-geometric rough paths in\nterms of their bracket extension, we use the same framework to define\nmanifold-valued rough differential equations (RDEs) driven by quasi-geometric\nrough paths. These results extend previous work on $3 > p$-rough paths\n[ABCRF22], itself a generalisation of the Ito calculus on manifolds developed\nby Meyer and Emery [Mey81, E89, E90], to the setting of non-geometric rough\ncalculus of arbitrarily low regularity.\n""]","[('rough path theory', 0.6322948336601257), ('rough paths', 0.6299737095832825), ('geometric rough path', 0.6043637990951538), ('rough path', 0.5799274444580078), ('rough differential', 0.5558889508247375), ('rough differential equations', 0.5412273406982422), ('driven rough', 0.5251142382621765), ('geometric rough', 0.522034764289856), ('unbounded rough', 0.5071966052055359), ('rough stochastic', 0.43973803520202637)]"
369,369,79,369_nematic liquid crystals_nematic liquid crystal_nematic liquid_liquid crystals,"['nematic liquid crystals', 'nematic liquid crystal', 'nematic liquid', 'liquid crystals', 'liquid crystal', 'navier stokes system', 'navier stokes equations', 'nematic', 'navier stokes', 'hydrodynamics']","[""Global Well-posedness and Long-time Behavior of the General\n  Ericksen--Leslie System in 2D under a Magnetic Field   In this paper, we investigate the global well-posedness and long-time\nbehavior of the two-dimensional general Ericksen--Leslie system for a nematic\nliquid crystal in a constant magnetic field. The PDE system consists of\nNavier--Stokes equations and the harmonic heat flow equation for the\norientations of liquid crystal molecules. For incompressible nematic liquid\ncrystal fluids with either isotropic or anisotropic properties in torus\n$\\mathbb{T}^2$, we derive the global well-posedness of strong solutions through\nhigher-order energy estimates combined with compactness methods and acquire the\nlong-time behavior of the solutions by using the \\L ojasiewicz--Simon\ninequality after obtaining the boundedness of the nematic liquid crystal\nmolecules' angle.\n"", 'Singularity formation for full Ericksen-Leslie system of nematic liquid\n  crystal flows in dimension two   In this paper, we prove the singularity formation for Poiseuille laminar flow\nof full Ericksen-Leslie system modeling nematic liquid crystal flows in\ndimension two. The singularity is due to the geometric effect at the origin.\n', 'A note on the Stochastic Ericksen-Leslie equations for nematic liquid\n  crystals   In this note we prove the existence and uniqueness of local maximal smooth\nsolution of the stochastic simplified Ericksen-Leslie systems modelling the\ndynamics of nematic liquid crystals under stochastic perturbations.\n']","[('nematic liquid crystals', 0.6692168712615967), ('nematic liquid crystal', 0.6397054195404053), ('nematic liquid', 0.575665295124054), ('liquid crystals', 0.5380709767341614), ('liquid crystal', 0.4880436062812805), ('navier stokes system', 0.449400395154953), ('navier stokes equations', 0.416167289018631), ('nematic', 0.403351366519928), ('navier stokes', 0.40269002318382263), ('hydrodynamics', 0.39862632751464844)]"
370,370,79,370_coagulation_weak solutions_weak solutions continuous_conserving solutions,"['coagulation', 'weak solutions', 'weak solutions continuous', 'conserving solutions', 'classical solutions', 'fragmentation models', 'fragmentation', 'growth fragmentation', 'flux solutions', 'solutions continuous']","['Discrete Coagulation-Fragmentation equations with multiplicative\n  coagulation kernel and constant fragmentation kernel   Here, we study a discrete Coagulation-Fragmentation equation with a\nmultiplicative coagulation kernel and a constant fragmentation kernel, which is\ncritical. We apply the discrete Bernstein transform to the original\nCoagulation-Fragmentation equation to get two new singular Hamilton-Jacobi\nequations and use viscosity solution methods to analyze them. We obtain\nwell-posedness, regularity, and long-time behaviors of the viscosity solutions\nto the Hamilton-Jacobi equations in certain ranges, which imply the\nwell-posedness and long-time behaviors of mass-conserving solutions to the\nCoagulation-Fragmentation equation. The results obtained provide some\ndefinitive answers to a conjecture posed in [11,10], and are counterparts to\nthose for the continuous case studied in [32].\n', 'Coagulation-Fragmentation equations with multiplicative coagulation\n  kernel and constant fragmentation kernel   We study a critical case of Coagulation-Fragmentation equations with\nmultiplicative coagulation kernel and constant fragmentation kernel. Our method\nis based on the study of viscosity solutions to a new singular Hamilton-Jacobi\nequation, which results from applying the Bernstein transform to the original\nCoagulation-Fragmentation equation. Our results include wellposedness,\nregularity and long-time behaviors of viscosity solutions to the\nHamilton-Jacobi equation in certain regimes, which have implications to\nwellposedness and long-time behaviors of \\emph{mass-conserving} solutions to\nthe Coagulation-Fragmentation equation.\n', 'Mass-conserving weak solutions to Oort-Hulst-Safronov coagulation\n  equation with singular rates   Existence of global weak solutions to the continuous Oort-Hulst-Safronov\n(OHS) coagulation equation is investigated for coagulation kernels capturing a\nsingularity near zero and growing linearly at infinity. The proof mainly relies\non a relation, between classical Smoluchowski coagulation equation (SCE) and\nOHS coagulation equation, which is introduced in [16] as generalized\ncoagulation equation. Moreover, all weak solutions formulated in a suitable\nsense are demonstrated to be mass-conserving. We obtain here a similar result\nfor OHS coagulation equation as the one in [6] for SCE.\n']","[('coagulation', 0.48731693625450134), ('weak solutions', 0.42593106627464294), ('weak solutions continuous', 0.37288910150527954), ('conserving solutions', 0.3680550158023834), ('classical solutions', 0.33930352330207825), ('fragmentation models', 0.32461753487586975), ('fragmentation', 0.31416141986846924), ('growth fragmentation', 0.3097873628139496), ('flux solutions', 0.30852189660072327), ('solutions continuous', 0.3037676513195038)]"
371,371,79,371_definable minimal structure_definable minimal_every definable_definable sets,"['definable minimal structure', 'definable minimal', 'every definable', 'definable sets', 'locally minimal', 'definable subsets', 'minimal structures', 'definable version', 'structures minimal', 'minimal structure']","['Approximation and zero set of definable functions in a definably\n  complete locally o-minimal structure   We consider a definably complete locally o-minimal expansion of an ordered\nfield. We treat two topics in this paper. The first topic is a definable\n$\\mathcal C^r$ approximation of a definable $\\mathcal C^{r-1}$ map between\ndefinable $\\mathcal C^r$ submanifolds in the definable $\\mathcal C^{r-1}$\ntopology. The second topic is the imbedding theorem for definably compact\ndefinable $\\mathcal C^r$ manifolds. We demonstrate that a definably normal\ndefinable $\\mathcal C^r$ manifold is a definably $\\mathcal C^r$ diffeomorphic\nto a definable $\\mathcal C^r$ submanifold. It enables us to show that the\ndefinable quotient of a definably compact definable $\\mathcal C^r$ group by a\ndefinable subgroup exists.\n', ""Tameness of definably complete locally o-minimal structures and\n  definable bounded multiplication   We first show that the projection image of a discrete definable set is again\ndiscrete for an arbitrary definably complete locally o-minimal structure. This\nfact together with the results in a previous paper implies tame dimension\ntheory and decomposition theorem into good-shaped definable subsets called\nquasi-special submanifolds. Using this fact, in the latter part of this paper,\nwe investigate definably complete locally o-minimal expansions of ordered\ngroups when the restriction of multiplication to an arbitrary bounded open box\nis definable. Similarly to o-minimal expansions of ordered fields,\n{\\L}ojasiewicz's inequality, Tietze extension theorem and affiness of\npsudo-definable spaces hold true for such structures under the extra assumption\nthat the domains of definition and the psudo-definable spaces are definably\ncompact. Here, a pseudo-definable space is a topological spaces having finite\ndefinable atlases. We also demonstrate Michael's selection theorem for\ndefinable set-valued functions with definably compact domains of definition.\n"", 'Definable quotients in locally o-minimal structures   Let $\\mathcal F=(F, +. \\cdot, <, 0, 1, \\dots)$ be a definably complete\nlocally o-minimal expansion of an ordered field. We demonstrate the existence\nof definable quotients of definable sets by definable equivalence relations\nwhen several technical conditions are satisfied. These conditions are satisfied\nwhen $X$ is a locally closed definable subset of $F^n$ and there is a definable\nproper action of a definable group $G$ on $X$.\n']","[('definable minimal structure', 0.7417447566986084), ('definable minimal', 0.6895357370376587), ('every definable', 0.5720868706703186), ('definable sets', 0.5707852840423584), ('locally minimal', 0.5706207156181335), ('definable subsets', 0.5548571944236755), ('minimal structures', 0.5542487502098083), ('definable version', 0.5531508326530457), ('structures minimal', 0.5457032918930054), ('minimal structure', 0.5383472442626953)]"
372,372,79,372_prior distributions_posterior predictive distribution_posterior inference_posterior distributions,"['prior distributions', 'posterior predictive distribution', 'posterior inference', 'posterior distributions', 'bayes estimators', 'bayesian estimation', 'posterior predictive', 'prior distribution', 'posteriors', 'generalized bayes']","['Relations Between the Conditional Normalized Maximum Likelihood\n  Distributions and the Latent Information Priors   We reveal the relations between the conditional normalized maximum likelihood\n(CNML) distributions and Bayesian predictive densities based on the latent\ninformation priors (LIPs). In particular, CNML3, which is one type of CNML\ndistributions, is investigated. The Bayes projection of a predictive density,\nwhich is an information projection of the predictive density on a set of\nBayesian predictive densities, is considered. We prove that the sum of the\nBayes projection divergence of CNML3 and the conditional mutual information is\nasymptotically constant. This result implies that the Bayes projection of CNML3\n(BPCNML3) is asymptotically identical to the Bayesian predictive density based\non LIP. In addition, under some stronger assumptions, we show that BPCNML3\nexactly coincides with the Bayesian predictive density based on LIP.\n', 'Accuracy of Gaussian approximation in nonparametric Bernstein -- von\n  Mises Theorem   The prominent Bernstein -- von Mises (BvM) result claims that the posterior\ndistribution after centering by the efficient estimator and standardizing by\nthe square root of the total Fisher information is nearly standard normal. In\nparticular, the prior completely washes out from the asymptotic posterior\ndistribution. This fact is fundamental and justifies the Bayes approach from\nthe frequentist viewpoint. In the nonparametric setup the situation changes\ndramatically and the impact of prior becomes essential even for the contraction\nof the posterior; see [vdV2008], [Bo2011], [CaNi2013,CaNi2014] for different\nmodels like Gaussian regression or i.i.d. model in different weak topologies.\nThis paper offers another non-asymptotic approach to studying the behavior of\nthe posterior for a special but rather popular and useful class of statistical\nmodels and for Gaussian priors. First we derive tight finite sample bounds on\nposterior contraction in terms of the so called effective dimension of the\nparameter space. Our main results describe the accuracy of Gaussian\napproximation of the posterior. In particular, we show that restricting to the\nclass of all centrally symmetric credible sets around pMLE allows to get\nGaussian approximation up to order (n^{-1}). We also show that the posterior\ndistribution mimics well the distribution of the penalized maximum likelihood\nestimator (pMLE) and reduce the question of reliability of credible sets to\nconsistency of the pMLE-based confidence sets. The obtained results are\nspecified for nonparametric log-density estimation and generalized regression.\n', 'Enriched standard conjugate priors and the right invariant prior for\n  Wishart distributions   The prediction of the variance-covariance matrix of the multivariate normal\ndistribution is important in the multivariate analysis. We investigated\nBayesian predictive distributions for Wishart distributions under the\nKullback-Leibler divergence. The conditional reducibility of the family of\nWishart distributions enables us to decompose the risk of a Bayesian predictive\ndistribution. We considered a recently introduced class of prior distributions,\nwhich is called the family of enriched standard conjugate prior distributions,\nand compared the Bayesian predictive distributions based on these prior\ndistributions. Furthermore, we studied the performance of the Bayesian\npredictive distribution based on the reference prior distribution in the family\nand showed that there exists a prior distribution in the family that dominates\nthe reference prior distribution. Our study provides new insight into the\nmultivariate analysis when there exists an ordered inferential importance for\nthe independent variables.\n']","[('prior distributions', 0.5922869443893433), ('posterior predictive distribution', 0.5913994312286377), ('posterior inference', 0.5881401896476746), ('posterior distributions', 0.5864154696464539), ('bayes estimators', 0.5639004707336426), ('bayesian estimation', 0.538489043712616), ('posterior predictive', 0.5384443998336792), ('prior distribution', 0.5374892950057983), ('posteriors', 0.5299583673477173), ('generalized bayes', 0.5249616503715515)]"
373,373,79,373_supersonic flow_euler flows_steady euler equations_shock solutions,"['supersonic flow', 'euler flows', 'steady euler equations', 'shock solutions', 'compressible euler equations', 'shocks', 'potential flow', 'euler poisson system', 'steady euler', 'solutions euler poisson']","['Transonic shocks for steady Euler flows with an external force in an\n  axisymmetric perturbed cylinder   We concern the structural stability of transonic shocks for the steady Euler\nsystem with an external force in an axisymmetric perturbed cylinder. For a\nclass of external forces, we first prove the existence and uniqueness of the\ntransonic shock solution to the one-dimensional steady Euler system with an\nexternal force, which shows that the external force has a stabilization effect\non the transonic shock in the flat cylinder and the shock position is uniquely\ndetermined. We then establish the existence and stability of the transonic\nshock solution under axisymmetric perturbations of the incoming supersonic\nflow, the nozzle boundary, the exit pressure and the external force. Different\nfrom the transonic shock problem in two-dimensional nozzles, there exists a\nsingularity along the symmetric axis for axisymmetric flows. We introduce an\ninvertible modified Lagrangian transformation to overcome this difficulty and\nstraighten the streamline. One of the key elements in the analysis is to\nutilize the deformation-curl decomposition to effectively decouple the\nhyperbolic and elliptic modes in the steady axisymmetric Euler system with an\nexternal force. Another one is an equivalent reformulation of the\nRankine-Hugoniot conditions so that the shock front is uniquely determined by\nan algebraic equation.\n', 'Uniqueness of Transonic Shock Solutions for Two-Dimensional Steady\n  Compressible Euler Flows in an Expanding Nozzle   In this paper, we are trying to show the uniqueness of transonic shock\nsolutions in an expanding nozzle under certain conditions and assumptions on\nthe boundary data and the shock solution. The idea is to compare two transonic\nshock solutions and show that they should coincide if the perturbation of the\nnozzle is sufficiently small. To this end, a condition on the pressure of the\nflow across the shock front is proposed, such that a priori estimates for the\nsubsonic flow behind the shock front could be established without the\nassumption that it is a small perturbation of the unperturbed uniform subsonic\nstate. With the help of these estimates, the uniqueness of the position of the\nintersection point between the shock front and the nozzle boundary could be\nfurther established by demonstrating the monotonicity of the solvability\ncondition for the elliptic sub-problem of the subsonic flow behind the shock\nfront. Then, via contraction arguments, two transonic shock solutions could be\nverified to coincide as the perturbation is small, which leads to the\nuniqueness of the transonic shock solution.\n', 'Structural Stability of Transonic Shock Flows with an External Force   This paper is devoted to the structural stability of a transonic shock\npassing through a flat nozzle for two-dimensional steady compressible flows\nwith an external force. We first establish the existence and uniqueness of one\ndimensional transonic shock solutions to the steady Euler system with an\nexternal force by prescribing suitable pressure at the exit of the nozzle when\nthe upstream flow is a uniform supersonic flow. It is shown that the external\nforce helps to stabilize the transonic shock in flat nozzles and the shock\nposition is uniquely determined. Then we are concerned with the structural\nstability of these transonic shoc solutions when the exit pressure is suitably\nperturbed. One of the new ingredients in our analysis is to use the\ndeformation-curl decomposition to the steady Euler system developed in\n\\cite{WengX2019} to deal with the transonic shock problem.\n']","[('supersonic flow', 0.5381531119346619), ('euler flows', 0.49902528524398804), ('steady euler equations', 0.4807656705379486), ('shock solutions', 0.4643316864967346), ('compressible euler equations', 0.43051785230636597), ('shocks', 0.3949955701828003), ('potential flow', 0.3814949095249176), ('euler poisson system', 0.38061726093292236), ('steady euler', 0.36908647418022156), ('solutions euler poisson', 0.3603183329105377)]"
374,374,79,374_c_0 semigroups_c_0 semigroup_operator semigroups_strongly continuous semigroups,"['c_0 semigroups', 'c_0 semigroup', 'operator semigroups', 'strongly continuous semigroups', 'continuous semigroups', 'semigroup bounded', 'semigroups banach', 'semigroups', 'semigroups general', 'semigroups hilbert']","['On asymptotics for $C_0$-semigroups   We stretch the spectral bound equal growth bound condition along with a\ngeneralized Lyapunov stability theorem, known to hold for $C_0$-semigroups of\nnormal operators on complex Hilbert spaces, to $C_0$-semigroups of scalar type\nspectral operators on complex Banach spaces. For such semigroups, we obtain\nexponential estimates with the best stability constants. We also extend to a\nBanach space setting a celebrated characterization of uniform exponential\nstability for $C_0$-semigroups on complex Hilbert spaces and thereby acquire a\ncharacterization of uniform exponential stability for scalar type spectral and\neventually norm-continuous $C_0$-semigroups.\n', 'Characterizations of the Crandall--Pazy Class of $C_0$-semigroups on\n  Hilbert Spaces and Their Application to Decay Estimates   We investigate immediately differentiable $C_0$-semigroups $(e^{-tA})_{t \\geq\n0}$ satisfying $\\sup_{0 < t <1} t^{1/\\beta}\\|Ae^{-tA}\\| < \\infty$ for some $0 <\n\\beta \\leq 1$. Such $C_0$-semigroups are referred to as the Crandall--Pazy\nclass of $C_0$-semigroups. In the Hilbert space setting, we present two\ncharacterizations of the Crandall--Pazy class. We then apply these\ncharacterizations to estimate decay rates for Crank--Nicolson schemes with\nsmooth initial data when the associated abstract Cauchy problem is governed by\nan exponentially stable $C_0$-semigroup in the Crandall--Pazy class. The first\napproach is based on a functional calculus called the $\\mathcal{B}$-calculus.\nThe second approach builds upon estimates derived from Lyapunov equations and\nimproves the decay estimate obtained in the first approach, under the\nadditional assumption that $-A^{-1}$ generates a bounded $C_0$-semigroup.\n', ""On the regularity of scalar type spectral $C_0$-semigroups   We show that, for the $C_0$-semigroups of scalar type spectral operators, a\nwell-known necessary condition for the generation of eventually norm-continuous\n$C_0$-semigroups, formulated exclusively in terms of the location of the\nspectrum of the semigroup's generator in the complex plane, is also sufficient\nand, in fact, characterizes the generators of immediately norm-continuous such\nsemigroups.\n  Combining characterizations of the immediate differentiability and the Gevrey\nultradifferentiability of scalar type spectral $C_0$-semigroups with the\ngeneration theorem, found earlier by the author, we arrive at respective\ncharacterizations of the generation of such semigroups.\n  We further establish characterizations of the generation of eventually\ndifferentiable and immediately compact scalar type spectral $C_0$-semigroups\nalso in terms of the generator's spectrum and show that, for such semigroups,\neventual compactness implies immediate.\n  All the obtained results are instantly transferred to the $C_0$-semigroups of\nnormal operators.\n""]","[('c_0 semigroups', 0.740020215511322), ('c_0 semigroup', 0.7138640284538269), ('operator semigroups', 0.6977649927139282), ('strongly continuous semigroups', 0.6962099075317383), ('continuous semigroups', 0.6893165111541748), ('semigroup bounded', 0.6752175092697144), ('semigroups banach', 0.6722471117973328), ('semigroups', 0.6282438635826111), ('semigroups general', 0.6268917918205261), ('semigroups hilbert', 0.6171889901161194)]"
375,375,79,375_length geodesic_closed geodesics_simple closed geodesics_simple closed geodesic,"['length geodesic', 'closed geodesics', 'simple closed geodesics', 'simple closed geodesic', 'closed geodesic', 'geodesic surfaces', 'geodesics closed', 'geodesics riemannian', 'simple geodesic', 'curvature geodesic']","['The length of the shortest closed geodesic on positively curved\n  2-spheres   We show that the shortest closed geodesic on a 2-sphere with non-negative\ncurvature has length bounded above by three times the diameter. We prove a new\nisoperimetric inequality for 2-spheres with pinched curvature; this allows us\nto improve our bound on the length of the shortest closed geodesic in the\npinched curvature setting.\n', 'From curve shortening to flat link stability and Birkhoff sections of geodesic flows We employ the curve shortening flow to establish three new results on the dynamics of geodesic flows of closed Riemannian surfaces. The first one is the stability, under $C^0$-small perturbations of the Riemannian metric, of certain flat links of closed geodesics. The second one is a forced existence theorem for closed connected orientable Riemannian surfaces: for surfaces of positive genus, the existence of a contractible simple closed geodesic $\\gamma$ forces the existence of infinitely many closed geodesics intersecting $\\gamma$ in every primitive free homotopy class of loops; for the 2-sphere, the existence of two disjoint simple closed geodesics forces the existence of a third one intersecting both. The final result asserts the existence of Birkhoff sections for the geodesic flow of any closed connected orientable Riemannian surface.', 'Minimizing closed geodesics on polygons and disks   In this paper we study 1/k geodesics, those closed geodesics that minimize on\nall subintervals of length $L/k$, where $L$ is the length of the geodesic. We\ndevelop new techniques to study the minimizing properties of these curves on\ndoubled polygons, and demonstrate a sequence of doubled polygons whose closed\ngeodesics exhibit unbounded minimizing properties. We also compute the length\nof the shortest closed geodesic on doubled odd-gons and show that this length\napproaches 4 times the diameter.\n']","[('length geodesic', 0.7613329887390137), ('closed geodesics', 0.7600989937782288), ('simple closed geodesics', 0.7563445568084717), ('simple closed geodesic', 0.7343205213546753), ('closed geodesic', 0.7256487607955933), ('geodesic surfaces', 0.720312774181366), ('geodesics closed', 0.7098394632339478), ('geodesics riemannian', 0.6985927224159241), ('simple geodesic', 0.6962644457817078), ('curvature geodesic', 0.6936958432197571)]"
376,376,79,376_pricing hedging_asset pricing_arbitrage free_martingale optimal transport,"['pricing hedging', 'asset pricing', 'arbitrage free', 'martingale optimal transport', 'arbitrage', 'martingale optimal', 'semimartingales', 'martingale', 'financial markets', 'hedging']","['No-arbitrage conditions and pricing from discrete-time to\n  continuous-time strategies   In this paper, a general framework is developed for continuous-time financial\nmarket models defined from simple strategies through conditional topologies\nthat avoid stochastic calculus and do not necessitate semimartingale models. We\nthen compare the usual no-arbitrage conditions of the literature, e.g. the\nusual no-arbitrage conditions NFL, NFLVR and NUPBR and the recent AIP\ncondition. With appropriate pseudo-distance topologies, we show that they hold\nin continuous time if and only if they hold in discrete time. Moreover, the\nsuper-hedging prices in continuous time coincide with the discrete-time\nsuper-hedging prices, even without any no-arbitrage condition.\n', 'Super-hedging-pricing formulas and Immediate-Profit arbitrage for market\n  models under random horizon   In this paper, we consider the discrete-time setting, and the market model\ndescribed by (S,F,T)$. Herein F is the ``public"" flow of information which is\navailable to all agents overtime, S is the discounted price process of\nd-tradable assets, and T is an arbitrary random time whose occurrence might not\nbe observable via F. Thus, we consider the larger flow G which incorporates F\nand makes T an observable random time. This framework covers the credit risk\ntheory setting, the life insurance setting and the setting of employee stock\noption valuation. For the stopped model (S^T,G) and for various vulnerable\nclaims, based on this model, we address the super-hedging pricing valuation\nproblem and its intrinsic Immediate-Profit arbitrage (IP hereafter for short).\nOur first main contribution lies in singling out the impact of change of prior\nand/or information on conditional essential supremum, which is a vital tool in\nsuper-hedging pricing. The second main contribution consists of describing as\nexplicit as possible how the set of super-hedging prices expands under the\nstochasticity of T and its risks, and we address the IP arbitrage for (S^T,G)\nas well. The third main contribution resides in elaborating as explicit as\npossible pricing formulas for vulnerable claims, and singling out the various\ninformational risks in the prices\' dynamics.\n', 'Pricing and hedging for a sticky diffusion   We introduce a financial market model featuring a risky asset whose price\nfollows a sticky geometric Brownian motion and a riskless asset that grows with\na constant interest rate $r\\in \\mathbb R $. We prove that this model satisfies\nNo Arbitrage (NA) and No Free Lunch with Vanishing Risk (NFLVR) only when $r=0\n$. Under this condition, we derive the corresponding arbitrage-free pricing\nequation, assess replicability and representation of the replication strategy.\nWe then show that all locally bounded replicable payoffs for the standard\nBlack--Scholes model are also replicable for the sticky model. Last, we\nevaluate via numerical experiments the impact of hedging in discrete time and\nof misrepresenting price stickiness.\n']","[('pricing hedging', 0.5562582612037659), ('asset pricing', 0.4642876386642456), ('arbitrage free', 0.4443102478981018), ('martingale optimal transport', 0.4397875666618347), ('arbitrage', 0.43526315689086914), ('martingale optimal', 0.4332718253135681), ('semimartingales', 0.42639437317848206), ('martingale', 0.42539092898368835), ('financial markets', 0.42518162727355957), ('hedging', 0.41913920640945435)]"
377,377,79,377_incompleteness_completeness_undecidability_formal theory,"['incompleteness', 'completeness', 'undecidability', 'formal theory', 'formal systems', 'theorems', 'provability', 'computably enumerable', 'undecidable', 'arithmetical']","['On Constructivity and the Rosser Property: a closer look at some\n  G\\""odelean proofs   The proofs of Kleene, Chaitin and Boolos for G\\""odel\'s First Incompleteness\nTheorem are studied from the perspectives of constructivity and the Rosser\nproperty. A proof of the incompleteness theorem has the Rosser property when\nthe independence of the true but unprovable sentence can be shown by assuming\nonly the (simple) consistency of the theory. It is known that G\\""odel\'s own\nproof for his incompleteness theorem does not have the Rosser property, and we\nshow that neither do Kleene\'s or Boolos\' proofs. However, we show that a\nvariant of Chaitin\'s proof can have the Rosser property. The proofs of G\\""odel,\nRosser and Kleene are constructive in the sense that they explicitly construct,\nby algorithmic ways, the independent sentence(s) from the theory. We show that\nthe proofs of Chaitin and Boolos are not constructive, and they prove only the\nmere existence of the independent sentences.\n', 'A Machine-Assisted Proof of G\\""odel\'s Incompleteness Theorems for the\n  Theory of Hereditarily Finite Sets   A formalisation of G\\""odel\'s incompleteness theorems using the Isabelle proof\nassistant is described. This is apparently the first mechanical verification of\nthe second incompleteness theorem. The work closely follows {\\\'S}wierczkowski\n(2003), who gave a detailed proof using hereditarily finite set theory. The\nadoption of this theory is generally beneficial, but it poses certain technical\nissues that do not arise for Peano arithmetic. The formalisation itself should\nbe useful to logicians, particularly concerning the second incompleteness\ntheorem, where existing proofs are lacking in detail.\n', ""Some reflections on the relationship between logical incompleteness and\n  concrete incompleteness   In this paper, we aim to conceptually examine the relationship between\nlogical incompleteness and concrete incompleteness which both study the\nincompleteness phenomenon. We argue for two main theses. Firstly, the current\nresearch on concrete incompleteness reals both similarities and differences\nbetween logical incompleteness and concrete incompleteness. Similarities\nbetween them are not universal, and differences between them are essential.\nSecondly, concrete incompleteness is a higher order phenomenon over logical\nincompleteness. This verifies that Hilbert's concrete and intuitive proof\ntheory provides us essential new information from non-concrete and\nnon-intuitive ideal proofs. We examine similarities between logical\nincompleteness and concrete incompleteness from two aspects: equivalences\nbetween logical incompleteness and concrete incompleteness, and the ubiquity of\nthe incompleteness phenomenon in both logical incompleteness and concrete\nincompleteness. We examine differences between logical incompleteness and\nconcrete incompleteness from five aspects: (1) the influence on Hilbert's\nprogram; (2) properties of independent sentences; (3) the intensionality\nproblem; (4) the relationship with ordinal analysis; (5) the limit of\nprovability.\n""]","[('incompleteness', 0.6439491510391235), ('completeness', 0.49630966782569885), ('undecidability', 0.49108561873435974), ('formal theory', 0.4696025550365448), ('formal systems', 0.4380451738834381), ('theorems', 0.426035076379776), ('provability', 0.41886967420578003), ('computably enumerable', 0.41485869884490967), ('undecidable', 0.39864376187324524), ('arithmetical', 0.3956137001514435)]"
378,378,78,378_fundamental groupoids_topological fundamental group_fundamental groupoid_fundamental groups,"['fundamental groupoids', 'topological fundamental group', 'fundamental groupoid', 'fundamental groups', 'fundamental group', 'fundamental group pi_1', 'universal covering space', 'topological fundamental', 'topological groups', 'topological group']","['Topological fundamental groupoid. III. Haar systems on the fundamental\n  groupoid   Let $X$ be a path connected, locally path connected and semilocally simply\nconnected space; let $\\tilde{X}$ be its universal cover. We discuss the\nexistence and description of a Haar system on the fundamental groupoid\n$\\Pi_1(X)$ of $X$. The existence of a Haar system on $\\Pi_1(X)$ is justified\nwhen $X$ is a second countable, locally compact and Hausdorff. We provide\nequivalent criteria for the existence of the Haar system on a locally compact\n(locally Hausdorff) fundamental groupoid in terms of certain measures on $X$\nand $\\tilde{X}$. $\\mathrm{C}^*(\\Pi_1(X))$ is described using a result of Muhly,\nRenault and Williams. Finally, two formulae for the Haar system on $\\Pi_1(X)$\nin terms of measures on $X$ or $\\tilde{X}$ are given.\n', 'Dense products in fundamental groupoids   Infinitary operations, such as products indexed by countably infinite linear\norders, arise naturally in the context of fundamental groups and groupoids.\nDespite the fact that the usual binary operation of the fundamental group\ndetermines the operation of the fundamental groupoid, we show that, for a\nlocally path-connected metric space, the well-definedness of countable dense\nproducts in the fundamental group need not imply the well-definedness of\ncountable dense products in the fundamental groupoid. Additionally, we show the\nfundamental groupoid $\\Pi_1(X)$ has well-defined dense products if and only if\n$X$ admits a generalized universal covering space.\n', 'Topological Fundamental Groupoid. II. An action category of the\n  fundamental groupoid   For a path connected, locally path connected and semilocally simply connected\nspace $X$, let $\\Pi_1(X)$ denote its topologised fundamental groupoid as\nestablished in the first article of this series. Let $\\mathcal{E}$ be the\ncategory of $\\Pi_1(X)$-spaces in which the momentum maps are local\nhomeomorphisms. We show that this category is isomorphic to that of covering\nspaces of $X$. Using this, we give different characterisations for free or\nproper actions of the fundamental groupoid in $\\mathcal{E}$.\n']","[('fundamental groupoids', 0.6871073246002197), ('topological fundamental group', 0.683088481426239), ('fundamental groupoid', 0.6586177945137024), ('fundamental groups', 0.6471946239471436), ('fundamental group', 0.6341830492019653), ('fundamental group pi_1', 0.6341117024421692), ('universal covering space', 0.6134421825408936), ('topological fundamental', 0.5835886001586914), ('topological groups', 0.5685991644859314), ('topological group', 0.5418099761009216)]"
379,379,78,379_time fractional diffusion_fractional diffusion_order time fractional_fractional derivative,"['time fractional diffusion', 'fractional diffusion', 'order time fractional', 'fractional derivative', 'time fractional', 'fractional evolution equations', 'fractional order', 'fractional nonlocal', 'discrete fractional', 'tempered fractional']","['Sharp pointwise-in-time error estimate of L1 scheme for nonlinear\n  subdiffusion equations   An essential feature of the subdiffusion equations with the $\\alpha$-order\ntime fractional derivative is the weak singularity at the initial time. The\nweak regularity of the solution is usually characterized by a regularity\nparameter $\\sigma\\in (0,1)\\cup(1,2)$. Under this general regularity assumption,\nwe here obtain the pointwise-in-time error estimate of the widely used L1\nscheme for nonlinear subdiffusion equations. To the end, we present a refined\ndiscrete fractional-type Gr\\""onwall inequality and a rigorous analysis for the\ntruncation errors. Numerical experiments are provided to demonstrate the\neffectiveness of our theoretical analysis.\n', 'A discrete Gr\\""{o}nwall inequality with application to numerical schemes\n  for subdiffusion problems   We consider a class of numerical approximations to the Caputo fractional\nderivative. Our assumptions permit the use of nonuniform time steps, such as is\nappropriate for accurately resolving the behavior of a solution whose\nderivatives are singular at~$t=0$. The main result is a type of fractional\nGr\\""{o}nwall inequality and we illustrate its use by outlining some stability\nand convergence estimates of schemes for fractional reaction-subdiffusion\nproblems. This approach extends earlier work that used the familiar L1\napproximation to the Caputo fractional derivative, and will facilitate the\nanalysis of higher order and linearized fast schemes.\n', 'Numerical analysis of linear and nonlinear time-fractional subdiffusion\n  equations   In this paper, a new type of the discrete fractional Gr{\\""o}nwall inequality\nis developed, which is applied to analyze the stability and convergence of a\nGalerkin spectral method for a linear time-fractional subdiffusion equation.\nBased on the temporal-spatial error splitting argument technique, the discrete\nfractional Gr{\\""o}nwall inequality is also applied to prove the unconditional\nconvergence of a semi-implicit Galerkin spectral method for a nonlinear\ntime-fractional subdiffusion equation.\n']","[('time fractional diffusion', 0.6052443981170654), ('fractional diffusion', 0.6009534001350403), ('order time fractional', 0.5524219274520874), ('fractional derivative', 0.5036751627922058), ('time fractional', 0.4916575253009796), ('fractional evolution equations', 0.4912415146827698), ('fractional order', 0.48502296209335327), ('fractional nonlocal', 0.46050047874450684), ('discrete fractional', 0.4563896656036377), ('tempered fractional', 0.4498540461063385)]"
380,380,78,380_golay complementary sequences_complementary sequences_complementary pairs_complementary sets,"['golay complementary sequences', 'complementary sequences', 'complementary pairs', 'complementary sets', 'generalized boolean', 'golay complementary', 'zc sequences', 'boolean functions', 'sequence pairs', 'sequences constructed']","[""A Direct and Generalized Construction of Polyphase Complementary Set\n  with Low PMEPR and High Code-Rate for OFDM System   A major drawback of orthogonal frequency division multiplexing (OFDM) systems\nis their high peak-to-mean envelope power ratio (PMEPR). The PMEPR problem can\nbe solved by adopting large codebooks consisting of complementary sequences\nwith low PMEPR. In this paper, we present a new construction of polyphase\ncomplementary sets (CSs) using generalized Boolean functions (GBFs), which\ngeneralizes Schmidt's construction in 2007, Paterson's construction in 2000 and\nGolay complementary pairs (GCPs) given by Davis and Jedwab in 1999. Compared\nwith Schmidt's approach, our proposed CSs lead to lower PMEPR with higher\ncode-rate for sequences constructed from higher-order ($\\geq 3$) GBFs. We\nobtain polyphase complementary sequences with maximum PMEPR of $2^{k+1}$ and\n$2^{k+2}-2M$ where $k,M$ are non-negative integers that can be easily derived\nfrom the GBF associated with the CS.\n"", 'A Construction of 2-D Z-Complementary Array Code Sets with Flexible Even\n  Row Lengths and Applications in Massive MIMO   The need for two-dimensional (2-D) arrays with good 2-D correlation\nproperties and flexible parameters has been of great interest due to their\napplication in the field of wireless communications such as massive multiple\ninput multiple output (MIMO), phased array antenna, multi-carrier code division\nmultiple access (MC-CDMA), 2D-MC-CDMA, etc. In this paper, we propose a direct\nconstruction of a 2-D Z-complementary array code set (ZCACS) with flexible\nparameters. For this purpose, we first propose a construction of inter-group\ncomplementary (IGC) code sets using multivariable function and by using this\nconstruction 2-D Z-complementary array code (ZCAC) and 2-D ZCAC set (ZCACS) are\nprovided. In some special case, the proposed 2-D ZCAC reduces to a 2-D\nZ-complementary array pair (ZCAP), which is not reported till date. The\npeak-to-mean envelope power ratio (PMEPR) of row and column sequences of 2-D\nZCAC is shown to be better than the existing ones for use in MC-CDMA. 2-D Golay\ncomplementary array set (GCAS) and Golay complementary set (GCS) are derived\nfrom the proposed construction, which can be applied in omnidirectional\nprecoding (OP) based transmission through massive MIMO. The proposed\nconstruction can support a more flexible number of antennas for a uniform\nrectangular array (URA) to transmit space-time block coded (STBC) data, than\nthe existing constructions. The bit-error-rate (BER) simulation result also\nshows the performance benefits of derived 2-D GCAS and GCS compared to the\nexisting ones.\n', 'Two-Dimensional Golay Complementary Array Sets from Generalized Boolean\n  Functions   The one-dimensional (1-D) Golay complementary set (GCS) has many well-known\nproperties and has been widely employed in engineering. The concept of 1-D GCS\ncan be extended to the two-dimensional (2-D) Golay complementary array set\n(GCAS) where the 2-D aperiodic autocorrelation of constituent arrays sum to\nzero except for the 2-D zero shift. The 2-D GCAS includes the 2-D Golay\ncomplementary array pair (GCAP) as a special case when the set size is 2. In\nthis paper, 2-D generalized Boolean functions are introduced and novel\nconstructions of 2-D GCAPs, 2-D GCASs, and 2-D Golay complementary array mates\nbased on generalized Boolean functions are proposed. Explicit expressions of\n2-D Boolean functions for 2-D GCAPs and 2-D GCASs are given. Therefore, they\nare all direct constructions without the aid of other existing 1-D or 2-D\nsequences. Moreover, for the column sequences and row sequences of the\nconstructed 2-D GCAPs, their peak-to-average power ratio (PAPR) properties are\nalso investigated.\n']","[('golay complementary sequences', 0.6312750577926636), ('complementary sequences', 0.5379337668418884), ('complementary pairs', 0.517177402973175), ('complementary sets', 0.45214200019836426), ('generalized boolean', 0.43368053436279297), ('golay complementary', 0.41992977261543274), ('zc sequences', 0.3955727815628052), ('boolean functions', 0.37639838457107544), ('sequence pairs', 0.3581572473049164), ('sequences constructed', 0.356512188911438)]"
381,381,78,381_distributive lattices_distributive lattice_lattice poset_complete lattice,"['distributive lattices', 'distributive lattice', 'lattice poset', 'complete lattice', 'relation algebras', 'lattices', 'lattice', 'pseudocomplemented', 'finite distributive', 'semilattices']","['Algebras describing pseudocomplemented, relatively pseudocomplemented\n  and sectionally pseudocomplemented posets   In order to be able to use methods of Universal Algebra for investigating\nposets, we assign to every pseudocomplemented poset, to every relatively\npseudocomplemented poset and to every sectionally pseudocomplemented poset a\ncertain algebra (based on a commutative directoid or on a lambda-lattice) which\nsatisfies certain identities and implications. We show that the assigned\nalgebras fully characterize the given corresponding posets. It turns out that\nthe assigned algebras satisfy strong congruence properties which can be\ntransferred back to the posets. We also mention applications of such posets in\ncertain non-classical logics.\n', 'Filters and ideals in pseudocomplemented posets   We study ideals and filters of posets and of pseudocomplemented posets and\nshow a version of the Separation Theorem, known for ideals and filters in\nlattices and semilattices, within this general setting. We extend the concept\nof a *-ideal already introduced by Rao for pseudocomplemented distributive\nlattices and by Talukder, Chakraborty and Begum for pseudocomplemented\nsemilattices to pseudocomplemented posets. We derive several important\nproperties of such ideals. Especially, we explain connections between prime\nfilters, ultrafilters, filters satisfying the *-condition and dense elements.\nFinally, we prove a Separation Theorem for *-ideals.\n', 'Properties and special filters of pseudocomplemented posets   Investigating the structure of pseudocomplemented lattices started ninety\nyears ago with papers by V. Glivenko, G. Birkhoff and O. Frink and this\nstructure was essentially developed by G. Gr\\""atzer. In recent years, some\nspecial filters in pseudocomplemented and Stone lattices have been studied by\nM. Sambasiva Rao. However, in some applications, in particular in non-classical\nlogics with unsharp logical connectives, pseudocomplemented posets instead of\nlattices are used. This motivated us to develop an algebraic theory of\npseudocomplemented posets, i.e. we derive identities and inequalities holding\nin such posets and we use them in order to characterize the so-called Stone\nposets. Then we adopt several concepts of special filters and we investigate\ntheir properties in pseudocomplemented posets. Moreover, we show how properties\nof these filters influence algebraic properties of the underlying\npseudocomplemented posets.\n']","[('distributive lattices', 0.7121371030807495), ('distributive lattice', 0.6728543639183044), ('lattice poset', 0.6287254691123962), ('complete lattice', 0.5268056988716125), ('relation algebras', 0.5203328728675842), ('lattices', 0.5166617035865784), ('lattice', 0.47857001423835754), ('pseudocomplemented', 0.4715483784675598), ('finite distributive', 0.4435392916202545), ('semilattices', 0.44221121072769165)]"
382,382,78,382_operators graphs_graphs spectral_operator graph_quantum graphs,"['operators graphs', 'graphs spectral', 'operator graph', 'quantum graphs', 'schr odinger operators', 'quantum graph', 'compact metric graphs', 'odinger operators', 'schr odinger operator', 'spectral theory']","['Comparing the spectrum of Schr\\""odinger operators on quantum graphs   We study Schr\\""odinger operators on compact finite metric graphs subject to\n$\\delta$-coupling and standard boundary conditions. We compare the $n$-th\neigenvalues of those self-adjoint realizations and derive an asymptotic result\nfor the mean value of deviations. By doing this, we generalize recent results\nfrom Rudnick et al. obtained for domains in $\\mathbb{R}^2$ to the setting of\nquantum graphs. This also leads to a generalization of related results\npreviously and independently obtained in [arXiv:2212.09143] and\n[arXiv:2212.12531] for metric graphs. In addition, based on our main result, we\nintroduce some notions of circumference for a (quantum) graph which might prove\nuseful in the future.\n', 'Surgery transformations and spectral estimates of $\\delta$ beam\n  operators   We introduce $\\delta$ type vertex conditions for beam operators, the fourth\nderivative operator, on metric graphs and study the effect of certain\ngeometrical alterations (graph surgery) of the graph on the spectra of beam\noperators on compact metric graphs. Results are obtained for a class of vertex\nconditions which can be seen as an analogue of {\\delta} vertex conditions for\nquantum graphs. There are a number of possible candidates of {\\delta} type\nconditions for beam operators. We develop surgery principles and record the\nmonotonicity properties of the spectrum, keeping in view the possibility that\nvertex conditions may change within the same class after certain graph\nalterations. We also demonstrate the applications of surgery principles by\nobtaining several lower and upper estimates on the eigenvalues.\n', 'The Krein-von Neumann extension for Schr\\""odinger operators on metric\n  graphs   The Krein-von Neumann extension is studied for Schr\\""odinger operators on\nmetric graphs. Among other things, its vertex conditions are expressed\nexplicitly, and its relation to other self-adjoint vertex conditions (e.g.\ncontinuity-Kirchhoff) is explored. A variational characterisation for its\npositive eigenvalues is obtained. Based on this, the behaviour of its\neigenvalues under perturbations of the metric graph is investigated, and\nso-called surgery principles are established. Moreover, isoperimetric\neigenvalue inequalities are obtained.\n']","[('operators graphs', 0.6146266460418701), ('graphs spectral', 0.6094761490821838), ('operator graph', 0.6016937494277954), ('quantum graphs', 0.5793662071228027), ('schr odinger operators', 0.5630861520767212), ('quantum graph', 0.5612211227416992), ('compact metric graphs', 0.5282479524612427), ('odinger operators', 0.5266996622085571), ('schr odinger operator', 0.5247525572776794), ('spectral theory', 0.506464421749115)]"
383,383,78,383_ricci solitons_invariant ricci_ricci tensor_metrics lie groups,"['ricci solitons', 'invariant ricci', 'ricci tensor', 'metrics lie groups', 'ricci curvature', 'ricci soliton', 'generalized ricci', 'lorentzian metrics', 'lie groups', 'generalized ricci flow']","['Canonical connections and algebraic Ricci solitons of three-dimensional\n  Lorentzian Lie groups   In this paper, we compute canonical connections and Kobayashi-Nomizu\nconnections and their curvature on three-dimensional Lorentzian Lie groups with\nsome product structure. We define algebraic Ricci solitons associated to\ncanonical connections and Kobayashi-Nomizu connections. We classify algebraic\nRicci solitons associated to canonical connections and Kobayashi-Nomizu\nconnections on three-dimensional Lorentzian Lie groups with some product\nstructure.\n', 'Left-invariant Ricci collineations associated to canonical connections\n  on three-dimensional Lorentzian Lie groups   In this paper, we classify Left-invariant Ricci collineations associated to\ncanonical connections and Kobayashi-Nomizu connections on three-dimensional\nLorentzian Lie groups.\n', 'Affine Ricci solitons of three-dimensional Lorentzian Lie groups   In this paper, we classify affine Ricci solitons associated to canonical\nconnections and Kobayashi-Nomizu connections and perturbed canonical\nconnections and perturbed Kobayashi-Nomizu connections on three-dimensional\nLorentzian Lie groups with some product structure.\n']","[('ricci solitons', 0.6132519841194153), ('invariant ricci', 0.6004853844642639), ('ricci tensor', 0.5687137842178345), ('metrics lie groups', 0.5677045583724976), ('ricci curvature', 0.5654342770576477), ('ricci soliton', 0.5627171397209167), ('generalized ricci', 0.5623127818107605), ('lorentzian metrics', 0.5278225541114807), ('lie groups', 0.5142693519592285), ('generalized ricci flow', 0.5086314678192139)]"
384,384,78,384_automorphism group affine_automorphisms affine_algebraic groups_groups affine,"['automorphism group affine', 'automorphisms affine', 'algebraic groups', 'groups affine', 'affine algebraic variety', 'algebraic group', 'affine varieties', 'algebraic subgroups', 'algebraic varieties', 'algebraic subgroup']","['When is the automorphism group of an affine variety linear?   Let $Aut_{alg}(X)$ be the subgroup of the group of regular automorphisms\n$Aut(X)$ of an affine algebraic variety $X$ generated by all connected\nalgebraic subgroups. We prove that if $dim X \\ge 2$ and if $Aut_{alg}(X)$ is\nrich enough, $Aut_{alg}(X)$ is not linear, i.e., it cannot be embedded into\n$GL_n(K)$, where $K$ is an algebraically closed field of characteristic zero.\nMoreover, $Aut(X)$ is isomorphic to an algebraic group as an abstract group\nonly if the connected component of $Aut(X)$ is either the algebraic torus or a\ndirect limit of commutative unipotent groups. Finally, we prove that for an\nuncountable $K$ the group of birational transformations of $X$ cannot be\nisomorphic to the group of automorphisms of an affine variety if $X$ is endowed\nwith a rational action of a positive-dimensional linear algebraic group.\n', 'Maximal commutative unipotent subgroups and a characterization of affine\n  spherical varieties   We describe maximal commutative unipotent subgroups of the automorphism group\n$\\mathrm{Aut}(X)$ of an irreducible affine variety $X$. Further we show that a\ngroup isomorphism $\\mathrm{Aut}(X) \\to \\mathrm{Aut}(Y)$ maps unipotent elements\nto unipotent elements, where $Y$ is irreducible and affine. Using this result,\nwe show that the automorphism group detects sphericity and the weight-monoid.\n  As an application, we show that an affine toric variety different from an\nalgebraic torus is determined by its automorphism group among normal\nirreducible affine varieties and we show that a smooth affine spherical variety\ndifferent from an algebraic torus is determined by its automorphism group (up\nto an automorphism of the base field) among smooth irreducible affine\nvarieties.\n', 'When is the automorphism group of an affine variety nested?   For an affine algebraic variety $X$, we study the subgroup\n$\\mathrm{Aut}_{\\text{alg}}(X)$ of the group of regular automorphisms\n$\\mathrm{Aut}(X)$ of $X$ generated by all the connected algebraic subgroups. We\nprove that $\\mathrm{Aut}_{\\text{alg}}(X)$ is nested, i.e., is a direct limit of\nalgebraic subgroups of $\\mathrm{Aut}(X)$, if and only if all the\n$\\mathbb{G}_a$-actions on $X$ commute. Moreover, we describe the structure of\nsuch a group $\\mathrm{Aut}_{\\text{alg}}(X)$.\n']","[('automorphism group affine', 0.6595730185508728), ('automorphisms affine', 0.6288237571716309), ('algebraic groups', 0.6234959363937378), ('groups affine', 0.5937581062316895), ('affine algebraic variety', 0.584550678730011), ('algebraic group', 0.5843175053596497), ('affine varieties', 0.5733441114425659), ('algebraic subgroups', 0.5713752508163452), ('algebraic varieties', 0.561937689781189), ('algebraic subgroup', 0.5507652163505554)]"
385,385,78,385_radiative transport_radiative transfer_radiation transport_thermal radiation,"['radiative transport', 'radiative transfer', 'radiation transport', 'thermal radiation', 'transfer equations', 'radiative', 'boltzmann transport', 'scattering', 'radiation', 'diffusion limit']","['Remarks on the Radiative Transfer Equations for Climatology   Using theoretical and numerical arguments we discuss some of the commonly\naccepted approximations for the radiative transfer equations in climatology.\n', 'Numerical analysis of a spherical harmonic discontinuous Galerkin method\n  for scaled radiative transfer equations with isotropic scattering   In highly diffusion regimes when the mean free path $\\varepsilon$ tends to\nzero, the radiative transfer equation has an asymptotic behavior which is\ngoverned by a diffusion equation and the corresponding boundary condition.\nGenerally, a numerical scheme for solving this problem has the truncation error\ncontaining an $\\varepsilon^{-1}$ contribution, that leads to a nonuniform\nconvergence for small $\\varepsilon$. Such phenomenons require high resolutions\nof discretizations, which degrades the performance of the numerical scheme in\nthe diffusion limit. In this paper, we first provide a--priori estimates for\nthe scaled spherical harmonic ($P_N$) radiative transfer equation. Then we\npresent an error analysis for the spherical harmonic discontinuous Galerkin\n(DG) method of the scaled radiative transfer equation showing that, under some\nmild assumptions, its solutions converge uniformly in $\\varepsilon$ to the\nsolution of the scaled radiative transfer equation. We further present an\noptimal convergence result for the DG method with the upwind flux on Cartesian\ngrids. Error estimates of $\\left(1+\\mathcal{O}(\\varepsilon)\\right)h^{k+1}$\n(where $h$ is the maximum element length) are obtained when tensor product\npolynomials of degree at most $k$ are used.\n', 'A Variable Eddington Factor Model for Thermal Radiative Transfer with\n  Closure based on Data-Driven Shape Function   A new variable Eddington factor (VEF) model is presented for nonlinear\nproblems of thermal radiative transfer (TRT). The VEF model is a data-driven\none that acts on known (a-priori) radiation-diffusion solutions for material\ntemperatures in the TRT problem. A linear auxiliary problem is constructed for\nthe radiative transfer equation (RTE) with opacities and emission source\nevaluated at the known material temperatures. The solution to this RTE\napproximates the specific intensity distribution for the problem in all\nphase-space and time. It is applied as a shape function to define the Eddington\ntensor for the presented VEF model. The shape function computed via the\nauxiliary RTE problem will capture some degree of transport effects within the\nTRT problem. The VEF moment equations closed with this approximate Eddington\ntensor will thus carry with them these captured transport effects. In this\nstudy, the temperature data comes from multigroup $P_1$, $P_{1/3}$, and\nflux-limited diffusion radiative transfer (RT) models. The proposed VEF model\ncan be interpreted as a transport-corrected diffusion reduced-order model.\nNumerical results are presented on the Fleck-Cummings test problem which models\na supersonic wavefront of radiation. The presented VEF model is shown to\nreliably improve accuracy by 1-2 orders of magnitude compared to the considered\nradiation-diffusion model solutions to the TRT problem.\n']","[('radiative transport', 0.6808843016624451), ('radiative transfer', 0.6546933054924011), ('radiation transport', 0.5630890130996704), ('thermal radiation', 0.5059009194374084), ('transfer equations', 0.4679494798183441), ('radiative', 0.43669334053993225), ('boltzmann transport', 0.39475610852241516), ('scattering', 0.3470453917980194), ('radiation', 0.3468194305896759), ('diffusion limit', 0.3418880105018616)]"
386,386,77,386_elliptic optimal control_parabolic optimal control_parabolic optimal_elliptic optimal,"['elliptic optimal control', 'parabolic optimal control', 'parabolic optimal', 'elliptic optimal', 'distributed optimal control', 'optimal control problems', 'optimal control governed', 'neumann boundary control', 'finite element discretization', 'variational discretization']","['Robust finite element solvers for distributed hyperbolic optimal control\n  problems   We propose, analyze, and test new robust iterative solvers for systems of\nlinear algebraic equations arising from the space-time finite element\ndiscretization of reduced optimality systems defining the approximate solution\nof hyperbolic distributed, tracking-type optimal control problems with both the\nstandard $L^2$ and the more general energy regularizations. In contrast to the\nusual time-stepping approach, we discretize the optimality system by space-time\ncontinuous piecewise-linear finite element basis functions which are defined on\nfully unstructured simplicial meshes. If we aim at the asymptotically best\napproximation of the given desired state $y_d$ by the computed finite element\nstate $y_{\\varrho h}$, then the optimal choice of the regularization parameter\n$\\varrho$ is linked to the space-time finite element mesh-size $h$ by the\nrelations $\\varrho=h^4$ and $\\varrho=h^2$ for the $L^2$ and the energy\nregularization, respectively. For this setting, we can construct robust\n(parallel) iterative solvers for the reduced finite element optimality systems.\nThese results can be generalized to variable regularization parameters adapted\nto the local behavior of the mesh-size that can heavily change in the case of\nadaptive mesh refinements. The numerical results illustrate the theoretical\nfindings firmly.\n', 'Space-time finite element methods for distributed optimal control of the\n  wave equation   We consider space-time tracking type distributed optimal control problems for\nthe wave equation in the space-time domain $Q:= \\Omega \\times (0,T) \\subset\n{\\mathbb{R}}^{n+1}$, where the control is assumed to be in the energy space\n$[H_{0;,0}^{1,1}(Q)]^*$, rather than in $L^2(Q)$ which is more common. While\nthe latter ensures a unique state in the Sobolev space $H^{1,1}_{0;0,}(Q)$,\nthis does not define a solution isomorphism. Hence we use an appropriate state\nspace $X$ such that the wave operator becomes an isomorphism from $X$ onto\n$[H_{0;,0}^{1,1}(Q)]^*$. Using space-time finite element spaces of piecewise\nlinear continuous basis functions on completely unstructured but shape regular\nsimplicial meshes, we derive a priori estimates for the error\n$\\|\\widetilde{u}_{\\varrho h}-\\overline{u}\\|_{L^2(Q)}$ between the computed\nspace-time finite element solution $\\widetilde{u}_{\\varrho h}$ and the target\nfunction $\\overline{u}$ with respect to the regularization parameter $\\varrho$,\nand the space-time finite element mesh-size $h$, depending on the regularity of\nthe desired state $\\overline{u}$. These estimates lead to the optimal choice\n$\\varrho=h^2$ in order to define the regularization parameter $\\varrho$ for a\ngiven space-time finite element mesh size $h$, or to determine the required\nmesh size $h$ when $\\varrho$ is a given constant representing the costs of the\ncontrol. The theoretical results will be supported by numerical examples with\ntargets of different regularities, including discontinuous targets.\nFurthermore, an adaptive space-time finite element scheme is proposed and\nnumerically analyzed.\n', 'Robust space-time finite element error estimates for parabolic\n  distributed optimal control problems with energy regularization   We consider space-time tracking optimal control problems for linear\npara\\-bo\\-lic initial boundary value problems that are given in the space-time\ncylinder $Q = \\Omega \\times (0,T)$, and that are controlled by the right-hand\nside $z_\\varrho$ from the Bochner space $L^2(0,T;H^{-1}(\\Omega))$. So it is\nnatural to replace the usual $L^2(Q)$ norm regularization by the energy\nregularization in the $L^2(0,T;H^{-1}(\\Omega))$ norm. We derive a priori\nestimates for the error $\\|\\widetilde{u}_{\\varrho h} - \\bar{u}\\|_{L^2(Q)}$\nbetween the computed state $\\widetilde{u}_{\\varrho h}$ and the desired state\n$\\bar{u}$ in terms of the regularization parameter $\\varrho$ and the space-time\nfinite element mesh-size $h$, and depending on the regularity of the desired\nstate $\\bar{u}$. These estimates lead to the optimal choice $\\varrho = h^2$.\nThe approximate state $\\widetilde{u}_{\\varrho h}$ is computed by means of a\nspace-time finite element method using piecewise linear and continuous basis\nfunctions on completely unstructured simplicial meshes for $Q$. The theoretical\nresults are quantitatively illustrated by a series of numerical examples in two\nand three space dimensions.\n']","[('elliptic optimal control', 0.6193254590034485), ('parabolic optimal control', 0.5842732787132263), ('parabolic optimal', 0.5319536328315735), ('elliptic optimal', 0.5085748434066772), ('distributed optimal control', 0.49811848998069763), ('optimal control problems', 0.48735374212265015), ('optimal control governed', 0.47869381308555603), ('neumann boundary control', 0.477764368057251), ('finite element discretization', 0.4769255518913269), ('variational discretization', 0.4718341827392578)]"
387,387,77,387_potential scattering_scattering theory_scattering matrices_scattering states,"['potential scattering', 'scattering theory', 'scattering matrices', 'scattering states', 'scattering properties', 'scattering general', 'quantum scattering', 'limit scattering', 'scattering matrix', 'stationary scattering']","['Transfer matrix for long-range potentials   We extend the notion of the transfer matrix of potential scattering to a\nlarge class of long-range potentials $v(x)$ and derive its basic properties. We\noutline a dynamical formulation of the time-independent scattering theory for\nthis class of potentials where we identify their transfer matrix with the\n$S$-matrix of a certain effective non-unitary two-level quantum system. For\nsufficiently large values of $|x|$, we express $v(x)$ as the sum of a\nshort-range potential and an exactly solvable long-range potential. Using this\nresult and the composition property of the transfer matrix, we outline an\napproximation scheme for solving the scattering problem for $v(x)$. To\ndemonstrate the effectiveness of this scheme, we construct an exactly solvable\nlong-range potential and compare the exact values of its reflection and\ntransmission coefficients with those we obtain using our approximation scheme.\n', ""Stationary scattering theory, the $N$-body long-range case   Within the class of Derezi{\\'n}ski-Enss pair-potentials which includes\nCoulomb potentials and for which asymptotic completeness is known \\cite{De}, we\nshow that all entries of the $N$-body quantum scattering matrix have a\nwell-defined meaning at any given non-threshold energy. As a function of the\nenergy parameter the scattering matrix is weakly continuous. This result\ngeneralizes a similar one obtained previously by Yafaev for systems of\nparticles interacting by short-range potentials \\cite{Ya1}. As for Yafaev's\npaper we do not make any assumption on the decay of channel eigenstates. The\nmain part of the proof consists in establishing a number of Kato-smoothness\nbounds needed for justifying a new formula for the scattering matrix. Similarly\nwe construct and show strong continuity of channel wave matrices for all\nnon-threshold energies. Away from a set of measure zero we show that the\nscattering and channel wave matrices constitute a well-defined `scattering\ntheory', in particular at such energies the scattering matrix is unitary,\nstrongly continuous and characterized by asymptotics of minimum generalized\neigenfunctions.\n"", 'Long-range potential scattering: Converting long-range potential to\n  short-range potential by tortoise coordinate   Inspired by general relativity, we suggest an approach for long-range\npotential scattering. In scattering theory, there is a general theory for\nshort-range potential scattering, but there is no general theory for long-range\npotential scattering. This is because the scattering boundary conditions for\nall short-range potentials are the same, but for different long-range\npotentials are different. In this paper, by introducing tortoise coordinates,\nwe convert long-range potential scattering to short-range potential scattering.\nThis allows us to deal with long-range potential scattering as short-range\npotential scattering. An explicit expression of the scattering wave function\nfor long-range potential scattering is presented, in which the scattering wave\nfunction is represented by the tortoise coordinate and the scattering phase\nshift. We show that the long-range potential scattering wave function is just\nthe short-range potential scattering wave function with a replacement of a\ncommon coordinate by a tortoise coordinate. The approach applies not only to\nscattering but also applies to bound states. Furthermore, in terms of tortoise\ncoordinates, we suggest a classification scheme for potentials. We also discuss\nthe duality between tortoise coordinates.\n']","[('potential scattering', 0.6818814873695374), ('scattering theory', 0.6649898290634155), ('scattering matrices', 0.650175929069519), ('scattering states', 0.646491527557373), ('scattering properties', 0.6445941925048828), ('scattering general', 0.6360308527946472), ('quantum scattering', 0.629141092300415), ('limit scattering', 0.6284510493278503), ('scattering matrix', 0.621843695640564), ('stationary scattering', 0.619804322719574)]"
388,388,77,388_homology graph_magnitude homology_homology theory_path homology,"['homology graph', 'magnitude homology', 'homology theory', 'path homology', 'homology theories', 'homology', 'homology groups', 'homology simplicial', 'simplicial homology', 'homology classes']","['The reachability homology of a directed graph   The last decade has seen the development of path homology and magnitude\nhomology -- two homology theories of directed graphs, each satisfying classic\nproperties such as Kunneth and Mayer-Vietoris theorems. Recent work of Asao has\nshown that magnitude homology and path homology are related, appearing in\ndifferent pages of a certain spectral sequence. Here we study the target of\nthat spectral sequence, which we call reachability homology. We prove that it\nsatisfies appropriate homotopy invariance, Kunneth, excision, and\nMayer-Vietoris theorems, these all being stronger than the corresponding\nproperties for either magnitude or path homology.\n', 'Eulerian magnitude homology: subgraph structure and random graphs   In this paper we explore the connection between the ranks of the magnitude\nhomology groups of a graph and the structure of its subgraphs. To this end, we\nintroduce variants of magnitude homology called eulerian magnitude homology and\ndiscriminant magnitude homology. Leveraging the combinatorics of the\ndifferential in magnitude homology, we illustrate a close relationship between\nthe ranks of the eulerian magnitude homology groups on the first diagonal and\ncounts of subgraphs which fall in specific classes. We leverage these tools to\nstudy limiting behavior of the eulerian magnitude homology groups for\nErdos-Renyi random graphs and random geometric graphs, producing for both\nmodels a vanishing threshold for the eulerian magnitude homology groups on the\nfirst diagonal. This in turn provides a characterization of the generators for\nthe corresponding magnitude homology groups. Finally, we develop an explicit\nasymptotic estimate the expected rank of eulerian magnitude homology along the\nfirst diagonal for these random graph models.\n', ""Bigraded path homology and the magnitude-path spectral sequence   Two important invariants of directed graphs, namely magnitude homology and\npath homology, have recently been shown to be intimately connected: there is a\n'magnitude-path spectral sequence' or 'MPSS' in which magnitude homology\nappears as the first page, and in which path homology appears as an axis of the\nsecond page. In this paper we study the homological and computational\nproperties of the spectral sequence, and in particular of the full second page,\nwhich we now call 'bigraded path homology'. We demonstrate that every page of\nthe MPSS deserves to be regarded as a homology theory in its own right,\nsatisfying excision and Kunneth theorems (along with a homotopy invariance\nproperty already established by Asao), and that magnitude homology and bigraded\npath homology also satisfy Mayer-Vietoris theorems. We construct a homotopy\ntheory of graphs (in the form of a cofibration category structure) in which\nweak equivalences are the maps inducing isomorphisms on bigraded path homology,\nstrictly refining an existing structure based on ordinary path homology. And we\nprovide complete computations of the MPSS for two important families of graphs\n- the directed and bi-directed cycles - which demonstrate the power of both the\nMPSS, and bigraded path homology in particular, to distinguish graphs that\nordinary path homology cannot.\n""]","[('homology graph', 0.7327029705047607), ('magnitude homology', 0.6395251154899597), ('homology theory', 0.6367390155792236), ('path homology', 0.6269773840904236), ('homology theories', 0.6217542886734009), ('homology', 0.6027653217315674), ('homology groups', 0.5957625508308411), ('homology simplicial', 0.5833982229232788), ('simplicial homology', 0.5789279937744141), ('homology classes', 0.5709219574928284)]"
389,389,77,389_inequalities polynomials_bernstein inequalities_extremal polynomials_bernstein type inequality,"['inequalities polynomials', 'bernstein inequalities', 'extremal polynomials', 'bernstein type inequality', 'polynomial approximation', 'bernstein inequality', 'orthonormal polynomials', 'chebyshev polynomials', 'asymptotic lower bound', 'orthogonal polynomials']","['A Note on Sharp Multivariate Bernstein- and Markov-Type Inequalities   Let $V$ be a symmetric convex body in $\\R^m$.\n  We prove sharp Bernstein-type inequalities for entire functions of\nexponential type with the spectrum in $V$ and discuss certain properties of the\nextremal functions. Markov-type inequalities with sharp constants\n  for algebraic polynomials on $V$ and certain\n  non-symmetric convex bodies are proved as well.\n', 'Sharp Constants of Approximation Theory. III. Certain Polynomial\n  Inequalities of Different Metrics on Convex Sets   Let $V\\subset\\R^m$ be a centrally symmetric convex body and let\n$V^*\\subset\\R^m$ be its polar. We prove limit relations between the sharp\nconstants in the multivariate Markov-Bernstein-Nikolskii type inequalities for\nalgebraic polynomials on $V^*$ and the corresponding constants for entire\nfunctions of exponential type with the spectrum in $V$.\n', 'On Properties of a Regular Simplex Inscribed into a Ball   Let $B$ be a Euclidean ball in ${\\mathbb R}^n$ and let $C(B)$ be a space\nof~continuous functions $f:B\\to{\\mathbb R}$ with the uniform norm\n$\\|f\\|_{C(B)}:=\\max_{x\\in B}|f(x)|.$ By $\\Pi_1\\left({\\mathbb R}^n\\right)$ we\nmean a set of polynomials of degree $\\leq 1$, i.e., a set of linear functions\nupon ${\\mathbb R}^n$. The interpolation projector $P:C(B)\\to \\Pi_1({\\mathbb\nR}^n)$ with the nodes $x^{(j)}\\in B$ is defined by the equalities\n$Pf\\left(x^{(j)}\\right)= f\\left(x^{(j)}\\right)$, $j=1,$ $\\ldots,$ $ n+1$. The\nnorm of $P$ as an operator from $C(B)$ to $C(B)$ can be calculated by the\nformula $\\|P\\|_B=\\max_{x\\in B}\\sum |\\lambda_j(x)|.$ Here $\\lambda_j$ are the\nbasic Lagrange polynomials corresponding to the $n$-dimensional nondegenerate\nsimplex $S$ with the vertices $x^{(j)}$. Let $P^\\prime$ be a projector having\nthe nodes in the vertices \\linebreak of a regular simplex inscribed into the\nball. We describe the points $y\\in B$ with the property $\\|P^\\prime\\|_B=\\sum\n|\\lambda_j(y)|$. Also we formulate a geometric conjecture which implies that\n$\\|P^\\prime\\|_B$ is equal to the minimal norm of an interpolation projector\nwith nodes in $B$. We prove that this conjecture holds true at least for\n$n=1,2,3,4$.\n  Keywords: regular simplex, ball, linear interpolation, projector, norm\n']","[('inequalities polynomials', 0.5399311184883118), ('bernstein inequalities', 0.500100314617157), ('extremal polynomials', 0.49802035093307495), ('bernstein type inequality', 0.4923955202102661), ('polynomial approximation', 0.4474357068538666), ('bernstein inequality', 0.441413015127182), ('orthonormal polynomials', 0.43575844168663025), ('chebyshev polynomials', 0.4055422246456146), ('asymptotic lower bound', 0.38733887672424316), ('orthogonal polynomials', 0.38680267333984375)]"
390,390,77,390_low rank approximation_low rank approximations_dynamical low rank_rank adaptive,"['low rank approximation', 'low rank approximations', 'dynamical low rank', 'rank adaptive', 'rank approximation', 'splitting integrator', 'rank approximations', 'equations low rank', 'integrators', 'low rank matrix']","['A rank-adaptive robust integrator for dynamical low-rank approximation   A rank-adaptive integrator for the dynamical low-rank approximation of matrix\nand tensor differential equations is presented. The fixed-rank integrator\nrecently proposed by two of the authors is extended to allow for an adaptive\nchoice of the rank, using subspaces that are generated by the integrator\nitself. The integrator first updates the evolving bases and then does a\nGalerkin step in the subspace generated by both the new and old bases, which is\nfollowed by rank truncation to a given tolerance. It is shown that the adaptive\nlow-rank integrator retains the exactness, robustness and symmetry-preserving\nproperties of the previously proposed fixed-rank integrator. Beyond that, up to\nthe truncation tolerance, the rank-adaptive integrator preserves the norm when\nthe differential equation does, it preserves the energy for Schr\\""odinger\nequations and Hamiltonian systems, and it preserves the monotonic decrease of\nthe functional in gradient flows. Numerical experiments illustrate the\nbehaviour of the rank-adaptive integrator.\n', 'A parallel rank-adaptive integrator for dynamical low-rank approximation   This work introduces a parallel and rank-adaptive matrix integrator for\ndynamical low-rank approximation. The method is related to the previously\nproposed rank-adaptive basis update & Galerkin (BUG) integrator but differs\nsignificantly in that all arising differential equations, both for the basis\nand the Galerkin coefficients, are solved in parallel. Moreover, this approach\neliminates the need for a potentially costly coefficient update with augmented\nbasis matrices. The integrator also incorporates a new step rejection strategy\nthat enhances the robustness of both the parallel integrator and the BUG\nintegrator. By construction, the parallel integrator inherits the robust error\nbound of the BUG and projector-splitting integrators. Comparisons of the\nparallel and BUG integrators are presented by a series of numerical experiments\nwhich demonstrate the efficiency of the proposed method, for problems from\nradiative transfer and radiation therapy.\n', 'Robust high-order low-rank BUG integrators based on explicit Runge-Kutta\n  methods   In this work, we propose high-order basis-update & Galerkin (BUG) integrators\nbased on explicit Runge-Kutta methods for large-scale matrix differential\nequations. These dynamical low-rank integrators are high-order extensions of\nthe BUG integrator and are constructed by performing a BUG step at each stage\nof the Runge-Kutta method. In this way, the resulting Runge-Kutta BUG\nintegrator is robust to the presence of small singular values and does not\ninvolve backward time-integration steps. We provide an error bound, which shows\nthat the Runge-Kutta BUG integrator retains the order of convergence of the\nassociated Runge-Kutta method until the error reaches a plateau corresponding\nto the low-rank truncation error and which vanishes as the rank becomes full.\nThis error bound is finally validated experimentally on three numerical test\ncases. The results demonstrate the high-order convergence of the Runge-Kutta\nBUG integrator and its superior accuracy compared to other dynamical low-rank\nintegrators proposed in the literature.\n']","[('low rank approximation', 0.49701786041259766), ('low rank approximations', 0.4949898421764374), ('dynamical low rank', 0.47361627221107483), ('rank adaptive', 0.4663763642311096), ('rank approximation', 0.46607378125190735), ('splitting integrator', 0.46116504073143005), ('rank approximations', 0.4597302973270416), ('equations low rank', 0.4318618178367615), ('integrators', 0.42969462275505066), ('low rank matrix', 0.42024171352386475)]"
391,391,77,391_tractability results_tractability_information complexity_linear functionals,"['tractability results', 'tractability', 'information complexity', 'linear functionals', 'functions finite dimensional', 'discretization provides', 'approximation functions', 'type discretization', 'continuous linear functionals', 'kernel hilbert spaces']","['On the power of standard information for tractability for\n  $L_2$-approximation in the average case setting   We study multivariate approximation in the average case setting with the\nerror measured in the weighted $L_2$ norm. We consider algorithms that use\nstandard information $\\Lambda^{\\rm std}$ consisting of function values or\ngeneral linear information $\\Lambda^{\\rm all}$ consisting of arbitrary\ncontinuous linear functionals. We investigate the equivalences of various\nnotions of algebraic and exponential tractability for $\\Lambda^{\\rm std}$ and\n$\\Lambda^{\\rm all}$ for the absolute error criterion, and show that the power\nof $\\Lambda^{\\rm std}$ is the same as that of $\\Lambda^{\\rm all}$ for all\nnotions of algebraic and exponential tractability without any condition.\nSpecifically, we solve Open Problems 116-118 and almost solve Open Problem 115\nas posed by E.Novak and H.Wo\\\'zniakowski in the book: Tractability of\nMultivariate Problems, Volume III: Standard Information for Operators, EMS\nTracts in Mathematics, Z\\""urich, 2012.\n', 'Tractability of non-homogeneous tensor product problems in the worst\n  case setting   We study multivariate linear tensor product problems with some special\nproperties in the worst case setting. We consider algorithms that use finitely\nmany continuous linear functionals. We use a unified method to investigate\ntractability of the above multivariate problems, and obtain necessary and\nsufficient conditions for strong polynomial tractability, polynomial\ntractability, quasi-polynomial tractability, uniformly weak tractability,\n$(s,t)$-weak tractability, and weak tractability. Our results can apply to\nmultivariate approximation problems with kernels corresponding to Euler\nkernels, Wiener kernels, Korobov kernels, Gaussian kernels, and analytic\nKorobov kernels.\n', 'Tractability of approximation in the weighted Korobov space in the\n  worst-case setting -- a complete picture   In this paper, we study tractability of $L_2$-approximation of one-periodic\nfunctions from weighted Korobov spaces in the worst-case setting. The\nconsidered weights are of product form. For the algorithms we allow information\nfrom the class $\\Lambda^{{\\rm all}}$ consisting of all continuous linear\nfunctionals and from the class $\\Lambda^{{\\rm std}}$, which only consists of\nfunction evaluations.\n  We provide necessary and sufficient conditions on the weights of the function\nspace for quasi-polynomial tractability, uniform weak tractability, weak\ntractability and $(\\sigma,\\tau)$-weak tractability. Together with the already\nknown results for strong polynomial and polynomial tractability, our findings\nprovide a complete picture of the weight conditions for all current standard\nnotions of tractability.\n']","[('tractability results', 0.47732973098754883), ('tractability', 0.4533868134021759), ('information complexity', 0.44834470748901367), ('linear functionals', 0.4032503664493561), ('functions finite dimensional', 0.39063650369644165), ('discretization provides', 0.3811548054218292), ('approximation functions', 0.3762529492378235), ('type discretization', 0.36860665678977966), ('continuous linear functionals', 0.344745010137558), ('kernel hilbert spaces', 0.3444209396839142)]"
392,392,75,392_information bottleneck_information bottleneck ib_deep neural_variational information,"['information bottleneck', 'information bottleneck ib', 'deep neural', 'variational information', 'learned representation', 'bottleneck', 'information decomposition', 'bottleneck ib', 'representation learning', 'learned representations']","['Disentangled Information Bottleneck   The information bottleneck (IB) method is a technique for extracting\ninformation that is relevant for predicting the target random variable from the\nsource random variable, which is typically implemented by optimizing the IB\nLagrangian that balances the compression and prediction terms. However, the IB\nLagrangian is hard to optimize, and multiple trials for tuning values of\nLagrangian multiplier are required. Moreover, we show that the prediction\nperformance strictly decreases as the compression gets stronger during\noptimizing the IB Lagrangian. In this paper, we implement the IB method from\nthe perspective of supervised disentangling. Specifically, we introduce\nDisentangled Information Bottleneck (DisenIB) that is consistent on compressing\nsource maximally without target prediction performance loss (maximum\ncompression). Theoretical and experimental results demonstrate that our method\nis consistent on maximum compression, and performs well in terms of\ngeneralization, robustness to adversarial attack, out-of-distribution\ndetection, and supervised disentangling.\n', 'Flexible Variational Information Bottleneck: Achieving Diverse\n  Compression with a Single Training   Information Bottleneck (IB) is a widely used framework that enables the\nextraction of information related to a target random variable from a source\nrandom variable. In the objective function, IB controls the trade-off between\ndata compression and predictiveness through the Lagrange multiplier $\\beta$.\nTraditionally, to find the trade-off to be learned, IB requires a search for\n$\\beta$ through multiple training cycles, which is computationally expensive.\nIn this study, we introduce Flexible Variational Information Bottleneck (FVIB),\nan innovative framework for classification task that can obtain optimal models\nfor all values of $\\beta$ with single, computationally efficient training. We\ntheoretically demonstrate that across all values of reasonable $\\beta$, FVIB\ncan simultaneously maximize an approximation of the objective function for\nVariational Information Bottleneck (VIB), the conventional IB method. Then we\nempirically show that FVIB can learn the VIB objective as effectively as VIB.\nFurthermore, in terms of calibration performance, FVIB outperforms other IB and\ncalibration methods by enabling continuous optimization of $\\beta$. Our codes\nare available at https://github.com/sotakudo/fvib.\n', ""Elastic Information Bottleneck   Information bottleneck is an information-theoretic principle of\nrepresentation learning that aims to learn a maximally compressed\nrepresentation that preserves as much information about labels as possible.\nUnder this principle, two different methods have been proposed, i.e.,\ninformation bottleneck (IB) and deterministic information bottleneck (DIB), and\nhave gained significant progress in explaining the representation mechanisms of\ndeep learning algorithms. However, these theoretical and empirical successes\nare only valid with the assumption that training and test data are drawn from\nthe same distribution, which is clearly not satisfied in many real-world\napplications. In this paper, we study their generalization abilities within a\ntransfer learning scenario, where the target error could be decomposed into\nthree components, i.e., source empirical error, source generalization gap (SG),\nand representation discrepancy (RD). Comparing IB and DIB on these terms, we\nprove that DIB's SG bound is tighter than IB's while DIB's RD is larger than\nIB's. Therefore, it is difficult to tell which one is better. To balance the\ntrade-off between SG and the RD, we propose an elastic information bottleneck\n(EIB) to interpolate between the IB and DIB regularizers, which guarantees a\nPareto frontier within the IB framework. Additionally, simulations and real\ndata experiments show that EIB has the ability to achieve better domain\nadaptation results than IB and DIB, which validates the correctness of our\ntheories.\n""]","[('information bottleneck', 0.5808712840080261), ('information bottleneck ib', 0.5486969947814941), ('deep neural', 0.45689716935157776), ('variational information', 0.45300284028053284), ('learned representation', 0.4505176544189453), ('bottleneck', 0.4495852589607239), ('information decomposition', 0.446396142244339), ('bottleneck ib', 0.43348976969718933), ('representation learning', 0.41702166199684143), ('learned representations', 0.41116711497306824)]"
393,393,75,393_cahn hilliard equations_hilliard equations_cahn hilliard system_analysis cahn hilliard,"['cahn hilliard equations', 'hilliard equations', 'cahn hilliard system', 'analysis cahn hilliard', 'hilliard navier stokes', 'hilliard degenerate mobility', 'hilliard system', 'surface diffusion', 'cahn hilliard type', 'cahn hilliard degenerate']","['Abstract error analysis for Cahn--Hilliard type equations with dynamic\n  boundary conditions   This work addresses the problem of solving the Cahn-Hilliard equation\nnumerically. For that we introduce an abstract formulation for Cahn-Hilliard\ntype equations with dynamic boundary conditions, we conduct the spatial\nsemidiscretization via finite elements and prove error bounds based on the\ntechnique of energy estimates. The variational formulation for\nCahn-Hilliard/Cahn-Hilliard coupling, will apply to a larger abstract class of\nproblems and is similar to the usual weak formulation of parabolic problems. In\ncontrast to problems with non dynamic boundary conditions, the Hilbert spaces\n$L^2(\\Omega)$ and $H^1(\\Omega)$ are exchanged with the spaces\n$L^2(\\Omega)\\times L^2(\\Gamma)$ and $\\lbrace v\\in H^1(\\Omega): \\gamma v \\in\nH^1(\\Gamma)\\rbrace$, respectively. Because we are considering a fourth-order\ndifferential equation, which will be described by a system of two second-order\ndifferential equations, the variational formulation also consists of a system\nof two equations.\n', 'An efficient and convergent finite element scheme for Cahn--Hilliard\n  equations with dynamic boundary conditions   The Cahn--Hilliard equation is a widely used model that describes amongst\nothers phase separation processes of binary mixtures or two-phase flows. In the\nrecent years, different types of boundary conditions for the Cahn--Hilliard\nequation were proposed and analyzed. In this publication, we are concerned with\nthe numerical treatment of a recent model which introduces an additional\nCahn--Hilliard type equation on the boundary as closure for the Cahn--Hilliard\nequation in the domain [C. Liu, H. Wu, Arch. Ration. Mech. An., 2019]. By\nidentifying a mapping between the phase-field parameter and the chemical\npotential inside of the domain, we are able to postulate an efficient,\nunconditionally energy stable finite element scheme. Furthermore, we establish\nthe convergence of discrete solutions towards suitable weak solutions of the\noriginal model. This serves also as an additional pathway to establish\nexistence of weak solutions. Furthermore, we present simulations underlining\nthe practicality of the proposed scheme and investigate its experimental order\nof convergence.\n', 'A sturcture-preserving, upwind-SAV scheme for the degenerate\n  Cahn--Hilliard equation with applications to simulating surface diffusion   This paper establishes a structure-preserving numerical scheme for the\nCahn--Hilliard equation with degenerate mobility. First, by applying a finite\nvolume method with upwind numerical fluxes to the degenerate Cahn--Hilliard\nequation rewritten by the scalar auxiliary variable (SAV) approach, we\ncreatively obtain an unconditionally bound-preserving, energy-stable and\nfully-discrete scheme, which, for the first time, addresses the boundedness of\nthe classical SAV approach under $H^{-1}$-gradient flow. Then, a\ndimensional-splitting technique is introduced in high-dimensional cases, which\ngreatly reduces the computational complexity while preserves original\nstructural properties. Numerical experiments are presented to verify the\nbound-preserving and energy-stable properties of the proposed scheme. Finally,\nby applying the proposed structure-preserving scheme, we numerically\ndemonstrate that surface diffusion can be approximated by the Cahn--Hilliard\nequation with degenerate mobility and Flory--Huggins potential when the\nabsolute temperature is sufficiently low, which agrees well with the\ntheoretical result by using formal asymptotic analysis.wn theoretically by\nformal matched asymptotics.\n']","[('cahn hilliard equations', 0.7240265011787415), ('hilliard equations', 0.6889084577560425), ('cahn hilliard system', 0.6076458692550659), ('analysis cahn hilliard', 0.581264078617096), ('hilliard navier stokes', 0.5719852447509766), ('hilliard degenerate mobility', 0.568988025188446), ('hilliard system', 0.5462570786476135), ('surface diffusion', 0.4721023738384247), ('cahn hilliard type', 0.4572918713092804), ('cahn hilliard degenerate', 0.45558953285217285)]"
394,394,75,394_tournament_round robin_tournaments_teams,"['tournament', 'round robin', 'tournaments', 'teams', 'matches', 'competitions', 'first round', 'ranking', 'soccer', 'gambling']","['Increasing competitiveness by imbalanced groups: The example of the\n  48-team FIFA World Cup   A match played in a sports tournament can be called stakeless if at least one\nteam is indifferent to its outcome because it already has qualified or has been\neliminated. Such a game threatens fairness since teams may not exert full\neffort without incentives. This paper suggests a novel classification for\nstakeless matches according to their expected outcome: they are more costly if\nthe indifferent team is more likely to win by playing honestly. Our approach is\nillustrated with the 2026 FIFA World Cup, the first edition of the competition\nwith 48 teams. We propose a novel format based on imbalanced groups, which\ndrastically reduces the probability of stakeless matches played by the\nstrongest teams according to Monte Carlo simulations. The new design also\nincreases the uncertainty of match outcomes and requires fewer matches.\nGoverning bodies in sports are encouraged to consider our innovative idea in\norder to enhance the competitiveness of their tournaments.\n', 'Best Strategy for Each Team in The Regular Season to Win Champion in The\n  Knockout Tournament   In J. Schwenk.(2018) [\'What is the Correct Way to Seed a Knockout\nTournament?\' Retrieved from The American Mathematical Monthly], Schwenk\nidentified a surprising weakness in the standard method of seeding a single\nelimination (or knockout) tournament. In particular, he showed that for a\ncertain probability model for the outcomes of games it can be the case that the\ntop seeded team would be less likely to win the tournament than the second\nseeded team. This raises the possibility that in certain situations it might be\nadvantageous for a team to intentionally lose a game in an attempt to get a\nmore optimal (though possibly lower) seed in the tournament. We examine this\nquestion in the context of a four team league which consists of a round robin\n""regular season"" followed by a single elimination tournament with seedings\ndetermined by the results from the regular season [4]. Using the same\nprobability model as Schwenk we show that there are situations where it is\nindeed optimal for a team to intentionally lose. Moreover, we show how a team\ncan make the decision as to whether or not it should intentionally lose. We did\ntwo detailed analysis. One is for the situation where other teams always try to\nwin every game. The other is for the situation where other teams are smart\nenough, namely they can also lose some games intentionally if necessary. The\nanalysis involves computations in both probability and (multi-player) game\ntheory.\n', 'Tournament schedules and incentives in a double round-robin tournament\n  with four teams   In a round-robin tournament, a team may lack the incentive to win if its\nfinal rank does not depend on the outcome of the matches still to be played.\nThis paper introduces a classification scheme to determine these weakly (where\none team is indifferent) or strongly (where both teams are indifferent)\nstakeless matches in a double round-robin contest with four teams. The\nprobability that such matches arise can serve as a novel fairness criterion to\ncompare and evaluate match schedules. Our approach is illustrated by the UEFA\nChampions League group stage. A simulation model is built to compare the 12\nvalid schedules for the group matches. Some schedules are shown to be dominated\nby other schedules. It is found that the strongest team should play at home in\nthe last round against one of the middle teams, depending on the preferences of\nthe tournament organiser. Choosing an optimal sequence of matches with respect\nto the proposed metric can help to avoid uninteresting matches.\n']","[('tournament', 0.5333236455917358), ('round robin', 0.5081331729888916), ('tournaments', 0.49522364139556885), ('teams', 0.47144073247909546), ('matches', 0.4601212441921234), ('competitions', 0.42588740587234497), ('first round', 0.39873409271240234), ('ranking', 0.3780086636543274), ('soccer', 0.3763379156589508), ('gambling', 0.3724209666252136)]"
395,395,75,395_exclusion processes_symmetric exclusion process_asymmetric exclusion_asymmetric simple exclusion,"['exclusion processes', 'symmetric exclusion process', 'asymmetric exclusion', 'asymmetric simple exclusion', 'exclusion process', 'simple exclusion process', 'zero range processes', 'exclusion process tasep', 'boundary dynamics', 'symmetric simple exclusion']","['Multi species asymmetric simple exclusion process with impurity\n  activated flips   We obtain an exact matrix product steady state for a class of multi species\nasymmetric simple exclusion process with impurities, under periodic boundary\ncondition. Alongside the usual hopping dynamics, an additional flip dynamics is\nactivated only in the presence of impurities. Although the microscopic dynamics\nrenders the system to be non-ergodic, exact analytical results for observables\nare obtained in steady states for a specific class of initial configurations.\nInteresting physical features including negative differential mobility and\ntransition of correlations from negative to positive with changing vacancy\ndensity, have been observed. We discuss plausible connections of this exactly\nsolvable model with multi lane asymmetric simple exclusion processes as well as\nenzymatic chemical reactions.\n', 'Weak reservoirs are superexponentially irrelevant for misanthrope\n  processes   We provide a short proof for the exponential equivalence between misanthrope\nprocesses in contact with weak reservoirs and those with impermeable\nboundaries. As a consequence, we can derive both the hydrodynamic limit and the\nlarge deviations of the totally asymmetric simple exclusion process (TASEP) in\ncontact with weak reservoirs. This extends a recent result which proved the\nhydrodynamic behaviour of a vanishing viscocity approximation of the TASEP in\ncontact with weak reservoirs. Further applications to a class of asymmetric\nexclusion processes with long jumps are discussed.\n', 'Coupling hydrodynamics of several Facilitated Exclusion Processes with\n  closed boundaries   In this paper, we prove the hydrodynamic limit for the ergodic dynamics of\nthe Facilitated Exclusion Process with closed boundaries in the symmetric,\nasymmetric and weakly asymmetric regimes. For this, we couple it with a Simple\nExclusion Process by constructing a mapping that transforms the facilitated\ndynamics into the simple one. As the hydrodynamic behaviour of the simple\nexclusion process with closed boundaries has been extensively studied, we can\ndeduce the corresponding hydrodynamics for the facilitated exclusion process.\n']","[('exclusion processes', 0.5918699502944946), ('symmetric exclusion process', 0.5777075886726379), ('asymmetric exclusion', 0.5339664220809937), ('asymmetric simple exclusion', 0.521884024143219), ('exclusion process', 0.5132913589477539), ('simple exclusion process', 0.5109306573867798), ('zero range processes', 0.46276918053627014), ('exclusion process tasep', 0.4546809196472168), ('boundary dynamics', 0.43443524837493896), ('symmetric simple exclusion', 0.4209282696247101)]"
396,396,75,396_switched systems_switching systems_linear switching_switched system,"['switched systems', 'switching systems', 'linear switching', 'switched system', 'switching system', 'lyapunov functions stability', 'based lyapunov', 'fast switching', 'hybrid dynamical systems', 'lyapunov technique']","['Stability of Reset and Impulsive Continuous-time Linear Switched Systems   We study stability issue of reset and impulsive switched systems. We find\ntime constraints (dwell time and flee time) on switching signals which\nstabilize a given reset switched system. For a given collection of matrices, we\nfind an assignment of resets and time constraints on switching signals which\nguarantee stability of the reset switched system. Similar results are obtained\nfor impulsive switched systems as well. Two techniques, namely, analysis of\nflow of the system and the multiple Lyapunov function approach is used to\nobtain the results. The results are later generalized to obtain mode-dependent\ntime constraints for stability of these systems.\n', 'Converse Lyapunov Results for Stability of Switched Systems with Average\n  Dwell-Time   This article provides a characterization of stability for switched nonlinear\nsystems under average dwell-time constraints, in terms of necessary and\nsufficient conditions involving multiple Lyapunov functions. Earlier converse\nresults focus on switched systems with dwell-time constraints only, and the\nresulting inequalities depend on the flow of individual subsystems. With the\nhelp of a counterexample, we show that a lower bound that guarantees stability\nfor dwell-time switching signals may not necessarily imply stability for\nswitching signals with same lower bound on the average dwell-time. Based on\nthese two observations, we provide a converse result for the average dwell-time\nconstrained systems in terms of inequalities which do not depend on the flow of\nindividual subsystems and are easier to check. The particular case of linear\nswitched systems is studied as a corollary to our main result.\n', 'A Simple Loop Dwell Time Approach for Stability of Switched Systems   We introduce a novel concept of simple loop dwell time and use it to give\nsufficient conditions for stability of a continuous-time linear switched system\nwhere switching between subsystems is governed by an underlying graph. We\npresent a slow-fast switching mechanism to ensure stability of the system. We\nalso consider switched systems with both stable and unstable subsystems, and\nobtain bounds on the dwell time in the stable subsystem and flee time from the\nunstable subsystem that guarantee the stability of the system.\n']","[('switched systems', 0.6064746975898743), ('switching systems', 0.5921393632888794), ('linear switching', 0.5803369283676147), ('switched system', 0.5739593505859375), ('switching system', 0.5484576225280762), ('lyapunov functions stability', 0.460043728351593), ('based lyapunov', 0.4305814206600189), ('fast switching', 0.4261157512664795), ('hybrid dynamical systems', 0.406753271818161), ('lyapunov technique', 0.40304896235466003)]"
397,397,75,397_cahn hilliard equations_hilliard equations_solutions cahn hilliard_cahn hilliard system,"['cahn hilliard equations', 'hilliard equations', 'solutions cahn hilliard', 'cahn hilliard system', 'coupled cahn hilliard', 'nonlocal cahn hilliard', 'cahn hilliard degenerate', 'stokes cahn hilliard', 'solutions nonlocal', 'convective cahn hilliard']","['Existence and local asymptotics for a system of cross-diffusion\n  equations with nonlocal Cahn-Hilliard terms   We study a nonlocal Cahn-Hilliard model for a multicomponent mixture with\ncross-diffusion effects and degenerate mobility. The nonlocality is described\nby means of a symmetric singular kernel. We define a notion of weak solution\nadapted to possible degeneracies and prove, as our first main result, its\nglobal-in-time existence. The proof relies on an application of the formal\ngradient flow structure of the system (to overcome the lack of a-priori\nestimates), combined with an extension of the boundedness-by-entropy method, in\nturn involving a careful analysis of an auxiliary variational problem. This\nallows to obtain solutions to an approximate, time-discrete system. Letting the\ntime step size go to zero, we recover the desired nonlocal weak solution where,\ndue to their low regularity, the Cahn-Hilliard terms require a special\ntreatment.\n  Finally, we prove convergence of solutions for this class of nonlocal\nCahn-Hilliard equations to their local counterparts.\n', 'Degenerate nonlocal Cahn-Hilliard equations: well-posedness, regularity\n  and local asymptotics   Existence and uniqueness of solutions for nonlocal Cahn-Hilliard equations\nwith degenerate potential is shown. The nonlocality is described by means of a\nsymmetric singular kernel not falling within the framework of any previous\nexistence theory. A convection term is also taken into account. Building upon\nthis novel existence result, we prove convergence of solutions for this class\nof nonlocal Cahn-Hilliard equations to their local counterparts, as the\nnonlocal convolution kernels approximate a Dirac delta. Eventually, we show\nthat, under suitable assumptions on the data, the solutions to the nonlocal\nCahn-Hilliard equations exhibit further regularity, and the nonlocal-to-local\nconvergence is verified in a stronger topology.\n', 'Cahn-Hilliard Equations on Random Walk Spaces   In this paper we study a nonlocal Cahn-Hilliard model (CHE) in the framework\nof random walk spaces, which includes as particular cases, the CHE on locally\nfinite weighted connected graphs, the CHE determined by finite Markov chains or\nthe Cahn-Hilliard Equations driven by convolution integrable kernels. We\nconsider different transitions for the phase and the chemical potential, and a\nlarge class of potentials including obstacle ones. We prove existence and\nuniqueness of solutions in $L^1$ of the Cahn-Hilliard Equation. We also show\nthat the Cahn-Hilliard equation is the gradient flow of the Ginzburg-Landau\nfree energy functional on an appropriate Hilbert space. We finally study the\nasymptotic behaviour of the solutions.\n']","[('cahn hilliard equations', 0.7212889194488525), ('hilliard equations', 0.6555029153823853), ('solutions cahn hilliard', 0.6183039546012878), ('cahn hilliard system', 0.5908727645874023), ('coupled cahn hilliard', 0.5872452259063721), ('nonlocal cahn hilliard', 0.5810753703117371), ('cahn hilliard degenerate', 0.5343356132507324), ('stokes cahn hilliard', 0.5329737663269043), ('solutions nonlocal', 0.52117919921875), ('convective cahn hilliard', 0.5197079181671143)]"
398,398,75,398_anisotropic surface energy_anisotropic surface_variational formulation_surface diffusion,"['anisotropic surface energy', 'anisotropic surface', 'variational formulation', 'surface diffusion', 'finite element methods', 'surface diffusion flow', 'surface finite element', 'surface energies', 'surface energy', 'anisotropic']","['A symmetrized parametric finite element method for anisotropic surface\n  diffusion in 3D   For the evolution of a closed surface under anisotropic surface diffusion\nwith a general anisotropic surface energy $\\gamma(\\boldsymbol{n})$ in three\ndimensions (3D), where $\\boldsymbol{n}$ is the unit outward normal vector, by\nintroducing a novel symmetric positive definite surface energy matrix\n$\\boldsymbol{Z}_k(\\boldsymbol{n})$ depending on a stabilizing function\n$k(\\boldsymbol{n})$ and the Cahn-Hoffman $\\boldsymbol{\\xi}$-vector, we present\na new symmetrized variational formulation for anisotropic surface diffusion\nwith weakly or strongly anisotropic surface energy, which preserves two\nimportant structures including volume conservation and energy dissipation. Then\nwe propose a structural-preserving parametric finite element method (SP-PFEM)\nto discretize the symmetrized variational problem, which preserves the volume\nin the discretized level. Under a relatively mild and simple condition on\n$\\gamma(\\boldsymbol{n})$, we show that SP-PFEM is unconditionally energy-stable\nfor almost all anisotropic surface energies $\\gamma(\\boldsymbol{n})$ arising in\npractical applications. Extensive numerical results are reported to demonstrate\nthe efficiency and accuracy as well as energy dissipation of the proposed\nSP-PFEM for solving anisotropic surface diffusion in 3D.\n', 'An energy-stable parametric finite element method for anisotropic\n  surface diffusion   We propose an energy-stable parametric finite element method (ES-PFEM) to\ndiscretize the motion of a closed curve under surface diffusion with an\nanisotropic surface energy $\\gamma(\\theta)$ -- anisotropic surface diffusion --\nin two dimensions, while $\\theta$ is the angle between the outward unit normal\nvector and the vertical axis. By introducing a positive definite surface energy\n(density) matrix $G(\\theta)$, we present a new and simple variational\nformulation for the anisotropic surface diffusion and prove that it satisfies\narea/mass conservation and energy dissipation. The variational problem is\ndiscretized in space by the parametric finite element method and area/mass\nconservation and energy dissipation are established for the\nsemi-discretization. Then the problem is further discretized in time by a\n(semi-implicit) backward Euler method so that only a linear system is to be\nsolved at each time step for the full-discretization and thus it is efficient.\nWe establish well-posedness of the full-discretization and identify some simple\nconditions on $\\gamma(\\theta)$ such that the full-discretization keeps energy\ndissipation and thus it is unconditionally energy-stable. Finally the ES-PFEM\nis applied to simulate solid-state dewetting of thin films with anisotropic\nsurface energies, i.e. the motion of an open curve under anisotropic surface\ndiffusion with proper boundary conditions at the two triple points moving along\nthe horizontal substrate. Numerical results are reported to demonstrate the\nefficiency and accuracy as well as energy dissipation of the proposed ES-PFEM.\n', 'A unified structure-preserving parametric finite element method for\n  anisotropic surface diffusion   We propose and analyze a unified structure-preserving parametric finite\nelement method (SP-PFEM) for the anisotropic surface diffusion of curves in two\ndimensions $(d=2)$ and surfaces in three dimensions $(d=3)$ with an arbitrary\nanisotropic surface energy density $\\gamma(\\boldsymbol{n})$, where\n$\\boldsymbol{n}\\in \\mathbb{S}^{d-1}$ represents the outward unit vector. By\nintroducing a novel unified surface energy matrix\n$\\boldsymbol{G}_k(\\boldsymbol{n})$ depending on $\\gamma(\\boldsymbol{n})$, the\nCahn--Hoffman $\\boldsymbol{\\xi}$-vector and a stabilizing function\n$k(\\boldsymbol{n}):\\ \\mathbb{S}^{d-1}\\to {\\mathbb R}$, we obtain a unified and\nconservative variational formulation for the anisotropic surface diffusion via\ndifferent surface differential operators including the surface gradient\noperator, the surface divergence operator and the surface Laplace--Beltrami\noperator. A SP-PFEM discretization is presented for the variational problem. In\norder to establish the unconditional energy stability of the proposed SP-PFEM\nunder a very mild condition on $\\gamma(\\boldsymbol{n})$, we propose a new\nframework via {\\sl local energy estimate} for proving energy\nstability/structure-preserving properties of the parametric finite element\nmethod for the anisotropic surface diffusion. This framework sheds light on how\nto prove unconditional energy stability of other numerical methods for\ngeometric partial differential equations. Extensive numerical results are\nreported to demonstrate the efficiency and accuracy as well as\nstructure-preserving properties of the proposed SP-PFEM for the anisotropic\nsurface diffusion with arbitrary anisotropic surface energy density\n$\\gamma(\\boldsymbol{n})$ arising from different applications.\n']","[('anisotropic surface energy', 0.5993136167526245), ('anisotropic surface', 0.5358702540397644), ('variational formulation', 0.5315506458282471), ('surface diffusion', 0.508649468421936), ('finite element methods', 0.49449944496154785), ('surface diffusion flow', 0.4888797104358673), ('surface finite element', 0.45603322982788086), ('surface energies', 0.44424769282341003), ('surface energy', 0.421956330537796), ('anisotropic', 0.3965432941913605)]"
399,399,74,399_stability couette flow_couette flow_near couette flow_steady navier stokes,"['stability couette flow', 'couette flow', 'near couette flow', 'steady navier stokes', 'navier boundary conditions', '2d navier stokes', 'navier stokes equations', 'dimensional navier stokes', 'navier stokes', 'linearized navier stokes']","['Transition threshold for the 3D Couette flow in a finite channel   In this paper, we study nonlinear stability of the 3D plane Couette flow\n$(y,0,0)$ at high Reynolds number ${Re}$ in a finite channel $\\mathbb{T}\\times\n[-1,1]\\times \\mathbb{T}$. It is well known that the plane Couette flow is\nlinearly stable for any Reynolds number. However, it could become nonlinearly\nunstable and transition to turbulence for small but finite perturbations at\nhigh Reynolds number. This is so-called Sommerfeld paradox. One resolution of\nthis paradox is to study the transition threshold problem, which is concerned\nwith how much disturbance will lead to the instability of the flow and the\ndependence of disturbance on the Reynolds number. This work shows that if the\ninitial velocity $v_0$ satisfies $\\|v_0-(y,0,0)\\|_{H^2}\\le c_0{Re}^{-1}$ for\nsome $c_0>0$ independent of $Re$, then the solution of the 3D Navier-Stokes\nequations is global in time and does not transition away from the Couette flow\nin the $L^\\infty$ sense, and rapidly converges to a streak solution for $t\\gg\nRe^{\\frac 13}$ due to the mixing-enhanced dissipation effect. This result\nconfirms the transition threshold conjecture proposed by Trefethen et\nal.(Science, 261(1993), 578-584). To this end, we develop the resolvent\nestimate method to establish the space-time estimates for the full linearized\nNavier-Stokes system around the flow $(V(t,y,z), 0,0)$, where $V(t,y,z)$ is a\nsmall perturbation(but independent of $Re$) of the Couette flow $y$.\n', 'Stability threshold for 2D shear flows near Couette of the Navier-Stokes\n  equation   In this paper, we consider the stability threshold of the 2D shear flow\n$(U(y),0)^{\\top}$ of the Navier-Stokes equation at high Reynolds number $Re$.\nWhen the shear flow is near in Sobolev norm to the Couette flow $(y,0)^{\\top}$\nin some sense, we prove that if the initial data $u_0$ satisfies\n$\\|u_0-(U(y),0)^{\\top}\\|\\leq \\epsilon Re^{-1/3}$, then the solution of the 2D\nNavier-Stokes equation approaches to some shear flow which is also close to the\nCouette flow for $t\\gg Re^{1/3}$, as $t\\to\\infty$.\n', 'Stability threshold of the 2D Couette flow in Sobolev spaces   We study the stability threshold of the 2D Couette flow in Sobolev spaces at\nhigh Reynolds number $Re$. We prove that if the initial vorticity $\\Omega_{in}$\nsatisfies $\\|\\Omega_{in}-(-1)\\|_{H^{\\sigma}}\\leq \\epsilon Re^{-1/3}$, then the\nsolution of the 2D Navier-Stokes equation approaches to some shear flow which\nis also close to Couette flow for time $t\\gg Re^{1/3}$ by a mixing-enhanced\ndissipation effect and then converges back to Couette flow when $t\\to +\\infty$.\n']","[('stability couette flow', 0.6498288512229919), ('couette flow', 0.5631622076034546), ('near couette flow', 0.5622454881668091), ('steady navier stokes', 0.5580193996429443), ('navier boundary conditions', 0.5225887298583984), ('2d navier stokes', 0.5204209089279175), ('navier stokes equations', 0.5132118463516235), ('dimensional navier stokes', 0.5084714889526367), ('navier stokes', 0.5060442090034485), ('linearized navier stokes', 0.5057677626609802)]"
400,400,74,400_tau tilting modules_tilting modules_tau tilting module_tilting module,"['tau tilting modules', 'tilting modules', 'tau tilting module', 'tilting module', 'tau tilting theory', 'tau tilting finite', 'support tau tilting', 'tilting theory', 'tau tilting', 'rigid modules']","['Tau-tilting modules over trivial extenstions   We study (support) $\\tau$-tilting modules over the trivial extensions of\nfinite dimensional algebras. More precisely, we construct two classes of\n(support)$\\tau$-tilting modules in terms of the adjoint functors which extend\nand generalize the results on (support) $\\tau$-tilting modules over triangular\nmatrix rings given by Gao-Huang.\n', 'A construction of support $\\tau$-tilting modules over $\\tau$-tilting\n  finite algebras   The notion of (semi)bricks, regarded as a generalization of (semi)simple\nmodules, appeared in a paper of Ringel in 1976. In recent years, there has been\nseveral new developments motivated by links to {\\tau}-tilting theory studied by\nDemonet-Iyama-Jasso and Asai. In this paper, we will discuss how to glue\nsemibricks along a recollement with the intermediate extension functor similar\nto gluing simple modules by Beilinson-Bernstein-Deligne. As an application, we\ninvestigate the behavior of {\\tau}-tilting finite under recollements of module\ncategories of algebras. Moreover, we give some examples to show the\nconstruction of support {\\tau}-tilting modules over {\\tau}-tilting finite\nalgebras by gluing semibricks via recollements.\n', 'Normal subgroups and support $\\tau$-tilting modules   Let $\\tilde{G}$ be a finite group, $G$ a normal subgroup of $\\tilde{G}$ and\n$k$ an algebraically closed field of characteristic $p>0$. The first main\nresult in this paper is to show that support $\\tau$-tilting\n$k\\tilde{G}$-modules satisfying some properties are support $\\tau$-tilting\nmodules as $kG$-modules too. As the second main result, we give equivalent\nconditions for support $\\tau$-tilting $k\\tilde{G}$-modules to satisfy the above\nproperties, and show that the set of the support $\\tau$-tilting\n$k\\tilde{G}$-modules with the properties is isomorphic to the set of\n$\\tilde{G}$-invariant support $\\tau$-tilting $kG$-modules as partially ordered\nsets. As an application, we show that the set of $\\tilde{G}$-invariant support\n$\\tau$-tilting $kG$-modules is isomorphic to the set of support $\\tau$-tilting\n$k\\tilde{G}$-modules in the case that the index $G$ in $\\tilde{G}$ is a\n$p$-power. As a further application, we give a feature of vertices of\nindecomposable $\\tau$-rigid $k\\tilde{G}$-modules. Finally, we give the block\nversions of the above results.\n']","[('tau tilting modules', 0.7767847776412964), ('tilting modules', 0.7334574460983276), ('tau tilting module', 0.7268770933151245), ('tilting module', 0.6666305661201477), ('tau tilting theory', 0.63116055727005), ('tau tilting finite', 0.5985439419746399), ('support tau tilting', 0.5802391171455383), ('tilting theory', 0.5486263632774353), ('tau tilting', 0.542215883731842), ('rigid modules', 0.5203795433044434)]"
401,401,74,401_variational problems_minimization energy functional_existence minimizers_nonlocal perimeter,"['variational problems', 'minimization energy functional', 'existence minimizers', 'nonlocal perimeter', 'minimizers', 'energy minimisers', 'constrained minimizers', 'minimization energy', 'perimeter functional', 'nonlocal potentials']","[""Existence and nonexistence of minimizers for classical capillarity\n  problems in presence of nonlocal repulsion and gravity   We investigate, under a volume constraint and among sets contained in a\nEuclidean half-space, the minimization problem of an energy functional given by\nthe sum of a capillarity perimeter, a nonlocal interaction term and a\ngravitational potential energy. The capillarity perimeter assigns a constant\nweight to the portion of the boundary touching the boundary of the half-space.\nThe nonlocal term is represented by a double integral of a positive kernel $g$,\nwhile the gravitational term is represented by the integral of a positive\npotential $G$.\n  We first establish existence of volume-constrained minimizers in the small\nmass regime, together with several qualitative properties of minimizers. The\nexistence result holds for rather general choices of kernels in the nonlocal\ninteraction term, including attractive-repulsive ones. When the nonlocal kernel\n$g(x)=1/|x|^\\beta$ with $\\beta \\in (0,2]$, we also obtain nonexistence of\nvolume constrained minimizers in the large mass regime. Finally, we prove a\ngeneralized existence result of minimizers holding for all masses and general\nnonlocal interaction terms, meaning that the infimum of the problem is realized\nby a finite disjoint union of sets thought located at ``infinite distance'' one\nfrom the other.\n  These results stem from an application of quantitative isoperimetric\ninequalities for the capillarity problem in a half-space.\n"", ""Large mass minimizers for isoperimetric problems with integrable\n  nonlocal potentials   This paper is concerned with volume-constrained minimization problems derived\nfrom Gamow's liquid drop model for the atomic nucleus, involving the\ncompetition of a perimeter term and repulsive nonlocal potentials. We consider\na large class of potentials, given by general radial nonnegative kernels which\nare integrable on $\\mathbb{R}^n$, such as Bessel potentials, and study the\nbehavior of the problem for large masses (i.e., volumes). Contrarily to the\nsmall mass case, where the nonlocal term becomes negligible compared to the\nperimeter, here the nonlocal term explodes compared to it. However, using the\nintegrability of those kernels, we rewrite the problem as the minimization of\nthe difference between the classical perimeter and a nonlocal perimeter, which\nconverges to a multiple of the classical perimeter as the mass goes to\ninfinity. Renormalizing to a fixed volume, we show that, if the first moment of\nthe kernels is smaller than an explicit threshold, the problem admits\nminimizers of arbitrarily large mass, which contrasts with the usual case of\nRiesz potentials. In addition, we prove that, any sequence of minimizers\nconverges to the ball as the mass goes to infinity. Finally, we study the\nstability of the ball, and show that our threshold on the first moment of the\nkernels is sharp in the sense that large balls go from stable to unstable. A\ndirect consequence of the instability of large balls above this threshold is\nthat there exist nontrivial compactly supported kernels for which the problems\nadmit minimizers which are not balls, that is, symmetry breaking occurs.\n"", 'Isoperimetry and stability properties of balls with respect to nonlocal\n  energies   We obtain a sharp quantitative isoperimetric inequality for nonlocal\n$s$-perimeters, uniform with respect to $s$ bounded away from $0$. This allows\nus to address local and global minimality properties of balls with respect to\nthe volume-constrained minimization of a free energy consisting of a nonlocal\n$s$-perimeter plus a non-local repulsive interaction term. In the particular\ncase $s =1$ the $s$-perimeter coincides with the classical perimeter, and our\nresults improve the ones of Kn\\""upfer and Muratov concerning minimality of\nballs of small volume in isoperimetric problems with a competition between\nperimeter and a nonlocal potential term. More precisely, their result is\nextended to its maximal range of validity concerning the type of nonlocal\npotentials considered, and is also generalized to the case where local\nperimeters are replaced by their nonlocal counterparts.\n']","[('variational problems', 0.5880261659622192), ('minimization energy functional', 0.5835803151130676), ('existence minimizers', 0.5725557208061218), ('nonlocal perimeter', 0.5622467994689941), ('minimizers', 0.5569162368774414), ('energy minimisers', 0.5508268475532532), ('constrained minimizers', 0.5385622978210449), ('minimization energy', 0.5324543714523315), ('perimeter functional', 0.528986930847168), ('nonlocal potentials', 0.511475145816803)]"
402,402,74,402_density functional theory_density functional_functional theory_distributional potentials,"['density functional theory', 'density functional', 'functional theory', 'distributional potentials', 'theory dft', 'densities', 'classical density', 'ground state density', 'state density', 'electron density']","['A rigorous formulation of Density Functional Theory for spinless\n  electrons in one dimension   In this paper, we present a completely rigorous formulation of Kohn-Sham\ndensity functional theory for spinless electrons living in one dimensional\nspace. More precisely, we consider Schr\\""odinger operators of the form\n$H_N(v,w) = -\\Delta + \\sum_{i\\neq j}^N w(x_i,x_j) + \\sum_{j=1}^N v(x_i)$ acting\non $\\wedge^N \\mathrm{L}^2([0,1])$, where the external and interaction\npotentials $v$ and $w$ belong to a suitable class of distributions. In this\nsetting, we obtain a complete characterization of the set of pure-state\n$v$-representable densities on the interval. Then, we prove a Hohenberg-Kohn\ntheorem that applies to the class of distributional potentials studied here.\nLastly, we establish the differentiability of the exchange-correlation\nfunctional and therefore the existence of a unique exchange-correlation\npotential. We then combine these results to provide a rigorous formulation of\nthe Kohn-Sham scheme. In particular, these results show that the Kohn-Sham\nscheme is rigorously exact in this setting.\n', 'Dissociation limit in Kohn-Sham density functional theory   We consider the dissociation limit for molecules of the type $X_2$ in the\nKohn-Sham density functional theory setting, where $X$ can be any element with\n$N$ electrons. We prove that when the two atoms in the system are torn\ninfinitely far apart, the energy of the system convergences to $\\min\n\\limits_{\\alpha \\in [0,N]} \\big( I^{X}_{\\alpha} + I^{X}_{2N-\\alpha} \\big)$,\nwhere $I^{X}_{\\alpha}$ denotes the energy of the atom with $\\alpha$ electrons\nsurrounding it. Depending on the ""strength"" of the exchange this minimum might\nnot be equal to the symmetric splitting $2I^{X}_{N}$. We show numerically that\nfor the $H_2$-molecule with Dirac exchange this gives the expected result of\ntwice the energy of a H-atom $2 I^{H}_1$.\n', 'Mathematical Elements of Density Functional Theory   We review some of the basic mathematical results about density functional\ntheory.\n']","[('density functional theory', 0.797637939453125), ('density functional', 0.6754052639007568), ('functional theory', 0.5078844428062439), ('distributional potentials', 0.4866584539413452), ('theory dft', 0.4854942560195923), ('densities', 0.4564504027366638), ('classical density', 0.4513125717639923), ('ground state density', 0.44981709122657776), ('state density', 0.42366838455200195), ('electron density', 0.41507768630981445)]"
403,403,74,403_riemannian optimization_optimization riemannian manifolds_optimization riemannian_riemannian gradient descent,"['riemannian optimization', 'optimization riemannian manifolds', 'optimization riemannian', 'riemannian gradient descent', 'optimization manifolds', 'manifold optimization', 'algorithms riemannian', 'conjugate gradient methods', 'optimization stiefel manifold', 'riemannian conjugate gradient']","['Sufficient Descent Riemannian Conjugate Gradient Method   This paper considers sufficient descent Riemannian conjugate gradient methods\nwith line search algorithms. We propose two kinds of sufficient descent\nnonlinear conjugate gradient methods and prove these methods satisfy the\nsufficient descent condition even on Riemannian manifolds. One is the hybrid\nmethod combining the Fletcher-Reeves-type method with the\nPolak-Ribiere-Polyak-type method, and the other is the Hager-Zhang-type method,\nboth of which are generalizations of those used in Euclidean space. Also, we\ngeneralize two kinds of line search algorithms that are widely used in\nEuclidean space. In addition, we numerically compare our generalized methods by\nsolving several Riemannian optimization problems. The results show that the\nperformance of the proposed hybrid method greatly depends regardless of the\ntype of line search used. Meanwhile, the Hager-Zhang-type method has the fast\nconvergence property regardless of the type of line search used.\n', 'Negative curvature obstructs acceleration for strongly geodesically\n  convex optimization, even with exact first-order oracles   Hamilton and Moitra (2021) showed that, in certain regimes, it is not\npossible to accelerate Riemannian gradient descent in the hyperbolic plane if\nwe restrict ourselves to algorithms which make queries in a (large) bounded\ndomain and which receive gradients and function values corrupted by a (small)\namount of noise. We show that acceleration remains unachievable for any\ndeterministic algorithm which receives exact gradient and function-value\ninformation (unbounded queries, no noise). Our results hold for the classes of\nstrongly and nonstrongly geodesically convex functions, and for a large class\nof Hadamard manifolds including hyperbolic spaces and the symmetric space\n$\\mathrm{SL}(n) / \\mathrm{SO}(n)$ of positive definite $n \\times n$ matrices of\ndeterminant one. This cements a surprising gap between the complexity of convex\noptimization and geodesically convex optimization: for hyperbolic spaces,\nRiemannian gradient descent is optimal on the class of smooth and and strongly\ngeodesically convex functions, in the regime where the condition number scales\nwith the radius of the optimization domain. The key idea for proving the lower\nbound consists of perturbing the hard functions of Hamilton and Moitra (2021)\nwith sums of bump functions chosen by a resisting oracle.\n', 'Riemannian conjugate gradient methods: General framework and specific\n  algorithms with convergence analyses   This paper proposes a novel general framework of Riemannian conjugate\ngradient methods, that is, conjugate gradient methods on Riemannian manifolds.\nThe conjugate gradient methods are important first-order optimization\nalgorithms both in Euclidean spaces and on Riemannian manifolds. While various\ntypes of conjugate gradient methods are studied in Euclidean spaces, there have\nbeen fewer studies on those on Riemannian manifolds. In each iteration of the\nRiemannian conjugate gradient methods, the previous search direction must be\ntransported to the current tangent space so that it can be added to the\nnegative gradient of the objective function at the current point. There are\nseveral approaches to transport a tangent vector to another tangent space.\nTherefore, there are more variants of the Riemannian conjugate gradient methods\nthan the Euclidean case. In order to investigate them in more detail, the\nproposed framework unifies the existing Riemannian conjugate gradient methods\nsuch as ones utilizing a vector transport or inverse retraction and also\ndevelops other methods that have not been covered in previous studies.\nFurthermore, sufficient conditions for the convergence of a class of algorithms\nin the proposed framework are clarified. Moreover, the global convergence\nproperties of several specific types of algorithms are extensively analyzed.\nThe analyses provide the theoretical results for some algorithms in a more\ngeneral setting than the existing studies and completely new developments for\nthe other algorithms. Numerical experiments are performed to confirm the\nvalidity of the theoretical results. The results also compare the performances\nof several specific algorithms in the proposed framework.\n']","[('riemannian optimization', 0.7590447664260864), ('optimization riemannian manifolds', 0.752141535282135), ('optimization riemannian', 0.7429322004318237), ('riemannian gradient descent', 0.7220861911773682), ('optimization manifolds', 0.6775408387184143), ('manifold optimization', 0.6748816967010498), ('algorithms riemannian', 0.6631847620010376), ('conjugate gradient methods', 0.6542012095451355), ('optimization stiefel manifold', 0.6167433261871338), ('riemannian conjugate gradient', 0.602773904800415)]"
404,404,74,404_toric varieties_complete toric varieties_projective toric varieties_projective toric variety,"['toric varieties', 'complete toric varieties', 'projective toric varieties', 'projective toric variety', 'complete toric variety', 'toric variety', 'projective toric', 'affine toric varieties', 'conjecture toric', 'affine toric']","['F-blowups and essential divisors for toric varieties   We investigate the relation between essential divisors and F-blowups, in\nparticular, address the problem whether all essential divisors appear on the\n$e$-th F-blowup for large enough $e$. Focusing on the case of normal affine\ntoric varieties, we establish a simple sufficient condition for a divisor over\nthe given toric variety to appear on the normalized limit F-blowup as a prime\ndivisor. As a corollary, we show that if a normal toric variety has a crepant\nresolution, then the above problem has a positive answer, provided that we use\nthe notion of essential divisors in the sense of Bouvier and\nGonzalez-Sprinberg. We also provide an example of toric threefold singularities\nfor which a non-essential divisor appears on an F-blowup.\n', 'Stable rationality of hypersurfaces of mock toric variety I   We introduce a mock toric variety, a generalization of a toric variety. For a\nnon-toric example, Del-Pezzo surfaces are mock toric varieties. These new\nvarieties inherit some properties of mock toric varieties. In application, we\ngive sufficient conditions for the concrete construction of a strictly toroidal\nmodel of a hypersurface in a mock toric variety.\n', 'Irrational toric varieties and secondary polytopes   The space of torus translations and degenerations of a projective toric\nvariety forms a toric variety associated to the secondary fan of the integer\npoints in the polytope corresponding to the toric variety. This is used to\nidentify a moduli space of real degenerations with the secondary polytope. A\nconfiguration A of real vectors gives an irrational projective toric variety in\na simplex. We identify a space of translations and degenerations of the\nirrational projective toric variety with the secondary polytope of A. For this,\nwe develop a theory of irrational toric varieties associated to arbitrary fans.\nWhen the fan is rational, the irrational toric variety is the nonnegative part\nof the corresponding classical toric variety. When the fan is the normal fan of\na polytope, the irrational toric variety is homeomorphic to that polytope.\n']","[('toric varieties', 0.8165759444236755), ('complete toric varieties', 0.8117119073867798), ('projective toric varieties', 0.8092436790466309), ('projective toric variety', 0.7966701984405518), ('complete toric variety', 0.7950587272644043), ('toric variety', 0.7754994034767151), ('projective toric', 0.7658342719078064), ('affine toric varieties', 0.7562578916549683), ('conjecture toric', 0.7323623299598694), ('affine toric', 0.6806918382644653)]"
405,405,74,405_entropy solutions scalar_solutions scalar conservation_scalar conservation laws_solutions conservation laws,"['entropy solutions scalar', 'solutions scalar conservation', 'scalar conservation laws', 'solutions conservation laws', 'nonlocal conservation laws', 'scalar conservation law', 'hyperbolic conservation laws', 'entropy solutions', 'entropy weak', 'convex entropy']","['Minimal Entropy Conditions for Scalar Conservation Laws with General\n  Convex Fluxes   We are concerned with the minimal entropy conditions for one-dimensional\nscalar conservation laws with general convex flux functions. For such scalar\nconservation laws, we prove that a single entropy-entropy flux pair\n$(\\eta(u),q(u))$ with $\\eta(u)$ of strict convexity is sufficient to single out\nan entropy solution from a broad class of weak solutions in $L^\\infty_{\\rm\nloc}$ that satisfy the inequality: $\\eta(u)_t+q(u)_x\\leq \\mu$ in the\ndistributional sense for some non-negative Radon measure $\\mu$. Furthermore, we\nextend this result to the class of weak solutions in $L^p_{\\rm loc}$, based on\nthe asymptotic behavior of the flux function $f(u)$ and the entropy function\n$\\eta(u)$ at infinity. The proofs are based on the equivalence between the\nentropy solutions of one-dimensional scalar conservation laws and the viscosity\nsolutions of the corresponding Hamilton-Jacobi equations, as well as the\nbilinear form and commutator estimates as employed similarly in the theory of\ncompensated compactness.\n', 'Higher regularity for entropy solutions of conservation laws with\n  geometrically constrained discontinuous flux   For the Burgers equation, the entropy solution becomes instantly BV with only\n$L^\\infty$ initial data. For conservation laws with genuinely nonlinear\ndiscontinuous flux, it is well known that the BV regularity of entropy\nsolutions is lost. Recently, this regularity has been proved to be fractional\nwith s = 1/2. Moreover, for less nonlinear flux the solution has still a\nfractional regularity 0 < s \\leq 1/2. The resulting general rule is the\nregularity of entropy solutions for a discontinuous flux is less than for a\nsmooth flux. In this paper, an optimal geometric condition on the discontinuous\nflux is used to recover the same regularity as for the smooth flux with the\nsame kind of nonlinearity.\n', ""$L^1$-Contraction Property of Entropy Solutions for Scalar Conservation\n  Laws with Minimal Regularity Assumptions on the Flux   This paper is concerned with entropy solutions of scalar conservation laws of\nthe form $\\partial_{t}u+\\diver f=0$ in $\\mathbb{R}^d\\times(0,\\infty)$. The flux\n$f=f(x,u)$ depends explicitly on the spatial variable $x$. Using an extension\nof Kruzkov's method, we establish the $L^1$-contraction property of entropy\nsolutions under minimal regularity assumptions on the flux.\n""]","[('entropy solutions scalar', 0.6057782769203186), ('solutions scalar conservation', 0.5651147961616516), ('scalar conservation laws', 0.5630073547363281), ('solutions conservation laws', 0.5546779632568359), ('nonlocal conservation laws', 0.5538472533226013), ('scalar conservation law', 0.5523650050163269), ('hyperbolic conservation laws', 0.5506081581115723), ('entropy solutions', 0.5188858509063721), ('entropy weak', 0.5180320143699646), ('convex entropy', 0.5056545734405518)]"
406,406,74,406_distributionally robust optimization_portfolio optimization_optimal portfolio_portfolio optimization problems,"['distributionally robust optimization', 'portfolio optimization', 'optimal portfolio', 'portfolio optimization problems', 'robust optimization', 'portfolio selection', 'constrained portfolio', 'portfolio allocation', 'portfolio management', 'distributionally robust']","['Robust portfolio optimization for recommender systems considering\n  uncertainty of estimated statistics   This paper is concerned with portfolio optimization models for creating\nhigh-quality lists of recommended items to balance the accuracy and diversity\nof recommendations. However, the statistics (i.e., expectation and covariance\nof ratings) required for mean--variance portfolio optimization are subject to\ninevitable estimation errors. To remedy this situation, we focus on robust\noptimization techniques that derive reliable solutions to uncertain\noptimization problems. Specifically, we propose a robust portfolio optimization\nmodel that copes with the uncertainty of estimated statistics based on the\ncardinality-based uncertainty sets. This robust portfolio optimization model\ncan be reduced to a mixed-integer linear optimization problem, which can be\nsolved exactly using mathematical optimization solvers. Experimental results\nusing two publicly available rating datasets demonstrate that our method can\nimprove not only the recommendation accuracy but also the diversity of\nrecommendations compared with conventional mean--variance portfolio\noptimization models. Notably, our method has the potential to improve the\nrecommendation quality of various rating prediction algorithms.\n', 'Wasserstein-Kelly Portfolios: A Robust Data-Driven Solution to Optimize\n  Portfolio Growth   We introduce a robust variant of the Kelly portfolio optimization model,\ncalled the Wasserstein-Kelly portfolio optimization. Our model, taking a\nWasserstein distributionally robust optimization (DRO) formulation, addresses\nthe fundamental issue of estimation error in Kelly portfolio optimization by\ndefining a ``ball"" of distributions close to the empirical return distribution\nusing the Wasserstein metric and seeking a robust log-optimal portfolio against\nthe worst-case distribution from the Wasserstein ball. Enhancing the Kelly\nportfolio using Wasserstein DRO is a natural step to take, given many\nsuccessful applications of the latter in areas such as machine learning for\ngenerating robust data-driven solutions. However, naive application of\nWasserstein DRO to the growth-optimal portfolio problem can lead to several\nissues, which we resolve through careful modelling. Our proposed model is both\npractically motivated and efficiently solvable as a convex program. Using\nempirical financial data, our numerical study demonstrates that the\nWasserstein-Kelly portfolio can outperform the Kelly portfolio in out-of-sample\ntesting across multiple performance metrics and exhibits greater stability.\n', 'Portfolio Optimization with Entropic Value-at-Risk   The entropic value-at-risk (EVaR) is a new coherent risk measure, which is an\nupper bound for both the value-at-risk (VaR) and conditional value-at-risk\n(CVaR). As important properties, the EVaR is strongly monotone over its domain\nand strictly monotone over a broad sub-domain including all continuous\ndistributions, while well-known monotone risk measures, such as VaR and CVaR\nlack these properties. A key feature for a risk measure, besides its financial\nproperties, is its applicability in large-scale sample-based portfolio\noptimization. If the negative return of an investment portfolio is a\ndifferentiable convex function, the portfolio optimization with the EVaR\nresults in a differentiable convex program whose number of variables and\nconstraints is independent of the sample size, which is not the case for the\nVaR and CVaR. This enables us to design an efficient algorithm using\ndifferentiable convex optimization. Our extensive numerical study shows the\nhigh efficiency of the algorithm in large scales, compared to the existing\nconvex optimization software packages. The computational efficiency of the EVaR\nportfolio optimization approach is also compared with that of CVaR-based\nportfolio optimization. This comparison shows that the EVaR approach generally\nperforms similarly, and it outperforms as the sample size increases. Moreover,\nthe comparison of the portfolios obtained for a real case by the EVaR and CVaR\napproaches shows that the EVaR approach can find portfolios with better\nexpectations and VaR values at high confidence levels.\n']","[('distributionally robust optimization', 0.6322900056838989), ('portfolio optimization', 0.6057041883468628), ('optimal portfolio', 0.5760486721992493), ('portfolio optimization problems', 0.5576682686805725), ('robust optimization', 0.5346884727478027), ('portfolio selection', 0.5269837379455566), ('constrained portfolio', 0.5003700852394104), ('portfolio allocation', 0.49566376209259033), ('portfolio management', 0.4715350568294525), ('distributionally robust', 0.47129860520362854)]"
407,407,73,407_holomorphic line bundles_holomorphic line bundle_bergman kernels_holomorphic sections,"['holomorphic line bundles', 'holomorphic line bundle', 'bergman kernels', 'holomorphic sections', 'holomorphic vector bundle', 'hermitian holomorphic', 'hermitian line bundle', 'bergman kernel', 'holomorphic section', 'bundles hermitian']","['Equidistribution for Random Polynomials and Systems of Random Holomorphic Sections This article addresses an equidistribution problem concerning the zeros of systems of random holomorphic sections of positive line bundles on compact K\\""{a}hler manifolds and random polynomials on $\\mathbb{C}^{m}$ in the setting of the weighted pluripotential theory. For random polynomials, we consider non-orthonormal bases and prove an equidistribution result which is more general than the ones acquired before for non-discrete probability measures. More precisely, our result demonstrates that the equidistribution holds true even when the random coefficients in the basis representation are not independent and identically distributed (i.i.d.), and moreover, they are not constrained to any particular probability distribution. For random holomorphic sections, by extending the concept of a sequence of asymptotically Bernstein-Markov measures introduced by Bayraktar, Bloom and Levenberg in their recent paper to the setting of holomorphic line bundles over compact Kahler manifolds, we derive a global equidistribution, variance estimate and expected distribution theorems related to the zeros of systems of random holomorphic sections for large tensor powers of a fixed holomorphic line bundle for any codimension k, generalizing a previous result of Bayraktar in his 2016 paper and giving also a positive answer to a question posed in the same paper, asking whether the equidistribution is true for non-projective manifolds. For both random holomorphic polynomials on $\\mathbb{C}^{m}$ and systems of random holomorphic sections, the variance estimation method detailed in another paper of the author with Bojnik is significant.', 'Equidistribution for weakly holomorphic sections of line bundles on\n  algebraic curves   We prove the convergence of the normalized Fubini-Study measures and the\nlogarithms of the Bergman kernels of various Bergman spaces of holomorphic and\nweakly holomorphic sections associated to a singular Hermitian holomorphic line\nbundle on an algebraic curve. Using this, we study the asymptotic distribution\nof the zeros of random sequences of sections in these spaces.\n', 'Universality results for zeros of random holomorphic sections   In this work we prove an universality result regarding the equidistribution\nof zeros of random holomorphic sections associated to a sequence of singular\nHermitian holomorphic line bundles on a compact K\\""ahler complex space $X$.\nNamely, under mild moment assumptions, we show that the asymptotic distribution\nof zeros of random holomorphic sections is independent of the choice of the\nprobability measure on the space of holomorphic sections. In the case when $X$\nis a compact K\\""ahler manifold, we also prove an off-diagonal exponential decay\nestimate for the Bergman kernels of a sequence of positive line bundles on $X$.\n']","[('holomorphic line bundles', 0.5950692892074585), ('holomorphic line bundle', 0.5661104321479797), ('bergman kernels', 0.545159101486206), ('holomorphic sections', 0.5367096662521362), ('holomorphic vector bundle', 0.5216360688209534), ('hermitian holomorphic', 0.5086067318916321), ('hermitian line bundle', 0.4966665506362915), ('bergman kernel', 0.4950961470603943), ('holomorphic section', 0.4890747666358948), ('bundles hermitian', 0.4831976592540741)]"
408,408,73,408_skein module_skein theory_skein relations_skein,"['skein module', 'skein theory', 'skein relations', 'skein', 'algebras quantum', 'kauffman bracket', 'frobenius map', 'invariant knots', 'quantum tori', 'frobenius']","['Skeins on tori   We analyze the $G$-skein theory invariants of the 3-torus $T^3$ and the\ntwo-torus $T^2$, for the groups $G = GL_N, SL_N$ and for generic quantum\nparameter. We obtain formulas for the dimension of the skein module of $T^3$,\nand we describe the algebraic structure of the skein category of $T^2$ --\nnamely of the $n$-point relative skein algebras.\n  The case $n=N$ (the Schur-Weyl case) is special in our analysis. We construct\nan isomorphism between the $N$-point relative skein algebra and the double\naffine Hecke algebra at specialized parameters. As a consequence, we prove that\nall tangles in the relative $N$-point skein algebra are in fact equivalent to\nlinear combinations of braids, modulo skein relations. More generally for $n$\nan integer multiple of $N$, we construct a surjective homomorphism from an\nappropriate DAHA to the $n$-point relative skein algebra.\n  In the case $G=SL_2$ corresponding to the Kauffman bracket we give proofs\ndirectly using skein relations. Our analysis of skein categories in higher rank\nhinges instead on the combinatorics of multisegment representations when\nrestricting from DAHA to AHA and nonvanishing properties of parabolic sign\nidempotents upon them.\n', 'Center of the stated skein algebra   The stated skein algebra is a generalization of the Kauffman bracket skein\nalgebra introduced in the study of quantum trace maps. When the quantum\nparameter is a root of unity, the stated skein algebra has a big center and is\nfinitely generated as a module over the center. We give the center a simple\ndescription and calculate the dimension over center of the stated skein\nalgebra.\n', 'Faithfullness of geometric action of skein algebras   We show that the action of the Kauffman bracket skein algebra of a surface\n$\\Sigma$ on the skein module of the handlebody bounded by $\\Sigma$ is faithful\nif and only if the quantum parameter is not a root of 1.\n']","[('skein module', 0.6613759994506836), ('skein theory', 0.6544811725616455), ('skein relations', 0.6378319263458252), ('skein', 0.5716791749000549), ('algebras quantum', 0.4162183701992035), ('kauffman bracket', 0.38531988859176636), ('frobenius map', 0.36766135692596436), ('invariant knots', 0.3395243287086487), ('quantum tori', 0.3220579922199249), ('frobenius', 0.29347389936447144)]"
409,409,73,409_association schemes_association scheme_schemes obtained_class association scheme,"['association schemes', 'association scheme', 'schemes obtained', 'class association scheme', 'terwilliger algebra', 'schemes', 'schemes determine', 'schemes class', 'scheme mathcal', 'association']","['On Terwilliger $\\mathbb{F}$-algebras of factorial association schemes   The Terwilliger algebras of association schemes over an arbitrary field\n$\\mathbb{F}$ were called the Terwilliger $\\mathbb{F}$-algebras of association\nschemes in [8]. In this paper, we study the Terwilliger $\\mathbb{F}$-algebras\nof factorial association schemes. We determine the $\\mathbb{F}$-dimensions, the\ncenters, the semisimplicity, the Jacobson radicals, and the algebraic\nstructures of the Terwilliger $\\mathbb{F}$-algebras of factorial association\nschemes.\n', ""Bivariate $Q$-polynomial structures for the nonbinary Johnson scheme and\n  the association scheme obtained from attenuated spaces   The study of $P$-polynomial association schemes (distance-regular graphs) and\n$Q$-polynomial association schemes, and in particular $P$- and $Q$-polynomial\nassociation schemes, has been a central theme not only in the theory of\nassociation schemes but also in the whole study of algebraic combinatorics in\ngeneral. Leonard's theorem (1982) says that the spherical functions (or the\ncharacter tables) of $P$- and $Q$-polynomial association schemes are described\nby Askey-Wilson orthogonal polynomials or their relatives. These polynomials\nare one-variable orthogonal polynomials. It seems that the new attempt to\ndefine and study higher rank $P$- and $Q$-polynomial association schemes had\nbeen hoped for, but had gotten only limited success. The first very successful\nattempt was initiated recently by Bernard-Cramp\\'{e}-d'Andecy-Vinet-Zaimi\n[arXiv:2212.10824], and then followed by Bannai-Kurihara-Zhao-Zhu\n[arXiv:2305.00707]. The general theory and some explicit examples of families\nof higher rank (multivariate) $P$- and/or $Q$-polynomial association schemes\nhave been obtained there. The main purpose of the present paper is to prove\nthat some important families of association schemes are shown to be bivariate\n$Q$-polynomial. Namely, we show that all the nonbinary Johnson association\nschemes and all the attenuated space association schemes are bivariate\n$Q$-polynomial. It should be noted that the parameter restrictions needed in\nthe previous papers are completely lifted in this paper. Our proofs are done by\nexplicitly calculating the Krein parameters of these association schemes. At\nthe end, we mention some speculations and indications of what we can expect in\nthe future study.\n"", ""A note on modular Terwilliger algebras of association schemes   Let $p$ denote a prime number. In this note, we focus on the modular\nTerwilliger algebras of association schemes defined in [3]. We define the\nprimary module of a modular Terwilliger algebra of an association scheme and\ndetermine all its composition factors up to isomorphism. We then characterize\nthe $p'$-valenced association schemes by some properties of their modular\nTerwilliger algebras. The corollaries about the modular Terwilliger algebras of\nassociation schemes are given.\n""]","[('association schemes', 0.6842932105064392), ('association scheme', 0.6309466361999512), ('schemes obtained', 0.5762040019035339), ('class association scheme', 0.5710912346839905), ('terwilliger algebra', 0.5448213815689087), ('schemes', 0.5442129373550415), ('schemes determine', 0.475030779838562), ('schemes class', 0.46161332726478577), ('scheme mathcal', 0.4303923547267914), ('association', 0.4272582530975342)]"
410,410,72,410_pair correlations_pair correlation_low discrepancy sequences_poissonian,"['pair correlations', 'pair correlation', 'low discrepancy sequences', 'poissonian', 'correlation functions', 'sequences small', 'statistical correlation', 'correlations', 'discrepancy sequences', 'sequences']","['P-adic Poissonian Pair Correlations via the Monna Map   Although the existence of sequences in the p-adic integers with Poissonian\npair correlations has already been shown, no explicit examples had been found\nso far. In this note we discuss how to transfer real sequences with Poissonian\npair correlations to the p-adic setting by making use of the Monna map.\n', 'On Inhomogeneous Poissonian Pair Correlations We study the notion of inhomogeneous Poissonian pair correlations, proving several properties that show similarities and differences to its homogeneous counterpart. In particular, we show that sequences with inhomogeneous Poissonian pair correlations need not be uniformly distributed, contrary to what was till recently believed.', 'Sequences with almost Poissonian Pair Correlations   Although a generic uniformly distributed sequence has Poissonian pair\ncorrelations, only one explicit example has been found up to now. Additionally,\nit is even known that many classes of uniformly distributed sequences, like van\nder Corput sequences, Kronecker sequences and LS sequences, do not have\nPoissonian pair correlations. In this paper, we show that van der Corput\nsequences and the Kronecker sequence for the golden mean are as close to having\nPoissonian pair correlations as possible: they both have $\\alpha$-pair\ncorrelations for all $0 < \\alpha < 1$ but not for $\\alpha = 1$ which\ncorresponds to Poissonian pair correlations.\n']","[('pair correlations', 0.4912514090538025), ('pair correlation', 0.46936506032943726), ('low discrepancy sequences', 0.44649606943130493), ('poissonian', 0.4061199426651001), ('correlation functions', 0.40167373418807983), ('sequences small', 0.3858182728290558), ('statistical correlation', 0.3820165693759918), ('correlations', 0.3760518729686737), ('discrepancy sequences', 0.3757084012031555), ('sequences', 0.3549329340457916)]"
411,411,72,411_optimal pricing_dynamic pricing_pricing problems_assortment,"['optimal pricing', 'dynamic pricing', 'pricing problems', 'assortment', 'discrete choice models', 'demand models', 'choice models', 'pricing', 'revenue management', 'retail']","['Revenue Management Under the Markov Chain Choice Model with Joint Price\n  and Assortment Decisions   Finding the optimal product prices and product assortment are two fundamental\nproblems in revenue management. Usually, a seller needs to jointly determine\nthe prices and assortment while managing a network of resources with limited\ncapacity. However, there is not yet a tractable method to efficiently solve\nsuch a problem. Existing papers studying static joint optimization of price and\nassortment cannot incorporate resource constraints. Then we study the revenue\nmanagement problem with resource constraints and price bounds, where the prices\nand the product assortments need to be jointly determined over time. We showed\nthat under the Markov chain (MC) choice model (which subsumes the multinomial\nlogit (MNL) model), we could reformulate the choice-based joint optimization\nproblem as a tractable convex conic optimization problem. We also proved that\nan optimal solution with a constant price vector exists even with constraints\non resources. In addition, a solution with both constant assortment and price\nvector can be optimal when there is no resource constraint.\n', 'PASTA: Pessimistic Assortment Optimization   We consider a class of assortment optimization problems in an offline\ndata-driven setting. A firm does not know the underlying customer choice model\nbut has access to an offline dataset consisting of the historically offered\nassortment set, customer choice, and revenue. The objective is to use the\noffline dataset to find an optimal assortment. Due to the combinatorial nature\nof assortment optimization, the problem of insufficient data coverage is likely\nto occur in the offline dataset. Therefore, designing a provably efficient\noffline learning algorithm becomes a significant challenge. To this end, we\npropose an algorithm referred to as Pessimistic ASsortment opTimizAtion (PASTA\nfor short) designed based on the principle of pessimism, that can correctly\nidentify the optimal assortment by only requiring the offline data to cover the\noptimal assortment under general settings. In particular, we establish a regret\nbound for the offline assortment optimization problem under the celebrated\nmultinomial logit model. We also propose an efficient computational procedure\nto solve our pessimistic assortment optimization problem. Numerical studies\ndemonstrate the superiority of the proposed method over the existing baseline\nmethod.\n', ""A Model of Competitive Assortment Planning Algorithm   With a novel search algorithm or assortment planning or assortment\noptimization algorithm that takes into account a Bayesian approach to\ninformation updating and two-stage assortment optimization techniques, the\ncurrent research provides a novel concept of competitiveness in the digital\nmarketplace. Via the search algorithm, there is competition between the\nplatform, vendors, and private brands of the platform. The current paper\nsuggests a model and discusses how competition and collusion arise in the\ndigital marketplace through assortment planning or assortment optimization\nalgorithm. Furthermore, it suggests a model of an assortment algorithm free\nfrom collusion between the platform and the large vendors. The paper's major\nconclusions are that collusive assortment may raise a product's purchase\nlikelihood but fail to maximize expected revenue. The proposed assortment\nplanning, on the other hand, maintains competitiveness while maximizing\nexpected revenue.\n""]","[('optimal pricing', 0.5974754095077515), ('dynamic pricing', 0.5037583708763123), ('pricing problems', 0.4973328113555908), ('assortment', 0.49214664101600647), ('discrete choice models', 0.4899616539478302), ('demand models', 0.46093741059303284), ('choice models', 0.45782703161239624), ('pricing', 0.45367565751075745), ('revenue management', 0.4310216009616852), ('retail', 0.40351253747940063)]"
412,412,72,412_distinct distances_maximum number points_distinct distance_distances points,"['distinct distances', 'maximum number points', 'distinct distance', 'distances points', 'finite points', 'distinct triangles', 'point sets', 'point configurations', 'optimal point', 'integer distance']","[""Distinct Angles in General Position   The Erd\\H{o}s distinct distance problem is a ubiquitous problem in discrete\ngeometry. Somewhat less well known is Erd\\H{o}s' distinct angle problem, the\nproblem of finding the minimum number of distinct angles between $n$\nnon-collinear points in the plane. Recent work has introduced bounds on a wide\narray of variants of this problem, inspired by similar variants in the distance\nsetting.\n  In this short note, we improve the best known upper bound for the minimum\nnumber of distinct angles formed by $n$ points in general position from\n$O(n^{\\log_2(7)})$ to $O(n^2)$. Before this work, similar bounds relied on\nprojections onto a generic plane from higher dimensional space. In this paper,\nwe employ the geometric properties of a logarithmic spiral, sidestepping the\nneed for a projection.\n  We also apply this configuration to reduce the upper bound on the largest\ninteger such that any set of $n$ points in general position has a subset of\nthat size with all distinct angles. This bound is decreased from\n$O(n^{\\log_2(7)/3})$ to $O(n^{1/2})$.\n"", 'Distinct Angles and Angle Chains in Three Dimensions   In 1946, Erd\\H{o}s posed the distinct distance problem, which seeks to find\nthe minimum number of distinct distances between pairs of points selected from\nany configuration of $n$ points in the plane. The problem has since been\nexplored along with many variants, including ones that extend it into higher\ndimensions. Less studied but no less intriguing is Erd\\H{o}s\' distinct angle\nproblem, which seeks to find point configurations in the plane that minimize\nthe number of distinct angles. In their recent paper ""Distinct Angles in\nGeneral Position,"" Fleischmann, Konyagin, Miller, Palsson, Pesikoff, and Wolf\nuse a logarithmic spiral to establish an upper bound of $O(n^2)$ on the minimum\nnumber of distinct angles in the plane in general position, which prohibits\nthree points on any line or four on any circle.\n  We consider the question of distinct angles in three dimensions and provide\nbounds on the minimum number of distinct angles in general position in this\nsetting. We focus on pinned variants of the question, and we examine explicit\nconstructions of point configurations in $\\mathbb{R}^3$ which use\nself-similarity to minimize the number of distinct angles. Furthermore, we\nstudy a variant of the distinct angles question regarding distinct angle chains\nand provide bounds on the minimum number of distinct chains in $\\mathbb{R}^2$\nand $\\mathbb{R}^3$.\n', ""Distinct Angle Problems and Variants   The Erd\\H{o}s distinct distance problem is a ubiquitous problem in discrete\ngeometry. Less well known is Erd\\H{o}s' distinct angle problem, the problem of\nfinding the minimum number of distinct angles between $n$ non-collinear points\nin the plane. The standard problem is already well understood. However, it\nadmits many of the same variants as the distinct distance problem, many of\nwhich are unstudied.\n  We provide upper and lower bounds on a broad class of distinct angle\nproblems. We show that the number of distinct angles formed by $n$ points in\ngeneral position is $O(n^{\\log_2(7)})$, providing the first non-trivial bound\nfor this quantity. We introduce a new class of asymptotically optimal point\nconfigurations with no four cocircular points. Then, we analyze the sensitivity\nof asymptotically optimal point sets to perturbation, yielding a much broader\nclass of asymptotically optimal configurations. In higher dimensions we show\nthat a variant of Lenz's construction admits fewer distinct angles than the\noptimal configurations in two dimensions.\n  We also show that the minimum size of a maximal subset of $n$ points in\ngeneral position admitting only unique angles is $\\Omega(n^{1/5})$ and\n$O(n^{\\log_2(7)/3})$. We also provide bounds on the partite variants of the\nstandard distinct angle problem.\n""]","[('distinct distances', 0.5189416408538818), ('maximum number points', 0.484149694442749), ('distinct distance', 0.460813969373703), ('distances points', 0.4577624797821045), ('finite points', 0.4488392472267151), ('distinct triangles', 0.4467434585094452), ('point sets', 0.4337937831878662), ('point configurations', 0.4289490878582001), ('optimal point', 0.42679134011268616), ('integer distance', 0.42033135890960693)]"
413,413,72,413_sparse identification nonlinear_identification nonlinear dynamics_sparse identification_identification nonlinear,"['sparse identification nonlinear', 'identification nonlinear dynamics', 'sparse identification', 'identification nonlinear', 'sparse regression', 'nonlinear dynamics sindy', 'sparse optimization', 'dynamics sindy', 'systems sparse', 'kalman smoothing']","['EKF-SINDy: Empowering the extended Kalman filter with sparse\n  identification of nonlinear dynamics   Measured data from a dynamical system can be assimilated into a predictive\nmodel by means of Kalman filters. Nonlinear extensions of the Kalman filter,\nsuch as the Extended Kalman Filter (EKF), are required to enable the joint\nestimation of (possibly nonlinear) system dynamics and of input parameters. To\nconstruct the evolution model used in the prediction phase of the EKF, we\npropose to rely on the Sparse Identification of Nonlinear Dynamics (SINDy).\nSINDy enables to identify the evolution model directly from preliminary\nacquired data, thus avoiding possible bias due to wrong assumptions and\nincorrect modelling of the system dynamics. Moreover, the numerical integration\nof a SINDy model leads to great computational savings compared to alternate\nstrategies based on, e.g., finite elements. Last, SINDy allows an immediate\ndefinition of the Jacobian matrices required by the EKF to identify system\ndynamics and properties, a derivation that is usually extremely involved with\nphysical models. As a result, combining the EKF with SINDy provides a\ndata-driven computationally efficient, easy-to-apply approach for the\nidentification of nonlinear systems, capable of robust operation even outside\nthe range of training of SINDy. To demonstrate the potential of the approach,\nwe address the identification of a linear non-autonomous system consisting of a\nshear building model excited by real seismograms, and the identification of a\npartially observed nonlinear system. The challenge arising from the use of\nSINDy when the system state is not entirely accessible has been relieved by\nmeans of time-delay embedding. The great accuracy and the small uncertainty\nassociated with the state identification, where the state has been augmented to\ninclude system properties, underscores the great potential of the proposed\nstrategy, paving the way for the setting of predictive digital twins in\ndifferent fields.\n', 'Sparsifying Priors for Bayesian Uncertainty Quantification in Model\n  Discovery   We propose a probabilistic model discovery method for identifying ordinary\ndifferential equations (ODEs) governing the dynamics of observed multivariate\ndata. Our method is based on the sparse identification of nonlinear dynamics\n(SINDy) framework, in which target ODE models are expressed as a sparse linear\ncombinations of pre-specified candidate functions. Promoting parsimony through\nsparsity in SINDy leads to interpretable models that generalize to unknown\ndata. Instead of targeting point estimates of the SINDy (linear combination)\ncoefficients, in this work we estimate these coefficients via sparse Bayesian\ninference. The resulting method, uncertainty quantification SINDy (UQ-SINDy),\nquantifies not only the uncertainty in the values of the SINDy coefficients due\nto observation errors and limited data, but also the probability of inclusion\nof each candidate function in the linear combination. UQ-SINDy promotes\nrobustness against observation noise and limited data, interpretability (in\nterms of model selection and inclusion probabilities), and generalization\ncapacity for out-of-sample forecast. Sparse inference for UQ-SINDy employs\nMarkov Chain Monte Carlo, and we explore two sparsifying priors: the\nspike-and-slab prior, and the regularized horseshoe prior. We apply UQ-SINDy to\nsynthetic nonlinear data sets from a Lotka-Volterra model and a nonlinear\noscillator, and to a real-world data set of lynx and hare populations. We find\nthat UQ-SINDy is able to discover accurate and meaningful models even in the\npresence of noise and limited data samples.\n', 'Ensemble-SINDy: Robust sparse model discovery in the low-data,\n  high-noise limit, with active learning and control   Sparse model identification enables the discovery of nonlinear dynamical\nsystems purely from data; however, this approach is sensitive to noise,\nespecially in the low-data limit. In this work, we leverage the statistical\napproach of bootstrap aggregating (bagging) to robustify the sparse\nidentification of nonlinear dynamics (SINDy) algorithm. First, an ensemble of\nSINDy models is identified from subsets of limited and noisy data. The\naggregate model statistics are then used to produce inclusion probabilities of\nthe candidate functions, which enables uncertainty quantification and\nprobabilistic forecasts. We apply this ensemble-SINDy (E-SINDy) algorithm to\nseveral synthetic and real-world data sets and demonstrate substantial\nimprovements to the accuracy and robustness of model discovery from extremely\nnoisy and limited data. For example, E-SINDy uncovers partial differential\nequations models from data with more than twice as much measurement noise as\nhas been previously reported. Similarly, E-SINDy learns the Lotka Volterra\ndynamics from remarkably limited data of yearly lynx and hare pelts collected\nfrom 1900-1920. E-SINDy is computationally efficient, with similar scaling as\nstandard SINDy. Finally, we show that ensemble statistics from E-SINDy can be\nexploited for active learning and improved model predictive control.\n']","[('sparse identification nonlinear', 0.6653997898101807), ('identification nonlinear dynamics', 0.6219236850738525), ('sparse identification', 0.5790945291519165), ('identification nonlinear', 0.5744889974594116), ('sparse regression', 0.5140687823295593), ('nonlinear dynamics sindy', 0.4886881411075592), ('sparse optimization', 0.4735393226146698), ('dynamics sindy', 0.45282962918281555), ('systems sparse', 0.44591793417930603), ('kalman smoothing', 0.40779945254325867)]"
414,414,72,414_rota baxter algebras_rota baxter algebra_algebras rota baxter_rota baxter operators,"['rota baxter algebras', 'rota baxter algebra', 'algebras rota baxter', 'rota baxter operators', 'rota baxter operator', 'baxter algebras', 'relative rota baxter', 'baxter algebra', 'lie algebras', 'baxter operators']","['Lie n-algebras and cohomologies of relative Rota-Baxter operators on\n  n-Lie algebras   Based on the differential graded Lie algebra controlling deformations of an\n$n$-Lie algebra with a representation (called an n-LieRep pair), we construct a\nLie n-algebra, whose Maurer-Cartan elements characterize relative Rota-Baxter\noperators on n-LieRep pairs. The notion of an n-pre-Lie algebra is introduced,\nwhich is the underlying algebraic structure of the relative Rota-Baxter\noperator. We give the cohomology of relative Rota-Baxter operators and study\ninfinitesimal deformations and extensions of order m deformations to order m+1\ndeformations of relative Rota-Baxter operators through the cohomology groups of\nrelative Rota-Baxter operators. Moreover, we build the relation between the\ncohomology groups of relative Rota-Baxter operators on n-LieRep pairs and those\non (n+1)-LieRep pairs by certain linear functions.\n', 'Lie theory and cohomology of relative Rota-Baxter operators   In this paper, we establish a local Lie theory for relative Rota-Baxter\noperators of weight $1$. First we recall the category of relative Rota-Baxter\noperators of weight $1$ on Lie algebras and construct a cohomology theory for\nthem. We use the second cohomology group to study infinitesimal deformations of\nrelative Rota-Baxter operators and modified $r$-matrices. Then we introduce a\ncohomology theory of relative Rota-Baxter operators on a Lie group. We\nconstruct the differentiation functor from the category of relative Rota-Baxter\noperators on Lie groups to that on Lie algebras, and extend it to the\ncohomology level by proving the Van Est theorem between the two cohomology\ntheories. We integrate a relative Rota-Baxter operator of weight 1 on a Lie\nalgebra to a local relative Rota-Baxter operator on the corresponding Lie\ngroup, and show that the local integration and differentiation are adjoint to\neach other. Finally, we give two applications of our integration of Rota-Baxter\noperators: one is to give an explicit formula for the factorization problem,\nand the other is to provide an integration for matched pairs.\n', 'Representations and cohomologies of relative Rota-Baxter Lie algebras\n  and applications   In this paper, first we give the notion of a representation of a relative\nRota-Baxter Lie algebra and introduce the cohomologies of a relative\nRota-Baxter Lie algebra with coefficients in a representation. Then we classify\nabelian extensions of relative Rota-Baxter Lie algebras using the second\ncohomology group, and classify skeletal relative Rota-Baxter Lie 2-algebras\nusing the third cohomology group as applications. At last, using the\nestablished general framework of representations and cohomologies of relative\nRota-Baxter Lie algebras, we give the notion of representations of Rota-Baxter\nLie algebras, which is consistent with representations of Rota-Baxter\nassociative algebras in the literature, and introduce the cohomologies of\nRota-Baxter Lie algebras with coefficients in a representation. Applications\nare also given to classify abelian extensions of Rota-Baxter Lie algebras and\nskeletal Rota-Baxter Lie 2-algebras.\n']","[('rota baxter algebras', 0.8021764159202576), ('rota baxter algebra', 0.7702881693840027), ('algebras rota baxter', 0.7196706533432007), ('rota baxter operators', 0.7171759605407715), ('rota baxter operator', 0.6800022721290588), ('baxter algebras', 0.6700299382209778), ('relative rota baxter', 0.6263338327407837), ('baxter algebra', 0.624234676361084), ('lie algebras', 0.58626788854599), ('baxter operators', 0.5841808915138245)]"
415,415,72,415_parking functions_parking_number cars_combinatorial,"['parking functions', 'parking', 'number cars', 'combinatorial', 'park', 'characterization permutation', 'functions length', 'permutation invariant', 'functions introduced', 'buses']","['Vacillating parking functions   For any integers $1\\leq k\\leq n$, we introduce a new family of parking\nfunctions called $k$-vacillating parking functions of length $n$. The parking\nrule for $k$-vacillating parking functions allows a car with preference $p$ to\npark in the first available spot in encounters among the parking spots numbered\n$p$, $p-k$, and $p+k$ (in that order and if those spots exists). In this way,\n$k$-vacillating parking functions are a modification of Naples parking\nfunctions, which allow for backwards movement of a car, and of $\\ell$-interval\nparking functions, which allow a car to park in its preference or up to $\\ell$\nspots in front of its preference. Among our results, we establish a\ncombinatorial interpretation for the numerator of the $n$th convergent of the\ncontinued fraction of $\\sqrt{2}$, as the number of non-decreasing\n$1$-vacillating parking functions of length~$n$. Our main result gives a\nproduct formula for the enumeration of $k$-vacillating parking functions of\nlength $n$ based on the number of $1$-vacillating parking functions of smaller\nlength. We conclude with some directions for further research.\n', 'Connecting $k$-Naples parking functions and obstructed parking functions\n  via involutions   Parking functions were classically defined for $n$ cars attempting to park on\na one-way street with $n$ parking spots, where cars only drive forward.\nSubsequently, parking functions have been generalized in various ways,\nincluding allowing cars the option of driving backward. The set $PF_{n,k}$ of\n$k$-Naples parking functions have cars who can drive backward a maximum of $k$\nsteps before driving forward. A recursive formula for $|PF_{n,k}|$ has been\nobtained, though deriving a closed formula for $|PF_{n,k}|$ appears difficult.\nIn addition, an important subset $B_{n,k}$ of $PF_{n,k}$, called the contained\n$k$-Naples parking functions, has been shown, with a non-bijective proof, to\nhave the same cardinality as that of the set $PF_n$ of classical parking\nfunctions, independent of $k$.\n  In this paper, we study $k$-Naples parking functions in the more general\ncontext of $m$ cars and $n$ parking spots, for any $m \\leq n$. We use various\nparking function involutions to establish a bijection between the contained\n$k$-Naples parking functions and the classical parking functions, from which it\ncan be deduced that the two sets have the same number of ties. Then we extend\nthis bijection to inject the set of $k$-Naples parking functions into a certain\nset of obstructed parking functions, providing an upper bound for the\ncardinality of the former set.\n', 'Metered Parking Functions   We introduce a generalization of parking functions called $t$-metered\n$(m,n)$-parking functions, in which one of $m$ cars parks among $n$ spots per\nhour then leaves after $t$ hours. We characterize and enumerate these sequences\nfor $t=1$, $t=m-2$, and $t=n-1$, and provide data for other cases. We\ncharacterize the $1$-metered parking functions by decomposing them into\nsections based on which cars are unlucky, and enumerate them using a Lucas\nsequence recursion. Additionally, we establish a new combinatorial\ninterpretation of the numerator of the continued fraction $n-1/(n-1/\\cdots)$\n($n$ times) as the number of $1$-metered $(n,n)$-parking functions. We\nintroduce the $(m,n)$-parking function shuffle in order to count\n$(m-2)$-metered $(m,n)$-parking functions, which also yields an expression for\nthe number of $(m,n)$-parking functions with any given first entry. As a\nspecial case, we find that the number of $(m-2)$-metered $(m, m-1)$-parking\nfunctions is equal to the sum of the first entries of classical parking\nfunction of length $m-1$. We enumerate the $(n-1)$-metered $(m,n)$-parking\nfunctions in terms of the number of classical parking functions of length $n$\nwith certain parking outcomes, which we show are periodic sequences with period\n$n$. We conclude with an array of open problems.\n']","[('parking functions', 0.6706756353378296), ('parking', 0.5539387464523315), ('number cars', 0.4135991930961609), ('combinatorial', 0.41086676716804504), ('park', 0.3859894871711731), ('characterization permutation', 0.37441471219062805), ('functions length', 0.3533335030078888), ('permutation invariant', 0.3143352270126343), ('functions introduced', 0.3137834370136261), ('buses', 0.31041181087493896)]"
416,416,72,416_simply connected manifolds_connected manifolds_surfaces manifolds_spheres manifolds,"['simply connected manifolds', 'connected manifolds', 'surfaces manifolds', 'spheres manifolds', 'simply connected manifold', 'manifolds', 'topological manifold', 'homotopy spheres', 'connected manifold', 'surfaces manifold']","[""Direct and indirect constructions of locally flat surfaces in\n  4-manifolds   There are two main approaches to building locally flat embedded surfaces in\n4-manifolds: direct methods which geometrically manipulate a given map of a\nsurface, and more indirect methods using surgery theory. Both methods rely on\nFreedman--Quinn's disc embedding theorem. These are the lecture notes for a\nminicourse giving an introduction to both methods, by sketching the proofs of\nthe following results: every primitive second homology class in a closed,\nsimply connected 4-manifold is represented by a locally flat torus\n(Lee--Wilczy\\'{n}ski); and every Alexander polynomial one knot in $S^3$ is\ntopologically slice (Freedman--Quinn).\n"", 'Topologically isotopic and smoothly inequivalent 2-spheres in simply\n  connected 4-manifolds whose complement has a prescribed fundamental group   We describe a procedure to construct infinite sets of pairwise smoothly\ninequivalent 2-spheres in simply connected 4-manifolds, which are topologically\nisotopic and whose complement has a prescribed fundamental group that satisfies\nsome conditions. This class of groups include finite cyclic groups and the\nbinary icosahedral group. These are the first known examples of knotting\nphenomena in 4-manifolds with such properties. Examples of locally flat\nembedded 2-spheres in non-smoothable 4-manifolds are also given.\n', ""Pseudo-isotopies of simply connected 4-manifolds   Perron and Quinn gave independent proofs in 1986 that every topological\npseudo-isotopy of a simply-connected, compact topological 4-manifold is\nisotopic to the identity. Another result of Quinn is that every smooth\npseudo-isotopy of a simply-connected, compact, smooth 4-manifold is smoothly\nstably isotopic to the identity. From this he deduced that\n$\\pi_4(\\operatorname{TOP}(4)/\\operatorname{O}(4)) =0$. A replacement criterion\nis used at a key juncture in Quinn's proofs, but the justification given for it\nis incorrect. We provide different arguments that bypass the replacement\ncriterion, thus completing Quinn's proofs of both the topological and the\nstable smooth pseudo-isotopy theorems. We discuss the replacement criterion and\nstate it as an open problem.\n""]","[('simply connected manifolds', 0.6222572922706604), ('connected manifolds', 0.6051391959190369), ('surfaces manifolds', 0.5907193422317505), ('spheres manifolds', 0.5811100602149963), ('simply connected manifold', 0.5725117325782776), ('manifolds', 0.5688417553901672), ('topological manifold', 0.5635130405426025), ('homotopy spheres', 0.5578122735023499), ('connected manifold', 0.5542427897453308), ('surfaces manifold', 0.5416324138641357)]"
417,417,72,417_dislocations_dislocation_brittle materials_elasticity,"['dislocations', 'dislocation', 'brittle materials', 'elasticity', 'elastic energy', 'threshold dynamics', 'grain boundaries', 'grain boundary', 'dynamics', 'strain gradient']","[""A New Formulation of Coupling and Sliding Motions of Grain Boundaries\n  Based on Dislocation Structure   A continuum model of the two dimensional low angle grain boundary motion and\nthe dislocation structure evolution on the grain boundaries has been developed\nin Ref. [48]. The model is based on the motion and reaction of the constituent\ndislocations of the grain boundaries. The long-range elastic interaction\nbetween dislocations is included in the continuum model, and it maintains a\nstable dislocation structure described by the Frank's formula for grain\nboundaries. In this paper, we develop a new continuum model for the coupling\nand sliding motions of grain boundaries that avoids the time-consuming\ncalculation of the long-range elastic interaction. In this model, the\nlong-range elastic interaction is replaced by a constraint of the Frank's\nformula. The constrained evolution problem in our new continuum model is\nfurther solved by using the projection method. Effects of the coupling and\nsliding motions in our new continuum model and relationship with the classical\nmotion by curvature model are discussed. The continuum model is validated by\ncomparisons with discrete dislocation dynamics model and the early continuum\nmodel [48] in which the long-range dislocation interaction is explicitly\ncalculated.\n"", 'Discrete Dislocations Dynamics with annihilation as the limit of the\n  Peierls-Nabarro model in one dimension   Plasticity of metals is the emergent phenomenon of many crystal defects\n(dislocations) which interact and move on microscopic time and length scales.\nTwo of the commonly used models to describe such dislocation dynamics are the\nPeierls-Nabarro model and the so-called discrete dislocation dynamics model.\n  However, the consistency between these two models is known only for a few\nnumber of dislocations or up to the first time at which two dislocations\ncollide. In this paper we resolve these restrictions, and establish the\nconsistency for any number of dislocations and without any restriction on their\ninitial position or orientation.\n  In more detail, the evolutive Peierls-Nabarro model which we consider\ndescribes the evolution of a phase-field function $v_\\e(t,x)$ which represents\nthe atom deformation in a crystal. The model is a reaction-diffusion equation\nof Allen-Cahn type with the half Laplacian. The small parameter $\\ep$ is the\nratio between the atomic distance and the typical distance between phase\ntransitions in $v_\\e$. The position of a phase transition determines the\nposition of a dislocation, and the sign of the transition (up or down)\ndetermines the orientation.\n  The goal of this paper is to derive the asymptotic behavior of the function\n$v_\\e$ as $\\ep\\to0$ up to arbitrary end time $T$; in particular beyond\ncollisions. We prove that $v_\\e$ converges to a piecewise constant function\n$v$, whose jump points in the spatial variable satisfy the ODE system which\nrepresents discrete dislocation dynamics with annihilation. Our proof method is\nto explicitly construct and patch together several sub- and supersolutions of\n$v_\\e$, and to show that they converge to the same limit $v$.\n', 'From the Peierls-Nabarro model to the equation of motion of the\n  dislocation continuum   We consider a semi-linear integro-differential equation in dimension one\nassociated to the half Laplacian %This model describes the evolution of phase\ntransitions associated to dislocations. whose solution represents the atom\ndislocation in a crystal. The equation comprises the evolutive version of the\nclassical Peierls-Nabarro model. We show that for a large number of\ndislocations, the solution, properly rescaled, converges to the solution of a\nwell known equation called by Head \\cite{H} ""the equation of motion of the\ndislocation continuum"". The limit equation is a model for the macroscopic\ncrystal plasticity with density of dislocations. In particular, we recover the\nso called Orowan\'s law which states that dislocations move at a velocity\nproportional to the effective stress.\n']","[('dislocations', 0.5610136389732361), ('dislocation', 0.5431692600250244), ('brittle materials', 0.3465258777141571), ('elasticity', 0.3296327590942383), ('elastic energy', 0.3262615501880646), ('threshold dynamics', 0.3251006007194519), ('grain boundaries', 0.31719139218330383), ('grain boundary', 0.3108021914958954), ('dynamics', 0.2997433543205261), ('strain gradient', 0.287410706281662)]"
418,418,72,418_compression distributed_communication compression_gradient compression_distributed optimization,"['compression distributed', 'communication compression', 'gradient compression', 'distributed optimization', 'efficient distributed learning', 'compressed communication', 'distributed training', 'bidirectional compression', 'distributed learning', 'distributed stochastic gradient']","['EF21: A New, Simpler, Theoretically Better, and Practically Faster Error\n  Feedback   Error feedback (EF), also known as error compensation, is an immensely\npopular convergence stabilization mechanism in the context of distributed\ntraining of supervised machine learning models enhanced by the use of\ncontractive communication compression mechanisms, such as Top-$k$. First\nproposed by Seide et al (2014) as a heuristic, EF resisted any theoretical\nunderstanding until recently [Stich et al., 2018, Alistarh et al., 2018].\nHowever, all existing analyses either i) apply to the single node setting only,\nii) rely on very strong and often unreasonable assumptions, such global\nboundedness of the gradients, or iterate-dependent assumptions that cannot be\nchecked a-priori and may not hold in practice, or iii) circumvent these issues\nvia the introduction of additional unbiased compressors, which increase the\ncommunication cost. In this work we fix all these deficiencies by proposing and\nanalyzing a new EF mechanism, which we call EF21, which consistently and\nsubstantially outperforms EF in practice. Our theoretical analysis relies on\nstandard assumptions only, works in the distributed heterogeneous data setting,\nand leads to better and more meaningful rates. In particular, we prove that\nEF21 enjoys a fast $O(1/T)$ convergence rate for smooth nonconvex problems,\nbeating the previous bound of $O(1/T^{2/3})$, which was shown a bounded\ngradients assumption. We further improve this to a fast linear rate for PL\nfunctions, which is the first linear convergence result for an EF-type method\nnot relying on unbiased compressors. Since EF has a large number of\napplications where it reigns supreme, we believe that our 2021 variant, EF21,\ncan a large impact on the practice of communication efficient distributed\nlearning.\n', ""EF-BV: A Unified Theory of Error Feedback and Variance Reduction\n  Mechanisms for Biased and Unbiased Compression in Distributed Optimization   In distributed or federated optimization and learning, communication between\nthe different computing units is often the bottleneck and gradient compression\nis widely used to reduce the number of bits sent within each communication\nround of iterative methods. There are two classes of compression operators and\nseparate algorithms making use of them. In the case of unbiased random\ncompressors with bounded variance (e.g., rand-k), the DIANA algorithm of\nMishchenko et al. (2019), which implements a variance reduction technique for\nhandling the variance introduced by compression, is the current state of the\nart. In the case of biased and contractive compressors (e.g., top-k), the EF21\nalgorithm of Richt\\'arik et al. (2021), which instead implements an\nerror-feedback mechanism, is the current state of the art. These two classes of\ncompression schemes and algorithms are distinct, with different analyses and\nproof techniques. In this paper, we unify them into a single framework and\npropose a new algorithm, recovering DIANA and EF21 as particular cases. Our\ngeneral approach works with a new, larger class of compressors, which has two\nparameters, the bias and the variance, and includes unbiased and biased\ncompressors as particular cases. This allows us to inherit the best of the two\nworlds: like EF21 and unlike DIANA, biased compressors, like top-k, whose good\nperformance in practice is recognized, can be used. And like DIANA and unlike\nEF21, independent randomness at the compressors allows to mitigate the effects\nof compression, with the convergence rate improving when the number of parallel\nworkers is large. This is the first time that an algorithm with all these\nfeatures is proposed. We prove its linear convergence under certain conditions.\nOur approach takes a step towards better understanding of two so-far distinct\nworlds of communication-efficient distributed learning.\n"", ""Error Compensated Distributed SGD Can Be Accelerated   Gradient compression is a recent and increasingly popular technique for\nreducing the communication cost in distributed training of large-scale machine\nlearning models. In this work we focus on developing efficient distributed\nmethods that can work for any compressor satisfying a certain contraction\nproperty, which includes both unbiased (after appropriate scaling) and biased\ncompressors such as RandK and TopK. Applied naively, gradient compression\nintroduces errors that either slow down convergence or lead to divergence. A\npopular technique designed to tackle this issue is error compensation/error\nfeedback. Due to the difficulties associated with analyzing biased compressors,\nit is not known whether gradient compression with error compensation can be\ncombined with Nesterov's acceleration. In this work, we show for the first time\nthat error compensated gradient compression methods can be accelerated. In\nparticular, we propose and study the error compensated loopless Katyusha\nmethod, and establish an accelerated linear convergence rate under standard\nassumptions. We show through numerical experiments that the proposed method\nconverges with substantially fewer communication rounds than previous error\ncompensated algorithms.\n""]","[('compression distributed', 0.6065275073051453), ('communication compression', 0.6006171107292175), ('gradient compression', 0.5904747247695923), ('distributed optimization', 0.5803897976875305), ('efficient distributed learning', 0.5754527449607849), ('compressed communication', 0.561447262763977), ('distributed training', 0.556502640247345), ('bidirectional compression', 0.550220251083374), ('distributed learning', 0.5312035083770752), ('distributed stochastic gradient', 0.5283000469207764)]"
419,419,71,419_optimal controller_optimal regret_regret optimal_regret minimization,"['optimal controller', 'optimal regret', 'regret optimal', 'regret minimization', 'adaptive regret', 'robust regret', 'regret adaptive', 'dynamic regret', 'control linear time', 'estimation control']","['Regret-optimal measurement-feedback control   We consider measurement-feedback control in linear dynamical systems from the\nperspective of regret minimization. Unlike most prior work in this area, we\nfocus on the problem of designing an online controller which competes with the\noptimal dynamic sequence of control actions selected in hindsight, instead of\nthe best controller in some specific class of controllers. This formulation of\nregret is attractive when the environment changes over time and no single\ncontroller achieves good performance over the entire time horizon. We show that\nin the measurement-feedback setting, unlike in the full-information setting,\nthere is no single offline controller which outperforms every other offline\ncontroller on every disturbance, and propose a new $H_2$-optimal offline\ncontroller as a benchmark for the online controller to compete against. We show\nthat the corresponding regret-optimal online controller can be found via a\nnovel reduction to the classical Nehari problem from robust control and present\na tight data-dependent bound on its regret.\n', 'Regret-Optimal LQR Control   We consider the infinite-horizon LQR control problem. Motivated by\ncompetitive analysis in online learning, as a criterion for controller design\nwe introduce the dynamic regret, defined as the difference between the LQR cost\nof a causal controller (that has only access to past disturbances) and the LQR\ncost of the \\emph{unique} clairvoyant one (that has also access to future\ndisturbances) that is known to dominate all other controllers. The regret\nitself is a function of the disturbances, and we propose to find a causal\ncontroller that minimizes the worst-case regret over all bounded energy\ndisturbances. The resulting controller has the interpretation of guaranteeing\nthe smallest regret compared to the best non-causal controller that can see the\nfuture. We derive explicit formulas for the optimal regret and for the\nregret-optimal controller for the state-space setting. These explicit solutions\nare obtained by showing that the regret-optimal control problem can be reduced\nto a Nehari extension problem that can be solved explicitly. The regret-optimal\ncontroller is shown to be linear and can be expressed as the sum of the\nclassical $H_2$ state-feedback law and an $n$-th order controller ($n$ is the\nstate dimension), and its construction simply requires a solution to the\nstandard LQR Riccati equation and two Lyapunov equations. Simulations over a\nrange of plants demonstrate that the regret-optimal controller interpolates\nnicely between the $H_2$ and the $H_\\infty$ optimal controllers, and generally\nhas $H_2$ and $H_\\infty$ costs that are simultaneously close to their optimal\nvalues. The regret-optimal controller thus presents itself as a viable option\nfor control systems design.\n', 'Regret-optimal control in dynamic environments   We consider control in linear time-varying dynamical systems from the\nperspective of regret minimization. Unlike most prior work in this area, we\nfocus on the problem of designing an online controller which minimizes regret\nagainst the best dynamic sequence of control actions selected in hindsight\n(dynamic regret), instead of the best fixed controller in some specific class\nof controllers (static regret). This formulation is attractive when the\nenvironment changes over time and no single controller achieves good\nperformance over the entire time horizon. We derive the state-space structure\nof the regret-optimal controller via a novel reduction to $H_{\\infty}$ control\nand present a tight data-dependent bound on its regret in terms of the energy\nof the disturbance. Our results easily extend to the model-predictive setting\nwhere the controller can anticipate future disturbances and to settings where\nthe controller only affects the system dynamics after a fixed delay. We present\nnumerical experiments which show that our regret-optimal controller\ninterpolates between the performance of the $H_2$-optimal and\n$H_{\\infty}$-optimal controllers across stochastic and adversarial\nenvironments.\n']","[('optimal controller', 0.6203005313873291), ('optimal regret', 0.604501485824585), ('regret optimal', 0.593945324420929), ('regret minimization', 0.5903175473213196), ('adaptive regret', 0.5822970271110535), ('robust regret', 0.5797488689422607), ('regret adaptive', 0.5696468353271484), ('dynamic regret', 0.5550806522369385), ('control linear time', 0.5237324237823486), ('estimation control', 0.5076760649681091)]"
420,420,71,420_arbitrary precision_precision algorithms_mixed precision algorithms_rounding error analysis,"['arbitrary precision', 'precision algorithms', 'mixed precision algorithms', 'rounding error analysis', 'precision floating point', 'precision arithmetic', 'floating point numbers', 'floating point arithmetic', 'mixed precision', 'probabilistic error bounds']","[""On Stochastic Rounding with Few Random Bits   Large-scale numerical computations make increasing use of low-precision (LP)\nfloating point formats and mixed precision arithmetic, which can be enhanced by\nthe technique of stochastic rounding (SR), that is, rounding an intermediate\nhigh-precision value up or down randomly as a function of the value's distance\nto the two rounding candidates. Stochastic rounding requires, in addition to\nthe high-precision input value, a source of random bits. As the provision of\nhigh-quality random bits is an additional computational cost, it is of interest\nto require as few bits as possible while maintaining the desirable properties\nof SR in a given computation, or computational domain. This paper examines a\nnumber of possible implementations of few-bit stochastic rounding (FBSR), and\nshows how several natural implementations can introduce sometimes significant\nbias into the rounding process, which are not present in the case of\ninfinite-bit, infinite-precision examinations of these implementations. The\npaper explores the impact of these biases in machine learning examples, and\nhence opens another class of configuration parameters of which practitioners\nshould be aware when developing or adopting low-precision floating point. Code\nis available at\nhttp://github.com/graphcore-research/arith25-stochastic-rounding.\n"", 'Numerical Fuzz: A Type System for Rounding Error Analysis   Algorithms operating on real numbers are implemented as floating-point\ncomputations in practice, but floating-point operations introduce roundoff\nerrors that can degrade the accuracy of the result. We propose $\\Lambda_{num}$,\na functional programming language with a type system that can express\nquantitative bounds on roundoff error. Our type system combines a sensitivity\nanalysis, enforced through a linear typing discipline, with a novel graded\nmonad to track the accumulation of roundoff errors. We prove that our type\nsystem is sound by relating the denotational semantics of our language to the\nexact and floating-point operational semantics. To demonstrate our system, we\ninstantiate $\\Lambda_{num}$ with error metrics proposed in the numerical\nanalysis literature and we show how to incorporate rounding operations that\nfaithfully model aspects of the IEEE 754 floating-point standard. To show that\n$\\Lambda_{num}$ can be a useful tool for automated error analysis, we develop a\nprototype implementation for $\\Lambda_{num}$ that infers error bounds that are\ncompetitive with existing tools, while often running significantly faster.\nFinally, we consider semantic extensions of our graded monad to bound error\nunder more complex rounding behaviors, such as non-deterministic and randomized\nrounding.\n', ""Probabilistic Error Analysis For Sequential Summation of Real Floating\n  Point Numbers   We derive two probabilistic bounds for the relative forward error in the\nfloating point summation of $n$ real numbers, by representing the roundoffs as\nindependent, zero-mean, bounded random variables. The first probabilistic bound\nis based on Azuma's concentration inequality, and the second on the\nAzuma-Hoeffding Martingale. Our numerical experiments illustrate that the\nprobabilistic bounds, with a stringent failure probability of $10^{-16}$, can\nbe 1-2 orders of magnitude tighter than deterministic bounds. We performed the\nnumerical experiments in Julia by summing up to $n=10^7$ single precision\n(binary32) floating point numbers, and up to $n=10^4$ half precision (binary16)\nfloating point numbers. We simulated exact computation with double precision\n(binary64). The bounds tend to be tighter when all summands have the same sign.\n""]","[('arbitrary precision', 0.6567695140838623), ('precision algorithms', 0.6379656791687012), ('mixed precision algorithms', 0.6303492784500122), ('rounding error analysis', 0.6251690983772278), ('precision floating point', 0.621599018573761), ('precision arithmetic', 0.5878729224205017), ('floating point numbers', 0.5838916897773743), ('floating point arithmetic', 0.5751509666442871), ('mixed precision', 0.5403457880020142), ('probabilistic error bounds', 0.5361748337745667)]"
421,421,71,421_abelian lie groups_abelian lie group_abelian lie algebra_abelian lie,"['abelian lie groups', 'abelian lie group', 'abelian lie algebra', 'abelian lie', 'almost abelian lie', 'lie groups', 'structures lie groups', 'solvable lie groups', 'compact lie groups', 'lie algebras']","['Harmonic almost complex structures on almost abelian Lie groups and\n  solvmanifolds   An almost abelian Lie group is a solvable Lie group with a codimension-one\nnormal abelian subgroup. We characterize almost Hermitian structures on almost\nabelian Lie groups where the almost complex structure is harmonic with respect\nto the Hermitian metric. Also, we adapt the Gray-Hervella classification of\nalmost Hermitian structures to the family of almost abelian Lie groups. We\nprovide several examples of harmonic almost complex structures in different\nGray-Hervella classes on some associated compact almost abelian solvmanifolds.\n', 'Balanced Hermitian structures on almost abelian Lie algebras   We study balanced Hermitian structures on almost abelian Lie algebras, i.e.\non Lie algebras with a codimension-one abelian ideal. In particular, we\nclassify six-dimensional almost abelian Lie algebras which carry a balanced\nstructure. It has been conjectured by A. Fino and L. Vezzoni that a compact\ncomplex manifold admitting both a balanced metric and a SKT metric necessarily\nhas a K\\""ahler metric: we prove this conjecture for compact almost abelian\nsolvmanifolds with left-invariant complex structures. Moreover, we investigate\nthe behaviour of the flow of balanced metrics introduced by L. Bedulli and L.\nVezzoni and of the anomaly flow by D. H. Phong, S. Picard and X. Zhang on\nalmost abelian Lie groups. In particular, we show that the anomaly flow\npreserves the balanced condition and that locally conformally K\\""ahler metrics\nare fixed points.\n', 'Generalized K\\""ahler almost abelian Lie groups   We study left-invariant generalized K\\""ahler structures on almost abelian Lie\ngroups, i.e., on solvable Lie groups with a codimension-one abelian normal\nsubgroup. In particular, we classify six-dimensional almost abelian Lie groups\nwhich admit a left-invariant complex structure and establish which of those\nhave a left-invariant Hermitian structure whose fundamental 2-form is $\\partial\n\\bar \\partial$-closed. We obtain a classification of six-dimensional\ngeneralized K\\""ahler almost abelian Lie groups and determine the 6-dimensional\ncompact almost abelian solvmanifolds admitting an invariant generalized\nK\\""ahler structure. Moreover, we prove some results in relation to the\nexistence of holomorphic Poisson structures and to the pluriclosed flow.\n']","[('abelian lie groups', 0.7529777884483337), ('abelian lie group', 0.7300997376441956), ('abelian lie algebra', 0.7291752099990845), ('abelian lie', 0.6729624271392822), ('almost abelian lie', 0.6698938012123108), ('lie groups', 0.6172395944595337), ('structures lie groups', 0.6051972508430481), ('solvable lie groups', 0.5894522070884705), ('compact lie groups', 0.5880084037780762), ('lie algebras', 0.5661044716835022)]"
422,422,71,422_discontinuous galerkin methods_galerkin methods_based discontinuous galerkin_discontinuous galerkin,"['discontinuous galerkin methods', 'galerkin methods', 'based discontinuous galerkin', 'discontinuous galerkin', 'finite difference methods', 'discontinuous galerkin dg', 'hybridizable discontinuous galerkin', 'discontinuous galerkin time', 'finite volume methods', 'galerkin']","['An energy-based summation-by-parts finite difference method for the wave\n  equation in second order form   We develop a new finite difference method for the wave equation in second\norder form. The finite difference operators satisfy a summation-by-parts (SBP)\nproperty. With boundary conditions and material interface conditions imposed\nweakly by the simultaneous-approximation-term (SAT) method, we derive energy\nestimates for the semi-discretization. In addition, error estimates are derived\nby the normal mode analysis. The proposed method is termed as energy-based\nbecause of its similarity with the energy-based discontinuous Galerkin method.\nWhen imposing the Dirichlet boundary condition and material interface\nconditions, the traditional SBP-SAT discretization uses a penalty term with a\nmesh-dependent parameter, which is not needed in our method. Furthermore,\nnumerical dissipation can be added to the discretization through the boundary\nand interface conditions. We present numerical experiments that verify\nconvergence and robustness of the proposed method.\n', 'Upwind summation by parts finite difference methods for large scale\n  elastic wave simulations in 3D complex geometries   High-order accurate summation-by-parts (SBP) finite difference (FD) methods\nconstitute efficient numerical methods for simulating large-scale hyperbolic\nwave propagation problems. Traditional SBP FD operators that approximate\nfirst-order spatial derivatives with central-difference stencils often have\nspurious unresolved numerical wave-modes in their computed solutions. Recently\nderived high order accurate upwind SBP operators based upwind FD stencils have\nthe potential to suppress these poisonous spurious wave-modes on marginally\nresolved computational grids. In this paper, we demonstrate that not all high\norder upwind SBP FD operators are applicable. Numerical dispersion relation\nanalysis shows that odd-order upwind SBP FD operators also support spurious\nunresolved high-frequencies on marginally resolved meshes. Meanwhile,\neven-order upwind SBP FD operators (of order 2, 4, 6) do not support spurious\nunresolved high frequency wave modes and also have better numerical dispersion\nproperties. We discretise the three space dimensional (3D) elastic wave\nequation on boundary-conforming curvilinear meshes. Using the energy method we\nprove that the semi-discrete approximation is stable and energy-conserving. We\nderive a priori error estimate and prove the convergence of the numerical\nerror. Numerical experiments for the 3D elastic wave equation in complex\ngeometries corroborate the theoretical analysis. Numerical simulations of the\n3D elastic wave equation in heterogeneous media with complex non-planar free\nsurface topography are given, including numerical simulations of community\ndeveloped seismological benchmark problems. Computational results show that\neven-order upwind SBP FD operators are more efficient, robust and less prone to\nnumerical dispersion errors on marginally resolved meshes when compared to the\nodd-order upwind and traditional SBP FD operators.\n', 'A finite difference - discontinuous Galerkin method for the wave\n  equation in second order form   We develop a hybrid spatial discretization for the wave equation in second\norder form, based on high-order accurate finite difference methods and\ndiscontinuous Galerkin methods. The hybridization combines computational\nefficiency of finite difference methods on Cartesian grids and geometrical\nflexibility of discontinuous Galerkin methods on unstructured meshes. The two\nspatial discretizations are coupled by a penalty technique at the interface\nsuch that the overall semidiscretization satisfies a discrete energy estimate\nto ensure stability. In addition, optimal convergence is obtained in the sense\nthat when combining a fourth order finite difference method with a\ndiscontinuous Galerkin method using third order local polynomials, the overall\nconvergence rate is fourth order. Furthermore, we use a novel approach to\nderive an error estimate for the semidiscretization by combining the energy\nmethod and the normal mode analysis for a corresponding one dimensional model\nproblem. The stability and accuracy analysis are verified in numerical\nexperiments.\n']","[('discontinuous galerkin methods', 0.7233380079269409), ('galerkin methods', 0.6489315032958984), ('based discontinuous galerkin', 0.6344971656799316), ('discontinuous galerkin', 0.5778234601020813), ('finite difference methods', 0.5723057389259338), ('discontinuous galerkin dg', 0.5508369207382202), ('hybridizable discontinuous galerkin', 0.5465832352638245), ('discontinuous galerkin time', 0.5062845349311829), ('finite volume methods', 0.4712658226490021), ('galerkin', 0.4619188606739044)]"
423,423,71,423_stable phase retrieval_phase retrieval via_retrieval phase retrieval_phase retrieval,"['stable phase retrieval', 'phase retrieval via', 'retrieval phase retrieval', 'phase retrieval', 'phase retrieval problems', 'phase retrieval phase', 'retrieval phase', 'dimensional phase', 'one dimensional phase', 'dual frames']","['Classifying weak phase retrieval   We will give several surprising equivalences and consequences of weak phase\nretrieval. These results give a complete understanding of the difference\nbetween weak phase retrieval and phase retrieval. We also answer two\nlongstanding open problems on weak phase retrieval: (1) We show that the\nfamilies of weak phase retrievable frames $\\{x_{i}\\}_{i=1}^{m}$ in\n$\\mathbb{R}^n$ are not dense in the family of $m$-element sets of vectors in\n$\\mathbb{R}^n$ for all $m\\ge 2n-2$; (2) We show that any frame\n$\\{x_i\\}_{i=1}^{2n-2}$ containing one or more canonical basis vectors in\n$\\mathbb{R}^n$ cannot do weak phase retrieval. We provide numerous examples to\nshow that the obtained results are best possible.\n', 'Characterization of (weak) phase retrieval dual frames   Recovering a signal up to a unimodular constant from the magnitudes of linear\nmeasurements has been popular and well studied in recent years. However,\nnumerous unsolved problems regarding phase retrieval still exist. Given a phase\nretrieval frame, may the family of phase retrieval dual frames be classified?\nAnd is such a family dense in the set of dual frames? Can we present the\nequivalent conditions for a family of vectors to do weak phase retrieval in\ncomplex Hilbert space case? What is the connection between phase, weak phase\nand norm retrieval? In this context, we aim to deal with these open problems\nconcerning phase retrieval dual frames, weak phase retrieval frames, and\nspecially investigate equivalent conditions for identifying these features. We\nprovide some characterizations of alternate dual frames of a phase retrieval\nframe which yield phase retrieval in finite dimensional Hilbert spaces.\nMoreover, for some classes of frames, we show that the family of phase\nretrieval dual frames is open and dense in the set of dual frames.\n  Then, we study weak phase retrieval problem. Among other things, we obtain\nsome equivalent conditions on a family of vectors to do phase retrieval in\nterms of weak phase retrieval.\n', 'A note on (weak) phase and norm retrievable Real Hilbert space frames\n  and projections   \\begin{abstract} In this manuscript, we answer a list of longstanding open\nproblems on weak phase retrieval including: (1) A complete classification of\nthe vectors $\\{x_i\\}_{i=1}^2$ in $\\RR^3$ that do weak phase retrieval; (2) We\nshow that frames doing weak phase retrieval in $\\RR^n$ must span $\\RR^n$; (3)\nWe give an example of a set of vectors doing phase retrieval but their\northogonal complement hyperplanes fail weak phase retrieval; (4) We give a\nclassification of weak phase retrievable frames - which makes clear the\ndifference between phase retrieval and weak phase retrieval; (5) We classify\nwhen weak phase retrievable frames also do norm retrieval. We then introduce\nthe notion of weak phase retrieval by projections and develop their basic\nproperties. We then look at phase (norm) retrieval by projections. We end with\nsome open problems.\n  We provide numerous examples to show that our results are best possible.\n\\end{abstract}\n']","[('stable phase retrieval', 0.707198441028595), ('phase retrieval via', 0.6783788204193115), ('retrieval phase retrieval', 0.6639207005500793), ('phase retrieval', 0.6579474806785583), ('phase retrieval problems', 0.6133785247802734), ('phase retrieval phase', 0.5945379137992859), ('retrieval phase', 0.5222489237785339), ('dimensional phase', 0.4465582072734833), ('one dimensional phase', 0.421712189912796), ('dual frames', 0.3726435601711273)]"
424,424,71,424_fourier restriction estimates_restriction estimates_restriction estimate_fourier restriction theory,"['fourier restriction estimates', 'restriction estimates', 'restriction estimate', 'fourier restriction theory', 'estimates hyperbolic', 'fourier restriction', 'bilinear restriction', 'paraboloids', 'restriction extension', 'decoupling estimates']","['On decoupling and restriction estimates   In this short note, we prove that the restriction conjecture for the\n(hyperbolic) paraboloid in $\\mathbb{R}^d$ implies the $l^p$-decoupling theorem\nfor the (hyperbolic) paraboloid in $\\mathbb{R}^{2d-1}$. In particular, this\ngives a simple proof of the $l^p$ decoupling theorem for the (hyperbolic)\nparaboloid in $\\mathbb{R}^3$.\n', 'An endpoint estimate of the bilinear paraboloid restriction operator   In Fourier restriction problems, a cone and a paraboloid are model surfaces.\nThe sharp bilinear cone restriction estimate was first shown by Wolff, and\nlater the endpoint was obtained by Tao. For a paraboloid, the sharp $L^2$\nbilinear restriction estimate was obtained by Tao, but the endpoint was\nremained open. In this paper we prove the endpoint $L^2$ bilinear restriction\nestimate for a paraboloid.\n', 'Restriction and decoupling estimates for the hyperbolic paraboloid in $\\mathbb{R}^3$ We prove bilinear $\\ell^2$-decoupling and refined bilinear decoupling inequalities for the truncated hyperbolic paraboloid in $\\mathbb{R}^3$. As an application, we prove the associated restriction estimate in the range $p>22/7$, matching an earlier result for the elliptic paraboloid.']","[('fourier restriction estimates', 0.5777525901794434), ('restriction estimates', 0.5252439379692078), ('restriction estimate', 0.49860477447509766), ('fourier restriction theory', 0.4933471083641052), ('estimates hyperbolic', 0.47609299421310425), ('fourier restriction', 0.45049962401390076), ('bilinear restriction', 0.4213803708553314), ('paraboloids', 0.37997663021087646), ('restriction extension', 0.3775838315486908), ('decoupling estimates', 0.3767317533493042)]"
425,425,71,425_entropy information_shannon entropy_entropy shannon_generalized entropy,"['entropy information', 'shannon entropy', 'entropy shannon', 'generalized entropy', 'entropy measures', 'entropy measure', 'information theoretic', 'entropy relative entropy', 'conditional entropy', 'relative entropy']","['Introduction to Logical Entropy and its Relationship to Shannon Entropy   We live in the information age. Claude Shannon, as the father of the\ninformation age, gave us a theory of communications that quantified an ""amount\nof information,"" but, as he pointed out, ""no concept of information itself was\ndefined."" Logical entropy provides that definition. Logical entropy is the\nnatural measure of the notion of information based on distinctions,\ndifferences, distinguishability, and diversity. It is the (normalized)\nquantitative measure of the distinctions of a partition on a set--just as the\nBoole-Laplace logical probability is the normalized quantitative measure of the\nelements of a subset of a set. And partitions and subsets are mathematically\ndual concepts--so the logic of partitions is dual in that sense to the usual\nBoolean logic of subsets, and hence the name ""logical entropy."" The logical\nentropy of a partition has a simple interpretation as the probability that a\ndistinction or dit (elements in different blocks) is obtained in two\nindependent draws from the underlying set. The Shannon entropy is shown to also\nbe based on this notion of information-as-distinctions; it is the average\nminimum number of binary partitions (bits) that need to be joined to make all\nthe same distinctions of the given partition. Hence all the concepts of simple,\njoint, conditional, and mutual logical entropy can be transformed into the\ncorresponding concepts of Shannon entropy by a uniform non-linear dit-bit\ntransform. And finally logical entropy linearizes naturally to the\ncorresponding quantum concept. The quantum logical entropy of an observable\napplied to a state is the probability that two different eigenvalues are\nobtained in two independent projective measurements of that observable on that\nstate.\n  Keywords: logical entropy, Shannon entropy, partitions, MaxEntropy, quantum\nlogical entropy, von Neumann entropy\n', ""Information Decomposition Diagrams Applied beyond Shannon Entropy: A\n  Generalization of Hu's Theorem   In information theory, one major goal is to find useful functions that\nsummarize the amount of information contained in the interaction of several\nrandom variables. Specifically, one can ask how the classical Shannon entropy,\nmutual information, and higher interaction information relate to each other.\nThis is answered by Hu's theorem, which is widely known in the form of\ninformation diagrams: it relates shapes in a Venn diagram to information\nfunctions, thus establishing a bridge from set theory to information theory. In\nthis work, we view random variables together with the joint operation as a\nmonoid that acts by conditioning on information functions, and entropy as a\nfunction satisfying the chain rule of information. This abstract viewpoint\nallows to prove a generalization of Hu's theorem. It applies to Shannon and\nTsallis entropy, (Tsallis) Kullback-Leibler Divergence, cross-entropy,\nKolmogorov complexity, submodular information functions, and the generalization\nerror in machine learning. Our result implies for Chaitin's Kolmogorov\ncomplexity that the interaction complexities of all degrees are in expectation\nclose to Shannon interaction information. For well-behaved probability\ndistributions on increasing sequence lengths, this shows that the per-bit\nexpected interaction complexity and information asymptotically coincide, thus\nshowing a strong bridge between algorithmic and classical information theory.\n"", ""Learn your entropy from informative data: an axiom ensuring the\n  consistent identification of generalized entropies   Shannon entropy, a cornerstone of information theory, statistical physics and\ninference methods, is uniquely identified by the Shannon-Khinchin or\nShore-Johnson axioms. Generalizations of Shannon entropy, motivated by the\nstudy of non-extensive or non-ergodic systems, relax some of these axioms and\nlead to entropy families indexed by certain `entropic' parameters. In general,\nthe selection of these parameters requires pre-knowledge of the system or\nencounters inconsistencies. Here we introduce a simple axiom for any entropy\nfamily: namely, that no entropic parameter can be inferred from a completely\nuninformative (uniform) probability distribution. When applied to the\nUffink-Jizba-Korbel and Hanel-Thurner entropies, the axiom selects only R\\'enyi\nentropy as viable. It also extends consistency with the Maximum Likelihood\nprinciple, which can then be generalized to estimate the entropic parameter\npurely from data, as we confirm numerically. Remarkably, in a generalized\nmaximum-entropy framework the axiom implies that the maximized log-likelihood\nalways equals minus Shannon entropy, even if the inferred probability\ndistribution maximizes a generalized entropy and not Shannon's, solving a\nseries of problems encountered in previous approaches.\n""]","[('entropy information', 0.794343888759613), ('shannon entropy', 0.7100279927253723), ('entropy shannon', 0.7048062086105347), ('generalized entropy', 0.695746898651123), ('entropy measures', 0.6811944246292114), ('entropy measure', 0.6766042709350586), ('information theoretic', 0.6656215786933899), ('entropy relative entropy', 0.6447096467018127), ('conditional entropy', 0.6339763402938843), ('relative entropy', 0.6302649974822998)]"
426,426,70,426_fuzzy numbers_fuzzy theory_fuzzy sets_triangular fuzzy numbers,"['fuzzy numbers', 'fuzzy theory', 'fuzzy sets', 'triangular fuzzy numbers', 'fuzzy inference', 'based fuzzy', 'type fuzzy', 'fuzzy measures', 'intuitionistic fuzzy', 'fuzzy']","['Properties of f correlated fuzzy numbers   This paper presents some concepts of the theory of interactive fuzzy numbers,\nand mainly, a class of interactive fuzzy numbers, called $f$-correlated fuzzy\nnumbers. We start from the foundations of general fuzzy mathematics and go\nthrough operations and the notion of interactivity for fuzzy numbers. The main\nresult is that $f$-correlation preserve the shape of certains fuzzy numbers.\nMore specificaly, if two fuzzy numbers are $f$ correlated, and one is a LR-type\nfuzzy number, the other is also a LR-type fuzzy number. This paper also\npresents some operations with the $f$-correlated fuzzy numbers wich are\ninteresting to applications like biomathematics.\n', 'Fuzzy Calculus with Noval Approach Using Fuzzy Functions   This article deals with the complexity involved in fuzzy derivatives when\nboth input and output are from nonempty, convex, and compact fuzzy space.\nConsider a fuzzy valued mapping, and for fuzzy differentiation of fuzzy valued\nfunction, we propose Modified Hukuhara derivative. To evaluate this derivative,\nwe need to take the parametric form of, input and the mapping which is involved\nin it. Our definition gives a more realistic explanation of fuzzy derivatives,\nunder this derivative, we also develop fuzzy Taylor series along with its\nconvergence. Lastly, we solve a fully fuzzy differential equation with initial\ncondition using Fuzzy Taylor series.\n', 'A study on fuzzy plane and its application on fuzzy plane fitting   In this paper, I obtain an $S$-type fuzzy point when two fuzzy numbers for\ntwo independent variables and a corresponding fuzzy number for the dependent\nvariable are given. A comprehensive study on a conceptualization of a fuzzy\nplane as a collection of fuzzy numbers, or fuzzy points is proposed. A\nperpendicular fuzzy distance from a fuzzy point to a fuzzy plane is also\nrevisited. An application of the proposed fuzzy plane is made to fit a fuzzy\nplane to the available data sets of imprecise locations in $\\mathbb{R}^3$.\nMoreover, a degree of fuzzily fitted fuzzy plane to the given data sets of\nfuzzy points is defined. All the fuzzy geometric construction and\ncharacteristics of fuzzy planes are explored with the help of same and inverse\npoints ideas. All the study is supported by numerical examples and illustrated\nby fuzzy geometrical figures. This study provides a framework for developing a\nfuzzy plane-fitting model that will benefit the fields of curve detecting and\nfitting, image processing for industrial and scientific applications, signal\nprocessing, and problems of shape recognition.\n']","[('fuzzy numbers', 0.756867527961731), ('fuzzy theory', 0.7021488547325134), ('fuzzy sets', 0.6816055178642273), ('triangular fuzzy numbers', 0.6587856411933899), ('fuzzy inference', 0.6461561918258667), ('based fuzzy', 0.6455037593841553), ('type fuzzy', 0.6314517855644226), ('fuzzy measures', 0.6264473795890808), ('intuitionistic fuzzy', 0.6138861775398254), ('fuzzy', 0.5884905457496643)]"
427,427,70,427_general relativity_gravity theories_theories gravity_einstein gravity,"['general relativity', 'gravity theories', 'theories gravity', 'einstein gravity', 'theory gravity', 'teleparallel gravity', 'flat spacetime', 'gravity models', 'modified gravity', 'gravitational field']","['Is spacetime curved? Assessing the underdetermination of general\n  relativity and teleparallel gravity   Realism about general relativity (GR) seems to imply realism about spacetime\ncurvature. The existence of the teleparallel equivalent of general relativity\n(TEGR) calls this into question, for (a) TEGR is set in a torsionful but flat\nspacetime, and (b) TEGR is empirically equivalent to GR. Knox (2011) claims\nthat there is no genuine underdetermination between GR and TEGR; we call this\nverdict into question by isolating and addressing her individual arguments. In\naddition, we anticipate and evaluate two further worries for realism about the\ntorsionful spacetimes of TEGR, which we call the ""problem of\noperationalisability"" and the ""problem of visualisability"".\n', ""Wald's entropy in Coincident General Relativity   The equivalence principle and its universality enables the geometrical\nformulation of gravity. In the standard formulation of General Relativity \\'a\nla Einstein, the gravitational interaction is geometrized in terms of the\nspacetime curvature. However, if we embrace the geometrical character of\ngravity, two alternative, though equivalent, formulations of General Relativity\nemerge in flat spacetimes, in which gravity is fully ascribed either to torsion\nor to non-metricity. The latter allows a much simpler formulation of General\nRelativity oblivious to the affine spacetime structure, the Coincident General\nRelativity. The entropy of a black hole can be computed using the Euclidean\npath integral approach, which strongly relies on the addition of boundary or\nregulating terms in the standard formulation of General Relativity. A more\nfundamental derivation can be performed using Wald's formula, in which the\nentropy is directly related to Noether charges and is applicable to general\ntheories with diffeomorphism invariance. In this work we extend Wald's Noether\ncharge method for calculating black hole entropy to spacetimes endowed with\nnon-metricity. Using this method, we show that Coincident General Relativity\nwith an improved action principle gives the same entropy as the well-known\nentropy in standard General Relativity. Furthermore the first law of black hole\nthermodynamics holds and an explicit expression for the energy appearing in the\nfirst law is obtained.\n"", ""A Unified Approach to Geometric Modifications of Gravity   This thesis studies modified theories of gravity from a geometric viewpoint.\nWe review the motivations for considering alternatives to General Relativity\nand cover the mathematical foundations of gravitational theories in Riemannian\nand non-Riemannian geometries. Then, starting from the decomposition of the\nEinstein-Hilbert action into bulk and boundary terms, we construct new\nmodifications of General Relativity. These modifications break diffeomorphism\ninvariance or local Lorentz invariance, allowing one to bypass Lovelock's\ntheorem while remaining second-order and without introducing additional fields.\nIn the metric-affine framework, we introduce a new Einstein-Cartan-type theory\nwith propagating torsion. Important comparisons are made with the modified\nteleparallel theories, and we construct a unified framework encompassing all\nthese theories. The equivalence between theories that break fundamental\nsymmetries in the Riemannian setting and non-Riemannian theories of gravity is\nexplored in detail. This leads to a dual interpretation of teleparallel\ngravity, one in terms of geometric quantities and the other in terms of\nnon-covariant objects. We then study the cosmological applications of these\nmodified theories, making use of dynamical systems techniques. One key result\nis that the modified Einstein-Cartan theories can drive inflation in the early\nuniverse, replacing the initial cosmological singularity of General Relativity.\nTo conclude, we discuss the viability of these modifications and possible\nfuture directions, examining their significance and relevance to the broader\nfield of gravitational physics.\n""]","[('general relativity', 0.6620340347290039), ('gravity theories', 0.6008008718490601), ('theories gravity', 0.5941246747970581), ('einstein gravity', 0.5847780704498291), ('theory gravity', 0.5606460571289062), ('teleparallel gravity', 0.5460583567619324), ('flat spacetime', 0.5382315516471863), ('gravity models', 0.5365902781486511), ('modified gravity', 0.5162702798843384), ('gravitational field', 0.5132985711097717)]"
428,428,70,428_stochastic quantization_stochastic pdes_quantum field theory_parabolic stochastic,"['stochastic quantization', 'stochastic pdes', 'quantum field theory', 'parabolic stochastic', 'singular stochastic', 'quantum fields', 'singular stochastic partial', 'quantum field', 'quantization', 'stochastic partial differential']","['A stochastic PDE approach to large N problems in quantum field theory: a\n  survey   In this survey we review some recent rigorous results on large N problems in\nquantum field theory, stochastic quantization and singular stochastic PDEs, and\ntheir mean field limit problems. In particular we discuss the O(N) linear sigma\nmodel on two and three dimensional torus. The stochastic quantization procedure\nleads to a coupled system of N interacting $\\Phi^4$ equations. In d = 2, we\nshow uniform in N bounds for the dynamics and convergence to a mean-field\nsingular SPDE. For large enough mass or small enough coupling, the invariant\nmeasures (i.e. the O(N) linear sigma model) converge to the massive Gaussian\nfree field, the unique invariant measure of the mean-field dynamics, in a\nWasserstein distance. We also obtain tightness for certain O(N) invariant\nobservables as random fields in suitable Besov spaces as $N\\to \\infty$, along\nwith exact descriptions of the limiting correlations. In d = 3, the estimates\nbecome more involved since the equation is more singular. We discuss in this\ncase how to prove convergence to the massive Gaussian free field. The proofs of\nthese results build on the recent progress of singular SPDE theory and combine\nmany new techniques such as uniform in N estimates and dynamical mean field\ntheory. These are based on joint papers with Scott Smith, Rongchan Zhu and\nXiangchan Zhu.\n', ""Stochastic quantization associated with the $\\exp(\\Phi)_2$-quantum field\n  model driven by space-time white noise on the torus   We consider a quantum field model with exponential interactions on the\ntwo-dimensional torus, which is called the $\\exp (\\Phi)_{2}$-quantum field\nmodel or H{\\o}egh-Krohn's model. In the present paper, we study the stochastic\nquantization of this model by singular stochastic partial differential\nequations, which is recently developed. By the method, we construct a unique\ntime-global solution and the invariant probability measure of the corresponding\nstochastic quantization equation, and identify with an infinite-dimensional\ndiffusion process, which has been constructed by the Dirichlet form approach.\n"", 'A simple construction of the sine-Gordon model via stochastic\n  quantization   We present a simple PDE construction of the sine-Gordon measure below the\nfirst threshold ($\\be^2 < 4\\pi$), in both the finite and infinite volume\nsettings, by studying the corresponding parabolic sine-Gordon model. We also\nestablish pathwise global well-posedness of the hyperbolic sine-Gordon model in\nfinite volume for $\\be^2 < 2\\pi$.\n']","[('stochastic quantization', 0.6170191168785095), ('stochastic pdes', 0.5428388714790344), ('quantum field theory', 0.5200030207633972), ('parabolic stochastic', 0.5044676065444946), ('singular stochastic', 0.4915240705013275), ('quantum fields', 0.48142120242118835), ('singular stochastic partial', 0.4711681306362152), ('quantum field', 0.461696982383728), ('quantization', 0.45796826481819153), ('stochastic partial differential', 0.4522290527820587)]"
429,429,70,429_hochschild cohomology_hochschild cohomology groups_first hochschild cohomology_hochschild homology,"['hochschild cohomology', 'hochschild cohomology groups', 'first hochschild cohomology', 'hochschild homology', 'gerstenhaber algebra structure', 'cohomology coefficients', 'cohomology twisted', 'cohomology symmetric', 'classical cohomology', 'gerstenhaber algebra']","['On the first relative Hochschild cohomology and contracted fundamental\n  group   In this paper we investigate the Lie algebra structure of the first relative\nHochschild cohomology and its relation with the relative notion of fundamental\ngroup. Let $A,B$ be finite-dimensional basic $k$-algebras over an algebraically\nclosed field of characteristic zero, such that $Q_B$ is a subquiver of $Q_A$.\nWe show that if the complement of $Q_A$ by the arrows of $Q_B$ is a simple\ndirected graph, then the first relative Hochschild cohomology\n$\\text{HH}^1(A|B)$ is a solvable Lie algebra. We also compute the Lie algebra\nstructure of the first relative Hochschild cohomology for radical square zero\nalgebras and for dual extension algebras of directed monomial algebras.\nFinally, we introduce the notion of fundamental group for a pair of an algebra\n$A$ and a subalgebra $B$ and we construct the relative version of the map from\nthe dual fundamental group into the first Hochschild cohomology.\n', 'Hochschild cohomology of twisted tensor products   For a tensor product of algebras twisted by a bicharacter, we completely\ndescribe its Hochschild cohomology, as a Gerstenhaber algebra, in terms of the\nHochschild cohomology of its component parts. This description generalizes a\nresult of Bergh and Oppermann. It allows us to significantly simplify various\ncalculations in the literature, and to compute Hochschild cohomology for a\nnumber of new examples.\n', 'Traces, Schubert calculus, and Hochschild cohomology of category\n  $\\mathcal{O}$   We discuss how the Hochschild cohomology of a dg category can be computed as\nthe trace of its Serre functor. Applying this approach to the principal block\nof the Bernstein--Gelfand--Gelfand category $\\mathcal{O}$, we obtain its\nHochschild cohomology as the compactly supported cohomology of an associated\nspace. Equivalently, writing $\\mathcal{O}$ as modules over the endomorphism\nalgebra $A$ of a minimal projective generator, this is the Hochschild\ncohomology of $A$. In particular our computation gives the Euler characteristic\nof the Hochschild cohomology of $\\mathcal{O}$ in type A.\n']","[('hochschild cohomology', 0.7434208989143372), ('hochschild cohomology groups', 0.7255613207817078), ('first hochschild cohomology', 0.7159214019775391), ('hochschild homology', 0.6983351707458496), ('gerstenhaber algebra structure', 0.6206328272819519), ('cohomology coefficients', 0.5811200141906738), ('cohomology twisted', 0.5673642754554749), ('cohomology symmetric', 0.565127432346344), ('classical cohomology', 0.5603671073913574), ('gerstenhaber algebra', 0.5598496198654175)]"
430,430,70,430_convergence fourier series_convergence fourier_convergence summability_approximations fourier,"['convergence fourier series', 'convergence fourier', 'convergence summability', 'approximations fourier', 'fourier series', 'summability methods', 'summability', 'almost everywhere convergence', 'integrable functions', 'everywhere convergence']","['Lebesgue and Vilenkin-Lebesgue points and a. e. Convergence of N\\""orlund\n  means with respect to Vilenkin systems of integrable functions   In this paper we derive converge of N\\""orlund means of Vilenkin-Fourier\nseries with monotone coefficients of integrable functions in Lebesgue and\nVilinkin-Lebesgue points. Moreover, we discuss pointwise and norm convergence\nin $L_p$ norms of such N\\""orlund means.\n', 'Convergence and Strong Summability of the Two-dimensional\n  Vilenkin-Fourier Series   In this paper we investigate convergence and strong summability of the\ntwo-dimensional Vilenkin-Fourier series in the martingale Hardy spaces.\n', 'On the almost everywhere and norm convergences of N\\""orlund means with\n  respect to Vilenkin systems   Unlike the classical theory of Fourier series which deals with decomposition\nof a function into sinusoidal waves the Vilenkin (Walsh) functions are\nrectangular waves. The development of the theory of Vilenkin-Fourier series has\nbeen strongly influenced by the classical theory of trigonometric series but\nthere are a lot of differences also. The aim of my master thesis is to discuss,\ndevelop and apply the newest developments of this fascinating theory connected\nto modern harmonic analysis. In particular, we investigate N\\""orlund means but\nonly in the case when their coefficients are monotone and prove convergence in\nLebesgue and Vilenkin-Lebesgue points. Since almost everywhere points are\nLebesgue and Vilenkin-Lebesgue points for any integrable functions we obtain\nalmost everywhere convergence of such summability methods.\n']","[('convergence fourier series', 0.556429386138916), ('convergence fourier', 0.5309114456176758), ('convergence summability', 0.5266607999801636), ('approximations fourier', 0.49333474040031433), ('fourier series', 0.45677655935287476), ('summability methods', 0.44128987193107605), ('summability', 0.4384327530860901), ('almost everywhere convergence', 0.42663079500198364), ('integrable functions', 0.42606398463249207), ('everywhere convergence', 0.4040256142616272)]"
431,431,70,431_symplectic manifolds_symplectic manifold_symplectic geometry_canonical symplectic,"['symplectic manifolds', 'symplectic manifold', 'symplectic geometry', 'canonical symplectic', 'symplectic reduction', 'symplectic structure', 'symplectic actions', 'reduction symplectic', 'actions symplectic', 'structure symplectic']","[""From Symplectic to Poisson. A Study of Reduction and a Proposal Towards\n  Implosion   The imploded cross-section of a symplectic manifold is a stratified space\nallowing for an abelianization of its symplectic reduction. After recalling\nsymplectic and Poisson reduction and reviewing the basics of symplectic\nimplosion, we prove a cross-section theorem for Poisson manifolds, generalizing\nthe Guillemin-Sternberg theorem for symplectic manifolds, which constitutes a\nfirst step towards Poisson implosion. On our way, we find and fix a mistake in\nthe proof of Guillemin-Sternberg's theorem, and we identify Poisson\ntransversals as the right analogue to symplectic submanifolds in this context.\n"", ""Stacky Hamiltonian actions and symplectic reduction   We introduce the notion of a Hamiltonian action of an \\'etale Lie group stack\non an \\'etale symplectic stack and establish versions of the Kirwan convexity\ntheorem, the Meyer-Marsden-Weinstein symplectic reduction theorem, and the\nDuistermaat-Heckman theorem in this context.\n"", 'Stratification of the transverse momentum map   Given a Hamiltonian action of a proper symplectic groupoid (for instance, a\nHamiltonian action of a compact Lie group), we show that the transverse\nmomentum map admits a natural constant rank stratification. To this end, we\nconstruct a refinement of the canonical stratification associated to the Lie\ngroupoid action (the orbit type stratification, in the case of a Hamiltonian\nLie group action) that seems not to have appeared before, even in the\nliterature on Hamiltonian Lie group actions. This refinement turns out to be\ncompatible with the Poisson geometry of the Hamiltonian action: it is a Poisson\nstratification of the orbit space, each stratum of which is a regular Poisson\nmanifold that admits a natural proper symplectic groupoid integrating it. The\nmain tools in our proofs (which we believe could be of independent interest)\nare a version of the Marle-Guillemin-Sternberg normal form theorem for\nHamiltonian actions of proper symplectic groupoids and a notion of equivalence\nbetween Hamiltonian actions of symplectic groupoids, closely related to Morita\nequivalence between symplectic groupoids.\n']","[('symplectic manifolds', 0.7501591444015503), ('symplectic manifold', 0.7317120432853699), ('symplectic geometry', 0.7174208164215088), ('canonical symplectic', 0.7080197930335999), ('symplectic reduction', 0.7020606398582458), ('symplectic structure', 0.6955626010894775), ('symplectic actions', 0.6895765066146851), ('reduction symplectic', 0.6851004362106323), ('actions symplectic', 0.6746052503585815), ('structure symplectic', 0.6636552810668945)]"
432,432,70,432_fusion systems_theory fusion_fusion_representations fusion,"['fusion systems', 'theory fusion', 'fusion', 'representations fusion', 'systems groups', 'systems prime', 'sylow subgroups', 'class groups', 'centralizers', 'systems maximal']","['Fusion systems with some sporadic J-components   Aschbacher\'s program for the classification of simple fusion systems of ""odd""\ntype at the prime 2 has two main stages: the classification of 2-fusion systems\nof subintrinsic component type and the classification of 2-fusion systems of\nJ-component type. We make a contribution to the latter stage by classifying\n2-fusion systems with a J-component isomorphic to the 2-fusion systems of\nseveral sporadic groups under the assumption that the centralizer of such a\ncomponent is cyclic.\n', 'Proving a conjecture for fusion systems on a class of groups   We prove the conjecture that exotic and block-exotic fusion systems coincide\nholds for all fusion systems on exceptional $p$-groups of maximal nilpotency\nclass, where $p \\geq 5$. This is done by considering a family of exotic fusion\nsystems discovered by Parker and Stroth. Together with a previous result by the\nauthor, which we also generalise in this paper, and a result by Grazian and\nParker this implies the conjecture for fusion systems on such groups.\nConsidering small primes, there are no exotic fusion systems on $2$-groups of\nmaximal class and for $p = 3$, we prove block-exoticity of two exotic fusion\nsystems described by Diaz--Ruiz--Viruel.\n', 'Fusion systems on a Sylow $p$-subgroup of $SU_4(p)$   We determine, for $p$ odd, all saturated fusion systems on a Sylow\n$p$-subgroup $S$ of the unitary group $SU_4(p)$ and we prove that they are all\nrealizable by finite groups. In particular, we prove that $S$ does not support\nany exotic fusion systems.\n']","[('fusion systems', 0.6558826565742493), ('theory fusion', 0.6090428233146667), ('fusion', 0.5724871754646301), ('representations fusion', 0.4946197271347046), ('systems groups', 0.4513149559497833), ('systems prime', 0.3853203356266022), ('sylow subgroups', 0.3782992660999298), ('class groups', 0.37717458605766296), ('centralizers', 0.3716740310192108), ('systems maximal', 0.36099159717559814)]"
433,433,70,433_terahertz thz communications_terahertz communications_terahertz thz communication_thz communications,"['terahertz thz communications', 'terahertz communications', 'terahertz thz communication', 'thz communications', 'terahertz thz band', 'thz systems', 'thz communication', 'hybrid beamforming architecture', 'terahertz thz', 'hybrid beamforming']","['Terahertz Near-Field Communications and Sensing   This article focuses on the near-field effect in terahertz (THz)\ncommunications and sensing systems. By equipping with extremely large-scale\nantenna arrays (ELAAs), the near-field region in THz systems can be possibly\nextended to hundreds of meters in proximity to THz transceivers, which\nnecessitates the consideration of near-field effect in the THz band both for\nthe communications and sensing. We first review the main characteristics of the\nnear-field region in the THz bands. The signal propagation in the near-field\nregion is characterized by spherical waves rather than planar waves in the\nfar-field region. This distinction introduces a new distance dimension to the\ncommunication and sensing channels, which brings new opportunities and\nchallenges for both THz communications and sensing. More particularly, 1) For\nTHz communications, the near-field effect enables a new mechanism for\nbeamforming, namely, beamfocusing, in the focusing region. Furthermore, in THz\nmultiple-input and multiple-output (MIMO) systems, the near-field effect can be\nexploited to combat the multiplexing gain degradation caused by the sparse THz\nchannels. To address the near-field beam split effect caused by the\nconventional frequency-independent hybrid beamforming architecture in THz\nwideband communications, we propose a pair of wideband beamforming optimization\napproaches by a new hybrid beamforming architecture based on true-time-delayers\n(TTDs). 2) For THz sensing, joint angle and distance sensing can be achieved in\nthe near-field region. Additionally, the near-field beam split becomes a\nbeneficial effect for enhancing the sensing performance by focusing on multiple\npossible target locations rather than a drawback encountered in communications.\nFinally, several topics for future research are discussed.\n', 'Hybrid Beamforming for Terahertz Wireless Communications: Challenges,\n  Architectures, and Open Problems   Terahertz (THz) communications are regarded as a pillar technology for the\nsixth generation (6G) wireless systems, by offering multi-ten-GHz bandwidth. To\novercome the short transmission distance and huge propagation loss,\nultra-massive (UM) MIMO systems that employ sub-millimeter wavelength antennas\narray are proposed to enable an enticingly high array gain. In the UM-MIMO\nsystems, hybrid beamforming stands out for its great potential in promisingly\nhigh data rate and reduced power consumption. In this paper, challenges and\nfeatures of the THz hybrid beamforming design are investigated, in light of the\ndistinctive THz peculiarities. Specifically, we demonstrate that the spatial\ndegree-of-freedom (SDoF) is less than 5, which is caused by the extreme\nsparsity of the THz channel. The blockage problem caused by the huge reflection\nand scattering losses, as high as 15 dB or over, is studied. Moreover, we\nanalyze the challenges led by the array containing 1024 or more antennas,\nincluding the requirement for intelligent subarray architecture, strict energy\nefficiency, and propagation characterization based on spherical-wave\npropagation mechanisms. Owning up to hundreds of GHz bandwidth, beam squint\neffect could cause over 5~dB array gain loss, when the fractional bandwidth\nexceeds 10%. Inspired by these facts, three novel THz-specific hybrid\nbeamforming architectures are presented, including widely-spaced\nmulti-subarray, dynamic array-of-subarrays, and true-time-delay-based\narchitectures. We also demonstrate the potential data rate, power consumption,\nand array gain capabilities for THz communications. As a roadmap of THz hybrid\nbeamforming design, multiple open problems and potential research directions\nare elaborated.\n', 'Beamforming Technologies for Ultra-Massive MIMO in Terahertz\n  Communications   Terahertz (THz) communications with a frequency band $0.1-10$ THz are\nenvisioned as a promising solution to future high-speed wireless communication.\nAlthough with tens of gigahertz available bandwidth, THz signals suffer from\nsevere free-spreading loss and molecular-absorption loss, which limit the\nwireless transmission distance. To compensate for the propagation loss, the\nultra-massive multiple-input-multiple-output (UM-MIMO) can be applied to\ngenerate a high-gain directional beam by beamforming technologies. In this\npaper, a review of beamforming technologies for THz UM-MIMO systems is\nprovided. Specifically, we first present the system model of THz UM-MIMO and\nidentify its channel parameters and architecture types. Then, we illustrate the\nbasic principles of beamforming via UM-MIMO and discuss the far-field and\nnear-field assumptions in THz UM-MIMO. Moreover, an important beamforming\nstrategy in THz band, i.e., beam training, is introduced wherein the beam\ntraining protocol and codebook design approaches are summarized. The\nintelligent-reflecting-surface (IRS)-assisted joint beamforming and multi-user\nbeamforming in THz UM-MIMO systems are studied, respectively. The\nspatial-wideband effect and frequency-wideband effect in the THz beamforming\nare analyzed and the corresponding solutions are provided. Further, we present\nthe corresponding fabrication techniques and illuminate the emerging\napplications benefiting from THz beamforming. Open challenges and future\nresearch directions on THz UM-MIMO systems are finally highlighted.\n']","[('terahertz thz communications', 0.6684570908546448), ('terahertz communications', 0.6599503755569458), ('terahertz thz communication', 0.6105765104293823), ('thz communications', 0.5866559743881226), ('terahertz thz band', 0.5182515382766724), ('thz systems', 0.50868159532547), ('thz communication', 0.4941602051258087), ('hybrid beamforming architecture', 0.4622153043746948), ('terahertz thz', 0.45512232184410095), ('hybrid beamforming', 0.45081108808517456)]"
434,434,69,434_discretization stochastic_stochastic allen cahn_approximations stochastic_stochastic allen,"['discretization stochastic', 'stochastic allen cahn', 'approximations stochastic', 'stochastic allen', 'approximation stochastic', 'stochastic wave equations', 'parabolic stochastic', 'parabolic stochastic partial', 'stochastic semilinear', 'nonlinear stochastic']","['Lower and upper bounds for strong approximation errors for numerical\n  approximations of stochastic heat equations   Optimal upper and lower error estimates for strong full-discrete numerical\napproximations of the stochastic heat equation driven by space-time white noise\nare obtained. In particular, we establish the optimality of strong convergence\nrates for full-discrete approximations of stochastic Allen-Cahn equations with\nspace-time white noise which have recently been obtained in [Becker, S., Gess,\nB., Jentzen, A., and Kloeden, P. E., Strong convergence rates for explicit\nspace-time discrete numerical approximations of stochastic Allen-Cahn\nequations. arXiv:1711.02423 (2017)].\n', 'Strong convergence rates for explicit space-time discrete numerical\n  approximations of stochastic Allen-Cahn equations   The scientific literature contains a number of numerical approximation\nresults for stochastic partial differential equations (SPDEs) with\nsuperlinearly growing nonlinearities but, to the best of our knowledge, none of\nthem prove strong or weak convergence rates for full-discrete numerical\napproximations of space-time white noise driven SPDEs with superlinearly\ngrowing nonlinearities. In particular, in the scientific literature there\nexists neither a result which proves strong convergence rates nor a result\nwhich proves weak convergence rates for full-discrete numerical approximations\nof stochastic Allen-Cahn equations. In this article we bridge this gap and\nestablish strong convergence rates for full-discrete numerical approximations\nof space-time white noise driven SPDEs with superlinearly growing\nnonlinearities such as stochastic Allen-Cahn equations. Moreover, we also\nestablish lower bounds for strong temporal and spatial approximation errors\nwhich demonstrate that our strong convergence rates are essentially sharp and\ncan, in general, not be improved.\n', 'An efficient explicit full-discrete scheme for strong approximation of\n  stochastic Allen-Cahn equation   In Becker and Jentzen (2019) and Becker et al. (2017), an explicit temporal\nsemi-discretization scheme and a space-time full-discretization scheme were,\nrespectively, introduced and analyzed for the additive noise-driven stochastic\nAllen-Cahn type equations, with strong convergence rates recovered. The present\nwork aims to propose a different explicit full-discrete scheme to numerically\nsolve the stochastic Allen-Cahn equation with cubic nonlinearity, perturbed by\nadditive space-time white noise. The approximation is easily implementable,\nperforming the spatial discretization by a spectral Galerkin method and the\ntemporal discretization by a kind of nonlinearity-tamed accelerated exponential\nintegrator scheme. Error bounds in a strong sense are analyzed for both the\nspatial semi-discretization and the spatio-temporal full discretization, with\nconvergence rates in both space and time explicitly identified. It turns out\nthat the obtained convergence rate of the new scheme is, in the temporal\ndirection, twice as high as existing ones in the literature. Numerical results\nare finally reported to confirm the previous theoretical findings.\n']","[('discretization stochastic', 0.6437339186668396), ('stochastic allen cahn', 0.6279503703117371), ('approximations stochastic', 0.6002830266952515), ('stochastic allen', 0.5761711001396179), ('approximation stochastic', 0.5729718208312988), ('stochastic wave equations', 0.544739305973053), ('parabolic stochastic', 0.5128073692321777), ('parabolic stochastic partial', 0.5073893666267395), ('stochastic semilinear', 0.5026876330375671), ('nonlinear stochastic', 0.49634894728660583)]"
435,435,69,435_output feedback stabilization_boundary feedback_boundary stabilization_feedback boundary,"['output feedback stabilization', 'boundary feedback', 'boundary stabilization', 'feedback boundary', 'feedback stabilization', 'boundary control', 'output feedback controller', 'output feedback control', 'pde backstepping', 'pde systems']","['Boundary Output Feedback Stabilization of Reaction-Diffusion PDEs with\n  Delayed Boundary Measurement   This paper addresses the boundary output feedback stabilization of general\n1-D reaction-diffusion PDEs with delayed boundary measurement. The output takes\nthe form of a either Dirichlet or Neumann trace. The output delay can be\narbitrarily large. The control strategy is composed of a finite-dimensional\nobserver that is used to observe a delayed version of the first modes of the\nPDE and a predictor component which is employed to obtain the control input to\nbe applied at current time. For any given value of the output delay, we assess\nthe stability of the resulting closed-loop system provided the order of the\nobserver is selected large enough. Taking advantage of this result, we discuss\nthe extension of the control strategy to the case of simultaneous input and\noutput delays.\n', 'Boundary Output Feedback Stabilization of State Delayed\n  Reaction-Diffusion PDEs   This paper studies the boundary output feedback stabilization of general 1-D\nreaction-diffusion PDEs in the presence of a state delay in the reaction term.\nThe control input applies through a Robin boundary condition while the system\noutput is selected as a either Dirichlet or Neumann boundary trace. The control\nstrategy takes the form of a finite-dimensional observer-based controller with\nfeedback and observer gains that are computed in order to dominate the state\ndelayed term. For any arbitrarily given value of the state delay, we show the\nexponential stability of the resulting closed-loop system provided the order of\nthe observer is selected large enough.\n', 'Observer-Based Output-Feedback Backstepping Stabilization of Continua of\n  Hyperbolic PDEs and Application to Large-Scale $n+m$ Coupled Hyperbolic PDEs   We develop a non-collocated, observer-based output-feedback law for a class\nof continua of linear hyperbolic PDE systems, which are viewed as the continuum\nversion of $n+m$, general heterodirectional hyperbolic systems as $n\\to\\infty$.\nThe design relies on the introduction of a novel, continuum PDE backstepping\ntransformation, which enables the construction of a Lyapunov functional for the\nestimation error system. Stability under the observer-based output-feedback law\nis established by using the Lyapunov functional construction for the estimation\nerror system and proving well-posedness of the complete closed-loop system,\nwhich allows utilization of the separation principle.\n  Motivated by the fact that the continuum-based designs may provide\ncomputationally tractable control laws for large-scale, $n+m$ systems, we then\nutilize the control/observer kernels and the observer constructed for the\ncontinuum system to introduce an output-feedback control design for the\noriginal $n+m$ system. We establish exponential stability of the resulting\nclosed-loop system, which consists of a mixed $n+m$-continuum PDE system\n(comprising the plant-observer dynamics), introducing a virtual continuum\nsystem with resets, which enables utilization of the continuum approximation\nproperty of the solutions of the $n+m$ system by its continuum counterpart (for\nlarge $n$). We illustrate the potential computational complexity/flexibility\nbenefits of our approach via a numerical example of stabilization of a\nlarge-scale $n+m$ system, for which we employ the continuum observer-based\ncontroller, while the continuum-based stabilizing control/observer kernels can\nbe computed in closed form.\n']","[('output feedback stabilization', 0.5635818839073181), ('boundary feedback', 0.5615407228469849), ('boundary stabilization', 0.5592047572135925), ('feedback boundary', 0.5249781608581543), ('feedback stabilization', 0.5144673585891724), ('boundary control', 0.4985077381134033), ('output feedback controller', 0.49661922454833984), ('output feedback control', 0.4917483925819397), ('pde backstepping', 0.4548260569572449), ('pde systems', 0.45023688673973083)]"
436,436,69,436_phase retrieval via_phase retrieval_retrieval phase retrieval_phase retrieval phase,"['phase retrieval via', 'phase retrieval', 'retrieval phase retrieval', 'phase retrieval phase', 'compressed sensing', 'compressive sensing', 'recovering sparse', 'sparse signals', 'sparse signal', 'recover sparse']","['Inertial Proximal ADMM for Separable Multi-Block Convex Optimizations\n  and Compressive Affine Phase Retrieval   Separable multi-block convex optimization problem appears in many\nmathematical and engineering fields. In the first part of this paper, we\npropose an inertial proximal ADMM to solve a linearly constrained separable\nmulti-block convex optimization problem, and we show that the proposed inertial\nproximal ADMM has global convergence under mild assumptions on the\nregularization matrices. Affine phase retrieval arises in holography, data\nseparation and phaseless sampling, and it is also considered as a\nnonhomogeneous version of phase retrieval that has received considerable\nattention in recent years. Inspired by convex relaxation of vector sparsity and\nmatrix rank in compressive sensing and by phase lifting in phase retrieval, in\nthe second part of this paper, we introduce a compressive affine phase\nretrieval via lifting approach to connect affine phase retrieval with\nmulti-block convex optimization, and then based on the proposed inertial\nproximal ADMM for multi-block convex optimization, we propose an algorithm to\nrecover sparse real signals from their (noisy) affine quadratic measurements.\nOur numerical simulations show that the proposed algorithm has satisfactory\nperformance for affine phase retrieval of sparse real signals.\n', 'Strong convexity of affine phase retrieval   The recovery of a signal from the intensity measurements with some entries\nbeing known in advance is termed as {\\em affine phase retrieval}. In this\npaper, we prove that a natural least squares formulation for the affine phase\nretrieval is strongly convex on the entire space under some mild conditions,\nprovided the measurements are complex Gaussian random vecotrs and the\nmeasurement number $m \\gtrsim d \\log d$ where $d$ is the dimension of signals.\nBased on the result, we prove that the simple gradient descent method for the\naffine phase retrieval converges linearly to the target solution with high\nprobability from an arbitrary initial point. These results show an essential\ndifference between the affine phase retrieval and the classical phase\nretrieval, where the least squares formulations for the classical phase\nretrieval are non-convex.\n', 'Solving phase retrieval with random initial guess is nearly as good as\n  by spectral initialization   The problem of recovering a signal $\\mathbf{x}\\in \\mathbb{R}^n$ from a set of\nmagnitude measurements $y_i=|\\langle \\mathbf{a}_i, \\mathbf{x} \\rangle |, \\;\ni=1,\\ldots,m$ is referred as phase retrieval, which has many applications in\nfields of physical sciences and engineering. In this paper we show that the\nsmoothed amplitude flow model for phase retrieval has benign geometric\nstructure under the optimal sampling complexity. In particular, we show that\nwhen the measurements $\\mathbf{a}_i\\in \\mathbb{R}^n$ are Gaussian random\nvectors and the number of measurements $m\\ge Cn$, our smoothed amplitude flow\nmodel has no spurious local minimizers with high probability, ie., the target\nsolution $\\mathbf{x}$ is the unique global minimizer (up to a global phase) and\nthe loss function has a negative directional curvature around each saddle\npoint. Due to this benign geometric landscape, the phase retrieval problem can\nbe solved by the gradient descent algorithms without spectral initialization.\nNumerical experiments show that the gradient descent algorithm with random\ninitialization performs well even comparing with state-of-the-art algorithms\nwith spectral initialization in empirical success rate and convergence speed.\n']","[('phase retrieval via', 0.7242335081100464), ('phase retrieval', 0.691697359085083), ('retrieval phase retrieval', 0.6267639398574829), ('phase retrieval phase', 0.6167480945587158), ('compressed sensing', 0.5794746279716492), ('compressive sensing', 0.558795690536499), ('recovering sparse', 0.5358235836029053), ('sparse signals', 0.5068024396896362), ('sparse signal', 0.47604697942733765), ('recover sparse', 0.4490545392036438)]"
437,437,69,437_expander graphs_expander graph_spectral expander_vertex expansion,"['expander graphs', 'expander graph', 'spectral expander', 'vertex expansion', 'ramanujan graphs', 'expanders', 'edge expansion', 'expansion small', 'spectral expansion', 'expansion defined']","['New Cosystolic Expanders from Tensors Imply Explicit Quantum LDPC Codes\n  with $\\Omega(\\sqrt{n}\\log^kn)$ Distance   In this work we introduce a new notion of expansion in higher dimensions that\nis stronger than the well studied cosystolic expansion notion, and is termed\n{\\em Collective-cosystolic expansion}.\n  We show that tensoring two cosystolic expanders yields a new cosystolic\nexpander, assuming one of the complexes in the product, is not only cosystolic\nexpander, but rather a collective cosystolic expander.\n  We then show that the well known bounded degree cosystolic expanders, the\nRamanujan complexes are, in fact, collective cosystolic expanders. This enables\nus to construct new bounded degree cosystolic expanders, by tensoring of\nRamanujan complexes.\n  Using our new constructed bounded degree cosystolic expanders we construct\n{\\em explicit} quantum LDPC codes of distance $\\sqrt{n} \\log^k n$ for any $k$,\nimproving a recent result of Evra et. al. \\cite{EKZ}, and setting a new record\nfor distance of explicit quantum LDPC codes.\n  The work of \\cite{EKZ} took advantage of the high dimensional expansion\nnotion known as cosystolic expansion, that occurs in Ramanujan complexes. Our\nimprovement is achieved by considering tensor product of Ramanujan complexes,\nand using their newly derived property, the collective cosystolic expansion.\n', ""New High Dimensional Expanders from Covers   We present a new construction of high dimensional expanders based on covering\nspaces of simplicial complexes. High dimensional expanders (HDXs) are\nhypergraph analogues of expander graphs. They have many uses in theoretical\ncomputer science, but unfortunately only few constructions are known which have\narbitrarily small local spectral expansion.\n  We give a randomized algorithm that takes as input a high dimensional\nexpander $X$ (satisfying some mild assumptions). It outputs a sub-complex $Y\n\\subseteq X$ that is a high dimensional expander and has infinitely many\nsimplicial covers. These covers form new families of bounded-degree high\ndimensional expanders. The sub-complex $Y$ inherits $X$'s underlying graph and\nits links are sparsifications of the links of $X$. When the size of the links\nof $X$ is $O(\\log |X|)$, this algorithm can be made deterministic. Our\nalgorithm is based on the groups and generating sets discovered by Lubotzky,\nSamuels and Vishne (2005), that were used to construct the first discovered\nhigh dimensional expanders. We show these groups give rise to many more\n``randomized'' high dimensional expanders.\n  In addition, our techniques also give a random sparsification algorithm for\nhigh dimensional expanders, that maintains its local spectral properties. This\nmay be of independent interest.\n"", 'Combinatorics via Closed Orbits: Number Theoretic Ramanujan Graphs are\n  not Unique Neighbor Expanders   The question of finding expander graphs with strong vertex expansion\nproperties such as unique neighbor expansion and lossless expansion is central\nto computer science. A barrier to constructing these is that strong notions of\nexpansion could not be proven via the spectral expansion paradigm.\n  A very symmetric and structured family of optimal spectral expanders (i.e.,\nRamanujan graphs) was constructed using number theory by Lubotzky, Phillips and\nSarnak, and was subsequently generalized by others. We call such graphs Number\nTheoretic Ramanujan Graphs. These graphs are not only spectrally optimal, but\nalso posses strong symmetries and rich structure. Thus, it has been widely\nconjectured that number theoretic Ramanujan graphs are lossless expanders, or\nat least unique neighbor expanders.\n  In this work we disprove this conjecture, by showing that there are number\ntheoretic Ramanujan graphs that are not even unique neighbor expanders. This is\ndone by introducing a new combinatorial paradigm that we term the closed orbit\nmethod.\n  The closed orbit method allows one to construct finite combinatorial objects\nwith extermal substructures. This is done by observing that there exist\ninfinite combinatorial structures with extermal substructures, coming from an\naction of a subgroup of the automorphism group of the structure. The crux of\nour idea is a systematic way to construct a finite quotient of the infinite\nstructure containing a simple shadow of the infinite substructure, which\nmaintains its extermal combinatorial property.\n  Other applications of the method are to the edge expansion of number\ntheoretic Ramanujan graphs and vertex expansion of Ramanujan complexes.\nFinally, in the field of graph quantum ergodicity we produce number theoretic\nRamanujan graphs with an eigenfunction of small support that corresponds to the\nzero eigenvalue. This again contradicts common expectations.\n']","[('expander graphs', 0.6640743017196655), ('expander graph', 0.5776554942131042), ('spectral expander', 0.5770860910415649), ('vertex expansion', 0.5534707903862), ('ramanujan graphs', 0.5279740691184998), ('expanders', 0.5153231620788574), ('edge expansion', 0.4913121163845062), ('expansion small', 0.48499050736427307), ('spectral expansion', 0.4827525317668915), ('expansion defined', 0.46735748648643494)]"
438,438,69,438_quandles_quandle_arising groups_knot theory,"['quandles', 'quandle', 'arising groups', 'knot theory', 'groups generators', 'associated groups', 'automorphisms', 'trivial idempotents', 'non trivial idempotents', 'idempotents']","['Nilpotent quandles   A nilpotent quandle is a quandle whose inner automorphism group is nilpotent.\nSuch quandles have been called reductive in previous works, but it turns out\nthat their behaviour is in fact very close to nilpotency for groups. In\nparticular, we show that it is easy to characterise generating sets of such\nquandles, and that they have the Hopf property. We also show how to construct\nfree nilpotent quandles from free nilpotent groups. We then use the properties\nof nilpotent quandles to describe a simple presentation of their associated\ngroup, and we use this to recover the classification of abelian quandles by\nLebed and Mortier [LM21]. We also study reduced quandles, and we show that the\nreduced fundamental quandle is equivalent, as an invariant of links, to the\nreduced peripheral system, sharpening a previous result of Hughes [Hug11].\nFinally, we give a characterisation of nilpotency in terms of the associated\ninvariants of braids.\n', 'Idempotents, free products and quandle coverings   In this paper, we investigate idempotents in quandle rings and relate them\nwith quandle coverings. We prove that integral quandle rings of quandles of\nfinite type that are non-trivial coverings over nice base quandles admit\ninfinitely many non-trivial idempotents, and give their complete description.\nWe show that the set of all these idempotents forms a quandle in itself. As an\napplication, we deduce that the quandle ring of the knot quandle of a\nnon-trivial long knot admit non-trivial idempotents. We consider free products\nof quandles and prove that integral quandle rings of free quandles have only\ntrivial idempotents, giving an infinite family of quandles with this property.\nWe also give a description of idempotents in quandle rings of unions and\ncertain twisted unions of quandles.\n', 'Derivations of quandles   The aim of this paper is to propose a theory of derivations for quandles.\nGiven a quandle $A$ admitting an action by a quandle $Q$, derivations from $Q$\nto $A$ are introduced as twisted analogues of quandle homomorphisms. It is\nshown that for each quandle $Q$ there exists a unique $Q$-quandle\n$\\mathcal{A}_Q$ (the derived quandle of $Q$) such that derivations from $Q$ to\nany $Q$-quandle $A$ are in bijective correspondence with $Q$-quandle\nhomomorphisms from $\\mathcal{A}_Q$ to $A$. Further, it is proved that the set\nof all derivations to an abelian $Q$-quandle $A$ has the structure of an\nabelian quandle, and inherits many other properties from $A$. In the end, the\nideas are extended to the setting of virtual quandles.\n']","[('quandles', 0.6069127917289734), ('quandle', 0.5649697184562683), ('arising groups', 0.4019137918949127), ('knot theory', 0.39837929606437683), ('groups generators', 0.3452865183353424), ('associated groups', 0.3422608971595764), ('automorphisms', 0.33807599544525146), ('trivial idempotents', 0.3321877717971802), ('non trivial idempotents', 0.3284178376197815), ('idempotents', 0.3268849849700928)]"
439,439,69,439_triangles whose_triangles_triangles two_hyperbolic triangles,"['triangles whose', 'triangles', 'triangles two', 'hyperbolic triangles', 'triangles common', 'equilateral triangles', 'spherical triangles', 'triangle', 'triangle three', 'triangle triangle']","[""Heron triangles and the hunt for unicorns   A Heron triangle is one that has all integer side lengths and integer area,\nwhich takes its name from Heron of Alexandria's area formula. From a more\nrelaxed point of view, if rescaling is allowed, then one can define a Heron\ntriangle to be one whose side lengths and area are all rational numbers. A\nperfect triangle is a Heron triangle with all three medians being rational.\nAccording to a longstanding conjecture, no such triangle exists, so perfect\ntriangles are as rare as unicorns.\n  However, if perfect is the enemy of good, then perhaps it is best to insist\non only two of the medians being rational. Buchholz and Rathbun found an\ninfinite family of Heron triangles with two rational medians, which they were\nable to associate with the set of rational points on an elliptic curve\n$E(\\mathbb{Q})$. Here we describe a recently discovered explicit formula for\nthe sides, area and medians of these (almost perfect) triangles, expressed in\nterms of a pair of integer sequences: these are Somos sequences, which first\nbecame popular thanks to David Gale's column in Mathematical Intelligencer.\n"", 'Amicable Heron triangles   A Heron triangle is a triangle whose side lengths and area are integers. Two\nHeron triangles are amicable if the perimeter of one is the area of the other.\nWe show, using elementary techniques, that there is only one pair of amicable\nHeron triangles.\n', 'Spherical Heron triangles and elliptic curves   We define spherical Heron triangles (spherical triangles with ""rational""\nside-lengths and angles) and parametrize them via rational points of certain\nfamilies of elliptic curves. We show that the congruent number problem has\ninfinitely many solutions for most areas in the spherical setting and we find a\nspherical Heron triangle with rational medians. We also explore the question of\nspherical triangles with a single rational median or a single a rational area\nbisector (median splitting the triangle in half), and discuss various problems\ninvolving isosceles spherical triangles.\n']","[('triangles whose', 0.5954829454421997), ('triangles', 0.5940314531326294), ('triangles two', 0.5714617967605591), ('hyperbolic triangles', 0.5615163445472717), ('triangles common', 0.5507704019546509), ('equilateral triangles', 0.5456045866012573), ('spherical triangles', 0.5294310450553894), ('triangle', 0.5234453082084656), ('triangle three', 0.5076762437820435), ('triangle triangle', 0.4800568222999573)]"
440,440,69,440_compact topological group_topological groups_groups topological_compact groups,"['compact topological group', 'topological groups', 'groups topological', 'compact groups', 'topological group', 'locally compact group', 'group topology', 'compact group', 'abelian topological', 'countably compact']","['On the continuity of the inverse in (strongly) paratopological\n  gyrogroups   In this paper, we consider the continuity of the inverse in (strongly)\nparatopological gyrogroups. The conclusions are established as follows: (1) A\ncompact Hausdorff paratopological gyrogroup $G$ is a topological gyrogroup. (2)\nA Hausdorff locally compact strongly paratopological gyrogroup is a topological\ngyrogroup. (3) If $G$ is locally compact strongly paratopological\ngyrocommutative gyrogroup (without any separation restrictions), then $G$ is a\nstrongly topological gyrogroup. (4) Every regular feebly compact strongly\nparatopological gyrogroup is a topological gyrogroup. (5) If a Hausdorff\nstrongly paratopological gyrogroup $G$ is countablly compact and topologically\nperiodic, then $G$ is a strongly topological gyrogroup.\n', 'The strong Pytkeev property and strong countable completeness in\n  (strongly) topological gyrogroups   A topological gyrogroup is a gyrogroup endowed with a topology such that the\nbinary operation is jointly continuous and the inverse mapping is also\ncontinuous. In this paper, it is proved that if $G$ is a sequential topological\ngyrogroup with an $\\omega^{\\omega}$-base, then $G$ has the strong Pytkeev\nproperty. Moreover, some equivalent conditions about $\\omega^{\\omega}$-base and\nstrong Pytkeev property are given in Baire topological gyrogroups. Finally, it\nis shown that if $G$ is a strongly countably complete strongly topological\ngyrogroup, then $G$ contains a closed, countably compact, admissible\nsubgyrogroup $P$ such that the quotient space $G/P$ is metrizable and the\ncanonical homomorphism $\\pi :G\\rightarrow G/P$ is closed.\n', 'Separability in (strongly) topological gyrogroups   Separability is one of the most basic and important topological properties.\nIn this paper, the separability in (strongly) topological gyrogroups is\nstudied. It is proved that every first-countable left {\\omega}-narrow strongly\ntopological gyrogroup is separable. Furthermore, it is shown that if a\nfeathered strongly topological gyrogroup G is isomorphic to a subgyrogroup of a\nseparable strongly topological gyrogroup, then G is separable. Therefore, if a\nmetrizable strongly topological gyrogroup G is isomorphic to a subgyrogroup of\na separable strongly topological gyrogroup, then G is separable, and if a\nlocally compact strongly topological gyrogroup G is isomorphic to a\nsubgyrogroup of a separable strongly topological gyrogroup, then G is\nseparable.\n']","[('compact topological group', 0.6590691208839417), ('topological groups', 0.6589993834495544), ('groups topological', 0.6424903869628906), ('compact groups', 0.6147348284721375), ('topological group', 0.6021379828453064), ('locally compact group', 0.6002689599990845), ('group topology', 0.583915114402771), ('compact group', 0.5675554275512695), ('abelian topological', 0.5044041275978088), ('countably compact', 0.4936213493347168)]"
441,441,69,441_groups definable_definable minimal_type definable_groups fields,"['groups definable', 'definable minimal', 'type definable', 'groups fields', 'every definable', 'definable', 'algebraic groups', 'absolute galois groups', 'galois groups', 'definable sets']","['One-dimensional subgroups and connected components in non-abelian\n  $p$-adic definable groups   We generalize two of our previous results on abelian definable groups in\n$p$-adically closed fields to the non-abelian case. First, we show that if $G$\nis a definable group that is not definably compact, then $G$ has a\none-dimensional definable subgroup which is not definably compact. This is a\n$p$-adic analogue of the Peterzil-Steinhorn theorem for o-minimal theories.\nSecond, we show that if $G$ is a group definable over the standard model\n$\\mathbb{Q}_p$, then $G^0 = G^{00}$. As an application, definably amenable\ngroups over $\\mathbb{Q}_p$ are open subgroups of algebraic groups, up to finite\nfactors. We also prove that $G^0 = G^{00}$ when $G$ is a definable subgroup of\na linear algebraic group, over any model.\n', 'On groups with definable $f$-generics definable in $p$-adically closed\n  fields   The aim of this paper is to develop the theory of groups definable in the\n$p$-adic field ${\\mathbb Q}_p$, with ``definable $f$-generics"" in the sense of\nan ambient saturated elementary extension of ${\\mathbb Q}_p$. We call such\ngroups definable $f$-generic groups.\n  So, by a ``definable f-generic\'\' or dfg group we mean a definable group in a\nsaturated model with a global f-generic type which is definable over a small\nmodel. In the present context the group is definable over ${\\mathbb Q}_p$, and\nthe small model will be ${\\mathbb Q}_p$ itself. The notion of a dfg group is\ndual, or rather opposite to that of an fsg group (group with ``finitely\nsatisfiable generics"") and is a useful tool to describe the analogue of torsion\nfree o-minimal groups in the $p$-adic context.\n  In the current paper our group will be definable over ${\\mathbb Q}_p$ in an\nambient saturated elementary extension $\\mathbb K$ of ${\\mathbb Q}_p$, so as to\nmake sense of the notions of $f$-generic etc. In this paper we will show that\nevery definable $f$-generic group definable in ${\\mathbb Q}_p$ is virtually\nisomorphic to a finite index subgroup of a trigonalizable algebraic group over\n${\\mathbb Q}_p$. This is analogous to the $o$-minimal context, where every\nconnected torsion free group definable in $\\mathbb R$ is isomorphic to a\ntrigonalizable algebraic group (Lemma 3.4, \\cite{COS}). We will also show that\nevery open definable $f$-generic subgroup of a definable $f$-generic group has\nfinite index, and every $f$-generic type of a definable $f$-generic group is\nalmost periodic, which gives a positive answer to the problem raised in\n\\cite{P-Y} of whether $f$-generic types coincide with almost periodic types in\nthe $p$-adic case.\n', 'Abelian groups definable in $p$-adically closed fields   Recall that a group $G$ has finitely satisfiable generics ($fsg$) or\ndefinable $f$-generics ($dfg$) if there is a global type $p$ on $G$ and a small\nmodel $M_0$ such that every left translate of $p$ is finitely satisfiable in\n$M_0$ or definable over $M_0$, respectively. We show that any abelian group\ndefinable in a $p$-adically closed field is an extension of a definably compact\n$fsg$ definable group by a $dfg$ definable group. We discuss an approach which\nmight prove a similar statement for interpretable abelian groups. In the case\nwhere $G$ is an abelian group definable in the standard model $\\mathbb{Q}_p$,\nwe show that $G^0 = G^{00}$, and that $G$ is an open subgroup of an algebraic\ngroup, up to finite factors. This latter result can be seen as a rough\nclassification of abelian definable groups in $\\mathbb{Q}_p$.\n']","[('groups definable', 0.615484893321991), ('definable minimal', 0.53328537940979), ('type definable', 0.5021486878395081), ('groups fields', 0.48309510946273804), ('every definable', 0.47211411595344543), ('definable', 0.4455510973930359), ('algebraic groups', 0.44361788034439087), ('absolute galois groups', 0.43314874172210693), ('galois groups', 0.431674063205719), ('definable sets', 0.4300747513771057)]"
442,442,68,442_stochastic games_sum stochastic games_markov games_games convergence,"['stochastic games', 'sum stochastic games', 'markov games', 'games convergence', 'zero sum games', 'equilibrium game', 'nash equilibrium game', 'nash equilibrium', 'learning dynamics', 'learning agents']","[""Synchronization in Learning in Periodic Zero-Sum Games Triggers\n  Divergence from Nash Equilibrium   Learning in zero-sum games studies a situation where multiple agents\ncompetitively learn their strategy. In such multi-agent learning, we often see\nthat the strategies cycle around their optimum, i.e., Nash equilibrium. When a\ngame periodically varies (called a ``periodic'' game), however, the Nash\nequilibrium moves generically. How learning dynamics behave in such periodic\ngames is of interest but still unclear. Interestingly, we discover that the\nbehavior is highly dependent on the relationship between the two speeds at\nwhich the game changes and at which players learn. We observe that when these\ntwo speeds synchronize, the learning dynamics diverge, and their time-average\ndoes not converge. Otherwise, the learning dynamics draw complicated cycles,\nbut their time-average converges. Under some assumptions introduced for the\ndynamical systems analysis, we prove that this behavior occurs. Furthermore,\nour experiments observe this behavior even if removing these assumptions. This\nstudy discovers a novel phenomenon, i.e., synchronization, and gains insight\nwidely applicable to learning in periodic games.\n"", 'Towards convergence to Nash equilibria in two-team zero-sum games   Contemporary applications of machine learning in two-team e-sports and the\nsuperior expressivity of multi-agent generative adversarial networks raise\nimportant and overlooked theoretical questions regarding optimization in\ntwo-team games. Formally, two-team zero-sum games are defined as multi-player\ngames where players are split into two competing sets of agents, each\nexperiencing a utility identical to that of their teammates and opposite to\nthat of the opposing team. We focus on the solution concept of Nash equilibria\n(NE). We first show that computing NE for this class of games is\n$\\textit{hard}$ for the complexity class ${\\mathrm{CLS}}$. To further examine\nthe capabilities of online learning algorithms in games with full-information\nfeedback, we propose a benchmark of a simple -- yet nontrivial -- family of\nsuch games. These games do not enjoy the properties used to prove convergence\nfor relevant algorithms. In particular, we use a dynamical systems perspective\nto demonstrate that gradient descent-ascent, its optimistic variant, optimistic\nmultiplicative weights update, and extra gradient fail to converge (even\nlocally) to a Nash equilibrium. On a brighter note, we propose a first-order\nmethod that leverages control theory techniques and under some conditions\nenjoys last-iterate local convergence to a Nash equilibrium. We also believe\nour proposed method is of independent interest for general min-max\noptimization.\n', 'Nash Equilibria for Exchangeable Team against Team Games, their Mean\n  Field Limit, and Role of Common Randomness   We study stochastic mean-field games among finite number of teams with large\nfinite as well as infinite number of decision makers. For this class of games\nwithin static and dynamic settings, we establish the existence of a Nash\nequilibrium, and show that a Nash equilibrium exhibits exchangeability in the\nfinite decision maker regime and symmetry in the infinite one. To arrive at\nthese existence and structural theorems, we endow the set of randomized\npolicies with a suitable topology under various decentralized information\nstructures, which leads to the desired convexity and compactness of the set of\nrandomized policies. Then, we establish the existence of a randomized Nash\nequilibrium that is exchangeable (not necessarily symmetric) among decision\nmakers within each team for a general class of exchangeable stochastic games.\nAs the number of decision makers within each team goes to infinity (that is for\nthe mean-field game among teams), using a de Finetti representation theorem, we\nshow existence of a randomized Nash equilibrium that is symmetric (i.e.,\nidentical) among decision makers within each team and also independently\nrandomized. Finally, we establish that a Nash equilibrium for a class of\nmean-field games among teams (which is symmetric) constitutes an approximate\nNash equilibrium for the corresponding pre-limit (exchangeable) game among\nteams with large but finite number of decision makers. We thus show that common\nrandomness is not necessary for large team-against-team games, unlike the case\nwith small sized teams.\n']","[('stochastic games', 0.6388931274414062), ('sum stochastic games', 0.6335944533348083), ('markov games', 0.6007513403892517), ('games convergence', 0.5717445015907288), ('zero sum games', 0.569260835647583), ('equilibrium game', 0.564379870891571), ('nash equilibrium game', 0.5642666816711426), ('nash equilibrium', 0.5358735918998718), ('learning dynamics', 0.5358541011810303), ('learning agents', 0.5328167080879211)]"
443,443,68,443_anderson models_driven gaussian noise_parabolic anderson_gaussian noise white,"['anderson models', 'driven gaussian noise', 'parabolic anderson', 'gaussian noise white', 'gaussian noise', 'gaussian noises', 'stochastic heat', 'noise spatial', 'driven gaussian', 'fractional noise']","['Functional central limit theorems for spatial averages of the parabolic\n  Anderson model with delta initial condition in dimension $d\\geq 1$   Let $\\{u(t,x)\\}_{t>0,x\\in{{\\mathbb R}^{d}}}$ denote the solution to a\n$d$-dimensional parabolic Anderson model with delta initial condition and\ndriven by a multiplicative noise that is white in time and has a spatially\nhomogeneous covariance given by a nonnegative-definite measure $f$. Let\n$S_{N,t}:=N^{-d}\\int_{{[0,N]}^d}{[U(t,x)-1]}{\\rm d}x$ denote the spatial\naverage on ${{\\mathbb R}^{d}}$. We obtain various functional central limit\ntheorems (CLTs) for spatial averages based on the quantitative analysis of $f$\nand spatial dimension $d$. In particular, when $f$ is given by Riesz kernel,\nthat is, $f({\\rm x})={\\Vert x \\Vert}^{-\\beta}{\\rm d}x$, $\\beta\\in(0,2\\wedge\nd)$, the functional CLT is also based on the index $\\beta$.\n', ""Convergence of densities of spatial averages of the parabolic Anderson\n  model driven by colored noise   In this paper, we present a rate of convergence in the uniform norm for the\ndensities of spatial averages of the solution to the d-dimensional parabolic\nAnderson model driven by a Gaussian multiplicative noise, which is white in\ntime and has a spatial covariance given by the Riesz kernel. The proof is based\non the combination of Malliavin calculus techniques and the Stein's method for\nnormal approximations.\n"", 'Fractal Geometry of the Valleys of the Parabolic Anderson Equation   We study the macroscopic fractal properties of the deep valleys of the\nsolution of the $(1+1)$-dimensional parabolic Anderson equation $${\\partial\n\\over \\partial t}u(t,x) =\\frac{1}{2} {\\partial^2 \\over \\partial x^2} u(t,x) +\nu(t,x)\\dot{W}(t,x),t>0, x\\in {\\bf R},\\quad\n  u(0,x) \\equiv u_0(x),x\\in {\\bf R}, $$ where $\\dot{W}$ is the time-space white\nnoise and $0<\\inf_{x\\in {\\bf R}} u_0(x)\\leq \\sup_{x\\in {\\bf R}} u_0(x)<\\infty.$\nUnlike the macroscopic multifractality of the tall peaks, we show that valleys\nof the parabolic Anderson equation are macroscopically monofractal. In fact,\nthe macroscopic Hausdorff dimension (introduced by Barlow and Taylor [J. Phys.\nA 22 (1989) 2621--2628; Proc. Lond. Math. Soc. (3) 64 (1992) 125--152]) of the\nvalleys undergoes a phase transition at a point which does not depend on the\ninitial data. The key tool of our proof is a lower bound to the lower tail\nprobability of the parabolic Anderson equation. Such lower bound is obtained\nfor the first time in this paper and will be derived by utilizing the\nconnection between the parabolic Anderson equation and the Kardar-Parisi-Zhang\nequation. Our techniques of proving this lower bound can be extended to other\nmodels in the KPZ universality class including the KPZ fixed point.\n']","[('anderson models', 0.49170786142349243), ('driven gaussian noise', 0.48054054379463196), ('parabolic anderson', 0.4676809310913086), ('gaussian noise white', 0.4674839675426483), ('gaussian noise', 0.43646979331970215), ('gaussian noises', 0.4252844452857971), ('stochastic heat', 0.417334645986557), ('noise spatial', 0.3911520838737488), ('driven gaussian', 0.38881155848503113), ('fractional noise', 0.3840440809726715)]"
444,444,68,444_reduced basis methods_reduced order modeling_basis methods_reduced basis rb,"['reduced basis methods', 'reduced order modeling', 'basis methods', 'reduced basis rb', 'reduced order models', 'reduced basis', 'empirical interpolation', 'based reduction', 'orthogonal decomposition', 'discrete empirical interpolation']","['Uncertainty quantification for nonlinear solid mechanics using reduced\n  order models with Gaussian process regression   Uncertainty quantification (UQ) tasks, such as sensitivity analysis and\nparameter estimation, entail a huge computational complexity when dealing with\ninput-output maps involving the solution of nonlinear differential problems,\nbecause of the need to query expensive numerical solvers repeatedly.\nProjection-based reduced order models (ROMs), such as the Galerkin-reduced\nbasis (RB) method, have been extensively developed in the last decades to\novercome the computational complexity of high fidelity full order models\n(FOMs), providing remarkable speedups when addressing UQ tasks related with\nparameterized differential problems. Nonetheless, constructing a\nprojection-based ROM that can be efficiently queried usually requires extensive\nmodifications to the original code, a task which is non-trivial for nonlinear\nproblems, or even not possible at all when proprietary software is used.\nNon-intrusive ROMs - which rely on the FOM as a black box - have been recently\ndeveloped to overcome this issue. In this work, we consider ROMs exploiting\nproper orthogonal decomposition to construct a reduced basis from a set of FOM\nsnapshots, and Gaussian process regression (GPR) to approximate the RB\nprojection coefficients. Two different approaches, namely a global GPR and a\ntensor-decomposition-based GPR, are explored on a set of 3D time-dependent\nsolid mechanics examples. Finally, the non-intrusive ROM is exploited to\nperform global sensitivity analysis (relying on both screening and\nvariance-based methods) and parameter estimation (through Markov chain Monte\nCarlo methods), showing remarkable computational speedups and very good\naccuracy compared to high-fidelity FOMs.\n', 'An EIM-degradation free reduced basis method via over collocation and\n  residual hyper reduction-based error estimation   The need for multiple interactive, real-time simulations using different\nparameter values has driven the design of fast numerical algorithms with\ncertifiable accuracies. The reduced basis method (RBM) presents itself as such\nan option. RBM features a mathematically rigorous error estimator which drives\nthe construction of a low-dimensional subspace. A surrogate solution is then\nsought in this low-dimensional space approximating the parameter-induced high\nfidelity solution manifold. However when the system is nonlinear or its\nparameter dependence nonaffine, this efficiency gain degrades tremendously, an\ninherent drawback of the application of the empirical interpolation method\n(EIM).\n  In this paper, we augment and extend the EIM approach as a direct solver, as\nopposed to an assistant, for solving nonlinear partial differential equations\non the reduced level. The resulting method, called Reduced Over-Collocation\nmethod (ROC), is stable and capable of avoiding the efficiency degradation. Two\ncritical ingredients of the scheme are collocation at about twice as many\nlocations as the number of basis elements for the reduced approximation space,\nand an efficient error indicator for the strategic building of the reduced\nsolution space. The latter, the main contribution of this paper, results from\nan adaptive hyper reduction of the residuals for the reduced solution.\nTogether, these two ingredients render the proposed R2-ROC scheme both offline-\nand online-efficient. A distinctive feature is that the efficiency degradation\nappearing in traditional RBM approaches that utilize EIM for nonlinear and\nnonaffine problems is circumvented, both in the offline and online stages.\nNumerical tests on different families of time-dependent and steady-state\nnonlinear problems demonstrate the high efficiency and accuracy of our R2-ROC\nand its superior stability performance.\n', 'Generative Reduced Basis Method   We present a generative reduced basis (RB) approach to construct reduced\norder models for parametrized partial differential equations. Central to this\napproach is the construction of generative RB spaces that provide rapidly\nconvergent approximations of the solution manifold. We introduce a generative\nsnapshot method to generate significantly larger sets of snapshots from a small\ninitial set of solution snapshots. This method leverages multivariate nonlinear\ntransformations to enrich the RB spaces, allowing for a more accurate\napproximation of the solution manifold than commonly used techniques such as\nproper orthogonal decomposition and greedy sampling. The key components of our\napproach include (i) a Galerkin projection of the full order model onto the\ngenerative RB space to form the reduced order model; (ii) a posteriori error\nestimates to certify the accuracy of the reduced order model; and (iii) an\noffline-online decomposition to separate the computationally intensive model\nconstruction, performed once during the offline stage, from the real-time model\nevaluations performed many times during the online stage. The error estimates\nallow us to efficiently explore the parameter space and select parameter points\nthat maximize the accuracy of the reduced order model. Through numerical\nexperiments, we demonstrate that the generative RB method not only improves the\naccuracy of the reduced order model but also provides tight error estimates.\n']","[('reduced basis methods', 0.6810027956962585), ('reduced order modeling', 0.5378035306930542), ('basis methods', 0.5173454880714417), ('reduced basis rb', 0.45655325055122375), ('reduced order models', 0.45084348320961), ('reduced basis', 0.44971659779548645), ('empirical interpolation', 0.415083110332489), ('based reduction', 0.3781919479370117), ('orthogonal decomposition', 0.37807920575141907), ('discrete empirical interpolation', 0.3705623149871826)]"
445,445,68,445_latin squares_orthogonal latin squares_latin square_squares,"['latin squares', 'orthogonal latin squares', 'latin square', 'squares', 'squares order', 'combinatorial designs', 'square order', 'latin hypercube', 'orthogonal latin', 'mutually orthogonal latin']","[""Recent results on Choi's orthogonal Latin squares   Choi Seok-Jeong studied Latin squares at least 60 years earlier than Euler\nalthough this was less known. He introduced a pair of orthogonal Latin squares\nof order 9 in his book. Interestingly, his two orthogonal non-double-diagonal\nLatin squares produce a magic square of order 9, whose theoretical reason was\nnot studied. There have been a few studies on Choi's Latin squares of order 9.\nThe most recent one is Ko-Wei Lih's construction of Choi's Latin squares of\norder 9 based on the two $3 \\times 3$ orthogonal Latin squares.\n  In this paper, we give a new generalization of Choi's orthogonal Latin\nsquares of order 9 to orthogonal Latin squares of size $n^2$ using the\nKronecker product including Lih's construction. We find a geometric description\nof Choi's orthogonal Latin squares of order 9 using the dihedral group $D_8$.\nWe also give a new way to construct magic squares from two orthogonal\nnon-double-diagonal Latin squares, which explains why Choi's Latin squares\nproduce a magic square of order 9.\n"", 'Do K33-Free Latin Squares Exist?   We discuss the problem of existence of latin squares without a substructure\nconsisting of six elements $(r_1,c_2,l_3)$, $(r_2,c_3,l_1)$, $(r_3,c_1,l_2)$,\n$(r_2,c_1,l_3)$, $(r_3,c_2,l_1)$, $(r_1,c_3,l_2)$. Equivalently, the\ncorresponding latin square graph does not have an induced subgraph isomorphic\nto $K_{3,3}$. The exhaustive search [Brouwer, Wanless. Universally\nnoncommutative loops. 2011] says that there are no such latin squares of order\nfrom $3$ to $11$, and there are only two $K_{3,3}$-free latin squares of order\n$8$, up to equivalence. We repeat the search, establishing also the number of\nlatin $m$-by-$n$ rectangles for each $m$ and $n$ less or equal to $11$. As a\nswitched combination of two orthogonal latin squares of order $8$, we construct\na $K_{3,3}$-free (universally noncommutative) latin square of order $16$.\n  Keywords: latin square; transversal; trade; pattern avoiding; eigenfunction;\nuniversally noncommutative loops.\n', 'Uniform semi-Latin squares and their pairwise-variance aberrations   For integers $n>2$ and $k>0$, an $(n\\times n)/k$ semi-Latin square is an\n$n\\times n$ array of $k$-subsets (called blocks) of an $nk$-set (of\ntreatments), such that each treatment occurs once in each row and once in each\ncolumn of the array. A semi-Latin square is uniform if every pair of blocks,\nnot in the same row or column, intersect in the same positive number of\ntreatments. We show that when a uniform $(n\\times n)/k$ semi-Latin square\nexists, the Schur optimal $(n\\times n)/k$ semi-Latin squares are precisely the\nuniform ones. We then compare uniform semi-Latin squares using the criterion of\npairwise-variance (PV) aberration, introduced by J.P. Morgan for affine\nresolvable designs, and determine the uniform $(n\\times n)/k$ semi-Latin\nsquares with minimum PV aberration when there exist $n-1$ mutually orthogonal\nLatin squares (MOLS) of order $n$. These do not exist when $n=6$, and the\nsmallest uniform semi-Latin squares in this case have size $(6\\times 6)/10$. We\npresent a complete classification of the uniform $(6\\times 6)/10$ semi-Latin\nsquares, and display the one with least PV aberration. We give a construction\nproducing a uniform $((n+1)\\times (n+1))/((n-2)n)$ semi-Latin square when there\nexist $n-1$ MOLS of order $n$, and determine the PV aberration of such a\nuniform semi-Latin square. Finally, we describe how certain affine resolvable\ndesigns and balanced incomplete-block designs (BIBDs) can be constructed from\nuniform semi-Latin squares. From the uniform $(6\\times 6)/10$ semi-Latin\nsquares we classified, we obtain (up to block design isomorphism) exactly 16875\naffine resolvable designs for 72 treatments in 36 blocks of size 12 and 8615\nBIBDs for 36 treatments in 84 blocks of size 6. In particular, this shows that\nthere are at least 16875 pairwise non-isomorphic orthogonal arrays\n$\\mathrm{OA}(72,6,6,2)$.\n']","[('latin squares', 0.6889646053314209), ('orthogonal latin squares', 0.6724368333816528), ('latin square', 0.5975907444953918), ('squares', 0.5134188532829285), ('squares order', 0.49816128611564636), ('combinatorial designs', 0.4095515012741089), ('square order', 0.37511396408081055), ('latin hypercube', 0.3717191815376282), ('orthogonal latin', 0.3524201810359955), ('mutually orthogonal latin', 0.3514713943004608)]"
446,446,67,446_optimal clustering_unsupervised clustering_clustering methods_clustering fundamental,"['optimal clustering', 'unsupervised clustering', 'clustering methods', 'clustering fundamental', 'optimal number clusters', 'clustering high', 'spectral clustering', 'clustering algorithms', 'clustering', 'means clustering']","['The information bottleneck and geometric clustering   The information bottleneck (IB) approach to clustering takes a joint\ndistribution $P\\!\\left(X,Y\\right)$ and maps the data $X$ to cluster labels $T$\nwhich retain maximal information about $Y$ (Tishby et al., 1999). This\nobjective results in an algorithm that clusters data points based upon the\nsimilarity of their conditional distributions $P\\!\\left(Y\\mid X\\right)$. This\nis in contrast to classic ""geometric clustering\'\' algorithms such as $k$-means\nand gaussian mixture models (GMMs) which take a set of observed data points\n$\\left\\{ \\mathbf{x}_{i}\\right\\} _{i=1:N}$ and cluster them based upon their\ngeometric (typically Euclidean) distance from one another. Here, we show how to\nuse the deterministic information bottleneck (DIB) (Strouse and Schwab, 2017),\na variant of IB, to perform geometric clustering, by choosing cluster labels\nthat preserve information about data point location on a smoothed dataset. We\nalso introduce a novel method to choose the number of clusters, based on\nidentifying solutions where the tradeoff between number of clusters used and\nspatial information preserved is strongest. We apply this approach to a variety\nof simple clustering problems, showing that DIB with our model selection\nprocedure recovers the generative cluster labels. We also show that, in\nparticular limits of our model parameters, clustering with DIB and IB is\nequivalent to $k$-means and EM fitting of a GMM with hard and soft assignments,\nrespectively. Thus, clustering with (D)IB generalizes and provides an\ninformation-theoretic perspective on these classic algorithms.\n', 'Some notes on the $k$-means clustering for missing data   The classical $k$-means clustering requires a complete data matrix without\nmissing entries. As a natural extension of the $k$-means clustering for missing\ndata, the $k$-POD clustering has been proposed, which ignores the missing\nentries in the $k$-means clustering. This paper shows the inconsistency of the\n$k$-POD clustering even under the missing completely at random mechanism. More\nspecifically, the expected loss of the $k$-POD clustering can be represented as\nthe weighted sum of the expected $k$-means losses with parts of variables.\nThus, the $k$-POD clustering converges to the different clustering from the\n$k$-means clustering as the sample size goes to infinity. This result indicates\nthat although the $k$-means clustering works well, the $k$-POD clustering may\nfail to capture the hidden cluster structure. On the other hand, for\nhigh-dimensional data, the $k$-POD clustering could be a suitable choice when\nthe missing rate in each variable is low.\n', 'A provable initialization and robust clustering method for general\n  mixture models   Clustering is a fundamental tool in statistical machine learning in the\npresence of heterogeneous data. Most recent results focus primarily on optimal\nmislabeling guarantees when data are distributed around centroids with\nsub-Gaussian errors. Yet, the restrictive sub-Gaussian model is often invalid\nin practice since various real-world applications exhibit heavy tail\ndistributions around the centroids or suffer from possible adversarial attacks\nthat call for robust clustering with a robust data-driven initialization. In\nthis paper, we present initialization and subsequent clustering methods that\nprovably guarantee near-optimal mislabeling for general mixture models when the\nnumber of clusters and data dimensions are finite. We first introduce a hybrid\nclustering technique with a novel multivariate trimmed mean type centroid\nestimate to produce mislabeling guarantees under a weak initialization\ncondition for general error distributions around the centroids. A matching\nlower bound is derived, up to factors depending on the number of clusters. In\naddition, our approach also produces similar mislabeling guarantees even in the\npresence of adversarial outliers. Our results reduce to the sub-Gaussian case\nin finite dimensions when errors follow sub-Gaussian distributions. To solve\nthe problem thoroughly, we also present novel data-driven robust initialization\ntechniques and show that, with probabilities approaching one, these initial\ncentroid estimates are sufficiently good for the subsequent clustering\nalgorithm to achieve the optimal mislabeling rates. Furthermore, we demonstrate\nthat the Lloyd algorithm is suboptimal for more than two clusters even when\nerrors are Gaussian and for two clusters when error distributions have heavy\ntails. Both simulated data and real data examples further support our robust\ninitialization procedure and clustering algorithm.\n']","[('optimal clustering', 0.6640930771827698), ('unsupervised clustering', 0.6129897236824036), ('clustering methods', 0.5813641548156738), ('clustering fundamental', 0.5767962336540222), ('optimal number clusters', 0.5672590136528015), ('clustering high', 0.5541749000549316), ('spectral clustering', 0.5424906015396118), ('clustering algorithms', 0.542026698589325), ('clustering', 0.541009247303009), ('means clustering', 0.518790602684021)]"
447,447,67,447_finite coloring_number monochromatic_finite colouring_coloring mathbb,"['finite coloring', 'number monochromatic', 'finite colouring', 'coloring mathbb', 'number colors', 'contains monochromatic', 'colorings', 'monochromatic', 'every coloring', 'coloring']","['Almost-monochromatic sets and the chromatic number of the plane   In a colouring of $\\mathbb{R}^d$ a pair $(S,s_0)$ with $S\\subseteq\n\\mathbb{R}^d$ and with $s_0\\in S$ is \\emph{almost monochromatic} if $S\\setminus\n\\{s_0\\}$ is monochromatic but $S$ is not. We consider questions about finding\nalmost monochromatic similar copies of pairs $(S,s_0)$ in colourings of\n$\\mathbb{R}^d$, $\\mathbb{Z}^d$, and in $\\mathbb{Q}$ under some restrictions on\nthe colouring.\n  Among other results, we characterise those $(S,s_0)$ with $S\\subseteq\n\\mathbb{Z}$ for which every finite colouring of $\\mathbb{R}$ without an\ninfinite monochromatic arithmetic progression contains an almost monochromatic\nsimilar copy of $(S,s_0)$. We also show that if $S\\subseteq \\mathbb{Z}^d$ and\n$s_0$ is outside of the convex hull of $S\\setminus \\{s_0\\}$, then every finite\ncolouring of $\\mathbb{R}^d$ without a similar monochromatic copy of\n$\\mathbb{Z}^d$ contains an almost monochromatic similar copy of $(S,s_0)$.\n  Further, we propose an approach of finding almost-monochromatic sets that\nmight lead to a non-computer assisted proof of $\\chi(\\R^2)\\geq 5$.\n', 'Integer colorings with no rainbow $k$-term arithmetic progression   In this paper, we study the rainbow Erd\\H{o}s-Rothschild problem with respect\nto $k$-term arithmetic progressions. For a set of positive integers $S\n\\subseteq [n]$, an $r$-coloring of $S$ is \\emph{rainbow $k$-AP-free} if it\ncontains no rainbow $k$-term arithmetic progression. Let $g_{r,k}(S)$ denote\nthe number of rainbow $k$-AP-free $r$-colorings of $S$. For sufficiently large\n$n$ and fixed integers $r\\ge k\\ge 3$, we show that $g_{r,k}(S)<g_{r,k}([n])$\nfor any proper subset $S\\subset [n]$. Further, we prove that $\\lim_{n\\to\n\\infty}g_{r,k}([n])/(k-1)^n= \\binom{r}{k-1}$. Our result is asymptotically best\npossible and implies that, almost all rainbow $k$-AP-free $r$-colorings of\n$[n]$ use only $k-1$ colors.\n', ""Gallai-Schur Triples and Related Problems   Schur's Theorem states that, for any $r \\in \\mathbb{Z}^+$, there exists a\nminimum integer $S(r)$ such that every $r$-coloring of $\\{1,2,\\dots,S(r)\\}$\nadmits a monochromatic solution to $x+y=z$. Recently, Budden determined the\nrelated Gallai-Schur numbers; that is, he determined the minimum integer\n$GS(r)$ such that every $r$-coloring of $\\{1,2,\\dots,GS(r)\\}$ admits either a\nrainbow or monochromatic solution to $x+y=z$. In this article we consider\nproblems that have been solved in the monochromatic setting under a\nmonochromatic-rainbow paradigm. In particular, we investigate Gallai-Schur\nnumbers when $x \\neq y$, we consider $x+y+b=z$ and $x+y<z$, and we investigate\nthe asymptotic minimum number of rainbow and monochromatic solutions to $x+y=z$\nand $x+y<z$.\n""]","[('finite coloring', 0.628470778465271), ('number monochromatic', 0.6013121008872986), ('finite colouring', 0.5375729203224182), ('coloring mathbb', 0.5179001092910767), ('number colors', 0.49306055903434753), ('contains monochromatic', 0.4918515086174011), ('colorings', 0.4827929735183716), ('monochromatic', 0.481559693813324), ('every coloring', 0.47254785895347595), ('coloring', 0.45024389028549194)]"
448,448,67,448_conditions optimal control_optimal control problems_optimal control governed_optimal control,"['conditions optimal control', 'optimal control problems', 'optimal control governed', 'optimal control', 'second order optimality', 'time optimal control', 'optimality conditions', 'optimality conditions optimal', 'sufficient optimality conditions', 'necessary optimality conditions']","['Regularity of multipliers and second-order optimality conditions for\n  semilinear parabolic optimal control problems with mixed pointwise\n  constraints   A class of optimal control problems governed by semilinear parabolic\nequations with mixed pointwise constraints is considered. We give some criteria\nunder which the first and second-order optimality conditions are of KKT-type.\nWe then prove that the Lagrange multipliers belong to $L^p$-spaces. Moreover,\nwe show that if the initial value is good enough and boundary $\\partial\\Omega$\nhas a property of positive geometric density, then multipliers and optimal\nsolutions are H\\""{o}lder continuous.\n', 'Strong Stationarity Conditions for Optimal Control Problems Governed by\n  a Rate-Independent Evolution Variational Inequality   We prove strong stationarity conditions for optimal control problems that are\ngoverned by a prototypical rate-independent evolution variational inequality,\ni.e., first-order necessary optimality conditions in the form of a primal-dual\nmultiplier system that are equivalent to the purely primal notion of Bouligand\nstationarity. Our analysis relies on recent results on the Hadamard directional\ndifferentiability of the scalar stop operator and a new concept of temporal\npolyhedricity that generalizes classical ideas of Mignot. The established\nstrong stationarity system is compared with known optimality conditions for\noptimal control problems governed by elliptic obstacle-type variational\ninequalities and stationarity systems obtained by regularization.\n', 'Second-order Optimality Conditions for Time-Optimal Control Problems\n  Governed by Semilinear Parabolic Equations   A class of time-optimal control problems governed by semilinear parabolic\nequations with mixed pointwise constraints and final point constraints is\nconsidered. By introducing the so-called locally optimal solution to\ntime-optimal control problems, we establish first and second-order necessary\noptimality conditions of KKT-type and second-order sufficient conditions for\nlocally optimal solutions to the problem.\n']","[('conditions optimal control', 0.6671512126922607), ('optimal control problems', 0.6228211522102356), ('optimal control governed', 0.6037992238998413), ('optimal control', 0.5978503823280334), ('second order optimality', 0.5970962643623352), ('time optimal control', 0.5969749093055725), ('optimality conditions', 0.5780145525932312), ('optimality conditions optimal', 0.5701553821563721), ('sufficient optimality conditions', 0.5688384175300598), ('necessary optimality conditions', 0.5597127676010132)]"
449,449,67,449_bayesian networks_bayesian network_probabilistic graphical_graphical models,"['bayesian networks', 'bayesian network', 'probabilistic graphical', 'graphical models', 'gaussian graphical models', 'probabilistic reasoning', 'linear bayesian', 'probabilistic', 'dependency graphs', 'causal inference']","[""Are Bayesian networks typically faithful?   Faithfulness is a ubiquitous assumption in causal inference, often motivated\nby the fact that the faithful parameters of linear Gaussian and discrete\nBayesian networks are typical, and the folklore belief that this should also\nhold for other classes of Bayesian networks. We address this open question by\nshowing that among all Bayesian networks over a given DAG, the faithful\nBayesian networks are indeed `typical': they constitute a dense, open set with\nrespect to the total variation metric. However, this does not imply that\nfaithfulness is typical in restricted classes of Bayesian networks, as are\noften considered in statistical applications. To this end we consider the class\nof Bayesian networks parametrised by conditional exponential families, for\nwhich we show that under mild regularity conditions, the faithful parameters\nconstitute a dense, open set and the unfaithful parameters have Lebesgue\nmeasure zero, extending the existing results for linear Gaussian and discrete\nBayesian networks. Finally, we show that the aforementioned results also hold\nfor Bayesian networks with latent variables.\n"", 'Markov Equivalence of Max-Linear Bayesian Networks   Max-linear Bayesian networks have emerged as highly applicable models for\ncausal inference via extreme value data. However, conditional independence (CI)\nfor max-linear Bayesian networks behaves differently than for classical\nGaussian Bayesian networks. We establish the parallel between the two theories\nvia tropicalization, and establish the surprising result that the Markov\nequivalence classes for max-linear Bayesian networks coincide with the ones\nobtained by regular CI. Our paper opens up many problems at the intersection of\nextreme value statistics, causal inference and tropical geometry.\n', 'Conditional Independence in Max-linear Bayesian Networks   Motivated by extreme value theory, max-linear Bayesian networks have been\nrecently introduced and studied as an alternative to linear structural equation\nmodels. However, for max-linear systems the classical independence results for\nBayesian networks are far from exhausting valid conditional independence\nstatements. We use tropical linear algebra to derive a compact representation\nof the conditional distribution given a partial observation, and exploit this\nto obtain a complete description of all conditional independence relations. In\nthe context-specific case, where conditional independence is queried relative\nto a specific value of the conditioning variables, we introduce the notion of a\nsource DAG to disclose the valid conditional independence relations. In the\ncontext-free case we characterize conditional independence through a modified\nseparation concept, $\\ast$-separation, combined with a tropical eigenvalue\ncondition. We also introduce the notion of an impact graph which describes how\nextreme events spread deterministically through the network and we give a\ncomplete characterization of such impact graphs. Our analysis opens up several\ninteresting questions concerning conditional independence and tropical\ngeometry.\n']","[('bayesian networks', 0.6471065878868103), ('bayesian network', 0.6324957013130188), ('probabilistic graphical', 0.5581830143928528), ('graphical models', 0.5419754981994629), ('gaussian graphical models', 0.5406574606895447), ('probabilistic reasoning', 0.49647200107574463), ('linear bayesian', 0.4774758815765381), ('probabilistic', 0.47607001662254333), ('dependency graphs', 0.4691443145275116), ('causal inference', 0.426326185464859)]"
450,450,67,450_irreducible polynomials_polynomials irreducible_number irreducible factors_polynomials finite fields,"['irreducible polynomials', 'polynomials irreducible', 'number irreducible factors', 'polynomials finite fields', 'factorization polynomials', 'polynomials integer coefficients', 'irreducibility criterion', 'number irreducible', 'irreducible factors', 'monic polynomials']","['Prime numbers and factorization of polynomials   In this article, we obtain upper bounds on the number of irreducible factors\nof some classes of polynomials having integer coefficients, which in particular\nyield some of the well known irreducibility criteria. For devising our results,\nwe use the information about prime factorization of the values taken by such\npolynomials at sufficiently large integer arguments along with the information\nabout their root location in the complex plane. Further, these techniques are\nextended to bivariate polynomials over arbitrary fields using non-Archimedean\nabsolute values, yielding extensions of the irreducibility results of M. Ram\nMurty and S. Weintraub to bivariate polynomials.\n', 'Improved error bounds for the number of irreducible polynomials and\n  self-reciprocal irreducible monic polynomials with prescribed coefficients\n  over a finite field   A polynomial is called self-reciprocal (or palindromic) if the sequence of\nits coefficients is palindromic. In this paper we obtain improved error bounds\nfor the number of irreducible polynomials and self-reciprocal irreducible monic\npolynomials with prescribed coefficients over a finite field. The improved\nbounds imply that self-reciprocal irreducible monic polynomials with degree\n$2d$ always exist provided that the number of prescribed leading coefficients\nis slightly less than $ d/2$.\n', 'Irreducibility criterion, irreducible factors, Newton polygon techniques   Jakhar shown that for $f(x)=a_nx^n + a_{n-1}x^{n-1}+\\cdot+ a_0$ ($a_0\\neq 0$)\nis a polynomial with rational coefficients, if there exists a prime integer $p$\nsatisfying $\\nu_p(a_n)=0$ and $n\\nu_p(a_i)\\ge (n-i)\\nu_p(a_0)> 0$ for every\n$0\\le i\\le n-1$, then $f(x)$ has at most $gcd(\\nu_p(a_0),n)$ irreducible\nfactors over the field $\\mathbb{Q}$ of rational numbers and each irreducible\nfactor has degree at least $n/gcd(\\nu_p(a_0),n)$. The goal of this paper is to\ngeneralize this criterion in the following context: Let $(K,\\nu)$ be a rank one\ndiscrete valued field, $R_\\nu$ its valuation ring and $\\mathbb{F}_\\nu$ its\nresidue field. Assume that $f(x)=\\phi^n(x) + a_{n- 1}(x)\\phi^{n-1}(x)+\\cdot+\na_0(x)\\in R_\\nu[x]$, with for every $i=0,\\dots,n-1$, $a_i(x)\\in R_\\nu[x]$, and\n$a_0(x)\\neq 0$ for some monic polynomial $\\phi\\in R_\\nu[x]$ with\n$\\overline{\\phi}$ is irreducible in $\\mathbb{F}_\\nu[x]$. If for every $0\\le\ni\\le n-1$, $n\\nu_p(a_i)\\ge (n-i)\\nu_p(a_0)>0$,} then $f(x)$ has at most\n$gcd(\\nu_p(a_0(x)),n)$ irreducible factors over the field $K^h$ and so over $K$\nand each irreducible factor has degree at least $n/gcd(\\nu_p(a_0),n)$, where\n$K^h$ is the henselization of $(K,\\nu)$.\n']","[('irreducible polynomials', 0.6165496706962585), ('polynomials irreducible', 0.5998358726501465), ('number irreducible factors', 0.57880038022995), ('polynomials finite fields', 0.5739825367927551), ('factorization polynomials', 0.5648220181465149), ('polynomials integer coefficients', 0.5489695072174072), ('irreducibility criterion', 0.5409563183784485), ('number irreducible', 0.5370399951934814), ('irreducible factors', 0.5282518863677979), ('monic polynomials', 0.5270919799804688)]"
451,451,67,451_constraint satisfaction_constraint satisfaction problems_complexity dichotomy_categorical structures,"['constraint satisfaction', 'constraint satisfaction problems', 'complexity dichotomy', 'categorical structures', 'finite structures', 'relational structures', 'complexity classes', 'proof systems', 'proof complexity', 'complexity classification']","[""Proof complexity of CSP   The CSP (constraint satisfaction problems) is a class of problems deciding\nwhether there exists a homomorphism from an instance relational structure to a\ntarget one. The CSP dichotomy is a profound result recently proved by Zhuk\n(2020, J. ACM, 67) and Bulatov (2017, FOCS, 58). It establishes that for any\nfixed target structure, CSP is either NP-complete or $p$-time solvable. Zhuk's\nalgorithm solves CSP in polynomial time for constraint languages having a weak\nnear-unanimity polymorphism.\n  For negative instances of $p$-time CSPs, it is reasonable to explore their\nproof complexity. We show that the soundness of Zhuk's algorithm can be proved\nin a theory of bounded arithmetic, namely in the theory $V^1$ augmented by\nthree special universal algebra axioms. This implies that any propositional\nproof system that simulates both Extended Resolution and a theory that proves\nthe three axioms admits $p$-size proofs of all negative instances of a fixed\n$p$-time CSP.\n"", '\\omega-categorical structures avoiding height 1 identities   The algebraic dichotomy conjecture for Constraint Satisfaction Problems\n(CSPs) of reducts of (infinite) finitely bounded homogeneous structures states\nthat such CSPs are polynomial-time tractable if the model-complete core of the\ntemplate has a pseudo-Siggers polymorphism, and NP-complete otherwise.\n  One of the important questions related to the dichotomy conjecture is\nwhether, similarly to the case of finite structures, the condition of having a\npseudo-Siggers polymorphism can be replaced by the condition of having\npolymorphisms satisfying a fixed set of identities of height 1, i.e.,\nidentities which do not contain any nesting of functional symbols. We provide a\nnegative answer to this question by constructing for each non-trivial set of\nheight 1 identities a structure within the range of the conjecture whose\npolymorphisms do not satisfy these identities, but whose CSP is tractable\nnevertheless.\n  An equivalent formulation of the dichotomy conjecture characterizes\ntractability of the CSP via the local satisfaction of non-trivial height 1\nidentities by polymorphisms of the structure. We show that local satisfaction\nand global satisfaction of non-trivial height 1 identities differ for\n$\\omega$-categorical structures with less than doubly exponential orbit growth,\nthereby resolving one of the main open problems in the algebraic theory of such\nstructures.\n', 'Topology is relevant (in a dichotomy conjecture for infinite-domain\n  constraint satisfaction problems)   The algebraic dichotomy conjecture for Constraint Satisfaction Problems\n(CSPs) of reducts of (infinite) finitely bounded homogeneous structures states\nthat such CSPs are polynomial-time tractable when the model-complete core of\nthe template has a pseudo-Siggers polymorphism, and NP-complete otherwise.\n  One of the important questions related to this conjecture is whether,\nsimilarly to the case of finite structures, the condition of having a\npseudo-Siggers polymorphism can be replaced by the condition of having\npolymorphisms satisfying a fixed set of identities of height 1, i.e.,\nidentities which do not contain any nesting of functional symbols. We provide a\nnegative answer to this question by constructing for each non-trivial set of\nheight 1 identities a structure whose polymorphisms do not satisfy these\nidentities, but whose CSP is tractable nevertheless.\n  An equivalent formulation of the dichotomy conjecture characterizes\ntractability of the CSP via the local satisfaction of non-trivial height 1\nidentities by polymorphisms of the structure. We show that local satisfaction\nand global satisfaction of non-trivial height 1 identities differ for\n$\\omega$-categorical structures with less than double exponential orbit growth,\nthereby resolving one of the main open problems in the algebraic theory of such\nstructures.\n']","[('constraint satisfaction', 0.5693583488464355), ('constraint satisfaction problems', 0.532406747341156), ('complexity dichotomy', 0.5217820405960083), ('categorical structures', 0.46494656801223755), ('finite structures', 0.46486642956733704), ('relational structures', 0.4617173969745636), ('complexity classes', 0.45548179745674133), ('proof systems', 0.43313589692115784), ('proof complexity', 0.42851608991622925), ('complexity classification', 0.422303706407547)]"
452,452,67,452_modular lattices_lattices introduced_planar lattices_lattices general,"['modular lattices', 'lattices introduced', 'planar lattices', 'lattices general', 'finite lattices', 'lattices short', 'finite distributive lattices', 'lattices', 'lattices two', 'congruence lattices']","[""On slim rectangular lattices   Let $L$ be a slim, planar, semimodular lattice (slim means that it does not\ncontain an ${\\mathsf M}_3$-sublattice). We call the interval $I = [o, i]$ of\n$L$ \\emph{rectangular}, if there are complementary $a, b \\in I$ such that $a$\nis to the left of $b$. We claim that a rectangular interval of a slim\nrectangular lattice is also a slim rectangular lattice. We will present some\napplications, including a recent result of G. Cz\\'edli.\n  In a paper with E. Knapp about a dozen years ago, we introduced natural\ndiagrams} for slim rectangular lattices. Five years later, G. Cz\\'edli\nintroduced ${\\E C}_1$-diagrams} We prove that they are the same.\n"", 'Slim patch lattices as absolute retracts and maximal lattices   Patch lattices, introduced by G. Cz\\\'edli and E.T. Schmidt in 2013, are the\nbuilding stones for slim (and so necessarily finite and planar) semimodular\nlattices with respect to gluing. Slim semimodular lattices were introduced by\nG. Gr\\""atzer and E. Knapp in 2007, and they have been intensively studied since\nthen. Outside lattice theory, these lattices played the main role in adding a\nuniqueness part to the classical Jordan--H\\""older theorem for groups by G.\nCz\\\'edli and E.T. Schmidt in 2011, and they also led to results in\ncombinatorial geometry. In this paper, we prove that slim patch lattices are\nexactly the absolute retracts with more than two elements for the category of\nslim semimodular lattices with length-preserving lattice embeddings as\nmorphisms. Also, slim patch lattices are the same as the maximal objects $L$ in\nthis category such that $|L|>2$. Furthermore, slim patch lattices are\ncharacterized as the algebraically closed lattices $L$ in this category such\nthat $|L|>2$. Finally, we prove that if we consider $\\{0,1\\}$-preserving\nlattice homomorphisms rather than length-preserving ones, then the absolute\nretracts for the class of slim semimodular lattices are the at most 4-element\nboolean lattices.\n', 'Lamps in slim rectangular planar semimodular lattices   A planar (upper) semimodular lattice $L$ is slim if the five-element\nnondistributive modular lattice $M_3$ does not occur among its sublattices.\n(Planar lattices are finite by definition.) Slim rectangular lattices as\nparticular slim planar semimodular lattices were defined by G. Gr\\""atzer and E.\nKnapp in 2007. In 2009, they also proved that the congruence lattices of slim\nplanar semimodular lattices with at least three elements are the same as those\nof slim rectangular lattices. In order to provide an effective tool for\nstudying these congruence lattices, we introduce the concept of lamps of slim\nrectangular lattices and prove several of their properties. Lamps and several\ntools based on them allow us to prove in a new and easy way that the congruence\nlattices of slim planar semimodular lattices satisfy the two previously known\nproperties. Also, we use lamps to prove that these congruence lattices satisfy\nfour new properties including the two-pendant four-crown property and the\nforbidden marriage property.\n']","[('modular lattices', 0.6779797077178955), ('lattices introduced', 0.6768861413002014), ('planar lattices', 0.6715413331985474), ('lattices general', 0.6671714186668396), ('finite lattices', 0.6614130735397339), ('lattices short', 0.65742427110672), ('finite distributive lattices', 0.657025933265686), ('lattices', 0.6569386124610901), ('lattices two', 0.6545324921607971), ('congruence lattices', 0.6542240381240845)]"
453,453,66,453_plato_mathematician_history mathematics_mathematicians,"['plato', 'mathematician', 'history mathematics', 'mathematicians', 'modern mathematical', 'ptolemy', 'mathematical knowledge', 'mathematics', 'euclid', 'greek']","[""Clairaut, Euler and the figure of the Earth   The sphericity of the form of the Earth was questioned around the year 1687,\nprimarily, by Isaac Newton who deduced from his theory of universal gravitation\nthat the Earth has the form of a spheroid flattened at the poles and elongated\nat the equator. In France, somepreeminent geographers were not convinced by\nNewton's arguments, and about the same period, based on empirical measurements,\nthey emitted another theory, claiming that on the contrary, the Earth has the\nform of a spheroid flattened at the equator and elongated at the poles. To find\nthe real figure of the Earth became one of the major questions that were\ninvestigated by geographers, astronomers, mathematicians and other scientists\nin the eighteenth century, and the work done around this question had an impact\non the development of all these fields. In this paper, we review the work of\nthe eighteenth-century French mathematician, astronomer and geographer\nAlexis-Claude Clairaut related to the question of the figure of the Earth. We\nreport on the relation between this work and that of Leonhard Euler. At the\nsame time, we comment on the impact of the question of the figure of the Earth\non mathematics, astronomy and hydrostatics. Finally, we review some later\nmathematical developments that are due to various authors that were motivated\nby this question. It is interesting to see how a question on geography had such\nan impact on the theoretical sciences. The final version of this paper will\nappear in Ganita Bh{\\=a}r{\\=a}t{\\=i}, (Indian Mathematics) the Bulletin of the\nIndian Society for History of Mathematics.\n"", ""Truth and Knowledge: the Incorrect Definition of `Powers' by\n  Theaetetus-A New Interpretation of Theaetetus (147d7-148b2)   In a first article (referred here as B-O), we studied the first part of the\nso-called 'mathematical part' of Plato's Theaetetus, i.e. Theodorus' lesson. In\nthe present one, we consider the sequel and the end of the passage\n(147d7-148b2), as well as its philosophical interpretation in connection with\nthe whole dialogue. As in the previous article, we analyze it simultaneously\nfrom the mathematical, the historical and the philosophical points of view, a\nnecessity to understand it. Our strategy is once again to take seriously\nPlato's text, not as the dream of a poet. Our analysis casts a new light on\nthis passage, as an essential testimony for both Plato's philosophy and for\nhistory of mathematics. Plato's relation to Theodorus and Theaetetus is more\ncomplex than usually claimed; the search for a definition of knowledge\nconducted in a large part of the dialogue and even in some other dialogues is\nrooted in the mathematical passage; it needs a reevaluation of its connection\nto Euclid's Elements, in particular the proposition X.9, as well as a supposed\nEuclid's 'catastrophic' mistake (to quote Jean Itard) on incommensurability. In\na nutshell, the passage has to be understood differently than in the usual\ninterpretations gathered together under the collective so-called name 'Modern\nStandard Interpretation' (or MSI). Both articles form a whole. They are both\naimed to an audience without any particular mathematical background, and\nrequire only elementary mathematical knowledge, essentially of high\nschool-level. Some more complex points are developed in an Appendix at the end\nof the article.\n"", ""Theodorus' lesson in Plato's Theaetetus (147d1-d6) Revisited-A New\n  Perspective   This article is the first part of a study of the so-called 'mathematical\npart' of Plato's Theaetetus (147d-148b). The subject of this 'mathematical\npart' is the irrationality, one of the most important topics in early Greek\nmathematics. As of huge interest for mathematicians, historians of mathematics\nas well as of philosophy, there had been an avalanche of studies about it. In\nour work, we revisit this question, for we think something is missing: a global\nanalysis of Plato's text, from these three points of view simultaneously:\nhistory, mathematics and philosophy. It is what we have undertook through a new\ntranslation, a new interpretation of the mathematical lesson about irrational\nmagnitudes and a novel interpretation of the whole passage from these three\npoints of view. Our guideline is considering Plato's writings seriously, not as\nsome playful work. This simple rule is indeed surprisingly constraining, but it\nallows us to get a rare direct glance inside pre-Euclidean mathematics, in\ncontradiction with the 'Main Standard Interpretation' prevailing in history of\nmathematics as well as in history of philosophy. This study had been divided in\ntwo parts for editorial reasons. In the present article, we propose an analysis\nof the first part of this 'mathematical part', Theodorus' lesson. In the second\narticle (Brisson-Ofman (to appear)), we present the sequel of the lesson and a\nphilosophical interpretation of the 'mathematical part' within the framework of\nthe entire dialogue. Both articles form a whole. They are both aimed to an\naudience without any particular mathematical background, and require only\nelementary mathematical knowledge, essentially of high school-level. Some more\ndelicate points are nevertheless developed in the Appendices.\n""]","[('plato', 0.5039989352226257), ('mathematician', 0.4897053837776184), ('history mathematics', 0.47836726903915405), ('mathematicians', 0.4480035603046417), ('modern mathematical', 0.4465402364730835), ('ptolemy', 0.437541127204895), ('mathematical knowledge', 0.4308575391769409), ('mathematics', 0.4005937874317169), ('euclid', 0.39122024178504944), ('greek', 0.3611803352832794)]"
454,454,66,454_multipartite entanglement_entanglement measures_maximally entangled states_multipartite quantum,"['multipartite entanglement', 'entanglement measures', 'maximally entangled states', 'multipartite quantum', 'entanglement theory', 'distillable entanglement', 'entanglement', 'bipartite quantum states', 'entangled states', 'maximally entangled']","['Entanglement monogamy via multivariate trace inequalities   Entropy is a fundamental concept in quantum information theory that allows to\nquantify entanglement and investigate its properties, for example its monogamy\nover multipartite systems. Here, we derive variational formulas for relative\nentropies based on restricted measurements of multipartite quantum systems. By\ncombining these with multivariate matrix trace inequalities, we recover and\nsometimes strengthen various existing entanglement monogamy inequalities. In\nparticular, we give direct, matrix-analysis-based proofs for the faithfulness\nof squashed entanglement by relating it to the relative entropy of entanglement\nmeasured with one-way local operations and classical communication, as well as\nfor the faithfulness of conditional entanglement of mutual information by\nrelating it to the separably measured relative entropy of entanglement. We\ndiscuss variations of these results using the relative entropy to states with\npositive partial transpose, and multipartite setups. Our results simplify and\ngeneralize previous derivations in the literature that employed operational\narguments about the asymptotic achievability of information-theoretic tasks.\n', 'Constructing Multipartite Planar Maximally Entangled States from Phase\n  States and Quantum Secret Sharing Protocol   In this paper, we explore the construction of Planar Maximally Entangled\n(PME) states from phase states. PME states form a class of $n$-partite states\nin which any subset of adjacent particles whose size is less than or equal to\nhalf the total number of particles is in a fully entangled state. This property\nis essential to ensuring the robustness and stability of PME states in various\nquantum information applications. We introduce phase states for a set of\nso-called noninteracting $n$ particles and describe their corresponding\nseparable density matrices. These phase states, although individually\nseparable, serve as a starting point for the generation of entangled states\nwhen subjected to unitary dynamics. Using this method, we suggest a way to make\ncomplex multi-qubit states by watching how unconnected phase states change over\ntime with a certain unitary interaction operator. In addition, we show how to\nderive PME states from these intricate phase states for two-, three-, four-,\nand K-qubit systems. This construction method for PME states represents a\nsignificant advance over absolutely maximally entangled (AME) states, as it\nprovides a more accessible and versatile resource for quantum information\nprocessing. Not only does it enable the creation of a broader class of\nmultipartite entangled states, overcoming the limitations of AME states,\nnotably their restricted availability in low-dimensional systems; for example,\nthe absence of a four-qubit AME state, but it also offers a systematic\nconstruction method for any even number of qudits, paving the way for practical\napplications in key quantum technologies such as teleportation, secret sharing\nand error correction, where multipartite entanglement plays a central role in\nprotocol efficiency.\n', 'Multipartite entanglement measures   The main concern of this paper is how to define proper measures of\nmultipartite entanglement for mixed quantum states. Since the structure of\npartial separability and multipartite entanglement is getting complicated if\nthe number of subsystems exceeds two, one can not expect the existence of an\nultimate scalar entanglement measure, which grasps even a small part of the\nrich hierarchical structure of multipartite entanglement, and some higher order\nstructure characterizing that is needed. In this paper we make some steps\ntowards this direction.\n  First, we reveal the lattice-theoretic structure of the partial separability\nclassification, introduced earlier [Sz. Szalay and Z. Kokenyesi, Phys. Rev. A\n86, 032341 (2012)]. It turns out that, mathematically, the structure of the\nentanglement classes is the up-set lattice of the structure of the different\nkinds of partial separability, which is the down-set lattice of the lattice of\nthe partitions of the subsystems. It turns also out that, physically, this\nstructure is related to the LOCC convertibility: If a state from a class can be\nmapped into another one, then that class can be found higher in the hierarchy.\n  Second, we introduce the notion of multipartite monotonicity, expressing that\na given set of entanglement monotones, while measuring the different kinds of\nentanglement, shows also the same hierarchical structure as the entanglement\nclasses. Then we construct such hierarchies of entanglement measures, and\npropose a physically well-motivated one, being the direct multipartite\ngeneralization of the entanglement of formation based on the entanglement\nentropy, motivated by the notion of statistical distinguishability. The\nmultipartite monotonicity shown by this set of measures motivates us to\nconsider the measures to be the different manifestations of some ""unified""\nnotion of entanglement.\n']","[('multipartite entanglement', 0.7728949785232544), ('entanglement measures', 0.6769061088562012), ('maximally entangled states', 0.6730167865753174), ('multipartite quantum', 0.6721490025520325), ('entanglement theory', 0.6660071611404419), ('distillable entanglement', 0.6612447500228882), ('entanglement', 0.6515666246414185), ('bipartite quantum states', 0.640624463558197), ('entangled states', 0.636874258518219), ('maximally entangled', 0.6177203059196472)]"
455,455,66,455_existence global attractors_existence global attractor_exponential attractors_attractors time,"['existence global attractors', 'existence global attractor', 'exponential attractors', 'attractors time', 'infinite dimensional dynamical', 'existence time dependent', 'diffusion unbounded', 'dimensional dynamical', 'global attractors', 'establish existence regularity']","['Existence and upper semicontinuity of pullback attractors for Kirchhoff\n  wave equations in time-dependent spaces   In this paper, we shall investigate the existence and upper semicontinuity of\npullback attractors for non-autonomous Kirchhoff wave equations with a strong\ndamping in the time-dependent space $X_t$. After deriving the existence and\nuniqueness of solutions by the Faedo-Galerkin approximation method, we\nestablish the existence of pullback attractors. Later on, we prove the upper\nsemicontinuity of pullback attractors between the Kirchhoff-type wave equations\nwith $\\delta \\geq 0$ and the conventional wave equations with $\\delta=0$ by a\nseries of complex energy estimates.\n', 'Continuity of the attractors in time-dependent spaces and applications   In this paper, we investigate the continuity of the attractors in\ntime-dependent phase spaces. (i) We establish two abstract criteria on the\nupper semicontinuity and the residual continuity of the pullback $\\mathscr\nD$-attractor with respect to the perturbations, and an equivalence criterion\nbetween their continuity and the pullback equi-attraction, which generalize the\ncontinuity theory of attractors developed recently in [27,28] to that in\ntime-dependent spaces. (ii) We propose the notion of pullback $\\mathscr\nD$-exponential attractor, which includes the notion of time-dependent\nexponential attractor [33] as its spacial case, and establish its existence and\nH\\""{o}lder continuity criterion via quasi-stability method introduced\noriginally by Chueshov and Lasiecka [12,13]. (iii) We apply above-mentioned\ncriteria to the semilinear damped wave equations with perturbed time-dependent\nspeed of propagation: $\\e\\rho(t) u_{tt}+\\alpha u_t -\\Delta u+f(u)=g$, with\nperturbation parameter $\\e\\in(0, 1]$, to realize above mentioned continuity of\npullback $\\mathscr D$ and $\\mathscr D$-exponential attractors in time-dependent\nphase spaces, and the method developed here allows to overcome the difficulty\nof the hyperbolicity of the model. These results deepen and extend recent\ntheory of attractors in time-dependent spaces in literatures [15,20,19].\n', 'Existence and dimensions of global attractors for a delayed\n  reaction-diffusion equation on an unbounded domain   The purpose of this paper is to investigate the existence and Hausdorff\ndimension as well as fractal dimension of global attractors for a delayed\nreaction-diffusion equation on an unbounded domain. The noncompactness of the\ndomain causes the Laplace operator has a continuous spectrum, the semigroup\ngenerated by the linear part and the Sobolev embeddings are no longer compact,\nmaking the problem more difficult compared with the equations on bounded\ndomains. We first obtain the existence of an absorbing set for the infinite\ndimensional dynamical system generated by the equation by a priori estimate of\nthe solutions. Then, we show the asymptotic compactness of the solution\nsemiflow by an uniform a priori estimates for far-field values of solutions\ntogether with the Arzel\\`a-Ascoli theorem, which facilitates us to show the\nexistence of global attractors. By decomposing the solution into three parts\nand establishing a squeezing property of each part, we obtain the explicit\nupper estimation of both Hausdorff and fractal dimension of the global\nattractors, which only depend on the inner characteristic of the equation,\nwhile not related to the entropy number compared with the existing literature.\n']","[('existence global attractors', 0.5759610533714294), ('existence global attractor', 0.5617557168006897), ('exponential attractors', 0.5226115584373474), ('attractors time', 0.5164950489997864), ('infinite dimensional dynamical', 0.4909083843231201), ('existence time dependent', 0.4449940323829651), ('diffusion unbounded', 0.43921607732772827), ('dimensional dynamical', 0.4353099465370178), ('global attractors', 0.41519853472709656), ('establish existence regularity', 0.4093858599662781)]"
456,456,66,456_maximum number edges_planar graph vertices_vertex planar graph_number edges vertex,"['maximum number edges', 'planar graph vertices', 'vertex planar graph', 'number edges vertex', 'planar graph', 'vertex planar', 'extremal graphs', 'tur number graph', 'number edges', 'vertex free']","[""Planar Tur\\'an number of two adjacent cycles The planar Tur\\'an number of $H$, denoted by $ex_{\\mathcal{P}}(n,H)$, is the maximum number of edges in an $n$-vertex $H$-free planar graph. The planar Tur\\'an number of $k(k\\geq 3)$ vertex-disjoint union of cycles is the trivial value $3n-6$. We determine the planar Tur\\'an number of $C_{3}\\text{-}C_{3}$ and $C_{3}\\text{-}C_{4}$, where $C_{k}\\text{-}C_{\\ell}$ denotes the graph consisting of two disjoint cycles $C_k$ with an edge connecting them."", ""The planar Tur\\'an number of double star $S_{2,4}$   Planar Tur\\'an number $ex_{\\mathcal{P}}(n,H)$ of $H$ is the maximum number of\nedges in an $n$-vertex planar graph which does not contain $H$ as a subgraph.\nGhosh, Gy\\H{o}ri, Paulos and Xiao initiated the topic of the planar Tur\\'an\nnumber for double stars. In this paper, we prove that\n$ex_{\\mathcal{P}}(n,S_{2,4})\\leq \\frac{31}{14}n$ for $n\\geq 1$, and show that\nequality holds for infinitely many integers $n$.\n"", ""Planar Tur\\'an number of the 7-cycle   The $\\textit{planar Tur\\'an number}$ $\\textrm{ex}_{\\mathcal P}(n,H)$ of a\ngraph $H$ is the maximum number of edges in an $n$-vertex planar graph without\n$H$ as a subgraph. Let $C_{\\ell}$ denote the cycle of length $\\ell$. The planar\nTur\\'an number $\\textrm{ex}_{\\mathcal P}(n,C_{\\ell})$ behaves differently for\n$\\ell\\le 10$ and for $\\ell\\ge 11$, and it is known when $\\ell \\in \\{3,4,5,6\\}$.\nWe prove that $\\textrm{ex}_{\\mathcal P}(n,C_7) \\le \\frac{18n}{7} -\n\\frac{48}{7}$ for all $n > 38$, and show that equality holds for infinitely\nmany integers $n$.\n""]","[('maximum number edges', 0.5546605587005615), ('planar graph vertices', 0.5392929315567017), ('vertex planar graph', 0.5330348014831543), ('number edges vertex', 0.5271874666213989), ('planar graph', 0.5039851665496826), ('vertex planar', 0.4971644878387451), ('extremal graphs', 0.4968205988407135), ('tur number graph', 0.4807385206222534), ('number edges', 0.4580439329147339), ('vertex free', 0.45229020714759827)]"
457,457,66,457_abelian defect_blocks finite groups_defect group_block algebras,"['abelian defect', 'blocks finite groups', 'defect group', 'block algebras', 'morita equivalence classes', 'group block', 'conjecture blocks', 'corresponding blocks', 'equivalences morita type', 'picard groups']","['2-blocks with an abelian defect group and a freely acting cyclic\n  inertial quotient   We study blocks with an abelian defect group and a cyclic inertial quotient\nacting freely but not transitively. We prove that when p=2, such blocks are\ninertial, i.e. basic Morita equivalent to their Brauer correspondent. Together\nwith a result of the second author on Singer cycle actions on homocyclic defect\ngroups, this completes the classification of 2-blocks with a cyclic inertial\nquotient acting freely on an abelian defect group.\n', ""Brou\\'e's Conjecture for 2-blocks with elementary abelian defect groups\n  of order 32   The first author has recently classified the Morita equivalence classes of\n2-blocks B of finite groups with elementary abelian defect group of order 32.\nIn all but three cases he proved that the Morita equivalence class determines\nthe inertial quotient of B. We finish the remaining cases by utilizing the\ntheory of lower defect groups. As a corollary, we verify Brou\\'e's Abelian\nDefect Group Conjecture in this situation.\n"", ""Morita equivalence classes of $2$-blocks with abelian defect groups of\n  rank $4$   We classify all $2$-blocks with abelian defect groups of rank $4$ up to\nMorita equivalence. The classification holds for blocks over a suitable\ndiscrete valuation ring as well as for those over an algebraically closed\nfield. An application is that Brou\\'{e}'s abelian defect group conjecture holds\nfor all blocks under consideration here.\n""]","[('abelian defect', 0.6014416813850403), ('blocks finite groups', 0.5893712639808655), ('defect group', 0.5319609642028809), ('block algebras', 0.4966319501399994), ('morita equivalence classes', 0.45066753029823303), ('group block', 0.444175660610199), ('conjecture blocks', 0.4433278441429138), ('corresponding blocks', 0.44204768538475037), ('equivalences morita type', 0.42973560094833374), ('picard groups', 0.428396999835968)]"
458,458,66,458_fractional differential equations_hilfer fractional derivative_nonlinear fractional differential_fractional integro differential,"['fractional differential equations', 'hilfer fractional derivative', 'nonlinear fractional differential', 'fractional integro differential', 'fractional differential', 'fractional derivatives', 'type fractional differential', 'riemann liouville fractional', 'fractional derivative', 'nonlinear fractional']","['On the Nonlinear $\\Psi$-Hilfer Hybrid Fractional Differential Equations   In this paper, we initially derive the equivalent fractional integral\nequation to $\\Psi$-Hilfer hybrid fractional differential equations and through\nit, we prove the existence of a solution in the weighted space. The primary\nobjective of the paper is to obtain estimates on $\\Psi$-Hilfer derivative and\nutilize it to derive the hybrid fractional differential inequalities involving\n$\\Psi$-Hilfer derivative. With the assistance of these fractional differential\ninequalities, we determine the existence of extremal solutions, comparison\ntheorems and uniqueness of the solution.\n', ""On the Nonlinear $\\Psi$-Hilfer Fractional Differential Equations   We consider the nonlinear Cauchy problem for $ \\Psi $- Hilfer fractional\ndifferential equations and investigate the existence, interval of existence and\nuniqueness of solution in the weighted space of functions. The continuous\ndependence of solutions on initial conditions is proved via Weissinger fixed\npoint theorem. Picard's successive approximation method has been developed to\nsolve nonlinear Cauchy problem for differential equations with $ \\Psi $- Hilfer\nfractional derivative and an estimation have been obtained for the error bound.\nFurther, by Picard's successive approximation, we derive the representation\nformula for the solution of linear Cauchy problem for $ \\Psi $-Hilfer\nfractional differential equation with constant coefficient and variable\ncoefficient in terms of Mittag-Leffler function and Generalized (Kilbas-Saigo)\nMittag-Leffler function.\n"", 'Nonlocal Boundary Value Problem for Generalized Hilfer Implicit\n  Fractional Differential Equations   In this paper, we derive the equivalent fractional integral equation to the\nnonlinear implicit fractional differential equations involving $\\varphi$-Hilfer\nfractional derivative subject to nonlocal fractional integral boundary\nconditions. The existence of a solution, Ulam-Hyers, and Ulam-Hyers-Rassias\nstability has been acquired by means equivalent fractional integral equation.\nOur investigations depend on the fixed point theorem due to Krasnoselskii and\nthe Gronwall inequality involving $\\varphi$-Riemann--Liouville fractional\nintegral. An example is provided to show the utilization of primary outcomes.\n']","[('fractional differential equations', 0.6864091157913208), ('hilfer fractional derivative', 0.6749805808067322), ('nonlinear fractional differential', 0.6513458490371704), ('fractional integro differential', 0.6033055782318115), ('fractional differential', 0.5974915623664856), ('fractional derivatives', 0.5963417291641235), ('type fractional differential', 0.5862515568733215), ('riemann liouville fractional', 0.5855101346969604), ('fractional derivative', 0.5849968791007996), ('nonlinear fractional', 0.5793638229370117)]"
459,459,66,459_conformal prediction_conformal inference_conformity_methods conformal,"['conformal prediction', 'conformal inference', 'conformity', 'methods conformal', 'conformalized', 'conformal', 'weighted conformal', 'non conformity', 'prediction methods', 'prediction cp']","['Unifying Different Theories of Conformal Prediction   This paper presents a unified framework for understanding the methodology and\ntheory behind several different methods in the conformal prediction literature,\nwhich includes standard conformal prediction (CP), weighted conformal\nprediction (WCP), nonexchangeable conformal prediction (NexCP), and\nrandomly-localized conformal prediction (RLCP), among others. At the crux of\nour framework is the idea that conformal methods are based on revealing partial\ninformation about the data at hand, and positing a conditional distribution for\nthe data given the partial information. Different methods arise from different\nchoices of partial information, and of the corresponding (approximate)\nconditional distribution. In addition to recovering and unifying existing\nresults, our framework leads to both new theoretical guarantees for existing\nmethods, and new extensions of the conformal methodology.\n', 'Localized Conformal Prediction: A Generalized Inference Framework for\n  Conformal Prediction   We propose a new inference framework called localized conformal prediction.\nIt generalizes the framework of conformal prediction by offering a\nsingle-test-sample adaptive construction that emphasizes a local region around\nthis test sample, and can be combined with different conformal score\nconstructions. The proposed framework enjoys an assumption-free finite sample\nmarginal coverage guarantee, and it also offers additional local coverage\nguarantees under suitable assumptions. We demonstrate how to change from\nconformal prediction to localized conformal prediction using several conformal\nscores, and we illustrate a potential gain via numerical examples.\n', 'Conformal prediction with localization   We propose a new method called localized conformal prediction, where we can\nperform conformal inference using only a local region around a new test sample\nto construct its confidence interval. Localized conformal inference is a\nnatural extension to conformal inference. It generalizes the method of\nconformal prediction to the case where we can break the data exchangeability,\nso as to give the test sample a special role. To our knowledge, this is the\nfirst work that introduces such a localization to the framework of conformal\nprediction. We prove that our proposal can also have assumption-free and finite\nsample coverage guarantees, and we compare the behaviors of localized conformal\nprediction and conformal prediction in simulations.\n']","[('conformal prediction', 0.8031665086746216), ('conformal inference', 0.6939605474472046), ('conformity', 0.5734134912490845), ('methods conformal', 0.5389817953109741), ('conformalized', 0.5241352915763855), ('conformal', 0.5057578682899475), ('weighted conformal', 0.49680426716804504), ('non conformity', 0.4957426190376282), ('prediction methods', 0.45694443583488464), ('prediction cp', 0.43643811345100403)]"
460,460,66,460_quantile regression_regression quantile_quantile estimation_conditional quantiles,"['quantile regression', 'regression quantile', 'quantile estimation', 'conditional quantiles', 'quantile functions', 'conditional quantile', 'quantile based', 'quantile', 'quantile loss', 'quantiles']","['Smoothed Quantile Regression with Large-Scale Inference   Quantile regression is a powerful tool for learning the relationship between\na response variable and a multivariate predictor while exploring heterogeneous\neffects. In this paper, we consider statistical inference for quantile\nregression with large-scale data in the ""increasing dimension"" regime. We\nprovide a comprehensive and in-depth analysis of a convolution-type smoothing\napproach that achieves adequate approximation to computation and inference for\nquantile regression. This method, which we refer to as {\\it{conquer}}, turns\nthe non-differentiable quantile loss function into a twice-differentiable,\nconvex and locally strongly convex surrogate, which admits a fast and scalable\nBarzilai-Borwein gradient-based algorithm to perform optimization, and\nmultiplier bootstrap for statistical inference. Theoretically, we establish\nexplicit non-asymptotic bounds on both estimation and Bahadur-Kiefer\nlinearization errors, from which we show that the asymptotic normality of the\nconquer estimator holds under a weaker requirement on the number of the\nregressors than needed for conventional quantile regression. Moreover, we prove\nthe validity of multiplier bootstrap confidence constructions. Our numerical\nstudies confirm the conquer estimator as a practical and reliable approach to\nlarge-scale inference for quantile regression. Software implementing the\nmethodology is available in the \\texttt{R} package \\texttt{conquer}.\n', 'A Simplified Condition For Quantile Regression   Quantile regression is effective in modeling and inferring the conditional\nquantile given some predictors and has become popular in risk management due to\nwide applications of quantile-based risk measures. When forecasting risk for\neconomic and financial variables, quantile regression has to account for\nheteroscedasticity, which raises the question of whether the identification\ncondition on residuals in quantile regression is equivalent to one independent\nof heteroscedasticity. In this paper, we present some identification conditions\nunder three probability models and use them to establish simplified conditions\nin quantile regression.\n', ""Bayesian joint quantile autoregression   Quantile regression continues to increase in usage, providing a useful\nalternative to customary mean regression. Primary implementation takes the form\nof so-called multiple quantile regression, creating a separate regression for\neach quantile of interest. However, recently, advances have been made in joint\nquantile regression, supplying a quantile function which avoids crossing of the\nregression across quantiles. Here, we turn to quantile autoregression (QAR),\noffering a fully Bayesian version. We extend the initial quantile regression\nwork of Koenker and Xiao (2006) in the spirit of Tokdar and Kadane (2012). We\noffer a directly interpretable parametric model specification for QAR. Further,\nwe offer a p-th order QAR(p) version, a multivariate QAR(1) version, and a\nspatial QAR(1) version. We illustrate with simulation as well as a temperature\ndataset collected in Arag\\'on, Spain.\n""]","[('quantile regression', 0.8011374473571777), ('regression quantile', 0.7843177914619446), ('quantile estimation', 0.7394453287124634), ('conditional quantiles', 0.6395343542098999), ('quantile functions', 0.6373835206031799), ('conditional quantile', 0.6373003125190735), ('quantile based', 0.6255989074707031), ('quantile', 0.6181362271308899), ('quantile loss', 0.5913863778114319), ('quantiles', 0.5893331170082092)]"
461,461,65,461_conformal field theory_liouville conformal field_conformal field theories_liouville conformal,"['conformal field theory', 'liouville conformal field', 'conformal field theories', 'liouville conformal', 'conformal bootstrap', 'conformal field', 'dimensional conformal field', 'dimensional conformal', 'conformal', 'liouville theory']","[""Segal's axioms and bootstrap for Liouville Theory In 1987 Graeme Segal gave a functorial definition of Conformal Field Theory (CFT) that was designed to capture the mathematical essence of the Conformal Bootstrap formalism pioneered in physics by Belavin-Polyakov-Zamolodchikov. In Segal's formulation the basic objects of CFT, the correlation functions of conformal primary fields, are viewed as functions on the moduli space of Riemann surfaces with marked points which behave naturally under gluing of surfaces. In this paper we give a probabilistic realization of Segal's axioms in Liouville Conformal Field Theory (LCFT) which is a CFT that plays a fundamental role in the theory of random surfaces and two dimensional quantum gravity. Then we use Segal's axioms to express the correlation functions of LCFT in terms of the basic objects of LCFT: its {\\it spectrum} and its {\\it structure constants}, determined in earlier works by the authors. As a consequence, we obtain a formula for the correlation functions as multiple integrals over the spectrum of LCFT, the structure of these integrals being associated to a pant decomposition of the surface. The integrand is the modulus squared of a function called conformal block: its structure is encoded by the commutation relations of an algebra of operators called the Virasoro algebra and it depends holomorphically on the moduli of the surface with marked points. The integration measure involves a product of structure constants, which have an explicit expression, the so called DOZZ formula."", ""Conformal Bootstrap for surfaces with boundary in Liouville CFT. Part 1:\n  Segal axioms   This paper is the first part of the proof of the conformal bootstrap for\nLiouville conformal field theory on surfaces with a boundary, devoted to\nSegal's axioms in this context. We introduce the notion of Segal's amplitudes\non surfaces with corners and prove the gluing property for such amplitudes. The\nsemi-group of half-annuli and its generator are studied and we develop the\nnecessary material for proving its spectral decomposition using scattering\ntheory in the companion paper \\cite{GRW2}. The Segal gluing properties and the\nspectral decomposition allows us to prove the conformal bootstrap formula for\ncorrelation functions of Liouville conformal field theory with a boundary. This\nhas several important applications to the study of conformal blocks\n(analyticity and convergence) in \\cite{remypreprint}, in the construction of a\nunitary representation of mapping class group in the space of conformal blocks,\nand the study of random moduli \\cite{ARSmoduliRPM} in Liouville quantum\ngravity.\n"", 'Stress-Energy in Liouville Conformal Field Theory on Compact Riemann\n  Surfaces   We derive the conformal Ward identities for the correlation functions of the\nStress--Energy tensor in probabilistic Liouville Conformal Field Theory on\ncompact Riemann surfaces by varying the correlation functions with respect to\nthe background metric. The conformal Ward identities show that the correlation\nfunctions of the Stress--Energy tensor can be expressed as a differential\noperator with meromorphic coefficient acting on the correlation functions of\nthe primary fields of Liouville Conformal Field Theory.\n  Variations of the metric come in three different forms: reparametrizations,\nconformal scalings and deformations of the conformal structure. Conformal\nsymmetry makes it easy to treat variations of the metric that do not deform the\nconformal structure. Variations that deform the conformal structure have to be\ntreated separately, and this part of the computation relies on regularity and\nintegrability properties of the correlation functions of Liouville Conformal\nField Theory.\n']","[('conformal field theory', 0.7105077505111694), ('liouville conformal field', 0.7091464400291443), ('conformal field theories', 0.70110684633255), ('liouville conformal', 0.6841360330581665), ('conformal bootstrap', 0.6121594309806824), ('conformal field', 0.6072519421577454), ('dimensional conformal field', 0.592595636844635), ('dimensional conformal', 0.5772327780723572), ('conformal', 0.5593013763427734), ('liouville theory', 0.5490968227386475)]"
462,462,65,462_ehrhart polynomials_rational polytopes_ehrhart polynomial_polytopes lattice,"['ehrhart polynomials', 'rational polytopes', 'ehrhart polynomial', 'polytopes lattice', 'ehrhart quasi polynomial', 'rational polytope', 'lattice polytopes', 'lattice polytope', 'polynomials lattice', 'reflexive polytopes']","['A new class of magic positive Ehrhart polynomials of reflexive polytopes   The magic positivity of Ehrhart polynomials is a useful tool for proving the\nreal-rootedness of the $h^\\ast$-polynomials. In this paper, we provide a new\nclass of reflexive polytopes whose Ehrhart polynomials are magic positive.\nFirst, we prove that the Ehrhart polynomials of Stasheff polytopes are magic\npositive. Second, we provide a partial proof of the magic positivity of the\nEhrhart polynomials of the dual polytopes of the symmetric edge polytopes of\ncycles.\n', 'Ehrhart Functions of Weighted Lattice Points   This paper studies three different ways to assign weights to the lattice\npoints of a convex polytope and discusses the algebraic and combinatorial\nproperties of the resulting weighted Ehrhart functions and their generating\nfunctions and associated rings. These will be called $q$-weighted,\n$r$-weighted, and $s$-weighted Ehrhart functions, respectively. The key\nquestions we investigate are \\emph{When are the weighted Ehrhart series\nrational functions and which classical Ehrhart theory properties are preserved?\nAnd, when are the abstract formal power series the Hilbert series of Ehrhart\nrings of some polytope?} We prove generalizations about weighted Ehrhart\n$h^*$-coefficients of $q$-weighted Ehrhart series, and show $q$- and\n$s$-weighted Ehrhart reciprocity theorems. Then, we show the $q$- and\n$r$-weighted Ehrhart rings are the (classical) Ehrhart rings of weight lifting\npolytopes.\n', ""Stanley's non-Ehrhart-positive order polytopes   We say a polytope is Ehrhart positive if all the coefficients in its Ehrhart\npolynomial are positive. Answering an Ehrhart positivity question posed on\nMathoverflow, Stanley provided an example of a non-Ehrhart-positive order\npolytope of dimension $21$. Stanley's example comes from a certain family of\norder polytopes. In this paper, we study the Ehrhart positivity question on\nthis family of polytopes. By giving explicit formulas for the coefficients of\nthe Ehrhart polynomials of these polytopes in terms of Bernolli numbers, we\ndetermine the sign of each Ehrhart coefficient of each polytope in the family.\n  As a consequence of our result, we conclude that for any positive integer $d\n\\ge 21,$ there exists an order polytope of dimension $d$ that is not Ehrhart\npositive, and for any positive integer $\\ell$, there exists an order polytope\nwhose Ehrhart polynomial has precisely $\\ell$ negative coefficients, which\nanswers a question posed by Hibi. We finish this article by discussing the\nexistence of lower-dimensional order polytopes whose Ehrhart polynomials have a\nnegative coefficient.\n""]","[('ehrhart polynomials', 0.6471689343452454), ('rational polytopes', 0.6245351433753967), ('ehrhart polynomial', 0.6062913537025452), ('polytopes lattice', 0.5852457284927368), ('ehrhart quasi polynomial', 0.5805622935295105), ('rational polytope', 0.5713094472885132), ('lattice polytopes', 0.568119466304779), ('lattice polytope', 0.5301533341407776), ('polynomials lattice', 0.5075013041496277), ('reflexive polytopes', 0.5045790672302246)]"
463,463,65,463_efficient compression_neural network compression_lossless compression_compression scheme,"['efficient compression', 'neural network compression', 'lossless compression', 'compression scheme', 'compression', 'compression algorithms', 'network compression', 'compression methods', 'lossy compression', 'compression techniques']","[""An Error-Bounded Lossy Compression Method with Bit-Adaptive Quantization\n  for Particle Data   This paper presents error-bounded lossy compression tailored for particle\ndatasets from diverse scientific applications in cosmology, fluid dynamics, and\nfusion energy sciences. As today's high-performance computing capabilities\nadvance, these datasets often reach trillions of points, posing significant\nvisualization, analysis, and storage challenges. While error-bounded lossy\ncompression makes it possible to represent floating-point values with strict\npointwise accuracy guarantees, the lack of correlations in particle data's\nstorage ordering often limits the compression ratio. Inspired by\nquantization-encoding schemes in SZ lossy compressors, we dynamically determine\nthe number of bits to encode particles of the dataset to increase the\ncompression ratio. Specifically, we utilize a k-d tree to partition particles\ninto subregions and generate ``bit boxes'' centered at particles for each\nsubregion to encode their positions. These bit boxes ensure error control while\nreducing the bit count used for compression. We comprehensively evaluate our\nmethod against state-of-the-art compressors on cosmology, fluid dynamics, and\nfusion plasma datasets.\n"", 'Enhancing ZFP: A Statistical Approach to Understanding and Reducing Error Bias in a Lossy Floating-Point Compression Algorithm The amount of data generated and gathered in scientific simulations and data collection applications is continuously growing, putting mounting pressure on storage and bandwidth concerns. A means of reducing such issues is data compression; however, lossless data compression is typically ineffective when applied to floating-point data. Thus, users tend to apply a lossy data compressor, which allows for small deviations from the original data. It is essential to understand how the error from lossy compression impacts the accuracy of the data analytics. Thus, we must analyze not only the compression properties but the error as well. In this paper, we provide a statistical analysis of the error caused by ZFP compression, a state-of-the-art, lossy compression algorithm explicitly designed for floating-point data. We show that the error is indeed biased and propose simple modifications to the algorithm to neutralize the bias and further reduce the resulting error.', 'Black-Box Statistical Prediction of Lossy Compression Ratios for\n  Scientific Data   Lossy compressors are increasingly adopted in scientific research, tackling\nvolumes of data from experiments or parallel numerical simulations and\nfacilitating data storage and movement. In contrast with the notion of entropy\nin lossless compression, no theoretical or data-based quantification of lossy\ncompressibility exists for scientific data. Users rely on trial and error to\nassess lossy compression performance. As a strong data-driven effort toward\nquantifying lossy compressibility of scientific datasets, we provide a\nstatistical framework to predict compression ratios of lossy compressors. Our\nmethod is a two-step framework where (i) compressor-agnostic predictors are\ncomputed and (ii) statistical prediction models relying on these predictors are\ntrained on observed compression ratios. Proposed predictors exploit spatial\ncorrelations and notions of entropy and lossyness via the quantized entropy. We\nstudy 8+ compressors on 6 scientific datasets and achieve a median percentage\nprediction error less than 12%, which is substantially smaller than that of\nother methods while achieving at least a 8.8x speedup for searching for a\nspecific compression ratio and 7.8x speedup for determining the best compressor\nout of a collection.\n']","[('efficient compression', 0.6626338362693787), ('neural network compression', 0.6618268489837646), ('lossless compression', 0.6378976106643677), ('compression scheme', 0.6190735697746277), ('compression', 0.6048305034637451), ('compression algorithms', 0.599842369556427), ('network compression', 0.5975890159606934), ('compression methods', 0.5954598188400269), ('lossy compression', 0.5922426581382751), ('compression techniques', 0.5890854001045227)]"
464,464,65,464_commutative group schemes_group schemes_commutative group scheme_schemes,"['commutative group schemes', 'group schemes', 'commutative group scheme', 'schemes', 'reductive groups', 'affine schemes', 'torsors', 'group scheme', 'schemes give', 'reductive group']","['Generically isotropic reductive group schemes are locally isotropic   Let $R$ be a semilocal geometrically factorial Noetherian domain of\ncharacteristic zero. We show that a reductive $R$-group scheme is isotropic if\nit is generically isotropic. We derive various consequences, in particular for\nthe Grothenieck-Serre conjecture and for homotopic invariance of torsors.\n', 'Generically trivial torsors under constant groups   We resolve the Grothendieck-Serre question over an arbitrary base field $k$:\nfor a smooth $k$-group scheme $G$ and a smooth $k$-variety $X$, we show that\nevery generically trivial $G$-torsor over $X$ trivializes Zariski semilocally\non $X$. This was known when $G$ is reductive or when $k$ is perfect, and to\nsettle it in general we uncover a wealth of new arithmetic phenomena over\nimperfect $k$. We build our arguments on new purity theorems for torsors under\npseudo-complete, pseudo-proper, and pseudo-finite $k$-groups, for instance,\nrespectively, under wound unipotent $k$-groups, under pseudo-abelian varieties,\nand under the kernels $\\mathrm{Ker}(i_G)$ of comparison maps $i_G$ that relate\npseudo-reductive groups to restrictions of scalars of reductive groups. We then\ndeduce an Auslander-Buchsbaum extension theorem for torsors under\nquasi-reductive $k$-groups; for instance, we show that torsors over\n$\\mathbb{A}^2_k \\setminus \\{(0,0)\\}$ under wound unipotent $k$-groups extend to\ntorsors over $\\mathbb{A}^2_k$. For a quasi-reductive $k$-group $G$, this\nextension theorem allows us to quickly classify $G$-torsors over\n$\\mathbb{P}^1_k$ by an argument that already simplifies the reductive case and\nto establish Birkhoff, Cartan, and Iwasawa decompositions for $G(k((t)))$. We\ncombine these new results with deep inputs from recent work on the structure of\npseudo-reductive and quasi-reductive $k$-groups to show an unramifiedness\nstatement for the Whitehead group (the unstable $K_1$-group) of a\nquasi-reductive $k$-group, and then use it to argue that, for a smooth\n$k$-group $G$ and a semilocal $k$-algebra $A$, every $G$-torsor over\n$\\mathbb{P}^1_A$ trivial at $\\{t = \\infty\\}$ is also trivial at $\\{t = 0\\}$,\nwhich is known to imply the Grothendieck--Serre conclusion via geometric\narguments. To achieve all this, we develop and heavily use the structure theory\nof $k$-group schemes locally of finite type.\n', ""The Bass--Quillen conjecture for torsors over valuation rings   For a valuation ring $V$, a smooth $V$-algebra $A$, and a reductive $V$-group\nscheme $G$ satisfying a certain natural isotropicity condition, we prove that\nevery Nisnevich $G$-torsor on $\\mathbb{A}^N_A$ descends to a $G$-torsor on $A$.\nAs a corollary, we generalize Raghunathan's theorem on torsors over affine\nspaces to a relative setting. We also extend several affine representability\nresults of Asok, Hoyois, and Wendt from equi-characteristics to mixed\ncharacteristics. Our proof relies on previous work on the purity of reductive\ntorsors over smooth relative curves and the Grothendieck--Serre conjecture for\nconstant reductive group schemes.\n""]","[('commutative group schemes', 0.602130115032196), ('group schemes', 0.5981515049934387), ('commutative group scheme', 0.527291476726532), ('schemes', 0.5012729167938232), ('reductive groups', 0.49710533022880554), ('affine schemes', 0.4746985137462616), ('torsors', 0.4672471582889557), ('group scheme', 0.4656130373477936), ('schemes give', 0.4622882604598999), ('reductive group', 0.4606578052043915)]"
465,465,64,465_rankin selberg functions_selberg functions_rankin selberg_chi primitive dirichlet,"['rankin selberg functions', 'selberg functions', 'rankin selberg', 'chi primitive dirichlet', 'primitive dirichlet character', 'subconvexity bound', 'subconvex bound', 'primitive dirichlet', 'subconvexity bounds', 'mathrm gl _2']","['Hybrid subconvexity bounds for twists of $\\rm GL(3)$ $L$-functions   Let $\\pi$ be a $SL(3,\\mathbb Z)$ Hecke-Maass cusp form and $\\chi$ a primitive\nDirichlet character of prime power conductor $\\mathfrak{q}=p^k$ with $p$ prime.\nIn this paper we will prove the following subconvexity bound $$\nL\\left(\\frac{1}{2}+it,\\pi\\times \\chi\\right)\\ll_{\\pi,\\varepsilon}\np^{3/4}\\big(\\mathfrak{q}(1+|t|)\\big)^{3/4-3/40+\\varepsilon}, $$ for any\n$\\varepsilon >0$ and $t \\in \\mathbb{R}$.\n', 'Hybrid bounds for ${\\rm{GL}}(4)\\times {\\rm{GL}}(1)$ twisted\n  $L$-functions   Let $P,M$ be a two primes such that $(P,M)=1$. Let $\\Pi$ be a normalized\nHecke-Maa\\ss\\ form on ${\\rm{GL}}(4)$ of level $P$, and $\\chi$ a primitive\nDirichlet character modulo $M$. In this paper, we study the hybrid subconvexity\nproblem for $L(s, \\Pi\\otimes \\chi)$ simultaneously in the level and conductor\naspects. Among other things, we prove a hybrid subconvex bound, so long as\n$M^{1/5}<P<M^{2/5}$.\n', 'Subconvexity for $GL(1)$ twists of Rankin-Selberg $L$-functions   Let $f$ and $g$ be two holomorphic or Hecke-Maass primitive cusp forms for\n$SL(2,\\mathbb{Z})$ and $\\chi$ be a primitive Dirichlet character of modulus\n$p$, an odd prime. A subconvex bound for the central values of the\nRankin-Selberg $L$-functions is $L(s, f \\otimes g \\otimes \\chi)$ is given by\n$$L(\\frac{1}{2}, f \\otimes g \\otimes \\chi)\n\\ll_{f,g,\\epsilon}p^{\\frac{27}{28}+\\epsilon} ,$$ for any $\\epsilon > 0$, where\nthe implied constant depends only on the forms $f,g$ and $\\epsilon$. Here the\nconvexity bound has exponent $1+\\epsilon$, which was improved to\n$1-\\frac{1}{1324}$ (see \\cite{HM}). Our bound reduces it further to $1-\n\\frac{1}{28}$. The main ingredients is to reduce the original problem to a\n$GL(2) \\times GL(2)$ shifted convolution sum problem.\n']","[('rankin selberg functions', 0.5750684142112732), ('selberg functions', 0.49104830622673035), ('rankin selberg', 0.47504696249961853), ('chi primitive dirichlet', 0.4329797029495239), ('primitive dirichlet character', 0.4176907539367676), ('subconvexity bound', 0.36713069677352905), ('subconvex bound', 0.3603423833847046), ('primitive dirichlet', 0.35973066091537476), ('subconvexity bounds', 0.35925331711769104), ('mathrm gl _2', 0.3335503935813904)]"
466,466,64,466_tikhonov regularization parameter_tikhonov regularization term_tikhonov regularization_tikhonov regularized,"['tikhonov regularization parameter', 'tikhonov regularization term', 'tikhonov regularization', 'tikhonov regularized', 'regularization parameter', 'constrained convex optimization', 'accelerated gradient methods', 'convex optimization', 'strongly convex', 'convex optimization via']","['Fast convergence rates and trajectory convergence of a Tikhonov\n  regularized inertial primal\\mbox{-}dual dynamical system with time scaling\n  and vanishing damping   A Tikhonov regularized inertial primal\\mbox{-}dual dynamical system with time\nscaling and vanishing damping is proposed for solving a linearly constrained\nconvex optimization problem in Hilbert spaces. The system under consideration\nconsists of two coupled second order differential equations and its convergence\nproperties depend upon the decaying speed of the product of the time scaling\nparameter and the Tikhonov regularization parameter (named the rescaled\nregularization parameter) to zero. When the rescaled regularization parameter\nconverges rapidly to zero, the system enjoys fast convergence rates of the\nprimal-dual gap, the feasibility violation, the objective residual, and the\ngradient norm of the objective function along the trajectory, and the weak\nconvergence of the trajectory to a primal-dual solution of the linearly\nconstrained convex optimization problem. When the rescaled regularization\nparameter converges slowly to zero, the generated primal trajectory converges\nstrongly to the minimal norm solution of the problem under suitable conditions.\nFinally, numerical experiments are performed to illustrate the theoretical\nfindings.\n', ""Accelerated gradient methods combining Tikhonov regularization with\n  geometric damping driven by the Hessian   In a Hilbert setting, for convex differentiable optimization, we consider\naccelerated gradient dynamics combining Tikhonov regularization with\nHessian-driven damping. The Tikhonov regularization parameter is assumed to\ntend to zero as time tends to infinity, which preserves equilibria. The\npresence of the Tikhonov regularization term induces a strong convexity\nproperty which vanishes asymptotically. To take advantage of the exponential\nconvergence rates attached to the heavy ball method in the strongly convex\ncase, we consider the inertial dynamic where the viscous damping coefficient is\ntaken proportional to the square root of the Tikhonov regularization parameter,\nand therefore also converges towards zero. Moreover, the dynamic involves a\ngeometric damping which is driven by the Hessian of the function to be\nminimized, which induces a significant attenuation of the oscillations. Under\nan appropriate tuning of the parameters, based on Lyapunov's analysis, we show\nthat the trajectories have at the same time several remarkable properties: they\nprovide fast convergence of values, fast convergence of gradients towards zero,\nand strong convergence to the minimum norm minimizer. This study extends a\nprevious paper by the authors where similar issues were examined but without\nthe presence of Hessian driven damping.\n"", 'Tikhonov regularized second-order plus first-order primal-dual dynamical\n  systems with asymptotically vanishing damping for linear equality constrained\n  convex optimization problems   In this paper, in the setting of Hilbert spaces, we consider a Tikhonov\nregularized second-order plus first-order primal-dual dynamical system with\nasymptotically vanishing damping for a linear equality constrained convex\noptimization problem. The convergence properties of the proposed dynamical\nsystem depend heavily upon the choice of the Tikhonov regularization parameter.\nWhen the Tikhonov regularization parameter decreases rapidly to zero, we\nestablish the fast convergence rates of the primal-dual gap, the objective\nfunction error, the feasibility measure, and the gradient norm of the objective\nfunction along the trajectory generated by the system. When the Tikhonov\nregularization parameter tends slowly to zero, we prove that the primal\ntrajectory of the Tikhonov regularized dynamical system converges strongly to\nthe minimal norm solution of the linear equality constrained convex\noptimization problem. Numerical experiments are performed to illustrate the\nefficiency of our approach.\n']","[('tikhonov regularization parameter', 0.6208226680755615), ('tikhonov regularization term', 0.5745869874954224), ('tikhonov regularization', 0.5717356204986572), ('tikhonov regularized', 0.5402715802192688), ('regularization parameter', 0.4997090697288513), ('constrained convex optimization', 0.49571993947029114), ('accelerated gradient methods', 0.4801374673843384), ('convex optimization', 0.47841694951057434), ('strongly convex', 0.4714740812778473), ('convex optimization via', 0.4710109233856201)]"
467,467,64,467_multiple zeta values_multiple zeta_double zeta values_multiple zeta functions,"['multiple zeta values', 'multiple zeta', 'double zeta values', 'multiple zeta functions', 'tate algebras', 'zeta values', 'double zeta', 'zeta functions', 'zeta', 'finite fields']","['Elliptic multizetas and the elliptic double shuffle relations   We define an elliptic generating series whose coefficients, the elliptic\nmultizetas, are related to the elliptic analogues of multiple zeta values\nintroduced by Enriquez as the coefficients of his elliptic associator; both\nsets of coefficients lie in $\\mathcal{O}(\\mathfrak{H})$, the ring of functions\non the Poincar\\\'e upper half-plane $\\mathfrak H$. The elliptic multizetas\ngenerate a $\\mathbb Q$-algebra $\\mathcal{E}$ which is an elliptic analogue of\nthe algebra of multiple zeta values. Working modulo $2\\pi i$, we show that the\nalgebra $\\mathcal{E}$ decomposes into a geometric and an arithmetic part and\nstudy the precise relationship between the elliptic generating series and the\nelliptic associator defined by Enriquez. We show that the elliptic multizetas\nsatisfy a double shuffle type family of algebraic relations similar to the\ndouble shuffle relations satisfied by multiple zeta values. We prove that these\nelliptic double shuffle relations give all algebraic relations among elliptic\nmultizetas if (a) the classical double shuffle relations give all algebraic\nrelations among multiple zeta values and (b) the elliptic double shuffle Lie\nalgebra has a certain natural semi-direct product structure analogous to that\nestablished by Enriquez for the elliptic Grothendieck-Teichm\\""uller Lie\nalgebra.\n', ""Multiple zeta values with varying constant fields   Multiple zeta values associated with function fields with varying constant\nfields are dealt with simultaneously. Thakur introduced multiple zeta values in\nthe arithmetic of positive characteristic function fields, and the definition\ndepends on the field of constants of the chosen function field. Using\nPapanikolas' theory on the relationship between the $t$-motivic Galois group\nand the periods of a pre-$t$-motive, we show that there exist no algebraic\nrelations which relate multiple zeta values with different constants field.\n"", ""AGZT-Lectures on formal multiple zeta values   Formal multiple zeta values allow to study multiple zeta values by algebraic\nmethods in a way that the open question about their transcendence is\ncircumvented. In this note we show that Hoffman's basis conjecture for formal\nmultiple zeta values is implied by the free odd generation conjecture for the\ndouble shuffle Lie algebra. We use the concept of a post-Lie structure for a\nconvenient approach to the multiplication on the double shuffle group. From\nthis, we get a coaction on the algebra of formal multiple zeta values. This in\nturn allows us to follow the proof of Brown's celebrated and unconditional\ntheorem for the same result in the context of motivic multiple zeta values. We\nneed the free odd generation conjecture twice: at first it gives a formula for\nthe graded dimensions and secondly it is a key to derive a lift of the Zagier\nformula to the formal context.\n""]","[('multiple zeta values', 0.6074334383010864), ('multiple zeta', 0.5769208073616028), ('double zeta values', 0.5765171051025391), ('multiple zeta functions', 0.5764449238777161), ('tate algebras', 0.5737501382827759), ('zeta values', 0.56546550989151), ('double zeta', 0.5293262004852295), ('zeta functions', 0.4848848581314087), ('zeta', 0.4751836061477661), ('finite fields', 0.4078332185745239)]"
468,468,64,468_electrical impedance tomography_impedance tomography_impedance tomography eit_tomography based,"['electrical impedance tomography', 'impedance tomography', 'impedance tomography eit', 'tomography based', 'electrical impedance', 'tomography', 'conductivity boundary', 'tomography eit', 'boundary measurements', 'complete electrode']","['Immersed Boundary Method for the Complete Electrode Model in Electrical\n  Impedance Tomography   We propose an immersed boundary scheme for the numerical resolution of the\nComplete Electrode Model in Electrical Impedance Tomography, that we use as a\nmain ingredient in the resolution of inverse problems in medical imaging. Such\nmethod allows to use a Cartesian mesh without accurate discretization of the\nboundary, which is useful in situations where the boundary is complicated\nand/or changing. We prove the convergence of our method, and illustrate its\nefficiency with two dimensional direct and inverse problems.\n', 'Weak Galerkin Method for Electrical Impedance Tomography   In this work, we propose and analyse a weak Galerkin method for the\nelectrical impedance tomography based on a bounded variation regularization. We\nuse the complete electrode model as the forward system that is approximated by\na weak Galerkin method with lowest order. The error estimates are studied for\nthe forward problem, which are used to establish the convergence of this weak\nGalerkin algorithm for the inverse problem. Numerical examples are presented to\nverify the effectiveness and efficiency of the weak Galerkin algorithm for the\nelectrical impedance tomography.\n', 'Mumford-Shah regularization in electrical impedance tomography with\n  complete electrode model   In electrical impedance tomography, we aim to solve the conductivity within a\ntarget body through electrical measurements made on the surface of the target.\nThis inverse conductivity problem is severely ill-posed, especially in real\napplications with only partial boundary data available. Thus regularization has\nto be introduced. Conventionally regularization promoting smooth features is\nused, however, the Mumford--Shah regularizer familiar for image segmentation is\nmore appropriate for targets consisting of several distinct objects or\nmaterials. It is, however, numerically challenging. We show theoretically\nthrough $\\Gamma$-convergence that a modification of the Ambrosio--Tortorelli\napproximation of the Mumford--Shah regularizer is applicable to electrical\nimpedance tomography, in particular the complete electrode model of boundary\nmeasurements. With numerical and experimental studies, we confirm that this\nfunctional works in practice and produces higher quality results than typical\nregularizations employed in electrical impedance tomography when the\nconductivity of the target consists of distinct smoothly-varying regions.\n']","[('electrical impedance tomography', 0.7275944948196411), ('impedance tomography', 0.6414700746536255), ('impedance tomography eit', 0.5895735025405884), ('tomography based', 0.4696519374847412), ('electrical impedance', 0.46740737557411194), ('tomography', 0.4565812945365906), ('conductivity boundary', 0.44715574383735657), ('tomography eit', 0.4406236410140991), ('boundary measurements', 0.4237327575683594), ('complete electrode', 0.4062657058238983)]"
469,469,64,469_hyperelliptic curves genus_hyperelliptic curve genus_hyperelliptic curves_hyperelliptic curve,"['hyperelliptic curves genus', 'hyperelliptic curve genus', 'hyperelliptic curves', 'hyperelliptic curve', 'jacobian varieties', 'genus curves', 'jacobians curves', 'curves genus', 'jacobian variety', 'families hyperelliptic']","['Hyperelliptic Curves with Maximal Galois Action on the Torsion Points of\n  their Jacobians   In this article, we show that in each of four standard families of\nhyperelliptic curves, there is a density-$1$ subset of members with the\nproperty that their Jacobians have adelic Galois representation with image as\nlarge as possible. This result constitutes an explicit application of a general\ntheorem on arbitrary rational families of abelian varieties to the case of\nfamilies of Jacobians of hyperelliptic curves. Furthermore, we provide explicit\nexamples of hyperelliptic curves of genus $2$ and $3$ over $\\mathbb Q$ whose\nJacobians have such maximal adelic Galois representations.\n', 'Quadratic torsion orders on Jacobian varieties   We establish the existence of hyperelliptic curves of genus $g\\ge 2$ defined\nover $\\mathbb{Q}$ whose Jacobians possess rational torsion points of order $N$\nwhere $N=4g^2+2g-2$ or $4g^2+ 2g -4$. For $N=2g^2+7g+1$, we introduce a\n$1$-parameter family of hyperelliptic curves of genus $g$ over $\\mathbb{Q}$\nwith a rational torsion point of order $N$ on their Jacobians.\n', 'Translating the discrete logarithm problem on Jacobians of genus 3\n  hyperelliptic curves with $(\\ell,\\ell,\\ell)$-isogenies   We give an algorithm to compute $(\\ell,\\ell,\\ell)$-isogenies from the\nJacobians of genus three hyperelliptic curves to the Jacobians of\nnon-hyperelliptic curves. An important application is to reduce the discrete\nlogarithm problem in the Jacobian of a hyperelliptic curve to the corresponding\nproblem in the Jacobian of a non-hyperelliptic curve.\n']","[('hyperelliptic curves genus', 0.7583663463592529), ('hyperelliptic curve genus', 0.7432161569595337), ('hyperelliptic curves', 0.7394399642944336), ('hyperelliptic curve', 0.6814892888069153), ('jacobian varieties', 0.6144089698791504), ('genus curves', 0.6093424558639526), ('jacobians curves', 0.5936639308929443), ('curves genus', 0.5916022658348083), ('jacobian variety', 0.5900390148162842), ('families hyperelliptic', 0.579734742641449)]"
470,470,64,470_branching random walks_branching random walk_random walks_galton watson trees,"['branching random walks', 'branching random walk', 'random walks', 'galton watson trees', 'biased random walk', 'galton watson tree', 'reinforced random walks', 'trees random', 'tree random', 'random walk']","['The frog model on Galton-Watson trees   We consider an interacting particle system on trees known as the frog model:\ninitially, a single active particle begins at the root and\ni.i.d.~$\\mathrm{Poiss}(\\lambda)$ many inactive particles are placed at each\nnon-root vertex. Active particles perform discrete time simple random walk and\nactivate the inactive particles they encounter. We show that for Galton-Watson\ntrees with offspring distributions $Z$ satisfying $\\mathbf{P}(Z \\geq 2) = 1$\nand $\\mathbf{E}[Z^{4 + \\epsilon}] < \\infty$ for some $\\epsilon > 0$, there is a\ncritical value $\\lambda_c\\in(0,\\infty)$ separating recurrent and transient\nregimes for almost surely every tree, thereby answering a question of\nHoffman-Johnson-Junge. In addition, we also establish that this critical\nparameter depends on the entire offspring distribution, not just the maximum\nvalue of $Z$, answering another question of Hoffman-Johnson-Junge and showing\nthat the frog model and contact process behave differently on Galton-Watson\ntrees.\n', 'Differentiability of the speed of biased random walks on Galton-Watson\n  trees   We prove that the speed of a $\\lambda$-biased random walk on a supercritical\nGalton-Watson tree is differentiable for $\\lambda$ such that the walk is\nballistic and obeys a central limit theorem, and give an expression of the\nderivative using a certain $2$-dimensional Gaussian random variable. The proof\nheavily uses the renewal structure of Galton-Watson trees that was introduced\nby Lyons-Pemantle-Peres.\n', 'On transience of frogs on Galton-Watson trees   We consider a random interacting particle system, known as the frog model, on\ninfinite Galton-Watson trees allowing offspring zero and one. The system starts\nwith one awake particle (frog) at the root of the tree and a random number of\nsleeping particles at the other vertices. Awake frogs move according to simple\nrandom walk on the tree and as soon as they encounter sleeping frogs, those\nwill wake up and move independently according to simple random walk. The frog\nmodel is called transient, if there are almost surely only finitely many\nparticles returning to the root. In this paper we prove a zero-one law for\ntransience of the frog model and show the existence of a transient phase for\ncertain classes of Galton-Watson trees.\n']","[('branching random walks', 0.701907753944397), ('branching random walk', 0.6874219179153442), ('random walks', 0.5908543467521667), ('galton watson trees', 0.5906566977500916), ('biased random walk', 0.5851370096206665), ('galton watson tree', 0.5635023713111877), ('reinforced random walks', 0.5487191677093506), ('trees random', 0.5390554666519165), ('tree random', 0.5324928164482117), ('random walk', 0.5323582887649536)]"
471,471,64,471_differential uniformity_functions finite fields_differential properties_permutation polynomials,"['differential uniformity', 'functions finite fields', 'differential properties', 'permutation polynomials', 'multiplicative differential', 'uniformity also', 'uniform permutations', 'ciphers', 'perfect nonlinear functions', 'zero differential']","['Investigations of c-Differential Uniformity of Permutations with Carlitz\n  Rank 3   The $c$-differential uniformity is recently proposed to reflect resistance\nagainst some variants of differential attack. Finding functions with low\n$c$-differential uniformity is attracting attention from many researchers. For\neven characteristic, it is known that permutations of low Carlitz rank have\ngood cryptographic parameters, for example, low differential uniformity, high\nnonlinearity, etc. In this paper we show that permutations with low Carlitz\nrank have low $c$-differential uniformity. We also investigate $c$-differential\nuniformity of permutations with Carlitz rank 3 in detail.\n', 'A connection between the boomerang uniformity and the extended\n  differential in odd characteristic and applications   This paper makes the first bridge between the classical\ndifferential/boomerang uniformity and the newly introduced $c$-differential\nuniformity. We show that the boomerang uniformity of an odd APN function is\ngiven by the maximum of the entries (except for the first row/column) of the\nfunction\'s $(-1)$-Difference Distribution Table. In fact, the boomerang\nuniformity of an odd permutation APN function equals its $(-1)$-differential\nuniformity. We next apply this result to easily compute the boomerang\nuniformity of several odd APN functions. In the second part we give two classes\nof differentially low-uniform functions obtained by modifying the inverse\nfunction. The first class of permutations (CCZ-inequivalent to the inverse)\nover a finite field $\\mathbb{F}_{p^n}$ ($p$, an odd prime) is obtained from the\ncomposition of the inverse function with an order-$3$ cycle permutation, with\ndifferential uniformity $3$ if $p=3$ and $n$ is odd; $5$ if $p=13$ and $n$ is\neven; and $4$ otherwise. The second class is a family of binomials and we show\nthat their differential uniformity equals~$4$. We next complete the open case\nof $p=3$ in the investigation started by G\\"" olo\\u glu and McGuire (2014), for\n$p\\geq 5$, and continued by K\\""olsch (2021), for $p=2$, $n\\geq 5$, on the\ncharacterization of $L_1(X^{p^n-2})+L_2(X)$ (with linearized $L_1,L_2$) being a\npermutation polynomial. Finally, we extend to odd characteristic a result of\nCharpin and Kyureghyan (2010) providing an upper bound for the differential\nuniformity of the function and its switched version via a trace function.\n', 'On the second-order zero differential spectra of some power functions\n  over finite fields   Boukerrou et al. (IACR Trans. Symmetric Cryptol. 2020(1), 331-362) introduced\nthe notion of Feistel Boomerang Connectivity Table (FBCT), the Feistel\ncounterpart of the Boomerang Connectivity Table (BCT), and the Feistel\nboomerang uniformity (which is the same as the second-order zero differential\nuniformity in even characteristic). FBCT is a crucial table for the analysis of\nthe resistance of block ciphers to power attacks such as differential and\nboomerang attacks. It is worth noting that the coefficients of FBCT are related\nto the second-order zero differential spectra of functions. In this paper, by\ncarrying out certain finer manipulations of solving specific equations over the\nfinite field $\\mathbb{F}_{p^n}$, we explicitly determine the second-order zero\ndifferential spectra of some power functions with low differential uniformity,\nand show that our considered functions also have low second-order zero\ndifferential uniformity. Our study pushes further former investigations on\nsecond-order zero differential uniformity and Feistel boomerang differential\nuniformity for a power function $F$.\n']","[('differential uniformity', 0.5266542434692383), ('functions finite fields', 0.4195200800895691), ('differential properties', 0.41569435596466064), ('permutation polynomials', 0.40549784898757935), ('multiplicative differential', 0.40398740768432617), ('uniformity also', 0.3854975402355194), ('uniform permutations', 0.3834455609321594), ('ciphers', 0.382006973028183), ('perfect nonlinear functions', 0.37897437810897827), ('zero differential', 0.37443453073501587)]"
472,472,64,472_free cumulants_free probability theory_non commutative probability_cumulants,"['free cumulants', 'free probability theory', 'non commutative probability', 'cumulants', 'moment cumulant', 'commutative probability space', 'monotone independence', 'free probability', 'cumulant', 'shuffle algebra']","[""Cumulant-cumulant relations in free probability theory from Magnus'\n  expansion   Relations between moments and cumulants play a central role in both classical\nand non-commutative probability theory. The latter allows for several distinct\nfamilies of cumulants corresponding to different types of independences: free,\nBoolean and monotone. Relations among those cumulants have been studied\nrecently. In this work we focus on the problem of expressing with a closed\nformula multivariate monotone cumulants in terms of free and Boolean cumulants.\nIn the process we introduce various constructions and statistics on\nnon-crossing partitions. Our approach is based on a pre-Lie algebra structure\non cumulant functionals. Relations among cumulants are described in terms of\nthe pre-Lie Magnus expansion combined with results on the continuous\nBaker-Campbell-Hausdorff formula due to A. Murua.\n"", 'Conditionally monotone cumulants via shuffle algebra   In this work we study conditional monotone cumulants and additive convolution\nin the shuffle-algebraic approach to non-commutative probability. We describe\nc-monotone cumulants as an infinitesimal character and identify the c-monotone\nadditive convolution as an associative operation in the set of pairs of\ncharacters in the dual of a double tensor Hopf algebra. In this algebraic\nframework, we understand previous results on c-monotone cumulants and prove a\ncombinatorial formula that relates c-free and c-monotone cumulants. We also\nidentify the notion of $t$-Boolean cumulants in the shuffle-algebraic approach\nand introduce the corresponding notion of $t$-monotone cumulants as a\nparticular case of c-monotone cumulants.\n', 'Relations between infinitesimal non-commutative cumulants   Boolean, free and monotone cumulants as well as relations among them, have\nproven to be important in the study of non-commutative probability theory.\nQuite notably, Boolean cumulants were successfully used to study free infinite\ndivisibility via the Boolean Bercovici--Pata bijection. On the other hand, in\nrecent years the concept of infinitesimal non-commutative probability has been\ndeveloped, together with the notion of infinitesimal cumulants which can be\nuseful in the context of combinatorial questions.\n  In this paper, we show that the known relations among free, Boolean and\nmonotone cumulants still hold in the infinitesimal framework. Our approach is\nbased on the use of Grassmann algebra. Formulas involving infinitesimal\ncumulants can be obtained by applying a formal derivation to known formulas.\n  The relations between the various types of cumulants turn out to be captured\nvia the shuffle algebra approach to moment-cumulant relations in\nnon-commutative probability theory. In this formulation, (free, Boolean and\nmonotone) cumulants are represented as elements of the Lie algebra of\ninfinitesimal characters over a particular combinatorial Hopf algebra. The\nlatter consists of the graded connected double tensor algebra defined over a\nnon-commutative probability space and is neither commutative nor cocommutative.\nIn this note it is shown how the shuffle algebra approach naturally extends to\nthe notion of infinitesimal non-commutative probability space. The basic step\nconsists in replacing the base field as target space of linear Hopf algebra\nmaps by the Grassmann algebra over the base field. We also consider the\ninfinitesimal analog of the Boolean Bercovici--Pata map.\n']","[('free cumulants', 0.5851132869720459), ('free probability theory', 0.5654887557029724), ('non commutative probability', 0.4718267619609833), ('cumulants', 0.46808645129203796), ('moment cumulant', 0.468056321144104), ('commutative probability space', 0.46741795539855957), ('monotone independence', 0.4578694701194763), ('free probability', 0.4176594316959381), ('cumulant', 0.4138374626636505), ('shuffle algebra', 0.4106959402561188)]"
473,473,64,473_stochastic maximum principle_stochastic optimal control_optimal control stochastic_stochastic maximum,"['stochastic maximum principle', 'stochastic optimal control', 'optimal control stochastic', 'stochastic maximum', 'stochastic control', 'backward stochastic differential', 'principle optimal control', 'stochastic control systems', 'stochastic optimal', 'backward stochastic partial']","[""Stochastic maximum principle for optimal control problem with varying\n  terminal time and non-convex control domain   In this paper, we consider a varying terminal time structure for the\nstochastic optimal control problem under state constraints, in which the\nterminal time varies with the mean value of the state. In this new stochastic\noptimal control system, the control domain does not need to be convex and the\ndiffusion coefficient contains the control variable. To overcome the difficulty\nin the proof of the related Pontryagin's stochastic maximum principle, we\ndevelop asymptotic first- and second-order adjoint equations for the varying\nterminal time, and then establish its variational equation. In the end, two\nexamples are given to verify the main results of this study.\n"", ""On Stochastic Maximum Principle: A Backward Stochastic Partial\n  Differential Equations Point of View   In this paper, we consider a class of stochastic control problems for\nstochastic differential equations with random coefficients. The control domain\nneed not to be convex but the control process is not allowed to enter in\ndiffusion term. Moreover, the terminal cost involves a non linear term of the\nexpected value of terminal state. Our purpose is to derive a new version of the\nPontryagin's stochastic maximum principle by adopting an idea inspired from the\nwork of Peng [S. Peng, Maximum Principle for Stochastic Optimal Control with\nNonconvex Control Domain, Lecture Notes in Control & Information Sciences, 114,\n(1990), pp. 724-732]. More specifically, we show that if we combine the spike\nperturbation of the optimal control combined with the stochastic Feynman-Kac\nrepresentation of linear backward stochastic partial differential equations\n(BSPDE, for short), a new version of the stochastic maximum principle can be\nderived. We also investigate sufficient conditions of optimality. In the last\npart of this paper, motivated by our version of SMP, an interesting class of\nforward backward stochastic partial differential equations is naturally\nintroduced and the solvability of such kind of equations is briefly presented.\n"", 'Stochastic maximum principle for recursive optimal control problems with\n  varying terminal time   This paper introduces a new recursive stochastic optimal control problem\ndriven by a forward-backward stochastic differential equations (FBSDEs), where\nthe ter?minal time varies according to the constraints of the state of the\nforward equation. This new optimal control problem can be used to describe the\ninvestment portfolio problems with the varying investment period. Based on\nnovel \\r{ho}-moving variational and adjoint equations, we establish the\nstochastic maximum principle for this optimal control problem including the\nclassical optimal control problem as a particular case. Furthermore, we propose\nan example to verify our main results.\n']","[('stochastic maximum principle', 0.755662739276886), ('stochastic optimal control', 0.7549058198928833), ('optimal control stochastic', 0.7384849190711975), ('stochastic maximum', 0.6602541208267212), ('stochastic control', 0.6596713662147522), ('backward stochastic differential', 0.6289165616035461), ('principle optimal control', 0.6266623139381409), ('stochastic control systems', 0.6225612759590149), ('stochastic optimal', 0.6125560998916626), ('backward stochastic partial', 0.6032155752182007)]"
474,474,64,474_gorenstein algebras_gorenstein algebra_artinian algebras_graded algebras,"['gorenstein algebras', 'gorenstein algebra', 'artinian algebras', 'graded algebras', 'algebras codimension', 'gorenstein', 'monomial algebras', 'artinian', 'jacobian algebra', 'lefschetz']","['Lefschetz properties for jacobian rings of cubic fourfolds and other\n  Artinian algebras   In this paper, we exploit some geometric-differential techniques to prove the\nstrong Lefschetz property in degree $1$ for a complete intersection standard\nArtinian Gorenstein algebra of codimension $6$ presented by quadrics. We prove\nalso some strong Lefschetz properties for the same kind of Artinian algebras in\nhigher codimensions. Moreover, we analyze some loci that come naturally into\nthe picture of ""special"" Artinian algebras: for them, we give some geometric\ndescriptions and show a connection between the non emptiness of the so-called\nnon-Lefschetz locus in degree $1$ and the ""lifting"" of a weak Lefschetz\nproperty to an algebra from one of its quotients.\n', 'Lefschetz properties of some codimension three Artinian Gorenstein\n  algebras   Codimension two Artinian algebras $A$ have the strong and weak Lefschetz\nproperties provided the characteristic is zero or greater than the socle\ndegree. It is open to what extent such results might extend to codimension\nthree AG algebras - the most promising results so far have concerned the weak\nLefschetz property for such algebras. We here show that every standard-graded\ncodimension three Artinian Gorenstein algebra $A$ having low maximum value of\nthe Hilbert function - at most six - has the strong Lefschetz property,\nprovided that the characteristic is zero. When the characteristic is greater\nthan the socle degree of $A$, we show that $A$ is almost strong Lefschetz. This\nquite modest result is nevertheless arguably the most encompassing so far\nconcerning the strong Lefschetz property for graded codimension three AG\nalgebras.\n', 'Hilbert Functions of Artinian Gorenstein algebras with the Strong\n  Lefschetz Property   We prove that a sequence $h$ of non-negative integers is the Hilbert function\nof some Artinian Gorenstein algebra with the strong Lefschetz property if and\nonly if it is an SI-sequence. This generalizes the result by T. Harima which\ncharacterizes the Hilbert functions of Artinian Gorenstein algebras with the\nweak Lefschetz property. We also provide classes of Artinian Gorenstein\nalgebras obtained from the ideal of points in $\\mathbb{P}^n$ such that some of\ntheir higher Hessians have non-vanishing determinants. Consequently, we provide\nfamilies of such algebras satisfying the SLP.\n']","[('gorenstein algebras', 0.7360035181045532), ('gorenstein algebra', 0.6930315494537354), ('artinian algebras', 0.6080862879753113), ('graded algebras', 0.4917362630367279), ('algebras codimension', 0.4672408998012543), ('gorenstein', 0.436754047870636), ('monomial algebras', 0.42949819564819336), ('artinian', 0.3927019536495209), ('jacobian algebra', 0.3847786486148834), ('lefschetz', 0.3827832341194153)]"
475,475,63,475_distributed matrix_matrix computations_matrix multiplication_secure distributed,"['distributed matrix', 'matrix computations', 'matrix multiplication', 'secure distributed', 'coded distributed', 'matrix computation', 'coded computation', 'codes distributed', 'distributed computing', 'communication computation']","['GASP Codes for Secure Distributed Matrix Multiplication   We consider the problem of secure distributed matrix multiplication (SDMM) in\nwhich a user wishes to compute the product of two matrices with the assistance\nof honest but curious servers. We construct polynomial codes for SDMM by\nstudying a combinatorial problem on a special type of addition table, which we\ncall the degree table. The codes are based on arithmetic progressions, and are\nthus named GASP (Gap Additive Secure Polynomial) Codes. GASP Codes are shown to\noutperform all previously known polynomial codes for secure distributed matrix\nmultiplication in terms of download rate.\n', ""Speeding Up Private Distributed Matrix Multiplication via Bivariate\n  Polynomial Codes   We consider the problem of private distributed matrix multiplication under\nlimited resources. Coded computation has been shown to be an effective solution\nin distributed matrix multiplication, both providing privacy against the\nworkers and boosting the computation speed by efficiently mitigating\nstragglers. In this work, we propose the use of recently-introduced bivariate\npolynomial codes to further speed up private distributed matrix multiplication\nby exploiting the partial work done by the stragglers rather than completely\nignoring them. We show that the proposed approach reduces the average\ncomputation time of private distributed matrix multiplication compared to its\ncompetitors in the literature while improving the upload communication cost and\nthe workers' storage efficiency.\n"", ""Bivariate Polynomial Codes for Secure Distributed Matrix Multiplication   We consider the problem of secure distributed matrix multiplication (SDMM).\nCoded computation has been shown to be an effective solution in distributed\nmatrix multiplication, both providing privacy against workers and boosting the\ncomputation speed by efficiently mitigating stragglers. In this work, we\npresent a non-direct secure extension of the recently introduced bivariate\npolynomial codes. Bivariate polynomial codes have been shown to be able to\nfurther speed up distributed matrix multiplication by exploiting the partial\nwork done by the stragglers rather than completely ignoring them while reducing\nthe upload communication cost and/or the workers' storage's capacity needs. We\nshow that, especially for upload communication or storage constrained settings,\nthe proposed approach reduces the average computation time of SDMM compared to\nits competitors in the literature.\n""]","[('distributed matrix', 0.573223888874054), ('matrix computations', 0.5590437054634094), ('matrix multiplication', 0.5170714259147644), ('secure distributed', 0.5143439769744873), ('coded distributed', 0.5108539462089539), ('matrix computation', 0.5050907731056213), ('coded computation', 0.49766916036605835), ('codes distributed', 0.4945460259914398), ('distributed computing', 0.47574833035469055), ('communication computation', 0.467773973941803)]"
476,476,63,476_subdivision_linear schemes_quasi interpolation_hermite interpolation,"['subdivision', 'linear schemes', 'quasi interpolation', 'hermite interpolation', 'schemes', 'schemes widely', 'generalized hermite', 'subdivided', 'class schemes', 'ridge functions']","['Multivariate Generalized Hermite Subdivision Schemes   Due to properties such as interpolation, smoothness, and spline connections,\nHermite subdivision schemes employ fast iterative algorithms for geometrically\nmodeling curves/surfaces in CAGD and for building Hermite wavelets in numerical\nPDEs. In this paper we introduce a notion of generalized Hermite (dyadic)\nsubdivision schemes and then we characterize their convergence, smoothness and\nunderlying matrix masks with or without interpolation properties. We also\nintroduce the notion of linear-phase moments for achieving the\npolynomial-interpolation property. For any given positive integer m, we\nconstructively prove that there always exist convergent smooth generalized\nHermite subdivision schemes with linear-phase moments such that their basis\nvector functions are spline functions in $C^m$ and have linearly independent\ninteger shifts. As byproducts, our results resolve convergence, smoothness and\nexistence of Lagrange, Hermite, or Birkhoff subdivision schemes. Even in\ndimension one our results significantly generalize and extend many known\nresults on extensively studied univariate Hermite subdivision schemes. To\nillustrate the theoretical results in this paper, we provide examples of\nconvergent generalized Hermite subdivision schemes with symmetric matrix masks\nhaving short support and smooth basis vector functions with or without\ninterpolation property.\n', 'Multivariate Vector Subdivision Schemes with a General Matrix-valued\n  Filter   Subdivision schemes are closely related to splines and wavelets and have\nnumerous applications in CAGD and numerical differential equations. Subdivision\nschemes employ a scalar filter; that is, scalar subdivision schemes, have been\nextensively studied in the literature. In contrast, subdivision schemes with a\nmatrix filter, which are the so-called vector subdivision schemes, are far from\nbeing well understood. So far, only vector subdivision schemes that use special\nmatrix-valued filters have been well-investigated, such as the Lagrange and\nHermite subdivision schemes. To the best of our knowledge, it remains unclear\nhow to define and characterize the convergence of a vector subdivision scheme\nthat uses a general matrix-valued filter. Though filters from Lagrange and\nHermite subdivision schemes have nice properties and are widely used in\npractice, filters not from either subdivision scheme appear in many\napplications. Hence, it is necessary to study vector subdivision schemes with a\ngeneral matrix-valued filter. In this paper, from the perspective of a vector\ncascade algorithm, we show that there is only one meaningful way to define a\nvector subdivision scheme. We will analyze the convergence of the newly defined\nvector subdivision scheme and show that it is equivalent to the convergence of\nthe corresponding vector cascade algorithm. Applying our theory, we show that\nexisting results on the convergence of Lagrange and Hermite subdivision schemes\ncan be easily obtained and improved. Finally, we will present some examples of\nvector subdivision schemes to illustrate our main results.\n', 'Analysis and convergence of Hermite subdivision schemes   Hermite interpolation property is desired in applied and computational\nmathematics. Hermite and vector subdivision schemes are of interest in CAGD for\ngenerating subdivision curves and in computational mathematics for building\nHermite wavelets to numerically solve partial differential equations. In\ncontrast to well-studied scalar subdivision schemes, Hermite and vector\nsubdivision schemes employ matrix-valued masks and vector input data, which\nmake their analysis much more complicated and difficult than their scalar\ncounterparts. Despite recent progresses on Hermite subdivision schemes, several\nkey questions still remain unsolved, for example, characterization of Hermite\nmasks, factorization of matrix-valued masks, and convergence of Hermite\nsubdivision schemes. In this paper, we shall study Hermite subdivision schemes\nthrough investigating vector subdivision operators acting on vector polynomials\nand establishing the relations among Hermite subdivision schemes, vector\ncascade algorithms and refinable vector functions. This approach allows us to\nresolve several key problems on Hermite subdivision schemes including\ncharacterization of Hermite masks, factorization of matrix-valued masks, and\nconvergence of Hermite subdivision schemes.\n']","[('subdivision', 0.4758419692516327), ('linear schemes', 0.457271546125412), ('quasi interpolation', 0.431007444858551), ('hermite interpolation', 0.4290284514427185), ('schemes', 0.39579540491104126), ('schemes widely', 0.3793403208255768), ('generalized hermite', 0.3707045912742615), ('subdivided', 0.3636758029460907), ('class schemes', 0.3503813147544861), ('ridge functions', 0.3419687747955322)]"
477,477,63,477_random waves_random wave_euclidean random_random gaussian,"['random waves', 'random wave', 'euclidean random', 'random gaussian', 'gaussian random', 'fluctuations number', 'length random', 'random spherical', 'asymptotic variance', 'non gaussian']","['Boundary effect on the nodal length for Arithmetic Random Waves, and\n  spectral semi-correlations   We test M. Berry\'s ansatz on nodal deficiency in presence of boundary. The\nsquare billiard is studied, where the high spectral degeneracies allow for the\nintroduction of a Gaussian ensemble of random Laplace eigenfunctions\n(""boundary-adapted arithmetic random waves""). As a result of a precise\nasymptotic analysis, two terms in the asymptotic expansion of the expected\nnodal length are derived, in the high energy limit along a generic sequence of\nenergy levels. It is found that the precise nodal deficiency or surplus of the\nnodal length depends on arithmetic properties of the energy levels, in an\nexplicit way.\n  To obtain the said results we apply the Kac-Rice method for computing the\nexpected nodal length of a Gaussian random field. Such an application uncovers\nmajor obstacles, e.g. the occurrence of ""bad"" subdomains, that, one hopes,\ncontribute insignificantly to the nodal length. Fortunately, we were able to\nreduce this contribution to a number theoretic question of counting the\n""spectral semi-correlations"", a concept joining the likes of ""spectral\ncorrelations"" and ""spectral quasi-correlations"" in having impact on the nodal\nlength for arithmetic dynamical systems.\n  This work rests on several breakthrough techniques of J. Bourgain, whose\ninterest in the subject helped shaping it to high extent, and whose fundamental\nwork on spectral correlations, joint with E. Bombieri, has had a crucial impact\non the field.\n', ""Spectral quasi correlations and phase-transitions for the nodal length\n  of Arithmetic Random Waves   Spectral quasi correlations are small sums of lattice points lying on the\nsame circle; we show that, for generic integers representable as the sum of two\nsquares, there are no spectral quasi-correlations. Moreover, we apply our\nresult to study the nodal length of Arithmetic Random Waves at small scales: we\nshow that there exists a phase-transition for the distribution of the nodal\nlength at a logarithmic power above Planck-scale. Furthermore, we give strong\nevidence for the existence of an intermediate phase between Arithmetic and\nBerry's random waves.\n"", ""Nodal Statistics of Planar Random Waves   We consider Berry's random planar wave model (1977) for a positive Laplace\neigenvalue $E>0$, both in the real and complex case, and prove limit theorems\nfor the nodal statistics associated with a smooth compact domain, in the\nhigh-energy limit ($E\\to \\infty$). Our main result is that both the nodal\nlength (real case) and the number of nodal intersections (complex case) verify\na Central Limit Theorem, which is in sharp contrast with the non-Gaussian\nbehaviour observed for real and complex arithmetic random waves on the flat\n$2$-torus, see Marinucci et al. (2016) and Dalmao et al. (2016). Our findings\ncan be naturally reformulated in terms of the nodal statistics of a single\nrandom wave restricted to a compact domain diverging to the whole plane. As\nsuch, they can be fruitfully combined with the recent results by Canzani and\nHanin (2016), in order to show that, at any point of isotropic scaling and for\nenergy levels diverging sufficently fast, the nodal length of any Gaussian\npullback monochromatic wave verifies a central limit theorem with the same\nscaling as Berry's model. As a remarkable byproduct of our analysis, we\nrigorously confirm the asymptotic behaviour for the variances of the nodal\nlength and of the number of nodal intersections of isotropic random waves, as\nderived in Berry (2002).\n""]","[('random waves', 0.5687032341957092), ('random wave', 0.5546650290489197), ('euclidean random', 0.45282459259033203), ('random gaussian', 0.4416176378726959), ('gaussian random', 0.42195427417755127), ('fluctuations number', 0.405129998922348), ('length random', 0.3934871256351471), ('random spherical', 0.38275766372680664), ('asymptotic variance', 0.3805796504020691), ('non gaussian', 0.3685644567012787)]"
478,478,63,478_systems controllability_controllability linear_controllability analysis_controllability matrix,"['systems controllability', 'controllability linear', 'controllability analysis', 'controllability matrix', 'minimal controllability', 'controllability system', 'controllability', 'controllability observability', 'controllability conditions', 'controllability can']","['Estimation of Strong Structural Controllable Subspace of Network:\n  Equitable Partition Method   In this paper, the strong structural controllability of the network is\nanalyzed. Based on the unified definition of equitable partition for kinds of\nscene, the upper bound of the strong structural controllable subspace in\ndifferent scenarios is given, and the strong structural observability is\nanalyzed by using the characteristics of the dual system. Finally, the\npractical significance when the dimension of the strong structural controllable\nsubspace is less than the number of individuals is given, and an invariant\nattribute of strong structural controllability analysis is proposed.\n', 'Composition Rules for Strong Structural Controllability and Minimum\n  Input Problem in Diffusively-Coupled Networks   This paper presents new results and reinterpretation of existing conditions\nfor strong structural controllability in a structured network determined by the\nzero/non-zero patterns of edges. For diffusively-coupled networks with\nself-loops, we first establish a necessary and sufficient condition for strong\nstructural controllability, based on the concepts of dedicated and sharing\nnodes. Subsequently, we define several conditions for strong structural\ncontrollability across various graph types by decomposing them into disjoint\npath graphs. We further extend our findings by introducing a composition rule,\nfacilitating the analysis of strong structural controllability in larger\nnetworks. This rule allows us to determine the strong structural\ncontrollability of connected graphs called pactus graphs (a generalization of\nthe well-known cactus graph) by consideration of the strong structural\ncontrollability of its disjoint component graphs. In this process, we introduce\nthe notion of a component input node, which is a state node that functions\nidentically to an external input node. Based on this concept, we present an\nalgorithm with approximate polynomial complexity to determine the minimum\nnumber of external input nodes required to maintain strong structural\ncontrollability in a diffusively-coupled network with self-loops.\n', 'The Controllability and Structural Controllability of Laplacian Dynamics   In this paper, classic controllability and structural controllability under\ntwo protocols are investigated. For classic controllability, the multiplicity\nof eigenvalue zero of general Laplacian matrix $L^*$ is shown to be determined\nby the sum of the numbers of zero circles, identical nodes and opposite pairs,\nwhile it is always simple for the Laplacian $L$ with diagonal entries in\nabsolute form. For a fixed structurally balanced topology, the controllable\nsubspace is proved to be invariant even if the antagonistic weights are\nselected differently under the corresponding protocol with $L$. For a graph\nexpanded from a star graph rooted from a single leader, the dimension of\ncontrollable subspace is two under the protocol associated with $L^*$. In\naddition, the system is structurally controllable under both protocols if and\nonly if the topology without unaccessible nodes is connected. As a reinforcing\ncase of structural controllability, strong structural controllability requires\nthe system to be controllable for any choice of weights. The connection between\nfather nodes and child nodes affects strong structural controllability because\nit determines the linear relationship of the control information from father\nnodes. This discovery is a major factor in establishing the sufficient\nconditions on strong structural controllability for multi-agent systems under\nboth protocols, rather than for complex networks, about latter results are\nalready abundant.\n']","[('systems controllability', 0.6486363410949707), ('controllability linear', 0.6393600702285767), ('controllability analysis', 0.6369073987007141), ('controllability matrix', 0.6344345808029175), ('minimal controllability', 0.6115476489067078), ('controllability system', 0.6105129718780518), ('controllability', 0.6027651429176331), ('controllability observability', 0.6013805866241455), ('controllability conditions', 0.5984927415847778), ('controllability can', 0.5539373159408569)]"
479,479,63,479_lossless compression_image compression_lossy compression_compression performance,"['lossless compression', 'image compression', 'lossy compression', 'compression performance', 'compression rate', 'efficient compression', 'rate distortion', 'compression methods', 'compression', 'compression algorithms']","['Universal Representations for Classification-enhanced Lossy Compression   In lossy compression, the classical tradeoff between compression rate and\nreconstruction distortion has traditionally guided algorithm design. However,\nBlau and Michaeli [5] introduced a generalized framework, known as the\nrate-distortion-perception (RDP) function, incorporating perceptual quality as\nan additional dimension of evaluation. More recently, the\nrate-distortion-classification (RDC) function was investigated in [19],\nevaluating compression performance by considering classification accuracy\nalongside distortion. In this paper, we explore universal representations,\nwhere a single encoder is developed to achieve multiple decoding objectives\nacross various distortion and classification (or perception) constraints. This\nuniversality avoids retraining encoders for each specific operating point\nwithin these tradeoffs. Our experimental validation on the MNIST dataset\nindicates that a universal encoder incurs only minimal performance degradation\ncompared to individually optimized encoders for perceptual image compression\ntasks, aligning with prior results from [23]. Nonetheless, we also identify\nthat in the RDC setting, reusing an encoder optimized for one specific\nclassification-distortion tradeoff leads to a significant distortion penalty\nwhen applied to alternative points.\n', 'A Rate-Distortion-Classification Approach for Lossy Image Compression   In lossy image compression, the objective is to achieve minimal signal\ndistortion while compressing images to a specified bit rate. The increasing\ndemand for visual analysis applications, particularly in classification tasks,\nhas emphasized the significance of considering semantic distortion in\ncompressed images. To bridge the gap between image compression and visual\nanalysis, we propose a Rate-Distortion-Classification (RDC) model for lossy\nimage compression, offering a unified framework to optimize the trade-off\nbetween rate, distortion, and classification accuracy. The RDC model is\nextensively analyzed both statistically on a multi-distribution source and\nexperimentally on the widely used MNIST dataset. The findings reveal that the\nRDC model exhibits desirable properties, including monotonic non-increasing and\nconvex functions, under certain conditions. This work provides insights into\nthe development of human-machine friendly compression methods and Video Coding\nfor Machine (VCM) approaches, paving the way for end-to-end image compression\ntechniques in real-world applications.\n', 'Analysis and Enhancement of Lossless Image Compression in JPEG-XL   As the demand for digital information grows in fields like medicine, remote\nsensing, and archival, efficient image compression becomes crucial. This paper\nfocuses on lossless image compression, vital for managing the increasing volume\nof image data without quality loss. Current research emphasizes techniques such\nas predictive coding, transform coding, and context modeling to improve\ncompression ratios. This study evaluates lossless compression in JPEG XL, the\nlatest standard in the JPEG family, and aims to enhance its compression ratio\nby modifying the codebase. Results show that while overall compression levels\nare below the original codec, one prediction method improves compression for\nspecific image types. This study offers insights into enhancing lossless\ncompression performance and suggests possibilities for future advancements in\nthis area.\n']","[('lossless compression', 0.6087267398834229), ('image compression', 0.6059099435806274), ('lossy compression', 0.5776505470275879), ('compression performance', 0.5611299276351929), ('compression rate', 0.5593934059143066), ('efficient compression', 0.5555649399757385), ('rate distortion', 0.5357561111450195), ('compression methods', 0.5208307504653931), ('compression', 0.519421398639679), ('compression algorithms', 0.5091071724891663)]"
480,480,63,480_group schemes_fundamental groups_etale fundamental_fundamental group,"['group schemes', 'fundamental groups', 'etale fundamental', 'fundamental group', 'abelian varieties', 'fundamental group mathbb', 'schemes', 'variety algebraically closed', 'abelian variety', 'conjecture etale']","[""The tame fundamental group schemes of curves in positive characteristic   The tame fundamental group scheme for an algebraic variety is the maximal\nlinearly reductive quotient of Nori's fundamental group scheme. In this paper,\nwe study the tame fundamental group schemes of smooth curves defined over\nalgebraically closed fields of positive characteristic and develop the theory\nof cospecialization maps for them. As a result, we see that the tame\nfundamental group schemes heavily depend on the curves. We also see that\nnumerical invariants of curves can be reconstructed from the tame fundamental\ngroup schemes.\n"", ""The section conjecture for the toric fundamental group over $p$-adic\n  fields   The toric fundamental group is the Tannaka dual of a category of vector\nbundles which become direct sums of line bundles on a finite \\'etale cover. It\nis an extension of the \\'etale fundamental group scheme by a projective limit\nof tori.\n  Grothendieck's section conjecture for the \\'etale fundamental group implies\nthe analogous statement for the toric fundamental group. We call this the toric\nsection conjecture. We prove that a resolution of the toric section conjecture\nwould reduce the original one to particular cases about which more is known,\nmainly due to J. Stix.\n  We prove that abelian varieties over $p$-adic fields satisfy the toric\nsection conjecture, and give strong evidence that it holds for hyperbolic\ncurves over $p$-adic fields, too.\n"", 'A note on certain Tannakian group schemes   In this note, we prove that the F-fundamental group scheme is birational\ninvariant for smooth projective varieties. We prove that the F-fundamental\ngroup scheme is naturally a quotient of the Nori fundamental group scheme. For\nelliptic curves, it turns out that the F-fundamental group scheme and the Nori\nfundamental group scheme coincides. We also consider an extension of the Nori\nfundamental group scheme in positive characteristic using semi-essentially\nfinite vector bundles and prove that in this way, we do not get a non-trivial\nextension of the Nori fundamental group scheme for elliptic curves, unlike in\ncharacteristic zero.\n']","[('group schemes', 0.5616292357444763), ('fundamental groups', 0.5542318224906921), ('etale fundamental', 0.5300147533416748), ('fundamental group', 0.5270683169364929), ('abelian varieties', 0.51651531457901), ('fundamental group mathbb', 0.49789679050445557), ('schemes', 0.4877047836780548), ('variety algebraically closed', 0.486341267824173), ('abelian variety', 0.4826926290988922), ('conjecture etale', 0.48142093420028687)]"
481,481,63,481_yang baxter solutions_solutions yang baxter_theoretic yang baxter_quantum yang baxter,"['yang baxter solutions', 'solutions yang baxter', 'theoretic yang baxter', 'quantum yang baxter', 'baxter solutions', 'solutions yang', 'yang baxter', 'solutions quantum', 'groups solutions', 'theoretic yang']","['A characterization of finite simple set-theoretic solutions of the\n  Yang-Baxter equation   In this paper we present a characterization of finite simple involutive\nnon-degenerate set-theoretic solutions of the Yang-Baxter equation by means of\nleft braces and we provide some significant examples.\n', 'Indecomposable involutive set-theoretical solutions to the Yang-Baxter\n  equation of size $p^2$   The quantum Yang-Baxter equation is a braiding condition on vector spaces\nwhich is of high relevance in several fields of mathematics, such as knot\ntheory and quantum group theory. Their combinatorial counterpart are\nset-theoretic solutions to the Yang--Baxter equation, whose investigation is\nstrongly driven by the study of algebraic objects called (skew) braces. In this\narticle, we focus on indecomposable involutive non-degenerate set-theoretic\nsolutions to the Yang-Baxter equation. More specifically, through a thorough\nanalysis of their associated braces, we give a full classification of those\nwhich are of size $p^2$, for $p$ a prime.\n', 'Enumeration of set-theoretic solutions to the Yang-Baxter equation   We use Constraint Satisfaction methods to enumerate and construct\nset-theoretic solutions to the Yang-Baxter equation of small size. We show that\nthere are 321931 involutive solutions of size nine, 4895272 involutive\nsolutions of size ten and 422449480 non-involutive solution of size eight. Our\nmethod is then used to enumerate non-involutive biquandles.\n']","[('yang baxter solutions', 0.7274637818336487), ('solutions yang baxter', 0.6957356333732605), ('theoretic yang baxter', 0.6372444033622742), ('quantum yang baxter', 0.6245448589324951), ('baxter solutions', 0.6140480637550354), ('solutions yang', 0.5185389518737793), ('yang baxter', 0.4996185600757599), ('solutions quantum', 0.4738007187843323), ('groups solutions', 0.46086952090263367), ('theoretic yang', 0.4398537278175354)]"
482,482,63,482_numerical approximation semilinear_approximation methods_numerical approximation_semilinear pdes,"['numerical approximation semilinear', 'approximation methods', 'numerical approximation', 'semilinear pdes', 'approximation schemes', 'stochastic galerkin methods', 'semilinear heat equations', 'elliptic pdes', 'approximation semilinear', 'semilinear parabolic partial']","['Multilevel Picard approximations for high-dimensional semilinear\n  second-order PDEs with Lipschitz nonlinearities   The recently introduced full-history recursive multilevel Picard (MLP)\napproximation methods have turned out to be quite successful in the numerical\napproximation of solutions of high-dimensional nonlinear PDEs. In particular,\nthere are mathematical convergence results in the literature which prove that\nMLP approximation methods do overcome the curse of dimensionality in the\nnumerical approximation of nonlinear second-order PDEs in the sense that the\nnumber of computational operations of the proposed MLP approximation method\ngrows at most polynomially in both the reciprocal $1/\\epsilon$ of the\nprescribed approximation accuracy $\\epsilon>0$ and the PDE dimension $d\\in\n\\mathbb{N}=\\{1,2,3, \\ldots\\}$. However, in each of the convergence results for\nMLP approximation methods in the literature it is assumed that the coefficient\nfunctions in front of the second-order differential operator are affine linear.\nIn particular, until today there is no result in the scientific literature\nwhich proves that any semilinear second-order PDE with a general time horizon\nand a non affine linear coefficient function in front of the second-order\ndifferential operator can be approximated without the curse of dimensionality.\nIt is the key contribution of this article to overcome this obstacle and to\npropose and analyze a new type of MLP approximation method for semilinear\nsecond-order PDEs with possibly nonlinear coefficient functions in front of the\nsecond-order differential operators. In particular, the main result of this\narticle proves that this new MLP approximation method does indeed overcome the\ncurse of dimensionality in the numerical approximation of semilinear\nsecond-order PDEs.\n', 'Overcoming the curse of dimensionality in the numerical approximation of\n  high-dimensional semilinear elliptic partial differential equations   Recently, so-called full-history recursive multilevel Picard (MLP)\napproximation schemes have been introduced and shown to overcome the curse of\ndimensionality in the numerical approximation of semilinear parabolic partial\ndifferential equations (PDEs) with Lipschitz nonlinearities. The key\ncontribution of this article is to introduce and analyze a new variant of MLP\napproximation schemes for certain semilinear elliptic PDEs with Lipschitz\nnonlinearities and to prove that the proposed approximation schemes overcome\nthe curse of dimensionality in the numerical approximation of such semilinear\nelliptic PDEs.\n', 'Numerical simulations for full history recursive multilevel Picard\n  approximations for systems of high-dimensional partial differential equations   One of the most challenging issues in applied mathematics is to develop and\nanalyze algorithms which are able to approximately compute solutions of\nhigh-dimensional nonlinear partial differential equations (PDEs). In\nparticular, it is very hard to develop approximation algorithms which do not\nsuffer under the curse of dimensionality in the sense that the number of\ncomputational operations needed by the algorithm to compute an approximation of\naccuracy $\\epsilon > 0$ grows at most polynomially in both the reciprocal\n$1/\\epsilon$ of the required accuracy and the dimension $d \\in \\mathbb{N}$ of\nthe PDE. Recently, a new approximation method, the so-called full history\nrecursive multilevel Picard (MLP) approximation method, has been introduced\nand, until today, this approximation scheme is the only approximation method in\nthe scientific literature which has been proven to overcome the curse of\ndimensionality in the numerical approximation of semilinear PDEs with general\ntime horizons. It is a key contribution of this article to extend the MLP\napproximation method to systems of semilinear PDEs and to numerically test it\non several example PDEs. More specifically, we apply the proposed MLP\napproximation method in the case of Allen-Cahn PDEs, Sine-Gordon-type PDEs,\nsystems of coupled semilinear heat PDEs, and semilinear Black-Scholes PDEs in\nup to 1000 dimensions. The presented numerical simulation results suggest in\nthe case of each of these example PDEs that the proposed MLP approximation\nmethod produces very accurate results in short runtimes and, in particular, the\npresented numerical simulation results indicate that the proposed MLP\napproximation scheme significantly outperforms certain deep learning based\napproximation methods for high-dimensional semilinear PDEs.\n']","[('numerical approximation semilinear', 0.577593982219696), ('approximation methods', 0.5028925538063049), ('numerical approximation', 0.49057093262672424), ('semilinear pdes', 0.4715627431869507), ('approximation schemes', 0.4654906988143921), ('stochastic galerkin methods', 0.4595715403556824), ('semilinear heat equations', 0.4514892101287842), ('elliptic pdes', 0.4385432004928589), ('approximation semilinear', 0.4330664873123169), ('semilinear parabolic partial', 0.3970268964767456)]"
483,483,63,483_optimal power flow_ac optimal power_ac power flow_ac optimal,"['optimal power flow', 'ac optimal power', 'ac power flow', 'ac optimal', 'power flow', 'power flow opf', 'power grid', 'power flow equations', 'current optimal power', 'optimal power']","[""Differentiable Optimization for Deep Learning-Enhanced DC Approximation\n  of AC Optimal Power Flow   The growing scale of power systems and the increasing uncertainty introduced\nby renewable energy sources necessitates novel optimization techniques that are\nsignificantly faster and more accurate than existing methods. The AC Optimal\nPower Flow (AC-OPF) problem, a core component of power grid optimization, is\noften approximated using linearized DC Optimal Power Flow (DC-OPF) models for\ncomputational tractability, albeit at the cost of suboptimal and inefficient\ndecisions. To address these limitations, we propose a novel deep learning-based\nframework for network equivalency that enhances DC-OPF to more closely mimic\nthe behavior of AC-OPF. The approach utilizes recent advances in differentiable\noptimization, incorporating a neural network trained to predict adjusted nodal\nshunt conductances and branch susceptances in order to account for nonlinear\npower flow behavior. The model can be trained end-to-end using modern deep\nlearning frameworks by leveraging the implicit function theorem. Results\ndemonstrate the framework's ability to significantly improve prediction\naccuracy, paving the way for more reliable and efficient power systems.\n"", 'Learning to Solve AC Optimal Power Flow by Differentiating through\n  Holomorphic Embeddings   Alternating current optimal power flow (AC-OPF) is one of the fundamental\nproblems in power systems operation. AC-OPF is traditionally cast as a\nconstrained optimization problem that seeks optimal generation set points\nwhilst fulfilling a set of non-linear equality constraints -- the power flow\nequations. With increasing penetration of renewable generation, grid operators\nneed to solve larger problems at shorter intervals. This motivates the research\ninterest in learning OPF solutions with neural networks, which have fast\ninference time and is potentially scalable to large networks. The main\ndifficulty in solving the AC-OPF problem lies in dealing with this equality\nconstraint that has spurious roots, i.e. there are assignments of voltages that\nfulfill the power flow equations that however are not physically realizable.\nThis property renders any method relying on projected-gradients brittle because\nthese non-physical roots can act as attractors. In this paper, we show\nefficient strategies that circumvent this problem by differentiating through\nthe operations of a power flow solver that embeds the power flow equations into\na holomorphic function. The resulting learning-based approach is validated\nexperimentally on a 200-bus system and we show that, after training, the\nlearned agent produces optimized power flow solutions reliably and fast.\nSpecifically, we report a 12x increase in speed and a 40% increase in\nrobustness compared to a traditional solver. To the best of our knowledge, this\napproach constitutes the first learning-based approach that successfully\nrespects the full non-linear AC-OPF equations.\n', ""Improving the Accuracy of DC Optimal Power Flow Formulations via\n  Parameter Optimization   DC Optimal Power Flow (DC-OPF) problems optimize the generators' active power\nsetpoints while satisfying constraints based on the DC power flow\nlinearization. The computational tractability advantages of DC-OPF problems\ncome at the expense of inaccuracies relative to AC Optimal Power Flow (AC-OPF)\nproblems which accurately model the nonlinear steady-state behavior of power\ngrids. This paper proposes an algorithm that significantly improves the\naccuracy of the generators' active power setpoints from DC-OPF problems with\nrespect to the corresponding AC-OPF problems over a specified range of\noperating conditions. Using sensitivity information in a machine\nlearning-inspired methodology, this algorithm tunes coefficient and bias\nparameters in the DC power flow approximation to improve the accuracy of the\nresulting DC-OPF solutions. Employing the Truncated Newton Conjugate-Gradient\n(TNC) method -- a Quasi-Newton optimization technique -- this parameter tuning\noccurs during an offline training phase, with the resulting parameters then\nused in online computations. Numerical results underscore the algorithm's\nefficacy with accuracy improvements in squared two-norm and $\\infty$-norm\nlosses of up to $90\\%$ and $79\\%$, respectively, relative to traditional DC-OPF\nformulations.\n""]","[('optimal power flow', 0.5480743050575256), ('ac optimal power', 0.5040249228477478), ('ac power flow', 0.45992571115493774), ('ac optimal', 0.4550696611404419), ('power flow', 0.45172393321990967), ('power flow opf', 0.44556885957717896), ('power grid', 0.4416418671607971), ('power flow equations', 0.4300520718097687), ('current optimal power', 0.42112356424331665), ('optimal power', 0.41454291343688965)]"
484,484,63,484_dividends_dividend_markov additive process_stochastic control,"['dividends', 'dividend', 'markov additive process', 'stochastic control', 'levy processes', 'surplus process', 'markov additive', 'process optimal', 'optimality', 'risk theory']","[""An optimization dichotomy for capital injections and absolutely\n  continuous dividend strategies   We consider an optimal stochastic control problem in which a firm's\ncash/surplus process is controlled by dividend payments and capital injections.\nStockholders aim to maximize their dividend stream minus the cost of injecting\ncapital, if needed. We consider absolutely continuous dividend policies subject\nto a level-dependent upper bound on the dividend rate while we allow for\ngeneral capital injections behavior. We prove that the optimal strategy can\nonly be of two types: dividends are paid according to a \\textit{mean-reverting}\nstrategy with capital injections performed each time the cash process reaches\nzero; or, dividends are paid according to another \\textit{mean-reverting}\nstrategy and no injection of capital is ever made, until ruin is reached. We\ngive a complete solution to this problem and characterize this dichotomy by\ncomparing (the derivatives of) the value functions at zero of two sub-problems.\nThe first sub-problem is concerned solely with the maximization of dividends,\nwhile the second sub-problem is the corresponding bail-out optimal dividend\nproblem for which we provide also a complete solution.\n"", ""On De Finetti's control under Poisson observations: optimality of a\n  double barrier strategy in a Markov additive model   In this paper we consider the De Finetti's optimal dividend and capital\ninjection problem under a Markov additive model. We assume that the surplus\nprocess before dividends and capital injections follows a spectrally positive\nMarkov additive process. Dividend payments are made only at the jump times of\nan independent Poisson process. Capitals are required to be injected whenever\nneeded to ensure a non-negative surplus process to avoid bankruptcy. Our\npurpose is to characterize the optimal periodic dividend and capital injection\nstrategy that maximizes the expected total discounted dividends subtracted by\nthe total discounted costs of capital injection. To this end, we first consider\nan auxiliary optimal periodic dividend and capital injection problem with final\npayoff under a single spectrally positive L\\'evy process and conjecture that\nthe optimal strategy is a double barrier strategy. Using the fluctuation theory\nand excursion-theoretical approach of the spectrally positive L\\'evy process\nand the Hamilton-Jacobi-Bellman inequality approach of the control theory, we\nare able to verify the conjecture that some double barrier periodic dividend\nand capital injection strategy solves the auxiliary problem. With the results\nfor the auxiliary control problem and a fixed point argument for recursive\niterations induced by the dynamic programming principle, the optimality of a\nregime-modulated double barrier periodic dividend and capital injection\nstrategy is proved for our target control problem.\n"", 'Optimal ratcheting of dividend payout under Brownian motion surplus   This paper is concerned with a long standing optimal dividend payout problem\nsubject to the so-called ratcheting constraint, that is, the dividend payout\nrate shall be non-decreasing over time and is thus self-path-dependent. The\nsurplus process is modeled by a drifted Brownian motion process and the aim is\nto find the optimal dividend ratcheting strategy to maximize the expectation of\nthe total discounted dividend payouts until the ruin time. Due to the\nself-path-dependent control constraint, the standard control theory cannot be\ndirectly applied to tackle the problem. The related Hamilton-Jacobi-Bellman\n(HJB) equation is a new type of variational inequality. In the literature, it\nis only shown to have a viscosity solution, which is not strong enough to\nguarantee the existence of an optimal dividend ratcheting strategy. This paper\nproposes a novel partial differential equation method to study the HJB\nequation. We not only prove the the existence and uniqueness of the solution in\nsome stronger functional space, but also prove the strict monotonicity,\nboundedness, and $C^\\infty$-smoothness of the dividend ratcheting free\nboundary. Based on these results, we eventually derive an optimal dividend\nratcheting strategy, and thus solve the open problem completely. Economically\nspeaking, we find that if the surplus volatility is above an explicit\nthreshold, then one should pay dividends at the maximum rate, regardless the\nsurplus level. Otherwise, by contrast, the optimal dividend ratcheting strategy\nrelays on the surplus level and one should only ratchet up the dividend payout\nrate when the surplus level touches the dividend ratcheting free boundary.\nMoreover, our numerical results suggest that one should invest into those\ncompanies with stable dividend payout strategies since their income rates\nshould be higher and volatility rates smaller.\n']","[('dividends', 0.49920588731765747), ('dividend', 0.47229570150375366), ('markov additive process', 0.42522016167640686), ('stochastic control', 0.40502607822418213), ('levy processes', 0.36901596188545227), ('surplus process', 0.3542971611022949), ('markov additive', 0.35388848185539246), ('process optimal', 0.3493140637874603), ('optimality', 0.3413011431694031), ('risk theory', 0.3352701961994171)]"
485,485,63,485_viscous hamilton jacobi_convex hamilton jacobi_solutions hamilton jacobi_existence viscosity solutions,"['viscous hamilton jacobi', 'convex hamilton jacobi', 'solutions hamilton jacobi', 'existence viscosity solutions', 'hamilton jacobi equations', 'viscous hamilton', 'existence viscosity', 'convex hamilton', 'convergence viscosity', 'viscosity solutions']","['The selection problem for a new class of perturbations of\n  Hamilton-Jacobi equations and its applications   This paper studies a perturbation problem given by the equation:\n\\begin{equation*} H(x, d_xu_\\lambda, \\lambda u_\\lambda(x))+\\lambda\nV(x,\\lambda)=c \\quad \\text{in $M$}, \\end{equation*} where $M$ is a closed\nmanifold and $\\lambda>0$ is a perturbation parameter. The Hamiltonian\n$H(x,p,u):T^*M\\times \\mathbb{R}\\to \\mathbb{R}$ satisfies certain convexity,\nsuperlinearity, and monotonicity conditions. $\\lambda\nV(\\cdot,\\lambda):M\\to\\mathbb{R}$ converges to zero as $\\lambda\\to 0$. First, we\nstudy the asymptotic behavior of the viscosity solution\n$u_\\lambda:M\\to\\mathbb{R}$ as $\\lambda$ approaches zero. This perturbation\nproblem explores the combined effects of both the vanishing discount process\nand potential perturbations, leading to a new selection principle that extends\nbeyond the classical vanishing discount approach. Additionally, we apply this\nprinciple to Hamilton-Jacobi equations with $u$-independent Hamiltonians,\nresulting in the introduction of a new solution operator. This operator\nprovides new insights into the variational characterization of viscosity\nsolutions and Mather measures.\n', ""On the negative limit of viscosity solutions for discounted\n  Hamilton-Jacobi equations   Suppose $M$ is a closed Riemannian manifold. For a $C^2$ generic (in the\nsense of Ma\\~n\\'e) Tonelli Hamiltonian $H: T^*M\\rightarrow\\mathbb{R}$, the\nminimal viscosity solution $u_\\lambda^-:M\\rightarrow \\mathbb{R}$ of the\nnegative discounted equation \\[-\\lambda u+H(x,d_xu)=c(H),\\quad x\\in M,\\\n\\lambda>0 \\] with the Ma\\~n\\'e's critical value $c(H)$ converges to a uniquely\nestablished viscosity solution $u_0^-$ of the critical Hamilton-Jacobi equation\n\\[ H(x,d_x u)=c(H),\\quad x\\in M \\] as $\\lambda\\rightarrow 0_+$. We also propose\na dynamical interpretation of $u_0^-$.\n"", 'Convergence of solutions for some degenerate discounted Hamilton--Jacobi\n  equations   We study solutions of Hamilton--Jacobi equations of the form $$\\lambda\n\\alpha(x) u_\\lambda(x) + H(x, D_x u_\\lambda) = c,$$\n  where $\\alpha$ is a nonnegative function, $\\lambda$ a positive constant, $c$\na constant and $H $ a convex coercive Hamiltonian. Under suitable conditions on\n$\\alpha$ we prove that the functions $u_\\lambda$ converge as $\\lambda\\to 0$ to\na function $u_0$ that is a solution of the critical equation $H(x, D_x u_0) =\nc$.\n']","[('viscous hamilton jacobi', 0.6327298879623413), ('convex hamilton jacobi', 0.6288728713989258), ('solutions hamilton jacobi', 0.6039184331893921), ('existence viscosity solutions', 0.5780844688415527), ('hamilton jacobi equations', 0.5732761025428772), ('viscous hamilton', 0.5586130619049072), ('existence viscosity', 0.5216942429542542), ('convex hamilton', 0.5071069598197937), ('convergence viscosity', 0.4984537959098816), ('viscosity solutions', 0.4887389540672302)]"
486,486,63,486_simplicial complexes_simplicial complex_random geometric graph_hypergraphs random,"['simplicial complexes', 'simplicial complex', 'random geometric graph', 'hypergraphs random', 'simplicial', 'random hypergraph', 'topology random', 'random geometric', 'random clique', 'random dimensional']","['Ample simplicial complexes   Motivated by potential applications in network theory, engineering and\ncomputer science, we study $r$-ample simplicial complexes. These complexes can\nbe viewed as finite approximations to the Rado complex which has a remarkable\nproperty of {\\it indestructibility,} in the sense that removing any finite\nnumber of its simplexes leaves a complex isomorphic to itself. We prove that an\n$r$-ample simplicial complex is simply connected and $2$-connected for $r$\nlarge. The number $n$ of vertexes of an $r$-ample simplicial complex satisfies\n$\\exp(\\Omega(\\frac{2^r}{\\sqrt{r}}))$. We use the probabilistic method to\nestablish the existence of $r$-ample simplicial complexes with $n$ vertexes for\nany $n>r 2^r 2^{2^r}$. Finally, we introduce the iterated Paley simplicial\ncomplexes, which are explicitly constructed $r$-ample simplicial complexes with\nnearly optimal number of vertexes.\n', ""Central limit theorems for Soft random simplicial complexes   A soft random graph $G(n,r,p)$ can be obtained from the random geometric\ngraph $G(n,r)$ by keeping every edge in $G(n,r)$ with probability $p$. The soft\nrandom simplicial complexes is a model for random simplicial complexes built\nover the soft random graph $G(n,r,p)$. This new model depends on a probability\nvector $\\rho$ which allows the simplicial complexes to present randomness in\nall dimensions. In this article, we use a normal approximation theorem to prove\ncentral limit theorems for the number of $k$-faces and for the Euler's\ncharacteristic for soft random simplicial complexes.\n"", ""Law of large numbers for Betti numbers of homogeneous and spatially\n  independent random simplicial complexes   The Linial-Meshulam complex model is a natural higher-dimensional analog of\nthe Erd\\H{o}s-R\\'enyi graph model. In recent years, Linial and Peled\nestablished a limit theorem for Betti numbers of Linial-Meshulam complexes with\nan appropriate scaling of the underlying parameter. The present paper aims to\nextend that result to more-general random simplicial complex models. We\nintroduce a class of homogeneous and spatially independent random simplicial\ncomplexes, including the Linial-Meshulam complex model and the random clique\ncomplex model as special cases, and we study the asymptotic behavior of their\nBetti numbers. Moreover, we obtain the convergence of the empirical spectral\ndistributions of their Laplacians. A key element in the argument is the local\nweak convergence of simplicial complexes. Inspired by the work of Linial and\nPeled, we establish the local weak limit theorem for homogeneous and spatially\nindependent random simplicial complexes.\n""]","[('simplicial complexes', 0.5944415330886841), ('simplicial complex', 0.5620343685150146), ('random geometric graph', 0.5047833323478699), ('hypergraphs random', 0.5039939284324646), ('simplicial', 0.4867057800292969), ('random hypergraph', 0.443040668964386), ('topology random', 0.43720677495002747), ('random geometric', 0.43413013219833374), ('random clique', 0.43124207854270935), ('random dimensional', 0.43001478910446167)]"
487,487,63,487_sphere packings_bounds sphere packing_sphere packing_packing bound,"['sphere packings', 'bounds sphere packing', 'sphere packing', 'packing bound', 'sphere packing density', 'packing density', 'packing densities', 'packing covering', 'ball packings', 'packing mathbb']","[""Bounds for totally separable translative packings in the plane   A packing of translates of a convex domain in the Euclidean plane is said to\nbe totally separable if any two packing elements can be separated by a line\ndisjoint from the interior of every packing element. This notion was introduced\nby G. Fejes T\\'oth and L. Fejes T\\'oth (1973) and has attracted significant\nattention. In this paper we prove an analogue of Oler's inequality for totally\nseparable translative packings of convex domains and then we derive from it\nsome new results. This includes finding the largest density of totally\nseparable translative packings of an arbitrary convex domain and finding the\nsmallest area convex hull of totally separable packings (resp., totally\nseparable soft packings) generated by given number of translates of a convex\ndomain (resp., soft convex domain). Finally, we determine the largest covering\nratio (that is, the largest fraction of the plane covered by the soft disks) of\nan arbitrary totally separable soft disk packing with given soft parameter.\n"", ""Density of triangulated ternary disc packings   We consider ternary disc packings of the plane, i.e. the packings using discs\nof three different radii. Packings in which each ''hole'' is bounded by three\npairwise tangent discs are called triangulated. There are 164 pairs $(r,s)$,\n$1{>}r{>}s$, allowing triangulated packings by discs of radii 1, $r$ and $s$.\nIn this paper, we enhance existing methods of dealing with maximal-density\npackings in order to find ternary triangulated packings which maximize the\ndensity among all the packings with the same disc radii. We showed for 16 pairs\nthat the density is maximized by a triangulated ternary packing; for 15 other\npairs, we proved the density to be maximized by a triangulated packing using\nonly two sizes of discs; for 40 pairs, we found non-triangulated packings\nstrictly denser than any triangulated one; finally, we classified the remaining\ncases where our methods are not applicable.\n"", 'On contact numbers of locally separable unit sphere packings   The contact number of a packing of finitely many balls in Euclidean $d$-space\nis the number of touching pairs of balls in the packing. A prominent subfamily\nof sphere packings is formed by the so-called totally separable sphere\npackings: here, a packing of balls in Euclidean $d$-space is called totally\nseparable if any two balls can be separated by a hyperplane such that it is\ndisjoint from the interior of each ball in the packing. Bezdek, Szalkai and\nSzalkai (Discrete Math. 339(2): 668-676, 2016) upper bounded the contact\nnumbers of totally separable packings of $n$ unit balls in Euclidean $d$-space\nin terms of $n$ and $d$. In this paper we improve their upper bound and extend\nthat new upper bound to the so-called locally separable packings of unit balls.\nWe call a packing of unit balls a locally separable packing if each unit ball\nof the packing together with the unit balls that are tangent to it form a\ntotally separable packing. In the plane, we prove a crystallization result by\ncharacterizing all locally separable packings of $n$ unit disks having maximum\ncontact number.\n']","[('sphere packings', 0.6722238063812256), ('bounds sphere packing', 0.6599403619766235), ('sphere packing', 0.6526076793670654), ('packing bound', 0.6494789719581604), ('sphere packing density', 0.6379593014717102), ('packing density', 0.6268922686576843), ('packing densities', 0.6107833981513977), ('packing covering', 0.6016293168067932), ('ball packings', 0.5285456776618958), ('packing mathbb', 0.5281727910041809)]"
488,488,62,488_skew braces_skew brace_symmetric skew_skew,"['skew braces', 'skew brace', 'symmetric skew', 'skew', 'theory skew', 'left braces', 'skew left', 'braces', 'brace', 'left brace']","['On two-sided skew braces   In order to study two-sided skew braces, we introduce the notion of weakly\ntrivial skew braces. We give a classification of such skew braces and show that\nthey are essential in the study of two-sided skew braces. As an application, we\nobtain new and generalize known results relating the additive and\nmultiplicative group of two-sided skew braces. Further, we show that two a\npriori different notions of prime and semi-prime skew braces, as introduced by\nKonovalov, Smoktunowicz and Vendramin, coincide for two-sided skew braces.\n', ""Central series' and ($n$)-isoclinism of skew left braces   The aim of this article is to advance the knowledge on the theory of skew\nleft braces. We introduce a subclass of skew left braces, which we denote by\n$\\mathcal{I}_n$, $n \\ge 1$, such that elements of the annihilator and lower\ncentral series' interact `nicely' with respect to commutation. That allows us\nto define a concept of $n$-isoclinism of skew left braces in $\\mathcal{I}_n$,\nby using a concept of brace commutator words, which we have introduced. We\nprove results on $1$-isoclinism (isoclinism) of skew left braces analogous to\nimportant results in group theory. For any two symmetric $n$-isoclinic skew\nleft braces $A$ and $B$, we prove that, there exist skew left braces $C$ and\n$R$ such that both $A$ and $B$ are $n$-isoclinic to both $C$ and $R$ and (i)\n$A$ and $B$ are quotient skew left braces of $C$; (ii) $A$ and $B$ are sub-skew\nleft braces of $R$. Connections between a skew left brace and the group which\noccurs as a natural semi-direct product of additive and multiplicative groups\nof the skew left brace are investigated, and it is proved that $n$-isoclinism\nis preserved from braces to groups. We also show that various nilpotency\nconcepts on skew left braces are invariant under $n$-isoclinism.\n"", 'Aspects of the Category SKB of Skew Braces   We examine the pointed protomodular category SKB of left skew braces. We\nstudy the notion of commutator of ideals in a left skew brace. Notice that in\nthe literature, ""product"" of ideals of skew braces is often considered. We show\nthat Huq=Smith for left skew braces. Finally, we give a set of generators for\nthe commutator of two ideals, and prove that every ideal of a left skew brace\nhas a centralizer.\n']","[('skew braces', 0.7390409708023071), ('skew brace', 0.6907340288162231), ('symmetric skew', 0.5855985283851624), ('skew', 0.5433050394058228), ('theory skew', 0.5334663391113281), ('left braces', 0.5188145637512207), ('skew left', 0.5156097412109375), ('braces', 0.511692464351654), ('brace', 0.4683283269405365), ('left brace', 0.4497099816799164)]"
489,489,62,489_hypersurfaces mean curvature_boundary hypersurfaces_convex hypersurfaces_hypersurfaces hyperbolic,"['hypersurfaces mean curvature', 'boundary hypersurfaces', 'convex hypersurfaces', 'hypersurfaces hyperbolic', 'hypersurfaces hyperbolic space', 'generalized mean curvature', 'hypersurfaces', 'hypersurfaces mean', 'mean curvature prescribed', 'hypersurface']","['Compactness of capillary hypersurfaces with mean curvature prescribed by\n  ambient functions   We prove a compactness result for capillary hypersurfaces with mean curvature\nprescribed by ambient functions, which generalizes the results of Sch\\""atzle\nand Bellettini to the capillary case. The proof relies on extending the\ndefinition of (unoriented) curvature varifolds with capillary boundary\nintroduced by Wang-Zhang to the context of oriented integral varifolds. We also\ndiscuss the case when the mean curvature of the boundary is prescribed.\n', 'Regularity of minimal surfaces with capillary boundary conditions   We prove $\\varepsilon$-regularity theorems for varifolds with capillary\nboundary condition in a Riemannian manifold. These varifolds were first\nintroduced by Kagaya-Tonegawa \\cite{KaTo}. We establish a uniform first\nvariation control for all such varifolds (and free-boundary varifolds\ngenerally) satisfying a sharp density bound and prove that if a capillary\nvarifold has bounded mean curvature and is close to a capillary half-plane with\nangle not equal to $\\tfrac{\\pi}{2}$, then it coincides with a $C^{1,\\alpha}$\nproperly embedded hypersurface. We apply our theorem to deduce regularity at a\ngeneric point along the boundary in the region where the density is strictly\nless than $1$.\n', ""Anisotropic mean curvature type flow and capillary Alexandrov-Fenchel\n  inequalities   In this paper, an anisotropic volume-preserving mean curvature type flow for\nstar-shaped anisotropic $\\omega_0$-capillary hypersurfaces in the half-space is\nstudied, and the long-time existence and smooth convergence to a capillary\nWulff shape are obtained. If the initial hypersurface is strictly convex, the\nsolution of this flow remains to be strictly convex for all $t>0$ by adopting a\nnew approach applicable to anisotropic capillary setting. In analogy with\nclosed hypersurfaces, if the $\\omega_0$-capillary Wulff shape is a\n$\\theta$-capillary hypersurface with constant contact angle $\\theta$, the\nquermassintegrals for anisotropic capillary hypersurfaces match the mixed\nvolume of two $\\theta$-capillary convex bodies. Thus, generalized\nquermassintegrals for anisotropic capillary hypersurfaces with general Wulff\nshapes (i.e., the $\\omega_0$-capillary Wulff shape has a variable contact\nangle) can be defined, which satisfy certain monotonicity properties along the\nflow. As applications, we establish an anisotropic capillary isoperimetric\ninequality for star-shaped anisotropic capillary hypersurfaces and a family of\nnew Alexandrov-Fenchel inequalities for strictly convex anisotropic capillary\nhypersurfaces. In particular, we provide a flow's method to derive the\nAlexandrov-Fenchel inequalities for two $\\theta$-capillary hypersurfaces,\ndemonstrated in [30] (arXiv:2408.13655) from the view of point in convex\ngeometry.\n""]","[('hypersurfaces mean curvature', 0.6499007940292358), ('boundary hypersurfaces', 0.5924600958824158), ('convex hypersurfaces', 0.5805371999740601), ('hypersurfaces hyperbolic', 0.5671579241752625), ('hypersurfaces hyperbolic space', 0.5535412430763245), ('generalized mean curvature', 0.5297123193740845), ('hypersurfaces', 0.5277754664421082), ('hypersurfaces mean', 0.524685800075531), ('mean curvature prescribed', 0.5164006352424622), ('hypersurface', 0.49543413519859314)]"
490,490,62,490_anosov representations_group representations_representations introduced_representations,"['anosov representations', 'group representations', 'representations introduced', 'representations', 'representations sl', 'representations finitely generated', 'representations finitely', 'representations closed', 'discrete representations', 'relatively hyperbolic groups']","['Reducible Suspensions of Anosov Representations   We study through the lens of Anosov representations the dynamical properties\nof reducible suspensions of linear representations of non-elementary hyperbolic\ngroups, which are linear representations preserving and acting weakly\nunipotently on a proper non-zero subspace. We characterize when reducible\nsuspensions are discrete and (almost) faithful, quasi-isometrically embedded,\nand Anosov. Anosov reducible suspensions correspond to points in bounded convex\ndomains in a finite-dimensional real vector space. Stronger characterizations\nof such domains for symmetric Anosov representations allow us to find\ndeformations of Borel Anosov representations which retain some but not all of\nthe Anosov conditions and to compute examples of non-Anosov limits of Anosov\nrepresentations.\n', 'Topological restrictions on relatively Anosov representations   We obtain restrictions on which groups can admit relatively Anosov\nrepresentations into specified target Lie groups, by examining the topology of\npossible Bowditch boundaries and how they interact with the Anosov limit maps.\nFor instance, we prove that, up to finite index, any group admitting a\nrelatively Anosov representation into SL(3,R) is a free group or surface group,\nand any group admitting a relatively k-Anosov representation into Sp(2m,R),\nwhere k is an odd integer between 1 and m, is a surface group or a free product\nof nilpotent groups.\n  We also obtain a characterization of groups admitting relatively 1-Anosov\nrepresentations into SL(4,R), general bounds on the dimension of the Bowditch\nboundary of groups admitting relatively Anosov representations into SL(d,R),\nstatements relating spheres in the Bowditch boundary to the (non-)existence of\nrelatively Anosov representations, and a characterization of groups of\ncohomological dimension at least d-1 admitting relatively 1-Anosov\nrepresentations into SL(d,R).\n', 'Cusped Hitchin representations and Anosov representations of\n  geometrically finite Fuchsian groups   We develop a theory of Anosov representation of geometrically finite Fuchsian\ngroups in SL(d,R) and show that cusped Hitchin representations are Borel Anosov\nin this sense. We establish analogues of many properties of traditional Anosov\nrepresentations. In particular, we show that our Anosov representations are\nstable under type-preserving deformations and that their limit maps vary\nanalytically. We also observe that our Anosov representations fit into the\nprevious frameworks of relatively Anosov and relatively dominated\nrepresentations developed by Kapovich-Leeb and Zhu.\n']","[('anosov representations', 0.7431021928787231), ('group representations', 0.5515949130058289), ('representations introduced', 0.5375238060951233), ('representations', 0.5358865857124329), ('representations sl', 0.5277115106582642), ('representations finitely generated', 0.5168331861495972), ('representations finitely', 0.5098429918289185), ('representations closed', 0.5033633708953857), ('discrete representations', 0.49604612588882446), ('relatively hyperbolic groups', 0.4943126440048218)]"
491,491,62,491_random forests_random forest_regression trees_trees forests,"['random forests', 'random forest', 'regression trees', 'trees forests', 'tree forest', 'forests', 'tree models', 'forest', 'regression tree', 'decision trees']","['Exogenous Randomness Empowering Random Forests   We offer theoretical and empirical insights into the impact of exogenous\nrandomness on the effectiveness of random forests with tree-building rules\nindependent of training data. We formally introduce the concept of exogenous\nrandomness and identify two types of commonly existing randomness: Type I from\nfeature subsampling, and Type II from tie-breaking in tree-building processes.\nWe develop non-asymptotic expansions for the mean squared error (MSE) for both\nindividual trees and forests and establish sufficient and necessary conditions\nfor their consistency. In the special example of the linear regression model\nwith independent features, our MSE expansions are more explicit, providing more\nunderstanding of the random forests\' mechanisms. It also allows us to derive an\nupper bound on the MSE with explicit consistency rates for trees and forests.\nGuided by our theoretical findings, we conduct simulations to further explore\nhow exogenous randomness enhances random forest performance. Our findings\nunveil that feature subsampling reduces both the bias and variance of random\nforests compared to individual trees, serving as an adaptive mechanism to\nbalance bias and variance. Furthermore, our results reveal an intriguing\nphenomenon: the presence of noise features can act as a ""blessing"" in enhancing\nthe performance of random forests thanks to feature subsampling.\n', 'Minimax Rates for High-Dimensional Random Tessellation Forests   Random forests are a popular class of algorithms used for regression and\nclassification. The algorithm introduced by Breiman in 2001 and many of its\nvariants are ensembles of randomized decision trees built from axis-aligned\npartitions of the feature space. One such variant, called Mondrian forests, was\nproposed to handle the online setting and is the first class of random forests\nfor which minimax rates were obtained in arbitrary dimension. However, the\nrestriction to axis-aligned splits fails to capture dependencies between\nfeatures, and random forests that use oblique splits have shown improved\nempirical performance for many tasks. In this work, we show that a large class\nof random forests with general split directions also achieve minimax optimal\nconvergence rates in arbitrary dimension. This class includes STIT forests, a\ngeneralization of Mondrian forests to arbitrary split directions, as well as\nrandom forests derived from Poisson hyperplane tessellations. These are the\nfirst results showing that random forest variants with oblique splits can\nobtain minimax optimality in arbitrary dimension. Our proof technique relies on\nthe novel application of the theory of stationary random tessellations in\nstochastic geometry to statistical learning theory.\n', 'Asymptotic Properties of High-Dimensional Random Forests   As a flexible nonparametric learning tool, the random forests algorithm has\nbeen widely applied to various real applications with appealing empirical\nperformance, even in the presence of high-dimensional feature space. Unveiling\nthe underlying mechanisms has led to some important recent theoretical results\non the consistency of the random forests algorithm and its variants. However,\nto our knowledge, almost all existing works concerning random forests\nconsistency in high dimensional setting were established for various modified\nrandom forests models where the splitting rules are independent of the\nresponse; a few exceptions assume simple data generating models with binary\nfeatures. In light of this, in this paper we derive the consistency rates for\nthe random forests algorithm associated with the sample CART splitting\ncriterion, which is the one used in the original version of the algorithm, in a\ngeneral high-dimensional nonparametric regression setting through a\nbias-variance decomposition analysis. Our new theoretical results show that\nrandom forests can indeed adapt to high dimensionality and allow for\ndiscontinuous regression function. Our bias analysis characterizes explicitly\nhow the random forests bias depends on the sample size, tree height, and column\nsubsampling parameter. Some limitations on our current results are also\ndiscussed.\n']","[('random forests', 0.6068018078804016), ('random forest', 0.5975457429885864), ('regression trees', 0.5601415038108826), ('trees forests', 0.5339198112487793), ('tree forest', 0.5095943212509155), ('forests', 0.4905528426170349), ('tree models', 0.4656199514865875), ('forest', 0.4621380567550659), ('regression tree', 0.4558812975883484), ('decision trees', 0.4510056674480438)]"
492,492,62,492_ultrametric spaces_ultrametric space_pseudometric spaces_semimetric spaces,"['ultrametric spaces', 'ultrametric space', 'pseudometric spaces', 'semimetric spaces', 'ultrametrics', 'ultrametric', 'universal spaces', 'metrizable space', 'arbitrary metric space', 'proper metric spaces']","[""Constructions of Urysohn universal ultrametric spaces   In this paper, we give new constructions of Urysohn universal ultrametric\nspaces. We first characterize a Urysohn universal ultrametric subspace of the\nspace of all continuous functions whose images contain the zero, from a\nzero-dimensional compact Hausdorff space without isolated points into the space\nof non-negative real numbers equipped with the nearly discrete topology. As a\nconsequence, the whole function space is Urysohn universal, which can be\nconsidered as a non-Archimedean analog of Banach--Mazur theorem. As a more\napplication, we prove that the space of all continuous pseudo-ultrametrics on a\nzero-dimensional compact Hausdorff space with an accumulation point is a\nUrysohn universal ultrametric space. This result can be considered as a variant\nof Wan's construction of Urysohn universal ultrametric space via the\nGromov--Hausdorff ultrametric space.\n"", 'Ultrametric preserving functions and weak similarities of ultrametric\n  spaces   Let $WS(X, d)$ be the class of ultrametric spaces which are weakly similar to\nultrametric space $(X, d)$. The main results of the paper completely describe\nthe ultrametric spaces $(X, d)$ for which the equality $$ \\rho(x, y) =\nf(d(\\Phi(x), \\Phi(y))) $$ holds for every $(Y, \\rho) \\in WS(X, d)$, every weak\nsimilarity $\\Phi \\colon Y \\to X$, and all $x$, $y \\in Y$ with some ultrametric\n(pseudoultrametric) preserving function $f$ depending on $\\Phi$.\n', 'Characterizations of Urysohn universal ultrametric spaces   In this paper, using the existence of infinite equidistant subsets of closed\nballs, we characterize the injectivity of ultrametric spaces for finite\nultrametric spaces, which also gives a characterization of the Urysohn\nuniversal ultrametric spaces. As an application, we find that the operations of\nthe Cartesian product and the hyperspaces preserve the structures of the\nUrysohn universal ultrametric spaces. Namely, let $(X, d)$ be the Urysohn\nuniversal ultrametric space. Then we show that $(X\\times X, d\\times d)$ is\nisometric to $(X, d)$. Next we prove that the hyperspace consisting of all\nnon-empty compact subsets of $(X, d)$ and symmetric products of $(X, d)$ are\nisometric to $(X, d)$. We also establish that every complete ultrametric space\ninjective for finite ultrametric space contains a subspace isometric to $(X,\nd)$.\n']","[('ultrametric spaces', 0.8508307933807373), ('ultrametric space', 0.7994542717933655), ('pseudometric spaces', 0.6059825420379639), ('semimetric spaces', 0.6031386852264404), ('ultrametrics', 0.5941691994667053), ('ultrametric', 0.5572716593742371), ('universal spaces', 0.5096129775047302), ('metrizable space', 0.5065327286720276), ('arbitrary metric space', 0.4727352261543274), ('proper metric spaces', 0.45323482155799866)]"
493,493,62,493_image registration_diffeomorphic image_smooth interpolation_deformation metric,"['image registration', 'diffeomorphic image', 'smooth interpolation', 'deformation metric', 'large deformation', 'diffeomorphic', 'krylov solver', 'registration', 'medical imaging', 'shape matching']","['Fast GPU 3D Diffeomorphic Image Registration   3D image registration is one of the most fundamental and computationally\nexpensive operations in medical image analysis. Here, we present a\nmixed-precision, Gauss--Newton--Krylov solver for diffeomorphic registration of\ntwo images. Our work extends the publicly available CLAIRE library to GPU\narchitectures. Despite the importance of image registration, only a few\nimplementations of large deformation diffeomorphic registration packages\nsupport GPUs. Our contributions are new algorithms to significantly reduce the\nrun time of the two main computational kernels in CLAIRE: calculation of\nderivatives and scattered-data interpolation. We deploy (i) highly-optimized,\nmixed-precision GPU-kernels for the evaluation of scattered-data interpolation,\n(ii) replace Fast-Fourier-Transform (FFT)-based first-order derivatives with\noptimized 8th-order finite differences, and (iii) compare with state-of-the-art\nCPU and GPU implementations. As a highlight, we demonstrate that we can\nregister $256^3$ clinical images in less than 6 seconds on a single NVIDIA\nTesla V100. This amounts to over 20$\\times$ speed-up over the current version\nof CLAIRE and over 30$\\times$ speed-up over existing GPU implementations.\n', 'CLAIRE: Scalable GPU-Accelerated Algorithms for Diffeomorphic Image\n  Registration in 3D   We present our work on scalable, GPU-accelerated algorithms for diffeomorphic\nimage registration. The associated software package is termed CLAIRE. Image\nregistration is a non-linear inverse problem. It is about computing a spatial\nmapping from one image of the same object or scene to another. In diffeomorphic\nimage registration, the set of admissible spatial transformations is restricted\nto maps that are smooth, one-to-one, and have a smooth inverse. We formulate\ndiffeomorphic image registration as a variational problem governed by transport\nequations. We use an inexact, globalized (Gauss--)Newton--Krylov method for\nnumerical optimization. We consider semi-Lagrangian methods for numerical time\nintegration. Our solver features mixed-precision, hardware-accelerated\ncomputational kernels for optimal computational throughput. We use the\nmessage-passing interface for distributed-memory parallelism and deploy our\ncode on modern high-performance computing architectures. Our solver allows us\nto solve clinically relevant problems in under four seconds on a single GPU. It\ncan also be applied to large-scale 3D imaging applications with data that is\ndiscretized on meshes with billions of voxels. We demonstrate that our\nnumerical framework yields high-fidelity results in only a few seconds, even if\nwe search for an optimal regularization parameter.\n', 'Diffeomorphic Image Registration with An Optimal Control Relaxation and\n  Its Implementation   Image registration has played an important role in image processing problems,\nespecially in medical imaging applications. It is well known that when the\ndeformation is large, many variational models cannot ensure diffeomorphism. In\nthis paper, we propose a new registration model based on an optimal control\nrelaxation constraint for large deformation images, which can theoretically\nguarantee that the registration mapping is diffeomorphic. We present an\nanalysis of optimal control relaxation for indirectly seeking the diffeomorphic\ntransformation of Jacobian determinant equation and its registration\napplications, including the construction of diffeomorphic transformation as a\nspecial space. We also provide an existence result for the control increment\noptimization problem in the proposed diffeomorphic image registration model\nwith an optimal control relaxation. Furthermore, a fast iterative scheme based\non the augmented Lagrangian multipliers method (ALMM) is analyzed to solve the\ncontrol increment optimization problem, and a convergence analysis is followed.\nFinally, a grid unfolding indicator is given, and a robust solving algorithm\nfor using the deformation correction and backtrack strategy is proposed to\nguarantee that the solution is diffeomorphic. Numerical experiments show that\nthe registration model we proposed can not only get a diffeomorphic mapping\nwhen the deformation is large, but also achieves the state-of-the-art\nperformance in quantitative evaluations in comparing with other classical\nmodels.\n']","[('image registration', 0.5349790453910828), ('diffeomorphic image', 0.42347922921180725), ('smooth interpolation', 0.4148949086666107), ('deformation metric', 0.3672361671924591), ('large deformation', 0.3615803122520447), ('diffeomorphic', 0.3574073612689972), ('krylov solver', 0.353678822517395), ('registration', 0.35043004155158997), ('medical imaging', 0.34712281823158264), ('shape matching', 0.34604841470718384)]"
494,494,62,494_dynamics open quantum_open quantum systems_quantum stochastic_quantum stochastic differential,"['dynamics open quantum', 'open quantum systems', 'quantum stochastic', 'quantum stochastic differential', 'open quantum system', 'open quantum', 'quantum systems', 'quantum master', 'quantum evolution', 'stochastic schr odinger']","['On a tilted Liouville-master equation of open quantum systems   A tilted Liouville-master equation in Hilbert space is presented for\nMarkovian open quantum systems. We demonstrate that it is the unraveling of the\ntilted quantum master equation. The latter is widely used in the analysis and\ncalculations of stochastic thermodynamic quantities in quantum stochastic\nthermodynamics.\n', 'Unified analysis of non-Markovian open quantum systems in Gaussian\n  environment using superoperator formalism   We present perturbative error bounds for the non-Markovian dynamics of\nobservables in open quantum systems interacting with Gaussian environments,\ngoverned by general Liouville dynamics. This extends the work of [Mascherpa et\nal., Phys. Rev. Lett. 118, 100401, 2017], which demonstrated qualitatively\ntighter bounds over the standard Gr\\""onwall-type analysis, where the joint\nsystem-environment evolution is unitary. Our results apply to systems with both\nbosonic and fermionic environments. Our approach utilizes a superoperator\nformalism, which avoids the need for formal coherent state path integral\ncalculations, or the dilation of Lindblad dynamics into an equivalent unitary\nframework with infinitely many degrees of freedom. This enables a unified\ntreatment of a wide range of open quantum systems. These findings provide a\nsolid theoretical basis for various recently developed pseudomode methods in\nsimulating open quantum system dynamics.\n', ""Classical correspondence beyond the Ehrenfest time for open quantum systems with general Lindbladians Quantum and classical systems evolving under the same formal Hamiltonian $H$ may dramatically differ after the Ehrenfest timescale $t_E \\sim \\log(\\hbar^{-1})$, even as $\\hbar \\to 0$. Coupling the system to a Markovian environment results in a Lindblad equation for the quantum evolution. Its classical counterpart is given by the Fokker-Planck equation on phase space, which describes Hamiltonian flow with friction and diffusive noise. The quantum and classical evolutions may be compared via the Wigner-Weyl representation. Due to decoherence, they are conjectured to match closely for times far beyond the Ehrenfest timescale as $\\hbar \\to 0$. We prove a version of this correspondence, bounding the error between the quantum and classical evolutions for any sufficiently regular Hamiltonian $H(x,p)$ and Lindblad functions $L_k(x,p)$. The error is small when the strength of the diffusion $D$ associated to the Lindblad functions satisfies $D \\gg \\hbar^{4/3}$, which allows vanishing noise in the classical limit. Our method uses a time-dependent semiclassical mixture of variably squeezed Gaussian states. The states evolve according to a local harmonic approximation to the Lindblad dynamics. Both the exact quantum trajectory and its classical counterpart can be expressed as perturbations of this semiclassical mixture, with the errors bounded using Duhamel's principle. We present heuristic arguments suggesting the $4/3$ exponent is optimal and defines a boundary in the sense that asymptotically weaker diffusion permits a breakdown of quantum-classical correspondence at the Ehrenfest timescale. In a shorter companion paper, we treat the special case of Hamiltonians that decompose into kinetic and potential energy with linear Lindblad operators, with explicit bounds that can be applied directly to physical systems.""]","[('dynamics open quantum', 0.6719533801078796), ('open quantum systems', 0.6622845530509949), ('quantum stochastic', 0.6370878219604492), ('quantum stochastic differential', 0.6304714679718018), ('open quantum system', 0.618060290813446), ('open quantum', 0.5829629898071289), ('quantum systems', 0.5778173804283142), ('quantum master', 0.5441465377807617), ('quantum evolution', 0.5375780463218689), ('stochastic schr odinger', 0.5318816900253296)]"
495,495,62,495_generalized hypergeometric functions_confluent hypergeometric functions_hypergeometric functions_gauss hypergeometric functions,"['generalized hypergeometric functions', 'confluent hypergeometric functions', 'hypergeometric functions', 'gauss hypergeometric functions', 'hypergeometric identities', 'generalized hypergeometric', 'hypergeometric series', 'identities hypergeometric', 'confluent hypergeometric', 'gaussian hypergeometric']","[""Rodrigues formula and linear independence for values of hypergeometric\n  functions with parameters vary   In this article, we prove a generalized Rodrigues formula for a wide class of\nholonomic Laurent series, which yields a new linear independence criterion\nconcerning their values at algebraic points. This generalization yields a new\nconstruction of Pad\\'e approximations including those for Gauss hypergeometric\nfunctions. In particular, we obtain a linear independence criterion over a\nnumber field concerning values of Gauss hypergeometric functions, allowing the\nparameters of Gauss hypergeometric functions to vary.\n"", 'Unveiling new perspectives of hypergeometric functions using umbral\n  techniques   The umbral restyling of hypergeometric functions is shown to be a useful and\nefficient approach in simplifying the associated computational technicalities.\nIn this article, the authors provide a general introduction to the umbral\nversion of Gauss hypergeometric functions and extend the formalism to certain\ngeneralized forms of these functions. It is shown that suggested approach is\nparticularly efficient for evaluating integrals involving hypergeometric\nfunctions and their combination with other special functions.\n', 'On digamma series convertible into hypergeometric series   Series containing the digamma function arise when calculating the parametric\nderivatives of the hypergeometric functions and play a role in evaluation of\nFeynman diagrams. As these series are typically non-hypergeometric, a few\ninstances when they are summable in terms of hypergeometric functions are of\nimportance. In this paper, we convert multi-term identities for the generalized\nhypergeometric functions evaluated at unity into identities connecting them to\nthe digamma series via the appropriate limiting process. The resulting formulas\ncan be viewed as hypergeometric expressions for the $1$-norm of the gradient of\nthe generalized hypergeometric function with respect to all its parameters and\nseem to have no direct analogues in the literature.\n']","[('generalized hypergeometric functions', 0.8559032678604126), ('confluent hypergeometric functions', 0.8187122344970703), ('hypergeometric functions', 0.8105894327163696), ('gauss hypergeometric functions', 0.8042767643928528), ('hypergeometric identities', 0.7738474607467651), ('generalized hypergeometric', 0.7711834907531738), ('hypergeometric series', 0.7549129724502563), ('identities hypergeometric', 0.7479950189590454), ('confluent hypergeometric', 0.7308114171028137), ('gaussian hypergeometric', 0.7257722616195679)]"
496,496,62,496_manifold learning_manifold hypothesis_dimensional manifold_manifolds,"['manifold learning', 'manifold hypothesis', 'dimensional manifold', 'manifolds', 'manifolds euclidean', 'manifold', 'riemannian manifolds', 'manifolds particular', 'underlying manifold', 'riemannian manifold']","['Distance Measure Based on an Embedding of the Manifold of K-Component\n  Gaussian Mixture Models into the Manifold of Symmetric Positive Definite\n  Matrices   In this paper, a distance between the Gaussian Mixture Models(GMMs) is\nobtained based on an embedding of the K-component Gaussian Mixture Model into\nthe manifold of the symmetric positive definite matrices. Proof of embedding of\nK-component GMMs into the manifold of symmetric positive definite matrices is\ngiven and shown that it is a submanifold. Then, proved that the manifold of\nGMMs with the pullback of induced metric is isometric to the submanifold with\nthe induced metric. Through this embedding we obtain a general lower bound for\nthe Fisher-Rao metric. This lower bound is a distance measure on the manifold\nof GMMs and we employ it for the similarity measure of GMMs. The effectiveness\nof this framework is demonstrated through an experiment on standard machine\nlearning benchmarks, achieving accuracy of 98%, 92%, and 93.33% on the UIUC,\nKTH-TIPS, and UMD texture recognition datasets respectively.\n', 'Estimation of Local Geometric Structure on Manifolds from Noisy Data   A common observation in data-driven applications is that high-dimensional\ndata have a low intrinsic dimension, at least locally. In this work, we\nconsider the problem of point estimation for manifold-valued data. Namely,\ngiven a finite set of noisy samples of $\\mathcal{M}$, a $d$ dimensional\nsubmanifold of $\\mathbb{R}^D$, and a point $r$ near the manifold we aim to\nproject $r$ onto the manifold. Assuming that the data was sampled uniformly\nfrom a tubular neighborhood of a $k$-times smooth boundaryless and compact\nmanifold, we present an algorithm that takes $r$ from this neighborhood and\noutputs $\\hat p_n\\in \\mathbb{R}^D$, and $\\widehat{T_{\\hat p_n}\\mathcal{M}}$ an\nelement in the Grassmannian $Gr(d, D)$. We prove that as the number of samples\n$n\\to\\infty$, the point $\\hat p_n$ converges to $\\mathbf{p}\\in \\mathcal{M}$,\nthe projection of $r$ onto $\\mathcal{M}$, and $\\widehat{T_{\\hat\np_n}\\mathcal{M}}$ converges to $T_{\\mathbf{p}}\\mathcal{M}$ (the tangent space\nat that point) with high probability. Furthermore, we show that $\\hat p_n$\napproaches the manifold with an asymptotic rate of $n^{-\\frac{k}{2k + d}}$, and\nthat $\\hat p_n, \\widehat{T_{\\hat p_n}\\mathcal{M}}$ approach $\\mathbf{p}$ and\n$T_{\\mathbf{p}}\\mathcal{M}$ correspondingly with asymptotic rates of\n$n^{-\\frac{k-1}{2k + d}}$.\n', 'Non-Parametric Estimation of Manifolds from Noisy Data   A common observation in data-driven applications is that high dimensional\ndata has a low intrinsic dimension, at least locally. In this work, we consider\nthe problem of estimating a $d$ dimensional sub-manifold of $\\mathbb{R}^D$ from\na finite set of noisy samples. Assuming that the data was sampled uniformly\nfrom a tubular neighborhood of $\\mathcal{M}\\in \\mathcal{C}^k$, a compact\nmanifold without boundary, we present an algorithm that takes a point $r$ from\nthe tubular neighborhood and outputs $\\hat p_n\\in \\mathbb{R}^D$, and\n$\\widehat{T_{\\hat p_n}\\mathcal{M}}$ an element in the Grassmanian $Gr(d, D)$.\nWe prove that as the number of samples $n\\to\\infty$ the point $\\hat p_n$\nconverges to $p\\in \\mathcal{M}$ and $\\widehat{T_{\\hat p_n}\\mathcal{M}}$\nconverges to $T_p\\mathcal{M}$ (the tangent space at that point) with high\nprobability. Furthermore, we show that the estimation yields asymptotic rates\nof convergence of $n^{-\\frac{k}{2k + d}}$ for the point estimation and\n$n^{-\\frac{k-1}{2k + d}}$ for the estimation of the tangent space. These rates\nare known to be optimal for the case of function estimation.\n']","[('manifold learning', 0.699824869632721), ('manifold hypothesis', 0.5947431921958923), ('dimensional manifold', 0.5744516849517822), ('manifolds', 0.5519105195999146), ('manifolds euclidean', 0.5517706274986267), ('manifold', 0.5461164116859436), ('riemannian manifolds', 0.5346787571907043), ('manifolds particular', 0.5331147313117981), ('underlying manifold', 0.5310053825378418), ('riemannian manifold', 0.521573543548584)]"
497,497,62,497_folding_foldings_obtained folding_origami,"['folding', 'foldings', 'obtained folding', 'origami', 'folds', 'paperfolding', 'fold', 'foldable', 'bending', 'folded']","['Flat origami is Turing Complete   ""Flat origami"" refers to the folding of flat, zero-curvature paper such that\nthe finished object lies in a plane. Mathematically, flat origami consists of a\ncontinuous, piecewise isometric map $f:P\\subseteq\\mathbb{R}^2\\to\\mathbb{R}^2$\nalong with a layer ordering $\\lambda_f:P\\times P\\to \\{-1,1\\}$ that tracks which\npoints of $P$ are above/below others when folded. The set of crease lines that\na flat origami makes (i.e., the set on which the mapping $f$ is\nnon-differentiable) is called its ""crease pattern."" Flat origami mappings and\ntheir layer orderings can possess surprisingly intricate structure. For\ninstance, determining whether or not a given straight-line planar graph drawn\non $P$ is the crease pattern for some flat origami has been shown to be an\nNP-complete problem, and this result from 1996 led to numerous explorations in\ncomputational aspects of flat origami. In this paper we prove that flat\norigami, when viewed as a computational device, is Turing complete, or more\nspecifically P-complete. We do this by showing that flat origami crease\npatterns with ""optional creases"" (creases that might be folded or remain\nunfolded depending on constraints imposed by other creases or inputs) can be\nconstructed to simulate Rule 110, a one-dimensional cellular automaton that was\nproven to be Turing complete by Matthew Cook in 2004.\n', 'The Folding Mathematics   Origami is the art of paper folding, and it borrows its name from two\nJapanese words \\emph{ori} and \\emph{kami}. In Japanese, {ori} means folding,\nand the paper is called {kami}. While origami is just a hobby to most, there is\na lot more to it. If you fold a square sheet of paper into any of the\ntraditional origami model (for example the flapping bird) and unfold it, you\ncan see crease patterns. These crease patterns tell us that there is a lot of\ngeometry hidden behind the folds.\n  In this article, we investigate the symbiotic relationship between\nmathematics and origami. The first part of this article explores the utility of\norigami in education. We will see how origami could become an effective way of\nteaching methods of geometry, mainly because of its experiential nature.\nComplex origami patterns cannot be created out of thin air. They usually\ninvolve understanding deep mathematical theories and the ability to apply them\nto paper folding. In the second part of the article, we attempt to provide a\nglimpse of this beautiful connection between origami and mathematics.\n', 'Rigid folding equations of degree-6 origami vertices   Rigid origami, with applications ranging from nano-robots to unfolding solar\nsails in space, describes when a material is folded along straight crease line\nsegments while keeping the regions between the creases planar. Prior work has\nfound explicit equations for the folding angles of a flat-foldable degree-4\norigami vertex and some cases of degree-6 vertices. We extend this work to\ngeneralized symmetries of the degree-6 vertex where all sector angles equal\n$60^\\circ$. We enumerate the different viable rigid folding modes of these\ndegree-6 crease patterns and then use $2^{nd}$-order Taylor expansions and\nprior rigid folding techniques to find algebraic folding angle relationships\nbetween the creases. This allows us to explicitly compute the configuration\nspace of these degree-6 vertices, and in the process we uncover new\nexplanations for the effectiveness of Weierstrass substitutions in modeling\nrigid origami. These results expand the toolbox of rigid origami mechanisms\nthat engineers and materials scientists may use in origami-inspired designs.\n']","[('folding', 0.6424164772033691), ('foldings', 0.6208420395851135), ('obtained folding', 0.6089639067649841), ('origami', 0.6063122749328613), ('folds', 0.5653497576713562), ('paperfolding', 0.5633963942527771), ('fold', 0.5131834149360657), ('foldable', 0.49920976161956787), ('bending', 0.4796355366706848), ('folded', 0.4650580585002899)]"
498,498,62,498_collision avoidance constraints_collision avoidance_obstacle avoidance_trajectory planning,"['collision avoidance constraints', 'collision avoidance', 'obstacle avoidance', 'trajectory planning', 'motion planning', 'avoidance constraints', 'planning control', 'collision free', 'control barrier functions', 'obstacle']","['A Differentiable Signed Distance Representation for Continuous Collision\n  Avoidance in Optimization-Based Motion Planning   This paper proposes a new set of conditions for exactly representing\ncollision avoidance constraints within optimization-based motion planning\nalgorithms. The conditions are continuously differentiable and therefore\nsuitable for use with standard nonlinear optimization solvers. The method\nrepresents convex shapes using a support function representation and is\ntherefore quite general. For collision avoidance involving polyhedral or\nellipsoidal shapes, the proposed method introduces fewer variables and\nconstraints than existing approaches. Additionally the proposed method can be\nused to rigorously ensure continuous collision avoidance as the vehicle\ntransitions between the discrete poses determined by the motion planning\nalgorithm. Numerical examples demonstrate how this can be used to prevent\nproblems of corner cutting and passing through obstacles which can occur when\ncollision avoidance is only enforced at discrete time steps.\n', 'Safety-Critical Planning and Control for Dynamic Obstacle Avoidance\n  Using Control Barrier Functions   Dynamic obstacle avoidance is a challenging topic for optimal control and\noptimization-based trajectory planning problems. Many existing works use\nControl Barrier Functions (CBFs) to enforce safety constraints for control\nsystems. CBFs are typically formulated based on the distance to obstacles, or\nintegrated with path planning algorithms as a safety enhancement tool. However,\nthese approaches usually require knowledge of the obstacle boundary equations\nor have very slow computational efficiency. In this paper, we propose a\nframework based on model predictive control (MPC) with discrete-time high-order\nCBFs (DHOCBFs) to generate a collision-free trajectory. The DHOCBFs are first\nobtained from convex polytopes generated through grid mapping, without the need\nto know the boundary equations of obstacles. Additionally, a path planning\nalgorithm is incorporated into this framework to ensure the global optimality\nof the generated trajectory. We demonstrate through numerical examples that our\nframework allows a unicycle robot to safely and efficiently navigate tight,\ndynamically changing environments with both convex and nonconvex obstacles. By\ncomparing our method to established CBF-based benchmarks, we demonstrate\nsuperior computing efficiency, length optimality, and feasibility in trajectory\ngeneration and obstacle avoidance.\n', 'Control Barrier Functions in UGVs for Kinematic Obstacle Avoidance: A\n  Collision Cone Approach   In this paper, we propose a new class of Control Barrier Functions (CBFs) for\nUnmanned Ground Vehicles (UGVs) that help avoid collisions with kinematic\n(non-zero velocity) obstacles. While the current forms of CBFs have been\nsuccessful in guaranteeing safety/collision avoidance with static obstacles,\nextensions for the dynamic case have seen limited success. Moreover, with the\nUGV models like the unicycle or the bicycle, applications of existing CBFs have\nbeen conservative in terms of control, i.e., steering/thrust control has not\nbeen possible under certain scenarios. Drawing inspiration from the classical\nuse of collision cones for obstacle avoidance in trajectory planning, we\nintroduce its novel CBF formulation with theoretical guarantees on safety for\nboth the unicycle and bicycle models. The main idea is to ensure that the\nvelocity of the obstacle w.r.t. the vehicle is always pointing away from the\nvehicle. Accordingly, we construct a constraint that ensures that the velocity\nvector always avoids a cone of vectors pointing at the vehicle. The efficacy of\nthis new control methodology is later verified by Pybullet simulations on\nTurtleBot3 and F1Tenth.\n']","[('collision avoidance constraints', 0.7147361636161804), ('collision avoidance', 0.6281982660293579), ('obstacle avoidance', 0.5917373299598694), ('trajectory planning', 0.5339030623435974), ('motion planning', 0.4889644980430603), ('avoidance constraints', 0.4674803614616394), ('planning control', 0.4570924937725067), ('collision free', 0.43197357654571533), ('control barrier functions', 0.41382378339767456), ('obstacle', 0.4092254936695099)]"
499,499,62,499_waveform inversion fwi_waveform inversion_full waveform inversion_inversion fwi,"['waveform inversion fwi', 'waveform inversion', 'full waveform inversion', 'inversion fwi', 'seismic inversion', 'full waveform', 'nonlinear ill posed', 'inversion', 'waveform', 'alternating direction multipliers']","['Efficient extended-search space full-waveform inversion with unknown\n  source signatures   Full waveform inversion (FWI) requires an accurate estimation of source\nsignatures. Due to the coupling between the source signatures and the\nsubsurface model, small errors in the former can translate into large errors in\nthe latter. When direct methods are used to solve the forward problem,\nclassical frequency-domain FWI efficiently processes multiple sources for\nsource signature and wavefield estimations once a single Lower-Upper (LU)\ndecomposition of the wave-equation operator has been performed. However, this\nefficient FWI formulation is based on the exact solution of the wave equation\nand hence is highly sensitive to the inaccuracy of the velocity model due to\nthe cycle skipping pathology. Recent extended-space FWI variants tackle this\nsensitivity issue through a relaxation of the wave equation combined with data\nassimilation, allowing the wavefields to closely match the data from the first\ninversion iteration. Then, the subsurface parameters are updated by minimizing\nthe wave-equation violations. When the wavefields and the source signatures are\njointly estimated with this approach, the extended wave equation operator\nbecomes source dependent, hence making direct methods ineffective. In this\npaper, we propose a simple method to bypass this issue and estimate source\nsignatures efficiently during extended FWI. The proposed method replaces each\nsource with a blended source during each data-assimilated wavefield\nreconstruction to make the extended wave equation operator source independent.\nBesides computational efficiency, the additional degrees of freedom introduced\nby spatially distributing the sources allows for a better signature estimation\nat the physical location when the velocity model is rough. Numerical tests on\nthe Marmousi II and 2004 BP salt synthetic models confirm the efficiency and\nthe robustness of the proposed method.\n', 'An extended Gauss-Newton method for full waveform inversion   Full waveform inversion (FWI) is a large-scale nonlinear ill-posed problem\nfor which computationally expensive Newton-type methods can become trapped in\nundesirable local minima, particularly when the initial model lacks a\nlow-wavenumber component and the recorded data lacks low-frequency content. A\nmodification to the Gauss-Newton (GN) method is proposed to address these\nissues. The standard GN system for multisource multireceiver FWI is\nreformulated into an equivalent matrix equation form, with the solution\nbecoming a diagonal matrix rather than a vector as in the standard system. The\nsearch direction is transformed from a vector to a matrix by relaxing the\ndiagonality constraint, effectively adding a degree of freedom to the\nsubsurface offset axis. The relaxed system can be explicitly solved with only\nthe inversion of two small matrices that deblur the data residual matrix along\nthe source and receiver dimensions, which simplifies the inversion of the\nHessian matrix. When used to solve the extended source FWI objective function,\nthe Extended GN (EGN) method integrates the benefits of both model and source\nextension. The EGN method effectively combines the computational effectiveness\nof the reduced FWI method with the robustness characteristics of extended\nformulations and offers a promising solution for addressing the challenges of\nFWI. It bridges the gap between these extended formulations and the reduced FWI\nmethod, enhancing inversion robustness while maintaining computational\nefficiency. The robustness and stability of the EGN algorithm for waveform\ninversion are demonstrated numerically.\n', '$\\omega$-FWI: Robust full-waveform inversion with Fourier-based metric   Full-waveform inversion is a cutting-edge methodology for recovering\nhigh-resolution subsurface models. However, one of the main conventional\nfull-waveform optimization problems challenges is cycle-skipping, usually\nleading us to an inaccurate local minimum model. A highly investigated track to\nalleviate this challenge involves designing a more global measure of misfit\nbetween the observed and modelled data beyond the sample-to-sample comparison.\nHowever, most of these approaches admit relatively smooth inversion results.\nHere, we introduce a novel misfit function based on the Fourier-based metric.\nThis metric has been successfully applied in molecular physics for solving the\nBoltzmann equation, and we adapt it to full-waveform inversion. This misfit\nfunction exploits the power spectrum information between the modelled and\nobserved data to provide low-wavenumber velocity model updates early, and more\nhigh resolution updates as we approach the solution. Thus, it also can be\nreformulated as a weighted $\\ell_{2}$-norm in a quadratic case, which can be\nseen as a simple extension for conventional full-waveform inversion. Thus,\ndespite its robustness to cycle skipping, it is capable of delivering\nhigh-resolution models synonymous to conventional FWI. Considering its\nfrequency domain utilization, we refer to this inversion method as\n$\\omega$-FWI. Through the synthetic Marmousi model example, this method\nsuccessfully recovers an accurate velocity model, starting from a linearly\nincreasing model even for the case of noisy observed data and the lack of low\nfrequencies below 3 Hz and 5Hz, in which the conventional $\\ell_{2}$-norm\nfull-waveform inversion suffers from cycle skipping.\n']","[('waveform inversion fwi', 0.6693663001060486), ('waveform inversion', 0.6633883118629456), ('full waveform inversion', 0.663212776184082), ('inversion fwi', 0.49878743290901184), ('seismic inversion', 0.4664880931377411), ('full waveform', 0.44185447692871094), ('nonlinear ill posed', 0.3871942162513733), ('inversion', 0.38529232144355774), ('waveform', 0.383637398481369), ('alternating direction multipliers', 0.3421293795108795)]"
500,500,62,500_khovanov homology_homology khovanov_homology knot_homology link,"['khovanov homology', 'homology khovanov', 'homology knot', 'homology link', 'link homology', 'homology coefficients', 'knot floer homology', 'homology', 'link floer homology', 'homology also']","['Khovanov homology detects $T(2,6)$   We show if $L$ is any link in $S^3$ whose Khovanov homology is isomorphic to\nthe Khovanov homology of $T(2,6)$ then $L$ is isotopic to $T(2,6)$. We show\nthis for unreduced Khovanov homology with $\\mathbb{Z}$ coefficients.\n', 'Symplectic annular Khovanov homology and fixed point localizations   We introduce a new version of symplectic annular Khovanov homology and\nestablish spectral sequences from (i) the symplectic annular Khovanov homology\nof a knot to the link Floer homology of the lift of the annular axis in the\ndouble branched cover; (ii) the symplectic Khovanov homology of a two-periodic\nknot to the symplectic annular Khovanov homology of its quotient; and (iii) the\nsymplectic Khovanov homology of a strongly invertible knot to the cone of the\naxis-moving map between the symplectic annular Khovanov homology of the two\nresolutions of its quotient.\n', 'An Introduction to Khovanov Homology   This paper is an introduction to Khovanov homology, starting with the\nKauffman bracket state summation, emphasizing the Bar-Natan Canopoloy and\ntangle cobordism approach. The paper discusses a simplicial approach to\nKhovanov homology and a quantum model for it so that the graded Euler\ncharacteristic that produces the Jones polynomial from Khovanov homology\nbecomes the trace of a unitary transformation on a Hilbert space associated\nwith the Khovanov Homology.\n']","[('khovanov homology', 0.8069881200790405), ('homology khovanov', 0.7883487343788147), ('homology knot', 0.661383330821991), ('homology link', 0.6424472332000732), ('link homology', 0.6361256837844849), ('homology coefficients', 0.5747525095939636), ('knot floer homology', 0.5669403076171875), ('homology', 0.5521819591522217), ('link floer homology', 0.5354429483413696), ('homology also', 0.5346258282661438)]"
501,501,61,501_dual quaternions_dual quaternion_quaternion matrices_quaternion hermitian,"['dual quaternions', 'dual quaternion', 'quaternion matrices', 'quaternion hermitian', 'quaternion valued', 'quaternions', 'quaternionic', 'quaternion', 'matrices dual', 'hermitian matrices']","['Minimax principle for right eigenvalues of dual quaternion matrices and\n  their generalized inverses   Dual quaternions can represent rigid body motion in 3D spaces, and have found\nwide applications in robotics, 3D motion modelling and control, and computer\ngraphics. In this paper, we introduce three different right linear independency\nfor a set of dual quaternion vectors, and study some related basic properties\nfor the set of dual quaternion vectors and dual quaternion matrices. We present\na minimax principle for right eigenvalues of dual quaternion Hermitian\nmatrices. Based upon a newly established Cauchy-Schwarz inequality for dual\nquaternion vectors and singular value decomposition of dual quaternion\nmatrices, we propose an important inequality for singular values of dual\nquaternion matrices. We finally introduce the concept of generalized inverse of\ndual quaternion matrices, and present the necessary and sufficient conditions\nfor a dual quaternion matrix to be one of four types of generalized inverses of\nanother dual quaternion matrix.\n', 'Eigenvalues and Singular Values of Dual Quaternion Matrices   The poses of $m$ robotics in $n$ time points may be represented by an $m\n\\times n$ dual quaternion matrix. In this paper, we study the spectral theory\nof dual quaternion matrices. We introduce right and left eigenvalues for square\ndual quaternion matrices. If a right eigenvalue is a dual number, then it is\nalso a left eigenvalue. In this case, this dual number is called an eigenvalue\nof that dual quaternion matrix. We show that the right eigenvalues of a dual\nquaternion Hermitian matrix are dual numbers. Thus, they are eigenvalues. An $n\n\\times n$ dual quaternion Hermitian matrix is shown to have exactly $n$\neigenvalues. It is positive semidefinite, or positive definite, if and only if\nall of its eigenvalues are nonnegative, or positive and appreciable, dual\nnumbers, respectively. We present a unitary decomposition of a dual quaternion\nHermitian matrix, and the singular value decomposition for a general dual\nquaternion matrix. The singular values of a dual quaternion matrix are\nnonnegative dual numbers.\n', 'Standard Dual Quaternion Optimization and Its Applications in Hand-Eye\n  Calibration and SLAM   Several common dual quaternion functions, such as the power function, the\nmagnitude function, the $2$-norm function and the $k$th largest eigenvalue of a\ndual quaternion Hermitian matrix, are standard dual quaternion functions, i.e.,\nthe standard parts of their function values depend upon only the standard parts\nof their dual quaternion variables. Furthermore, the sum, product, minimum,\nmaximum and composite functions of two standard dual functions, the logarithm\nand the exponential of standard unit dual quaternion functions, are still\nstandard dual quaternion functions. On the other hand, the dual quaternion\noptimization problem, where objective and constraint function values are dual\nnumbers but variables are dual quaternions, naturally arises from applications.\nWe show that to solve an equality constrained dual quaternion optimization\nproblem, we only need to solve two quaternion optimization problems. If the\ninvolved dual quaternion functions are all standard, the optimization problem\nis called a standard dual quaternion optimization problem, and some better\nresults hold. Then, we show that the dual quaternion optimization problems\narising from the hand-eye calibration problem and the simultaneous localization\nand mapping (SLAM) problem are equality constrained standard dual quaternion\noptimization problems.\n']","[('dual quaternions', 0.7368823289871216), ('dual quaternion', 0.7323687672615051), ('quaternion matrices', 0.690557599067688), ('quaternion hermitian', 0.6495280861854553), ('quaternion valued', 0.6282325387001038), ('quaternions', 0.5846021175384521), ('quaternionic', 0.5707897543907166), ('quaternion', 0.5636573433876038), ('matrices dual', 0.537486732006073), ('hermitian matrices', 0.5346131324768066)]"
502,502,61,502_valuation rings_transcendental extensions_key polynomials_algebraic extensions,"['valuation rings', 'transcendental extensions', 'key polynomials', 'algebraic extensions', 'valuation ring', 'algebraic extension', 'extensions valued', 'algebraic closure', 'valuation theoretic', 'key polynomial']","['Minimal limit key polynomials   In this paper, we extend the theory of minimal limit key polynomials of\nvaluations on the polynomial ring $\\kx$. We use the theory of cuts on ordered\nabelian groups to show that the previous results on bounded sets of key\npolynomials of rank-one valuations, extend to vertically bounded sets of key\npolynomials of valuations of an arbitrary rank. We discuss as well properties\nof minimal limit key polynomials in the vertically unbounded case.\n', ""Invariants of limit key polynomials   Let $\\nu$ be a valuation of arbitrary rank on the polynomial ring $K[x]$ with\ncoefficients in a field $K$. We prove comparison theorems between\nMacLane-Vaqui\\'e key polynomials for valuations $\\mu\\le\\nu$ and abstract key\npolynomials for $\\nu$.\n  Also, some results on invariants attached to limit key polynomials are\nobtained. In particular, if $\\operatorname{char}(K)=0$ we show that all limit\nkey polynomials of unbounded continuous MacLane chains have numerical character\nequal to one.\n"", ""Key polynomials for simple extensions of valued fields   Let $\\iota:K\\hookrightarrow L\\cong K(x)$ be a simple transcendental extension\nof valued fields, where $K$ is equipped with a valuation $\\nu$ of rank 1. That\nis, we assume given a rank 1 valuation $\\nu$ of $K$ and its extension $\\nu'$ to\n$L$. Let $(R_\\nu,M_\\nu,k_\\nu)$ denote the valuation ring of $\\nu$. The purpose\nof this paper is to present a refined version of MacLane's theory of key\npolynomials, similar to those considered by M. Vaqui\\'e, and reminiscent of\nrelated objects studied by Abhyankar and Moh (approximate roots) and T.C. Kuo.\n  Namely, we associate to $\\iota$ a countable well ordered set $$\n\\mathbf{Q}=\\{Q_i\\}_{i\\in\\Lambda}\\subset K[x]; $$ the $Q_i$ are called {\\bf key\npolynomials}. Key polynomials $Q_i$ which have no immediate predecessor are\ncalled {\\bf limit key polynomials}. Let $\\beta_i=\\nu'(Q_i)$.\n  We give an explicit description of the limit key polynomials (which may be\nviewed as a generalization of the Artin--Schreier polynomials). We also give an\nupper bound on the order type of the set of key polynomials. Namely, we show\nthat if $\\operatorname{char}\\ k_\\nu=0$ then the set of key polynomials has\norder type at most $\\omega$, while in the case $\\operatorname{char}\\ k_\\nu=p>0$\nthis order type is bounded above by $\\omega\\times\\omega$, where $\\omega$ stands\nfor the first infinite ordinal.\n""]","[('valuation rings', 0.5446714758872986), ('transcendental extensions', 0.5413507223129272), ('key polynomials', 0.5391252040863037), ('algebraic extensions', 0.5232682824134827), ('valuation ring', 0.5168200731277466), ('algebraic extension', 0.5034975409507751), ('extensions valued', 0.4968920648097992), ('algebraic closure', 0.4863630533218384), ('valuation theoretic', 0.4825505316257477), ('key polynomial', 0.4605458974838257)]"
503,503,61,503_zero forcing_zero forcing number_graphs zero_graph zero,"['zero forcing', 'zero forcing number', 'graphs zero', 'graph zero', 'graph families', 'forcing sets', 'sets graphs', 'graph size', 'graphs', 'graphs including']","['Characterization of Graphs With Failed Skew Zero Forcing Number of 1   Given a graph $G$, the zero forcing number of $G$, $Z(G)$, is the smallest\ncardinality of any set $S$ of vertices on which repeated applications of the\nforcing rule results in all vertices being in $S$. The forcing rule is: if a\nvertex $v$ is in $S$, and exactly one neighbor $u$ of $v$ is not in $S$, then\n$u$ is added to $S$ in the next iteration. Hence the failed zero forcing number\nof a graph was defined to be the size of the largest set of vertices which\nfails to force all vertices in the graph. A similar property called skew zero\nforcing was defined so that if there is exactly one neighbor $u$ of $v$ is not\nin $S$, then $u$ is added to $S$ in the next iteration. The difference is that\nvertices that are not in $S$ can force other vertices. This leads to the failed\nskew zero forcing number of a graph, which is denoted by $F^{-}(G)$. In this\npaper we provide a complete characterization of all graphs with $F^{-}(G)=1$.\nFetcie, Jacob, and Saavedra showed that the only graphs with a failed zero\nforcing number of $1$ are either: the union of two isolated vertices; $P_3$;\n$K_3$; or $K_4$. In this paper we provide a surprising result: changing the\nforcing rule to a skew-forcing rule results in an infinite number of graphs\nwith $F^{-}(G)=1$.\n', 'The zero forcing span of a graph   In zero forcing, the focus is typically on finding the minimum cardinality of\nany zero forcing set in the graph; however, the number of cardinalities between\n$0$ and the number of vertices in the graph for which there are both zero\nforcing sets and sets that fail to be zero forcing sets is not well known. In\nthis paper, we introduce the zero forcing span of a graph, which is the number\nof distinct cardinalities for which there are sets that are zero forcing sets\nand sets that are not. We introduce the span within the context of standard\nzero forcing and skew zero forcing as well as for standard zero forcing on\ndirected graphs. We characterize graphs with high span and low span of each\ntype, and also investigate graphs with special zero forcing polynomials.\n', 'Minimum rank and failed zero forcing number of graphs   Let $G$ be a simple, finite, and undirected graph with vertices each given an\ninitial coloring of either blue or white. Zero forcing on graph $G$ is an\niterative process of forcing its white vertices to become blue after a finite\napplication of a specified color-change rule. We say that an initial set $S$ of\nblue vertices of $G$ is a zero forcing set for $G$ under the specified\ncolor-change rule if a finite number of iterations of zero forcing results to\nan updated coloring where all vertices of $G$ are blue. Otherwise, we say that\n$S$ is a failed zero forcing set for $G$ under the specified color-change rule.\nIt is not difficult to see that any subset of a failed zero forcing set is also\nfailed. Hence, our interest lies on the maximum possible cardinality of a\nfailed zero forcing set, which we refer to as the failed zero forcing number of\n$G$. In this paper, we consider two color-change rules $-$ standard and\npositive semidefinite. We compute for the failed zero forcing numbers of\nseveral graph families. Furthermore, under each graph family, we characterize\nthe graphs $G$ for which the failed zero forcing number is equal to the minimum\nrank of $G$.\n']","[('zero forcing', 0.594649076461792), ('zero forcing number', 0.5865803360939026), ('graphs zero', 0.5784080624580383), ('graph zero', 0.5447729229927063), ('graph families', 0.5050793886184692), ('forcing sets', 0.4924146831035614), ('sets graphs', 0.4525030851364136), ('graph size', 0.4465179741382599), ('graphs', 0.4455445408821106), ('graphs including', 0.44362378120422363)]"
504,504,61,504_curve shortening flow_curvature flows_shortening flow_curve shortening,"['curve shortening flow', 'curvature flows', 'shortening flow', 'curve shortening', 'curvature flow', 'inverse curvature flow', 'flow curves', 'preserving curvature', 'convex curves', 'flow curve']","['Non-uniqueness of curve shortening flow   We formulate a uniqueness conjecture for curve shortening flow of proper\ncurves on certain symmetric surfaces and give an example of a non-flat metric\non the plane with respect to which curve shortening flow is not unique. That\nis, with respect to a suitably chosen metric, we construct a non-static\nsolution to curve shortening flow starting from a properly embedded geodesic.\n', 'Curve shortening flows on surfaces that are not convex at infinity   The behavior of the curve shortening flow has been extensively studied. Gage,\nHamilton, and Grayson proved that, under the curve shortening flow, an embedded\nclosed curve in the Euclidean plane becomes convex after a finite time and then\nshrinks to a point while remaining convex. Moreover, Grayson extended these\nresults to surfaces that are convex at infinity and proved results similar to\nthose for plane curves. In this paper, we study the curve shortening flow on\nsurfaces that are not convex at infinity. Specifically, we consider a warped\nproduct of a unit circle and an open interval with a strictly increasing\nwarping function. In this setting, we can define a graph property for curves\nwithin these warped products. It is known that this graph property is preserved\nalong the curve shortening flow. Similarly to the behavior of the curve\nshortening flow in the plane, we prove that the curve becomes a graph after a\nfinite time under the curve shortening flow.\n', 'Convex Ancient Solutions to Anisotropic Curve Shortening Flow   We construct a translating solution to anisotropic curve shortening flow and\nshow that for a given anisotropic factor $g:S^1\\to\\mathbb{R}_+$, and a given\ndirection and speed, this translator is unique. We then construct an ancient\ncompact solution to anisotropic curve shortening flow, and show that this\nsolution, along with the appropriate translating solution, are the unique\nsolutions to anisotropic curve shortening flow that lie in a slab of a given\nwidth and no smaller.\n']","[('curve shortening flow', 0.751459002494812), ('curvature flows', 0.6374607086181641), ('shortening flow', 0.6162655353546143), ('curve shortening', 0.6145198345184326), ('curvature flow', 0.61402827501297), ('inverse curvature flow', 0.6016814708709717), ('flow curves', 0.5711679458618164), ('preserving curvature', 0.5621747374534607), ('convex curves', 0.5593223571777344), ('flow curve', 0.5488513112068176)]"
505,505,61,505_hamiltonicity graphs_hamilton cycles_contains hamilton cycle_hamilton cycle,"['hamiltonicity graphs', 'hamilton cycles', 'contains hamilton cycle', 'hamilton cycle', 'hamiltonian graph', 'hamiltonian cycles', 'random directed graphs', 'random graphs', 'binomial random graph', 'pseudorandom graphs']","['Hamilton Cycles in Random Graphs: a bibliography   We provide an annotated bibliography for the study of Hamilton cycles in\nrandom graphs and hypergraphs.\n', 'Finding Hamilton cycles in random intersection graphs   The construction of the random intersection graph model is based on a random\nfamily of sets. Such structures, which are derived from intersections of sets,\nappear in a natural manner in many applications. In this article we study the\nproblem of finding a Hamilton cycle in a random intersection graph. To this end\nwe analyse a classical algorithm for finding Hamilton cycles in random graphs\n(algorithm HAM) and study its efficiency on graphs from a family of random\nintersection graphs (denoted here by G(n,m,p)). We prove that the threshold\nfunction for the property of HAM constructing a Hamilton cycle in G(n,m,p) is\nthe same as the threshold function for the minimum degree at least two. Until\nnow, known algorithms for finding Hamilton cycles in G(n,m,p) were designed to\nwork in very small ranges of parameters and, unlike HAM, used the structure of\nthe family of random sets.\n', 'Covering Random Digraphs with Hamilton Cycles   A covering of a digraph $D$ by Hamilton cycles is a collection of directed\nHamilton cycles (not necessarily edge-disjoint) that together cover all the\nedges of $D$. We prove that for $1/2 \\geq p\\geq \\frac{\\log^{20} n}{n}$, the\nrandom digraph $D_{n,p}$ typically admits an optimal Hamilton cycle covering.\nSpecifically, the edges of $D_{n,p}$ can be covered by a family of $t$ Hamilton\ncycles, where $t$ is the maximum of the the in-degree and out-degree of the\nvertices in $D_{n,p}$. Notably, $t$ is the best possible bound, and our\nassumption on $p$ is optimal up to a polylogarithmic factor.\n']","[('hamiltonicity graphs', 0.663780152797699), ('hamilton cycles', 0.6352989077568054), ('contains hamilton cycle', 0.6108763217926025), ('hamilton cycle', 0.6044806838035583), ('hamiltonian graph', 0.5914243459701538), ('hamiltonian cycles', 0.5839307904243469), ('random directed graphs', 0.5801255702972412), ('random graphs', 0.5689408183097839), ('binomial random graph', 0.5651730895042419), ('pseudorandom graphs', 0.5614422559738159)]"
506,506,61,506_photoacoustic tomography_quantitative photoacoustic_photoacoustic_reconstruction algorithms,"['photoacoustic tomography', 'quantitative photoacoustic', 'photoacoustic', 'reconstruction algorithms', 'optical tomography', 'image reconstruction', 'diffuse optical tomography', 'tomography', 'compressed sensing', 'imaging modality']","['Analysis for Full Field Photoacoustic Tomography with Variable Sound\n  Speed   Photoacoustic tomography (PAT) is a non-invasive imaging modality that\nrequires recovering the initial data of the wave equation from certain\nmeasurements of the solution outside the object. In the standard PAT\nmeasurement setup, the used data consist of time-dependent signals measured on\nan observation surface. In contrast, the measured data from the recently\ninvented full-field detection technique provide the solution of the wave\nequation on a spatial domain at a single instant in time. While reconstruction\nusing classical PAT data has been extensively studied, not much is known for\nthe full field PAT problem. In this paper, we build mathematical foundations of\nthe latter problem for variable sound speed and settle its uniqueness and\nstability. Moreover, we introduce an exact inversion method using time-reversal\nand study its convergence. Our results demonstrate the suitability of both the\nfull field approach and the proposed time-reversal technique for high\nresolution photoacoustic imaging.\n', 'Well-posedness for Photoacoustic Tomography with Fabry-Perot Sensors   In the mathematical analysis of photoacoustic imaging, it is usually assumed\nthat the acoustic pressure (Dirichlet data) is measured on a detection surface.\nHowever, actual ultrasound detectors gather data of a different type. In this\npaper, we propose a more realistic mathematical model of ultrasound\nmeasurements acquired by the Fabry--Perot sensor. This modeling incorporates\ndirectional response of such sensors. We study the solvability of the resulting\nphotoacoustic tomography problem, concluding that the problem is well-posed\nunder certain assumptions. Numerical reconstructions are implemented using the\nLandweber iterations, after discretization of the governing equations using the\nfinite element method.\n', 'Sampling and resolution in sparse view photoacoustic tomography   We investigate resolution in photoacoustic tomography (PAT). Using Shannon\ntheory, we investigate the theoretical resolution limit of sparse view PAT\ntheoretically, and empirically demonstrate that all reconstruction methods used\nexceed this limit.\n']","[('photoacoustic tomography', 0.8082677125930786), ('quantitative photoacoustic', 0.7143515348434448), ('photoacoustic', 0.6356012225151062), ('reconstruction algorithms', 0.5501888394355774), ('optical tomography', 0.5488844513893127), ('image reconstruction', 0.5201607346534729), ('diffuse optical tomography', 0.5072025060653687), ('tomography', 0.5019213557243347), ('compressed sensing', 0.4544423818588257), ('imaging modality', 0.42212849855422974)]"
507,507,61,507_holomorphic vector bundles_holomorphic vector bundle_hermitian vector bundles_hermitian metrics,"['holomorphic vector bundles', 'holomorphic vector bundle', 'hermitian vector bundles', 'hermitian metrics', 'singular hermitian', 'hermitian holomorphic', 'hermitian metric', 'stein manifolds', 'vector bundles', 'metrics holomorphic']","['Optimal $L^2$ extension for holomorphic vector bundles with singular\n  hermitian metrics   In the present paper, we study the properties of singular Nakano positivity\nof singular hermitian metrics on holomorphic vector bundles, and establish an\noptimal $L^2$ extension theorem for holomorphic vector bundles with singular\nhermitian metrics on weakly pseudoconvex K\\""{a}hler manifolds. As applications,\nwe give a necessary condition for the holding of the equality in optimal $L^2$\nextension theorem, and present singular hermitian holomorphic vector bundle\nversions of some $L^2$ extension theorems with optimal estimate.\n', ""Multiplier Submodule Sheaves and a problem of Lempert   In this article, we establish an $L^2$ extension theorem for Nakano\nsemi-positive singular Hermitian metrics on holomorphic vector bundles, and the\nstrong openness and stability properties of the multiplier submodule sheaves\nassociated to Nakano semi-positive singular Hermitian metrics on holomorphic\nvector bundles.\n  We solve affirmatively a question of Lempert on the preservation of Nakano\nsemi-positivity under limit of an increasing metrics based on\nDeng-Ning-Wang-Zhou's characterization of Nakano positivity.\n"", 'Nakano positivity of singular Hermitian metrics and vanishing theorems\n  of Demailly-Nadel-Nakano type   In this article, we propose a definition of Nakano semi-positivity of\nsingular Hermitian metrics on holomorphic vector bundles. By using this\npositivity notion, we establish $L^2$-estimates for holomorphic vector bundles\nwith Nakano positive singular Hermitian metrics. We also show vanishing\ntheorems, which generalize both Nakano type and Demailly-Nadel type vanishing\ntheorems. As applications, we specifically construct globally Nakano\nsemi-positive singular Hermitian metrics for several bundles, and prove\nvanishing theorems associated with them.\n']","[('holomorphic vector bundles', 0.6605112552642822), ('holomorphic vector bundle', 0.6272302269935608), ('hermitian vector bundles', 0.6269044876098633), ('hermitian metrics', 0.5331854820251465), ('singular hermitian', 0.5095834732055664), ('hermitian holomorphic', 0.5083897709846497), ('hermitian metric', 0.5051353573799133), ('stein manifolds', 0.4971466064453125), ('vector bundles', 0.49545687437057495), ('metrics holomorphic', 0.48542648553848267)]"
508,508,61,508_langevin dynamics_underdamped langevin dynamics_overdamped langevin dynamics_langevin equations,"['langevin dynamics', 'underdamped langevin dynamics', 'overdamped langevin dynamics', 'langevin equations', 'underdamped langevin', 'langevin type', 'overdamped langevin', 'stochastic differential equations', 'langevin', 'dynamics brownian']","['Some properties on the reversibility and the linear response theory of\n  Langevin dynamics   Linear response theory is a fundamental framework studying the macroscopic\nresponse of a physical system to an external perturbation. This paper focuses\non the rigorous mathematical justification of linear response theory for\nLangevin dynamics. We give some equivalent characterizations for reversible\noverdamped/underdamped Langevin dynamics, which is the unperturbed reference\nsystem. Then we clarify sufficient conditions for the smoothness and\nexponential convergence to the invariant measure for the overdamped case. We\nalso clarify those sufficient conditions for the underdamped case, which\ncorresponds to hypoellipticity and hypocoercivity. Based on these, the\nasymptotic dependence of the response function on the small perturbation is\nproved in both finite and infinite time horizons. As applications, Green-Kubo\nrelations and linear response theory for a generalized Langevin dynamics are\nalso proved in a rigorous fashion.\n', 'Quantitative hydrodynamic limits of the Langevin dynamics for gradient\n  interface models   We study the Langevin dynamics corresponding to the $\\nabla\\phi$ (or\nGinzburg-Landau) interface model with a uniformly convex interaction potential.\nWe interpret these Langevin dynamics as a nonlinear parabolic equation forced\nby white noise, which turns the problem into a nonlinear homogenization\nproblem. Using quantitative homogenization methods, we prove a quantitative\nhydrodynamic limit, obtain the $C^2$ regularity of the surface tension, prove a\nlarge-scale Lipschitz-type estimate for the trajectories of the dynamics, and\nshow that the fluctuation-dissipation relation can be seen as a commutativity\nof homogenization and linearization. Finally, we explain why we believe our\ntechniques can be adapted to the setting of degenerate (non-uniformly) convex\ninteraction potentials.\n', 'Hypocoercivity meets lifts   We unify the variational hypocoercivity framework established by D.\nAlbritton, S. Armstrong, J.-C. Mourrat, and M. Novack, with the notion of\nsecond-order lifts of reversible diffusion processes, recently introduced by A.\nEberle and F. L\\""orler. We give an abstract, yet fully constructive,\npresentation of the theory, so that it can be applied to a large class of\nlinear kinetic equations. As this hypocoercivity technique does not twist the\nreference norm, we can recover accurate and sharp convergence rates in various\nmodels. Among those, adaptive Langevin dynamics (ALD) is discussed in full\ndetail and we show that for near-quadratic potentials, with suitable choices of\nparameters, it is a near-optimal second-order lift of the overdamped Langevin\ndynamics. As a further consequence, we observe that the Generalised Langevin\nEquation (GLE) is a also a second-order lift, as the standard (kinetic)\nLangevin dynamics are, of the overdamped Langevin dynamics. Then, convergence\nof (GLE) cannot exceed ballistic speed, i.e. the square root of the rate of the\noverdamped regime. We illustrate this phenomenon with explicit computations in\na benchmark Gaussian case.\n']","[('langevin dynamics', 0.7950067520141602), ('underdamped langevin dynamics', 0.7577980756759644), ('overdamped langevin dynamics', 0.755357563495636), ('langevin equations', 0.7523316740989685), ('underdamped langevin', 0.5530759692192078), ('langevin type', 0.5491297245025635), ('overdamped langevin', 0.5444380044937134), ('stochastic differential equations', 0.5364617705345154), ('langevin', 0.5338810682296753), ('dynamics brownian', 0.5245683193206787)]"
509,509,61,509_mimo broadcast_broadcast channel_broadcast_mimo multiple access,"['mimo broadcast', 'broadcast channel', 'broadcast', 'mimo multiple access', 'multiple access channels', 'fading channels', 'multiple access channel', 'transmit antennas', 'channels', 'channel state information']","['The DoF Region of Two-User MIMO Broadcast Channel with Delayed\n  Imperfect-Quality CSIT   The channel state information at the transmitter (CSIT) play an important\nrole in the performance of wireless networks. The CSIT model can be delayed and\nimperfect-quality, since the feedback link has a delay and the channel state\ninformation (CSI) feedback has distortion. In this paper, we thus characterize\nthe degrees-of-freedom (DoF) region of the two-user multiple-input\nmultiple-output (MIMO) broadcast channel with delayed imperfect-quality CSIT,\nwhere the antenna configurations can be arbitrary. The converse proof of DoF\nregion is based on the enhancement of physically degraded channel. The\nachievability proof of DoF region is through a novel transmission scheme\ndesign, where the duration of each phase and the amount of transmitted symbols\nare configured based on the imperfect-quality of delayed CSIT. As a result, we\nshow that the DoF region with delayed imperfect-quality CSIT is located between\nthe DoF region with no CSIT and the DoF region with delayed CSIT.\n', 'Achievable DoF Regions of Three-User MIMO Broadcast Channel with Delayed\n  CSIT   For the two-user multiple-input multiple-output (MIMO) broadcast channel with\ndelayed channel state information at the transmitter (CSIT) and arbitrary\nantenna configurations, all the degrees-of-freedom (DoF) regions are obtained.\nHowever, for the three-user MIMO broadcast channel with delayed CSIT and\narbitrary antenna configurations, the DoF region of order-2 messages is still\nunclear and only a partial achievable DoF region of order-1 messages is\nobtained, where the order-2 messages and order-1 messages are desired by two\nreceivers and one receiver, respectively. In this paper, for the three-user\nMIMO broadcast channel with delayed CSIT and arbitrary antenna configurations,\nwe first design transmission schemes for order-2 messages and order-1 messages.\nNext, we propose to analyze the achievable DoF region of transmission scheme by\ntransformation approach. In particular, we transform the decoding condition of\ntransmission scheme w.r.t. phase duration into the achievable DoF region w.r.t.\nachievable DoF, through achievable DoF tuple expression connecting phase\nduration and achievable DoF. As a result, the DoF region of order-2 messages is\ncharacterized and an achievable DoF region of order-1 messages is completely\nexpressed. Besides, for order-1 messages, we derive the sufficient condition,\nunder which the proposed achievable DoF region is the DoF region.\n', 'The DoF Region of Order-(K-1) Messages for the K-user MIMO Broadcast\n  Channel with Delayed CSIT   This paper theoretically characterizes the degrees-of-freedom (DoF) region of\norder-$(K-1)$ messages for the $K$-user multiple-input multiple-output (MIMO)\nbroadcast channel with delayed channel state information at the transmitter\n(CSIT) and arbitrary antenna configurations, where the transmitter has $M$\nantennas and the receiver $i=1,2,\\cdots,K$ has $N_i$ antennas. For the\nconverse, we first derive the DoF region of order-$(K-1)$ messages for the\n$K$-user MIMO broadcast channel with no CSIT and arbitrary antenna\nconfigurations with the aid of the proposed Genie-bound, and then establish the\nDoF outer region. For the achievability, we first design a 2-phase transmission\nscheme, and then propose a backward/forward cancellation algorithm for\ndecoding. Specifically, we efficiently derive the achievable DoF region from\nthe designed transmission scheme by transformation approach. The main\nimplication of this paper is that for the order-$(K-1)$ messages of $K$-user\nMIMO broadcast channel, the DoF region with delayed CSIT is larger than the DoF\nregion with no CSIT when $N_2<M$, where $N_1 \\le N_2 \\le \\cdots \\le N_K$.\n']","[('mimo broadcast', 0.6343712210655212), ('broadcast channel', 0.5854736566543579), ('broadcast', 0.49332165718078613), ('mimo multiple access', 0.4929204285144806), ('multiple access channels', 0.4812326431274414), ('fading channels', 0.4738999307155609), ('multiple access channel', 0.47046878933906555), ('transmit antennas', 0.4437200427055359), ('channels', 0.42930030822753906), ('channel state information', 0.42867642641067505)]"
510,510,61,510_topological complexity_higher topological complexity_complexity map_equivariant topological,"['topological complexity', 'higher topological complexity', 'complexity map', 'equivariant topological', 'complexity group', 'homotopy invariants', 'topological complexities', 'complexity several', 'homotopy invariant', 'complexity']","[""Equivariant and Invariant Parametrized Topological Complexity For a $G$-equivariant fibration $p \\colon E\\to B$, we introduce and study the invariant analogue of Cohen, Farber and Weinberger's parametrized topological complexity, called the invariant parametrized topological complexity. This notion generalizes the invariant topological complexity introduced by Lubawski and Marzantowicz. We establish the equivariant fibrewise homotopy invariance of this notion and derive several bounds, including a cohomological lower bound and a dimensional upper bound. Additionally, we compare invariant parametrized topological complexity with other well-known invariants. When $G$ is a compact Lie group acting freely on $E$, we show that the invariant parametrized topological complexity of the $G$-fibration $p \\colon E\\to B$ coincides with the parametrized topological complexity of the induced fibration $\\overline{p} \\colon \\overline{E} \\to \\overline{B}$ between the orbit spaces. Finally, we compute the invariant parametrized topological complexity of equivariant Fadell-Neuwirth fibrations, which measures the complexity of motion planning in presence of obstacles having unknown positions such that the order in which they are placed is irrelevant.\n  Apart from this, we establish several bounds, including a cohomological lower bound, an equivariant homotopy dimension-connectivity upper bound and various product inequalities for the equivariant sectional category. Applying them, we obtain some interesting results for equivariant and invariant parametrized topological complexity of a $G$-fibration."", 'LS-category and topological complexity of Milnor manifolds and\n  corresponding generalized projective product spaces   Milnor manifolds are a class of certain codimension-$1$ submanifolds of the\nproduct of projective spaces. In this paper, we study the LS-category and\ntopological complexity of these manifolds. We determine the exact value of the\nLS-category and in many cases, the topological complexity of these manifolds.\nWe also obtain tight bounds on the topological complexity of these manifolds.\nIt is known that Milnor manifolds admit $\\mathbb{Z}_2$ and circle actions. We\ncompute bounds on the equivariant LS-category and equivariant topological\ncomplexity of these manifolds. Finally, we describe the mod-$2$ cohomology\nrings of some generalized projective product spaces corresponding to Milnor\nmanifolds and use this information to compute the bound on LS-category and\ntopological complexity of these spaces.\n', 'Directed LS category and directed parametrized topological complexity   We introduce and study a parametrized analogue of the directed topological\ncomplexity, originally developed by Goubault, Farber, and Sagnier. We establish\nthe fibrewise basic dihomotopy invariance of directed parametrized topological\ncomplexity and explore its relationship with the parametrized topological\ncomplexity. In addition, we introduce the concept of the directed\nLusternik$-$Schnirelmann (LS) category, prove its basic dihomotopy invariance,\nand investigate its connections with both directed topological complexity and\ndirected parametrized topological complexity. As an application, we show that\nthe directed LS category of the directed spheres is equal to two.\n']","[('topological complexity', 0.6264715790748596), ('higher topological complexity', 0.6142130494117737), ('complexity map', 0.5187938809394836), ('equivariant topological', 0.516747772693634), ('complexity group', 0.49527445435523987), ('homotopy invariants', 0.4808940887451172), ('topological complexities', 0.4548664391040802), ('complexity several', 0.45200905203819275), ('homotopy invariant', 0.45084652304649353), ('complexity', 0.4376457929611206)]"
511,511,61,511_warped product manifolds_warped product metric_manifolds warped_product riemannian manifolds,"['warped product manifolds', 'warped product metric', 'manifolds warped', 'product riemannian manifolds', 'warped product spaces', 'product manifolds', 'product manifold', 'warped product space', 'warped products', 'riemannian manifolds']","['Remarks on metallic warped product manifolds   We characterize the metallic structure on the product of two metallic\nmanifolds in terms of metallic maps and provide a necessary and sufficient\ncondition for the warped product of two locally metallic Riemannian manifolds\nto be locally metallic. The particular case of product manifolds is discussed\nand an example of metallic warped product Riemannian manifold is provided.\n', 'Warped product pointwise bi-slant submanifolds in metallic Riemannian\n  manifolds   In this paper, we study some properties of warped product pointwise bi-slant\nsubmanifolds in locally metallic Riemannian manifolds and we construct some\nexamples in Euclidean spaces.\n', 'Warped product submanifolds in metallic Riemannian manifolds   In this paper, we study the existence of proper warped product submanifolds\nin metallic (or Golden) Riemannian manifolds and we discuss about\nsemi-invariant, semi-slant and, respectively, hemi-slant warped product\nsubmanifolds in metallic and Golden Riemannian manifolds. Also, we provide some\nexamples of warped product submanifolds in Euclidean spaces.\n']","[('warped product manifolds', 0.8393812775611877), ('warped product metric', 0.7366539239883423), ('manifolds warped', 0.7146445512771606), ('product riemannian manifolds', 0.7126454710960388), ('warped product spaces', 0.6810364127159119), ('product manifolds', 0.6653791666030884), ('product manifold', 0.6591536402702332), ('warped product space', 0.6438052654266357), ('warped products', 0.6300831437110901), ('riemannian manifolds', 0.6191053986549377)]"
512,512,61,512_equivariant cohomology_gkm manifold_torus manifolds_manifolds,"['equivariant cohomology', 'gkm manifold', 'torus manifolds', 'manifolds', 'toric manifolds', 'manifold 2n', 'manifold', 'equivariant', 'manifolds locally', 'equivariantly formal']","[""The GKM correspondence in dimension 6   It follows from the GKM description of equivariant cohomology that the GKM\ngraph of a GKM manifold has free equivariant graph cohomology, and satisfies a\nPoincar\\'e duality condition. We prove that these conditions are sufficient for\nan abstract $3$-valent $T^2$-GKM graph to be realizable by a simply-connected\n$6$-dimensional GKM manifold. Our realization has the property that any closed\nstratum of a finite isotropy group contains a fixed point. Furthermore, we\nargue that in case there exists a fixed point in whose vicinity there occur at\nmost two distinct finite nontrivial isotropy groups such a realization is\nunique up to equivariant homeomorphism, thus establishing a complexity one GKM\ncorrespondence in dimension $6$. We show that the statement on equivariant\nuniqueness is false without the two conditions on the finite isotropies by\nproviding counterexamples in presence of a fixed point with three distinct\nneighbouring finite isotropy groups, as well as an example of a\nsimply-connected integer GKM manifold with a closed stratum of a finite\nisotropy group which does not contain any fixed point.\n"", 'How is a graph not like a manifold?   For an equivariantly formal action of a compact torus $T$ on a smooth\nmanifold $X$ with isolated fixed points we investigate the global homological\nproperties of the graded poset $S(X)$ of face submanifolds. We prove that the\ncondition of $j$-independency of tangent weights at each fixed point implies\n$(j+1)$-acyclicity of the skeleta $S(X)_r$ for $r>j+1$. This result provides a\nnecessary topological condition for a GKM graph to be a GKM graph of some GKM\nmanifold. We use particular acyclicity arguments to describe the equivariant\ncohomology algebra of an equivariantly formal manifold of dimension $2n$ with\nan $(n-1)$-independent action of $(n-1)$-dimensional torus, under certain\ncolorability assumptions on its GKM graph. This description relates the\nequivariant cohomology algebra to the face algebra of a simplicial poset. Such\nobservation underlines certain similarity between actions of complexity one and\ntorus manifolds.\n', 'Equivariantly formal 2-torus actions of complexity one   In this paper we study a specific class of actions of a $2$-torus\n$\\mathbb{Z}_2^k$ on manifolds, namely, the actions of complexity one in general\nposition. We describe the orbit space of equivariantly formal $2$-torus actions\nof complexity one in general position and restricted complexity one actions in\nthe case of small covers. It is observed that the orbit spaces of such actions\nare topological manifolds. If the action is equivariantly formal, we prove that\nthe orbit space is a $\\mathbb{Z}_2$-homology sphere. We study a particular\nsubclass of these $2$-torus actions: restrictions of small covers to a subgroup\nof index 2 in general position. The subgroup of this form exists if and only if\nthe small cover is orientable, and in this case we prove that the orbit space\nof a restricted $2$-torus action is homeomorphic to a sphere.\n']","[('equivariant cohomology', 0.598688006401062), ('gkm manifold', 0.5930532813072205), ('torus manifolds', 0.5598386526107788), ('manifolds', 0.5480840802192688), ('toric manifolds', 0.5283799767494202), ('manifold 2n', 0.5272412300109863), ('manifold', 0.48927244544029236), ('equivariant', 0.48812535405158997), ('manifolds locally', 0.48245057463645935), ('equivariantly formal', 0.4810764491558075)]"
513,513,61,513_anosov flows_anosov flow_anosov diffeomorphisms_flows manifolds,"['anosov flows', 'anosov flow', 'anosov diffeomorphisms', 'flows manifolds', 'flow manifold', 'examples anosov', 'pseudo anosov', 'hyperbolic three manifold', 'anosov', 'flow closed manifold']","['Anomalous Anosov flows revisited   This paper is devoted to higher dimensional Anosov flows and consists of two\nparts. In the first part, we investigate fiberwise Anosov flows on affine torus\nbundles which fiber over 3-dimensional Anosov flows. We provide a dichotomy\nresult for such flows --- they are either suspensions of Anosov diffeomorphisms\nor the stable and unstable distributions have equal dimensions.\n  In the second part, we give a new surgery type construction of Anosov flows,\nwhich yields non-transitive Anosov flows in all odd dimensions.\n', 'Anosov flows on Dehn surgeries on the figure-eight knot   The purpose of this paper is to classify Anosov flows on the 3-manifolds\nobtained by Dehn surgeries on the figure-eight knot. This set of 3-manifolds is\ndenoted by M(r) (r is a ratioanl number), which contains the first class of\nhyperbolic 3-manifolds admitting Anosov flows in history, discovered by\nGoodman. Combining with the classification of Anosov flows on the sol-manifold\nM(0) due to Plante, we have: 1. if r is an integer, up to topological\nequivalence, M(r) exactly carries a unique Anosov flow, which is constructed by\nGoodman by doing a Dehn-Fried-Goodman surgery on a suspension Anosov flow; 2.\nif r is not an integer, M(r) does not carry any Anosov flow. As a consequence\nof the second result, we get infinitely many closed orientable hyperbolic\n3-manifolds which carry taut foliations but does not carry any Anosov flow. The\nfundamental tool in the proofs is the set of branched surfaces built by\nSchwider, which is used to carry essential laminations on M(r).\n', ""Goodman surgery and projectively Anosov flows   We introduce a generalization of Goodman surgery to the category of\nprojectively Anosov flows. This construction is performed along a knot that is\nsimultaneously Legendrian and transverse for a supporting bi-contact structure.\nIf the flow is Anosov there is a particular class of supporting bi-contact\nstructures that induce Lorentzian metrics satisfying Barbot's criterion of\nhyperbolicity. Foulon and Hasselblatt construct new contact Anosov flows by\nsurgery from a geodesic flow. We generalize their result showing that in any\ncontact Anosov flow there is a family of Legendrian knots that can be used to\nproduce new contact Anosov flows by surgery. Outside of the realm of Anosov\nflows we generate new examples of projectively Anosov flows on hyperbolic\n3-manifolds. These flows contain an invariant submanifold of genus g>0. We also\ngive some application to contact geometry: we interpret the bi-contact surgery\nin terms of classic contact-Legendrian surgery and admissible-inadmissible\ntransverse surgery and we deduce some (hyper)tightness result for contact and\ntransverse surgeries.\n""]","[('anosov flows', 0.7368488907814026), ('anosov flow', 0.6928591728210449), ('anosov diffeomorphisms', 0.66829913854599), ('flows manifolds', 0.617516040802002), ('flow manifold', 0.5735312700271606), ('examples anosov', 0.5522007346153259), ('pseudo anosov', 0.5506640076637268), ('hyperbolic three manifold', 0.5430340766906738), ('anosov', 0.5287063717842102), ('flow closed manifold', 0.5276111364364624)]"
514,514,61,514_quantum cryptography_quantum secure_efficient quantum_quantum private,"['quantum cryptography', 'quantum secure', 'efficient quantum', 'quantum private', 'based quantum', 'key distribution', 'quantum', 'secret key', 'scheme quantum', 'cryptography']","['Information-Theoretic Secure Key Sharing for Wide-Area Mobile\n  Applications   With the rapid growth of handheld devices in the internet of things (IoT)\nnetworks, mobile applications have become ubiquitous in everyday life. As\ntechnology is developed, so do also the risks and threats associated with it,\nespecially in the forthcoming quantum era. Existing IoT networks, however, lack\na quantum-resistant secret key sharing scheme to meet confidential message\ntransmission demands in wide-area mobile applications. To address this issue,\nthis article proposes a new scheme, channel reciprocity (CR) based quantum key\ndistribution (QKD) CR-QKD, which accomplishes the goal of secret key sharing by\ncombining emerging techniques of QKD and CR-based key generation (CRKG).\nExploiting laws of quantum physics and properties of wireless channels, the\nproposed scheme is able to ensure the secrecy of the key, even against\ncomputationally unbounded adversaries. The basic mechanism is elaborated for a\nsingle-user case and it is extended into a multi-user case by redesigning a\nmulti-user edge forwarding strategy. In addition, to make CR-QKD more\npractical, some enhancement strategies are studied to reduce the time delay and\nto improve the secret key generation rate in a secure manner. A prototype of\nCR-QKD is demonstrated in a metropolitan area network, where secret keys are\nshared between two remote IoT devices that are roughly fifteen kilometers apart\nfrom each other. The experimental results have verified that CR-QKD allows a\nsecret key rate of 424 bits per second with a retransmission rate of 2.1%.\n', 'High-dimensional coherent one-way quantum key distribution   High-dimensional quantum key distribution (QKD) offers secure communication,\nwith secure key rates that surpass those achievable by QKD protocols utilizing\ntwo-dimensional encoding. However, existing high-dimensional QKD protocols\nrequire additional experimental resources, such as multiport interferometers\nand multiple detectors, thus raising the cost of practical high-dimensional\nsystems and limiting their use. Here, we present and analyze a novel protocol\nfor arbitrary-dimensional QKD, that requires only the hardware of a standard\ntwo-dimensional system. We provide security proofs against individual attacks\nand coherent attacks, setting an upper and lower bound on the secure key rates.\nThen, we test the new high-dimensional protocol in a standard two-dimensional\nQKD system over a 40 km fiber link. The new protocol yields a two-fold\nenhancement of the secure key rate compared to the standard two-dimensional\ncoherent one-way protocol, without introducing any hardware modifications to\nthe system. This work, therefore, holds great potential to enhance the\nperformance of already deployed time-bin QKD systems through a software update\nalone. Furthermore, its applications extend across different encoding schemes\nof QKD qudits.\n', 'QKD Based on Time-Entangled Photons and its Key-Rate Promise   For secure practical systems, quantum key distribution (QKD) must provide\nhigh key rates over long distances. Time-entanglement-based QKD promises to\nincrease the secret key rate and distribution distances compared to other QKD\nimplementations. This article describes the major steps in QKD protocols,\nfocusing on the nascent QKD technology based on high-dimensional time-bin\nentangled photons. We overview state-of-the-art from the information and coding\ntheory perspective. In particular, we discuss the key rate loss due to\nsingle-photon detector imperfections. We hope the open questions posed and\ndiscussed in this paper will inspire information and coding theorists to\ncontribute to and impact fledgling quantum applications and influence future\nquantum communication systems.\n']","[('quantum cryptography', 0.6806862354278564), ('quantum secure', 0.6574891209602356), ('efficient quantum', 0.5407142043113708), ('quantum private', 0.5154941082000732), ('based quantum', 0.4681846797466278), ('key distribution', 0.46137675642967224), ('quantum', 0.45435941219329834), ('secret key', 0.4535849392414093), ('scheme quantum', 0.44883522391319275), ('cryptography', 0.44430768489837646)]"
515,515,60,515_compact ahler manifolds_ahler manifolds_manifolds compact ahler_compact ahler manifold,"['compact ahler manifolds', 'ahler manifolds', 'manifolds compact ahler', 'compact ahler manifold', 'hyperk ahler manifolds', 'hyper ahler manifolds', 'ahler manifold', 'hyperk ahler manifold', 'compact ahler', 'ahler spaces']","['On the dual positive cones and the algebraicity of a compact K\\""ahler manifold We investigate the algebraicity of compact K\\""ahler manifolds admitting a positive rational Hodge class of bidimension $(1,1)$. We prove that if the dual K\\""ahler cone of a compact K\\""ahler manifold $X$ contains a rational class as an interior point, then its Albanese variety is projective. As a consequence, we answer the Oguiso--Peternell problem for Ricci-flat compact K\\""ahler manifolds. We also study related algebraicity problems for threefolds.', 'Algebraic approximations of compact K\\""ahler manifolds of algebraic\n  codimension 1   For every compact K\\""ahler manifold $X$ of algebraic dimension $a(X) = \\dim X\n- 1$, we prove that $X$ has arbitrarily small deformations to some projective\nmanifolds.\n', 'A characterization of uniruled compact K\\""ahler manifolds   We adapt Bost\'s algebraicity characterization to the situation of a germ in a\ncompact K\\""ahler manifold. As a consequence, we extend the algebraic\nintegrability criteria of Campana-P\\u{a}un and of Druel to foliations on\ncompact K\\""ahler manifolds. As an application, we prove that a compact K\\""ahler\nmanifold is uniruled if and only if its canonical line bundle is not\npseudoeffective.\n']","[('compact ahler manifolds', 0.7993425726890564), ('ahler manifolds', 0.7858462929725647), ('manifolds compact ahler', 0.7852358222007751), ('compact ahler manifold', 0.7752997279167175), ('hyperk ahler manifolds', 0.7710613012313843), ('hyper ahler manifolds', 0.768036425113678), ('ahler manifold', 0.7560639977455139), ('hyperk ahler manifold', 0.7468293905258179), ('compact ahler', 0.6476287841796875), ('ahler spaces', 0.6470850110054016)]"
516,516,60,516_decoding complexity_access massive mimo_massive mimo_orthogonal multiple access,"['decoding complexity', 'access massive mimo', 'massive mimo', 'orthogonal multiple access', 'fading channels', 'decoding', 'successive interference cancellation', 'unsourced random access', 'interference cancellation', 'random access massive']","[""Unsourced Random Access with a Massive MIMO Receiver Using Multiple\n  Stages of Orthogonal Pilots   We study the problem of unsourced random access (URA) over Rayleigh\nblock-fading channels with a receiver equipped with multiple antennas. We\nemploy multiple stages of orthogonal pilots, each of which is randomly picked\nfrom a codebook. In the proposed scheme, each user encodes its message using a\npolar code and appends it to the selected pilot sequences to construct its\ntransmitted signal. Accordingly, the received signal consists of superposition\nof the users' signals each composed of multiple orthogonal pilot parts and a\npolar coded part. We use an iterative approach for decoding the transmitted\nmessages along with a suitable successive interference cancellation scheme.\nPerformance of the proposed scheme is illustrated via extensive set of\nsimulation results which show that it significantly outperforms the existing\napproaches for URA over multiple-input multiple-output fading channels.\n"", 'Pilot-Based Unsourced Random Access with a Massive MIMO Receiver in the\n  Quasi-Static Fading Regime   In this work we treat the unsourced random access problem on a Rayleigh\nblock-fading AWGN channel with multiple receive antennas. Specifically, we\nconsider the slowly fading scenario where the coherence block-length is large\ncompared to the number of active users and the message can be transmitted in\none coherence block. Unsourced random access refers to a form of grant-free\nrandom access where users are considered to be a-priori indistinguishable and\nthe receiver recovers a list of transmitted messages up to permutation. In this\nwork we show that, when the coherence block length is large enough, a\nconventional approach based on the transmission of non-orthogonal pilot\nsequences with subsequent channel estimation and Maximum-Ratio-Combining (MRC)\nprovides a simple energy-efficient solution whose performance can be well\napproximated in closed form. For the finite block-length simulations we use a\nrandomly sub-sampled DFT matrix as pilot matrix, a low-complexity approximate\nmessage passing algorithm for activity detection and a state-of-the-art polar\ncode as single-user error correction code with a successive-cancellation-list\ndecoder. These simulations prove the scalability of the presented approach and\nthe quality of the analysis.\n', 'Design and Analysis of Massive Uncoupled Unsourced Random Access with\n  Bayesian Joint Decoding   In this paper, we investigate unsourced random access for massive\nmachine-type communications (mMTC) in the sixth-generation (6G) wireless\nnetworks. Firstly, we establish a high-efficiency uncoupled framework for\nmassive unsourced random access without extra parity check bits. Then, we\ndesign a low-complexity Bayesian joint decoding algorithm, including codeword\ndetection and stitching. In particular, we present a Bayesian codeword\ndetection approach by exploiting Bayes-optimal divergence-free orthogonal\napproximate message passing in the case of unknown priors. The output long-term\nchannel statistic information is well leveraged to stitch codewords for\nrecovering the original message. Thus, the spectral efficiency is improved by\navoiding the use of parity bits. Moreover, we analyze the performance of the\nproposed Bayesian joint decoding-based massive uncoupled unsourced random\naccess scheme in terms of computational complexity and error probability of\ndecoding. Furthermore, by asymptotic analysis, we obtain some useful insights\nfor the design of massive unsourced random access. Finally, extensive\nsimulation results confirm the effectiveness of the proposed scheme in 6G\nwireless networks.\n']","[('decoding complexity', 0.49901971220970154), ('access massive mimo', 0.49773862957954407), ('massive mimo', 0.4804563820362091), ('orthogonal multiple access', 0.46978387236595154), ('fading channels', 0.4657641649246216), ('decoding', 0.4574897587299347), ('successive interference cancellation', 0.4413185119628906), ('unsourced random access', 0.42018598318099976), ('interference cancellation', 0.4080773890018463), ('random access massive', 0.404352605342865)]"
517,517,60,517_orbits class_line classes_liebler line classes_family orbits,"['orbits class', 'line classes', 'liebler line classes', 'family orbits', 'orbits points', 'quartic forms', 'projective space mathrm', 'twisted cubic', 'orbits', 'line incidence']","['Incidence matrices for the class $\\mathcal{O}_6$ of lines external to\n  the twisted cubic in $\\mathrm{PG}(3,q)$   We consider the structures of the plane-line and point-line incidence\nmatrices of the projective space $\\mathrm{PG}(3,q)$ connected with orbits of\nplanes, points, and lines under the stabilizer group of the twisted cubic. In\nthe literature, lines are partitioned into classes, each of which is a union of\nline orbits. In this paper, for all $q$, even and odd, we determine the\nincidence matrices connected with a family of orbits of the class named\n$\\mathcal{O}_6$. This class contains lines external to the twisted cubic. The\nconsidered family include an essential part of all $\\mathcal{O}_6$ orbits,\nwhose complete classification is an open problem.\n', 'Further results on orbits and incidence matrices for the class\n  $\\mathcal{O}_6$ of lines external to the twisted cubic in $\\mathrm{PG}(3,q)$   In the literature, lines of the projective space $\\mathrm{PG}(3,q)$ are\npartitioned into classes, each of which is a union of line orbits under the\nstabilizer group of the twisted cubic. The least studied class is named\n$\\mathcal{O}_6$. This class contains lines external to the twisted cubic which\nare not its chords or axes and do not lie in any of its osculating planes. For\neven and odd $q$, we propose a new family of orbits of $\\mathcal{O}_6$ and\ninvestigate in detail their stabilizer groups and the corresponding submatrices\nof the point-line and plane-line incidence matrices. To obtain these\nsubmatrices, we explored the number of solutions of cubic and quartic equations\nconnected with intersections of lines (including the tangents to the twisted\ncubic), points, and planes in $\\mathrm{PG}(3,q)$.\n', 'Twisted cubic and orbits of lines in $\\mathrm{PG}(3,q)$, II   In the projective space $\\mathrm{PG}(3,q)$, we consider the orbits of lines\nunder the stabilizer group of the twisted cubic. In the literature, lines of\n$\\mathrm{PG}(3,q)$ are partitioned into classes, each of which is a union of\nline orbits. In this paper, all classes of lines consisting of a unique orbit\nare found. For the remaining line types, with one exception, it is proved that\nthey consist exactly of two or three orbits; sizes and structures of these\norbits are determined. Also, the subgroups of the stabilizer group of the\ntwisted cubic fixing lines of the orbits are obtained. Problems which remain\nopen for one type of lines are formulated and, for $5\\le q\\le37$ and $q=64$, a\nsolution is provided.\n']","[('orbits class', 0.5249767899513245), ('line classes', 0.4794791638851166), ('liebler line classes', 0.46747949719429016), ('family orbits', 0.4487634003162384), ('orbits points', 0.441826730966568), ('quartic forms', 0.432918518781662), ('projective space mathrm', 0.41721397638320923), ('twisted cubic', 0.40265342593193054), ('orbits', 0.40227988362312317), ('line incidence', 0.39774754643440247)]"
518,518,60,518_graph matching_matching algorithms_matching graph_matching vertices,"['graph matching', 'matching algorithms', 'matching graph', 'matching vertices', 'exact matching', 'matching', 'vertex correspondence', 'matching strategy', 'graph alignment', 'edge correlation']","[""Random Graph Matching with Improved Noise Robustness   Graph matching, also known as network alignment, refers to finding a\nbijection between the vertex sets of two given graphs so as to maximally align\ntheir edges. This fundamental computational problem arises frequently in\nmultiple fields such as computer vision and biology. Recently, there has been a\nplethora of work studying efficient algorithms for graph matching under\nprobabilistic models. In this work, we propose a new algorithm for graph\nmatching: Our algorithm associates each vertex with a signature vector using a\nmultistage procedure and then matches a pair of vertices from the two graphs if\ntheir signature vectors are close to each other. We show that, for two\nErd\\H{o}s--R\\'enyi graphs with edge correlation $1-\\alpha$, our algorithm\nrecovers the underlying matching exactly with high probability when $\\alpha \\le\n1 / (\\log \\log n)^C$, where $n$ is the number of vertices in each graph and $C$\ndenotes a positive universal constant. This improves the condition $\\alpha \\le\n1 / (\\log n)^C$ achieved in previous work.\n"", 'The Phantom Alignment Strength Conjecture: Practical use of graph\n  matching alignment strength to indicate a meaningful graph match   The alignment strength of a graph matching is a quantity that gives the\npractitioner a measure of the correlation of the two graphs, and it can also\ngive the practitioner a sense for whether the graph matching algorithm found\nthe true matching. Unfortunately, when a graph matching algorithm fails to find\nthe truth because of weak signal, there may be ""phantom alignment strength""\nfrom meaningless matchings that, by random noise, have fewer disagreements than\naverage (sometimes substantially fewer); this alignment strength may give the\nmisleading appearance of significance. A practitioner needs to know what level\nof alignment strength may be phantom alignment strength and what level\nindicates that the graph matching algorithm obtained the true matching and is a\nmeaningful measure of the graph correlation. The {\\it Phantom Alignment\nStrength Conjecture} introduced here provides a principled and practical means\nto approach this issue. We provide empirical evidence for the conjecture, and\nexplore its consequences.\n', 'Deep graph matching meets mixed-integer linear programming: Relax at\n  your own risk ?   Graph matching is an important problem that has received widespread\nattention, especially in the field of computer vision. Recently,\nstate-of-the-art methods seek to incorporate graph matching with deep learning.\nHowever, there is no research to explain what role the graph matching algorithm\nplays in the model. Therefore, we propose an approach integrating a MILP\nformulation of the graph matching problem. This formulation is solved to\noptimal and it provides inherent baseline. Meanwhile, similar approaches are\nderived by releasing the optimal guarantee of the graph matching solver and by\nintroducing a quality level. This quality level controls the quality of the\nsolutions provided by the graph matching solver. In addition, several\nrelaxations of the graph matching problem are put to the test. Our experimental\nevaluation gives several theoretical insights and guides the direction of deep\ngraph matching methods.\n']","[('graph matching', 0.7304831743240356), ('matching algorithms', 0.6561830639839172), ('matching graph', 0.6559106707572937), ('matching vertices', 0.5915506482124329), ('exact matching', 0.5882946848869324), ('matching', 0.5580474138259888), ('vertex correspondence', 0.5313360691070557), ('matching strategy', 0.5212876796722412), ('graph alignment', 0.4946323335170746), ('edge correlation', 0.473112553358078)]"
519,519,60,519_instanton moduli_sasakian manifolds_instantons_instantons also,"['instanton moduli', 'sasakian manifolds', 'instantons', 'instantons also', 'deformed hermitian yang', '_2 manifolds', 'g_2 manifolds', 'instanton', 'g_2 manifold', 'spin manifolds']","['Deformations of Asymptotically Conical $G_2$-Instantons   We develop the deformation theory of instantons on asymptotically conical\n$G_2$-manifolds, where an asymptotic connection at infinity is fixed. A\nspinorial approach is adopted to relate the space of deformations to the kernel\nof a twisted Dirac operator on the $G_2$-manifold and to the eigenvalues of a\ntwisted Dirac operator on the nearly K\\""ahler link. This framework is then used\nto calculate the virtual dimension of the moduli spaces of $G_2$-instantons on\nwhich several known examples live. One such example considered is the\n$G_2$-instanton of G\\""unaydin-Nicolai, which lives on $R^7$. As an application\nof the deformation theory, we show how knowledge of the virtual dimension of\nthe moduli space allows us to prove that unobstructed connections in the moduli\nspace are $G_2$-invariant. By classifying such connections we prove a\nuniqueness result for unobstructed $G_2$-instantons on the principal\n$G_2$-bundle over $R^7$.\n', 'Examples of deformed Spin(7)-instantons/Donaldson-Thomas connections   We construct examples of deformed Hermitian Yang-Mills connections and\ndeformed Spin(7)-instantons (also called Spin(7) deformed Donaldson-Thomas\nconnections) on the cotangent bundle of $\\mathbb{C}\\mathbb{P}^2$ endowed with\nthe Calabi hyperK\\""ahler structure. Deformed Spin(7)-instantons on cones over\n3-Sasakian 7-manifolds are also constructed. We show that these can be used to\ndistinguish between isometric structures and also between Sp(2) and Spin(7)\nholonomy cones. To the best of our knowledge, these are the first non-trivial\nexamples of deformed Spin(7)-instantons.\n', 'Examples of deformed G_2-instantons/Donaldson-Thomas connections   In this note, we provide the first non-trivial examples of deformed\nG_2-instantons, originally called deformed Donaldson-Thomas connections. As a\nconsequence, we see how deformed G_2-instantons can be used to distinguish\nbetween nearly parallel G_2-structures and isometric G_2-structures on\n3-Sasakian 7-manifolds. Our examples give non-trivial deformed G_2-instantons\nwith obstructed deformation theory and situations where the moduli space of\ndeformed G_2-instantons has components of different dimensions. We finally\nstudy the relation between our examples and a Chern-Simons type functional\nwhich has deformed G_2-instantons as critical points.\n']","[('instanton moduli', 0.5707650184631348), ('sasakian manifolds', 0.5348260998725891), ('instantons', 0.5334477424621582), ('instantons also', 0.529183566570282), ('deformed hermitian yang', 0.48007336258888245), ('_2 manifolds', 0.4797575771808624), ('g_2 manifolds', 0.475161075592041), ('instanton', 0.46929964423179626), ('g_2 manifold', 0.4555666744709015), ('spin manifolds', 0.44736602902412415)]"
520,520,60,520_mapping class groups_mapping class group_subgroup mapping class_orientable surface genus,"['mapping class groups', 'mapping class group', 'subgroup mapping class', 'orientable surface genus', 'group closed orientable', 'class group closed', 'subgroup mapping', 'class groups', 'surface genus', 'cyclic covers']","['General primitivity in the mapping class group   For $g\\geq 2$, let $\\mathrm{Mod}(S_g)$ be the mapping class group of the\nclosed orientable surface $S_g$ of genus $g$. In this paper, we obtain\nnecessary and sufficient conditions under which a given pseudo-periodic mapping\nclass can be a root of another up to conjugacy. Using this characterization,\nthe canonical decomposition of (non-periodic) mapping classes, and some known\nalgorithms, we give an algorithm for determining the conjugacy classes of roots\nof arbitrary mapping classes. Furthermore, we derive realizable bounds on the\ndegrees of roots of pseudo-periodic mapping classes in $\\mathrm{Mod}(S_g)$, the\nTorelli group, the level-$m$ subgroup of $\\mathrm{Mod}(S_g)$, and the\ncommutator subgroup of $\\mathrm{Mod}(S_2)$. In particular, we show that the\nhighest possible (realizable) degree of a root of a pseudo-periodic mapping\nclass $F$ is $3q(F)(g+1)(g+2)$, where $q(F)$ is a unique positive integer\nassociated with the conjugacy class of $F$. Moreover, this bound is realized by\na root of a power of a Dehn twist about a separating curve of genus $[g/2]$ in\n$S_g$, where $g\\equiv 0,9 \\pmod{12}$. Finally, for $g\\geq 3$, we show that any\npseudo-periodic mapping class having a nontrivial periodic component that is\nnot the hyperelliptic involution, normally generates $\\mathrm{Mod}(S_g)$.\nConsequently, we establish that $\\mathrm{Mod}(S_g)$ is normally generated by a\nroot of bounding pair map or a root of a nontrivial power of a Dehn twist.\n', 'The liftable mapping class group of balanced superelliptic covers   The hyperelliptic mapping class group has been studied in various contexts\nwithin topology and algebraic geometry. What makes this study tractable is that\nthere is a surjective map from the hyperelliptic mapping class group to a\nmapping class group of a punctured sphere. The more general family of\nsuperelliptic mapping class groups does not, in general, surject on to a\nmapping class group of a punctured sphere, but on to a finite index subgroup.\nWe call this finite index subgroup the liftable mapping class group. In order\nto initiate the generalization of results on the hyperelliptic mapping class\ngroup to the broader family of superelliptic mapping class groups, we study an\nintermediate family called the balanced superelliptic mapping class group. We\ncompute the index of the liftable mapping class group in the full mapping class\ngroup of the sphere and show that the liftable mapping class group is\nindependent of the degree of the cover. We also build a presentation for the\nliftable mapping class group, compute its abelianization, and show that the\nbalanced superelliptic mapping class group has finite abelianization. Although\nour calculations focus on the subfamily of balanced superelliptic mapping class\ngroups, our techniques can be extended to any superelliptic mapping class\ngroup, even those not within the balanced family.\n', 'Generating the liftable mapping class groups of cyclic covers of spheres   For $g\\geq 2$, let $\\mathrm{Mod}(S_g)$ be the mapping class group of closed\norientable surface $S_g$ of genus $g$. In this paper, we derive a finite\ngenerating set for the liftable mapping class groups corresponding to\nfinite-sheeted regular branched cyclic covers of spheres. As an application, we\nprovide an algorithm to derive presentations of these liftable mapping class\ngroups, and the normalizers and centralizers of periodic mapping classes\ncorresponding to these covers. Furthermore, we determine the isomorphism\nclasses of the normalizers of irreducible periodic mapping classes in\n$\\mathrm{Mod}(S_g)$. Moreover, we derive presentations for the liftable mapping\nclass groups corresponding to covers induced by certain reducible periodic\nmapping classes. Consequently, we derive a presentation for the centralizer and\nnormalizer of a reducible periodic mapping class in $\\mathrm{Mod}(S_g)$ of the\nhighest order $2g+2$. As final applications of our results, we recover the\ngenerating sets of the liftable mapping class groups of the hyperelliptic cover\nobtained by Birman-Hilden and the balanced superelliptic cover obtained by\nGhaswala-Winarski.\n']","[('mapping class groups', 0.5341042280197144), ('mapping class group', 0.5215731263160706), ('subgroup mapping class', 0.5110412240028381), ('orientable surface genus', 0.4970936179161072), ('group closed orientable', 0.47015607357025146), ('class group closed', 0.4466570317745209), ('subgroup mapping', 0.4461509585380554), ('class groups', 0.4450928568840027), ('surface genus', 0.4415581226348877), ('cyclic covers', 0.4404545724391937)]"
521,521,59,521_traffic control_automated vehicles cavs_connected automated vehicles_autonomous vehicles cavs,"['traffic control', 'automated vehicles cavs', 'connected automated vehicles', 'autonomous vehicles cavs', 'traffic scenarios', 'connected autonomous vehicles', 'automated vehicles', 'human driven vehicles', 'automated vehicle', 'mixed traffic']","['Mixed platoon control of automated and human-driven vehicles at a\n  signalized intersection: dynamical analysis and optimal control   The emergence of Connected and Automated Vehicles (CAVs) promises better\ntraffic mobility for future transportation systems. Existing research mostly\nfocused on fully-autonomous scenarios, while the potential of CAV control at a\nmixed traffic intersection where human-driven vehicles (HDVs) also exist has\nbeen less explored. This paper proposes a notion of ""1+n"" mixed platoon,\nconsisting of one leading CAV and n following HDVs, and formulates a\nplatoon-based optimal control framework for CAV control at a signalized\nintersection. Based on the linearized dynamics model of the ""1+n"" mixed\nplatoon, fundamental properties including stability and controllability are\nunder rigorous theoretical analysis. Then, a constrained optimal control\nframework is established, aiming at improving the global traffic efficiency and\nfuel consumption at the intersection via direct control of the CAV. A\nhierarchical event-triggered algorithm is also designed for practical\nimplementation of the optimal control method between adjacent mixed platoons\nwhen approaching the intersection. Extensive numerical simulations at multiple\ntraffic volumes and market penetration rates validate the greater benefits of\nthe mixed platoon based method, compared with traditional trajectory\noptimization methods for one single CAV.\n', 'Decentralized Optimal Coordination of Connected and Automated Vehicles\n  for Multiple Traffic Scenarios   Connected and automated vehicles (CAVs) provide the most intriguing\nopportunity to optimize energy consumption and travel time. Several approaches\nhave been proposed in the literature that allow CAVs to coordinate in\nsituations where there is a potential conflict, for example, in signalized\nintersections, merging at roadways and roundabouts, to reduce energy\nconsumption and optimize traffic flow. In this paper, we consider the problem\nof coordinating CAVs in a corridor consisting of multiple traffic scenarios. We\nformulate a two-level optimization problem in which we maximize traffic\nthroughput in the upper-level problem, and derive a closed-form analytical\nsolution that yields the optimal control input for each CAV, in terms of fuel\nconsumption, in the low-level problem. We validate the effectiveness of the\nsolution through simulation under 100% CAVpenetration rate. Fuel consumption\nand travel time for the vehicles are significantly reduced compared to a\nbaseline scenario consisting of human-driven vehicles.\n', ""Addressing Mixed Traffic Through Platooning of Vehicles   Connected and automated vehicles (CAVs) provide the most intriguing\nopportunity for enabling users to better monitor transportation network\nconditions and make better operating decisions to improve safety and reduce\npollution, energy consumption, and travel delays. While several studies have\nshown the benefits of CAVs in reducing energy and alleviating traffic\ncongestion in specific traffic scenarios, e.g., crossing signal-free\nintersections, merging at roadways and roundabouts, cruising in congested\ntraffic, passing through speed reduction zones, and lane-merging or passing\nmaneuvers, most of these efforts have focused on 100% CAV penetration rates\nwithout considering human-driven vehicles (HDVs). One key question that still\nremains unanswered is ``how can CAVs and HDVs be coordinated safely?'' In this\npaper, we report on an optimal control framework to coordinate CAVs and HDVs at\nany traffic scenario. The idea is to directly control the CAVs to force the\ntrailing HDVs to form platoons. Thus, we indirectly control the HDVs by\ncoordinating the platoon of HDVs led by CAVs.\n""]","[('traffic control', 0.6099854111671448), ('automated vehicles cavs', 0.5983742475509644), ('connected automated vehicles', 0.595649003982544), ('autonomous vehicles cavs', 0.5387541055679321), ('traffic scenarios', 0.5233027338981628), ('connected autonomous vehicles', 0.5194181799888611), ('automated vehicles', 0.5096039772033691), ('human driven vehicles', 0.5037647485733032), ('automated vehicle', 0.5036025047302246), ('mixed traffic', 0.4695597290992737)]"
522,522,59,522_facility location problems_cost optimization_facility location_programming lp relaxation,"['facility location problems', 'cost optimization', 'facility location', 'programming lp relaxation', 'facility', 'facilities', 'location models', 'integer programming', 'location decisions', 'location problems']","[""An O(loglog n)-Approximation for Submodular Facility Location   In the Submodular Facility Location problem (SFL) we are given a collection\nof $n$ clients and $m$ facilities in a metric space. A feasible solution\nconsists of an assignment of each client to some facility. For each client, one\nhas to pay the distance to the associated facility. Furthermore, for each\nfacility $f$ to which we assign the subset of clients $S^f$, one has to pay the\nopening cost $g(S^f)$, where $g(\\cdot)$ is a monotone submodular function with\n$g(\\emptyset)=0$.\n  SFL is APX-hard since it includes the classical (metric uncapacitated)\nFacility Location problem (with uniform facility costs) as a special case.\nSvitkina and Tardos [SODA'06] gave the current-best $O(\\log n)$ approximation\nalgorithm for SFL. The same authors pose the open problem whether SFL admits a\nconstant approximation and provide such an approximation for a very restricted\nspecial case of the problem.\n  We make some progress towards the solution of the above open problem by\npresenting an $O(\\log\\log n)$ approximation. Our approach is rather flexible\nand can be easily extended to generalizations and variants of SFL. In more\ndetail, we achieve the same approximation factor for the practically relevant\ngeneralizations of SFL where the opening cost of each facility $f$ is of the\nform $p_f+g(S^f)$ or $w_f\\cdot g(S^f)$, where $p_f,w_f \\geq 0$ are input\nvalues.\n  We also obtain an improved approximation algorithm for the related Universal\nStochastic Facility Location problem. In this problem one is given a classical\n(metric) facility location instance and has to a priori assign each client to\nsome facility. Then a subset of active clients is sampled from some given\ndistribution, and one has to pay (a posteriori) only the connection and opening\ncosts induced by the active clients. The expected opening cost of each facility\n$f$ can be modelled with a submodular function of the set of clients assigned\nto $f$.\n"", 'A row generation method for inverse continuous facility location problem   In a single facility location problem, a set of points is given and the goal\nis finding the optimal location of new facility respect to given criteria such\nas minimizing time, cost and distances between the clients and facilities. On\nthe other side, the inverse models try to modify the parameters of the problem\nwith the minimum cost such that a given point becomes optimal. In this paper,\nwe introduce a novel algorithm for the general case of the inverse single\nfacility location problem with variable weights in the plane. The convergence\nand optimality conditions of the algorithm are presented. Then in the special\ncases, the inverse minisum and minimax single facility location problems are\nconsidered and the algorithm tested on some instances. The results indicate the\nefficiency of the algorithm on these instances.\n', ""Inverse single facility location problem in the plane with variable\n  coordinates   In traditional facility location problems, a set of points is provided, and\nthe objective is to determine the best location for a new facility based on\ncriteria such as minimizing cost, time, and distances between clients and\nfacilities. Conversely, inverse single facility location problems focus on\nadjusting the problem's parameters at minimal cost to make a specific point\noptimal. In this paper, we present an algorithm for the general case of the\ninverse single facility location problem with variable coordinates in a\ntwo-dimensional space. We outline the optimality conditions of this algorithm.\nAdditionally, we examine the specific case namely the inverse minisum single\nfacility location problem and test the algorithm on various instances. The\nresults demonstrate the algorithm's effectiveness in these scenarios.\n""]","[('facility location problems', 0.601440966129303), ('cost optimization', 0.5646630525588989), ('facility location', 0.483258455991745), ('programming lp relaxation', 0.46497368812561035), ('facility', 0.441272109746933), ('facilities', 0.4133220613002777), ('location models', 0.4060271084308624), ('integer programming', 0.4058842658996582), ('location decisions', 0.3922431766986847), ('location problems', 0.39215022325515747)]"
523,523,59,523_liebler sets_cameron liebler sets_liebler line classes_polar spaces,"['liebler sets', 'cameron liebler sets', 'liebler line classes', 'polar spaces', 'sets generators', 'projective spaces', 'dimensional projective space', 'projective subspaces', 'sets projective', 'cameron liebler line']","['On two non-existence results for Cameron-Liebler $k$-sets in\n  $\\mathrm{PG}(n,q)$   This paper focuses on non-existence results for Cameron-Liebler $k$-sets. A\nCameron-Liebler $k$-set is a collection of $k$-spaces in $\\mathrm{PG}(n,q)$ or\n$\\mathrm{AG}(n,q)$ admitting a certain parameter $x$, which is dependent on the\nsize of this collection. One of the main research questions remains the\n(non-)existence of Cameron-Liebler $k$-sets with parameter $x$. This paper\nimproves two non-existence results. First we show that the parameter of a\nnon-trivial Cameron-Liebler $k$-set in $\\mathrm{PG}(n,q)$ should be larger than\n$q^{n-\\frac{5k}{2}-1}$, which is an improvement of an earlier known lower\nbound. Secondly, we prove a modular equality on the parameter $x$ of\nCameron-Liebler $k$-sets in $\\mathrm{PG}(n,q)$ with\n$x<\\frac{q^{n-k}-1}{q^{k+1}-1}$, $n\\geq 2k+1$, $n-k+1\\geq 7$ and $n-k$ even. In\nthe affine case we show a similar result for $n-k+1\\geq 3$ and $n-k$ even. This\nis a generalization of earlier known modular equalities in the projective and\naffine case.\n', ""Cameron-Liebler sets of generators in finite classical polar spaces   Cameron-Liebler sets were originally defined as collections of lines (`line\nclasses') in $\\mathrm{PG}(3,q)$ sharing certain properties with line classes of\nsymmetric tactical decompositions. While there are many equivalent\ncharacterisations, these objects are defined as sets of lines whose\ncharacteristic vector lies in the image of the transpose of the point-line\nincidence matrix of $\\mathrm{PG}(3,q)$, and so combinatorially they behave like\na union of pairwise disjoint point-pencils. Recently, the concept of a\nCameron-Liebler set has been generalised to several other settings. In this\narticle we introduce Cameron-Liebler sets of generators in finite classical\npolar spaces. For each of the polar spaces we give a list of characterisations\nthat mirrors those for Cameron-Liebler line sets, and also prove some\nclassification results.\n"", 'Cameron-Liebler sets of k-spaces in PG(n,q)   Cameron-Liebler sets of k-spaces were introduced recently by Y. Filmus and F.\nIhringer. We list several equivalent definitions for these Cameron-Liebler\nsets, by making a generalization of known results about Cameron-Liebler line\nsets in PG(n, q) and Cameron-Liebler sets of k-spaces in PG(2k + 1, q). We also\npresent a classification result.\n']","[('liebler sets', 0.6231690645217896), ('cameron liebler sets', 0.5839786529541016), ('liebler line classes', 0.48691168427467346), ('polar spaces', 0.43504729866981506), ('sets generators', 0.42141562700271606), ('projective spaces', 0.4131200611591339), ('dimensional projective space', 0.4029794931411743), ('projective subspaces', 0.40208402276039124), ('sets projective', 0.39951062202453613), ('cameron liebler line', 0.37910395860671997)]"
524,524,59,524_stability inverse source_inverse source problems_inverse scattering problems_stability inverse,"['stability inverse source', 'inverse source problems', 'inverse scattering problems', 'stability inverse', 'inverse boundary value', 'inverse boundary', 'inverse scattering', 'stability estimates', 'inverse obstacle', 'frequency inverse']","['Increasing stability for inverse acoustic source problems in the time\n  domain   This paper is concerned with inverse source problems for the acoustic wave\nequation in the full space R^3, where the source term is compactly supported in\nboth time and spatial variables. The main goal is to investigate increasing\nstability for the wave equation in terms of the interval length of given\nparameters (e.g., bandwith of the temporal component of the source function).\nWe establish increasing stability estimates of the L^2 -norm of the source\nfunction by using only the Dirichlet boundary data. Our method relies on the\nHuygens principle, the Fourier transform and explicit bounds for the\ncontinuation of analytic functions.\n', 'Increasing stability for inverse acoustic source problems   In this paper, we show the increasing stability of the inverse source\nproblems for the acoustic wave equation in the full space R3.The goal is to\nunderstand increasing stability for wave equation in the time domain. If the\ntime and spatial variables of the source term can be separated with compact\nsupport, the increasing stability estimates of the $L^2$-norm of the acoustic\nsource function can be established. The stability estimates consist of two\nparts: the Lipschitz type data discrepancy and the high time tail of the source\nfunctions. As the time increases, the latter decreases and thus becomes\nnegligible.\n', 'Increasing stability for the inverse source problems in electrodynamics   We are concerned with increasing stability in the inverse source problems for\nthe time-dependent Maxwell equations in R^3 , where the source term is\ncompactly supported in both time and spatial variables. By using the Fourier\ntransform, sharp bounds of the analytic continuation and the Huygens principle,\nincreasing stability estimates of the L^2 -norm of the source function are\nobtained. The main goal of this paper is to understand increasing stability for\nthe Maxwell equations in the time domain.\n']","[('stability inverse source', 0.5718381404876709), ('inverse source problems', 0.5328972339630127), ('inverse scattering problems', 0.5155634880065918), ('stability inverse', 0.5016095042228699), ('inverse boundary value', 0.4957756996154785), ('inverse boundary', 0.4864320456981659), ('inverse scattering', 0.4766538739204407), ('stability estimates', 0.46886521577835083), ('inverse obstacle', 0.4461193382740021), ('frequency inverse', 0.4458314776420593)]"
525,525,59,525_extreme value distribution_generalized extreme value_extreme value theory_extreme value analysis,"['extreme value distribution', 'generalized extreme value', 'extreme value theory', 'extreme value analysis', 'generalized extreme', 'extreme value', 'distribution estimators', 'heavy tailed distributions', 'multivariate extremes', 'distribution estimator']","['Smooth tail index estimation   Both parametric distribution functions appearing in extreme value theory -\nthe generalized extreme value distribution and the generalized Pareto\ndistribution - have log-concave densities if the extreme value index gamma is\nin [-1,0]. Replacing the order statistics in tail index estimators by their\ncorresponding quantiles from the distribution function that is based on the\nestimated log-concave density leads to novel smooth quantile and tail index\nestimators. These new estimators aim at estimating the tail index especially in\nsmall samples. Acting as a smoother of the empirical distribution function, the\nlog-concave distribution function estimator reduces estimation variability to a\nmuch greater extent than it introduces bias. As a consequence, Monte Carlo\nsimulations demonstrate that the smoothed version of the estimators are well\nsuperior to their non-smoothed counterparts, in terms of mean squared error.\n', 'On tail inference in iid settings with nonnegative extreme value index   In extreme value inference it is a fundamental problem how the target value\nis required to be extreme by the extreme value theory. In iid settings this\nstudy both theoretically and numerically compares tail estimators, which are\nbased on either or both of the extreme value theory and the nonparametric\nsmoothing. This study considers tail probability estimation and mean excess\nfunction estimation.\n  This study assumes that the extreme value index of the underlying\ndistribution is nonnegative. Specifically, the Hall class or the Weibull class\nof distributions is supposed in order to obtain the convergence rates of the\nestimators. This study investigates the nonparametric kernel type estimators,\nthe fitting estimators to the generalized Pareto distribution and the plug-in\nestimators of the Hall distribution, which was proposed by Hall and Weissman\n(1997). In simulation studies the mean squared errors of the estimators in some\nfinite sample cases are compared.\n', 'Parametric and nonparametric probability distribution estimators of\n  sample maximum   Extreme value theory has constructed asymptotic properties of the sample\nmaximum. This study concerns probability distribution estimation of the sample\nmaximum. The traditional approach is parametric fitting to the limiting\ndistribution -- the generalized extreme value distribution; however, the model\nin non-limiting cases is misspecified to a certain extent. We propose a plug-in\ntype of nonparametric estimator that does not need model specification.\nAsymptotic properties of the distribution estimator are derived. The simulation\nstudy numerically investigates the relative performance in finite-sample cases.\n  This study assumes that the underlying distribution of the original sample\nbelongs to one of the Hall class, the Weibull class or the bounded class, whose\ntypes of the limiting distributions are all different: the Frechet, Gumbel or\nWeibull. It is proven that the convergence rate of the parametric fitting\nestimator depends on both the extreme value index and the second-order\nparameter and gets slower as the extreme value index tends to zero. On the\nother hand, the rate of the nonparametric estimator is proven to be independent\nof the extreme value index under certain conditions. The numerical performances\nof the parametric fitting estimator and the nonparametric estimator are\ncompared, which shows that the nonparametric estimator performs better,\nespecially for the extreme value index close to zero. Finally, we report two\nreal case studies: the Potomac River peak stream flow (cfs) data and the Danish\nFire Insurance data.\n']","[('extreme value distribution', 0.7152676582336426), ('generalized extreme value', 0.6565033793449402), ('extreme value theory', 0.6266049146652222), ('extreme value analysis', 0.6093490719795227), ('generalized extreme', 0.5796033143997192), ('extreme value', 0.5416560173034668), ('distribution estimators', 0.5403727293014526), ('heavy tailed distributions', 0.5129364728927612), ('multivariate extremes', 0.5124903917312622), ('distribution estimator', 0.5022273659706116)]"
526,526,59,526_fading distribution_fading models_fading channels_fading parameters,"['fading distribution', 'fading models', 'fading channels', 'fading parameters', 'fading channel', 'arbitrary fading', 'nakagami fading', 'fading', 'mu fading', 'ftr fading']","['A Comprehensive Analysis of 5G Heterogeneous Cellular Systems operating\n  over $\\kappa$-$\\mu$ Shadowed Fading Channels   Emerging cellular technologies such as those proposed for use in 5G\ncommunications will accommodate a wide range of usage scenarios with diverse\nlink requirements. This will include the necessity to operate over a versatile\nset of wireless channels ranging from indoor to outdoor, from line-of-sight\n(LOS) to non-LOS, and from circularly symmetric scattering to environments\nwhich promote the clustering of scattered multipath waves. Unfortunately, many\nof the conventional fading models adopted in the literature to develop network\nmodels lack the flexibility to account for such disparate signal propagation\nmechanisms. To bridge the gap between theory and practical channels, we\nconsider $\\kappa$-$\\mu$ shadowed fading, which contains as special cases, the\nmajority of the linear fading models proposed in the open literature, including\nRayleigh, Rician, Nakagami-m, Nakagami-q, One-sided Gaussian, $\\kappa$-$\\mu$,\n$\\eta$-$\\mu$, and Rician shadowed to name but a few. In particular, we apply an\northogonal expansion to represent the $\\kappa$-$\\mu$ shadowed fading\ndistribution as a simplified series expression. Then using the series\nexpressions with stochastic geometry, we propose an analytic framework to\nevaluate the average of an arbitrary function of the SINR over $\\kappa$-$\\mu$\nshadowed fading channels. Using the proposed method, we evaluate the spectral\nefficiency, moments of the SINR, bit error probability and outage probability\nof a $K$-tier HetNet with $K$ classes of BSs, differing in terms of the\ntransmit power, BS density, shadowing characteristics and small-scale fading.\nBuilding upon these results, we provide important new insights into the network\nperformance of these emerging wireless applications while considering a diverse\nrange of fading conditions and link qualities.\n', 'The {\\kappa}-{\\mu} Shadowed Fading Model with Integer Fading Parameters   We show that the popular and general {\\kappa}-{\\mu} shad- owed fading model\nwith integer fading parameters {\\mu} and m can be represented as a mixture of\nsquared Nakagami (or Gamma) distributions. Thus, its PDF and CDF can be\nexpressed in closed-form in terms of a finite number of elementary functions\n(powers and exponentials). The main implications arising from such connection\nare then discussed, which can be summarized as: (1) the performance evaluation\nof communication systems operating in {\\kappa}-{\\mu} shadowed fading becomes as\nsimple as if a Nakagami fading channel was assumed; (2) the {\\kappa}-{\\mu}\nshadowed distribution can be used to approximate the {\\kappa}-{\\mu}\ndistribution us- ing a closed-form representation in terms of elementary\nfunctions, by choosing a sufficiently large value of m; and (3) restricting the\nparameters {\\mu} and m to take integer values has limited impact in practice\nwhen fitting the {\\kappa}-{\\mu} shadowed fading model to field measurements. As\nan application example, the average channel capacity of communication systems\noperating under {\\kappa}-{\\mu} shadowed fading is obtained in closed-form.\n', 'The Multi-cluster Fluctuating Two-Ray Fading Model   We introduce a new class of fading channels, built as the superposition of\ntwo fluctuating specular components with random phases, plus a clustering of\nscattered waves: the Multi-cluster Fluctuating Two-Ray (MFTR) fading channel.\nThe MFTR model emerges as a natural generalization of both the fluctuating\ntwo-ray (FTR) and the $\\kappa$-$\\mu$ shadowed fading models through a more\ngeneral yet equally mathematically tractable model. This generalization enables\nthe presence of additional multipath clusters in the purely ray-based FTR\nmodel, and the convenience of the new underlying fading channel model is\ndiscussed in depth. Then, we derive all the chief probability functions of the\nMFTR model (e.g., probability density function (PDF), cumulative density\nfunction (CDF), and moment generation function) in closed-form, having {a\nmathematical complexity similar to} other fading models in the\nstate-of-the-art. We also provide two additional analytical formulations for\nthe PDF and the CDF: (i) in terms of a continuous mixture of $\\kappa$-$\\mu$\nshadowed distributions, and (ii) as an infinite discrete mixture of Gamma\ndistributions. Such expressions enable to conduct performance analysis under\nMFTR fading by directly leveraging readily available results for the\n$\\kappa$-$\\mu$ shadowed or Nakagami-$m$ cases, respectively. The performance of\nwireless communications systems undergoing MFTR fading is exemplified in terms\nof a classical benchmarking metric like the outage probability, both in exact\nand asymptotic forms, and the amount of fading.\n']","[('fading distribution', 0.6712777018547058), ('fading models', 0.661210834980011), ('fading channels', 0.6384114027023315), ('fading parameters', 0.635501503944397), ('fading channel', 0.6275188326835632), ('arbitrary fading', 0.6077556610107422), ('nakagami fading', 0.48504239320755005), ('fading', 0.47777217626571655), ('mu fading', 0.44885388016700745), ('ftr fading', 0.4028159976005554)]"
527,527,59,527_reductive algebraic groups_connected reductive subgroup_reductive algebraic group_connected reductive group,"['reductive algebraic groups', 'connected reductive subgroup', 'reductive algebraic group', 'connected reductive group', 'reductive groups', 'reductive subgroup', 'reductive group', 'reductive groups let', 'split reductive groups', 'connected reductive algebraic']","['Jordan classes and Lusztig strata in disconnected reductive groups   Let $G$ be a non-connected reductive algebraic group over an algebraically\nclosed field $\\mathbb{K}$ and let $D$ be a connected component of $G$. We\ninvestigate Jordan classes of $D$ and we obtain a description of the regular\npart of the closure of a Jordan class in terms of induction of\n$G^{\\circ}$-orbits. We use this result to show that Lusztig strata in a\nnon-connected reductive algebraic group are locally closed.\n', 'Complete reducibility in bad characteristic   Let $G$ be a simple algebraic group of exceptional type over an algebraically\nclosed field of characteristic $p > 0$. This paper continues a long-standing\neffort to classify the connected reductive subgroups of $G$. Having previously\ncompleted the classification when $p$ is sufficiently large, we focus here on\nthe case that $p$ is bad for $G$. We classify the connected reductive subgroups\nof $G$ which are not $G$-completely reducible, whose simple components have\nrank at least $3$. For each such subgroup $X$, we determine the action of $X$\non the adjoint module $L(G)$ and on a minimal non-trivial $G$-module, and the\nconnected centraliser of $X$ in $G$. As corollaries we obtain information on:\nsubgroups which are maximal among connected reductive subgroups; products of\ncommuting $G$-completely reducible subgroups; subgroups with trivial connected\ncentraliser; and subgroups which act indecomposably on an adjoint or minimal\nmodule for $G$.\n', ""Complete reducibility of subgroups of reductive algebraic groups over\n  nonperfect fields IV: An $F_4$ example   Let $k$ be a nonperfect separably closed field. Let $G$ be a connected\nreductive algebraic group defined over $k$. We study rationality problems for\nSerre's notion of complete reducibility of subgroups of $G$. In particular, we\npresent the first example of a connected nonabelian $k$-subgroup $H$ of $G$\nthat is $G$-completely reducible but not $G$-completely reducible over $k$, and\nthe first example of a connected nonabelian $k$-subgroup $H'$ of $G$ that is\n$G$-completely reducible over $k$ but not $G$-completely reducible. This is\nnew: all previously known such examples are for finite (or non-connected) $H$\nand $H'$ only.\n""]","[('reductive algebraic groups', 0.6985800862312317), ('connected reductive subgroup', 0.6702807545661926), ('reductive algebraic group', 0.6694273352622986), ('connected reductive group', 0.6497764587402344), ('reductive groups', 0.6456801295280457), ('reductive subgroup', 0.6451141834259033), ('reductive group', 0.6098848581314087), ('reductive groups let', 0.6022993922233582), ('split reductive groups', 0.5917857885360718), ('connected reductive algebraic', 0.5614116191864014)]"
528,528,59,528_mmwave mimo_hybrid massive mimo_mmwave communications_mmwave systems,"['mmwave mimo', 'hybrid massive mimo', 'mmwave communications', 'mmwave systems', 'millimeter wave mmwave', 'massive mimo systems', 'massive mimo', 'millimeter wave massive', 'millimeter wave', 'hybrid beamforming']","['Partially-Connected Hybrid Beamforming for Spectral Efficiency\n  Maximization via a Weighted MMSE Equivalence   Hybrid beamforming (HBF) is an attractive technology for practical massive\nmultiple-input and multiple-output (MIMO) millimeter wave (mmWave) systems.\nCompared with the fully-connected HBF architecture, the partially-connected one\ncan further reduce the hardware cost and power consumption. However, the\nspecial block diagonal structure of its analog beamforming matrix brings\nadditional design challenges. In this paper, we develop effective HBF\nalgorithms for spectral efficiency maximization (SEM) in mmWave massive MIMO\nsystems with the partially-connected architecture. One main contribution is\nthat we prove the equivalence of the SEM problem and a matrix weighted sum mean\nsquare error minimization (WMMSE) problem, which leads to a convenient\nalgorithmic approach to directly tackle the SEM problem. Specifically, we\ndecompose the equivalent WMMSE problem into the hybrid precoding and hybrid\ncombining subproblems, for which both the optimal digital precoder and combiner\nhave closed-form solutions. For the more challenging analog precoder and\ncombiner, we propose an element iteration based algorithm and a manifold\noptimization based algorithm. Finally, the hybrid precoder and combiner are\nalternatively updated. The overall HBF algorithms are proved to monotonously\nincrease the spectral efficiency and converge. Furthermore, we also propose\nmodified algorithms with reduced computational complexity and finite-resolution\nphase shifters. Simulation results demonstrate that the proposed HBF algorithms\nachieve significant performance gains over conventional algorithms.\n', 'Beamspace Precoding and Beam Selection for Wideband Millimeter-Wave MIMO\n  Relying on Lens Antenna Arrays   Millimeter-wave (mmWave) multiple-input multiple-out (MIMO) systems relying\non lens antenna arrays are capable of achieving a high antenna-gain at a\nconsiderably reduced number of radio frequency (RF) chains via beam selection.\nHowever, the traditional beam selection network suffers from significant\nperformance loss in wideband systems due to the effect of beam squint. In this\npaper, we propose a phase shifter-aided beam selection network, which enables a\nsingle RF chain to support multiple focused-energy beams, for mitigating the\nbeam squint in wideband mmWave MIMO systems. Based on this architecture, we\nadditionally design an efficient transmit precoder (TPC) for maximizing the\nachievable sum-rate, which is composed of beam selection and beamspace\nprecoding. Specifically, we decouple the design problems of beamspace precoding\nand beam selection by exploiting the fact that the beam selection matrix has a\nlimited number of candidates. For the beamspace precoding design, we propose a\nsuccessive interference cancellation (SIC)-based method, which decomposes the\nassociated optimization problem into a series of subproblems and solves them\nsuccessively. For the beam selection design, we propose an energy-max beam\nselection method for avoiding the high complexity of exhaustive search, and\nderive the number of required beams for striking an attractive trade-off\nbetween the hardware cost and system performance. Our simulation results show\nthat the proposed beamspace precoding and beam selection methods achieve both a\nhigher sum-rate and a higher energy efficiency than its conventional\ncounterparts.\n', 'Practical Hybrid Beamforming for Millimeter Wave Massive MIMO Full\n  Duplex with Limited Dynamic Range   Full Duplex (FD) radio has emerged as a promising solution to increase the\ndata rates by up to a factor of two via simultaneous transmission and reception\nin the same frequency band. This paper studies a novel hybrid beamforming\n(HYBF) design to maximize the weighted sum-rate (WSR) in a single-cell\nmillimeter wave (mmWave) massive multiple-input-multiple-output (mMIMO) FD\nsystem. Motivated by practical considerations, we assume that the multi-antenna\nusers and hybrid FD base station (BS) suffer from the limited dynamic range\n(LDR) noise due to non-ideal hardware and an impairment aware HYBF approach is\nadopted by integrating the traditional LDR noise model in the mmWave band. In\ncontrast to the conventional HYBF schemes, our design also considers the joint\nsum-power and the practical per-antenna power constraints. A novel\ninterference, self-interference (SI) and LDR noise aware optimal power\nallocation scheme for the uplink (UL) users and FD BS is also presented to\nsatisfy the joint constraints. The maximum achievable gain of a multi-user\nmmWave FD system over a fully digital half duplex (HD) system with different\nLDR noise levels and numbers of the radio-frequency (RF) chains is\ninvestigated. Simulation results show that our design outperforms the HD system\nwith only a few RF chains at any LDR noise level. The advantage of having\namplitude control at the analog stage is also examined, and additional gain for\nthe mmWave FD system becomes evident when the number of RF chains at the hybrid\nFD BS is small.\n']","[('mmwave mimo', 0.5896348357200623), ('hybrid massive mimo', 0.5877441167831421), ('mmwave communications', 0.5753423571586609), ('mmwave systems', 0.5725988745689392), ('millimeter wave mmwave', 0.5672420263290405), ('massive mimo systems', 0.5625055432319641), ('massive mimo', 0.5482810735702515), ('millimeter wave massive', 0.5427452325820923), ('millimeter wave', 0.5364566445350647), ('hybrid beamforming', 0.520703136920929)]"
529,529,58,529_vector approximate message_generalized approximate message_compressed sensing_approximate message passing,"['vector approximate message', 'generalized approximate message', 'compressed sensing', 'approximate message passing', 'optimal orthogonal', 'signal estimation', 'sensing matrices', 'signal recovery', 'vector approximate', 'message passing algorithms']","[""Memory AMP   Approximate message passing (AMP) is a low-cost iterative\nparameter-estimation technique for certain high-dimensional linear systems with\nnon-Gaussian distributions. AMP only applies to independent identically\ndistributed (IID) transform matrices, but may become unreliable (e.g., perform\npoorly or even diverge) for other matrix ensembles, especially for\nill-conditioned ones. To solve this issue, orthogonal/vector AMP (OAMP/VAMP)\nwas proposed for general right-unitarily-invariant matrices. However, the\nBayes-optimal OAMP/VAMP (BO-OAMP/VAMP) requires a high-complexity linear\nminimum mean square error (MMSE) estimator. This prevents OAMP/VAMP from being\nused in large-scale systems.\n  To address the drawbacks of AMP and BO-OAMP/VAMP, this paper offers a memory\nAMP (MAMP) framework based on the orthogonality principle, which ensures that\nestimation errors in MAMP are asymptotically IID Gaussian. To realize the\nrequired orthogonality for MAMP, we provide an orthogonalization procedure for\nthe local memory estimators. In addition, we propose a Bayes-optimal MAMP\n(BO-MAMP), in which a long-memory matched filter is used for interference\nsuppression. The complexity of BO-MAMP is comparable to AMP. To asymptotically\ncharacterize the performance of BO-MAMP, a state evolution is derived. The\nrelaxation parameters and damping vector in BO-MAMP are optimized based on\nstate evolution. Most crucially, the state evolution of the optimized BO-MAMP\nconverges to the same fixed point as that of the high-complexity BO-OAMP/VAMP\nfor all right-unitarily-invariant matrices, and achieves the Bayes optimal MSE\npredicted by the replica method if its state evolution has a unique fixed\npoint. Finally, simulations are provided to verify the theoretical results'\nvalidity and accuracy.\n"", 'A Concise Tutorial on Approximate Message Passing   High-dimensional signal recovery of standard linear regression is a key\nchallenge in many engineering fields, such as, communications, compressed\nsensing, and image processing. The approximate message passing (AMP) algorithm\nproposed by Donoho \\textit{et al} is a computational efficient method to such\nproblems, which can attain Bayes-optimal performance in independent identical\ndistributed (IID) sub-Gaussian random matrices region. A significant feature of\nAMP is that the dynamical behavior of AMP can be fully predicted by a scalar\nequation termed station evolution (SE). Although AMP is optimal in IID\nsub-Gaussian random matrices, AMP may fail to converge when measurement matrix\nis beyond IID sub-Gaussian. To extend the region of random measurement matrix,\nan expectation propagation (EP)-related algorithm orthogonal AMP (OAMP) was\nproposed, which shares the same algorithm with EP, expectation consistent (EC),\nand vector AMP (VAMP). This paper aims at giving a review for those algorithms.\nWe begin with the worst case, i.e., least absolute shrinkage and selection\noperator (LASSO) inference problem, and then give the detailed derivation of\nAMP derived from message passing. Also, in the Bayes-optimal setting, we give\nthe Bayes-optimal AMP which has a slight difference from AMP for LASSO. In\naddition, we review some AMP-related algorithms: OAMP, VAMP, and Memory AMP\n(MAMP), which can be applied to more general random matrices.\n', 'Memory Approximate Message Passing   Approximate message passing (AMP) is a low-cost iterative\nparameter-estimation technique for certain high-dimensional linear systems with\nnon-Gaussian distributions. However, AMP only applies to independent\nidentically distributed (IID) transform matrices, but may become unreliable for\nother matrix ensembles, especially for ill-conditioned ones. To handle this\ndifficulty, orthogonal/vector AMP (OAMP/VAMP) was proposed for general\nright-unitarily-invariant matrices. However, the Bayes-optimal OAMP/VAMP\nrequires high-complexity linear minimum mean square error estimator. To solve\nthe disadvantages of AMP and OAMP/VAMP, this paper proposes a memory AMP\n(MAMP), in which a long-memory matched filter is proposed for interference\nsuppression. The complexity of MAMP is comparable to AMP. The asymptotic\nGaussianity of estimation errors in MAMP is guaranteed by the orthogonality\nprinciple. A state evolution is derived to asymptotically characterize the\nperformance of MAMP. Based on the state evolution, the relaxation parameters\nand damping vector in MAMP are optimized. For all right-unitarily-invariant\nmatrices, the optimized MAMP converges to OAMP/VAMP, and thus is Bayes-optimal\nif it has a unique fixed point. Finally, simulations are provided to verify the\nvalidity and accuracy of the theoretical results.\n']","[('vector approximate message', 0.5316614508628845), ('generalized approximate message', 0.4936504364013672), ('compressed sensing', 0.48419004678726196), ('approximate message passing', 0.47763141989707947), ('optimal orthogonal', 0.44967764616012573), ('signal estimation', 0.4291739761829376), ('sensing matrices', 0.4233035743236542), ('signal recovery', 0.419937402009964), ('vector approximate', 0.4159371852874756), ('message passing algorithms', 0.40895000100135803)]"
530,530,58,530_hilbert schemes points_hilbert scheme points_points hilbert scheme_hilbert schemes,"['hilbert schemes points', 'hilbert scheme points', 'points hilbert scheme', 'hilbert schemes', 'hilbert scheme', 'punctual hilbert schemes', 'schemes points', 'schemes points mathbb', 'scheme points', 'points hilbert']","['Irrational components of the Hilbert scheme of points   We construct irrational irreducible components of the Hilbert scheme of\npoints of affine n-dimensional space, for n at least 12. We start with\nirrational components of the Hilbert scheme of curves in P^3 and use methods\ndeveloped by Jelisiejew to relate these to irreducible components of the\nHilbert schemes of points of A^n. The result solves Problem XX of [J.\nJelisiejew, Open problems in deformations of Artinian algebras, Hilbert schemes\nand around, arXiv:2307.08777, 2023].\n', 'Unexpected but recurrent phenomena for Quot and Hilbert schemes of\n  points   We investigate some aspects of the geometry of two classical generalisations\nof the Hilbert schemes of points. Precisely, we show that parity conjecture for\n$\\text{Quot}_r^d\\mathbb{A}^3$ already fails for $d=8$ and $r=2$ and that lots\nof the elementary components of the nested Hilbert schemes of points on smooth\nquasi-projective varieties of dimension at least 4 are generically non-reduced.\nWe also deduce that nested Hilbert schemes of points on smooth surfaces have\ngenerically non-reduced components. Finally, we give an infinite family of\nelementary components of the classical Hilbert schemes of points.\n', 'Hilbert schemes of points and Fulton-MacPherson compactifications   We relate Hilbert schemes of points and Fulton-MacPherson compactifications\nby an interpolating stability condition. We then derive wall-crossings formulas\nand some applications for the enumerative geometry of Hilbert schemes.\n']","[('hilbert schemes points', 0.8351036906242371), ('hilbert scheme points', 0.8229315280914307), ('points hilbert scheme', 0.8010462522506714), ('hilbert schemes', 0.789676308631897), ('hilbert scheme', 0.7458274960517883), ('punctual hilbert schemes', 0.730219841003418), ('schemes points', 0.6911960244178772), ('schemes points mathbb', 0.6519202589988708), ('scheme points', 0.6036329865455627), ('points hilbert', 0.5883411169052124)]"
531,531,58,531_supersymmetric field theory_supersymmetric field_supersymmetric_supersymmetries,"['supersymmetric field theory', 'supersymmetric field', 'supersymmetric', 'supersymmetries', 'cal supersymmetric', 'supergravity', 'supersymmetry', 'mathcal superconformal', 'superconformal', 'mathcal super yang']","['$\\mathcal{N}=3$ conformal superspace in four dimensions   We develop a superspace formulation for ${\\cal N}=3$ conformal supergravity\nin four spacetime dimensions as a gauge theory of the superconformal group\n$\\mathsf{SU}(2,2|3)$. Upon imposing certain covariant constraints, the algebra\nof conformally covariant derivatives $\\nabla_A =\n(\\nabla_a,\\nabla_\\alpha^i,\\bar{\\nabla}_i^{\\dot \\alpha})$ is shown to be\ndetermined in terms of a single primary chiral spinor superfield, the\nsuper-Weyl spinor $W_\\alpha$ of dimension $+1/2$ and its conjugate. Associated\nwith $W_\\alpha$ is its primary descendant $B^i{}_j$ of dimension $+2$, the\nsuper-Bach tensor, which determines the equation of motion for conformal\nsupergravity. As an application of this construction, we present two different\nbut equivalent action principles for ${\\cal N}=3$ conformal supergravity. We\ndescribe the model for linearised $\\mathcal{N}=3$ conformal supergravity in an\narbitrary conformally flat background and demonstrate that it possesses\n$\\mathsf{U}(1)$ duality invariance. Additionally, upon degauging certain local\nsymmetries, our superspace geometry is shown to reduce to the $\\mathsf{U}(3)$\nsuperspace constructed by Howe more than four decades ago. Further degauging\nproves to lead to a new superspace formalism, called $\\mathsf{SU}(3) $\nsuperspace, which can also be used to describe ${\\mathcal N}=3$ conformal\nsupergravity. Our conformal superspace setting opens up the possibility to\nformulate the dynamics of the off-shell ${\\mathcal N}=3$ super Yang-Mills\ntheory coupled to conformal supergravity.\n', ""Superspace approaches to $\\mathcal{N}=1$ supergravity   The superspace formalism for $\\mathcal{N}=1$ supergravity in four dimensions\nis a powerful geometric setting to engineer off-shell supergravity-matter\ntheories, including higher-derivative couplings. This review provides a unified\ndescription of the three superspace approaches to $\\mathcal{N}=1$ conformal\nsupergravity: (i) conformal superspace; (ii) $\\mathsf{U}(1)$ superspace; and\n(iii) the Grimm-Wess-Zumino formalism. The prepotential formulation for the\nlatter is discussed. We briefly describe the known off-shell formulations for\nPoincar\\'e and anti-de Sitter supergravity theories as conformal supergravity\ncoupled to certain compensators. As simple applications of the formalism, we\npresent the superfield equations of motion for various off-shell formulations\nfor pure Poincar\\'e and anti-de Sitter supergravity, and show that every\nsolution of these equations is also a solution of the equations of motion for\nconformal supergravity.\n"", 'Covariant superspace approaches to ${\\cal N}=2$ supergravity   We provide a unified description of the three covariant superspace approaches\nto ${\\cal N}=2$ conformal supergravity in four dimensions: (i) conformal\nsuperspace; (ii) $\\mathsf{U}(2)$ superspace; and (iii) $\\mathsf{SU}(2)$\nsuperspace. Each of them can be used to formulate general supergravity-matter\nsystems, although conformal superspace has the largest structure group and is\nintimately related to the superconformal tensor calculus. We review the\nstructure of covariant projective multiplets and demonstrate how they are used\nto describe pure and matter-coupled supergravity, including locally\nsuperconformal off-shell sigma models. Higher-derivative invariants,\ntopological invariants and super-Weyl anomalies are also briefly discussed.\n']","[('supersymmetric field theory', 0.6267067790031433), ('supersymmetric field', 0.5848659873008728), ('supersymmetric', 0.5704357624053955), ('supersymmetries', 0.5678916573524475), ('cal supersymmetric', 0.5578714609146118), ('supergravity', 0.5469289422035217), ('supersymmetry', 0.5445941686630249), ('mathcal superconformal', 0.519738495349884), ('superconformal', 0.4867018759250641), ('mathcal super yang', 0.4832058548927307)]"
532,532,58,532_bundles moduli space_moduli vector bundles_bundles moduli_bundle moduli,"['bundles moduli space', 'moduli vector bundles', 'bundles moduli', 'bundle moduli', 'stable bundles', 'bundles curves', 'moduli spaces stable', 'stable vector bundles', 'moduli space stable', 'bundles surfaces']","[""Positivity of the Poincar\\'e bundle on the moduli space of vector\n  bundles and its applications   We prove that the normalized Poincar\\'e bundle on the moduli space of stable\nrank $r$ vector bundles with a fixed determinant on a smooth projective curve\n$X$ induces a family of nef vector bundles on the moduli space. Two\napplications follow. We show that when the genus of $X$ is large, the derived\ncategory of $X$ is embedded into the derived category of the moduli space for\narbitrary rank and coprime degree, which extends the results of Narasimhan,\nFonarev-Kuznetsov, and Belmans-Mukhopadhyay. As the second application, we\nconstruct a family of ACM bundles on the moduli space. A key ingredient of our\nproof is the investigation of birational geometry of the moduli spaces of\nparabolic bundles.\n"", 'Universal Chern classes on the moduli of bundles   The goal of this paper is to construct universal cohomology classes on the\nmoduli space of stable bundles over a curve when it is not a fine moduli space,\ni.e. when the rank and degree are not coprime. More precisely, we show that\ncertain Chern classes of the universal bundle on the product of the curve with\nthe moduli stack of bundles lift to the product of the curve with the moduli\nspace of stable bundles.\n', 'Projectivity of good moduli spaces of vector bundles on stacky curves   Moduli of vector bundles on stacky curves behave similarly to moduli of\nvector bundles on curves, except there are additional numerical invariants\ngiving many different notions of stability. We apply the existence criterion\nfor good moduli spaces of stacks to show that the moduli stack of semistable\nvector bundles on a stacky curve has a proper good moduli space. We\nmoduli-theoretically prove that a natural determinantal line bundle on this\nmoduli space is ample, thus proving this moduli space is projective. Our\nmethods give effective bounds for when a power of this line bundle is\nbasepoint-free. As a special case, we obtain new and effective constructions of\nmoduli spaces of parabolic bundles.\n']","[('bundles moduli space', 0.7735928893089294), ('moduli vector bundles', 0.7666133642196655), ('bundles moduli', 0.762732744216919), ('bundle moduli', 0.716746985912323), ('stable bundles', 0.6936160326004028), ('bundles curves', 0.6801590323448181), ('moduli spaces stable', 0.6781517267227173), ('stable vector bundles', 0.6686015129089355), ('moduli space stable', 0.646569550037384), ('bundles surfaces', 0.6398494839668274)]"
533,533,58,533_steiner triple systems_steiner triple system_steiner quadruple system_steiner quadruple,"['steiner triple systems', 'steiner triple system', 'steiner quadruple system', 'steiner quadruple', 'steiner systems', 'steiner triple', 'steiner system', 'steiner', 'triple systems', 'triple system']","['Almost all Steiner triple systems have perfect matchings   We show that for any n divisible by 3, almost all order-n Steiner triple\nsystems have a perfect matching (also known as a parallel class or resolution\nclass). In fact, we prove a general upper bound on the number of perfect\nmatchings in a Steiner triple system and show that almost all Steiner triple\nsystems essentially attain this maximum. We accomplish this via a general\ntheorem comparing a uniformly random Steiner triple system to the outcome of\nthe triangle removal process, which we hope will be useful for other problems.\nOur methods can also be adapted to other types of designs; for example, we\nsketch a proof of the theorem that almost all Latin squares have transversals.\n', 'Extensions of Steiner Triple Systems   In this article we study extensions of Steiner triple systems by means of the\nassociated Steiner loops. We recognize that the set of Veblen points of a\nSteiner triple system corresponds to the center of the Steiner loop. We\ninvestigate extensions of Steiner loops, focusing in particular on the case of\nSchreier extensions, which provide a powerful method for constructing Steiner\ntriple systems containing Veblen points.\n', 'The number of the non-full-rank Steiner triple systems   The $p$-rank of a Steiner triple system $B$ is the dimension of the linear\nspan of the set of characteristic vectors of blocks of $B$, over GF$(p)$. We\nderive a formula for the number of different Steiner triple systems of order\n$v$ and given $2$-rank $r_2$, $r_2<v$, and a formula for the number of Steiner\ntriple systems of order $v$ and given $3$-rank $r_3$, $r_3<v-1$. Also, we prove\nthat there are no Steiner triple systems of $2$-rank smaller than $v$ and, at\nthe same time, $3$-rank smaller than $v-1$. Our results extend previous work on\nenumerating Steiner triple systems according to the rank of their codes, mainly\nby Tonchev, V.A.Zinoviev and D.V.Zinoviev for the binary case and by Jungnickel\nand Tonchev for the ternary case.\n']","[('steiner triple systems', 0.8026636838912964), ('steiner triple system', 0.7676563858985901), ('steiner quadruple system', 0.6855132579803467), ('steiner quadruple', 0.6727777719497681), ('steiner systems', 0.6609475612640381), ('steiner triple', 0.6502804756164551), ('steiner system', 0.6462374925613403), ('steiner', 0.5403807759284973), ('triple systems', 0.5379380583763123), ('triple system', 0.47362127900123596)]"
534,534,58,534_domination number graph_domination graphs_dominating graph_total domination number,"['domination number graph', 'domination graphs', 'dominating graph', 'total domination number', 'domination numbers', 'domination number', 'domination parameters', 'total dominating', 'domination total', 'dominating number']","['(Independent) Roman Domination Parameterized by Distance to Cluster   Given a graph $G=(V,E)$, a function $f:V\\to \\{0,1,2\\}$ is said to be a\n\\emph{Roman Dominating function} (RDF) if for every $v\\in V$ with $f(v)=0$,\nthere exists a vertex $u\\in N(v)$ such that $f(u)=2$. A Roman Dominating\nfunction $f$ is said to be an \\emph{Independent Roman Dominating function}\n(IRDF), if $V_1\\cup V_2$ forms an independent set, where $V_i=\\{v\\in\nV~\\vert~f(v)=i\\}$, for $i\\in \\{0,1,2\\}$. The total weight of $f$ is equal to\n$\\sum_{v\\in V} f(v)$, and is denoted as $w(f)$. The \\emph{Roman Domination\nNumber} (resp. \\emph{Independent Roman Domination Number}) of $G$, denoted by\n$\\gamma_R(G)$ (resp. $i_R(G)$), is defined as min$\\{w(f)~\\vert~f$ is an RDF\n(resp. IRDF) of $G\\}$. For a given graph $G$, the problem of computing\n$\\gamma_R(G)$ (resp. $i_R(G)$) is defined as the \\emph{Roman Domination\nproblem} (resp. \\emph{Independent Roman Domination problem}).\n  In this paper, we examine structural parameterizations of the (Independent)\nRoman Domination problem. We propose fixed-parameter tractable (FPT) algorithms\nfor the (Independent) Roman Domination problem in graphs that are $k$ vertices\naway from a cluster graph. These graphs have a set of $k$ vertices whose\nremoval results in a cluster graph. We refer to $k$ as the distance to the\ncluster graph. Specifically, we prove the following results when parameterized\nby the deletion distance $k$ to cluster graphs: we can find the Roman\nDomination Number (and Independent Roman Domination Number) in time\n$4^kn^{O(1)}$. In terms of lower bounds, we show that the Roman Domination\nnumber can not be computed in time $2^{\\epsilon k}n^{O(1)}$, for any\n$0<\\epsilon <1$ unless a well-known conjecture, SETH fails. In addition, we\nalso show that the Roman Domination problem parameterized by distance to\ncluster, does not admit a polynomial kernel unless NP $\\subseteq$ coNP$/$poly.\n', 'Outer independent double Roman domination number of graphs   A double Roman dominating function of a graph $G$ is a function\n$f:V(G)\\rightarrow \\{0,1,2,3\\}$ having the property that for each vertex $v$\nwith $f(v)=0$, there exists $u\\in N(v)$ with $f(u)=3$, or there are $u,w\\in\nN(v)$ with $f(u)=f(w)=2$, and if $f(v)=1$, then $v$ is adjacent to a vertex\nassigned at least $2$ under $f$. The double Roman domination number\n$\\gamma_{dR}(G)$ is the minimum weight $f(V(G))=\\sum_{v\\in V(G)}f(v)$ among all\ndouble Roman dominating functions of $G$. An outer independent double Roman\ndominating function is a double Roman dominating function $f$ for which the set\nof vertices assigned $0$ under $f$ is independent. The outer independent double\nRoman domination number $\\gamma_{oidR}(G)$ is the minimum weight taken over all\nouter independent double Roman dominating functions of $G$.\n  In this work, we present some contributions to the study of outer independent\ndouble Roman domination in graphs. Characterizations of the families of all\nconnected graphs with small outer independent double Roman domination numbers,\nand tight lower and upper bounds on this parameter are given. We moreover bound\nthis parameter for a tree $T$ from below by two times the vertex cover number\nof $T$ plus one. We also prove that the decision problem associated with\n$\\gamma_{oidR}(G)$ is NP-complete even when restricted to planar graphs with\nmaximum degree at most four. Finally, we give an exact formula for this\nparameter concerning the corona graphs.\n', 'Roman domination number of zero-divisor graphs over commutative rings   For a graph $G= (V, E)$, a Roman dominating function is a map $f : V\n\\rightarrow \\{0, 1, 2\\}$ satisfies the property that if $f(v) = 0$, then $v$\nmust have adjacent to at least one vertex $u$ such that $f(u)= 2$. The weight\nof a Roman dominating function $f$ is the value $f(V)= \\Sigma_{u \\in V} f(u)$,\nand the minimum weight of a Roman dominating function on $G$ is called the\nRoman domination number of $G$, denoted by $\\gamma_R(G)$. The main focus of\nthis paper is to study the Roman domination number of zero-divisor graph\n$\\Gamma(R)$ and find the bounds of the Roman domination number of\n$T(\\Gamma(R))$.\n']","[('domination number graph', 0.6281771063804626), ('domination graphs', 0.6197737455368042), ('dominating graph', 0.5445478558540344), ('total domination number', 0.4967099130153656), ('domination numbers', 0.48516520857810974), ('domination number', 0.4800700545310974), ('domination parameters', 0.4761878252029419), ('total dominating', 0.41867101192474365), ('domination total', 0.41161027550697327), ('dominating number', 0.3937092125415802)]"
535,535,58,535_stone duality_dualities_duality theorems_duality,"['stone duality', 'dualities', 'duality theorems', 'duality', 'category compact', 'dually equivalent', 'dual equivalence', 'spaces category', 'regular spaces', 'equivalent category']","['Raney extensions of frames: topological aspects   We explore a pointfree approach to spaces which extends the category of $T_0$\nspaces. Our pointfree objects are Raney extensions, pairs $(L,C)$ where $C$ is\na coframe, $L\\subseteq C$ is a frame which meet-generates it, and the inclusion\n$L\\subseteq C$ preserves the frame operations as well as the strongly exact\nmeets. We show that the category $\\mathbf{Raney}$ extends that of $T_0$ spaces,\nby showing the existence of an adjunction which extends that between frames and\nspaces. We map a space $X$ to the pair $(\\Omega(X),\\mathcal{U}(X))$, where\n$\\Omega(X)$ are its opens and $\\mathcal{U}(X)$ its saturated sets. The spectrum\nfunctor $\\mathsf{pt}_R$ maps a Raney extension $(L,C)$ to the collection of\ncompletely join-prime elements of $C$, suitably topologized. For a frame $L$\nthe spectra of the largest and the smallest Raney extensions over it are,\nrespectively, the classical spectrum $\\mathsf{pt}(L)$ and the $T_D$ spectrum\n$\\mathsf{pt}_D(L)$.\n  We characterize sobriety as well as the $T_D$ and the $T_1$ axioms for spaces\nin terms of algebraic properties of their Raney duals. We use this to define\nsobriety for general Raney extensions, as well as the $T_D$ and $T_1$\nproperties, and show that a sober coreflection always exists, whereas a $T_D$\nreflection exists when we restrict morphisms to exact maps. We show that a\nframe is subfit if and only if it admits a $T_1$ Raney extension, and that a\nsubfit frame is scattered if and only if it admits a unique Raney extension.\n  We show that the dual adjunction between frames and spaces restricts to a\ndual adjunction between the category of $T_D$ spaces and the category of\n$\\mathbf{Frm}_{\\mathcal{E}}$ of frames and exact maps, and that exact\nsublocales (sublocales whose surjection is exact) form a subcolocale of the\ncoframe of all sublocales.\n', 'A generalization of de Vries duality to closed relations between compact\n  Hausdorff spaces   Stone duality generalizes to an equivalence between the categories\n$\\mathsf{Stone}^{\\mathsf{R}}$ of Stone spaces and closed relations and\n$\\mathsf{BA}^\\mathsf{S}$ of boolean algebras and subordination relations.\nSplitting equivalences in $\\mathsf{Stone}^{\\mathsf{R}}$ yields a category that\nis equivalent to the category $\\mathsf{KHaus}^\\mathsf{R}$ of compact Hausdorff\nspaces and closed relations. Similarly, splitting equivalences in\n$\\mathsf{BA}^\\mathsf{S}$ yields a category that is equivalent to the category\n$\\mathsf{DeV^S}$ of de Vries algebras and compatible subordination relations.\nApplying the machinery of allegories then yields that\n$\\mathsf{KHaus}^\\mathsf{R}$ is equivalent to $\\mathsf{DeV^S}$, thus resolving a\nproblem recently raised in the literature.\n  The equivalence between $\\mathsf{KHaus}^\\mathsf{R}$ and $\\mathsf{DeV^S}$\nfurther restricts to an equivalence between the category ${\\mathsf{KHaus}}$ of\ncompact Hausdorff spaces and continuous functions and the wide subcategory\n$\\mathsf{DeV^F}$ of $\\mathsf{DeV^S}$ whose morphisms satisfy additional\nconditions. This yields an alternative to de Vries duality. One advantage of\nthis approach is that composition of morphisms is usual relation composition.\n', 'Extensions of the Stone Duality to the category BooleSp   In [G. Dimov and E. Ivanova-Dimova, Two extensions of the Stone Duality to\nthe category of zero-dimensional Hausdorff spaces, arXiv:1901.04537v4, 1--33],\nextending the Stone Duality Theorem, we proved two duality theorems for the\ncategory ZDHaus of zero-dimensional Hausdorff spaces and continuous maps. Now\nwe derive from them the extension of the Stone Duality Theorem to the category\nBooleSp of zero-dimensional locally compact Hausdorff spaces and continuous\nmaps obtained in [G. Dimov, Some generalizations of the Stone Duality Theorem,\nPublicationes Mathematicae Debrecen, 80 (2012), 255--293], as well as two new\nduality theorems for the category BooleSp.\n']","[('stone duality', 0.5825828909873962), ('dualities', 0.5708863735198975), ('duality theorems', 0.531975269317627), ('duality', 0.5188266634941101), ('category compact', 0.5160791873931885), ('dually equivalent', 0.5094999670982361), ('dual equivalence', 0.48268967866897583), ('spaces category', 0.47910958528518677), ('regular spaces', 0.4466950595378876), ('equivalent category', 0.4251900911331177)]"
536,536,57,536_stochastic differential game_stochastic differential games_stochastic differential equations_stackelberg equilibrium,"['stochastic differential game', 'stochastic differential games', 'stochastic differential equations', 'stackelberg equilibrium', 'stochastic linear quadratic', 'linear quadratic stochastic', 'backward stochastic differential', 'stackelberg game', 'stochastic differential', 'quadratic stochastic']","['A Linear-Quadratic Stackelberg Differential Game with Mixed\n  Deterministic and Stochastic Controls   This paper is concerned with a linear-quadratic (LQ) Stackelberg differential\ngame with mixed deterministic and stochastic controls. Here in the game, the\nfollower is a random controller which means that the follower can choose\nadapted random processes, while the leader is a deterministic controller which\nmeans that the leader can choose only deterministic time functions. An\nopen-loop Stackelberg equilibrium solution is considered. First, an optimal\ncontrol process of the follower is obtained by maximum principle of controlled\nstochastic differential equation (SDE), which is a linear functional of optimal\nstate variable and control variable of the leader, via a classical Riccati\nequation. Then an optimal control function of the leader is got via a direct\ncalculation of derivative of cost functional, by the solution to a system of\nmean-field forward-backward stochastic differential equations (MF-FBSDEs). And\nit is represented as a functional of expectation of optimal state variable,\ntogether with solutions to a two-point boundary value problem of ordinary\ndifferential equation (ODE), by a system consisting of two coupled Riccati\nequations. The solvability of this new system of Riccati equation is discussed.\n', 'Stackelberg Stochastic Differential Game with Asymmetric Noisy\n  Observations   This paper is concerned with a Stackelberg stochastic differential game with\nasymmetric noisy observation, with one follower and one leader. In our model,\nthe follower cannot observe the state process directly, but could observe a\nnoisy observation process, while the leader can completely observe the state\nprocess. Open-loop Stackelberg equilibrium is considered. The follower first\nsolve an stochastic optimal control problem with partial observation, the\nmaximum principle and verification theorem are obtained. Then the leader turns\nto solve an optimal control problem for a conditional mean-field\nforward-backward stochastic differential equation, and both maximum principle\nand verification theorem are proved. An linear-quadratic Stackelberg stochastic\ndifferential game with asymmetric noisy observation is discussed to illustrate\nthe theoretical results in this paper. With the aid of some Riccati equations,\nthe open-loop Stackelberg equilibrium admits its state estimate feedback\nrepresentation.\n', 'Zero-Sum Stackelberg Stochastic Linear-Quadratic Differential Games   The paper is concerned with a zero-sum Stackelberg stochastic\nlinear-quadratic (LQ, for short) differential game over finite horizons. Under\na fairly weak condition, the Stackelberg equilibrium is explicitly obtained by\nfirst solving a forward stochastic LQ optimal control problem (SLQ problem, for\nshort) and then a backward SLQ problem. Two Riccati equations are derived in\nconstructing the Stackelberg equilibrium. An interesting finding is that the\ndifference of these two Riccati equations coincides with the Riccati equation\nassociated with the zero-sum Nash stochastic LQ differential game, which\nimplies that the Stackelberg equilibrium and the Nash equilibrium are actually\nidentical. Consequently, the Stackelberg equilibrium admits a linear state\nfeedback representation, and the Nash game can be solved in a leader-follower\nmanner.\n']","[('stochastic differential game', 0.6371510028839111), ('stochastic differential games', 0.6138809323310852), ('stochastic differential equations', 0.5607272982597351), ('stackelberg equilibrium', 0.5482807159423828), ('stochastic linear quadratic', 0.540931224822998), ('linear quadratic stochastic', 0.5365339517593384), ('backward stochastic differential', 0.5190718173980713), ('stackelberg game', 0.5035554766654968), ('stochastic differential', 0.4999921917915344), ('quadratic stochastic', 0.49899807572364807)]"
537,537,57,537_consensus based optimization_consensus convergence_global optimization methods_global optimization,"['consensus based optimization', 'consensus convergence', 'global optimization methods', 'global optimization', 'global minimizers', 'based global optimization', 'global optimization problems', 'global minimizer', 'nonsmooth nonconvex optimization', 'swarm optimization']","['Discrete Consensus-Based Optimization   We propose Discrete Consensus-Based Optimization (DCBO), a fully discrete\nversion of the Consensus-Based Optimization (CBO) framework. DCBO is a\nmulti-agent method for the global optimization of possibly non-convex and\nnon-differentiable functions. It aligns with the CBO paradigm, which promotes a\nconsensus among agents towards a global optimum through simple stochastic\ndynamics amenable to rigorous mathematical analysis. Despite the promises,\nthere has been a gap between the analysis of CBO and the actual behavior of the\nagents from its time-discrete implementation, as the former has focused on the\nsystem of continuous stochastic differential equations defining the model or\nits mean-field approximation. In particular, direct analysis of CBO-type\nalgorithms with heterogeneous stochasticity is very challenging. DCBO\ndistinguishes itself from these approaches in the sense that it has no\ncontinuous counterpart, thanks to the replacement of the ""softmin"" operator\nwith the ""hardmin"" one, which is inherently discrete. Yet, it maintains the\noperational principles of CBO and allows for rich mathematical analysis. We\npresent conditions, independent of the number of agents, for achieving a\nconsensus or convergence and study the circumstances under which global\noptimization occurs. We test DCBO on a large number of benchmark functions to\nshow its merits. We also demonstrate that DCBO is applicable to a diverse range\nof real-world problems, including neural network training, compressed sensing,\nand portfolio optimization, with competitive performance.\n', 'On the mean-field limit for the consensus-based optimization   This paper is concerned with the large particle limit for the consensus-based\noptimization (CBO), which was postulated in the pioneering works [6,28]. In\norder to solve this open problem, we adapt a compactness argument by first\nproving the tightness of the empirical measures $\\{\\mu^N\\}_{N\\geq 2}$\nassociated to the particle system and then verifying that the limit measure\n$\\mu$ is the unique weak solution to the mean-field CBO equation. Such results\nare extended to the model of particle swarm optimization (PSO).\n', 'Convergence of Anisotropic Consensus-Based Optimization in Mean-Field\n  Law   In this paper we study anisotropic consensus-based optimization (CBO), a\nmulti-agent metaheuristic derivative-free optimization method capable of\nglobally minimizing nonconvex and nonsmooth functions in high dimensions. CBO\nis based on stochastic swarm intelligence, and inspired by consensus dynamics\nand opinion formation. Compared to other metaheuristic algorithms like particle\nswarm optimization, CBO is of a simpler nature and therefore more amenable to\ntheoretical analysis. By adapting a recently established proof technique, we\nshow that anisotropic CBO converges globally with a dimension-independent rate\nfor a rich class of objective functions under minimal assumptions on the\ninitialization of the method. Moreover, the proof technique reveals that CBO\nperforms a convexification of the optimization problem as the number of agents\ngoes to infinity, thus providing an insight into the internal CBO mechanisms\nresponsible for the success of the method. To motivate anisotropic CBO from a\npractical perspective, we further test the method on a complicated\nhigh-dimensional benchmark problem, which is well understood in the machine\nlearning literature.\n']","[('consensus based optimization', 0.7130618095397949), ('consensus convergence', 0.5700045228004456), ('global optimization methods', 0.5477051734924316), ('global optimization', 0.5413480401039124), ('global minimizers', 0.5351935625076294), ('based global optimization', 0.5233585834503174), ('global optimization problems', 0.5233027935028076), ('global minimizer', 0.49346527457237244), ('nonsmooth nonconvex optimization', 0.4876555800437927), ('swarm optimization', 0.4798206090927124)]"
538,538,57,538_hanson wright inequality_wright inequality_matrix concentration inequalities_inequalities gaussian,"['hanson wright inequality', 'wright inequality', 'matrix concentration inequalities', 'inequalities gaussian', 'concentration inequality', 'moment inequalities', 'concentration inequalities', 'deviation inequality', 'norm concentration', 'sub gaussian']","['Uniform Hanson-Wright Type Deviation Inequalities for\n  $\\alpha$-Subexponential Random Vectors   This paper is devoted to uniform versions of the Hanson-Wright inequality for\na random vector with independent centered $\\alpha$-subexponential entries,\n$0<\\alpha\\le 1$. Our method relies upon a novel decoupling inequality and a\ncomparison of weak and strong moments. As an application, we use the derived\ninequality to prove the restricted isometry property of partial random\ncirculant matrices generated by standard $\\alpha$-subexponential random\nvectors, $0<\\alpha\\le 1$.\n', 'Sparse Hanson-Wright Inequalities with Applications   We derive new Hanson-Wright-type inequalities tailored to the quadratic forms\nof random vectors with sparse independent components. Specifically, we consider\ncases where the components of the random vector are sparse\n$\\alpha$-subexponential random variables with $\\alpha>0$. When $\\alpha=\\infty$,\nthese inequalities can be seen as quadratic generalizations of the classical\nBernstein and Bennett inequalities for sparse bounded random vectors. To\nestablish this quadratic generalization, we also develop new Bersntein-type and\nBennett-type inequalities for linear forms of sparse $\\alpha$-subexponential\nrandom variables that go beyond the bounded case $(\\alpha=\\infty)$. Our proof\nrelies on a novel combinatorial method for estimating the moments of both\nrandom linear forms and quadratic forms.\n  We present two key applications of these new sparse Hanson-Wright\ninequalities: (1) A local law and complete eigenvector delocalization for\nsparse $\\alpha$-subexponential Hermitian random matrices, generalizing the\nresult of He et al. (2019) beyond sparse Bernoulli random matrices. To the best\nof our knowledge, this is the first local law and complete delocalization\nresult for sparse $\\alpha$-subexponeitial random matrices down to the\nnear-optimal sparsity $p\\geq \\frac{\\mathrm{polylog}(n)}{n}$ when $\\alpha\\in\n(0,2)$ as well as for unbounded sparse sub-gaussian random matrices down to the\noptimal sparsity $p\\gtrsim \\frac{\\log n}{n}.$ (2) Concentration of the\nEuclidean norm for the linear transformation of a sparse\n$\\alpha$-subexponential random vector, improving on the results of G\\""otze et\nal. (2021) for sparse sub-exponential random vectors.\n', 'A note on the improved sparse Hanson-Wright inequalities In this paper, we establish sparse Hanson-Wright inequalities for quadratic forms of sparse $\\alpha$-sub-exponential random vectors where $\\alpha \\in (0,2]$. When only considering the regime $0 < \\alpha \\leq 1$, we derive a sharper sparse Hanson-Wright inequality that achieves optimality in certain special cases. These results generalize some classical Hanson-Wright inequalities without sparse structure.']","[('hanson wright inequality', 0.6652339100837708), ('wright inequality', 0.5363143086433411), ('matrix concentration inequalities', 0.535497784614563), ('inequalities gaussian', 0.5314407348632812), ('concentration inequality', 0.46162497997283936), ('moment inequalities', 0.4512241780757904), ('concentration inequalities', 0.43929582834243774), ('deviation inequality', 0.41865620017051697), ('norm concentration', 0.41285794973373413), ('sub gaussian', 0.41162869334220886)]"
539,539,57,539_inventory management_inventory models_inventory control_stochastic demand,"['inventory management', 'inventory models', 'inventory control', 'stochastic demand', 'inventory systems', 'inventory', 'stochastic dynamic programming', 'inventory levels', 'initial inventory', 'demand process']","['Asymptotically Optimal Inventory Control for Assemble-to-Order Systems   We consider Assemble-to-Order (ATO) inventory systems with a general Bill of\nMaterials and general deterministic lead times. Unsatisfied demands are always\nbacklogged. We apply a four-step asymptotic framework to develop inventory\npolicies for minimizing the long-run average expected total inventory cost. Our\napproach features a multi-stage Stochastic Program (SP) to establish a lower\nbound on the inventory cost and determine parameter values for inventory\ncontrol. Our replenishment policy deviates from the conventional constant base\nstock policies to accommodate non-identical lead times. Our component\nallocation policy differentiates demands based on backlog costs, Bill of\nMaterials, and component availabilities. We prove that our policy is\nasymptotically optimal on the diffusion scale, that is, as the longest lead\ntime grows, the percentage difference between the average cost under our policy\nand its lower bound converges to zero. In developing these results, we\nformulate a broad Stochastic Tracking Model and prove general convergence\nresults from which the asymptotic optimality of our policy follows as\nspecialized corollaries.\n', 'Inventory Management Under Stochastic Demand: A Simulation-Optimization\n  Approach   This study presents a comprehensive approach to optimizing inventory\nmanagement under stochastic demand by leveraging Monte Carlo Simulation (MCS)\nwith grid search and Bayesian optimization. By using a business case of\nhistorical demand data and through the comparison of periodic review (p, Q) and\ncontinuous review (r, Q) inventory policies, it demonstrates that the (r, Q)\npolicy significantly increases expected profit by dynamically managing\ninventory levels based on daily demand and lead time considerations. The\nintegration of random and conditional sampling techniques highlights critical\nperiods of high demand, providing deeper insights into demand patterns. While\nconditional sampling reduces execution time, it yields slightly lower profits\ncompared to random sampling. Though Bayesian optimization marginally\noutperforms grid search in identifying optimal reorder quantities and points,\nhowever, given the stochastic nature of the algorithm, this can change with\nmultiple runs. This study accentuates the effectiveness of advanced simulation\nand optimization techniques in addressing complex inventory challenges,\nultimately supporting more informed and profitable inventory management\ndecisions. The simulation model and optimization framework are open-source and\nwritten in Python, promoting transparency and enabling other researchers and\npractitioners to replicate and build upon this work. This contributes to the\nadvancement of knowledge and the development of more effective inventory\nmanagement solutions.\n', 'Exploiting random lead times for significant inventory cost savings   We study the classical single-item inventory system in which unsatisfied\ndemands are backlogged. Replenishment lead times are random, independent\nidentically distributed, causing orders to cross in time. We develop a new\ninventory policy to exploit implications of lead time randomness and order\ncrossover, and evaluate its performance by asymptotic analysis and simulations.\nOur policy does not follow the basic principle of Constant Base Stock (CBS)\npolicy, or more generally, (s,S) and (r,Q) policies, which is to keep the\ninventory position within a fixed range. Instead, it uses the current inventory\nlevel (= inventory-on-hand minus backlog) to set a dynamic target for inventory\nin-transit, and place orders to follow this target. Our policy includes CBS\npolicy as a special case, under a particular choice of a policy parameter. We\nshow that our policy can significantly reduce the average inventory cost\ncompared with CBS policy. Specifically, we prove that if the lead time is\nexponentially distributed, then under our policy, with properly chosen policy\nparameters, the expected (absolute) inventory level scales as $o(\\sqrt{r})$, as\nthe demand rate $r\\to\\infty$. In comparison, it is known to scale as\n$\\Theta(\\sqrt{r})$ under CBS policy. In particular, this means that, as\n$r\\to\\infty$, the average inventory cost under our policy vanishes in\ncomparison with that under CBS policy. Furthermore, our simulations show that\nthe advantage of our policy remains to be substantial under non-exponential\nlead time distributions, and may even be greater than under exponential\ndistribution. We also use simulations to compare GBS to an optimal policy for\nsome cases where computing the optimal cost is tractable. The results show that\nour policy removes a majority of excess costs of CBS policy over the minimum\ncost, leading to much smaller optimality gaps.\n']","[('inventory management', 0.6054854393005371), ('inventory models', 0.5932982563972473), ('inventory control', 0.5823553800582886), ('stochastic demand', 0.5450937747955322), ('inventory systems', 0.544512152671814), ('inventory', 0.511051595211029), ('stochastic dynamic programming', 0.47663700580596924), ('inventory levels', 0.45930203795433044), ('initial inventory', 0.4562068581581116), ('demand process', 0.44768646359443665)]"
540,540,56,540_quantum relative entropy_quantum entropy_entropy quantum_quantum information theory,"['quantum relative entropy', 'quantum entropy', 'entropy quantum', 'quantum information theory', 'information quantum', 'quantum information', 'von neumann entropy', 'enyi divergences', 'enyi divergence', 'inequality quantum']","[""The strong converse exponent of discriminating infinite-dimensional\n  quantum states   The sandwiched R\\'enyi divergences of two finite-dimensional density\noperators quantify their asymptotic distinguishability in the strong converse\ndomain. This establishes the sandwiched R\\'enyi divergences as the\noperationally relevant ones among the infinitely many quantum extensions of the\nclassical R\\'enyi divergences for R\\'enyi parameter $\\alpha>1$. The known proof\nof this goes by showing that the sandwiched R\\'enyi divergence coincides with\nthe regularized measured R\\'enyi divergence, which in turn is proved by\nasymptotic pinching, a fundamentally finite-dimensional technique. Thus, while\nthe notion of the sandwiched R\\'enyi divergences was extended recently to\ndensity operators on an infinite-dimensional Hilbert space (even for states of\na von Neumann algebra), these quantities were so far lacking an operational\ninterpretation similar to the finite-dimensional case, and it has also been\nopen whether they coincide with the regularized measured R\\'enyi divergences.\nIn this paper we fill this gap by answering both questions in the positive for\ndensity operators on an infinite-dimensional Hilbert space, using a simple\nfinite-dimensional approximation technique.\n  We also initiate the study of the sandwiched R\\'enyi divergences, and the\nrelated problem of the strong converse exponent, for pairs of positive\nsemi-definite operators that are not necessarily trace-class. This is\ninteresting from the purely mathematical point of view of extending the concept\nof R\\'enyi (and other) divergences to settings beyond the standard one of\npositive trace-class operators (positive normal functionals in the von Neumann\nalgebra setting). In this spirit, we also discuss the definition and some\nproperties of the more general family of R\\'enyi $(\\alpha,z)$-divergences of\npositive semi-definite operators on an infinite-dimensional separable Hilbert\nspace.\n"", ""Quantum R\\'enyi divergences and the strong converse exponent of state\n  discrimination in operator algebras   The sandwiched R\\'enyi $\\alpha$-divergences of two finite-dimensional quantum\nstates play a distinguished role among the many quantum versions of R\\'enyi\ndivergences as the tight quantifiers of the trade-off between the two error\nprobabilities in the strong converse domain of state discrimination. In this\npaper we show the same for the sandwiched R\\'enyi divergences of two normal\nstates on an injective von Neumann algebra, thereby establishing the\noperational significance of these quantities. Moreover, we show that in this\nsetting, again similarly to the finite-dimensional case, the sandwiched R\\'enyi\ndivergences coincide with the regularized measured R\\'enyi divergences, another\ndistinctive feature of the former quantities. Our main tool is an approximation\ntheorem (martingale convergence) for the sandwiched R\\'enyi divergences, which\nmay be used for the extension of various further results from the\nfinite-dimensional to the von Neumann algebra setting.\n  We also initiate the study of the sandwiched R\\'enyi divergences of pairs of\nstates on a $C^*$-algebra, and show that the above operational interpretation,\nas well as the equality to the regularized measured R\\'enyi divergence, holds\nmore generally for pairs of states on a nuclear $C^*$-algebra.\n"", ""Optimized quantum f-divergences   The quantum relative entropy is a measure of the distinguishability of two\nquantum states, and it is a unifying concept in quantum information theory:\nmany information measures such as entropy, conditional entropy, mutual\ninformation, and entanglement measures can be realized from it. As such, there\nhas been broad interest in generalizing the notion to further understand its\nmost basic properties, one of which is the data processing inequality. The\nquantum f-divergence of Petz is one generalization of the quantum relative\nentropy, and it also leads to other relative entropies, such as the Petz--Renyi\nrelative entropies. In this contribution, I introduce the optimized quantum\nf-divergence as a related generalization of quantum relative entropy. I prove\nthat it satisfies the data processing inequality, and the method of proof\nrelies upon the operator Jensen inequality, similar to Petz's original\napproach. Interestingly, the sandwiched Renyi relative entropies are particular\nexamples of the optimized f-divergence. Thus, one benefit of this approach is\nthat there is now a single, unified approach for establishing the data\nprocessing inequality for both the Petz--Renyi and sandwiched Renyi relative\nentropies, for the full range of parameters for which it is known to hold.\n""]","[('quantum relative entropy', 0.6298792362213135), ('quantum entropy', 0.5938050746917725), ('entropy quantum', 0.5891563892364502), ('quantum information theory', 0.5836425423622131), ('information quantum', 0.5596954822540283), ('quantum information', 0.5519769787788391), ('von neumann entropy', 0.5374349355697632), ('enyi divergences', 0.516111433506012), ('enyi divergence', 0.48102372884750366), ('inequality quantum', 0.4718809723854065)]"
541,541,56,541_cancer cells_cancer cell_tumor cells_tumour cells,"['cancer cells', 'cancer cell', 'tumor cells', 'tumour cells', 'tumor growth', 'cancer treatment', 'tumour growth', 'cancer', 'breast cancer', 'chemotherapy']","[""Evaluation of Entropy and Fractal Dimension as Biomarkers for Tumor\n  Growth and Treatment Response using Cellular Automata   Cell-based models provide a helpful approach for simulating complex systems\nthat exhibit adaptive, resilient qualities, such as cancer. Their focus on\nindividual cell interactions makes them a particularly appropriate strategy to\nstudy the effects of cancer therapies, which often are designed to disrupt\nsingle-cell dynamics. In this work, we also propose them as viable methods for\nstudying the time evolution of cancer imaging biomarkers (IBM). We propose a\ncellular automata model for tumor growth and three different therapies:\nchemotherapy, radiotherapy, and immunotherapy, following well-established\nmodeling procedures documented in the literature. The model generates a\nsequence of tumor images, from which time series of two biomarkers: entropy and\nfractal dimension, is obtained. Our model shows that the fractal dimension\nincreased faster at the onset of cancer cell dissemination, while entropy was\nmore responsive to changes induced in the tumor by the different therapy\nmodalities. These observations suggest that the predictive value of the\nproposed biomarkers could vary considerably with time. Thus, it is important to\nassess their use at different stages of cancer and for different imaging\nmodalities. Another observation derived from the results was that both\nbiomarkers varied slowly when the applied therapy attacked cancer cells in a\nscattered fashion along the automatons' area, leaving multiple independent\nclusters of cells at the end of the treatment. Thus, patterns of change of\nsimulated biomarkers time series could reflect on essential qualities of the\nspatial action of a given cancer intervention.\n"", 'Mathematical modeling of tumor-immune system interactions: the effect of\n  rituximab on breast cancer immune response   tBregs are a newly discovered subcategory of B regulatory cells, which are\ngenerated by breast cancer, resulting in the increase of Tregs and therefore in\nthe death of NK cells. In this study, we use a mathematical and computational\napproach to investigate the complex interactions between the aforementioned\ncells as well as CD8$^+$ T cells, CD4$^+$ T cells and B cells. Furthermore, we\nuse data fitting to prove that the functional response regarding the lysis of\nbreast cancer cells by NK cells has a ratio-dependent form. Additionally, we\ninclude in our model the concentration of rituximab - a monoclonal antibody\nthat has been suggested as a potential breast cancer therapy - and test its\neffect, when the standard, as well as experimental dosages, are administered.\n', 'A mathematical model of Breast cancer (ER+) with excess estrogen: Mixed\n  treatments using Ketogenic diet, endocrine therapy and Immunotherapy   Breast Cancer is a major public health problem and the most common diagnosed\nmalignancy in woman. There have been significant developments in clinical\napproaches and theoretical experimental to understand the interactions of\ncancer cells dynamics with the immune system, also developments on analytical\nand computational models to help provide insights into clinical observations\nfor a better understanding of cancer cells, but more are needed, especially at\nthe genetic and molecular levels mathematically. Treatments such as\nimmunotherapy, chemotherapy, hormone therapy, radiotherapy, and gene therapy\nare the main strategies in the fight against breast cancer. The present study\naims at investigating the effects of estrogen derived from recent models, but\nthis time combined with immunotherapy as a way to treat or inhibit the cancer\ngrowth by a mathematical model of breast cancer in situ, governed by a\nsimplified model of nonlinear-coupled ordinary differential equations, that\ncombines important interactions between natural cells, tumor cells, immune\ncells, ketogenic diet in the presence of an anticancer drug. Another\ncontribution was to introduce the inhibition effect epsilon for new results and\nconclusions, A qualitative study was performed and biological interpretations\nwere included to understand the conditions of stability in a realistic way.\n']","[('cancer cells', 0.48255226016044617), ('cancer cell', 0.47458213567733765), ('tumor cells', 0.46554940938949585), ('tumour cells', 0.4489360451698303), ('tumor growth', 0.4363931119441986), ('cancer treatment', 0.414428174495697), ('tumour growth', 0.4009222686290741), ('cancer', 0.37375637888908386), ('breast cancer', 0.3737190067768097), ('chemotherapy', 0.34050825238227844)]"
542,542,56,542_stochastic schr odinger_nonlinear schr odinger_schr odinger equations_critical nonlinear schr,"['stochastic schr odinger', 'nonlinear schr odinger', 'schr odinger equations', 'critical nonlinear schr', 'stochastic schr', 'odinger equations', 'nonlinear schr', 'stochastic nonlinear', 'critical nonlinear', 'fractional nonlinear schr']","['Qualitative quasi-invariance of low regularity Gaussian measures for the\n  1d quintic nonlinear Schr\\""odinger equation   We consider the 1d quintic nonlinear Schr\\""odinger equation (NLS) on the\ntorus with initial data distributed according to the Gaussian measures with\ncovariance operator $(1-\\Delta)^{-s}$, and denoted $\\mu_s$. For the full range\n$s>\\frac{9}{10}$, we prove that these Gaussian measures are quasi-invariant\nalong the flow of (NLS), meaning that the law of the solution at any time is\nabsolutely continuous with respect to the initial Gaussian measure. Moreover,\nthe condition $s>\\frac{9}{10}$ corresponds to the threshold where the Sobolev\nspace $H^{\\frac{2}{5}+}(\\mathbb{T})$ is of $\\mu_s$-full measure (it is of zero\n$\\mu_s$-measure otherwise). This is the lower regularity Sobolev space where we\ncurrently know that (NLS) is globally well-posed, thanks to a work by LI-WU-XU.\nThe present work extends the known threshold $s>\\frac{3}{2}$ for the\nquasi-invariance down to $s>\\frac{9}{10}$, but we do not obtain here\nquantitative results on the Radon-Nikodym derivatives. Our approach is based on\na work of Sun-Tzvetkov, combining a Poincar\\\'e-Dulac normal form reduction with\nenergy estimates. However, our main tool to obtain these energy estimates\ndiffers: we use the Bou\\\'e-Dupuis variational formula instead of Wiener Chaos.\n', 'Transport of low regularity Gaussian measures for the 1d quintic\n  nonlinear Schr\\""odinger equation   We consider the 1d nonlinear Schr\\""odinger equation (NLS) on the torus with\ninitial data distributed according to the Gaussian measure with covariance\noperator $(1 - \\Delta)^{-s}$, where $\\Delta$ is the Laplace operator. We prove\nthat the Gaussian measures are quasi-invariant along the flow of (NLS) for the\nfull range $s > \\frac{3}{2}$. This improves a previous result obtained by\nPlanchon, Tzvetkov and Visciglia (in 2019), where the quasi-invariance is\nproven for $s=2k$, for all integers $k\\geq 1$. In our approach, to prove the\nquasi-invariance, we directly establish an explicit formula for the\nRadon-Nikodym derivative $G_s(t,.)$ of the transported measures, which is\nobtained as the limit of truncated Radon-Nikodym derivatives $G_{s,N}(t,.)$ for\ntransported measures associated with a truncated system. We also prove that the\nRadon-Nikodym derivatives belong to $L^p$, $p>1$, with respect to\n$H^1(\\mathbb{T})$-cutoff Gaussian measures, relying on the introduction of\nweighted Gaussian measures produced by a normal form reduction, following a\nrecent work by Sun and Tzvetkov (in 2023). Additionally, we prove that the\ntruncated densities $G_{s,N}(t,.)$ converges to $G_s(t,.)$ in $L^p$ (with\nrespect to the $H^1(\\mathbb{T})$-cutoff Gaussian measures).\n', 'Global well-posedness of the energy-critical stochastic nonlinear Schr\\""odinger equation on the three-dimensional torus We study the Cauchy problem of the defocusing energy-critical stochastic nonlinear Schr\\""odinger equation (SNLS) on the three dimensional torus, forced by an additive noise. We adapt the atomic spaces framework in the context of the energy-critical nonlinear Schr\\""odinger equation, and employ probabilistic perturbation arguments in the context of stochastic PDEs, establishing the global well-posedness of the defocusing energy-critical quintic SNLS in the energy space. It is the first global well-posedness result for the periodic SNLS in a critical space.']","[('stochastic schr odinger', 0.6600659489631653), ('nonlinear schr odinger', 0.6388644576072693), ('schr odinger equations', 0.6111624836921692), ('critical nonlinear schr', 0.6095843315124512), ('stochastic schr', 0.5337492227554321), ('odinger equations', 0.5288882851600647), ('nonlinear schr', 0.5247098803520203), ('stochastic nonlinear', 0.5168464779853821), ('critical nonlinear', 0.46555382013320923), ('fractional nonlinear schr', 0.45550036430358887)]"
543,543,56,543_graph ramsey_ramsey properties_ramsey_randomly perturbed graphs,"['graph ramsey', 'ramsey properties', 'ramsey', 'randomly perturbed graphs', 'dense random graphs', 'number random graphs', 'random graphs', 'chromatic number', 'random graph g_', 'binomial random graph']","['Resolution of the Kohayakawa-Kreuter conjecture   A graph $G$ is said to be Ramsey for a tuple of graphs $(H_1,\\dots,H_r)$ if\nevery $r$-coloring of the edges of $G$ contains a monochromatic copy of $H_i$\nin color $i$, for some $i$. A fundamental question at the intersection of\nRamsey theory and the theory of random graphs is to determine the threshold at\nwhich the binomial random graph $G_{n,p}$ becomes a.a.s. Ramsey for a fixed\ntuple $(H_1,\\dots,H_r)$, and a famous conjecture of Kohayakawa and Kreuter\npredicts this threshold. Earlier work of Mousset-Nenadov-Samotij,\nBowtell-Hancock-Hyde, and Kuperwasser-Samotij-Wigderson has reduced this\nprobabilistic problem to a deterministic graph decomposition conjecture. In\nthis paper, we resolve this deterministic problem, thus proving the\nKohayakawa-Kreuter conjecture. Along the way, we prove a number of novel graph\ndecomposition results which may be of independent interest.\n', 'On the Kohayakawa-Kreuter conjecture   Let us say that a graph $G$ is Ramsey for a tuple $(H_1,\\dots,H_r)$ of graphs\nif every $r$-coloring of the edges of $G$ contains a monochromatic copy of\n$H_i$ in color $i$, for some $i \\in [r]$. A famous conjecture of Kohayakawa and\nKreuter, extending seminal work of R\\""odl and Ruci\\\'nski, predicts the\nthreshold at which the binomial random graph $G_{n,p}$ becomes Ramsey for\n$(H_1,\\dots,H_r)$ asymptotically almost surely. In this paper, we resolve the\nKohayakawa-Kreuter conjecture for almost all tuples of graphs. Moreover, we\nreduce its validity to the truth of a certain deterministic statement, which is\na clear necessary condition for the conjecture to hold. All of our results\nactually hold in greater generality, when one replaces the graphs\n$H_1,\\dots,H_r$ by finite families $\\mathcal{H}_1,\\dots,\\mathcal{H}_r$.\nAdditionally, we pose a natural (deterministic) graph-partitioning conjecture,\nwhich we believe to be of independent interest, and whose resolution would\nimply the Kohayakawa-Kreuter conjecture.\n', 'Ramsey games near the critical threshold   A well-known result of R\\""odl and Ruci\\\'nski states that for any graph $H$\nthere exists a constant $C$ such that if $p \\geq C n^{- 1/m_2(H)}$, then the\nrandom graph $G_{n,p}$ is a.a.s. $H$-Ramsey, that is, any $2$-colouring of its\nedges contains a monochromatic copy of $H$. Aside from a few simple exceptions,\nthe corresponding $0$-statement also holds, that is, there exists $c>0$ such\nthat whenever $p\\leq cn^{-1/m_2(H)}$ the random graph $G_{n,p}$ is a.a.s. not\n$H$-Ramsey.\n  We show that near this threshold, even when $G_{n,p}$ is not $H$-Ramsey, it\nis often extremely close to being $H$-Ramsey. More precisely, we prove that for\nany constant $c > 0$ and any strictly $2$-balanced graph $H$, if $p \\geq c\nn^{-1/m_2(H)}$, then the random graph $G_{n,p}$ a.a.s. has the property that\nevery $2$-edge-colouring without monochromatic copies of $H$ cannot be extended\nto an $H$-free colouring after $\\omega(1)$ extra random edges are added. This\ngeneralises a result by Friedgut, Kohayakawa, R\\""odl, Ruci\\\'nski and Tetali,\nwho in 2002 proved the same statement for triangles, and addresses a question\nraised by those authors. We also extend a result of theirs on the three-colour\ncase and show that these theorems need not hold when $H$ is not strictly\n$2$-balanced.\n']","[('graph ramsey', 0.6972663998603821), ('ramsey properties', 0.6678486466407776), ('ramsey', 0.531890332698822), ('randomly perturbed graphs', 0.5170877575874329), ('dense random graphs', 0.511830747127533), ('number random graphs', 0.5048694610595703), ('random graphs', 0.5014710426330566), ('chromatic number', 0.48348918557167053), ('random graph g_', 0.4770886301994324), ('binomial random graph', 0.46288537979125977)]"
544,544,56,544_truncated moment_moment solutions_generalized moment_moment matrices,"['truncated moment', 'moment solutions', 'generalized moment', 'moment matrices', 'moment sequences', 'moment problems', 'moment functional', 'dimensional moment', 'truncated matrix', 'moment matrix']","['Generalized truncated moment problems with unbounded sets   This paper studies generalized truncated moment problems with unbounded sets.\nFirst, we study geometric properties of the truncated moment cone and its dual\ncone of nonnegative polynomials. By the technique of homogenization, we give a\nconvergent hierarchy of Moment-SOS relaxations for approximating these cones.\nWith them, we give a Moment-SOS method for solving generalized truncated moment\nproblems with unbounded sets. Finitely atomic representing measures, or\ncertificates for their nonexistence, can be obtained by the proposed method.\nNumerical experiments and applications are also given.\n', 'The strong truncated Hamburger moment problem with and without gaps   The strong truncated Hamburger moment problem (STHMP) of degree\n$(-2k_1,2k_2)$ asks to find necessary and sufficient conditions for the\nexistence of a positive Borel measure, supported on $\\mathbb{R}\\setminus\n\\{0\\}$, such that $\\beta_i=\\int x^id\\mu\\; (-2k_1\\leq i\\leq 2k_2)$. Using the\nsolution of the truncated Hamburger moment problem and the properties of Hankel\nmatrices we solve the STHMP. Then, using the equivalence with the STHMP of\ndegree $(-2k,2k)$, we obtain the solution of the 2-dimensional truncated moment\nproblem (TMP) of degree $2k$ with variety $xy=1$, first solved by Curto and\nFialkow. Our addition to their result is the fact previously known only for\n$k=2$, that the existence of a measure is equivalent to the existence of a flat\nextension of the moment matrix. Further on, we solve the STHMP of degree\n$(-2k_1,2k_2)$ with one missing moment in the sequence, i.e., $\\beta_{-2k_1+1}$\nor $\\beta_{2k_2-1}$, which also gives the solution of the TMP with variety\n$x^2y=1$ as a special case, first studied by Fialkow.\n', 'On the Matricial Truncated Moment Problem. II   We continue the study of truncated matrix-valued moment problems begun in\narXiv:2310.00957. Let $q\\in\\mathbb{N}$. Suppose that\n$(\\mathcal{X},\\mathfrak{X})$ is a measurable space and $\\mathcal{E}$ is a\nfinite-dimensional vector space of measurable mappings of $\\mathscr{X}$ into\n$\\mathcal{H}_q$, the Hermitian $q\\times q$ matrices. A linear functional\n$\\Lambda$ on $\\mathcal{E}$ is called a moment functional if there exists a\npositive $\\mathcal{H}_q$-valued measure $\\mu$ on $(\\mathcal{X},\\mathfrak{X})$\nsuch that $\\Lambda(F)=\\int_\\mathcal{X} \\langle F, \\mathrm{d}\\mu\\rangle$ for\n$F\\in \\mathcal{E}$.\n  In this paper a number of special topics on the truncated matricial moment\nproblem are treated. We restate a result from (Mourrain and Schm\\""udgen, 2016)\nto obtain a matricial version of the flat extension theorem. Assuming that\n$\\mathcal{X}$ is a compact space and all elements of $ \\mathcal{E}$ are\ncontinuous on $\\mathcal{X}$ we characterize moment functionals in terms of\npositivity and obtain an ordered maximal mass representing measure for each\nmoment functional. The set of masses of representing measures at a fixed point\nand some related sets are studied. The class of commutative matrix moment\nfunctionals is investigated. We generalize the apolar scalar product for\nhomogeneous polynomials to the matrix case and apply this to the matricial\ntruncated moment problem.\n']","[('truncated moment', 0.5787633657455444), ('moment solutions', 0.49732154607772827), ('generalized moment', 0.48193612694740295), ('moment matrices', 0.4804365634918213), ('moment sequences', 0.4724515974521637), ('moment problems', 0.4640355110168457), ('moment functional', 0.45624157786369324), ('dimensional moment', 0.43664488196372986), ('truncated matrix', 0.4317488372325897), ('moment matrix', 0.4175755977630615)]"
545,545,56,545_geodesic ray transform_geodesic ray_riemannian geodesics_ray transforms,"['geodesic ray transform', 'geodesic ray', 'riemannian geodesics', 'ray transforms', 'sub riemannian geodesics', 'transform tensors', 'manifolds geodesic', 'geodesic flows', 'ray transform', 'geodesic vector']","['The Light Ray transform in Stationary and Static Lorentzian geometries   Given a Lorentzian manifold, the light ray transform of a function is its\nintegrals along null geodesics. This paper is concerned with the injectivity of\nthe light ray transform on functions and tensors, up to the natural gauge for\nthe problem. First, we study the injectivity of the light ray transform of a\nscalar function on a globally hyperbolic stationary Lorentzian manifold and\nprove injectivity holds if either a convex foliation condition is satisfied on\na Cauchy surface on the manifold or the manifold is real analytic and null\ngeodesics do not have cut points. Next, we consider the light ray transform on\ntensor fields of arbitrary rank in the more restrictive class of static\nLorentzian manifolds and show that if the geodesic ray transform on tensors\ndefined on the spatial part of the manifold is injective up to the natural\ngauge, then the light ray transform on tensors is also injective up to its\nnatural gauge. Finally, we provide applications of our results to some inverse\nproblems about recovery of coefficients for hyperbolic partial differential\nequations from boundary data.\n', ""The tensorial X-ray transform on asymptotically conic spaces   In this paper we show the invertibility of the geodesic X-ray transform on\none forms and 2-tensors on asymptotically conic manifolds, up to the natural\nobstruction, allowing existence of certain kinds of conjugate points. We use\nthe 1-cusp pseudodifferential operator algebra and its semiclassical foliation\nversion introduced and used by Vasy and Zachos, who showed the same type\ninvertibility on functions.\n  The complication of the invertibility of the tensorial X-ray transform,\ncompared with X-ray transform on functions, is caused by the natural kernel of\nthe transform consisting of `potential tensors'. We overcome this by arranging\na modified solenoidal gauge condition, under which we have the invertibility of\nthe X-ray transform.\n"", 'On mixed and transverse ray transforms on orientable surfaces   The geodesic ray transform, the mixed ray transform and the transverse ray\ntransform of a tensor field on a manifold can all be seen as what we call\nmixing ray transforms, compositions of the geodesic ray transform and an\ninvertible linear map on tensor fields. We show that the characterization of\nthe kernel and the stability of a mixing ray transform can be reduced to the\nsame properties of any other mixing ray transform. Our approach applies to\nvarious geometries and ray transforms, including the light ray transform. In\nparticular, we extend studies in de Hoop--Saksala--Zhai (2019) from compact\nsimple surfaces to orientable surfaces with solenoidally injective geodesic ray\ntransform. Our proofs are based on algebraic arguments.\n']","[('geodesic ray transform', 0.7036567330360413), ('geodesic ray', 0.5782729983329773), ('riemannian geodesics', 0.5392959117889404), ('ray transforms', 0.5378016233444214), ('sub riemannian geodesics', 0.5313126444816589), ('transform tensors', 0.5156800150871277), ('manifolds geodesic', 0.5092257857322693), ('geodesic flows', 0.5022864937782288), ('ray transform', 0.5006166100502014), ('geodesic vector', 0.48018917441368103)]"
546,546,56,546_reduced order modeling_reduced order models_parametric order reduction_order reduction parametric,"['reduced order modeling', 'reduced order models', 'parametric order reduction', 'order reduction parametric', 'reduced models', 'second order systems', 'reduced order', 'order models', 'order reduction', 'optimal reduced']","['A Unifying Framework for Interpolatory $\\mathcal{L}_2$-optimal\n  Reduced-order Modeling   We develop a unifying framework for interpolatory $\\mathcal{L}_2$-optimal\nreduced-order modeling for a wide classes of problems ranging from stationary\nmodels to parametric dynamical systems. We first show that the framework\nnaturally covers the well-known interpolatory necessary conditions for\n$\\mathcal{H}_2$-optimal model order reduction and leads to the interpolatory\nconditions for $\\mathcal{H}_2 \\otimes \\mathcal{L}_2$-optimal model order\nreduction of multi-input/multi-output parametric dynamical systems. Moreover,\nwe derive novel interpolatory optimality conditions for rational discrete\nleast-squares minimization and for $\\mathcal{L}_2$-optimal model order\nreduction of a class of parametric stationary models. We show that bitangential\nHermite interpolation appears as the main tool for optimality across different\ndomains. The theoretical results are illustrated on two numerical examples.\n', 'Balanced truncation for parametric linear systems using interpolation of\n  Gramians: a comparison of algebraic and geometric approaches   When balanced truncation is used for model order reduction, one has to solve\na pair of Lyapunov equations for two Gramians and uses them to construct a\nreduced-order model. Although advances in solving such equations have been\nmade, it is still the most expensive step of this reduction method. Parametric\nmodel order reduction aims to determine reduced-order models for\nparameter-dependent systems. Popular techniques for parametric model order\nreduction rely on interpolation. Nevertheless, the interpolation of Gramians is\nrarely mentioned, most probably due to the fact that Gramians are symmetric\npositive semidefinite matrices, a property that should be preserved by the\ninterpolation method. In this contribution, we propose and compare two\napproaches for Gramian interpolation. In the first approach, the interpolated\nGramian is computed as a linear combination of the data Gramians with positive\ncoefficients. Even though positive semidefiniteness is guaranteed in this\nmethod, the rank of the interpolated Gramian can be significantly larger than\nthat of the data Gramians. The second approach aims to tackle this issue by\nperforming the interpolation on the manifold of fixed-rank positive\nsemidefinite matrices. The results of the interpolation step are then used to\nconstruct parametric reduced-order models, which are compared numerically on\ntwo benchmark problems.\n', 'Generalizations of data-driven balancing: what to sample for different\n  balancing-based reduced models   The Quadrature-based Balanced Truncation (QuadBT) framework of\narXiv:2104.01006 is a ""non-intrusive"" reformulation of balanced truncation; a\nclassical projection-based model-order reduction technique for linear systems.\nQuadBT is non-intrusive in the sense that it builds approximate balanced\nreduced-order models entirely from system response data (e.g., transfer\nfunction measurements) without the need to reference an explicit state-space\nrealization of the underlying full-order model. In this work, we generalize and\nextend QuadBT to other types of balanced truncation model reduction. Namely, we\ndevelop non-intrusive implementations for balanced stochastic truncation,\npositive-real balanced truncation, and bounded-real balanced truncation. We\nshow that the data-driven construction of these balanced reduced-order models\nrequires sampling certain spectral factors associated with the system of\ninterest. Numerical examples are included in each case to validate our\napproach.\n']","[('reduced order modeling', 0.684229850769043), ('reduced order models', 0.6758138537406921), ('parametric order reduction', 0.614983081817627), ('order reduction parametric', 0.5838462114334106), ('reduced models', 0.5313328504562378), ('second order systems', 0.5039570927619934), ('reduced order', 0.47840091586112976), ('order models', 0.46832191944122314), ('order reduction', 0.46217080950737), ('optimal reduced', 0.43097180128097534)]"
547,547,56,547_port hamiltonian systems_port hamiltonian structure_port hamiltonian_hamiltonian systems,"['port hamiltonian systems', 'port hamiltonian structure', 'port hamiltonian', 'hamiltonian systems', 'hamiltonian systems one', 'hamiltonian system', 'hamiltonian structure', 'hamiltonian type', 'hamiltonian', 'dissipative hamiltonian']","['On Energy Conversion in Port-Hamiltonian Systems   We study port-Hamiltonian systems with two external ports, and the strategies\nand limitations for conversion of energy from one port into the other. It turns\nout that, apart from the cyclo-passivity of port-Hamiltonian systems, this is\nrelated to the internal connection structure of port-Hamiltonian systems. A\nsource of motivation for energy conversion is provided by thermodynamics, in\nparticular the Carnot theory of conversion of thermal into mechanical energy.\nThis is extended to general port-Hamiltonian systems which are satisfying\nstructural conditions on their topology; thus generalizing the Carnot-Clausius\ntheory of heat engines. In particular, the operation of Carnot cycles is\nextended, which is illustrated by the example of a precursor to the Stirling\nengine, as well as an electromagnetic actuator. Furthermore, alternative energy\nconversion control schemes such as energy-routers are discussed.\n', 'Linear port-Hamiltonian systems are generically controllable   The new concept of relative generic subsets is introduced. It is shown that\nthe set of controllable linear finite-dimensional port-Hamiltonian systems is a\nrelative generic subset of the set of all linear finite-dimensional\nport-Hamiltonian systems. This implies that a random, continuously distributed\nport-Hamiltonian system is almost surely controllable.\n', 'Port-Hamiltonian systems and monotonicity   The relationships between port-Hamiltonian systems modeling and the notion of\nmonotonicity are explored. The earlier introduced notion of incrementally\nport-Hamiltonian systems is extended to maximal cyclically monotone relations,\ntogether with their generating functions. This gives rise to new classes of\nincrementally port-Hamiltonian systems, with examples stemming from physical\nsystems modeling as well as from convex optimization. An in-depth treatment is\ngiven of the composition of maximal monotone and maximal cyclically monotone\nrelations, where in the latter case the resulting maximal cyclically monotone\nrelation is shown to be computable through the use of generating functions.\nFurthermore, connections are discussed with incremental versions of passivity,\nand it is shown how incrementally port-Hamiltonian systems with strictly convex\nHamiltonians are (maximal) equilibrium independent passive. Finally, the\nresults on compositionality of monotone relations are employed for a convex\noptimization approach to the computation of the equilibrium of interconnected\nincrementally port-Hamiltonian systems.\n']","[('port hamiltonian systems', 0.8495932817459106), ('port hamiltonian structure', 0.7872862815856934), ('port hamiltonian', 0.7712743878364563), ('hamiltonian systems', 0.6562238931655884), ('hamiltonian systems one', 0.6273617744445801), ('hamiltonian system', 0.5814061164855957), ('hamiltonian structure', 0.5699095726013184), ('hamiltonian type', 0.5518908500671387), ('hamiltonian', 0.5290038585662842), ('dissipative hamiltonian', 0.5201601982116699)]"
548,548,56,548_machine scheduling_scheduling problems_scheduling_job scheduling,"['machine scheduling', 'scheduling problems', 'scheduling', 'job scheduling', 'scheduling non', 'parallel machines', 'integer linear programming', 'linear programming', 'batch processing', 'schedules']","['Malleable scheduling beyond identical machines   In malleable job scheduling, jobs can be executed simultaneously on multiple\nmachines with the processing time depending on the number of allocated\nmachines. In this setting, jobs are required to be executed non-preemptively\nand in unison, in the sense that they occupy, during their execution, the same\ntime interval over all the machines of the allocated set. In this work, we\nstudy generalizations of malleable job scheduling inspired by standard\nscheduling on unrelated machines. Specifically, we introduce a general model of\nmalleable job scheduling, where each machine has a (possibly different) speed\nfor each job, and the processing time of a job $j$ on a set of allocated\nmachines $S$ depends on the total speed of $S$ with respect to $j$. For\nmachines with unrelated speeds, we show that the optimal makespan cannot be\napproximated within a factor less than $\\frac{e}{e-1}$, unless $P = NP$. On the\npositive side, we present polynomial-time algorithms with approximation ratios\n$\\frac{2e}{e-1}$ for machines with unrelated speeds, $3$ for machines with\nuniform speeds, and $7/3$ for restricted assignments on identical machines. Our\nalgorithms are based on deterministic LP rounding. They result in sparse\nschedules, in the sense that each machine shares at most one job with other\nmachines. We also prove lower bounds on the integrality gap of $1+\\varphi$ for\nunrelated speeds ($\\varphi$ is the golden ratio) and $2$ for uniform speeds and\nrestricted assignments. To indicate the generality of our approach, we show\nthat it also yields constant factor approximation algorithms for a variant\nwhere we determine the effective speed of a set of allocated machines based on\nthe $L_p$ norm of their speeds.\n', 'EPTAS for load balancing problem on parallel machines with a\n  non-renewable resource   The problem considered is the non-preemptive scheduling of independent jobs\nthat consume a resource (which is non-renewable and replenished regularly) on\nparallel uniformly related machines. The input defines the speed of machines,\nsize of jobs, the quantity of resource required by the jobs, the replenished\nquantities, and replenishment dates of the resource. Every job can start\nprocessing only after the required quantity of the resource is allocated to the\njob. The objective function is the minimization of the convex combination of\nthe makespan and an objective that is equivalent to the $l_p$-norm of the\nvector of loads of the machines. We present an EPTAS for this problem. Prior to\nour work only a PTAS was known in this non-renewable resource settings and this\nPTAS was only for the special case of our problem of makespan minimization on\nidentical machines.\n', 'Approximate and Robust Bounded Job Start Scheduling for Royal Mail\n  Delivery Offices   Motivated by mail delivery scheduling problems arising in Royal Mail, we\nstudy a generalization of the fundamental makespan scheduling P||Cmax problem\nwhich we call the bounded job start scheduling problem. Given a set of jobs,\neach specified by an integer processing time p_j, that have to be executed\nnon-preemptively by a set of m parallel identical machines, the objective is to\ncompute a minimum makespan schedule subject to an upper bound g<=m on the\nnumber of jobs that may simultaneously begin per unit of time. With perfect\ninput knowledge, we show that Longest Processing Time First (LPT) algorithm is\ntightly 2-approximate. After proving that the problem is strongly NP-hard even\nwhen g=1, we elaborate on improving the 2-approximation ratio for this case. We\ndistinguish the classes of long and short instances satisfying p_j>=m and\np_j<m, respectively, for each job j. We show that LPT is 5/3-approximate for\nthe former and optimal for the latter. Then, we explore scheduling long jobs in\nparallel with short jobs to obtain tightly satisfied packing and bounded job\nstart constraints. For a broad family of instances excluding degenerate\ninstances with many very long jobs, we derive a 1.985-approximation ratio. For\ngeneral instances, we require machine augmentation to obtain better than\n2-approximate schedules. Under uncertain job processing times, we exploit\nmachine augmentation and lexicographic optimization to propose a two-stage\nrobust optimization approach for bounded job start scheduling under uncertainty\naiming in a low number of used machines. Given a collection of schedules of\nmakespan <= D, this approach allows distinguishing which are the more robust.\nWe substantiate both the heuristics and our recovery approach numerically using\nRoyal Mail data. We show that, for the Royal Mail application, machine\naugmentation, i.e. short-term van rental, is especially relevant.\n']","[('machine scheduling', 0.6550276279449463), ('scheduling problems', 0.6176431179046631), ('scheduling', 0.5955268144607544), ('job scheduling', 0.5720775723457336), ('scheduling non', 0.5332529544830322), ('parallel machines', 0.5080031752586365), ('integer linear programming', 0.43542277812957764), ('linear programming', 0.3986499607563019), ('batch processing', 0.38202667236328125), ('schedules', 0.38081514835357666)]"
549,549,56,549_pezzo surfaces_del pezzo surfaces_pezzo surfaces degree_pezzo surface,"['pezzo surfaces', 'del pezzo surfaces', 'pezzo surfaces degree', 'pezzo surface', 'pezzo surface degree', 'del pezzo surface', 'bielliptic surfaces', 'rational surfaces', 'automorphism groups', 'surfaces characteristic']","['Automorphisms of del Pezzo surfaces in odd characteristic   We complete the classification of automorphism groups of del Pezzo surfaces\nover algebraically closed fields of odd positive characteristic.\n', 'Automorphisms of del Pezzo surfaces of degree 2 in characteristic 2   We find normal forms for del Pezzo surfaces of degree $2$ over algebraically\nclosed fields of characteristic $2$. For each normal form, we describe the\nstructure of the group of automorphisms of the surface. In particular, we\nclassify all finite groups that can act on such del Pezzo surfaces.\n', 'Automorphisms of del Pezzo surfaces in characteristic 2   We classify the automorphism groups of del Pezzo surfaces of degrees one and\ntwo over an algebraically closed field of characteristic two. This finishes the\nclassification of automorphism groups of del Pezzo surfaces in all\ncharacteristics.\n']","[('pezzo surfaces', 0.6984140276908875), ('del pezzo surfaces', 0.6948989629745483), ('pezzo surfaces degree', 0.6860026121139526), ('pezzo surface', 0.6337850093841553), ('pezzo surface degree', 0.6313581466674805), ('del pezzo surface', 0.6245940327644348), ('bielliptic surfaces', 0.5792259573936462), ('rational surfaces', 0.5593390464782715), ('automorphism groups', 0.5354884266853333), ('surfaces characteristic', 0.5199748277664185)]"
550,550,56,550_arrangements hyperplanes_hyperplane arrangements_free arrangements_arrangements associated,"['arrangements hyperplanes', 'hyperplane arrangements', 'free arrangements', 'arrangements associated', 'hyperplane arrangement', 'coxeter arrangements', 'arrangements', 'arrangement mathcal', 'arrangements article', 'arrangements let']","[""Vertex-weighted Digraphs and Freeness of Arrangements Between Shi and\n  Ish   We introduce and study a digraph analogue of Stanley's $\\psi$-graphical\narrangements from the perspectives of combinatorics and freeness. Our\narrangements form a common generalization of various classes of arrangements in\nliterature including the Catalan arrangement, the Shi arrangement, the Ish\narrangement, and especially the arrangements interpolating between Shi and Ish\nrecently introduced by Duarte and Guedes de Oliveira. The arrangements between\nShi and Ish all are proved to have the same characteristic polynomial with all\ninteger roots, thus raising the natural question of their freeness. We define\ntwo operations on digraphs, which we shall call king and coking elimination\noperations and prove that subject to certain conditions on the weight $\\psi$,\nthe operations preserve the characteristic polynomials and freeness of the\nassociated arrangements. As an application, we affirmatively prove that the\narrangements between Shi and Ish all are free, and among them only the Ish\narrangement has supersolvable cone.\n"", 'Freeness for restriction arrangements of the extended Shi and Catalan\n  arrangements   The extended Shi and Catalan arrangements are well investigated arrangements.\nIn this paper, we prove that the cone of the extended Catalan arrangement of\ntype A is always hereditarily free, while we determine the dimension in which\nthe cone of the extended Shi arrangement of type A is hereditarily free. For\nthis purpose, using digraphs, we define a class of arrangements which is closed\nunder restriction, and which contains the extended Shi and Catalan\narrangements. We also characterize the freeness for the cone of this\narrangement by graphical conditions.\n', ""Free arrangements with low exponents   In this article we show that any free hyperplane arrangement with exponents\n1's and 2's is a supersolvable arrangement. We conjecture that any free\narrangement with exponents 1's, 2's and exactly one 3, is also supersolvable,\nand we show this conjecture for hyperplane arrangements of ranks 4 and 5, and\nfor inductively free arrangements of any rank.\n""]","[('arrangements hyperplanes', 0.6828402876853943), ('hyperplane arrangements', 0.6568528413772583), ('free arrangements', 0.6080275177955627), ('arrangements associated', 0.6007117033004761), ('hyperplane arrangement', 0.5645509958267212), ('coxeter arrangements', 0.5416799783706665), ('arrangements', 0.5397939682006836), ('arrangement mathcal', 0.500292956829071), ('arrangements article', 0.4943998456001282), ('arrangements let', 0.4793594777584076)]"
551,551,56,551_mahler measures_mahler measure_measure polynomials_measure polynomial,"['mahler measures', 'mahler measure', 'measure polynomials', 'measure polynomial', 'measure algebraic', 'mahler', 'polynomials dynamical', 'corresponding elliptic', 'measures', 'laurent polynomials']","['An invariant property of Mahler measure   We exhibit a change of variables that maintains the Mahler measure of a given\npolynomial. This method leads to the construction of highly non-trivial\npolynomials with given Mahler measure and settles some conjectural numerical\nformulas due to Boyd and Brunault.\n', ""Generalized Mahler measures of Laurent polynomials   Following the work of Lal\\'in and Mittal on the Mahler measure over arbitrary\ntori, we investigate the definition of the generalized Mahler measure for all\nLaurent polynomials in two variables when they do not vanish on the integration\ntorus. We establish certain relations between the standard Mahler measure and\nthe generalized Mahler measure of such polynomials. Later we focus our\ninvestigation on a tempered family of polynomials originally studied by Boyd,\nnamely $Q_{r}(x, y) = x + \\frac{1}{x} + y + \\frac{1}{y} + r$ with $r \\in\n\\mathbb{C},$ and apply our results to this family. For the $r = 4$ case, we\nexplicitly calculate the generalized Mahler measure of $Q_4$ over any arbitrary\ntorus in terms of special values of the Bloch-Wigner dilogarithm. Finally, we\nextend our results to the several variable setting.\n"", 'Random walks through the areal Mahler measure: steps in the complex\n  plane   We study the areal Mahler measure of the two-variable, $k$-parameter family\n$x+y+k$ and prove explicit formulas that demonstrate its relation to the\nstandard Mahler measure of these polynomials. The proofs involve interpreting\nthe areal Mahler measure as a random walk in the complex plane and utilizing\nthe areal analogue of the Zeta Mahler function to arrive at the result. Using\nsimilar techniques, we also present formulas for a three-variable family\n$(x+1)(y+1)+kz$ in terms of the standard Mahler measure, along with terms that\ninvolve certain hypergeometric functions. For both families we show that its\nareal Mahler measure is, up to elementary functions, a linear combination of\nthe normal Mahler measure and the volume of the Deninger cycle of the\ncorresponding family.\n']","[('mahler measures', 0.7021769285202026), ('mahler measure', 0.6924634575843811), ('measure polynomials', 0.5804685950279236), ('measure polynomial', 0.5797693729400635), ('measure algebraic', 0.5076744556427002), ('mahler', 0.4778021275997162), ('polynomials dynamical', 0.4264625608921051), ('corresponding elliptic', 0.39934787154197693), ('measures', 0.35850003361701965), ('laurent polynomials', 0.35153627395629883)]"
552,552,55,552_particle swarm optimization_swarm optimization pso_particle swarm_swarm optimization,"['particle swarm optimization', 'swarm optimization pso', 'particle swarm', 'swarm optimization', 'optimization pso', 'evolutionary optimization', 'swarm intelligence', 'metaheuristic optimization', 'evolutionary algorithms', 'optimization algorithms']","['On enhancing efficiency and accuracy of particle swarm optimization\n  algorithms   The particle swarm optimization (PSO) algorithm has been recently introduced\nin the non--linear programming, becoming widely studied and used in a variety\nof applications. Starting from its original formulation, many variants for\nimprovement and specialization of the PSO have been already proposed, but\nwithout any definitive result, thus research in this area is nowadays still\nrather active. This paper goes in this direction, by proposing some\nmodifications to the basic PSO algorithm, aiming at enhancements in aspects\nthat impact on the efficiency and accuracy of the optimization algorithm. In\nparticular, variants of PSO based on fuzzy logics and Bayesian theory have been\ndeveloped, which show better, or competitive, performances when compared to\nboth the basic PSO formulation and a few other optimization algorithms taken\nfrom the literature.\n', 'Underdamped Particle Swarm Optimization   This article presents Underdamped Particle Swarm Optimization (UEPS), a novel\nmetaheuristic inspired by both the Particle Swarm Optimization (PSO) algorithm\nand the dynamic behavior of an underdamped system. The underdamped motion acts\nas an intermediate solution between undamped systems, which oscillate\nindefinitely, and overdamped systems, which stabilize without oscillation. In\nthe context of optimization, this type of motion allows particles to explore\nthe search space dynamically, alternating between exploration and exploitation,\nwith the ability to overshoot the optimal solution to explore new regions and\navoid getting trapped in local optima.\n  First, we review the concept of damped vibrations, an essential physical\nprinciple that describes how a system oscillates while losing energy over time,\nbehaving in an underdamped, overdamped, or critically damped manner. This\nunderstanding forms the foundation for applying these concepts to optimization,\nensuring a balanced management of exploration and exploitation. Furthermore,\nthe classical PSO algorithm is discussed, highlighting its fundamental features\nand limitations, providing the necessary context to understand how the\nunderdamped behavior improves PSO performance.\n  The proposed metaheuristic is evaluated using benchmark functions and classic\nengineering problems, demonstrating its high robustness and efficiency.\n', ""A Study of the Fundamental Parameters of Particle Swarm Optimizers   The range of applications of traditional optimization methods are limited by\nthe features of the object variables, and of both the objective and the\nconstraint functions. In contrast, population-based algorithms whose\noptimization capabilities are emergent properties, such as evolutionary\nalgorithms and particle swarm optimization, present almost no restriction on\nthose features and can handle different optimization problems with few or no\nadaptations. Their main drawbacks consist of their comparatively higher\ncomputational cost and difficulty in handling equality constraints. The\nparticle swarm optimization method is sometimes viewed as an evolutionary\nalgorithm because of their many similarities, despite not being inspired by the\nsame metaphor: they evolve a population of individuals taking into account\nprevious experiences and using stochastic operators to introduce new responses.\nThe advantages of evolutionary algorithms with respect to traditional methods\nhave been greatly discussed in the literature for decades. While the particle\nswarm optimizers share such advantages, their main desirable features when\ncompared to evolutionary algorithms are their lower computational cost and\neasier implementation, involving no operator design and few parameters to be\ntuned. However, even slight modifications of these parameters greatly influence\nthe dynamics of the swarm. This paper deals with the effect of the settings of\nthe parameters of the particles' velocity update equation on the behaviour of\nthe system.\n""]","[('particle swarm optimization', 0.821598470211029), ('swarm optimization pso', 0.747171938419342), ('particle swarm', 0.6957452297210693), ('swarm optimization', 0.6698147058486938), ('optimization pso', 0.6438214778900146), ('evolutionary optimization', 0.5541428327560425), ('swarm intelligence', 0.551301121711731), ('metaheuristic optimization', 0.5305026769638062), ('evolutionary algorithms', 0.5196970105171204), ('optimization algorithms', 0.5114336013793945)]"
553,553,55,553_invariants manifolds_seifert manifolds_invariants three_homology spheres,"['invariants manifolds', 'seifert manifolds', 'invariants three', 'homology spheres', 'quantum invariants', 'manifolds obtained', 'invariants', 'series invariants', 'three manifolds', 'integer homology']","['BPS Invariants for 3-Manifolds at Rational Level $K$   We consider the Witten-Reshetikhin-Turaev invariants or Chern-Simons\npartition function at or around roots of unity $q=e^{2\\pi i \\frac{1}{K}}$ with\nrational level $K=\\frac{r}{s}$ where $r$ and $s$ are coprime integers. From the\nexact expression for the $G=SU(2)$ Witten-Reshetikhin-Turaev invariants of\nSeifert manifolds at other roots of unity obtained by Lawrence and Rozansky, we\nprovide an expected form of the structure of the Witten-Reshetikhin-Turaev\ninvariants in terms of the homological blocks at other roots of unity. Also, we\ndiscuss the asymptotic expansion of knot invariants around roots of unity where\nwe take a limit different from the standard limit in the volume conjecture.\n', ""Witten-Reshetikhin-Turaev invariants and indefinite false theta\n  functions for plumbing indefinite H-graphs   Gukov--Pei--Putrov--Vafa conjectured the existence of $ q $-series whose\nradial limits are Witten--Reshetikhin--Turaev invariants and called them\nhomological blocks. For weakly negative definite plumbed 3-manifolds,\nGukov--Pei--Putrov--Vafa and Gukov-Manolescu constructed homological blocks. In\nthis paper, we construct indefinite false theta functions which are candidates\nof homological blocks for some plumbed $ 3 $-manifolds which are not weakly\nnegative definite. Moreover we prove that, for the Poincar\\'{e} homology\nsphere, our indefinite false theta function coincides with the original\nhomological block.\n"", 'BPS Invariants for Seifert Manifolds   We calculate the homological blocks for Seifert manifolds from the exact\nexpression for the $G=SU(N)$ Witten-Reshetikhin-Turaev invariants of Seifert\nmanifolds obtained by Lawrence, Rozansky, and Mari\\~no. For the $G=SU(2)$ case,\nit is possible to express them in terms of the false theta functions and their\nderivatives. For $G=SU(N)$, we calculate them as a series expansion and also\ndiscuss some properties of the contributions from the abelian flat connections\nto the Witten-Reshetikhin-Turaev invariants for general $N$. We also provide an\nexpected form of the $S$-matrix for general cases and the structure of the\nWitten-Reshetikhin-Turaev invariants in terms of the homological blocks.\n']","[('invariants manifolds', 0.5557800531387329), ('seifert manifolds', 0.5485147833824158), ('invariants three', 0.5234701633453369), ('homology spheres', 0.48964932560920715), ('quantum invariants', 0.4831371605396271), ('manifolds obtained', 0.48175930976867676), ('invariants', 0.4710147976875305), ('series invariants', 0.4619229733943939), ('three manifolds', 0.45480138063430786), ('integer homology', 0.44779014587402344)]"
554,554,55,554_boolean network_boolean networks_networks finite_control networks,"['boolean network', 'boolean networks', 'networks finite', 'control networks', 'boolean functions', 'network finite', 'network models', 'network structure', 'monotone boolean', 'boolean']","['Stability of Linear Boolean Networks   Stability is an important characteristic of network models that has\nimplications for other desirable aspects such as controllability. The stability\nof a Boolean network depends on various factors, such as the topology of its\nwiring diagram and the type of the functions describing its dynamics. In this\npaper, we study the stability of linear Boolean networks by computing Derrida\ncurves and quantifying the number of attractors and cycle lengths imposed by\ntheir network topologies. Derrida curves are commonly used to measure the\nstability of Boolean networks and several parameters such as the average\nin-degree K and the output bias p can indicate if a network is stable,\ncritical, or unstable. For random unbiased Boolean networks there is a critical\nconnectivity value Kc=2 such that if K<Kc networks operate in the ordered\nregime, and if K>Kc networks operate in the chaotic regime. Here, we show that\nfor linear networks, which are the least canalizing and most unstable, the\nphase transition from order to chaos already happens at an average in-degree of\nKc=1. Consistently, we also show that unstable networks exhibit a large number\nof attractors with very long limit cycles while stable and critical networks\nexhibit fewer attractors with shorter limit cycles. Additionally, we present\ntheoretical results to quantify important dynamical properties of linear\nnetworks. First, we present a formula for the proportion of attractor states in\nlinear systems. Second, we show that the expected number of fixed points in\nlinear systems is 2, while general Boolean networks possess on average one\nfixed point. Third, we present a formula to quantify the number of bijective\nlinear Boolean networks and provide a lower bound for the percentage of this\ntype of network.\n', 'Non-deterministic updates of Boolean networks   Boolean networks are discrete dynamical systems where each automaton has its\nown Boolean function for computing its state according to the configuration of\nthe network. The updating mode then determines how the configuration of the\nnetwork evolves over time. Many of updating modes from the literature,\nincluding synchronous and asynchronous modes, can be defined as the composition\nof elementary deterministic configuration updates, i.e., by functions mapping\nconfigurations of the network. Nevertheless, alternative dynamics have been\nintroduced using ad-hoc auxiliary objects, such as that resulting from binary\nprojections of Memory Boolean networks, or that resulting from additional\npseudo-states for Most Permissive Boolean networks. One may wonder whether\nthese latter dynamics can still be classified as updating modes of finite\nBoolean networks, or belong to a different class of dynamical systems. In this\npaper, we study the extension of updating modes to the composition of\nnon-deterministic updates, i.e., mapping sets of finite configurations. We show\nthat the above dynamics can be expressed in this framework, enabling a better\nunderstanding of them as updating modes of Boolean networks. More generally, we\nargue that non-deterministic updates pave the way to a unifying framework for\nexpressing complex updating modes, some of them enabling transitions that\ncannot be computed with elementary and non-elementary deterministic updates.\n', 'Modular Construction of Boolean Networks   Boolean networks have been used in a variety of settings, as models for\ngeneral complex systems as well as models of specific systems in diverse\nfields, such as biology, engineering, and computer science. Traditionally,\ntheir properties as dynamical systems have been studied through simulation\nstudies, due to a lack of mathematical structure. This paper uses a common\nmathematical technique to identify a class of Boolean networks with a ""simple""\nstructure and describes an algorithm to construct arbitrary extensions of a\ncollection of simple Boolean networks. In this way, all Boolean networks can be\nobtained from a collection of simple Boolean networks as building blocks. The\npaper furthermore provides a formula for the number of extensions of given\nsimple networks and, in some cases, provides a parametrization of those\nextensions. This has potential applications to the construction of networks\nwith particular properties, for instance in synthetic biology, and can also be\napplied to develop efficient control algorithms for Boolean network models.\n']","[('boolean network', 0.7214975953102112), ('boolean networks', 0.6995376944541931), ('networks finite', 0.5776644945144653), ('control networks', 0.5206179022789001), ('boolean functions', 0.5199163556098938), ('network finite', 0.49974173307418823), ('network models', 0.4717377722263336), ('network structure', 0.471189022064209), ('monotone boolean', 0.45400115847587585), ('boolean', 0.45288169384002686)]"
555,555,55,555_volterra integral equations_volterra integral_solving volterra_volterra equations,"['volterra integral equations', 'volterra integral', 'solving volterra', 'volterra equations', 'fredholm integral equations', 'volterra integro differential', 'singular integral equations', 'integral equations first', 'integral equations', 'integro differential equations']","['A sparse spectral method for Volterra integral equations using\n  orthogonal polynomials on the triangle   We introduce and analyse a sparse spectral method for the solution of\nVolterra integral equations using bivariate orthogonal polynomials on a\ntriangle domain. The sparsity of the Volterra operator on a weighted Jacobi\nbasis is used to achieve high efficiency and exponential convergence. The\ndiscussion is followed by a demonstration of the method on example Volterra\nintegral equations of the first and second kind with known analytic solutions\nas well as an application-oriented numerical experiment. We prove convergence\nfor both first and second kind problems, where the former builds on connections\nwith Toeplitz operators.\n', ""Relation between two Sinc-collocation methods for Volterra integral equations of the second kind and further improvement Two different Sinc-collocation methods for Volterra integral equations of the second kind have been independently proposed by Stenger and Rashidinia--Zarebnia. However, their relation remains unexplored. This study theoretically examines the solutions of these two methods, and reveals that they are not generally equivalent, despite coinciding at the collocation points. Strictly speaking, Stenger's method assumes that the kernel of the integral is a function of a single variable, but this study theoretically justifies the use of his method in general cases, i.e., the kernel is a function of two variables. Then, this study rigorously proves that both methods can attain the same, root-exponential convergence. In addition to the contribution, this study improves Stenger's method to attain significantly higher, almost exponential convergence. Numerical examples supporting the theoretical results are also provided."", ""Numerical solution of locally loaded Volterra integral equations   Volterra's integral equations with local and nonlocal loads represent the\nnovel class of integral equations that have attracted considerable attention in\nrecent years. These equations are a generalisation of the classic Volterra\nintegral equations, which were first introduced by Vito Volterra in the late\n19th century. The loaded Volterra integral equations are characterised by the\npresence of a load which complicates the process of their theoretical and\nnumerical study. Sometimes these equation are called the equations with\n``frozen'' argument. The present work is devoted to the study of Volterra\nequations with locally loaded integral operators. The existence and uniquness\ntheorems are proved. Among the main contributions is the collocation method for\napproximate solution of such equations based on the piecewise linear\napproximation. To confirm the convergence of the method, a number of numerical\nresults for solving model problems are provided.\n""]","[('volterra integral equations', 0.728187620639801), ('volterra integral', 0.6280444860458374), ('solving volterra', 0.5922694802284241), ('volterra equations', 0.5860403180122375), ('fredholm integral equations', 0.5344144701957703), ('volterra integro differential', 0.5234792232513428), ('singular integral equations', 0.520072340965271), ('integral equations first', 0.4759313464164734), ('integral equations', 0.4719547629356384), ('integro differential equations', 0.46335193514823914)]"
556,556,55,556_quantum metric_compact quantum_metric spectral_spectral metric,"['quantum metric', 'compact quantum', 'metric spectral', 'spectral metric', 'quantum groups', 'convergence quantum', 'algebras quantum', 'space quantum', 'spectral triples', 'quantum limits']","['External products of spectral metric spaces   In this paper, we present a characterization of compact quantum metric spaces\nin terms of finite dimensional approximations. This characterization naturally\nleads to the introduction of a matrix analogue of a compact quantum metric\nspace. As an application, we show that matrix compact quantum metric spaces are\nstable under minimal tensor products and more specifically that matrix spectral\nmetric spaces are stable under the external product operation on unital\nspectral triples. We present several noncommutative examples of matrix compact\nquantum metric spaces.\n', 'Inductive limits of compact quantum metric spaces   A compact quantum metric space is a unital $C^*$-algebra equipped with a\nLip-norm. Let $\\{(A_n, L_n)\\}$ be a sequence of compact quantum metric spaces,\nand let $\\phi_n:A_n\\to A_{n+1}$ be a unital $^*$-homomorphism preserving\nLipschitz elements for $n\\geq 1$. We show that there exists a compact quantum\nmetric space structure on the inductive limit $\\varinjlim(A_n,\\phi_n)$ by means\nof the inverse limit of the state spaces $\\{\\mathcal{S}(A_n)\\}$. We also give\nsome sufficient conditions that two inductive limits of compact quantum metric\nspaces are Lipschitz isomorphic.\n', ""Dynamics of compact quantum metric spaces   We provide a detailed study of actions of the integers on compact quantum\nmetric spaces, which includes general criteria ensuring that the associated\ncrossed product algebra is again a compact quantum metric space in a natural\nway. We moreover provide a flexible set of assumptions ensuring that a\ncontinuous family of *-automorphisms of a compact quantum metric space, yields\na field of crossed product algebras which varies continuously in Rieffel's\nquantum Gromov-Hausdorff distance. Lastly we show how our results apply to\ncontinuous families of Lip-isometric actions on compact quantum metric spaces\nand to families of diffeomorphisms of compact Riemannian manifolds which vary\ncontinuously in the Whitney C^1-topology.\n""]","[('quantum metric', 0.6420822143554688), ('compact quantum', 0.6407660841941833), ('metric spectral', 0.5221912860870361), ('spectral metric', 0.5211588144302368), ('quantum groups', 0.49257588386535645), ('convergence quantum', 0.48332858085632324), ('algebras quantum', 0.4693385064601898), ('space quantum', 0.4656340479850769), ('spectral triples', 0.4516122341156006), ('quantum limits', 0.4487766623497009)]"
557,557,55,557_polynomial lattice rules_lattice rules_lattice rule_lattice based,"['polynomial lattice rules', 'lattice rules', 'lattice rule', 'lattice based', 'polynomial lattice', 'rank lattices', 'lattice', 'rank lattice', 'lattice point sets', 'randomized algorithms']","['The analysis of vertex modified lattice rules in a non-periodic Sobolev\n  space   In a series of papers, in 1993, 1994 & 1996, Sloan & Niederreiter introduced\na modification of lattice rules for non-periodic functions, called ""vertex\nmodified lattice rules""\', and a particular breed called ""optimal vertex\nmodified lattice rules"". In the 1994 paper, Niederreiter & Sloan concentrate\nexplicitly on Fibonacci lattice rules, which are a particular good choice of\n2-dimensional lattice rules. Error bounds in this series of papers were given\nrelated to the star discrepancy.\n  In this paper we pose the problem in terms of the so-called unanchored\nSobolev space, which is a reproducing kernel Hilbert space often studied\nnowadays in which functions have $L_2$-integrable mixed first derivatives. It\nis known constructively that randomly shifted lattice rules, as well as\ndeterministic tent-transformed lattice rules and deterministic fully\nsymmetrized lattice rules can achieve close to $O(N^{-1})$ convergence in this\nspace, see Sloan, Kuo & Joe (2002) and Dick, Nuyens & Pillichshammer (2014)\nrespectively.\n  We derive a break down of the worst-case error of vertex modified lattice\nrules in the unanchored Sobolev space in terms of the worst-case error in a\nKorobov space, a multilinear space and some additional ""mixture term"". For the\n1-dimensional case this worst-case error is obvious and gives an explicit\nexpression for the trapezoidal rule. In the 2-dimensional case this mixture\nterm also takes on an explicit form for which we derive upper and lower bounds.\nFor this case we prove that there exist lattice rules with a nice worst-case\nerror bound with the additional mixture term of the form $N^{-1} \\log^2(N)$.\n', 'Construction-free median quasi-Monte Carlo rules for function spaces\n  with unspecified smoothness and general weights   We study quasi-Monte Carlo (QMC) integration of smooth functions defined over\nthe multi-dimensional unit cube. Inspired by a recent work of Pan and Owen, we\nstudy a new construction-free median QMC rule which can exploit the smoothness\nand the weights of function spaces adaptively. For weighted Korobov spaces, we\ndraw a sample of $r$ independent generating vectors of rank-1 lattice rules,\ncompute the integral estimate for each, and approximate the true integral by\nthe median of these $r$ estimates. For weighted Sobolev spaces, we use the same\napproach but with the rank-1 lattice rules replaced by high-order polynomial\nlattice rules. A major advantage over the existing approaches is that we do not\nneed to construct good generating vectors by a computer search algorithm, while\nour median QMC rule achieves almost the optimal worst-case error rate for the\nrespective function space with any smoothness and weights, with a probability\nthat converges to 1 exponentially fast as $r$ increases. Numerical experiments\nillustrate and support our theoretical findings.\n', 'Stability of lattice rules and polynomial lattice rules constructed by\n  the component-by-component algorithm   We study quasi-Monte Carlo (QMC) methods for numerical integration of\nmultivariate functions defined over the high-dimensional unit cube. Lattice\nrules and polynomial lattice rules, which are special classes of QMC methods,\nhave been intensively studied and the so-called component-by-component (CBC)\nalgorithm has been well-established to construct rules which achieve the almost\noptimal rate of convergence with good tractability properties for given\nsmoothness and set of weights. Since the CBC algorithm constructs rules for\ngiven smoothness and weights, not much is known when such rules are used for\nfunction classes with different smoothness and/or weights.\n  In this paper we prove that a lattice rule constructed by the CBC algorithm\nfor the weighted Korobov space with given smoothness and weights achieves the\nalmost optimal rate of convergence with good tractability properties for\ngeneral classes of smoothness and weights which satisfy some summability\nconditions. Such a stability result also can be shown for polynomial lattice\nrules in weighted Walsh spaces. We further give bounds on the weighted star\ndiscrepancy and discuss the tractability properties for these QMC rules. The\nresults are comparable to those obtained for Halton, Sobol and Niederreiter\nsequences.\n']","[('polynomial lattice rules', 0.5674009919166565), ('lattice rules', 0.5508448481559753), ('lattice rule', 0.5407083034515381), ('lattice based', 0.47958654165267944), ('polynomial lattice', 0.4355095326900482), ('rank lattices', 0.4335857927799225), ('lattice', 0.42821910977363586), ('rank lattice', 0.4151711165904999), ('lattice point sets', 0.3885737657546997), ('randomized algorithms', 0.3856908679008484)]"
558,558,55,558_millimeter wave_beam training_wave mmwave terahertz_beam training overhead,"['millimeter wave', 'beam training', 'wave mmwave terahertz', 'beam training overhead', 'mmwave terahertz', 'mmwave communications', 'millimeter wave mmwave', 'mmwave terahertz thz', 'mmwave communication', 'terahertz communication']","['Radar Aided 6G Beam Prediction: Deep Learning Algorithms and Real-World\n  Demonstration   This paper presents the first machine learning based real-world demonstration\nfor radar-aided beam prediction in a practical vehicular communication\nscenario. Leveraging radar sensory data at the communication terminals provides\nimportant awareness about the transmitter/receiver locations and the\nsurrounding environment. This awareness could be utilized to reduce or even\neliminate the beam training overhead in millimeter wave (mmWave) and\nsub-terahertz (THz) MIMO communication systems, which enables a wide range of\nhighly-mobile low-latency applications. In this paper, we develop deep learning\nbased radar-aided beam prediction approaches for mmWave/sub-THz systems. The\ndeveloped solutions leverage domain knowledge for radar signal processing to\nextract the relevant features fed to the learning models. This optimizes their\nperformance, complexity, and inference time. The proposed radar-aided beam\nprediction solutions are evaluated using the large-scale real-world dataset\nDeepSense 6G, which comprises co-existing mmWave beam training and radar\nmeasurements. In addition to completely eliminating the radar/communication\ncalibration overhead, the experimental results showed that the proposed\nalgorithms are able to achieve around $90\\%$ top-5 beam prediction accuracy\nwhile saving $93\\%$ of the beam training overhead. This highlights a promising\ndirection for addressing the beam management overhead challenges in mmWave/THz\ncommunication systems.\n', 'LiDAR Aided Future Beam Prediction in Real-World Millimeter Wave V2I\n  Communications   This paper presents the first large-scale real-world evaluation for using\nLiDAR data to guide the mmWave beam prediction task. A machine learning (ML)\nmodel that leverages the LiDAR sensory data to predict the current and future\nbeams was developed. Based on the large-scale real-world dataset, DeepSense 6G,\nthis model was evaluated in a vehicle-to-infrastructure communication scenario\nwith highly-mobile vehicles. The experimental results show that the developed\nLiDAR-aided beam prediction and tracking model can predict the optimal beam in\n$95\\%$ of the cases and with more than $90\\%$ reduction in the beam training\noverhead. The LiDAR-aided beam tracking achieves comparable accuracy\nperformance to a baseline solution that has perfect knowledge of the previous\noptimal beams, without requiring any knowledge about the previous optimal beam\ninformation and without any need for beam calibration. This highlights a\npromising solution for the critical beam alignment challenges in mmWave and\nterahertz communication systems.\n', 'Computer Vision Aided Beam Tracking in A Real-World Millimeter Wave\n  Deployment   Millimeter-wave (mmWave) and terahertz (THz) communications require\nbeamforming to acquire adequate receive signal-to-noise ratio (SNR). To find\nthe optimal beam, current beam management solutions perform beam training over\na large number of beams in pre-defined codebooks. The beam training overhead\nincreases the access latency and can become infeasible for high-mobility\napplications. To reduce or even eliminate this beam training overhead, we\npropose to utilize the visual data, captured for example by cameras at the base\nstations, to guide the beam tracking/refining process. We propose a machine\nlearning (ML) framework, based on an encoder-decoder architecture, that can\npredict the future beams using the previously obtained visual sensing\ninformation. Our proposed approach is evaluated on a large-scale real-world\ndataset, where it achieves an accuracy of $64.47\\%$ (and a normalized receive\npower of $97.66\\%$) in predicting the future beam. This is achieved while\nrequiring less than $1\\%$ of the beam training overhead of a corresponding\nbaseline solution that uses a sequence of previous beams to predict the future\none. This high performance and low overhead obtained on the real-world dataset\ndemonstrate the potential of the proposed vision-aided beam tracking approach\nin real-world applications.\n']","[('millimeter wave', 0.4696437120437622), ('beam training', 0.43816253542900085), ('wave mmwave terahertz', 0.43346068263053894), ('beam training overhead', 0.431839257478714), ('mmwave terahertz', 0.42110270261764526), ('mmwave communications', 0.4063487648963928), ('millimeter wave mmwave', 0.40585818886756897), ('mmwave terahertz thz', 0.3938080668449402), ('mmwave communication', 0.38885363936424255), ('terahertz communication', 0.38171449303627014)]"
559,559,55,559_5g nr_5g_sensing 6g_positioning accuracy,"['5g nr', '5g', 'sensing 6g', 'positioning accuracy', 'indoor localization', '5g mmwave', 'localization accuracy', 'localization sensing', 'cellular network', 'mmwave communication']","['Angle-based SLAM on 5G mmWave Systems: Design, Implementation, and\n  Measurement   Simultaneous localization and mapping (SLAM) is a key technology that\nprovides user equipment (UE) tracking and environment mapping services,\nenabling the deep integration of sensing and communication. The millimeter-wave\n(mmWave) communication, with its larger bandwidths and antenna arrays,\ninherently facilitates more accurate delay and angle measurements than sub-6\nGHz communication, thereby providing opportunities for SLAM. However, none of\nthe existing works have realized the SLAM function under the 5G New Radio (NR)\nstandard due to specification and hardware constraints. In this study, we\ninvestigate how 5G mmWave communication systems can achieve situational\nawareness without changing the transceiver architecture and 5G NR standard. We\nimplement 28 GHz mmWave transceivers that deploy OFDM-based 5G NR waveform with\n160 MHz channel bandwidth, and we realize beam management following the 5G NR.\nFurthermore, we develop an efficient successive cancellation-based angle\nextraction approach to obtain angles of arrival and departure from the\nreference signal received power measurements. On the basis of angle\nmeasurements, we propose an angle-only SLAM algorithm to track UE and map\nfeatures in the radio environment. Thorough experiments and ray tracing-based\ncomputer simulations verify that the proposed angle-based SLAM can achieve\nsub-meter level localization and mapping accuracy with a single base station\nand without the requirement of strict time synchronization. Our experiments\nalso reveal many propagation properties critical to the success of SLAM in 5G\nmmWave communication systems.\n', '5G NR Positioning Enhancements in 3GPP Release-18   New radio (NR) positioning in the Third Generation Partnership Project (3GPP)\nRelease 18 (Rel-18) enables 5G-advanced networks to achieve ultra-high accuracy\npositioning without dependence on global navigation satellite systems (GNSS)\nwith key enablers such as the carrier phase positioning technique, standardized\nfor the first time in a cellular communications standard and setting a new\nbaseline for future generations. In addition, Rel-18 NR supports positioning\nfunctionalities for reduced capability (RedCap) user equipment and bandwidth\naggregation for positioning measurements. Moreover, the low power solutions are\ndesigned for low power high accuracy positioning use cases. Lastly,\nsidelink-based positioning is introduced in Rel-18. This article constitutes a\ncomprehensive treatment of the Rel-18 NR positioning enhancements crucial for\nthe development of next-generation networks.\n', ""Dynamic Selective Positioning for High-Precision Accuracy in 5G NR V2X\n  Networks   The capability to achieve high-precision positioning accuracy has been\nconsidered as one of the most critical requirements for vehicle-to-everything\n(V2X) services in the fifth-generation (5G) cellular networks. The\nnon-line-of-sight (NLOS) connectivity, coverage, reliability requirements, the\nminimum number of available anchors, and bandwidth limitations are among the\nmain challenges to achieve high accuracy in V2X services. This work provides an\noverview of the potential solutions to provide the new radio (NR) V2X users\n(UEs) with high positioning accuracy in the future 3GPP releases. In\nparticular, we propose a novel selective positioning solution to dynamically\nswitch between different positioning technologies to improve the overall\npositioning accuracy in NR V2X services, taking into account the locations of\nV2X UEs and the accuracy of the collected measurements. Furthermore, we use\nhigh-fidelity system-level simulations to evaluate the performance gains of\nfusing the positioning measurements from different technologies in NR V2X\nservices. Our numerical results show that the proposed hybridized schemes\nachieve a positioning error $\\boldsymbol{\\leq}$ 3 m with $\\boldsymbol{\\approx}$\n76\\% availability compared to $\\boldsymbol{\\approx}$ 55\\% availability when\ntraditional positioning methods are used. The numerical results also reveal a\npotential gain of $\\boldsymbol{\\approx}$ 56\\% after leveraging the road-side\nunits (RSUs) to improve the tail of the UE's positioning error distribution,\ni.e., worst-case scenarios, in NR V2X services.\n""]","[('5g nr', 0.537726640701294), ('5g', 0.4851677417755127), ('sensing 6g', 0.4771285951137543), ('positioning accuracy', 0.47452059388160706), ('indoor localization', 0.4533942937850952), ('5g mmwave', 0.44704243540763855), ('localization accuracy', 0.4158201813697815), ('localization sensing', 0.41502076387405396), ('cellular network', 0.4006536304950714), ('mmwave communication', 0.35750389099121094)]"
560,560,55,560_porous medium equations_solutions porous medium_porous medium type_solutions porous,"['porous medium equations', 'solutions porous medium', 'porous medium type', 'solutions porous', 'equations porous', 'weak solutions', 'existence weak solutions', 'boundary solutions', 'nonnegative weak solutions', 'medium type equations']","['Regularity theory for fully nonlinear equations of porous medium-type   In this paper, we establish the regularity results for nonnegative viscosity\nsolutions to fully nonlinear equations of porous medium-type in bounded domains\nwith the zero Dirichlet boundary condition, to be precise, we prove the global\n$C^{2,\\alpha}$-estimates of viscosity solutions. In many PDE problems, the\n$C^{2,\\alpha}$-estimates have been obtained through Schauder-type estimates.\nHowever, the Schauder-type estimates are not applicable to the porous\nmedium-type equations. We provide techniques for handling porous medium-type\nequations so that the global $C^{2,\\alpha}$-estimates can be established.\n', 'Higher integrability in the obstacle problem for the fast diffusion\n  equation   We prove local higher integrability of the spatial gradient for solutions to\nobstacle problems of porous medium type in the fast diffusion case $m<1$. The\nresult holds for the natural range of exponents that is known from other\nregularity results for porous medium type equations. We also cover the case of\nsigned solutions.\n', 'Continuity up to the boundary for obstacle problems to porous medium\n  type equations   We show that signed weak solutions to obstacle problems for porous medium\ntype equations with Cauchy-Dirichlet boundary data are continuous up to the\nparabolic boundary, provided that the obstacle and boundary data are\ncontinuous. This result seems to be new even for signed solutions to the\n(obstacle free) Cauchy-Dirichlet problem to the singular porous medium\nequation, which is retrieved as a special case.\n']","[('porous medium equations', 0.7135329246520996), ('solutions porous medium', 0.6617616415023804), ('porous medium type', 0.5655531287193298), ('solutions porous', 0.5587399005889893), ('equations porous', 0.5571248531341553), ('weak solutions', 0.5431632995605469), ('existence weak solutions', 0.5338497757911682), ('boundary solutions', 0.5326562523841858), ('nonnegative weak solutions', 0.5198605060577393), ('medium type equations', 0.5070761442184448)]"
561,561,55,561_ridge regression_ridge regularization_ridge estimator_prediction risk,"['ridge regression', 'ridge regularization', 'ridge estimator', 'prediction risk', 'generalized cross validation', 'ridge', 'regularization', 'sample prediction', 'random matrix theory', 'regularization parameter']","['Subsample Ridge Ensembles: Equivalences and Generalized Cross-Validation   We study subsampling-based ridge ensembles in the proportional asymptotics\nregime, where the feature size grows proportionally with the sample size such\nthat their ratio converges to a constant. By analyzing the squared prediction\nrisk of ridge ensembles as a function of the explicit penalty $\\lambda$ and the\nlimiting subsample aspect ratio $\\phi_s$ (the ratio of the feature size to the\nsubsample size), we characterize contours in the $(\\lambda, \\phi_s)$-plane at\nany achievable risk. As a consequence, we prove that the risk of the optimal\nfull ridgeless ensemble (fitted on all possible subsamples) matches that of the\noptimal ridge predictor. In addition, we prove strong uniform consistency of\ngeneralized cross-validation (GCV) over the subsample sizes for estimating the\nprediction risk of ridge ensembles. This allows for GCV-based tuning of full\nridgeless ensembles without sample splitting and yields a predictor whose risk\nmatches optimal ridge risk.\n', 'Asymptotically free sketched ridge ensembles: Risks, cross-validation,\n  and tuning   We employ random matrix theory to establish consistency of generalized cross\nvalidation (GCV) for estimating prediction risks of sketched ridge regression\nensembles, enabling efficient and consistent tuning of regularization and\nsketching parameters. Our results hold for a broad class of asymptotically free\nsketches under very mild data assumptions. For squared prediction risk, we\nprovide a decomposition into an unsketched equivalent implicit ridge bias and a\nsketching-based variance, and prove that the risk can be globally optimized by\nonly tuning sketch size in infinite ensembles. For general subquadratic\nprediction risk functionals, we extend GCV to construct consistent risk\nestimators, and thereby obtain distributional convergence of the GCV-corrected\npredictions in Wasserstein-2 metric. This in particular allows construction of\nprediction intervals with asymptotically correct coverage conditional on the\ntraining data. We also propose an ""ensemble trick"" whereby the risk for\nunsketched ridge regression can be efficiently estimated via GCV using small\nsketched ridge ensembles. We empirically validate our theoretical results using\nboth synthetic and real large-scale datasets with practical sketches including\nCountSketch and subsampled randomized discrete cosine transforms.\n', ""The distribution of Ridgeless least squares interpolators   The Ridgeless minimum $\\ell_2$-norm interpolator in overparametrized linear\nregression has attracted considerable attention in recent years. While it seems\nto defy the conventional wisdom that overfitting leads to poor prediction,\nrecent research reveals that its norm minimizing property induces an `implicit\nregularization' that helps prediction in spite of interpolation. This renders\nthe Ridgeless interpolator a theoretically tractable proxy that offers useful\ninsights into the mechanisms of modern machine learning methods.\n  This paper takes a different perspective that aims at understanding the\nprecise stochastic behavior of the Ridgeless interpolator as a statistical\nestimator. Specifically, we characterize the distribution of the Ridgeless\ninterpolator in high dimensions, in terms of a Ridge estimator in an associated\nGaussian sequence model with positive regularization, which plays the role of\nthe prescribed implicit regularization in the context of prediction risk. Our\ndistributional characterizations hold for general random designs and extend\nuniformly to positively regularized Ridge estimators. As a demonstration of the\nanalytic power of these characterizations, we derive approximate formulae for a\ngeneral class of weighted $\\ell_q$ risks for Ridge(less) estimators that were\npreviously available only for $\\ell_2$. Our theory also provides certain\nfurther conceptual reconciliation with the conventional wisdom: given any data\ncovariance, a certain amount of regularization in Ridge regression remains\nbeneficial for `most' signals across various statistical tasks including\nprediction, estimation and inference, as long as the noise level is\nnon-trivial. Surprisingly, optimal tuning can be achieved simultaneously for\nall the designated statistical tasks by a single generalized or $k$-fold\ncross-validation scheme, despite being designed specifically for tuning\nprediction risk.\n""]","[('ridge regression', 0.5725917220115662), ('ridge regularization', 0.5664570331573486), ('ridge estimator', 0.5568039417266846), ('prediction risk', 0.4053715467453003), ('generalized cross validation', 0.4016422629356384), ('ridge', 0.3963067829608917), ('regularization', 0.3800205588340759), ('sample prediction', 0.37578052282333374), ('random matrix theory', 0.3738304674625397), ('regularization parameter', 0.3645648658275604)]"
562,562,55,562_valued convex_valuation theory_convex bodies_finite convex,"['valued convex', 'valuation theory', 'convex bodies', 'finite convex', 'convex functions', 'valuations', 'convex geometry', 'valuation', 'finite valued', 'space valuations']","['Smooth valuations on convex functions   We construct valuations on the space of finite-valued convex functions using\nintegration of differential forms over the differential cycle associated to a\nconvex function. We describe the kernel of this procedure and show that the\nintersection of this space of smooth valuations with the space of all\ncontinuous dually epi-translation invariant valuations on convex functions is\ndense in the latter. As an application, we obtain a description of\n1-homogeneous, continuous, dually epi-translation invariant valuations that are\ninvariant with respect to a compact subgroup operating transitively on the unit\nsphere.\n', 'From valuations on convex bodies to convex functions   A geometric framework relating valuations on convex bodies to valuations on\nconvex functions is introduced. It is shown that a classical result by McMullen\ncan be used to obtain a characterization of continuous, epi-translation\ninvariant, and n-epi-homogeneous valuations on convex functions, which was\npreviously established by Colesanti, Ludwig, and Mussnig. Following an approach\nby Goodey and Weil, a new characterization of 1-epi-homogeneous valuations is\nobtained.\n', 'The support of dually epi-translation invariant valuations on convex\n  functions   We study dually epi-translation invariant valuations on cones of convex\nfunctions containing the space of finite-valued convex functions. The existence\nof a homogeneous decomposition is used to associate a distribution to every\nvaluation of this type similar to the Goodey-Weil embedding for translation\ninvariant valuations on convex bodies. The relation between the valuation and\nits associated distribution is used to establish a notion of support for\nvaluations. As an application, we show that there are no $\\mathrm{SL}(n)$ or\ntranslation invariant valuations except constant valuations in this class and\nwe discuss which valuations on finite-valued convex functions can be extended\nto larger cones. In addition, we examine some topological properties of spaces\nof valuations with compact support.\n']","[('valued convex', 0.5761333107948303), ('valuation theory', 0.5334601998329163), ('convex bodies', 0.5064535140991211), ('finite convex', 0.4982152581214905), ('convex functions', 0.4798067510128021), ('valuations', 0.46919432282447815), ('convex geometry', 0.46209731698036194), ('valuation', 0.4608435332775116), ('finite valued', 0.4474365711212158), ('space valuations', 0.42639774084091187)]"
563,563,55,563_steiner trees_steiner tree_minimum spanning tree_spanning trees,"['steiner trees', 'steiner tree', 'minimum spanning tree', 'spanning trees', 'spanning tree', 'steiner', 'minimum spanning', 'weighted tree', 'adjacency', 'shortest paths']","['The Central Spanning Tree Problem   Spanning trees are an important primitive in many data analysis tasks, when a\ndata set needs to be summarized in terms of its ""skeleton"", or when a\ntree-shaped graph over all observations is required for downstream processing.\nPopular definitions of spanning trees include the minimum spanning tree and the\noptimum distance spanning tree, a.k.a. the minimum routing cost tree. When\nsearching for the shortest spanning tree but admitting additional branching\npoints, even shorter spanning trees can be realized: Steiner trees.\nUnfortunately, both minimum spanning and Steiner trees are not robust with\nrespect to noise in the observations; that is, small perturbations of the\noriginal data set often lead to drastic changes in the associated spanning\ntrees. In response, we make two contributions when the data lies in a Euclidean\nspace: on the theoretical side, we introduce a new optimization problem, the\n""(branched) central spanning tree"", which subsumes all previously mentioned\ndefinitions as special cases. On the practical side, we show empirically that\nthe (branched) central spanning tree is more robust to noise in the data, and\nas such is better suited to summarize a data set in terms of its skeleton. We\nalso propose a heuristic to address the NP-hard optimization problem, and\nillustrate its use on single cell RNA expression data from biology and 3D point\nclouds of plants.\n', 'Local Search for Weighted Tree Augmentation and Steiner Tree   We present a technique that allows for improving on some relative greedy\nprocedures by well-chosen (non-oblivious) local search algorithms. Relative\ngreedy procedures are a particular type of greedy algorithm that start with a\nsimple, though weak, solution, and iteratively replace parts of this starting\nsolution by stronger components. Some well-known applications of relative\ngreedy algorithms include approximation algorithms for Steiner Tree and, more\nrecently, for connectivity augmentation problems.\n  The main application of our technique leads to a\n$(1.5+\\epsilon)$-approximation for Weighted Tree Augmentation, improving on a\nrecent relative greedy based method with approximation factor $1+\\ln 2 +\n\\epsilon\\approx 1.69$. Furthermore, we show how our local search technique can\nbe applied to Steiner Tree, leading to an alternative way to obtain the\ncurrently best known approximation factor of $\\ln 4 + \\epsilon$. Contrary to\nprior methods, our approach is purely combinatorial without the need to solve\nan LP. Nevertheless, the solution value can still be bounded in terms of the\nwell-known hypergraphic LP, leading to an alternative, and arguably simpler,\ntechnique to bound its integrality gap by $\\ln 4$.\n', 'Lower bounds for the integrality gap of the bi-directed cut formulation\n  of the Steiner Tree Problem   In this work, we study the metric Steiner Tree problem on graphs focusing on\ncomputing lower bounds for the integrality gap of the bi-directed cut (BCR)\nformulation and introducing a novel formulation, the Complete Metric (CM)\nmodel, specifically designed to address the weakness of the BCR formulation on\nmetric instances. A key contribution of our work is extending the Gap problem,\npreviously explored in the context of the Traveling Salesman problems, to the\nmetric Steiner Tree problem. To tackle the Gap problem for Steiner Tree\ninstances, we first establish several structural properties of the CM\nformulation. We then classify the isomorphism classes of the vertices within\nthe CM polytope, revealing a correspondence between the vertices of the BCR and\nCM polytopes. Computationally, we exploit these structural properties to design\ntwo complementary heuristics for finding nontrivial small metric Steiner\ninstances with a large integrality gap. We present several vertices for graphs\nwith a number of nodes <=10, which realize the best-known lower bounds on the\nintegrality gap for the CM and the BCR formulations. We conclude the paper by\npresenting two new conjectures on the integrality gap of the BCR and CM\nformulations for small graphs.\n']","[('steiner trees', 0.6721805930137634), ('steiner tree', 0.6232283115386963), ('minimum spanning tree', 0.5395301580429077), ('spanning trees', 0.5295649170875549), ('spanning tree', 0.4824182093143463), ('steiner', 0.4669835567474365), ('minimum spanning', 0.46320265531539917), ('weighted tree', 0.4368390142917633), ('adjacency', 0.4254823625087738), ('shortest paths', 0.41221946477890015)]"
564,564,55,564_selmer groups elliptic_selmer groups_supersingular elliptic curves_groups elliptic curves,"['selmer groups elliptic', 'selmer groups', 'supersingular elliptic curves', 'groups elliptic curves', 'selmer group', 'theory elliptic curves', 'groups elliptic', 'elliptic curves', 'iwasawa invariants', 'elliptic curves let']","['$\\Lambda$-submodules of finite index of anticyclotomic plus and minus\n  Selmer groups of elliptic curves   Let $p$ be an odd prime and $K$ an imaginary quadratic field where $p$\nsplits. Under appropriate hypotheses, Bertolini showed that the Selmer group of\na $p$-ordinary elliptic curve over the anticyclotomic $\\mathbb Z_p$-extension\nof $K$ does not admit any proper $\\Lambda$-submodule of finite index, where\n$\\Lambda$ is a suitable Iwasawa algebra. We generalize this result to the plus\nand minus Selmer groups (in the sense of Kobayashi) of $p$-supersingular\nelliptic curves. In particular, in our setting the plus/minus Selmer groups\nhave $\\Lambda$-corank one, so they are not $\\Lambda$-cotorsion. As an\napplication of our main theorem, we prove results in the vein of\nGreenberg-Vatsal on Iwasawa invariants of $p$-congruent elliptic curves,\nextending to the supersingular case results for $p$-ordinary elliptic curves\ndue to Hatley-Lei.\n', 'On the signed Selmer groups for motives at non-ordinary primes in\n  $\\mathbb{Z}_p^2$-extensions   Generalizing the work of Kobayashi and the second author for elliptic curves\nwith supersingular reduction at the prime $p$, B\\""uy\\""ukboduk and Lei\nconstructed multi-signed Selmer groups over the cyclotomic\n$\\mathbb{Z}_p$-extension of a number field $F$ for more general non-ordinary\nmotives. In particular, their construction applies to abelian varieties over\n$F$ with good supersingular reduction at all the primes of $F$ above $p$. In\nthis article, we scrutinize the case in which $F$ is imaginary quadratic, and\nprove a control theorem (that generalizes Kim\'s control theorem for elliptic\ncurves) of multi-signed Selmer groups of non-ordinary motives over the maximal\nabelian pro-$p$ extension of $F$ that is unramified outside $p$, which is the\n$\\mathbb{Z}_p^2$-extension of $F$. We apply it to derive a sufficient condition\nwhen these multi-signed Selmer groups are cotorsion over the corresponding\ntwo-variable Iwasawa algebra. Furthermore, we compare the Iwasawa\n$\\mu$-invariants of multi-signed Selmer groups over the\n$\\mathbb{Z}_p^2$-extension for two such representations which are congruent\nmodulo $p$.\n', 'Conjecture A and $\\mu$-invariant for Selmer groups of supersingular\n  elliptic curves   Let $p$ be an odd prime and let $E$ be an elliptic curve defined over a\nnumber field $F$ with good reduction at primes above $p$. In this survey\narticle, we give an overview of some of the important results proven for the\nfine Selmer group and the signed Selmer groups over cyclotomic towers as well\nas the signed Selmer groups over $\\mathbb{Z}_p^2$-extensions of an imaginary\nquadratic field where $p$ splits completely. We only discuss the algebraic\naspects of these objects through Iwasawa theory. We also attempt to give some\nof the recent results implying the vanishing of the $\\mu$-invariant under the\nhypothesis of Conjecture A. Moreover, we draw an analogy between the classical\nSelmer group in the ordinary reduction case and that of the signed Selmer\ngroups of Kobayashi in the supersingular reduction case. We highlight\nproperties of signed Selmer groups (when $E$ has good supersingular reduction)\nwhich are completely analogous to the classical Selmer group (when $E$ has good\nordinary reduction). In this survey paper, we do not present any proofs,\nhowever we have tried to give references of the discussed results for the\ninterested reader.\n']","[('selmer groups elliptic', 0.7022711634635925), ('selmer groups', 0.6084024906158447), ('supersingular elliptic curves', 0.5808296799659729), ('groups elliptic curves', 0.575124204158783), ('selmer group', 0.5607745051383972), ('theory elliptic curves', 0.5601499080657959), ('groups elliptic', 0.4996313154697418), ('elliptic curves', 0.49871039390563965), ('iwasawa invariants', 0.4869324564933777), ('elliptic curves let', 0.482587605714798)]"
565,565,54,565_convex quadratic programming_mixed integer convex_integer convex_convex hull,"['convex quadratic programming', 'mixed integer convex', 'integer convex', 'convex hull', 'convex relaxations', 'integer nonlinear optimization', 'polyhedral relaxations', 'general linear programming', 'optimization formulations', 'linear programming']","[""Outer Approximation With Conic Certificates For Mixed-Integer Convex\n  Problems   A mixed-integer convex (MI-convex) optimization problem is one that becomes\nconvex when all integrality constraints are relaxed. We present a\nbranch-and-bound LP outer approximation algorithm for an MI-convex problem\ntransformed to MI-conic form. The polyhedral relaxations are refined with\n$\\mathcal{K}^*$ cuts derived from conic certificates for continuous primal-dual\nconic subproblems. Under the assumption that all subproblems are well-posed,\nthe algorithm detects infeasibility or unboundedness or returns an optimal\nsolution in finite time. Using properties of the conic certificates, we show\nthat the $\\mathcal{K}^*$ cuts imply certain practically-relevant guarantees\nabout the quality of the polyhedral relaxations, and demonstrate how to\nmaintain helpful guarantees when the LP solver uses a positive feasibility\ntolerance. We discuss how to disaggregate $\\mathcal{K}^*$ cuts in order to\ntighten the polyhedral relaxations and thereby improve the speed of\nconvergence, and propose fast heuristic methods of obtaining useful\n$\\mathcal{K}^*$ cuts. Our new open source MI-conic solver Pajarito\n(http://github.com/JuliaOpt/Pajarito.jl) uses an external mixed-integer linear\n(MILP) solver to manage the search tree and an external continuous conic solver\nfor subproblems. Benchmarking on a library of mixed-integer second-order cone\n(MISOCP) problems, we find that Pajarito greatly outperforms Bonmin (the\nleading open source alternative) and is competitive with CPLEX's specialized\nMISOCP algorithm. We demonstrate the robustness of Pajarito by solving diverse\nMI-conic problems involving mixtures of positive semidefinite, second-order,\nand exponential cones, and provide evidence for the practical value of our\nanalyses and enhancements of $\\mathcal{K}^*$ cuts.\n"", 'On the convex hull of convex quadratic optimization problems with\n  indicators   We consider the convex quadratic optimization problem with indicator\nvariables and arbitrary constraints on the indicators. We show that a convex\nhull description of the associated mixed-integer set in an extended space with\na quadratic number of additional variables consists of a single positive\nsemidefinite constraint (explicitly stated) and linear constraints. In\nparticular, convexification of this class of problems reduces to describing a\npolyhedral set in an extended formulation. While the vertex representation of\nthis polyhedral set is exponential and an explicit linear inequality\ndescription may not be readily available in general, we derive a compact\nmixed-integer linear formulation whose solutions coincide with the vertices of\nthe polyhedral set. We also give descriptions in the original space of\nvariables: we provide a description based on an infinite number of\nconic-quadratic inequalities, which are ``finitely generated."" In particular,\nit is possible to characterize whether a given inequality is necessary to\ndescribe the convex hull. The new theory presented here unifies several\npreviously established results, and paves the way toward utilizing polyhedral\nmethods to analyze the convex hull of mixed-integer nonlinear sets.\n', 'Convexification of bilinear terms over network polytopes   It is well-known that the McCormick relaxation for the bilinear constraint\n$z=xy$ gives the convex hull over the box domains for $x$ and $y$. In network\napplications where the domain of bilinear variables is described by a network\npolytope, the McCormick relaxation, also referred to as linearization, fails to\nprovide the convex hull and often leads to poor dual bounds. We study the\nconvex hull of the set containing bilinear constraints $z_{i,j}=x_iy_j$ where\n$x_i$ represents the arc-flow variable in a network polytope, and $y_j$ is in a\nsimplex. For the case where the simplex contains a single $y$ variable, we\nintroduce a systematic procedure to obtain the convex hull of the above set in\nthe original space of variables, and show that all facet-defining inequalities\nof the convex hull can be obtained explicitly through identifying a special\ntree structure in the underlying network. For the generalization where the\nsimplex contains multiple $y$ variables, we design a constructive procedure to\nobtain an important class of facet-defining inequalities for the convex hull of\nthe underlying bilinear set that is characterized by a special forest structure\nin the underlying network. Computational experiments are presented to evaluate\nthe effectiveness of the proposed methods.\n']","[('convex quadratic programming', 0.6327882409095764), ('mixed integer convex', 0.6046164631843567), ('integer convex', 0.6011295914649963), ('convex hull', 0.5758158564567566), ('convex relaxations', 0.5650365352630615), ('integer nonlinear optimization', 0.5364458560943604), ('polyhedral relaxations', 0.5263542532920837), ('general linear programming', 0.5084383487701416), ('optimization formulations', 0.5052669644355774), ('linear programming', 0.5036247372627258)]"
566,566,54,566_permutation matrices_matrix entries_matrices bounded_binary matrix,"['permutation matrices', 'matrix entries', 'matrices bounded', 'binary matrix', 'matrix rows', 'submatrix', 'partitioned matrix', 'submatrices', 'matrices order', 'regular matrices']","['An exact characterization of saturation for permutation matrices   A 0-1 matrix $M$ contains a 0-1 matrix pattern $P$ if we can obtain $P$ from\n$M$ by deleting rows and/or columns and turning arbitrary 1-entries into 0s.\nThe saturation function $\\mathrm{sat}(P,n)$ for a 0-1 matrix pattern $P$\nindicates the minimum number of 1s in an $n \\times n$ 0-1 matrix that does not\ncontain $P$, but changing any 0-entry into a 1-entry creates an occurrence of\n$P$. Fulek and Keszegh recently showed that each pattern has a saturation\nfunction either in $O(1)$ or in $\\Theta(n)$. We fully classify the saturation\nfunctions of permutation matrices.\n', 'Multivalued forbidden numbers of two-rowed configurations -- the missing\n  cases   The present paper considers extremal combinatorics questions in the language\nof matrices. An $s$-matrix is a matrix with entries in $\\{0,1,\\ldots, s-1\\}$.\nAn $s$-matrix is simple if it has no repeated columns. A matrix $F$ is a\nconfiguration in a matrix $A$, denoted $F\\prec A$, if it is a row/column\npermutation of a submatrix of $A$. $\\text{Avoid}(m,s,F)$ is the set of\n$m$-rowed, simple $s$-matrices not containing a configuration of $F$ and\n$\\text{forb}(m,s, F)=\\max\\{|A|\\colon A \\in \\text{Avoid}(m,s,F)\\}$. Dillon and\nSali initiated the systematic study of $\\text{forb}(m,s, F)$ for $2$-matrices\n$F$, and computed $\\text{forb}(m,s, F)$ for all 2-rowed $F$ when $s>3$. In this\npaper we tackle the remaining cases when $s=3$. In particular, we determine the\nasymptotics of $\\text{forb}(m,3,p\\cdot K_2)-\\text{forb}(m,3,p\\cdot I_2)$ for\n$p>3$, where $K_2$ is the $2\\times 4$ simple $2$-matrix and $I_2$ is the\n$2\\times 2$ identity matrix, as well as the exact values of\n$\\text{forb}(m,3,F)$ for many 2-rowed $2$-matrices $F$.\n', 'An intermediate case of exponential multivalued forbidden matrix\n  configuration   The forbidden number forb$(m,F)$, which denotes the maximum number of\ndistinct columns in an $m$-rowed $(0,1)$-matrix with no submatrix that is a row\nand column permutation of $F$, has been widely studied in extremal set theory.\nRecently, this function was extended to $r$-matrices, whose entries lie in\n$\\{0,1,\\cdots,r-1\\}$. forb$(m,r,F)$ is the maximum number of distinct columns\nin an $r$-matrix with no submatrix that is a row and column permutation of $F$.\nWhile forb$(m,F)$ is polynomial in $m$, forb$(m,r,F)$ is exponential for $r\\geq\n3$. Recently, forb$(m,r,F)$ was studied for some small $(0,1)$-matrices $F$,\nand exact values were determined in some cases. In this paper we study\nforb$(m,r,M)$ for $M=\\begin{bmatrix}0&1\\\\0&1\\\\1&0\\end{bmatrix}$, which is the\nsmallest matrix for which this forbidden number is unknown. Interestingly, it\nturns out that this problem is closely linked with the following optimisation\nproblem. For each triangle in the complete graph $K_m$, pick one of its edges.\nLet $m_e$ denote the number of times edge $e$ is picked. For each\n$\\alpha\\in\\mathbb{R}$, what is $H(m,\\alpha)=\\max\\sum_{e\\in\nE(K_m)}\\alpha^{m_e}$? We establish a relationship between forb$(m,r,M)$ and\n$H(m,(r-1)/(r-2))$, find upper and lower bounds for $H(m,\\alpha)$, and use them\nto significantly improve known bounds for forb$(m,r,M)$.\n']","[('permutation matrices', 0.5066666603088379), ('matrix entries', 0.4693513810634613), ('matrices bounded', 0.42343586683273315), ('binary matrix', 0.42057672142982483), ('matrix rows', 0.41099777817726135), ('submatrix', 0.4081539213657379), ('partitioned matrix', 0.40441974997520447), ('submatrices', 0.39641860127449036), ('matrices order', 0.3888341784477234), ('regular matrices', 0.3874637186527252)]"
567,567,54,567_surface integrals_fast multipole_layer potentials_fast multipole fmm,"['surface integrals', 'fast multipole', 'layer potentials', 'fast multipole fmm', 'double layer potential', 'multipole', 'layer potential', 'multipole fmm', 'single layer potential', 'quadrature expansion']","['On the Approximation of Local Expansions of Laplace Potentials by the\n  Fast Multipole Method   In this paper, we present a generalization of the classical error bounds of\nGreengard-Rokhlin for the Fast Multipole Method (FMM) for Laplace potentials in\nthree dimensions, extended to the case of local expansion (instead of point)\ntargets. We also present a complementary, less sharp error bound proven via\napproximation theory whose applicability is not restricted to Laplace\npotentials. Our study is motivated by the GIGAQBX FMM, an algorithm for the\nfast, high-order accurate evaluation of layer potentials near and on the source\nlayer. GIGAQBX is based on the FMM, but unlike a conventional FMM, which is\ndesigned to evaluate potentials at point-shaped targets, GIGAQBX evaluates\nlocal expansions of potentials at ball-shaped targets. Although the accuracy\n(or the acceleration error, i.e., error due to the approximation of the\npotential by the fast algorithm) of the conventional FMM is well understood,\nthe acceleration error of FMM-based algorithms applied to the evaluation of\nlocal expansions has not been as well studied. The main contribution of this\npaper is a proof of a set of hypotheses first demonstrated numerically in the\npaper ""A Fast Algorithm for Quadrature by Expansion in Three Dimensions,"" which\npertain to the accuracy of FMM approximation of local expansions of Laplace\npotentials in three dimensions. These hypotheses are also essential to the\nthree-dimensional error bound for GIGAQBX, which was previously stated\nconditionally on their truth and can now be stated unconditionally.\n', ""Fast Multipole Method for 3-D Linearized Poisson-Boltzmann Equation in\n  Layered Media   In this paper, we propose a fast multipole method (FMM) for 3-D linearized\nPoisson-Boltzmann (PB) equation in layered media. The main framework of the\nalgorithm is analogous to the FMM for Helmholtz and Laplace equation in layered\nmedia [1,2], using an extension of the Funk-Hecke formula for pure imaginary\nwave number. Moreover, a recurrence formula is provided for the run-time\ncomputation of the Sommerfeld-type integrals used in the FMM algorithm. Due to\nthe similarity between Helmholtz and linearized PB equation, the recurrence\nformula can also be used for the FMM of Helmholtz equation in layered media\nwith minor changes as mentioned in [1] . Numerical results validate that the\nFMM for interactions of charges under screen's potentials in layered media has\nthe same accuracy and CPU complexity as the classic FMM for charge interactions\nin free space.\n"", 'Fast multipole method for 3-D Laplace equation in layered media   In this paper, a fast multipole method (FMM) is proposed for 3-D Laplace\nequation in layered media. The potential due to charges embedded in layered\nmedia is decomposed into a free space component and four types of reaction\nfield components, and the latter can be associated with the potential of a\npolarization source defined for each type. New multipole expansions (MEs) and\nlocal expansions (LEs), as well as the multipole to local (M2L) translation\noperators are derived for the reaction components, based on which the FMMs for\nreaction components are then proposed. The resulting FMM for charge\ninteractions in layered media is a combination of using the classic FMM for the\nfree space components and the new FMMs for the reaction field components. With\nthe help of a recurrence formula for the run-time computation of the\nSommerfeld-type integrals used in M2L translation operators, pre-computations\nof a large number of tables are avoided. The new FMMs for the reaction\ncomponents are found to be much faster than the classic FMM for the free space\ncomponents due to the separation of equivalent polarization charges and the\nassociated target charges by a material interface. As a result, the FMM for\npotential in layered media costs almost the same as the classic FMM in the free\nspace case. Numerical results validate the fast convergence of the MEs for the\nreaction components, and the O(N) complexity of the FMM with a given truncation\nnumber p for charge interactions in 3-D layered media.\n']","[('surface integrals', 0.5168631076812744), ('fast multipole', 0.4874567985534668), ('layer potentials', 0.4661477208137512), ('fast multipole fmm', 0.4607246220111847), ('double layer potential', 0.45141011476516724), ('multipole', 0.4299156367778778), ('layer potential', 0.42927780747413635), ('multipole fmm', 0.4256751537322998), ('single layer potential', 0.42496681213378906), ('quadrature expansion', 0.40934431552886963)]"
568,568,54,568_ginzburg landau equations_magnetization dynamics_landau equations_landau lifshitz gilbert,"['ginzburg landau equations', 'magnetization dynamics', 'landau equations', 'landau lifshitz gilbert', 'landau lifshitz', 'magnetization', 'ferromagnetic', 'magnetisation', 'landau', 'lifshitz gilbert']","['Recent results for the Landau-Lifshitz equation   We give a survey on some recent results concerning the Landau-Lifshitz\nequation, a fundamental nonlinear PDE with a strong geometric content,\ndescribing the dynamics of the magnetization in ferromagnetic materials. We\nrevisit the Cauchy problem for the anisotropic Landau-Lifshitz equation,\nwithout dissipation, for smooth solutions, and also in the energy space in\ndimension one. We also examine two approximations of the Landau-Lifshitz\nequation given by of the Sine-Gordon equation and cubic Schr\\""odinger\nequations, arising in certain singular limits of strong easy-plane and\neasy-axis anisotropy, respectively.\n  Concerning localized solutions, we review the orbital and asymptotic\nstability problems for a sum of solitons in dimension one, exploiting the\nvariational nature of the solitons in the hydrodynamical framework.\n  Finally, we survey results concerning the existence, uniqueness and stability\nof self-similar solutions (expanders and shrinkers) for the isotropic\nLandau-Lifshitz equation with Gilbert term. Since expanders are associated with\na singular initial condition with a jump discontinuity, we also review their\nwell-posedness in spaces linked to the BMO space.\n', 'Well-Posedness and Finite Element Approximation for the\n  Landau-Lifshitz-Gilbert Equation with Spin-Torques   Spin currents act on ferromagnets by exerting a torque on the magnetisation.\nThis torque is modelled by appending additional terms to the\nLandau-Lifshitz-Gilbert equation motivating the study of the non-homogeneous\nLandau-Lifshitz-Gilbert equation. We first prove the existence and uniqueness\nof high regularity local solutions to this equation using the Faedo-Galerkin\nmethod. Then we construct a numerical method for the problem and prove that it\nconverges to a global weak solution of the PDE. Numerical simulations of the\nproblem are also included.\n', 'On numerical aspects of parameter identification for the\n  Landau-Lifshitz-Gilbert equation in Magnetic Particle Imaging   The Landau-Lifshitz-Gilbert equation yields a mathematical model to describe\nthe evolution of the magnetization of a magnetic material, particularly in\nresponse to an external applied magnetic field. It allows one to take into\naccount various physical effects, such as the exchange within the magnetic\nmaterial itself. In particular, the Landau-Lifshitz-Gilbert equation encodes\nrelaxation effects, i.e., it describes the time-delayed alignment of the\nmagnetization field with an external magnetic field. These relaxation effects\nare an important aspect in magnetic particle imaging, particularly in the\ncalibration process. In this article, we address the data-driven modeling of\nthe system function in magnetic particle imaging, where the\nLandau-Lifshitz-Gilbert equation serves as the basic tool to include relaxation\neffects in the model. We formulate the respective parameter identification\nproblem both in the all-at-once and the reduced setting, present reconstruction\nalgorithms that yield a regularized solution and discuss numerical experiments.\nApart from that, we propose a practical numerical solver to the nonlinear\nLandau-Lifshitz-Gilbert equation, not via the classical finite element method,\nbut through solving only linear PDEs in an inverse problem framework.\n']","[('ginzburg landau equations', 0.5615898966789246), ('magnetization dynamics', 0.5580888390541077), ('landau equations', 0.5548179149627686), ('landau lifshitz gilbert', 0.5341891646385193), ('landau lifshitz', 0.47455108165740967), ('magnetization', 0.44522619247436523), ('ferromagnetic', 0.4228179454803467), ('magnetisation', 0.4204021692276001), ('landau', 0.38645055890083313), ('lifshitz gilbert', 0.3803773820400238)]"
569,569,54,569_supersingular elliptic curves_class elliptic curves_isogeny class_elliptic curves,"['supersingular elliptic curves', 'class elliptic curves', 'isogeny class', 'elliptic curves', 'isogeny', 'isogeny based cryptography', 'elliptic curves defined', 'isogeny based', 'elliptic curve', 'supersingular elliptic']","['Higher-degree supersingular group actions   We investigate the isogeny graphs of supersingular elliptic curves over\n$\\mathbb{F}_{p^2}$ equipped with a $d$-isogeny to their Galois conjugate. These\ncurves are interesting because they are, in a sense, a generalization of curves\ndefined over $\\mathbb{F}_p$, and there is an action of the ideal class group of\n$\\mathbb{Q}(\\sqrt{-dp})$ on the isogeny graphs. We investigate constructive and\ndestructive aspects of these graphs in isogeny-based cryptography, including\ngeneralizations of the CSIDH cryptosystem and the Delfs-Galbraith algorithm.\n', 'A classification of isogeny-torsion graphs of $\\mathbb{Q}$-isogeny\n  classes of elliptic curves   Let $\\mathcal{E}$ be a $\\mathbb{Q}$-isogeny class of elliptic curves defined\nover $\\mathbb{Q}$. The isogeny graph associated to $\\mathcal{E}$ is a graph\nwhich has a vertex for each elliptic curve in the $\\mathbb{Q}$-isogeny class\n$\\mathcal{E}$, and an edge for each cyclic $\\mathbb{Q}$-isogeny of prime degree\nbetween elliptic curves in the isogeny class, with the degree recorded as a\nlabel of the edge. In this paper, we define an isogeny-torsion graph to be an\nisogeny graph where, in addition, we label each vertex with the abstract group\nstructure of the torsion subgroup over $\\mathbb{Q}$ of the corresponding\nelliptic curve. Then, the main result of the article is a classification of all\nthe possible isogeny-torsion graphs that occur for $\\mathbb{Q}$-isogeny classes\nof elliptic curves defined over the rationals.\n', 'Orientations and cycles in supersingular isogeny graphs   The paper concerns several theoretical aspects of oriented supersingular\n$\\ell$-isogeny volcanoes and their relationship to closed walks in the\nsupersingular $\\ell$-isogeny graph. Our main result is a bijection between the\nrims of the union of all oriented supersingular $\\ell$-isogeny volcanoes over\n$\\overline{\\mathbb{F}}_p$ (up to conjugation of the orientations), and isogeny\ncycles (non-backtracking closed walks which are not powers of smaller walks) of\nthe supersingular $\\ell$-isogeny graph over $\\overline{\\mathbb{F}}_p$. The\nexact proof and statement of this bijection are made more intricate by special\nbehaviours arising from extra automorphisms and the ramification of $p$ in\ncertain quadratic orders. We use the bijection to count isogeny cycles of given\nlength in the supersingular $\\ell$-isogeny graph exactly as a sum of class\nnumbers of these orders, and also give an explicit upper bound by estimating\nthe class numbers.\n']","[('supersingular elliptic curves', 0.6762767434120178), ('class elliptic curves', 0.6265339851379395), ('isogeny class', 0.6215174794197083), ('elliptic curves', 0.61449134349823), ('isogeny', 0.611928403377533), ('isogeny based cryptography', 0.5815449357032776), ('elliptic curves defined', 0.5811377763748169), ('isogeny based', 0.5646113753318787), ('elliptic curve', 0.5311540961265564), ('supersingular elliptic', 0.5106186270713806)]"
570,570,54,570_biharmonic maps_harmonic biharmonic_biharmonic_hypersurfaces riemannian,"['biharmonic maps', 'harmonic biharmonic', 'biharmonic', 'hypersurfaces riemannian', 'biharmonicity', 'submanifolds riemannian', 'riemannian submersions', 'hypersurfaces euclidean', 'hypersurfaces space forms', 'submanifolds euclidean']","['Remarks on constructing biharmonic and conformal biharmonic maps to\n  spheres   Biharmonic and conformal biharmonic maps are two fourth-order generalizations\nof the well-studied notion of harmonic maps in Riemannian geometry. In this\narticle we consider maps into the Euclidean sphere and investigate a geometric\nalgorithm that aims at rendering a given harmonic map either biharmonic or\nconformally biharmonic.\n  For biharmonic maps we find that in the case of a closed domain the maximum\nprinciple imposes strong restrictions on our approach, whereas there is more\nflexibility when we have a non-compact domain and we highlight this difference\nby a number of examples.\n  Concerning conformal biharmonic maps we show that our algorithm produces\nexplicit critical points for maps between spheres. Moreover, it turns out that\nwe do not get strong restrictions as we obtain for biharmonic maps, such that\nour algorithm might produce additional conformal biharmonic maps between\nspheres beyond the ones found in this article.\n', '$f$-Biharmonic submanifolds in space forms and $f$-biharmonic Riemannian\n  submersions from 3-manifolds   $f$-Biharmonic maps are generalizations of harmonic maps and biharmonic maps.\nIn this paper, we obtain some descriptions of $f$-biharmonic curves in a space\nform. We also obtain a complete classification of proper $f$-biharmonic\nisometric immersions of a developable surface in $\\r^3$ by proving that a\nproper $f$-biharmonic developable surface exists only in the case where the\nsurface is a cylinder. Based on this, we show that a proper biharmonic\nconformal immersion of a developable surface into $\\r^3$ exists only in the\ncase when the surface is a cylinder. Riemannian submersions can be viewed as\nthe dual notion of isometric immersions (i.e., submanifolds). We also study\n$f$-biharmonicity of Riemannian submersions from 3-space forms by using the\nintegrability data. Examples are given of proper $f$-biharmonic Riemannian\nsubmersions and $f$-biharmonic surfaces and curves.\n', 'On conformal biharmonic maps and hypersurfaces   In this article we initiate a thorough geometric study of the conformal\nbienergy functional which consists of the standard bienergy augmented by two\nadditional curvature terms. The conformal bienergy is conformally invariant in\ndimension four and its precise structure is motivated by the Paneitz operator\nfrom conformal geometry. The critical points of the conformal bienergy are\ncalled conformal biharmonic maps.\n  Besides establishing a number of basic results on conformal biharmonic maps,\nwe pay special attention to conformal biharmonic hypersurfaces in space forms.\nFor hypersurfaces in spheres, we determine all conformal biharmonic\nhyperspheres and then we classify all conformal biharmonic generalized Clifford\ntori. Moreover, in sharp contrast to biharmonic hypersurfaces, we show that\nthere also exist conformal biharmonic hypersurfaces of hyperbolic space,\npointing out a fundamental difference between biharmonic and conformal\nbiharmonic hypersurfaces.\n  Finally, we also study the stability of the conformal biharmonic hyperspheres\nin spheres and explicitly compute their index and nullity. In particular, we\nobtain that the index of the equator $\\mathbb{S}^4$ of $\\mathbb{S}^5$ is zero,\ni.e., it is stable, while the index of the equator $\\mathbb{S}^5$ of\n$\\mathbb{S}^6$ is seven.\n']","[('biharmonic maps', 0.7640111446380615), ('harmonic biharmonic', 0.722446084022522), ('biharmonic', 0.6398043632507324), ('hypersurfaces riemannian', 0.6263751983642578), ('biharmonicity', 0.6071684956550598), ('submanifolds riemannian', 0.5582473874092102), ('riemannian submersions', 0.5461894869804382), ('hypersurfaces euclidean', 0.5364722609519958), ('hypersurfaces space forms', 0.5340084433555603), ('submanifolds euclidean', 0.522759735584259)]"
571,571,54,571_compact ahler manifolds_ahler manifolds_compact kahler manifolds_compact ahler manifold,"['compact ahler manifolds', 'ahler manifolds', 'compact kahler manifolds', 'compact ahler manifold', 'kahler manifolds', 'ahler manifold', 'ahler manifolds non', 'kahler manifold', 'compact kahler', 'positive currents']","[""Loss of mass of non-pluripolar products   It is a well-known fact that the non-pluripolar self-products of a closed\npositive (1,1)-current in a big nef cohomology class on a compact Kahler\nmanifold are not of full mass in the presence of positive Lelong numbers of the\ncurrent in consideration. In this paper, we give a quantitative version of the\nlast property. Our proof involves a generalization of Demailly's comparison of\nLelong numbers to the setting of density currents, a reversed\nAlexandrov-Fenchel inequality, and the notion of relative non-pluripolar\nproducts.\n"", 'The generalized Lelong numbers and intersection theory   Let $X$ be a complex manifold of dimension $k,$ and $(V,\\omega)$ be a\nK\\""ahler submanifold of dimension $l$ in $X,$ and $B\\Subset V$ be a domain with\n$\\mathcal{C}^2$-smooth boundary. Let $T$ be a positive plurisubharmonic current\non $X$ such that $T$ satisfies a reasonable approximation condition on $X$ and\nnear $\\partial B.$ In our previous work we introduce the concept of the\ngeneralized Lelong numbers $\\nu_j(T,B)\\in\\mathbb{R}$ of $T$ along $B$ for\n$0\\leq j\\leq l.$ When $l=0,$ $V=B$ is a single point $x,$ $\\nu_0(T,B)$ is none\nother than the classical Lelong number of $T$ at $x.$\n  This article has five purposes: Firstly, we formulate the notion of the\ngeneralized Lelong number of $T$ associated to every closed smooth $(j,j)$-form\non $V.$ This concept extends the previous notion of the generalized Lelong\nnumbers. We also establish their basic properties. Secondly, we define the\nhorizontal dimension $\\hbar$ of such a current $T$ along $B.$ Next, we\ncharacterize $\\hbar$ in terms of the generalized Lelong numbers. We also\nestablish a Siu\'s upper-semicontinuity type theorem for the generalized Lelong\nnumbers. In their above-mentioned context, Dinh and Sibony introduced some\ncohomology classes which may be regarded as their analogues of the classical\nLelong numbers. Our third objective is to generalize their notion to the\nbroader context where $T$ is (merely) positive pluriharmonic. Moreover, we also\nestablish a formula relating Dinh-Sibony classes and the generalized Lelong\nnumbers. Fourthly, we obtain an effective sufficient condition for defining the\nintersection of $m$ positive closed currents in the sense of Dinh-Sibony\'s\ntheory of tangent currents on a compact K\\""ahler manifold. Finally, we\nestablish an effective sufficient condition for the continuity of the above\nintersection.\n', 'Positive plurisubharmonic currents: Generalized Lelong numbers and\n  Tangent theorems   Dinh--Sibony theory of tangent and density currents is a recent but powerful\ntool to study positive closed currents. Over twenty years ago, Alessandrini and\nBassanelli initiated the theory of the Lelong number of a positive\nplurisubharmonic current in $\\mathbb{C}^k$ along a linear subspace. Although\nthe latter theory is intriguing, it has not yet been explored in-depth since\nthen. Introducing the concept of the generalized Lelong numbers and studying\nthese new numerical values, we extend both theories to a more general class of\npositive plurisubharmonic currents and in a more general context of ambient\nmanifolds.\n  More specifically, in the first part of our article, we consider a positive\nplurisubharmonic current $T$ of bidegree $(p,p)$ on a complex manifold $X$ of\ndimension $k,$ and let $V\\subset X$ be a K\\""ahler submanifold of dimension $l$\nand $B$ a relatively compact piecewise $\\mathcal{C}^2$-smooth open subset of\n$V.$ We define the notion of the $j$-th Lelong number of $T$ along $B$ for\nevery $j$ with $\\max(0,l-p)\\leq j\\leq \\min(l,k-p)$ and prove their existence as\nwell as their basic properties.\n  Our method relies on some Lelong-Jensen formulas for the normal bundle to $V$\nin $X,$ which are of independent interest.\n  The second part of our article is devoted to geometric characterizations of\nthe generalized Lelong numbers. As a consequence of this study, we show that\nthe top degree Lelong number of $T$ along $B$ is totally intrinsic. This is a\ngeneralization of the fundamental result of Siu (for positive closed currents)\nand of Alessandrini--Bassanelli (for positive plurisubharmonic currents) on the\nindependence of Lelong numbers at a single point on the choice of coordinates.\n']","[('compact ahler manifolds', 0.5545623302459717), ('ahler manifolds', 0.5501444339752197), ('compact kahler manifolds', 0.5386043787002563), ('compact ahler manifold', 0.5360661149024963), ('kahler manifolds', 0.532922089099884), ('ahler manifold', 0.5258020758628845), ('ahler manifolds non', 0.524488627910614), ('kahler manifold', 0.5166493058204651), ('compact kahler', 0.5148895382881165), ('positive currents', 0.4538809359073639)]"
572,572,54,572_vehicle routing_capacitated vehicle routing_vehicle routing problems_deep reinforcement learning,"['vehicle routing', 'capacitated vehicle routing', 'vehicle routing problems', 'deep reinforcement learning', 'vehicle', 'traveling salesman', 'deep learning', 'travelling salesman', 'vehicles', 'deep reinforcement']","['A deep learning Attention model to solve the Vehicle Routing Problem and\n  the Pick-up and Delivery Problem with Time Windows   SNCF, the French public train company, is experimenting to develop new types\nof transportation services by tackling vehicle routing problems. While many\ndeep learning models have been used to tackle efficiently vehicle routing\nproblems, it is difficult to take into account time related constraints. In\nthis paper, we solve the Capacitated Vehicle Routing Problem with Time Windows\n(CVRPTW) and the Capacitated Pickup and Delivery Problem with Time Windows\n(CPDPTW) with a constructive iterative Deep Learning algorithm. We use an\nAttention Encoder-Decoder structure and design a novel insertion heuristic for\nthe feasibility check of the CPDPTW. Our models yields results that are better\nthan best known learning solutions on the CVRPTW. We show the feasibility of\ndeep learning techniques for solving the CPDPTW but witness the limitations of\nour iterative approach in terms of computational complexity.\n', 'Deep Reinforcement Learning for Solving the Heterogeneous Capacitated\n  Vehicle Routing Problem   Existing deep reinforcement learning (DRL) based methods for solving the\ncapacitated vehicle routing problem (CVRP) intrinsically cope with homogeneous\nvehicle fleet, in which the fleet is assumed as repetitions of a single\nvehicle. Hence, their key to construct a solution solely lies in the selection\nof the next node (customer) to visit excluding the selection of vehicle.\nHowever, vehicles in real-world scenarios are likely to be heterogeneous with\ndifferent characteristics that affect their capacity (or travel speed),\nrendering existing DRL methods less effective. In this paper, we tackle\nheterogeneous CVRP (HCVRP), where vehicles are mainly characterized by\ndifferent capacities. We consider both min-max and min-sum objectives for\nHCVRP, which aim to minimize the longest or total travel time of the vehicle(s)\nin the fleet. To solve those problems, we propose a DRL method based on the\nattention mechanism with a vehicle selection decoder accounting for the\nheterogeneous fleet constraint and a node selection decoder accounting for the\nroute construction, which learns to construct a solution by automatically\nselecting both a vehicle and a node for this vehicle at each step. Experimental\nresults based on randomly generated instances show that, with desirable\ngeneralization to various problem sizes, our method outperforms the\nstate-of-the-art DRL method and most of the conventional heuristics, and also\ndelivers competitive performance against the state-of-the-art heuristic method,\ni.e., SISR. Additionally, the results of extended experiments demonstrate that\nour method is also able to solve CVRPLib instances with satisfactory\nperformance.\n', ""A Deep Reinforcement Learning Approach for Solving the Traveling\n  Salesman Problem with Drone   Reinforcement learning has recently shown promise in learning quality\nsolutions in many combinatorial optimization problems. In particular, the\nattention-based encoder-decoder models show high effectiveness on various\nrouting problems, including the Traveling Salesman Problem (TSP).\nUnfortunately, they perform poorly for the TSP with Drone (TSP-D), requiring\nrouting a heterogeneous fleet of vehicles in coordination -- a truck and a\ndrone. In TSP-D, the two vehicles are moving in tandem and may need to wait at\na node for the other vehicle to join. State-less attention-based decoder fails\nto make such coordination between vehicles. We propose a hybrid model that uses\nan attention encoder and a Long Short-Term Memory (LSTM) network decoder, in\nwhich the decoder's hidden state can represent the sequence of actions made. We\nempirically demonstrate that such a hybrid model improves upon a purely\nattention-based model for both solution quality and computational efficiency.\nOur experiments on the min-max Capacitated Vehicle Routing Problem (mmCVRP)\nalso confirm that the hybrid model is more suitable for the coordinated routing\nof multiple vehicles than the attention-based model. The proposed model\ndemonstrates comparable results as the operations research baseline methods.\n""]","[('vehicle routing', 0.5047167539596558), ('capacitated vehicle routing', 0.4767903983592987), ('vehicle routing problems', 0.4429205656051636), ('deep reinforcement learning', 0.44116660952568054), ('vehicle', 0.3952752351760864), ('traveling salesman', 0.3913218379020691), ('deep learning', 0.3911551833152771), ('travelling salesman', 0.38640621304512024), ('vehicles', 0.3807438015937805), ('deep reinforcement', 0.3753458857536316)]"
573,573,54,573_hadamard matrices_hadamard matrices order_hadamard matrix_hadamard matrix order,"['hadamard matrices', 'hadamard matrices order', 'hadamard matrix', 'hadamard matrix order', 'hadamard conjecture', 'matrices introduced', 'dimensional hadamard', 'hadamard powers', 'hadamard', 'matrices whose entries']","['Implementing Hadamard Matrices in SageMath   Hadamard matrices are $(-1, +1)$ square matrices with mutually orthogonal\nrows. The Hadamard conjecture states that Hadamard matrices of order $n$ exist\nwhenever $n$ is $1$, $2$, or a multiple of $4$. However, no construction is\nknown that works for all values of $n$, and for some orders no Hadamard matrix\nhas yet been found. Given the many practical applications of these matrices, it\nwould be useful to have a way to easily check if a construction for a Hadamard\nmatrix of order $n$ exists, and in case to create it. This project aimed to\naddress this, by implementing constructions of Hadamard and skew Hadamard\nmatrices to cover all known orders less than or equal to $1000$ in SageMath, an\nopen-source mathematical software. Furthermore, we implemented some additional\nmathematical objects, such as complementary difference sets and T-sequences,\nwhich were not present in SageMath but are needed to construct Hadamard\nmatrices.\n  This also allows to verify the correctness of the results given in the\nliterature; within the $n\\leq 1000$ range, just one order, $292$, of a skew\nHadamard matrix claimed to have a known construction, required a fix.\n', ""A database of constructions of Hadamard matrices   Hadamard matrices of order $n$ are conjectured to exist whenever $n$ is $1$,\n$2$, or a multiple of $4$; a similar conjecture exists for skew Hadamard\nmatrices. We provide constructions covering orders $\\le 1208$ of all known\nHadamard and skew Hadamard matrices in the open-source software SageMath. This\nallowed us to verify the correctness of results given in the literature. Within\nthis range, just one order, $292$, of a skew Hadamard matrix claimed to have a\nknown construction, required a fix.\n  We also produce the up to date tables, for $n \\le 2999$ (resp. $n\\le 999$ for\nskew case), of the minimum exponents $m$ such that a (skew) Hadamard matrix of\norder $2^m n$ is known, improving over 100 entries in the previously published\nsources. We explain how tables' entries are related to Riesel numbers. As a\nby-product of the latter, we show that the Paley constructions of\n(skew-)Hadamard matrices do not work for the order $2^m 509203$, for any $m$.\n"", 'On Some Quaternionic Hadamard Matrices of Small Order   We introduce Hadamard matrices whose entries are quaternionic. We then go on\nto provide classification of quaternionic Hadamard matrices of circulant core\nof orders 2 through 5. We also introduce quaternionic Hadamard matrices of\nButson type and ways to create quaternionic Hadamard matrices from real and\ncomplex Hadamard matrices. Examples are shown that showcase how Hadamard\nmatrices over the quaternions are richer than Hadamard matrices over the\ncomplex numbers.\n']","[('hadamard matrices', 0.8248621821403503), ('hadamard matrices order', 0.7964359521865845), ('hadamard matrix', 0.7600660920143127), ('hadamard matrix order', 0.7531813979148865), ('hadamard conjecture', 0.6325342059135437), ('matrices introduced', 0.5978678464889526), ('dimensional hadamard', 0.5908184051513672), ('hadamard powers', 0.5608043670654297), ('hadamard', 0.5597406625747681), ('matrices whose entries', 0.5592418313026428)]"
574,574,54,574_sparse pca_robust pca_component analysis sparse_component analysis pca,"['sparse pca', 'robust pca', 'component analysis sparse', 'component analysis pca', 'principal component analysis', 'robust principal component', 'pca', 'analysis pca', 'robust principal', 'principal components']","['Efficient Sparse PCA via Block-Diagonalization   Sparse Principal Component Analysis (Sparse PCA) is a pivotal tool in data\nanalysis and dimensionality reduction. However, Sparse PCA is a challenging\nproblem in both theory and practice: it is known to be NP-hard and current\nexact methods generally require exponential runtime. In this paper, we propose\na novel framework to efficiently approximate Sparse PCA by (i) approximating\nthe general input covariance matrix with a re-sorted block-diagonal matrix,\n(ii) solving the Sparse PCA sub-problem in each block, and (iii) reconstructing\nthe solution to the original problem. Our framework is simple and powerful: it\ncan leverage any off-the-shelf Sparse PCA algorithm and achieve significant\ncomputational speedups, with a minor additive error that is linear in the\napproximation error of the block-diagonal matrix. Suppose $g(k, d)$ is the\nruntime of an algorithm (approximately) solving Sparse PCA in dimension $d$ and\nwith sparsity constant $k$. Our framework, when integrated with this algorithm,\nreduces the runtime to $\\mathcal{O}\\left(\\frac{d}{d^\\star} \\cdot g(k, d^\\star)\n+ d^2\\right)$, where $d^\\star \\leq d$ is the largest block size of the\nblock-diagonal matrix. For instance, integrating our framework with the\nBranch-and-Bound algorithm reduces the complexity from $g(k, d) =\n\\mathcal{O}(k^3\\cdot d^k)$ to $\\mathcal{O}(k^3\\cdot d \\cdot (d^\\star)^{k-1})$,\ndemonstrating exponential speedups if $d^\\star$ is small. We perform\nlarge-scale evaluations on many real-world datasets: for exact Sparse PCA\nalgorithm, our method achieves an average speedup factor of 100.50, while\nmaintaining an average approximation error of 0.61%; for approximate Sparse PCA\nalgorithm, our method achieves an average speedup factor of 6.00 and an average\napproximation error of -0.91%, meaning that our method oftentimes finds better\nsolutions.\n', 'Sparse PCA on fixed-rank matrices   Sparse PCA is the optimization problem obtained from PCA by adding a sparsity\nconstraint on the principal components. Sparse PCA is NP-hard and hard to\napproximate even in the single-component case. In this paper we settle the\ncomputational complexity of sparse PCA with respect to the rank of the\ncovariance matrix. We show that, if the rank of the covariance matrix is a\nfixed value, then there is an algorithm that solves sparse PCA to global\noptimality, whose running time is polynomial in the number of features. We also\nprove a similar result for the version of sparse PCA which requires the\nprincipal components to have disjoint supports.\n', 'Extended Principal Component Analysis   Principal Component Analysis (PCA) is a transform for finding the principal\ncomponents (PCs) that represent features of random data. PCA also provides a\nreconstruction of the PCs to the original data. We consider an extension of PCA\nwhich allows us to improve the associated accuracy and diminish the numerical\nload, in comparison with known techniques. This is achieved due to the special\nstructure of the proposed transform which contains two matrices $T_0$ and\n$T_1$, and a special transformation $\\mathcal{f}$ of the so called auxiliary\nrandom vector $\\mathbf w$. For this reason, we call it the three-term PCA. In\nparticular, we show that the three-term PCA always exists, i.e. is applicable\nto the case of singular data. Both rigorous theoretical justification of the\nthree-term PCA and simulations with real-world data are provided.\n']","[('sparse pca', 0.7785629630088806), ('robust pca', 0.6730216145515442), ('component analysis sparse', 0.6523062586784363), ('component analysis pca', 0.6108027100563049), ('principal component analysis', 0.6069961190223694), ('robust principal component', 0.591234564781189), ('pca', 0.5691501498222351), ('analysis pca', 0.5459249019622803), ('robust principal', 0.5410550832748413), ('principal components', 0.5356019139289856)]"
575,575,53,575_network centrality_centrality measures_centrality_networks vertices,"['network centrality', 'centrality measures', 'centrality', 'networks vertices', 'complex networks', 'network analysis', 'network science', 'network adjacency', 'centralization', 'important nodes']","['Harmonic Centrality in Some Graph Families   One of the more recent measures of centrality in social network analysis is\nthe normalized harmonic centrality. A variant of the closeness centrality,\nharmonic centrality sums the inverse of the geodesic distances of each node to\nother nodes where it is 0 if there is no path from one node to another. It is\nthen normalized by dividing it by m-1, where m is the number of nodes of the\ngraph. In this paper, we present notions regarding the harmonic centrality of\nsome important classes of graphs.\n', 'Fast computation of matrix function-based centrality measures for\n  layer-coupled multiplex networks   Centrality measures identify and rank the most influential entities of\ncomplex networks. In this paper, we generalize matrix function-based centrality\nmeasures, which have been studied extensively for single-layer and temporal\nnetworks in recent years to layer-coupled multiplex networks. The layers of\nthese networks can reflect different relationships and interactions between\nentities or changing interactions over time. We use the supra-adjacency matrix\nas network representation, which has already been used to generalize\neigenvector centrality to temporal and multiplex networks. With a suitable\nchoice of edge weights, the definition of single-layer matrix function-based\ncentrality measures in terms of walks on networks carries over naturally to the\nmultilayer case. In contrast to other walk-based centralities, matrix\nfunction-based centralities are parameterized measures, which have been shown\nto interpolate between (local) degree and (global) eigenvector centrality in\nthe single-layer case. As the explicit evaluation of the involved matrix\nfunction expressions becomes infeasible for medium to large-scale networks, we\npresent highly efficient approximation techniques from numerical linear\nalgebra, which rely on Krylov subspace methods, Gauss quadrature, and\nstochastic trace estimation. We present extensive numerical studies on\nsynthetic and real-world multiplex transportation, communication, and\ncollaboration networks. The comparison with established multilayer centrality\nmeasures shows that our framework produces meaningful rankings of nodes,\nlayers, and node-layer pairs. Furthermore, our experiments corroborate the\ntheoretically indicated linear computational complexity of the employed\nnumerical methods for sparse supra-adjacency matrices, which allows the\nefficient treatment of large-scale networks with the number of node-layer pairs\nof order $10^7$ or higher.\n', 'Centrality measures for graphons: Accounting for uncertainty in networks   As relational datasets modeled as graphs keep increasing in size and their\ndata-acquisition is permeated by uncertainty, graph-based analysis techniques\ncan become computationally and conceptually challenging. In particular, node\ncentrality measures rely on the assumption that the graph is perfectly known --\na premise not necessarily fulfilled for large, uncertain networks. Accordingly,\ncentrality measures may fail to faithfully extract the importance of nodes in\nthe presence of uncertainty. To mitigate these problems, we suggest a\nstatistical approach based on graphon theory: we introduce formal definitions\nof centrality measures for graphons and establish their connections to\nclassical graph centrality measures. A key advantage of this approach is that\ncentrality measures defined at the modeling level of graphons are inherently\nrobust to stochastic variations of specific graph realizations. Using the\ntheory of linear integral operators, we define degree, eigenvector, Katz and\nPageRank centrality functions for graphons and establish concentration\ninequalities demonstrating that graphon centrality functions arise naturally as\nlimits of their counterparts defined on sequences of graphs of increasing size.\nThe same concentration inequalities also provide high-probability bounds\nbetween the graphon centrality functions and the centrality measures on any\nsampled graph, thereby establishing a measure of uncertainty of the measured\ncentrality score. The same concentration inequalities also provide\nhigh-probability bounds between the graphon centrality functions and the\ncentrality measures on any sampled graph, thereby establishing a measure of\nuncertainty of the measured centrality score.\n']","[('network centrality', 0.7047029733657837), ('centrality measures', 0.6981902122497559), ('centrality', 0.5895329117774963), ('networks vertices', 0.5262851119041443), ('complex networks', 0.5112992525100708), ('network analysis', 0.5018473863601685), ('network science', 0.5003154873847961), ('network adjacency', 0.5000029802322388), ('centralization', 0.4732985198497772), ('important nodes', 0.4599999189376831)]"
576,576,53,576_measures fourier_almost periodicity_measure fourier_almost periodic,"['measures fourier', 'almost periodicity', 'measure fourier', 'almost periodic', 'periodic distributions', 'periodic sets', 'measure', 'measures', 'bounded measure', 'tempered distributions']","['Pure Point Diffraction and Mean, Besicovitch and Weyl Almost Periodicity   We show that a translation bounded measure has pure point diffraction if and\nonly if it is mean almost periodic. We then go on and show that a translation\nbounded measure solves what we call the phase problem if and only if it is\nBesicovitch almost periodic. Finally, we show that a translation bounded\nmeasure solves the phase problem independent of the underlying van Hove\nsequence if and only if it is Weyl almost periodic. These results solve\nfundamental issues in the theory of pure point diffraction and answer questions\nof Lagarias.\n', 'On the Fourier Analysis of Measures with Meyer Set Support   In this paper we show the existence of the generalized Eberlein decomposition\nfor Fourier transformable measures with Meyer set support. We prove that each\nof the three components is also Fourier transformable and has Meyer set\nsupport. We obtain that each of the pure point, absolutely continuous and\nsingular continuous components of the Fourier transform is a strong almost\nperiodic measure, and hence is either trivial or has relatively dense support.\nWe next prove that the Fourier transform of a measure with Meyer set support is\nnorm almost periodic, and hence so is each of the pure point, absolutely\ncontinuous and singular continuous components. We show that a measure with\nMeyer set support is Fourier transformable if and only if it is a linear\ncombination of positive definite measures, which can be chosen with Meyer set\nsupport, solving a particular case of an open problem. We complete the paper by\ndiscussing some applications to the diffraction of weighted Dirac combs with\nMeyer set support.\n', 'On Weakly Almost Periodic Measures   We study the diffraction and dynamical properties of translation bounded\nweakly almost periodic measures. We prove that the dynamical hull of a weakly\nalmost periodic measure is a weakly almost periodic dynamical system with\nunique minimal component given by the hull of the strongly almost periodic\ncomponent of the measure. In particular the hull is minimal if and only if the\nmeasure is strongly almost periodic and the hull is always measurably conjugate\nto a torus and has pure point spectrum with continuous eigenfunctions. As an\napplication we show the stability of the class of weighted Dirac combs with\nMeyer set or FLC support and deduce that such measures have either trivial or\nlarge pure point respectively continuous spectrum. We complement these results\nby investigating the Eberlein convolution of two weakly almost periodic\nmeasures. Here, we show that it is unique and a strongly almost periodic\nmeasure. We conclude by studying the Fourier-Bohr coefficients of weakly almost\nperiodic measures.\n']","[('measures fourier', 0.6879010796546936), ('almost periodicity', 0.6286703944206238), ('measure fourier', 0.6280233860015869), ('almost periodic', 0.5788630247116089), ('periodic distributions', 0.5179911851882935), ('periodic sets', 0.4664420783519745), ('measure', 0.45926353335380554), ('measures', 0.4568881392478943), ('bounded measure', 0.45468512177467346), ('tempered distributions', 0.44849804043769836)]"
577,577,53,577_polytopes vertices_polytope vertices_edge polytopes_reflexive polytopes,"['polytopes vertices', 'polytope vertices', 'edge polytopes', 'reflexive polytopes', 'dimensional polytope', 'polytopes', 'dual polytope', 'reflexive polytope', 'simple polytope', 'simplicial polytopes']","[""A lower bound theorem for $d$-polytopes with $2d+2$ vertices   We establish a lower bound theorem for the number of $k$-faces ($1\\le k\\le\nd-2$) in a $d$-dimensional polytope $P$ (abbreviated as a $d$-polytope) with\n$2d+2$ vertices, building on the known case for $k=1$. There are two distinct\nlower bounds depending on the number of facets in the $d$-polytope. We identify\nall minimisers for $d\\le 5$. If $P$ has $d+2$ facets, the lower bound is tight\nwhen $d$ is odd. For $d\\ge 5$ and $P$ with at least $d+3$ facets, the lower\nbound is always tight. Moreover, for $1\\le k\\le {d/3}-2$, minimisers among\n$d$-polytopes with $2d+2$ vertices are those with at least $d+3$ facets, while\nfor ${0.4d}\\le k\\le d-1$, the lower bound arises from $d$-polytopes with $d+2$\nfacets. These results support Pineda-Villavicencio's lower bound conjecture for\n$d$-polytopes with at most $3d-1$ vertices.\n"", ""A Positive Answer to B\\'ar\\'any's Question on Face Numbers of Polytopes   Despite a full characterization of the face vectors of simple and simplicial\npolytopes, the face numbers of general polytopes are poorly understood. Around\n1997, B\\'ar\\'any asked whether for all convex $d$-polytopes $P$ and all $0 \\leq\nk \\leq d-1$, $f_k(P) \\geq \\min\\{f_0(P), f_{d-1}(P)\\}$. We answer B\\'ar\\'any's\nquestion in the affirmative and prove a stronger statement: for all convex\n$d$-polytopes $P$ and all $0 \\leq k \\leq d-1$, \\[ \\frac{f_k(P)}{f_0(P)} \\geq\n\\frac{1}{2}\\biggl[{\\lceil \\frac{d}{2} \\rceil \\choose k} + {\\lfloor \\frac{d}{2}\n\\rfloor \\choose k}\\biggr], \\qquad \\frac{f_k(P)}{f_{d-1}(P)} \\geq\n\\frac{1}{2}\\biggl[{\\lceil \\frac{d}{2} \\rceil \\choose d-k-1} + {\\lfloor\n\\frac{d}{2} \\rfloor \\choose d-k-1}\\biggr]. \\] In the former, equality holds\nprecisely when $k=0$ or when $k=1$ and $P$ is simple. In the latter, equality\nholds precisely when $k=d-1$ or when $k=d-2$ and $P$ is simplicial.\n"", 'Reflexive polytopes arising from edge polytopes   It is known that every lattice polytope is unimodularly equivalent to a face\nof some reflexive polytope. A stronger question is to ask whether every\n$(0,1)$-polytope is unimodularly equivalent to a facet of some reflexive\npolytope. A large family of $(0,1)$-polytopes are the edge polytopes of finite\nsimple graphs. In the present paper, it is shown that, by giving a new class of\nreflexive polytopes, each edge polytope is unimodularly equivalent to a facet\nof some reflexive polytope. Furthermore, we extend the characterization of\nnormal edge polytopes to a characterization of normality for these new\nreflexive polytopes.\n']","[('polytopes vertices', 0.6839759945869446), ('polytope vertices', 0.6730940937995911), ('edge polytopes', 0.6613056659698486), ('reflexive polytopes', 0.6525644063949585), ('dimensional polytope', 0.6518339514732361), ('polytopes', 0.6427150964736938), ('dual polytope', 0.6318151354789734), ('reflexive polytope', 0.6311408281326294), ('simple polytope', 0.6257333159446716), ('simplicial polytopes', 0.6222288012504578)]"
578,578,53,578_delay differential equations_delay differential_delay equations_differential delay,"['delay differential equations', 'delay differential', 'delay equations', 'differential delay', 'linear delay differential', 'solutions delay', 'delay systems', 'functional differential equations', 'state dependent delay', 'delay parameter']","[""On solution manifolds of some differential equations with more general\n  state-dependent delay   Differential equations with state-dependent delays define a semiflow of\ncontinuously differentiable solution operators in general only on the\nassociated {\\it solution manifold} in the Banach space\n$C^1_n=C^1([-h,0],\\mathbb{R}^n)$. For a prototypic example we develop a new\nproof that its solution manifold is diffeomorphic to an open subset of the\nsubspace given by $\\phi'(0)=0$, without recourse to a restrictive hypothesis\nabout the form of delays which is instrumental in earlier work on the nature of\nsolution manifolds. The new proof uses the framework of algebraic-delay\nsystems.\n"", 'Parameterization method for state-dependent delay perturbation of an\n  ordinary differential equation   We consider state-dependent delay equations (SDDE) obtained by adding delays\nto a planar ordinary differential equation with a limit cycle. These situations\nappear in models of several physical processes, where small delay effects are\nadded. Even if the delays are small, they are very singular perturbations since\nthe natural phase space of an SDDE is an infinite dimensional space.\n  We show that the SDDE admits solutions which resemble the solutions of the\nODE. That is, there exist a periodic solution and a two parameter family of\nsolutions whose evolution converges to the periodic solution. Even if the phase\nspace of the SDDE is naturally a space of functions, we show that there are\ninitial values which lead to solutions similar to that of the ODE.\n  The method of proof bypasses the theory of existence, uniqueness, dependence\non parameters of SDDE. We consider the class of functions of time that have a\nwell defined behavior (e.g. periodic, or asymptotic to periodic) and derive a\nfunctional equation which imposes that they are solutions of the SDDE. These\nfunctional equations are studied using methods of functional analysis. We\nprovide a result in ""a posteriori"" format: Given an approximate solution of the\nfunctional equation, which has some good condition numbers, we prove that there\nis true solution close to the approximate one. Thus, we can use the result to\nvalidate the results of numerical computations. The method of proof leads also\nto practical algorithms. In a companion paper, we present the implementation\ndetails and representative results.\n  One feature of the method presented here is that it allows to obtain smooth\ndependence on parameters for the periodic solutions and their slow stable\nmanifolds without studying the smoothness of the flow (which seems to be\nproblematic for SDDEs, for now the optimal result on smoothness of the flow is\n$C^1$).\n', ""Topologies of continuity for Carath\\'{e}odory delay differential\n  equations with applications in non-autonomous dynamics   We study some already introduced and some new strong and weak topologies of\nintegral type to provide continuous dependence on continuous initial data for\nthe solutions of non-autonomous Carath\\'eodory delay differential equations. As\na consequence, we obtain new families of continuous skew-product semiflows\ngenerated by delay differential equations whose vector fields belong to such\nmetric topological vector spaces of Lipschitz Carath\\'eodory functions.\nSufficient conditions for the equivalence of all or some of the considered\nstrong or weak topologies are also given. Finally, we also provide results of\ncontinuous dependence of the solutions as well as of continuity of the\nskew-product semiflows generated by Carath\\'eodory delay differential equations\nwhen the considered phase space is a Sobolev space.\n""]","[('delay differential equations', 0.7437011003494263), ('delay differential', 0.6293702721595764), ('delay equations', 0.6289461851119995), ('differential delay', 0.6233406662940979), ('linear delay differential', 0.6214284300804138), ('solutions delay', 0.5660370588302612), ('delay systems', 0.5383453965187073), ('functional differential equations', 0.5148991346359253), ('state dependent delay', 0.5061132311820984), ('delay parameter', 0.4831099510192871)]"
579,579,53,579_galton watson trees_galton watson tree_watson trees_trees critical,"['galton watson trees', 'galton watson tree', 'watson trees', 'trees critical', 'random trees', 'tree conditioned', 'generated trees', 'watson tree', 'random tree', 'trees']","[""Conditioning Bienaym{\\'e}-Galton-Watson trees to have large\n  sub-populations   We study the local limit in distribution of Bienaym{\\'e}-Galton-Watson trees\nconditioned on having large sub-populations. Assuming a generic and aperiodic\ncondition on the offspring distribution, we prove the existence of a limit\ngiven by a Kesten's tree associated with a certain critical offspring\ndistribution.\n"", ""Critical exponential tiltings for size-conditioned multitype\n  Bienaym\\'e--Galton--Watson trees   We consider here multitype Bienaym\\'e--Galton--Watson trees, under the\nconditioning that the numbers of vertices of given type satisfy some linear\nrelations. We prove that, under some smoothness conditions on the offspring\ndistribution $\\mathbf{\\zeta}$, there exists a critical offspring distribution\n$\\tilde{\\mathbf{\\zeta}}$ such that the trees with offspring distribution\n$\\mathbf{\\zeta}$ and $\\tilde{\\mathbf{\\zeta}}$ have the same law under our\nconditioning. This allows us in a second time to characterize the local limit\nof such trees, as their size goes to infinity. Our main tool is a notion of\nexponential tilting for multitype Bienaym\\'e--Galton--Watson trees.\n"", 'Invariance and attraction properties of Galton-Watson trees   We give a description of invariants and attractors of the critical and\nsubcritical Galton-Watson tree measures under the operation of Horton pruning\n(cutting tree leaves with subsequent series reduction). Under a regularity\ncondition, the class of invariant measures consists of the critical binary\nGalton-Watson tree and a one-parameter family of critical Galton-Watson trees\nwith offspring distribution $\\{q_k\\}$ that has a power tail $q_k\\sim\nCk^{-(1+1/q_0)}$, where $q_0\\in(1/2,1)$. Each invariant measure has a non-empty\ndomain of attraction under consecutive Horton pruning, specified by the tail\nbehavior of the initial Galton-Watson offspring distribution. The invariant\nmeasures satisfy the Toeplitz property for the Tokunaga coefficients and obey\nthe Horton law with exponent $R = (1-q_0)^{-1/q_0}$.\n']","[('galton watson trees', 0.6364066004753113), ('galton watson tree', 0.5927675366401672), ('watson trees', 0.5685687065124512), ('trees critical', 0.5674169659614563), ('random trees', 0.5657873749732971), ('tree conditioned', 0.5326477885246277), ('generated trees', 0.5226263999938965), ('watson tree', 0.5116195678710938), ('random tree', 0.49587926268577576), ('trees', 0.48195046186447144)]"
580,580,53,580_toeplitz matrices_matrices toeplitz_toeplitz matrices generated_toeplitz matrix,"['toeplitz matrices', 'matrices toeplitz', 'toeplitz matrices generated', 'toeplitz matrix', 'block toeplitz matrices', 'toeplitz operators', 'symmetric toeplitz', 'toeplitz systems', 'tridiagonal toeplitz', 'matrix sequences']","['A note on eigenvalues and singular values of variable Toeplitz matrices\n  and matrix-sequences, with application to variable two-step BDF\n  approximations to parabolic equations   Here, we consider a more general class of matrix-sequences and we prove that\nthey belong to the maximal $*$-algebra of generalized locally Toeplitz (GLT)\nmatrix-sequences. Then, we identify the associated GLT symbols and GLT\nmomentary symbols in the general setting and in the specific case, by providing\nin both cases a spectral and singular value analysis. More specifically, we use\nthe GLT tools in order to study the asymptotic behaviour of the eigenvalues and\nsingular values of the considered BDF matrix-sequences, in connection with the\ngiven non-uniform grids. Numerical examples, visualizations, and open problems\nend the present work.\n', 'A Note on Generalized Locally Toeplitz Operators   Generalized Locally Toeplitz (GLT) matrix sequences arise from large linear\nsystems that approximate Partial Differential Equations (PDEs), Fractional\nDifferential Equations (FDEs), and Integro-Differential Equations (IDEs). GLT\nsequences of matrices have been developed to study the spectral/singular value\nbehaviour of the numerical approximations to various PDEs, Fades and IDEs.\nThese approximations can be achieved using any discretization method on\nappropriate grids through local techniques such as Finite Differences, Finite\nElements, Finite Volumes, Isogeometric Analysis, and Discontinuous Galerkin\nmethods. Spectral and singular value symbols are essential for analyzing the\neigenvalue and singular value distributions of matrix sequences in the Weyl\nsense. In this article, we provide a comprehensive overview of the\noperator-theoretic aspect of GLT sequences. The theory of GLT sequences, along\nwith findings on the asymptotic spectral distribution of perturbed matrix\nsequences, is a highly effective and successful method for calculating the\nspectral symbol f. Therefore, developing an automatic procedure to compute the\nspectral symbols of these matrix sequences would be advantageous, a task that\nAhmed Ratnani, N S Sarathkumar, S. Serra-Capizzano have partially undertaken.\nAs an application of the theory developed here, we propose an automatic\nprocedure for computing the symbol of the underlying sequences of matrices,\nassuming they form a GLT sequence that meets mild conditions.\n', 'Toeplitz Momentary Symbols: definition, results, and limitations in the\n  spectral analysis of Structured Matrices   A powerful tool for analyzing and approximating the singular values and\neigenvalues of structured matrices is the theory of GLT sequences. By the GLT\ntheory one can derive a function, which describes the singular value or the\neigenvalue distribution of the sequence, the latter under precise assumptions.\nHowever, for small values of the matrix size of the considered sequence, the\napproximations may not be as good as it is desirable, since in the construction\nof the GLT symbol one disregards small norm and low-rank perturbations. On the\nother hand, LFA can be used to construct polynomial symbols in a similar manner\nfor discretizations, where the geometric information is present, but the small\nnorm perturbations are retained. The main focus of this paper is the\nintroduction of the concept of sequence of ""Toeplitz momentary symbols"",\nassociated with a given sequence of truncated Toeplitz-like matrices. We\nconstruct the symbol in the same way as in the GLT theory, but we keep the\ninformation of the small norm contributions. The low-rank contributions are\nstill disregarded, and we give an idea on the reason why this is negligible in\ncertain cases and why it is not in other cases, being aware that in presence of\nhigh nonnormality the same low-rank perturbation can produce a dramatic change\nin the eigenvalue distribution. Moreover, a difference with respect to the LFA\nsymbols is that GLT symbols and Toeplitz momentary symbols are more general and\nare applicable to a larger class of matrices. We show the applicability of the\napproach which leads to higher accuracy in some cases when compared with the\nGLT symbol. Finally, since for many applications and their analysis it is often\nnecessary to consider non-square Toeplitz matrices, we formalize and provide\nsome useful definitions, applicable for non-square Toeplitz momentary symbols.\n']","[('toeplitz matrices', 0.7590765357017517), ('matrices toeplitz', 0.7464879751205444), ('toeplitz matrices generated', 0.7420318126678467), ('toeplitz matrix', 0.7348496913909912), ('block toeplitz matrices', 0.71797114610672), ('toeplitz operators', 0.6518711447715759), ('symmetric toeplitz', 0.6343663930892944), ('toeplitz systems', 0.6268385052680969), ('tridiagonal toeplitz', 0.6021559238433838), ('matrix sequences', 0.5148468613624573)]"
581,581,53,581_climate models_bifurcations_bifurcation_bifurcation analysis,"['climate models', 'bifurcations', 'bifurcation', 'bifurcation analysis', 'tipping point', 'induced tipping', 'tipping points', 'oscillations', 'climate change', 'global climate']","['Tipping mechanisms in a carbon cycle model   Rate-induced tipping (R-tipping) occurs when a ramp parameter changes rapidly\nenough to cause the system to tip between co-existing, attracting states, while\nnoise-induced tipping (N-tipping) occurs when there are random transitions\nbetween two attractors of the underlying deterministic system. This work\ninvestigates R-tipping and N-tipping events in a carbonate system in the upper\nocean, in which the key objective is understanding how the system undergoes\ntipping away from a stable fixed point in a bistable regime. While R-tipping\naway from the fixed point is straightforward, N-tipping poses challenges due to\na periodic orbit forming the basin boundary for the attracting fixed point of\nthe underlying deterministic system. Furthermore, in the case of N-tipping, we\nare interested in the case where noise is away from the small noise limit, as\nit is more appropriate for the application. We compute the most probable escape\npath (MPEP) for our system, resulting in a firm grasp on the least action path\nin an asymmetric system of higher scale. Our analysis shows that the carbon\ncycle model is susceptible to both tipping mechanisms when using the standard\nformulations.\n', 'Uniting Parametric Uncertainty and Tipping Diagrams   Various subsystems of the Earth system may undergo critical transitions by\npassing a so-called tipping point, under sustained changes to forcing. For\nexample, the Atlantic Meridional Overturning Circulation (AMOC) is of\nparticular importance for North Atlantic heat transport and is thought to be\npotentially at risk of tipping. Given a model of such a subsystem that\naccurately includes the relevant physical processes, whether tipping occurs or\nnot, will depend on model parameters that typically are uncertain. Reducing\nthis parametric uncertainty is important to understand the likelihood of\ntipping behavior being present in the system and possible tipping locations. In\nthis letter, we develop improved estimates for the parametric uncertainty by\ninferring probability distributions for the model parameters based on physical\nconstraints and by using a Bayesian inversion technique. To visualize the\nimpact of parametric uncertainty, we extend classical tipping diagrams by\nvisualizing probabilistic bifurcation curves according to the inferred\ndistribution of the model parameter. Furthermore, we highlight the uncertain\nlocations of tipping points along the probabilistic bifurcation curves. We\nshowcase our probabilistic visualizations of the tipping behavior using a\nsimple box-model of the AMOC, the Stommel-Cessi model [5].\n', 'Signatures consistent with multi-frequency tipping in the Atlantic\n  meridional overturning circulation   The early detection of tipping points, which describe a rapid departure from\na stable state, is an important theoretical and practical challenge. Tipping\npoints are most commonly associated with the disappearance of steady-state or\nperiodic solutions at fold bifurcations. We discuss here multi-frequency\ntipping (M-tipping), which is tipping due to the disappearance of an attracting\ntorus. M-tipping is a generic phenomenon in systems with at least two intrinsic\nor external frequencies that can interact and, hence, is relevant to a wide\nvariety of systems of interest. We show that the more complicated sequence of\nbifurcations involved in M-tipping provides a possible consistent explanation\nfor as yet unexplained behavior observed near tipping in climate models for the\nAtlantic meridional overturning circulation. More generally, this work provides\na path towards identifying possible early-warning signs of tipping in\nmultiple-frequency systems.\n']","[('climate models', 0.5048434734344482), ('bifurcations', 0.45939743518829346), ('bifurcation', 0.4437396824359894), ('bifurcation analysis', 0.42380547523498535), ('tipping point', 0.39182770252227783), ('induced tipping', 0.3764795660972595), ('tipping points', 0.3666541576385498), ('oscillations', 0.35940080881118774), ('climate change', 0.3574243485927582), ('global climate', 0.35260340571403503)]"
582,582,53,582_fracture networks_porous media flow_flow porous media_darcy flow,"['fracture networks', 'porous media flow', 'flow porous media', 'darcy flow', 'flow porous', 'fracture', 'fractured', 'fractures', 'finite volume scheme', 'porous media']","['A hybrid-mixed finite element method for single-phase Darcy flow in\n  fractured porous media   We present a hybrid-mixed finite element method for\n  a novel hybrid-dimensional model of single-phase Darcy flow in a fractured\nporous media. In this model, the fracture is treated as an $(d-1)$-dimensional\ninterface within the $d$-dimensional fractured porous domain, for $d=2, 3$. Two\nclasses of fracture are distinguished based on the permeability magnitude ratio\nbetween the fracture and its surrounding medium: when the permeability in the\nfracture is (significantly) larger than in its surrounding medium, it is\nconsidered as a {\\it conductive} fracture; when the permeability in the\nfracture is (significantly) smaller than in its surrounding medium, it is\nconsidered as a {\\it blocking} fracture. The conductive fractures are treated\nusing the classical hybrid-dimensional approach of the interface model where\npressure is assumed to be continuous across the fracture interfaces, while the\nblocking fractures are treated using the recent Dirac-$\\delta$ function\napproach where normal component of Darcy velocity is assumed to be continuous\nacross the interface. Due to the use of Dirac-$\\delta$ function approach for\nthe blocking fractures, our numerical scheme allows for nonconforming meshes\nwith respect to the blocking fractures. This is the major novelty of our model\nand numerical discretization. Moreover, our numerical scheme produces locally\nconservative velocity approximations and leads to a symmetric positive definite\nlinear system involving pressure degrees of freedom on the mesh skeleton only.\nThe performance of the proposed method is demonstrated by various benchmark\ntest cases in both two- and three-dimensions. Numerical results indicate that\nthe proposed scheme is highly competitive with existing methods in the\nliterature.\n', 'Geometric model of the fracture as a manifold immersed in porous media   In this work, we analyze the flow filtration process of slightly compressible\nfluids in porous media containing man made fractures with complex geometries.\nWe model the coupled fracture-porous media system where the linear Darcy flow\nis considered in porous media and the nonlinear Forchheimer equation is used\ninside the fracture. We develop a model to examine the flow inside fractures\nwith complex geometries and variable thickness, on a Riemannian manifold. The\nfracture is represented as the normal variation of a surface immersed in\n$\\mathbb{R}^3$. Using operators of Laplace Beltrami type and geometric\nidentities, we model an equation that describes the flow in the fracture. A\nreduced model is obtained as a low dimensional BVP. We then couple the model\nwith the porous media. Theoretical and numerical analysis have been performed\nto compare the solutions between the original geometric model and the reduced\nmodel in reservoirs containing fractures with complex geometries. We prove that\nthe two solutions are close, and therefore, the reduced model can be\neffectively used in large scale simulators for long and thin fractures with\ncomplicated geometry.\n', 'A five field formulation for flow simulations in porous media with\n  fractures and barriers via an optimization based domain decomposition method   The present work deals with the numerical resolution of coupled 3D-2D\nproblems arising from the simulation of fluid flow in fractured porous media\nmodeled via the Discrete Fracture and Matrix (DFM) model. According to the DFM\nmodel, fractures are represented as planar interfaces immersed in a 3D porous\nmatrix and can behave as preferential flow paths, in the case of conductive\nfractures, or can actually be a barrier for the flow, when, instead, the\npermeability in the normal-to-fracture direction is small compared to the\npermeability of the matrix. Consequently, the pressure solution in a DFM can be\ndiscontinuous across a barrier, as a result of the geometrical dimensional\nreduction operated on the fracture.\n  The present work is aimed at developing a numerical scheme suitable for the\nsimulation of the flow in a DFM with fractures and barriers, using a mesh for\nthe 3D matrix non conforming to the fractures and that is ready for domain\ndecomposition. This is achieved starting from a PDE-constrained optimization\nmethod, currently available in literature only for conductive fractures in a\nDFM. First, a novel formulation of the optimization problem is defined to\naccount for non permeable fractures. These are described by a filtration-like\ncoupling at the interface with the surrounding porous matrix. Also the extended\nfinite element method with discontinuous enrichment functions is used to\nreproduce the pressure solution in the matrix around a barrier.\n  The method is presented here in its simplest form, for clarity of exposition,\ni.e. considering the case of a single fracture in a 3D domain, also providing a\nproof of the well posedness of the resulting discrete problem. Four validation\nexamples are proposed to show the viability and the effectiveness of the\nmethod.\n']","[('fracture networks', 0.548383891582489), ('porous media flow', 0.4655747413635254), ('flow porous media', 0.46192091703414917), ('darcy flow', 0.41419076919555664), ('flow porous', 0.4041970372200012), ('fracture', 0.3828469216823578), ('fractured', 0.37078291177749634), ('fractures', 0.36413612961769104), ('finite volume scheme', 0.34907498955726624), ('porous media', 0.3359956741333008)]"
583,583,53,583_flow constraints_minimum cost flow_cost flow_multi commodity flow,"['flow constraints', 'minimum cost flow', 'cost flow', 'multi commodity flow', 'flow network', 'minimum flow', 'flow formulations', 'flow decomposition', 'max flow min', 'maximum flow']","['Solving Unsplittable Network Flow Problems with Decision Diagrams   In unsplittable network flow problems, certain nodes must satisfy a\ncombinatorial requirement that the incoming arc flows cannot be split or merged\nwhen routed through outgoing arcs. This so-called ""no-split no-merge""\nrequirement arises in unit train scheduling where train consists should remain\nintact at stations that lack necessary equipment and manpower to attach/detach\nthem. Solving the unsplittable network flow problems with standard\nmixed-integer programming formulations is computationally difficult due to the\nlarge number of binary variables needed to determine matching pairs between\nincoming and outgoing arcs of nodes with no-split no-merge constraint. In this\npaper, we study a stochastic variant of the unit train scheduling problem where\nthe demand is uncertain. We develop a novel decision diagram (DD)-based\nframework that decomposes the underlying two-stage formulation into a master\nproblem that contains the combinatorial requirements, and a subproblem that\nmodels a continuous network flow problem. The master problem is modeled by a DD\nin a transformed space of variables with a smaller dimension, leading to a\nsubstantial improvement in solution time. Similarly to the Benders\ndecomposition technique, the subproblems output cutting planes that are used to\nrefine the master DD. Computational experiments show a significant improvement\nin solution time of the DD framework compared with that of standard methods.\n', 'Robust Minimum Cost Flow Problem Under Consistent Flow Constraints   The robust minimum cost flow problem under consistent flow constraints\n(RobMCF$\\equiv$) is a new extension of the minimum cost flow (MCF) problem. In\nthe RobMCF$\\equiv$ problem, we consider demand and supply that are subject to\nuncertainty. For all demand realizations, however, we require that the flow\nvalue on an arc needs to be equal if it is included in the predetermined arc\nset given. The objective is to find feasible flows that satisfy the equal flow\nrequirements while minimizing the maximum occurring cost among all demand\nrealizations.\n  In the case of a discrete set of scenarios, we derive structural results\nwhich point out the differences with the polynomial time solvable MCF problem\non networks with integral capacities. In particular, the Integral Flow Theorem\nof Dantzig and Fulkerson does not hold. For this reason, we require integral\nflows in the entire paper. We show that the RobMCF$\\equiv$ problem is strongly\n$\\mathcal{NP}$-hard on acyclic digraphs by a reduction from the $(3,B2)$-Sat\nproblem. Further, we demonstrate that the RobMCF$\\equiv$ problem is weakly\n$\\mathcal{NP}$-hard on series-parallel digraphs by providing a reduction from\nPartition and a pseudo-polynomial algorithm based on dynamic programming.\nFinally, we propose a special case on series-parallel digraphs for which we can\nsolve the RobMCF$\\equiv$ problem in polynomial time.\n', 'A Tight Max-Flow Min-Cut Duality Theorem for Non-Linear Multicommodity\n  Flows   The Max-Flow Min-Cut theorem is the classical duality result for the Max-Flow\nproblem, which considers flow of a single commodity. We study a multiple\ncommodity generalization of Max-Flow in which flows are composed of real-valued\nk-vectors through networks with arc capacities formed by regions in \\R^k. Given\nthe absence of a clear notion of ordering in the multicommodity case, we define\nthe generalized max flow as the feasible region of all flow values.\n  We define a collection of concepts and operations on flows and cuts in the\nmulticommodity setting. We study the mutual capacity of a set of cuts, defined\nas the set of flows that can pass through all cuts in the set. We present a\nmethod to calculate the mutual capacity of pairs of cuts, and then generalize\nthe same to a method of calculation for arbitrary sets of cuts. We show that\nthe mutual capacity is exactly the set of feasible flows in the network, and\nhence is equal to the max flow. Furthermore, we present a simple class of the\nmulticommodity max flow problem where computations using this tight duality\nresult could run significantly faster than default brute force computations.\n  We also study more tractable special cases of the multicommodity max flow\nproblem where the objective is to transport a maximum real or integer multiple\nof a given vector through the network. We devise an augmenting cycle search\nalgorithm that reduces the optimization problem to one with m constraints in at\nmost \\R^{(m-n+1)k} space from one that requires mn constraints in \\R^{mk} space\nfor a network with n nodes and m edges. We present efficient algorithms that\ncompute eps-approximations to both the ratio and the integer ratio maximum flow\nproblems.\n']","[('flow constraints', 0.650623619556427), ('minimum cost flow', 0.6360247731208801), ('cost flow', 0.5561113953590393), ('multi commodity flow', 0.5506693720817566), ('flow network', 0.532760739326477), ('minimum flow', 0.5316399931907654), ('flow formulations', 0.5111958384513855), ('flow decomposition', 0.5090819597244263), ('max flow min', 0.5083338022232056), ('maximum flow', 0.4998980164527893)]"
584,584,52,584_jacobian conjecture_jacobian_jacobian determinant_jacobian matrix,"['jacobian conjecture', 'jacobian', 'jacobian determinant', 'jacobian matrix', 'polynomial maps', 'vanishing conjecture', 'conjecture dimensions', 'polynomial mappings', 'conjecture characteristic', 'polynomial map']","['Jacobian conjecture in $\\mathbb R^2$   Jacobian conjecture states that if $F:\\ \\mathbb C^n(\\mathbb R^n)\\rightarrow\n\\mathbb C^n(\\mathbb R^n)$ is a polynomial map such that the Jacobian of $F$ is\na nonzero constant, then $F$ is injective. This conjecture is still open for\nall $n\\ge 2$, and for both $\\mathbb C^n$ and $\\mathbb R^n$. Here we provide a\npositive answer to the Jacobian conjecture in $\\mathbb R^2$ via the tools from\nthe theory of dynamical systems.\n', 'Characteristic p approaches to the Jacobian Conjecture   We present several versions of the Jacobian Conjecture in positive\ncharacteristic each of which if true would imply the Jacobian conjecture in\ncharacteristic 0. We test these characteristic p versions of the conjecture\nagainst several families of Jacobian pairs in characteristic p. Based on the\nresults we propose a characteristic p approach to solving the Jacobian\nConjecture in characteristic 0.\n', ""The necessary and sufficient conditions for the real Jacobian conjecture   The real Jacobian conjecture claims that if\n$F=\\left(f^1,\\ldots,f^n\\right):\\mathbb{R}^n\\rightarrow \\mathbb{R}^n$ is a\npolynomial map such that $\\det DF$ is nowhere zero, then $F$ is a global\ninjective.\n  The first part is to study the two-dimensional real Jacobian conjecture via\nthe method of the qualitative theory of dynamical systems. By Bendixson\ncompactification, an induced polynomial differential system can be obtained\nfrom the Hamiltonian system associated to polynomial map $F$. We prove that the\nfollowing statements are equivalent: (A) $F$ is a global injective; (B) the\norigin of induced system is a center; (C) the origin of induced system is a\nmonodromic singular point; (D) the origin of induced system has no hyperbolic\nsectors; (E) induced system has a $C^k$ first integral with an isolated minimun\nat the origin and $k\\in\\mathbb{N}^{+}\\cup\\{\\infty\\}$. Moreover, applying the\nabove results we present a necessary and sufficient condition for the validity\nof the two-dimensional real Jacobian conjecture, which is an algebraic\ncriterion. By definition a criterion function, $F$ is a global injective if and\nonly if the limit of criterion function is infinite as\n$\\left|x\\right|+\\left|y\\right|$ tends to infinity. This algebraic criterion\nimproves the main result of Braun et al [J. Differential Equations {\\bf 260}\n(2016) 5250-5258].\n  In the second part, the necessary and sufficient conditions on the\n$n$-dimensional real Jacobian conjecture is obtained. Using the tool from the\nnonlinear functional analysis, $F$ is a global injective if and only if\n$\\parallel F\\left(\\mathbf{x}\\right)\\parallel$ approaches to infinite as\n$\\parallel\\mathbf{x}\\parallel\\rightarrow\\infty$, which is a generalization of\nthe above algebraic criterion. As an application, we give an alternate proof of\nthe Cima's result on the $n$-dimensional real Jacobian conjecture [Nonlinear\nAnal. {\\bf 26} (1996) 877-885].\n""]","[('jacobian conjecture', 0.791641116142273), ('jacobian', 0.6024095416069031), ('jacobian determinant', 0.5814048051834106), ('jacobian matrix', 0.5321245789527893), ('polynomial maps', 0.4801611304283142), ('vanishing conjecture', 0.45821526646614075), ('conjecture dimensions', 0.4536340832710266), ('polynomial mappings', 0.4506003260612488), ('conjecture characteristic', 0.4483993649482727), ('polynomial map', 0.4444870352745056)]"
585,585,52,585_nernst planck equations_poisson nernst planck_planck equations_ions,"['nernst planck equations', 'poisson nernst planck', 'planck equations', 'ions', 'planck system', 'ionic', 'poisson boltzmann', 'planck navier', 'nernst planck navier', 'ion']","[""Integral equation method for the 1D steady-state Poisson-Nernst-Planck\n  equations   An integral equation method is presented for the 1D steady-state\nPoisson-Nernst-Planck equations modeling ion transport through membrane\nchannels. The differential equations are recast as integral equations using\nGreen's 3rd identity yielding a fixed-point problem for the electric potential\ngradient and ion concentrations. The integrals are discretized by a combination\nof midpoint and trapezoid rules and the resulting algebraic equations are\nsolved by Gummel iteration. Numerical tests for electroneutral and\nnon-electroneutral systems demonstrate the method's 2nd order accuracy and\nability to resolve sharp boundary layers. The method is applied to a 1D model\nof the K$^+$ ion channel with a fixed charge density that ensures cation\nselectivity. In these tests, the proposed integral equation method yields\npotential and concentration profiles in good agreement with published results.\n"", ""On the equilibrium of the Poisson-Nernst-Planck-Bikermann model\n  equipping with the steric and correlation effects   The Poisson-Nernst-Planck-Bikermann (PNPB) model, in which the ions and water\nmolecules are treated as different species with non-uniform sizes and valences\nwith interstitial voids, can describe the steric and correlation effects in\nionic solution neglected by the Poisson-Nernst-Planck and Poisson-Boltzmann\ntheories with point charge assumption. In the PNPB model, the electric\npotential is governed by the fourth-order Poisson-Bikermann (4PBik) equation\ninstead of the Poisson equation so that it can describe the correlation effect.\nWhat's more, the steric potential is included in the ionic and water fluxes as\nwell as the equilibrium Fermi-like distributions which characterizes the steric\neffect quantitatively.\n  In this work, after doing a nondimensionalization step, we analyze the\nself-adjointness and the kernel of the fourth-order operator of the 4PBik\nequation. Also, we show the positivity of the void volume function and the\nconvexity of the free energy. Following these properties, the well-posedness of\nthe PNPB model in equilibrium is given. Furthermore, because the PNPB model has\nan energy dissipated structure, we adopt a finite volume scheme which preserves\nthe energy dissipated property at the semi-discrete level. After that, various\nnumerical investigations are given to show the parameter dependence of the\nsteric effect to the steady state.\n"", 'An inverse averaging finite element method for solving the size-modified\n  Poisson-Nernst-Planck equations in ion channel simulations   In this work, we introduce an inverse averaging finite element method (IAFEM)\nfor solving the size-modified Poisson-Nernst-Planck (SMPNP) equations.\nComparing with the classical Poisson-Nernst-Planck (PNP) equations, the SMPNP\nequations add a nonlinear term to each of the Nernst-Planck (NP) fluxes to\ndescribe the steric repulsion which can treat multiple nonuniform particle\nsizes in simulations. Since the new terms include sums and gradients of ion\nconcentrations, the nonlinear coupling of SMPNP equations is much stronger than\nthat of PNP equations. By introducing a generalized Slotboom transform, each of\nthe size-modified NP equation is transformed into a self-adjoint equation with\nexponentially behaved coefficient, which has similar simple form to the\nstandard NP equation with the Slotboom transformation. This treatment enables\nemploying our recently developed inverse averaging technique to deal with the\nexponential coefficients of the reformulated formulations, featured with\nadvantages of numerical stability and flux conservation especially in strong\nnonlinear and convection-dominated cases. Comparing with previous stabilization\nmethods, the IAFEM proposed in this paper can still possess the numerical\nstability when dealing with convection-dominated problems. And it is more\nconcise and easier to be numerically implemented. Numerical experiments about a\nmodel problem with analytic solutions are presented to verify the accuracy and\norder of IAFEM for SMPNP equations. Studies about the size-effects of a sphere\nmodel and an ion channel system are presented to show that our IAFEM is more\neffective and robust than the traditional finite element method (FEM) when\nsolving SMPNP equations in simulations of biological systems.\n']","[('nernst planck equations', 0.5028902292251587), ('poisson nernst planck', 0.48824986815452576), ('planck equations', 0.4568244516849518), ('ions', 0.4455103576183319), ('planck system', 0.42010197043418884), ('ionic', 0.4139557480812073), ('poisson boltzmann', 0.41371777653694153), ('planck navier', 0.3851510286331177), ('nernst planck navier', 0.37874001264572144), ('ion', 0.37506619095802307)]"
586,586,52,586_stability rotating_stars_star_astrophysics,"['stability rotating', 'stars', 'star', 'astrophysics', 'euler poisson equations', 'stellar', 'stability criterion', 'euler poisson system', 'galaxies', 'boson stars']","['Nonlinear stability of non-rotating gaseous stars   For the non-rotating gaseous stars modeled by the compressible Euler-Poisson\nsystem with general pressure law, Lin and Zeng [18] proved a turning point\nprinciple, which gives the sharp linear stability/instability criteria for the\nnon-rotating gaseous stars. In this paper, we prove that the sharp linear\nstability criterion for the non-rotating stars also implies nonlinear orbital\nstability against general perturbations provided the global weak solutions\nexist. If the perturbations are further restricted to be spherically symmetric,\nthen nonlinear stability holds true unconditionally in the sense that the\nexistence of global weak solutions near the non-rotating star can be proved.\n', 'Separable Hamiltonian PDEs and Turning point principle for stability of\n  gaseous stars   We consider stability of non-rotating gaseous stars modeled by the\nEuler-Poisson system. Under general assumptions on the equation of states, we\nproved a turning point principle (TPP) that the stability of the stars is\nentirely determined by the mass-radius curve parameterized by the center\ndensity. In particular, the stability can only change at extrema (i.e. local\nmaximum or minimum points) of the total mass. For very general equation of\nstates, TPP implies that for increasing center density the stars are stable up\nto the first mass maximum and unstable beyond this point until next mass\nextremum (a minimum). Moreover, we get a precise counting of unstable modes and\nexponential trichotomy estimates for the linearized Euler-Poisson system. To\nprove these results, we develop a general framework of separable Hamiltonian\nPDEs. The general approach is flexible and can be used for many other problems\nincluding stability of rotating and magnetic stars, relativistic stars and\ngalaxies.\n', 'Stability of rotating gaseous stars   We consider stability of rotating gaseous stars modeled by the Euler-Poisson\nsystem with general equation of states. When the angular velocity of the star\nis Rayleigh stable, we proved a sharp stability criterion for axi-symmetric\nperturbations. We also obtained estimates for the number of unstable modes and\nexponential trichotomy for the linearized Euler-Poisson system. By using this\nstability criterion, we proved that for a family of slowly rotating stars\nparameterized by the center density with fixed angular velocity profile, the\nturning point principle is not true. That is, unlike the case of non-rotating\nstars, the change of stability of the rotating stars does not occur at extrema\npoints of the total mass. By contrast, we proved that the turning point\nprinciple is true for the family of slowly rotating stars with fixed angular\nmomentum distribution. When the angular velocity is Rayleigh unstable, we\nproved linear instability of rotating stars. Moreover, we gave a complete\ndescription of the spectra and sharp growth estimates for the linearized\nEuler-Poisson equation.\n']","[('stability rotating', 0.43998730182647705), ('stars', 0.4382312595844269), ('star', 0.40996667742729187), ('astrophysics', 0.39446714520454407), ('euler poisson equations', 0.39367735385894775), ('stellar', 0.3890090882778168), ('stability criterion', 0.382023423910141), ('euler poisson system', 0.3802114725112915), ('galaxies', 0.37533289194107056), ('boson stars', 0.3623967468738556)]"
587,587,52,587_chemical reaction networks_reaction networks_biochemical reaction networks_reaction network,"['chemical reaction networks', 'reaction networks', 'biochemical reaction networks', 'reaction network', 'stochastic reaction', 'networks stochastic', 'markov chains', 'reaction systems', 'models reaction', 'markov chain']","['Sensitivity of steady states in networks with application to Markov\n  chains and chemical reaction networks   We consider steady states of dynamics that have an underlying network\nstructure. We study how a steady state responds to small perturbations in the\nnetwork parameters and how this sensitivity is connected to the network\nstructure. We introduce a prototypical linear response equation and determine\nits sensitivity. This abstract result is applied to study the sensitivity of\nsteady states in two common dynamics on networks: continuous-time Markov chains\nand deterministically modelled chemical reaction networks. For continuous-time\nMarkov chains, we are able to efficiently compute the signs of the response in\nterms of the underlying network structure. The study of chemical reaction\nnetworks extends the sensitivity analysis to open systems with more complex\nnetwork structures.\n', 'Identifiability of SDEs for reaction networks Biochemical reaction networks are widely applied across scientific disciplines to model complex dynamic systems. We investigate the diffusion approximation of reaction networks with mass-action kinetics, focusing on the identifiability of the generator of the associated stochastic differential equations. We derive conditions under which the law of the diffusion approximation is identifiable and provide theorems for verifying identifiability in practice. Notably, our results show that some reaction networks have non-identifiable reaction rates, even when the law of the corresponding stochastic process is completely known. Moreover, we show that reaction networks with distinct graphical structures can generate the same diffusion law under specific choices of reaction rates. Finally, we compare our framework with identifiability results in the deterministic ODE setting and the discrete continuous-time Markov chain models for reaction networks.', 'Fast reactions with non-interacting species in stochastic reaction\n  networks   We consider stochastic reaction networks modeled by continuous-time Markov\nchains. Such reaction networks often contain many reactions, potentially\noccurring at different time scales, and have unknown parameters (kinetic rates,\ntotal amounts). This makes their analysis complex. We examine stochastic\nreaction networks with non-interacting species that often appear in examples of\ninterest (e.g. in the two-substrate Michaelis Menten mechanism).\nNon-interacting species typically appear as intermediate (or transient)\nchemical complexes that are depleted at a fast rate. We embed the Markov\nprocess of the reaction network into a one-parameter family under a two\ntime-scale approach, such that molecules of non-interacting species are\ndegraded fast. We derive simplified reaction networks where the non-interacting\nspecies are eliminated and that approximate the scaled Markov process in the\nlimit as the parameter becomes small. Then, we derive sufficient conditions for\nsuch reductions based on the reaction network structure for both homogeneous\nand time-varying stochastic settings, and study examples and properties of the\nreduction.\n']","[('chemical reaction networks', 0.6441124081611633), ('reaction networks', 0.6277099251747131), ('biochemical reaction networks', 0.6231732368469238), ('reaction network', 0.6180610060691833), ('stochastic reaction', 0.6173568964004517), ('networks stochastic', 0.5874063372612), ('markov chains', 0.4969191253185272), ('reaction systems', 0.4630500376224518), ('models reaction', 0.45952659845352173), ('markov chain', 0.4547452926635742)]"
588,588,52,588_spline functions_spline basis functions_spline interpolation_polynomial spline,"['spline functions', 'spline basis functions', 'spline interpolation', 'polynomial spline', 'splines basis', 'splines defined', 'spline basis', 'spline curves', 'spline approximation', 'splines']","['Polynomial and trigonometric splines   Classes of simple polynomial and simple trigonometric splines given by\nFourier series are considered. It is shown that the class of simple\ntrigonometric splines includes the class of simple polynomial splines. For some\nparameter values, the polynomial splines coincide with the trigonometric ones;\nthis allows to transfer to such trigonometric splines all the results obtained\nfor polynomial splines. Thus, it was possible to combine two powerful theories\n- the theory of trigonometric Fourier series and the theory of simple\npolynomial splines. The above material is illustrated by numerous examples.\n', 'About some properties of simple trigonometric splines   The class $Ts(r,f)$ the trigonometric interpolation splines depending on the\nparameter vectors, selected convergence factors and interpolation factors is\nconsidered. The main properties of simple interpolation trigonometric splines\nare given, which are also transferred to periodic simple interpolation\npolynomial splines. These results lead to the possibility of combining the\ntheory of simple polynomial interpolation splines and the basics of the theory\nof simple trigonometric splines into a single theory - the theory of\ninterpolation splines\n', 'B-splines and kernels of trigonometric interpolation splines   This article focuses on trigonometric Riemann B-splines and Riemann kernels\nof trigonometric interpolation splines of arbitrary order; it is shown that\ntrigonometric interpolation splines are a convolution of trigonometric\nB-splines with corresponding kernels. Theoretical statements are followed by\nexamples, and the results are applicable in many practical areas.\n']","[('spline functions', 0.7563902735710144), ('spline basis functions', 0.7491527199745178), ('spline interpolation', 0.7403860092163086), ('polynomial spline', 0.7366668581962585), ('splines basis', 0.7265335917472839), ('splines defined', 0.714167594909668), ('spline basis', 0.6895570755004883), ('spline curves', 0.6751521229743958), ('spline approximation', 0.6674691438674927), ('splines', 0.6577062606811523)]"
589,589,52,589_elastic scattering_inverse scattering theory_inverse scattering_scattering theory,"['elastic scattering', 'inverse scattering theory', 'inverse scattering', 'scattering theory', 'scattering', 'medium scattering', 'scattering problems', 'electromagnetic scattering', 'non scattering', 'wave field']","[""On corners scattering stably and stable shape determination by a single\n  far-field pattern   In this paper, we establish two sharp quantitative results for the direct and\ninverse time-harmonic acoustic wave scattering. The first one is concerned with\nthe recovery of the support of an inhomogeneous medium, independent of its\ncontents, by a single far-field measurement. For this challenging inverse\nscattering problem, we establish a sharp stability estimate of logarithmic type\nwhen the medium support is a polyhedral domain in $\\mathbb{R}^n$, $n=2,3$. The\nsecond one is concerned with the stability for corner scattering. More\nprecisely if an inhomogeneous scatterer, whose support has a corner, is probed\nby an incident plane-wave, we show that the energy of the scattered far-field\npossesses a positive lower bound depending only on the geometry of the corner\nand bounds on the refractive index of the medium there. This implies the\nimpossibility of approximate invisibility cloaking by a device containing a\ncorner and made of isotropic material. Our results sharply quantify the\nqualitative corner scattering results in the literature, and the corresponding\nproofs involve much more subtle analysis and technical arguments. As a\nsignificant byproduct of this study, we establish a quantitative Rellich's\ntheorem that continues smallness of the wave field from the far-field up to the\ninterior of the inhomogeneity. The result is of significant mathematical\ninterest for its own sake and is surprisingly not yet known in the literature.\n"", 'Stable determination of an elastic medium scatterer by a single\n  far-field measurement and beyond   We are concerned with the time-harmonic elastic scattering due to an\ninhomogeneous elastic material inclusion located inside a uniformly homogeneous\nisotropic medium. We establish a sharp stability estimate of logarithmic type\nin determining the support of the elastic scatterer, independent of its\nmaterial content, by a single far-field measurement when the support is a\nconvex polyhedral domain in $\\mathbb{R}^n$, $n=2,3$. Our argument in\nestablishing the stability result is localized around a corner of the medium\nscatterer. This enables us to further establish a byproduct result by proving\nthat if a generic medium scatterer, not necessary to be a polyhedral shape,\npossesses a corner, then there exists a positive lower bound of the scattered\nfar-field patterns. The latter result indicates that if an elastic material\nobject possesses a corner on its support, then it scatters every incident wave\nstably and invisibility phenomenon does not occur.\n', 'Unique determination by a single far-field measurement for an inverse\n  elastic problem   This paper is concerned with the unique identification of the shape of a\nscatterer through a single far-field pattern in an inverse elastic medium\nscattering problem with a generalized transmission boundary condition. The\nuniqueness issue by a single far-field measurement is a challenging problem in\ninverse scattering theory, which has a long and colorful history. In this\npaper, we demonstrate the well-posedness of the direct problem by the\nvariational approach. We establish the uniqueness results by a single far-field\nmeasurement under a generic scenario when dealing with underlying elastic\nscatterers exhibiting polygonal-nest or polygonal-cell structures. Furthermore,\nfor a polygonal-nest or polygonal-cell structure scatterer associated with\ndensity and boundary impedance parameters as piecewise constants, we show that\nthese physical quantities can be uniquely determined simultaneously by a single\nfar-field measurement. The corresponding proof relies heavily on examining the\nsingular behaviour of a coupled PDE system near a corner in a microlocal\nmanner.\n']","[('elastic scattering', 0.6389300227165222), ('inverse scattering theory', 0.5869908928871155), ('inverse scattering', 0.581352949142456), ('scattering theory', 0.5590956807136536), ('scattering', 0.5530143976211548), ('medium scattering', 0.5320357084274292), ('scattering problems', 0.530455470085144), ('electromagnetic scattering', 0.5221232175827026), ('non scattering', 0.5195671319961548), ('wave field', 0.424030601978302)]"
590,590,52,590_area preserving diffeomorphisms_area preserving homeomorphisms_preserving surface diffeomorphisms_diffeomorphisms surfaces,"['area preserving diffeomorphisms', 'area preserving homeomorphisms', 'preserving surface diffeomorphisms', 'diffeomorphisms surfaces', 'surface diffeomorphisms', 'area preserving maps', 'preserving diffeomorphisms', 'hamiltonian diffeomorphisms', 'area preserving surface', 'diffeomorphisms']","[""Periodic Floer homology and the smooth closing lemma for area-preserving\n  surface diffeomorphisms   We prove a very general Weyl-type law for Periodic Floer Homology, estimating\nthe action of twisted Periodic Floer Homology classes over essentially any\ncoefficient ring in terms of the grading and the degree, and recovering the\nCalabi invariant of Hamiltonians in the limit. We also prove a strong\nnon-vanishing result, showing that under a monotonicity assumption which holds\nfor a dense set of maps, the Periodic Floer Homology has infinite rank. An\napplication of these results yields that a $C^{\\infty}$-generic area-preserving\ndiffeomorphism of a closed surface has a dense set of periodic points. This\nsettles Smale's tenth problem in the special case of area-preserving\ndiffeomorphisms of closed surfaces.\n"", 'A $C^{\\infty}$ closing lemma on torus   Asaoka & Irie recently proved a $C^{\\infty}$ closing lemma of Hamiltonian\ndiffeomorphisms of closed surfaces. We reformulated their techniques into a\nmore general perturbation lemma for area-preserving diffeomorphism and proved a\n$C^{\\infty}$ closing lemma for area-preserving diffeomorphisms on a torus that\nis isotopic to identity. i.e., we show that the set of periodic orbits is dense\nfor a generic diffeomorphism isotopic to identity area-preserving\ndiffeomorphism on torus. The main tool is the flux vector of area-preserving\ndiffeomorphisms which is, different from Hamiltonian cases, non-zero in\ngeneral.\n', 'Generic density of periodic orbits of area-preserving maps on punctured\n  surfaces   We study the dynamics of area-preserving maps in a non-compact setting. We\nshow that the $C^{\\infty}$-closing lemma holds for area-preserving\ndiffeomorphisms on a closed surface with finitely many points removed. As a\ncorollary, a $C^{\\infty}$-generic area-preserving diffeomorphism on such a\nsurface has a dense set of periodic points. For area-preserving maps on a\nfinitely punctured 2-sphere, we establish a more quantitative result regarding\nthe equidistribution of periodic orbits. The proof of this result involves a\nPFH Weyl law for rational area-preserving homeomorphisms, which may be of\nindependent interest.\n']","[('area preserving diffeomorphisms', 0.7402252554893494), ('area preserving homeomorphisms', 0.6511232852935791), ('preserving surface diffeomorphisms', 0.6442357897758484), ('diffeomorphisms surfaces', 0.5909556746482849), ('surface diffeomorphisms', 0.5855881571769714), ('area preserving maps', 0.577867865562439), ('preserving diffeomorphisms', 0.5719179511070251), ('hamiltonian diffeomorphisms', 0.5707530379295349), ('area preserving surface', 0.5659522414207458), ('diffeomorphisms', 0.5403804183006287)]"
591,591,52,591_linear system identification_learning dynamics_state estimator_linear dynamical systems,"['linear system identification', 'learning dynamics', 'state estimator', 'linear dynamical systems', 'identification linear', 'linear time invariant', 'finite time analysis', 'unknown nonlinear systems', 'linear dynamical system', 'learning stable']","['Non-asymptotic System Identification for Linear Systems with Nonlinear\n  Policies   This paper considers a single-trajectory system identification problem for\nlinear systems under general nonlinear and/or time-varying policies with i.i.d.\nrandom excitation noises. The problem is motivated by safe learning-based\ncontrol for constrained linear systems, where the safe policies during the\nlearning process are usually nonlinear and time-varying for satisfying the\nstate and input constraints. In this paper, we provide a non-asymptotic error\nbound for least square estimation when the data trajectory is generated by any\nnonlinear and/or time-varying policies as long as the generated state and\naction trajectories are bounded. This significantly generalizes the existing\nnon-asymptotic guarantees for linear system identification, which usually\nconsider i.i.d. random inputs or linear policies. Interestingly, our error\nbound is consistent with that for linear policies with respect to the\ndependence on the trajectory length, system dimensions, and excitation levels.\nLastly, we demonstrate the applications of our results by safe learning with\nrobust model predictive control and provide numerical analysis.\n', ""Finite Sample Identification of Partially Observed Bilinear Dynamical\n  Systems   We consider the problem of learning a realization of a partially observed\nbilinear dynamical system (BLDS) from noisy input-output data. Given a single\ntrajectory of input-output samples, we provide a finite time analysis for\nlearning the system's Markov-like parameters, from which a balanced realization\nof the bilinear system can be obtained. Our bilinear system identification\nalgorithm learns the system's Markov-like parameters by regressing the outputs\nto highly correlated, nonlinear, and heavy-tailed covariates. Moreover, the\nstability of BLDS depends on the sequence of inputs used to excite the system.\nThese properties, unique to partially observed bilinear dynamical systems, pose\nsignificant challenges to the analysis of our algorithm for learning the\nunknown dynamics. We address these challenges and provide high probability\nerror bounds on our identification algorithm under a uniform stability\nassumption. Our analysis provides insights into system theoretic quantities\nthat affect learning accuracy and sample complexity. Lastly, we perform\nnumerical experiments with synthetic data to reinforce these insights.\n"", 'Non-asymptotic Identification of Linear Dynamical Systems Using Multiple\n  Trajectories   This paper considers the problem of linear time-invariant (LTI) system\nidentification using input/output data. Recent work has provided non-asymptotic\nresults on partially observed LTI system identification using a single\ntrajectory but is only suitable for stable systems. We provide finite-time\nanalysis for learning Markov parameters based on the ordinary least-squares\n(OLS) estimator using multiple trajectories, which covers both stable and\nunstable systems. For unstable systems, our results suggest that the Markov\nparameters are harder to estimate in the presence of process noise. Without\nprocess noise, our upper bound on the estimation error is independent of the\nspectral radius of system dynamics with high probability. These two features\nare different from fully observed LTI systems for which recent work has shown\nthat unstable systems with a bigger spectral radius are easier to estimate.\nExtensive numerical experiments demonstrate the performance of our OLS\nestimator.\n']","[('linear system identification', 0.5255639553070068), ('learning dynamics', 0.46315762400627136), ('state estimator', 0.44029805064201355), ('linear dynamical systems', 0.43920475244522095), ('identification linear', 0.4389808177947998), ('linear time invariant', 0.42111778259277344), ('finite time analysis', 0.41725799441337585), ('unknown nonlinear systems', 0.41005411744117737), ('linear dynamical system', 0.4056509733200073), ('learning stable', 0.4036725163459778)]"
592,592,52,592_groebner bases_gr obner basis_groebner basis_computing gr obner,"['groebner bases', 'gr obner basis', 'groebner basis', 'computing gr obner', 'compute gr obner', 'obner basis', 'groebner', 'basis algorithms', 'gr obner bases', 'obner basis respect']","['A Signature-Based Gr\\""obner Basis Algorithm with Tail-Reduced Reductors\n  (M5GB)   Gr\\""obner bases are an important tool in computational algebra and,\nespecially in cryptography, often serve as a boilerplate for solving systems of\npolynomial equations. Research regarding (efficient) algorithms for computing\nGr\\""obner bases spans a large body of dedicated work that stretches over the\nlast six decades. The pioneering work of Bruno Buchberger in 1965 can be\nconsidered as the blueprint for all subsequent Gr\\""obner basis algorithms to\ndate. Among the most efficient algorithms in this line of work are\nsignature-based Gr\\""obner basis algorithms, with the first of its kind\npublished in the late 1990s by Jean-Charles Faug\\`ere under the name F5. In\naddition to signature-based approaches, Rusydi Makarim and Marc Stevens\ninvestigated a different direction to efficiently compute Gr\\""obner bases,\nwhich they published in 2017 with their algorithm M4GB. The ideas behind M4GB\nand signature-based approaches are conceptually orthogonal to each other\nbecause each approach addresses a different source of inefficiency in\nBuchberger\'s initial algorithm by different means.\n  We amalgamate those orthogonal ideas and devise a new Gr\\""obner basis\nalgorithm, called M5GB, that combines the concepts of both worlds. In that\ncapacity, M5GB merges strong signature-criteria to eliminate redundant S-pairs\nwith concepts for fast polynomial reductions borrowed from M4GB. We provide\nproofs of termination and correctness and a proof-of-concept implementation in\nC++ by means of the Mathic library. The comparison with a state-of-the-art\nsignature-based Gr\\""obner basis algorithm (implemented via the same library)\nvalidates our expectations of an overall faster runtime for quadratic\noverdefined polynomial systems that have been used in comparisons before in the\nliterature and are also part of cryptanalytic challenges.\n', 'Learning to Compute Gr\\""obner Bases   Solving a polynomial system, or computing an associated Gr\\""obner basis, has\nbeen a fundamental task in computational algebra. However, it is also known for\nits notorious doubly exponential time complexity in the number of variables in\nthe worst case. This paper is the first to address the learning of Gr\\""obner\nbasis computation with Transformers. The training requires many pairs of a\npolynomial system and the associated Gr\\""obner basis, raising two novel\nalgebraic problems: random generation of Gr\\""obner bases and transforming them\ninto non-Gr\\""obner ones, termed as backward Gr\\""obner problem. We resolve these\nproblems with 0-dimensional radical ideals, the ideals appearing in various\napplications. Further, we propose a hybrid input embedding to handle\ncoefficient tokens with continuity bias and avoid the growth of the vocabulary\nset. The experiments show that our dataset generation method is a few orders of\nmagnitude faster than a naive approach, overcoming a crucial challenge in\nlearning to compute Gr\\""obner bases, and Gr\\""obner computation is learnable in\na particular class.\n', 'The GroebnerWalk.jl package for OSCAR   Computing Gr\\""obner bases is known to have a very high upper bound on\ncomputation time with respect to input length. Due to the connection between\npolyhedral geometry and Gr\\""obner bases through the Gr\\""obner fan, one can\nattempt an incremental approach to compute Gr\\""obner bases. First computing a\nGr\\""obner basis with respect to an `easy\' term order and transforming that\nresult to a Gr\\""obner basis with respect to the desired term order by using\ninformation about this polyhedral fan is done by a family of algorithms termed\nas Gr\\""obner walk. We implemented two variants of the Gr\\""obner walk in the\ncomputer algebra system OSCAR and compared their performance with classical\nGr\\""obner basis methods already found in OSCAR.\n']","[('groebner bases', 0.6213439702987671), ('gr obner basis', 0.5847278833389282), ('groebner basis', 0.5782039165496826), ('computing gr obner', 0.5716066956520081), ('compute gr obner', 0.5396527051925659), ('obner basis', 0.537919282913208), ('groebner', 0.516010046005249), ('basis algorithms', 0.509105920791626), ('gr obner bases', 0.507167398929596), ('obner basis respect', 0.497378408908844)]"
593,593,52,593_area minimizing surfaces_minimal surface_boundary regularity_integral currents,"['area minimizing surfaces', 'minimal surface', 'boundary regularity', 'integral currents', 'submanifold sigma', 'interior regularity', 'integral varifolds', 'minimal cones', 'minimizing surfaces', 'dimensional minimal']","['Unique continuation for area minimizing currents   The main goal of this work is to prove an instance of the unique continuation\nprinciple for area minimizing integral currents. More precisely, consider an\n$m$-dimensional area minimizing integral current and an $m$-dimensional minimal\nsurface, both contained in $\\mathbb{R}^{n+m}$ with $n\\geq 1$. We show that if,\nin an integral sense, the current has infinite order of contact with the\nminimal surface at a point, then the current and the minimal surface coincide\nin a neighborhood of that point.\n', 'Regularity of area minimizing currents mod $p$   We establish a first general partial regularity theorem for area minimizing\ncurrents $\\mathrm{mod}(p)$, for every $p$, in any dimension and codimension.\nMore precisely, we prove that the Hausdorff dimension of the interior singular\nset of an $m$-dimensional area minimizing current $\\mathrm{mod}(p)$ cannot be\nlarger than $m-1$. Additionally, we show that, when $p$ is odd, the interior\nsingular set is $(m-1)$-rectifiable with locally finite $(m-1)$-dimensional\nmeasure.\n', 'The Fine Structure of the Singular Set of Area-Minimizing Integral\n  Currents III: Frequency 1 Flat Singular Points and $\\mathcal{H}^{m-2}$-a.e.\n  Uniqueness of Tangent Cones   We consider an area-minimizing integral current $T$ of codimension higher\nthan 1 ins a smooth Riemannian manifold $\\Sigma$. We prove that $T$ has a\nunique tangent cone, which is a superposition of planes, at\n$\\mathcal{H}^{m-2}$-a.e. point in its support. In combination with works of the\nfirst and third authors, we conclude that the singular set of $T$ is countably\n$(m-2)$-rectifiable.\n']","[('area minimizing surfaces', 0.5018146634101868), ('minimal surface', 0.44186270236968994), ('boundary regularity', 0.4414539635181427), ('integral currents', 0.440019428730011), ('submanifold sigma', 0.4376963675022125), ('interior regularity', 0.4260050654411316), ('integral varifolds', 0.42377978563308716), ('minimal cones', 0.42231783270835876), ('minimizing surfaces', 0.41237398982048035), ('dimensional minimal', 0.4066006541252136)]"
594,594,52,594_compact quantum groups_compact quantum group_discrete quantum groups_quantum groups,"['compact quantum groups', 'compact quantum group', 'discrete quantum groups', 'quantum groups', 'quantum groups quantum', 'groups quantum', 'small quantum groups', 'quantum subgroups', 'quantum group', 'quantum subgroup']","[""Bornological quantum groups as locally compact quantum groups   Bornological quantum groups were introduced by Voigt in order to generalize\nthe theory of algebraic quantum groups in the sense of van Daele. In particular\nthe class of bornological quantum groups contains all classical locally compact\ngroups. In this paper we prove that a bornological quantum group gives rise to\na locally compact quantum group, in a similar way to Kustermans and van Daele's\nresult for algebraic quantum groups. We show that the bornological quantum\ngroups, although more general than the algebraic ones, share most of their nice\nproperties. We also argue that bornological quantum groups, when they occur as\ndense subalgebras of locally compact quantum groups, are useful tools for\nstudying locally compact quantum groups. For instance, we show that the simple\ndefinition of a bornological closed quantum subgroup yields a closed subgroup\nof the locally compact quantum group in the sense of Vaes or Wooronowicz.\n"", 'Introduction to compact and discrete quantum groups   These are notes from introductory lectures at the graduate school\n""Topological Quantum Groups"" in B\\k{e}dlewo (June 28--July 11, 2015). The notes\npresent the passage from Hopf algebras to compact quantum groups and sketch the\nnotion of discrete quantum groups viewed as duals of compact quantum groups.\n', 'On certain invariants of compact quantum groups   We introduce and study a number of invariants of locally compact quantum\ngroups defined by their scaling and modular groups and the spectrum of their\nmodular elements. Focusing mainly on compact quantum groups we consider the\nquestion whether triviality of one of the invariants is equivalent to the\nquantum group being of Kac type and show that it has a positive answer in many\ncases including duals of second countable type $\\mathrm{I}$ discrete quantum\ngroups. We perform a complete calculation of the invariants for all\n$q$-deformations of compact, simply connected, semisimple Lie groups as well as\nfor some non-compact quantum groups and the compact quantum groups\n$\\operatorname{U}_F^+$. Finally we introduce a family of conditions for\ndiscrete quantum groups which for classical discrete groups are all equivalent\nto the fact that the group is i.c.c. We show that the above mentioned question\nabout characterization of Kac type quantum groups by one of our invariants has\na positive answer for duals of discrete quantum groups satisfying such an\ni.c.c.-type condition and illustrate this with the example of\n$\\operatorname{U}_F^+$.\n']","[('compact quantum groups', 0.8467414975166321), ('compact quantum group', 0.8106592893600464), ('discrete quantum groups', 0.764532208442688), ('quantum groups', 0.7620022892951965), ('quantum groups quantum', 0.7248157858848572), ('groups quantum', 0.720363199710846), ('small quantum groups', 0.7177827954292297), ('quantum subgroups', 0.7048670649528503), ('quantum group', 0.6898833513259888), ('quantum subgroup', 0.6650700569152832)]"
595,595,52,595_invariant riemannian metrics_manifolds geodesic_metrics lie groups_riemannian manifolds,"['invariant riemannian metrics', 'manifolds geodesic', 'metrics lie groups', 'riemannian manifolds', 'geodesic orbit', 'pseudo riemannian manifolds', 'riemannian metrics', 'metric geodesic', 'geodesic completeness', 'invariant riemannian']","['The Structure of Geodesic Orbit Lorentz Nilmanifolds   The geodesic orbit property is useful and interesting in Riemannian geometry.\nIt implies homogeneity and has important classes of Riemannian manifolds as\nspecial cases. Those classes include weakly symmetric Riemannian manifolds and\nnaturally reductive Riemannian manifolds. The corresponding results for\nindefinite metric manifolds are much more delicate than in Riemannian\nsignature, but in the last few years important corresponding structural results\nwere proved for geodesic orbit Lorentz manifolds. Here we carry out a major\nstep in the structural analysis of geodesic orbit Lorentz nilmanifolds. Those\nare the geodesic orbit Lorentz manifolds $M = G/H$ such that a nilpotent\nanalytic subgroup of $G$ is transitive on $M$. Suppose that there is a\nreductive decomposition $\\mathfrak{g} = \\mathfrak{h} \\oplus \\mathfrak{n}$\n(vector space direct sum) with $\\mathfrak{n}$ nilpotent. When the metric is\nnondegenerate on $[\\mathfrak{n},\\mathfrak{n}]$ we show that $\\mathfrak{n}$ is\nabelian or 2-step nilpotent (this is the same result as for geodesic orbit\nRiemannian nilmanifolds), and when the metric is degenerate on\n$[\\mathfrak{n},\\mathfrak{n}]$ we show that $\\mathfrak{n}$ is a Lorentz double\nextension corresponding to a geodesic orbit Riemannian nilmanifold. In the\nlatter case we construct examples to show that the number of nilpotency steps\nis unbounded.\n', 'Pseudo-Riemannian geodesic orbit nilmanifolds of signature\n  $\\boldsymbol{(n-2,2)}$   The geodesic orbit property is useful and interesting in itself, and it plays\na key role in Riemannian geometry. It implies homogeneity and has important\nclasses of Riemannian manifolds as special cases. Those classes include weakly\nsymmetric Riemannian manifolds and naturally reductive Riemannian manifolds.\nThe corresponding results for indefinite metric manifolds are much more\ndelicate than in Riemannian signature, but in the last few years important\ncorresponding structural results were proved for geodesic orbit Lorentz\nmanifolds. Here we extend Riemannian and Lorentz results to trans-Lorentz\nnilmanifolds. Those are the geodesic orbit pseudo Riemannian manifolds $M =\nG/H$ of signature $(n-2,2)$ such that a nilpotent analytic subgroup of $G$ is\ntransitive on $M$. For that we suppose that there is a reductive decomposition\n$\\g = \\h \\oplus \\n \\text{ (vector space direct sum) with } [\\h,\\n] \\subset \\n$\nand $\\n$ nilpotent. When the metric is nondegenerate on $[\\n,\\n]$ we show that\n$\\n$ is abelian or 2-step nilpotent. That is the same result as for geodesic\norbit Riemannian and Lorentz nilmanifolds. When the metric is degenerate on\n$[\\n,\\n]$ we show that $\\n$ is a double extension of a geodesic orbit\nnilmanifold of either Riemannian or Lorentz signature.\n', 'On the Geometric Orbit Property for Lorentz Manifolds   The geodesic orbit property has been studied intensively for Riemannian\nmanifolds. Geodesic orbit spaces are homogeneous and allow simplifications of\nmany structural questions using the Lie algebra of the isometry group. Weakly\nsymmetric Riemannian manifolds are geodesic orbit spaces. Here we define\n""naturally reductive"" for pseudo-Riemannian manifolds and note that they are\ngeodesic orbit spaces. A few years ago two of the authors proved that weakly\nsymmetric pseudo-Riemannian manifolds are geodesic orbit spaces. In particular\nthese results apply to pseudo-Riemannian Lorentz manifolds. There our main\nresults are Theorems 4.2 and 5.1. In the Riemannian case the nilpotent isometry\ngroup for a geodesic orbit nilmanifold is abelian or $2$-step nilpotent.\nExamples show that this fails dramatically in the pseudo-Riemannian case. Here\nwe concentrate on the geodesic orbit property for Lorentz nilmanifolds $G/H$\nwith $G = N \\rtimes H$ and $N$ nilpotent. When the metric is nondegenerate on\n$[\\mathfrak{n},\\mathfrak{n}]$, Theorem 4.2 shows that $N$ either is at most\n$2$-step nilpotent as in the Riemannian situation, or is $4$-step nilpotent,\nbut cannot be $3$-step nilpotent. Examples show that these bounds are the best\npossible. Surprisingly, Theorem 5.1 shows that $N$ is at most $2$-step\nnilpotent when the metric is degenerate on $[\\mathfrak{n},\\mathfrak{n}]$. Both\ntheorems give additional structural information and specialize to naturally\nreductive and to weakly symmetric Lorentz nilmanifolds.\n  Key Words: Geodesic Orbit Space; Lorentz nilmanifold; Weakly Symmetric Space;\nNaturally Reductive Space; Pseudo-Riemannian Manifold.\n']","[('invariant riemannian metrics', 0.684596598148346), ('manifolds geodesic', 0.664558470249176), ('metrics lie groups', 0.6186991930007935), ('riemannian manifolds', 0.6110048890113831), ('geodesic orbit', 0.607198178768158), ('pseudo riemannian manifolds', 0.6064746975898743), ('riemannian metrics', 0.6004126071929932), ('metric geodesic', 0.5999941229820251), ('geodesic completeness', 0.5945535898208618), ('invariant riemannian', 0.5938571095466614)]"
596,596,52,596_bounded analytic functions_bohr radius_bounded analytic_analytic functions unit,"['bounded analytic functions', 'bohr radius', 'bounded analytic', 'analytic functions unit', 'analytic functions', 'class analytic functions', 'harmonic mappings', 'sum_ infty a_nz', 'analytic functions defined', 'analytic']","['Bohr-Rogosinski and improved Bohr type inequalities for certain fully\n  starlike harmonic mappings   The classical Bohr inequality states that if $ f $ is an analytic function\nwith the power series representation $ f(z)=\\sum_{n=0}^{\\infty}a_nz^n $ in the\nunit disk $ \\mathbb{D}:=\\{z\\in\\mathbb{C} : |z|<1\\} $ such that $ |f(z)|\\leq 1 $\nfor all $ z\\in\\mathbb{D} $, then \\begin{equation*}\n  \\sum_{n=0}^{\\infty}|a_n|r^n\\leq 1\\;\\; \\text{for}\\;\\; |z|=r\\leq\\frac{1}{3}\n\\end{equation*} and the constant $ 1/3 $ cannot be improved. The constant $\nr_0=1/3 $ is known as Bohr radius and the inequality $\n\\sum_{n=0}^{\\infty}|a_n|r^n\\leq 1 $ is known as Bohr inequality. Let $\n\\mathcal{H} $ be the class of complex-valued harmonic mappings $ f=h+\\bar{g}$\ndefined in the unit disk $ \\mathbb{D} $, where $ h $ and $ g $ are analytic\nfunctions in $ \\mathbb{D} $ with the normalization $ h(0)=0=h^{\\prime}(0)-1 $\nand $ g(0)=0 $. Let $ \\mathcal{H}_{0}=\\{f=h+\\bar{g}\\in\\mathcal{H} :\ng^{\\prime}(0)=0\\}. $ Let $ \\mathcal{P}^{0}_{\\mathcal{H}}(M)\n:=\\{f=h+\\overline{g} \\in \\mathcal{H}_{0}: \\real (zh^{\\prime\\prime}(z))>\n-M+|zg^{\\prime\\prime}(z)|,\\; z \\in \\mathbb{D},\\; M>0\\} $. Functions in the\nclass $ \\mathcal{P}^{0}_{\\mathcal{H}}(M) $ are called fully starlike univalent\nfunctions for $ 0<M<1/\\log 4 $. In this paper, we obtain the sharp\nBohr-Rogosinski type inequality and improved Bohr inequality and the\ncorresponding Bohr radius for the class $ \\mathcal{P}_{\\mathcal{H}}^{0}(M) $.\n', 'Bohr phenomenon for certain classes of harmonic mappings   Bohr phenomenon for analytic functions $ f $ where $\nf(z)=\\sum_{n=0}^{\\infty}a_nz^n $, first introduced by Harald Bohr in $ 1914 $,\ndeals with finding the largest radius $ r_f $, $ 0<r_f<1 $, such that the\ninequality $ \\sum_{n=0}^{\\infty}|a_nz^n|<1 $ holds whenever $ |f(z)|<1 $ holds\nin the unit disk $ \\mathbb{D}=\\{z\\in\\mathbb{C} : |z|<1\\} $. The Bohr phenomenon\nfor the harmonic functions of the form $ f(z)=h+\\overline{g} $, where $\nh(z)=\\sum_{n=0}^{\\infty}a_nz^n $ and $ g(z)=\\sum_{n=1}^{\\infty}b_nz^n $ is to\nfind the largest radius $ r_f $, $ 0<r_f<1 $ such that \\begin{equation*}\n  \\sum_{n=1}^{\\infty}\\left(|a_n|+|b_n|\\right)|z|^n\\leq d(f(0),\\partial\nf(\\mathbb{D})) \\end{equation*} holds for $ |z|\\leq r_f $, where $\nd(f(0),\\partial f(\\mathbb{D})) $ is the Euclidean distance between $ f(0) $ and\nthe boundary of $ f(\\mathbb{D}) $. In this paper, we prove several improved\nversions of the sharp Bohr radius for the classes of harmonic and univalent\nfunctions. Further, we prove several corollaries as a consequence of the main\nresults.\n', ""Bohr inequalities for unimodular bounded functions on simply connected\n  domains   Let $ \\mathcal{H}(\\mathbb{D}) $ be the class of analytic functions in the\nunit disk $ \\mathbb{D} : =\\{z\\in\\mathbb{C} : |z|<1\\} $. The classical Bohr's\ninequality states that if a power series $ f(z)=\\sum_{n=0}^{\\infty}a_nz^n $\nconverges in $ \\mathbb{D} $ and $ |f(z)|<1 $ for $ z\\in\\mathbb{D} $, then\n  \\begin{equation*}\n  \\sum_{n=0}^{\\infty}|a_n|r^n\\leq 1\\;\\;\\mbox{for}\\;\\; r\\leq \\frac{1}{3}\n  \\end{equation*} and the constant $ 1/3 $ cannot be improved. The constant $\n1/3 $ is known as Bohr radius. In this paper, we study Bohr phenomenon for\nanalytic as well as harmonic mappings on simply connected domains. We prove\nseveral sharp results on improved Bohr radius for analytic functions as well as\nfor harmonic mappings on simply connected domains.\n""]","[('bounded analytic functions', 0.46719855070114136), ('bohr radius', 0.4519573748111725), ('bounded analytic', 0.44456619024276733), ('analytic functions unit', 0.4083241820335388), ('analytic functions', 0.4035034775733948), ('class analytic functions', 0.38655251264572144), ('harmonic mappings', 0.3756464123725891), ('sum_ infty a_nz', 0.3717479407787323), ('analytic functions defined', 0.3692020773887634), ('analytic', 0.35117271542549133)]"
597,597,52,597_urn models_urn schemes_urns_urn,"['urn models', 'urn schemes', 'urns', 'urn', 'olya urns', 'number balls', 'draws', 'balls bins', 'olya urn', 'balls']","[""A new method for computing the expected hitting time between arbitrary\n  different configurations of the multiple-urn Ehrenfest model   We study a multiple-urn version of the Ehrenfest model. In this setting, we\ndenote the n urns by Urn 1 to Urn n, where n>=2. Initially, M balls are\nrandomly placed in the n urns. At each subsequent step, a ball is selected and\nput into the other n-1 urns with equal probability. The expected hitting time\nleading to a change of the M balls' status is computed using the method of\nstopping times. As a corollary, we obtain the expected hitting time of moving\nall the M balls from Urn 1 to Urn 2. This proves a conjecture which was\nrecently made in Chen et al.(2017).\n"", ""Urns with Multiple Drawings and Graph-Based Interaction   Consider a finite undirected graph and place an urn with balls of two colours\nat each vertex. At every discrete time step, for each urn, a fixed number of\nballs are drawn from that same urn with probability $p$, and from a randomly\nchosen neighbour of that urn with probability $1-p$. Based on what is drawn,\nthe urns then reinforce themselves or their neighbours. For every ball of a\ngiven colour in the sample, in case of P\\'olya-type reinforcement, a constant\nmultiple of balls of that colour is added while in case of Friedman-type\nreinforcement, balls of the other colour are reinforced. These different\nchoices for reinforcement give rise to multiple models. In this paper, we study\nthe convergence of the fraction of balls of either colour across urns for all\nof these models. We show that in most cases the urns synchronize, that is, the\nfraction of balls of either colour in each urn converges to the same limit\nalmost surely. A different kind of asymptotic behaviour is observed on\nbipartite graphs. We also prove similar results for the case of finite directed\ngraphs.\n"", 'Feedback Interacting Urn Models   We introduce and discuss a special type of feedback interacting urn model\nwith deterministic interaction. This is a generalisation of the very well known\nEggenberger and Polya (1923) urn model. In our model, balls are added to a\nparticular urn depending on the replacement matrix of that urn and the color of\nball chosen from some other urn. This urn model can help in studying how\nvarious interacting models might behave in real life in the long run. We have\nalso introduced a special type of interacting urn model with non-deterministic\ninteraction and studied its behaviour. Furthermore, we have provided some nice\nexamples to illustrate the various consequences of these interacting urn\nmodels.\n']","[('urn models', 0.6244636178016663), ('urn schemes', 0.5442214608192444), ('urns', 0.4535621106624603), ('urn', 0.41076335310935974), ('olya urns', 0.3631264865398407), ('number balls', 0.3552396893501282), ('draws', 0.35325855016708374), ('balls bins', 0.34416908025741577), ('olya urn', 0.33704817295074463), ('balls', 0.33525803685188293)]"
598,598,52,598_chow group zero_higher chow groups_chow groups_smooth projective varieties,"['chow group zero', 'higher chow groups', 'chow groups', 'smooth projective varieties', 'group zero cycles', 'projective varieties', 'chow group', 'quotient varieties', 'quasi projective', 'zero cycles']","[""Zero-cycles on normal varieties   We prove an extension of the Kato-Saito class field theory for smooth\nprojective schemes over a finite field to schemes with singularities. As an\napplication, we obtain Bloch's formula for the Chow groups of 0-cycles on such\nschemes. We identify the Chow group of 0-cycles on a normal projective scheme\nover an algebraically closed field to the Suslin homology of its regular locus.\nOur final result is a Roitman torsion theorem for smooth quasi-projective\nschemes over algebraically closed fields. This completes the missing\n$p$-torsion part in the torsion theorem of Spiess and Szamuely.\n"", 'Cycle class maps for Chow groups of zero-cycles with modulus   For a quasi-projective smooth scheme X of pure dimension d over a field k and\nan effective Cartier divisor D on X whose support is a simple normal crossing\ndivisor, we construct a cycle class map from the Chow group of zero-cycles with\nmodulus to the top cohomology of the dth relative Milnor K-sheaf.\n', 'Zero-cycles with modulus and relative $K$-theory   We construct a cycle class map from the higher Chow groups of 0-cycles to the\nrelative $K$-theory of a modulus pair. We show that this induces a\npro-isomorphism between the additive higher Chow groups of relative 0-cycles\nand relative $K$-theory of truncated polynomial rings over a regular semi-local\nring, essentially of finite type over a characteristic zero field.\n']","[('chow group zero', 0.6121647953987122), ('higher chow groups', 0.5692532062530518), ('chow groups', 0.5075135231018066), ('smooth projective varieties', 0.4909512996673584), ('group zero cycles', 0.48911306262016296), ('projective varieties', 0.4863366484642029), ('chow group', 0.4674281179904938), ('quotient varieties', 0.4468742311000824), ('quasi projective', 0.4317098557949066), ('zero cycles', 0.42893943190574646)]"
599,599,52,599_yang mills connections_yang mills theory_dual yang mills_hermitian yang mills,"['yang mills connections', 'yang mills theory', 'dual yang mills', 'hermitian yang mills', 'yang mills fields', 'yang mills higgs', 'yang mills', 'mills connections', 'mills theory', 'su yang mills']","[""The stability for F-Yang-Mills functional on CP^n   In this paper, we study the critical points of $F$-Yang-Mills functional on\n$\\mathbb{C}P^n$, which are called $F$-Yang-Mills connections. We prove that if\n$(2+\\frac4n)F''(x)x+(n+1)F'(x)<0$, then the weakly stable $F$-Yang-Mills\nconnection on $\\mathbb{C}P^n$ must be flat. Moreover, if\n$(2+\\frac4n)F''(x)x+(n+1)F'(x)=0$, we obtain the structure of curvatures\ncorresponding to weakly stable connections. We also show a gap theorem for\n$F$-Yang-Mills connections on $\\mathbb{C}P^n$.\n"", ""A Simons type condition for instability of $F$-Yang-Mills connections   $F$-Yang-Mills connections are critical points of $F$-Yang Mills functional\non the space of connections of a principal fiber bundle, which is a\ngeneralization of Yang-Mills connections, $p$-Yang-Mills connections and\nexponential Yang-Mills connections and so on. Here, $F$ is a strictly\nincreasing $C^{2}$-function. In this paper, we extend Simons theorem for an\ninstability of Yang-Mills connections to $F$-Yang-Mills connections. We derive\na sufficient condition that any non-flat, $F$-Yang-Mills connection over convex\nhypersurfaces in a Euclidean space is instable. In the sphere case, this\ncondition is expressed by an inequality with respect to its dimension and a\ndegree of the differential of the function $F$. The proofs of the results are\ngiven by extending Kobayashi-Ohnita-Takeuchi's calculation to $F$-Yang-Mills\nconnections.\n"", 'Stability and energy identity for Yang-Mills-Higgs pairs   In this paper, we study the properties of the critical points of\nYang-Mills-Higgs functional, which are called Yang-Mills-Higgs pairs. We first\nconsider the properties of weakly stable Yang-Mills-Higgs pairs on a vector\nbundle over S^n (n > 3). When n > 3, we prove that the norm of its Higgs field\nis 1 and the connection is actually Yang-Mills. More precisely, its curvature\nvanishes when n > 4. We also use the bubble-neck decomposition to prove the\nenergy identity of a sequence of Yang-Mills-Higgs pairs over a 4-dimensional\ncompact manifold with uniformly bounded energy. We show there is a subsequence\nconverges smoothly to a Yang-Mills-Higgs pair up to gauge modulo finitely many\n4-dimensional spheres with Yang-Mills connections.\n']","[('yang mills connections', 0.6773803234100342), ('yang mills theory', 0.6461192965507507), ('dual yang mills', 0.63357013463974), ('hermitian yang mills', 0.6220141649246216), ('yang mills fields', 0.6057571172714233), ('yang mills higgs', 0.592616081237793), ('yang mills', 0.5099999308586121), ('mills connections', 0.5085885524749756), ('mills theory', 0.5074515342712402), ('su yang mills', 0.4879157245159149)]"
600,600,52,600_multiuser communications_movable antennas mas_movable antennas_movable antenna ma,"['multiuser communications', 'movable antennas mas', 'movable antennas', 'movable antenna ma', 'movable antenna', 'wireless communication performance', 'antennas mas', 'antenna positions', 'antenna ma', 'antenna position']","[""Multiuser Communications with Movable-Antenna Base Station Via Antenna\n  Position Optimization   This paper studies the deployment of multiple movable antennas (MAs) at the\nbase station (BS) for enhancing the multiuser communication performance. First,\nwe model the multiuser channel in the uplink to characterize the wireless\nchannel variation caused by MAs' movement at the BS. Then, an optimization\nproblem is formulated to maximize the minimum achievable rate among multiple\nusers for MA-aided uplink multiuser communications by jointly optimizing the\nMAs' positions, their receive combining at the BS, and the transmit power of\nusers, under the constraints of finite moving region of MAs, minimum inter-MA\ndistance, and maximum transmit power of each user. To solve this challenging\nnon-convex optimization problem, a two-loop iterative algorithm is proposed by\nleveraging the particle swarm optimization (PSO) method. Specifically, the\nouter-loop updates the positions of a set of particles, where each particle's\nposition represents one realization of the antenna positioning vector (APV) of\nall MAs. The inner-loop implements the fitness evaluation for each particle in\nterms of the max-min achievable rate of multiple users with its corresponding\nAPV, where the receive combining matrix of the BS and the transmit power of\neach user are optimized by applying the block coordinate descent (BCD)\ntechnique. Simulation results show that the antenna position optimization for\nMAs-aided BS can significantly improve the rate performance as compared to\nconventional BS with fixed-position antennas (FPAs).\n"", 'Multiuser Communications Aided by Cross-Linked Movable Antenna Array:\n  Architecture and Optimization   Movable antenna (MA) has been regarded as a promising technology to enhance\nwireless communication performance by enabling flexible antenna movement.\nHowever, the hardware cost of conventional MA systems scales with the number of\nmovable elements due to the need for independently controllable driving\ncomponents. To reduce hardware cost, we propose in this paper a novel\narchitecture named cross-linked MA (CL-MA) array, which enables the collective\nmovement of multiple antennas in both horizontal and vertical directions. To\nevaluate the performance benefits of the CL-MA array, we consider an uplink\nmultiuser communication scenario. Specifically, we aim to minimize the total\ntransmit power while satisfying a given minimum rate requirement for each user\nby jointly optimizing the horizontal and vertical antenna position vectors\n(APVs), the receive combining at the base station (BS), and the transmit power\nof users. A globally lower bound on the total transmit power is derived, with\nclosed-form solutions for the APVs obtained under the condition of a single\nchannel path for each user. For the more general case of multiple channel\npaths, we develop a low-complexity algorithm based on discrete antenna position\noptimization. Additionally, to further reduce antenna movement overhead, a\nstatistical channel-based antenna position optimization approach is proposed,\nallowing for unchanged APVs over a long time period. Simulation results\ndemonstrate that the proposed CL-MA schemes significantly outperform\nconventional fixed-position antenna (FPA) systems and closely approach the\ntheoretical lower bound on the total transmit power. Compared to the\ninstantaneous channel-based CL-MA optimization, the statistical channel-based\napproach incurs a slight performance loss but achieves significantly lower\nmovement overhead, making it an appealing solution for practical wireless\nsystems.\n', ""Multiuser Communications with Movable-Antenna Base Station: Joint\n  Antenna Positioning, Receive Combining, and Power Control   Movable antenna (MA) is an emerging technology which enables a local movement\nof the antenna in the transmitter/receiver region for improving the channel\ncondition and communication performance. In this paper, we study the deployment\nof multiple MAs at the base station (BS) for enhancing the multiuser\ncommunication performance. First, we model the multiuser channel in the uplink\nto characterize the wireless channel variation due to MAs' movements at the BS.\nThen, an optimization problem is formulated to maximize the minimum achievable\nrate among multiple users for MA-aided uplink multiuser communications by\njointly optimizing the MAs' positions, their receive combining at the BS, and\nthe transmit power of users, under the constraints of finite moving region for\nMAs, minimum inter-MA distance, and maximum transmit power of each user. To\nsolve this challenging non-convex optimization problem, a two-loop iterative\nalgorithm is proposed by leveraging the particle swarm optimization (PSO)\nmethod. Specifically, the outer-loop updates the positions of a set of\nparticles, where each particle's position represents one realization of the\nantenna position vector (APV) of all MAs. The inner-loop implements the fitness\nevaluation for each particle in terms of the max-min achievable rate of\nmultiple users with its corresponding APV, where the receive combining matrix\nof the BS and the transmit power of each user are optimized by applying the\nblock coordinate descent (BCD) technique. Simulation results show that the\nantenna position optimization for MAs-aided BSs can significantly improve the\nrate performance as compared to conventional BSs with fixed-position antennas\n(FPAs).\n""]","[('multiuser communications', 0.5311717391014099), ('movable antennas mas', 0.5073432922363281), ('movable antennas', 0.4847365617752075), ('movable antenna ma', 0.47404319047927856), ('movable antenna', 0.4680345356464386), ('wireless communication performance', 0.4656793177127838), ('antennas mas', 0.43591150641441345), ('antenna positions', 0.4319903552532196), ('antenna ma', 0.42925408482551575), ('antenna position', 0.4288038909435272)]"
601,601,51,601_drinfeld modules finite_drinfeld modules_drinfeld module_drinfeld modular,"['drinfeld modules finite', 'drinfeld modules', 'drinfeld module', 'drinfeld modular', 'modules rank', 'rank drinfeld', 'module rank', 'isogeny classes', '_q finite field', 'adic galois representation']","['Drinfeld Module and Weil pairing over Dedekind domain of class number\n  two   The primary objective of this paper is to derive explicit formulas for rank\none and rank two Drinfeld modules over a specific domain denoted by A. This\ndomain corresponds to the projective line associated with an infinite place of\ndegree two. To achieve the goals, we construct a pair of standard Drinfeld\nmodules whose coefficients are in the Hilbert class field of A. We demonstrate\nthat the period lattice of the exponential functions corresponding to both\nmodules behaves similarly to the period lattice of the Carlitz module, the\nstandard rank one Drinfeld module defined over rational function field.\nMoreover, we employ Andersons t-motive to obtain the complete family of rank\ntwo Drinfeld modules. This family is parameterized by the invariant J =\n\\lambda^{q^2+1} which effectively serves as the counterpart of the j-invariant\nfor elliptic curves. Building upon the concepts introduced by van~der~Heiden,\nparticularly with regard to rank two Drinfeld modules, we are able to\nreformulate the Weil pairing of Drinfeld modules of any rank using a\nspecialized polynomial in multiple variables known as the Weil operator. As an\nillustrative example, we provide a detailed examination of a more explicit\nformula for the Weil pairing and the Weil operator of rank two Drinfeld modules\nover the domain A.\n', 'Orders occurring as endomorphism ring of a Drinfeld module in some\n  isogeny classes of Drinfeld modules of higher ranks   The question we propose to answer throughout this paper is the following:\nGiven an isogeny class of Drinfeld modules over a finite field, what are the\norders of the corresponding endomorphism algebra (which is an isogeny\ninvariant) that occur as endomorphism ring of a Drinfeld module in that isogeny\nclass? It is worth mentioning that this question is different from the ones\ninvestigated by the authors Kuhn, Pink in [6] and Garai, Papikian in [3]. The\nformer authors rather provided an answer to the question, given a Drinfeld\nmodule {\\phi}, how does one efficiently compute the endomorphism ring of\n{\\phi}? The importance of our question resides in the fact that it might be\nvery helpful to better understand isogeny graphs of Drinfeld modules of higher\nrank (r > 2) and may be reopen the debate concerning the application to\nisogeny-based cryptography. We answer that question for the case whereby the\nendomorphism algebra is a field by providing a necessary and sufficient\ncondition for a given order to be the endomorphism ring of a Drinfeld module.\nWe apply our result to rank r = 3 Drinfeld modules and explicitly compute those\norders occurring as endomorphism rings of rank 3 Drinfeld modules over a finite\nfield.\n', ""Explicit description of isogeny and isomorphism classes of Drinfeld\n  modules over finite field   When travelling from the number fields theory to the function fields theory,\none cannot miss the deep analogy between rank 1 Drinfeld modules and the group\nof root of unity and the analogy between rank 2 Drinfeld modules and elliptic\ncurves. But so far, there is no known structure in number fields theory that is\nanalogous to the Drinfeld modules of higher rank r > 2. In this paper we\ninvestigate the classes of those Drinfeld modules of higher rank r > 2. We\ndescribe explicitly the Weil polynomials defining the isogeny classes of rank r\nDrinfeld modules for any rank r > 2. our explicit description of the Weil\npolynomials depends heavily on Yu's classification of isogeny classes (analogue\nof Honda-Tate at abelian varieties). Actually Yu has also explicitly did that\nwork for r = 2. To complete the classification, we define the new notion of\nfine isomorphy invariants for any rank r Drinfeld module and we prove that the\nfine isomorphy invariants together with J-invariants completely determine the\nL-isomorphism classes of rank r Drinfeld modules defined over the finite field\nL.\n""]","[('drinfeld modules finite', 0.6660834550857544), ('drinfeld modules', 0.593525230884552), ('drinfeld module', 0.5236316323280334), ('drinfeld modular', 0.512085497379303), ('modules rank', 0.46785658597946167), ('rank drinfeld', 0.466763436794281), ('module rank', 0.45952144265174866), ('isogeny classes', 0.42578932642936707), ('_q finite field', 0.4133080542087555), ('adic galois representation', 0.41229093074798584)]"
602,602,51,602_acoustic waves_acoustic wave_propagation acoustic waves_propagation acoustic,"['acoustic waves', 'acoustic wave', 'propagation acoustic waves', 'propagation acoustic', 'wave equations', 'ultrasonic', 'acoustics', 'acoustic', 'nonlinearities', 'acoustic pressure']","['Boundary stabilization of the linear MGT equation with partially\n  absorbing boundary data and degenerate viscoelasticity   The Jordan--Moore--Gibson--Thompson (JMGT) equation is a well-established and\nrecently widely studied model for nonlinear acoustics (NLA). It is a\nthird-order (in time) semilinear Partial Differential Equation (PDE) model with\nthe distinctive feature of predicting the propagation of ultrasound waves at\n\\textit{finite} speed due to heat phenomenon know as \\textit{second sound}\nwhich leads to the hyperbolic character of heat propagation. In this paper, we\nconsider the problem of stabilizability of the linear (known as) MGT--equation.\nWe consider a special geometry that is suitable for studying the problem of\ncontrolling (from the boundary) the acoustic pressure involved in medical\ntreatments like lithotripsy, thermotherapy, sonochemistry, or any other\nprocedures using High Intensity Focused Ultrasound (HIFU).\n', ""Asymptotic behaviors for the Jordan-Moore-Gibson-Thompson equation in\n  the viscous case   In this paper, we study large-time behaviors for a fundamental model in\nnonlinear acoustics, precisely, the viscous Jordan-Moore-Gibson-Thompson (JMGT)\nequation in the whole space $\\mathbb{R}^n$. This model describes nonlinear\nacoustics in perfect gases under irrotational flow and equipping Cattaneo's law\nof heat conduction. By employing refined WKB analysis and Fourier analysis, we\nderive first- and second-order asymptotic profiles of solution to the\nMoore-Gibson-Thompson (MGT) equation as $t\\gg 1$, which illustrates novel\noptimal estimates for the solutions even subtracting its profiles. Concerning\nthe nonlinear JMGT equation, via suggesting a new decomposition of nonlinear\nportion, we investigate the existence and large-time profiles of global (in\ntime) small data Sobolev solutions with suitable regularity. These results help\nbridge a new connection between the JMGT equation and diffusion-waves as\n$t\\gg1$.\n"", 'Time-fractional Moore-Gibson-Thompson equations   In this paper, we consider several time-fractional generalizations of the\nJordan-Moore-Gibson-Thompson (JMGT) equations in nonlinear acoustics as well as\ntheir linear Moore-Gibson-Thompson (MGT) versions. Following the procedure\ndescribed in Jordan (2014), these time-fractional acoustic equations are\nderived from four fractional versions of the Maxwell-Cattaneo law in Compte and\nMetzler (1997). Additionally to providing well-posedness results for each of\nthem, we also study the respective limits as the fractional order tends to one,\nleading to the classical third order in time (J)MGT equation.\n']","[('acoustic waves', 0.4705714285373688), ('acoustic wave', 0.46758076548576355), ('propagation acoustic waves', 0.45636796951293945), ('propagation acoustic', 0.45423203706741333), ('wave equations', 0.443844199180603), ('ultrasonic', 0.41037750244140625), ('acoustics', 0.3934442698955536), ('acoustic', 0.39048248529434204), ('nonlinearities', 0.386278361082077), ('acoustic pressure', 0.3741256594657898)]"
603,603,51,603_kac moody algebras_kac moody algebra_moody lie algebras_moody algebras,"['kac moody algebras', 'kac moody algebra', 'moody lie algebras', 'moody algebras', 'moody algebra', 'symmetrizable kac moody', 'lie algebras', 'kac moody lie', 'lie algebra mathfrak', 'lie superalgebras']","['On a Class of Indefinite Kac-Moody Algebras   In this paper, we study a special class of indefinite Kac-Moody algebras.\nBased on the study of hyperbolic Kac-Moody algebras, we give the definition of\n$N_k$ type Kac-Moody algebras and study some properties of this special type\nKac-Moody algebras.\n', '$\\pi$-systems and the embedding problem for rank $2$ Kac-Moody Lie\n  algebras   $\\pi$-systems are fundamental in the study of Kac-Moody Lie algebras since\nthey arise naturally in the embedding problems. Dynkin introduced them first\nand showed how they also appear in the classification of semisimple subalgebras\nof a semisimple Lie algebra. In this article, we explicitly classify the\n$\\pi$-systems associated to rank $2$ Kac-Moody Lie algebras and prove that in\nmost of the cases they are linearly independent. This classification allows us\nto determine the root generated subalgebras and which in turn determines all\npossible Kac-Moody algebras that can be embedded in a rank $2$ Kac-Moody\nalgebra as subalgebras generated by real root vectors. Additionally, following\nthe work of Naito we provide examples illustrating how Borcherds Kac-Moody\nalgebras can also be embedded inside a rank $2$ Kac-Moody algebra.\n', 'N-Extended Lorentzian Kac-Moody algebras   We investigate a class of Kac-Moody algebras previously not considered. We\nrefer to them as n-extended Lorentzian Kac-Moody algebras defined by their\nDynkin diagrams through the connection of an $A_n$ Dynkin diagram to the node\ncorresponding to the affine root. The cases $n=1$ and $n=2$ correspond to the\nwell studied over and very extended Kac-Moody algebras, respectively, of which\nthe particular examples of $E_{10}$ and $E_{11}$ play a prominent role in\nstring and M-theory. We construct closed generic expressions for their\nassociated roots, fundamental weights and Weyl vectors. We use these quantities\nto calculate specific constants from which the nodes can be determined that\nwhen deleted decompose the n-extended Lorentzian Kac-Moody algebras into simple\nLie algebras and Lorentzian Kac-Moody algebra. The signature of these constants\nalso serves to establish whether the algebras possess $SO(1,2)$ and/or\n$SO(3)$-principal subalgebras.\n']","[('kac moody algebras', 0.861343264579773), ('kac moody algebra', 0.8127442598342896), ('moody lie algebras', 0.7869264483451843), ('moody algebras', 0.7369333505630493), ('moody algebra', 0.6632618308067322), ('symmetrizable kac moody', 0.6393943428993225), ('lie algebras', 0.6287389397621155), ('kac moody lie', 0.5666267275810242), ('lie algebra mathfrak', 0.5600702166557312), ('lie superalgebras', 0.5530683398246765)]"
604,604,51,604_cusped hyperbolic manifolds_cusped hyperbolic manifold_volume hyperbolic manifolds_hyperbolic manifolds,"['cusped hyperbolic manifolds', 'cusped hyperbolic manifold', 'volume hyperbolic manifolds', 'hyperbolic manifolds', 'manifolds hyperbolic', 'hyperbolic manifold', 'closed hyperbolic manifolds', 'orientable hyperbolic', 'hyperbolic three', 'finite volume hyperbolic']","['Embedding closed hyperbolic 3-manifolds in small volume hyperbolic\n  4-manifolds   In this paper we study existence and lack thereof of closed embedded\norientable co-dimension one totally geodesic submanifolds of minimal volume\ncusped orientable hyperbolic manifolds.\n', 'Hyperbolic 3-manifolds of low cusp volume   We classify the complete hyperbolic 3-manifolds admitting a maximal cusp of\nvolume at most 2.62. We use this to show that the figure-8 knot complement is\nthe unique 1-cusped hyperbolic 3-manifold with nine or more non-hyperbolic\nfillings; to show that the figure-8 knot complement and its sister are the\nunique hyperbolic 3-manifolds with minimal volume maximal cusps; and to extend\nresults on determining low volume closed and cusped hyperbolic 3-manifolds.\n', ""Guts and The Minimal Volume Orientable Hyperbolic 3-Manifold with 3\n  Cusps   The minimal volume of orientable hyperbolic manifolds with a given number of\ncusps has been found for $0,1,2,4$ cusps, while the minimal volume of 3-cusped\norientable hyperbolic manifolds remains unknown. By using guts in sutured\nmanifolds and pared manifolds, we are able to show that for an orientable\nhyperbolic 3-manifold with 3 cusps such that every second homology class is\nlibroid, its volume is at least $5.49\\ldots = 6 \\times $Catalan's constant.\n""]","[('cusped hyperbolic manifolds', 0.7633167505264282), ('cusped hyperbolic manifold', 0.73630690574646), ('volume hyperbolic manifolds', 0.7145212292671204), ('hyperbolic manifolds', 0.6847983598709106), ('manifolds hyperbolic', 0.6791417002677917), ('hyperbolic manifold', 0.6539127230644226), ('closed hyperbolic manifolds', 0.6455258131027222), ('orientable hyperbolic', 0.6024537086486816), ('hyperbolic three', 0.58144211769104), ('finite volume hyperbolic', 0.5665795207023621)]"
605,605,51,605_wasserstein gradient flows_wasserstein gradient flow_gradient flow wasserstein_wasserstein gradient,"['wasserstein gradient flows', 'wasserstein gradient flow', 'gradient flow wasserstein', 'wasserstein gradient', 'flow wasserstein', 'gradient flow formulation', 'gradient flows', 'wasserstein metric', 'gradient flows space', 'metric gradient flow']","['Lagrangian schemes for Wasserstein gradient flows   This paper reviews different numerical methods for specific examples of\nWasserstein gradient flows: we focus on nonlinear Fokker-Planck equations,but\nalso discuss discretizations of the parabolic-elliptic Keller-Segel model and\nof the fourth order thin film equation. The methods under review are of\nLagrangian nature, that is, the numerical approximations trace the\ncharacteristics of the underlying transport equation rather than solving the\nevolution equation for the mass density directly. The two main approaches are\nbased on integrating the equation for the Lagrangian maps on the one hand, and\non solution of coupled ODEs for individual mass particles on the other hand.\n', ""The back-and-forth method for Wasserstein gradient flows   We present a method to efficiently compute Wasserstein gradient flows. Our\napproach is based on a generalization of the back-and-forth method (BFM)\nintroduced by Jacobs and L\\'eger to solve optimal transport problems. We evolve\nthe gradient flow by solving the dual problem to the JKO scheme. In general,\nthe dual problem is much better behaved than the primal problem. This allows us\nto efficiently run large-scale simulations for a large class of internal\nenergies including singular and non-convex energies.\n"", ""A new flow dynamic approach for Wasserstein gradient flows   We develop in this paper a new regularized flow dynamic approach to construct\nefficient numerical schemes for Wasserstein gradient flows in Lagrangian\ncoordinates. Instead of approximating the Wasserstein distance which needs to\nsolve constrained minimization problems, we reformulate the problem using the\nBenamou-Brenier's flow dynamic approach, leading to algorithms which only need\nto solve unconstrained minimization problem in $L^2$ distance. Our schemes\nautomatically inherit some essential properties of Wasserstein gradient systems\nsuch as positivity-preserving, mass conservative and energy dissipation. We\npresent ample numerical simulations of Porous-Medium equations, Keller-Segel\nequations and Aggregation equations to validate the accuracy and stability of\nthe proposed schemes. Compared to numerical schemes in Eulerian coordinates,\nour new schemes can capture sharp interfaces for various Wasserstein gradient\nflows using relatively smaller number of unknowns.\n""]","[('wasserstein gradient flows', 0.8286130428314209), ('wasserstein gradient flow', 0.7934304475784302), ('gradient flow wasserstein', 0.7837318778038025), ('wasserstein gradient', 0.7101649641990662), ('flow wasserstein', 0.6782558560371399), ('gradient flow formulation', 0.5889840722084045), ('gradient flows', 0.5883603096008301), ('wasserstein metric', 0.5852901935577393), ('gradient flows space', 0.5672669410705566), ('metric gradient flow', 0.5593248605728149)]"
606,606,51,606_anderson acceleration_acceleration methods_accelerating convergence_newton iteration,"['anderson acceleration', 'acceleration methods', 'accelerating convergence', 'newton iteration', 'convergence acceleration', 'fixed point iterations', 'fixed point iteration', 'accelerated', 'point iterations', 'fixed point methods']","['Composite Anderson acceleration method with dynamic window-sizes and\n  optimized damping   In this paper, we propose and analyze a set of fully non-stationary Anderson\nacceleration algorithms with dynamic window sizes and optimized damping.\nAlthough Anderson acceleration (AA) has been used for decades to speed up\nnonlinear solvers in many applications, most authors are simply using and\nanalyzing the stationary version of Anderson acceleration (sAA) with fixed\nwindow size and a constant damping factor. The behavior and potential of the\nnon-stationary version of Anderson acceleration methods remain an open\nquestion. Since most efficient linear solvers use composable algorithmic\ncomponents. Similar ideas can be used for AA to solve nonlinear systems. Thus\nin the present work, to develop non-stationary Anderson acceleration\nalgorithms, we first propose two systematic ways to dynamically alternate the\nwindow size $m$ by composition. One simple way to package sAA(m) with sAA(n) in\neach iteration is applying sAA(m) and sAA(n) separately and then average their\nresults. It is an additive composite combination. The other more important way\nis the multiplicative composite combination, which means we apply sAA(m) in the\nouter loop and apply sAA(n) in the inner loop. By doing this, significant gains\ncan be achieved. Secondly, to make AA to be a fully non-stationary algorithm,\nwe need to combine these strategies with our recent work on the non-stationary\nAnderson acceleration algorithm with optimized damping (AAoptD), which is\nanother important direction of producing non-stationary AA and nice performance\ngains have been observed. Moreover, we also investigate the rate of convergence\nof these non-stationary AA methods under suitable assumptions. Finally, our\nnumerical results show that some of these proposed non-stationary Anderson\nacceleration algorithms converge faster than the stationary sAA method and they\nmay significantly reduce the storage and time to find the solution in many\ncases.\n', 'Anderson Acceleration as a Krylov Method with Application to Asymptotic\n  Convergence Analysis   Anderson acceleration (AA) is widely used for accelerating the convergence of\nnonlinear fixed-point methods $x_{k+1}=q(x_{k})$, $x_k \\in \\mathbb{R}^n$, but\nlittle is known about how to quantify the convergence acceleration provided by\nAA. As a roadway towards gaining more understanding of convergence acceleration\nby AA, we study AA($m$), i.e., Anderson acceleration with finite window size\n$m$, applied to the case of linear fixed-point iterations $x_{k+1}=M x_{k}+b$.\nWe write AA($m$) as a Krylov method with polynomial residual update formulas,\nand derive recurrence relations for the AA($m$) polynomials. Writing AA($m$) as\na Krylov method immediately implies that $k$ iterations of AA($m$) cannot\nproduce a smaller residual than $k$ iterations of GMRES without restart (but\nwithout implying anything about the relative convergence speed of (windowed)\nAA($m$) versus restarted GMRES($m$)). We find that the AA($m$) residual\npolynomials observe a periodic memory effect where increasing powers of the\nerror iteration matrix $M$ act on the initial residual as the iteration number\nincreases. We derive several further results based on these polynomial residual\nupdate formulas, including orthogonality relations, a lower bound on the AA(1)\nacceleration coefficient $\\beta_k$, and explicit nonlinear recursions for the\nAA(1) residuals and residual polynomials that do not include the acceleration\ncoefficient $\\beta_k$. Using these recurrence relations we also derive new\nresidual convergence bounds for AA(1) in the linear case, demonstrating how the\nper-iteration residual reduction $||r_{k+1}||/||r_{k}||$ depends strongly on\nthe residual reduction in the previous iteration and on the angle between the\nprior residual vectors $r_k$ and $r_{k-1}$. We apply these results to study the\ninfluence of the initial guess on the asymptotic convergence factor of AA(1),\nand to study AA(1) residual convergence patterns.\n', 'Anderson acceleration of gradient methods with energy for optimization\n  problems   Anderson acceleration (AA) as an efficient technique for speeding up the\nconvergence of fixed-point iterations may be designed for accelerating an\noptimization method. We propose a novel optimization algorithm by adapting\nAnderson acceleration to the energy adaptive gradient method (AEGD)\n[arXiv:2010.05109]. The feasibility of our algorithm is examined in light of\nconvergence results for AEGD, though it is not a fixed-point iteration. We also\nquantify the accelerated convergence rate of AA for gradient descent by a\nfactor of the gain at each implementation of the Anderson mixing. Our\nexperimental results show that the proposed algorithm requires little tuning of\nhyperparameters and exhibits superior fast convergence.\n']","[('anderson acceleration', 0.6059589982032776), ('acceleration methods', 0.49620574712753296), ('accelerating convergence', 0.49507251381874084), ('newton iteration', 0.4835720360279083), ('convergence acceleration', 0.48123618960380554), ('fixed point iterations', 0.46517136693000793), ('fixed point iteration', 0.4546765387058258), ('accelerated', 0.42470917105674744), ('point iterations', 0.3885803520679474), ('fixed point methods', 0.38733404874801636)]"
607,607,51,607_tree theorems_tangles_tangle_tree decompositions,"['tree theorems', 'tangles', 'tangle', 'tree decompositions', 'tree decomposition', 'locally finite graphs', 'infinite graphs', 'spanning trees', 'finite graphs', 'graphs infinite']","[""A tree-of-tangles theorem for infinite tangles   Carmesin has extended Robertson and Seymour's tree-of-tangles theorem to the\ninfinite tangles of locally finite infinite graphs. We extend it further to the\ninfinite tangles of all infinite graphs.\n  Our result has a number of applications for the topology of infinite graphs,\nsuch as their end spaces and their compactifications.\n"", 'Tangle-tree duality in abstract separation systems   We prove a general width duality theorem for combinatorial structures with\nwell-defined notions of cohesion and separation. These might be graphs and\nmatroids, but can be much more general or quite different. The theorem asserts\na duality between the existence of high cohesiveness somewhere local and a\nglobal overall tree structure.\n  We describe cohesive substructures in a unified way in the format of tangles:\nas orientations of low-order separations satisfying certain consistency axioms.\nThese axioms can be expressed without reference to the underlying structure,\nsuch as a graph or matroid, but just in terms of the poset of the separations\nthemselves. This makes it possible to identify tangles, and apply our\ntangle-tree duality theorem, in very diverse settings.\n  Our result implies all the classical duality theorems for width parameters in\ngraph minor theory, such as path-width, tree-width, branch-width or rank-width.\nIt yields new, tangle-type, duality theorems for tree-width and path-width. It\nimplies the existence of width parameters dual to cohesive substructures such\nas $k$-blocks, edge-tangles, or given subsets of tangles, for which no width\nduality theorems were previously known.\n  Abstract separation systems can be found also in structures quite unlike\ngraphs and matroids. For example, our theorem can be applied to image analysis\nby capturing the regions of an image as tangles of separations defined as\nnatural partitions of its set of pixels. It can be applied in big data contexts\nby capturing clusters as tangles. It can be applied in the social sciences,\ne.g. by capturing as tangles the few typical mindsets of individuals found by a\nsurvey. It could also be applied in pure mathematics, e.g. to separations of\ncompact manifolds.\n', ""Refining trees of tangles in abstract separation systems: inessential\n  parts   Robertson and Seymour proved two fundamental theorems about tangles in\ngraphs: the tree-of-tangles theorem, which says that every graph has a\ntree-decomposition such that distinguishable tangles live in different nodes of\nthe tree, and the tangle-tree duality theorem, which says that graphs without a\n$k$-tangle have a tree-decomposition that witnesses the non-existence of such\ntangles, in that $k$-tangles would have to live in a node but no node is large\nenough to accommodate one.\n  Erde combined these two fundamental theorems into one, by constructing a\nsingle tree-decomposition such that every node either accommodates a single\n$k$-tangle or is too small to accommodate one. Such a tree-decomposition thus\nshows at a glance how many $k$-tangles a graph has and where they are.\n  The two fundamental theorems have since been extended to abstract separation\nsystems, which support tangles in more general discrete structures. In this\npaper we extend Erde's unified theorem to such general systems.\n""]","[('tree theorems', 0.5448997020721436), ('tangles', 0.5394032597541809), ('tangle', 0.5283288955688477), ('tree decompositions', 0.48516157269477844), ('tree decomposition', 0.4313061535358429), ('locally finite graphs', 0.4217003583908081), ('infinite graphs', 0.41983890533447266), ('spanning trees', 0.4127034842967987), ('finite graphs', 0.40692704916000366), ('graphs infinite', 0.3973032534122467)]"
608,608,51,608_free matching_matching problems_matchings_matching,"['free matching', 'matching problems', 'matchings', 'matching', 'random matching', 'matching minimum', 'preference lists', 'matched', 'matching maximum', 'bipartite']","['Instances of small size with no weakly stable matching for three-sided\n  problem with complete cyclic preferences   Given $n$ men, $n$ women, and $n$ dogs, we assume that each man has a\ncomplete preference list of women, while each woman does a complete preference\nlist of dogs, and each dog does a complete preference list of men. We study the\nso-called 3D-CYC problem, i.e., a three-dimensional problem with cyclic\npreferences. We understand a matching as a collection of $n$ nonintersecting\ntriples, each of which contains a man, a woman, and a dog. A matching is said\nto be nonstable, if one can find a man, a woman, and a dog, which belong to\ndifferent triples and prefer each other to their current partners in the\ncorresponding triples. Otherwise, the matching is said to be stable. According\nto the conjecture proposed by Eriksson, S\\""ostrand, and Strimling (2006), the\nproblem of finding a stable matching (the problem 3DSM-CYC) always has a\nsolution. However, Lam and Paxton have proposed an algorithm for constructing\npreference lists in 3DSM-CYC of size $n=90$, which has allowed them to disprove\nthe mentioned conjecture. The question on the existence of counterexamples of a\nlesser size remained open. The main value of this paper consists in reducing\nthe size of the counterexample to $n=20$. At the end part of the paper, we\ndiscuss a new variant of 3DSM, whose solution always exists.\n', 'Finding Stable Matchings in PhD Markets with Consistent Preferences and\n  Cooperative Partners   We introduce a new algorithm for finding stable matchings in multi-sided\nmatching markets. Our setting is motivated by a PhD market of students,\nadvisors, and co-advisors, and can be generalized to supply chain networks\nviewed as $n$-sided markets. In the three-sided PhD market, students primarily\ncare about advisors and then about co-advisors (consistent preferences), while\nadvisors and co-advisors have preferences over students only (hence they are\ncooperative). A student must be matched to one advisor and one co-advisor, or\nnot at all. In contrast to previous work, advisor-student and\nstudent-co-advisor pairs may not be mutually acceptable (e.g., a student may\nnot want to work with an advisor or co-advisor and vice versa). We show that\nthree-sided stable matchings always exist, and present an algorithm that, in\ntime quadratic in the market size (up to log factors), finds a three-sided\nstable matching using any two-sided stable matching algorithm as matching\nengine. We illustrate the challenges that arise when not all advisor-co-advisor\npairs are compatible. We then generalize our algorithm to $n$-sided markets\nwith quotas and show how they can model supply chain networks. Finally, we show\nhow our algorithm outperforms the baseline given by [Danilov, 2003] in terms of\nboth producing a stable matching and a larger number of matches on a synthetic\ndataset.\n', 'Stable Marriage with One-Sided Preference   Many countries around the world, including Korea, use the school choice\nlottery system. However, this method has a problem in that many students are\nassigned to less-preferred schools based on the lottery results. In addition,\nthe task of finding a good assignment with ties often has a time complexity of\nNP, making it a very difficult problem to improve the quality of the\nassignment.\n  In this paper, we prove that the problem of finding a stable matching that\nmaximizes the student-oriented preference utility in a two-sided market with\none-sided preference can be solved in polynomial time, and we verify through\nexperiments that the quality of assignment is improved. The main contributions\nof this paper are as follows. We found that stable student-oriented allocation\nin a two-sided market with one-sided preferences is the same as stable\nallocation in a two-sided market with symmetric preferences. In addition, we\ndefined a method to quantify the quality of allocation from a preference\nutilitarian perspective. Based on the above two, it was proven that the problem\nof finding a stable match that maximizes the preference utility in a two-sided\nmarket with homogeneous preferences can be reduced to an allocation problem. In\nthis paper, through an experiment, we quantitatively verified that optimal\nstudent assignment assigns more students to schools of higher preference, even\nin situations where many students are assigned to schools of low preference\nusing the existing assignment method.\n']","[('free matching', 0.6098833680152893), ('matching problems', 0.5929465293884277), ('matchings', 0.5906234383583069), ('matching', 0.5533781051635742), ('random matching', 0.5203653573989868), ('matching minimum', 0.4816785454750061), ('preference lists', 0.44951513409614563), ('matched', 0.4382687211036682), ('matching maximum', 0.42643502354621887), ('bipartite', 0.40602701902389526)]"
609,609,51,609_oscillatory integrals_gaussian quadrature rules_gaussian quadrature_high order quadrature,"['oscillatory integrals', 'gaussian quadrature rules', 'gaussian quadrature', 'high order quadrature', 'quadrature formulas', 'numerical integration', 'quadrature rules', 'explicit error bounds', 'integration rules', 'type integrals']","['A Filon-Clenshaw-Curtis-Smolyak rule for multi-dimensional oscillatory\n  integrals with application to a UQ problem for the Helmholtz equation   In this paper, we combine the Smolyak technique for multi-dimensional\ninterpolation with the Filon-Clenshaw-Curtis (FCC) rule for one-dimensional\noscillatory integration, to obtain a new Filon-Clenshaw-Curtis-Smolyak (FCCS)\nrule for oscillatory integrals with linear phase over the $d-$dimensional cube\n$[-1,1]^d$. By combining stability and convergence estimates for the FCC rule\nwith error estimates for the Smolyak interpolation operator, we obtain an error\nestimate for the FCCS rule, consisting of the product of a Smolyak-type error\nestimate multiplied by a term that decreases with\n$\\mathcal{O}(k^{-\\tilde{d}})$, where $k$ is the wavenumber and $\\tilde{d}$ is\nthe number of oscillatory dimensions. If all dimensions are oscillatory, a\nhigher negative power of $k$ appears in the estimate. As an application, we\nconsider the forward problem of uncertainty quantification (UQ) for a\none-space-dimensional Helmholtz problem with wavenumber $k$ and a random\nheterogeneous refractive index, depending in an affine way on $d$ i.i.d.\nuniform random variables. After applying a classical hybrid\nnumerical-asymptotic approximation, expectations of functionals of the solution\nof this problem can be formulated as a sum of oscillatory integrals over\n$[-1,1]^d$, which we compute using the FCCS rule. We give numerical results for\nthe FCCS rule and the UQ algorithm showing that accuracy improves when both $k$\nand the order of the rule increase. We also give results for dimension-adaptive\nsparse grid FCCS quadrature showing its efficiency as dimension increases.\n', 'Gaussian quadrature rules for composite highly oscillatory integrals   Highly oscillatory integrals of composite type arise in electronic\nengineering and their calculations is a challenging problem. In this paper, we\npropose two Gaussian quadrature rules for computing such integrals. The first\none is constructed based on the classical theory of orthogonal polynomials and\nits nodes and weights can be computed efficiently by using tools of numerical\nlinear algebra. We show that the rate of convergence of this rule depends\nsolely on the regularity of the non-oscillatory part of the integrand. The\nsecond one is constructed with respect to a sign-changing function and the\nclassical theory of Gaussian quadrature can not be used anymore. We explore\ntheoretical properties of this Gaussian quadrature, including the trajectories\nof the quadrature nodes and the convergence rate of these nodes to the\nendpoints of the integration interval, and prove its asymptotic error estimate\nunder suitable hypotheses. Numerical experiments are presented to demonstrate\nthe performance of the proposed methods.\n', 'Modified Filon-Clenshaw-Curtis rules for oscillatory integrals with a\n  nonlinear oscillator   Filon-Clenshaw-Curtis rules are among rapid and accurate quadrature rules for\ncomputing highly oscillatory integrals. In the implementation of the\nFilon-Clenshaw-Curtis rules in the case when the oscillator function is not\nlinear, its inverse should be evaluated at some points. In this paper, we solve\nthis problem by introducing an approach based on the interpolation, which leads\nto a class of modifications of the original Filon-Clenshaw-Curtis rules. In the\nabsence of stationary points, two kinds of modified Filon-Clenshaw-Curtis rules\nare introduced. For each kind, an error estimate is given theoretically, and\nthen illustrated by some numerical experiments. Also, some numerical\nexperiments are carried out for a comparison of the accuracy and the efficiency\nof the two rules. In the presence of stationary points, the idea is applied to\nthe composite Filon-Clenshaw-Curtis rules on graded meshes. An error estimate\nis given theoretically, and then illustrated by some numerical experiments.\n']","[('oscillatory integrals', 0.6106595396995544), ('gaussian quadrature rules', 0.5925812721252441), ('gaussian quadrature', 0.5313867926597595), ('high order quadrature', 0.5296556353569031), ('quadrature formulas', 0.5277127027511597), ('numerical integration', 0.5238021016120911), ('quadrature rules', 0.46367567777633667), ('explicit error bounds', 0.4467110335826874), ('integration rules', 0.42468592524528503), ('type integrals', 0.4140947461128235)]"
610,610,51,610_population covariance matrices_large sample covariance_sample covariance matrices_linear spectral statistics,"['population covariance matrices', 'large sample covariance', 'sample covariance matrices', 'linear spectral statistics', 'spectral statistics', 'random matrix theory', 'eigenvalue statistics', 'limiting spectral distribution', 'spiked eigenvalues', 'population covariance matrix']","[""A CLT for the LSS of large dimensional sample covariance matrices with\n  unbounded dispersions   In this paper, we establish the central limit theorem (CLT) for linear\nspectral statistics (LSS) of large-dimensional sample covariance matrix when\nthe population covariance matrices are not uniformly bounded, which is a\nnontrivial extension of the Bai-Silverstein theorem (BST) (2004). The latter\nhas strongly stimulated the development of high-dimensional statistics,\nespecially the application of random matrix theory to statistics. However, the\nassumption of uniform boundedness of the population covariance matrices is\nfound strongly limited to the applications of BST. The aim of this paper is to\nremove the blockages to the applications of BST. The new CLT, allows the spiked\neigenvalues to exist and tend to infinity. It is interesting to note that the\nroles of either spiked eigenvalues or the bulk eigenvalues or both of the two\nare dominating in the CLT.\n  Moreover, the results are checked by simulation studies with various\npopulation settings. The CLT for LSS is then applied for testing the hypothesis\nthat a covariance matrix $ \\bSi $ is equal to an identity matrix. For this, the\nasymptotic distributions for the corrected likelihood ratio test (LRT) and\nNagao's trace test (NT) under alternative are derived, and we also propose the\nasymptotic power of LRT and NT under certain alternatives.\n"", ""A CLT for the LSS of large dimensional sample covariance matrices with\n  diverging spikes   In this paper, we establish the central limit theorem (CLT) for linear\nspectral statistics (LSSs) of a large-dimensional sample covariance matrix when\nthe population covariance matrices are involved with diverging spikes. This\nconstitutes a nontrivial extension of the Bai-Silverstein theorem (BST) (Ann\nProbab 32(1):553--605, 2004), a theorem that has strongly influenced the\ndevelopment of high-dimensional statistics, especially in the applications of\nrandom matrix theory to statistics. Recently, there has been a growing\nrealization that the assumption of uniform boundedness of the population\ncovariance matrices in the BST is not satisfied in some fields, such as\neconomics, where the variances of principal components may diverge as the\ndimension tends to infinity. Therefore, in this paper, we aim to eliminate this\nobstacle to applications of the BST. Our new CLT accommodates spiked\neigenvalues, which may either be bounded or tend to infinity. A distinguishing\nfeature of our result is that the variance in the new CLT is related to both\nspiked eigenvalues and bulk eigenvalues, with dominance being determined by the\ndivergence rate of the largest spiked eigenvalues. The new CLT for LSS is then\napplied to test the hypothesis that the population covariance matrix is the\nidentity matrix or a generalized spiked model. The asymptotic distributions of\nthe corrected likelihood ratio test statistic and the corrected Nagao's trace\ntest statistic are derived under the alternative hypothesis. Moreover, we\npresent power comparisons between these two LSSs and Roy's largest root test.\nIn particular, we demonstrate that except for the case in which the number of\nspikes is equal to one, the LSSs could exhibit higher asymptotic power than\nRoy's largest root test.\n"", 'Asymptotic independence of spiked eigenvalues and linear spectral\n  statistics for large sample covariance matrices   We consider general high-dimensional spiked sample covariance models and show\nthat their leading sample spiked eigenvalues and their linear spectral\nstatistics are asymptotically independent when the sample size and dimension\nare proportional to each other. As a byproduct, we also establish the central\nlimit theorem of the leading sample spiked eigenvalues by removing the block\ndiagonal assumption on the population covariance matrix, which is commonly\nneeded in the literature. Moreover, we propose consistent estimators of the\n$L_4$ norm of the spiked population eigenvectors. Based on these results, we\ndevelop a new statistic to test the equality of two spiked population\ncovariance matrices. Numerical studies show that the new test procedure is more\npowerful than some existing methods.\n']","[('population covariance matrices', 0.5943713784217834), ('large sample covariance', 0.5873129963874817), ('sample covariance matrices', 0.5862782001495361), ('linear spectral statistics', 0.576336145401001), ('spectral statistics', 0.5642995834350586), ('random matrix theory', 0.5607863068580627), ('eigenvalue statistics', 0.5596984028816223), ('limiting spectral distribution', 0.5559484362602234), ('spiked eigenvalues', 0.5510962009429932), ('population covariance matrix', 0.5378568768501282)]"
611,611,51,611_commutative semiring_idempotent semirings_semirings_idempotent semiring,"['commutative semiring', 'idempotent semirings', 'semirings', 'idempotent semiring', 'semiring', 'semifields', 'prime ideals', 'reduced ring', 'commutative rings', 'maximal ideals']","['Some remarks on the comparability of ideals in semirings   A semiring is uniserial if its ideals are totally ordered by inclusion.\nFirst, we show that a semiring $S$ is uniserial if and only if the matrix\nsemiring $M_n(S)$ is uniserial. As a generalization of valuation semirings, we\nalso investigate those semirings whose prime ideals are linearly ordered by\ninclusion. For example, we prove that the prime ideals of a commutative\nsemiring $S$ are linearly ordered if and only if for each $x,y \\in S$, there is\na positive integer $n$ such that either $x|y^n$ or $y|x^n$. Then, we introduce\nand characterize pseudo-valuation semidomains. It is shown that prime ideals of\npseudo-valuation semidomains and also of the divided ones are linearly ordered.\n', ""Lattices, Spectral Spaces, and Closure Operations on Idempotent\n  Semirings   Spectral spaces, introduced by Hochster, are topological spaces homeomorphic\nto the prime spectra of commutative rings. In this paper we study spectral\nspaces in perspective of idempotent semirings which are algebraic structures\nreceiving a lot of attention due to its several applications to tropical\ngeometry. We first prove that a space is spectral if and only if it is the\n\\emph{prime $k$-spectrum} of an idempotent semiring. In fact, we enrich\nHochster's theorem by constructing a subcategory of idempotent semirings which\nis antiequivalent to the category of spectral spaces. We further provide\nexamples of spectral spaces arising from sets of congruence relations of\nsemirings. In particular, we prove that the \\emph{space of valuations} and the\n\\emph{space of prime congruences} on an idempotent semiring are spectral, and\nthere is a natural bijection of sets between the two; this shows a stark\ndifference between rings and idempotent semirings. We then develop several\naspects of commutative algebra of semirings. We mainly focus on the notion of\n\\emph{closure operations} for semirings, and provide several examples. In\nparticular, we introduce an \\emph{integral closure operation} and a\n\\emph{Frobenius closure operation} for idempotent semirings.\n"", ""Algebraic properties of expectation semirings   In this paper, we investigate the algebraic properties of the expectation\nsemirings which are semiring version of the concept of trivial extension in\nring theory. We discuss ideals, primes, maximals and primary ideals of these\nsemirings. We also discuss the distinguished elements such as the units,\nidempotents, and zero-divisors of the expectations semirings. Similar to their\ncounterparts in ring theory, we introduce pr\\'{e}simplifiable, domainlike,\nclean, almost clean, and weakly clean semiring and see when an expectation\nsemiring is one of these semirings.\n""]","[('commutative semiring', 0.7479601502418518), ('idempotent semirings', 0.7180318832397461), ('semirings', 0.714269757270813), ('idempotent semiring', 0.6744199991226196), ('semiring', 0.6571899652481079), ('semifields', 0.5602231621742249), ('prime ideals', 0.5106940865516663), ('reduced ring', 0.49636465311050415), ('commutative rings', 0.4702248275279999), ('maximal ideals', 0.46681469678878784)]"
612,612,51,612_control barrier functions_control constraints_state control constraints_safety constraints,"['control barrier functions', 'control constraints', 'state control constraints', 'safety constraints', 'safety critical control', 'control barrier', 'lyapunov barrier functions', 'control lyapunov barrier', 'control barrier cbf', 'control bounds']","['Predictive Control Barrier Functions: Bridging model predictive control\n  and control barrier functions   In this paper, we establish a connection between model predictive control\n(MPC) techniques and Control Barrier Functions (CBFs). Recognizing the\nsimilarity between CBFs and Control Lyapunov Functions (CLFs), we propose a\nsafe MPC formulation that ensures invariance and safety without relying on\nexplicit stability conditions. The value function of our proposed safe MPC is a\nCBF, which we refer to as the Predictive Control Barrier Function (PCBF),\nsimilar to traditional MPC formulations which encode stability by having value\nfunctions as CLFs. Our formulation is simpler than previous PCBF approaches and\nis based on weaker assumptions while proving a similar theorem that guarantees\nsafety recovery. Notably, our safe MPC formulation does not require the value\nfunction to be strictly decreasing to ensure convergence to a safe invariant\nset. Numerical examples demonstrate the effectiveness of our approach in\nguaranteeing safety and constructing non-conservative CBFs.\n', 'Optimal Control Barrier Functions: Maximizing the Action Space Subject\n  to Control Bounds   This letter addresses the constraint compatibility problem of control barrier\nfunctions (CBFs), which occurs when a safety-critical CBF requires a system to\napply more control effort than it is capable of generating. This inevitably\nleads to a safety violation, which transitions the system to an unsafe (and\npossibly dangerous) trajectory. We resolve the constraint compatibility problem\nby constructing a control barrier function that maximizes the feasible action\nspace for first and second-order constraints, and we prove that the optimal CBF\nencodes a dynamical motion primitive. Furthermore, we show that this dynamical\nmotion primitive contains an implicit model for the future trajectory for\ntime-varying components of the system. We validate our optimal CBF in\nsimulation, and compare its behavior with a linear CBF.\n', 'Composing Control Barrier Functions for Complex Safety Specifications   The increasing complexity of control systems necessitates control laws that\nguarantee safety w.r.t. complex combinations of constraints. In this letter, we\npropose a framework to describe compositional safety specifications with\ncontrol barrier functions (CBFs). The specifications are formulated as Boolean\ncompositions of state constraints, and we propose an algorithmic way to create\na single continuously differentiable CBF that captures these constraints and\nenables safety-critical control. We describe the properties of the proposed\nCBF, and we demonstrate its efficacy by numerical simulations.\n']","[('control barrier functions', 0.6491319537162781), ('control constraints', 0.6295250654220581), ('state control constraints', 0.6108224987983704), ('safety constraints', 0.6017189621925354), ('safety critical control', 0.5821799039840698), ('control barrier', 0.5656638741493225), ('lyapunov barrier functions', 0.5600019693374634), ('control lyapunov barrier', 0.5585483908653259), ('control barrier cbf', 0.5521830320358276), ('control bounds', 0.5328438878059387)]"
613,613,51,613_flocking behavior_cucker smale flocking_flocking_smale flocking,"['flocking behavior', 'cucker smale flocking', 'flocking', 'smale flocking', 'flock', 'collective dynamics', 'flocks', 'asymptotic dynamics', 'collective motion', 'cucker smale type']","[""Finite flocking time of the nonlinear Cucker--Smale model with Rayleigh\n  friction type using the discrete $p$-Laplacian   The study of collective behavior in multi-agent systems has attracted the\nattention of many researchers due to its wide range of applications. Among\nthem, the Cucker-Smale model was developed to study the phenomenon of flocking,\nand various types of extended models have been actively proposed and studied in\nrecent decades.\n  In this study, we address open questions of the Cucker--Smale model with\nnorm-type Rayleigh friction: {\\bf (i)} The positivity of the communication\nweight, {\\bf (ii)} The convergence of the norm of the velocities of agents,\n{\\bf (iii)} The direction of the velocities of agents. For problems (i) and\n(ii), we present the nonlinear Cucker--Smale model with norm-type Rayleigh\nfriction, where the nonlinear Cucker--Smale model is generalized to a nonlinear\nmodel by applying a discrete $p$-Laplacian operator. For this model, we present\nconditions that guarantee that the norm for velocities of agents converges to 0\nor a positive value, and we also show that the regular communication weight\nsatisfies the conditions given in this study. In particular, we present a\ncondition for the initial configuration to obtain that the norm of agent\nvelocities converges to only some positive value.\n  By contrast, problem (iii) is not solved by the norm-type nonlinear model.\nThus, we propose a nonlinear Cucker--Smale model with a vector-type Rayleigh\nfriction for problem (iii). In parallel to the first model, we show that the\ndirection of the agents' velocities can be controlled by parameters in the\nnonlinear Cucker--Smale model with the vector-type Rayleigh friction.\n"", 'Interplay of geometric constraint and bonding force in the emergent\n  behaviors of relativistic Cucker-Smale flocks   We present the relativistic analogue of the Cucker-Smale model with a bonding\nforce on Riemannian manifold, and study its emergent dynamics. The Cucker-Smale\nmodel serves a prototype example of mechanical flocking models, and it has been\nextensively studied from various points of view. Recently, the authors studied\ncollision avoidance and asymptotic flocking of the Cucker-Smale model with a\nbonding force on the Euclidean space. In this paper, we provide an analytical\nframework for collision avoidance and asymptotic flocking of the proposed model\non Riemannian manifolds. Our analytical framework is explicitly formulated in\nterms of system parameters, initial data and the injectivity radius of the\nambient manifold, and we study how the geometric information of an ambient\nmanifold can affect the flocking dynamics.\n', 'Asymptotic dynamics for the Cucker-Smale model with velocity control   We study the Cucker-Smale model with a velocity control function. The\nCucker-Smale model design the emergence of consensus in terms of flocking. A\nproposed model encompasses several Cucker-Smale models, such as a speed limit\nmodel, a relativistic model, and an almost unit speed model. We provide\ncollective behaviors of the proposed model, like mono or bi-cluster flocking,\nsticking, and collision avoidance, depending on the regularity and singularity\nof communication weight at the origin. In particular, we provide a sufficient\nframework to guarantee a positive lower bound of the distance between agents\nunder strongly singular communications.\n']","[('flocking behavior', 0.6503498554229736), ('cucker smale flocking', 0.6260586977005005), ('flocking', 0.5623850226402283), ('smale flocking', 0.5541673898696899), ('flock', 0.517275869846344), ('collective dynamics', 0.5159062743186951), ('flocks', 0.5038080215454102), ('asymptotic dynamics', 0.49501579999923706), ('collective motion', 0.4650108814239502), ('cucker smale type', 0.4436056613922119)]"
614,614,51,614_satellite communications_satellite communication_satellite networks_multi satellite,"['satellite communications', 'satellite communication', 'satellite networks', 'multi satellite', 'leo satellite communication', 'interference management', 'satellite', 'satellite systems', 'leo satellite', 'integrated satellite']","['Distributed Rate-Splitting Multiple Access for Multilayer Satellite\n  Communications   Future wireless networks, in particular, 5G and beyond, are anticipated to\ndeploy dense Low Earth Orbit (LEO) satellites to provide global coverage and\nbroadband connectivity. However, the limited frequency band and the coexistence\nof multiple constellations bring new challenges for interference management. In\nthis paper, we propose a robust multilayer interference management scheme for\nspectrum sharing in heterogeneous satellite networks with statistical channel\nstate information (CSI) at the transmitter (CSIT) and receivers (CSIR). In the\nproposed scheme, Rate-Splitting Multiple Access (RSMA), as a general and\npowerful framework for interference management and multiple access strategies,\nis implemented distributedly at GEO and LEO satellites, coined Distributed-RSMA\n(D-RSMA). By doing so, D-RSMA aims to mitigate the interference and boost the\nuser fairness of the overall multilayer satellite system. Specifically, we\nstudy the problem of jointly optimizing the GEO/LEO precoders and message\nsplits to maximize the minimum rate among User Terminals (UTs) subject to a\ntransmit power constraint at all satellites. A robust algorithm is proposed to\nsolve the original non-convex optimization problem. Numerical results\ndemonstrate the effectiveness and robustness towards network load and CSI\nuncertainty of our proposed D-RSMA scheme. Benefiting from the interference\nmanagement capability, D-RSMA provides significant max-min fairness performance\ngains compared to several benchmark schemes.\n', 'Holographic Metasurface-Based Beamforming for Multi-Altitude LEO\n  Satellite Networks   Low Earth Orbit (LEO) satellite networks are capable of improving the global\nInternet service coverage. In this context, we propose a hybrid beamforming\ndesign for holographic metasurface based terrestrial users in multi-altitude\nLEO satellite networks. Firstly, the holographic beamformer is optimized by\nmaximizing the downlink channel gain from the serving satellite to the\nterrestrial user. Then, the digital beamformer is designed by conceiving a\nminimum mean square error (MMSE) based detection algorithm for mitigating the\ninterference arriving from other satellites. To dispense with excessive\noverhead of full channel state information (CSI) acquisition of all satellites,\nwe propose a low-complexity MMSE beamforming algorithm that only relies on the\ndistribution of the LEO satellite constellation harnessing stochastic geometry,\nwhich can achieve comparable throughput to that of the algorithm based on the\nfull CSI in the case of a dense LEO satellite deployment. Furthermore, it\noutperforms the maximum ratio combining (MRC) algorithm, thanks to its\ninter-satellite interference mitigation capacity. The simulation results show\nthat our proposed holographic metasurface based hybrid beamforming architecture\nis capable of outperforming the state-of-the-art antenna array architecture in\nterms of its throughput, given the same physical size of the transceivers.\nMoreover, we demonstrate that the beamforming performance attained can be\nsubstantially improved by taking into account the mutual coupling effect,\nimposed by the dense placement of the holographic metasurface elements.\n', 'Rate-Splitting Multiple Access for GEO-LEO Coexisting Satellite Systems:\n  A Traffic-Aware Throughput Maximization Precoder Design   The frequency coexistence between geostationary orbit (GEO) and low earth\norbit (LEO) satellite systems is expected to be a promising approach for\nrelieving spectrum scarcity. However, it is essential to manage mutual\ninterference between GEO and LEO satellite systems for frequency coexistence.\nSpecifically, \\emph{in-line interference}, caused by LEO satellites moving near\nthe line-of-sight path between GEO satellite and GEO users (GUs), can\nsignificantly degrade GEO system throughput. This paper put forth a novel\nrate-splitting multiple access (RSMA) with a super-common message for GEO-LEO\ncoexisting satellite systems (CSS). By employing a super-common message that\nGUs can decode, GUs can mitigate the in-line interference by successive\ninterference cancellation (SIC). Moreover, we formulate a traffic-aware\nthroughput maximization (TTM) problem to satisfy the heterogeneous traffic\ndemands of users by minimizing total unmet throughput demands (or user\ndissatisfaction). By doing so, the TTM precoder can be flexibly adjusted\naccording to the interference leakage from LEO satellites to GUs and target\ntraffic demands. Numerical results confirm that our proposed method ensures\nseamless connectivity even in the GEO-LEO in-line interference regime under\nimperfect channel state information (CSI) at both the transmitter and receiver.\n']","[('satellite communications', 0.6399053335189819), ('satellite communication', 0.6159931421279907), ('satellite networks', 0.5898683667182922), ('multi satellite', 0.5765540599822998), ('leo satellite communication', 0.568963348865509), ('interference management', 0.4922533631324768), ('satellite', 0.48568403720855713), ('satellite systems', 0.4800630807876587), ('leo satellite', 0.4655263423919678), ('integrated satellite', 0.45009955763816833)]"
615,615,50,615_finite field elements_primitive polynomials_finite fields_elements finite field,"['finite field elements', 'primitive polynomials', 'finite fields', 'elements finite field', 'finite fields mathbb', 'mathbb f_q', 'finite field', 'finite field mathbb', 'mathbb finite field', 'finite fields let']","['Inverses of $r$-primitive $k$-normal elements over finite fields   Let $r$, $n$ be positive integers, $k$ be a non-negative integer and $q$ be\nany prime power such that $r\\mid q^n-1.$ An element $\\alpha$ of the finite\nfield $\\mathbb{F}_{q^n}$ is called an {\\it $r$-primitive} element, if its\nmultiplicative order is $(q^n-1)/r$, and it is called a {\\it $k$-normal}\nelement over $\\mathbb{F}_q$, if the greatest common divisor of the polynomials\n$m_\\alpha(x)=\\sum_{i=1}^{n} \\alpha^{q^{i-1}}x^{n-i}$ and $x^n-1$ is of degree\n$k.$ In this article, we define the characteristic function for the set of\n$k$-normal elements, and with the help of this, we establish a sufficient\ncondition for the existence of an element $\\alpha$ in $\\mathbb{F}_{q^n}$, such\nthat $\\alpha$ and $\\alpha^{-1}$ both are simultaneously $r$-primitive and\n$k$-normal over $\\mathbb{F}_q$. Moreover, for $n>6k$, we show that there always\nexists an $r$-primitive and $k$-normal element $\\alpha$ such that $\\alpha^{-1}$\nis also $r$-primitive and $k$-normal in all but finitely many fields\n$\\mathbb{F}_{q^n}$ over $\\mathbb{F}_q$, where $q$ and $n$ are such that $r\\mid\nq^n-1$ and there exists a $k$-degree polynomial $g(x)\\mid x^n-1$ over\n$\\mathbb{F}_q$. In particular, we discuss the existence of an element $\\alpha$\nin $\\mathbb{F}_{q^n}$ such that $\\alpha$ and $\\alpha^{-1}$ both are\nsimultaneously $1$-primitive and $1$-normal over $\\mathbb{F}_q$.\n', 'About $r$- primitive and $k$-normal elements in finite fields   In 2013, Huczynska, Mullen, Panario and Thomson introduced the concept of\n$k$-normal elements: an element $\\alpha \\in \\mathbb{F}_{q^n}$ is $k$-normal\nover $\\mathbb{F}_q$ if the greatest common divisor of the polynomials\n$g_{\\alpha}(x)= \\alpha x^{n-1}+\\alpha^qx^{n-2}+\\ldots\n+\\alpha^{q^{n-2}}x+\\alpha^{q^{n-1}}$ and $x^n-1$ in $\\mathbb{F}_{q^n}[x]$ has\ndegree $k$, generalizing the concept of normal elements (normal in the usual\nsense is $0$-normal). In this paper we discuss the existence of $r$-primitive,\n$k$-normal elements in $\\mathbb{F}_{q^n}$ over $\\mathbb{F}_{q}$, where an\nelement $\\alpha \\in \\mathbb{F}_{q^n}^*$ is $r$-primitive if its multiplicative\norder is $\\frac{q^n-1}{r}$. We provide many general results about the existence\nof this class of elements and we work a numerical example over finite fields of\ncharacteristic $11$.\n', 'Pairs of $r$-primitive and $k$-normal elements in finite fields   Let $\\mathbb{F}_{q^n}$ be a finite field with $q^n$ elements and $r$ be a\npositive divisor of $q^n-1$. An element $\\alpha \\in \\mathbb{F}_{q^n}^*$ is\ncalled $r$-primitive if its multiplicative order is $(q^n-1)/r$. Also, $\\alpha\n\\in \\mathbb{F}_{q^n}$ is $k$-normal over $\\mathbb{F}_q$ if the greatest common\ndivisor of the polynomials $g_{\\alpha}(x) = \\alpha x^{n-1}+ \\alpha^q x^{n-2} +\n\\ldots + \\alpha^{q^{n-2}}x + \\alpha^{q^{n-1}}$ and $x^n-1$ in\n$\\mathbb{F}_{q^n}[x]$ has degree $k$. These concepts generalize the ideas of\nprimitive and normal elements, respectively. In this paper, we consider\nnon-negative integers $m_1,m_2,k_1,k_2$, positive integers $r_1,r_2$ and\nrational functions $F(x)=F_1(x)/F_2(x) \\in \\mathbb{F}_{q^n}(x)$ with $\\deg(F_i)\n\\leq m_i$ for $i\\in\\{ 1,2\\}$ satisfying certain conditions and we present\nsufficient conditions for the existence of $r_1$-primitive $k_1$-normal\nelements $\\alpha \\in \\mathbb{F}_{q^n}$ over $\\mathbb{F}_q$, such that\n$F(\\alpha)$ is an $r_2$-primitive $k_2$-normal element over $\\mathbb{F}_q$.\nFinally as an example we study the case where $r_1=2$, $r_2=3$, $k_1=2$,\n$k_2=1$, $m_1=2$ and $m_2=1$, with $n \\ge 7$.\n']","[('finite field elements', 0.5421686172485352), ('primitive polynomials', 0.5058491826057434), ('finite fields', 0.5045954585075378), ('elements finite field', 0.5003438591957092), ('finite fields mathbb', 0.4893413782119751), ('mathbb f_q', 0.48656943440437317), ('finite field', 0.48482733964920044), ('finite field mathbb', 0.4686537981033325), ('mathbb finite field', 0.4651802182197571), ('finite fields let', 0.46078377962112427)]"
616,616,50,616_representations lie groups_representations lie_irreducible unitary representation_real reductive groups,"['representations lie groups', 'representations lie', 'irreducible unitary representation', 'real reductive groups', 'real reductive group', 'irreducible representations', 'representations pi', 'representations compact', 'irreducible representation', 'unitary representation']","[""Symmetry breaking operators for real reductive groups of rank one   For a pair of real reductive groups $G'\\subset G$ we consider the space ${\\rm\nHom}_{G'}(\\pi|_{G'},\\tau)$ of intertwining operators between spherical\nprincipal series representations $\\pi$ of $G$ and $\\tau$ of $G'$, also called\n\\emph{symmetry breaking operators}. Restricting to those pairs $(G,G')$ where\n${\\rm dim\\,Hom}_{G'}(\\pi|_{G'},\\tau)<\\infty$ and $G$ and $G'$ are of real rank\none, we classify all symmetry breaking operators explicitly in terms of their\ndistribution kernels. This generalizes previous work by Kobayashi--Speh for\n$(G,G')=({\\rm O}(1,n+1),{\\rm O}(1,n))$ to the reductive pairs $$ (G,G') = ({\\rm\nU}(1,n+1;\\mathbb{F}),{\\rm U}(1,m+1;\\mathbb{F})\\times F) \\qquad \\mbox{with\n$\\mathbb{F}=\\mathbb{C},\\mathbb{H},\\mathbb{O}$ and $F<{\\rm U}(n-m;\\mathbb{F})$.}\n$$ In most cases, all symmetry breaking operators can be constructed using one\nmeromorphic family of distributions whose poles and residues we describe in\ndetail. In addition to this family, there may occur some sporadic symmetry\nbreaking operators which we determine explicitly.\n"", 'On the direct integral decomposition in branching laws for real\n  reductive groups   The restriction of an irreducible unitary representation $\\pi$ of a real\nreductive group $G$ to a reductive subgroup $H$ decomposes into a direct\nintegral of irreducible unitary representations $\\tau$ of $H$ with\nmultiplicities $m(\\pi,\\tau)\\in\\mathbb{N}\\cup\\{\\infty\\}$. We show that on the\nsmooth vectors of $\\pi$, the direct integral is pointwise defined. This implies\nthat $m(\\pi,\\tau)$ is bounded above by the dimension of the space\n$\\operatorname{Hom}_H(\\pi^\\infty|_H,\\tau^\\infty)$ of intertwining operators\nbetween the smooth vectors, also called symmetry breaking operators, and\nprovides a precise relation between these two concepts of multiplicity.\n', ""Strong multiplicity one theorems for locally homogeneous spaces of\n  compact type   Let $G$ be a compact connected semisimple Lie group, let $K$ be a closed\nsubgroup of $G$, let $\\Gamma$ be a finite subgroup of $G$, and let $\\tau$ be a\nfinite-dimensional representation of $K$. For $\\pi$ in the unitary dual\n$\\widehat G$ of $G$, denote by $n_\\Gamma(\\pi)$ its multiplicity in\n$L^2(\\Gamma\\backslash G)$.\n  We prove a strong multiplicity one theorem in the spirit of Bhagwat and\nRajan, for the $n_\\Gamma(\\pi)$ for $\\pi$ in the set $\\widehat G_\\tau$ of\nirreducible $\\tau$-spherical representations of $G$. More precisely, for\n$\\Gamma$ and $\\Gamma'$ finite subgroups of $G$, we prove that if\n$n_{\\Gamma}(\\pi)= n_{\\Gamma'}(\\pi)$ for all but finitely many $\\pi\\in \\widehat\nG_\\tau$, then $\\Gamma$ and $\\Gamma'$ are $\\tau$-representation equivalent, that\nis, $n_{\\Gamma}(\\pi)=n_{\\Gamma'}(\\pi)$ for all $\\pi\\in \\widehat G_\\tau$.\n  Moreover, when $\\widehat G_\\tau$ can be written as a finite union of strings\nof representations, we prove a finite version of the above result. For any\nfinite subset $\\widehat {F}_{\\tau}$ of $\\widehat G_{\\tau}$ verifying some mild\nconditions, the values of the $n_\\Gamma(\\pi)$ for $\\pi\\in\\widehat F_{\\tau}$\ndetermine the $n_\\Gamma(\\pi)$'s for all $\\pi \\in \\widehat G_\\tau$. In\nparticular, for two finite subgroups $\\Gamma$ and $\\Gamma'$ of $G$, if\n$n_\\Gamma(\\pi) = n_{\\Gamma'}(\\pi)$ for all $\\pi\\in \\widehat F_{\\tau}$ then the\nequality holds for every $\\pi \\in \\widehat G_\\tau$. We use algebraic methods\ninvolving generating functions and some facts from the representation theory of\n$G$.\n""]","[('representations lie groups', 0.5242888331413269), ('representations lie', 0.4930185377597809), ('irreducible unitary representation', 0.4657241404056549), ('real reductive groups', 0.4617254436016083), ('real reductive group', 0.4566650986671448), ('irreducible representations', 0.4547811448574066), ('representations pi', 0.4515068829059601), ('representations compact', 0.44772660732269287), ('irreducible representation', 0.4431324005126953), ('unitary representation', 0.43975791335105896)]"
617,617,50,617_decoding performance_decoding_belief propagation decoder_based decoding,"['decoding performance', 'decoding', 'belief propagation decoder', 'based decoding', 'neural decoders', 'decoders', 'decoder', 'propagation bp decoding', 'based decoders', 'propagation decoder']","['Pruning and Quantizing Neural Belief Propagation Decoders   We consider near maximum-likelihood (ML) decoding of short linear block\ncodes. In particular, we propose a novel decoding approach based on neural\nbelief propagation (NBP) decoding recently introduced by Nachmani et al. in\nwhich we allow a different parity-check matrix in each iteration of the\nalgorithm. The key idea is to consider NBP decoding over an overcomplete\nparity-check matrix and use the weights of NBP as a measure of the importance\nof the check nodes (CNs) to decoding. The unimportant CNs are then pruned. In\ncontrast to NBP, which performs decoding on a given fixed parity-check matrix,\nthe proposed pruning-based neural belief propagation (PB-NBP) typically results\nin a different parity-check matrix in each iteration. For a given complexity in\nterms of CN evaluations, we show that PB-NBP yields significant performance\nimprovements with respect to NBP. We apply the proposed decoder to the decoding\nof a Reed-Muller code, a short low-density parity-check (LDPC) code, and a\npolar code. PB-NBP outperforms NBP decoding over an overcomplete parity-check\nmatrix by 0.27-0.31 dB while reducing the number of required CN evaluations by\nup to 97%. For the LDPC code, PB-NBP outperforms conventional belief\npropagation with the same number of CN evaluations by 0.52 dB. We further\nextend the pruning concept to offset min-sum decoding and introduce a\npruning-based neural offset min-sum (PB-NOMS) decoder, for which we jointly\noptimize the offsets and the quantization of the messages and offsets. We\ndemonstrate performance 0.5 dB from ML decoding with 5-bit quantization for the\nReed-Muller code.\n', 'Boosting Learning for LDPC Codes to Improve the Error-Floor Performance   Low-density parity-check (LDPC) codes have been successfully commercialized\nin communication systems due to their strong error correction capabilities and\nsimple decoding process. However, the error-floor phenomenon of LDPC codes, in\nwhich the error rate stops decreasing rapidly at a certain level, presents\nchallenges for achieving extremely low error rates and deploying LDPC codes in\nscenarios demanding ultra-high reliability. In this work, we propose training\nmethods for neural min-sum (NMS) decoders to eliminate the error-floor effect.\nFirst, by leveraging the boosting learning technique of ensemble networks, we\ndivide the decoding network into two neural decoders and train the post decoder\nto be specialized for uncorrected words that the first decoder fails to\ncorrect. Secondly, to address the vanishing gradient issue in training, we\nintroduce a block-wise training schedule that locally trains a block of weights\nwhile retraining the preceding block. Lastly, we show that assigning different\nweights to unsatisfied check nodes effectively lowers the error-floor with a\nminimal number of weights. By applying these training methods to standard LDPC\ncodes, we achieve the best error-floor performance compared to other decoding\nmethods. The proposed NMS decoder, optimized solely through novel training\nmethods without additional modules, can be integrated into existing LDPC\ndecoders without incurring extra hardware costs. The source code is available\nat https://github.com/ghy1228/LDPC_Error_Floor .\n', 'Pruning Neural Belief Propagation Decoders   We consider near maximum-likelihood (ML) decoding of short linear block codes\nbased on neural belief propagation (BP) decoding recently introduced by\nNachmani et al.. While this method significantly outperforms conventional BP\ndecoding, the underlying parity-check matrix may still limit the overall\nperformance. In this paper, we introduce a method to tailor an overcomplete\nparity-check matrix to (neural) BP decoding using machine learning. We consider\nthe weights in the Tanner graph as an indication of the importance of the\nconnected check nodes (CNs) to decoding and use them to prune unimportant CNs.\nAs the pruning is not tied over iterations, the final decoder uses a different\nparity-check matrix in each iteration. For Reed-Muller and short low-density\nparity-check codes, we achieve performance within 0.27 dB and 1.5 dB of the ML\nperformance while reducing the complexity of the decoder.\n']","[('decoding performance', 0.5488951802253723), ('decoding', 0.5309605598449707), ('belief propagation decoder', 0.5270020961761475), ('based decoding', 0.5249950885772705), ('neural decoders', 0.5195695757865906), ('decoders', 0.510630190372467), ('decoder', 0.4980385899543762), ('propagation bp decoding', 0.49302297830581665), ('based decoders', 0.4834640324115753), ('propagation decoder', 0.4801415801048279)]"
618,618,50,618_crystal basis_kac moody algebras_crystal operators_quantum affine algebras,"['crystal basis', 'kac moody algebras', 'crystal operators', 'quantum affine algebras', 'moody algebras', 'kashiwara crystals', 'crystals type', 'crystal structure', 'crystal bases', 'demazure crystals']","[""Adapted Sequences and Polyhedral Realizations of Crystal Bases for\n  highest weight modules   The polyhedral realizations for crystal bases of the integrable highest\nweight modules of $U_q(\\mathfrak{g})$ have been introduced in ([T.Nakashima, J.\nAlgebra, vol.219, no. 2, (1999)]), which describe the crystal bases as sets of\nlattice points in the infinite $\\mathbb{Z}$-lattice $\\mathbb{Z}^{\\infty}$ given\nby some system of linear inequalities, where $\\mathfrak{g}$ is a symmetrizable\nKac-Moody Lie algebra. To construct the polyhedral realization, we need to fix\nan infinite sequence $\\iota$ from the indices of the simple roots. If the pair\n($\\iota$,$\\lambda$) ($\\lambda$: a dominant integral weight) satisfies the\n`ample' condition then there are some procedure to calculate the sets of linear\ninequalities.\n  In this article, we show that if $\\iota$ is an adapted sequence (defined in\nour paper [Y.Kanakubo, T.Nakashima, arXiv:1904.10919]) then the pair ($\\iota$,\n$\\lambda$) satisfies the ample condition for any dominant integral weight\n$\\lambda$ in the case $\\mathfrak{g}$ is a classical Lie algebra. Furthermore,\nwe reveal the explicit forms of the polyhedral realizations of the crystal\nbases $B(\\lambda)$ associated with arbitrary adapted sequences $\\iota$ in terms\nof column tableaux. As an application, we will give a combinatorial description\nof the function $\\varepsilon_i^*$ on the crystal base $B(\\infty)$.\n"", 'A Demazure Character Formula for the Product Monomial Crystal   The product monomial crystal was defined by Kamnitzer, Tingley, Webster,\nWeekes, and Yacobi for any semisimple simply-laced Lie algebra $\\mathfrak{g}$,\nand depends on a collection of parameters $\\mathbf{R}$. We show that a family\nof truncations of this crystal are Demazure crystals, and give a Demazure-type\nformula for the character of each truncation, and the crystal itself. This\ncharacter formula shows that the product monomial crystal is the crystal of a\ngeneralised Demazure module, as defined by Lakshmibai, Littelmann and Magyar.\nIn type $A$, we show the product monomial crystal is the crystal of a\ngeneralised Schur module associated to a column-convex diagram depending on\n$\\mathbf{R}$.\n', 'On Combinatorial Models for Affine Crystals   The tableau model for Kirillov-Reshetikhin (KR) crystals, which are finite\ndimensional crystals corresponding to certain affine Lie algebras, is commonly\nused for its ease of crystal operator calculations. However, its simplicity\nmakes quite complex the calculation of statistics such as: keys (used to\nexpress Demazure characters), the crystal energy function (an affine grading on\ntensor products of KR crystals), and the combinatorial R-matrix (an affine\ncrystal isomorphism permuting factors in a tensor product of KR crystals). It\nhas been shown that these calculations are much simpler with the added\nstructure in the quantum alcove model for KR crystals. In this paper, we give\nan explicit description of the crystal isomorphism between the mentioned\nrealizations of KR crystals in all classical Lie types.\n']","[('crystal basis', 0.5591942667961121), ('kac moody algebras', 0.5395922064781189), ('crystal operators', 0.5387303829193115), ('quantum affine algebras', 0.5231804847717285), ('moody algebras', 0.49388808012008667), ('kashiwara crystals', 0.48609188199043274), ('crystals type', 0.4772756099700928), ('crystal structure', 0.47438162565231323), ('crystal bases', 0.46790051460266113), ('demazure crystals', 0.4634953439235687)]"
619,619,50,619_killing tensor_killing vector fields_killing fields_killing vectors,"['killing tensor', 'killing vector fields', 'killing fields', 'killing vectors', 'riemannian manifolds', 'riemannian manifold', 'conformal killing', 'killing vector', 'lorentzian manifolds', 'lorentzian manifold']","[""Killing vector fields on semi-Riemannian product manifolds   Hano's theorem states that the space of Killing vector fields of a complete\nsimply connected Riemannian manifold is isomorphic to the direct sum of the\nKilling vector fields of the factors in its de Rham decomposition. We prove a\ngeneralisation of this theorem to manifolds with indefinite metrics that\nrequires an assumption on the factors, and show by example why this assumption\nis needed.\n"", 'Conformal Killing tensors and their Killing scales   We address the problem of how to characterise when a rank-two conformal\nKilling tensor is the trace-free part of a Killing tensor for a metric in the\nconformal class. We call such a metric a Killing scale. Our approach is via\ndifferential prolongation using conformally invariant tractor calculus. First,\nwe show that there is a useful partial prolongation of the conformal Killing\nequation to a simplified equation for sections of some tractor bundle. We then\nuse this partial prolongation to provide such an invariant characterisation in\nterms of the scale tractor and this partial prolongation. This captures\ninvariantly the relevant Bertrand--Darboux equation. We show that Einstein\nKilling scales have a special place in the theory. On conformally flat\nmanifolds, we give the full prolongation of the conformally Killing equation to\na conformally invariant connection on a tractor bundle. Using this, we provide\na characterisation of (non-scalar flat) Einstein Killing scales by an algebraic\nequation for the scale tractors corresponding to such metrics. This also\nprovides an algebraic description of the linear subspace of conformal Killing\ntensors that are compatible with a given Einstein Killing scale. For\ncompleteness and to introduce the main ideas, we also study analogous questions\nfor conformal Killing vectors.\n', 'Quadratic Killing tensors on symmetric spaces which are not generated by\n  Killing vector fields   Every Killing tensor field on the space of constant curvature and on the\ncomplex projective space can be decomposed into the sum of symmetric tensor\nproducts of Killing vector fields (equivalently, every polynomial in the\nvelocities integral of the geodesic flow is a polynomial in the linear\nintegrals). This fact led to the natural question on whether this property is\nshared by Killing tensor fields on all Riemannian symmetric spaces. We answer\nthis question in the negative by constructing explicit examples of quadratic\nKilling tensor fields which are not quadratic forms in the Killing vector\nfields on the quaternionic projective spaces $\\mathbb{H} P^n, n \\ge 3$, and on\nthe Cayley projective plane $\\mathbb{O} P^2$.\n']","[('killing tensor', 0.7060989737510681), ('killing vector fields', 0.6658459901809692), ('killing fields', 0.5858469605445862), ('killing vectors', 0.5790470242500305), ('riemannian manifolds', 0.5774942636489868), ('riemannian manifold', 0.546369731426239), ('conformal killing', 0.5421743392944336), ('killing vector', 0.535679042339325), ('lorentzian manifolds', 0.5323808193206787), ('lorentzian manifold', 0.49343693256378174)]"
620,620,50,620_theories extending_constructive theory_valued models_intuitionistic,"['theories extending', 'constructive theory', 'valued models', 'intuitionistic', 'countable models', 'axiom choice', 'existence models', 'models theory', 'classical logic', 'axioms']","['Choice and independence of premise rules in intuitionistic set theory   Choice and independence of premise principles play an important role in\ncharacterizing Kreisel\'s modified realizability and G\\""odel\'s Dialectica\ninterpretation. In this paper we show that a great many intuitionistic set\ntheories are closed under the corresponding rules for finite types over\n$\\mathbb{N}$. It is also shown that the existence property (or existential\ndefinability property) holds for statements of the form $\\exists y^{\\sigma}\\,\n\\varphi(y)$, where the variable $y$ ranges over objects of finite type\n$\\sigma$. This applies in particular to ${\\sf CZF}$ (Constructive\nZermelo-Fraenkel set theory) and ${\\sf IZF}$ (Intuitionistic Zermelo-Fraenkel\nset theory), two systems known not to have the general existence property. On\nthe technical side, the paper uses a method that amalgamates generic\nrealizability for set theory with truth, whereby the underlying partial\ncombinatory algebra is required to contain all objects of finite type.\n', 'Extensional realizability and choice for dependent types in\n  intuitionistic set theory   In ""Extensional realizability for intuitionistic set theory"", we introduced\nan extensional variant of generic realizability, where realizers act\nextensionally on realizers, and showed that this form of realizability provides\n""inner"" models of $\\sf CZF$ (constructive Zermelo-Fraenkel set theory) and $\\sf\nIZF$ (intuitionistic Zermelo-Fraenkel set theory), that further validate ${\\sf\nAC}_{\\sf FT}$ (the axiom of choice in all finite types). In this paper, we show\nthat extensional generic realizability validates several choice principles for\ndependent types, all exceeding ${\\sf AC}_{\\sf FT}$. We then show that adding\nsuch choice principles does not change the arithmetic part of either $\\sf CZF$\nor $\\sf IZF$.\n', ""Extensional realizability for intuitionistic set theory   In generic realizability for set theories, realizers treat unbounded\nquantifiers generically. To this form of realizability, we add another layer of\nextensionality by requiring that realizers ought to act extensionally on\nrealizers, giving rise to a realizability universe $\\mathrm{V_{ex}}(A)$ in\nwhich the axiom of choice in all finite types ${\\sf AC}_{{\\sf FT}}$ is\nrealized, where $A$ stands for an arbitrary partial combinatory algebra. This\nconstruction furnishes 'inner models' of many set theories that additionally\nvalidate ${\\sf AC}_{{\\sf FT}}$, in particular it provides a self-validating\nsemantics for $\\sf CZF$ (Constructive Zermelo-Fraenkel set theory) and $\\sf\nIZF$ (Intuitionistic Zermelo-Fraenkel set theory). One can also add large set\naxioms and many other principles.\n""]","[('theories extending', 0.5012504458427429), ('constructive theory', 0.49250322580337524), ('valued models', 0.46664437651634216), ('intuitionistic', 0.4491322636604309), ('countable models', 0.4441967308521271), ('axiom choice', 0.4381404221057892), ('existence models', 0.42313843965530396), ('models theory', 0.4185433089733124), ('classical logic', 0.41770970821380615), ('axioms', 0.4058234989643097)]"
621,621,50,621_dimensional harmonic oscillator_quantum harmonic_dimensional harmonic_harmonic oscillator potential,"['dimensional harmonic oscillator', 'quantum harmonic', 'dimensional harmonic', 'harmonic oscillator potential', 'harmonic oscillator', 'coherent states', 'supersymmetric quantum mechanics', 'energy spectrum', 'excitation modes', 'quantization conditions']","['Confined One Dimensional Harmonic Oscillator as a Two-Mode System   The one-dimensional harmonic oscillator in a box problem is possibly the\nsimplest example of a two-mode system. This system has two exactly solvable\nlimits, the harmonic oscillator and a particle in a (one-dimensional) box. Each\nof the two limits has a characteristic spectral structure describing the two\ndifferent excitation modes of the system. Near each of these limits, one can\nuse perturbation theory to achieve an accurate description of the eigenstates.\nAway from the exact limits, however, one has to carry out a matrix\ndiagonalization because the basis-state mixing that occurs is typically too\nlarge to be reproduced in any other way. An alternative to casting the problem\nin terms of one or the other basis set consists of using an ""oblique"" basis\nthat uses both sets. Through a study of this alternative in this\none-dimensional problem, we are able to illustrate practical solutions and\ninfer the applicability of the concept for more complex systems, such as in the\nstudy of complex nuclei where oblique-basis calculations have been successful.\nKeywords: one-dimensional harmonic oscillator, particle in a box, exactly\nsolvable models, two-mode system, oblique basis states, perturbation theory,\ncoherent states, adiabatic mixing.\n', 'Confined One Dimensional Harmonic Oscillator as a Two-Mode System   The one-dimensional harmonic oscillator in a box problem is possibly the\nsimplest example of a two-mode system. This system has two exactly solvable\nlimits, the harmonic oscillator and a particle in a (one-dimensional) box. Each\nof the two limits has a characteristic spectral structure describing the two\ndifferent excitation modes of the system. Near each of these limits, one can\nuse perturbation theory to achieve an accurate description of the eigenstates.\nAway from the exact limits, however, one has to carry out a matrix\ndiagonalization because the basis-state mixing that occurs is typically too\nlarge to be reproduced in any other way. An alternative to casting the problem\nin terms of one or the other basis set consists of using an ""oblique"" basis\nthat uses both sets. Through a study of this alternative in this\none-dimensional problem, we are able to illustrate practical solutions and\ninfer the applicability of the concept for more complex systems, such as in the\nstudy of complex nuclei where oblique-basis calculations have been successful.\nKeywords: one-dimensional harmonic oscillator, particle in a box, exactly\nsolvable models, two-mode system, oblique basis states, perturbation theory,\ncoherent states, adiabatic mixing.\n', 'Confined One Dimensional Harmonic Oscillator as a Two-Mode System   The one-dimensional harmonic oscillator in a box problem is possibly the\nsimplest example of a two-mode system. This system has two exactly solvable\nlimits, the harmonic oscillator and a particle in a (one-dimensional) box. Each\nof the two limits has a characteristic spectral structure describing the two\ndifferent excitation modes of the system. Near each of these limits, one can\nuse perturbation theory to achieve an accurate description of the eigenstates.\nAway from the exact limits, however, one has to carry out a matrix\ndiagonalization because the basis-state mixing that occurs is typically too\nlarge to be reproduced in any other way. An alternative to casting the problem\nin terms of one or the other basis set consists of using an ""oblique"" basis\nthat uses both sets. Through a study of this alternative in this\none-dimensional problem, we are able to illustrate practical solutions and\ninfer the applicability of the concept for more complex systems, such as in the\nstudy of complex nuclei where oblique-basis calculations have been successful.\nKeywords: one-dimensional harmonic oscillator, particle in a box, exactly\nsolvable models, two-mode system, oblique basis states, perturbation theory,\ncoherent states, adiabatic mixing.\n']","[('dimensional harmonic oscillator', 0.5852524042129517), ('quantum harmonic', 0.5241262316703796), ('dimensional harmonic', 0.4502199590206146), ('harmonic oscillator potential', 0.44647690653800964), ('harmonic oscillator', 0.4449795186519623), ('coherent states', 0.4237481653690338), ('supersymmetric quantum mechanics', 0.41242504119873047), ('energy spectrum', 0.40529268980026245), ('excitation modes', 0.40284332633018494), ('quantization conditions', 0.39904719591140747)]"
622,622,50,622_voting systems_majority voting_ballot_voting,"['voting systems', 'majority voting', 'ballot', 'voting', 'number voters', 'elections', 'voter', 'polling', 'votes', 'voters']","[""Tradeoffs in Hierarchical Voting Systems   Condorcet's jury theorem states that the correct outcome is reached in direct\nmajority voting systems with sufficiently large electorates as long as each\nvoter's independent probability of voting for that outcome is greater than 0.5.\nYet, in situations where direct voting systems are infeasible, such as due to\nhigh implementation and infrastructure costs, hierarchical voting systems\nprovide a reasonable alternative. We study differences in outcome precision\nbetween hierarchical and direct voting systems for varying group sizes,\nabstention rates, and voter competencies. Using asymptotic expansions of the\nderivative of the reliability function (or Banzhaf number), we first prove that\nindirect systems differ most from their direct counterparts when group size and\nnumber are equal to each other, and therefore to $\\sqrt{N_{\\rm d}}$, where\n$N_{\\rm d}$ is the total number of voters in the direct system. In multitier\nsystems, we prove that this difference is maximized when group size equals\n$\\sqrt[n]{N_{\\rm d}}$, where $n$ is the number of hierarchical levels. Second,\nwe show that while direct majority rule always outperforms hierarchical voting\nfor homogeneous electorates that vote with certainty, as group numbers and size\nincrease, hierarchical majority voting gains in its ability to represent all\neligible voters. Furthermore, when voter abstention and competency are\ncorrelated within groups, hierarchical systems often outperform direct voting,\nwhich we show by using a generating function approach that is able to\nanalytically characterize heterogeneous voting systems.\n"", 'Recognizing distributed approval voting forms and correspondences   Each voter $i \\in I$ has $\\alpha_i$ cards that (s)he distributes among the\ncandidates $a \\in A$ as a measure of approval. One (or several) candidate(s)\nwho received the maximum number of cards is (are) elected. We provide\npolynomial algorithms to recognize voting forms and voting correspondences\ngenerated by such voting schemes in cases when either the number of candidates\nor the number of voters is equal to $2$. We prove that for two voters, if\n$\\alpha_2 \\geq \\alpha_1-2\\geq 0$ then the unique voting correspondence has\ndistinct rows. We also characterize voting forms with distinct rows.\n', 'Noise Stability of Ranked Choice Voting   We conjecture that Borda count is the ranked choice voting method that best\npreserves the outcome of an election with randomly corrupted votes, among all\nfair voting methods with small influences satisfying the Condorcet Loser\nCriterion. This conjecture is an adaptation of the Plurality is Stablest\nConjecture to the setting of ranked choice voting. Since the plurality function\ndoes not satisfy the Condorcet Loser Criterion, our new conjecture is not\ndirectly related to the Plurality is Stablest Conjecture. Nevertheless, we show\nthat the Plurality is Stablest Conjecture implies our new Borda count is\nStablest conjecture. We therefore deduce that Borda count is stablest for\nelections with three candidates when the corrupted votes are nearly\nuncorrelated with the original votes. We also adapt a dimension reduction\nargument to this setting, showing that the optimal ranked choice voting method\nis ""low-dimensional.""\n  The Condorcet Loser Criterion asserts that a candidate must lose an election\nif each other candidate is preferred in head-to-head comparisons. Lastly, we\ndiscuss a variant of our conjecture with the Condorcet Winner Criterion as a\nconstraint instead of the Condorcet Loser Criterion. In this case, we have no\nguess for the most stable ranked choice voting method.\n']","[('voting systems', 0.7061023116111755), ('majority voting', 0.5919284820556641), ('ballot', 0.5442880392074585), ('voting', 0.5346370339393616), ('number voters', 0.5295928120613098), ('elections', 0.5253397226333618), ('voter', 0.5107036828994751), ('polling', 0.48946613073349), ('votes', 0.4821479320526123), ('voters', 0.48135024309158325)]"
623,623,50,623_fluid rigid body_viscous incompressible_incompressible viscous_incompressible viscous fluid,"['fluid rigid body', 'viscous incompressible', 'incompressible viscous', 'incompressible viscous fluid', 'incompressible navier stokes', 'viscous incompressible fluid', 'fluid rigid', 'navier stokes equations', 'viscous compressible fluid', 'rigid bodies']","['A uniqueness result for 3D incompressible fluid-rigid body interaction\n  problem   We study a 3D nonlinear moving boundary fluid-structure interaction problem\ndescribing the interaction of the fluid flow with a rigid body. The fluid flow\nis governed by 3D incompressible Navier-Stokes equations, while the motion of\nthe rigid body is described by a system of ordinary differential equations\ncalled Euler equations for the rigid body. The equations are fully coupled via\ndynamical and kinematic coupling conditions. We consider two different kinds of\nkinematic coupling conditions: no-slip and slip. In both cases we prove a\ngeneralization of the well-known weak-strong uniqueness result for the\nNavier-Stokes equations to the fluid-rigid body system. More precisely, we\nprove that weak solutions that additionally satisfy Prodi-Serrin $L^r-L^s$\ncondition are unique in the class of Leray-Hopf weak solutions.\n', 'The vanishing limit of a rigid body in three-dimensional viscous\n  incompressible fluid   We consider the evolution of a small rigid body in an incompressible viscous\nfluid filling the whole space $\\rline^3$. When the small rigid body shrinks to\na ""massless"" point in the sense that its density is constant, we prove that the\nsolution of the fluid-rigid body system converges to a solution of the\nNavier-Stokes equations in the full space. Based on some $L^p-L^q$ estimates of\nthe fluid-structure semigroup and a fixed point argument, we obtain a uniform\nestimate of velocity of the rigid body. This allows us to construct admissible\ntest functions which plays a key role in the procedure of passing to the limit.\n', 'On the small rigid body limit in 3D incompressible flows   We consider the evolution of a small rigid body in an incompressible viscous\nfluid filling the whole space. The motion of the fluid is modelled by the\nNavier-Stokes equations, whereas the motion of the rigid body is described by\nthe conservation law of linear and angular momentum. Under the assumption that\nthe diameter of the rigid body tends to zero and that the density of the rigid\nbody goes to infinity, we prove that the solution of the fluid-rigid body\nsystem converges to a solution of the Navier-Stokes equations in the full space\nwithout rigid body.\n']","[('fluid rigid body', 0.6486569046974182), ('viscous incompressible', 0.6048112511634827), ('incompressible viscous', 0.60201096534729), ('incompressible viscous fluid', 0.6018893718719482), ('incompressible navier stokes', 0.6002814769744873), ('viscous incompressible fluid', 0.5932202339172363), ('fluid rigid', 0.5809428691864014), ('navier stokes equations', 0.5476133823394775), ('viscous compressible fluid', 0.540245532989502), ('rigid bodies', 0.5352464318275452)]"
624,624,50,624_drazin inverse_banach algebras_generalized inverses_generalized drazin,"['drazin inverse', 'banach algebras', 'generalized inverses', 'generalized drazin', 'banach algebra', 'banach algebra mathcal', 'inverse generalized', 'invertible elements', 'multilinear algebra', 'operator matrices']","['Drazin and g-Drazin invertibility of combinations of three Banach\n  algebra elements   Consider a complex unital Banach algebra $\\mathcal{A}.$ For\n$x_1,x_2,x_3\\in\\mathcal{A},$ in this paper, we establish that under certain\nassumptions on $x_1,x_2,x_3$, Drazin (resp. g-Drazin) invertibility of any\nthree elements among $x_1,x_2,x_3$ and $x_1+x_2+x_3\\text{ }(\\text{or\n}x_1x_2+x_1x_3+x_2x_3)$ ensure the Drazin (resp. g-Drazin) invertibility of the\nremaining one. As a consequence for two idempotents $p,q\\in\\mathcal{A},$ this\nresult indicates the equivalence between Drazin (resp. g-Drazin) invertibility\nof\n$$\\lambda_1p+\\gamma_1q-\\lambda_1pq+\\lambda_2\\left(pqp-(pq)^2\\right)+\\cdots+\\lambda_m\\left((pq)^{m-1}p-(pq)^m\\right)$$\nand\n$$\\lambda_1-\\lambda_1pq+\\lambda_2\\left(pqp-(pq)^2\\right)+\\cdots+\\lambda_m\\left((pq)^{m-1}p-(pq)^m\\right),$$\nwhere $\\gamma_1,\\lambda_i\\in\\mathbb{C}$ for $i=1,2,\\cdots,m,$ with\n$\\lambda_1\\gamma_1\\neq0.$ Furthermore, for $x_1,x_2$, we establish that the\nDrazin (resp. g-Drazin) invertibility of any two elements among $x_1,x_2$ and\n$x_1+x_2$ indicates the Drazin (resp. g-Drazin) invertibility of the remaining\none, provided that $x_1x_2=\\alpha(x_1+x_2)$ for some $\\alpha\\in\\mathbb{C}$.\nAdditionally, if it exists, we furnish a new formula to represent the Drazin\n(resp. g-Drazin) inverse of any element among $x_1,x_2$ and $x_1+x_2$, by using\nthe other two elements and their Drazin (resp. g-Drazin) inverse.\n', ""Some New Results on Pseudo n-Strong Drazin Inverses in Rings   In this paper, we give a further study in-depth of the pseudo $n$-strong\nDrazin inverses in an associative unital ring $R$. The characterizations of\nelements $a,b\\in R$ for which $aa^{\\tiny{\\textcircled{\\qihao\nD}}}=bb^{\\tiny{\\textcircled{\\qihao D}}}$ are provided, and some new equivalent\nconditions on pseudo $n$-strong Drazin inverses are obtained. In particular, we\nshow that an element $a\\in R$ is pseudo $n$-strong Drazin invertible if, and\nonly if, $a$ is $p$-Drazin invertible and $a-a^{n+1}\\in \\sqrt{J(R)}$ if, and\nonly if, there exists $e^2=e\\in {\\rm comm}^2(a)$ such that $ae\\in \\sqrt{J(R)}$\nand $1-(a+e)^n\\in \\sqrt{J(R)}$. We also consider pseudo $n$-strong Drazin\ninverses with involution, and discuss the extended versions of Cline's formula\nand Jacobson's lemma of this new class of generalized inverses. Likewise, we\ndefine and explore the so-called {\\it pseudo $\\pi$-polar} rings and demonstrate\ntheir relationships with periodic rings and strongly $\\pi$-regular rings,\nrespectively.\n"", ""Extensions of Jacobson's lemma for generalized inverses in a ring   Let $R$ be an associative ring with unit $1$, and $a, b, c\\in R$ satisfy\n$a(ba)^{2}=abaca=acaba=(ac)^{2}a$, this paper proves that $1-ac$ has\ngeneralized Drazin inverse (Drazin inverse, pseudo Drazin inverse,\nrespectively) if and only if $1-ba$ has generalized Drazin inverse (Drazin\ninverse, pseudo Drazin inverse, respectively). In particular, we obtain new\ncommon spectral properties for $ac$ and $ba$ in Banach algebras. As\napplications, new extension of Jacobson's lemma for B-Fredholm elements and\ngeneralized Fredholm elements in rings is established.\n""]","[('drazin inverse', 0.6052400469779968), ('banach algebras', 0.5553942322731018), ('generalized inverses', 0.5173655152320862), ('generalized drazin', 0.509171187877655), ('banach algebra', 0.4996313154697418), ('banach algebra mathcal', 0.4693065583705902), ('inverse generalized', 0.4282206594944), ('invertible elements', 0.41347047686576843), ('multilinear algebra', 0.41207945346832275), ('operator matrices', 0.40104711055755615)]"
625,625,50,625_reduced dynamics_nonlinear modes_nonlinear structures_nonlinear dynamics,"['reduced dynamics', 'nonlinear modes', 'nonlinear structures', 'nonlinear dynamics', 'systems spectral', 'nonlinear reduction', 'reduction nonlinear', 'reduced order models', 'periodic systems', 'finite element models']","['Nonlinear analysis of forced mechanical systems with internal resonance\n  using spectral submanifolds, Part II: Bifurcation and quasi-periodic response   In Part I of this paper, we have used spectral submanifold (SSM) theory to\nconstruct reduced-order models for harmonically excited mechanical systems with\ninternal resonances. In that setting, extracting forced response curves formed\nby periodic orbits of the full system was reduced to locating the solution\nbranches of equilibria of the corresponding reduced-order model. Here we use\nbifurcations of the equilibria of the reduced-order model to predict\nbifurcations of the periodic response of the full system. Specifically, we\nidentify Hopf bifurcations of equilibria and limit cycles in reduced models on\nSSMs to predict the existence of two-dimensional and three-dimensional\nquasi-periodic attractors and repellers in periodically forced mechanical\nsystems of arbitrary dimension. We illustrate the accuracy and efficiency of\nthese computations on finite-element models of beams and plates.\n', ""Nonlinear analysis of forced mechanical systems with internal resonance\n  using spectral submanifolds, Part I: Periodic response and forced response\n  curve   We show how spectral submanifold theory can be used to construct\nreduced-order models for harmonically excited mechanical systems with internal\nresonances. Efficient calculations of periodic and quasi-periodic responses\nwith the reduced-order models are discussed in this paper and its companion,\nPart II, respectively. The dimension of a reduced-order model is determined by\nthe number of modes involved in the internal resonance, independently of the\ndimension of the full system. The periodic responses of the full system are\nobtained as equilibria of the reduced-order model on spectral submanifolds. The\nforced response curve of periodic orbits then becomes a manifold of equilibria,\nwhich can be easily extracted using parameter continuation. To demonstrate the\neffectiveness and efficiency of the reduction, we compute the forced response\ncurves of several high-dimensional nonlinear mechanical systems, including the\nfinite-element models of a von K\\'arm\\'an beam and a plate.\n"", 'Fast computation and characterization of forced response surfaces via\n  spectral submanifolds and parameter continuation   For mechanical systems subject to periodic excitation, forced response curves\n(FRCs) depict the relationship between the amplitude of the periodic response\nand the forcing frequency. For nonlinear systems, this functional relationship\nis different for different forcing amplitudes. Forced response surfaces (FRSs),\nwhich relate the response amplitude to both forcing frequency and forcing\namplitude, are then required in such settings. Yet, FRSs have been rarely\ncomputed in the literature due to the higher numerical effort they require.\nHere, we use spectral submanifolds (SSMs) to construct reduced-order models\n(ROMs) for high-dimensional mechanical systems and then use multidimensional\nmanifold continuation of fixed points of the SSM-based ROMs to efficiently\nextract the FRSs. Ridges and trenches in an FRS characterize the main features\nof the forced response. We show how to extract these ridges and trenches\ndirectly without computing the FRS via reduced optimization problems on the\nROMs. We demonstrate the effectiveness and efficiency of the proposed approach\nby calculating the FRSs and their ridges and trenches for a plate with a 1:1\ninternal resonance and for a shallow shell with a 1:2 internal resonance.\n']","[('reduced dynamics', 0.5322452187538147), ('nonlinear modes', 0.4609927535057068), ('nonlinear structures', 0.4592623710632324), ('nonlinear dynamics', 0.44371408224105835), ('systems spectral', 0.4374871551990509), ('nonlinear reduction', 0.4344729781150818), ('reduction nonlinear', 0.4294452965259552), ('reduced order models', 0.40673887729644775), ('periodic systems', 0.3959250748157501), ('finite element models', 0.3869994580745697)]"
626,626,50,626_strongly regular graphs_strongly regular graph_graphs strongly regular_regular graphs,"['strongly regular graphs', 'strongly regular graph', 'graphs strongly regular', 'regular graphs', 'regular graphs give', 'regular graph', 'regular graph vertices', 'graphs strongly', 'divisible design', 'graphs construction']","['Strongly regular graphs decomposable into a divisible design graph and a\n  Hoffman coclique   In 2022, the second author found a prolific construction of strongly regular\ngraphs, which is based on joining a coclique and a divisible design graph with\ncertain parameters. The construction produces strongly regular graphs with the\nsame parameters as the complement of the symplectic graph $\\mathsf{Sp}(2d,q)$.\n  In this paper, we determine the parameters of strongly regular graphs which\nadmit a decomposition into a divisible design graph and a coclique attaining\nthe Hoffman bound. In particular, it is shown that when the least eigenvalue of\nsuch a strongly regular graph is a prime power, its parameters coincide with\nthose of the complement of $\\mathsf{Sp}(2d,q)$. Furthermore, a generalization\nof the construction is discussed.\n', '$q$-Analogs of divisible design graphs and Deza graphs   Divisible design graphs were introduced in 2011 by Haemers, Kharaghani and\nMeulenberg. In this paper, we introduce the notion of $q$-analogs of divisible\ndesign graphs and show that all $q$-analogs of divisible design graphs come\nfrom spreads, and are actually $q$-analogs of strongly regular graphs. Deza\ngraphs were introduced by Erickson, Fernando, Haemers and Hardy in 1999. In\nthis paper, we introduce $q$-analogs of Deza graphs. Further, we determine\npossible parameters, give examples of $q$-analogs of Deza graphs and\ncharacterize all non-strongly regular $q$-analogs of Deza graphs with the\nsmallest parameters.\n', 'Deza graphs with parameters $(n,k,k-1,a)$ and $\\beta=1$   A Deza graph with parameters $(n,k,b,a)$ is a $k$-regular graph with $n$\nvertices in which any two vertices have $a$ or $b$ ($a\\leq b$) common\nneighbours. A Deza graph is strictly Deza if it has diameter $2$, and is not\nstrongly regular. In an earlier paper, the two last authors et el.\ncharacterized the strictly Deza graphs with $b=k-1$ and $\\beta > 1$, where\n$\\beta$ is the number of vertices with $b$ common neighbours with a given\nvertex. Here we deal with the case $\\beta=1$, thus we complete the\ncharacterization of strictly Deza graphs with $b=k-1$. It follows that all Deza\ngraphs with $b=k-1$ and $\\beta=1$ can be made from special strongly regular\ngraphs, and we present several examples of such strongly regular graphs.\n  A divisible design graph is a special Deza graph, and a Deza graph with\n$\\beta=1$ is a divisible design graph. The present characterization reveals an\nerror in a paper on divisible design graphs by the second author et al. We\ndiscuss the cause and the consequences of this mistake and give the required\nerrata.\n']","[('strongly regular graphs', 0.7047820091247559), ('strongly regular graph', 0.6837820410728455), ('graphs strongly regular', 0.6784238219261169), ('regular graphs', 0.6591888070106506), ('regular graphs give', 0.6264156699180603), ('regular graph', 0.6234698295593262), ('regular graph vertices', 0.6172063946723938), ('graphs strongly', 0.5738462209701538), ('divisible design', 0.5359910130500793), ('graphs construction', 0.5079412460327148)]"
627,627,49,627_contact manifolds_contact manifold_reeb orbits_closed orbits,"['contact manifolds', 'contact manifold', 'reeb orbits', 'closed orbits', 'three manifold', 'transverse foliations', 'reeb flows', 'convex contact', 'flows dimension three', 'contact homology']","['Homoclinic orbits, Reeb chords and nice Birkhoff sections for Reeb flows\n  in 3D   We prove that for a $C^\\infty$-generic contact form defining a given\nco-oriented contact structure on a closed $3$-manifold, every hyperbolic\nperiodic Reeb orbit admits a transverse homoclinic connection in each of the\nbranches of its stable and unstable manifolds. We exploit this result to prove\nthat for a $C^\\infty$-generic contact form defining a given co-oriented contact\nstructure, given any finite collection $\\Gamma$ of periodic Reeb orbits and any\nLegendrian link $L$, there exists a global surface of section (embedded\nBirkhoff section) for the Reeb flow that contains $\\Gamma$ in its boundary, and\nthat contains in its interior a Legendrian link that is Legendrian isotopic to\n$L$ by a $C^0$-small isotopy. Finally we prove that if the Reeb vector field\nadmits a $\\partial$-strong Birkhoff section then every Legendrian knot has\ninfinitely many geometrically distinct Reeb chords, except possibly when the\nambient manifold is a lens space or the sphere and the Reeb flow has exactly\ntwo periodic orbits. In particular, $C^\\infty$-generically on the contact form\nthere are infinitely many geometrically distinct Reeb chords for every\nLegendrian knot. In the case of geodesic flows, every Legendrian knot has\ninfinitely many disjoint chords, without any further assumptions.\n', 'The action spectrum characterizes closed contact 3-manifolds all of\n  whose Reeb orbits are closed   A classical theorem due to Wadsley implies that, on a connected contact\nmanifold all of whose Reeb orbits are closed, there is a common period for the\nReeb orbits. In this paper we show that, for any Reeb flow on a closed\nconnected 3-manifold, the following conditions are actually equivalent: (1)\nevery Reeb orbit is closed; (2) all closed Reeb orbits have a common period;\n(3) the action spectrum has rank 1. We also show that, on a fixed closed\nconnected 3-manifold, a contact form with an action spectrum of rank 1 is\ndetermined (up to pull-back by diffeomorphisms) by the set of minimal periods\nof its closed Reeb orbits.\n', 'Contact three-manifolds with exactly two simple Reeb orbits   It is known that every contact form on a closed three-manifold has at least\ntwo simple Reeb orbits, and a generic contact form has infinitely many. We show\nthat if there are exactly two simple Reeb orbits, then the contact form is\nnondegenerate. Combined with a previous result, this implies that the\nthree-manifold is diffeomorphic to the three-sphere or a lens space, and the\ntwo simple Reeb orbits are the core circles of a genus one Heegaard splitting.\nWe also obtain further information about the Reeb dynamics and the contact\nstructure. For example the Reeb flow has a disk-like global surface of section\nand so its dynamics are described by a pseudorotation; the contact struture is\nuniversally tight; and in the case of the three-sphere, the contact volume and\nthe periods and rotation numbers of the simple Reeb orbits satisfy the same\nrelations as for an irrational ellipsoid.\n']","[('contact manifolds', 0.5523893237113953), ('contact manifold', 0.5275592803955078), ('reeb orbits', 0.5185915231704712), ('closed orbits', 0.49824342131614685), ('three manifold', 0.4891386330127716), ('transverse foliations', 0.446301132440567), ('reeb flows', 0.43870604038238525), ('convex contact', 0.43625304102897644), ('flows dimension three', 0.427286833524704), ('contact homology', 0.4250692129135132)]"
628,628,49,628_isogeometric framework_based isogeometric analysis_isogeometric analysis_isogeometric galerkin,"['isogeometric framework', 'based isogeometric analysis', 'isogeometric analysis', 'isogeometric galerkin', 'galerkin isogeometric', 'spline functions', 'isogeometric analysis iga', 'isogeometric', 'spline spaces', 'spline space']","['$C^1$ isogeometric spline space for trilinearly parameterized\n  multi-patch volumes   We study the space of $C^1$ isogeometric spline functions defined on\ntrilinearly parameterized multi-patch volumes. Amongst others, we present a\ngeneral framework for the design of the $C^1$ isogeometric spline space and of\nan associated basis, which is based on the two-patch construction [7], and\nwhich works uniformly for any possible multi-patch configuration. The presented\nmethod is demonstrated in more detail on the basis of a particular subclass of\ntrilinear multi-patch volumes, namely for the class of trilinearly\nparameterized multi-patch volumes with exactly one inner edge. For this\nspecific subclass of trivariate multi-patch parameterizations, we further\nnumerically compute the dimension of the resulting $C^1$ isogeometric spline\nspace and use the constructed $C^1$ isogeometric basis functions to numerically\nexplore the approximation properties of the $C^1$ spline space by performing\n$L^2$ approximation.\n', '$C^s$-smooth isogeometric spline spaces over planar multi-patch\n  parameterizations   The design of globally $C^s$-smooth ($s \\geq 1$) isogeometric spline spaces\nover multi-patch geometries is a current and challenging topic of research in\nthe framework of isogeometric analysis. In this work, we extend the recent\nmethods [25,28] and [31-33] for the construction of $C^1$-smooth and\n$C^2$-smooth isogeometric spline spaces over particular planar multi-patch\ngeometries to the case of $C^s$-smooth isogeometric multi-patch spline spaces\nof an arbitrary selected smoothness $s \\geq 1$. More precisely, for any $s \\geq\n1$, we study the space of $C^s$-smooth isogeometric spline functions defined on\nplanar, bilinearly parameterized multi-patch domains, and generate a particular\n$C^s$-smooth subspace of the entire $C^s$-smooth isogeometric multi-patch\nspline space. We further present the construction of a basis for this\n$C^s$-smooth subspace, which consists of simple and locally supported\nfunctions. Moreover, we use the $C^s$-smooth spline functions to perform $L^2$\napproximation on bilinearly parameterized multi-patch domains, where the\nobtained numerical results indicate an optimal approximation power of the\nconstructed $C^s$-smooth subspace.\n', 'The Argyris isogeometric space on unstructured multi-patch planar\n  domains   Multi-patch spline parametrizations are used in geometric design and\nisogeometric analysis to represent complex domains. We deal with a particular\nclass of $C^0$ planar multi-patch spline parametrizations called\nanalysis-suitable $G^1$ (AS-$G^{1}$) multi-patch parametrizations (Collin,\nSangalli, Takacs; CAGD, 2016). This class of parametrizations has to satisfy\nspecific geometric continuity constraints, and is of importance since it allows\nto construct, on the multi-patch domain, $C^1$ isogeometric spaces with optimal\napproximation properties. It was demonstrated in (Kapl, Sangalli, Takacs; CAD,\n2018) that AS-$G^1$ multi-patch parametrizations are suitable for modeling\ncomplex planar multi-patch domains.\n  In this work, we construct a basis, and an associated dual basis, for a\nspecific $C^1$ isogeometric spline space $\\mathcal{W}$ over a given AS-$G^1$\nmulti-patch parametrization. We call the space $\\mathcal{W}$ the Argyris\nisogeometric space, since it is $C^1$ across interfaces and $C^2$ at all\nvertices and generalizes the idea of Argyris finite elements to tensor-product\nsplines. The considered space $\\mathcal{W}$ is a subspace of the entire $C^1$\nisogeometric space $\\mathcal{V}^{1}$, which maintains the reproduction\nproperties of traces and normal derivatives along the interfaces. Moreover, it\nreproduces all derivatives up to second order at the vertices. In contrast to\n$\\mathcal{V}^{1}$, the dimension of $\\mathcal{W}$ does not depend on the domain\nparametrization, and $\\mathcal{W}$ admits a basis and dual basis which possess\na simple explicit representation and local support.\n  We conclude the paper with some numerical experiments, which exhibit the\noptimal approximation order of the Argyris isogeometric space $\\mathcal{W}$ and\ndemonstrate the applicability of our approach for isogeometric analysis.\n']","[('isogeometric framework', 0.6271073222160339), ('based isogeometric analysis', 0.6059540510177612), ('isogeometric analysis', 0.5673235058784485), ('isogeometric galerkin', 0.5536587834358215), ('galerkin isogeometric', 0.5311634540557861), ('spline functions', 0.5261503458023071), ('isogeometric analysis iga', 0.5018710494041443), ('isogeometric', 0.4909915328025818), ('spline spaces', 0.4562542140483856), ('spline space', 0.45293575525283813)]"
629,629,49,629_positive mass asymptotically_dimensional asymptotically flat_static spacetimes_asymptotically flat initial,"['positive mass asymptotically', 'dimensional asymptotically flat', 'static spacetimes', 'asymptotically flat initial', 'minkowski space', 'asymptotically flat', 'spherically symmetric', 'flat asymptotically', 'spacetimes', 'null energy condition']","['A tilted spacetime positive mass theorem   We show a spacetime positive mass theorem for asymptotically flat initial\ndata sets with a noncompact boundary. We develop a mass type invariant and a\nboundary dominant energy condition. Our proof is based on spinors.\n', 'Density and positive mass theorems for initial data sets with boundary   We prove a harmonic asymptotics density theorem for asymptotically flat\ninitial data sets with compact boundary that satisfy the dominant energy\ncondition. We use this to settle the spacetime positive mass theorem, with\nrigidity, for initial data sets with apparent horizon boundary in dimensions\nless than $8$ without a spin assumption.\n', 'Stability of the Spacetime Positive Mass Theorem in Spherical Symmetry   The rigidity statement of the positive mass theorem asserts that an\nasymptotically flat initial data set for the Einstein equations with zero ADM\nmass, and satisfying the dominant energy condition, must arise from an\nembedding into Minkowski space. In this paper we address the question of what\nhappens when the mass is merely small. In particular, we formulate a conjecture\nfor the stability statement associated with the spacetime version of the\npositive mass theorem, and give examples to show how it is basically sharp if\ntrue. This conjecture is then established under the assumption of spherical\nsymmetry in all dimensions. More precisely, it is shown that a sequence of\nasymptotically flat initial data satisfying the dominant energy condition,\nwithout horizons except possibly at an inner boundary, and with ADM masses\ntending to zero must arise from isometric embeddings into a sequence of static\nspacetimes converging to Minkowski space in the pointed volume preserving\nintrinsic flat sense. The difference of second fundamental forms coming from\nthe embeddings and initial data must converge to zero in $L^p$, $1\\leq p<2$. In\naddition some minor tangential results are also given, including the spacetime\nversion of the Penrose inequality with rigidity statement in all dimensions for\nspherically symmetric initial data, as well as symmetry inheritance properties\nfor outermost apparent horizons.\n']","[('positive mass asymptotically', 0.4849907457828522), ('dimensional asymptotically flat', 0.4799441993236542), ('static spacetimes', 0.45302969217300415), ('asymptotically flat initial', 0.4218403995037079), ('minkowski space', 0.4134734272956848), ('asymptotically flat', 0.40399083495140076), ('spherically symmetric', 0.37903881072998047), ('flat asymptotically', 0.37115025520324707), ('spacetimes', 0.36671486496925354), ('null energy condition', 0.36556077003479004)]"
630,630,49,630_hodge conjecture_conjecture hodge_variation hodge structures_hodge structures,"['hodge conjecture', 'conjecture hodge', 'variation hodge structures', 'hodge structures', 'hodge theory', 'mixed hodge structures', 'variation hodge structure', 'variations hodge', 'hodge structure', 'hodge numbers']","['Height Pairing on Higher Cycles and Mixed Hodge Structures   For a smooth, projective complex variety, we introduce several mixed Hodge\nstructures associated to higher algebraic cycles. Most notably, we introduce a\nmixed Hodge structure for a pair of higher cycles which are in the refined\nnormalized complex and intersect properly. In a special case, this mixed Hodge\nstructure is an oriented biextension, and its height agrees with the higher\narchimedean height pairing introduced in a previous paper by the first two\nauthors. We also compute a non-trivial example of this height given by\nBloch-Wigner dilogarithm function. Finally we study the variation of mixed\nHodge structures of Hodge-Tate type, and show that the height extends\ncontinuously to degenerate situations.\n', 'On the distribution of the Hodge locus   Given a polarizable $\\mathbb{Z}$-variation of Hodge structures $\\mathbb{V}$\nover a complex smooth quasi-projective base $S$, a classical result of Cattani,\nDeligne and Kaplan says that its Hodge locus (i.e. the locus where exceptional\nHodge tensors appear) is a countable union of irreducible algebraic\nsubvarieties of $S$, called the special subvarieties for $\\mathbb{V}$. Our main\nresult in this paper is that, if the level of $\\mathbb{V}$ is at least $3$,\nthis Hodge locus is in fact a finite union of such special subvarieties (hence\nis algebraic), at least if we restrict ourselves to the Hodge locus factorwise\nof positive period dimension. For instance the Hodge locus of positive period\ndimension of the universal family of degree $d$ smooth hypersurfaces in\n$\\mathbf{P}^{n+1}_\\mathbb{C}$, $n\\geq 3, d\\geq 5$ and $(n,d)\\neq (4,5)$, is\nalgebraic. On the other hand we prove that in level $1$ or $2$, the Hodge locus\nis analytically dense in $S^{an}$ as soon as it contains one typical special\nsubvariety. These results follow from a complete elucidation of the\ndistribution in $S$ of the special subvarieties in terms of typical/atypical\nintersections, with the exception of the atypical special subvarieties of zero\nperiod dimension.\n', 'On the fields of definition of Hodge loci   A polarizable variation of Hodge structure over a smooth complex quasi\nprojective variety $S$ is said to be defined over a number field $L$ if $S$ and\nthe algebraic connection associated to the variation are both defined over $L$.\nConjecturally any special subvariety (also called ""an irreducible component of\nthe Hodge locus) for such variations is defined over $\\overline{\\mathbb{Q}}$,\nand its Galois conjugates are also special subvarieties. We prove this\nconjecture for special subvarieties satisfying a simple monodromy condition. As\na corollary we reduce the conjecture that special subvarieties for variation of\nHodge structures defined over a number field are defined over\n$\\overline{\\mathbb{Q}}$ to the case of special points.\n']","[('hodge conjecture', 0.6839228272438049), ('conjecture hodge', 0.6781579256057739), ('variation hodge structures', 0.6565886735916138), ('hodge structures', 0.6497602462768555), ('hodge theory', 0.6383296847343445), ('mixed hodge structures', 0.6348170042037964), ('variation hodge structure', 0.6319117546081543), ('variations hodge', 0.6293762922286987), ('hodge structure', 0.6284515261650085), ('hodge numbers', 0.6195225119590759)]"
631,631,49,631_moore penrose inverses_penrose generalized inverse_moore penrose inverse_penrose inverses,"['moore penrose inverses', 'penrose generalized inverse', 'moore penrose inverse', 'penrose inverses', 'matrix dual', 'inverse matrices', 'generalized inverses', 'inverse dual', 'penrose inverse', 'generalized inverse']","['A new generalized inverse of matrices from core-EP decomposition   A new generalized inverse for a square matrix $H\\in\\mathbb{C}^{n\\times n}$,\ncalled CCE-inverse, is established by the core-EP decomposition and\nMoore-Penrose inverse $H^{\\dag}$. We propose some characterizations of the\nCCE-inverse. Furthermore, two canonical forms of the CCE-inverse are presented.\nAt last, we introduce the definitions of CCE-matrices and $k$-CCE matrices, and\nprove that CCE-matrices are the same as $i$-EP matrices studied by Wang and Liu\nin [The weak group matrix, Aequationes Mathematicae, 93(6): 1261-1273, 2019].\n', 'A Genuine Extension of The Moore-Penrose Inverse to Dual Matrices   The Moore-Penrose inverse is a genuine extension of the matrix inverse. Given\na complex matrix, there uniquely exists another complex matrix satisfying the\nfour Moore-Penrose conditions, and if the original matrix is nonsingular, it is\nexactly the inverse of that matrix. In the last one and half decade, in the\nstudy of approximate synthesis in kinematic, two generalizations of the\nMoore-Penrose inverse appeared for dual real matrices,including Moore-Penrose\ndual generalized inverse and dual Moore-Penrose generalized inverse (DMPGI).\nDMPGI satisfies the four Moore-Penrose conditions, but does not exist for\nuncountably many dual real matrices. %Another generalization, called\nMoore-Penrose dual generalized inverse (MPDGI), is different from DMPGI even if\nDMPGI exists. In this paper, based upon the singular value decomposition of\ndual matrices, we extend the first Moore-Penrose condition to dual matrices and\nintroduce a genuine extension of the Moore-Penrose inverse to dual matrices,\nreferred to as GMPI. Given a dual complex matrix, its GMPI is the unique dual\ncomplex matrix which satisfy the first extended and the other three\nMoore-Penrose conditions. If the original matrix is a complex matrix, its GMPI\nis exactly the Moore-Penrose inverse of that matrix. And if the original matrix\nis a dual real matrix and its DMPGI exists, its GMPI coincides with its DMPGI.\n', 'Further results on weighted core-EP inverse of matrices   In this paper, we introduce the notation of $E$-weighted core-EP and\n$F$-weighted dual core-EP inverse of matrices. We then obtain a few explicit\nexpressions for the weighted core-EP inverse of matrices through other\ngeneralized inverses. Further, we discuss the existence of generalized weighted\nMoore-Penrose inverse and additive properties of the weighted core-EP inverse\nof matrices. In addition to these, we propose the star weighted core-EP and\nweighted core-EP star class of matrices for solving the system of matrix\nequations. We further elaborate on this theory by producing a few\nrepresentation and characterization of star weighted core-EP and weighted\ncore-EP star classes of matrices.\n']","[('moore penrose inverses', 0.689298689365387), ('penrose generalized inverse', 0.6547641158103943), ('moore penrose inverse', 0.6485008001327515), ('penrose inverses', 0.6135396957397461), ('matrix dual', 0.5959499478340149), ('inverse matrices', 0.5952804088592529), ('generalized inverses', 0.594093918800354), ('inverse dual', 0.5851373076438904), ('penrose inverse', 0.5701401829719543), ('generalized inverse', 0.5562636852264404)]"
632,632,49,632_higgs bundles_higgs bundle_space higgs bundles_moduli space higgs,"['higgs bundles', 'higgs bundle', 'space higgs bundles', 'moduli space higgs', 'higgs sheaves', 'parabolic higgs', 'bundle moduli', 'bundles', 'bundles smooth', 'parabolic bundles']","[""On Fourier-Mukai transforms of upward flows for Hitchin systems   We consider the moduli space of semistable Higgs bundles on a smooth\nprojective curve. Motivated by mirror symmetry, Hausel and Hitchin showed that\nover an open of the locus of smooth Hitchin fibers, the duality of\nDonagi-Pantev intertwines certain Lagrangian upward flows with hyperholomorphic\nvector bundles constructed from universal Higgs bundles. Using Arinkin's sheaf\nand some codimension estimates, we show a generalization of this result over\nthe entire Hitchin base, for Higgs bundles of arbitrary degree.\n"", 'Higgs bundles -- Recent applications   We present an overview of some recent applications of Higgs bundles and the\nHitchin fibration.\n', 'Generalizations of parabolic Higgs bundles, real structures and\n  integrability   We introduce a notion of quasi-antisymmetric Higgs $G$-bundles over curves\nwith marked points. They are endowed with additional structures, which replace\nthe parabolic structures at marked points in the parabolic Higgs bundles. The\nlatter means that the coadjoint orbits are attached to the marked points. The\nmoduli spaces of parabolic Higgs bundles are the phase spaces of complex\ncompletely integrable systems. In our case the coadjoint orbits are replaced by\nthe cotangent bundles over some special symmetric spaces in such a way that the\nmoduli space of the modified Higgs bundles are still phase spaces of complex\ncompletely integrable systems. We show that the moduli space of the parabolic\nHiggs bundles is the symplectic quotient of the moduli space of the\nquasi-antisymmetric Higgs bundle with respect to the action of product of\nCartan subgroups. Also, by changing the symmetric spaces we introduce\nquasi-compact and quasi-normal Higgs bundles. Then the fixed point sets of real\ninvolutions acting on their moduli spaces are the phase spaces of real\ncompletely integrable systems. Several examples are given including integrable\nextensions of the ${\\rm SL}(2)$ Euler-Arnold top, two-body elliptic\nCalogero-Moser system and the rational ${\\rm SL}(2)$ Gaudin system together\nwith its real reductions.\n']","[('higgs bundles', 0.7563750147819519), ('higgs bundle', 0.732689380645752), ('space higgs bundles', 0.7094482183456421), ('moduli space higgs', 0.6554529666900635), ('higgs sheaves', 0.6346598267555237), ('parabolic higgs', 0.6053459048271179), ('bundle moduli', 0.5976796746253967), ('bundles', 0.5951946377754211), ('bundles smooth', 0.5913069844245911), ('parabolic bundles', 0.5884205102920532)]"
633,633,49,633_quantum graphs quantum_quantum graphs_graphs quantum_graph quantum,"['quantum graphs quantum', 'quantum graphs', 'graphs quantum', 'graph quantum', 'quantum graph', 'classical graphs', 'graphs isomorphic', 'graph isomorphism', 'cayley graphs abelian', 'isomorphism graphs']","[""Almost all trees have quantum symmetry   From the work of Erd\\H{o}s and R\\'{e}nyi from 1963 it is known that almost\nall graphs have no symmetry. In 2017, Lupini, Man\\v{c}inska and Roberson proved\na quantum counterpart: Almost all graphs have no quantum symmetry. Here, the\nnotion of quantum symmetry is phrased in terms of Banica's definition of\nquantum automorphism groups of finite graphs from 2005, in the framework of\nWoronowicz's compact quantum groups. Now, Erd\\H{o}s and R\\'{e}nyi also proved a\ncomplementary result in 1963: Almost all trees do have symmetry. The crucial\npoint is the almost sure existence of a cherry in a tree. But even more is\ntrue: We almost surely have two cherries in a tree - and we derive that almost\nall trees have quantum symmetry. We give an explicit proof of this quantum\ncounterpart of Erd\\H{o}s and R\\'{e}nyi's result on trees.\n"", ""On the quantum symmetry of distance-transitive graphs   In this article, we study quantum automorphism groups of distance-transitive\ngraphs. We show that the odd graphs, the Hamming graphs $H(n,3)$, the Johnson\ngraphs $J(n,2)$ and the Kneser graphs $K(n,2)$ do not have quantum symmetry. We\nalso give a table with the quantum automorphism groups of all cubic\ndistance-transitive graphs. Furthermore, with one graph missing, we can now\ndecide whether or not a distance-regular graph of order $\\leq 20$ has quantum\nsymmetry. Moreover, we prove that the Hoffman-Singleton graph has no quantum\nsymmetry. On a final note, we present an example of a pair of graphs with the\nsame intersection array (the Shrikhande graph and the $4 \\times 4$ rook's\ngraph), where one of them has quantum symmetry and the other one does not.\n"", 'Solution group representations as quantum symmetries of graphs   In 2019, Aterias et al. constructed pairs of quantum isomorphic,\nnon-isomorphic graphs from linear constraint systems. This article deals with\nquantum automorphisms and quantum isomorphisms of colored versions of those\ngraphs. We show that the quantum automorphism group of such a colored graph is\nthe dual of the homogeneous solution group of the underlying linear constraint\nsystem. Given a vertex- and edge-colored graph with certain properties, we\nconstruct an uncolored graph that has the same quantum automorphism group as\nthe colored graph we started with. Using those results, we obtain the first\nknown example of a graph that has quantum symmetry and finite quantum\nautomorphism group. Furthermore, we construct a pair of quantum isomorphic,\nnon-isomorphic graphs that both have no quantum symmetry.\n']","[('quantum graphs quantum', 0.7812669277191162), ('quantum graphs', 0.7809606790542603), ('graphs quantum', 0.776302695274353), ('graph quantum', 0.7402753233909607), ('quantum graph', 0.7167310118675232), ('classical graphs', 0.5911139845848083), ('graphs isomorphic', 0.5778074264526367), ('graph isomorphism', 0.5770379304885864), ('cayley graphs abelian', 0.5731438398361206), ('isomorphism graphs', 0.5714489817619324)]"
634,634,49,634_material models_physics informed neural_material parameters_solid mechanics,"['material models', 'physics informed neural', 'material parameters', 'solid mechanics', 'microstructures', 'recurrent neural network', 'neural networks', 'heterogeneous materials', 'microstructure', 'neural network']","['A Microstructure-based Graph Neural Network for Accelerating Multiscale\n  Simulations   Simulating the mechanical response of advanced materials can be done more\naccurately using concurrent multiscale models than with single-scale\nsimulations. However, the computational costs stand in the way of the practical\napplication of this approach. The costs originate from microscale Finite\nElement (FE) models that must be solved at every macroscopic integration point.\nA plethora of surrogate modeling strategies attempt to alleviate this cost by\nlearning to predict macroscopic stresses from macroscopic strains, completely\nreplacing the microscale models. In this work, we introduce an alternative\nsurrogate modeling strategy that allows for keeping the multiscale nature of\nthe problem, allowing it to be used interchangeably with an FE solver for any\ntime step. Our surrogate provides all microscopic quantities, which are then\nhomogenized to obtain macroscopic quantities of interest. We achieve this for\nan elasto-plastic material by predicting full-field microscopic strains using a\ngraph neural network (GNN) while retaining the microscopic constitutive\nmaterial model to obtain the stresses. This hybrid data-physics graph-based\napproach avoids the high dimensionality originating from predicting full-field\nresponses while allowing non-locality to arise. By training the GNN on a\nvariety of meshes, it learns to generalize to unseen meshes, allowing a single\nmodel to be used for a range of microstructures. The embedded microscopic\nconstitutive model in the GNN implicitly tracks history-dependent variables and\nleads to improved accuracy. We demonstrate for several challenging scenarios\nthat the surrogate can predict complex macroscopic stress-strain paths. As the\ncomputation time of our method scales favorably with the number of elements in\nthe microstructure compared to the FE method, our method can significantly\naccelerate FE2 simulations.\n', 'Learning Memory and Material Dependent Constitutive Laws   We propose and study a neural operator framework for learning memory- and\nmaterial microstructure-dependent constitutive laws for heterogeneous\nmaterials. We work in the two-scale setting where homogenization theory\nprovides a systematic approach to deriving macroscale constitutive laws,\nobviating the need to resolve complex microstructure repeatedly. However, the\nunit cell problems defining these constitutive models are typically not\namenable to explicit evaluation. It is therefore of interest to learn\nconstitutive models from data generated by the unit cell problem. Our proposed\nframework models homogenized constitutive laws with both memory- and\nmicrostructure-dependence through the use of Markovian recurrent and Fourier\nneural operators. The homogenization problem for Kelvin-Voigt viscoelastic\nmaterials is studied to provide firm theoretical foundations for our model. The\ntheoretical properties of the cell problem in this Kelvin-Voigt setting\nmotivate the proposed learning framework; and are also used to prove a\nuniversal approximation theorem for the learned macroscale constitutive model.\nNumerical experiments show that the proposed learning framework accurately\nlearns memory- and microstructure-dependent viscoelastic and\nelasto-viscoplastic constitutive models, beyond the setting of the theory.\nFurthermore, we show that the learned constitutive models can be successfully\ndeployed in macroscale simulation of material deformation for different\nmicrostructures without retraining.\n', 'Physically recurrent neural network for rate and path-dependent\n  heterogeneous materials in a finite strain framework   In this work, a hybrid physics-based data-driven surrogate model for the\nmicroscale analysis of heterogeneous material is investigated. The proposed\nmodel benefits from the physics-based knowledge contained in the constitutive\nmodels used in the full-order micromodel by embedding them in a neural network.\nFollowing previous developments, this paper extends the applicability of the\nphysically recurrent neural network (PRNN) by introducing an architecture\nsuitable for rate-dependent materials in a finite strain framework. In this\nmodel, the homogenized deformation gradient of the micromodel is encoded into a\nset of deformation gradients serving as input to the embedded constitutive\nmodels. These constitutive models compute stresses, which are combined in a\ndecoder to predict the homogenized stress, such that the internal variables of\nthe history-dependent constitutive models naturally provide physics-based\nmemory for the network. To demonstrate the capabilities of the surrogate model,\nwe consider a unidirectional composite micromodel with transversely isotropic\nelastic fibers and elasto-viscoplastic matrix material. The extrapolation\nproperties of the surrogate model trained to replace such micromodel are tested\non loading scenarios unseen during training, ranging from different\nstrain-rates to cyclic loading and relaxation. Speed-ups of three orders of\nmagnitude with respect to the runtime of the original micromodel are obtained.\n']","[('material models', 0.5387968420982361), ('physics informed neural', 0.4200875759124756), ('material parameters', 0.4154379963874817), ('solid mechanics', 0.403278648853302), ('microstructures', 0.373250812292099), ('recurrent neural network', 0.37243789434432983), ('neural networks', 0.3667760491371155), ('heterogeneous materials', 0.3565627336502075), ('microstructure', 0.3552679121494293), ('neural network', 0.35131001472473145)]"
635,635,49,635_nonlinear boussinesq_viscous boussinesq_two dimensional boussinesq_boussinesq equations,"['nonlinear boussinesq', 'viscous boussinesq', 'two dimensional boussinesq', 'boussinesq equations', 'boussinesq system', 'dimensional boussinesq system', 'boussinesq approximation', 'dimensional boussinesq', 'boussinesq', 'stability sobolev']","[""On the Boussinesq equations with non-monotone temperature profiles   In this article we consider the asymptotic stability of the two-dimensional\nBoussinesq equations with partial dissipation near a combination of Couette\nflow and temperature profiles $T(y)$. As a first main result we show that if\n$T'$ is of size at most $\\nu^{1/3}$ in a suitable norm, then the linearized\nBoussinesq equations with only vertical dissipation of the velocity but not of\nthe temperature are stable. Thus, mixing enhanced dissipation can suppress\nRayleigh-B\\'enard instability in this linearized case. We further show that\nthese results extend to the (forced) nonlinear equations with vertical\ndissipation in both temperature and velocity.\n"", 'On Enhanced Dissipation for the Boussinesq Equations   In this article we consider the stability and damping problem for the 2D\nBoussinesq equations with partial dissipation near a two parameter family of\nstationary solutions which includes Couette flow and hydrostatic balance.\n  In the first part we show that for the linearized problem in an infinite\nperiodic channel the evolution is asymptotically stable if any diffusion\ncoefficient is non-zero. In particular, this imposes weaker conditions than for\nexample vertical diffusion. Furthermore, we study the interaction of shear\nflow, hydrostatic balance and partial dissipation.\n  In a second part we adapt the methods used by Bedrossian, Vicol and Wang in\nthe Navier-Stokes problem and combine them with cancellation properties of the\nBoussinesq equations to establish small data stability and enhanced dissipation\nresults for the nonlinear Boussinesq problem with full dissipation.\n', 'The stabilizing effect of the temperature on buoyancy-driven fluids   The Boussinesq system for buoyancy driven fluids couples the momentum\nequation forced by the buoyancy with the convection-diffusion equation for the\ntemperature. One fundamental issue on the Boussinesq system is the stability\nproblem on perturbations near the hydrostatic balance. This problem can be\nextremely difficult when the system lacks full dissipation. This paper solves\nthe stability problem for a two-dimensional Boussinesq system with only\nvertical dissipation and horizontal thermal diffusion. We establish the\nstability for the nonlinear system and derive precise large-time behavior for\nthe linearized system. The results presented in this paper reveal a remarkable\nphenomenon for buoyancy driven fluids. That is, the temperature actually\nsmooths and stabilizes the fluids. If the temperature were not present, the\nfluid is governed by the 2D Navier-Stokes with only vertical dissipation and\nits stability remains open. It is the coupling and interaction between the\ntemperature and the velocity in the Boussinesq system that makes the stability\nproblem studied here possible. Mathematically the system can be reduced to\ndegenerate and damped wave equations that fuel the stabilization.\n']","[('nonlinear boussinesq', 0.665182888507843), ('viscous boussinesq', 0.660558819770813), ('two dimensional boussinesq', 0.6447146534919739), ('boussinesq equations', 0.6434515714645386), ('boussinesq system', 0.5950853824615479), ('dimensional boussinesq system', 0.588531494140625), ('boussinesq approximation', 0.5642362833023071), ('dimensional boussinesq', 0.5635280013084412), ('boussinesq', 0.5125750303268433), ('stability sobolev', 0.446853905916214)]"
636,636,48,636_optimal beamforming_output mimo_mimo_user mimo,"['optimal beamforming', 'output mimo', 'mimo', 'user mimo', 'beamforming design', 'beamforming', 'passive beamforming', 'channel state information', 'alternating optimization', 'transmit power']","['Reconfigurable Intelligent Surface-Aided MISO Systems with Statistical\n  CSI: Channel Estimation, Analysis and Optimization   This paper investigates the reconfigurable reflecting surface (RIS)-aided\nmultiple-input-single-output (MISO) systems with imperfect channel state\ninformation (CSI), where RIS-related channels are modeled by Rician fading.\nConsidering the overhead and complexity in practical systems, we employ the\nlow-complexity maximum ratio combining (MRC) beamforming at the base station\n(BS), and configure the phase shifts of the RIS based on long-term statistical\nCSI. Specifically, we first estimate the overall channel matrix based on the\nlinear minimum mean square error (LMMSE) estimator, and evaluate the\nperformance of MSE and normalized MSE (NMSE). Then, with the estimated channel,\nwe derive the closed-form expressions of the ergodic rate. The derived\nexpressions show that with Rician RIS-related channels, the rate can maintain\nat a non-zero value when the transmit power is scaled down proportionally to\n$1/M$ or $1/N^2$, where $M$ and $N$ are the number of antennas and reflecting\nelements, respectively. However, if all the RIS-related channels are fully\nRayleigh, the transmit power of each user can only be scaled down\nproportionally to $1/\\sqrt{M}$ or $1/N$. Finally, numerical results verify the\npromising benefits from the RIS to traditional MISO systems.\n', 'Statistical CSI Based Beamforming for Reconfigurable Intelligent Surface\n  Aided MISO Systems with Channel Correlation   Reconfigurable intelligent surface (RIS) is a promising candidate technology\nof the upcoming Sixth Generation (6G) communication system for its ability to\nprovide unprecedented spectral and energy efficiency increment through passive\nbeamforming. However, it is challenging to obtain instantaneous channel state\ninformation (I-CSI) for RIS, which obliges us to use statistical channel state\ninformation (S-CSI) to achieve passive beamforming. In this paper, RIS-aided\nmultiple-input single-output (MISO) multi-user downlink communication system\nwith correlated channels is investigated. Then, we formulate the problem of\njoint beamforming design at the AP and RIS to maximize the sum ergodic spectral\nefficiency (ESE) of all users to improve the network capacity. Since it is too\nhard to compute sum ESE, an ESE approximation is adopted to reformulate the\nproblem into a more tractable form. Then, we present two joint beamforming\nalgorithms, namely the singular value decomposition-gradient descent (SVD-GD)\nalgorithm and the fractional programming-gradient descent (FP-GD) algorithm.\nSimulation results show the effectiveness of our proposed algorithms and\nvalidate that 2-bits quantizer is enough for RIS phase shifts implementation.\n', 'Sum-Rate Maximization of RIS-Aided Multi-User MIMO Systems With\n  Statistical CSI   This paper investigates a reconfigurable intelligent surface (RIS)-aided\nmulti-user multiple-input multiple-output (MIMO) system by considering only the\nstatistical channel state information (CSI) at the base station (BS). We aim to\nmaximize its sum-rate via the joint optimization of beamforming at the BS and\nphase shifts at the RIS. However, the multi-user MIMO transmissions and the\nspatial correlations make the optimization cumbersome. For tractability, a\ndeterministic approximation is derived for the sum-rate under a large number of\nthe reflecting elements. By adopting the approximate sum-rate for maximization,\nthe optimal designs of the transmit beamforming and the phase shifts can be\ndecoupled and solved in closed-forms individually. More specifically, the\nglobal optimality of the transmit beamforming can be guaranteed by using the\nwater-filling algorithm and a sub-optimal solution of phase shifts can be\nobtained by using the projected gradient ascent (PGA) algorithm. By comparing\nto the case of the instantaneous CSI assumed at the BS, the proposed algorithm\nbased on statistical CSI can achieve comparable performance but with much lower\ncomplexity and signaling overhead, which is more affordable and appealing for\npractical applications. Moreover, the impact of spatial correlation is\nthoroughly examined by using majorization theory.\n']","[('optimal beamforming', 0.5271108746528625), ('output mimo', 0.4996911287307739), ('mimo', 0.4373053014278412), ('user mimo', 0.3997352421283722), ('beamforming design', 0.39768052101135254), ('beamforming', 0.3865744173526764), ('passive beamforming', 0.37881696224212646), ('channel state information', 0.3676014542579651), ('alternating optimization', 0.35944581031799316), ('transmit power', 0.33343833684921265)]"
637,637,48,637_operator manifolds_dirac operators_dirac operator_associated dirac operator,"['operator manifolds', 'dirac operators', 'dirac operator', 'associated dirac operator', 'compact manifolds boundary', 'manifolds boundary', 'manifold boundary', 'riemannian spin manifold', 'boundary spectral', 'dimensional compact manifolds']","['Dirac-Witten Operators and the Kastler-Kalau-Walze type theorem for\n  manifolds with boundary   In this paper, we obtain two Lichnerowicz type formulas for the Dirac-Witten\noperators. And we give the proof of Kastler-Kalau-Walze type theorems for the\nDirac-Witten operators on 4-dimensional and 6- dimensional compact manifolds\nwith (resp.without) boundary\n', 'A Kastler-Kalau-Walze type theorem for the $J$-twist of the Dirac\n  operator with torsion   In this paper, we give a Lichnerowicz type formula for the $J$-twist of the\nDirac operator with torsion. And we prove a Kastler-Kalau-Walze type theorem\nfor the $J$-twist of the Dirac operator with torsion on 4-dimensional and\n6-dimensional almost product Riemannian spin manifold with boundary.\n', 'The generalized noncommutative residue and the Kastler-Kalau-Walze type\n  theorem   In this paper, we define the generalized noncommutative residue of the Dirac\noperator. And we give the proof of Kastler-Kalau-Walze type theorems for the\ngeneralized noncommutative residue on 4-dimensional and 6-dimensional compact\nmanifolds with (resp.without) boundary.\n']","[('operator manifolds', 0.6125748753547668), ('dirac operators', 0.5824159383773804), ('dirac operator', 0.5689877867698669), ('associated dirac operator', 0.5537378191947937), ('compact manifolds boundary', 0.5478976964950562), ('manifolds boundary', 0.535584568977356), ('manifold boundary', 0.5294363498687744), ('riemannian spin manifold', 0.5041033029556274), ('boundary spectral', 0.48290345072746277), ('dimensional compact manifolds', 0.4828580319881439)]"
638,638,48,638_kink solutions_kinks_kink_soliton dynamics,"['kink solutions', 'kinks', 'kink', 'soliton dynamics', 'field theories dimensions', 'field theory models', 'field theories', 'field theory', 'scalar field theories', 'theories dimensions']","['Deformations of Kink Tails   We study the asymptotic properties of kinks in connection with the\ndeformation procedure. We show that, upon deformation of the field-theoretic\nmodel, the asymptotics of kinks can change or remain unchanged, depending on\nthe properties of the deforming function. The cases of both explicit and\nimplicit kinks are considered. In addition, we show that the the deformation\nprocedure can be applied to the important case of implicit kinks. We also prove\nthat for any kink with a power-law tail, the stability potential decreases as\nthe inverse square of the coordinate. The physical consequences of the\ndeformation are discussed: the change of the kink mass, as well as the\nasymptotic behavior of the kink-antikink force.\n', ""Exotic Final States in the $\\varphi^8$ Multi-Kink Collisions   We study final states in the scattering of kinks and antikinks of the\n$\\varphi^8$ field-theoretic model. We use the initial conditions in the form of\ntwo, three or four static or moving kinks. In the numerical experiments we\nobserve a number of different processes such as emergence of static and moving\noscillons, change of the kink's topological sector, scattering of an oscillon\nby a kink, production of kink-antikink pairs in oscillon-oscillon collisions.\nIn antikink-kink collisions for asymmetric kinks, we found resonance phenomena\n-- escape windows.\n"", 'Classification of kink clusters for scalar fields in dimension 1+1   We consider a real scalar field equation in dimension 1+1 with an even,\npositive self-interaction potential having two non-degenerate zeros (vacua) 1\nand -1. Such a model admits non-trivial static solutions called kinks and\nantikinks. We define a kink n-cluster to be a solution approaching, for large\npositive times, a superposition of n alternating kinks and antikinks whose\nvelocities converge to $0$. They can be equivalently characterized as the\nsolutions of minimal possible energy containing n transitions between the\nvacua, or as the solutions whose kinetic energy decays to 0 in large time.\n  Our first main result is a determination of the main-order asymptotic\nbehavior of any kink n-cluster. The proof relies on a reduction,using\nappropriately chosen modulation parameters, to an n-body problem with\nattractive exponential interactions. We then construct a kink n-cluster for any\nprescribed initial positions of the kinks and antikinks, provided that their\nmutual distances are sufficiently large. Next, we prove that the set of all the\nkink n-clusters is an n-dimensional topological manifold, and we show how it\ncan be parametrized by the positions of the kinks in the configuration. The\nproof relies on energy estimates and the contraction mapping principle, using\nthe Lyapunov-Schmidt reduction technique. Finally, we show that kink clusters\nare universal profiles for the formation/collapse of multikink configurations.\nIn this sense, they can be interpreted as forming the stable/unstable manifold\nof the multikink state given by a superposition of n infinitely separated\nalternating kinks and antikinks.\n']","[('kink solutions', 0.5317065715789795), ('kinks', 0.4455612301826477), ('kink', 0.40807467699050903), ('soliton dynamics', 0.3889233469963074), ('field theories dimensions', 0.36036422848701477), ('field theory models', 0.34937357902526855), ('field theories', 0.3376745581626892), ('field theory', 0.3282959759235382), ('scalar field theories', 0.3231489658355713), ('theories dimensions', 0.32046443223953247)]"
639,639,48,639_deep learning dl_deep learning_network dnn_wireless communications,"['deep learning dl', 'deep learning', 'network dnn', 'wireless communications', 'wireless channel', 'wireless communication', 'deep neural networks', 'deep learning based', 'deep neural network', 'deep neural']","['Science-Informed Deep Learning (ScIDL) With Applications to Wireless\n  Communications   Given the extensive and growing capabilities offered by deep learning (DL),\nmore researchers are turning to DL to address complex challenges in\nnext-generation (xG) communications. However, despite its progress, DL also\nreveals several limitations that are becoming increasingly evident. One\nsignificant issue is its lack of interpretability, which is especially critical\nfor safety-sensitive applications. Another significant consideration is that DL\nmay not comply with the constraints set by physics laws or given security\nstandards, which are essential for reliable DL. Additionally, DL models often\nstruggle outside their training data distributions, which is known as poor\ngeneralization. Moreover, there is a scarcity of theoretical guidance on\ndesigning DL algorithms. These challenges have prompted the emergence of a\nburgeoning field known as science-informed DL (ScIDL). ScIDL aims to integrate\nexisting scientific knowledge with DL techniques to develop more powerful\nalgorithms. The core objective of this article is to provide a brief tutorial\non ScIDL that illustrates its building blocks and distinguishes it from\nconventional DL. Furthermore, we discuss both recent applications of ScIDL and\npotential future research directions in the field of wireless communications.\n', 'From Multilayer Perceptron to GPT: A Reflection on Deep Learning\n  Research for Wireless Physical Layer   Most research studies on deep learning (DL) applied to the physical layer of\nwireless communication do not put forward the critical role of the\naccuracy-generalization trade-off in developing and evaluating practical\nalgorithms. To highlight the disadvantage of this common practice, we revisit a\ndata decoding example from one of the first papers introducing DL-based\nend-to-end wireless communication systems to the research community and\npromoting the use of artificial intelligence (AI)/DL for the wireless physical\nlayer. We then put forward two key trade-offs in designing DL models for\ncommunication, namely, accuracy versus generalization and compression versus\nlatency. We discuss their relevance in the context of wireless communications\nuse cases using emerging DL models including large language models (LLMs).\nFinally, we summarize our proposed evaluation guidelines to enhance the\nresearch impact of DL on wireless communications. These guidelines are an\nattempt to reconcile the empirical nature of DL research with the rigorous\nrequirement metrics of wireless communications systems.\n', 'Robust Deep Learning-Based Physical Layer Communications: Strategies and\n  Approaches   Deep learning (DL) has emerged as a transformative technology with immense\npotential to reshape the sixth-generation (6G) wireless communication network.\nBy utilizing advanced algorithms for feature extraction and pattern\nrecognition, DL provides unprecedented capabilities in optimizing the network\nefficiency and performance, particularly in physical layer communications.\nAlthough DL technologies present the great potential, they also face\nsignificant challenges related to the robustness, which are expected to\nintensify in the complex and demanding 6G environment. Specifically, current DL\nmodels typically exhibit substantial performance degradation in dynamic\nenvironments with time-varying channels, interference of noise and different\nscenarios, which affect their effectiveness in diverse real-world applications.\nThis paper provides a comprehensive overview of strategies and approaches for\nrobust DL-based methods in physical layer communications. First we introduce\nthe key challenges that current DL models face. Then we delve into a detailed\nexamination of DL approaches specifically tailored to enhance robustness in 6G,\nwhich are classified into data-driven and model-driven strategies. Finally, we\nverify the effectiveness of these methods by case studies and outline future\nresearch directions.\n']","[('deep learning dl', 0.594598114490509), ('deep learning', 0.5073696970939636), ('network dnn', 0.493927538394928), ('wireless communications', 0.47367873787879944), ('wireless channel', 0.4652799665927887), ('wireless communication', 0.4507967233657837), ('deep neural networks', 0.44675058126449585), ('deep learning based', 0.4457560181617737), ('deep neural network', 0.4436316192150116), ('deep neural', 0.4425448477268219)]"
640,640,48,640_novikov algebras_algebras associative algebras_zinbiel algebras_dimensional associative algebras,"['novikov algebras', 'algebras associative algebras', 'zinbiel algebras', 'dimensional associative algebras', 'associative algebras', 'algebras derived', 'non associative algebras', 'algebras obtained', 'algebras describe', 'associative algebras associative']","['On Pre-Novikov Algebras and Derived Zinbiel Variety   For a non-associative algebra $A$ with a derivation $d$, its derived algebra\n$A^{(d)}$ is the same space equipped with new operations $a\\succ b = d(a)b$,\n$a\\prec b = ad(b)$, $a,b\\in A$. Given a variety ${\\rm Var}$ of algebras, its\nderived variety is generated by all derived algebras $A^{(d)}$ for all $A$ in\n${\\rm Var}$ and for all derivations $d$ of $A$. The same terminology is applied\nto binary operads governing varieties of non-associative algebras. For example,\nthe operad of Novikov algebras is the derived one for the operad of\n(associative) commutative algebras. We state a sufficient condition for every\nalgebra from a derived variety to be embeddable into an appropriate\ndifferential algebra of the corresponding variety. We also find that for ${\\rm\nVar} = {\\rm Zinb}$, the variety of Zinbiel algebras, there exist algebras from\nthe derived variety (which coincides with the class of pre-Novikov algebras)\nthat cannot be embedded into a Zinbiel algebra with a derivation.\n', 'Novikov algebras and their primitive ideals   The aim of this paper is to study the primitive ideals of Novikov algebras.\nIn terms of modular maximal right ideals, a characterization of the primitive\nideals of a Novikov algebra has been obtained. We prove a Chevalley-Jacobson\ndensity-type theorem for primitive Novikov algebras. We obtain some\nequivalences between prime, simple, and primitive Novikov algebras. We describe\na subalgebra of a Novikov algebra as a Novikov algebra of endomorphisms.\n', 'On quadratic Novikov algebras   A quadratic Novikov algebra is a Novikov algebra $(A, \\circ)$ with a\nsymmetric and nondegenerate bilinear form $B(\\cdot,\\cdot)$ satisfying $B(a\\circ\nb, c)=-B(b, a\\circ c+c\\circ a)$ for all $a$, $b$, $c\\in A$. This notion\nappeared in the theory of Novikov bialgebras. In this paper, we first\ninvestigate some properties of quadratic Novikov algebras and give a\ndecomposition theorem of quadratic Novikov algebras. Then we present a\nclassification of quadratic Novikov algebras of dimensions $2$ and $3$ over\n$\\mathbb{C}$ up to isomorphism. Finally, a construction of quadratic Novikov\nalgebras called double extension is presented and we show that any quadratic\nNovikov algebra containing a nonzero isotropic ideal can be obtained by double\nextensions. Based on double extension, an example of quadratic Novikov algebras\nof dimension 4 is given.\n']","[('novikov algebras', 0.8179489374160767), ('algebras associative algebras', 0.6548816561698914), ('zinbiel algebras', 0.6365542411804199), ('dimensional associative algebras', 0.632917582988739), ('associative algebras', 0.6126910448074341), ('algebras derived', 0.6126843690872192), ('non associative algebras', 0.6072324514389038), ('algebras obtained', 0.590986967086792), ('algebras describe', 0.5573858618736267), ('associative algebras associative', 0.5507645606994629)]"
641,641,48,641_isometric deformations_finite element formulation_finite element implementation_isogeometric analysis,"['isometric deformations', 'finite element formulation', 'finite element implementation', 'isogeometric analysis', 'elasticity', 'elastic', 'isogeometric', 'element formulation', 'thin shells', 'thin structures']","['An efficient displacement-based isogeometric formulation for\n  geometrically exact viscoelastic beams   We propose a novel approach to the linear viscoelastic problem of\nshear-deformable geometrically exact beams. The generalized Maxwell model for\none-dimensional solids is here efficiently extended to the case of arbitrarily\ncurved beams undergoing finite displacement and rotations. High efficiency is\nachieved by combining a series of distinguishing features, that are i) the\nformulation is displacement-based, therefore no additional unknowns, other than\nincremental displacements and rotations, are needed for the internal variables\nassociated with the rate-dependent material; ii) the governing equations are\ndiscretized in space using the isogeometric collocation method, meaning that\nelements integration is totally bypassed; iii) finite rotations are updated\nusing the incremental rotation vector, leading to two main benefits: minimum\nnumber of rotation unknowns (the three components of the incremental rotation\nvector) and no singularity problems; iv) the same $\\rm SO(3)$-consistent\nlinearization of the governing equations and update procedures as for\nnon-rate-dependent linear elastic material can be used; v) a standard\nsecond-order accurate time integration scheme is made consistent with the\nunderlying geometric structure of the kinematic problem. Moreover, taking full\nadvantage of the isogeometric analysis features, the formulation permits\naccurately representing beams and beam structures with highly complex initial\nshape and topology, paving the way for a large number of potential applications\nin the field of architectured materials, meta-materials, morphing/programmable\nobjects, topological optimizations, etc. Numerical applications are finally\npresented in order to demonstrate attributes and potentialities of the proposed\nformulation.\n', 'Fast and accurate elastic analysis of laminated composite plates via\n  isogeometric collocation and an equilibrium-based stress recovery approach   A novel approach which combines isogeometric collocation and an\nequilibrium-based stress recovery technique is applied to analyze laminated\ncomposite plates. Isogeometric collocation is an appealing strong form\nalternative to standard Galerkin approaches, able to achieve high order\nconvergence rates coupled with a significantly reduced computational cost.\nLaminated composite plates are herein conveniently modeled considering only one\nelement through the thickness with homogenized material properties. This\nguarantees accurate results in terms of displacements and in-plane stress\ncomponents. To recover an accurate out-of-plane stress state, equilibrium is\nimposed in strong form as a post-processing correction step, which requires the\nshape functions to be highly continuous. This continuity demand is fully\ngranted by isogeometric analysis properties, and excellent results are obtained\nusing a minimal number of collocation points per direction, particularly for\nincreasing values of length-to-thickness plate ratio and number of layers.\n', 'Unified high-order multi-scale method for mechanical behavior simulation\n  and strength prediction of composite plate and shell structures   The complicated mesoscopic configurations of composite plate and shell\nstructures requires a huge amount of computational overhead for directly\nsimulating their mechanical problems. In this paper, a unified high-order\nmulti-scale method, which can effectively simulate the mechanical behavior and\npredict yield strength of composite plates and shells, is developed. Firstly,\nthrough the multiscale asymptotic analysis of multi-scale elastic equations in\nthe orthogonal curvilinear coordinate system, a high-order multi-scale model is\nestablished, which can uniformly and effectively analyze the mechanical\nbehavior of composite plate and shell structures. Moreover, the error\nestimation of the high-order multi-scale solutions is derived. Then, combining\nwith the material strength theory, a high-order multi-scale model for the\nstrength prediction of composite plate and shell structures is established.\nNext, based on the established high-order multi-scale model, a multi-scale\nalgorithm is developed which can not only efficiently and accurately simulate\nthe mechanical behaviors of composite plate and shell structures, but also\npredict their yield strength. Finally, the effectiveness of the established\nhigh-order multi-scale method is verified by extensive numerical experiments.\nThe numerical experimental results indicate that the high-order multi-scale\nmethod can more accurately capture the meso-scale oscillatory behaviors of\ncomposite plate and shell structures. The unified high-order multi-scale method\nestablished in this paper is not only suitable for the prediction of mechanical\nproperties of composite plate and shell structures, but also can be further\nextended to the prediction of multi-field coupling properties of composite\nplate and shell structures.\n']","[('isometric deformations', 0.45764923095703125), ('finite element formulation', 0.4503491222858429), ('finite element implementation', 0.43359628319740295), ('isogeometric analysis', 0.4302140474319458), ('elasticity', 0.39450255036354065), ('elastic', 0.3767453134059906), ('isogeometric', 0.36888420581817627), ('element formulation', 0.3669884502887726), ('thin shells', 0.35813066363334656), ('thin structures', 0.3505023121833801)]"
642,642,48,642_moduli spaces curves_cycles moduli spaces_moduli space curves_moduli spaces,"['moduli spaces curves', 'cycles moduli spaces', 'moduli space curves', 'moduli spaces', 'tautological ring', 'moduli space mathcal', 'classes moduli space', 'tautological classes', 'moduli spaces stable', 'curves genus']","[""Logarithmic tautological rings of the moduli spaces of curves We define the logarithmic tautological rings of the moduli spaces of Deligne-Mumford stable curves (together with a set of additive generators lifting the decorated strata classes of the standard tautological rings). While these algebras are infinite dimensional, a connection to polyhedral combinatorics via a new theory of homological piecewise polynomials allows an effective study. A complete calculation is given in genus 0 via the algebra of piecewise polynomials on the cone stack of the associated Artin fan (lifting Keel's presentation of the Chow ring of $\\overline{\\mathcal{M}}_{0,n}$). Counterexamples to the simplest generalizations in genus 1 are presented. We show, however, that the structure of the log tautological rings is determined by the complete knowledge of all relations in the standard tautological rings of the moduli spaces of curves. In particular, Pixton's conjecture concerning relations in the standard tautological rings lifts to a complete conjecture for relations in the log tautological rings of the moduli spaces of curves. Several open questions are discussed.\n  We develop the entire theory of logarithmic tautological classes in the context of arbitrary smooth normal crossings pairs $(X,D)$ with explicit formulas for intersection products. As a special case, we give an explicit set of additive generators of the full logarithmic Chow ring of $(X,D)$ in terms of Chow classes on the strata of $X$ and piecewise polynomials on the cone stack."", 'On the Chow and cohomology rings of moduli spaces of stable curves   In this paper, we ask: for which $(g, n)$ is the rational Chow or cohomology\nring of $\\overline{\\mathcal{M}}_{g,n}$ generated by tautological classes? This\nquestion has been fully answered in genus $0$ by Keel (the Chow and cohomology\nrings are tautological for all $n$) and genus $1$ by Belorousski (the rings are\ntautological if and only if $n \\leq 10$). For $g \\geq 2$, work of van Zelm\nshows the Chow and cohomology rings are not tautological once $2g + n \\geq 24$,\nleaving finitely many open cases. Here, we prove that the Chow and cohomology\nrings of $\\overline{\\mathcal{M}}_{g,n}$ are isomorphic and generated by\ntautological classes for $g = 2$ and $n \\leq 9$ and for $3 \\leq g \\leq 7$ and\n$2g + n \\leq 14$. For such $(g, n)$, this implies that the tautological ring is\nGorenstein and $\\overline{\\mathcal{M}}_{g,n}$ has polynomial point count.\n', 'The H-tautological ring   We extend the theory of tautological classes on moduli spaces of stable\ncurves to the more general setting of moduli spaces of admissible Galois covers\nof curves, introducing the so-called H-tautological ring. The main new feature\nis the existence of restriction-corestriction morphisms remembering\nintermediate quotients of Galois covers, which are a rich source of new\nclasses. In particular, our new framework includes classes of Harris-Mumford\nadmissible covers on moduli spaces of curves, which are known in some (and\nspeculatively many more) examples to lie outside the usual tautological ring.\nWe give additive generators for the H-tautological ring and show that their\nintersections may be algorithmically computed, building on work of Schmitt-van\nZelm. As an application, we give a method for computing integrals of\nHarris-Mumford loci against tautological classes of complementary dimension,\nrecovering and giving a mild generalization of a recent quasi-modularity result\nof the author for covers of elliptic curves.\n']","[('moduli spaces curves', 0.617355227470398), ('cycles moduli spaces', 0.5926262140274048), ('moduli space curves', 0.5921061038970947), ('moduli spaces', 0.5677377581596375), ('tautological ring', 0.5574291944503784), ('moduli space mathcal', 0.5452510714530945), ('classes moduli space', 0.5432203412055969), ('tautological classes', 0.5414977073669434), ('moduli spaces stable', 0.5370203852653503), ('curves genus', 0.5263619422912598)]"
643,643,48,643_graph homology_graph complex_moduli spaces curves_cohomology moduli,"['graph homology', 'graph complex', 'moduli spaces curves', 'cohomology moduli', 'cohomology moduli spaces', 'moduli space curves', 'cohomology moduli space', 'weight cohomology', 'moduli spaces', 'supported cohomology']","['Weight 11 compactly supported cohomology of moduli spaces of curves   We study the weight 11 part of the compactly supported cohomology of the\nmoduli space of curves $M_{g,n}$, using graph complex techniques, with\nparticular attention to the case $n = 0$. As applications, we prove new\nnonvanishing results for the cohomology of $M_g$, and exponential growth with\n$g$, in a wide range of degrees.\n', ""Hairy graphs to ribbon graphs via a fixed source graph complex   We show that the hairy graph complex $(HGC_{n,n},d)$ appears as an associated\ngraded complex of the oriented graph complex $(OGC_{n+1},d)$, subject to the\nfiltration on the number of targets, or equivalently sources, called the fixed\nsource graph complex. The fixed source graph complex $(OGC_1,d_0)$ maps into\nthe ribbon graph complex $RGC$, which models the moduli space of Riemann\nsurfaces with marked points. The full differential $d$ on the oriented graph\ncomplex $OGC_{n+1}$ corresponds to the deformed differential $d+h$ on the hairy\ngraph complex $HGC_{n,n}$, where $h$ adds a hair. This deformed complex\n$(HGC_{n,n},d+h)$ is already known to be quasi-isomorphic to standard\nKontsevich's graph complex $GC^2_n$. This gives a new connection between the\nstandard and the oriented version of Kontsevich's graph complex.\n"", 'Oriented hairy graphs and moduli spaces of curves   We discuss a graph complex formed by directed acyclic graphs with external\nlegs. This complex comes in particular with a map to the ribbon graph complex\ncomputing the (compactly supported) cohomology of the moduli space of points\n$\\mathcal M_{g,n}$, extending an earlier result of Merkulov-Willwacher. It is\nfurthermore quasi-isomorphic to the hairy graph complex computing the weight 0\npart of the compactly supported cohomology of $\\mathcal{M}_{g,n}$ according to\nChan-Galatius-Payne. Hence we can naturally connect the works\nChan-Galatius-Payne and of Merkulov-Willwacher and the ribbon graph complex and\nobtain a fairly satisfying picture of how all the pieces and various graph\ncomplexes fit together, at least in weight zero.\n']","[('graph homology', 0.5695045590400696), ('graph complex', 0.523385226726532), ('moduli spaces curves', 0.519324779510498), ('cohomology moduli', 0.5177637338638306), ('cohomology moduli spaces', 0.5176759362220764), ('moduli space curves', 0.5149717330932617), ('cohomology moduli space', 0.5088376998901367), ('weight cohomology', 0.46872538328170776), ('moduli spaces', 0.44646593928337097), ('supported cohomology', 0.4440521001815796)]"
644,644,48,644_optimal stopping problems_optimal stopping_optimal stopping time_stopping problems,"['optimal stopping problems', 'optimal stopping', 'optimal stopping time', 'stopping problems', 'stopping times', 'stochastic control problems', 'stopping time', 'stochastic control', 'singular stochastic control', 'stopping']","['On the continuity of optimal stopping surfaces for jump-diffusions   We show that optimal stopping surfaces $(t,y)\\mapsto x_*(t,y)$ arising from\ntime-inhomogeneous optimal stopping problems on two-dimensional jump-diffusions\n$(X,Y)$ are continuous (jointly in time and space) under mild monotonicity and\nregularity assumptions of local nature.\n', 'Exact optimal stopping for multidimensional linear switching diffusions   The paper studies a class of multidimensional optimal stopping problems with\ninfinite horizon for linear switching diffusions. There are two main novelties\nin the optimal problems considered: the underlying stochastic process has\ndiscontinuous paths and the cost function is not necessarily integrable on the\nentire time horizon, where the latter is often a key assumption in classical\noptimal stopping theory for diffusions, cf. [22, Corollary 2.9]. Under\nrelatively mild conditions, we show, for the class of multidimensional optimal\nstopping problems under consideration, that the first entry time of the\nstopping region is an optimal stopping time. Further, we prove that the\ncorresponding optimal stopping boundaries can be represented as the unique\nsolution to a nonlinear integral equation. We conclude with an application of\nour results to the problem of quickest real-time detection of a Markovian\ndrift.\n', 'On the monotonicity of the stopping boundary for time-inhomogeneous\n  optimal stopping problems   We consider a class of time-inhomogeneous optimal stopping problems and we\nprovide sufficient conditions on the data of the problem that guarantee\nmonotonicity of the optimal stopping boundary. In our setting,\ntime-inhomogeneity stems not only from the reward function but, in particular,\nfrom the time dependence of the drift coefficient of the one-dimensional\nstochastic differential equation (SDE) which drives the stopping problem. In\norder to obtain our results, we mostly employ probabilistic arguments: we use a\ncomparison principle between solutions of the SDE computed at different\nstarting times, and martingale methods of optimal stopping theory. We also show\na variant of the main theorem, which weakens one of the assumptions and\nadditionally relies on the renowned connection between optimal stopping and\nfree-boundary problems.\n']","[('optimal stopping problems', 0.7586783170700073), ('optimal stopping', 0.7324041724205017), ('optimal stopping time', 0.7295541763305664), ('stopping problems', 0.5962411165237427), ('stopping times', 0.592441976070404), ('stochastic control problems', 0.5237237215042114), ('stopping time', 0.5132967233657837), ('stochastic control', 0.4982474446296692), ('singular stochastic control', 0.4735577702522278), ('stopping', 0.46595627069473267)]"
645,645,48,645_finite mixture models_mixture models_finite mixtures_finite mixture,"['finite mixture models', 'mixture models', 'finite mixtures', 'finite mixture', 'mixture components', 'process mixture', 'mixture distribution', 'mixtures', 'mixture', 'bayesian nonparametric']","[""Evidence estimation in finite and infinite mixture models and\n  applications   Estimating the model evidence - or mariginal likelihood of the data - is a\nnotoriously difficult task for finite and infinite mixture models and we\nreexamine here different Monte Carlo techniques advocated in the recent\nliterature, as well as novel approaches based on Geyer (1994) reverse logistic\nregression technique, Chib (1995) algorithm, and Sequential Monte Carlo (SMC).\nApplications are numerous. In particular, testing for the number of components\nin a finite mixture model or against the fit of a finite mixture model for a\ngiven dataset has long been and still is an issue of much interest, albeit yet\nmissing a fully satisfactory resolution. Using a Bayes factor to find the right\nnumber of components K in a finite mixture model is known to provide a\nconsistent procedure. We furthermore establish the consistence of the Bayes\nfactor when comparing a parametric family of finite mixtures against the\nnonparametric 'strongly identifiable' Dirichlet Process Mixture (DPM) model.\n"", 'Clustering consistency with Dirichlet process mixtures   Dirichlet process mixtures are flexible non-parametric models, particularly\nsuited to density estimation and probabilistic clustering. In this work we\nstudy the posterior distribution induced by Dirichlet process mixtures as the\nsample size increases, and more specifically focus on consistency for the\nunknown number of clusters when the observed data are generated from a finite\nmixture. Crucially, we consider the situation where a prior is placed on the\nconcentration parameter of the underlying Dirichlet process. Previous findings\nin the literature suggest that Dirichlet process mixtures are typically not\nconsistent for the number of clusters if the concentration parameter is held\nfixed and data come from a finite mixture. Here we show that consistency for\nthe number of clusters can be achieved if the concentration parameter is\nadapted in a fully Bayesian way, as commonly done in practice. Our results are\nderived for data coming from a class of finite mixtures, with mild assumptions\non the prior for the concentration parameter and for a variety of choices of\nlikelihood kernels for the mixture.\n', 'Bayesian mixture models (in)consistency for the number of clusters   Bayesian nonparametric mixture models are common for modeling complex data.\nWhile these models are well-suited for density estimation, recent results\nproved posterior inconsistency of the number of clusters when the true number\nof components is finite, for the Dirichlet process and Pitman--Yor process\nmixture models. We extend these results to additional Bayesian nonparametric\npriors such as Gibbs-type processes and finite-dimensional representations\nthereof. The latter include the Dirichlet multinomial process, the recently\nproposed Pitman-Yor, and normalized generalized gamma multinomial processes. We\nshow that mixture models based on these processes are also inconsistent in the\nnumber of clusters and discuss possible solutions. Notably, we show that a\npost-processing algorithm introduced for the Dirichlet process can be extended\nto more general models and provides a consistent method to estimate the number\nof components.\n']","[('finite mixture models', 0.7649624347686768), ('mixture models', 0.7097166180610657), ('finite mixtures', 0.6440296769142151), ('finite mixture', 0.6124605536460876), ('mixture components', 0.5371478796005249), ('process mixture', 0.5222703218460083), ('mixture distribution', 0.5168867707252502), ('mixtures', 0.5009558200836182), ('mixture', 0.49402764439582825), ('bayesian nonparametric', 0.4731227159500122)]"
646,646,48,646_solutions critical regularity_global well posedness_local well posedness_critical sobolev space,"['solutions critical regularity', 'global well posedness', 'local well posedness', 'critical sobolev space', 'muskat', 'viscosities', 'critical sobolev', 'viscosity', 'invariant sobolev', 'posedness']","['Global well-posedness for the three dimensional Muskat problem in the\n  critical Sobolev space   We prove that the 3D stable Muskat problem is globally well-posed in the\ncritical Sobolev space $\\dot H^2 \\cap \\dot W^{1,\\infty}$ provided that the\nsemi-norm $\\Vert f_0 \\Vert_{\\dot H^{2}}$ is small enough. Consequently, this\nallows the Lipschitz semi-norm to be arbitrarily large. The proof is based on a\nnew formulation of the 3D Muskat problem that allows to capture the hidden\noscillatory nature of the problem. The latter formulation allows to prove the\n$\\dot H^{2}$ {\\emph{a priori}} estimates. In the literature, all the known\nglobal existence results for the 3D Muskat problem are for small slopes (less\nthan 1). This is the first arbitrary large slope theorem for the 3D stable\nMuskat problem.\n', 'The vanishing surface tension limit of the Muskat problem   The Muskat problem, in its general setting, concerns the interface evolution\nbetween two incompressible fluids of different densities and viscosities in\nporous media. The interface motion is driven by gravity and capillarity forces,\nwhere the latter is due to surface tension. To leading order, both the Muskat\nproblems with and without surface tension effect are scaling invariant in the\nSobolev space $H^{1+\\frac{d}{2}}(\\mathbb{R}^d)$, where $d$ is the dimension of\nthe interface. We prove that for any subcritical data satisfying the\nRayleigh-Taylor condition, solutions of the Muskat problem with surface tension\n$\\frak{s}$ converge to the unique solution of the Muskat problem without\nsurface tension locally in time with the rate $\\sqrt{\\frak{s}}$ when\n$\\frak{s}\\to 0$. This allows for initial interfaces that have unbounded or even\nnot locally square integrable curvature. If in addition the initial curvature\nis square integrable, we obtain the convergence with optimal rate $\\frak{s}$.\n', 'Regularity of solutions to the Muskat equation   In this paper, we show that if a solution to the Muskat problem in the case\nof different densities and the same viscosity is sufficiently smooth, then it\nmust be analytic except at the points where a turnover of the fluids happens.\n']","[('solutions critical regularity', 0.5123879313468933), ('global well posedness', 0.5032236576080322), ('local well posedness', 0.4764489531517029), ('critical sobolev space', 0.43991535902023315), ('muskat', 0.4362015724182129), ('viscosities', 0.4263180196285248), ('critical sobolev', 0.4258410930633545), ('viscosity', 0.41092169284820557), ('invariant sobolev', 0.40665072202682495), ('posedness', 0.3878284990787506)]"
647,647,48,647_gradient estimates positive_emery ricci curvature_riemannian manifolds nonnegative_manifolds nonnegative ricci,"['gradient estimates positive', 'emery ricci curvature', 'riemannian manifolds nonnegative', 'manifolds nonnegative ricci', 'gradient estimates nonlinear', 'equations riemannian manifolds', 'type gradient estimate', 'gradient estimates', 'curvature conditions', 'equations riemannian']","[""Gradient estimates for nonlinear elliptic equations involving the Witten\n  Laplacian on smooth metric measure spaces and implications   This article presents new local and global gradient estimates of Li-Yau type\nfor positive solutions to a class of nonlinear elliptic equations on smooth\nmetric measure spaces involving the Witten Laplacian. The estimates are derived\nunder natural lower bounds on the associated Bakry-\\'Emery Ricci curvature\ntensor and find utility in proving general Harnack inequalities and\nLiouville-type theorems to mention a few. The results here unify, extend and\nimprove various existing results in the literature for special nonlinearities\nalready of huge interest and applications. Some important consequences are\npresented and discussed.\n"", ""Souplet-Zhang and Hamilton type gradient estimates for nonlinear\n  elliptic equations on smooth metric measure spaces   In this article we present new gradient estimates for positive solutions to a\nclass of nonlinear elliptic equations involving the f-Laplacian on a smooth\nmetric measure space. The gradient estimates of interest are of Souplet-Zhang\nand Hamilton types respectively and are established under natural lower bounds\non the generalised Bakry-\\'Emery Ricci curvature tensor. From these estimates\nwe derive amongst other things Harnack inequalities and general global\nconstancy and Liouville-type theorems. The results and approach undertaken here\nprovide a unified treatment and extend and improve various existing results in\nthe literature. Some implications and applications are presented and discussed.\n"", 'Some gradient estimates for nonlinear heat-type equations on smooth\n  metric measure spaces with compact boundary   In this paper we prove some Hamilton type and Li-Yau type gradient estimates\non positive solutions to generalized nonlinear parabolic equations on smooth\nmetric measure space with compact boundary. The geometry of the space in terms\nof lower bounds on the weighted Bakry-Emery Ricci curvature tensor and weighted\nmean curvature of the boundary are key in proving generalized local and global\ngradient estimates. Various applications of these gradient estimates in terms\nof parabolic Harnack inequalities and Liouville type results are discussed.\nFurther consequences to some specific models informed by the nature of the\nnonlinearities are highlighted.\n']","[('gradient estimates positive', 0.5724435448646545), ('emery ricci curvature', 0.557473361492157), ('riemannian manifolds nonnegative', 0.5491749048233032), ('manifolds nonnegative ricci', 0.5454241037368774), ('gradient estimates nonlinear', 0.5448678731918335), ('equations riemannian manifolds', 0.5429112315177917), ('type gradient estimate', 0.5013286471366882), ('gradient estimates', 0.4995534420013428), ('curvature conditions', 0.49858906865119934), ('equations riemannian', 0.49735406041145325)]"
648,648,48,648_string amplitudes_string theory_selberg integrals_superstring theory,"['string amplitudes', 'string theory', 'selberg integrals', 'superstring theory', 'modular forms', 'amplitudes', 'eisenstein series', 'holomorphic modular forms', 'modular invariant', 'scattering amplitudes']","[""Integrating three-loop modular graph functions and transcendentality of\n  string amplitudes   Modular graph functions (MGFs) are $\\mathrm{SL}(2,\\mathbb{Z})$-invariant\nfunctions on the Poincar\\'e upper half-plane associated with Feynman graphs of\na conformal scalar field on a torus. The low-energy expansion of genus-one\nsuperstring amplitudes involves suitably regularized integrals of MGFs over the\nfundamental domain for $\\mathrm{SL}(2,\\mathbb{Z})$. In earlier work, these\nintegrals were evaluated for all MGFs up to two loops and for higher loops up\nto weight six. These results led to the conjectured uniform transcendentality\nof the genus-one four-graviton amplitude in Type II superstring theory. In this\npaper, we explicitly evaluate the integrals of several infinite families of\nthree-loop MGFs and investigate their transcendental structure. Up to weight\nseven, the structure of the integral of each individual MGF is consistent with\nthe uniform transcendentality of string amplitudes. Starting at weight eight,\nthe transcendental weights obtained for the integrals of individual MGFs are no\nlonger consistent with the uniform transcendentality of string amplitudes.\nHowever, in all the cases we examine, the violations of uniform\ntranscendentality take on a special form given by the integrals of triple\nproducts of non-holomorphic Eisenstein series. If Type II superstring\namplitudes do exhibit uniform transcendentality, then the special combinations\nof MGFs which enter the amplitudes must be such that these integrals of triple\nproducts of Eisenstein series precisely cancel one another. Whether this indeed\nis the case poses a novel challenge to the conjectured uniform\ntranscendentality of genus-one string amplitudes.\n"", 'Single-valued integration and superstring amplitudes in genus zero   We study open and closed string amplitudes at tree-level in string\nperturbation theory using the methods of single-valued integration which were\ndeveloped in the prequel to this paper. Using dihedral coordinates on the\nmoduli spaces of curves of genus zero with marked points, we define a canonical\nregularisation of both open and closed string perturbation amplitudes at tree\nlevel, and deduce that they admit a Laurent expansion in Mandelstam variables\nwhose coefficients are multiple zeta values (resp. single-valued multiple zeta\nvalues). Furthermore, we prove the existence of a motivic Laurent expansion\nwhose image under the period map is the open string expansion, and whose image\nunder the single-valued period map is the closed string expansion. This proves\nthe recent conjecture of Stieberger that closed string amplitudes are the\nsingle-valued projections of (motivic lifts of) open string amplitudes.\n  Finally, applying a variant of the single-valued formalism for cohomology\nwith coefficients yields the KLT formula expressing closed string amplitudes as\nquadratic expressions in open string amplitudes.\n', 'Modular Graph Forms and Scattering Amplitudes in String Theory   In this thesis, we investigate the low-energy expansion of scattering\namplitudes of closed strings at one-loop level (i.e. at genus one) in a\nten-dimensional Minkowski background using a special class of functions called\nmodular graph forms. These allow for a systematic evaluation of the low-energy\nexpansion and satisfy many non-trivial algebraic and differential relations. We\nstudy these relations in detail, leading to basis decompositions for a large\nnumber of modular graph forms which greatly reduce the complexity of the\nexpansions of the integrals appearing in the amplitude. One of the results of\nthis thesis is a Mathematica package which automatizes these simplifications.\nWe use these techniques to compute the leading low-energy orders of the\nscattering amplitude of four gluons in the heterotic string at one-loop level.\n  Furthermore, we study a generating function which conjecturally contains the\ntorus integrals of all perturbative closed-string theories. We write this\ngenerating function in terms of iterated integrals of holomorphic Eisenstein\nseries and use this approach to arrive at a more rigorous characterization of\nthe space of modular graph forms than was possible before.\n  For tree-level string amplitudes, the single-valued map of multiple zeta\nvalues maps open-string amplitudes to closed-string amplitudes. The definition\nof a suitable one-loop generalization, a so-called elliptic single-valued map,\nis an active area of research and we provide a new perspective on this topic\nusing our generating function of torus integrals.\n  The original version of this thesis, as submitted in June 2020 to the\nHumboldt University Berlin, is available under the DOI 10.18452/21829. The\npresent text contains minor updates compared to this version, reflecting\nfurther developments in the literature, in particular concerning the\nconstruction of an elliptic single-valued map.\n']","[('string amplitudes', 0.5842167735099792), ('string theory', 0.5353040099143982), ('selberg integrals', 0.4911847710609436), ('superstring theory', 0.466799795627594), ('modular forms', 0.4596395790576935), ('amplitudes', 0.4548826217651367), ('eisenstein series', 0.43109026551246643), ('holomorphic modular forms', 0.42609816789627075), ('modular invariant', 0.4138498306274414), ('scattering amplitudes', 0.4048449397087097)]"
649,649,48,649_finite element methods_multiscale methods_multiscale finite element_multiscale basis functions,"['finite element methods', 'multiscale methods', 'multiscale finite element', 'multiscale basis functions', 'multiscale pdes', 'multiscale basis', 'multiscale problems', 'generalized multiscale finite', 'heterogeneous multiscale', 'generalized multiscale']","['Iterative Oversampling Technique for Constraint Energy Minimizing\n  Generalized Multiscale Finite Element Method in the Mixed Formulation   In this paper, we develop an iterative scheme to construct multiscale basis\nfunctions within the framework of the Constraint Energy Minimizing Generalized\nMultiscale Finite Element Method (CEM-GMsFEM) for the mixed formulation. The\niterative procedure starts with the construction of an energy minimizing\nsnapshot space that can be used for approximating the solution of the model\nproblem. A spectral decomposition is then performed on the snapshot space to\nform global multiscale space. Under this setting, each global multiscale basis\nfunction can be split into a non-decaying and a decaying parts. The\nnon-decaying part of a global basis is localized and it is fixed during the\niteration. Then, one can approximate the decaying part via a modified\nRichardson scheme with an appropriately defined preconditioner. Using this set\nof iterative-based multiscale basis functions, first-order convergence with\nrespect to the coarse mesh size can be shown if sufficiently many times of\niterations with regularization parameter being in an appropriate range are\nperformed. Numerical results are presented to illustrate the effectiveness and\nefficiency of the proposed computational multiscale method.\n', 'An iterative constraint energy minimizing generalized multiscale finite\n  element method for contact problem   This work presents an Iterative Constraint Energy Minimizing Generalized\nMultiscale Finite Element Method (ICEM-GMsFEM) for solving the contact problem\nwith high contrast coefficients. The model problem can be characterized by a\nvariational inequality, where we add a penalty term to convert this problem\ninto a non-smooth and non-linear unconstrained minimizing problem. The\ncharacterization of the minimizer satisfies the variational form of a mixed\nDirilect-Neumann-Robin boundary value problem. So we apply CEM-GMsFEM\niteratively and introduce special boundary correctors along with multiscale\nspaces to achieve an optimal convergence rate. Numerical results are conducted\nfor different highly heterogeneous permeability fields, validating the fast\nconvergence of the CEM-GMsFEM iteration in handling the contact boundary and\nillustrating the stability of the proposed method with different sets of\nparameters. We also prove the fast convergence of the proposed iterative\nCEM-GMsFEM method and provide an error estimate of the multiscale solution\nunder a mild assumption.\n', 'Constraint energy minimizing generalized multiscale finite element\n  method for convection diffusion equation   In this paper we present and analyze a constraint energy minimizing\ngeneralized multiscale finite element method for convection diffusion equation.\nTo define the multiscale basis functions, we first build an auxiliary\nmultiscale space by solving local spectral problems motivated by analysis. Then\nconstraint energy minimization performed in oversampling domains is exploited\nto construct the multiscale space. The resulting multiscale basis functions\nhave a good decay property even for high contrast diffusion and convection\ncoefficients. Furthermore, if the number of oversampling layer is chosen\nproperly, we can prove that the convergence rate is proportional to the coarse\nmesh size. Our analysis also indicates that the size of the oversampling domain\nweakly depends on the contrast of the heterogeneous coefficients. Several\nnumerical experiments are presented illustrating the performances of our\nmethod.\n']","[('finite element methods', 0.5890632271766663), ('multiscale methods', 0.583855926990509), ('multiscale finite element', 0.563180685043335), ('multiscale basis functions', 0.5604422092437744), ('multiscale pdes', 0.5568943619728088), ('multiscale basis', 0.5313199162483215), ('multiscale problems', 0.5289488434791565), ('generalized multiscale finite', 0.4912639260292053), ('heterogeneous multiscale', 0.4824080169200897), ('generalized multiscale', 0.48219993710517883)]"
650,650,47,650_dedekind domains_noetherian domains_dedekind domain_valuation rings,"['dedekind domains', 'noetherian domains', 'dedekind domain', 'valuation rings', 'maximal ideals', 'noetherian domain', 'local rings', 'noetherian rings', 'associated prime ideals', 'minimal prime ideals']","['Revisiting G-Dedekind domains   Let $R$ be an integral domain with $qf(R)=K$ and let $F(R)$ be the set of\nnonzero fractional ideals of $R.$ Call $R$ a dually compact domain (DCD) if for\neach $I\\in F(R)$ the ideal $I_{v}=(I^{-1})^{-1}$ is a finite intersection of\nprincipal fractional ideals. We characterize DCDs and show that the class of\nDCDs properly contains various classes of integral domains, such as Noetherian,\nMori and Krull domains. In addition we show that a Schreier DCD is a GCD domain\nwith the property that for each $A\\in F(R)$ the ideal $A_{v}$ is principal. We\nshow that a domain $R$ is G-Dedekind domain (i.e. has the property that $A_{v}$\nis invertible for each $A\\in F(R)$) if and only if $R$ is a DCD satisfying the\nproperty $\\ast :$ for all pairs of subsets\n$\\{a_{1},...,a_{m}\\},\\{b_{1},...b_{n}\\}\\subseteq K\\backslash \\{0\\},$ $(\\cap\n_{i=1}^{m}(a_{i})(\\cap _{j=1}^{n}(b_{j}))=\\cap _{i,j=1}^{m,n}a_{i}b_{j}$. We\ndiscuss what the appropriate name for G-Dedekind domains and related notions\nshould be. We also make some observations about how the DCDs behave under\nlocalizations and polynomial ring extensions.\n', 'Constructing Noncatenary Quasi-Excellent Precompletions   Let $T$ be a local (Noetherian) ring and let $Q_1$ and $Q_2$ be prime ideals\nof $T$. We find sufficient conditions for there to exist a quasi-excellent\nlocal subring $B$ of $T$ satisfying the following conditions: (1) the\ncompletion of $B$ at its maximal ideal is isomorphic to the completion of $T$\nat its maximal ideal, (2) $B \\cap Q_1 = B \\cap Q_2$, (3) the set of prime\nideals of $T/(Q_1 \\cap Q_2)$ of positive height is the same as the set of prime\nideals of $B/(B \\cap Q_1)$ of positive height when viewed as partially ordered\nsets, and (4) for $i = 1$ and for $i = 2$, there is a coheight preserving\nbijection between the minimal prime ideals of $T_{Q_i}$ and the minimal prime\nideals of $B_{B \\cap Q_1}$. Intuitively, this means that $T$ contains a\nquasi-excellent local subring in which $Q_1$ and $Q_2$ are ""glued together"" and\nsuch that both the completion and desirable properties of the prime spectrum\nare preserved. We use this result to show that certain complete local rings are\nthe completion of a quasi-excellent local ring whose prime spectrum, when\nviewed as a partially ordered set, contains interesting noncatenary finite\nsubsets.\n', 'Boundness in almost Dedekind domains   We study different form of boundness for ideals of almost Dedekind domains,\ngeneralizing the notions of critical ideals, radical factorization, and\nSP-domains. We show that every almost Dedekind domain has at least one\nnoncritical maximal ideals and, indeed, the set of noncritical maximal ideals\nis dense in the maximal space, with respect to the constructible topology; as a\nconsequence, we show that every almost Dedekind domain is SP-scattered, and in\nparticular that the group $\\mathrm{Inv}(D)$ of invertible ideals of an almost\nDedekind domain $D$ is always free. If $D$ is an almost Dedekind domain with\nnonzero Jacobson radical, we also show that there is at least one element whose\nideal function is bounded.\n']","[('dedekind domains', 0.6730853915214539), ('noetherian domains', 0.6150155067443848), ('dedekind domain', 0.6040382385253906), ('valuation rings', 0.5932872295379639), ('maximal ideals', 0.5797446966171265), ('noetherian domain', 0.5792582631111145), ('local rings', 0.5577030777931213), ('noetherian rings', 0.5438986420631409), ('associated prime ideals', 0.5276409387588501), ('minimal prime ideals', 0.5226598978042603)]"
651,651,47,651_clifford algebras_clifford algebra_clifford geometric_geometric algebras,"['clifford algebras', 'clifford algebra', 'clifford geometric', 'geometric algebras', 'geometric algebra', 'algebras arbitrary dimension', 'clifford', 'quaternions', 'heisenberg algebra', 'algebras arbitrary']","[""Development of the Method of Averaging in Clifford Geometric Algebras   We develop the method of averaging in Clifford (geometric) algebras suggested\nby the author in previous papers. We consider operators constructed using two\ndifferent sets of anticommuting elements of real or complexified Clifford\nalgebras. These operators generalize Reynolds operators from the representation\ntheory of finite groups. We prove a number of new properties of these\noperators. Using the generalized Reynolds operators, we give a complete proof\nof the generalization of Pauli's theorem to the case of Clifford algebras of\narbitrary dimension. The results can be used in geometry, physics, engineering,\ncomputer science, and other applications.\n"", 'Algorithmic computation of multivector inverses and characteristic\n  polynomials in non-degenerate Clifford algebras   The power of Clifford or, geometric, algebra lies in its ability to represent\ngeometric operations in a concise and elegant manner. Clifford algebras provide\nthe natural generalizations of complex, dual numbers and quaternions into\nnon-commutative multivectors. The paper demonstrates an algorithm for the\ncomputation of inverses of such numbers in a non-degenerate Clifford algebra of\nan arbitrary dimension. The algorithm is a variation of the\nFaddeev-LeVerrier-Souriau algorithm and is implemented in the open-source\nComputer Algebra System Maxima. Symbolic and numerical examples in different\nClifford algebras are presented.\n', 'On computing the determinant, other characteristic polynomial\n  coefficients, and inverse in Clifford algebras of arbitrary dimension   In this paper, we solve the problem of computing the inverse in Clifford\nalgebras of arbitrary dimension. We present basis-free formulas of different\ntypes (explicit and recursive) for the determinant, other characteristic\npolynomial coefficients, adjugate, and inverse in real Clifford algebras (or\ngeometric algebras) over vector spaces of arbitrary dimension $n$. The formulas\ninvolve only the operations of multiplication, summation, and operations of\nconjugation without explicit use of matrix representation. We use methods of\nClifford algebras (including the method of quaternion typification proposed by\nthe author in previous papers and the method of operations of conjugation of\nspecial type presented in this paper) and generalizations of numerical methods\nof matrix theory (the Faddeev-LeVerrier algorithm based on the Cayley-Hamilton\ntheorem; the method of calculating the characteristic polynomial coefficients\nusing Bell polynomials) to the case of Clifford algebras in this paper. We\npresent the construction of operations of conjugation of special type and study\nrelations between these operations and the projection operations onto fixed\nsubspaces of Clifford algebras. We use this construction in the analytical\nproof of formulas for the determinant, other characteristic polynomial\ncoefficients, adjugate, and inverse in Clifford algebras. The basis-free\nformulas for the inverse give us basis-free solutions to linear algebraic\nequations, which are widely used in computer science, image and signal\nprocessing, physics, engineering, control theory, etc. The results of this\npaper can be used in symbolic computation.\n']","[('clifford algebras', 0.8155835270881653), ('clifford algebra', 0.7903597950935364), ('clifford geometric', 0.7011298537254333), ('geometric algebras', 0.6247924566268921), ('geometric algebra', 0.5542518496513367), ('algebras arbitrary dimension', 0.5370621085166931), ('clifford', 0.5250276923179626), ('quaternions', 0.5174680352210999), ('heisenberg algebra', 0.44475841522216797), ('algebras arbitrary', 0.433689683675766)]"
652,652,47,652_factor models_factor analysis_matrix factor_decomposition factor,"['factor models', 'factor analysis', 'matrix factor', 'decomposition factor', 'principal components analysis', 'principal component analysis', 'latent factors', 'factors factor', 'high dimensional factor', 'component analysis pca']","[""Factor Strength Estimation in Vector and Matrix Time Series Factor\n  Models   Most factor modelling research in vector or matrix-valued time series assume\nall factors are pervasive/strong and leave weaker factors and their\ncorresponding series to the noise. Weaker factors can in fact be important to a\ngroup of observed variables, for instance a sector factor in a large portfolio\nof stocks may only affect particular sectors, but can be important both in\ninterpretations and predictions for those stocks. While more recent factor\nmodelling researches do consider ``local'' factors which are weak factors with\nsparse corresponding factor loadings, there are real data examples in the\nliterature where factors are weak because of weak influence on most/all\nobserved variables, so that the corresponding factor loadings are not sparse\n(non-local). As a first in the literature, we propose estimators of factor\nstrengths for both local and non-local weak factors, and prove their\nconsistency with rates of convergence spelt out for both vector and\nmatrix-valued time series factor models. Factor strength has an important\nindication in what estimation procedure of factor models to follow, as well as\nthe estimation accuracy of various estimators (Chen and Lam, 2024). Simulation\nresults show that our estimators have good performance in recovering the true\nfactor strengths, and an analysis on the NYC taxi traffic data indicates the\nexistence of weak factors in the data which may not be localized.\n"", ""Statistical properties of matrix decomposition factor analysis Numerous estimators have been proposed for factor analysis, and their statistical properties have been extensively studied. In the early 2000s, a novel matrix factorization-based approach, known as Matrix Decomposition Factor Analysis (MDFA), was introduced and has been actively developed in computational statistics. The MDFA estimator offers several advantages, including the guarantee of proper solutions (i.e., no Heywood cases) and the extensibility to $\\ell_0$-sparse estimation. However, the MDFA estimator does not appear to be formulated as a classical M-estimator or a minimum discrepancy function estimator. and the statistical properties of the MDFA estimator have remained largely unexplored. Although the MDFA estimator minimizes a loss function resembling that of principal component analysis (PCA), it empirically behaves more like consistent estimators used in factor analysis than like PCA itself. This raises a fundamental question: Can matrix decomposition factor analysis truly be regarded as ``factor analysis''? To address this problem, we establish the consistency and asymptotic normality of the MDFA estimator. Notably, the MDFA estimator can be formulated as a semiparametric profile likelihood estimator, and we derive the explicit form of the profile likelihood. Surprisingly, we discover that the profile likelihood is the squared Bures-Wasserstein distance between the sample covariance matrix and the modeled covariance matrix. Thus, the MDFA estimator is finally a minimum discrepancy function estimator in factor analysis, and we can easily extend MDFA for structural equation modeling (SEM). Numerical experiments demonstrate that MDFA performs competitively with other established estimators, suggesting it is a theoretically grounded and computationally appealing alternative for factor analysis."", 'Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A\n  Critical Review   We review Quasi Maximum Likelihood estimation of factor models for\nhigh-dimensional panels of time series. We consider two cases: (1) estimation\nwhen no dynamic model for the factors is specified (Bai and Li, 2012, 2016);\n(2) estimation based on the Kalman smoother and the Expectation Maximization\nalgorithm thus allowing to model explicitly the factor dynamics (Doz et al.,\n2012, Barigozzi and Luciani, 2019). Our interest is in approximate factor\nmodels, i.e., when we allow for the idiosyncratic components to be mildly\ncross-sectionally, as well as serially, correlated. Although such setting\napparently makes estimation harder, we show, in fact, that factor models do not\nsuffer of the {\\it curse of dimensionality} problem, but instead they enjoy a\n{\\it blessing of dimensionality} property. In particular, given an approximate\nfactor structure, if the cross-sectional dimension of the data, $N$, grows to\ninfinity, we show that: (i) identification of the model is still possible, (ii)\nthe mis-specification error due to the use of an exact factor model\nlog-likelihood vanishes. Moreover, if we let also the sample size, $T$, grow to\ninfinity, we can also consistently estimate all parameters of the model and\nmake inference. The same is true for estimation of the latent factors which can\nbe carried out by weighted least-squares, linear projection, or Kalman\nfiltering/smoothing. We also compare the approaches presented with: Principal\nComponent analysis and the classical, fixed $N$, exact Maximum Likelihood\napproach. We conclude with a discussion on efficiency of the considered\nestimators.\n']","[('factor models', 0.5944709777832031), ('factor analysis', 0.4926369786262512), ('matrix factor', 0.48232969641685486), ('decomposition factor', 0.4792507290840149), ('principal components analysis', 0.476398229598999), ('principal component analysis', 0.4733233153820038), ('latent factors', 0.4731725752353668), ('factors factor', 0.4594159424304962), ('high dimensional factor', 0.45731741189956665), ('component analysis pca', 0.443287193775177)]"
653,653,47,653_greedy basis_weak greedy_greedy algorithms_greedy approximation,"['greedy basis', 'weak greedy', 'greedy algorithms', 'greedy approximation', 'greedy type', 'variants greedy', 'greedy', 'chebyshev greedy', 'bases quasi', 'bases banach spaces']","['Weak weight-semi-greedy Markushevich bases   We introduce and study the notion of weak weight-semi-greedy Markushevich\nbases - which extends the concepts of weight semi-greedy and weak semi-greedy\nMarkushevich bases. In particular, we study conditions under which such bases\nare weight almost greedy. We also define the notion of weak weight almost\ngreedy bases, and prove that this formally weaker concept is equivalent to that\nconcept of weight almost greedy bases. Finally, we study some parameters\ninvolving the weak thresholding and Chebyshevian greedy algorithms.\n', 'Performance of the Thresholding Greedy Algorithm with Larger Greedy Sums   The goal of this paper is to study the performance of the Thresholding Greedy\nAlgorithm (TGA) when we increase the size of greedy sums by a constant factor\n$\\lambda\\geqslant 1$. We introduce the so-called $\\lambda$-almost greedy and\n$\\lambda$-partially greedy bases. The case when $\\lambda = 1$ gives us the\nclassical definitions of almost greedy and (strong) partially greedy bases. We\nshow that a basis is almost greedy if and only if it is $\\lambda$-almost greedy\nfor all (some) $\\lambda \\geqslant 1$. However, for each $\\lambda > 1$, there\nexists an unconditional basis that is $\\lambda$-partially greedy but is not\n$1$-partially greedy. Furthermore, we investigate and give examples when a\nbasis is\n  1. not almost greedy with constant $1$ but is $\\lambda$-almost greedy with\nconstant $1$ for some $\\lambda > 1$, and\n  2. not strong partially greedy with constant $1$ but is $\\lambda$-partially\ngreedy with constant $1$ for some $\\lambda > 1$.\n  Finally, we prove various characterizations of different greedy-type bases.\n', 'Bidemocratic bases and their connections with other greedy-type bases   In nonlinear greedy approximation theory, bidemocratic bases have\ntraditionally played the role of dualizing democratic, greedy, quasi-greedy, or\nalmost greedy bases. In this article we shift the viewpoint and study them for\ntheir own sake, just as we would with any other kind of greedy-type bases. In\nparticular we show that bidemocratic bases need not be quasi-greedy, despite\nthe fact that they retain a strong unconditionality flavor which brings them\nvery close to being quasi-greedy. Our constructive approach gives that for each\n$1<p<\\infty$ the space $\\ell_p$ has a bidemocratic basis which is not\nquasi-greedy. We also present a novel method for constructing conditional\nquasi-greedy bases which are bidemocratic, and provide a characterization of\nbidemocratic bases in terms of the new concepts of truncation quasi-greediness\nand partially democratic bases.\n']","[('greedy basis', 0.6815626621246338), ('weak greedy', 0.675078272819519), ('greedy algorithms', 0.6226357817649841), ('greedy approximation', 0.6185528039932251), ('greedy type', 0.5670069456100464), ('variants greedy', 0.5464649796485901), ('greedy', 0.5182775855064392), ('chebyshev greedy', 0.4853537380695343), ('bases quasi', 0.4631064832210541), ('bases banach spaces', 0.45016881823539734)]"
654,654,47,654_gas flow_gas flows_flow gas_simulation optimization,"['gas flow', 'gas flows', 'flow gas', 'simulation optimization', 'flow networks', 'pipelines', 'pipeline', 'flow dynamics', 'nonlinear program', 'gas power']","['Modeling Gas Flow Directions as State Variables: Does it Provide More\n  Flexibility to Power Systems?   As a common practice, the direction of natural gas flow in every pipeline is\ndetermined ex-ante for simplification purposes, and treated as a given\nparameter within the scheduling problem. However, in integrated gas and\nelectric power networks with a large share of intermittent renewable power\nsupply, it is no longer straightforward to optimally predetermine the gas flow\ndirections. A wrong predetermination of gas flow directions may result in\nfeasible but not necessarily optimal schedules. We propose a mixed-integer\nlinear optimization model to determine the optimal gas flow directions while\nscheduling the system. This unlocks additional flexibility to power systems,\nprovided that a tight coordination between power and gas systems exists. The\nincreased flexibility, although it comes at the cost of increased computational\ncomplexity, is quantified by comparing the total operational cost of the entire\nsystem with bidirectional gas flows as opposed to unidirectional gas flows. We\nnumerically show that modeling gas flow directions as state variables may bring\nadded value not only in the meshed but also in the radial gas networks.\n', 'Modeling and Optimization of Steady Flow of Natural Gas and Hydrogen\n  Mixtures in Pipeline Networks   We extend the canonical problems of simulation and optimization of\nsteady-state gas flows in pipeline networks with compressors to the transport\nof mixtures of highly heterogeneous gases injected throughout a network. Our\nstudy is motivated by proposed projects to blend hydrogen generated using clean\nenergy into existing natural gas pipeline systems as part of efforts to reduce\nthe reliance of energy systems on fossil fuels. Flow in a pipe is related to\nendpoint pressures by a basic Weymouth equation model, with an ideal gas\nequation of state, where the wave speed depends on the hydrogen concentration.\nAt vertices, in addition to mass balance, we also consider mixing of incoming\nflows of varying hydrogen concentrations. The problems of interest are the\nheterogeneous gas flow simulation (HGFS), which determines system pressures and\nflows given fixed boundary conditions and compressor settings, as well as the\nheterogeneous gas flow optimization (HGFO), which extremizes an objective by\ndetermining optimal boundary conditions and compressor settings. We examine\nconditions for uniqueness of solutions to the HGFS, as well as compare and\ncontrast mixed-integer and continuous nonlinear programming formulations for\nthe HGFO. We develop computational methods to solve both problems, and examine\ntheir performance using four test networks of increasing complexity.\n', 'Relaxations of the Steady Optimal Gas Flow Problem for a Non-Ideal Gas   Natural gas ranks second in consumption among primary energy sources in the\nUnited States. The majority of production sites are in remote locations, hence\nnatural gas needs to be transported through a pipeline network equipped with a\nvariety of physical components such as compressors, valves, etc. Thus, from the\npoint of view of both economics and reliability, it is desirable to achieve\noptimal transportation of natural gas using these pipeline networks. The\nphysics that governs the flow of natural gas through various components in a\npipeline network is governed by nonlinear and non-convex equality and\ninequality constraints and the most general steady-flow operations problem\ntakes the form of a Mixed Integer Nonlinear Program. In this paper, we consider\none example of steady-flow operations -- the Optimal Gas Flow (OGF) problem for\na natural gas pipeline network that minimizes the production cost subject to\nthe physics of steady-flow of natural gas. The ability to quickly determine\nglobal optimal solution and a lower bound to the objective value of the OGF for\ndifferent demand profiles plays a key role in efficient day-to-day operations.\nOne strategy to accomplish this relies on tight relaxations to the nonlinear\nconstraints of the OGF. Currently, many nonlinear constraints that arise due to\nmodeling the non-ideal equation of state either do not have relaxations or have\nrelaxations that scale poorly for realistic network sizes. In this work, we\ncombine recent advancements in the development of polyhedral relaxations for\nunivariate functions to obtain tight relaxations that can be solved within a\nfew seconds on a standard laptop. We demonstrate the quality of these\nrelaxations through extensive numerical experiments on very large scale test\nnetworks available in the literature and find that the proposed relaxation is\nable to prove optimality in 92% of the instances.\n']","[('gas flow', 0.5055714249610901), ('gas flows', 0.4903213679790497), ('flow gas', 0.4883020520210266), ('simulation optimization', 0.40590205788612366), ('flow networks', 0.3990994393825531), ('pipelines', 0.3983598053455353), ('pipeline', 0.3975408673286438), ('flow dynamics', 0.3821418583393097), ('nonlinear program', 0.36982262134552), ('gas power', 0.3588160276412964)]"
655,655,47,655_topological recursion_orantin topological recursion_generalized topological_refined topological,"['topological recursion', 'orantin topological recursion', 'generalized topological', 'refined topological', 'theory topological', 'formula topological', 'maps topological', 'topological', 'eynard orantin topological', 'orantin topological']","['Topological recursion for fully simple maps from ciliated maps   Ordinary maps satisfy topological recursion for a certain spectral curve $(x,\ny)$. We solve a conjecture from arXiv:1710.07851 that claims that fully simple\nmaps, which are maps with non self-intersecting disjoint boundaries, satisfy\ntopological recursion for the exchanged spectral curve $(y, x)$, making use of\nthe topological recursion for ciliated maps arXiv:2105.08035.\n', 'Degenerate and irregular topological recursion We use the theory of $x-y$ duality to propose a new definition / construction for the correlation differentials of topological recursion; we call it ""generalized topological recursion"". This new definition coincides with the original topological recursion of Chekhov-Eynard-Orantin in the regular case and allows, in particular, to get meaningful answers in a variety of irregular and degenerate situations.', 'Topological recursion on transalgebraic spectral curves and Atlantes Hurwitz numbers Given a spectral curve with exponential singularities (which we call a ""transalgebraic spectral curve""), we extend the definition of topological recursion to include contributions from the exponential singularities in a way that is compatible with limits of sequences of spectral curves. This allows us to prove the topological recursion/quantum curve correspondence for a large class of transalgebraic spectral curves. As an application, we find that Atlantes Hurwitz numbers, which were previously thought to fall outside the scope of topological recursion, satisfy (our extended version of) topological recursion, and we construct the corresponding quantum curve directly from topological recursion.']","[('topological recursion', 0.7022286653518677), ('orantin topological recursion', 0.6306807398796082), ('generalized topological', 0.559557318687439), ('refined topological', 0.5473858118057251), ('theory topological', 0.5244976282119751), ('formula topological', 0.5047589540481567), ('maps topological', 0.4723914861679077), ('topological', 0.4673829674720764), ('eynard orantin topological', 0.45494452118873596), ('orantin topological', 0.43463677167892456)]"
656,656,47,656_reachable sets_discrete time systems_reachability analysis_nonlinear control systems,"['reachable sets', 'discrete time systems', 'reachability analysis', 'nonlinear control systems', 'backward reachable', 'time invariant systems', 'nonlinear control affine', 'nonlinear systems', 'systems unknown dynamics', 'reachability']","['Efficient space-time discretizations for tracking the boundaries of\n  reachable sets   The reachable sets of nonlinear control systems can in general only be\nnumerically approximated, and are often very expensive to calculate. In this\npaper, we propose an algorithm that tracks only the boundaries of the reachable\nsets and that chooses the temporal and spatial discretizations in a non-uniform\nway to reduce the computational complexity.\n', 'On the Convergence of the Backward Reachable Sets of Robust Controlled\n  Invariant Sets For Discrete-time Linear Systems   This paper considers discrete-time linear systems with bounded additive\ndisturbances, and studies the convergence properties of the backward reachable\nsets of robust controlled invariant sets (RCIS). Under a simple condition, we\nprove that the backward reachable sets of an RCIS are guaranteed to converge to\nthe maximal RCIS in Hausdorff distance, with an exponential convergence rate.\nWhen all sets are represented by polytopes, this condition can be checked\nnumerically via a linear program. We discuss how the developed condition\ngeneralizes the existing conditions in the literature for (controlled)\ninvariant sets of systems without disturbances (or without control inputs).\n', 'Tight Decomposition Functions for Continuous-Time Mixed-Monotone Systems\n  with Disturbances   The vector field of a mixed-monotone system is decomposable via a\ndecomposition function into increasing (cooperative) and decreasing\n(competitive) components, and this decomposition allows for, e.g., efficient\ncomputation of reachable sets and forward invariant sets. A main challenge in\nthis approach, however, is identifying an appropriate decomposition function.\nIn this work, we show that any continuous-time dynamical system with a\nLipschitz continuous vector field is mixed-monotone, and we provide a\nconstruction for the decomposition function that yields the tightest\napproximation of reachable sets when used with the standard tools for\nmixed-monotone systems. Our construction is similar to that recently proposed\nby Yang and Ozay for computing decomposition functions of discrete-time systems\n[1] where we make appropriate modifications for the continuous-time setting and\nalso extend to the case with unknown disturbance inputs. As in [1], our\ndecomposition function construction requires solving an optimization problem\nfor each point in the state-space; however, we demonstrate through example how\ntight decomposition functions can sometimes be calculated in closed form. As a\nsecond contribution, we show how under-approximations of reachable sets can be\nefficiently computed via the mixed-monotonicity property by considering the\nbackward-time dynamics.\n']","[('reachable sets', 0.557508647441864), ('discrete time systems', 0.49263903498649597), ('reachability analysis', 0.4584164023399353), ('nonlinear control systems', 0.45506542921066284), ('backward reachable', 0.4361404776573181), ('time invariant systems', 0.43578314781188965), ('nonlinear control affine', 0.43133673071861267), ('nonlinear systems', 0.4123663604259491), ('systems unknown dynamics', 0.4094490110874176), ('reachability', 0.4084196388721466)]"
657,657,47,657_manifolds positive ricci_positive ricci curvature_ricci curvatures_ricci curvature positive,"['manifolds positive ricci', 'positive ricci curvature', 'ricci curvatures', 'ricci curvature positive', 'metric positive ricci', 'ricci curvature', 'intermediate ricci curvature', 'curvature manifolds', 'curvature metrics', 'positively curved manifolds']","['Generalized Surgery on Riemannian Manifolds of Positive Ricci Curvature   The surgery theorem of Wraith states that positive Ricci curvature is\npreserved under surgery if certain metric and dimensional conditions are\nsatisfied. We generalize this theorem as follows: Instead of attaching a\nproduct of a sphere and a disc, we glue a sphere bundle over a manifold with a\nso-called core metric, a type of metric which was recently introduced by\nBurdick to construct metrics of positive Ricci curvature on connected sums. As\napplications we construct core metrics on 2-sphere bundles, where the base\nadmits a core metric, and obtain new examples of 6-manifolds with metrics of\npositive Ricci curvature.\n', 'Positive Intermediate Ricci Curvature on Fibre Bundles   We prove a canonical variation-type result for submersion metrics with\npositive intermediate Ricci curvatures. This can then be used in conjunction\nwith surgery techniques to establish the existence of metrics with positive\nintermediate Ricci curvatures on a wide range of examples which had previously\nonly been known to admit positive Ricci curvature, such as highly connected\nmanifolds and exotic spheres. Further, we extend results of the second author\non the moduli space of metrics with positive Ricci curvature to positive\nintermediate Ricci curvatures.\n', 'Metrics of Positive Ricci Curvature on Simply-Connected Manifolds of\n  Dimension $6k$   A consequence of the surgery theorem of Gromov and Lawson is that every\nclosed, simply-connected 6-manifold admits a Riemannian metric of positive\nscalar curvature. For metrics of positive Ricci curvature it is widely open\nwhether a similar result holds; there are no obstructions known for those\nmanifolds to admit a metric of positive Ricci curvature, while the number of\nexamples known is limited. In this article we introduce a new description of\ncertain $6k$-dimensional manifolds via labeled bipartite graphs and use an\nearlier result of the author to construct metrics of positive Ricci curvature\non these manifolds. In this way we obtain many new examples, both spin and\nnon-spin, of $6k$-dimensional manifolds with a metric of positive Ricci\ncurvature.\n']","[('manifolds positive ricci', 0.802105724811554), ('positive ricci curvature', 0.7511956691741943), ('ricci curvatures', 0.7431906461715698), ('ricci curvature positive', 0.7341055274009705), ('metric positive ricci', 0.7224867939949036), ('ricci curvature', 0.7070626020431519), ('intermediate ricci curvature', 0.7052057981491089), ('curvature manifolds', 0.6722880601882935), ('curvature metrics', 0.6556221842765808), ('positively curved manifolds', 0.6210565567016602)]"
658,658,47,658_mean curvature flows_preserving curvature flow_mean curvature flow_curvature flows,"['mean curvature flows', 'preserving curvature flow', 'mean curvature flow', 'curvature flows', 'preserving mean curvature', 'curvature flow', 'curvature flow two', 'curvature flow planar', 'volume preserving mean', 'mean curvature']","['Weak-strong uniqueness for volume-preserving mean curvature flow   In this note, we derive a stability and weak-strong uniqueness principle for\nvolume-preserving mean curvature flow. The proof is based on a new notion of\nvolume-preserving gradient flow calibrations, which is a natural extension of\nthe concept in the case without volume preservation recently introduced by\nFischer et al. [arXiv:2003.05478]. The first main result shows that any strong\nsolution with certain regularity is calibrated. The second main result consists\nof a stability estimate in terms of a relative entropy, which is valid in the\nclass of distributional solutions to volume-preserving mean curvature flow.\n', 'Consistency of the flat flow solution to the volume preserving mean\n  curvature flow   We consider the flat flow solution, obtained via discrete minimizing movement\nscheme, to the volume preserving mean curvature flow starting from\nC^{1,1}-regular set. We prove the consistency principle which states that (any)\nsuch flat flow agrees with the classical solution as long as the latter exists.\nIn particular, the flat flow is unique and smooth up to the first singular\ntime. We obtain the result by proving the full regularity for the discrete time\napproximation of the flat flow such that the regularity estimates are stable\nwith respect to the time discretization. Our method can also be applied in the\ncase of the mean curvature flow and thus it provides an alternative proof, not\nrelying on comparison principle, for the consistency between the flat flow\nsolution and the classical solution for C^{1,1}-regular initial sets.\n', 'Long time behaviour of discrete volume preserving mean curvature flows   In this paper we analyse the Euler implicit scheme for the volume preserving\nmean curvature flow. We prove the exponential convergence of the scheme to a\nfinite union of disjoint balls with equal volume for any bounded initial set\nwith finite perimeter.\n']","[('mean curvature flows', 0.7509297132492065), ('preserving curvature flow', 0.7471238374710083), ('mean curvature flow', 0.727931559085846), ('curvature flows', 0.6832051277160645), ('preserving mean curvature', 0.6678305864334106), ('curvature flow', 0.6613397598266602), ('curvature flow two', 0.6243576407432556), ('curvature flow planar', 0.596878170967102), ('volume preserving mean', 0.5722289681434631), ('mean curvature', 0.5538213849067688)]"
659,659,47,659_epidemic models_epidemic dynamics_epidemic network_epidemic spread,"['epidemic models', 'epidemic dynamics', 'epidemic network', 'epidemic spread', 'epidemic outbreak', 'epidemics', 'epidemic', 'sir epidemic', 'spread infectious', 'outbreak']","['Clustering for epidemics on networks: a geometric approach   Infectious diseases typically spread over a contact network with millions of\nindividuals, whose sheer size is a tremendous challenge to analysing and\ncontrolling an epidemic outbreak. For some contact networks, it is possible to\ngroup individuals into clusters. A high-level description of the epidemic\nbetween a few clusters is considerably simpler than on an individual level.\nHowever, to cluster individuals, most studies rely on equitable partitions, a\nrather restrictive structural property of the contact network. In this work, we\nfocus on Susceptible-Infected-Susceptible (SIS) epidemics, and our contribution\nis threefold. First, we propose a geometric approach to specify all networks\nfor which an epidemic outbreak simplifies to the interaction of only a few\nclusters. Second, for the complete graph and any initial viral state vectors,\nwe derive the closed-form solution of the nonlinear differential equations of\nthe N-Intertwined Mean-Field Approximation (NIMFA) of the SIS process. Third,\nby relaxing the notion of equitable partitions, we derive low-complexity\napproximations and bounds for epidemics on arbitrary contact networks. Our\nresults are an important step towards understanding and controlling epidemics\non large networks.\n', 'Edge Deletion Algorithms for Minimizing Spread in SIR Epidemic Models   This paper studies algorithmic strategies to effectively reduce the number of\ninfections in susceptible-infected-recovered (SIR) epidemic models. We consider\na Markov chain SIR model and its two instantiations in the deterministic SIR\n(D-SIR) model and the independent cascade SIR (IC-SIR) model. We investigate\nthe problem of minimizing the number of infections by restricting contacts\nunder realistic constraints. Under moderate assumptions on the reproduction\nnumber, we prove that the infection numbers are bounded by supermodular\nfunctions in the D-SIR model and the IC-SIR model for large classes of random\nnetworks. We propose efficient algorithms with approximation guarantees to\nminimize infections. The theoretical results are illustrated by numerical\nsimulations.\n', 'Network-based analysis of stochastic SIR epidemic models with random and\n  proportionate mixing   In this paper, we outline the theory of epidemic percolation networks and\ntheir use in the analysis of stochastic SIR epidemic models on undirected\ncontact networks. We then show how the same theory can be used to analyze\nstochastic SIR models with random and proportionate mixing. The epidemic\npercolation networks for these models are purely directed because undirected\nedges disappear in the limit of a large population. In a series of simulations,\nwe show that epidemic percolation networks accurately predict the mean outbreak\nsize and probability and final size of an epidemic for a variety of epidemic\nmodels in homogeneous and heterogeneous populations. Finally, we show that\nepidemic percolation networks can be used to re-derive classical results from\nseveral different areas of infectious disease epidemiology. In an appendix, we\nshow that an epidemic percolation network can be defined for any\ntime-homogeneous stochastic SIR model in a closed population and prove that the\ndistribution of outbreak sizes given the infection of any given node in the SIR\nmodel is identical to the distribution of its out-component sizes in the\ncorresponding probability space of epidemic percolation networks. We conclude\nthat the theory of percolation on semi-directed networks provides a very\ngeneral framework for the analysis of stochastic SIR models in closed\npopulations.\n']","[('epidemic models', 0.7630548477172852), ('epidemic dynamics', 0.7325147390365601), ('epidemic network', 0.7314288020133972), ('epidemic spread', 0.6435247659683228), ('epidemic outbreak', 0.6341221928596497), ('epidemics', 0.6249572038650513), ('epidemic', 0.6135359406471252), ('sir epidemic', 0.5621971487998962), ('spread infectious', 0.4953671991825104), ('outbreak', 0.47243747115135193)]"
660,660,47,660_knot polynomials_knot invariants_polynomials knots_knot theory,"['knot polynomials', 'knot invariants', 'polynomials knots', 'knot theory', 'knot invariant', 'homfly polynomial', 'homfly pt polynomial', 'knots links', 'link invariants', 'torus knots']","['Colored HOMFLY-PT polynomials of quasi-alternating $3$-braid knots   Obtaining a closed-form expression for the colored HOMFLY-PT polynomials of\nknots from $3$-strand braids carrying arbitrary $SU(N)$ representation is a\nchallenging problem. In this paper, we confine our interest to twisted\ngeneralized hybrid weaving knots which we denote hereafter by\n$\\hat{Q}_3(m_1,-m_2,n,\\ell)$. This family of knots not only generalizes the\nwell-known class of weaving knots but also contains an infinite family of\nquasi-alternating knots. Interestingly, we obtain a closed-form expression for\nthe HOMFLY-PT polynomial of $\\hat{Q}_3(m_1,-m_2,n,\\ell)$ using a modified\nversion of the Reshitikhin-Turaev method. In addition, we compute the exact\ncoefficients of the Jones polynomials and the Alexander polynomials of\nquasi-alternating knots $\\hat{Q}_3(1,-1,n,\\pm 1)$. For these homologically-thin\nknots, such coefficients are known to be the ranks of their Khovanov and link\nFloer homologies, respectively. We also show that the asymptotic behaviour of\nthe coefficients of the Alexander polynomial is trapezoidal. On the other hand,\nwe compute the $[r]$-colored HOMFLY-PT polynomials of quasi alternating knots\nfor small values of $r$. Remarkably, the study of the determinants of certain\ntwisted weaving knots leads to establish a connection with enumerative geometry\nrelated to $m^{th}$ Lucas numbers, denoted hereafter as $L_{m,2n}$. At the end,\nwe verify that the reformulated invariants satisfy Ooguri-Vafa conjecture and\nwe express certain BPS integers in terms of hyper-geometric functions ${}_2\n{\\bf F}_1\\left[a,b, c;z\\right]$.\n', 'The HOMFLY-PT polynomial and HZ factorisation   The Harer-Zagier (HZ) transform maps the HOMFLY-PT polynomial into a rational\nfunction. For some special knots and links, the latter admits a simple\nfactorised form, which is referred to as HZ factorisation. This property is\npreserved under full twists and concatenation with the Jucys-Murphy braid,\nwhich are hence used to generate infinite HZ-factorisable families. For such\nfamilies, the HOMFLY-PT polynomial can be fully encoded in two sets of\nintegers, corresponding to the numerator and denominator exponents, which turn\nout to be related to the Khovanov homology and its Euler characteristics.\nMoreover, a relation between the HOMFLY-PT and Kauffman polynomials, which was\noriginally found for torus knots, is now proven for several such families.\nInterestingly, this relation is equivalent to the vanishing of the two-crosscap\nBPS invariants in topological string theory. It is conjectured that the\nHOMFLY-PT-Kauffman relation provides a criterion for HZ factorisability.\n', 'Closed 4-braids and the Jones unknot conjecture   The Jones problem is a question whether there is a non-trivial knot with the\ntrivial Jones polynomial in one variable $q$. The answer to this fundamental\nquestion is still unknown despite numerous attempts to explore it. In braid\npresentation the case of 4-strand braids is already open. S. Bigelow showed in\n2000 that if the Burau representation for four-strand braids is unfaithful,\nthen there is an infinite number of non-trivial knots with the trivial\ntwo-variable HOMFLY-PT polynomial and hence, with the trivial Jones polynomial,\nsince it is obtained from the HOMFLY-PT polynomial by the specialisation of one\nof the variables $A=q^2$.\n  In this paper, we study four-strand braids and ask whether there are\nnon-trivial knots with the trivial Jones polynomial but a non-trivial HOMFLY-PT\npolynomial. We have discovered that there is a whole 1-parameter family,\nparameterised by the writhe number, of 2-variable polynomials that can be\nHOMFLY-PT polynomials of some knots. We explore various properties of the\nobtained hypothetical HOMFLY-PT polynomials and suggest several checks to test\nthese formulas. A generalisation is also proposed for the case of a large\nnumber of strands.\n']","[('knot polynomials', 0.7060946226119995), ('knot invariants', 0.6598513126373291), ('polynomials knots', 0.6533944010734558), ('knot theory', 0.622239351272583), ('knot invariant', 0.6149289608001709), ('homfly polynomial', 0.5667487382888794), ('homfly pt polynomial', 0.559173583984375), ('knots links', 0.5397434234619141), ('link invariants', 0.5315389037132263), ('torus knots', 0.5174547433853149)]"
661,661,47,661_fourier multiplier operators_fourier integral operators_graded lie_besov spaces,"['fourier multiplier operators', 'fourier integral operators', 'graded lie', 'besov spaces', 'compact lie groups', 'boundedness fourier', 'lie groups results', 'pseudo differential operators', 'lie groups', 'differential operators']","['$L^p$-bounds for pseudo-differential operators on graded Lie groups   In this work we obtain sharp $L^p$-estimates for pseudo-differential\noperators on arbitrary graded Lie groups.\n  The results are presented within the setting of the global symbolic calculus\non graded Lie groups by using the Fourier analysis associated to every graded\nLie group which extends the usual one due to H\\""ormander on $\\mathbb{R}^n$. The\nmain result extends the classical Fefferman\'s sharp theorem on the\n$L^p$-boundedness of pseudo-differential operators for H\\""ormander classes on\n$\\mathbb{R}^n$ to general graded Lie groups, also adding the borderline\n$\\rho=\\delta$ case.\n', '$L^p$-$L^q$ boundedness of pseudo-differential operators on graded Lie\n  groups   In this paper we establish the $L^p$-$L^q$ estimates for global\npseudo-differential operators on graded Lie groups. We provide both necessary\nand sufficient conditions for the $L^p$-$L^q$ boundedness of\npseudo-differential operators associated with the global H\\""ormander symbol\nclasses on graded Lie groups, within the range $1<p\\leq 2 \\leq q<\\infty$.\nAdditionally, we present a sufficient condition for the $L^p$-$L^q$ estimates\nof pseudo-differential operators within the range $1<p\\leq q\\leq 2$ or $2\\leq\np\\leq q<\\infty$. The proofs rely on estimates of the Riesz and Bessel\npotentials associated with Rockland operators, along with previously\nestablished results on $L^p$-boundedness of global pseudo-differential\noperators on graded Lie groups. Notably, as a byproduct, we also establish the\nsharpness of the Sobolev embedding theorem for the inhomogeneous Sobolev spaces\non graded Lie groups.\n', 'Littlewood-Paley theorem, Nikolskii inequality, Besov spaces, Fourier\n  and spectral multipliers on graded Lie groups   In this paper we investigate Besov spaces on graded Lie groups. We prove a\nNikolskii type inequality (or the Reverse H\\""older inequality) on graded Lie\ngroups and as consequence we obtain embeddings of Besov spaces. We prove a\nversion of the Littlewood-Paley theorem on graded Lie groups. The results are\napplied to obtain embedding properties of Besov spaces and multiplier theorems\nfor both spectral and Fourier multipliers in Besov spaces on graded Lie groups.\nIn particular, we give a number of sufficient conditions for the boundedness of\nFourier multipliers in Besov spaces.\n']","[('fourier multiplier operators', 0.5598655939102173), ('fourier integral operators', 0.49802008271217346), ('graded lie', 0.49735715985298157), ('besov spaces', 0.4751419723033905), ('compact lie groups', 0.46927422285079956), ('boundedness fourier', 0.4588750898838043), ('lie groups results', 0.4584991931915283), ('pseudo differential operators', 0.44986066222190857), ('lie groups', 0.4465295672416687), ('differential operators', 0.43690812587738037)]"
662,662,47,662_lagrangian floer homology_floer cohomology_lagrangian floer theory_floer homology,"['lagrangian floer homology', 'floer cohomology', 'lagrangian floer theory', 'floer homology', 'lagrangian tori', 'lagrangian correspondence', 'symplectic cohomology', 'symplectic manifolds', 'theory symplectic', 'symplectic topology']","[""Chekanov torus and Gelfand--Zeitlin torus in $S^2 \\times S^2$   The Chekanov torus was the first known \\emph{exotic} torus, a monotone\nLagrangian torus that is not Hamiltonian isotopic to the standard monotone\nLagrangian torus. We explore the relationship between the Chekanov torus in\n$S^2 \\times S^2$ and a monotone Lagrangian torus which had been introduced\nbefore Chekanov's construction \\cite{Chekanov}. We prove that the monotone\nLagrangian torus fiber in a certain Gelfand--Zeitlin system is Hamiltonian\nisotopic to the Chekanov torus in $S^2 \\times S^2$.\n"", ""Construction of holomorphic quilts in Cartesian product of closed\n  surfaces   In this article, we modify the proof of holomorphic quilts from Wehrheim and\nWoodward in \\cite{wehrheim2009floer} to construct a specific type of immersed\nholomorphic quilt, where the symplectic manifolds are closed surfaces. The\napplication is to compare Lagrangian Floer theory with quilted Lagrangian Floer\ntheory, as they relate through Lagrangian correspondence. A potential example\nis provided to support Bottman and Wehrheim's conjecture\n\\cite{bottman2018gromov} regarding the isomorphism between Lagrangian Floer\nhomology and quilted Lagrangian Floer homology after twisting by bounding\ncochains.\n"", 'Equivariant Lagrangian Floer theory on compact toric manifolds   We define an equivariant Lagrangian Floer theory for Lagrangian torus fibers\nin a compact symplectic toric manifold equipped with a subtorus action. We show\nthat the set of all Lagrangian torus fibers with weak bounding cochain data\nwhose equivariant Lagrangian Floer cohomology is non-zero can be identified\nwith a rigid analytic space. We prove that the set of these Lagrangian torus\nfibers is the tropicalization of the rigid analytic space. This provides a way\nto locate them in the moment polytope. Moreover, we prove that the dimension of\nsuch a rigid analytic space is equal to the dimension of the subtorus when the\nsymplectic manifold is $\\mathbb{CP}^n$ or has complex dimension less than or\nequal to 2. We also show that the Lagrangian submanifolds with non-trivial\nequivariant Floer cohomology are non-displaceable by $G$-equivariant\nHamiltonian diffeomorphisms.\n']","[('lagrangian floer homology', 0.7413482666015625), ('floer cohomology', 0.6254222989082336), ('lagrangian floer theory', 0.6228628754615784), ('floer homology', 0.6090953350067139), ('lagrangian tori', 0.5730302929878235), ('lagrangian correspondence', 0.5635759234428406), ('symplectic cohomology', 0.5615831017494202), ('symplectic manifolds', 0.5605863332748413), ('theory symplectic', 0.556178092956543), ('symplectic topology', 0.550443708896637)]"
663,663,47,663_microscopy_electron microscopy_microscope_fluorescence,"['microscopy', 'electron microscopy', 'microscope', 'fluorescence', 'resolution three dimensional', 'super resolution', 'superresolution', 'molecule', 'fluorescent', 'molecules']","[""COL0RME: Super-resolution microscopy based on sparse\n  blinking/fluctuating fluorophore localization and intensity estimation   To overcome the physical barriers caused by light diffraction,\nsuper-resolution techniques are often applied in fluorescence microscopy.\nState-of-the-art approaches require specific and often demanding acquisition\nconditions to achieve adequate levels of both spatial and temporal resolution.\nAnalyzing the stochastic fluctuations of the fluorescent molecules provides a\nsolution to the aforementioned limitations, as sufficiently high\nspatio-temporal resolution for live-cell imaging can be achieved by using\ncommon microscopes and conventional fluorescent dyes. Based on this idea, we\npresent COL0RME, a method for COvariance-based $\\ell_0$ super-Resolution\nMicroscopy with intensity Estimation, which achieves good spatio-temporal\nresolution by solving a sparse optimization problem in the covariance domain\nand discuss automatic parameter selection strategies. The method is composed of\ntwo steps: the former where both the emitters' independence and the sparse\ndistribution of the fluorescent molecules are exploited to provide an accurate\nlocalization; the latter where real intensity values are estimated given the\ncomputed support. The paper is furnished with several numerical results both on\nsynthetic and real fluorescence microscopy images and several comparisons with\nstate-of-the art approaches are provided. Our results show that COL0RME\noutperforms competing methods exploiting analogously temporal fluctuations; in\nparticular, it achieves better localization, reduces background artifacts and\navoids fine parameter tuning.\n"", 'DeepCEL0 for 2D Single Molecule Localization in Fluorescence Microscopy   In fluorescence microscopy, Single Molecule Localization Microscopy (SMLM)\ntechniques aim at localizing with high precision high density fluorescent\nmolecules by stochastically activating and imaging small subsets of blinking\nemitters. Super Resolution (SR) plays an important role in this field since it\nallows to go beyond the intrinsic light diffraction limit. In this work, we\npropose a deep learning-based algorithm for precise molecule localization of\nhigh density frames acquired by SMLM techniques whose $\\ell_{2}$-based loss\nfunction is regularized by positivity and $\\ell_{0}$-based constraints. The\n$\\ell_{0}$ is relaxed through its Continuous Exact $\\ell_{0}$ (CEL0)\ncounterpart. The arising approach, named DeepCEL0, is parameter-free, more\nflexible, faster and provides more precise molecule localization maps if\ncompared to the other state-of-the-art methods. We validate our approach on\nboth simulated and real fluorescence microscopy data.\n', 'Random Conical Tilt Reconstruction without Particle Picking in\n  Cryo-electron Microscopy   We propose a method to reconstruct the 3-D molecular structure from\nmicrographs collected at just one sample tilt angle in the random conical tilt\nscheme in cryo-electron microscopy. Our method uses autocorrelation analysis on\nthe micrographs to estimate features of the molecule which are invariant under\ncertain nuisance parameters such as the positions of molecular projections in\nthe micrographs. This enables us to reconstruct the molecular structure\ndirectly from micrographs, completely circumventing the need for particle\npicking. We demonstrate reconstructions with simulated data and investigate the\neffect of the missing-cone region. These results show promise to reduce the\nsize limit for single particle reconstruction in cryo-electron microscopy.\n']","[('microscopy', 0.6155019998550415), ('electron microscopy', 0.5423734188079834), ('microscope', 0.49007949233055115), ('fluorescence', 0.46248793601989746), ('resolution three dimensional', 0.3879648745059967), ('super resolution', 0.37996920943260193), ('superresolution', 0.3552004396915436), ('molecule', 0.3474215269088745), ('fluorescent', 0.3455808758735657), ('molecules', 0.3256196975708008)]"
664,664,47,664_multiobjective optimization_multiobjective optimization problems_multi objective optimization_single objective optimization,"['multiobjective optimization', 'multiobjective optimization problems', 'multi objective optimization', 'single objective optimization', 'objective optimization', 'quasi newton methods', 'composite optimization problems', 'methods multiobjective', 'objective optimization problems', 'free optimization']","['A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert\n  Spaces   The efficient optimization method for locally Lipschitz continuous\nmultiobjective optimization problems from [1] is extended from\nfinite-dimensional problems to general Hilbert spaces. The method iteratively\ncomputes Pareto critical points, where in each iteration, an approximation of\nthe subdifferential is computed in an efficient manner and then used to compute\na common descent direction for all objective functions. To prove convergence,\nwe present some new optimality results for nonsmooth multiobjective\noptimization problems in Hilbert spaces. Using these, we can show that every\naccumulation point of the sequence generated by our algorithm is Pareto\ncritical under common assumptions. Computational efficiency for finding Pareto\ncritical points is numerically demonstrated for multiobjective optimal control\nof an obstacle problem.\n', 'The Quasi-Newton Method for the Composite Multiobjective Optimization\n  Problems   In this paper, we introduce several new quasi-Newton methods for the\ncomposite multiobjective optimization problems (in short, CMOP) with Armijo\nline search. These multiobjective versions of quasi-Newton methods include BFGS\nquasi-Newnon method, self-scaling BFGS quasi-Newnon method, and Huang BFGS\nquasi-Newnon method. Under some suitable conditions, we show that each\naccumulation point of the sequence generated by these algorithms, if exists, is\nboth a Pareto stationary point and a Pareto optimal point of (CMOP).\n', 'Proximal Quasi-Newton Methods for Multiobjective Optimization Problems   We introduce some new proximal quasi-Newton methods for unconstrained\nmultiobjective optimization problems (in short, UMOP), where each objective\nfunction is the sum of a twice continuously differentiable strongly convex\nfunction and a proper lower semicontinuous convex but not necessarily\ndifferentiable function. We propose proximal BFGS method, proximal self-scaling\nBFGS method, and proximal Huang BFGS method for (UMOP) with both line searches\nand without line searches cases. Under mild assumputions, we show that each\naccumulation point of the sequence generated by these algorithms, if exists, is\na Pareto stationary point of the (UMOP). Moreover, we present their\napplications in both constrained multiobjective optimization problems and\nrobust multiobjective optimization problems. In particular, for robust\nmultiobjective optimization problems, we show that the subproblems of proximal\nquasi-Newton algorithms can be regarded as quadratic minimization problems with\nquadratic inequality constraints. Numerical experiments are also carried out to\nverify the effectiveness of the proposed proximal quasi-Newton methods.\n']","[('multiobjective optimization', 0.7071401476860046), ('multiobjective optimization problems', 0.6972857117652893), ('multi objective optimization', 0.6157368421554565), ('single objective optimization', 0.5806984901428223), ('objective optimization', 0.5273964405059814), ('quasi newton methods', 0.5202102065086365), ('composite optimization problems', 0.5195668935775757), ('methods multiobjective', 0.5113826394081116), ('objective optimization problems', 0.5112406611442566), ('free optimization', 0.5092450976371765)]"
665,665,47,665_invariant gibbs measures_gibbs measures_invariant gibbs_translation invariant gibbs,"['invariant gibbs measures', 'gibbs measures', 'invariant gibbs', 'translation invariant gibbs', 'gibbs measure', 'generalized gibbs', 'gibbs states', 'uniqueness gibbs', 'gibbs distributions', 'states gibbs']","['Gradient Gibbs measures with periodic boundary laws of a generalized SOS\n  model on a Cayley tree   We consider Gradient Gibbs measures corresponding to a periodic boundary law\nfor a generalized SOS model with spin values from a countable set, on Cayley\ntrees. On the Cayley tree, detailed information on Gradient Gibbs measures for\nmodels of SOS type are given in \\cite{3, 16,8,11} and we continue the works for\nthe generalized SOS model. Namely, in this paper, the problem of finding\nGradient Gibbs measures that correspond to periodic boundary laws is reduced to\na functional equation and by solving the equation all Gradient Gibbs measures\nwith 4 periodic boundary laws are found.\n', 'A new set of Gibbs measures for the SOS model on a Cayley tree   The phase transition phenomenon is one of the central problems of statistical\nmechanics. It occurs when the model possesses multiple Gibbs measures. In this\npaper, we consider a three-state SOS (solid-on-solid) model on a Cayley tree.\nWe reduce description of Gibbs measures to solving of a non-linear functional\nequation, which each solution of the equation corresponds to a Gibbs measure.\nWe give some sufficiency conditions on the existence of multiple Gibbs measures\nfor the model. We give a review of some known (translation-invariant, periodic,\nnon-periodic) Gibbs measures of the model and compare them with our new\nmeasures. We show that the Gibbs measures found in the paper differ from the\nknown Gibbs measures, i.e, we show that these measures are new.\n', 'Extremality of translation-invariant Gibbs measures for the Potts-SOS\n  model on the Cayley tree   In this paper, we consider the Potts-SOS model where the spin takes values in\nthe set $\\{0, 1, 2\\}$ on the Cayley tree of order two. We describe all the\ntranslation-invariant splitting Gibbs measures for this model in some\nconditions. Moreover, we investigate whether these Gibbs measures are extremal\nor non-extremal in the set of all Gibbs measures.\n']","[('invariant gibbs measures', 0.7461772561073303), ('gibbs measures', 0.7082025408744812), ('invariant gibbs', 0.6992498636245728), ('translation invariant gibbs', 0.6852949261665344), ('gibbs measure', 0.6699492335319519), ('generalized gibbs', 0.6494030952453613), ('gibbs states', 0.6146137118339539), ('uniqueness gibbs', 0.5752289891242981), ('gibbs distributions', 0.5546828508377075), ('states gibbs', 0.5473077297210693)]"
666,666,47,666_hurwitz numbers_double hurwitz numbers_monotone hurwitz numbers_spin hurwitz numbers,"['hurwitz numbers', 'double hurwitz numbers', 'monotone hurwitz numbers', 'spin hurwitz numbers', 'double hurwitz', 'monotone hurwitz', 'hurwitz', 'spin hurwitz', 'numbers genus', 'branched covers']","['Towards studying the structure of triple Hurwitz numbers   Going beyond the studies of single and double Hurwitz numbers, we report some\nprogress towards studying Hurwitz numbers which correspond to ramified\ncoverings of the Riemann sphere involving three nonsimple branch points. We\nfirst prove a recursion which implies a fundamental identity of Frobenius\nenumerating factorizations of a permutation in group algebra theory. We next\napply the recursion to study Hurwitz numbers involving three nonsimple branch\npoints (besides simple ones),two of them having deterministic ramification\nprofiles while the remaining one having a prescribed number of preimages. The\nrecursion allows us to obtain recurrences as well as explicit formulas for\nthese numbers which also generalize a number of existing results on single and\ndouble Hurwitz numbers. The case where one of the nonsimple branch points with\ndeterministic profile has a unique preimage (one-part quasi-triple Hurwitz\nnumbers {or $(1,m)$-part triple Hurwitz numbers}) is particularly studied in\ndetail. We prove an attractive dimension-reduction formula from which any\none-part quasi-triple Hurwitz number can be reduced to quasi-triple Hurwitz\nnumbers where both with deterministic profiles are fully ramified. We also\nobtain the polynomiality of one-part quasi-triple Hurwitz numbers analogous to\nthat implied by the remarkable ELSV formula for single Hurwitz numbers, and\ndiscuss the potential connection to intersection theory.\n', 'Asymptotics for real monotone double Hurwitz numbers   In recent years, monotone double Hurwitz numbers were introduced as a\nnaturally combinatorial modification of double Hurwitz numbers. Monotone double\nHurwitz numbers share many structural properties with their classical\ncounterparts, such as piecewise polynomaility, while the quantitative\nproperties of these two numbers are quite different. We consider real analogues\nof monotone double Hurwitz numbers and study the asymptotics for these real\nanalogues. The key ingredient is an interpretation of real tropical covers with\narbitrary splittings as factorizations in the symmetric group which generalizes\nthe result from Guay-Paquet, Markwig, and Rau (Int. Math. Res. Not. IMRN,\n2016(1):258-293, 2016). By using the above interpretation, we consider three\ntypes of real analogues of monotone double Hurwitz numbers: real monotone\ndouble Hurwitz numbers relative to simple splittings, relative to arbitrary\nsplittings and real mixed double Hurwitz numbers. Under certain conditions, we\nfind lower bounds for these real analogues, and obtain logarithmic asymptotics\nfor real monotone double Hurwitz numbers relative to arbitrary splittings and\nreal mixed double Hurwitz numbers. In particular, under given conditions real\nmixed double Hurwitz numbers are logarithmically equivalent to complex double\nHurwitz numbers. We construct a family of real tropical covers and use them to\nshow that real monotone double Hurwitz numbers relative to simple splittings\nare logarithmically equivalent to monotone double Hurwitz numbers with specific\nconditions. This is consistent with the logarithmic equivalence of real double\nHurwitz numbers and complex double Hurwitz numbers.\n', 'Double Hurwitz numbers: polynomiality, topological recursion and\n  intersection theory   Double Hurwitz numbers enumerate branched covers of $\\mathbb{CP}^1$ with\nprescribed ramification over two points and simple ramification elsewhere. In\ncontrast to the single case, their underlying geometry is not well understood.\nIn previous work by the second- and third-named authors, the double Hurwitz\nnumbers were conjectured to satisfy a polynomiality structure and to be\ngoverned by the topological recursion, analogous to existing results concerning\nsingle Hurwitz numbers. In this paper, we resolve these conjectures by a\ncareful analysis of the semi-infinite wedge representation for double Hurwitz\nnumbers, by pushing further methods previously used for other Hurwitz problems.\nWe deduce a preliminary version of an ELSV-like formula for double Hurwitz\nnumbers, by deforming the Johnson-Pandharipande-Tseng formula for orbifold\nHurwitz numbers and using properties of the topological recursion under\nvariation of spectral curves. In the course of this analysis, we unveil certain\nvanishing properties of the Chiodo classes.\n']","[('hurwitz numbers', 0.7314913272857666), ('double hurwitz numbers', 0.7286462187767029), ('monotone hurwitz numbers', 0.708986759185791), ('spin hurwitz numbers', 0.6492388248443604), ('double hurwitz', 0.5616515874862671), ('monotone hurwitz', 0.5471787452697754), ('hurwitz', 0.48606163263320923), ('spin hurwitz', 0.4817800521850586), ('numbers genus', 0.4765354096889496), ('branched covers', 0.389589786529541)]"
667,667,47,667_topological complexity_higher topological complexity_planning algorithms_motion planning,"['topological complexity', 'higher topological complexity', 'planning algorithms', 'motion planning', 'complexity topological', 'path planning', 'complexity map', 'topological complexities', 'complexity', 'planning']","['Rational sequential parametrized topological complexity   Sequential parametrized topological complexity is a numerical homotopy\ninvariant of a fibration, which arose in the robot motion planning problem with\nexternal constraints. In this paper, we study sequential parametrized\ntopological complexity in view of rational homotopy theory. We generalize\nresults on topological complexity, and in particular, give an explicit\nalgebraic upper bound for sequential parametrized topological complexity when a\nfibration admits a certain decomposition, which is a generalization of the\nresult of Hamoun, Rami and Vandembroucq on topological complexity.\n', 'Parametrized motion planning and topological complexity   In this paper we study paramertized motion planning algorithms which provide\nuniversal and flexible solutions to diverse motion planning problems. Such\nalgorithms are intended to function under a variety of external conditions\nwhich are viewed as parameters and serve as part of the input of the algorithm.\nContinuing a recent paper, we study further the concept of parametrized\ntopological complexity. We analyse in full detail the problem of controlling a\nswarm of robots in the presence of multiple obstacles in Euclidean space which\nserved for us a natural motivating example. We present an explicit parametrized\nmotion planning algorithm solving the motion planning problem for any number of\nrobots and obstacles.. This algorithm is optimal, it has minimal possible\ntopological complexity for any d odd. Besides, we describe a modification of\nthis algorithm which is optimal for d even. We also analyse the parametrized\ntopological complexity of sphere bundles using the Stiefel - Whitney\ncharacteristic classes.\n', 'A Motion Planning Algorithm in a Figure Eight Track   We design a motion planning algorithm to coordinate the movements of two\nrobots along a figure eight track, in such a way that no collisions occur. We\nuse a topological approach to robot motion planning that relates instabilities\nin motion planning algorithms to topological features of configuration spaces.\nThe topological complexity of a configuration space is an invariant that\nmeasures the complexity of motion planning algorithms. We show that the\ntopological complexity of our problem is 3 and construct an explicit algorithm\nwith three continuous instructions.\n']","[('topological complexity', 0.5969145894050598), ('higher topological complexity', 0.5844911932945251), ('planning algorithms', 0.5727782845497131), ('motion planning', 0.5712460279464722), ('complexity topological', 0.569426953792572), ('path planning', 0.535179853439331), ('complexity map', 0.4539560079574585), ('topological complexities', 0.4361104667186737), ('complexity', 0.4175169765949249), ('planning', 0.41454797983169556)]"
668,668,47,668_totally nonnegative matrices_nonnegative matrices_matrices max_nonnegative matrix,"['totally nonnegative matrices', 'nonnegative matrices', 'matrices max', 'nonnegative matrix', 'positive semidefinite matrices', 'hadamard product matrices', 'largest eigenvalue matrix', 'joint spectral radius', 'spectral radius', 'semidefinite matrices']","['Dynamics of products of nonnegative matrices   The aim of this manuscript is to understand the dynamics of products of\nnonnegative matrices. We extend a well known consequence of the\nPerron-Frobenius theorem on the periodic points of a nonnegative matrix to\nproducts of finitely many nonnegative matrices associated to a word and later\nto products of nonnegative matrices associated to a word, possibly of infinite\nlength. We also make use of an appropriate definition of the exponential map\nand the logarithm map on the positive orthant of $\\mathbb{R}^{n}$ and explore\nthe relationship between the periodic points of certain subhomogeneous maps\ndefined through the above functions and the periodic points of matrix products,\nmentioned above.\n', 'A bound on the joint spectral radius using the diagonals   The primary aim of this paper is to establish bounds on the joint spectral\nradius for a finite set of nonnegative matrices based on their diagonal\nelements. The efficacy of this approach is evaluated in comparison to existing\nand related results in the field. In particular, let $\\Sigma$ be any finite set\nof $D\\times D$ nonnegative matrices with the largest value $U$ and the smallest\nvalue $V$ over all positive entries. For each $i=1,\\dots,D$, let $m_i$ be any\nnumber so that there exist $A_1,\\dots,A_{m_i}\\in\\Sigma$ satisfying $(A_1\\dots\nA_{m_i})_{i,i} > 0$, or let $m_i=1$ if there are no such matrices. We prove\nthat the joint spectral radius $\\rho(\\Sigma)$ is bounded by \\[\n  \\max_i \\sqrt[m_i]{\\max_{A_1,\\dots,A_{m_i}\\in\\Sigma} (A_1\\dots A_{m_i})_{i,i}}\n\\le \\rho(\\Sigma) \\le \\max_i \\sqrt[m_i]{\\left(\\frac{UD}{V}\\right)^{3D^2}\n\\max_{A_1,\\dots,A_{m_i}\\in\\Sigma} (A_1\\dots A_{m_i})_{i,i}}. \\]\n', ""On the joint spectral radius of nonnegative matrices   We give an effective bound of the joint spectral radius $\\rho(\\Sigma)$ for a\nfinite set $\\Sigma$ of nonnegative matrices: For every $n$,\n  \\[\n  \\sqrt[n]{\\left(\\frac{V}{UD}\\right)^{D} \\max_C \\max_{i,j\\in C}\n\\max_{A_1,\\dots,A_n\\in\\Sigma}(A_1\\dots A_n)_{i,j}} \\le \\rho(\\Sigma)\n  \\le \\sqrt[n]{D \\max_C \\max_{i,j\\in C} \\max_{A_1,\\dots,A_n\\in\\Sigma}(A_1\\dots\nA_n)_{i,j}},\n  \\] where $D\\times D$ is the dimension of the matrices, $U,V$ are respectively\nthe largest entry and the smallest entry over all the positive entries of the\nmatrices in $\\Sigma$, and $C$ is taken over all strongly connected components\nin the dependency graph. The dependency graph is a directed graph where the\nvertices are the dimensions and there is an edge from $i$ to $j$ if and only if\n$A_{i,j}\\ne 0$ for some matrix $A\\in\\Sigma$.\n  Furthermore, a bound on the norm is also given: If $\\rho(\\Sigma)>0$ then\nthere exist a nonnegative integer $r$ and two positive numbers $\\alpha,\\beta$\nso that for every $n$,\n  \\[\n  \\alpha n^r{\\rho(\\Sigma)}^n \\le \\max_{A_1,\\dots,A_n\\in\\Sigma} \\|A_1\\dots A_n\\|\n\\le \\beta n^r{\\rho(\\Sigma)}^n.\n  \\]\n  Corollaries of the approach include a simple proof for the joint spectral\ntheorem for finite sets of nonnegative matrices and the convergence rate of\nsome sequences. The method in use is mostly based on Fekete's lemma, for both\nsubmultiplicative and supermultiplicative sequences.\n""]","[('totally nonnegative matrices', 0.6510918736457825), ('nonnegative matrices', 0.630473792552948), ('matrices max', 0.5688862800598145), ('nonnegative matrix', 0.5662618279457092), ('positive semidefinite matrices', 0.5654721856117249), ('hadamard product matrices', 0.49042069911956787), ('largest eigenvalue matrix', 0.4834378957748413), ('joint spectral radius', 0.4725141227245331), ('spectral radius', 0.46222877502441406), ('semidefinite matrices', 0.45765089988708496)]"
669,669,46,669_spanning trees graphs_disjoint spanning trees_trees spanning_spanning trees,"['spanning trees graphs', 'disjoint spanning trees', 'trees spanning', 'spanning trees', 'spanning trees graph', 'number spanning trees', 'graph spanning tree', 'spanning tree graph', 'spanning tree', 'trees graphs']","['Spectral conditions for spanning $k$-trees or $k$-ended-trees of graphs   Let $G$ be a connected graph of order $n$. a spanning $k$-tree of $G$ is a\nspanning tree with the maximum degree at most $k$ and a spanning $k$-ended-tree\nof $G$ is a spanning tree with at most $k$ leaves, where $k\\geq2$ is an\ninteger. In this paper, we prove some tight spectral conditions for the\nexistence of a spanning $k$-tree in $t$-connected graphs. Some of our results\ngeneralize the result of Fan, Goryainov, Huang and Lin (2022) and improve the\nspectral condition for a Hamilton path of Fiedler and Nikiforov (2010). For\nwhether $t$-connected graphs contain a spanning $k$-ended-tree, we present two\nspectral conditions which are improvements of the results of Ao, Liu and Yuan\n(2023).\n', ""Fan's condition for completely independent spanning trees   Spanning trees $T_1,T_2, \\dots,T_k$ of $G$ are $k$ completely independent\nspanning trees if, for any two vertices $u,v\\in V(G)$, the paths from $u$ to\n$v$ in these $k$ trees are pairwise edge-disjoint and internal vertex-disjoint.\nHasunuma proved that determining whether a graph contains $k$ completely\nindependent spanning trees is NP-complete, even for $k = 2$. Araki posed the\nquestion of whether certain known sufficient conditions for hamiltonian cycles\nare also also guarantee two completely independent spanning trees? In this\npaper, we affirmatively answer this question for the Fan-type condition.\nPrecisely, we proved that if $G$ is a connected graph such that each pair of\nvertices at distance 2 has degree sum at least $|V(G)|$, then $G$ has two\ncompletely independent spanning trees.\n"", 'Completely Independent Spanning Trees in Line Graphs   Completely independent spanning trees in a graph $G$ are spanning trees of\n$G$ such that for any two distinct vertices of $G$, the paths between them in\nthe spanning trees are pairwise edge-disjoint and internally vertex-disjoint.\nIn this paper, we present a tight lower bound on the maximum number of\ncompletely independent spanning trees in $L(G)$, where $L(G)$ denotes the line\ngraph of a graph $G$. Based on a new characterization of a graph with $k$\ncompletely independent spanning trees, we also show that for any complete graph\n$K_n$ of order $n \\geq 4$, there are $\\lfloor \\frac{n+1}{2} \\rfloor$ completely\nindependent spanning trees in $L(K_n)$ where the number $\\lfloor \\frac{n+1}{2}\n\\rfloor$ is optimal, such that $\\lfloor \\frac{n+1}{2} \\rfloor$ completely\nindependent spanning trees still exist in the graph obtained from $L(K_n)$ by\ndeleting any vertex (respectively, any induced path of order at most\n$\\frac{n}{2}$) for $n = 4$ or odd $n \\geq 5$ (respectively, even $n \\geq 6$).\nConcerning the connectivity and the number of completely independent spanning\ntrees, we moreover show the following, where $\\delta(G)$ denotes the minimum\ndegree of $G$. $\\ $ $\\bullet$ Every $2k$-connected line graph $L(G)$ has $k$\ncompletely independent spanning trees if $G$ is not super edge-connected or\n$\\delta(G) \\geq 2k$. $\\ $ $\\bullet$ Every $(4k-2)$-connected line graph $L(G)$\nhas $k$ completely independent spanning trees if $G$ is regular. $\\ $ $\\bullet$\nEvery $(k^2+2k-1)$-connected line graph $L(G)$ with $\\delta(G) \\geq k+1$ has\n$k$ completely independent spanning trees.\n']","[('spanning trees graphs', 0.6725278496742249), ('disjoint spanning trees', 0.6711954474449158), ('trees spanning', 0.6540799736976624), ('spanning trees', 0.6407349705696106), ('spanning trees graph', 0.6203998327255249), ('number spanning trees', 0.6183883547782898), ('graph spanning tree', 0.5963211059570312), ('spanning tree graph', 0.5842069983482361), ('spanning tree', 0.5718297362327576), ('trees graphs', 0.5562441349029541)]"
670,670,46,670_domino tilings_polygonal domains_limit shapes_tilings,"['domino tilings', 'polygonal domains', 'limit shapes', 'tilings', 'lozenge tilings', 'lattice paths', 'limit shape', 'aztec diamond', 'dominoes', 'shapes']","['Fluctuations of the Arctic curve in the tilings of the Aztec diamond on\n  restricted domains   We consider uniform random domino tilings of the restricted Aztec diamond\nwhich is obtained by cutting off an upper triangular part of the Aztec diamond\nby a horizontal line. The restriction line asymptotically touches the arctic\ncircle that is the limit shape of the north polar region in the unrestricted\nmodel. We prove that the rescaled boundary of the north polar region in the\nrestricted domain converges to the Airy$_2$ process conditioned to stay below a\nparabola with explicit continuous statistics and the finite dimensional\ndistribution kernels. The limit is the hard-edge tacnode process which was\nfirst discovered in the framework of non-intersecting Brownian bridges. The\nproof relies on a random walk representation of the correlation kernel of the\nnon-intersecting line ensemble which corresponds to a random tiling.\n', ""Domino tilings of the Aztec diamond with doubly periodic weightings   In this paper we consider domino tilings of the Aztec diamond with doubly\nperiodic weightings. In particular a family of models which, for any $ k \\in\n\\mathbb{N} $, includes models with $ k $ smooth regions is analyzed as the size\nof the Aztec diamond tends to infinity. We use a non-intersecting paths\nformulation and give a double integral formula for the correlation kernel of\nthe Aztec diamond of finite size. By a classical steepest descent analysis of\nthe correlation kernel we obtain the local behavior in the smooth and rough\nregions as the size of the Aztec diamond tends to infinity. From the mentioned\nlimit the macroscopic picture such as the arctic curves and in particular the\nnumber of smooth regions is deduced. Moreover we compute the limit of the\nheight function and as a consequence we confirm, in the setting of this paper,\nthat the limit in the rough region fulfills the complex Burgers' equation, as\nstated by Kenyon and Okounkov.\n"", ""Boundary dents, the arctic circle and the arctic ellipse   The original motivation for this paper goes back to the mid-1990's, when\nJames Propp was interested in natural situations when the number of domino\ntilings of a region increases if some of its unit squares are deleted. Guided\nin part by the intuition one gets from earlier work on parallels between the\nnumber of tilings of a region with holes and the 2D Coulomb energy of the\ncorresponding system of electric charges, we consider Aztec diamond regions\nwith unit square defects along two adjacent sides. We show that for large\nregions, if these defects are at fixed distances from a corner, the ratio\nbetween the number of domino tilings of the Aztec diamond with defects and the\nnumber of tilings of the entire Aztec diamond approaches a Delannoy number.\n  When the locations of the defects are not fixed but instead approach given\npoints on the boundary of the scaling limit $S$ (a square) of the Aztec\ndiamonds, we prove that, provided the line segment connecting these points is\noutside the circle inscribed in $S$, this ratio has the same asymptotics as the\nDelannoy number corresponding to the locations of the defects; if the segment\ncrosses the circle, the asymptotics is radically different. We use this to\ndeduce (under the assumption that an arctic curve exists) that the arctic curve\nfor domino tilings of Aztec diamonds is the circle inscribed in $S$. We also\ndiscuss counterparts of this phenomenon for lozenge tilings of hexagons.\n""]","[('domino tilings', 0.5201013684272766), ('polygonal domains', 0.4523870050907135), ('limit shapes', 0.43485257029533386), ('tilings', 0.4267529845237732), ('lozenge tilings', 0.40705642104148865), ('lattice paths', 0.3934832811355591), ('limit shape', 0.3914043605327606), ('aztec diamond', 0.39038532972335815), ('dominoes', 0.370918333530426), ('shapes', 0.37035173177719116)]"
671,671,46,671_dimensional coulomb gases_2d coulomb gas_coulomb gases_two dimensional coulomb,"['dimensional coulomb gases', '2d coulomb gas', 'coulomb gases', 'two dimensional coulomb', 'coulomb gas', '2d coulomb', 'dimensional coulomb', 'coulomb', 'gas particles', 'fluctuations linear']","['Two-Dimensional Coulomb Gas on an Elliptic Annulus   It is well-known that two-dimensional Coulomb gases at a special inverse\ntemperature $\\beta = 2$ can be analyzed by using the orthogonal polynomial\nmethod borrowed from the theory of random matrices. In this paper, such Coulomb\ngas molecules are studied when they are distributed on an elliptic annulus, and\nthe asymptotic forms of the molecule correlation functions in the thermodynamic\nlimit are evaluated. For that purpose, two-dimensional orthogonality relations\nof the Chebyshev polynomials on an elliptic annulus are utilized.\n', 'The two-dimensional Coulomb plasma: quasi-free approximation and central\n  limit theorem   For the two-dimensional one-component Coulomb plasma, we derive an asymptotic\nexpansion of the free energy up to order $N$, the number of particles of the\ngas, with an effective error bound $N^{1-\\kappa}$ for some constant $\\kappa >\n0$. This expansion is based on approximating the Coulomb gas by a quasi-free\nYukawa gas. Further, we prove that the fluctuations of the linear statistics\nare given by a Gaussian free field at any positive temperature. Our proof of\nthis central limit theorem uses a loop equation for the Coulomb gas, the free\nenergy asymptotics, and rigidity bounds on the local density fluctuations of\nthe Coulomb gas, which we obtained in a previous paper.\n', 'Non-rigidity Properties of the Coulomb Gas   We prove existence of infinite volume $d$-dimensional Coulomb gases which are\nnot number rigid for $d \\geq 3$. This makes the Coulomb gas the Gibbs point\nprocess with the longest range pairwise interaction (i.e.\\ with the smallest\n$s$ in the interaction kernel $g(x) = |x|^{-s}$) for which number non-rigidity\nhas been proved in $d \\geq 3$. We rule out properties stronger than number\nrigidity for the two-dimensional Coulomb gas.\n']","[('dimensional coulomb gases', 0.6818965077400208), ('2d coulomb gas', 0.633505642414093), ('coulomb gases', 0.6008849143981934), ('two dimensional coulomb', 0.5432865619659424), ('coulomb gas', 0.5276135802268982), ('2d coulomb', 0.5086796283721924), ('dimensional coulomb', 0.5066767930984497), ('coulomb', 0.3974767029285431), ('gas particles', 0.37467896938323975), ('fluctuations linear', 0.34853002429008484)]"
672,672,46,672_ordinals_ordinal_reflection principles_transfinite induction,"['ordinals', 'ordinal', 'reflection principles', 'transfinite induction', 'linear orders', 'theoretic', 'order type', 'well ordering', 'consistency strength', 'base theory']","[""The Order of Reflection   Extending Aanderaa's classical result that $\\pi^1_1<\\sigma^1_1$, we determine\nthe order between any two patterns of iterated $\\Sigma^1_1$- and\n$\\Pi^1_1$-reflection. We show that this \\emph{linear reflection order} is a\nprewellordering of length $\\omega^\\omega$. This requires considering the\nrelationship between linear and some \\emph{non-linear} reflection patterns,\nsuch as $\\sigma^1_1\\wedge\\pi^1_1$, the pattern of simultaneous $\\Sigma^1_1$-\nand $\\Pi^1_1$-reflection.\n"", 'A characterization of ordinal analysis   Ordinal analysis induces a partition of $\\Sigma^1_1$-definable and\n$\\Pi^1_1$-sound theories whereby two theories are equivalent if they have the\nsame proof-theoretic ordinal. We show that no equivalence relation $\\equiv$ is\nfiner than the ordinal analysis partition if both: (1) $T\\equiv U$ whenever $T$\nand $U$ prove the same $\\Pi^1_1$ sentences; (2) $T\\equiv T+U$ for every set $U$\nof true $\\Sigma^1_1$ sentences. In fact, no such equivalence relation makes a\nsingle distinction that the ordinal analysis partition does not make.\n', 'Reflection ranks and ordinal analysis   It is well-known that natural axiomatic theories are well-ordered by\nconsistency strength. However, it is possible to construct descending chains of\nartificial theories with respect to consistency strength. We provide an\nexplanation of this well-orderness phenomenon by studying a coarsening of the\nconsistency strength order, namely, the $\\Pi^1_1$ reflection strength order. We\nprove that there are no descending sequences of $\\Pi^1_1$ sound extensions of\n$\\mathsf{ACA}_0$ in this order. Accordingly, we can attach a rank in this\norder, which we call reflection rank, to any $\\Pi^1_1$ sound extension of\n$\\mathsf{ACA}_0$. We prove that for any $\\Pi^1_1$ sound theory $T$ extending\n$\\mathsf{ACA}_0^+$, the reflection rank of $T$ equals the proof-theoretic\nordinal of $T$. We also prove that the proof-theoretic ordinal of $\\alpha$\niterated $\\Pi^1_1$ reflection is $\\varepsilon_\\alpha$. Finally, we use our\nresults to provide straightforward well-foundedness proofs of ordinal notation\nsystems based on reflection principles.\n']","[('ordinals', 0.5226213335990906), ('ordinal', 0.4730663299560547), ('reflection principles', 0.4057880938053131), ('transfinite induction', 0.40332359075546265), ('linear orders', 0.35559695959091187), ('theoretic', 0.33820316195487976), ('order type', 0.3327895998954773), ('well ordering', 0.32798832654953003), ('consistency strength', 0.3257976472377777), ('base theory', 0.3227144479751587)]"
673,673,46,673_equivariant homotopy theory_equivariant stable homotopy_equivariant homotopy_equivariant stable,"['equivariant homotopy theory', 'equivariant stable homotopy', 'equivariant homotopy', 'equivariant stable', 'equivariant cohomology', 'stable homotopy theory', 'equivariant algebraic', 'genuine equivariant', 'equivariant', 'categories twisted']","['Twisted ambidexterity in equivariant homotopy theory   We develop the concept of twisted ambidexterity in a parametrized presentably\nsymmetric monoidal $\\infty$-category, which generalizes the notion of\nambidexterity by Hopkins and Lurie and the Wirthm\\""uller isomorphisms in\nequivariant stable homotopy theory, and is closely related to Costenoble-Waner\nduality. Our main result establishes the parametrized $\\infty$-category of\ngenuine $G$-spectra for a compact Lie group $G$ as the universal example of a\npresentably symmetric monoidal $\\infty$-category parametrized over $G$-spaces\nwhich is both stable and satisfies twisted ambidexterity for compact\n$G$-spaces. We further extend this result to the settings of orbispectra and\nproper genuine $G$-spectra for a Lie group $G$ which is not necessarily\ncompact.\n', 'The Adams isomorphism revisited   We establish abstract Adams isomorphisms in an arbitrary equivariantly\npresentable equivariantly semiadditive global category. This encompasses the\nwell-known Adams isomorphism in equivariant stable homotopy theory, and applies\nmore generally in the settings of $G$-Mackey functors, $G$-global homotopy\ntheory, and equivariant Kasparov categories.\n', 'Proper equivariant stable homotopy theory   This monograph introduces a framework for genuine proper equivariant stable\nhomotopy theory for Lie groups. The adjective `proper\' alludes to the feature\nthat equivalences are tested on compact subgroups, and that the objects are\nbuilt from equivariant cells with compact isotropy groups; the adjective\n`genuine\' indicates that the theory comes with appropriate transfers and\nWirthm\\""uller isomorphisms, and the resulting equivariant cohomology theories\nsupport the analog of an $RO(G)$-grading.\n  Our model for genuine proper $G$-equivariant stable homotopy theory is the\ncategory of orthogonal $G$-spectra; the equivalences are those morphisms that\ninduce isomorphisms of equivariant stable homotopy groups for all compact\nsubgroups of $G$. This class of $\\pi_*$-isomorphisms is part of a symmetric\nmonoidal stable model structure and the associated tensor triangulated homotopy\ncategory is compactly generated. Every orthogonal $G$-spectrum represents an\nequivariant cohomology theory on the category of $G$-spaces, depending only on\nthe `proper $G$-homotopy type\', tested by fixed points under all compact\nsubgroups.\n  An important special case are infinite discrete groups. For these, our\ngenuine equivariant theory is related to finiteness properties, in the sense of\ngeometric group theory; for example, the $G$-sphere spectrum is a compact\nobject in the equivariant homotopy category if the universal space for proper\n$G$-actions has a finite $G$-CW-model. For discrete groups, the represented\nequivariant cohomology theories on finite proper $G$-CW-complexes admit a more\nexplicit description in terms of parameterized equivariant homotopy theory,\nsuitably stabilized by $G$-vector bundles. Via this description, we can\nidentify the previously defined $G$-cohomology theories of equivariant stable\ncohomotopy and equivariant K-theory as cohomology theories represented by\nspecific orthogonal $G$-spectra.\n']","[('equivariant homotopy theory', 0.6713151335716248), ('equivariant stable homotopy', 0.6552557349205017), ('equivariant homotopy', 0.5968698859214783), ('equivariant stable', 0.5821713209152222), ('equivariant cohomology', 0.5689070820808411), ('stable homotopy theory', 0.5538592338562012), ('equivariant algebraic', 0.5185088515281677), ('genuine equivariant', 0.49710813164711), ('equivariant', 0.4875231981277466), ('categories twisted', 0.48527204990386963)]"
674,674,46,674_ultradifferentiable functions_ultradifferentiable_weighted spaces_gelfand shilov spaces,"['ultradifferentiable functions', 'ultradifferentiable', 'weighted spaces', 'gelfand shilov spaces', 'spaces weighted', 'weight functions', 'weight matrices', 'weight functions omega', 'ultradistributions', 'shilov spaces']","['Equality of ultradifferentiable classes by means of indices of mixed\n  O-regular variation   We characterize the equality between ultradifferentiable function classes\ndefined in terms of abstractly given weight matrices and in terms of the\ncorresponding matrix of associated weight functions by using new growth\nindices. These indices, defined by means of weight sequences and (associated)\nweight functions, are extending the notion of O-regular variation to a mixed\nsetting. Hence we are extending the known comparison results concerning classes\ndefined in terms of a single weight sequence and of a single weight function\nand give also these statements an interpretation expressed in O-regular\nvariation.\n', ""On the projective description of spaces of ultradifferentiable functions\n  of Roumieu type   We provide a projective description of the space\n$\\mathcal{E}^{\\{\\mathfrak{M}\\}}(\\Omega)$ of ultradifferentiable functions of\nRoumieu type, where $\\Omega$ is an arbitrary open set in $\\mathbb{R}^d$ and\n$\\mathfrak{M}$ is a weight matrix satisfying the analogue of Komatsu's\ncondition $(M.2)'$. In particular, we obtain in a unified way projective\ndescriptions of ultradifferentiable classes defined via a single weight\nsequence (Denjoy-Carleman approach) and via a weight function\n(Braun-Meise-Taylor approach) under considerably weaker assumptions than in\nearlier versions of these results.\n"", 'On generalized definitions of ultradifferentiable classes   We show that the ultradifferentiable-like classes of smooth functions\nintroduced and studied by S. Pilipovi\\\'c, N. Teofanov and F. Tomi\\\'c are\nspecial cases of the general framework of spaces of ultradifferentiable\nfunctions defined in terms of weight matrices in the sense of A. Rainer and the\nthird author. We study classes ""beyond geometric growth factors"" defined in\nterms of a weight sequence and an exponent sequence, prove that these new types\nadmit a weight matrix representation and transfer known results from the\nmatrix-type to such a non-standard ultradifferentiable setting.\n']","[('ultradifferentiable functions', 0.6510055661201477), ('ultradifferentiable', 0.5697295069694519), ('weighted spaces', 0.4668366611003876), ('gelfand shilov spaces', 0.41453787684440613), ('spaces weighted', 0.40318599343299866), ('weight functions', 0.40149012207984924), ('weight matrices', 0.37983012199401855), ('weight functions omega', 0.3728023171424866), ('ultradistributions', 0.37005814909935), ('shilov spaces', 0.3489963710308075)]"
675,675,46,675_sequences arbitrary_sequences various_binary alphabets_sequences well,"['sequences arbitrary', 'sequences various', 'binary alphabets', 'sequences well', 'sequences', 'sequences can', 'bruijn', 'finite alphabet', 'binary strings', 'de bruijn']","['To Infinity and Beyond: Continuing De Bruijn Sequences by Extending the\n  Alphabet   This article presents proof that the reverse of the Prefer Max De Bruijn\nsequence can be expanded into an infinite De Bruijn sequence by increasing the\nsize of the alphabet. Furthermore, we show that every De Bruijn sequence\npossessing this characteristic exhibits behavior similar to that of the reverse\nof the Prefer Max De Bruijn sequence.\n', 'Generalized Orthogonal de Bruijn and Kautz Sequences   A de Bruijn sequence of order $k$ over a finite alphabet is a cyclic sequence\nwith the property that it contains every possible $k$-sequence as a substring\nexactly once. Orthogonal de Bruijn sequences are collections of de Bruijn\nsequences of the same order, $k$, satisfying the joint constraint that every\n$(k+1)$-sequence appears as a substring in at most one of the sequences in the\ncollection. Both de Bruijn and orthogonal de Bruijn sequences have found\nnumerous applications in synthetic biology, although the latter remain largely\nunexplored in the coding theory literature. Here we study three relevant\npractical generalizations of orthogonal de Bruijn sequences where we relax\neither the constraint that every $(k+1)$-sequence appears exactly once, or that\nthe sequences themselves are de Bruijn rather than balanced de Bruijn\nsequences. We also provide lower and upper bounds on the number of fixed-weight\northogonal de Bruijn sequences. The paper concludes with parallel results for\northogonal nonbinary Kautz sequences, which satisfy similar constraints as de\nBruijn sequences except for only being required to cover all subsequences of\nlength $k$ whose maximum runlength equals to one.\n', ""Using alternating de Bruijn sequences to construct de Bruijn tori   A de Bruijn torus is the two dimensional generalization of a de Bruijn\nsequence. While some methods exist to generate these tori, only a few methods\nof construction are known. We present a novel method to generate de Bruijn tori\nwith rectangular windows by combining two variants de Bruijn sequences called\n`Alternating de Bruijn sequences' and `De Bruijn families'.\n""]","[('sequences arbitrary', 0.5277830362319946), ('sequences various', 0.5040925145149231), ('binary alphabets', 0.4802943170070648), ('sequences well', 0.45780467987060547), ('sequences', 0.4460950791835785), ('sequences can', 0.4451020061969757), ('bruijn', 0.43534377217292786), ('finite alphabet', 0.42908141016960144), ('binary strings', 0.4246056377887726), ('de bruijn', 0.42257237434387207)]"
676,676,46,676_knowledge graph_knowledge graphs_knowledge structure_graph embedding,"['knowledge graph', 'knowledge graphs', 'knowledge structure', 'graph embedding', 'knowledge', 'digital transformation', 'entities', 'semantic', 'embedding', 'ontologies']","[""Knowledge Sheaves: A Sheaf-Theoretic Framework for Knowledge Graph\n  Embedding   Knowledge graph embedding involves learning representations of entities --\nthe vertices of the graph -- and relations -- the edges of the graph -- such\nthat the resulting representations encode the known factual information\nrepresented by the knowledge graph and can be used in the inference of new\nrelations. We show that knowledge graph embedding is naturally expressed in the\ntopological and categorical language of \\textit{cellular sheaves}: a knowledge\ngraph embedding can be described as an approximate global section of an\nappropriate \\textit{knowledge sheaf} over the graph, with consistency\nconstraints induced by the knowledge graph's schema. This approach provides a\ngeneralized framework for reasoning about knowledge graph embedding models and\nallows for the expression of a wide range of prior constraints on embeddings.\nFurther, the resulting embeddings can be easily adapted for reasoning over\ncomposite relations without special training. We implement these ideas to\nhighlight the benefits of the extensions inspired by this new perspective.\n"", 'Representation-Enhanced Neural Knowledge Integration with Application to\n  Large-Scale Medical Ontology Learning   A large-scale knowledge graph enhances reproducibility in biomedical data\ndiscovery by providing a standardized, integrated framework that ensures\nconsistent interpretation across diverse datasets. It improves generalizability\nby connecting data from various sources, enabling broader applicability of\nfindings across different populations and conditions. Generating reliable\nknowledge graph, leveraging multi-source information from existing literature,\nhowever, is challenging especially with a large number of node sizes and\nheterogeneous relations. In this paper, we propose a general theoretically\nguaranteed statistical framework, called RENKI, to enable simultaneous learning\nof multiple relation types. RENKI generalizes various network models widely\nused in statistics and computer science. The proposed framework incorporates\nrepresentation learning output into initial entity embedding of a neural\nnetwork that approximates the score function for the knowledge graph and\ncontinuously trains the model to fit observed facts. We prove nonasymptotic\nbounds for in-sample and out-of-sample weighted MSEs in relation to the\npseudo-dimension of the knowledge graph function class. Additionally, we\nprovide pseudo-dimensions for score functions based on multilayer neural\nnetworks with ReLU activation function, in the scenarios when the embedding\nparameters either fixed or trainable. Finally, we complement our theoretical\nresults with numerical studies and apply the method to learn a comprehensive\nmedical knowledge graph combining a pretrained language model representation\nwith knowledge graph links observed in several medical ontologies. The\nexperiments justify our theoretical findings and demonstrate the effect of\nweighting in the presence of heterogeneous relations and the benefit of\nincorporating representation learning in nonparametric models.\n', 'Exploring the Enablers of Digital Transformation in Small and\n  Medium-Sized Enterprise   Recently, digital transformation has caught much attention of both academics\nand practitioners. With the advent of digital technologies,\nsmall-and-medium-sized enterprises (SMEs) have obtained the capacity to\ninitiate digital transformation initiatives in a similar fashion to large-sized\norganizations. The innate characteristics of digital technologies also favor\nSMEs in promoting initiation of digital transformation. However, the process\ndigital transformation in SMEs remains a black box and the existing findings of\ndigital transformation in SMEs are limited and remain fragmented. Considering\nthe important contribution SMEs can offer to nations and economies; it is\ntimely and relevant to conduct a profound analysis on digital transformation in\nSMEs. By conducting a thorough review of existing related literature in\nmanagement, information systems, and business disciplines, this book chapter\naims to understand both internal and external enablers of the digital\ntransformation in SMEs.\n']","[('knowledge graph', 0.5521101355552673), ('knowledge graphs', 0.544510543346405), ('knowledge structure', 0.47052285075187683), ('graph embedding', 0.4194835126399994), ('knowledge', 0.37838512659072876), ('digital transformation', 0.3639223575592041), ('entities', 0.3392196595668793), ('semantic', 0.32359397411346436), ('embedding', 0.31296077370643616), ('ontologies', 0.31196537613868713)]"
677,677,46,677_sobolev spaces_sobolev space_order sobolev spaces_sobolev mappings,"['sobolev spaces', 'sobolev space', 'order sobolev spaces', 'sobolev mappings', 'sobolev functions', 'metric measure spaces', 'spaces metric measure', 'functions sobolev', 'measure spaces', 'sobolev']","[""Capacitary density and removable sets for Newton-Sobolev functions in\n  metric spaces   In a complete metric space equipped with a doubling measure and supporting a\n$(1,1)$-Poincar\\'e inequality, we show that every set satisfying a suitable\ncapacitary density condition is removable for Newton-Sobolev functions.\n"", ""Characterizations of Sobolev functions via Besov-type energy functionals\n  in fractals   In the spirit of the ground-breaking result of Bourgain--Brezis--Mironescu,\nwe establish some characterizations of Sobolev functions in metric measure\nspaces including fractals like the Vicsek set, the Sierpi\\'{n}ski gasket and\nthe Sierpi\\'{n}ski carpet. As corollaries of our characterizations, we present\nequivalent norms on the Korevaar--Schoen--Sobolev space, and show that the\ndomain of a $p$-energy form is identified with a Besov-type function space\nunder a suitable $(p,p)$-Poincar\\'e inequality, capacity upper bound and the\nvolume doubling property.\n"", ""Korevaar-Schoen-Sobolev spaces and critical exponents in metric measure\n  spaces   We present developments in the theory of Korevaar-Schoen-Sobolev spaces on\nmetric measure spaces. While this theory coincides with those of Cheeger and\nShanmugalingam if the space is doubling and satisfies a Poincar\\'e inequality,\nit offers new perspectives in the context of fractals for which the approach by\nweak upper gradients is inadequate.\n""]","[('sobolev spaces', 0.6500704288482666), ('sobolev space', 0.6323177218437195), ('order sobolev spaces', 0.5821227431297302), ('sobolev mappings', 0.5393475294113159), ('sobolev functions', 0.5092771053314209), ('metric measure spaces', 0.4995458722114563), ('spaces metric measure', 0.49579089879989624), ('functions sobolev', 0.4951194226741791), ('measure spaces', 0.49142980575561523), ('sobolev', 0.47453442215919495)]"
678,678,46,678_extremum seeking_global minimiser_real time optimization_optimal point,"['extremum seeking', 'global minimiser', 'real time optimization', 'optimal point', 'time optimization', 'convergence optimum', 'extremum', 'local extrema', 'optimum', 'vector control']","['Extremum Seeking with Intermittent Measurements: A Lie-brackets Approach   Extremum seeking systems are powerful methods able to steer the input of a\n(dynamical) cost function towards an optimizer, without any prior knowledge of\nthe cost function. To achieve their objective, they typically combine\ntime-periodic signals with the on-line measurement of the cost. However, in\nsome practical applications, the cost can only be measured during some regular\ntime-intervals, and not continuously, contravening the classical extremum\nseeking framework. In this paper, we first analyze how existing Lie-bracket\nbased extremum seeking systems behave when being fed with intermittent\nmeasurements, instead of continuous ones. We then propose two modifications of\nthose schemes to improve both the convergence time and the steady-state\naccuracy in presence of intermittent measurements. The performances of the\ndifferent schemes are compared on a case study.\n', 'Extremum Seeking for Stefan PDE with Moving Boundary   This paper presents the design and analysis of the extremum seeking for\nstatic maps with input passed through a partial differential equation (PDE) of\nthe diffusion type defined on a time-varying spatial domain whose boundary\nposition is governed by an ordinary differential equation (ODE). This is the\nfirst effort to pursue an extension of extremum seeking from the heat PDE to\nthe Stefan PDE. We compensate the average-based actuation dynamics by a\ncontroller via backstepping transformation for the moving boundary, which is\nutilized to transform the original coupled PDE-ODE into a target system whose\nexponential stability of the average equilibrium of the average system is\nproved. The discussion for the delay-compensated extremum seeking control of\nthe Stefan problem is also presented and illustrated with numerical\nsimulations.\n', 'Extremum Seeking with High-Order Lie Bracket Approximations: Achieving\n  Exponential Decay Rate   This paper focuses on the further development of the Lie bracket\napproximation approach for extremum seeking systems. Classical results in this\narea provide extremum seeking algorithms with exponential convergence rates for\nquadratic-like cost functions, and polynomial decay rates for cost functions of\nhigher degrees. This paper proposes a novel control design approach that\nensures the motion of the extremum seeking system along directions associated\nwith higher-order Lie brackets, thereby ensuring exponential convergence for\ncost functions that are polynomial-like but with degree greater than two.\n']","[('extremum seeking', 0.6340025067329407), ('global minimiser', 0.5283120274543762), ('real time optimization', 0.4873504936695099), ('optimal point', 0.4580681622028351), ('time optimization', 0.44141092896461487), ('convergence optimum', 0.4265473484992981), ('extremum', 0.3648635149002075), ('local extrema', 0.3552035391330719), ('optimum', 0.35024601221084595), ('vector control', 0.35014981031417847)]"
679,679,46,679_metastable states_spin models_metastable behavior_curie weiss,"['metastable states', 'spin models', 'metastable behavior', 'curie weiss', 'metastability', 'phase transition', 'field spin', 'mean field spin', 'spins', 'glauber dynamics']","['Critical Regime in a Curie-Weiss Model with two Groups and Heterogeneous\n  Coupling   We discuss a Curie-Weiss model with two groups in the critical regime. This\nis the region where the central limit theorem does not hold any more but the\nmean magnetization still goes to zero as the number of spins grows. We show\nthat the total magnetization normalized by $N^{3/4}$ converges to a non-trivial\ndistribution which is not Gaussian, just as in the single-group Curie-Weiss\nmodel.\n', 'Energy Landscape and Metastability of Curie-Weis-Potts Model   In this paper, we thoroughly analyze the energy landscape of the\nCurie-Weiss-Potts model, which is a ferromagnetic spin system consisting of q\n$\\ge$ 3 spins defined on complete graphs. In particular, for the\nCurie-Weiss-Potts model with q $\\ge$ 3 spins and zero external field, we\ncompletely characterize all critical temperatures and phase transitions in view\nof the global structure of the energy landscape. We observe that there are\nthree critical temperatures and four different regimes for q < 5, whereas there\nare four critical temperatures and five different regimes for q $\\ge$ 5. Our\nanalysis extends the investigations performed in [M. Costeniuc, R. S. Ellis, H.\nTouchette: J. Math. Phys (2005)]; they provide the precise characterization of\nthe second critical temperatures for all q $\\ge$ 3 and in [Landim and Seo: J.\nStat. Phys. (2016)], which provides a complete analysis of the energy landscape\nfor q = 3. Based on our precise analysis of the energy landscape, we also\nperform a quantitative investigation of the metastable behavior of the\nheat-bath Glauber dynamics associated with the Curie-Weiss-Potts model.\n', 'Energy landscape of the two-component Curie-Weiss-Potts model with three\n  spins   In this paper, we investigate the energy landscape of the two-component spin\nsystems, known as the Curie-Weiss-Potts model, which is a generalization of the\nCurie-Weiss model consisting of $q\\ge3$ spins. In the energy landscape of a\nmulti-component model, the most important element is the relative strength\nbetween the inter-component interaction strength and the component-wise\ninteraction strength. If the inter-component interaction is stronger than the\ncomponent-wise interaction, we can expect all the components to be synchronized\nin the course of metastable transition. However, if the inter-component\ninteraction is relatively weaker, then the components will be desynchronized in\nthe course of metastable transition. For the two-component Curie-Weiss model,\nthe phase transition from synchronization to desynchronization has been\nprecisely characterized in studies owing to its mean-field nature. The purpose\nof this paper is to extend this result to the Curie-Weiss-Potts model with\nthree spins. We observe that the nature of the phase transition for the\nthree-spin case is entirely different from the two-spin case of the Curie-Weiss\nmodel, and the proof as well as the resulting phase diagram is fundamentally\ndifferent and exceedingly complicated.\n']","[('metastable states', 0.5133627653121948), ('spin models', 0.501051664352417), ('metastable behavior', 0.438105046749115), ('curie weiss', 0.41267672181129456), ('metastability', 0.4103182256221771), ('phase transition', 0.40998661518096924), ('field spin', 0.4018949568271637), ('mean field spin', 0.37668511271476746), ('spins', 0.37124577164649963), ('glauber dynamics', 0.3604836165904999)]"
680,680,46,680_cohomology groups_co homology groups_homology groups_equivariant homology,"['cohomology groups', 'co homology groups', 'homology groups', 'equivariant homology', 'lie group', 'connected lie group', 'cohomology', 'torsion homology', 'co homology', 'second homotopy group']","[""Spaces of commuting elements in the classical groups   Let $G$ be the classical group, and let Hom$(\\mathbb{Z}^m,G)$ denote the\nspace of commuting $m$-tuples in $G$. First, we refine the formula for the\nPoincar\\'e series of Hom$(\\mathbb{Z}^m,G)$ due to Ramras and Stafa by assigning\n(signed) integer partitions to (signed) permutations. Using the refined\nformula, we determine the top term of the Poincar\\'e series, and apply it to\nprove the dependence of the topology of Hom$(\\mathbb{Z}^m,G)$ on the parity of\n$m$ and the rational hyperbolicity of Hom$(\\mathbb{Z}^m,G)$ for $m\\ge 2$. Next,\nwe give a minimal generating set of the cohomology of Hom$(\\mathbb{Z}^m,G)$ and\ndetermine the cohomology in low dimensions. We apply these results to prove\nhomological stability for Hom$(\\mathbb{Z}^m,G)$ with the best possible stable\nrange. Baird proved that the cohomology of Hom$(\\mathbb{Z}^m,G)$ is identified\nwith a certain ring of invariants of the Weyl group of $G$, and our approach is\na direct calculation of this ring of invariants.\n"", 'Torsion in the space of commuting elements in a Lie group   Let $G$ be a compact connected Lie group, and let\n$\\mathrm{Hom}(\\mathbb{Z}^m,G)$ be the space of pairwise commuting $m$-tuples in\n$G$. We study the problem of which primes $p$ $\\mathrm{Hom}(\\mathbb{Z}^m,G)_1$,\nthe connected component of $\\mathrm{Hom}(\\mathbb{Z}^m,G)$ containing the\nelement $(1,\\ldots,1)$, has $p$-torsion in homology. We will prove that\n$\\mathrm{Hom}(\\mathbb{Z}^m,G)_1$ for $m\\ge 2$ has $p$-torsion in homology if\nand only if $p$ divides the order of the Weyl group of $G$ for $G=SU(n)$ and\nsome exceptional groups. We will also compute the top homology of\n$\\mathrm{Hom}(\\mathbb{Z}^m,G)_1$ and show that $\\mathrm{Hom}(\\mathbb{Z}^m,G)_1$\nalways has 2-torsion in homology whenever $G$ is simply-connected and simple.\nOur computation is based on a new homotopy decomposition of\n$\\mathrm{Hom}(\\mathbb{Z}^m,G)_1$, which is of independent interest and enables\nus to connect torsion in homology to the combinatorics of the Weyl group.\n', 'On the second homotopy group of spaces of commuting elements in Lie\n  groups   Let $G$ be a compact connected Lie group and $n\\geqslant 1$ an integer.\nConsider the space of ordered commuting $n$-tuples in $G$,\n$Hom(\\mathbb{Z}^n,G)$, and its quotient under the adjoint action,\n$Rep(\\mathbb{Z}^n,G):=Hom(\\mathbb{Z}^n,G)/G$. In this article we study and in\nmany cases compute the homotopy groups $\\pi_2(Hom(\\mathbb{Z}^n,G))$. For $G$\nsimply--connected and simple we show that $\\pi_2(Hom(\\mathbb{Z}^2,G))\\cong\n\\mathbb{Z}$ and $\\pi_2(Rep(\\mathbb{Z}^2,G))\\cong \\mathbb{Z}$, and that on these\ngroups the quotient map $Hom(\\mathbb{Z}^2,G)\\to Rep(\\mathbb{Z}^2,G)$ induces\nmultiplication by the Dynkin index of $G$. More generally we show that if $G$\nis simple and $Hom(\\mathbb{Z}^2,G)_{1}\\subseteq Hom(\\mathbb{Z}^2,G)$ is the\npath--component of the trivial homomorphism, then\n$H_2(Hom(\\mathbb{Z}^2,G)_{1};\\mathbb{Z})$ is an extension of the Schur\nmultiplier of $\\pi_1(G)^2$ by $\\mathbb{Z}$. We apply our computations to prove\nthat if $B_{com}G_{1}$ is the classifying space for commutativity at the\nidentity component, then $\\pi_4(B_{com}G_{1})\\cong \\mathbb{Z}\\oplus\n\\mathbb{Z}$, and we construct examples of non-trivial transitionally\ncommutative structures on the trivial principal $G$-bundle over the sphere\n$\\mathbb{S}^{4}$.\n']","[('cohomology groups', 0.58210688829422), ('co homology groups', 0.5480575561523438), ('homology groups', 0.5344223380088806), ('equivariant homology', 0.479054719209671), ('lie group', 0.4762938618659973), ('connected lie group', 0.4609653353691101), ('cohomology', 0.44665074348449707), ('torsion homology', 0.4388989806175232), ('co homology', 0.4356512725353241), ('second homotopy group', 0.4312891364097595)]"
681,681,46,681_lattice gauge theories_lattice gauge theory_lattice gauge_yang mills theory,"['lattice gauge theories', 'lattice gauge theory', 'lattice gauge', 'yang mills theory', 'gauge theories', 'yang mills theories', 'wilson loops', 'wilson loop', 'gauge theory', 'yang mills higgs']","['Wilson lines in the Abelian lattice Higgs model   Lattice gauge theories are lattice approximations of the Yang-Mills theory in\nphysics. The abelian lattice Higgs model is one of the simplest examples of a\nlattice gauge theory interacting with an external field. In a previous\npaper~\\cite{flv2021}, we calculated the leading order term of the expected\nvalue of Wilson loop observables in the low-temperature regime of the abelian\nlattice Higgs model on $ \\mathbb{Z}^4 ,$ with structure group $G = \\mathbb{Z}_n\n$ for some $ n \\geq 2. $ In the absence of a Higgs field, these are important\nobservables since they exhibit a phase transition which can be interpreted as\ndistinguishing between regions with and without quark confinement. However, in\nthe presence of a Higgs field, this is no longer the case, and a more relevant\nfamily of observables are so-called open Wilson lines. In this paper, we extend\nand refine the ideas introduced in~\\cite{flv2021} to calculate the leading\norder term of the expected value of the more general Wilson line observables.\nUsing our main result, we then calculate the leading order term of several\nnatural ratios of expected values and confirm the behavior predicted by\nphysicists.\n', 'Pure perimeter laws for Wilson lines observables   Several recent papers have studied the decay rate of the expectation of\nWilson loop and Wilson line observables in lattice gauge theory and the lattice\nHiggs model. These results have all been perturbative in the sense that the\nparameters need to scale with the length of the loop or line for the error term\nto be smaller than the estimate. In this paper, we further develop ideas\nfrom~\\cite{fv2023} and~\\cite{f2024} to give more detailed asymptotics for the\nexpectation of Wilson loop and Wilson line observables, which do not require\nthe parameters to be very large or very small for the error term to be small,\nthus improving the results of~\\cite{flv2022, flv2023, flv2020, f2022b}. In\nparticular, we show that Wilson line and loop observables have a pure parameter\nlaw in the Higgs and confinement phases of the lattice Higgs model.\n', 'Wilson loops in Ising lattice gauge theory   Wilson loop expectation in 4D $\\mathbb{Z}_2$ lattice gauge theory is computed\nto leading order in the weak coupling regime. This is the first example of a\nrigorous theoretical calculation of Wilson loop expectation in the weak\ncoupling regime of a 4D lattice gauge theory. All prior results are either\ninequalities or strong coupling expansions.\n']","[('lattice gauge theories', 0.7003953456878662), ('lattice gauge theory', 0.7003816366195679), ('lattice gauge', 0.6130776405334473), ('yang mills theory', 0.5325402617454529), ('gauge theories', 0.5309816002845764), ('yang mills theories', 0.5299404859542847), ('wilson loops', 0.5288560390472412), ('wilson loop', 0.5269350409507751), ('gauge theory', 0.5164684057235718), ('yang mills higgs', 0.4824645221233368)]"
682,682,46,682_invariant tori_invariant torus_integrable hamiltonian systems_dimensional tori,"['invariant tori', 'invariant torus', 'integrable hamiltonian systems', 'dimensional tori', 'nearly integrable hamiltonian', 'quasiperiodic solutions', 'integrable hamiltonians', 'hamiltonian systems', 'kam theory', 'quasiperiodic']","['Quasi-periodic motions on symplectic tori   The KAM (Kolmogorov-Arnold-Moser) theorem guarantees the stability of\nquasi-periodic invariant tori by perturbation in some Hamiltonian systems.\nMichel Herman proved a similar result for quasi-periodic motions, with\n$k$-dimensional involutive manifolds in Hamiltonian systems with $n$ degrees of\nfreedom $n \\leq k < 2n $. In this paper, we extend this result to the case of a\nquasi-periodic motion on symplectic tori $k = 2n$.\n', ""Singular KAM Theory   The question of the total measure of invariant tori in analytic,\nnearly--integrable Hamiltonian systems is considered. In 1985, Arnol'd, Kozlov\nand Neishtadt, in the Encyclopaedia of Mathematical Sciences \\cite{AKN1}, and\nin subsequent editions, conjectured that in $n=2$ degrees of freedom the\nmeasure of the non torus set of general analytic nearly--integrable systems\naway from critical points is exponentially small with the size $\\e$ of the\nperturbation, and that for $n\\ge 3$ the measure is, in general, of order $\\e$\n(rather than $\\sqrt\\e$ as predicted by classical KAM Theory). In the case of\ngeneric natural Hamiltonian systems, we prove lower bounds on the measure of\nprimary and secondary invariant tori, which are in agreement, up to a\nlogarithmic correction, with the above conjectures. The proof is based on a new\n{\\sl singular} KAM theory, particularly designed to study analytic properties\nin neighborhoods of the secular separatrices generated by the perturbation at\nsimple resonances.\n"", 'Biasymptotically quasiperiodic solutions for time-dependent Hamiltonians   In a previous work [Asymptotically quasiperiodic solutions for time-dependent\nHamiltonians, arXiv preprint arXiv:2211.06623 (2022)], we consider\ntime-dependent perturbations of a Hamiltonian vector field having an invariant\ntorus supporting quasiperiodic solutions. Assuming the perturbation decays\npolynomially fast as time tends to infinity, we prove the existence of an\nasymptotic KAM torus. An asymptotic KAM torus is a time-dependent family of\nembedded tori converging as time tends to infinity to the invariant torus\nassociated with the unperturbed system. Now, it is quite natural to wonder when\nwe have the existence of a biasymptotic KAM torus. That is a continuous\ntime-dependent family of embedded tori converging in the future and the past to\nsuitable quasiperiodic invariant tori.\n  In this work, we go one step further. We analyze time-dependent perturbations\nof integrable and near-integrable Hamiltonians. Assuming the perturbation\ndecays polynomially fast in time, we prove the existence of orbit converging to\nsome quasiperiodic solutions in the future and the past.\n']","[('invariant tori', 0.6452733278274536), ('invariant torus', 0.551091194152832), ('integrable hamiltonian systems', 0.5458289384841919), ('dimensional tori', 0.5268617272377014), ('nearly integrable hamiltonian', 0.5109813213348389), ('quasiperiodic solutions', 0.504986584186554), ('integrable hamiltonians', 0.49178680777549744), ('hamiltonian systems', 0.48399287462234497), ('kam theory', 0.48120367527008057), ('quasiperiodic', 0.4774192273616791)]"
683,683,46,683_quasi einstein manifold_einstein manifolds_einstein manifold_manifolds boundary,"['quasi einstein manifold', 'einstein manifolds', 'einstein manifold', 'manifolds boundary', 'manifold boundary', 'manifolds boundary establish', 'flat manifolds', 'einstein metrics', 'riemannian manifold', 'compact einstein']","['Compact quasi-Einstein manifolds with boundary   The goal of this article is to study compact quasi-Einstein manifolds with\nboundary. We provide boundary estimates for compact quasi-Einstein manifolds\nsimi\\-lar to previous results obtained for static and $V$-static spaces. In\naddition, we show that compact quasi-Einstein manifolds with connected boundary\nand satisfying a suitable pinching condition must be isometric, up to scaling,\nto the standard hemisphere $\\mathbb{S}_{+}^{n}.$\n', 'Rigidity of compact quasi-Einstein manifolds with boundary   In this article, we investigate the geometry of compact quasi-Einstein\nmanifolds with boundary. We establish the possible values for the constant\nscalar curvature of a compact quasi-Einstein manifold with boundary. Moreover,\nwe show that a $3$-dimensional simply connected compact $m$-quasi-Einstein\nmanifold with boundary and constant scalar curvature must be isometric, up to\nscaling, to either the standard hemisphere $\\mathbb{S}^{3}_{+}$, or the\ncylinder\n$\\left[0,\\frac{\\sqrt{m}}{\\sqrt{\\lambda}}\\,\\pi\\right]\\times\\mathbb{S}^2$ with\nthe product metric. For dimension $n=4,$ we prove that a $4$-dimensional simply\nconnected compact $m$-quasi-Einstein manifold $M^4$ with boundary and constant\nscalar curvature is isometric, up to scaling, to either the standard hemisphere\n$\\mathbb{S}^{4}_{+},$ or the cylinder\n$\\left[0,\\frac{\\sqrt{m}}{\\sqrt{\\lambda}}\\,\\pi\\right]\\times\\mathbb{S}^3$ with\nthe product metric, or the product space $\\mathbb{S}^{2}_{+}\\times\\mathbb{S}^2$\nwith the doubly warped product metric. Other related results for arbitrary\ndimensions are also discussed.\n', 'On quasi-Einstein manifolds with constant scalar curvature In this article, we study quasi-Einstein manifolds with constant scalar curvature. We provide a classification of compact and noncompact (possibly with boundary) $T$-flat quasi-Einstein manifolds with constant scalar curvature, where the $T$-tensor is directly related to the Cotton and Weyl tensors. Moreover, we construct new explicit examples of noncompact quasi-Einstein manifolds. In addition, we prove a complete classification of compact and noncompact (possibly with boundary) $3$-dimensional $m$-quasi-Einstein manifolds with constant scalar curvature.']","[('quasi einstein manifold', 0.7759039402008057), ('einstein manifolds', 0.711329996585846), ('einstein manifold', 0.690636932849884), ('manifolds boundary', 0.6448915004730225), ('manifold boundary', 0.6386608481407166), ('manifolds boundary establish', 0.6046327352523804), ('flat manifolds', 0.5718352198600769), ('einstein metrics', 0.5693192481994629), ('riemannian manifold', 0.5633817315101624), ('compact einstein', 0.5612713694572449)]"
684,684,46,684_maps manifolds_manifolds_simply connected manifolds_dimensional manifolds,"['maps manifolds', 'manifolds', 'simply connected manifolds', 'dimensional manifolds', 'connected manifolds', 'closed manifolds', 'manifolds admitting', 'manifolds whose', 'topology manifolds', 'spin manifolds']","[""Characterizing certain classes of $6$-dimensional closed and\n  simply-connected manifolds via special generic maps   The present paper finds new necessary and sufficient conditions for\n$6$-dimensional closed and simply-connected manifolds of certain classes to\nadmit special generic maps into certain Euclidean spaces.\n  The class of special generic maps naturally contains Morse functions with\nexactly two singular points on spheres in so-called Reeb's theorem,\ncharacterizing spheres topologically, and canonical projections of unit\nspheres. Our paper concerns variants of Reeb's theorem. Several results are\nknown e. g. the cases where the manifolds of the targets are the plane and some\ncases where the manifolds of the domains are closed and simply-connected. Our\npaper concerns $6$-dimensional versions of a result of Nishioka, determining\n$5$-dimensional closed and simply-connected manifolds admitting special generic\nmaps into Euclidean spaces completely. Closed and simply-connected manifolds\nare central geometric objects in (classical) algebraic topology and\ndifferential topology. The $6$-dimensional case is more complicated than the\n$5$-dimensional one: they are classified via explicit algebraic systems.\n"", '7-dimensional simply-connected spin manifolds whose integral cohomology\n  rings are isomorphic to that of ${\\mathbb{C}P}^2 \\times S^3$ admit round fold\n  maps   We have been interested in understanding the class of 7-dimensional closed\nand simply-connected manifolds in geometric and constructive ways. We have\nconstructed explicit fold maps, which are higher dimensional versions of Morse\nfunctions, on some of the manifolds, previously.\n  The studies have been motivated by studies of {\\it special generic} maps,\nhigher dimensional versions of Morse functions on homotopy spheres with exactly\ntwo singular points, characterizing them topologically except $4$-dimensional\ncases. The class contains canonical projections of unit spheres for example.\n  This class has been found to be interesting, restricting the topologies and\nthe differentiable structures of the manifolds strictly: Saeki, Sakuma and\nWrazidlo found explicit phenomena.\n  The present paper concerns fold maps on $7$-dimensional closed and\nsimply-connected spin manifolds whose integral cohomology rings are isomorphic\nto that of the product of the $2$-dimensional complex projective space and the\n$3$-dimensional sphere.\n', 'Restrictions on special generic maps into ${\\mathbb{R}}^5$ on\n  $6$-dimensional or higher dimensional closed and simply-connected manifolds   The class of special generic maps is a natural class of smooth maps\ncontaining Morse functions on spheres with exactly two singular points and\ncanonical projections of unit spheres. We find new restrictions on such maps on\n$6$-dimensional or higher dimensional closed and simply-connected manifolds\ninto ${\\mathbb{R}}^5$.\n  Spheres which are not diffeomorphic to unit spheres do not admit such maps\nwhose codimensions are negative in considerable cases. They restrict the\nhomeomorphism and the diffeomorphism types of the manifolds in general. On the\nother hands, some elementary manifolds admit special generic maps into suitable\nEuclidean spaces: manifolds represented as connected sums of products of unit\nspheres are of such examples. This motivates us to study the (non-)existence of\nspecial generic maps on elementary manifolds such as projective spaces and some\nclosed and simply-connected manifolds. For example, new explicit investigations\nof cohomology rings are keys in our new study.\n']","[('maps manifolds', 0.7033352255821228), ('manifolds', 0.6404151320457458), ('simply connected manifolds', 0.632663369178772), ('dimensional manifolds', 0.6275180578231812), ('connected manifolds', 0.6152242422103882), ('closed manifolds', 0.6103904247283936), ('manifolds admitting', 0.6041666865348816), ('manifolds whose', 0.5997612476348877), ('topology manifolds', 0.5972534418106079), ('spin manifolds', 0.5655500292778015)]"
685,685,45,685_elliptic operators_elliptic differential operator_approximations elliptic_operators periodic,"['elliptic operators', 'elliptic differential operator', 'approximations elliptic', 'operators periodic', 'estimates periodic', 'elliptic second order', 'elliptic periodic', 'higher order elliptic', 'elliptic systems', 'elliptic differential']","['Homogenization of the higher-order Schr\\""odinger-type equations with\n  periodic coefficients   In $L_2({\\mathbb R}^d; {\\mathbb C}^n)$, we consider a matrix strongly\nelliptic differential operator ${A}_\\varepsilon$ of order $2p$, $p \\geqslant\n2$. The operator ${A}_\\varepsilon$ is given by ${A}_\\varepsilon =\nb(\\mathbf{D})^* g(\\mathbf{x}/\\varepsilon) b(\\mathbf{D})$, $\\varepsilon >0$,\nwhere $g(\\mathbf{x})$ is a periodic, bounded, and positive definite\nmatrix-valued function, and $b(\\mathbf{D})$ is a homogeneous differential\noperator of order $p$. We prove that, for fixed $\\tau \\in {\\mathbb R}$ and\n$\\varepsilon \\to 0$, the operator exponential $e^{-i \\tau {A}_\\varepsilon}$\nconverges to $e^{-i \\tau {A}^0}$ in the norm of operators acting from the\nSobolev space $H^s({\\mathbb R}^d; {\\mathbb C}^n)$ (with a suitable $s$) into\n$L_2({\\mathbb R}^d; {\\mathbb C}^n)$. Here $A^0$ is the effective operator.\nSharp-order error estimate is obtained. The results are applied to\nhomogenization of the Cauchy problem for the Schr\\""odinger-type equation $i\n\\partial_\\tau {\\mathbf u}_\\varepsilon = {A}_\\varepsilon {\\mathbf u}_\\varepsilon\n+ {\\mathbf F}$, ${\\mathbf u}_\\varepsilon\\vert_{\\tau=0} = \\boldsymbol{\\phi}$.\n', 'Homogenization of hyperbolic equations with periodic coefficients in\n  ${\\mathbb R}^d$: sharpness of the results   In $L_2({\\mathbb R}^d;{\\mathbb C}^n)$, a selfadjoint strongly elliptic second\norder differential operator ${\\mathcal A}_\\varepsilon$ is considered. It is\nassumed that the coefficients of the operator ${\\mathcal A}_\\varepsilon$ are\nperiodic and depend on ${\\mathbf x}/\\varepsilon$, where $\\varepsilon >0$ is a\nsmall parameter. We find approximations for the operators $\\cos ( {\\mathcal\nA}_\\varepsilon^{1/2}\\tau)$ and ${\\mathcal A}_\\varepsilon^{-1/2}\\sin ( {\\mathcal\nA}_\\varepsilon^{1/2}\\tau)$ in the norm of operators acting from the Sobolev\nspace $H^s({\\mathbb R}^d)$ to $L_2({\\mathbb R}^d)$ (with suitable $s$). We also\nfind approximation with corrector for the operator ${\\mathcal\nA}_\\varepsilon^{-1/2}\\sin ( {\\mathcal A}_\\varepsilon^{1/2}\\tau)$ in the $(H^s\n\\to H^1)$-norm. The question about the sharpness of the results with respect to\nthe type of the operator norm and with respect to the dependence of estimates\non $\\tau$ is studied. The results are applied to study the behavior of the\nsolutions of the Cauchy problem for the hyperbolic equation $\\partial_\\tau^2\n{\\mathbf u}_\\varepsilon = - {\\mathcal A}_\\varepsilon {\\mathbf u}_\\varepsilon +\n{\\mathbf F}$.\n', 'Operator error estimates for homogenization of the nonstationary\n  Schr\\""{o}dinger-type equations: sharpness of the results   In $L_2 (\\mathbb{R}^d; \\mathbb{C}^n)$, we consider a selfadjoint matrix\nstrongly elliptic second order differential operator $\\mathcal{A}_\\varepsilon$\nwith periodic coefficients depending on $\\mathbf{x}/\\varepsilon$. We find\napproximations of the exponential $e^{-i \\tau \\mathcal{A}_\\varepsilon}$, $\\tau\n\\in \\mathbb{R}$, for small $\\varepsilon$ in the ($H^s \\to L_2$)-operator norm\nwith suitable $s$. The sharpness of the error estimates with respect to $\\tau$\nis discussed. The results are applied to study the behavior of the solution\n$\\mathbf{u}_\\varepsilon$ of the Cauchy problem for the Schr\\""{o}dinger-type\nequation $i\\partial_{\\tau} \\mathbf{u}_\\varepsilon = \\mathcal{A}_\\varepsilon\n\\mathbf{u}_\\varepsilon + \\mathbf{F}$.\n']","[('elliptic operators', 0.538303554058075), ('elliptic differential operator', 0.5167674422264099), ('approximations elliptic', 0.5107583403587341), ('operators periodic', 0.47462961077690125), ('estimates periodic', 0.44589561223983765), ('elliptic second order', 0.4435613751411438), ('elliptic periodic', 0.4042262136936188), ('higher order elliptic', 0.40199169516563416), ('elliptic systems', 0.3992117941379547), ('elliptic differential', 0.3869723081588745)]"
686,686,45,686_genus graphs_graphs surfaces_genus graph_orientable surface genus,"['genus graphs', 'graphs surfaces', 'genus graph', 'orientable surface genus', 'embeddings graphs', 'graph surface', 'genus embedding', 'graphs embedded', 'non orientable surfaces', 'orientable genus']","['The $\\mathbb{Z}_2$-genus of Kuratowski minors   A drawing of a graph on a surface is independently even if every pair of\nnonadjacent edges in the drawing crosses an even number of times. The\n$\\mathbb{Z}_2$-genus of a graph $G$ is the minimum $g$ such that $G$ has an\nindependently even drawing on the orientable surface of genus $g$. An\nunpublished result by Robertson and Seymour implies that for every $t$, every\ngraph of sufficiently large genus contains as a minor a projective $t\\times t$\ngrid or one of the following so-called $t$-Kuratowski graphs: $K_{3,t}$, or $t$\ncopies of $K_5$ or $K_{3,3}$ sharing at most two common vertices. We show that\nthe $\\mathbb{Z}_2$-genus of graphs in these families is unbounded in $t$; in\nfact, equal to their genus. Together, this implies that the genus of a graph is\nbounded from above by a function of its $\\mathbb{Z}_2$-genus, solving a problem\nposed by Schaefer and \\v{S}tefankovi\\v{c}, and giving an approximate version of\nthe Hanani-Tutte theorem on orientable surfaces. We also obtain an analogous\nresult for Euler genus and Euler $\\mathbb{Z}_2$-genus of graphs.\n', 'Excluded minors for the Klein Bottle II. Cascades   Graphs that are critical (minimal excluded minors) for embeddability in\nsurfaces are studied. In Part I, it was shown that graphs that are critical for\nembeddings into surfaces of Euler genus $k$ or for embeddings into\nnonorientable surface of genus $k$ are built from 3-connected components,\ncalled hoppers and cascades. In Part II, all cascades for Euler genus 2 are\nclassified. As a consequence, the complete list of obstructions of connectivity\n2 for embedding graphs into the Klein bottle is obtained.\n', ""On high genus extensions of Negami's conjecture   Negami's famous planar cover conjecture is equivalent to the statement that a\nconnected graph can be embedded in the projective plane if and only if it has a\nprojective planar cover. In 1999, Hlin\\v{e}n\\'y proposed extending this\nconjecture to higher genus non-orientable surfaces. In this paper, we put\nforward a natural extension that encompasses orientable surfaces as well; for\nevery compact surface $\\Sigma$, a connected graph $G$ has a finite cover\nembeddable in $\\Sigma$ if and only if $G$ is embeddable in a surface covered by\n$\\Sigma$.\n  As evidence toward this, we prove that for every surface $\\Sigma$, the\nconnected graphs with a finite cover embeddable in $\\Sigma$ have bounded Euler\ngenus. Moreover, we show that these extensions of Negami's conjecture are\ndecidable for every compact surface of sufficiently large Euler genus,\nsurpassing what is known for Negami's original conjecture. We also prove the\nnatural analogue for countable graphs embeddable into a compact (orientable)\nsurface. More precisely, we prove that a connected countable graph $G$ has a\nfinite ply cover that embeds into a compact (orientable) surface if and only if\n$G$ embeds into a compact (orientable) surface.\n  Our most general theorem, from which these results are derived, is that there\nis a constant $c>0$ such that for every surface $\\Sigma$, there exists a\ndecreasing function $p_\\Sigma:\\mathbb{N} \\to \\mathbb{N}$ with $\\lim_{g\\to\n\\infty}p_\\Sigma(g) =0$ such that every finite cover embeddable in $\\Sigma$ of\nany connected graph with Euler genus $g\\ge c$ has ply at most $p_\\Sigma(g)$.\n""]","[('genus graphs', 0.6726221442222595), ('graphs surfaces', 0.6672767400741577), ('genus graph', 0.6325106024742126), ('orientable surface genus', 0.5926876068115234), ('embeddings graphs', 0.5879006385803223), ('graph surface', 0.5743513703346252), ('genus embedding', 0.5641223788261414), ('graphs embedded', 0.5428010821342468), ('non orientable surfaces', 0.5401144623756409), ('orientable genus', 0.5396636128425598)]"
687,687,45,687_crystalline cohomology_adic hodge theory_adic formal scheme_prismatic cohomology,"['crystalline cohomology', 'adic hodge theory', 'adic formal scheme', 'prismatic cohomology', 'hodge theory', 'crystalline', 'adic completion', 'adic formal', 'crystals', 'adic hodge']","[""A prismatic approach to crystalline local systems   Let X be a smooth p-adic formal scheme. We show that integral crystalline\nlocal systems on the generic fiber of X are equivalent to prismatic F-crystals\nover the analytic locus of the prismatic site of X. As an application, we give\na prismatic proof of Fontaine's C_crys-conjecture, for general coefficients, in\nthe relative setting, and allowing ramified base fields. Along the way, we also\nestablish various foundational results for the cohomology of prismatic\nF-crystals, including various comparison theorems, Poincar\\'e duality, and\nFrobenius isogeny.\n"", 'Prismatic and $q$-crystalline sites of higher level   In this article, we define the $m$-prismatic site and the $m$-$q$-crystalline\nsite, which are higher level analogs of the prismatic site and the\n$q$-crystalline site respectively. We prove a certain equivalence between the\ncategory of crystals on the $m$-prismatic site (resp. the $m$-$q$-crystalline\nsite) and that on the prismatic site (resp. the $q$-crystalline site), which\ncan be regarded as the prismatic (resp. the $q$-crystalline) analog of the\nFrobenius descent due to Berthelot and the Cartier transform due to\nOgus-Vologodsky, Oyama and Xu. We also prove the equivalence between the\ncategory of crystals on the $m$-prismatic site and that on the\n$(m-1)$-$q$-crystalline site.\n', ""Finiteness and Duality for the cohomology of prismatic crystals   Let $(A, I)$ be a bounded prism, and $X$ be a smooth $p$-adic formal scheme\nover $\\Spf(A/I)$. We consider the notion of crystals on Bhatt--Scholze's\nprismatic site $(X/A)_{\\prism}$ of $X$ relative to $A$. We prove that if $X$ is\nproper over $\\Spf(A/I)$ of relative dimension $n$, then the cohomology of a\nprismatic crystal is a perfect complex of $A$-modules with tor-amplitude in\ndegrees $[0,2n]$. We also establish a Poincar\\'e duality for the reduced\nprismatic crystals, i.e. the crystals over the reduced structural sheaf of\n$(X/A)_{\\prism}$. The key ingredient is an explicit local description of\nreduced prismatic crystals in terms of Higgs modules.\n""]","[('crystalline cohomology', 0.6093465089797974), ('adic hodge theory', 0.5775978565216064), ('adic formal scheme', 0.575480580329895), ('prismatic cohomology', 0.5487120151519775), ('hodge theory', 0.4469429552555084), ('crystalline', 0.4465700089931488), ('adic completion', 0.4312492907047272), ('adic formal', 0.42861613631248474), ('crystals', 0.4108920693397522), ('adic hodge', 0.40052762627601624)]"
688,688,45,688_compressible euler equations_isentropic compressible euler_3d compressible euler_isentropic euler equations,"['compressible euler equations', 'isentropic compressible euler', '3d compressible euler', 'isentropic euler equations', 'dimensional compressible euler', 'shock formation', 'shock waves', 'euler flows', 'solutions compressible euler', 'compressible euler']","[""Formation of shifted shock for the 3D compressible Euler equations with\n  time-dependent damping   In this paper, we show the shock formation to the compressible Euler\nequations with time-dependent damping $\\frac{a\\p u}{(1+t)^{\\lam}}$ in three\nspatial dimensions without any symmetry conditions. It's well-known that for\n$\\lam>1$, the damping is too weak to prevent the shock formation for suitably\nlarge data. However, the classical results only showed the finite existence of\nthe solution. Follow the work by D.Christodoulou in\\cite{christodoulou2007},\nstarting from the initial isentropic and irrotational short pulse data, we show\nthe formation of shock is characterized by the collapse of the characteristic\nhypersurfaces and the vanishing of the inverse foliation density function\n$\\mu$, at which the first derivatives of the velocity and the density blow up,\nand the lifespan $T_{\\ast}(a,\\lam)$ is exponentially large. Moreover, the\ndamping effect will shift the time of shock formation $T_{\\ast}$. The methods\nin the paper can also be extended to the Euler equations with general\ntime-decay damping.\n"", 'Formation of point shocks for 3D compressible Euler   We consider the 3D isentropic compressible Euler equations with the ideal gas\nlaw. We provide a constructive proof of shock formation from smooth initial\ndatum of finite energy, with no vacuum regions, with nontrivial vorticity\npresent at the shock, and under no symmetry assumptions. We prove that for an\nopen set of Sobolev-class initial data which are a small $L^ \\infty $\nperturbation of a constant state, there exist smooth solutions to the Euler\nequations which form a generic stable shock in finite time. The blow up time\nand location can be explicitly computed, and solutions at the blow up time are\nsmooth except for a single point, where they are of cusp-type with H\\""{o}lder\n$C^ {\\frac{1}{3}}$ regularity. Our proof is based on the use of modulated\nself-similar variables that are used to enforce a number of constraints on the\nblow up profile, necessary to establish the stability in self-similar variables\nof the generic shock profile.\n', 'Shifted shock formation for the 3D compressible Euler equations with\n  damping and variation of the vorticity   In this paper, we consider the shock formation problem for the\n3-dimensional(3D) compressible Euler equations with damping inspired by the\nwork \\cite{BSV3Dfulleuler}. It will be shown that for a class of large data,\nthe damping can not prevent the formation of point shock, and the damping\neffect shifts the shock time and the wave amplitude while the shock location\nand the blow up direction remain the same with the information of this point\nshock being computed explicitly. Moreover, the vorticity is concentrated in the\nnon-blow-up direction, which varies exponentially due to the damping effect.\nOur proof is based on the estimates for the modulated self-similar variables\nand lower bounds for the Lagrangian trajectories.\n']","[('compressible euler equations', 0.5584918856620789), ('isentropic compressible euler', 0.5446354150772095), ('3d compressible euler', 0.5357376933097839), ('isentropic euler equations', 0.5290162563323975), ('dimensional compressible euler', 0.5287774801254272), ('shock formation', 0.5120683312416077), ('shock waves', 0.503206193447113), ('euler flows', 0.5007542371749878), ('solutions compressible euler', 0.4840829372406006), ('compressible euler', 0.46798235177993774)]"
689,689,45,689_gorenstein projective modules_gorenstein projective_modules gorenstein_finite gorenstein,"['gorenstein projective modules', 'gorenstein projective', 'modules gorenstein', 'finite gorenstein', 'gorenstein dimension', 'gorenstein injective', 'relative gorenstein', 'gorenstein flat', 'gorenstein ring', 'gorenstein rings']","['Stability of projectively coresolved Gorenstein flat modules   The stability of the class of projectively coresolved Gorenstein flat\nmodules, under the very Gorenstein process used to define them, is proven in\nthis paper. Moreover, a new characterization of the projectively coresolved\nGorenstein flat dimension is given.\n', 'Acyclic complexes and Gorenstein rings   For a given class of modules $\\mathcal{A}$, we denote by\n$\\widetilde{\\mathcal{A}}$ the class of exact complexes $X$ having all cycles in\n$\\mathcal{A}$, and by $dw(\\mathcal{A})$ the class of complexes $Y$ with all\ncomponents $Y_j$ in $\\mathcal{A}$. We use the notations $\\mathcal{GI}$\n$(\\mathcal{GF}, \\mathcal{GP})$ for the class of Gorenstein injective\n(Gorenstein flat, Gorenstein projective respectively) $R$-modules,\n$\\mathcal{DI}$ for Ding injective modules, and $\\mathcal{PGF}$ for projectively\ncoresolved Gorenstein flat modules (see section 2 for definitions). We prove\nthat the following are equivalent over any ring $R$: (1) Every exact complex of\ninjective modules is totally acyclic. (2) Every exact complex of Gorenstein\ninjective modules is in $\\widetilde{\\mathcal{GI}}$. (3) Every complex in\n$dw(\\mathcal{GI})$ is dg-Gorenstein injective. We show that the analogue result\nfor complexes of flat and Gorenstein flat modules also holds over arbitrary\nrings. if moreover, the ring is $n$-perfect for some integer $n \\ge 0$, then\nthe three equivalent statements for flat and Gorenstein flat modules are also\nequivalent with their counterparts for projective and projectively coresolved\nGorenstein flat modules. We also prove the following characterization of\nGorenstein rings: Let $R$ be a commutative coherent ring. The following\nstatements are equivalent: (1) every exact complex of FP-injective modules has\nall its cycles Ding injective modules. (2) every exact complex of injectives\nhas all its cycles Ding injective modules and every $R$-module M such that\n$M^+$ is Gorenstein flat is Ding injective. If moreover the ring $R$ has finite\nKrull dimension then statements (1), (2) above are also equivalent to (3) $R$\nis a Gorenstein ring (in the sense of Iwanaga).\n', 'Finiteness criteria for Gorenstein flat dimension and stability   Projectively coresolved Gorenstein flat modules were introduced recently by\nSaroch and Stovicek and were shown to be Gorenstein projective. While the\nrelation between Gorenstein projective and Gorenstein flat modules is not well\nunderstood, the class of projectively coresolved Gorenstein flat modules is\ncontained in the class of Gorenstein flat modules. This paper proves necessary\nand sufficient conditions for a module of finite Gorenstein flat dimension to\nbe projectively coresolved Gorenstein flat, or of finite flat dimension.\nStability results for the class of projectively coresolved Gorenstein flat\nmodules are also established.\n']","[('gorenstein projective modules', 0.8253125548362732), ('gorenstein projective', 0.7435633540153503), ('modules gorenstein', 0.7421517372131348), ('finite gorenstein', 0.665655255317688), ('gorenstein dimension', 0.665051281452179), ('gorenstein injective', 0.6370097994804382), ('relative gorenstein', 0.623832106590271), ('gorenstein flat', 0.6194303035736084), ('gorenstein ring', 0.6193505525588989), ('gorenstein rings', 0.6154393553733826)]"
690,690,45,690_mixed effects models_mixed models_bias estimators_effects models,"['mixed effects models', 'mixed models', 'bias estimators', 'effects models', 'likelihood estimator', 'bias estimation', 'asymptotic inference', 'empirical likelihood', 'consistent estimators', 'estimators']","['A Diagnostic for Bias in Linear Mixed Model Estimators Induced by\n  Dependence Between the Random Effects and the Corresponding Model Matrix   We explore how violations of the often-overlooked standard assumption that\nthe random effects model matrix in a linear mixed model is fixed (and thus\nindependent of the random effects vector) can lead to bias in estimators of\nestimable functions of the fixed effects. However, if the random effects of the\noriginal mixed model are instead also treated as fixed effects, or if the fixed\nand random effects model matrices are orthogonal with respect to the inverse of\nthe error covariance matrix (with probability one), or if the random effects\nand the corresponding model matrix are independent, then these estimators are\nunbiased. The bias in the general case is quantified and compared to a\nrandomized permutation distribution of the predicted random effects, producing\nan informative summary graphic for each estimator of interest. This is\ndemonstrated through the examination of sporting outcomes used to estimate a\nhome field advantage.\n', 'Asymptotic Results for Penalized Quasi-Likelihood Estimation in\n  Generalized Linear Mixed Models   Generalized Linear Mixed Models (GLMMs) are widely used for analysing\nclustered data. One well-established method of overcoming the integral in the\nmarginal likelihood function for GLMMs is penalized quasi-likelihood (PQL)\nestimation, although to date there are few asymptotic distribution results\nrelating to PQL estimation for GLMMs in the literature. In this paper, we\nestablish large sample results for PQL estimators of the parameters and random\neffects in independent-cluster GLMMs, when both the number of clusters and the\ncluster sizes go to infinity. This is done under two distinct regimes:\nconditional on the random effects (essentially treating them as fixed effects)\nand unconditionally (treating the random effects as random). Under the\nconditional regime, we show the PQL estimators are asymptotically normal around\nthe true fixed and random effects. Unconditionally, we prove that while the\nestimator of the fixed effects is asymptotically normally distributed, the\ncorrect asymptotic distribution of the so-called prediction gap of the random\neffects may in fact be a normal scale-mixture distribution under certain\nrelative rates of growth. A simulation study is used to verify the finite\nsample performance of our theoretical results.\n', 'Precise Asymptotics for Linear Mixed Models with Crossed Random Effects   We obtain an asymptotic normality result that reveals the precise asymptotic\nbehavior of the maximum likelihood estimators of parameters for a very general\nclass of linear mixed models containing cross random effects. In achieving the\nresult, we overcome theoretical difficulties that arise from random effects\nbeing crossed as opposed to the simpler nested random effects case. Our new\ntheory is for a class of Gaussian response linear mixed models which includes\ncrossed random slopes that partner arbitrary multivariate predictor effects and\ndoes not require the cell counts to be balanced. Statistical utilities include\nconfidence interval construction, Wald hypothesis test and sample size\ncalculations.\n']","[('mixed effects models', 0.5436911582946777), ('mixed models', 0.5092453360557556), ('bias estimators', 0.4351949989795685), ('effects models', 0.4085696041584015), ('likelihood estimator', 0.39224639534950256), ('bias estimation', 0.38828402757644653), ('asymptotic inference', 0.38768020272254944), ('empirical likelihood', 0.3851418197154999), ('consistent estimators', 0.3751668334007263), ('estimators', 0.3667672574520111)]"
691,691,45,691_entanglement entropy_topological entanglement entropy_bound entanglement_entanglement entropies,"['entanglement entropy', 'topological entanglement entropy', 'bound entanglement', 'entanglement entropies', 'entanglement spectrum', 'entanglement', 'topological entanglement', 'one dimensional quantum', 'interacting fermion', 'bipartite entanglement']","['Entanglement of inhomogeneous free fermions on hyperplane lattices   We introduce an inhomogeneous model of free fermions on a $(D-1)$-dimensional\nlattice with $D(D-1)/2$ continuous parameters that control the hopping strength\nbetween adjacent sites. We solve this model exactly, and find that the\neigenfunctions are given by multidimensional generalizations of Krawtchouk\npolynomials. We construct a Heun operator that commutes with the chopped\ncorrelation matrix, and compute the entanglement entropy numerically for\n$D=2,3,4$, for a wide range of parameters. For $D=2$, we observe oscillations\nin the sub-leading contribution to the entanglement entropy, for which we\nconjecture an exact expression. For $D>2$, we find logarithmic violations of\nthe area law for the entanglement entropy with nontrivial dependence on the\nparameters.\n', 'Entanglement Entropy Bounds for Droplet States of the XXZ Model on the\n  Strip   The scaling behavior of the entanglement entropy of droplet states in\nHeisenberg spin-1/2 XXZ model defined on a strip of width $M$ under the\npresence of a non-negative background magnetic field is investigated. Without\nany assumptions on $V$, a logarithmically corrected area law is shown. Assuming\nthat the values of $V$ are i.i.d. random variables, an area law in expectation\nis obtained.\n', 'Stability of the enhanced area law of the entanglement entropy   We consider a multi-dimensional continuum Schr\\""odinger operator which is\ngiven by a perturbation of the negative Laplacian by a compactly supported\npotential. We establish both an upper and a lower bound on the bipartite\nentanglement entropy of the ground state of the corresponding quasi-free Fermi\ngas. The bounds prove that the scaling behaviour of the entanglement entropy\nremains a logarithmically enhanced area law as in the unperturbed case of the\nfree Fermi gas. The central idea for the upper bound is to use a limiting\nabsorption principle for such kinds of Schr\\""odinger operators.\n']","[('entanglement entropy', 0.7098301649093628), ('topological entanglement entropy', 0.6960510015487671), ('bound entanglement', 0.6381599307060242), ('entanglement entropies', 0.5804762244224548), ('entanglement spectrum', 0.5325533747673035), ('entanglement', 0.5041516423225403), ('topological entanglement', 0.4930081069469452), ('one dimensional quantum', 0.48743748664855957), ('interacting fermion', 0.4861486554145813), ('bipartite entanglement', 0.4846138656139374)]"
692,692,45,692_inverse boundary problems_inverse boundary_dirichlet neumann map_inverse boundary value,"['inverse boundary problems', 'inverse boundary', 'dirichlet neumann map', 'inverse boundary value', 'neumann map', 'biharmonic operators', 'biharmonic operator', 'schr odinger equations', 'dirichlet neumann', 'odinger equations']","['Partial Data Inverse Problems for Nonlinear Magnetic Schr\\""odinger\n  Equations   We prove that the knowledge of the Dirichlet-to-Neumann map, measured on a\npart of the boundary of a bounded domain in $\\mathbb{R}^n, n\\geq2$, can\nuniquely determine, in a nonlinear magnetic Schr\\""odinger equation, the\nvector-valued magnetic potential and the scalar electric potential, both being\nnonlinear in the solution.\n', 'Partial data inverse problems for the nonlinear magnetic Schr\\""odinger\n  equation   In this paper, we study the partial data inverse problem for nonlinear\nmagnetic Schr\\""odinger equations. We show that the knowledge of the\nDirichlet-to-Neumann map, measured on an arbitrary part of the boundary,\ndetermines the time-dependent linear coefficients, electric and magnetic\npotentials, and nonlinear coefficients, provided that the divergence of the\nmagnetic potential is given. Additionally, we also investigate both the forward\nand inverse problems for the linear magnetic Schr\\""odinger equation with a\ntime-dependent leading term. In particular, all coefficients are uniquely\nrecovered from boundary data.\n', 'Inverse problems for nonlinear magnetic Schr\\""odinger equations on\n  conformally transversally anisotropic manifolds   We study the inverse boundary problem for a nonlinear magnetic Schr\\""odinger\noperator on a conformally transversally anisotropic Riemannian manifold of\ndimension $n\\ge 3$. Under suitable assumptions on the nonlinearity, we show\nthat the knowledge of the Dirichlet-to-Neumann map on the boundary of the\nmanifold determines the nonlinear magnetic and electric potentials uniquely. No\nassumptions on the transversal manifold are made in this result, whereas the\ncorresponding inverse boundary problem for the linear magnetic Schr\\""odinger\noperator is still open in this generality.\n']","[('inverse boundary problems', 0.6181885600090027), ('inverse boundary', 0.586825966835022), ('dirichlet neumann map', 0.5820659399032593), ('inverse boundary value', 0.5536119341850281), ('neumann map', 0.5250381827354431), ('biharmonic operators', 0.5160722136497498), ('biharmonic operator', 0.5135059952735901), ('schr odinger equations', 0.5105383396148682), ('dirichlet neumann', 0.490103542804718), ('odinger equations', 0.48944559693336487)]"
693,693,45,693_ring generalized_rings skew_power series rings_power series ring,"['ring generalized', 'rings skew', 'power series rings', 'power series ring', 'series rings', 'series ring', 'skew polynomial', 'polynomials skew', 'extensions rings', 'reduced ring']","['Bounded skew power series rings for inner $\\sigma$-derivations   We define and explore the bounded skew power series ring\n$R^+[[x;\\sigma,\\delta]]$ defined over a complete, filtered, Noetherian prime\nring $R$ with a commuting skew derivation $(\\sigma,\\delta)$. We establish\nprecise criteria for when this ring is well-defined, and for an appropriate\ncompletion $Q$ of $Q(R)$, we prove that if $Q$ has characteristic $p$, $\\delta$\nis an inner $\\sigma$-derivation and no positive power of $\\sigma$ is inner as\nan automorphism of $Q$, then $Q^+[[x;\\sigma,\\delta]]$ is often prime, and even\nsimple under certain mild restrictions on $\\delta$. It follows from this result\nthat $R^+[[x;\\sigma,\\delta]]$ is itself prime.\n', 'Skew Generalized Power Series Rings With the McCoy Property   Let $R$ be a ring, $(S,\\preceq)$ a strictly totally ordered monoid and\nsuppose also $\\omega:S\\rightarrow \\text{End}(R)$ is a monoid homomorphism. A\nskew generalized power series ring $R[[S,\\omega,\\preceq]]$ consists of all\nfunctions from a monoid $S$ to a coefficient ring $R$ whose support contains\nneither infinite descending chains nor infinite anti-chains, equipped with\npoint-wise addition and with multiplication given by convolution twisted by an\naction $\\omega$ of the monoid $S$ on the ring $R$.\n  Special cases of the skew generalized power series ring construction are the\nskew polynomial rings, skew Laurent polynomial rings, skew power series rings,\nskew Laurent series rings, skew monoid rings, skew group rings, skew\nMalcev-Neumann series rings and generalized power series rings as well as the\nuntwisted versions of all of these objects.\n  In the present article, we study the so-termed $(S,\\omega)$-McCoy condition\non $R$, that is a generalization of the standard McCoy condition from\npolynomials to skew generalized power series, thus generalizing some of the\nexisting results in the literature relevant to the subject.\n', 'Reduced Archimedean skew polynomial rings and skew power series rings   We characterize skew polynomial rings and skew power series rings that are\nreduced and right or left Archimedean.\n']","[('ring generalized', 0.5976601243019104), ('rings skew', 0.5931660532951355), ('power series rings', 0.5853309631347656), ('power series ring', 0.564516007900238), ('series rings', 0.5331981182098389), ('series ring', 0.5315434336662292), ('skew polynomial', 0.5167315006256104), ('polynomials skew', 0.5132293105125427), ('extensions rings', 0.5008906126022339), ('reduced ring', 0.4985293745994568)]"
694,694,45,694_leibniz algebras_lie leibniz algebras_leibniz algebra_lie algebras,"['leibniz algebras', 'lie leibniz algebras', 'leibniz algebra', 'lie algebras', 'subalgebras', 'lie algebra', 'dimensional leibniz', 'lie leibniz', 'every subalgebra', 'subalgebras ideals']","['Modularity conditions in Leibniz algebras   In this paper we continue the study of the subalgebra lattice of a Leibniz\nalgebra. In particular, we find out that solvable Leibniz algebras with an\nupper semi-modular lattice are either almost-abelian or have an abelian ideal\nspanned by the elements with square zero. We also study Leibniz algebras in\nwhich every subalgebra is a weak quasi-ideal, as well as modular symmetric\nLeibniz algebras.\n', 'Subinvariance in Leibniz Algebras   Leibniz algebras are certain generalizations of Lie algebras. Motivated by\nthe concept of subinvariance in group theory, Schenkman studied properties of\nsubinvariant subalgebras of a Lie algebra. In this paper we define subinvariant\nsubalgebras of Leibniz algebras and study their properties. It is shown that\nthe signature results on subinvariance in Lie algebras have analogs for Leibniz\nalgebras.\n', 'On Leibniz algebras, whose subalgebras are either ideals or\n  self-idealizing   A subalgebra S of a Leibniz algebra L is called self-idealizing in L if it\ncoincides with its idealizer IL(S). In this paper we study the structure of\nLeibniz algebras, whose subalgebras are either ideals or self-idealizing.\n']","[('leibniz algebras', 0.8803537487983704), ('lie leibniz algebras', 0.837924063205719), ('leibniz algebra', 0.8239427208900452), ('lie algebras', 0.6442869901657104), ('subalgebras', 0.5775814652442932), ('lie algebra', 0.5707260966300964), ('dimensional leibniz', 0.5549014806747437), ('lie leibniz', 0.5476409792900085), ('every subalgebra', 0.5382170677185059), ('subalgebras ideals', 0.5255522131919861)]"
695,695,45,695_hyperelliptic curves genus_supersingular elliptic curves_genus curves_curves genus,"['hyperelliptic curves genus', 'supersingular elliptic curves', 'genus curves', 'curves genus', 'hyperelliptic curves', 'non hyperelliptic curves', 'curve genus', 'curves genus mathbb', 'genus curve', 'hyperelliptic curve']","['Listing superspecial curves of genus three by using Richelot isogeny\n  graph   In algebraic geometry, superspecial curves are important research objects.\nWhile the number of superspecial genus-3 curves in characteristic $p$ is known,\nthe number of hyperelliptic ones among them has not been determined even for\nsmall $p$. In this paper, in order to compute the latter number, we give an\nalgorithm for computing the Richelot isogeny graph of superspecial abelian\nthreefolds by using theta functions. Our algorithm enables us to efficiently\nlist superspecial genus-3 curves, and we succeeded in counting hyperelliptic\ncurves among them when $11 \\leq p < 100$ by executing our algorithm in Magma.\n', 'Computing superspecial hyperelliptic curves of genus 4 with automorphism\n  group properly containing the Klein 4-group   In algebraic geometry, enumerating or finding superspecial curves in positive\ncharacteristic $p$ is important both in theory and in computation. In this\npaper, we propose feasible algorithms to enumerate or find superspecial\nhyperelliptic curves of genus $4$ with automorphism group properly containing\nthe Klein $4$-group. Executing the algorithms on Magma, we succeeded in\nenumerating such superspecial curves for every $p$ with $19 \\leq p < 500$, and\nin finding a single one for every $p$ with $19 \\leq p < 7000$.\n', 'On the existence of superspecial nonhyperelliptic curves of genus $4$   A curve over a perfect field $K$ of characteristic $p > 0$ is said to be\nsuperspecial if its Jacobian is isomorphic to a product of supersingular\nelliptic curves over the algebraic closure $\\overline{K}$. In recent years,\nisomorphism classes of superspecial nonhyperelliptic curves of genus $4$ over\nfinite fields in small characteristic have been enumerated. In particular, the\nnon-existence of superspecial curves of genus $4$ in characteristic $p = 7$ was\nproved. In this note, we give an elementary proof of the existence of\nsuperspecial nonhyperelliptic curves of genus $4$ for infinitely many primes\n$p$. Specifically, we prove that the variety $C_p : x^3+y^3+w^3= 2 y w + z^2 =\n0$ in the projective $3$-space with $p > 2$ is a superspecial curve of genus\n$4$ if and only if $p \\equiv 2 \\pmod{3}$. Our computational results show that\n$C_p$ with $p \\equiv 2 \\pmod 3$ are maximal curves over $\\mathbb{F}_{p^2}$ for\nall $3 \\leq p \\leq 269$.\n']","[('hyperelliptic curves genus', 0.7182863354682922), ('supersingular elliptic curves', 0.6514253616333008), ('genus curves', 0.6422585248947144), ('curves genus', 0.6420499086380005), ('hyperelliptic curves', 0.639897346496582), ('non hyperelliptic curves', 0.6209796071052551), ('curve genus', 0.6177716255187988), ('curves genus mathbb', 0.6092084646224976), ('genus curve', 0.6075043082237244), ('hyperelliptic curve', 0.5796400904655457)]"
696,696,45,696_triangulated categories_equivariant stability_triangulated category_stability manifolds,"['triangulated categories', 'equivariant stability', 'triangulated category', 'stability manifolds', 'triangulated category mathcal', 'yau triangulated category', 'stability manifold', 'calabi yau categories', 'space stability conditions', 'bounded derived category']","['Fusion-equivariant stability conditions and Morita duality   Given a triangulated category $D$ with an action of a fusion category $C$, we\nstudy the moduli space $Stab_{C}(D)$ of fusion-equivariant Bridgeland stability\nconditions on $D$. The main theorem is that the fusion-equivariant stability\nconditions form a closed, complex submanifold of the moduli space of stability\nconditions on $D$. As an application of this framework, we generalise a result\nof Macr\\`{i}--Mehrotra--Stellari by establishing a homeomorphism between the\nspace of $G$-invariant stability conditions on $D$ and the space of\n$rep(G)$-equivariant stability conditions on the equivariant category $D^G$. We\nalso describe applications to the study of stability conditions associated to\nMcKay quivers and to geometric stability conditions on free quotients of smooth\nprojective varieties.\n', 'On pseudo-Anosov autoequivalences   Motivated by results of Thurston, we prove that any autoequivalence of a\ntriangulated category induces a filtration by triangulated subcategories,\nprovided the existence of Bridgeland stability conditions. The filtration is\ngiven by the exponential growth rate of masses under iterates of the\nautoequivalence, and only depends on the choice of a connected component of the\nstability manifold. We then propose a new definition of pseudo-Anosov\nautoequivalences, and prove that our definition is more general than the one\npreviously proposed by Dimitrov, Haiden, Katzarkov, and Kontsevich. We\nconstruct new examples of pseudo-Anosov autoequivalences on the derived\ncategories of quintic Calabi-Yau threefolds and quiver Calabi-Yau categories.\nFinally, we prove that certain pseudo-Anosov autoequivalences on quiver\n3-Calabi-Yau categories act hyperbolically on the space of Bridgeland stability\nconditions.\n', ""Stability conditions on cyclic categories I: basic definitions and\n  examples   A triangulated category $\\mathcal{C}$ with a canonical Bott's isomorphism\n$[2]\\xrightarrow{\\sim}id$ is called a cyclic category in this paper. We give a\nnew notion of stability conditions on a $k$-linear Krull-Schmidt cyclic\ncategory. Given such a stability condition $\\sigma$, we can assign a Maslov\nindex to each basic loop in such a category. If all Maslov indexes vanish, we\nget $\\mathcal{C}',\\sigma'$ as the $\\mathbb{Z}$-lifts of $\\mathcal{C},\\sigma$\nrespectively such that $\\mathcal{C}'$ is a $\\mathbb{Z}$-graded triangulated\ncategory and $\\sigma'$ is a Bridgeland stability condition on $\\mathcal{C}'$.\nMoreover, we showed that there is an isomorphism\n$$Stab^{0,e}(\\mathcal{C})\\xrightarrow{\\simeq} BStab(\\mathcal{C}')$$ where\n$Stab^{0,e}(\\mathcal{C})$ denotes the equivalence classes of stability\nconditions which are deformation equivalent to $\\sigma$, and\n$BStab(\\mathcal{C}')$ denotes the space of Bridgeland stability conditions on\n$\\mathcal{C}'$.\n  We provide examples of stability conditions on a simple cyclic category. We\nalso discuss some interesting phenomena in these examples, such as the\nchirality symmetry breaking phenomenon and nontrivial monodromy. The chirality\nsymmetry breaking phenomenon involves stability conditions which can not be\nlifted to Bridgeland stability conditions.\n""]","[('triangulated categories', 0.5580572485923767), ('equivariant stability', 0.5408943295478821), ('triangulated category', 0.5294341444969177), ('stability manifolds', 0.5249542593955994), ('triangulated category mathcal', 0.522760808467865), ('yau triangulated category', 0.5187603831291199), ('stability manifold', 0.48530808091163635), ('calabi yau categories', 0.4432888925075531), ('space stability conditions', 0.43427619338035583), ('bounded derived category', 0.4286213517189026)]"
697,697,45,697_stochastic homogenization_estimates homogenization_homogenization elliptic equations_homogenization elliptic,"['stochastic homogenization', 'estimates homogenization', 'homogenization elliptic equations', 'homogenization elliptic', 'estimates stochastic', 'homogenization nonlinear', 'homogenization theory', 'homogenization results', 'quantitative homogenization', 'homogenized operator']","['Non-perturbative approach to the Bourgain-Spencer conjecture in\n  stochastic homogenization   In the context of stochastic homogenization, the Bourgain-Spencer conjecture\nstates that the ensemble-averaged solution of a divergence-form linear elliptic\nequation with random coefficients admits an intrinsic description in terms of\nhigher-order homogenized equations with an accuracy four times better than the\nalmost sure solution itself. While previous rigorous results were restricted to\na perturbative regime with small ellipticity ratio, we make the very first\nprogress in a non-perturbative setting, establishing half of the conjectured\noptimal accuracy. The validity of the full conjecture remains an open question\nand might in fact fail in general. Our approach involves the construction of a\nnew corrector theory in stochastic homogenization: while only a bounded number\nof correctors can be constructed as stationary random fields in a strong sense,\nwe show that twice as many stationary correctors can be defined in a\nSchwartz-like distributional sense on the probability space. We focus on the\nGaussian setting for the coefficient field, and the proof relies heavily on\nMalliavin calculus.\n', ""On Bourgain's approach to stochastic homogenization   In 2018, Bourgain pioneered a novel perturbative harmonic-analytic approach\nto the stochastic homogenization theory of discrete elliptic equations with\nweakly random i.i.d. coefficients. The approach was subsequently refined to\nshow that homogenized approximations of ensemble averages can be derived to a\nprecision four times better than almost sure homogenized approximations, which\nwas unexpected by the state-of-the-art homogenization theory. In this paper, we\ngrow this budding theory in various directions: First, we prove that the\napproach is robust by extending it to the continuum setting with exponentially\nmixing random coefficients. Second, we give a new proof via Malliavin calculus\nin the case of Gaussian coefficients, which avoids the main technicality of\nBourgain's original approach. This new proof also applies to strong Gaussian\ncorrelations with power-law decay. Third, we extend Bourgain's approach to the\nstudy of fluctuations by constructing weak correctors up to order $2d$, which\nalso clarifies the link between Bourgain's approach and the standard corrector\napproach to homogenization. Finally, we draw several consequences from those\ndifferent results, both for quantitative homogenization of ensemble averages\nand for asymptotic expansions of the annealed Green's function.\n"", 'The annealed Calderon-Zygmund estimate as convenient tool in\n  quantitative stochastic homogenization   This article is about the quantitative homogenization theory of linear\nelliptic equations in divergence form with random coefficients. We derive\ngradient estimates on the homogenization error, i.e. on the difference between\nthe actual solution and the two-scale expansion of the homogenized solution,\nboth in terms of strong norms (oscillation) and weak norms (fluctuation). These\nestimates are optimal in terms of scaling in the ratio between the microscopic\nand the macroscopic scale. The purpose of this article is to highlight the\nusage of the recently introduced annealed Calderon-Zygmund (CZ) estimates in\nobtaining the above, previously known, error estimates. Moreover, the article\nprovides a novel proof of these annealed CZ estimate that completely avoids\nquenched regularity theory, but rather relies on functional analysis. It is\nbased on the observation that even on the level of operator norms, the\nHelmholtz projection is close to the one for the homogenized coefficient (for\nwhich annealed CZ estimates are easily obtained). In this article, we strive\nfor simple proofs, and thus restrict ourselves to ensembles of coefficient\nfields that are local transformations of Gaussian random fields with integrable\ncorrelations and H\\""older continuous realizations. As in earlier work, we use\nthe natural objects from the general theory of homogenization, like the\n(potential and flux) correctors and the homogenization commutator. Both\noscillation and fluctuation estimates rely on a sensitivity calculus, i.e. on\nestimating how sensitively the quantity of interest does depend on an\ninfinitesimal change in the coefficient field, which is fed into the Spectral\nGap inequality. In this article, the annealed CZ estimate is the only form in\nwhich elliptic regularity theory enters.\n']","[('stochastic homogenization', 0.719310998916626), ('estimates homogenization', 0.6413835883140564), ('homogenization elliptic equations', 0.5429314374923706), ('homogenization elliptic', 0.5363515019416809), ('estimates stochastic', 0.5156412124633789), ('homogenization nonlinear', 0.5042369365692139), ('homogenization theory', 0.4994460642337799), ('homogenization results', 0.49492567777633667), ('quantitative homogenization', 0.48572206497192383), ('homogenized operator', 0.48488548398017883)]"
698,698,45,698_bernstein operators_approximation operators_operators approximation_operators approximate,"['bernstein operators', 'approximation operators', 'operators approximation', 'operators approximate', 'proposed operators', 'operators asymptotic', 'type operators', 'kantorovich operators', 'studied operators', 'operators']","['A class of Bernstein-type operators on the unit disk   We construct and study sequences of linear operators of Bernstein-type acting\non bivariate functions defined on the unit disk. To this end, we study\nBernstein-type operators under a domain transformation, we analyse the\nbivariate Bernstein-Stancu operators, and we introduce Bernstein-type operators\non disk quadrants by means of continuously differentiable transformations of\nthe function. We state convergence results for continuous functions and we\nestimate the rate of convergence. Finally some interesting numerical examples\nare given, comparing approximations using the shifted Bernstein-Stancu and the\nBernstein-type operator on disk quadrants.\n', 'Chlodowsky variant of Bernstein-type operators on the domain   In the present paper, we deal with Bernstein-Chlodowsky type operators for\napproximating functions on the domain. We first present Bernstein-Chlodowsky\ntype operators in two variables and then we discuss some examples of these\noperators under a domain transformation. Finally, we give bivarite shifted mth\nBernstein-Chlodowsky-Stancu operators and we present some figures for\napproximation properties of our operator.\n', ""Approximation of associated GBS operators by Szasz-Mirakjan type\n  operators   In this article, the approximation properties of the Szasz-Mirakjan type\noperators are studied for the function of two variables, and the rate of\nconvergence of the bivariate operators is determined in terms of total and\npartial modulus of continuity. An associated GBS (Generalized Boolean Sum)-form\nof the bivariate Szasz-Mirakjan type operators are considered for the function\nof two variables to find an approximation of B-continuous and B-differentiable\nfunction in the Bogel's space. Further, the degree of approximation of the GBS\ntype operators is found in terms of mixed modulus of smoothness and functions\nbelonging to the Lipschitz class as well as a pioneering result is obtained in\nterms of Peetre K-functional. Finally, the rate of convergence of the bivariate\nSzasz-Mirakjan type operators and the associated GBS type operators are\nexamined through graphical representation for the finite and infinite sum which\nshows that the rate of convergence of the associated GBS type operators is\nbetter than the bivariate Szasz-Mirakjan type operators.\n""]","[('bernstein operators', 0.665823221206665), ('approximation operators', 0.6486508250236511), ('operators approximation', 0.6383098363876343), ('operators approximate', 0.6029755473136902), ('proposed operators', 0.575474739074707), ('operators asymptotic', 0.5434933304786682), ('type operators', 0.5415695905685425), ('kantorovich operators', 0.5402398705482483), ('studied operators', 0.5358797907829285), ('operators', 0.520821750164032)]"
699,699,44,699_lyapunov exponents_maximal lyapunov exponent_lyapunov spectrum_lyapunov exponent,"['lyapunov exponents', 'maximal lyapunov exponent', 'lyapunov spectrum', 'lyapunov exponent', 'top lyapunov exponent', 'sets lyapunov', 'maximal lyapunov', 'lyapunov', 'ergodic measures', 'approximation lyapunov']","['Thermodynamic formalism of $GL_2(\\mathbb{R})$-cocycles with canonical\n  holonomies   We study singular value potentials of H\\""older continuous\n$GL_2(\\mathbb{R})$-cocycles over hyperbolic systems whose canonical holonomies\nconverge and are H\\""older continuous. Such cocycles include locally constant\n$GL_2(\\mathbb{R})$-cocycles as well as fiber-bunched\n$GL_2(\\mathbb{R})$-cocycles. We show that singular value potentials of\nirreducible such cocycles have unique equilibrium states. Among the reducible\ncocycles, we provide a characterization for cocycles whose singular value\npotentials have more than one equilibrium states.\n', 'H\\""older continuity of the Lyapunov exponent for Markov cocycles via\n  Furstenberg\'s Formula   This paper is concerned with the study of linear cocycles over uniformly\nergodic Markov shifts on a compact space of symbols. We establish the joint\nH\\""older continuity of the maximal Lyapunov exponent as a function of the\ncocycle and the transition kernel in the vicinity of any irreducible cocycle\nwith simple maximal Lyapunov exponent. Our approach, via Furstenberg\'s formula,\nshows the H\\""older continuous dependence on the data of the stationary measure\nof the projective cocycle and in particular provides a more computable H\\""older\nexponent.\n', 'Restricted variational principle of Lyapunov exponents for typical\n  cocycles   In this paper, we study the multifractal formalism of Lyapunov exponents for\ntypical cocycles. We establish a variational relation between the Legendre\ntransform of topological pressure of the generalized singular value function\nand measure-theoretic entropies. As a consequence, we show that the restricted\nvariational principle of Lyapunov exponents holds for typical cocycles.\n']","[('lyapunov exponents', 0.575231671333313), ('maximal lyapunov exponent', 0.5721226930618286), ('lyapunov spectrum', 0.5447952747344971), ('lyapunov exponent', 0.5437531471252441), ('top lyapunov exponent', 0.5334360003471375), ('sets lyapunov', 0.5298498868942261), ('maximal lyapunov', 0.5255438685417175), ('lyapunov', 0.5051527619361877), ('ergodic measures', 0.504288911819458), ('approximation lyapunov', 0.49955400824546814)]"
700,700,44,700_shape optimisation_shape optimization_shape optimization problems_optimal shape,"['shape optimisation', 'shape optimization', 'shape optimization problems', 'optimal shape', 'shape calculus', 'computing shape', 'constrained shape', 'shape functions', 'shape derivative', 'compute shape']","['PDE-constrained shape optimization: towards product shape spaces and\n  stochastic models   Shape optimization models with one or more shapes are considered in this\nchapter. Of particular interest for applications are problems in which where a\nso-called shape functional is constrained by a partial differential equation\n(PDE) describing the underlying physics. A connection can made between a\nclassical view of shape optimization and the differential-geometric structure\nof shape spaces. To handle problems where a shape functional depends on\nmultiple shapes, a theoretical framework is presented, whereby the optimization\nvariable can be represented as a vector of shapes belonging to a product shape\nspace. The multi-shape gradient and multi-shape derivative are defined, which\nallows for a rigorous justification of a steepest descent method with Armijo\nbacktracking. As long as the shapes as subsets of a hold-all domain do not\nintersect, solving a single deformation equation is enough to provide descent\ndirections with respect to each shape. Additionally, a framework for handling\nuncertainties arising from inputs or parameters in the PDE is presented. To\nhandle potentially high-dimensional stochastic spaces, a stochastic gradient\nmethod is proposed. A model problem is constructed, demonstrating how\nuncertainty can be introduced into the problem and the objective can be\ntransformed by use of the expectation. Finally, numerical experiments in the\ndeterministic and stochastic case are devised, which demonstrate the\neffectiveness of the presented algorithms.\n', 'A Novel $p$-Harmonic Descent Approach Applied to Fluid Dynamic Shape\n  Optimization   We introduce a novel method for the implementation of shape optimziation in\nfluid dynamics applications, where we propose to use the shape derivative to\ndetermine deformation fields with the help of the $p-$ Laplacian for $p > 2$.\nThis approach is closely related to the computation of steepest descent\ndirections of the shape functional in the $W^{1,\\infty}-$ topology. Our\napproach is demonstrated for shape optimization related to drag-minimal free\nfloating bodies. The method is validated against existing approaches with\nrespect to convergence of the optimization algorithm, the obtained shape, and\nregarding the quality of the computational grid after large deformations. Our\nnumerical results strongly indicate that shape optimization related to the\n$W^{1,\\infty}$-topology -- though numerically more demanding -- seems to be\nsuperior over the classical approaches invoking Hilbert space methods,\nconcerning the convergence, the obtained shapes and the mesh quality after\nlarge deformations, in particular when the optimal shape features sharp\ncorners.\n', 'Fireshape: a shape optimization toolbox for Firedrake   We introduce Fireshape, an open-source and automated shape optimization\ntoolbox for the finite element software Firedrake. Fireshape is based on the\nmoving mesh method and allows users with minimal shape optimization knowledge\nto tackle with ease challenging shape optimization problems constrained to\npartial differential equations (PDEs).\n']","[('shape optimisation', 0.7844696640968323), ('shape optimization', 0.7811776995658875), ('shape optimization problems', 0.7415656447410583), ('optimal shape', 0.6716670989990234), ('shape calculus', 0.6258940696716309), ('computing shape', 0.6197201013565063), ('constrained shape', 0.6116191744804382), ('shape functions', 0.5933371782302856), ('shape derivative', 0.5816140174865723), ('compute shape', 0.5745591521263123)]"
701,701,44,701_optimal impulse_stochastic differential game_stochastic differential games_optimal stopping,"['optimal impulse', 'stochastic differential game', 'stochastic differential games', 'optimal stopping', 'impulse control', 'impulse control problems', 'dynamic programming principle', 'control continuous time', 'stochastic differential', 'sum differential game']","['Non-Markovian Impulse Control Under Nonlinear Expectation   We consider a general type of non-Markovian impulse control problems under\nadverse non-linear expectation or, more specifically, the zero-sum game problem\nwhere the adversary player decides the probability measure. We show that the\nupper and lower value functions satisfy a dynamic programming principle (DPP).\nWe first prove the dynamic programming principle (DPP) for a truncated version\nof the upper value function in a straightforward manner. Relying on a uniform\nconvergence argument then enables us to show the DPP for the general setting.\nFollowing this, we use an approximation based on a combination of truncation\nand discretization to show that the upper and lower value functions coincide,\nthus establishing that the game has a value and that the DPP holds for the\nlower value function as well. Finally, we show that the DPP admits a unique\nsolution and give conditions under which a saddle-point for the game exists.\n  As an example, we consider a stochastic differential game (SDG) of impulse\nversus classical control of path-dependent stochastic differential equations\n(SDEs).\n', 'A Finite Horizon Optimal Stochastic Impulse Control Problem with A\n  Decision Lag   This paper studies an optimal stochastic impulse control problem in a finite\nhorizon with a decision lag, by which we mean that after an impulse is made, a\nfixed number units of time has to be elapsed before the next impulse is allowed\nto be made. The continuity of the value function is proved. A suitable version\nof dynamic programming principle is established, which takes into account the\ndependence of state process on the elapsed time. The corresponding\nHamilton-Jacobi-Bellman (HJB) equation is derived, which exhibit some special\nfeature of the problem. The value function of this optimal impulse control\nproblem is characterized as the unique viscosity solution to the corresponding\nHJB equation. An optimal impulse control is constructed provided the value\nfunction is given. Moreover, a limiting case with the waiting time approaching\n$0$ is discussed.\n', 'Zero-sum Stochastic Differential Games of Impulse Versus Continuous\n  Control by FBSDEs   We consider a stochastic differential game in the context of forward-backward\nstochastic differential equations, where one player implements an impulse\ncontrol while the opponent controls the system continuously. Utilizing the\nnotion of ""backward semigroups"" we first prove the dynamic programming\nprinciple (DPP) for a truncated version of the problem in a straightforward\nmanner. Relying on a uniform convergence argument then enables us to show the\nDPP for the general setting. In particular, this avoids technical constraints\nimposed in previous works dealing with the same problem. Moreover, our approach\nallows us to consider impulse costs that depend on the present value of the\nstate process in addition to unbounded coefficients.\n  Using the dynamic programming principle we deduce that the upper and lower\nvalue functions are both solutions (in viscosity sense) to the same\nHamilton-Jacobi-Bellman-Isaacs obstacle problem. By showing uniqueness of\nsolutions to this partial differential inequality we conclude that the game has\na value.\n']","[('optimal impulse', 0.6229838728904724), ('stochastic differential game', 0.6051530241966248), ('stochastic differential games', 0.6005265116691589), ('optimal stopping', 0.515313982963562), ('impulse control', 0.5081671476364136), ('impulse control problems', 0.5037730932235718), ('dynamic programming principle', 0.49247995018959045), ('control continuous time', 0.4335117042064667), ('stochastic differential', 0.43015575408935547), ('sum differential game', 0.4233149588108063)]"
702,702,44,702_semigroups_discrete semigroups_semigroup_commutative semigroups,"['semigroups', 'discrete semigroups', 'semigroup', 'commutative semigroups', 'commutative semigroup', 'sets strongly', 'subsemigroups', 'notions topological', 'notion central', 'combinatorial characterization']","['Exhibition of piecewise syndetic and broken IP sets near idempotent   Characterizations of ultrafilters belong to the smallest ideal of\nStone-\\v{C}ech compactification of a discrete semigroup are exhibited using\nsyndetic sets, strongly central sets and very strongly central sets\nrespectively. These lead to represent piecewise syndetic sets of a semigroup in\nterms of the sets that contain a broken $\\mathcal{A}$ set, where\n$\\mathcal{A}\\in\\{$ syndetic, quasi-central, central, strongly central, very\nstrongly central$\\}$. Also, a characterization of broken IP$^{n}$ sets using\nultrafilters, and the equivalence between the sets that contain a broken IP set\nand sets that contain a broken IP$^{n}$ are established, $n\\in \\mathbb{N}$.\nWithout assuming the countability of a semigroup, it is shown that piecewise\nsyndetic sets i.e., sets that contain a broken syndetic set (broken IP set)\nforce uniform recurrence (recurrence respectively) and vice versa. In addition,\nall the said results are established near idempotent of a semitopological\nsemigroup.\n', 'Dynamical characterization of central sets along filter   Using the notions of Topological dynamics, H. Furstenberg defined central\nsets and proved the Central Sets Theorem. Later V. Bergelson and N. Hindman\ncharacterized central sets in terms of algebra of the Stone-\\v{C}ech\nCompactification of discrete semigroup. They found that central sets are the\nmembers of the minimal idempotents of $\\beta S$, the Stone-\\v{C}ech\nCompactification of a semigroup $\\left(S,\\cdot\\right)$. We know that any closed\nsubsemigroup of $\\beta S$ is generated by a filter. We call a set $A$ to be a\n$\\mathcal{F}$-central set if it is a member of a minimal idempotent of a closed\nsubsemigroup of $\\beta S$, generated by the filter $\\mathcal{F}$. In this\narticle we will characterize the $\\mathcal{F}$-central sets dynamically.\n', 'A Study on Filter Version of Strongly Central Sets   Using the notions of Topological dynamics, H. Furstenberg defined central\nsets and proved the Central Sets Theorem. Later V. Bergelson and N. Hindman\ncharacterized central sets in terms of algebra of the Stone-\\v{C}ech\ncompactification of discrete semigroup. They found that central sets are the\nmembers of the minimal idempotents of \\b{eta}S, the Stone-\\v{C}ech\ncompactification of a semigroup (S, .). Hindman and leader introduced the\nnotion of Central set near zero algebraically. Later dynamical and\ncombinatorial characterization have also been established. For any given filter\nF in S a set A is said to be a F- central set if it is a member of a minimal\nidempotent of a closed subsemigroup of \\b{eta}S, generated by the filter F. In\na recent article Bergelson, Hindman and Strauss introduced strongly central and\nvery strongly central sets in [BHS]. They also dynamically characterized the\nsets in the same paper. In the present article we will characterize the\nstrongly F- central sets dynamically and combinatorially. Here we introduce the\nfilter version of strongly central sets and very strongly central sets. We also\nprovide dynamical and combinatorial characterization of such sets.\n']","[('semigroups', 0.5650152564048767), ('discrete semigroups', 0.535225510597229), ('semigroup', 0.5163434743881226), ('commutative semigroups', 0.49854257702827454), ('commutative semigroup', 0.46843183040618896), ('sets strongly', 0.4307766854763031), ('subsemigroups', 0.42654114961624146), ('notions topological', 0.4233023524284363), ('notion central', 0.4141101539134979), ('combinatorial characterization', 0.4020634889602661)]"
703,703,44,703_saturated graphs_saturation number_sat minimum_saturation,"['saturated graphs', 'saturation number', 'sat minimum', 'saturation', 'minimum number edges', 'bipartite graphs', 'weak saturation', 'extremal graphs', 'number edges graph', 'subgraph']","['Saturation Numbers for Linear Forests $P_6$ + $tP_2$   A graph $G$ is $H$-saturated if it contains no $H$ as a subgraph, but does\ncontain $H$ after the addition of any edge in the complement of $G$. The\nsaturation number, $sat (n, H)$, is the minimum number of edges of a graph in\nthe set of all $H$-saturated graphs with order $n$. In this paper, we determine\nthe saturation number $sat (n, P_6 + tP_2)$ for $n \\geq 10t/3 + 10$ and\ncharacterize the extremal graphs for $n >10t/3 + 20$.\n', 'The saturation number of $K_{3,3}$   A graph $G$ is called $F$-saturated if $G$ does not contain $F$ as a subgraph\n(not necessarily induced) but the addition of any missing edge to $G$ creates a\ncopy of $F$. The saturation number of $F$, denoted by $sat(n,F)$, is the\nminimum number of edges in an $n$-vertex $F$-saturated graph. Determining the\nsaturation number of complete partite graphs is one of the most important\nproblems in the study of saturation number. The value of $sat(n,K_{2,2})$ was\nshown to be $\\lfloor\\frac{3n-5}{2}\\rfloor$ by Ollmann, and a shorter proof was\nlater given by Tuza. For $K_{2,3}$, there has been a series of study aiming to\ndetermine $sat(n,K_{2,3})$ over the years. This was finally achieved by Chen\nwho confirmed a conjecture of Bohman, Fonoberova, and Pikhurko that $sat(n,\nK_{2,3})= 2n-3$ for all $n\\geq 5$. In this paper, we prove a conjecture of\nPikhurko and Schmitt that $sat(n, K_{3,3})=3n-9$ when $n \\geq 9$.\n', 'The saturation number of wheels   A graph $G$ is said to be $F$-free, if $G$ does not contain any copy of $F$.\n$G$ is said to be $F$-semi-saturated, if the addition of any nonedge $e \\not\n\\in E(G)$ would create a new copy of $F$ in $G+e$. $G$ is said to be\n$F$-saturated, if $G$ is $F$-free and $F$-semi-saturated. The saturation number\n$sat(n,F)$ (resp. semi-saturation number $ssat(n,F)$) is the minimum number of\nedges in an $F$-saturated (resp. $F$-semi-saturated) graph of order $n$. In\nthis paper we proved several results on the (semi)-saturation number of the\nwheel graph $W_k=K_1 \\vee C_k$. Let $k,n$ be positive integers with $k \\geq 8$\nand $n \\geq 56k^3$, we showed that $(s)sat(n,W_k)=n-1+(s)sat(n-1,C_k)$. We also\nestablish the lower bound of semi-saturation number of $W_k$ with restriction\non maximum degree.\n']","[('saturated graphs', 0.6762551069259644), ('saturation number', 0.5879009962081909), ('sat minimum', 0.4687013030052185), ('saturation', 0.4636145532131195), ('minimum number edges', 0.4529010057449341), ('bipartite graphs', 0.4314958155155182), ('weak saturation', 0.4217071235179901), ('extremal graphs', 0.42089512944221497), ('number edges graph', 0.4184594452381134), ('subgraph', 0.4142964482307434)]"
704,704,44,704_euclid_euclidean geometry_euclidean geometries_new geometry,"['euclid', 'euclidean geometry', 'euclidean geometries', 'new geometry', 'geometry', 'non euclidean geometries', 'euclidean', 'non euclidean', 'modern mathematics', 'axioms']","['On the Notion of Equal Figures in Euclid   Euclid uses an undefined notion of ""equal figures"", to which he applies the\ncommon notions about equals added to equals or subtracted from equals. When (in\nprevious work) we formalized Euclid Book~I for computer proof-checking, we had\nto add fifteen axioms about undefined relations ""equal triangles"" and ""equal\nquadrilaterals"" to replace Euclid\'s use of the common notions. In this paper,\nwe offer definitions of ""equal triangles"" and ""equal quadrilaterals"", that\nEuclid could have given, and prove that they have the required properties. This\nremoves the need for adding new axioms. The proof uses the theory of\nproportions. Hence we also discuss the ""early theory of proportions"", which has\na long history.\n', 'It is not ""B\\\'ezout\'s identity""   Given two non-zero integers $a$ and $b$ there exist integers $m$ and $n$ for\nwhich $am-bn =(a,b)$. An increasing number of mathematicians have been calling\nthis `B\\\'ezout\'s identity\', some encouraged by finding ""identit\\\'e de B\\\'ezout""\nin Bourbaki\'s \\emph{\'El\\\'ements de math\\\'ematique}. Moreover the observation\nthat if $\\gcd(a,b)=1$ then this is an `if and only if\' condition, is sometimes\ncalled the ""Bachet-B\\\'ezout theorem"".\n  However this is all in Euclid\'s work from around 300 B.C., when his writings\nare interpreted in context. So why does he not get credit? Some authors learned\nthe name ""B\\\'ezout\'s identity"" and have perhaps not consulted Euclid, so copied\nthe misattribution. Others, like some Nicolas Bourbaki collaborators, have\nperhaps browsed Euclid\'s results, but in a form written for the modern\nmathematician, and missed out on what he really did (though certainly others,\nsuch as Weil, did not). In this article we will carefully explain what Euclid\'s\narguments are and what his approach was. We will also share Kowalski\'s guess as\nto the reasons behind Bourbaki\'s misnomer.\n  To appreciate Euclid, you need to read his work in context: Lengths are the\ncentral object of study to the geometer Euclid, though he brilliantly developed\nthe theory of the numbers that measured those lengths. Today\'s mathematicians\nread his number theory results as being about abstract numbers not\nmeasurements. However the correct interpretation changes how these results are\nperceived; Euclid\'s proofs make clear Euclid\'s intentions.\n  These misperceptions reflect recent discussions about difficulties faced by\nindigenous people when learning mathematics. We discuss how some indigenous\ngroups may learn numbers in certain practical contexts, not as abstract\nentities, and struggle when curricula assume that we all share abstract numbers\nas a basic, primary fully-absorbed working tool.\n', 'Book I of Euclid\'s Elements and application of areas   We work through Book I of Euclid\'s Elements with our focus on application of\nareas (I.42, I.44, I.45). We summarize alternate constructions from medieval\neditions of Euclid\'s elements and ancient and medieval commentaries. We remark\nthat Euclid\'s proof of I.44 involves a seldom commented on use of\nsuperposition, but that several medieval editions of Euclid give constructions\nthat avoid the use of superposition. This use of superposition is also avoided\nin Ralph Abraham\'s ``VCE: The Visual Constructions of Euclid\'\' C#12, C#12B at\nhttp://www.visual-euclid.org/vce/contents.html\n  We collate the figures with the digitized editions of Euclid at (P)\nBiblioteca Apostolica Vaticana (BAV), Vat. gr. 190, (F) Biblioteca Medicea\nLaurenziana (BML), Plut. 28.03, (B) Bodleian, MS. D\'Orville 301, (V)\n\\""Osterreichische Nationalbibliothek, Cod. Phil. gr. 31, (b) Biblioteca\nComunale dell\'Archiginnasio, Collocazione A 19, (p) Biblioth\\`eque nationale de\nFrance, Grec 2466.\n']","[('euclid', 0.6077622175216675), ('euclidean geometry', 0.4579884111881256), ('euclidean geometries', 0.43431219458580017), ('new geometry', 0.41146212816238403), ('geometry', 0.4076915979385376), ('non euclidean geometries', 0.40646156668663025), ('euclidean', 0.4003154933452606), ('non euclidean', 0.3990643322467804), ('modern mathematics', 0.39890655875205994), ('axioms', 0.38902437686920166)]"
705,705,44,705_finite borel_finite graphs_closed graphs_locally finite borel,"['finite borel', 'finite graphs', 'closed graphs', 'locally finite borel', 'invariant borel', 'regular borel', 'chromatic numbers', 'chromatic number', 'every borel', 'graph admits']","['Jump operations for Borel graphs   We investigate the class of bipartite Borel graphs organized by the order of\nBorel homomorphism. We show that this class is unbounded by finding a jump\noperator for Borel graphs analogous to a jump operator of Louveau for Borel\nequivalence relations. The proof relies on a non-separation result for iterated\nFrechet ideals and filters due to Debs and Saint Raymond. We give a new proof\nof this fact using effective descriptive set theory. We also investigate an\nanalogue of the Friedman-Stanley jump for Borel graphs. This analogue does not\nyield a jump operator for bipartite Borel graphs. However, we use it to answer\na question of Kechris and Marks by showing that there is a Borel graph with no\nBorel homomorphism to a locally countable Borel graph, but each of whose\nconnected components has a countable Borel coloring.\n', 'Local Problems on Trees from the Perspectives of Distributed Algorithms,\n  Finitary Factors, and Descriptive Combinatorics   We study connections between distributed local algorithms, finitary factors\nof iid processes, and descriptive combinatorics in the context of regular\ntrees.\n  We extend the Borel determinacy technique of Marks coming from descriptive\ncombinatorics and adapt it to the area of distributed computing. Using this\ntechnique, we prove deterministic distributed $\\Omega(\\log n)$-round lower\nbounds for problems from a natural class of homomorphism problems.\nInterestingly, these lower bounds seem beyond the current reach of the powerful\nround elimination technique responsible for all substantial locality lower\nbounds of the last years. Our key technical ingredient is a novel ID graph\ntechnique that we expect to be of independent interest.\n  We prove that a local problem admits a Baire measurable coloring if and only\nif it admits a local algorithm with local complexity $O(\\log n)$, extending the\nclassification of Baire measurable colorings of Bernshteyn. A key ingredient of\nthe proof is a new and simple characterization of local problems that can be\nsolved in $O(\\log n)$ rounds. We complement this result by showing separations\nbetween complexity classes from distributed computing, finitary factors, and\ndescriptive combinatorics. Most notably, the class of problems that allow a\ndistributed algorithm with sublogarithmic randomized local complexity is\nincomparable with the class of problems with a Borel solution.\n  We hope that our treatment will help to view all three perspectives as part\nof a common theory of locality, in which we follow the insightful paper of\n[Bernshteyn -- arXiv 2004.04905].\n', ""Hyperfiniteness and Borel combinatorics   We study the relationship between hyperfiniteness and problems in Borel graph\ncombinatorics by adapting game-theoretic techniques introduced by Marks to the\nhyperfinite setting. We compute the possible Borel chromatic numbers and edge\nchromatic numbers of bounded degree acyclic hyperfinite Borel graphs and use\nthis to answer a question of Kechris and Marks about the relationship between\nBorel chromatic number and measure chromatic number. We also show that for\nevery $d > 1$ there is a $d$-regular acyclic hyperfinite Borel bipartite graph\nwith no Borel perfect matching. These techniques also give examples of\nhyperfinite bounded degree Borel graphs for which the Borel local lemma fails,\nin contrast to the recent results of Cs\\'oka, Grabowski, M\\'ath\\'e, Pikhurko,\nand Tyros.\n  Related to the Borel Ruziewicz problem, we show there is a continuous\nparadoxical action of $(\\mathbb{Z}/2\\mathbb{Z})^{*3}$ on a Polish space that\nadmits a finitely additive invariant Borel probability measure, but admits no\ncountably additive invariant Borel probability measure. In the context of\nstudying ultrafilters on the quotient space of equivalence relations under\n$\\mathrm{AD}$, we also construct an ultrafilter $U$ on the quotient of $E_0$\nwhich has surprising complexity. In particular, Martin's measure is\nRudin-Kiesler reducible to $U$.\n  We end with a problem about whether every hyperfinite bounded degree Borel\ngraph has a witness to its hyperfiniteness which is uniformly bounded below in\nsize.\n""]","[('finite borel', 0.49538353085517883), ('finite graphs', 0.48963046073913574), ('closed graphs', 0.4758804738521576), ('locally finite borel', 0.4618191719055176), ('invariant borel', 0.4575294852256775), ('regular borel', 0.4471170902252197), ('chromatic numbers', 0.4391625225543976), ('chromatic number', 0.4295004904270172), ('every borel', 0.42627838253974915), ('graph admits', 0.42096850275993347)]"
706,706,44,706_estimates heat kernels_heat kernel estimates_dirichlet heat kernel_heat kernels,"['estimates heat kernels', 'heat kernel estimates', 'dirichlet heat kernel', 'heat kernels', 'heat kernel', 'kernel estimates', 'dirichlet heat', 'estimates dirichlet', 'dimensional evy processes', 'parabolic harnack inequality']","[""Dirichlet Heat kernel estimates for a large class of anisotropic Markov\n  processes   Let $Z=(Z^{1}, \\ldots, Z^{d})$ be the d-dimensional L\\'evy {process} where\n{$Z^i$'s} are independent 1-dimensional L\\'evy {processes} with identical\njumping kernel $ \\nu^1(r) =r^{-1}\\phi(r)^{-1}$. Here $\\phi$ is {an} increasing\nfunction with weakly scaling condition of order $\\underline \\alpha, \\overline\n\\alpha\\in (0, 2)$. We consider a symmetric function $J(x,y)$ comparable to\n\\begin{align*}\n  \\begin{cases} \\nu^1(|x^i - y^i|)\\qquad&\\text{ if $x^i \\ne y^i$ for some $i$\nand $x^j = y^j$ for all $j \\ne i$}\\\\ 0\\qquad&\\text{ if $x^i \\ne y^i$ for more\nthan one index $i$}. \\end{cases} \\end{align*} Corresponding to the jumping\nkernel $J$, there exists an anisotropic Markov process $X$, see \\cite{KW22}. In\nthis article, we establish sharp two-sided Dirichlet heat kernel estimates for\n$X$ in $C^{1,1}$ open set, under certain regularity conditions. As an\napplication of the main results, we derive the Green function estimates.\n"", 'Heat kernel estimates for subordinate Markov processes and their\n  applications   In this paper, we establish sharp two-sided estimates for transition\ndensities of a large class of subordinate Markov processes. As applications, we\nshow that the parabolic Harnack inequality and H\\""older regularity hold for\nparabolic functions of such processes, and derive sharp two-sided Green\nfunction estimates.\n', 'Heat kernel estimates for Dirichlet forms degenerate at the boundary   The goal of this paper is to establish sharp two-sided estimates on the heat\nkernels of two types of purely discontinuous symmetric Markov processes in the\nupper half-space of $\\mathbb R^d$ with jump kernels degenerate at the boundary.\nThe jump kernels are of the form $J(x,y)=\\mathcal B(x,y)|x-y|^{-\\alpha-d}$,\n$\\alpha\\in (0,2)$, where the function $\\mathcal B$ depends on four parameters\nand may vanish at the boundary. Our results are the first sharp two-sided\nestimates for the heat kernels of non-local operators with jump kernels\ndegenerate at the boundary. The first type of processes are conservative Markov\nprocesses on $\\overline{\\mathbb R}^d_+$ with jump kernel $J(x,y)$. Depending on\nthe regions where the parameters belong, the heat kernels estimates have three\ndifferent forms, two of them are qualitatively different from all previously\nknown heat kernel estimates. The second type of processes are the processes\nabove killed either by a critical potential or upon hitting the boundary of the\nhalf-space. We establish that their heat kernel estimates have the approximate\nfactorization property with survival probabilities decaying as a power of the\ndistance to the boundary, where the power depends on the constant in the\ncritical potential.\n']","[('estimates heat kernels', 0.6934442520141602), ('heat kernel estimates', 0.6870437860488892), ('dirichlet heat kernel', 0.6384848952293396), ('heat kernels', 0.5552181601524353), ('heat kernel', 0.5197460651397705), ('kernel estimates', 0.517298698425293), ('dirichlet heat', 0.46336767077445984), ('estimates dirichlet', 0.4620548188686371), ('dimensional evy processes', 0.4605426788330078), ('parabolic harnack inequality', 0.44640570878982544)]"
707,707,44,707_thermodynamic systems_entropy principle_properties entropy_thermodynamic,"['thermodynamic systems', 'entropy principle', 'properties entropy', 'thermodynamic', 'thermodynamics', 'law thermodynamics', 'second law thermodynamics', 'entropy', 'entropy can', 'entropy production']","['Thermodynamics of Encoding and Encoders   Non-isolated systems have diverse coupling relations with the external\nenvironment. These relations generate complex thermodynamics and information\ntransmission between the system and its environment. The framework depicted in\nthe current research attempts to glance at the critical role of the internal\norders inside the non-isolated system in shaping the information thermodynamics\ncoupling. We characterize the coupling as a generalized encoding process, where\nthe system acts as an information thermodynamics encoder to encode the external\ninformation based on thermodynamics. We formalize the encoding process in the\ncontext of the nonequilibrium second law of thermodynamics, revealing an\nintrinsic difference in information thermodynamics characteristics between\ninformation thermodynamics encoders with and without internal correlations.\nDuring the information encoding process of an external source $\\mathsf{Y}$,\nspecific sub-systems in an encoder $\\mathsf{X}$ with internal correlations can\nexceed the information thermodynamics bound on\n$\\left(\\mathsf{X},\\mathsf{Y}\\right)$ and encode more information than system\n$\\mathsf{X}$ works as a whole. We computationally verify this theoretical\nfinding in an Ising model with a random external field and a neural data set of\nthe human brain during visual perception and recognition. Our analysis\ndemonstrates that the stronger internal correlation inside these systems\nimplies a higher possibility for specific sub-systems to encode more\ninformation than the global one. These findings may suggest a new perspective\nin studying information thermodynamics in diverse physical and biological\nsystems.\n', 'Mathematical Representation of Clausius\' and Kelvin\'s Statements of the\n  Second Law and Irreversibility   We provide a stochastic mathematical representation for Clausius\' and\nKelvin-Planck\'s statements of the Second Law of Thermodynamics in terms of the\nentropy productions of a finite, compact driven Markov system and its lift. A\nsurjective map is rigorously established through the lift when the state space\nis either a discrete graph or a continuous n-dimensional torus T^n. The\ncorresponding lifted processes have detailed balance thus a natural potential\nfunction but no stationary probability. We show that in the long-time limit the\nentropy production of the finite driven system precisely equals the potential\nenergy decrease in the lifted system. This theorem provides a dynamic\nfoundation for the two equivalent statements of Second Law of Thermodynamics, a\nla Kelvin\'s and Clausius\'. It suggests a modernized, combined statement: ""A\nmesoscopic engine that works in completing irreversible internal cycles\nstatistically has necessarily an external effect that lowering a weight\naccompanied by passing heat from a warmer to a colder body.""\n', 'The Role of Second Law of Thermodynamics in Continuum Physics: A Muschik\n  and Ehrentraut Theorem Revisited   Second law of thermodynamics imposes that in any thermodynamic process the\nentropy production must be nonnegative. In continuum physics such a requirement\nis fulfilled by postulating the constitutive equations which represent the\nmaterial properties of the bodies in such a way that second law of\nthermodynamics is satisfied in arbitrary processes. Such an approach, first\nassumed in some pioneering papers by Coleman and Noll \\cite{ColNol} and Coleman\nand Mizel \\cite{ColMiz}, in practice regards second law of thermodynamics as a\nrestriction on the constitutive equations, which must guarantee that any\nsolution of the balance laws satisfies also the entropy inequality. As observed\nby Muschik and Ehrentraut \\cite{MusEhr}, this is a useful operative assumption,\nbut not a consequence of general physical laws. Indeed, a different point of\nview, which regards second law of thermodynamics as a restriction on the\nthermodynamic processes, i.e., on the solutions of the system of balance laws,\nis possible. This is tantamount to assume that there are solutions of the\nbalance laws which satisfy the entropy inequality, and solutions which do not\nsatisfy it. In order to decide what is the correct approach, Muschik and\nErhentraut postulated an amendment to the second law, which makes explicit the\nevident but rather hidden assumption that in any point of the body the entropy\nproduction is zero if, and only if, this point is thermodynamic equilibrium.\nThen they proved that, given the amendment, second law of thermodynamics is\nnecessarily a restriction on the constitutive equations and not on the\nthermodynamic processes. In the present paper we revisit their proof, lighting\nup some geometric aspects which were hidden in Ref. \\cite{MusEhr}. Moreover, we\npropose an alternative formulation of second law of thermodynamics which\nincorporates the amendment.\n']","[('thermodynamic systems', 0.6658456325531006), ('entropy principle', 0.6545236110687256), ('properties entropy', 0.642338216304779), ('thermodynamic', 0.6374297738075256), ('thermodynamics', 0.6145360469818115), ('law thermodynamics', 0.6099252700805664), ('second law thermodynamics', 0.6086845993995667), ('entropy', 0.5886390209197998), ('entropy can', 0.5815935730934143), ('entropy production', 0.5775118470191956)]"
708,708,44,708_flocking behavior_hydrodynamics_flocking_hydrodynamic,"['flocking behavior', 'hydrodynamics', 'flocking', 'hydrodynamic', 'smale dynamics', 'solutions hydrodynamic', 'flocks', 'flock', 'hydrodynamic limit', 'kinetic fluid']","['Well-posedness and Long Time Behavior of the Euler Alignment System with\n  Adaptive Communication Strength   We study a new flocking model which has the versatility to capture the\nphysically realistic qualitative behavior of the Motsch-Tadmor model, while\nalso retaining the entropy law, which lends to a similar 1D global\nwell-posedness analysis to the Cucker-Smale model. This is an improvement to\nthe situation in the Cucker-Smale case, which may display the physically\nunrealistic behavior that large flocks overpower the dynamics of small, far\naway flocks; and it is an improvement in the situation in the Motsch-Tadmor\ncase, where 1D global well-posedness is not known. The new model was proposed\nin arXiv:2211.00117v3 and has a similar structure to the Cucker-Smale and\nMotsch-Tadmor hydrodynamic systems, but with a new feature: the communication\nstrength is not fixed, but evolves in time according to its own transport\nequation along the Favre-filtered velocity field. This transport of the\ncommunication strength is precisely what preserves the entropy law. A variety\nof phenomenological behavior can be obtained from various choices of the\ninitial communication strength, including the aforementioned Motsch-Tadmor-like\nbehavior. We develop the general well-posedness theory for the new model and\nstudy the long time behavior -- including alignment, strong flocking in 1D, and\nentropy estimates to estimate the distribution of the limiting flock, all of\nwhich extend the classical results of the Cucker-Smale case. In addition, we\nprovide numerical evidence to show the similar qualitative behavior\n', ""Swarming: hydrodynamic alignment with pressure   We study the swarming behavior of hydrodynamic alignment. Alignment reflects\nsteering towards a weighted average heading. We consider the class of so-called\n$p$-alignment hydrodynamics, based on $2p$-Laplacians, and weighted by a\ngeneral family of symmetric communication kernels. The main new aspect here is\nthe long time emergence behavior for a general class of pressure tensors\nwithout a closure assumption, beyond the mere requirement that they form an\nenergy dissipative process. We refer to such pressure laws as `entropic', and\nprove the flocking of $p$-alignment hydrodynamics, driven by singular kernels\nwith general class of entropic pressure tensors. These results indicate the\nrigidity of alignment in driving long-time flocking behavior despite the lack\nof thermodynamic closure.\n"", 'Inevitable monokineticity of strongly singular alignment   We prove that certain types of measure-valued mappings are monokinetic i.e.\nthe distribution of velocity is concentrated in a Dirac mass. These include\nweak measure-valued solutions to the strongly singular Cucker-Smale model with\nsingularity of order $\\alpha$ greater or equal to the dimension of the ambient\nspace. Consequently, we are able to answer a couple of open questions related\nto the singular Cucker-Smale model. First, we prove that weak measure-valued\nsolutions to the strongly singular Cucker-Smale kinetic equation are\nmonokinetic, under very mild assumptions that they are uniformly compactly\nsupported and weakly continuous in time. This can be interpreted as a rigorous\nderivation of the macroscopic fractional Euler-alignment system from kinetic\nCucker-Smale equation without the need to perform any hydrodynamical limit.\n  This suggests superior suitability of the macroscopic framework to describe\nlarge-crowd limits of strongly singular Cucker-Smale dynamics.\n  Second, we perform a direct micro- to macroscopic mean-field limit from the\nCucker-Smale particle system to the fractional Euler-alignment model. This\nleads to the final result -- existence of weak solutions to the fractional\nEuler-alignment system with almost arbitrary initial data in $\\mathbb{R}^1$,\nincluding the possibility of vacuum. Existence can be extended to\n$\\mathbb{R}^2$ under the a priori assumption that the density of the mean-field\nlimit has no atoms.\n']","[('flocking behavior', 0.5247926115989685), ('hydrodynamics', 0.450251042842865), ('flocking', 0.43959078192710876), ('hydrodynamic', 0.41765615344047546), ('smale dynamics', 0.416186660528183), ('solutions hydrodynamic', 0.39042773842811584), ('flocks', 0.3876889944076538), ('flock', 0.3851374089717865), ('hydrodynamic limit', 0.38260358572006226), ('kinetic fluid', 0.3415936231613159)]"
709,709,44,709_dimensional chaotic systems_dimensional chaotic_chaos theory_chaotic systems,"['dimensional chaotic systems', 'dimensional chaotic', 'chaos theory', 'chaotic systems', 'chaotic dynamical systems', 'chaotic dynamics', 'chaotic attractors', 'chaotic system', 'chaotic dynamical', 'chaotic behavior']","['A computable realization of Ruelle\'s formula for linear response of\n  statistics in chaotic systems   We present a computable reformulation of Ruelle\'s linear response formula for\nchaotic systems. The new formula, called Space-Split Sensitivity or S3,\nachieves an error convergence of the order ${\\cal O}(1/\\sqrt{N})$ using $N$\nphase points. The reformulation is based on splitting the overall sensitivity\ninto that to stable and unstable components of the perturbation. The unstable\ncontribution to the sensitivity is regularized using ergodic properties and the\nhyperbolic structure of the dynamics. Numerical examples of uniformly\nhyperbolic attractors are used to validate the S3 formula against a na\\""ive\nfinite-difference calculation; sensitivities match closely, with far fewer\nsample points required by S3.\n', ""Space-split algorithm for sensitivity analysis of discrete chaotic\n  systems with unstable manifolds of arbitrary dimension   Accurate approximations of the change of system's output and its statistics\nwith respect to the input are highly desired in computational dynamics.\nRuelle's linear response theory provides breakthrough mathematical machinery\nfor computing the sensitivity of chaotic dynamical systems, which enables a\nbetter understanding of chaotic phenomena. In this paper, we propose an\nalgorithm for sensitivity analysis of discrete chaos with an arbitrary number\nof positive Lyapunov exponents. We combine the concept of perturbation\nspace-splitting regularizing Ruelle's original expression together with\nmeasure-based parameterization of the expanding subspace. We use these tools to\nrigorously derive trajectory-following recursive relations that exponentially\nconverge, and construct a memory-efficient Monte Carlo scheme for derivatives\nof the output statistics. Thanks to the regularization and lack of simplifying\nassumptions on the behavior of the system, our method is immune to the common\nproblems of other popular systems such as the exploding tangent solutions and\nunphysicality of shadowing directions. We provide a ready-to-use algorithm,\nanalyze its complexity, and demonstrate several numerical examples of\nsensitivity computation of physically-inspired low-dimensional systems.\n"", ""Efficient computation of linear response of chaotic attractors with\n  one-dimensional unstable manifolds   This paper presents the space-split sensitivity or the S3 algorithm to\ntransform Ruelle's linear response formula into a well-conditioned\nergodic-averaging computation. We prove a decomposition of Ruelle's formula\nthat is differentiable on the unstable manifold, which we assume to be\none-dimensional. This decomposition of Ruelle's formula ensures that one of the\nresulting terms, the stable contribution, can be computed using a regularized\ntangent equation, similar to in a non-chaotic system. The remaining term, known\nas the unstable contribution, is regularized and converted into an efficiently\ncomputable ergodic average. In this process, we develop new algorithms, which\nmay be useful beyond linear response, to compute i) a fundamental statistical\nquantity we introduce called the density gradient, and ii) the unstable\nderivatives of the regularized tangent vector field and the unstable direction.\nWe prove that the S3 algorithm, which combines these computational ingredients\nthat enter the stable and unstable contribution, converges like a Monte Carlo\napproximation of Ruelle's formula. The algorithm presented here is hence a\nfirst step toward full-fledged applications of sensitivity analysis in chaotic\nsystems, wherever such applications have been limited due to lack of\navailability of long-term sensitivities.\n""]","[('dimensional chaotic systems', 0.6392607092857361), ('dimensional chaotic', 0.5914725661277771), ('chaos theory', 0.5914402604103088), ('chaotic systems', 0.5848188996315002), ('chaotic dynamical systems', 0.5772156119346619), ('chaotic dynamics', 0.5464558601379395), ('chaotic attractors', 0.5389350652694702), ('chaotic system', 0.5334853529930115), ('chaotic dynamical', 0.5331636667251587), ('chaotic behavior', 0.5079637765884399)]"
710,710,44,710_discrete morse theory_homology morse_morse theoretic_discrete morse,"['discrete morse theory', 'homology morse', 'morse theoretic', 'discrete morse', 'morse complex', 'morse functions', 'morse theory', 'morse sequence', 'simplicial complexes', 'associated simplicial complexes']","[""The Connectedness Homomorphism between Discrete Morse Complexes   Given two discrete Morse functions on a simplicial complex, we introduce the\n{\\em connectedness homomorphism} between the corresponding discrete Morse\ncomplexes. This concept leads to a novel framework for studying the\nconnectedness in discrete Morse theory at the chain complex level. In\nparticular, we apply it to describe a discrete analogy to `cusp-degeneration'\nof Morse complexes. A precise comparison between smooth case and our discrete\ncases is also given.\n"", ""Strong discrete Morse theory   The purpose of this work is to develop a version of Forman's discrete Morse\ntheory for simplicial complexes, based on internal strong collapses. Classical\ndiscrete Morse theory can be viewed as a generalization of Whitehead's\ncollapses, where each Morse function on a simplicial complex $K$ defines a\nsequence of elementary internal collapses. This reduction guarantees the\nexistence of a CW-complex that is homotopy equivalent to $K$, with cells\ncorresponding to the critical simplices of the Morse function. However, this\napproach lacks an explicit combinatorial description of the attaching maps,\nwhich limits the reconstruction of the homotopy type of $K$. By restricting\ndiscrete Morse functions to those induced by total orders on the vertices, we\ndevelop a strong discrete Morse theory, generalizing the strong collapses\nintroduced by Barmak and Minian. We show that, in this setting, the resulting\nreduced CW-complex is regular, enabling us to recover its homotopy type\ncombinatorially. We also provide an algorithm to compute this reduction and\napply it to obtain efficient structures for complexes in the library of\ntriangulations by Benedetti and Lutz.\n"", 'Gradient Vector Fields of Discrete Morse Functions and Watershed-cuts   In this paper, we study a class of discrete Morse functions, coming from\nDiscrete Morse Theory, that are equivalent to a class of simplicial stacks,\ncoming from Mathematical Morphology. We show that, as in Discrete Morse Theory,\nwe can see the gradient vector field of a simplicial stack (seen as a discrete\nMorse function) as the only relevant information we should consider. Last, but\nnot the least, we also show that the Minimum Spanning Forest of the dual graph\nof a simplicial stack is induced by the gradient vector field of the initial\nfunction. This result allows computing a watershed-cut from a gradient vector\nfield.\n']","[('discrete morse theory', 0.7448195815086365), ('homology morse', 0.7032551169395447), ('morse theoretic', 0.6960250735282898), ('discrete morse', 0.6809539794921875), ('morse complex', 0.6675131320953369), ('morse functions', 0.6510308384895325), ('morse theory', 0.6501314640045166), ('morse sequence', 0.6138629913330078), ('simplicial complexes', 0.5608404278755188), ('associated simplicial complexes', 0.5153635144233704)]"
711,711,44,711_kinetic transport_reaction diffusion systems_reaction diffusion_analysis kinetic,"['kinetic transport', 'reaction diffusion systems', 'reaction diffusion', 'analysis kinetic', 'kinetic', 'based kinetic', 'diffusion', 'nonlinear diffusion', 'aggregation diffusion', 'chemotaxis term']","[""Derivation of the bacterial run-and-tumble kinetic model : quantitative and strong convergence results During the past century, biologists and mathematicians investigated two mechanisms underlying bacteria motion: the run phase during which bacteria move in straight lines and the tumble phase in which they change their orientation. When surrounded by a chemical attractant, experiments show that bacteria increase their run time as moving up concentration gradients, leading to a biased random walk towards favorable regions. This observation raises the following question, which has drawn intense interest from both biological and mathematical communities: what cellular mechanisms enable bacteria to feel concentration gradients\\,? In this article, we investigate an asymptotic regime that was proposed to explain this ability thanks to internal mechanisms. More precisely, we derive the run-and-tumble kinetic equation with concentration's gradient dependent tumbling rate from a more comprehensive model, which incorporates internal cellular mechanisms. Our result improves on previous investigations, as we obtain strong convergence towards the gradient dependent kinetic model with quantitative and formally optimal convergence rates. The main ingredient consists in identifying a set of coordinates for the internal cellular dynamics in which concentration gradients arise explicitly. Then, we use relative entropy methods in order to capture quantitative measurement of the distance between the model incorporating cellular mechanisms and the one with concentration gradient dependent tumbling rate."", 'Effects of internal dynamics on chemotactic aggregation of bacteria   The effects of internal adaptation dynamics on the self-organized aggregation\nof chemotactic bacteria are investigated by Monte Carlo (MC) simulations based\non a two-stream kinetic transport equation coupled with a reaction-diffusion\nequation of the chemoattractant that bacteria produce. A remarkable finding is\na nonmonotonic behavior of the peak aggregation density with respect to the\nadaptation time; more specifically, aggregation is the most enhanced when the\nadaptation time is comparable to or moderately larger than the mean run time of\nbacteria. Another curious observation is the formation of a trapezoidal\naggregation profile occurring at a very large adaptation time, where the biased\nmotion of individual cells is rather hindered at the plateau regimes due to the\nboundedness of the tumbling frequency modulation. Asymptotic analysis of the\nkinetic transport system is also carried out, and a novel asymptotic equation\nis obtained at the large adaptation-time regime while the Keller-Segel type\nequations are obtained when the adaptation time is moderate. Numerical\ncomparison of the asymptotic equations with MC results clarifies that\ntrapezoidal aggregation is well described by the novel asymptotic equation, and\nthe nonmonotonic behavior of the peak aggregation density is interpreted as the\ntransient of the asymptotic solutions between different adaptation time\nregimes.\n', 'Kinetic chemotaxis tumbling kernel determined from macroscopic\n  quantities   Chemotaxis is the physical phenomenon that bacteria adjust their motions\naccording to chemical stimulus. A classical model for this phenomenon is a\nkinetic equation that describes the velocity jump process whose\ntumbling/transition kernel uniquely determines the effect of chemical stimulus\non bacteria. The model has been shown to be an accurate model that matches with\nbacteria motion qualitatively. For a quantitative modeling, biophysicists and\npractitioners are also highly interested in determining the explicit value of\nthe tumbling kernel. Due to the experimental limitations, measurements are\ntypically macroscopic in nature. Do macroscopic quantities contain enough\ninformation to recover microscopic behavior? In this paper, we give a positive\nanswer. We show that when given a special design of initial data, the\npopulation density, one specific macroscopic quantity as a function of time,\ncontains sufficient information to recover the tumbling kernel and its\nassociated damping coefficient. Moreover, we can read off the chemotaxis\ntumbling kernel using the values of population density directly from this\nspecific experimental design. This theoretical result using kinetic theory\nsheds light on how practitioners may conduct experiments in laboratories.\n']","[('kinetic transport', 0.517693042755127), ('reaction diffusion systems', 0.5051084160804749), ('reaction diffusion', 0.49913233518600464), ('analysis kinetic', 0.48656484484672546), ('kinetic', 0.47584205865859985), ('based kinetic', 0.41171079874038696), ('diffusion', 0.40859243273735046), ('nonlinear diffusion', 0.38766199350357056), ('aggregation diffusion', 0.3747609257698059), ('chemotaxis term', 0.37174493074417114)]"
712,712,44,712_eigenfunctions laplace beltrami_laplacian eigenfunctions_smooth compact riemannian_compact riemannian,"['eigenfunctions laplace beltrami', 'laplacian eigenfunctions', 'smooth compact riemannian', 'compact riemannian', 'laplace beltrami operator', 'compact riemannian manifold', 'sub laplacians', 'beltrami operator compact', 'estimates laplace', 'eigenfunctions laplace']","['Growth of high $L^p$ norms for eigenfunctions: an application of\n  geodesic beams   This work concerns $L^p$ norms of high energy Laplace eigenfunctions,\n$(-\\Delta_g-\\lambda^2)\\phi_\\lambda=0$, $\\|\\phi_\\lambda\\|_{L^2}=1$. In 1988,\nSogge gave optimal estimates on the growth of $\\|\\phi_\\lambda\\|_{L^p}$ for a\ngeneral compact Riemannian manifold. The goal of this article is to give\ngeneral dynamical conditions guaranteeing quantitative improvements in $L^p$\nestimates for $p>p_c$, where $p_c$ is the critical exponent. We also apply\nprevious results of the authors to obtain quantitative improvements in concrete\ngeometric settings including all product manifolds. These are the first results\nimproving estimates for the $L^p$ growth of eigenfunctions that only require\ndynamical assumptions. In contrast with previous improvements, our assumptions\nare local in the sense that they depend only on the geodesics passing through a\nshrinking neighborhood of a given set in $M$. Moreover, the article gives a\nstructure theorem for eigenfunctions which saturate the quantitatively improved\n$L^p$ bound. Modulo an error, the theorem describes these eigenfunctions as\nfinite sums of quasimodes which, roughly, approximate zonal harmonics on the\nsphere scaled by $1/\\sqrt{\\log \\lambda}$.\n', ""Fourier coefficients of restrictions of eigenfunctions   Let $\\{e_j\\}$ be an orthonormal basis of Laplace eigenfunctions of a compact\nRiemannian manifold $(M,g)$. Let $H \\subset M$ be a submanifold and let\n$\\{\\psi_k\\}$ be an orthonormal basis of Laplace eigenfunctions of $H$ with the\ninduced metric. We obtain joint asymptotics for the Fourier coefficients \\[\n  \\langle \\gamma_H e_j, \\psi_k \\rangle_{L^2(H)} = \\int_H e_j \\overline \\psi_k\n\\, dV_H, \\] of restrictions $\\gamma_H e_j$ of $e_j$ to $H$. In particular, we\nobtain asymptotics for the sums of the norm-squares of the Fourier coefficients\nover the joint spectrum $\\{(\\mu_k, \\lambda_j)\\}_{j,k - 0}^{\\infty}$ of the\n(square roots of the) Laplacian $\\Delta_M$ on $M$ and the Laplacian $\\Delta_H$\non $H$ in a family of suitably `thick' regions in $\\mathbb R^2$. Thick regions\ninclude (1) the truncated cone $\\mu_k/\\lambda_j \\in [a,b] \\subset (0,1)$ and\n$\\lambda_j \\leq \\lambda$, and (2) the slowly thickening strip $|\\mu_k -\nc\\lambda_j| \\leq w(\\lambda)$ and $\\lambda_j \\leq \\lambda$, where $w(\\lambda)$\nis monotonic and $1 \\ll w(\\lambda) \\lesssim \\lambda^{1 - 1/n}$. Key tools for\nobtaining these asymptotics include the composition calculus of Fourier\nintegral operators and a new multidimensional Tauberian theorem.\n"", 'Improvements for eigenfunction averages: An application of geodesic\n  beams   Let $(M,g)$ be a smooth, compact Riemannian manifold and $\\{\\phi_\\lambda \\}$\nan $L^2$-normalized sequence of Laplace eigenfunctions, $-\\Delta_g\\phi_\\lambda\n=\\lambda^2 \\phi_\\lambda$. Given a smooth submanifold $H \\subset M$ of\ncodimension $k\\geq 1$, we find conditions on the pair $(M,H)$, even when\n$H=\\{x\\}$, for which $$ \\Big|\\int_H\\phi_\\lambda\nd\\sigma_H\\Big|=O\\Big(\\frac{\\lambda^{\\frac{k-1}{2}}}{\\sqrt{\\log\n\\lambda}}\\Big)\\qquad \\text{or}\\qquad |\\phi_\\lambda(x)|=O\\Big(\\frac{\\lambda\n^{\\frac{n-1}{2}}}{\\sqrt{\\log \\lambda}}\\Big), $$ as $\\lambda\\to \\infty$. These\nconditions require no global assumption on the manifold $M$ and instead relate\nto the structure of the set of recurrent directions in the unit normal bundle\nto $H$. Our results extend all previously known conditions guaranteeing\nimprovements on averages, including those on sup-norms. For example, we show\nthat if $(M,g)$ is a surface with Anosov geodesic flow, then there are\nlogarithmically improved averages for any $H\\subset M$. We also find weaker\nconditions than having no conjugate points which guarantee $\\sqrt{\\log\n\\lambda}$ improvements for the $L^\\infty$ norm of eigenfunctions. Our results\nare obtained using geodesic beam techniques, which yield a mechanism for\nobtaining general quantitative improvements for averages and sup-norms.\n']","[('eigenfunctions laplace beltrami', 0.5458252429962158), ('laplacian eigenfunctions', 0.516021192073822), ('smooth compact riemannian', 0.48253461718559265), ('compact riemannian', 0.4744422733783722), ('laplace beltrami operator', 0.4595477283000946), ('compact riemannian manifold', 0.45229968428611755), ('sub laplacians', 0.45047691464424133), ('beltrami operator compact', 0.4479421079158783), ('estimates laplace', 0.4447207450866699), ('eigenfunctions laplace', 0.4394318759441376)]"
713,713,43,713_difference galois theory_differential galois theory_difference galois_differential galois,"['difference galois theory', 'differential galois theory', 'difference galois', 'differential galois', 'differential galois group', 'difference equations', 'differential transcendence', 'galois theory linear', 'galois theory', 'linear difference equations']","['Hypertranscendence and linear difference equations   After H\\""older proved his classical theorem about the Gamma function, there\nhas been a whole bunch of results showing that solutions to linear difference\nequations tend to be hypertranscendental i.e. they cannot be solution to an\nalgebraic differential equation). In this paper, we obtain the first complete\nresults for solutions to general linear difference equations associated with\nthe shift operator $x\\mapsto x+h$ ($h\\in\\mathbb{C}^*$), the $q$-difference\noperator $x\\mapsto qx$ ($q\\in\\mathbb{C}^*$ not a root of unity), and the Mahler\noperator $x\\mapsto x^p$ ($p\\geq 2$ integer). The only restriction is that we\nconstrain our solutions to be expressed as (possibly ramified) Laurent series\nin the variable $x$ with complex coefficients (or in the variable $1/x$ in some\nspecial case associated with the shift operator). Our proof is based on the\nparametrized difference Galois theory initiated by Hardouin and Singer. We also\ndeduce from our main result a general statement about algebraic independence of\nvalues of Mahler functions and their derivatives at algebraic points.\n', 'Computing differential Galois groups of second-order linear\n  $q$-difference equations   We apply the differential Galois theory for difference equations developed by\nHardouin and Singer to compute the differential Galois group for a second-order\nlinear $q$-difference equation with rational function coefficients. This Galois\ngroup encodes the possible polynomial differential relations among the\nsolutions of the equation. We apply our results to compute the differential\nGalois groups of several concrete $q$-difference equations, including for the\ncolored Jones polynomial of a certain knot.\n', 'Differential transcendence criteria for second-order linear difference\n  equations and elliptic hypergeometric functions   We develop general criteria that ensure that any non-zero solution of a given\nsecond-order difference equation is differentially transcendental, which apply\nuniformly in particular cases of interest, such as shift difference equations,\nq-dilation difference equations, Mahler difference equations, and elliptic\ndifference equations. These criteria are obtained as an application of\ndifferential Galois theory for difference equations. We apply our criteria to\nprove a new result to the effect that most elliptic hypergeometric functions\nare differentially transcendental.\n']","[('difference galois theory', 0.6130079627037048), ('differential galois theory', 0.5459491014480591), ('difference galois', 0.5059323310852051), ('differential galois', 0.5020899772644043), ('differential galois group', 0.4994033873081207), ('difference equations', 0.460208922624588), ('differential transcendence', 0.45734888315200806), ('galois theory linear', 0.43917325139045715), ('galois theory', 0.4332095980644226), ('linear difference equations', 0.4258568584918976)]"
714,714,43,714_compactifications moduli_compactification moduli space_compactification moduli_moduli space surfaces,"['compactifications moduli', 'compactification moduli space', 'compactification moduli', 'moduli space surfaces', 'elliptic k3 surfaces', 'surfaces moduli', 'toroidal compactification', 'k3 surfaces', 'compactifications', 'compact moduli']","['Compactifications of moduli spaces of K3 surfaces with a higher-order\n  nonsymplectic automorphism   We describe Baily-Borel, toroidal, and geometric -- using the KSBA stable\npairs -- compactifications of some moduli spaces of K3 surfaces with a\nnonsymplectic automorphism of order $3$ and $4$ for which the fixed locus of\nthe automorphism contains a curve of genus $\\ge2$. For order $3$, we treat all\nthe maximal-dimensional such families. We show that the toroidal and the KSBA\ncompactifications in these cases admit simple descriptions in terms of certain\n$ADE$ root lattices.\n', ""The KSBA compactification of the moduli space of $D_{1,6}$-polarized\n  Enriques surfaces   We describe a compactification by stable pairs (also known as KSBA\ncompactification) of the $4$-dimensional family of Enriques surfaces which\narise as the $\\mathbb{Z}_2^2$-covers of the blow up of $\\mathbb{P}^2$ at three\ngeneral points branched along a configuration of three pairs of lines. Up to a\nfinite group action, we show that this compactification is isomorphic to the\ntoric variety associated to the secondary polytope of the unit cube. We relate\nthe KSBA compactification considered to the Baily-Borel compactification of the\nsame family of Enriques surfaces. Part of the KSBA boundary has a toroidal\nbehavior, another part is isomorphic to the Baily-Borel compactification, and\nwhat remains is a mixture of these two. We relate the stable pair\ncompactification studied here with Looijenga's semitoric compactifications.\n"", ""Compactifications of moduli space of (quasi-)trielliptic K3 surfaces   We study the moduli space $\\mathcal{F}_{T_1}$ of quasi-trielliptic K3\nsurfaces of type I, whose general member is a smooth bidegree\n$(2,3)$-hypersurface of $\\mathbb{P}^1\\times \\mathbb{P}^2$. Such moduli space\nplays an important role in the study of the Hassett-Keel-Looijenga program of\nthe moduli space of degree $8$ quasi-polarized K3 surfaces.\n  In this paper, we consider several natural compactifications of\n$\\mathcal{F}_{T_1}$, such as the GIT compactification and arithmetic\ncompactifications. We give a complete analysis of GIT stability of\n$(2,3)$-hypersurfaces and provide a concrete description of the boundary of the\nGIT compactification. For the Baily--Borel compactification of the\nquasi-trielliptic K3 surfaces, we also compute the configurations of the\nboundary by classifying certain lattice embeddings. As an application, we show\nthat $(\\mathbb{P}^1\\times \\mathbb{P}^2,\\epsilon S)$ with small $\\epsilon$ is\nK-stable if $S$ is a K3 surface with at worst ADE singularities. This gives a\nconcrete description of the boundary of the K-stability compactification via\nthe identification of the GIT stability and the K-stability. We also discuss\nthe connection between the GIT, Baily--Borel compactification, and Looijenga's\ncompactifications by studying the projective models of quasi-trielliptic K3\nsurfaces.\n""]","[('compactifications moduli', 0.7279481291770935), ('compactification moduli space', 0.7078112959861755), ('compactification moduli', 0.7054637670516968), ('moduli space surfaces', 0.70524001121521), ('elliptic k3 surfaces', 0.6532180905342102), ('surfaces moduli', 0.6469427347183228), ('toroidal compactification', 0.6328083872795105), ('k3 surfaces', 0.6146141290664673), ('compactifications', 0.6125187873840332), ('compact moduli', 0.5994833111763)]"
715,715,43,715_pursuit evasion_strategies game_pursuit_differential game theory,"['pursuit evasion', 'strategies game', 'pursuit', 'differential game theory', 'optimal strategies', 'differential game', 'differential games', 'matrix game', 'attacker defender', 'defender']","['Pursuit-Evasion Game with Hybrid System of Dynamics   We consider a pursuit-evasion differential game with a Hybrid system of\ndynamics in Hilbert space with integral constraints on the control functions of\nplayers. We show that the pursuer has a winning strategy.\n', 'Analytical Pursuit-Evasion Game Strategy in Arbitrary Keplerian\n  Reference Orbits   This paper develops an analytical strategy for solving the linear quadratic\npursuit-evasion game in arbitrary Keplerian reference orbits. The motion of the\npursuer and evader is described using the controlled Tschauner-Hempel\nequations, and the optimal game strategies of the pursuer and evader are\npresented by the solution of the differential Riccati equation.The analytical\nsolution of the differential Riccati equation is presented for elliptic,\nparabolic, and hyperbolic reference orbits, thereby enabling an analytical\npursuit-evasion game strategy. Then, the procedure to solve the pursuit-evasion\ngame using this analytical strategy is proposed. Simulations of pursuit-evasion\ngame in elliptic, parabolic, and hyperbolic reference orbits validate the\neffectiveness of the developed analytical strategy. Results indicates that the\nanalytical strategy saves the CPU time by more than 99.8$\\%$ compared to the\nnumerical one, highlighting the efficiency of the developed strategy. The\ndeveloped analytical strategy is also applicable to pursuit-evasion game\nscenarios considering orbital disturbances. Compared to the conventional\nstrategy, which succeed in only two out of six test scenarios, the developed\nstrategy achieves success in all six cases, particularly demonstrating its\neffectiveness in high-eccentricity cases.\n', ""An Introduction to Pursuit-evasion Differential Games   Pursuit and evasion conflicts represent challenging problems with important\napplications in aerospace and robotics. In pursuit-evasion problems, synthesis\nof intelligent actions must consider the adversary's potential strategies.\nDifferential game theory provides an adequate framework to analyze possible\noutcomes of the conflict without assuming particular behaviors by the opponent.\nThis article presents an organized introduction of pursuit-evasion differential\ngames with an overview of recent advances in the area. First, a summary of the\nseminal work is outlined, highlighting important contributions. Next, more\nrecent results are described by employing a classification based on the number\nof players: one-pursuer-one-evader, N-pursuers-one-evader,\none-pursuer-M-evaders, and N-pursuer-M-evader games. In each scenario, a brief\nsummary of the literature is presented. Finally, two representative\npursuit-evasion differential games are studied in detail: the two-cutters and\nfugitive ship differential game and the active target defense differential\ngame. These problems provide two important applications and, more importantly,\nthey give great insight into the realization of cooperation between friendly\nagents in order to form a team and defeat the adversary.\n""]","[('pursuit evasion', 0.6632240414619446), ('strategies game', 0.5795261859893799), ('pursuit', 0.551235020160675), ('differential game theory', 0.5309648513793945), ('optimal strategies', 0.5017873048782349), ('differential game', 0.4896860122680664), ('differential games', 0.4797847270965576), ('matrix game', 0.45065176486968994), ('attacker defender', 0.43366119265556335), ('defender', 0.41593146324157715)]"
716,716,43,716_triangulation manifold_ideal triangulations_triangulated manifolds_triangulated manifold,"['triangulation manifold', 'ideal triangulations', 'triangulated manifolds', 'triangulated manifold', 'ideal triangulation', 'triangulations', 'triangulation', 'triangulation mathcal', 'graph triangulation', 'manifolds obtained']","['Essential loops in taut ideal triangulations   In this note we combinatorialise a technique of Novikov. We use this to prove\nthat, in a three-manifold equipped with a taut ideal triangulation, any\nvertical or normal loop is essential in the fundamental group.\n', 'Poor ideal three-edge triangulations are minimal   It is known that an ideal triangulation of a compact $3$-manifold with\nnonempty boundary is minimal if and only if it contains the minimum number of\nedges among all ideal triangulations of the manifold. Therefore, any ideal\none-edge triangulation (i.e., an ideal singular triangulation with exactly one\nedge) is minimal. Vesnin, Turaev, and the first author showed that an ideal\ntwo-edge triangulation is minimal if no $3$-$2$ Pachner move can be applied. In\nthis paper we show that any of the so-called poor ideal three-edge\ntriangulations is minimal. We exploit this property to construct minimal ideal\ntriangulations for an infinite family of hyperbolic $3$-manifolds with totally\ngeodesic boundary.\n', 'Efficient triangulations and boundary slopes   For a compact, irreducible, $\\partial$-irreducible, an-annular bounded\n3-manifold $M\\ne\\mathbb{B}^3$, then any triangulation $\\mathcal{T}$ of $M$ can\nbe modified to an ideal triangulation $\\mathcal{T}^*$ of $\\stackrel{\\circ}{M}$.\nWe use the inverse relationship of crushing a triangulation along a normal\nsurface and that of inflating an ideal triangulation to introduce and study\nboundary-efficient triangulations and end-efficient ideal triangulations. We\nprove that the topological conditions necessary for a compact 3-manifold $M$\nadmitting an annular-efficient triangulation are sufficient to modify any\ntriangulation of $M$ to a boundary-efficient triangulation which is also\nannular-efficient. From the proof we have for any ideal triangulation $T^*$ and\nany inflation $\\mathcal{T}_{\\Lambda}$, there is a bijective correspondence\nbetween the closed normal surfaces in $\\mathcal{T}^*$ and the closed normal\nsurfaces in $\\mathcal{T}_{\\Lambda}$ with corresponding normal surfaces being\nhomeomorphic. It follows that for an ideal triangulation $\\mathcal{T}^*$ that\nis $0$-efficient, $1$-efficient, or end-efficient, then any inflation\n$\\mathcal{T}_{\\Lambda}$ of $\\mathcal{T}^*$ is $0$-efficient, $1$-efficient, or\n$\\partial$-efficient, respectively. There are algorithms to decide if a given\ntriangulation or ideal triangulation of a $3$-manifold is one of these\nefficient triangulations. Finally, it is shown that for an annular-efficient\ntriangulation, there are only a finite number of boundary slopes for normal\nsurfaces of a bounded Euler characteristic; hence, in a compact, orientable,\nirreducible, $\\partial$-irreducible, and an-annular $3$-manifold, there are\nonly finitely many boundary slopes for incompressible and\n$\\partial$-incompressible surfaces of a bounded Euler characteristic.\n']","[('triangulation manifold', 0.7209374308586121), ('ideal triangulations', 0.715854823589325), ('triangulated manifolds', 0.7069114446640015), ('triangulated manifold', 0.6837923526763916), ('ideal triangulation', 0.6788793206214905), ('triangulations', 0.6476038098335266), ('triangulation', 0.603480339050293), ('triangulation mathcal', 0.5683703422546387), ('graph triangulation', 0.5568545460700989), ('manifolds obtained', 0.5193361043930054)]"
717,717,43,717_stability viscous_shock waves_shock wave_compressible navier stokes,"['stability viscous', 'shock waves', 'shock wave', 'compressible navier stokes', 'dispersive shock', 'barotropic navier stokes', 'time asymptotic stability', 'rarefaction waves', 'rarefaction wave', 'navier stokes poisson']","['Time-asymptotic stability of generic Riemann solutions for compressible\n  Navier-Stokes-Fourier equations   We establish the time-asymptotic stability of solutions to the\none-dimensional compressible Navier-Stokes-Fourier equations, with initial data\nperturbed from Riemann data that forms a generic Riemann solution. The Riemann\nsolution under consideration is composed of a viscous shock, a viscous contact\nwave, and a rarefaction wave. We prove that the perturbed solution of\nNavier-Stokes-Fourier converges, uniformly in space as time goes to infinity,\nto a viscous ansatz composed of viscous shock with time-dependent shift, a\nviscous contact wave and an inviscid rarefaction wave.\n  This is a first resolution of the challenging open problem associated with\nthe generic Riemann solution. Our approach relies on the method of\na-contraction with shifts, specifically applied to both the shock wave and the\ncontact discontinuity wave. It enables the application of a global energy\nmethod for the generic combination of three waves.\n', 'Stability of composite Wave of Planar Viscous Shock and Rarefaction for\n  3D Barotropic Navier-Stokes Equations   We prove the nonlinear time-asymptotic stability of the composite wave\nconsisting of a planar rarefaction wave and a planar viscous shock for the\nthree-dimensional (3D) compressible barotropic Navier-Stokes equations under\ngeneric perturbations, in particular, without zero-mass conditions. It is shown\nthat if the composite wave strength and the initial perturbations are suitably\nsmall, then 3D Navier-Stokes system admits a unique global-in-time strong\nsolution which time-asymptotically converges to the corresponding composite\nwave up to a time-dependent shift for planar viscous shock. Our proof is based\non the $a$-contraction method with time-dependent shift and suitable weight\nfunction.\n', 'Time-asymptotic stability of composite waves of degenerate Oleinik shock\n  and rarefaction for non-convex conservation laws   We are concerned with the large-time behavior of the solution to\none-dimensional (1D) cubic non-convex scalar viscous conservation laws. Due to\nthe inflection point of the cubic non-convex flux, the solution to the\ncorresponding inviscid Riemann problem can be the composite wave of a\ndegenerate Oleinik shock and a rarefaction wave and these two nonlinear waves\nare always attached together. We give a first proof of the time-asymptotic\nstability of this composite wave, up to a time-dependent shift to the viscous\nOleinik shock, for the viscous equation. The Oleinik shock wave strength can be\narbitrarily large. The main difficulty is due to the incompatibility of the\ntime-asymptotic stability proof framework of individual viscous shock by the\nso-called anti-derivative method and the direct $L^2$-energy method to\nrarefaction wave. Here we develop a new type of $a$-contraction method with\nsuitable weight function and the time-dependent shift to the viscous shock,\nwhich is motivated by [9,12]. Another difficulty comes from that the Oleinik\nshock and rarefaction wave are always attached together and their wave\ninteractions are very subtle. Therefore, the same time-dependent shift needs to\nbe equipped to both Oleinik shock and rarefaction wave such that the wave\ninteractions can be treated in our stability proof. Time-asymptotically, this\nshift function grows strictly sub-linear with respect to the time and then the\nshifted rarefaction wave is equivalent to the original self-similar rarefaction\nwave.\n']","[('stability viscous', 0.5291564464569092), ('shock waves', 0.4962676763534546), ('shock wave', 0.48060813546180725), ('compressible navier stokes', 0.4758514165878296), ('dispersive shock', 0.4705759882926941), ('barotropic navier stokes', 0.4659914970397949), ('time asymptotic stability', 0.4588632583618164), ('rarefaction waves', 0.4576541781425476), ('rarefaction wave', 0.44258785247802734), ('navier stokes poisson', 0.4409513771533966)]"
718,718,43,718_relu networks_neural networks relu_relu neural networks_mixed integer optimization,"['relu networks', 'neural networks relu', 'relu neural networks', 'mixed integer optimization', 'integer linear programming', 'integer optimization', 'mixed integer programming', 'trained neural', 'networks relu', 'robustness neural']","['Towards Optimal Branching of Linear and Semidefinite Relaxations for Neural Network Robustness Certification In this paper, we study certifying the robustness of ReLU neural networks against adversarial input perturbations. To diminish the relaxation error suffered by the popular linear programming (LP) and semidefinite programming (SDP) certification methods, we take a branch-and-bound approach to propose partitioning the input uncertainty set and solving the relaxations on each part separately. We show that this approach reduces relaxation error, and that the error is eliminated entirely upon performing an LP relaxation with a partition intelligently designed to exploit the nature of the ReLU activations. To scale this approach to large networks, we consider using a coarser partition whereby the number of parts in the partition is reduced. We prove that computing such a coarse partition that directly minimizes the LP relaxation error is NP-hard. By instead minimizing the worst-case LP relaxation error, we develop a closed-form branching scheme in the single-hidden layer case. We extend the analysis to the SDP, where the feasible set geometry is exploited to design a branching scheme that minimizes the worst-case SDP relaxation error. Experiments on MNIST, CIFAR-10, and Wisconsin breast cancer diagnosis classifiers demonstrate significant increases in the percentages of test samples certified. By independently increasing the input size and the number of layers, we empirically illustrate under which regimes the branched LP and branched SDP are best applied. Finally, we extend our LP branching method into a multi-layer branching heuristic, which attains comparable performance to prior state-of-the-art heuristics on large-scale, deep neural network certification benchmarks.', 'Feed-Forward Neural Networks as a Mixed-Integer Program   Deep neural networks (DNNs) are widely studied in various applications. A DNN\nconsists of layers of neurons that compute affine combinations, apply nonlinear\noperations, and produce corresponding activations. The rectified linear unit\n(ReLU) is a typical nonlinear operator, outputting the max of its input and\nzero. In scenarios like max pooling, where multiple input values are involved,\na fixed-parameter DNN can be modeled as a mixed-integer program (MIP). This\nformulation, with continuous variables representing unit outputs and binary\nvariables for ReLU activation, finds applications across diverse domains. This\nstudy explores the formulation of trained ReLU neurons as MIP and applies MIP\nmodels for training neural networks (NNs). Specifically, it investigates\ninteractions between MIP techniques and various NN architectures, including\nbinary DNNs (employing step activation functions) and binarized DNNs (with\nweights and activations limited to $-1,0,+1$). The research focuses on training\nand evaluating proposed approaches through experiments on handwritten digit\nclassification models. The comparative study assesses the performance of\ntrained ReLU NNs, shedding light on the effectiveness of MIP formulations in\nenhancing training processes for NNs.\n', 'Optimal training of integer-valued neural networks with mixed integer\n  programming   Recent work has shown potential in using Mixed Integer Programming (MIP)\nsolvers to optimize certain aspects of neural networks (NNs). However the\nintriguing approach of training NNs with MIP solvers is under-explored.\nState-of-the-art-methods to train NNs are typically gradient-based and require\nsignificant data, computation on GPUs, and extensive hyper-parameter tuning. In\ncontrast, training with MIP solvers does not require GPUs or heavy\nhyper-parameter tuning, but currently cannot handle anything but small amounts\nof data. This article builds on recent advances that train binarized NNs using\nMIP solvers. We go beyond current work by formulating new MIP models which\nimprove training efficiency and which can train the important class of\ninteger-valued neural networks (INNs). We provide two novel methods to further\nthe potential significance of using MIP to train NNs. The first method\noptimizes the number of neurons in the NN while training. This reduces the need\nfor deciding on network architecture before training. The second method\naddresses the amount of training data which MIP can feasibly handle: we provide\na batch training method that dramatically increases the amount of data that MIP\nsolvers can use to train. We thus provide a promising step towards using much\nmore data than before when training NNs using MIP models. Experimental results\non two real-world data-limited datasets demonstrate that our approach strongly\noutperforms the previous state of the art in training NN with MIP, in terms of\naccuracy, training time and amount of data. Our methodology is proficient at\ntraining NNs when minimal training data is available, and at training with\nminimal memory requirements -- which is potentially valuable for deploying to\nlow-memory devices.\n']","[('relu networks', 0.5187464952468872), ('neural networks relu', 0.5122368931770325), ('relu neural networks', 0.5121045708656311), ('mixed integer optimization', 0.5017260313034058), ('integer linear programming', 0.47655394673347473), ('integer optimization', 0.466467022895813), ('mixed integer programming', 0.46300581097602844), ('trained neural', 0.4559173285961151), ('networks relu', 0.44430607557296753), ('robustness neural', 0.44312193989753723)]"
719,719,43,719_curvature estimates_estimates curvature_curvature estimate_mean curvature operator,"['curvature estimates', 'estimates curvature', 'curvature estimate', 'mean curvature operator', 'mean curvature flow', 'curvature general', 'estimate curvature', 'mean curvature', 'curvature equations', 'mean curvature type']","['Gradient estimates for the Lagrangian mean curvature equation with\n  critical and supercritical phase   In this paper, we prove interior gradient estimates for the Lagrangian mean\ncurvature equation, if the Lagrangian phase is critical and supercritical and\n$C^{2}$. Combined with the a priori interior Hessian estimates proved in\n[Bha21, Bha22], this solves the Dirichlet boundary value problem for the\ncritical and supercritical Lagrangian mean curvature equation with $C^0$\nboundary data. We also provide a uniform gradient estimate for lower regularity\nphases that satisfy certain additional hypotheses.\n', 'Hessian estimates for shrinkers, expanders, translators, and rotators of\n  the Lagrangian Mean Curvature Flow   In this paper, we prove interior Hessian estimates for shrinkers, expanders,\ntranslators, and rotators of the Lagrangian mean curvature flow under the\nassumption that the Lagrangian phase is hypercritical. We further extend our\nresults to a broader class of Lagrangian mean curvature type equations.\n', 'Hessian Estimates for Lagrangian mean curvature equation   In this paper, we derive a priori interior Hessian estimates for Lagrangian\nmean curvature equation if the Lagrangian phase is supercritical and has\nbounded second derivatives.\n']","[('curvature estimates', 0.6733543872833252), ('estimates curvature', 0.6632091999053955), ('curvature estimate', 0.6460289359092712), ('mean curvature operator', 0.639062762260437), ('mean curvature flow', 0.6253466010093689), ('curvature general', 0.6212789416313171), ('estimate curvature', 0.6190338730812073), ('mean curvature', 0.6189190745353699), ('curvature equations', 0.6076040863990784), ('mean curvature type', 0.6025235652923584)]"
720,720,43,720_residuated lattices_residuated lattice_distributive lattice_lattices,"['residuated lattices', 'residuated lattice', 'distributive lattice', 'lattices', 'lattice', 'lattice ordered', 'residuated', 'algebras variety', 'boolean algebras', 'heyting algebras']","['Gluing residuated lattices   We introduce and characterize various gluing constructions for residuated\nlattices that intersect on a common subreduct, and which are subalgebras, or\nappropriate subreducts, of the resulting structure. Starting from the 1-sum\nconstruction (also known as ordinal sum for residuated structures), where\nalgebras that intersect only in the top element are glued together, we first\nconsider the gluing on a congruence filter, and then add a lattice ideal as\nwell. We characterize such constructions in terms of (possibly partial)\noperators acting on (possibly partial) residuated structures. As particular\nexamples of gluing constructions, we obtain the non-commutative version of some\nrotation constructions, and an interesting variety of semilinear residuated\nlattices that are 2-potent. This study also serves as a first attempt toward\nthe study of amalgamation of non-commutative residuated lattices, by\nconstructing an amalgam in the special case where the common subalgebra in the\nV-formation is either a special (congruence) filter or the union of a filter\nand an ideal.\n', 'Unilinear residuated lattices: axiomatization, varieties and FEP   We characterize all residuated lattices that have height equal to $3$ and\nshow that the variety they generate has continuum-many subvarieties. More\ngenerally, we study unilinear residuated lattices: their lattice is a union of\ndisjoint incomparable chains, with bounds added. We we give two general\nconstructions of unilinear residuated lattices, provide an axiomatization and a\nproof-theoretic calculus for the variety they generate, and prove the finite\nmodel property for various subvarieties.\n', 'Residuated lattices do not have the amalgamation property   We show that the variety of residuated lattices does not have the\namalgamation property.\n']","[('residuated lattices', 0.7975441813468933), ('residuated lattice', 0.7735671401023865), ('distributive lattice', 0.6480589509010315), ('lattices', 0.6314364075660706), ('lattice', 0.5854841470718384), ('lattice ordered', 0.5373907089233398), ('residuated', 0.47451725602149963), ('algebras variety', 0.4404121935367584), ('boolean algebras', 0.34431174397468567), ('heyting algebras', 0.34363672137260437)]"
721,721,43,721_polynomial systems_sparse polynomial_systems polynomials_solving systems polynomial,"['polynomial systems', 'sparse polynomial', 'systems polynomials', 'solving systems polynomial', 'sparse systems', 'systems polynomial equations', 'systems polynomial', 'polynomial system', 'system polynomial equations', 'sparse system']","['Decomposable sparse polynomial systems   The Macaulay2 package DecomposableSparseSystems implements methods for\nstudying and numerically solving decomposable sparse polynomial systems. We\ndescribe the structure of decomposable sparse systems and explain how the\nmethods in this package may be used to exploit this structure, with examples.\n', 'Khovanskii bases for semimixed systems of polynomial equations -- a case\n  of approximating stationary nonlinear Newtonian dynamics   We provide an approach to counting roots of polynomial systems, where each\npolynomial is a general linear combination of prescribed, fixed polynomials.\nOur tools rely on the theory of Khovanskii bases, combined with toric geometry,\nthe Bernstein-Khovanskii-Kushnirenko (BKK) Theorem, and fiber products.\n  As a direct application of this theory, we solve the problem of counting the\nnumber of approximate stationary states for coupled driven nonlinear\nresonators. We set up a system of polynomial equations that depends on three\nnumbers $N, n$ and $M$ and whose solutions model the stationary states. The\nparameter $N$ is the number of coupled resonators, $2n - 1$ is the degree of\nnonlinearity of the underlying differential equation, and $M$ is the number of\nfrequencies used in the approximation. We use our main theorems, that is, the\ngeneralized BKK Theorem and the Decoupling Theorem, to count the number of\n(complex) solutions of the polynomial system for an arbitrary degree of\nnonlinearity $2n - 1 \\geq 3$, any number of resonators $N \\geq 1$, and $M = 1$\nharmonic. We also solve the case $N = 1, n = 2$ and $M = 2$ and give a\ncomputational way to check the number of solutions for $N = 1, n = 2$ and $M\n\\geq 2$. This extends the results of arXiv:2208.08179.\n', 'Solving sparse polynomial systems using Groebner bases and resultants   Solving systems of polynomial equations is a central problem in nonlinear and\ncomputational algebra. Since Buchberger\'s algorithm for computing Gr\\""obner\nbases in the 60s, there has been a lot of progress in this domain. Moreover,\nthese equations have been employed to model and solve problems from diverse\ndisciplines such as biology, cryptography, and robotics. Currently, we have a\ngood understanding of how to solve generic systems from a theoretical and\nalgorithmic point of view. However, polynomial equations encountered in\npractice are usually structured, and so many properties and results about\ngeneric systems do not apply to them. For this reason, a common trend in the\nlast decades has been to develop mathematical and algorithmic frameworks to\nexploit specific structures of systems of polynomials.\n  Arguably, the most common structure is sparsity; that is, the polynomials of\nthe systems only involve a few monomials. Since Bernstein, Khovanskii, and\nKushnirenko\'s work on the expected number of solutions of sparse systems, toric\ngeometry has been the default mathematical framework to employ sparsity. In\nparticular, it is the crux of the matter behind the extension of classical\ntools to systems, such as resultant computations, homotopy continuation\nmethods, and most recently, Gr\\""obner bases. In this work, we will review these\nclassical tools, their extensions, and recent progress in exploiting sparsity\nfor solving polynomial systems.\n  This manuscript complements its homonymous tutorial presented at the\nconference ISSAC 2022.\n']","[('polynomial systems', 0.6677108407020569), ('sparse polynomial', 0.6226873993873596), ('systems polynomials', 0.6219503283500671), ('solving systems polynomial', 0.6162289977073669), ('sparse systems', 0.6122798323631287), ('systems polynomial equations', 0.603123128414154), ('systems polynomial', 0.5880126953125), ('polynomial system', 0.5706866383552551), ('system polynomial equations', 0.5623836517333984), ('sparse system', 0.5622580051422119)]"
722,722,43,722_adaptive mesh refinement_mesh refinement_adaptive mesh_mesh refinement amr,"['adaptive mesh refinement', 'mesh refinement', 'adaptive mesh', 'mesh refinement amr', 'mesh optimization', 'unstructured meshes', 'mesh adaptation', 'refined meshes', 'mesh generation', 'hexahedral meshes']","['On mesh refinement procedures for polygonal virtual elements   This work concerns adaptive refinement procedures for meshes of polygonal\nvirtual elements. Specifically, refinement procedures previously proposed by\nthe authors for structured meshes are generalized for the challenging case of\narbitrary element geometries arising in unstructured/Voronoi discretizations.\nHere, structured and unstructured meshes are considered and are created via\nVoronoi tessellation of sets of structured and unstructured seed points\nrespectively. The novel mesh refinement procedures for both structured and\nunstructured meshes allow for accurate and efficient application of the virtual\nelement method to challenging elastic problems in two-dimensions. The results\ndemonstrate that the high efficacy of the proposed refinement procedures on\nstructured meshes, as seen in previous work by the authors, is also achieved in\nthe case of unstructured/Voronoi meshes. The versatility and efficacy of the\nrefinement procedures demonstrated over a variety of mesh types indicates that\nthe procedures are well-suited to virtual element applications.\n', 'Smart Adaptive Mesh Refinement with NEMoSys   Adaptive mesh refinement (AMR) offers a practical solution to reduce the\ncomputational cost and memory requirement of numerical simulations that use\ncomputational meshes. In this work, we introduce a novel smart methodology for\nadaptive mesh refinement. Smart adaptive refinement blends classical AMR with\nmachine learning to address some of the known issues of the conventional\napproaches. We provide an algorithm for adaptive refinement. Subsequently, we\nintroduce a modular object-oriented structure for our smart AMR algorithm. Then\nwe present procedures used for the training of a smart AMR model. The study\nfollows with a demonstration of preliminary numerical studies indicating the\nfeasibility of performing adaptive mesh refinement on a few demonstrative\nproblems selected from the CFD domain. Finally, we conclude with a few comments\nabout future work.\n', 'A new quality preserving polygonal mesh refinement algorithm for Virtual\n  Element Methods   Mesh adaptivity is a useful tool for efficient solution to partial\ndifferential equations in very complex geometries. In the present paper we\ndiscuss the use of polygonal mesh refinement in order to tackle two common\nissues: first, adaptively refine a provided good quality polygonal mesh\npreserving quality, second, improve the quality of a coarse poor quality\npolygonal mesh during the refinement process on very complex domains. For\nfinite element methods and triangular meshes, convergence of a posteriori mesh\nrefinement algorithms and optimality properties have been widely investigated,\nwhereas convergence and optimality are still open problems for polygonal\nadaptive methods. In this article, we propose a new refinement method for\nconvex cells with the aim of introducing some properties useful to tackle\nconvergence and optimality for adaptive methods. The key issues in refining\nconvex general polygons are: a refinement dependent only on the marked cells\nfor refinement at each refinement step; a partial quality improvement, or, at\nleast, a non degenerate quality of the mesh during the refinement iterations; a\nbound of the number of unknowns of the discrete problem with respect to the\nnumber of the cells in the mesh. Although these properties are quite common for\nrefinement algorithms of triangular meshes, these issues are still open\nproblems for polygonal meshes\n']","[('adaptive mesh refinement', 0.8018457889556885), ('mesh refinement', 0.6981509327888489), ('adaptive mesh', 0.6964569091796875), ('mesh refinement amr', 0.6269924640655518), ('mesh optimization', 0.6093081831932068), ('unstructured meshes', 0.6035324335098267), ('mesh adaptation', 0.5950741171836853), ('refined meshes', 0.5902676582336426), ('mesh generation', 0.5695616602897644), ('hexahedral meshes', 0.5651450753211975)]"
723,723,43,723_fractal functions_fractal dimension_dimension fractal_fractals,"['fractal functions', 'fractal dimension', 'dimension fractal', 'fractals', 'non fractal', 'fractal', 'interpolation functions', 'solitons fractals', 'chaos solitons fractals', 'scaling functions']","['Box Dimension and Fractional Integrals of Multivariate Fractal\n  Interpolation Functions   In this article, we construct the multivariate fractal interpolation\nfunctions for a given data points and explore the existence of $\\alpha$-fractal\nfunction corresponding to the multivariate continuous function defined on\n$[0,1]\\times \\cdots \\times [0,1](q\\text{-times})$. The parameters are selected\nsuch that the corresponding fractal version preserves some of the original\nfunction\'s properties, for instance, if the given function is H\\""older\ncontinuous, then the corresponding $\\alpha$-fractal function is also H\\""older\ncontinuous. Moreover, we explore the restriction of the $\\alpha$-fractal\nfunction on the co-ordinate axis. Furthermore, the box dimension and Hausdorff\ndimension of the graph of the multivariate $\\alpha$-fractal function and its\nrestriction are investigated. In the last section, we prove that the mixed\nRiemann-Liouville fractional integral of fractal function satisfies a\nself-referential equation.\n', 'Fractal dimension for a class of complex-valued fractal interpolation\n  functions   There are many research papers dealing with fractal dimension of real-valued\nfractal functions in the recent literature. The main focus of the present paper\nis to study fractal dimension of complex-valued functions. This paper also\nhighlights the difference between dimensional results of the complex-valued and\nreal-valued fractal functions. In this paper, we study the fractal dimension of\nthe graph of complex-valued function $g(x)+i h(x)$, compare its fractal\ndimension with the graphs of functions $g(x)+h(x)$ and $(g(x),h(x))$ and also\nobtain some bounds. Moreover, we study the fractal dimension of the graph of\ncomplex-valued fractal interpolation function associated with a germ function\n$f$, base function $b$ and scaling functions $\\alpha_k$.\n', 'On Fractal Features and Fractal Linear Space About Fractal Continuous\n  Functions   This paper investigates fractal dimension of linear combination of fractal\ncontinuous functions with the same or different fractal dimensions. It has been\nproved that: (1) $BV_{I}$ all fractal continuous functions with bounded\nvariation is fractal linear space; (2) ${}^{1}D_{I}$ all fractal continuous\nfunctions with Box dimension one is a fractal linear space; (3) ${}^{s}D_{I}$\nall fractal continuous functions with identical Box dimension $s(1<s\\leq 2)$ is\nsurprisingly a non-fractal linear space, even non-fractal linear manifold,\nbeyond our initial expectation, because the Box dimension of linear combination\nof fractal continuous functions can take any real number in $[1,s)$ if it\nexists, and some different upper and lower Box dimension if it does not exit.\nThis attracts our interests to probe into fractal characteristics of\n${}^{s}D_{I}$, and get some suggesting results.\n']","[('fractal functions', 0.778420090675354), ('fractal dimension', 0.7163983583450317), ('dimension fractal', 0.7129349112510681), ('fractals', 0.6200358867645264), ('non fractal', 0.6086331605911255), ('fractal', 0.6083121299743652), ('interpolation functions', 0.5184624791145325), ('solitons fractals', 0.46711426973342896), ('chaos solitons fractals', 0.460711270570755), ('scaling functions', 0.42481163144111633)]"
724,724,43,724_crystal lattice_hexagonal lattice_lattice_lattices,"['crystal lattice', 'hexagonal lattice', 'lattice', 'lattices', 'square lattice', 'lattice structures', 'dimensional lattices', 'unimodular lattices', 'cubic lattice', 'triangular lattice']","[""On crystallization in the plane for pair potentials with an arbitrary\n  norm   We investigate two-dimensional crystallization phenomena, i.e. minimality of\na lattice's patch for interaction energies, with pair potentials of type\n$(x,y)\\mapsto V(\\|x-y\\|)$ where $\\|\\cdot\\|$ is an arbitrary norm on\n$\\mathbb{R}^2$ and $V:\\mathbb{R}_+^*\\to \\mathbb{R}$ is a function. For the\nHeitmann-Radin sticky disk potential $V=V_{\\text{HR}}$, we prove, using Brass'\nkey result from [Computational Geometry, 6:195--214, 1996], that\ncrystallization occurs for any fixed norm, with a classification of minimizers\nand minimal energies according to the kissing number associated to $\\|\\cdot\\|$.\nThe minimizer is proved to be, up to affine transform, a patch of the\ntriangular or the square lattice, which shows how to easily get anisotropy in a\ncrystallization phenomenon. We apply this result to the $p$-norms\n$\\|\\cdot\\|_p$, $p\\geq 1$, which allows us to construct an explicit family of\nnorms for which crystallization holds on any given lattice. We also solve part\nof a crystallization problem studied in [Arch. Ration. Mech. Anal.,\n240:987--1053] where points are constrained to be on $\\mathbb{Z}^2$. Moreover,\nwe numerically investigate the minimization problem for the energy per point\namong lattices for the Lennard-Jones potential $V=V_{\\text{LJ}}:r\\mapsto\nr^{-12}-2r^{-6}$ as well as the Epstein zeta function associated to a $p$-norm\n$\\|\\cdot\\|_p$, i.e. when $V=V_s:r\\mapsto r^{-s}$, $s>2$. Our simulations show a\nnew and unexpected phase transition for the minimizers with respect to $p$.\n"", 'On energy ground states among crystal lattice structures with prescribed\n  bonds   We consider pairwise interaction energies and we investigate their minimizers\namong lattices with prescribed minimal vectors (length and coordination\nnumber), i.e. the one corresponding to the crystal\'s bonds. In particular, we\nshow the universal minimality -- i.e. the optimality for all completely\nmonotone interaction potentials -- of strongly eutactic lattices among these\nstructures. This gives new optimality results for the square, triangular,\nsimple cubic (SC), face-centred-cubic (FCC) and body-centred-cubic (BCC)\nlattices in dimensions 2 and 3 when points are interacting through completely\nmonotone potentials. We also show the universal maximality of the triangular\nand FCC lattices among all lattices with prescribed bonds. Furthermore, we\napply our results to Lennard-Jones type potentials, showing the minimality of\nany universal minimizer (resp. maximizer) for small (resp. large) bond lengths,\nwhere the ranges of optimality are easily computable. Finally, a numerical\ninvestigation is presented where a phase transition of type\n""square-rhombic-triangular"" (resp. ""SC-rhombic-BCC-rhombic-FCC"") in dimension\n$d=2$ (resp. $d=3$) among lattices with more than 4 (resp. 6) bonds is\nobserved.\n', 'Three-dimensional lattice ground states for Riesz and Lennard-Jones type\n  energies   The Riesz potential $f_s(r)=r^{-s}$ is known to be an important building\nblock of many interactions, including Lennard-Jones type potentials\n$f_{n,m}^{\\rm{LJ}}(r):=a r^{-n}-b r^{-m}$, $n>m$ that are widely used in\nMolecular Simulations. In this paper, we investigate analytically and\nnumerically the minimizers among three-dimensional lattices of Riesz and\nLennard-Jones energies. We discuss the minimality of the Body-Centred-Cubic\nlattice (BCC), Face-Centred-Cubic lattice (FCC), Simple Hexagonal lattices (SH)\nand Hexagonal Close-Packing structure (HCP), globally and at fixed density. In\nthe Riesz case, new evidence of the global minimality at fixed density of the\nBCC lattice is shown for $s<0$ and the HCP lattice is computed to have higher\nenergy than the FCC (for $s>3/2$) and BCC (for $s<3/2$) lattices. In the\nLennard-Jones case with exponents $3<m<n$, the ground state among lattices is\nconfirmed to be a FCC lattice whereas a HCP phase occurs once added to the\ninvestigated structures. Furthermore, phase transitions of type ``FCC-SH"" and\n``FCC-HCP-SH"" (when the HCP lattice is added) as the inverse density $V$\nincreases are observed for a large spectrum of exponents $(n,m)$. In the SH\nphase, the variation of the ratio $\\Delta$ between the inter-layer distance $d$\nand the lattice parameter $a$ is studied as $V$ increases. In the critical\nregion of exponents $0<m<n<3$, the SH phase with an extreme value of the\nanisotropy parameter $\\Delta$ dominates. If one limits oneself to rigid\nlattices, the BCC-FCC-HCP phase diagram is found. For $-2<m<n<0$, the BCC\nlattice is the only energy minimizer. Choosing $-4<m<n<-2$, the FCC and SH\nlatices become minimizers.\n']","[('crystal lattice', 0.6024648547172546), ('hexagonal lattice', 0.5747079849243164), ('lattice', 0.5392190217971802), ('lattices', 0.5391175150871277), ('square lattice', 0.5340638160705566), ('lattice structures', 0.5306941270828247), ('dimensional lattices', 0.5268754363059998), ('unimodular lattices', 0.5223833322525024), ('cubic lattice', 0.5194195508956909), ('triangular lattice', 0.501747727394104)]"
725,725,43,725_inverse scattering_inverse scattering problems_inverse medium scattering_learning inverse,"['inverse scattering', 'inverse scattering problems', 'inverse medium scattering', 'learning inverse', 'full waveform inversion', 'waveform inversion', 'waveform inversion fwi', 'inverse medium', 'medium scattering', 'scattering']","[""Synergizing Deep Learning and Full-Waveform Inversion: Bridging\n  Data-Driven and Theory-Guided Approaches for Enhanced Seismic Imaging   This review explores the integration of deep learning (DL) with full-waveform\ninversion (FWI) for enhanced seismic imaging and subsurface characterization.\nIt covers FWI and DL fundamentals, geophysical applications (velocity\nestimation, deconvolution, tomography), and challenges (model complexity, data\nquality). The review also outlines future research directions, including\nhybrid, generative, and physics-informed models for improved accuracy,\nefficiency, and reliability in subsurface property estimation. The synergy\nbetween DL and FWI has the potential to transform geophysics, providing new\ninsights into Earth's subsurface.\n"", 'A Direct Sampling Method and Its Integration with Deep Learning for\n  Inverse Scattering Problems with Phaseless Data   We consider in this work an inverse acoustic scattering problem when only\nphaseless data is available. The inverse problem is highly nonlinear and\nill-posed due to the lack of the phase information. Solving inverse scattering\nproblems with phaseless data is important in applications as the collection of\nphysically acceptable phased data is usually difficult and expensive. A novel\ndirect sampling method (DSM) will be developed to effectively estimate the\nlocations and geometric shapes of the unknown scatterers from phaseless data\ngenerated by a very limited number of incident waves. With a careful\ntheoretical analysis of the behavior of the index function and some\nrepresentative numerical examples, the new DSM is shown to be computationally\nefficient, easy to implement, robust to large noise, and does not require any\nprior knowledge of the unknown scatterers. Furthermore, to fully exploit the\nindex functions obtained from the DSM, we also propose to integrate the DSM\nwith a deep learning technique (DSM-DL) to achieve high-quality\nreconstructions. Several challenging and representative numerical experiments\nare carried out to demonstrate the accuracy and robustness of reconstructions\nby DSM-DL. The DSM-DL networks trained by phased data are further theoretically\nand numerically shown to be able to solve problems with phaseless data.\nAdditionally, our numerical experiments also show the DSM-DL can solve inverse\nscattering problems with mixed types of scatterers, which renders its\napplications in many important practical scenarios.\n', 'A Direct Sampling-Based Deep Learning Approach for Inverse Medium\n  Scattering Problems   In this work, we focus on the inverse medium scattering problem (IMSP), which\naims to recover unknown scatterers based on measured scattered data. Motivated\nby the efficient direct sampling method (DSM) introduced in [23], we propose a\nnovel direct sampling-based deep learning approach (DSM-DL)for reconstructing\ninhomogeneous scatterers. In particular, we use the U-Net neural network to\nlearn the relation between the index functions and the true contrasts. Our\nproposed DSM-DL is computationally efficient, robust to noise, easy to\nimplement, and able to naturally incorporate multiple measured data to achieve\nhigh-quality reconstructions. Some representative tests are carried out with\nvarying numbers of incident waves and different noise levels to evaluate the\nperformance of the proposed method. The results demonstrate the promising\nbenefits of combining deep learning techniques with the DSM for IMSP.\n']","[('inverse scattering', 0.6195778250694275), ('inverse scattering problems', 0.6135947108268738), ('inverse medium scattering', 0.6030768156051636), ('learning inverse', 0.5455098748207092), ('full waveform inversion', 0.481564998626709), ('waveform inversion', 0.48120972514152527), ('waveform inversion fwi', 0.4784724712371826), ('inverse medium', 0.4622988700866699), ('medium scattering', 0.4610954523086548), ('scattering', 0.4550279974937439)]"
726,726,43,726_chip firing game_chip firing_directed graphs_chip,"['chip firing game', 'chip firing', 'directed graphs', 'chip', 'graph invariant', 'combinatorial game played', 'combinatorial game', 'chips', 'firing game', 'complete graphs']","['Periods and atomic firing sequences of parallel chip-firing games on\n  directed graphs   In 1992, Bitar and Goles introduced the parallel chip-firing game on\nundirected graphs. Two years later, Prisner extended the game to directed\ngraphs. While the properties of parallel chip-firing games on undirected graphs\nhave been extensively studied, their analogs for parallel chip-firing games on\ndirected graphs have been sporadic. In this paper, we prove the outstanding\nanalogs of the core results of parallel chip-firing games on undirected graphs\nfor those on directed graphs. We find the possible periods of a parallel\nchip-firing game on a directed simple cycle and introduce the method of\nGauss-Jordan elimination on a Laplacian-like matrix to establish a lower bound\non the maximum period of a parallel chip-firing game on an orientation of an\nundirected complete graph and an undirected complete bipartite graph. Finally,\nwe expand the method of motors by Jiang, Scully, and Zhang to directed graphs\nto show that a binary string $s$ can be the atomic firing sequence of a vertex\nin a parallel chip-firing game on a strongly connected directed graph if and\nonly if $s$ contains $1$ or $s=0$.\n', 'Sorting via chip-firing   We investigate a variant of the chip-firing process on the infinite path\ngraph: rather than treating the chips as indistinguishable, we label them with\npositive integers. To fire an unstable vertex, i.e. a vertex with more than one\nchip, we choose any two chips at that vertex and move the lesser-labeled chip\nto the left and the greater-labeled chip to the right. This labeled version of\nthe chip-firing process exhibits a remarkable confluence property, similar to\nbut subtler than the confluence that prevails for unlabeled chip-firing: when\nall chips start at the origin and the number of chips is even, the chips always\nend up in sorted order. Our proof of sorting relies upon an independently\ninteresting lemma concerning unlabeled chip- firing which says that\nstabilization preserves a natural partial order on configurations. We also\ndiscuss some extensions of this sorting phenomenon to other graphs (variants of\nthe infinite path), to other initial configurations, and to other\nCartan-Killing types.\n', 'Lattices in Chip-Firing   We analyze the poset of moves in chip-firing, as defined by Klivans and\nLiscio. Answering a question of Propp, we show that the move poset forms the\njoin-irreducibles of the poset of configurations. The proof involves a graph\naugmentation and an analysis of configurations in which only one firing move is\navailable. We then use this framework to analyze the problem of chip-firing on\na line, where the move poset is relevant to the problem of labeled chip-firing.\n']","[('chip firing game', 0.5997483730316162), ('chip firing', 0.5819966793060303), ('directed graphs', 0.48145607113838196), ('chip', 0.43760955333709717), ('graph invariant', 0.38891318440437317), ('combinatorial game played', 0.3694706857204437), ('combinatorial game', 0.3694310784339905), ('chips', 0.3616968095302582), ('firing game', 0.3612705171108246), ('complete graphs', 0.3606463372707367)]"
727,727,43,727_ornstein uhlenbeck processes_ornstein uhlenbeck process_generalized ornstein uhlenbeck_driven ornstein uhlenbeck,"['ornstein uhlenbeck processes', 'ornstein uhlenbeck process', 'generalized ornstein uhlenbeck', 'driven ornstein uhlenbeck', 'uhlenbeck processes', 'ornstein uhlenbeck type', 'uhlenbeck process', 'markov additive process', 'markov additive processes', 'ornstein uhlenbeck']","[""Markov-modulated generalized Ornstein-Uhlenbeck processes and an\n  application in risk theory   We derive the Markov-modulated generalized Ornstein-Uhlenbeck process by\nembedding a Markov-modulated random recurrence equation in continuous time. The\nobtained process turns out to be the unique solution of a certain stochastic\ndifferential equation driven by a bivariate Markov-additive process. We present\nthis stochastic differential equation as well as its solution explicitely in\nterms of the driving Markov-additive process. Moreover, we give necessary and\nsufficient conditions for strict stationarity of the Markov-modulated\ngeneralized Ornstein-Uhlenbeck process, and prove that its stationary\ndistribution is given by the distribution of a specific exponential functional\nof Markov-additive processes. Finally we propose an application of the\nMarkov-modulated generalized Ornstein-Uhlenbeck process as Markov-modulated\nrisk model with stochastic investment. This generalizes Paulsen's risk process\nto a Markov-switching environment. We derive a formula in this risk model that\nexpresses the ruin probability in terms of the distribution of an exponential\nfunctional of a Markov-additive process.\n"", 'Duals and time-reversed flows of generalized Ornstein-Uhlenbeck\n  processes   We derive explicit representations for the (Siegmund-) dual and the\ntime-reversed flow of generalized Ornstein-Uhlenbeck processes whenever these\nexist. It turns out that the dual and the process corresponding to the reversed\nstochastic flow are again generalized Ornstein-Uhlenbeck processes. Further, we\nobserve that the stationary distribution of the dual process provides\ninformation about the hitting time of zero of the original process.\n', ""Tempered stable distributions and finite variation Ornstein-Uhlenbeck\n  processes   Constructing \\Levy-driven Ornstein-Uhlenbeck processes is a task closely\nrelated to the notion of self-decomposability. In particular, their transition\nlaws are linked to the properties of what will be hereafter called the\n\\emph{a-reminder} of their self-decomposable stationary laws. In the present\nstudy we fully characterize the L\\'evy triplet of these a-reminder s and we\nprovide a general framework to deduce the transition laws of the finite\nvariation Ornstein-Uhlenbeck processes associated with tempered stable\ndistributions. We focus finally on the subclass of the exponentially-modulated\ntempered stable laws and we derive the algorithms for an exact generation of\nthe skeleton of Ornstein-Uhlenbeck processes related to such distributions,\nwith the further advantage of adopting a procedure computationally more\nefficient than those already available in the existing literature.\n""]","[('ornstein uhlenbeck processes', 0.8052793741226196), ('ornstein uhlenbeck process', 0.7665547132492065), ('generalized ornstein uhlenbeck', 0.7627850770950317), ('driven ornstein uhlenbeck', 0.6836860179901123), ('uhlenbeck processes', 0.6614883542060852), ('ornstein uhlenbeck type', 0.6217471957206726), ('uhlenbeck process', 0.5726487636566162), ('markov additive process', 0.5535878539085388), ('markov additive processes', 0.5454229116439819), ('ornstein uhlenbeck', 0.5346593856811523)]"
728,728,43,728_quaternion fourier transform_linear canonical transform_canonical transform_quaternion fourier,"['quaternion fourier transform', 'linear canonical transform', 'canonical transform', 'quaternion fourier', 'quaternion valued', 'quaternion', 'heisenberg uncertainty', 'transform theory', 'fourier transforms', 'integral transforms']","[""Quaternion Linear Canonical Wavelet Transform and The Corresponding\n  Uncertainty Inequalities   The linear canonical wavelet transform has been shown to be a valuable and\npowerful time-frequency analyzing tool for optics and signal processing. In\nthis article, we propose a novel transform called quaternion linear canonical\nwavelet transform which is designed to represent two dimensional\nquaternion-valued signals at different scales, locations and orientations. The\nproposed transform not only inherits the features of quaternion wavelet\ntransform but also has the capability of signal representation in quaternion\nlinear canonical domain. We investigate the fundamental properties of\nquaternion linear canonical wavelet transform including Parseval's formula,\nenergy conservation, inversion formula, and characterization of its range using\nthe machinery of quaternion linear canonical transform and its convolution. We\nconclude our investigation by deriving an analogue of the classical\nHeisenberg-Pauli-Weyl uncertainty inequality and the associated logarithmic and\nlocal versions for the quaternion linear canonical wavelet transform.\n"", 'Uncertainty Principles for Quaternion Windowed Offset Linear Canonical\n  Transform of Two Dimensional Signals   The offset linear canonical transform encompassing the numerous integral\ntransforms, is a promising tool for analyzing non-stationary signals with more\ndegrees of freedom. In this paper, we generalize the windowed offset linear\ncanonical transform for quaternion-valued signals, by introducing a novel\ntime-frequency transform namely the quaternion windowed offset linear canonical\ntransform of 2D quaternion-valued signals. We initiate our investigation by\nstudying some fundamental properties of the proposed transform including inner\nproduct relation, energy conservation, and reproducing formula by employing the\nmachinery of quaternion offset linear canonical transforms. Some uncertainty\nprinciples such as Heisenberg-Weyl, logarithmic and local uncertainty principle\nare also derived for quaternion windowed offset linear canonical transform.\nFinally, we gave an example of quaternion windowed offset linear canonical\ntransform.\n', ""Donoho Starks and Hardys Uncertainty Principles for the Shortotime\n  Quaternion Offset Linear Canonical Transform Donoho-Stark's and Hardy's\n  Uncertainty Principles for the Short-time Quaternion Offset Linear Canonical\n  Transform   The quaternion offset linear canonical transform (QOLCT) which is time\nshifted and frequency modulated version of the quaternion linear canonical\ntransform (QLCT) provides a more general framework of most existing signal\nprocessing tools. For the generalized QOLCT, the classical Heisenbergs and\nLiebs uncertainty principles have been studied recently. In this paper, we\nfirst define the shorttime quaternion offset linear canonical transform\n(STQOLCT) and drive its relationship with the quaternion Fourier transform\n(QFT). The crux of the paper lies in the generalization of several well known\nuncertainty principles for the STQOLCT, including Donoho Starks uncertainty\nprinciple, Hardys uncertainty principle, Beurlings uncertainty principle, and\nLogarithmic uncertainty principle.\n""]","[('quaternion fourier transform', 0.6546465158462524), ('linear canonical transform', 0.6097614169120789), ('canonical transform', 0.6016547679901123), ('quaternion fourier', 0.5909136533737183), ('quaternion valued', 0.5394992828369141), ('quaternion', 0.5184422135353088), ('heisenberg uncertainty', 0.5063701272010803), ('transform theory', 0.43341776728630066), ('fourier transforms', 0.42405378818511963), ('integral transforms', 0.41128382086753845)]"
729,729,43,729_sensitivity indices_based sensitivity analysis_sensitivity analysis_global sensitivity analysis,"['sensitivity indices', 'based sensitivity analysis', 'sensitivity analysis', 'global sensitivity analysis', 'based global sensitivity', 'global sensitivity', 'based sensitivity', 'sobol indices', 'sensitivity', 'high fidelity models']","['Sensitivity analysis for sets : application to pollutant concentration\n  maps   In the context of air quality control, our objective is to quantify the\nimpact of uncertain inputs such as meteorological conditions and traffic\nparameters on pollutant dispersion maps. It is worth noting that the majority\nof sensitivity analysis methods are designed to deal with scalar or vector\noutputs and are ill suited to a map-valued output space. To address this, we\npropose two classes of methods. The first technique focuses on pointwise\nindices. Sobol indices are calculated for each position on the map to obtain\nSobol index maps. Additionally, aggregated Sobol indices are calculated.\nAnother approach treats the maps as sets and proposes a sensitivity analysis of\na set-valued output with three different types of sensitivity indices. The\nfirst ones are inspired by Sobol indices but are adapted to sets based on the\ntheory of random sets. The second ones adapt universal indices defined for a\ngeneral metric output space. The last set indices use kernel-based sensitivity\nindices adapted to sets. The proposed methodologies are implemented to carry\nout an uncertainty analysis for time-averaged concentration maps of pollutants\nin an urban environment in the Greater Paris area. This entails taking into\naccount uncertain meteorological aspects, such as incoming wind speed and\ndirection, and uncertain traffic factors, such as injected traffic volume,\npercentage of diesel vehicles, and speed limits on the road network.\n', ""Risk of estimators for Sobol' sensitivity indices based on metamodels   Sobol' sensitivity indices allow to quantify the respective effects of random\ninput variables and their combinations on the variance of mathematical model\noutput. We focus on the problem of Sobol' indices estimation via a metamodeling\napproach where we replace the true mathematical model with a sample-based\napproximation to compute sensitivity indices. We propose a new method for\nindices quality control and obtain asymptotic and non-asymptotic risk bounds\nfor Sobol' indices estimates based on a general class of metamodels. Our\nanalysis is closely connected with the problem of nonparametric function\nfitting using the orthogonal system of functions in the random design setting.\nIt considers the relation between the metamodel quality and the error of the\ncorresponding estimator for Sobol' indices and shows the possibility of fast\nconvergence rates in the case of noiseless observations. The theoretical\nresults are complemented with numerical experiments for the approximations\nbased on multivariate Legendre and Trigonometric polynomials.\n"", ""Kernel-based ANOVA decomposition and Shapley effects -- Application to\n  global sensitivity analysis   Global sensitivity analysis is the main quantitative technique for\nidentifying the most influential input variables in a numerical simulation\nmodel. In particular when the inputs are independent, Sobol' sensitivity\nindices attribute a portion of the output of interest variance to each input\nand all possible interactions in the model, thanks to a functional ANOVA\ndecomposition. On the other hand, moment-independent sensitivity indices focus\non the impact of input variables on the whole output distribution instead of\nthe variance only, thus providing complementary insight on the inputs / output\nrelationship. Unfortunately they do not enjoy the nice decomposition property\nof Sobol' indices and are consequently harder to analyze. In this paper, we\nintroduce two moment-independent indices based on kernel-embeddings of\nprobability distributions and show that the RKHS framework used for their\ndefinition makes it possible to exhibit a kernel-based ANOVA decomposition.\nThis is the first time such a desirable property is proved for sensitivity\nindices apart from Sobol' ones. When the inputs are dependent, we also use\nthese new sensitivity indices as building blocks to design kernel-embedding\nShapley effects which generalize the traditional variance-based ones used in\nsensitivity analysis. Several estimation procedures are discussed and\nillustrated on test cases with various output types such as categorical\nvariables and probability distributions. All these examples show their\npotential for enhancing traditional sensitivity analysis with a kernel point of\nview.\n""]","[('sensitivity indices', 0.6388121247291565), ('based sensitivity analysis', 0.6156246066093445), ('sensitivity analysis', 0.6148877143859863), ('global sensitivity analysis', 0.5930317044258118), ('based global sensitivity', 0.5301598310470581), ('global sensitivity', 0.4845702052116394), ('based sensitivity', 0.4713711142539978), ('sobol indices', 0.4575245678424835), ('sensitivity', 0.42519134283065796), ('high fidelity models', 0.3941217362880707)]"
730,730,43,730_incompressible euler equations_solutions incompressible euler_compressible euler equations_dimensional incompressible euler,"['incompressible euler equations', 'solutions incompressible euler', 'compressible euler equations', 'dimensional incompressible euler', 'solutions compressible euler', 'incompressible euler', 'compressible euler system', 'isentropic compressible euler', '3d compressible euler', 'isentropic euler equations']","['A General Convex Integration Scheme for the Isentropic Compressible\n  Euler Equations   We prove via convex integration a result that allows to pass from a so-called\nsubsolution of the isentropic Euler equations (in space dimension at least $2$)\nto exact weak solutions. The method is closely related to the incompressible\nscheme established by De Lellis--Sz\\\'ekelyhidi, in particular we only perturb\nmomenta and not densities. Surprisingly, though, this turns out not to be a\nrestriction, as can be seen from our simple characterization of the\n$\\Lambda$-convex hull of the constitutive set. An important application of our\nscheme will be exhibited in forthcoming work by Gallenm\\""uller--Wiedemann.\n', 'An extension theorem for weak solutions of the 3d incompressible Euler\n  equations and applications to singular flows   We prove an extension theorem for local solutions of the 3d incompressible\nEuler equations. More precisely, we show that if a smooth vector field\nsatisfies the Euler equations in a spacetime region $\\Omega\\times(0,T)$, one\ncan choose an admissible weak solution on $\\mathbf R^3\\times (0,T)$ of class\n$C^\\beta$ for any $\\beta<1/3$ such that both fields coincide on $\\Omega\\times\n(0,T)$. Moreover, one controls the spatial support of the global solution. Our\nproof makes use of a new extension theorem for local subsolutions of the\nincompressible Euler equations and a $C^{1/3}$ convex integration scheme\nimplemented in the context of weak solutions with compact support in space. We\npresent two nontrivial applications of these ideas. First, we construct\ninfinitely many admissible weak solutions of class $C^\\beta_{\\text{loc}}$ with\nthe same vortex sheet initial data, which coincide with it at each time $t$\noutside a turbulent region of width $O(t)$. Second, given any smooth solution\n$v$ of the Euler equation on $\\mathbf T^3\\times(0,T)$ and any open set $U\n\\subset \\mathbf T^3$, we construct admissible weak solutions which coincide\nwith $v$ outside $U$ and are uniformly close to it everywhere at time 0, yet\nblow up dramatically on a subset of $U\\times (0,T)$ of full Hausdorff\ndimension. These solutions are of class $C^\\beta$ outside their singular set.\n', 'Convex Integration Applied to the Multi-Dimensional Compressible Euler\n  Equations   We shall deal with both the barotropic and the full compressible Euler system\nin multiple space dimensions. Both systems are particular examples of\nhyperbolic conservation laws. Whereas for scalar conservation laws there exists\na well-known complete well-posedness theory, and for one-dimensional systems\none also has achieved several results on existence and uniqueness, in the case\nof multi-dimensional systems there are even negative results regarding\nuniqueness: With the so-called convex integration method it is possible to show\nthat there exist initial data for which the compressible Euler equations in\nmultiple space dimensions admit infinitely many solutions. The convex\nintegration technique was originally developed in the context of differential\ninclusions and has later been applied in groundbreaking papers by De Lellis and\nSz\\\'ekelyhidi to the incompressible Euler equations which led to infinitely\nmany solutions. In the literature this result has been refined in order to\nobtain solutions for the compressible Euler system as well. The common feature\nof all of these non-uniqueness results for compressible Euler is an ansatz\nwhich reduces the compressible Euler equations to some kind of ""incompressible\nsystem"" for which a slight modification of the incompressible theory can be\napplied. In this work we present a first result of a direct application of\nconvex integration to the barotropic compressible Euler equations. With the\nhelp of this result we will show existence of initial data for which there are\ninfinitely many solutions both for the barotropic and full Euler system.\n']","[('incompressible euler equations', 0.6727304458618164), ('solutions incompressible euler', 0.6719345450401306), ('compressible euler equations', 0.6218205094337463), ('dimensional incompressible euler', 0.6168652772903442), ('solutions compressible euler', 0.5936595797538757), ('incompressible euler', 0.5837005972862244), ('compressible euler system', 0.5734442472457886), ('isentropic compressible euler', 0.5506113767623901), ('3d compressible euler', 0.5445399284362793), ('isentropic euler equations', 0.5299739837646484)]"
731,731,43,731_chaotic attractors_homoclinic bifurcations_lorenz attractor_chaotic attractor,"['chaotic attractors', 'homoclinic bifurcations', 'lorenz attractor', 'chaotic attractor', 'bifurcations', 'codimension bifurcations', 'global bifurcations', 'bifurcation', 'chaotic dynamics', 'strange attractors']","['Global and local bifurcations, three-dimensional Henon maps and discrete\n  Lorenz attractors   Lorenz attractors play an important role in the modern theory of dynamical\nsystems. The reason is that they are robust, i.e. preserve their chaotic\nproperties under various kinds of perturbations. This means that such\nattractors can exist in applied models and be observed in experiments. It is\nknown that discrete Lorenz attractors can appear in local and global\nbifurcations of multidimensional diffeomorphisms. However, to date, only\npartial cases were investigated. In this paper bifurcations of homoclinic and\nheteroclinic cycles with quadratic tangencies of invariant manifolds are\nstudied. A full list of such bifurcations, leading to the appearance of\ndiscrete Lorenz attractors is provided. In addition, with help of numerical\ntechniques, it was proved that if one reverses time in the diffeomorphisms\ndescribed above, the resulting systems also have such attractors. This result\nis an important step in the systematic studies of chaos and hyperchaos.\n', ""Multi-winged Lorenz attractors due to bifurcations of a periodic orbit\n  with multipliers $(-1,i,-i)$   We show that bifurcations of periodic orbits with multipliers $(-1,i,-i)$ can\nlead to the birth of pseudohyperbolic (i.e., robustly chaotic) Lorenz-like\nattractors of three different types: one is a discrete analogue of the\nclassical Lorenz attractor, and the other two are new. We call them two- and\nfour-winged ``Sim\\'o angels''. These three attractors exist in an\norientation-reversing, three-dimensional, quadratic H\\'enon map. Our analysis\nis based on a numerical study of a normal form for this bifurcation, a\nthree-dimensional system of differential equations with a Z4-symmetry. We\ninvestigate bifurcations in the normal form and describe those responsible for\nthe emergence of the Lorenz attractor and the continuous-time version of the\nSimo angels. Both for the normal form and the 3D H\\'enon map, we have found\nopen regions in the parameter space where the attractors are pseudohyperbolic,\nimplying that for every parameter value from these regions every orbit in the\nattractor has positive top Lyapunov exponent.\n"", 'On birth of discrete Lorenz attractors under bifurcations of 3D maps\n  with nontransversal heteroclinic cycles   Lorenz attractors are important objects in the modern theory of chaos. The\nreason from one side is that they are met in various natural applications\n(fluid dynamics, mechanics, laser dynamics, etc.). At the same time, Lorenz\nattractors are robust, in the sense that they are generally not destroyed by\nsmall perturbations (autonomous, non-autonomous, stochastic). This allows us to\nbe sure that the observed in the experiment object is exactly the chaotic\nattractor, rather than a long-time periodic orbit. Discrete-time analogs of the\nLorenz attractor possess even more complicated structure -- they allow\nhomoclinic tangencies of invariant manifolds within the attractor. Thus,\ndiscrete Lorenz attractors belong to the class of wild chaotic attractors.\nThese attractors can be born in codimension-three local and certain global\n(homoclinic and heteroclinic) bifurcations. While various homoclinic\nbifurcations leading to such attractors were studied, for heteroclinic cycles\nonly cases when at least one of the fixed points is saddle-focus were\nconsidered to date. In the present paper the case of a heteroclinic cycle\nconsisting of saddle fixed points with a quadratic tangency of invariant\nmanifolds, is considered. It is shown that in order to have a three-dimensional\nchaos such as the discrete Lorenz attractors, one needs to avoid the existence\nof lower-dimensional global invariant manifolds. Thus, it is assumed that\neither the quadratic tangency or the transversal heteroclinic orbit is\nnon-simple. The main result of the paper is the proof that the original system\nis the limiting point in the space of dynamical systems of a sequence of\ndomains in which the diffeomorphism possesses discrete Lorenz attractors.\n']","[('chaotic attractors', 0.6737517714500427), ('homoclinic bifurcations', 0.6667391061782837), ('lorenz attractor', 0.6424675583839417), ('chaotic attractor', 0.6282190680503845), ('bifurcations', 0.6115765571594238), ('codimension bifurcations', 0.5986031889915466), ('global bifurcations', 0.5948324799537659), ('bifurcation', 0.5765473246574402), ('chaotic dynamics', 0.5713034868240356), ('strange attractors', 0.5506657958030701)]"
732,732,43,732_meromorphic differentials_meromorphic differential_meromorphic forms_meromorphic,"['meromorphic differentials', 'meromorphic differential', 'meromorphic forms', 'meromorphic', 'riemann surfaces genus', 'riemann surfaces', 'strata differentials', 'regular singularities', 'prescribed singularities', 'riemann surface']","['Connected components of generalized strata of meromorphic differentials\n  with residue conditions   Generalized strata of meromorphic differentials are loci within the usual\nstrata of differentials where certain sets of residues sum to zero. They\nnaturally appear in the boundary of the multi-scale compactification of the\nusual strata. The classification of generalized strata is a key step towards\nunderstanding the irreducible components of the boundary strata of the\nmulti-scale compactification. The connected components of generalized strata of\nresidueless differentials were classified in \\cite{lee2023connected}. In the\npresent paper, we classify the connected components of generalized strata of\nmeromorphic differentials in full generality.\n', 'Towards a classification of connected components of the strata of\n  $k$-differentials   A $k$-differential on a Riemann surface is a section of the $k$-th power of\nthe canonical bundle. Loci of $k$-differentials with prescribed number and\nmultiplicities of zeros and poles form a natural stratification for the moduli\nspace of $k$-differentials. The classification of connected components of the\nstrata of $k$-differentials was known for holomorphic differentials,\nmeromorphic differentials and quadratic differentials with at worst simple\npoles by Kontsevich--Zorich, Boissy and Lanneau, respectively. Built on their\nwork we develop new techniques to study connected components of the strata of\n$k$-differentials for general $k$. As an application, we give a complete\nclassification of connected components of the strata of quadratic differentials\nwith arbitrary poles. Moreover, we distinguish certain components of the strata\nof $k$-differentials by generalizing the hyperelliptic structure and spin\nparity for higher $k$. We also describe an approach to determine explicitly\nparities of $k$-differentials in genus zero and one, which inspires an amusing\nconjecture in number theory. A key viewpoint we use is the notion of\nmulti-scale $k$-differentials introduced by\nBainbridge--Chen--Gendron--Grushevsky--M\\""oller for $k = 1$ and extended by\nCostantini--M\\""oller--Zachhuber for all $k$.\n', 'Connected components of strata of residueless meromorphic differentials   Generalized strata of meromorphic differentials are loci in the usual strata\nof differentials, where certain sets of residues sum up to zero. They appear\nnaturally in the boundary of the multi-scale compactification of the usual\nstrata. Enumerating the connected components of generalized strata is necessary\nto understand the boundary complex of the multi-scale compactification. In this\npaper we classify connected components of the strata of residueless meromorphic\ndifferentials, which are the strata with the maximum possible number of\nconditions imposed on the residues of the poles.\n']","[('meromorphic differentials', 0.6962834596633911), ('meromorphic differential', 0.6425826549530029), ('meromorphic forms', 0.6330592036247253), ('meromorphic', 0.5937296748161316), ('riemann surfaces genus', 0.5680715441703796), ('riemann surfaces', 0.5603175759315491), ('strata differentials', 0.5518587827682495), ('regular singularities', 0.5112094879150391), ('prescribed singularities', 0.5073444843292236), ('riemann surface', 0.5011501908302307)]"
733,733,42,733_quantum algorithms_quantum simulation_efficient quantum_quantum computing,"['quantum algorithms', 'quantum simulation', 'efficient quantum', 'quantum computing', 'quantum computers', 'based quantum', 'quantum linear', 'analog quantum', 'quantum dynamics', 'quantum circuits']","[""Quantum Circuits for the heat equation with physical boundary conditions\n  via Schrodingerisation   This paper explores the explicit design of quantum circuits for quantum\nsimulation of partial differential equations (PDEs) with physical boundary\nconditions. These equations and/or their discretized forms usually do not\nevolve via unitary dynamics, thus are not suitable for quantum simulation.\nBoundary conditions (either time-dependent or independent) make the problem\nmore difficult. To tackle this challenge, the Schrodingerisation method can be\nemployed, which converts linear partial and ordinary differential equations\nwith non-unitary dynamics into systems of Schrodinger-type equations, via the\nso-called warped phase transformation that maps the equation into one higher\ndimension. Despite advancements in Schrodingerisation techniques, the explicit\nimplementation of quantum circuits for solving general PDEs, especially with\nphysical boundary conditions, remains underdeveloped. We present two methods\nfor handling the inhomogeneous terms arising from time-dependent physical\nboundary conditions. One approach utilizes Duhamel's principle to express the\nsolution in integral form and employs linear combination of unitaries (LCU) for\ncoherent state preparation. Another method applies an augmentation to transform\nthe inhomogeneous problem into a homogeneous one. We then apply the quantum\nsimulation technique from [CJL23] to transform the resulting non-autonomous\nsystem to an autonomous system in one higher dimension. We provide detailed\nimplementations of these two methods and conduct a comprehensive complexity\nanalysis in terms of queries to the time evolution input oracle.\n"", 'High-precision quantum algorithms for partial differential equations   Quantum computers can produce a quantum encoding of the solution of a system\nof differential equations exponentially faster than a classical algorithm can\nproduce an explicit description. However, while high-precision quantum\nalgorithms for linear ordinary differential equations are well established, the\nbest previous quantum algorithms for linear partial differential equations\n(PDEs) have complexity $\\mathrm{poly}(1/\\epsilon)$, where $\\epsilon$ is the\nerror tolerance. By developing quantum algorithms based on adaptive-order\nfinite difference methods and spectral methods, we improve the complexity of\nquantum algorithms for linear PDEs to be $\\mathrm{poly}(d, \\log(1/\\epsilon))$,\nwhere $d$ is the spatial dimension. Our algorithms apply high-precision quantum\nlinear system algorithms to systems whose condition numbers and approximation\nerrors we bound. We develop a finite difference algorithm for the Poisson\nequation and a spectral algorithm for more general second-order elliptic\nequations.\n', 'Quantum simulation of Maxwell\'s equations via Schr\\""odingersation   We present quantum algorithms for electromagnetic fields governed by\nMaxwell\'s equations. The algorithms are based on the Schr\\""odingersation\napproach, which transforms any linear PDEs and ODEs with non-unitary dynamics\ninto a system evolving under unitary dynamics, via a warped phase\ntransformation that maps the equation into one higher dimension. In this paper,\nour quantum algorithms are based on either a direct approximation of Maxwell\'s\nequations combined with Yee\'s algorithm, or a matrix representation in terms of\nRiemann-Silberstein vectors combined with a spectral approach and an upwind\nscheme. We implement these algorithms with physical boundary conditions,\nincluding perfect conductor and impedance boundaries. We also solve Maxwell\'s\nequations for a linear inhomogeneous medium, specifically the interface\nproblem. Several numerical experiments are performed to demonstrate the\nvalidity of this approach. In addition, instead of qubits, the quantum\nalgorithms can also be formulated in the continuous variable quantum framework,\nwhich allows the quantum simulation of Maxwell\'s equations in analog quantum\nsimulation.\n']","[('quantum algorithms', 0.6465057730674744), ('quantum simulation', 0.5927127003669739), ('efficient quantum', 0.5765132308006287), ('quantum computing', 0.5438818335533142), ('quantum computers', 0.5084499716758728), ('based quantum', 0.5005735754966736), ('quantum linear', 0.49360156059265137), ('analog quantum', 0.47828951478004456), ('quantum dynamics', 0.47693949937820435), ('quantum circuits', 0.43961483240127563)]"
734,734,42,734_boundary estimates_solutions monge_mean curvature equations_degenerate monge amp,"['boundary estimates', 'solutions monge', 'mean curvature equations', 'degenerate monge amp', 'regularity free boundary', 'amp ere equations', 'ere equations', 'monge amp ere', 'regularity singular', 'estimates solutions']","['Asymptotic expansion at infinity of solutions of Monge-Amp\\`ere type\n  equations   We obtain a quantitative expansion at infinity of solutions for a kind of\nMonge-Amp\\`ere type equations that origin from mean curvature equations of\nLagrangian graph $(x,Du(x))$ and refine the previous study on zero mean\ncurvature equations and the Monge-Amp\\`ere equations.\n', 'The Anisotropic Convexity of Domains and the Boundary Estimate for Two\n  Monge-Amp\\`ere Equations   We study the exact effect of the anisotropic convexity of domains on the\nboundary estimate for two Monge-Amp\\`ere Equations: one is singular which is\nfrom the proper affine hyperspheres with constant mean curvature; the other is\ndegenerate which is from the Monge-Amp\\`ere eigenvalue problem. As a result, we\nobtain the sharp boundary boundary estimates and the optimal global H\\""older\nregularity for the two equations.\n', 'Continuity estimates for the gradient of solutions to the Monge-Amp\\`ere\n  equation with nature boundary conditions   We study the first derivative estimates for solutions to Monge-Amp\\`ere\nequations in terms of modulus of continuity. As a result, we establish the\noptimal global log-Lipschitz continuity for the gradient of solutions to the\nMonge-Amp\\`ere equation with natural boundary conditions.\n']","[('boundary estimates', 0.514440655708313), ('solutions monge', 0.49230241775512695), ('mean curvature equations', 0.48475199937820435), ('degenerate monge amp', 0.46837300062179565), ('regularity free boundary', 0.46010398864746094), ('amp ere equations', 0.44848358631134033), ('ere equations', 0.44674721360206604), ('monge amp ere', 0.44293826818466187), ('regularity singular', 0.43078741431236267), ('estimates solutions', 0.4209628701210022)]"
735,735,42,735_wave turbulence theory_turbulence theory_wave kinetic_wave turbulence,"['wave turbulence theory', 'turbulence theory', 'wave kinetic', 'wave turbulence', 'kinetic theory', 'kinetic equations', 'kinetic limit', 'nonlinear schr odinger', 'kinetic description', 'turbulence']","['Inhomogeneous turbulence for the Wick nonlinear Schr\\""odinger equation   We introduce a simplified model for wave turbulence theory -- the Wick NLS,\nof which the main feature is the absence of all self-interactions in the\ncorrelation expansions of its solutions. For this model, we derive several wave\nkinetic equations that govern the effective statistical behavior of its\nsolutions in various regimes. In the homogeneous setting, where the initial\ncorrelation is translation invariant, we obtain a wave kinetic equation similar\nto the one predicted by the formal theory. In the inhomogeneous setting, we\nobtain a wave kinetic equation that describes the statistical behavior of the\nwavepackets of the solutions, accounting for both the transport of wavepackets\nand collisions among them. Another wave kinetic equation, which seems new in\nthe literature, also appears in a certain scaling regime of this setting and\nprovides a more refined collision picture.\n', 'On the wave turbulence theory for a stochastic KdV type equation --\n  Generalization for the inhomogeneous kinetic limit   Starting from a stochastic Zakharov-Kuznetsov (ZK) equation on a lattice, the\nprevious work [ST21] by the last two authors gave a derivation of the\nhomogeneous 3-wave kinetic equation at the kinetic limit under very general\nassumptions: the initial condition is out of equilibrium, the dimension $d\\ge\n2$, the smallness of the nonlinearity $\\lambda$ is allowed to be independent of\nthe size of the lattice, the weak noise is chosen not to compete with the weak\nnonlinearity and not to inject energy into the equation. In the present work,\nwe build on the framework of [ST21], following the formal derivation of Spohn\n[Spo06] and inspired by previous work [HO21] of the first author and Olla, so\nthat the inhomogeneous 3-wave kinetic equation can also be obtained at the\nkinetic limit under analogous assumptions. Similar to the homogeneous case --\nand unlike the cubic nonlinear Schr\\""odinger equation -- the inhomogeneous\nkinetic description of the deterministic lattice ZK equation is unlikely to\nhappen due to the vanishing of the dispersion relation on a certain singular\nmanifold on which not only $3$-wave interactions but also all $n$-wave\ninteractions ($n\\ge3$) are allowed to happen, a phenomenon first observed by\nLukkarinen [Luk07]. To the best of our knowledge, our work provides the first\nrigorous derivation of a nonlinear inhomogeneous wave kinetic equation in the\nkinetic limit.\n', 'On the wave turbulence theory for a stochastic KdV type equation   Starting from the stochastic Zakharov-Kuznetsov equation, a multidimensional\nKdV type equation on a hypercubic lattice, we provide a derivation of the\n3-wave kinetic equation. We show that the two point correlation function can be\nasymptotically expressed as the solution of the 3-wave kinetic equation at the\nkinetic limit under very general assumptions: the initial condition is out of\nequilibrium, the dimension is $d\\ge 2$, the smallness of the nonlinearity\n$\\lambda$ is allowed to be independent of the size of the lattice, the weak\nnoise is chosen not to compete with the weak nonlinearity and not to inject\nenergy into the equation. Unlike the cubic nonlinear Schr\\""odinger equation,\nfor which such a general result is commonly expected without the noise, the\nkinetic description of the deterministic lattice ZK equation is unlikely to\nhappen. One of the key reasons is that the dispersion relation of the lattice\nZK equation leads to a singular manifold, on which not only $3$-wave\ninteractions but also all $m$-wave interactions ($m\\ge3$) are allowed to\nhappen. This phenomenon has been first observed by Lukkarinen\n\\cite{lukkarinen2007asymptotics} as a counterexample for which one of the main\ntools to derive kinetic equations from wave equations (the suppression of\ncrossings) fails to hold true. To the best of our knowledge, the work provides\nthe first rigorous derivation of nonlinear 3-wave kinetic equations. Also this\nis the first derivation for wave kinetic equations in the lattice setting and\nout-of-equilibrium.\n']","[('wave turbulence theory', 0.6120400428771973), ('turbulence theory', 0.5549706816673279), ('wave kinetic', 0.5194903612136841), ('wave turbulence', 0.5174102783203125), ('kinetic theory', 0.516202986240387), ('kinetic equations', 0.4883135259151459), ('kinetic limit', 0.44441622495651245), ('nonlinear schr odinger', 0.44301700592041016), ('kinetic description', 0.43300074338912964), ('turbulence', 0.4187701344490051)]"
736,736,42,736_rota baxter algebras_baxter algebras_algebras rota baxter_rota baxter operators,"['rota baxter algebras', 'baxter algebras', 'algebras rota baxter', 'rota baxter operators', 'rota baxter operator', 'yang baxter equations', 'lie bialgebras', 'leibniz algebras', 'baxter operators', 'baxter equations']","['Leibniz bialgebras, relative Rota-Baxter operators and the classical\n  Leibniz Yang-Baxter equation   In this paper, first we introduce the notion of a Leibniz bialgebra and show\nthat matched pairs of Leibniz algebras, Manin triples of Leibniz algebras and\nLeibniz bialgebras are equivalent. Then we introduce the notion of a (relative)\nRota-Baxter operator on a Leibniz algebra and construct the graded Lie algebra\nthat characterizes relative Rota-Baxter operators as Maurer-Cartan elements. By\nthese structures and the twisting theory of twilled Leibniz algebras, we\nfurther define the classical Leibniz Yang-Baxter equation, classical Leibniz\nr-matrices and triangular Leibniz bialgebras. Finally, we construct solutions\nof the classical Leibniz Yang-Baxter equation using relative Rota-Baxter\noperators and Leibniz-dendriform algebras.\n', 'Bialgebras, Frobenius algebras and associative Yang-Baxter equations for\n  Rota-Baxter algebras   Rota-Baxter operators and bialgebras go hand in hand in their applications,\nsuch as in the Connes-Kreimer approach to renormalization and the operator\napproach to the classical Yang-Baxter equation. We establish a bialgebra\nstructure that is compatible with the Rota-Baxter operator, called the\nRota-Baxter antisymmetric infinitesimal (ASI) bialgebra. This bialgebra is\ncharacterized by generalizations of matched pairs of algebras and double\nconstructions of Frobenius algebras to the context of Rota-Baxter algebras. The\nstudy of the coboundary case leads to an enrichment of the associative\nYang-Baxter equation (AYBE) to Rota-Baxter algebras. Antisymmetric solutions of\nthe equation are used to construct Rota-Baxter ASI bialgebras. The notions of\nan $\\mathcal{O}$-operator on a Rota-Baxter algebra and a Rota-Baxter dendriform\nalgebra are also introduced to produce solutions of the AYBE in Rota-Baxter\nalgebras and thus to provide Rota-Baxter ASI bialgebras. An unexpected\nbyproduct is that a Rota-Baxter ASI bialgebra of weight zero gives rise to a\nquadri-bialgebra instead of bialgebra constructions for the dendriform algebra.\n', 'Rota-Baxter Lie bialgebras, classical Yang-Baxter equations and special\n  L-dendriform bialgebras   We establish a bialgebra structure on Rota-Baxter Lie algebras following the\nManin triple approach to Lie bialgebras. Explicitly, Rota-Baxter Lie bialgebras\nare characterized by generalizing matched pairs of Lie algebras and Manin\ntriples of Lie algebras to the context of Rota-Baxter Lie algebras. The\ncoboundary case leads to the introduction of the admissible classical\nYang-Baxter equation (CYBE) in Rota-Baxter Lie algebras, for which the\nantisymmetric solutions give rise to Rota-Baxter Lie bialgebras. The notions of\n$\\mathcal{O}$-operators on Rota-Baxter Lie algebras and Rota-Baxter pre-Lie\nalgebras are introduced to produce antisymmetric solutions of the admissible\nCYBE. Furthermore, extending the well-known property that a Rota-Baxter Lie\nalgebra of weight zero induces a pre-Lie algebra, the Rota-Baxter Lie bialgebra\nof weight zero induces a bialgebra structure of independent interest, namely\nthe special L-dendriform bialgebra, which is equivalent to a Lie group with a\nleft-invariant flat pseudo-metric in geometry. This induction is also\ncharacterized as the inductions between the corresponding Manin triples and\nmatched pairs. Finally, antisymmetric solutions of the admissible CYBE in a\nRota-Baxter Lie algebra of weight zero give special L-dendriform bialgebras. In\nparticular, both Rota-Baxter algebras of weight zero and Rota-Baxter pre-Lie\nalgebras of weight zero can be used to construct special L-dendriform algebras.\n']","[('rota baxter algebras', 0.8043712973594666), ('baxter algebras', 0.7462326884269714), ('algebras rota baxter', 0.7439895272254944), ('rota baxter operators', 0.6709824204444885), ('rota baxter operator', 0.6332399249076843), ('yang baxter equations', 0.6224278807640076), ('lie bialgebras', 0.6213343739509583), ('leibniz algebras', 0.6186205148696899), ('baxter operators', 0.6054830551147461), ('baxter equations', 0.5913980603218079)]"
737,737,42,737_ising models_ferromagnetic ising_general ising_field ising,"['ising models', 'ferromagnetic ising', 'general ising', 'field ising', 'ising random', 'temperature ising', 'random regular graphs', 'ising', 'models dense', 'random graphs']","[""A Spectral Condition for Spectral Gap: Fast Mixing in High-Temperature\n  Ising Models   We prove that Ising models on the hypercube with general quadratic\ninteractions satisfy a Poincar\\'{e} inequality with respect to the natural\nDirichlet form corresponding to Glauber dynamics, as soon as the operator norm\nof the interaction matrix is smaller than $1$. The inequality implies a control\non the mixing time of the Glauber dynamics. Our techniques rely on a\nlocalization procedure which establishes a structural result, stating that\nIsing measures may be decomposed into a mixture of measures with quadratic\npotentials of rank one, and provides a framework for proving concentration\nbounds for high temperature Ising models.\n"", ""Sharp Signal Detection Under Ferromagnetic Ising Models   In this paper we study the effect of dependence on detecting a class of\nstructured signals in Ferromagnetic Ising models. Natural examples of our class\ninclude Ising Models on lattices, and Mean-Field type Ising Models such as\ndense Erd\\H{o}s-R\\'{e}nyi, and dense random regular graphs. Our results not\nonly provide sharp constants of detection in each of these cases and thereby\npinpoint the precise relationship of the detection problem with the underlying\ndependence, but also demonstrate how to be agnostic over the strength of\ndependence present in the respective models.\n"", 'Computational thresholds for the fixed-magnetization Ising model   The ferromagnetic Ising model is a model of a magnetic material and a central\ntopic in statistical physics. It also plays a starring role in the algorithmic\nstudy of approximate counting: approximating the partition function of the\nferromagnetic Ising model with uniform external field is tractable at all\ntemperatures and on all graphs, due to the randomized algorithm of Jerrum and\nSinclair. Here we show that hidden inside the model are hard computational\nproblems. For the class of bounded-degree graphs we find computational\nthresholds for the approximate counting and sampling problems for the\nferromagnetic Ising model at fixed magnetization (that is, fixing the number of\n$+1$ and $-1$ spins). In particular, letting $\\beta_c(\\Delta)$ denote the\ncritical inverse temperature of the zero-field Ising model on the infinite\n$\\Delta$-regular tree, and $\\eta_{\\Delta,\\beta,1}^+$ denote the mean\nmagnetization of the zero-field $+$ measure on the infinite $\\Delta$-regular\ntree at inverse temperature $\\beta$, we prove, for the class of graphs of\nmaximum degree $\\Delta$:\n  1. For $\\beta < \\beta_c(\\Delta)$ there is an FPRAS and efficient sampling\nscheme for the fixed-magnetization Ising model for all magnetizations $\\eta$.\n  2. For $\\beta > \\beta_c(\\Delta)$, there is an FPRAS and efficient sampling\nscheme for the fixed-magnetization Ising model for magnetizations $\\eta$ such\nthat $|\\eta| >\\eta_{\\Delta,\\beta,1}^+ $.\n  3. For $\\beta > \\beta_c(\\Delta)$, there is no FPRAS for the\nfixed-magnetization Ising model for magnetizations $\\eta$ such that $|\\eta|\n<\\eta_{\\Delta,\\beta,1}^+ $ unless NP=RP\\@.\n']","[('ising models', 0.5777818560600281), ('ferromagnetic ising', 0.5722146034240723), ('general ising', 0.4229792356491089), ('field ising', 0.41559159755706787), ('ising random', 0.40463486313819885), ('temperature ising', 0.39422526955604553), ('random regular graphs', 0.36646780371665955), ('ising', 0.3650401532649994), ('models dense', 0.3599972426891327), ('random graphs', 0.35811126232147217)]"
738,738,42,738_equivariant neural_symmetry groups_neural networks whose_equivariant functions,"['equivariant neural', 'symmetry groups', 'neural networks whose', 'equivariant functions', 'invariant equivariant', 'group equivariant', 'representations', 'symmetric tensors', 'neural networks provide', 'symmetries']","['How Jellyfish Characterise Alternating Group Equivariant Neural Networks   We provide a full characterisation of all of the possible alternating group\n($A_n$) equivariant neural networks whose layers are some tensor power of\n$\\mathbb{R}^{n}$. In particular, we find a basis of matrices for the learnable,\nlinear, $A_n$-equivariant layer functions between such tensor power spaces in\nthe standard basis of $\\mathbb{R}^{n}$. We also describe how our approach\ngeneralises to the construction of neural networks that are equivariant to\nlocal symmetries.\n', ""Brauer's Group Equivariant Neural Networks   We provide a full characterisation of all of the possible group equivariant\nneural networks whose layers are some tensor power of $\\mathbb{R}^{n}$ for\nthree symmetry groups that are missing from the machine learning literature:\n$O(n)$, the orthogonal group; $SO(n)$, the special orthogonal group; and\n$Sp(n)$, the symplectic group. In particular, we find a spanning set of\nmatrices for the learnable, linear, equivariant layer functions between such\ntensor power spaces in the standard basis of $\\mathbb{R}^{n}$ when the group is\n$O(n)$ or $SO(n)$, and in the symplectic basis of $\\mathbb{R}^{n}$ when the\ngroup is $Sp(n)$.\n"", 'Equivariant neural networks and piecewise linear representation theory   Equivariant neural networks are neural networks with symmetry. Motivated by\nthe theory of group representations, we decompose the layers of an equivariant\nneural network into simple representations. The nonlinear activation functions\nlead to interesting nonlinear equivariant maps between simple representations.\nFor example, the rectified linear unit (ReLU) gives rise to piecewise linear\nmaps. We show that these considerations lead to a filtration of equivariant\nneural networks, generalizing Fourier series. This observation might provide a\nuseful tool for interpreting equivariant neural networks.\n']","[('equivariant neural', 0.5847509503364563), ('symmetry groups', 0.5230075716972351), ('neural networks whose', 0.5065340399742126), ('equivariant functions', 0.5063589811325073), ('invariant equivariant', 0.4942556619644165), ('group equivariant', 0.49180275201797485), ('representations', 0.48064762353897095), ('symmetric tensors', 0.476574182510376), ('neural networks provide', 0.4745654761791229), ('symmetries', 0.4643433094024658)]"
739,739,42,739_finite group order_order finite group_finite groups_cyclic group order,"['finite group order', 'order finite group', 'finite groups', 'cyclic group order', 'groups order', 'finite groups let', 'finite group', 'subgroups finite group', 'let finite group', 'finite group let']","['An exact upper bound for the sum of powers of element orders in\n  non-cyclic finite groups   For a finite group $G$, let $\\psi(G)$ denote the sum of element orders of\n$G$. This function was introduced by Amiri, Amiri, and Isaacs in 2009 and they\nproved that for any finite group $G$ of order $n$, $\\psi(G)$ is maximum if and\nonly if $G \\simeq \\mathbb{Z}_n$ where $\\mathbb{Z}_n$ denotes the cyclic group\nof order $n$. Furthermore, Herzog, Longobardi, and Maj in 2018 proved that if\n$G$ is non-cyclic, $\\psi(G) \\leq \\frac{7}{11} \\psi(\\mathbb{Z}_n)$. Amiri and\nAmiri in 2014 introduced the function $\\psi_k(G)$ which is defined as the sum\nof the $k$-th powers of element orders of $G$ and they showed that for every\npositive integer $k$, $\\psi_k(G)$ is also maximum if and only if $G$ is cyclic.\n  In this paper, we have been able to prove that if $G$ is a non-cyclic group\nof order $n$, then $\\psi_k(G) \\leq \\frac{1+3.2^k}{1+2.4^k+2^k}\n\\psi_k(\\mathbb{Z}_n)$. Setting $k=1$ in our result, we immediately get the\nresult of Herzog et al. as a simple corollary. Besides, a recursive formula for\n$\\psi_k(G)$ is also obtained for finite abelian $p$-groups $G$, using which one\ncan explicitly find out the exact value of $\\psi_k(G)$ for finite abelian\ngroups $G$.\n', 'A generalization of a result on the sum of element orders of a finite\n  group   Let $G$ be a finite group and let $\\psi(G)$ denote the sum of element orders\nof $G$. It is well-known that the maximum value of $\\varphi$ on the set of\ngroups of order $n$, where $n$ is a positive integer, will occur at the cyclic\ngroup $C_n$. For nilpotent groups, we prove a natural generalization of this\nresult, obtained by replacing the element orders of $G$ with the element orders\nrelative to a certain subgroup $H$ of $G$.\n', ""Factorizations of groups of small order   Let $G$ be a finite group and let $A_1,\\ldots,A_k$ be a collection of subsets\nof $G$ such that $G=A_1\\ldots A_k$ is the product of all the $A_i$'s with\n$|G|=|A_1|\\ldots|A_k|$. We write $G=A_1\\cdot\\ldots\\cdot A_k$ and call this a\n$k$-fold factorization of $G$ of the form $(|A_1|,\\ldots,|A_k|)$ or more\nbriefly an $(|A_1|,\\ldots,|A_k|)$-factorization of $G$. Let $k\\geq2$ be a fixed\ninteger. If $G$ has an $(a_1,\\ldots,a_k)$-factorization, whenever\n$|G|=a_1\\ldots a_k$ with $a_i>1$, $i=1,\\ldots,k$, we say that $G$ is\n$k$-factorizable. We say that $G$ is multifold-factorizable if $G$ is\n$k$-factorizable for any possible integer $k\\geq2$. In this paper we prove that\nthere are exactly $6$ non-multifold-factorizable groups among the groups of\norder at most $60$. Here is their complete list: $A_4$, $(C_2\\times C_2)\\rtimes\nC_9$, $A_4\\times C_3$, $(C_2\\times C_2\\times C_2)\\rtimes C_7$, $A_5$,\n$A_4\\times C_5$. Some related open questions are presented.\n""]","[('finite group order', 0.6504666209220886), ('order finite group', 0.6388927698135376), ('finite groups', 0.5632821321487427), ('cyclic group order', 0.5628803968429565), ('groups order', 0.5529379844665527), ('finite groups let', 0.5510472059249878), ('finite group', 0.5474644899368286), ('subgroups finite group', 0.5268893837928772), ('let finite group', 0.521775484085083), ('finite group let', 0.5195640325546265)]"
740,740,42,740_curvature energy_energy critical points_knots_smooth critical,"['curvature energy', 'energy critical points', 'knots', 'smooth critical', 'elastic curves', 'point energy', 'regularity critical', 'knot', 'planar curves', 'bending energy']","['Optimal planar immersions of prescribed winding number and Arnold\n  invariants   Vladimir Arnold defined three invariants for generic planar immersions, i.e.\nplanar curves whose self-intersections are all transverse double points. We use\na variational approach to study these invariants by investigating a suitably\ntruncated knot energy, the tangent-point energy. We prove existence of energy\nminimizers for each truncation parameter ${\\delta} > 0$ in a class of\nimmersions with prescribed winding number and Arnold invariants, and establish\nGamma convergence of the truncated tangent-point energies to a limiting\nrenormalized tangent-point energy as ${\\delta\\to 0}$. Moreover, we show that\nany sequence of minimizers subconverges in ${C^1}$, and the corresponding limit\ncurve has the same topological invariants, self-intersects exclusively at right\nangles, and minimizes the renormalized tangent-point energy among all curves\nwith right self-intersection angles. In addition, the limit curve is an\nalmost-minimizer for all of the original truncated tangent-point energies as\nlong as the truncation parameter ${\\delta}$ is sufficiently small. Therefore,\nthis limit curve serves as an ""optimal"" curve in the class of generic planar\nimmersions with prescribed winding number and Arnold invariants.\n', ""On the Palais-Smale condition in geometric knot theory   We prove that various families of energies relevant in\n  geometric knot theory satisfy the Palais-Smale condition (PS)\n  on submanifolds of arclength para\\-metrized knots.\n  These energies\n  include linear combinations of the Euler-Bernoulli\n  bending energy with a wide variety of non-local\n  knot energies, such as\n  O'Hara's self-repulsive potentials $E^{\\alpha,p}$, generalized\n  tangent-point energies $\\TP^{(p,q)}$, and generalized integral\n  Menger curvature functionals $\\intM^{(p,q)}$. Even the\n  tangent-point energies $\\TP^{(p,2)}$ for $p\\in (4,5)$ alone\n  are shown to fulfill the (PS)-condition. For all energies mentioned\n  we can therefore prove existence of minimizing knots in any prescribed\n  ambient isotopy class, and we\n  provide long-time existence of their Hilbert-gradient flows,\n  and subconvergence to critical knots as time goes to infinity.\n  In addition, we prove $C^\\infty$-smoothness of all arclength constrained\n  critical knots, which shows in particular that these critical knots\n  are also critical for the energies on the larger open set of\n  regular knots under a fixed-length constraint.\n"", 'Tangent-point energies and ropelength as Gamma-limit of discrete\n  tangent-point energies on biarc curves   Using interpolation with biarc curves we prove $\\Gamma$-convergence of\ndiscretized tangent-point energies to the continuous tangent-point energies in\nthe $C^1$-topology, as well as to the ropelength functional. As a consequence\ndiscrete almost minimizing biarc curves converge to ropelength minimizers, and\nto minimizers of the continuous tangent-point energies. In addition, taking\npoint-tangent data from a given $C^{1,1}$-curve $\\gamma$, we establish\nconvergence of the discrete energies evaluated on biarc curves interpolating\nthese data, to the continuous tangent-point energy of $\\gamma$, together with\nan explicit convergence rate.\n']","[('curvature energy', 0.5001367330551147), ('energy critical points', 0.49397939443588257), ('knots', 0.45744362473487854), ('smooth critical', 0.4436820447444916), ('elastic curves', 0.42936185002326965), ('point energy', 0.4255892336368561), ('regularity critical', 0.419883131980896), ('knot', 0.41406306624412537), ('planar curves', 0.3892742395401001), ('bending energy', 0.3827558159828186)]"
741,741,42,741_coherent states_generalized coherent states_quantum coherent_coherent state,"['coherent states', 'generalized coherent states', 'quantum coherent', 'coherent state', 'generalized coherent', 'construct coherent', 'properties coherent', 'coherent', 'heisenberg algebra', 'quantum']","['Coherent states for equally spaced, homogeneous waveguide arrays   Coherent states for equally spaced, homogeneous waveguide arrays are defined,\nin the infinite, semiinfinite and finite cases, and resolutions of the identity\nare constructed, using different methods. In the infinite case, which\ncorresponds to Euclidean coherent states, a resolution of the identity with\ncoherent states on the circle and involving a nonlocal inner product is\nreviewed. In the semiinfinite case, which corresponds to London coherent\nstates, various construction are given (restricting to the circle with a\nnon-local scalar product, rescaling the coherent states, modifying them, or\nusing a non-tight frame). In the finite case, a construction in terms of\ncoherent states on the circle is given, and this construction is shown to be a\nregularization of the infinite and semiinfinite cases.\n', 'Coherent States for infinite homogeneous waveguide arrays: Cauchy\n  coherent states for $E(2)$   Perelomov coherent states for equally spaced, infinite homogeneous waveguide\narrays with Euclidean E(2) symmetry are defined, and a new resolution of the\nidentity is obtained. The key point to construct this novel resolution of the\nidentity is the fact that coherent states satisfy the Helmholtz equation (in\ncoherent states labels), and thus every coherent state belongs to a\none-parameter family uniquely determined by the Cauchy initial data of the\ncoherent state in a one-dimensional Cauchy set. For this reason we call\n\\textit{Cauchy coherent} states to these initial data. The novel, non-local\nresolution of the identity in terms of Cauchy coherent states is provided using\nframe theory. It is also shown that Perelomov coherent states for the Eucliean\nE(2) group have a simple and natural physical realization in these waveguide\narrays.\n', 'Ladder operators and coherent states for multi-step supersymmetric\n  rational extensions of the truncated oscillator   We construct ladder operators, $\\tilde{C}$ and $\\tilde{C^\\dagger}$, for a\nmulti-step rational extension of the harmonic oscillator on the half plane,\n$x\\ge0$. These ladder operators connect all states of the spectrum in only\ninfinite-dimensional representations of their polynomial Heisenberg algebra.\nFor comparison, we also construct two different classes of ladder operator\nacting on this system that form finite-dimensional as well as\ninfinite-dimensional representations of their respective polynomial Heisenberg\nalgebras. For the rational extension, we construct the position wavefunctions\nin terms of exceptional orthogonal polynomials. For a particular choice of\nparameters, we construct the coherent states, eigenvectors of $\\tilde{C}$ with\ngenerally complex eigenvalues, $z$, as superpositions of a subset of the energy\neigenvectors. Then we calculate the properties of these coherent states,\nlooking for classical or non-classical behaviour. We calculate the energy\nexpectation as a function of $|z|$. We plot position probability densities for\nthe coherent states and for the even and odd cat states formed from these\ncoherent states. We plot the Wigner function for a particular choice of $z$.\nFor these coherent states on one arm of a beamsplitter, we calculate the two\nexcitation number distribution and the linear entropy of the output state. We\nplot the standard deviations in $x$ and $p$ and find no squeezing in the regime\nconsidered. By plotting the Mandel $Q$ parameter for the coherent states as a\nfunction of $|z|$, we find that the number statistics is sub-Poissonian.\n']","[('coherent states', 0.7671739459037781), ('generalized coherent states', 0.7606347799301147), ('quantum coherent', 0.7073270082473755), ('coherent state', 0.7041916847229004), ('generalized coherent', 0.5844370722770691), ('construct coherent', 0.5504324436187744), ('properties coherent', 0.5002509355545044), ('coherent', 0.48749807476997375), ('heisenberg algebra', 0.42869120836257935), ('quantum', 0.4124872088432312)]"
742,742,42,742_optimal control finite_time optimal control_optimal control_optimal control problems,"['optimal control finite', 'time optimal control', 'optimal control', 'optimal control problems', 'quadratic optimal control', 'optimal control general', 'optimal controls', 'lq optimal control', 'nonlinear optimal control', 'turnpike']","[""Necessary conditions for turnpike property for generalized\n  linear-quadratic problems   In this paper, we develop several necessary conditions of turnpike property\nfor generalizaid linear-quadratic (LQ) optimal control problem in infinite\ndimensional setting. The term 'generalized' here means that both quadratic and\nlinear terms are considered in the running cost. The turnpike property reflects\nthe fact that over a sufficiently large time horizon, the optimal trajectories\nand optimal controls stay for most of the time close to a steady state of the\nsystem. We show that the turnpike property is strongly connected to certain\nsystem theoretical properties of the control system. We provide suitable\nconditions to characterize the turnpike property in terms of the detectability\nand stabilizability of the system. Subsequently, we show the equivalence\nbetween the exponential turnpike property for generalized LQ and LQ optimal\ncontrol problems.\n"", 'Strict Dissipativity and turnpike for LQ Optimal Control Problems with\n  Possibly Boundary Reference   In this paper we investigate the turnpike property for constrained LQ optimal\ncontrol problem in connection with dissipativity of the control system. We\ndetermine sufficient conditions to ensure the turnpike property in the case of\na turnpike reference possibly occurring on the boundary of the state constraint\nset.\n', ""Turnpike in optimal control and beyond: a survey   The turnpike principle is a fundamental concept in optimal control theory,\nstating that for a wide class of long-horizon optimal control problems, the\noptimal trajectory spends most of its time near a steady-state solution (the\n''turnpike'') rather than being influenced by the initial or final conditions.\nIn this article, we provide a survey on the turnpike property in optimal\ncontrol, adding several recent and novel considerations. After some historical\ninsights, we present an elementary proof of the exponential turnpike property\nfor linear-quadratic optimal control problems in finite dimension. Next, we\nshow an extension to nonlinear optimal control problems, with a local\nexponential turnpike property. On simple but meaningful examples, we illustrate\nthe local and global aspects of the turnpike theory, clarifying the global\npicture and raising new questions. We discuss key generalizations, in infinite\ndimension and other various settings, and review several applications of the\nturnpike theory across different fields.\n""]","[('optimal control finite', 0.5968241691589355), ('time optimal control', 0.5858653783798218), ('optimal control', 0.5837672352790833), ('optimal control problems', 0.5777828693389893), ('quadratic optimal control', 0.5762279033660889), ('optimal control general', 0.5667073130607605), ('optimal controls', 0.5598931312561035), ('lq optimal control', 0.5584486126899719), ('nonlinear optimal control', 0.5461187362670898), ('turnpike', 0.5412527322769165)]"
743,743,42,743_allen cahn equations_energy stable schemes_energy dissipation law_original energy dissipation,"['allen cahn equations', 'energy stable schemes', 'energy dissipation law', 'original energy dissipation', 'solving allen cahn', 'cahn equations', 'energy dissipation', 'runge kutta methods', 'energy stability', 'kutta methods']","['Stabilized exponential-SAV schemes preserving energy dissipation law and\n  maximum bound principle for the Allen-Cahn type equations   It is well-known that the Allen-Cahn equation not only satisfies the energy\ndissipation law but also possesses the maximum bound principle (MBP) in the\nsense that the absolute value of its solution is pointwise bounded for all time\nby some specific constant under appropriate initial/boundary conditions. In\nrecent years, the scalar auxiliary variable (SAV) method and many of its\nvariants have attracted much attention in numerical solution for gradient flow\nproblems due to their inherent advantage of preserving certain discrete\nanalogues of the energy dissipation law. However, existing SAV schemes usually\nfail to preserve the MBP when applied to the Allen-Cahn equation. In this\npaper, we develop and analyze new first- and second-order stabilized\nexponential-SAV schemes for a class of Allen-Cahn type equations, which are\nshown to simultaneously preserve the energy dissipation law and MBP in discrete\nsettings. In addition, optimal error estimates for the numerical solutions are\nrigorously obtained for both schemes. Extensive numerical tests and comparisons\nare also conducted to demonstrate the performance of the proposed schemes.\n', 'Maximum bound principle and original energy dissipation of arbitrarily\n  high-order rescaled exponential time differencing Runge-Kutta schemes for\n  Allen--Cahn equations   The energy dissipation law and the maximum bound principle are two critical\nphysical properties of the Allen--Cahn equations. While many existing\ntime-stepping methods are known to preserve the energy dissipation law, most\napply to a modified form of energy. In this work, we demonstrate that, when the\nnonlinear term of the Allen--Cahn equation is Lipschitz continuous, a class of\narbitrarily high-order exponential time differencing Runge--Kutta (ETDRK)\nschemes preserve the original energy dissipation property, under a mild\nstep-size constraint. Additionally, we guarantee the Lipschitz condition on the\nnonlinear term by applying a rescaling post-processing technique, which ensures\nthat the numerical solution unconditionally satisfies the maximum bound\nprinciple. Consequently, our proposed schemes maintain both the original energy\ndissipation law and the maximum bound principle and can achieve arbitrarily\nhigh-order accuracy. We also establish an optimal error estimate for the\nproposed schemes. Some numerical experiments are carried out to verify our\ntheoretical results.\n', 'Energy dissipation law and maximum bound principle-preserving linear\n  BDF2 schemes with variable steps for the Allen-Cahn equation   In this paper, we propose and analyze a linear, structure-preserving scalar\nauxiliary variable (SAV) method for solving the Allen--Cahn equation based on\nthe second-order backward differentiation formula (BDF2) with variable time\nsteps. To this end, we first design a novel and essential auxiliary functional\nthat serves twofold functions: (i) ensuring that a first-order approximation to\nthe auxiliary variable, which is essentially important for deriving the\nunconditional energy dissipation law, does not affect the second-order temporal\naccuracy of the phase function $\\phi$; and (ii) allowing us to develop\neffective stabilization terms that are helpful to establish the MBP-preserving\nlinear methods. Together with this novel functional and standard central\ndifference stencil, we then propose a linear, second-order variable-step BDF2\ntype stabilized exponential SAV scheme, namely BDF2-sESAV-I, which is shown to\npreserve both the discrete modified energy dissipation law under the temporal\nstepsize ratio $ 0 < r_{k} := \\tau_{k}/\\tau_{k-1} < 4.864 - \\delta $ with a\npositive constant $\\delta$ and the MBP under $ 0 < r_{k} < 1 + \\sqrt{2} $.\nMoreover, an analysis of the approximation to the original energy by the\nmodified one is presented. With the help of the kernel recombination technique,\noptimal $ H^{1}$- and $ L^{\\infty}$-norm error estimates of the variable-step\nBDF2-sESAV-I scheme are rigorously established. Numerical examples are carried\nout to verify the theoretical results and demonstrate the effectiveness and\nefficiency of the proposed scheme.\n']","[('allen cahn equations', 0.49694299697875977), ('energy stable schemes', 0.472444623708725), ('energy dissipation law', 0.4161089360713959), ('original energy dissipation', 0.4147806465625763), ('solving allen cahn', 0.4035598039627075), ('cahn equations', 0.39669954776763916), ('energy dissipation', 0.3930397033691406), ('runge kutta methods', 0.3882996439933777), ('energy stability', 0.3791588246822357), ('kutta methods', 0.36571934819221497)]"
744,744,42,744_satellite networks_satellite terrestrial networks_satellite network_satellite communications,"['satellite networks', 'satellite terrestrial networks', 'satellite network', 'satellite communications', 'satellite communication', 'leo satellite communication', 'satellite communication system', 'non terrestrial networks', 'satellite links', 'terrestrial networks']","['Stochastic Geometry-based Analysis of LEO Satellite Communication\n  Systems   This letter studies the performance of a low-earth orbit (LEO) satellite\ncommunication system where the locations of the LEO satellites are modeled as a\nbinomial point process (BPP) on a spherical surface. In particular, we study\nthe user coverage probability for a scenario where satellite gateways (GWs) are\ndeployed on the ground to act as a relay between the users and the LEO\nsatellites. We use tools from stochastic geometry to derive the coverage\nprobability for the described setup assuming that LEO satellites are placed at\nn different altitudes, given that the number of satellites at each altitude ak\nis Nk for all k. To resemble practical scenarios where satellite communication\ncan play an important role in coverage enhancement, we compare the performance\nof the considered setup with a scenario where the users are solely covered by a\nfiber-connected base station (referred to as anchored base station or ABS in\nthe rest of the paper) at a relatively far distance, which is a common\nchallenge in rural and remote areas. Using numerical results, we show the\nperformance gain, in terms of coverage probability, at rural and remote areas\nwhen LEO satellite communication systems are adopted. Finally, we draw multiple\nsystem-level insights regarding the density of GWs required to outperform the\nABS, as well as the number of LEO satellites and their altitudes.\n', 'A Novel Analytical Model for LEO and MEO Satellite Networks based on Cox\n  Point Processes   This work develops an analytical framework for downlink low Earth orbit (LEO)\nor medium Earth orbit (MEO) satellite communications, leveraging tools from\nstochastic geometry. We propose a tractable approach to the analysis of such\nsatellite communication systems, accounting for the fact that satellites are\nlocated on circular orbits. We accurately incorporate this geometric property\nof LEO or MEO satellite constellations by developing a Cox point process model\nthat jointly produces orbits and satellites on these orbits. Our work contrasts\nwith previous modeling studies that presumed satellite locations to be entirely\nrandom, thereby overlooking the fundamental fact that satellites are jointly\npositioned on orbits. Employing this Cox model, we analyze the network\nperformance experienced by users located on Earth. Specifically, we evaluate\nthe no-satellite probability of the proposed network and the Laplace transform\nof the interference created by such a network. Using it, we compute its SIR\n(signal-to-interference) distribution, namely its coverage probability. By\npresenting fundamental network performance as functions of key parameters, this\nmodel allows one to assess the statistical properties of downlink LEO or MEO\nsatellite communications and can thus be used as a system-level design tool to\noperate and optimize forthcoming complex LEO or MEO satellite networks.\n', 'Modeling and Analysis of Downlink Communications in a Heterogeneous LEO\n  Satellite Network   Low Earth Orbit (LEO) satellite networks connect millions of devices on Earth\nand offer various services, such as data communications, remote sensing, and\ndata harvesting. As the number of services increases, LEO satellite networks\nwill continue to grow, and many LEO satellite network operators will share the\nsame spectrum resources. We aim to examine the coexistence of such a future\nheterogeneous LEO satellite network by proposing a tractable spatial model and\nanalyzing the basic performance of downlink communications. We model a\nheterogeneous LEO satellite network as Cox point processes, ensuring satellites\nare located on various orbits. Then, we analyze two different access\ntechnologies for such a heterogeneous satellite network: closed access and open\naccess. For both cases, we derive the coverage probability and prove that the\ncoverage probability of the open access scenario outperforms that of the closed\naccess, and this coverage enhancement applies to all users. By providing\nessential network performance statistics as key distributional parameters and\nby presenting the fact that the Cox point process approximates a forthcoming\nfuture constellation with slight variation, the developed framework and\nanalysis will serve as a tractable instrument to design, evaluate, and optimize\nheterogeneous LEO satellite networks with numerous constellations.\n']","[('satellite networks', 0.6714313626289368), ('satellite terrestrial networks', 0.6673660278320312), ('satellite network', 0.642825722694397), ('satellite communications', 0.6257645487785339), ('satellite communication', 0.5927175283432007), ('leo satellite communication', 0.5803727507591248), ('satellite communication system', 0.5442667603492737), ('non terrestrial networks', 0.536840558052063), ('satellite links', 0.5219195485115051), ('terrestrial networks', 0.5190344452857971)]"
745,745,42,745_mixed integer optimization_integer nonlinear programming_integer quadratically constrained_integer nonlinear programs,"['mixed integer optimization', 'integer nonlinear programming', 'integer quadratically constrained', 'integer nonlinear programs', 'mixed integer programming', 'integer linear programs', 'integer optimization', 'nonlinear programming minlp', 'quadratic optimization', 'integer programming']","['Parabolic Approximation & Relaxation for MINLP   We propose an approach based on quadratic approximations for solving general\nMixed-Integer Nonlinear Programming (MINLP) problems. Specifically, our\napproach entails the global approximation of the epigraphs of constraint\nfunctions by means of paraboloids, which are polynomials of degree two with\nunivariate quadratic terms, and relies on a Lipschitz property only. These\napproximations are then integrated into the original problem. To this end, we\nintroduce a novel approach to compute globally valid epigraph approximations by\nparaboloids via a Mixed-Integer Linear Programming (MIP) model. We emphasize\nthe possibility of performing such approximations a-priori and providing them\nin form of a lookup table, and then present several ways of leveraging the\napproximations to tackle the original problem. We provide the necessary\ntheoretical background and conduct computational experiments on instances of\nthe MINLPLib. As a result, this approach significantly accelerates the solution\nprocess of MINLP problems, particularly those involving many trigonometric or\nfew exponential functions. In general, we highlight that the proposed technique\nis able to exploit advances in Mixed-Integer Quadratically-Constrained\nProgramming (MIQCP) to solve MINLP problems.\n', 'Enhancements of Discretization Approaches for Non-Convex Mixed-Integer\n  Quadratically Constraint Quadratic Programming: Part II   This is Part II of a study on mixed-integer programming (MIP) relaxation\ntechniques for the solution of non-convex mixed-integer quadratically\nconstrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation\nmethods for non-convex continuous variable products and extend the well-known\nMIP relaxation normalized multi-parametric disaggregation technique (NMDT),\napplying a sophisticated discretization to both variables. We refer to this\napproach as doubly discretized normalized multiparametric disaggregation\ntechnique (D-NMDT). In a comprehensive theoretical analysis, we underline the\ntheoretical advantages of the enhanced method D-NMDT compared to NMDT.\nFurthermore, we perform a broad computational study to demonstrate its\neffectiveness in terms of producing tight dual bounds for MIQCQPs. Finally, we\ncompare D-NMDT to the separable MIP relaxations from Part I and a\nstate-of-the-art MIQCQP solver.\n', 'Enhancements of Discretization Approaches for Non-Convex Mixed-Integer\n  Quadratically Constraint Quadratic Programming: Part I   We study mixed-integer programming (MIP) relaxation techniques for the\nsolution of non convex mixed-integer quadratically constrained quadratic\nprograms (MIQCQPs). We present MIP relaxation methods for non convex continuous\nvariable products. In Part I, we consider MIP relaxations based on separable\nreformulation. The main focus is the introduction of the enhanced separable MIP\nrelaxation for nonconvex quadratic products of the form z=xy, called hybrid\nseparable (HybS). Additionally, we introduce a logarithmic MIP relaxation for\nunivariate quadratic terms, called sawtooth relaxation. We combine the latter\nwith HybS and existing separable reformulations to derive MIP relaxations of\nMIQCQPs. We provide a comprehensive theoretical analysis of these techniques,\nunderlining the theoretical advantages of HybS compared to its predecessors. We\nperform a broad computational study to demonstrate the effectiveness of the\nenhanced MIP relaxation in terms of producing tight dual bounds for MIQCQPs. In\nPart II, we study MIP relaxations that extend the well-known MIP relaxation\nnormalized multiparametric disaggregation technique (NMDT) and present further\ntheoretical and computational analyses.\n']","[('mixed integer optimization', 0.6830683946609497), ('integer nonlinear programming', 0.6595961451530457), ('integer quadratically constrained', 0.6312302947044373), ('integer nonlinear programs', 0.624260425567627), ('mixed integer programming', 0.6224334239959717), ('integer linear programs', 0.6117438077926636), ('integer optimization', 0.6109567880630493), ('nonlinear programming minlp', 0.5650992393493652), ('quadratic optimization', 0.5577580332756042), ('integer programming', 0.5574216842651367)]"
746,746,42,746_truncated hypergeometric series_basic hypergeometric series_hypergeometric series_supercongruences,"['truncated hypergeometric series', 'basic hypergeometric series', 'hypergeometric series', 'supercongruences', 'truncated hypergeometric', 'th cyclotomic polynomial', 'cyclotomic polynomial', 'formulas basic hypergeometric', 'multiple basic hypergeometric', 'basic hypergeometric']","[""Further $q$-supercongruences from a transformation of Rahman   Employing a quadratic transformation formula of Rahman and the method of\n`creative microscoping' (introduced by the author and Zudilin in 2019), we\nprovide some new $q$-supercongruences for truncated basic hypergeometric\nseries. In particular, we confirm two recent conjectures of Liu and Wang. We\nalso propose some related conjectures on supercongruences and\n$q$-supercongruences.\n"", ""New q-supercongruences from the Bailey transformation   Inspired by the recent work of Guo, we establish some new q-supercongruences\nincluding q-analogues of some Ramannujan-type supercongruences, by using the\nBailey transformation formula and the `creative microscoping' method recently\nintroduced by Guo and Zudilin.\n"", 'Some $q$-supercongruences modulo the square and cube of a cyclotomic\n  polynomial   Two $q$-supercongruences of truncated basic hypergeometric series containing\ntwo free parameters are established by employing specific identities for basic\nhypergeometric series. The results partly extend two $q$-supercongruences that\nwere earlier conjectured by the same authors and involve $q$-supercongruences\nmodulo the square and the cube of a cyclotomic polynomial. One of the newly\nproved $q$-supercongruences is even conjectured to hold modulo the fourth power\nof a cyclotomic polynomial.\n']","[('truncated hypergeometric series', 0.5471616387367249), ('basic hypergeometric series', 0.5398809313774109), ('hypergeometric series', 0.5334280133247375), ('supercongruences', 0.5125811100006104), ('truncated hypergeometric', 0.46675583720207214), ('th cyclotomic polynomial', 0.44182825088500977), ('cyclotomic polynomial', 0.44155019521713257), ('formulas basic hypergeometric', 0.4232731759548187), ('multiple basic hypergeometric', 0.4181324243545532), ('basic hypergeometric', 0.41765865683555603)]"
747,747,42,747_positive semidefinite matrices_matrix inequalities_positive matrices_positive definite matrices,"['positive semidefinite matrices', 'matrix inequalities', 'positive matrices', 'positive definite matrices', 'semidefinite matrices', 'totally nonnegative matrices', 'positive semidefinite', 'partial trace', 'partial traces', 'block matrices']","[""A new matrix inequality involving partial traces   Let $A$ be an $m\\times m$ positive semidefinite block matrix with each block\nbeing $n$-square. We write $\\mathrm{tr}_1$ and $\\mathrm{tr}_2$ for the first\nand second partial trace, respectively. In this paper, we prove the following\ninequality \\[ (\\mathrm{tr} A)I_{mn} - (\\mathrm{tr}_2 A) \\otimes I_n \\ge \\pm\n\\bigl( I_m\\otimes (\\mathrm{tr}_1 A) -A\\bigr).\\] This inequality is not only a\ngeneralization of Ando's result [ILAS Conference (2014)] and Lin [Canad. Math.\nBull. 59 (2016) 585--591], but it also could be regarded as a complement of a\nrecent result of Choi [Linear Multilinear Algebra 66 (2018) 1619--1625].\nAdditionally, some new partial traces inequalities for positive semidefinite\nblock matrices are also included.\n"", 'Extensions of some matrix inequalities related to trace and partial\n  traces   We first present a determinant inequality related to partial traces for\npositive semidefinite block matrices. Our result extends a result of Lin\n[Czech. Math. J. 66 (2016)] and improves a result of Kuai [Linear Multilinear\nAlgebra 66 (2018)]. Moreover, we provide a unified treatment of a result of\nAndo [ILAS Conference (2014)] and a recent result of Li, Liu and Huang\n[Operators and Matrices 15 (2021)]. Furthermore, we also extend some\ndeterminant inequalities involving partial traces to a larger class of matrices\nwhose numerical ranges are contained in a sector. In addition, some extensions\non trace inequalities for positive semidefinite $2\\times 2$ block matrices are\nalso included.\n', 'Improvements on some partial trace inequalities for positive\n  semidefinite block matrices   We study matrix inequalities involving partial traces for positive\nsemidefinite block matrices. First of all, we present a new method to prove a\ncelebrated result of Choi [Linear Algebra Appl. 516 (2017)]. Our method also\nallows us to prove a generalization of another result of Choi [Linear\nMultilinear Algebra 66 (2018)]. Furthermore, we shall give an improvement on a\nrecent result of Li, Liu and Huang [Operators and Matrices 15 (2021)]. In\naddition, we include with some majorization inequalities involving partial\ntraces for two by two block matrices, and also provide inequalities related to\nthe unitarily invariant norms as well as the singular values, which can be\nviewed as slight extensions of two results of Lin [Linear Algebra Appl. 459\n(2014)] and [Electronic J. Linear Algebra 31 (2016)].\n']","[('positive semidefinite matrices', 0.6014244556427002), ('matrix inequalities', 0.599538266658783), ('positive matrices', 0.549420952796936), ('positive definite matrices', 0.5437739491462708), ('semidefinite matrices', 0.4876142740249634), ('totally nonnegative matrices', 0.4846913814544678), ('positive semidefinite', 0.4843551814556122), ('partial trace', 0.4526638388633728), ('partial traces', 0.44475027918815613), ('block matrices', 0.43761295080184937)]"
748,748,42,748_partial flag varieties_varieties combinatorial_tsetlin polytopes_toric varieties,"['partial flag varieties', 'varieties combinatorial', 'tsetlin polytopes', 'toric varieties', 'family polytopes', 'gelfand tsetlin polytopes', 'flag varieties', 'polytopes', 'partial flag variety', 'toric variety']","['Newton-Okounkov polytopes of flag varieties and marked chain-order\n  polytopes   Marked chain-order polytopes are convex polytopes constructed from a marked\nposet, which give a discrete family relating a marked order polytope with a\nmarked chain polytope. In this paper, we consider the Gelfand-Tsetlin poset of\ntype A, and realize the associated marked chain-order polytopes as\nNewton-Okounkov bodies of the flag variety. Our realization connects previous\nrealizations of Gelfand-Tsetlin polytopes and Feigin-Fourier-Littelmann-Vinberg\npolytopes as Newton-Okounkov bodies in a uniform way. As an application, we\nprove that the flag variety degenerates into the irreducible normal projective\ntoric variety corresponding to a marked chain-order polytope. We also construct\na specific basis of an irreducible highest weight representation which is\nnaturally parametrized by the set of lattice points in a marked chain-order\npolytope.\n', 'Newton-Okounkov bodies of flag varieties and combinatorial mutations   A Newton-Okounkov body is a convex body constructed from a projective variety\nwith a globally generated line bundle and with a higher rank valuation on the\nfunction field, which gives a systematic method of constructing toric\ndegenerations of projective varieties. Its combinatorial properties heavily\ndepend on the choice of a valuation, and it is a fundamental problem to relate\nNewton-Okounkov bodies associated with different kinds of valuations. In this\npaper, we address this problem for flag varieties using the framework of\ncombinatorial mutations which was introduced in the context of mirror symmetry\nfor Fano manifolds. By applying iterated combinatorial mutations, we connect\nspecific Newton-Okounkov bodies of flag varieties including string polytopes,\nNakashima-Zelevinsky polytopes, and FFLV polytopes.\n', 'Toric degenerations of partial flag varieties and combinatorial\n  mutations of matching field polytopes   We study toric degenerations arising from Gr\\""obner degenerations or the\ntropicalization of partial flag varieties. We produce a new family of toric\ndegenerations of partial flag varieties whose combinatorics are governed by\nmatching fields and combinatorial mutations of polytopes. We provide an\nexplicit description of the polytopes associated with the resulting toric\nvarieties in terms of matching field polytopes. These polytopes encode the\ncombinatorial data of monomial degenerations of Pl\\""ucker forms for the\nGrassmannians. We give a description of matching field polytopes of flag\nvarieties as Minkowski sums and show that all such polytopes are normal. The\npolytopes we obtain are examples of Newton-Okounkov bodies for particular\nfull-rank valuations for flag varieties. Furthermore, we study a certain\nexplicitly-defined large family of matching field polytopes and prove that all\npolytopes in this family are connected by combinatorial mutations. Finally, we\napply our methods to explicitly compute toric degenerations of small\nGrassmannians and flag varieties and obtain new families of toric\ndegenerations.\n']","[('partial flag varieties', 0.53626948595047), ('varieties combinatorial', 0.5263007283210754), ('tsetlin polytopes', 0.5222964882850647), ('toric varieties', 0.5222436785697937), ('family polytopes', 0.4893065392971039), ('gelfand tsetlin polytopes', 0.48692142963409424), ('flag varieties', 0.48473411798477173), ('polytopes', 0.48387134075164795), ('partial flag variety', 0.47761648893356323), ('toric variety', 0.47350600361824036)]"
749,749,42,749_nichols algebras_nichols algebras diagonal_nichols algebra_dimensional hopf algebras,"['nichols algebras', 'nichols algebras diagonal', 'nichols algebra', 'dimensional hopf algebras', 'hopf algebras', 'algebras hopf algebra', 'algebras finite dimensional', 'hopf algebra', 'semisimple hopf algebra', 'algebras hopf']","['Pre-Nichols algebras of one-parameter families of finite\n  Gelfand-Kirillov dimension   Between the braided vector spaces of diagonal type there exist some families\nwhose associated Nichols algebras are infinite dimensional but with finite\nGelfand-Kirillov dimension, called one-parameter families. We show that every\npre-Nichols algebra of finite Gelfand-Kirillov dimension of this kind with\nconnected diagram is necessarily the corresponding Nichols algebra, up to few\nexceptions. For each one of these exceptions we present a proper pre-Nichols\nalgebra by generators and relations, and prove that it is the corresponding\neminent pre-Nichols algebra.\n  This paper essentially ends the determination of the eminent pre-Nichols\nalgebras of diagonal type, the first step towards the classification of\npre-Nichols algebras of diagonal type with finite GKdim.\n', 'Finite dimensional Nichols algebras over Suzuki algebra I: simple\n  Yetter-Drinfeld modules of $A_{N\\,2n}^{\\mu\\lambda}$   The Suzuki algebra $A_{Nn}^{\\mu \\lambda}$ was introduced by Suzuki Satoshi in\n1998, which is a class of cosemisimple Hopf algebras. It is not categorically\nMorita-equivalent to a group algebra in general. In this paper, the author\ngives a complete set of simple Yetter-Drinfeld modules over the Suzuki algebra\n$A_{N\\,2n}^{\\mu\\lambda}$ and investigates the Nichols algebras over those\nsimple Yetter-Drinfeld modules. The involved finite dimensional Nichols\nalgebras of diagonal type are of Cartan type $A_1$, $A_1\\times A_1$, $A_2$,\n$A_2\\times A_2$, Super type ${\\bf A}_{2}(q;I_2)$ and the Nichols algebra\nufo(8). There are $64$, $4m$ and $m^2$-dimensional Nichols algebras of\nnon-diagonal type over $A_{N\\,2n}^{\\mu \\lambda}$. The $64$-dimensional Nichols\nalgebras are of dihedral rack type $\\Bbb{D}_4$. The $4m$ and $m^2$-dimensional\nNichols algebras $\\mathfrak{B}(V_{abe})$ discovered first by Andruskiewitsch\nand Giraldi can be realized in the category of Yetter-Drinfeld modules over\n$A_{Nn}^{\\mu \\lambda}$. By using a result of Masuoka, we prove that\n$\\dim\\mathfrak{B}(V_{abe})=\\infty$ under the condition $b^2=(ae)^{-1}$,\n$b\\in\\Bbb{G}_{m}$ for $m\\geq 5$.\n', 'Finite dimensional Nichols algebras over Suzuki algebra II: over simple\n  Yetter-Drinfeld modules of $A_{N\\,2n+1}^{\\mu\\lambda}$   In this paper, the author gives a complete set of simple Yetter-Drinfeld\nmodules over Suzuki algebra $A_{N\\,2n+1}^{\\mu\\lambda}$ and investigates the\nNichols algebras over those irreducible Yetter-Drinfeld modules. The finite\ndimensional Nichols algebras of diagonal type are of Cartan type $A_1$,\n$A_1\\times A_1$, $A_2$, Super type ${A}_{2}(q;I_2)$ and the Nichols algebra\n$\\mathfrak{ufo}(8)$. And the involved finite dimensional Nichols algebras of\nnon-diagonal type are $12$, $4m$ and $m^2$ dimensional. The left three unsolved\ncases are set as open problems.\n']","[('nichols algebras', 0.7661947011947632), ('nichols algebras diagonal', 0.7524921298027039), ('nichols algebra', 0.6924079060554504), ('dimensional hopf algebras', 0.6871837377548218), ('hopf algebras', 0.6458818912506104), ('algebras hopf algebra', 0.6231985688209534), ('algebras finite dimensional', 0.5944353342056274), ('hopf algebra', 0.5687422156333923), ('semisimple hopf algebra', 0.5434172749519348), ('algebras hopf', 0.5420476198196411)]"
750,750,41,750_quantum gibbs_quantum thermal_temperature quantum_quantum computers,"['quantum gibbs', 'quantum thermal', 'temperature quantum', 'quantum computers', 'quantum stochastic systems', 'quantum hamiltonians', 'markovian quantum', 'quantum master', 'quantum stochastic', 'open quantum systems']","['Reachability in Controlled Markovian Quantum Systems: An\n  Operator-Theoretic Approach   In quantum systems theory one of the fundamental problems boils down to:\nGiven an initial state, which final states can be reached by the dynamic system\nin question? Formulated in the framework of bilinear control systems, the\nevolution shall be governed by an inevitable Hamiltonian drift term, finitely\nmany control Hamiltonians allowing for (at least) piecewise constant control\namplitudes, plus a (possibly bang-bang switchable) noise term in\nKossakowski-Lindblad form.\n  Now assuming switchable coupling of finite-dimensional systems to a thermal\nbath of arbitrary temperature, the core problem of reachability boils down to\nstudying points in the standard simplex amenable to two types of controls that\ncan be used interleaved: Permutations within the simplex, and contractions by a\ndissipative one-parameter semigroup. We illustrate how the solutions of the\ncore problem pertain to the reachable set of the original controlled Markovian\nquantum system. This allows us to show that for global as well as local\nswitchable coupling to a temperature-zero bath one can generate every quantum\nstate from every initial state up to arbitrary precision. Moreover we present\nan inclusion for non-zero temperatures as a consequence of our results on\nd-majorization.\n  Then we consider infinite-dimensional open quantum-dynamical systems\nfollowing a unital Kossakowski-Lindblad master equation extended by controls.\nHere the drift Hamiltonian can be arbitrary, the finitely many control\nHamiltonians are bounded, and the switchable noise term is generated by a\nsingle compact normal operator. Via new majorization results of ours, we show\nthat such bilinear quantum control systems allow to approximately reach any\ntarget state majorized by the initial one, as up to now only has been known in\nfinite-dimensional analogues.\n', 'Optimal quantum algorithm for Gibbs state preparation   It is of great interest to understand the thermalization of open quantum\nmany-body systems, and how quantum computers are able to efficiently simulate\nthat process. A recently introduced disispative evolution, inspired by existing\nmodels of open system thermalization, has been shown to be efficiently\nimplementable on a quantum computer. Here, we prove that, at high enough\ntemperatures, this evolution reaches the Gibbs state in time scaling\nlogarithmically with system size. The result holds for Hamiltonians that\nsatisfy the Lieb-Robinson bound, such as local Hamiltonians on a lattice, and\nincludes long-range systems. To the best of our knowledge, these are the first\nresults rigorously establishing the rapid mixing property of high-temperature\nquantum Gibbs samplers, which is known to give the fastest possible speed for\nthermalization in the many-body setting. We then employ our result to the\nproblem of estimating partition functions at high temperature, showing an\nimproved performance over previous classical and quantum algorithms.\n', ""Quantum Thermal State Preparation   Preparing ground states and thermal states is essential for simulating\nquantum systems on quantum computers. Despite the hope for practical quantum\nadvantage in quantum simulation, popular state preparation approaches have been\nchallenged. Monte Carlo-style quantum Gibbs samplers have emerged as an\nalternative, but prior proposals have been unsatisfactory due to technical\nobstacles rooted in energy-time uncertainty. We introduce simple\ncontinuous-time quantum Gibbs samplers that overcome these obstacles by\nefficiently simulating Nature-inspired quantum master equations (Lindbladians).\nIn addition, we construct the first provably accurate and efficient algorithm\nfor preparing certain purified Gibbs states (called thermal field double states\nin high-energy physics) of rapidly thermalizing systems; this algorithm also\nbenefits from a quantum walk speedup. Our algorithms' costs have a provable\ndependence on temperature, accuracy, and the mixing time (or spectral gap) of\nthe relevant Lindbladian. We complete the first rigorous proof of finite-time\nthermalization for physically derived Lindbladians by developing a general\nanalytic framework for nonasymptotic secular approximation and approximate\ndetailed balance. Given the success of classical Markov chain Monte Carlo\n(MCMC) algorithms and the ubiquity of thermodynamics, we anticipate that\nquantum Gibbs sampling will become indispensable in quantum computing.\n""]","[('quantum gibbs', 0.6152254939079285), ('quantum thermal', 0.5855178236961365), ('temperature quantum', 0.5828031301498413), ('quantum computers', 0.5236903429031372), ('quantum stochastic systems', 0.5134966373443604), ('quantum hamiltonians', 0.508578360080719), ('markovian quantum', 0.5007844567298889), ('quantum master', 0.4842160940170288), ('quantum stochastic', 0.4825648069381714), ('open quantum systems', 0.4794980585575104)]"
751,751,41,751_holographic mimo_mimo communications_mimo systems_multiple output mimo,"['holographic mimo', 'mimo communications', 'mimo systems', 'multiple output mimo', 'mimo system', 'output mimo', 'spatial multiplexing', 'mimo based', 'antenna arrays', 'holographic']","['Channel Measurement for Holographic MIMO: Benefits and Challenges of\n  Spatial Oversampling   In this paper, the channel of an indoor holographic multiple-input\nmultiple-output (MIMO) system is measured. It is demonstrated through\nexperiments for the first time that the spatial oversampling of holographic\nMIMO systems is able to increase the capacity of a wireless communication\nsystem significantly. However, the antenna efficiency is the most crucial\nchallenge preventing us from getting the capacity improvement. An extended\nEM-compliant channel model is also proposed for holographic MIMO systems, which\nis able to take the non-isotropic characteristics of the propagation\nenvironment, the antenna pattern distortion, the antenna efficiency, and the\npolarization characteristics into consideration.\n', 'Electromagnetic-Compliant Channel Modeling and Performance Evaluation\n  for Holographic MIMO   Recently, the concept of holographic multiple-input multiple-output (MIMO) is\nemerging as one of the promising technologies beyond massive MIMO. Many\nchallenges need to be addressed to bring this novel idea into practice,\nincluding electromagnetic (EM)-compliant channel modeling and accurate\nperformance evaluation. In this paper, an EM-compliant channel model is\nproposed for the holographic MIMO systems, which is able to model both the\ncharacteristics of the propagation channel and the non-ideal factors caused by\nmutual coupling at the transceivers, including the antenna pattern distortion\nand the decrease of antenna efficiency. Based on the proposed channel model, a\nmore realistic performance evaluation is conducted to show the performance of\nthe holographic MIMO system in both the single-user and the multi-user\nscenarios. Key challenges and future research directions are further provided\nbased on the theoretical analyses and numerical results.\n', 'Effects of Mutual Coupling on Degree of Freedom and Antenna Efficiency\n  in Holographic MIMO Communications   The holographic multiple-input-multiple-output (MIMO) communications refer to\nthe MIMO systems built with ultra-dense antenna arrays, whose channel models\nand potential applications have attracted increasing attentions recently. When\nthe spacing between adjacent array elements is larger than half wavelength, the\neffect of mutual coupling can generally be neglected in current antenna\ndesigns. However, in holographic MIMO communications, the influence of strong\nmutual coupling on antenna characteristics is inevitable, resulting in\ndistorted radiation patterns and low radiation efficiencies. In this paper,\nstarting from the analytical correlation and efficiency models, we investigate\nhow the mutual coupling affects the capacity of a space-constrained MIMO system\nfrom the aspects of degree of freedom (DOF) and antenna efficiency. The\ninvolved fundamental concepts of correlation, DOF, efficiency and mutual\ncoupling are crucial for both antenna and wireless-communication engineers when\ndesigning emerging MIMO communication systems.\n']","[('holographic mimo', 0.7644466161727905), ('mimo communications', 0.5686900019645691), ('mimo systems', 0.5411375761032104), ('multiple output mimo', 0.522071123123169), ('mimo system', 0.511299192905426), ('output mimo', 0.5105807185173035), ('spatial multiplexing', 0.5009040236473083), ('mimo based', 0.4721406102180481), ('antenna arrays', 0.46571168303489685), ('holographic', 0.4570494592189789)]"
752,752,41,752_bilevel optimization problems_bilevel optimization_bilevel programming_optimality conditions,"['bilevel optimization problems', 'bilevel optimization', 'bilevel programming', 'optimality conditions', 'necessary optimality conditions', 'solving bilevel', 'optimality condition', 'bilevel program', 'bilevel programs', 'mathematical program complementarity']","['Relaxation methods for pessimistic bilevel optimization   We consider a smooth pessimistic bilevel optimization problem, where the\nlower-level problem is convex and satisfies the Slater constraint\nqualification. These assumptions ensure that the Karush-Kuhn-Tucker (KKT)\nreformulation of our problem is well-defined. We then introduce and study the\n(i) Scholtes, (ii) Lin and Fukushima, (iii) Kadrani, Dussault and Benchakroun,\n(iv) Steffensen and Ulbrich, and (v) Kanzow and Schwartz relaxation methods for\nthe KKT reformulation of our pessimistic bilevel program. These relaxations\nhave been extensively studied and compared for mathematical programs with\ncomplementatrity constraints (MPCCs). To the best of our knowledge, such a\nstudy has not been conducted for the pessimistic bilevel optimization problem,\nwhich is completely different from an MPCC, as the complemetatrity conditions\nare part of the objective function, and not in the feasible set of the problem.\nAfter introducing these relaxations, we provide convergence results for global\nand local optimal solutions, as well as suitable versions of the C- and\nM-stationarity points of our pessimistic bilevel optimization problem.\nNumerical results are also provided to illustrate the practical implementation\nof these relaxation algorithms, as well as some preliminary comparisons.\n', ""On a Computationally Ill-Behaved Bilevel Problem with a Continuous and\n  Nonconvex Lower Level   It is well known that bilevel optimization problems are hard to solve both in\ntheory and practice. In this paper, we highlight a further computational\ndifficulty when it comes to solving bilevel problems with continuous but\nnonconvex lower levels. Even if the lower-level problem is solved to\n$\\varepsilon$-feasibility regarding its nonlinear constraints for an\narbitrarily small but positive $\\varepsilon$, the obtained bilevel solution as\nwell as its objective value may be arbitrarily far away from the actual bilevel\nsolution and its actual objective value. This result even holds for bilevel\nproblems for which the nonconvex lower level is uniquely solvable, for which\nthe strict complementarity condition holds, for which the feasible set is\nconvex, and for which Slater's constraint qualification is satisfied for all\nfeasible upper-level decisions. Since the consideration of\n$\\varepsilon$-feasibility cannot be avoided when solving nonconvex problems to\nglobal optimality, our result shows that computational bilevel optimization\nwith continuous and nonconvex lower levels needs to be done with great care.\nFinally, we illustrate that the nonlinearities in the lower level are the key\nreason for the observed bad behavior by showing that linear bilevel problems\nbehave much better at least on the level of feasible solutions.\n"", 'Scholtes relaxation method for pessimistic bilevel optimization   When the lower-level optimal solution set-valued mapping of a bilevel\noptimization problem is not single-valued, we are faced with an ill-posed\nproblem, which gives rise to the optimistic and pessimistic bilevel\noptimization problems, as tractable algorithmic frameworks. However, solving\nthe pessimistic bilevel optimization problem is far more challenging than the\noptimistic one; hence, the literature has mostly been dedicated to the latter\nclass of the problem. The Scholtes relaxation has appeared to be one of the\nsimplest and most efficient ways to solve the optimistic bilevel optimization\nproblem in its Karush-Kuhn-Tucker (KKT) reformulation or the corresponding more\ngeneral mathematical program with complementarity constraints (MPCC). Inspired\nby such a success, this paper studies the potential of the Scholtes relaxation\nin the context of the pessimistic bilevel optimization problem. To proceed, we\nconsider a pessimistic bilevel optimization problem, where all the functions\ninvolved are at least continuously differentiable. Then assuming that the\nlower-level problem is convex, the KKT reformulation of the problem is\nconsidered under the Slater constraint qualification. Based on this KKT\nreformulation, we introduce the corresponding version of the Scholtes\nrelaxation algorithm. We then construct theoretical results ensuring that the\nlimit of a sequence of global/local optimal solutions (resp. stationary points)\nof the aforementioned Scholtes relaxation is a global/local optimal solution\n(resp. stationary point) of the KKT reformulation of the pessimistic bilevel\nprogram. The results are accompanied by technical constructions ensuring that\nthe Scholtes relaxation algorithm is well-defined or that the corresponding\nparametric optimization problem is more tractable.\n']","[('bilevel optimization problems', 0.755928635597229), ('bilevel optimization', 0.7551640272140503), ('bilevel programming', 0.6576176881790161), ('optimality conditions', 0.5643222332000732), ('necessary optimality conditions', 0.544077455997467), ('solving bilevel', 0.5411449074745178), ('optimality condition', 0.5367289781570435), ('bilevel program', 0.5341809988021851), ('bilevel programs', 0.5332731008529663), ('mathematical program complementarity', 0.5234434008598328)]"
753,753,41,753_manifolds nonnegative ricci_manifold positive_manifold positive scalar_manifold nonnegative ricci,"['manifolds nonnegative ricci', 'manifold positive', 'manifold positive scalar', 'manifold nonnegative ricci', 'manifolds nonnegative', 'noncompact manifolds nonnegative', 'contractible manifold', 'positive scalar curvature', 'manifold admit', 'manifold nonnegative']","['Some topological results of Ricci limit spaces   We study the topology of a Ricci limit space $(X,p)$, which is the\nGromov-Hausdorff limit of a sequence of complete $n$-manifolds $(M_i, p_i)$\nwith $\\mathrm{Ric}\\ge -(n-1)$. Our first result shows that, if $M_i$ has Ricci\nbounded covering geometry, i.e. the local Riemannian universal cover is\nnon-collapsed, then $X$ is semi-locally simply connected. In the process, we\nestablish a slice theorem for isometric pseudo-group actions on a closed ball\nin the Ricci limit space. In the second result, we give a description of the\nuniversal cover of $X$ if $M_i$ has a uniform diameter bound.\n', 'Contractible $3$-manifold and Positive scalar curvature (I)   In this work we prove that the Whitehead manifold has no complete metric of\npositive scalar curvature. This result can be generalized to the genus one\ncase. Precisely, we show that no contractible genus one $3$-manifold admits a\ncomplete metric of positive scalar curvature.\n', 'On open manifolds admitting no complete metric with positive scalar\n  curvature   In this paper, we investigate the topological obstruction problem for\npositive scalar curvature and uniformly positive scalar curvature on open\nmanifolds. We present a definition for open Schoen-Yau-Schick manifolds and\nprove that there is no complete metric with positive scalar curvature on these\nmanifolds. Similarly, we define weak Schoen-Yau-Shick manifolds by analogy,\nwhich are expected to admit no complete metrics with uniformly positive scalar\ncurvature.\n']","[('manifolds nonnegative ricci', 0.6354389786720276), ('manifold positive', 0.6282941699028015), ('manifold positive scalar', 0.6190166473388672), ('manifold nonnegative ricci', 0.6158062219619751), ('manifolds nonnegative', 0.6076884269714355), ('noncompact manifolds nonnegative', 0.6015065908432007), ('contractible manifold', 0.5980955362319946), ('positive scalar curvature', 0.5860158205032349), ('manifold admit', 0.5850512385368347), ('manifold nonnegative', 0.5826936960220337)]"
754,754,41,754_casimir_vacuum energy_quantum field theory_vacuum polarization,"['casimir', 'vacuum energy', 'quantum field theory', 'vacuum polarization', 'quantum field', 'spectral zeta', 'quantum scalar field', 'quantum electrodynamics', 'field boundary', 'quantum fluctuations']","['Critical Casimir Effect: Exact Results   In any medium there are fluctuations due to temperature or due to the quantum\nnature of its constituents. If a material body is immersed into such a medium,\nits shape and the properties of its constituents modify the properties of the\nsurrounding medium and its fluctuations. If in the same medium there is a\nsecond body then -- in addition to all direct interactions between them -- the\nmodifications due to the first body influence the modifications due to the\nsecond body. This mutual influence results in a force between these bodies. If\nthe excitations of the medium, which mediate the effective interaction between\nthe bodies, are massless, this force is long-ranged and nowadays known as a\nCasimir force. If the fluctuating medium consists of the confined\nelectromagnetic field in vacuum, one speaks of the quantum mechanical Casimir\neffect. In the case that the order parameter of material fields fluctuates -\nsuch as differences of number densities or concentrations - and that the\ncorresponding fluctuations of the order parameter are long-ranged, one speaks\nof the critical Casimir effect. This holds, e.g., in the case of systems which\nundergo a second-order phase transition and which are thermodynamically located\nnear the corresponding critical point, or for systems with a continuous\nsymmetry exhibiting Goldstone mode excitations. Here we review the currently\navailable exact results concerning the critical Casimir effect in systems\nencompassing the one-dimensional Ising, XY, and Heisenberg models, the\ntwo-dimensional Ising model, the Gaussian and the spherical models, as well as\nthe mean field results for the Ising and the XY model. Special attention is\npaid to the influence of the boundary conditions on the behavior of the Casimir\nforce.\n', 'Casimir pistons with generalized boundary conditions: a step forward   In this work we study the Casimir effect for massless scalar fields\npropagating in a piston geometry of the type $I\\times N$ where $I$ is an\ninterval of the real line and $N$ is a smooth compact Riemannian manifold. Our\nanalysis represents a generalization of previous results obtained for pistons\nconfigurations as we consider all possible boundary conditions that are allowed\nto be imposed on the scalar fields. We employ the spectral zeta function\nformalism in the framework of scattering theory in order to obtain an\nexpression for the Casimir energy and the corresponding Casimir force on the\npiston. We provide explicit results for the Casimir force when the manifold $N$\nis a $d$-dimensional sphere and a disk.\n', 'Fermionic Casimir Energy in Horava-Lifshitz Scenario   In this work, we investigate the violation of Lorentz symmetry through the\nCasimir effect. The Casimir effect is one of the most intriguing aspects of\nmodern physics, representing a macroscopic quantum-origin force between two\nneutral conducting surfaces, and it stands as a triumph of Quantum Field\nTheory. Here, we examine the Casimir effects associated with a massive\nfermionic quantum field confined in the region between two large and parallel\nplates within the Horava-Lifshitz framework of Lorentz symmetry violation. To\ncalculate the Casimir energy and consequently the Casimir pressure, we impose a\nMIT bag boundary condition on two plates, compatible with the higher-order\nderivative term in the modified Dirac equation. Our results indicate a strong\ninfluence of Lorentz violation on the Casimir effect. We observe that the\nCasimir energy is affected, both in intensity and sign, potentially exhibiting\nrepulsive or attractive force between the plates, depending on the critical\nexponent associated with the Horava-Lifshitz formalism.\n']","[('casimir', 0.6560659408569336), ('vacuum energy', 0.45561859011650085), ('quantum field theory', 0.44260072708129883), ('vacuum polarization', 0.41329920291900635), ('quantum field', 0.41313835978507996), ('spectral zeta', 0.3905617296695709), ('quantum scalar field', 0.382140576839447), ('quantum electrodynamics', 0.3778022825717926), ('field boundary', 0.36841925978660583), ('quantum fluctuations', 0.36747780442237854)]"
755,755,41,755_symplectic groups_symplectic group_invariant bilinear forms_bilinear forms,"['symplectic groups', 'symplectic group', 'invariant bilinear forms', 'bilinear forms', 'orthogonal groups', 'invariant bilinear', 'symplectic orthogonal', 'orthogonal symplectic', 'symplectic', 'non degenerate invariant']","['Normality theorem for elementary symplectic group with respect to an\n  alternating form   A.A. Suslin proved a normality theorem for an elementary linear group, which\nsays that an elementary linear group of size bigger than or equal to 3 over a\ncommutative ring with unity is normal in the general linear group of same size.\nSubsequently, V.I. Kopeiko extended this result of Suslin for a symplectic\ngroup defined with respect to the standard skew-symmetric matrix of even size.\nHere we generalise the result of Kopeiko for a symplectic group defined with\nrespect to any invertible skew-symmetric matrix of even size of Pfaffian one.\n', 'Normality of Vaserstein group   A.A. Suslin proved a normality theorem for an elementary linear group and\nV.I. Kopeiko extended this result of Suslin for a symplectic group defined with\nrespect to the standard skew-symmetric matrix of even size. We generalized the\nresult of Kopeiko for a symplectic group defined with respect to any invertible\nskew-symmetric matrix of Pfaffian one. Vaserstein group is an extension of a\nsymplectic group defined with respect to any invertible skew-symmetric matrix\nof Pfaffian one in the set up of projective modules. Here we prove a normality\ntheorem for Vaserstein group.\n', 'Equality of elementary symplectic group and symplectic group   V.I. Kopeiko proved that over a euclidean ring, the symplectic group defined\nwith respect to the standard skew-symmetric matrix is same as the elementary\nsymplectic group. Here we generalise the result of Kopeiko for a symplectic\ngroup defined with respect to any invertible skew-symmetric matrix of Pfaffian\none.\n']","[('symplectic groups', 0.6830794215202332), ('symplectic group', 0.6633754968643188), ('invariant bilinear forms', 0.6273150444030762), ('bilinear forms', 0.5343922972679138), ('orthogonal groups', 0.5186234712600708), ('invariant bilinear', 0.5131494998931885), ('symplectic orthogonal', 0.5078532695770264), ('orthogonal symplectic', 0.5039765238761902), ('symplectic', 0.48854875564575195), ('non degenerate invariant', 0.488335520029068)]"
756,756,41,756_tsunami_water waves_water wave_earthquake,"['tsunami', 'water waves', 'water wave', 'earthquake', 'waves', 'waves generated', 'nonlinear shallow water', 'shallow water equations', 'wave', 'wave propagation']","['Energy of tsunami waves generated by bottom motion   In the vast literature on tsunami research, few articles have been devoted to\nenergy issues. A theoretical investigation on the energy of waves generated by\nbottom motion is performed here. We start with the full incompressible Euler\nequations in the presence of a free surface and derive both dispersive and\nnon-dispersive shallow-water equations with an energy equation. It is shown\nthat dispersive effects only appear at higher order in the energy budget. Then\nwe solve the Cauchy-Poisson problem of tsunami generation for the linearized\nwater wave equations. Exchanges between potential and kinetic energies are\nclearly revealed.\n', 'The VOLNA code for the numerical modelling of tsunami waves: generation,\n  propagation and inundation   A novel tool for tsunami wave modelling is presented. This tool has the\npotential of being used for operational purposes: indeed, the numerical code\n\\VOLNA is able to handle the complete life-cycle of a tsunami (generation,\npropagation and run-up along the coast). The algorithm works on unstructured\ntriangular meshes and thus can be run in arbitrary complex domains. This paper\ncontains the detailed description of the finite volume scheme implemented in\nthe code. The numerical treatment of the wet/dry transition is explained. This\npoint is crucial for accurate run-up/run-down computations. Most existing\ntsunami codes use semi-empirical techniques at this stage, which are not always\nsufficient for tsunami hazard mitigation. Indeed the decision to evacuate\ninhabitants is based on inundation maps which are produced with this type of\nnumerical tools. We present several realistic test cases that partially\nvalidate our algorithm. Comparisons with analytical solutions and experimental\ndata are performed. Finally the main conclusions are outlined and the\nperspectives for future research presented.\n', 'Estimating earthquake-induced tsunami height probabilities without\n  sampling   Given a distribution of earthquake-induced seafloor elevations, we present a\nmethod to compute the probability of the resulting tsunamis reaching a certain\nsize on shore. Instead of sampling, the proposed method relies on optimization\nto compute the most likely fault slips that result in a seafloor deformation\ninducing a large tsunami wave. We model tsunamis induced by bathymetry change\nusing the shallow water equations on an idealized slice through the sea. The\nearthquake slip model is based on a sum of multivariate log-normal\ndistributions, and follows the Gutenberg-Richter law for moment magnitudes\n7--9. For a model problem inspired by the Tohoku-Oki 2011 earthquake and\ntsunami, we quantify annual probabilities of differently sized tsunami waves.\nOur method also identifies the most effective tsunami mechanisms. These\nmechanisms have smoothly varying fault slip patches that lead to an expansive\nbut moderately large bathymetry change. The resulting tsunami waves are\ncompressed as they approach shore and reach close-to-vertical leading wave edge\nclose to shore.\n']","[('tsunami', 0.6807753443717957), ('water waves', 0.4516889154911041), ('water wave', 0.44381582736968994), ('earthquake', 0.4075052738189697), ('waves', 0.37727221846580505), ('waves generated', 0.3770606219768524), ('nonlinear shallow water', 0.3735028803348541), ('shallow water equations', 0.37161070108413696), ('wave', 0.3452964425086975), ('wave propagation', 0.3438045084476471)]"
757,757,41,757_bergman projection_weighted bergman spaces_bergman spaces_bergman space,"['bergman projection', 'weighted bergman spaces', 'bergman spaces', 'bergman space', 'estimates bergman', 'bergman kernel', 'weighted bergman', 'bergman', 'projections', 'domains smooth boundary']","['Restricted type estimates on the Bergman projection of some singular\n  domains   We obtain (weighted) restricted type estimates for the Bergman projection\noperator on monomial polyhedra, a class of domains generalizing the Hartogs\ntriangle. From these estimates, we recapture $L^p$ boundedness results of the\nBergman projection on these domains. On some monomial polyhedra, we also\ndiscover that the Bergman projection could fail to be of weak type $(q_*,q_*)$\nwhere $q_*$ is the right endpoint of the interval of $L^p$-regularity of the\ndomain.\n', 'Sobolev mapping of some holomorphic projections   Sobolev irregularity of the Bergman projection on a family of domains\ncontaining the Hartogs triangle is shown. On the Hartogs triangle itself, a\nsub-Bergman projection is shown to satisfy better Sobolev norm estimates than\nits Bergman projection.\n', ""Weighted estimates for the Bergman projection on the Hartogs triangle   We apply modern techniques of dyadic harmonic analysis to obtain sharp\nestimates for the Bergman projection in weighted Bergman spaces. Our main\ntheorem focuses on the Bergman projection on the Hartogs triangle. The\nestimates of the operator norm are in terms of a Bekoll\\'e-Bonami type\nconstant. As an application of the results obtained, we give, for example, an\nupper bound for the $L^p$ norm of the Bergman projection on the generalized\nHartogs triangle $\\mathbb H_{m/n}$ in $\\mathbb C^2$.\n""]","[('bergman projection', 0.7386181950569153), ('weighted bergman spaces', 0.7353193759918213), ('bergman spaces', 0.7205063104629517), ('bergman space', 0.6664171814918518), ('estimates bergman', 0.6560797691345215), ('bergman kernel', 0.6452537178993225), ('weighted bergman', 0.6042468547821045), ('bergman', 0.547566831111908), ('projections', 0.3133254051208496), ('domains smooth boundary', 0.30423703789711)]"
758,758,41,758_sobolev inequalities_sobolev inequality_weighted sobolev space_sobolev embeddings,"['sobolev inequalities', 'sobolev inequality', 'weighted sobolev space', 'sobolev embeddings', 'weighted sobolev', 'sobolev spaces', 'trudinger moser type', 'korn inequality', 'int_ omega nabla', 'korn type inequalities']","['Korn inequalities for incompatible tensor fields in three space\n  dimensions with conformally invariant dislocation energy   Let $\\Omega \\subset \\mathbb{R}^3$ be an open and bounded set with Lipschitz\nboundary and outward unit normal $\\nu$. For $1<p<\\infty$ we establish an\nimproved version of the generalized $L^p$-Korn inequality for incompatible\ntensor fields $P$ in the new Banach space $$\n  W^{1,\\,p,\\,r}_0(\\operatorname{dev}\\operatorname{sym}\\operatorname{Curl};\n\\Omega,\\mathbb R^{3\\times3}) = \\{ P \\in L^p(\\Omega,\\mathbb R^{3\\times3}) \\mid\n\\operatorname{dev} \\operatorname{sym} \\operatorname{Curl} P \\in\nL^r(\\Omega,\\mathbb R^{3\\times3}),\\ \\operatorname{dev} \\operatorname{sym} (P\n\\times \\nu) = 0 \\text{ on $\\partial \\Omega$}\\} $$ where\n  $$ r \\in [1, \\infty), \\qquad \\frac1r \\le \\frac1p + \\frac13, \\qquad r >1 \\quad\n\\text{if $p = \\frac32$.}$$\n  Specifically, there exists a constant $c=c(p,\\Omega,r)>0$ such that the\ninequality\n  \\[ \\|P \\|_{L^p}\\leq c\\,\\left(\\|\\operatorname{sym} P \\|_{L^p} +\n\\|\\operatorname{dev}\\operatorname{sym} \\operatorname{Curl} P \\|_{L^{r}}\\right)\n\\] holds for all tensor fields $P\\in W^{1,\\,p, \\,\nr}_0(\\operatorname{dev}\\operatorname{sym}\\operatorname{Curl})$. Here,\n$\\operatorname{dev} X := X -\\frac13 \\operatorname{tr}(X)\\,\\mathbb{1}$ denotes\nthe deviatoric (trace-free) part of a $3 \\times 3$ matrix $X$ and the boundary\ncondition is understood in a suitable weak sense.\n', ""Ne\\v{c}as-Lions lemma revisited: An $L^p$-version of the generalized\n  Korn inequality for incompatible tensor fields   For $1<p<\\infty$ we prove an $L^p$-version of the generalized Korn inequality\nfor incompatible tensor fields $P$ in $ W^{1,\\,p}_0(\\operatorname{Curl};\n\\Omega,\\mathbb{R}^{3\\times3})$. More precisely, let $\\Omega\\subset\\mathbb{R}^3$\nbe a bounded Lipschitz domain. Then there exists a constant $c>0$ such that\n\\begin{equation*} \\| P\\|_{L^p(\\Omega,\\mathbb{R}^{3\\times3})}\\leq c\\,\\left(\n\\|\\operatorname{sym} P\\|_{L^p(\\Omega,\\mathbb{R}^{3\\times3})} + \\|\n\\operatorname{Curl}P \\|_{L^p(\\Omega,\n\\mathbb{R}^{3\\times3})}\\right)\\end{equation*} holds for all tensor fields $P\\in\nW^{1,\\,p}_0(\\operatorname{Curl}; \\Omega,\\mathbb{R}^{3\\times3})$, i.e., for all\n$P\\in W^{1,\\,p}(\\operatorname{Curl}; \\Omega,\\mathbb{R}^{3\\times3})$ with\nvanishing tangential trace $ P\\times \\nu=0 $ on $ \\partial\\Omega$ where $\\nu$\ndenotes the outward unit normal vector field to $\\partial\\Omega$. For\ncompatible $P=D u$ this recovers an $L^p$-version of the classical Korn's first\ninequality $$ \\|D u \\|_{L^p(\\Omega,\\mathbb{R}^{3\\times 3})} \\le c\\,\n\\|\\operatorname{sym}D u\\|_{L^p(\\Omega,\\mathbb{R}^{3\\times3})} \\quad \\text{with\n}D u \\times \\nu = 0 \\quad \\text{on $\\partial \\Omega$}, $$ and for\nskew-symmetric $P=A\\in\\mathfrak{so}(3)$ an $L^p$-version of the Poincar\\'{e}\ninequality $$ \\|A\\|_{L^p(\\Omega,\\mathfrak{so}(3))}\\le c\\, \\|\\operatorname{Curl}\nA\\|_{L^p(\\Omega,\\mathbb{R}^{3\\times3})} \\quad \\text{with } A \\times \\nu = 0 \\\n\\Leftrightarrow \\ A=0 \\quad \\text{on $\\partial \\Omega$}. $$\n"", '$L^p$-trace-free generalized Korn inequalities for incompatible tensor\n  fields in three space dimensions   For $1<p<\\infty$ we prove an $L^p$-version of the generalized trace-free Korn\ninequality for incompatible tensor fields $P$ in $\nW^{1,\\,p}_0(\\operatorname{Curl}; \\Omega,\\mathbb{R}^{3\\times3})$. More\nprecisely, let $\\Omega\\subset\\mathbb{R}^3$ be a bounded Lipschitz domain. Then\nthere exists a constant $c>0$ such that \\[ \\|{ P\n}\\|_{L^p(\\Omega,\\mathbb{R}^{3\\times3})}\\leq c\\,\\left(\\|{\\operatorname{dev}\n\\operatorname{sym} P }\\|_{L^p(\\Omega,\\mathbb{R}^{3\\times3})} + \\|{\n\\operatorname{dev} \\operatorname{Curl} P\n}\\|_{L^p(\\Omega,\\mathbb{R}^{3\\times3})}\\right) \\] holds for all tensor fields\n$P\\in W^{1,\\,p}_0(\\operatorname{Curl}; \\Omega,\\mathbb{R}^{3\\times3})$, i.e.,\nfor all $P\\in W^{1,\\,p}(\\operatorname{Curl}; \\Omega,\\mathbb{R}^{3\\times3})$\nwith vanishing tangential trace $ P\\times \\nu=0 $ on $ \\partial\\Omega$ where\n$\\nu$ denotes the outward unit normal vector field to $\\partial\\Omega$ and\n$\\operatorname{dev} P := P -\\frac13 \\operatorname{tr}(P)\\,\\mathbb{1}_3$ denotes\nthe deviatoric (trace-free) part of $P$. We also show the norm equivalence \\[\n\\|{ P }\\|_{L^p(\\Omega,\\mathbb{R}^{3\\times3})}+\\|{\\operatorname{Curl} P\n}\\|_{L^p(\\Omega,\\mathbb{R}^{3\\times3})}\\leq c\\,\\left(\\|{\\operatorname{dev}\n\\operatorname{sym} P }\\|_{L^p(\\Omega,\\mathbb{R}^{3\\times3})} + \\|{\n\\operatorname{dev}\\operatorname{Curl} P\n}\\|_{L^p(\\Omega,\\mathbb{R}^{3\\times3})}\\right) \\] for tensor fields $P\\in\nW^{1,\\,p}_0(\\operatorname{Curl}; \\Omega,\\mathbb{R}^{3\\times3})$. These\nestimates also hold true for tensor fields with vanishing tangential trace only\non a relatively open (non-empty) subset $\\Gamma \\subseteq \\partial\\Omega$ of\nthe boundary.\n']","[('sobolev inequalities', 0.5352504253387451), ('sobolev inequality', 0.5067548751831055), ('weighted sobolev space', 0.4971587061882019), ('sobolev embeddings', 0.49603700637817383), ('weighted sobolev', 0.4643005132675171), ('sobolev spaces', 0.4299454689025879), ('trudinger moser type', 0.42915403842926025), ('korn inequality', 0.412677526473999), ('int_ omega nabla', 0.4120519161224365), ('korn type inequalities', 0.39334815740585327)]"
759,759,41,759_convex risk measures_coherent risk measures_risk measures_risk measures risk,"['convex risk measures', 'coherent risk measures', 'risk measures', 'risk measures risk', 'conditional risk measures', 'risk measure', 'convex risk', 'measures risk', 'risk aversion', 'stochastic dominance']","['Quasi-Logconvex Measures of Risk   This paper introduces and fully characterizes the novel class of\nquasi-logconvex measures of risk, to stand on equal footing with the rich class\nof quasi-convex measures of risk. Quasi-logconvex risk measures naturally\ngeneralize logconvex return risk measures, just like quasi-convex risk measures\ngeneralize convex monetary risk measures. We establish their dual\nrepresentation and analyze their taxonomy in a few (sub)classification results.\nFurthermore, we characterize quasi-logconvex risk measures in terms of\nproperties of families of acceptance sets and provide their law-invariant\nrepresentation. Examples and applications to portfolio choice and capital\nallocation are also discussed.\n', 'Higher-Order Stochastic Dominance Constraints in Optimization   This contribution examines optimization problems that involve stochastic\ndominance constraints. These problems have uncountably many constraints. We\ndevelop methods to solve the optimization problem by reducing the constraints\nto a finite set of test points needed to verify stochastic dominance. This\nimproves both theoretical understanding and computational efficiency. Our\napproach introduces two formulations of stochastic\ndominance$\\unicode{x2013}$one employs expectation operators and another based\non risk measures$\\unicode{x2013}$allowing for efficient verification processes.\nAdditionally, we develop an optimization framework incorporating these\nstochastic dominance constraints. Numerical results validate the robustness of\nour method, showcasing its effectiveness for solving higher-order stochastic\ndominance problems, with applications to fields such as portfolio optimization.\n', 'Star-shaped Risk Measures   In this paper monetary risk measures that are positively superhomogeneous,\ncalled star-shaped risk measures, are characterized and their properties\nstudied. The measures in this class, which arise when the controversial\nsubadditivity property of coherent risk measures is dispensed with and positive\nhomogeneity is weakened, include all practically used risk measures, in\nparticular, both convex risk measures and Value-at-Risk. From a financial\nviewpoint, our relaxation of convexity is necessary to quantify the capital\nrequirements for risk exposure in the presence of liquidity risk, competitive\ndelegation, or robust aggregation mechanisms. From a decision theoretical\nperspective, star-shaped risk measures emerge from variational preferences when\nrisk mitigation strategies can be adopted by a rational decision maker.\n']","[('convex risk measures', 0.6564469933509827), ('coherent risk measures', 0.6481988430023193), ('risk measures', 0.6305280923843384), ('risk measures risk', 0.6193419098854065), ('conditional risk measures', 0.6098084449768066), ('risk measure', 0.5960701107978821), ('convex risk', 0.5939001441001892), ('measures risk', 0.5888017416000366), ('risk aversion', 0.5750283598899841), ('stochastic dominance', 0.5640048980712891)]"
760,760,41,760_legendrian knots_legendrian knot_torus knots_knots links,"['legendrian knots', 'legendrian knot', 'torus knots', 'knots links', 'transverse knots', 'knot types', 'knots', 'legendrian embeddings', 'knot type', 'knots standard']","['Spaces of Legendrian cables and Seifert fibered links   We determine the homotopy type of the spaces of several Legendrian knots and\nlinks with the maximal Thurston--Bennequin invariant. In particular, we give a\nrecursive formula of the homotopy type of the space of Legendrian embeddings of\nsufficiently positive cables, and determine the homotopy type of the space of\nLegendrian embeddings of Seifert fibered links, which include all torus knots\nand links, in the standard contact 3-sphere, except when one of the link\ncomponents is a negative torus knot. In general, we prove that the space of\ncontact structures on the complement of a sufficiently positive Legendrian\ncable with the maximal Thurston-Bennequin invariant is homotopy equivalent to\nthe space of contact structures on the complement of the underlying Legendrian\nknot, and prove that the space of contact structures on a Legendrian Seifert\nfibered space over a compact oriented surface with boundary is contractible.\nFrom this result, we find infinitely many new components of the space of\nLegendrian embeddings in the standard contact 3-sphere that satisfy an\ninjective h-principle. These include the spaces of Legendrian embeddings of an\nalgebraic link with the maximal Thurston--Bennequin invariant. In particular,\nthe inclusion of these Legendrian embedding spaces into the corresponding\nformal Legendrian embedding spaces is a homotopy injection.\n', 'Legendrian Torus and Cable Links   We give a classification of Legendrian torus links. Along the way, we give\nthe first classification of infinite families of Legendrian links where some\nsmooth symmetries of the link cannot be realized by Legendrian isotopies. We\nalso give the first family of links that are non-destabilizable but do not have\nmaximal Thurston-Bennequin invariant and observe a curious distribution of\nLegendrian torus knots that can be realized as the components of a Legendrian\ntorus link. This classification of Legendrian torus links leads to a\nclassification of transversal torus links.\n  We also give a classification of Legendrian and transversal cable links of\nknot types that are uniformly thick and Legendrian simple. Here we see some\nsimilarities with the classification of Legendrian torus links but also some\ndifferences. In particular, we show that there are Legendrian representatives\nof cable links of any uniformly thick knot type for which no symmetries of the\ncomponents can be realized by a Legendrian isotopy, others where only cyclic\npermutations of the components can be realized, and yet others where all smooth\nsymmetries are realizable.\n', ""On The Cost Function Associated With Legendrian Knots   In this article, we introduce a non-negative integer-valued function that\nmeasures the obstruction for converting topological isotopy between two\nLegendrian knots into a Legendrian isotopy. We refer to this function as the\nCost function. We show that the Cost function induces a metric on the set of\ntopologically isotopic Legendrian knots. Hence, the set of topologically\nisotopic Legendrian knots can be seen as a graph with path-metric given by the\nCost function. Legendrian simple knot types are shown to be characterized using\nthe Cost function. We also get a quantitative version of Fuchs-Tabachnikov's\nTheorem that says any two Legendrian knots in $(\\mathbb{S}^3,\\xi_{std})$ in the\nsame topological knot type become Legendrian isotopic after sufficiently many\nstabilizations. We compute the Cost function for Legendrian simple knots (for\nexample torus knots) and we note the behavior of Cost function for twist knots\nand cables of torus knots (some of which are Legendrian non-simple). We also\nconstruct examples of Legendrian representatives of 2-bridge knots and compute\nthe Cost between them. Further, we investigate the behavior of the Cost\nfunction under the connect sum operation. We conclude with some questions about\nthe Cost function, its relation with the standard contact structure, and the\ntopological knot type.\n""]","[('legendrian knots', 0.7725590467453003), ('legendrian knot', 0.71596360206604), ('torus knots', 0.6701808571815491), ('knots links', 0.654635488986969), ('transverse knots', 0.6463832855224609), ('knot types', 0.6163192987442017), ('knots', 0.5995162725448608), ('legendrian embeddings', 0.586093544960022), ('knot type', 0.5774387121200562), ('knots standard', 0.5719473958015442)]"
761,761,41,761_algebraic riccati equations_algebraic riccati_riccati equations_riccati type,"['algebraic riccati equations', 'algebraic riccati', 'riccati equations', 'riccati type', 'riccati', 'equations low rank', 'matrix equations', 'numerical solutions', 'solving large scale', 'iteration solving']","[""Using $LDL^{T}$ factorizations in Newton's method for solving general\n  large-scale algebraic Riccati equations   Continuous-time algebraic Riccati equations can be found in many disciplines\nin different forms. In the case of small-scale dense coefficient matrices,\nstabilizing solutions can be computed to all possible formulations of the\nRiccati equation. This is not the case when it comes to large-scale sparse\ncoefficient matrices. In this paper, we provide a reformulation of the\nNewton-Kleinman iteration scheme for continuous-time algebraic Riccati\nequations using indefinite symmetric low-rank factorizations. This allows the\napplication of the method to the case of general large-scale sparse coefficient\nmatrices. We provide convergence results for several prominent realizations of\nthe equation and show in numerical examples the effectiveness of the approach.\n"", 'Stochastic algebraic Riccati equations are almost as easy as\n  deterministic ones theoretically   Stochastic algebraic Riccati equations, also known as rational algebraic\nRiccati equations, arising in linear-quadratic optimal control for stochastic\nlinear time-invariant systems, were considered to be not easy to solve.\nThe-state-of-art numerical methods most rely on differentiability or\ncontinuity, such as Newton-type method, LMI method, or homotopy method. In this\npaper, we will build a novel theoretical framework and reveal the intrinsic\nalgebraic structure appearing in this kind of algebraic Riccati equations. This\nstructure guarantees that to solve them is almost as easy as to solve\ndeterministic/classical ones, which will shed light on the theoretical analysis\nand numerical algorithm design for this topic.\n', 'Decoupled Structure-Preserving Doubling Algorithm with Truncation for\n  Large-Scale Algebraic Riccati Equations   In \\emph{Guo et al, arXiv:2005.08288}, we propose a decoupled form of the\nstructure-preserving doubling algorithm (dSDA). The method decouples the\noriginal two to four coupled recursions, enabling it to solve large-scale\nalgebraic Riccati equations and other related problems. In this paper, we\nconsider the numerical computations of the novel dSDA for solving large-scale\ncontinuous-time algebraic Riccati equations with low-rank structures (thus\npossessing numerically low-rank solutions). With the help of a new truncation\nstrategy, the rank of the approximate solution is controlled. Consequently,\nlarge-scale problems can be treated efficiently. Illustrative numerical\nexamples are presented to demonstrate and confirm our claims.\n']","[('algebraic riccati equations', 0.7079675793647766), ('algebraic riccati', 0.6592796444892883), ('riccati equations', 0.6387003064155579), ('riccati type', 0.48878201842308044), ('riccati', 0.4875314235687256), ('equations low rank', 0.4357582628726959), ('matrix equations', 0.4077972173690796), ('numerical solutions', 0.38484910130500793), ('solving large scale', 0.3401500880718231), ('iteration solving', 0.3243492543697357)]"
762,762,41,762_bilayer graphene_graphene_electronic properties_bilayer,"['bilayer graphene', 'graphene', 'electronic properties', 'bilayer', 'models twisted', 'band structure', 'continuum pde', 'twisting', 'twisted', 'interlayer']","[""Modeling of electronic dynamics in twisted bilayer graphene   We consider the problem of numerically computing the quantum dynamics of an\nelectron in twisted bilayer graphene. The challenge is that atomic-scale models\nof the dynamics are aperiodic for generic twist angles because of the\nincommensurability of the layers. The Bistritzer-MacDonald PDE model, which is\nperiodic with respect to the bilayer's moir\\'e pattern, has recently been shown\nto rigorously describe these dynamics in a parameter regime. In this work, we\nfirst prove that the dynamics of the tight-binding model of incommensurate\ntwisted bilayer graphene can be approximated by computations on finite domains.\nThe main ingredient of this proof is a speed of propagation estimate proved\nusing Combes-Thomas estimates. We then provide extensive numerical computations\nwhich clarify the range of validity of the Bistritzer-MacDonald model.\n"", 'Bistritzer-MacDonald dynamics in twisted bilayer graphene   The Bistritzer-MacDonald (BM) model, introduced in \\cite{Bistritzer2011},\nattempts to capture the electronic properties of twisted bilayer graphene\n(TBG), even at incommensurate twist angles, by an effective periodic model over\nthe bilayer moir\\\'e pattern. Starting from a tight-binding model, we identify a\nregime where the BM model emerges as the effective dynamics for electrons\nmodeled as wave-packets spectrally concentrated at the monolayer Dirac points,\nup to error that can be rigorously estimated. Using measured values of relevant\nphysical constants, we argue that this regime is realized in TBG at the first\n""magic"" angle.\n', 'Spectral characterization of magic angles in twisted bilayer graphene   Twisted bilayer graphene (TBG) has been experimentally observed to exhibit\nalmost flat bands when the twisting occurs at certain magic angles. In this\nletter, we report new results on the continuum model of twisted bilayer\ngraphene and its electronic band structure. Under we show that in the\napproximation of vanishing AA-coupling, the magic angles (at which there exist\nentirely flat bands) are given as the eigenvalues of a non-hermitian operator,\nand that all bands start squeezing exponentially fast as the angle $\\theta$\ntends to $0$. In particular, as the interaction potential changes, the dynamics\nof magic angles involves the non-physical complex eigenvalues. Using our new\nspectral characterization, we show that the equidistant scaling of inverse\nmagic angles, is special for the choice of tunnelling potentials in the\ncontinuum model, and is not protected by symmetries. While we also show that\nthe protection of zero-energy states holds in the continuum model as long as\nparticle-hole symmetry is preserved, we observe that the existence of flat\nbands and the exponential squeezing are special properties of the chiral model.\n']","[('bilayer graphene', 0.6471819877624512), ('graphene', 0.5365777015686035), ('electronic properties', 0.380154013633728), ('bilayer', 0.37099403142929077), ('models twisted', 0.3545806109905243), ('band structure', 0.33140894770622253), ('continuum pde', 0.31555360555648804), ('twisting', 0.309405118227005), ('twisted', 0.304121732711792), ('interlayer', 0.30244290828704834)]"
763,763,41,763_topological semigroups_commutative semigroups_semigroups_semigroups semigroup,"['topological semigroups', 'commutative semigroups', 'semigroups', 'semigroups semigroup', 'commutative semigroup', 'semigroup finite', 'inverse semigroups', 'semigroup', 'semigroup mathcal', 'inverse semigroup']","['Characterizing categorically closed commutative semigroups   Let $\\mathcal C$ be a class of Hausdorff topological semigroups which\ncontains all zero-dimensional Hausdorff topological semigroups. A semigroup $X$\nis called $\\mathcal C$-$closed$ if $X$ is closed in each topological semigroup\n$Y\\in \\mathcal C$ containing $X$ as a discrete subsemigroup; $X$ is\n$projectively$ $\\mathcal C$-$closed$ if for each congruence $\\approx$ on $X$\nthe quotient semigroup $X/_\\approx$ is $\\mathcal C$-closed. A semigroup $X$ is\ncalled $chain$-$finite$ if for any infinite set $I\\subseteq X$ there are\nelements $x,y\\in I$ such that $xy\\notin\\{x,y\\}$. We prove that a semigroup $X$\nis $\\mathcal C$-closed if it admits a homomorphism $h:X\\to E$ to a chain-finite\nsemilattice $E$ such that for every $e\\in E$ the semigroup $h^{-1}(e)$ is\n$\\mathcal C$-closed. Applying this theorem, we prove that a commutative\nsemigroup $X$ is $\\mathcal C$-closed if and only if $X$ is periodic,\nchain-finite, all subgroups of $X$ are bounded, and for any infinite set\n$A\\subseteq X$ the product $AA$ is not a singleton. A commutative semigroup $X$\nis projectively $\\mathcal C$-closed if and only if $X$ is chain-finite, all\nsubgroups of $X$ are bounded and the union $H(X)$ of all subgroups in $X$ has\nfinite complement $X\\setminus H(X)$.\n', 'Subgroups of categorically closed semigroups   Let $\\mathcal C$ be a class of topological semigroups. A semigroup $X$ is\ncalled (1) $\\mathcal C$-$closed$ if $X$ is closed in every topological\nsemigroup $Y\\in\\mathcal C$ containing $X$ as a discrete subsemigroup, (2)\n$ideally$ $\\mathcal C$-$closed$ if for any ideal $I$ in $X$ the quotient\nsemigroup $X/I$ is $\\mathcal C$-closed; (3) $absolutely$ $\\mathcal C$-$closed$\nif for any homomorphism $h:X\\to Y$ to a topological semigroup $Y\\in\\mathcal C$,\nthe image $h[X]$ is closed in $Y$, (4) $injectively$ $\\mathcal C$-$closed$\n(resp. $\\mathcal C$-$discrete$) if for any injective homomorphism $h:X\\to Y$ to\na topological semigroup $Y\\in\\mathcal C$, the image $h[X]$ is closed (resp.\ndiscrete) in $Y$. Let $\\mathsf{T_{\\!z}S}$ be the class of Tychonoff\nzero-dimensional topological semigroups. For a semigroup $X$ let $V\\!E(X)$ be\nthe set of all viable idempotents of $X$, i.e., idempotents $e$ such that the\ncomplement $X\\setminus\\frac{H_e}e$ of the set $\\frac{H_e}e=\\{x\\in X:xe=ex\\in\nH_e\\}$ is an ideal in $X$. We prove the following results: (i) for any ideally\n$\\mathsf{T_{\\!z}S}$-closed semigroup $X$ each subgroup of the center\n$Z(X)=\\{z\\in X:\\forall x\\in X\\;\\;(xz=zx)\\}$ is bounded; (ii) for any\n$\\mathsf{T_{\\!z}S}$-closed semigroup $X$, each subgroup of the ideal center\n$I\\!Z(X)=\\{z\\in Z(X):zX\\subseteq Z(X)\\}$ is bounded; (iii) for any\n$\\mathsf{T_{\\!z}S}$-discrete or injectively $\\mathsf{T_{\\!z}S}$-closed\nsemigroup $X$, every subgroup of $Z(X)$ is finite, (iv) for any viable\nidempotent $e$ in an ideally (and absolutely) $\\mathsf{T_{\\!z}S}$-closed\nsemigroup $X$, the maximal subgroup $H_e$ is ideally (and absolutely)\n$\\mathsf{T_{\\!z}S}$-closed and has bounded (and finite) center $Z(H_e)$.\n', 'Categorically closed unipotent semigroups   Let $\\mathcal C$ be a class of $T_1$ topological semigroups, containing all\nHausdorff zero-dimensional topological semigroups. A semigroup $X$ is $\\mathcal\nC$-$closed$ if $X$ is closed in any topological semigroup $Y\\in\\mathcal C$ that\ncontains $X$ as a discrete subsemigroup; $X$ is $injectively$ $\\mathcal\nC$-$closed$ if for any (injective) homomorphism $h:X\\to Y$ to a topological\nsemigroup $Y\\in\\mathcal C$, the image $h[X]$ is closed in $Y$. A semigroup $X$\nis $unipotent$ if it contains a unique idempotent. We prove that a unipotent\ncommutative semigroup $X$ is (injectively) $\\mathcal C$-closed if and only if\n$X$ is bounded, nonsingular (and group-finite). This characterization implies\nthat for every injectively $\\mathcal C$-closed unipotent semigroup $X$, the\ncenter $Z(X)$ is injectively $\\mathcal C$-closed.\n']","[('topological semigroups', 0.7071312665939331), ('commutative semigroups', 0.6077237725257874), ('semigroups', 0.5992830991744995), ('semigroups semigroup', 0.5834299325942993), ('commutative semigroup', 0.5752526521682739), ('semigroup finite', 0.5659367442131042), ('inverse semigroups', 0.56577467918396), ('semigroup', 0.5595993995666504), ('semigroup mathcal', 0.5409469604492188), ('inverse semigroup', 0.5229026079177856)]"
764,764,41,764_sobolev regularity_construct divergence free_divergence free_divergence free vector,"['sobolev regularity', 'construct divergence free', 'divergence free', 'divergence free vector', 'divergence free velocity', 'lagrangian flow', 'free velocity field', 'advection diffusion equations', 'free vector fields', 'sobolev']","['Regularity estimates for the flow of BV autonomous divergence free\n  vector fields in $\\mathbb{R}^2$   We consider the regular Lagrangian flow X associated to a bounded\ndivergence-free vector field b with bounded variation. We prove a\nLusin-Lipschitz regularity result for X and we show that the Lipschitz constant\ngrows at most linearly in time. As a consequence we deduce that both geometric\nand analytical mixing have a lower bound of order $t^{-1}$ as $t \\to \\infty$.\n', 'Nonuniqueness of weak solutions for the transport equation at critical\n  space regularity   We consider the linear transport equations driven by an incompressible flow\nin dimensions $d\\geq 3$. For divergence-free vector fields $u \\in L^1_t\nW^{1,q}$, the celebrated DiPerna-Lions theory of the renormalized solutions\nestablished the uniqueness of the weak solution in the class $L^\\infty_t L^p$\nwhen $\\frac{1}{p} + \\frac{1}{q} \\leq 1$. For such vector fields, we show that\nin the regime $\\frac{1}{p} + \\frac{1}{q} > 1$, weak solutions are not unique in\nthe class $ L^1_t L^p$. One crucial ingredient in the proof is the use of both\ntemporal intermittency and oscillation in the convex integration scheme.\n', 'Nonuniqueness of trajectories on a set of full measure for Sobolev\n  vector fields   In this paper, we resolve an important long-standing question of Alberti\n\\cite{alberti2012generalized} that asks if there is a continuous vector field\nwith bounded divergence and of class $W^{1, p}$ for some $p \\geq 1$ such that\nthe ODE with this vector field has nonunique trajectories on a set of initial\nconditions with positive Lebesgue measure? This question belongs to the realm\nof well-known DiPerna--Lions theory for Sobolev vector fields $W^{1, p}$. In\nthis work, we design a divergence-free vector field in $W^{1, p}$ with $p < d$\nsuch that the set of initial conditions for which trajectories are not unique\nis a set of full measure. The construction in this paper is quite explicit; we\ncan write down the expression of the vector field at any point in time and\nspace. Moreover, our vector field construction is novel. We build a vector\nfield $\\boldsymbol{u}$ and a corresponding flow map $X^{\\boldsymbol{u}}$ such\nthat after finite time $T > 0$, the flow map takes the whole domain\n$\\mathbb{T}^d$ to a Cantor set $\\mathcal{C}_\\Phi$, i.e., $X^{\\boldsymbol{u}}(T,\n\\mathbb{T}^d) = \\mathcal{C}_\\Phi$ and the Hausdorff dimension of this Cantor\nset is strictly less than $d$. The flow map $X^{\\boldsymbol{u}}$ constructed as\nsuch is not a regular Lagrangian flow. The nonuniqueness of trajectories on a\nfull measure set is then deduced from the existence of the regular Lagrangian\nflow in the DiPerna--Lions theory.\n']","[('sobolev regularity', 0.5262590646743774), ('construct divergence free', 0.5204858779907227), ('divergence free', 0.5127483010292053), ('divergence free vector', 0.5000909566879272), ('divergence free velocity', 0.4931786358356476), ('lagrangian flow', 0.4594106376171112), ('free velocity field', 0.4575958549976349), ('advection diffusion equations', 0.4193286895751953), ('free vector fields', 0.41890597343444824), ('sobolev', 0.4174342751502991)]"
765,765,41,765_branching brownian_branching random walks_brownian motions_brownian motion,"['branching brownian', 'branching random walks', 'brownian motions', 'brownian motion', 'brownian motion first', 'branching random', 'brownian motion random', 'brownian', 'brownian motion conditioned', 'processes branching']","['Refined Large Deviation Principle for Branching Brownian Motion\n  Conditioned to Have a Low Maximum   Conditioning a branching Brownian motion to have an atypically low maximum\nleads to a suppression of the branching mechanism. In this note, we consider a\nbranching Brownian motion conditioned to have a maximum below $\\sqrt{2}\\alpha\nt$ ($\\alpha<1$). We study the precise effects of an early/late first branching\ntime and a low/high first branching location under this condition. We do so by\nimposing additional constraints on the first branching time and location. We\nobtain large deviation estimates, as well as the optimal first branching time\nand location given the additional constraints.\n', ""A simple backward construction of Branching Brownian motion with large\n  displacement and applications   In this article, we study the extremal processes of branching Brownian\nmotions conditioned on having an unusually large maximum. The limiting point\nmeasures form a one-parameter family and are the decoration point measures in\nthe extremal processes of several branching processes, including branching\nBrownian motions with variable speed and multitype branching Brownian motions.\nWe give a new, alternative representation of these point measures and we show\nthat they form a continuous family. This also yields a simple probabilistic\nexpression for the constant that appears in the large deviation probability of\nhaving a large displacement. As an application, we show that Bovier and Hartung\n(2015)'s results about variable speed branching Brownian motion also describe\nthe extremal point process of branching Ornstein-Uhlenbeck processes.\n"", 'The extremal process of branching Brownian motion with absorption   In this paper, we study branching Brownian motion with absorption, in which\nparticles undergo Brownian motions with drift and are killed upon reaching the\norigin. We prove that the extremal process of this branching Brownian motion\nwith absorption converges to a random shifted decorated Poisson point process.\nFurthermore, we show that the law of the right-most particle converges to the\nlaw of a random shifted Gumbel random variable.\n']","[('branching brownian', 0.7834295630455017), ('branching random walks', 0.6463106274604797), ('brownian motions', 0.6194354295730591), ('brownian motion', 0.5872563719749451), ('brownian motion first', 0.5800737142562866), ('branching random', 0.5632962584495544), ('brownian motion random', 0.5598203539848328), ('brownian', 0.5502726435661316), ('brownian motion conditioned', 0.5205345749855042), ('processes branching', 0.5004357695579529)]"
766,766,41,766_shuffling_shuffles_shuffle_shuffled,"['shuffling', 'shuffles', 'shuffle', 'shuffled', 'deck cards', 'randomly shuffled', 'symmetric group generated', 'alternating group', 'properties random walk', 'random walk']","['A look at generalized perfect shuffles   Standard perfect shuffles involve splitting a deck of $2n$ cards into two\nstacks and interlacing the cards from the stacks. There are two ways that this\ninterlacing can be done, commonly referred to as an in shuffle and an out\nshuffle, respectively. In 1983, Diaconis, Graham, and Kantor determined the\npermutation group generated by in and out shuffles on a deck of $2n$ cards for\nall $n$. Diaconis et al. concluded their work by asking whether similar results\ncan be found for so-called generalized perfect shuffles. For these new\nshuffles, we split a deck of $mn$ cards into $m$ stacks and similarly interlace\nthe cards with an in $m$-shuffle or out $m$-shuffle (denoted $I_m$ and $O_m$,\nrespectively). In this paper, we find the structure of the group generated by\nthese two shuffles for a deck of $m^k$ cards, together with $m^y$-shuffles, for\nall possible values of $m$, $k$, and $y$. The group structure is completely\ndetermined by $k/\\gcd(y,k)$ and the parity of $y/\\gcd(y,k)$. In particular, the\ngroup structure is independent of the value of $m$.\n', 'Random Walks on the Symmetric Group: Cutoff for One-sided Transposition\n  Shuffles   In this thesis we introduce a new type of card shuffle called the one-sided\ntransposition shuffle. At each step a card is chosen uniformly from the pack\nand then transposed with another card chosen uniformly from below it. This\ndefines a random walk on the symmetric group generated by a distribution which\nis non-constant on the conjugacy class of transpositions. Nevertheless, we\nprovide an explicit formula for all eigenvalues of the shuffle by demonstrating\na useful correspondence between eigenvalues and standard Young tableaux. This\nallows us to prove the existence of a total-variation cutoff for the one-sided\ntransposition shuffle at time $n\\log n$. We also study weighted generalisations\nof the one-sided transposition shuffle called biased one-sided transposition\nshuffles. We compute the full spectrum for every biased one-sided transposition\nshuffle, and prove the existence of a total variation cutoff for certain\nchoices of weighted distribution. In particular, we recover the eigenvalues and\nwell known mixing time of the classical random transposition shuffle. We study\nthe hyperoctahedral group as an extension of the symmetric group, and formulate\nthe one-sided transposition shuffle and random transposition shuffle as random\nwalks on this new group. We determine the spectrum of each hyperoctahedral\nshuffle by developing a correspondence between their eigenvalues and standard\nYoung bi-tableaux. We prove that the one-sided transposition shuffle on the\nhyperoctahedral group exhibits a cutoff at $n\\log n$, the same time as its\nsymmetric group counterpart. We conjecture that this results extends to the\nbiased one-sided transposition shuffles and the random transposition shuffle on\nthe hyperoctahedral group.\n', 'Automorphism Shuffles for Graphs and Hypergraphs and Its Applications   In card-based cryptography, a deck of physical cards is used to achieve\nsecure computation. A shuffle, which randomly permutes a card-sequence along\nwith some probability distribution, ensures the security of a card-based\nprotocol. The authors proposed a new class of shuffles called graph shuffles,\nwhich randomly permutes a card-sequence by an automorphism of a directed graph\n(New Generation Computing 2022). For a directed graph $G$ with $n$ vertices and\n$m$ edges, such a shuffle could be implemented with pile-scramble shuffles with\n$2(n+m)$ cards. In this paper, we study graph shuffles and give an\nimplementation, an application, and a slight generalization of them. First, we\npropose a new protocol for graph shuffles with $2n+m$ cards. Second, as a new\napplication of graph shuffles, we show that any cyclic group shuffle, which is\na shuffle over a cyclic group, is a graph shuffle associated with some graph.\nThird, we define a hypergraph shuffle, which is a shuffle by an automorphism of\na hypergraph, and show that any hypergraph shuffle can also be implemented with\npile-scramble shuffles.\n']","[('shuffling', 0.6173900961875916), ('shuffles', 0.6160478591918945), ('shuffle', 0.5892134308815002), ('shuffled', 0.5630918741226196), ('deck cards', 0.49927374720573425), ('randomly shuffled', 0.4933948516845703), ('symmetric group generated', 0.42931467294692993), ('alternating group', 0.4261987507343292), ('properties random walk', 0.4213132858276367), ('random walk', 0.4165121912956238)]"
767,767,41,767_module categories finite_module categories_finite tensor categories_module category,"['module categories finite', 'module categories', 'finite tensor categories', 'module category', 'finite tensor category', 'tensor categories', 'finite categories', 'tensor category', 'categories module', 'algebra category']","['(Co)ends for representations of tensor categories   We generalize the notion of ends and coends in category theory to the realm\nof module categories over finite tensor categories. We call this new concept\n""module (co)end"". This tool allows us to give different proofs to several known\nresults in the theory of representations of finite tensor categories. As a new\napplication, we present a description of the relative Serre functor for module\ncategories in terms of a module coend, in a analogous way as a Morita invariant\ndescription of the Nakayama functor of abelian categories presented in [J.\nFuchs, G. Schaumann and C. Schweigert, Eilenberg-Watts calculus for finite\ncategories and a bimodule Radford S^4 theorem, Trans. Amer. Math. Soc. 373\n(2020), 1-40]\n', 'On unimodular module categories   Let $\\mathcal{C}$ be a finite tensor category and $\\mathcal{M}$ an exact left\n$\\mathcal{C}$-module category. We call $\\mathcal{M}$ unimodular if the finite\nmultitensor category ${\\sf Rex}_{\\mathcal{C}}(\\mathcal{M})$ of right exact\n$\\mathcal{C}$-module endofunctors of $\\mathcal{M}$ is unimodular. In this\narticle, we provide various characterizations, properties, and examples of\nunimodular module categories. As our first application, we employ unimodular\nmodule categories to construct (commutative) Frobenius algebra objects in the\nDrinfeld center of any finite tensor category. When $\\mathcal{C}$ is a pivotal\ncategory, and $\\mathcal{M}$ is a unimodular, pivotal left $\\mathcal{C}$-module\ncategory, the Frobenius algebra objects are symmetric as well. Our second\napplication is a classification of unimodular module categories over the\ncategory of finite dimensional representations of a finite dimensional Hopf\nalgebra; this answers a question of Shimizu. Using this, we provide an example\nof a finite tensor category whose categorical Morita equivalence class does not\ncontain any unimodular tensor category.\n', 'Reconstruction of module categories in the infinite and non-rigid\n  settings   By building on the notions of internal projective and injective objects in a\nmodule category introduced by Douglas, Schommer-Pries, and Snyder, we extend\nthe reconstruction theory for module categories of Etingof and Ostrik. More\nexplicitly, instead of algebra objects in finite tensor categories, we consider\nquasi-finite coalgebra objects in locally finite tensor categories. Moreover,\nwe show that module categories over non-rigid monoidal categories can be\nreconstructed via lax module monads, which generalize algebra objects. For the\nmonoidal category of finite-dimensional comodules over a (non-Hopf) bialgebra,\nwe give this result a more concrete form, realizing module categories as\ncategories of contramodules over Hopf trimodule algebras -- this specializes to\nour tensor-categorical results in the Hopf case. In this context, we also give\na precise Morita theorem, as well as an analogue of the Eilenberg--Watts\ntheorem for lax module monads and, as a consequence, for Hopf trimodule\nalgebras. Using lax module functors we give a categorical proof of the variant\nof the fundamental theorem of Hopf modules which applies to Hopf trimodules. We\nalso give a characterization of fusion operators for a Hopf monad as coherence\ncells for a module functor structure, using which we similarly reinterpret and\nreprove the Hopf-monadic fundamental theorem of Hopf modules due to\nBrugui\\`eres, Lack, and Virelizier.\n']","[('module categories finite', 0.6869061589241028), ('module categories', 0.6480965614318848), ('finite tensor categories', 0.6324117183685303), ('module category', 0.6234549283981323), ('finite tensor category', 0.6166245341300964), ('tensor categories', 0.6023873090744019), ('finite categories', 0.5782325267791748), ('tensor category', 0.5740914940834045), ('categories module', 0.5579630136489868), ('algebra category', 0.5419987440109253)]"
768,768,41,768_levi civita connection_levi civita connections_noncommutative geometry_geometry noncommutative,"['levi civita connection', 'levi civita connections', 'noncommutative geometry', 'geometry noncommutative', 'pseudo riemannian metrics', 'noncommutative tori', 'noncommutative differential', 'riemannian geometry', 'riemannian metrics', 'non commutative geometry']","['A new look at Levi-Civita connection in noncommutative geometry   We prove the existence and uniqueness of Levi-Civita connections for strongly\nsigma-compatible pseudo-Riemannian metrics on tame differential calculi. Such\npseudo-Riemannian metrics properly contain the classes of bilinear metrics as\nwell as their conformal deformations. This extends the previous results in\nreferences 9 and 10. Star-compatibility of Levi-Civita connections for bilinear\npseudo-Riemannian metrics are also discussed.\n', 'Levi-Civita connections for a class of spectral triples   We give a new definition of Levi-Civita connection for a noncommutative\npseudo-Riemannian metric on a noncommutative manifold given by a spectral\ntriple. We prove the existence-uniqueness result for a class of modules of one\nforms over a large class of noncommutative manifolds, including the matrix\ngeometry of the fuzzy 3-sphere, the quantum Heisenberg manifolds and\nConnes-Landi deformations of spectral triples on the Connes-Dubois\nViolette-Rieffel-deformation of a compact manifold equipped with a free toral\naction. It is interesting to note that in the example of the quantum Heisenberg\nmanifold, the definition of metric compatibility given in the paper by Frolich\net al failed to ensure the existence of a unique Levi-Civita connection. In the\ncase of the matrix geometry, the Levi-Civita connection that we get coincides\nwith the unique real torsion-less unitary connection obtained by Frolich et al.\n', 'Projective real calculi and Levi-Civita connections   Based on its central role in the framework of real calculi, the existence of\nthe Levi-Civita connection for real calculi over projective modules is studied,\nwith a special emphasis placed on the simple module of N-dimensional complex\nvectors over the algebra of complex N-by-N matrices. It is demonstrated that\nexistence of the Levi-Civita connection in this case depends on the Lie algebra\ng of hermitian derivations, and necessary and sufficient conditions for the\npossibility of constructing a real calculus for which there exists a\nLevi-Civita connection are given in this case. Furthermore, in the general case\nof real calculi over projective modules, necessary and sufficient conditions\nfor the existence of the Levi-Civita connection are given in terms of explicit\nprojection coefficients.\n']","[('levi civita connection', 0.5733750462532043), ('levi civita connections', 0.5695621371269226), ('noncommutative geometry', 0.5657165050506592), ('geometry noncommutative', 0.5515169501304626), ('pseudo riemannian metrics', 0.5323153734207153), ('noncommutative tori', 0.5199761390686035), ('noncommutative differential', 0.5164893865585327), ('riemannian geometry', 0.5010925531387329), ('riemannian metrics', 0.4937524199485779), ('non commutative geometry', 0.48645368218421936)]"
769,769,41,769_mobile edge computing_edge computing mec_edge computing_computation offloading,"['mobile edge computing', 'edge computing mec', 'edge computing', 'computation offloading', 'edge servers', 'edge server', 'edge network', 'mobile edge', 'task offloading', 'fog computing']","['Latency Minimization for Task Offloading in Hierarchical Fog-Computing\n  C-RAN Networks   Fog-computing network combines the cloud computing and fog access points\n(FAPs) equipped with mobile edge computing (MEC) servers together to support\ncomputation-intensive tasks for mobile users. However, as FAPs have limited\ncomputational capabilities and are solely assisted by a remote cloud center in\nthe baseband processing unit (BBU) of the cloud radio access (C-RAN) network,\nthe latency benefits of this fog-computing C-RAN network may be worn off when\nfacing a large number of offloading requests. In this paper, we investigate the\ndelay minimization problem for task offloading in a hierarchical fog-computing\nC-RAN network, which consists of three tiers of computational services: MEC\nserver in radio units, MEC server in distributed units, and the cloud computing\nin central units. The receive beamforming vectors, task allocation, computing\nspeed for offloaded tasks in each server and the transmission bandwidth split\nof fronthaul links are optimized by solving the formulated mixed integer\nprogramming problem. The simulation results validate the superiority of the\nproposed hierarchical fog-computing C-RAN network in terms of the delay\nperformance.\n', ""Distributed Offloading in Multi-Access Edge Computing Systems: A\n  Mean-Field Perspective   Multi-access edge computing (MEC) technology is a promising solution to\nassist power-constrained IoT devices by providing additional computing\nresources for time-sensitive tasks. In this paper, we consider the problem of\noptimal task offloading in MEC systems with due consideration of the timeliness\nand scalability issues under two scenarios of equitable and priority access to\nthe edge server (ES). In the first scenario, we consider a MEC system\nconsisting of $N$ devices assisted by one ES, where the devices can split task\nexecution between a local processor and the ES, with equitable access to the\nES. In the second scenario, we consider a MEC system consisting of one primary\nuser, $N$ secondary users and one ES. The primary user has priority access to\nthe ES while the secondary users have equitable access to the ES amongst\nthemselves. In both scenarios, due to the power consumption associated with\nutilizing the local resource and task offloading, the devices must optimize\ntheir actions. Additionally, since the ES is a shared resource, other users'\noffloading activity serves to increase latency incurred by each user. We thus\nmodel both scenarios using a non-cooperative game framework. However, the\npresence of a large number of users makes it nearly impossible to compute the\nequilibrium offloading policies for each user, which would require a\nsignificant information exchange overhead between users. Thus, to alleviate\nsuch scalability issues, we invoke the paradigm of mean-field games to compute\napproximate Nash equilibrium policies for each user using their local\ninformation, and further study the trade-offs between increasing information\nfreshness and reducing power consumption for each user. Using numerical\nevaluations, we show that our approach can recover the offloading trends\ndisplayed under centralized solutions, and provide additional insights into the\nresults obtained.\n"", 'Joint Task Offloading and Resource Allocation for Streaming Application\n  in Cooperative Mobile Edge Computing   Mobile edge computing (MEC) enables resource-limited IoT devices to complete\ncomputation-intensive or delay-sensitive task by offloading the task to\nadjacent edge server deployed at the base station (BS), thus becoming an\nimportant technology in 5G and beyond. Due to channel occlusion, some users may\nnot be able to access the computation capability directly from the BS.\nConfronted with this issue, many other devices in the MEC system can serve as\ncooperative nodes to collect the tasks of these users and further forward them\nto the BS. In this paper, we study a MEC system in which multiple users\ncontinuously generate the tasks and offload the tasks to the BS through a\ncooperative node. As the tasks are continuously generated, users should\nsimultaneously execute the task generation in the current time frame and the\ntask offloading of the last time frame, i.e. the task is processed in a\nstreaming model. To optimize the power consumption of the users and the\ncooperative node for finishing these streaming tasks, we investigate the\nduration of each step in finishing the tasks together with multiuser offloading\nratio and bandwidth allocation within two cases: the BS has abundant\ncomputation capacity (Case I) and the BS has limited computation capacity (Case\nII). For both cases, the formulated optimization problems are nonconvex due to\nfractional structure of the objective function and complicated variable\ncoupling. To address this issue, we propose optimal solution algorithm with low\ncomplexity. Finally, simulation is carried out to verify the effectiveness of\nthe proposed methods and reveal the performance of the considered system.\n']","[('mobile edge computing', 0.5753289461135864), ('edge computing mec', 0.5734701156616211), ('edge computing', 0.5569068193435669), ('computation offloading', 0.5407795906066895), ('edge servers', 0.5079414248466492), ('edge server', 0.4939107894897461), ('edge network', 0.49219655990600586), ('mobile edge', 0.483723521232605), ('task offloading', 0.4791466295719147), ('fog computing', 0.4669122099876404)]"
770,770,40,770_support vector machine_support vector machines_machines svms_vector machines svms,"['support vector machine', 'support vector machines', 'machines svms', 'vector machines svms', 'machines svm', 'vector machine svm', 'vector machines svm', 'machine svm', 'svm', 'svms']","['Nonlinear Kernel Support Vector Machine with 0-1 Soft Margin Loss   Recent advance on linear support vector machine with the 0-1 soft margin loss\n($L_{0/1}$-SVM) shows that the 0-1 loss problem can be solved directly.\nHowever, its theoretical and algorithmic requirements restrict us extending the\nlinear solving framework to its nonlinear kernel form directly, the absence of\nexplicit expression of Lagrangian dual function of $L_{0/1}$-SVM is one big\ndeficiency among of them. In this paper, by applying the nonparametric\nrepresentation theorem, we propose a nonlinear model for support vector machine\nwith 0-1 soft margin loss, called $L_{0/1}$-KSVM, which cunningly involves the\nkernel technique into it and more importantly, follows the success on\nsystematically solving its linear task. Its optimal condition is explored\ntheoretically and a working set selection alternating direction method of\nmultipliers (ADMM) algorithm is introduced to acquire its numerical solution.\nMoreover, we firstly present a closed-form definition to the support vector\n(SV) of $L_{0/1}$-KSVM. Theoretically, we prove that all SVs of $L_{0/1}$-KSVM\nare only located on the parallel decision surfaces. The experiment part also\nshows that $L_{0/1}$-KSVM has much fewer SVs, simultaneously with a decent\npredicting accuracy, when comparing to its linear peer $L_{0/1}$-SVM and the\nother six nonlinear benchmark SVM classifiers.\n', 'A Novel Loss Function-based Support Vector Machine for Binary\n  Classification   The previous support vector machine(SVM) including $0/1$ loss SVM, hinge loss\nSVM, ramp loss SVM, truncated pinball loss SVM, and others, overlooked the\ndegree of penalty for the correctly classified samples within the margin. This\noversight affects the generalization ability of the SVM classifier to some\nextent. To address this limitation, from the perspective of confidence margin,\nwe propose a novel Slide loss function ($\\ell_s$) to construct the support\nvector machine classifier($\\ell_s$-SVM). By introducing the concept of proximal\nstationary point, and utilizing the property of Lipschitz continuity, we derive\nthe first-order optimality conditions for $\\ell_s$-SVM. Based on this, we\ndefine the $\\ell_s$ support vectors and working set of $\\ell_s$-SVM. To\nefficiently handle $\\ell_s$-SVM, we devise a fast alternating direction method\nof multipliers with the working set ($\\ell_s$-ADMM), and provide the\nconvergence analysis. The numerical experiments on real world datasets confirm\nthe robustness and effectiveness of the proposed method.\n', ""Chance constrained conic-segmentation support vector machine with\n  uncertain data   Support vector machines (SVM) is one of the well known supervised classes of\nlearning algorithms. Furthermore, the conic-segmentation SVM (CS-SVM) is a\nnatural multiclass analogue of the standard binary SVM, as CS-SVM models are\ndealing with the situation where the exact values of the data points are known.\nThis paper studies CS-SVM when the data points are uncertain or mislabelled.\nWith some properties known for the distributions, a chance-constrained CS-SVM\napproach is used to ensure the small probability of misclassification for the\nuncertain data. The geometric interpretation is presented to show how CS-SVM\nworks. Finally, we present experimental results to investigate the chance\nconstrained CS-SVM's performance.\n""]","[('support vector machine', 0.6449176073074341), ('support vector machines', 0.6419526934623718), ('machines svms', 0.6378724575042725), ('vector machines svms', 0.6313596963882446), ('machines svm', 0.6269855499267578), ('vector machine svm', 0.6261555552482605), ('vector machines svm', 0.6148266196250916), ('machine svm', 0.6136702299118042), ('svm', 0.5842292308807373), ('svms', 0.5740353465080261)]"
771,771,40,771_network nodes_gossip_neighboring nodes_communicate neighbors,"['network nodes', 'gossip', 'neighboring nodes', 'communicate neighbors', 'nodes network', 'gossiping', 'information nodes', 'nodes', 'dissemination', 'source nodes']","['Age of Gossip on Generalized Rings   We consider a gossip network consisting of a source forwarding updates and\n$n$ nodes placed geometrically in a ring formation. Each node gossips with\n$f(n)$ nodes on either side, thus communicating with $2f(n)$ nodes in total.\n$f(n)$ is a sub-linear, non-decreasing and positive function. The source keeps\nupdates of a process, that might be generated or observed, and shares them with\nthe nodes in the ring network. The nodes in the ring network communicate with\ntheir neighbors and disseminate these version updates using a push-style gossip\nstrategy. We use the version age metric to quantify the timeliness of\ninformation at the nodes. Prior to this work, it was shown that the version age\nscales as $O(n^{\\frac{1}{2}})$ in a ring network, i.e., when $f(n)=1$, and as\n$O(\\log{n})$ in a fully-connected network, i.e., when $2f(n)=n-1$. In this\npaper, we find an upper bound for the average version age for a set of nodes in\nsuch a network in terms of the number of nodes $n$ and the number of gossiped\nneighbors $2 f(n)$. We show that if $f(n) = \\Omega(\\frac{n}{\\log^2{n}})$, then\nthe version age still scales as $\\theta(\\log{n})$. We also show that if $f(n)$\nis a rational function, then the version age also scales as a rational\nfunction. In particular, if $f(n)=n^\\alpha$, then version age is\n$O(n^\\frac{1-\\alpha}{2})$. Finally, through numerical calculations we verify\nthat, for all practical purposes, if $f(n) = \\Omega(n^{0.6})$, the version age\nscales as $O(\\log{n})$.\n', 'ASUMAN: Age Sense Updating Multiple Access in Networks   We consider a fully-connected wireless gossip network which consists of a\nsource and $n$ receiver nodes. The source updates itself with a Poisson process\nand also sends updates to the nodes as Poisson arrivals. Upon receiving the\nupdates, the nodes update their knowledge about the source. The nodes gossip\nthe data among themselves in the form of Poisson arrivals to disperse their\nknowledge about the source. The total gossiping rate is bounded by a\nconstraint. The goal of the network is to be as timely as possible with the\nsource. In this work, we propose ASUMAN, a distributed opportunistic gossiping\nscheme, where after each time the source updates itself, each node waits for a\ntime proportional to its current age and broadcasts a signal to the other nodes\nof the network. This allows the nodes in the network which have higher age to\nremain silent and only the low-age nodes to gossip, thus utilizing a\nsignificant portion of the constrained total gossip rate. We calculate the\naverage age for a typical node in such a network with symmetric settings and\nshow that the theoretical upper bound on the age scales as $O(1)$. ASUMAN, with\nan average age of $O(1)$, offers significant gains compared to a system where\nthe nodes just gossip blindly with a fixed update rate in which case the age\nscales as $O(\\log n)$.\n', ""Age-Aware Gossiping in Network Topologies   We consider a fully-connected wireless gossip network which consists of a\nsource and $n$ receiver nodes. The source updates itself with a Poisson process\nand also sends updates to the nodes as Poisson arrivals. Upon receiving the\nupdates, the nodes update their knowledge about the source. The nodes gossip\nthe data among themselves in the form of Poisson arrivals to disperse their\nknowledge about the source. The total gossiping rate is bounded by a\nconstraint. The goal of the network is to be as timely as possible with the\nsource. We propose a scheme which we coin \\emph{age sense updating multiple\naccess in networks (ASUMAN)}, which is a distributed opportunistic gossiping\nscheme, where after each time the source updates itself, each node waits for a\ntime proportional to its current age and broadcasts a signal to the other nodes\nof the network. This allows the nodes in the network which have higher age to\nremain silent and only the low-age nodes to gossip, thus utilizing a\nsignificant portion of the constrained total gossip rate. We calculate the\naverage age for a typical node in such a network with symmetric settings, and\nshow that the theoretical upper bound on the age scales as $O(1)$. ASUMAN, with\nan average age of $O(1)$, offers significant gains compared to a system where\nthe nodes just gossip blindly with a fixed update rate, in which case the age\nscales as $O(\\log n)$. Further, we analyzed the performance of ASUMAN for\nfractional, finitely connected, sublinear and hierarchical cluster networks.\nFinally, we show that the $O(1)$ age scaling can be extended to asymmetric\nsettings as well. We give an example of power law arrivals, where nodes' ages\nscale differently but follow the $O(1)$ bound.\n""]","[('network nodes', 0.4799240529537201), ('gossip', 0.4629516005516052), ('neighboring nodes', 0.4588111937046051), ('communicate neighbors', 0.4378313422203064), ('nodes network', 0.436901330947876), ('gossiping', 0.42764124274253845), ('information nodes', 0.41998952627182007), ('nodes', 0.4146880507469177), ('dissemination', 0.3904307782649994), ('source nodes', 0.3890054523944855)]"
772,772,40,772_entropy power inequality_entropy inequality_inequality entropy_entropy inequalities,"['entropy power inequality', 'entropy inequality', 'inequality entropy', 'entropy inequalities', 'bounds entropy', 'generalized entropy', 'proof entropy', 'min entropy', 'entropy power', 'enyi entropy']","['On the problem of reversibility of the entropy power inequality   As was shown recently by the authors, the entropy power inequality can be\nreversed for independent summands with sufficiently concave densities, when the\ndistributions of the summands are put in a special position. In this note it is\nproved that reversibility is impossible over the whole class of convex\nprobability distributions. Related phenomena for identically distributed\nsummands are also discussed.\n', 'Two remarks on generalized entropy power inequalities   This note contributes to the understanding of generalized entropy power\ninequalities. Our main goal is to construct a counter-example regarding\nmonotonicity and entropy comparison of weighted sums of independent identically\ndistributed log-concave random variables. We also present a complex analogue of\na recent dependent entropy power inequality of Hao and Jog, and give a very\nsimple proof.\n', ""Prove Costa's Entropy Power Inequality and High Order Inequality for\n  Differential Entropy with Semidefinite Programming   Costa's entropy power inequality is an important generalization of Shannon's\nentropy power inequality. Related with Costa's entropy power inequality and a\nconjecture proposed by McKean in 1966, Cheng-Geng recently conjectured that\n$D(m,n): (-1)^{m+1}(\\partial^m/\\partial^m t)H(X_t)\\ge0$, where $X_t$ is the\n$n$-dimensional random variable in Costa's entropy power inequality and\n$H(X_t)$ the differential entropy of $X_t$. $D(1,n)$ and $D(2,n)$ were proved\nby Costa as consequences of Costa's entropy power inequality. Cheng-Geng proved\n$D(3,1)$ and $D(4,1)$. In this paper, we propose a systematical procedure to\nprove $D(m,n)$ and Costa's entropy power inequality based on semidefinite\nprogramming. Using software packages based on this procedure, we prove $D(3,n)$\nfor $n=2,3,4$ and give a new proof for Costa's entropy power inequality. We\nalso show that with the currently known constraints, $D(5,1)$ and $D(4,2)$\ncannot be proved with the procedure.\n""]","[('entropy power inequality', 0.8122025728225708), ('entropy inequality', 0.7987484335899353), ('inequality entropy', 0.7908479571342468), ('entropy inequalities', 0.7793954610824585), ('bounds entropy', 0.7008492946624756), ('generalized entropy', 0.6614972352981567), ('proof entropy', 0.6282062530517578), ('min entropy', 0.5982999205589294), ('entropy power', 0.590056836605072), ('enyi entropy', 0.5703683495521545)]"
773,773,40,773_fractional heat equations_existence solutions fractional_semilinear heat equations_fractional heat,"['fractional heat equations', 'existence solutions fractional', 'semilinear heat equations', 'fractional heat', 'fractional semilinear', 'heat fractional', 'semilinear heat', 'fractional parabolic equations', 'cauchy fractional', 'fractional laplacian']","['Existence of solutions to a fractional semilinear heat equation in\n  uniformly local weak Zygmund type spaces   In this paper we introduce uniformly local weak Zygmund type spaces, and\nobtain an optimal sufficient condition for the existence of solutions to the\ncritical fractional semilinear heat equation.\n', 'Existence of solutions to the fractional semilinear heat equation with a\n  singular inhomogeneous term   We study the existence of solutions to the fractional semilinear heat\nequation with a singular inhomogeneous term. For this aim, we establish decay\nestimates of the fractional heat semigroup in several uniformly local Zygumnd\nspaces. Furthermore, we apply the real interpolation method in uniformly local\nZygmund spaces to obtain sharp integral estimates on the inhomogeneous term and\nthe nonlinear term. This enables us to find sharp sufficient conditions for the\nexistence of solutions to the fractional semilinear heat equation with a\nsingular inhomogeneous term.\n', 'On a Fujita critical time-fractional semilinear heat equation in the\n  uniformly local weak Zygmund type space   In this paper, we derive sufficient conditions on initial data for the\nlocal-in-time solvability of a time-fractional semilinear heat equation with\nthe Fujita exponent in a uniformly local weak Zygmund type space. It is known\nthat the time-fractional problem with the Fujita exponent in the scale critical\nspace $L^1(\\mathbb{R}^N)$ exhibits the local-in-time solvability in contrast to\nthe unsolvability of the Fujita critical classical semilinear heat equation.\nOur new sufficient conditions take into account the fine structure of\nsingularities of the initial data, in order to show a natural correspondance\nbetween the time-fractional and the classical case for the local-in-time\nsolvability. We also apply our arguments to life span estimates for some\ntypical initial data.\n']","[('fractional heat equations', 0.682754397392273), ('existence solutions fractional', 0.6342089772224426), ('semilinear heat equations', 0.6184697151184082), ('fractional heat', 0.593367338180542), ('fractional semilinear', 0.5707215666770935), ('heat fractional', 0.5600273609161377), ('semilinear heat', 0.532633900642395), ('fractional parabolic equations', 0.5314821600914001), ('cauchy fractional', 0.5179908275604248), ('fractional laplacian', 0.5058573484420776)]"
774,774,40,774_gaussian multiplicative chaos_multiplicative chaos_gaussian multiplicative_fractional gaussian,"['gaussian multiplicative chaos', 'multiplicative chaos', 'gaussian multiplicative', 'fractional gaussian', 'gaussian free', 'correlated gaussian field', 'gaussian fields', 'non gaussian', 'correlated gaussian', 'gaussian field']","['Absolute continuity of non-Gaussian and Gaussian multiplicative chaos\n  measures   In this article, we consider the multiplicative chaos measure associated to\nthe log-correlated random Fourier series, or random wave model, with i.i.d.\ncoefficients taken from a general class of distributions. This measure was\nshown to be non-degenerate when the inverse temperature is subcritical by\nJunnila (Int. Math. Res. Not. 2020 (2020), no. 19, 6169-6196). When the\ncoefficients are Gaussian, this measure is an example of a Gaussian\nmultiplicative chaos (GMC), a well-studied universal object in the study of\nlog-correlated fields. In the case of non-Gaussian coefficients, the resulting\nchaos is not a GMC in general. However, for inverse temperature inside the\n$L^1$-regime, we construct a coupling between the non-Gaussian multiplicative\nchaos measure and a GMC such that the two are almost surely mutually absolutely\ncontinuous.\n', 'Critical Gaussian Multiplicative Chaos revisited   We present new, short and self-contained proofs of the convergence (with an\nadequate renormalization) of four different sequences to the critical Gaussian\nMultiplicative Chaos:(a) the derivative martingale (b) the critical martingale\n(c) the exponential of the mollified field (d) the subcritical Gaussian\nMultiplicative Chaos.\n', 'Uniqueness of supercritical Gaussian multiplicative chaos   We show that, for general convolution approximations to a large class of\nlog-correlated Gaussian fields, the properly normalised supercritical Gaussian\nmultiplicative chaos measures converge stably to a nontrivial limit. This limit\ndepends on the choice of regularisation only through a multiplicative constant\nand can be characterised as an integrated atomic measure with a random\nintensity expressed in terms of the critical Gaussian multiplicative chaos.\n']","[('gaussian multiplicative chaos', 0.8656043410301208), ('multiplicative chaos', 0.7239304184913635), ('gaussian multiplicative', 0.6616069078445435), ('fractional gaussian', 0.513420820236206), ('gaussian free', 0.5089482665061951), ('correlated gaussian field', 0.49537694454193115), ('gaussian fields', 0.49262535572052), ('non gaussian', 0.4912465214729309), ('correlated gaussian', 0.4824831187725067), ('gaussian field', 0.46855074167251587)]"
775,775,40,775_groups acting trees_locally finite tree_acting trees_locally compact groups,"['groups acting trees', 'locally finite tree', 'acting trees', 'locally compact groups', 'graph groups', 'local actions', 'regular trees', 'compact groups', 'groups acting', 'trees']","[""Discrete (P)-closed Groups Acting On Trees   Reid-Smith recently parametrised groups acting on trees with Tits'\nindependence property (P) using graph-based combinatorial structures known as\nlocal action diagrams. Properties of the acting (topological) group, such as\nbeing locally compact, compactly generated or simple, are reflected in its\nlocal action diagram. In this article we provide necessary and sufficient\nconditions on the local action diagram for the associated group to be discrete.\n"", ""Groups acting on trees with Tits' independence property (P)   A 1970 article of J. Tits concerning groups acting on trees introduced an\nindependence property $(\\mathrm{P})$ as a condition to produce the first\nexamples of nonlinear nondiscrete locally compact simple groups, answering a\nquestion of J. P. Serre. This property has become very important in the recent\ndevelopment of the theory of totally disconnected, locally compact (t.d.l.c.)\ngroups, with the majority of new constructions of compactly generated simple\nt.d.l.c. groups using $(\\mathrm{P})$ or related ideas.\n  In this paper we aim to advance the local-to-global theory of groups acting\non trees by developing a `local action' complement to classical Bass--Serre\ntheory. We describe, for a closed group $G$ of automorphisms of a (not\nnecessarily locally finite) tree $T$ something called a local action diagram: a\ngraph decorated with the local actions of $G$. A local action diagram plays a\nrole in our theory that is analogous to a graph of groups in Bass--Serre\ntheory. In place of the universal cover of a graph of groups, we define the\nuniversal group of a local action diagram. In this context, the groups\n$\\mathbf{U}(F)$ and $\\mathbf{U}(F_1, F_2)$ play analogous roles to the HNN\nextension and amalgamated free product respectively in Bass--Serre theory. We\nthen show how to determine whether the universal group has certain properties,\nsuch as geometric density, compact generation and simplicity, directly from the\nlocal action diagram.\n  Our theory allows us to completely describe all closed groups of\nautomorphisms of trees with Tits' independence property $(\\mathrm{P})$: they\nare precisely the universal groups of local action diagrams.\n"", ""An introduction to the local-to-global behaviour of groups acting on\n  trees and the theory of local action diagrams   The primary tool for analysing groups acting on trees is Bass--Serre Theory.\nIt is comprised of two parts: a decomposition result, in which an action is\ndecomposed via a graph of groups, and a construction result, in which graphs of\ngroups are used to build examples of groups acting on trees. The usefulness of\nthe latter for constructing new examples of `large' (e.g. nondiscrete) groups\nacting on trees is severely limited. There is a pressing need for new examples\nof such groups as they play an important role in the theory of locally compact\ngroups. An alternative `local-to-global' approach to the study of groups acting\non trees has recently emerged, inspired by a paper of Marc Burger and Shahar\nMozes, based on groups that are `universal' with respect to some specified\n`local' action. In recent work, the authors of this survey article have\ndeveloped a general theory of universal groups of local actions, that behaves,\nin many respects, like Bass--Serre Theory. We call this the theory of local\naction diagrams. The theory is powerful enough to completely describe all\nclosed groups of automorphisms of trees that enjoy Tits' Independence Property\n(P).\n  This article is an introductory survey of the local-to-global behaviour of\ngroups acting on trees and the theory of local action diagrams. The article\ncontains many ideas for future research projects.\n""]","[('groups acting trees', 0.7603524327278137), ('locally finite tree', 0.5954053997993469), ('acting trees', 0.5268598794937134), ('locally compact groups', 0.5156349539756775), ('graph groups', 0.49419254064559937), ('local actions', 0.48831790685653687), ('regular trees', 0.4845559298992157), ('compact groups', 0.4804549515247345), ('groups acting', 0.4772711396217346), ('trees', 0.454892635345459)]"
776,776,40,776_secant varieties_secant variety_projective algebraic geometry_algebraic curves,"['secant varieties', 'secant variety', 'projective algebraic geometry', 'algebraic curves', 'smooth projective curves', 'projective curves', 'projective varieties', 'veronese varieties', 'projective curve genus', 'projective variety']","['Singularities and syzygies of secant varieties of nonsingular projective\n  curves   In recent years, the equations defining secant varieties and their syzygies\nhave attracted considerable attention. The purpose of the present paper is to\nconduct a thorough study on secant varieties of curves by settling several\nconjectures and revealing interaction between singularities and syzygies. The\nmain results assert that if the degree of the embedding line bundle of a\nnonsingular curve of genus $g$ is greater than $2g+2k+p$ for nonnegative\nintegers $k$ and $p$, then the $k$-th secant variety of the curve has normal Du\nBois singularities, is arithmetically Cohen--Macaulay, and satisfies the\nproperty $N_{k+2, p}$. In addition, the singularities of the secant varieties\nare further classified according to the genus of the curve, and the\nCastelnuovo--Mumford regularities are also obtained as well. As one of the main\ntechnical ingredients, we establish a vanishing theorem on the Cartesian\nproducts of the curve, which may have independent interests and may find\napplications elsewhere.\n', ""Syzygies of algebraic varieties through symmetric products of algebraic\n  curves   This is a survey paper on recent work on syzygies of algebraic varieties. We\ndiscuss the gonality conjecture on weight-one syzygies of algebraic curves,\nsyzygies of secant varieties of algebraic curves, syzygies of tangent\ndevelopable surfaces and Green's conjecture on syzygies of canonical curves,\nand asymptotic syzygies of algebraic varieties. All results considered in this\npaper were proven using the geometry of symmetric products of algebraic curves.\n"", ""Syzygies of secant varieties of smooth projective curves and gonality\n  sequences   The purpose of this paper is to prove that one can read off the gonality\nsequence of a smooth projective curve from syzygies of secant varieties of the\ncurve embedded by a line bundle of sufficiently large degree. More precisely,\ntogether with Ein-Niu-Park's theorem, our main result shows that the gonality\nsequence of a smooth projective curve completely determines the shape of the\nminimal free resolutions of secant varieties of the curve of sufficiently large\ndegree. This is a natural generalization of the gonality conjecture on syzygies\nof smooth projective curves established by Ein-Lazarsfeld and Rathmann to the\nsecant varieties.\n""]","[('secant varieties', 0.6719602942466736), ('secant variety', 0.6184091567993164), ('projective algebraic geometry', 0.5682641863822937), ('algebraic curves', 0.5675867795944214), ('smooth projective curves', 0.5574034452438354), ('projective curves', 0.5536336898803711), ('projective varieties', 0.5528025031089783), ('veronese varieties', 0.5501539707183838), ('projective curve genus', 0.546302080154419), ('projective variety', 0.539887011051178)]"
777,777,40,777_monoids whose_class monoids_monoids_monoids also,"['monoids whose', 'class monoids', 'monoids', 'monoids also', 'category monoids', 'monoids called', 'schreier extensions', 'inverse monoids', 'class monoid', 'extensions groups']","['Brauer and Jones tied monoids   We introduce a ramified monoid, attached to each Brauer--type monoid, that\nis, to the symmetric group, to the Jones and Brauer monoids among others.\nRamified monoids correspond to a class of tied monoids which arise from knot\ntheory and are interesting in itself. The ramified monoid attached to the\nsymmetric group is the Coxeter-like version of the so--called tied braid\nmonoid. We give a presentation of the ramified monoid attached to the Brauer\nmonoid. Also, we introduce and studied two tied-like monoids that cannot be\ndescribed as ramified monoids. However, these monoids can also be regarded as\ntied versions of the Jones and Brauer monoids.\n', '$\\lambda$-Semidirect Products of Inverse Monoids are Weakly Schreier\n  Extensions   A split extension of monoids with kernel k: N -> G, cokernel e: G -> H and\nsplitting s: H -> G is weakly Schreier if each element g in G can be written g\n= k(n)se(g) for some n in N. The characterization of weakly Schreier extensions\nallows them to be viewed as something akin to a weak semidirect product. The\nmotivating examples of such extensions are the Artin glueings of topological\nspaces and, of course, the Schreier extensions of monoids which they\ngeneralise. In this paper we show that the lambda-semidirect products of\ninverse monoids are also examples of weakly Schreier extensions. The\ncharacterization of weakly Schreier extensions sheds some light on the\nstructure of lambda-semidirect products. The set of weakly Schreier extensions\nbetween two monoids comes equipped with a natural poset structure, which\ninduces an order on the set of lambda-semidirect products between two inverse\nmonoids. We show that Artin glueings are in fact lambda-semidirect products and\ninspired by this identify a class of Artin-like lambda-semidirect products. We\nshow that joins exist for this special class of lambda-semidirect product in\nthe aforementioned order.\n', 'On semidirect products of quantale enriched monoids   We consider monoids equipped with a compatible quantale valued relation, to\nwhich we call quantale enriched monoids, and study semidirect products of such\nstructures. It is well-known that semidirect products of monoids are closely\nrelated to Schreier split extensions which, in the setting of monoids, play the\nrole of split extensions of groups. We will thus introduce certain split\nextensions of quantale enriched monoids, which generalize the classical\nSchreier split extensions of monoids, and investigate their connections with\nsemidirect products. We then restrict our study to a class of quantale enriched\nmonoids whose behavior mimics the fact that the preorder on a preordered group\nis completely determined by its cone of positive elements. Finally, we\ninstantiate our results for preordered monoids and compare them with existing\nliterature.\n']","[('monoids whose', 0.6210724711418152), ('class monoids', 0.6125859618186951), ('monoids', 0.6107214689254761), ('monoids also', 0.5909309387207031), ('category monoids', 0.5866255760192871), ('monoids called', 0.5864188075065613), ('schreier extensions', 0.5655524730682373), ('inverse monoids', 0.5648877620697021), ('class monoid', 0.5438125133514404), ('extensions groups', 0.5377154350280762)]"
778,778,40,778_landau equations_classical landau_solutions landau_landau operator,"['landau equations', 'classical landau', 'solutions landau', 'landau operator', 'linear landau', 'estimates landau', 'uniqueness smooth solutions', 'smooth solutions', 'landau work', 'landau']","['Regularizing effect of the spatially homogeneous Landau equation with\n  soft potential   This paper investigates the Cauchy problem of the spatially homogeneous\nLandau equation with soft potential under the perturbation framework to global\nequilibrium. We prove that the solution to the Cauchy problem exhibits\nanalyticity in the time variable and the Gelfand-Shilov regularizing effect in\nthe velocity variables.\n', 'Analytic smoothing effect of the time variable for the spatially\n  homogeneous Landau equation   In this work, we study the Cauchy problem of the spatially homogeneous Landau\nequation with hard potentials in a close-to-quilibrium framework. We prove that\nthe solution to the Cauchy problem enjoys the analytic regularizing effect of\nthe time variable with an L2 initial datum for positive time. So that the\nsmoothing effect of Cauchy problem for the spatially homogeneous Landau\nequation with hard potentials is exactly same as heat equation.\n', 'A remark about time-analyticity of the linear Landau equation with soft\n  potential   In this note, we study the Cauchy problem of the linear spatially homogeneous\nLandau equation with soft potentials. We prove that the solution to the Cauchy\nproblem enjoys the analytic regularizing effect of the time variable with an L2\ninitial datum for positive time. So that the smoothing effect of Cauchy problem\nfor the linear spatially homogeneous Landau equation with soft potentials is\nsimilar to the heat equation.\n']","[('landau equations', 0.5826202630996704), ('classical landau', 0.5481441020965576), ('solutions landau', 0.5346319675445557), ('landau operator', 0.5057514309883118), ('linear landau', 0.5036828517913818), ('estimates landau', 0.45490995049476624), ('uniqueness smooth solutions', 0.44653671979904175), ('smooth solutions', 0.4308541417121887), ('landau work', 0.42803171277046204), ('landau', 0.41982290148735046)]"
779,779,40,779_algebras primitive_jordan algebras_generated algebras_primitive idempotents,"['algebras primitive', 'jordan algebras', 'generated algebras', 'primitive idempotents', 'algebras generated', 'algebras jordan', 'jordan algebra', 'algebras introduced', 'vertex operator algebras', 'associative algebra generated']","['On primitive $3$-generated axial algebras of Jordan type   Axial algebras of Jordan type $\\eta$ are commutative algebras generated by\nidempotents whose adjoint operators have the minimal polynomial dividing\n$(x-1)x(x-\\eta)$, where $\\eta\\not\\in\\{0,1\\}$ is fixed, with restrictive\nmultiplication rules. These properties generalize the Pierce decompositions for\nidempotents in Jordan algebras, where $\\frac{1}{2}$ is replaced with $\\eta$. In\nparticular, Jordan algebras generated by idempotents are axial algebras of\nJordan type $\\frac{1}{2}$. If $\\eta\\neq\\frac{1}{2}$ then it is known that axial\nalgebras of Jordan type $\\eta$ are factors of the so-called Matsuo algebras\ncorresponding to 3-transposition groups.\n  We call the generating idempotents {\\it axes} and say that an axis is {\\it\nprimitive} if its adjoint operator has 1-dimensional 1-eigenspace. It is known\nthat a subalgebra generated by two primitive axes has dimension at most three.\nThe 3-generated case has been opened so far. We prove that any axial algebra of\nJordan type generated by three primitive axes has dimension at most nine. If\nthe dimension is nine and $\\eta=\\frac{1}{2}$ then we either show how to find a\nproper ideal in this algebra or prove that the algebra is isomorphic to certain\nJordan matrix algebras.\n', 'Structure of primitive axial algebras   ""Fusion rules"" are laws of multiplication among eigenspaces of an idempotent.\nThis terminology is relatively new and is closely related to primitive axial\nalgebras, introduced recently by Hall, Rehren, and Shpectorov. Axial algebras,\nin turn, are closely related to $3$-transposition groups and vertex operator\nalgebras.\n  In earlier work we studied primitive axial algebras, not necessarily\ncommutative, and showed that they all have Jordan type. In this paper, we show\nthat all finitely generated primitive axial algebras are direct sums of\nspecifically described flexible finite dimensional noncommutative algebras, and\ncommutative axial algebras generated by primitive axes of the same type. In\nparticular,all primitive axial algebras are flexible. They also have Frobenius\nforms. We give a precise description of all the primitive axes of axial\nalgebras generated by two primitive axes.\n', 'Double axes and subalgebras of Monster type in Matsuo algebras   Axial algebras are a class of commutative non-associative algebras generated\nby idempotents, called axes, with adjoint action semi-simple and satisfying a\nprescribed fusion law. Axial algebras were introduced by Hall, Rehren and\nShpectorov \\cite{hrs,hrs1} as a broad generalisation of Majorana algebras of\nIvanov, whose axioms were derived from the properties of the Griess algebra for\nthe Monster sporadic simple group. The class of axial algebras of Monster type\nincludes Majorana algebras for the Monster and many other sporadic simple\ngroups, Jordan algebras for classical and some exceptional simple groups, and\nMatsuo algebras corresponding to $3$-transposition groups. Thus, axial algebras\nof Monster type unify several strands in the theory of finite simple groups.\n  It is shown here that double axes, i.e., sums of two orthogonal axes in a\nMatsuo algebra, satisfy the fusion law of Monster type $(2\\eta,\\eta)$.\nPrimitive subalgebras generated by two single or double axes are completely\nclassified and $3$-generated primitive subalgebras are classified in one of the\nthree cases. These classifications further lead to the general flip\nconstruction outputting a rich variety of axial algebras of Monster type. An\napplication of the flip construction to the case of Matsuo algebras related to\nthe symmetric groups results in three new explicit infinite series of such\nalgebras.\n']","[('algebras primitive', 0.5305128693580627), ('jordan algebras', 0.5283951163291931), ('generated algebras', 0.5243547558784485), ('primitive idempotents', 0.5035462379455566), ('algebras generated', 0.4883899986743927), ('algebras jordan', 0.48405885696411133), ('jordan algebra', 0.47789037227630615), ('algebras introduced', 0.47192466259002686), ('vertex operator algebras', 0.47092074155807495), ('associative algebra generated', 0.4658561944961548)]"
780,780,40,780_radiotherapy_inverse optimization_radiation therapy_inspired optimization,"['radiotherapy', 'inverse optimization', 'radiation therapy', 'inspired optimization', 'optimization', 'treatment planning', 'robust optimization', 'optimizing', 'treatment plans', 'layer optimization']","[""Bio-Inspired Strategies for Optimizing Radiation Therapy under\n  Uncertainties   Radiation therapy is a critical component of cancer treatment. However, the\ndelivery of radiation poses inherent challenges, particularly in minimizing\nradiation exposure to healthy organs surrounding the tumor site. One\nsignificant contributing factor to this challenge is the patient's respiration,\nwhich introduces uncertainties in the precise targeting of radiation. Managing\nthese uncertainties during radiotherapy is essential to ensure effective tumor\ntreatment while minimizing the adverse effects on healthy tissues. This\nresearch addresses the crucial objective of achieving a balanced dose\ndistribution during radiation therapy under conditions of respiration\nuncertainty. To tackle this issue, we begin by developing a motion uncertainty\nmodel employing probability density functions that characterize breathing\nmotion patterns. This model forms the foundation for our efforts to optimize\nradiation dose delivery. Next, we employ three bio-inspired optimization\ntechniques: Cuckoo search optimization (CSO), flower pollination algorithm\n(FPA), and bat search Optimization (BSO). Our research evaluates the dose\ndistribution in Gy on both the tumor and healthy organs by applying these\nbio-inspired optimization methods to identify the most effective approach. This\nresearch ultimately aids in refining the strategies used in radiation therapy\nplanning under the challenging conditions posed by respiration uncertainty.\nThrough the application of bio-inspired optimization techniques and a\ncomprehensive evaluation of dose distribution, we seek to improve the precision\nand safety of radiation therapy, thereby advancing cancer treatment outcomes.\n"", 'Superiorization as a novel strategy for linearly constrained inverse\n  radiotherapy treatment planning   We apply the superiorization methodology to the intensity-modulated radiation\ntherapy (IMRT) treatment planning problem. In superiorization, linear voxel\ndose inequality constraints are the fundamental modeling tool within which a\nfeasibility-seeking projection algorithm will seek a feasible point. This\nalgorithm is then perturbed with gradient descent steps to reduce a nonlinear\nobjective function. Within the open-source inverse planning toolkit matRad, we\nimplement a prototypical algorithmic framework for superiorization using the\nwell-established Agmon, Motzkin, and Schoenberg (AMS) feasibility-seeking\nprojection algorithm and common nonlinear dose optimization objective\nfunctions. Based on this prototype, we apply superiorization to\nintensity-modulated radiation therapy treatment planning and compare its\nperformance with feasibility-seeking and nonlinear constrained optimization.\nFor these comparisons, we use the TG119 water phantom and a head-and-neck\npatient of the CORT dataset. Bare feasibility-seeking with AMS confirms\nprevious studies, showing it can find solutions that are nearly equivalent to\nthose found by the established piece-wise least-squares optimization approach.\nThe superiorization prototype solved the linearly constrained planning problem\nwith similar performance to that of a general-purpose nonlinear constrained\noptimizer while showing smooth convergence in both constraint proximity and\nobjective function reduction. Superiorization is a useful alternative to\nconstrained optimization in radiotherapy inverse treatment planning. Future\nextensions with other approaches to feasibility-seeking, e.g., with dose-volume\nconstraints and more sophisticated perturbations, may unlock its full potential\nfor high-performant inverse treatment planning.\n', ""Improving Observed Decisions Quality using Inverse Optimization: A\n  Radiation Therapy Treatment Planning Application   In many applied optimization settings, parameters that define the constraints\nmay not guarantee the best possible solution, and superior solutions might\nexist that are infeasible for the given parameter values. Removing such\nconstraints, re-optimizing, and evaluating the new solution may be\ninsufficient, as the optimizer's preferences in selecting the existing\nsolutions might be lost. To address this issue, we present an inverse\noptimization-based model that takes an observed solution as input and aims to\nimprove upon it by projecting onto desired hyperplanes or expanding the\nfeasible set while balancing the distance to the observed decision to preserve\nthe optimizer's preferences.\n  We demonstrate the applicability of the model in the context of radiation\ntherapy treatment planning, an essential component of cancer treatment.\nRadiation therapy treatment planning is typically guided by expert-driven\nguidelines that define the optimization problem but remain mostly general. Our\nmodel provides an automated framework that learns new plans from available\nplans based on given clinical criteria, optimizing the desired effect without\ncompromising the remaining constraints.\n  The proposed approach is applied to a cohort of four prostate cancer\npatients, and the results demonstrate improvements in dose-volume histograms\nwhile maintaining comparable target coverage to clinically acceptable plans. By\noptimizing the parameters of the treatment planning problem and exploring the\nPareto frontier, our methodology uncovers previously unattainable solutions\nthat enhance organ-at-risk sparing without sacrificing target coverage. The\nframework's ability to handle multiple organs-at-risk and various dose-volume\nconstraints highlights its flexibility and potential for application to diverse\nradiation therapy treatment planning scenarios.\n""]","[('radiotherapy', 0.5163388252258301), ('inverse optimization', 0.5101374387741089), ('radiation therapy', 0.5050907731056213), ('inspired optimization', 0.47276803851127625), ('optimization', 0.44761088490486145), ('treatment planning', 0.4378269910812378), ('robust optimization', 0.39747729897499084), ('optimizing', 0.38654401898384094), ('treatment plans', 0.37173888087272644), ('layer optimization', 0.37153545022010803)]"
781,781,40,781_vehicle uav_vehicles uavs_aerial vehicles uavs_uav,"['vehicle uav', 'vehicles uavs', 'aerial vehicles uavs', 'uav', 'aerial vehicle uav', 'uav aided', 'uav based', 'secure communication', 'unmanned aerial vehicle', 'unmanned aerial vehicles']","['Integrated Sensing, Navigation, and Communication for Secure UAV\n  Networks with a Mobile Eavesdropper   This paper proposes an integrated sensing, navigation, and communication\n(ISNC) framework for safeguarding unmanned aerial vehicle (UAV)-enabled\nwireless networks against a mobile eavesdropping UAV (E-UAV). To cope with the\nmobility of the E-UAV, the proposed framework advocates the dual use of\nartificial noise transmitted by the information UAV (I-UAV) for simultaneous\njamming and sensing to facilitate navigation and secure communication. In\nparticular, the I-UAV communicates with legitimate downlink ground users, while\navoiding potential information leakage by emitting jamming signals, and\nestimates the state of the E-UAV with an extended Kalman filter based on the\nbackscattered jamming signals. Exploiting the estimated state of the E-UAV in\nthe previous time slot, the I-UAV determines its flight planning strategy,\npredicts the wiretap channel, and designs its communication resource allocation\npolicy for the next time slot. To circumvent the severe coupling between these\nthree tasks, a divide-and-conquer approach is adopted. The online navigation\ndesign has the objective to minimize the distance between the I-UAV and a\npre-defined destination point considering kinematic and geometric constraints.\nSubsequently, given the predicted wiretap channel, the robust resource\nallocation design is formulated as an optimization problem to achieve the\noptimal trade-off between sensing and communication in the next time slot,\nwhile taking into account the wiretap channel prediction error and the\nquality-of-service (QoS) requirements of secure communication. Simulation\nresults demonstrate the superior performance of the proposed design compared\nwith baseline schemes and validate the benefits of integrating sensing and\nnavigation into secure UAV communication systems.\n', 'Gridded UAV Swarm for Secrecy Rate Maximization with Unknown\n  Eavesdropper   This paper considers grid formation of an unmanned aerial vehicle (UAV) swarm\nfor maximizing the secrecy rate in the presence of an unknown eavesdropper. In\nparticular, the UAV swarm performs coordinated beamforming onto the null space\nof the legitimate channel to jam the eavesdropper located at an unknown\nlocation. By nulling the channel between the legitimate receiver and the UAV\nswarm, we obtain an optimal trajectory and jamming power allocation for each\nUAV enabling wideband single ray beamforming to improve the secrecy rate.\nResults obtained demonstrate the effectiveness of the proposed UAV-aided\njamming scheme as well as the optimal number of UAVs in the swarm necessary to\nobserve a saturation effect in the secrecy rate. We also show the optimal\nradius of the unknown but constrained location of the eavesdropper.\n', 'Dual-UAV-Enabled Secure Communication and Sensing for A2G-ISAC Systems with Maneuverable Jamming In this paper, we propose a dual-unmanned aerial vehicle (UAV)-enabled secure communication and sensing (SCS) scheme for an air-to-ground integrated sensing and communication (ISAC) system, in which a dual-functional source UAV and jamming UAV collaborate to enhance both the secure communication and target sensing performance. From a perspective of hybrid monostatitc-bistatic radar, the jamming UAV maneuvers to aid the source UAV to detect multiple ground targets by emitting artificial noise, meanwhile interfering with the ground eavesdropper. Residual interference is considered to reflect the effects of imperfect successive interference cancellation (SIC) on the receive signal-plus-interference-to-noise ratios, which results in a degraded system performance. To maximize the average secrecy rate (ASR), the dual-UAV trajectory and dual-UAV beamforming are jointly optimized subject to the transmit power budget, UAV maneuvering constraint, and sensing requirements. To tackle the highly complicated non-convex ASR maximization problem, the dual-UAV trajectory and dual-UAV beamforming are optimized for the secure communication (SC) purpose and the SCS purpose, sequentially. In the SC phase, a block coordinate descent algorithm is proposed to optimize the dual-UAV trajectory and dual-UAV beamforming iteratively, using the trust-region successive convex approximation (SCA) and semidefinite relaxation (SDR) techniques. Then, a weighted distance minimization problem is formulated to determine the dual-UAV maneuvering positions suitable for the SCS purpose, which is solved by a heuristic greedy algorithm, followed by the joint optimization of source beamforming and jamming beamforming.']","[('vehicle uav', 0.5117055773735046), ('vehicles uavs', 0.49320393800735474), ('aerial vehicles uavs', 0.49272382259368896), ('uav', 0.4837051331996918), ('aerial vehicle uav', 0.47725850343704224), ('uav aided', 0.4731946289539337), ('uav based', 0.466840922832489), ('secure communication', 0.44078558683395386), ('unmanned aerial vehicle', 0.43154579401016235), ('unmanned aerial vehicles', 0.42967382073402405)]"
782,782,40,782_lattice walks_lattice paths_walks mathbb_walk models,"['lattice walks', 'lattice paths', 'walks mathbb', 'walk models', 'closed walks', 'generating functions', 'number walks', 'walks confined', 'avoiding walks', 'walks']","['Counting quadrant walks via Tutte\'s invariant method (extended abstract)   In the 1970s, Tutte developed a clever algebraic approach, based on certain\n""invariants"" , to solve a functional equation that arises in the enumeration of\nproperly colored triangulations. The enumeration of plane lattice walks\nconfined to the first quadrant is governed by similar equations, and has led in\nthe past decade to a rich collection of attractive results dealing with the\nnature (algebraic, D-finite or not) of the associated generating function,\ndepending on the set of allowed steps. We first adapt Tutte\'s approach to prove\n(or reprove) the algebraicity of all quadrant models known or conjectured to be\nalgebraic (with one small exception). This includes Gessel\'s famous model, and\nthe first proof ever found for one model with weighted steps. To be applicable,\nthe method requires the existence of two rational functions called invariant\nand decoupling function respectively. When they exist, algebraicity comes out\n(almost) automatically. Then, we move to an analytic viewpoint which has\nalready proved very powerful, leading in particular to integral expressions of\nthe generating function in the non-D-finite cases, as well as to proofs of\nnon-D-finiteness. We develop in this context a weaker notion of invariant. Now\nall quadrant models have invariants, and for those that have in addition a\ndecoupling function, we obtain integral-free expressions of the generating\nfunction, and a proof that this series is differentially algebraic (that is,\nsatisfies a non-linear differential equation).\n', ""Square lattice walks avoiding a quadrant   In the past decade, a lot of attention has been devoted to the enumera-tion\nof walks with prescribed steps confined to a convex cone. In two dimensions,\nthis means counting walks in the first quadrant of the plane (possibly after a\nlinear transformation). But what about walks in non-convex cones? We\ninvestigate the two most natural cases: first, square lattice walks avoiding\nthe negative quadrant Q 1 = {(i, j) : i \\textless{} 0 and j \\textless{} 0}, and\nthen, square lattice walks avoiding the West quadrant Q 2 = {(i, j) : i\n\\textless{} j and i \\textless{} --j}. In both cases, the generating function\nthat counts walks starting from the origin is found to differ from a simple\nD-finite series by an algebraic one. We also obtain closed form expressions for\nthe number of n-step walks ending at certain prescribed endpoints, as a sum of\nthree hypergeometric terms. One of these terms already appears in the\nenumeration of square lattice walks confined to the cone {(i, j) : i +j $\\ge$ 0\nand j $\\ge$ 0}, known as Gessel's walks. In fact, the enumeration of Gessel's\nwalks follows, by the reflection principle, from the enumeration of walks\nstarting from (--1, 0) and avoiding Q 1. Their generating function turns out to\nbe purely algebraic (as the generating function of Gessel's walks). Another\napproach to Gessel's walks consists in counting walks that start from (--1, 1)\nand avoid the West quadrant Q 2. The associated generating function is D-finite\nbut transcendental.\n"", 'Enumeration of three quadrant walks with small steps and walks on other\n  M-quadrant cones   We address the enumeration of walks with small steps confined to a\ntwo-dimensional cone, for example the quarter plane, three-quarter plane or the\nslit plane. In the quarter plane case, the solutions for unweighted step-sets\nare already well understood, in the sense that it is known precisely for which\ncases the generating function is algebraic, D-finite or D-algebraic, and exact\nintegral expressions are known in all cases. We derive similar results in a\nmuch more general setting: we enumerate walks on an $M$-quadrant cone for any\npositive integer $M$, with weighted steps starting at any point. The main\nbreakthrough in this work is the derivation of an analytic functional equation\nwhich characterises the generating function of these walks, which is analogous\nto one now used widely for quarter-plane walks. In the case $M=3$, which\ncorresponds to walks avoiding a quadrant, we provide exact integral-expression\nsolutions for walks with weighted small steps which determine the generating\nfunction ${\\sf C}(x,y;t)$ counting these walks. Moreover, for each step-set and\nstarting point of the walk we determine whether the generating function ${\\sf\nC}(x,y;t)$ is algebraic, D-finite or D-algebraic as a function of $x$ and $y$.\nIn fact we provide results of this type for any $M$-quadrant cone, showing that\nthis nature is the same for any odd $M$. For $M$ even we find that the\ngenerating functions counting these walks are D-finite in $x$ and $y$, and\nalgebraic if and only if the starting point of the walk is on the same axis as\nthe boundaries of the cone.\n']","[('lattice walks', 0.6080119013786316), ('lattice paths', 0.5252193808555603), ('walks mathbb', 0.5045416355133057), ('walk models', 0.4934549927711487), ('closed walks', 0.4872417151927948), ('generating functions', 0.46715396642684937), ('number walks', 0.4651678502559662), ('walks confined', 0.44139495491981506), ('avoiding walks', 0.42412376403808594), ('walks', 0.42194029688835144)]"
783,783,40,783_monoids groups_inverse monoids_one relator groups_relator groups,"['monoids groups', 'inverse monoids', 'one relator groups', 'relator groups', 'free monoids', 'monoids', 'inverse monoid', 'sub semigroups', 'monoids also', 'relator group']","['Membership problems for positive one-relator groups and one-relation\n  monoids   Motivated by approaches to the word problem for one-relation monoids arising\nfrom work of Adian and Oganesian (1987), Guba (1997), and Ivanov, Margolis and\nMeakin (2001), we study the submonoid and rational subset membership problems\nin one-relation monoids and in positive one-relator groups. We give the first\nknown examples of positive one-relator groups with undecidable submonoid\nmembership problem, and apply this to give the first known examples of\none-relation monoids with undecidable submonoid membership problem. We\nconstruct several infinite families of one-relation monoids with undecidable\nsubmonoid membership problem, including examples that are defined by relations\nof the form $w=1$ but which are not groups, and examples defined by relations\nof the form $u=v$ where both of $u$ and $v$ are non-empty. As a consequence we\nobtain a classification of the right-angled Artin groups that can arise as\nsubgroups of one-relation monoids. We also give examples of monoids with a\nsingle defining relation of the form $aUb = a$, and examples of the form\n$aUb=aVa$, with undecidable rational subset membership problem. We give a\none-relator group defined by a freely reduced word of the form $uv^{-1}$ with\n$u, v$ positive words, in which the prefix membership problem is undecidable.\nFinally, we prove the existence of a special two-relator inverse monoid with\nundecidable word problem, and in which both the relators are positive words. As\na corollary, we also find a positive two-relator group with undecidable prefix\nmembership problem. In proving these results, we introduce new methods for\nproving undecidability of the rational subset membership problem in monoids and\ngroups, including by finding suitable embeddings of certain trace monoids.\n', 'On groups of units of special and one-relator inverse monoids   We investigate the groups of units of one-relator and special inverse\nmonoids. These are inverse monoids which are defined by presentations where all\nthe defining relations are of the form $r=1$. We develop new approaches for\nfinding presentations for the group of units of a special inverse monoid, and\napply these methods to give conditions under which the group admits a\npresentation with the same number of defining relations as the monoid. In\nparticular our results give sufficient conditions for the group of units of a\none-relator inverse monoid to be a one-relator group. When these conditions are\nsatisfied these results give inverse semigroup theoretic analogues of classical\nresults of Adjan for one-relator monoids, and Makanin for special monoids. In\ncontrast, we show that in general these classical results do not hold for\none-relator and special inverse monoids. In particular, we show that there\nexists a one-relator special inverse monoid whose group of units is not a\none-relator group (with respect to any generating set), and we show that there\nexists a finitely presented special inverse monoid whose group of units is not\nfinitely presented.\n', 'New results on the prefix membership problem for one-relator groups   In this paper we prove several results regarding decidability of the\nmembership problem for certain submonoids in amalgamated free products and HNN\nextensions of groups. These general results are then applied to solve the\nprefix membership problem for a number of classes of one-relator groups which\nare low in the Magnus-Moldavanski\\u{\\i} hierarchy. Since the prefix membership\nproblem for one-relator groups is intimately related to the word problem for\none-relator special inverse monoids in the $E$-unitary case (as discovered in\n2001 by Ivanov, Margolis and Meakin), these results yield solutions of the word\nproblem for several new classes of one-relator special inverse monoids. In\nestablishing these results, we introduce a new theory of conservative\nfactorisations of words which provides a link between the prefix membership\nproblem of a one-relator group and the group of units of the corresponding\none-relator special inverse monoid. Finally, we exhibit the first example of a\none-relator group, defined by a reduced relator word, that has an undecidable\nprefix membership problem.\n']","[('monoids groups', 0.687175989151001), ('inverse monoids', 0.6255816221237183), ('one relator groups', 0.5755302309989929), ('relator groups', 0.5514199137687683), ('free monoids', 0.5461199879646301), ('monoids', 0.5438664555549622), ('inverse monoid', 0.5230687260627747), ('sub semigroups', 0.5077781677246094), ('monoids also', 0.49365079402923584), ('relator group', 0.4885125160217285)]"
784,784,40,784_learning meta learning_meta learning_meta learning algorithms_agnostic meta learning,"['learning meta learning', 'meta learning', 'meta learning algorithms', 'agnostic meta learning', 'meta learning framework', 'meta reinforcement learning', 'learning meta', 'based meta learning', 'meta learned', 'meta learning maml']","['Modeling and Optimization Trade-off in Meta-learning   By searching for shared inductive biases across tasks, meta-learning promises\nto accelerate learning on novel tasks, but with the cost of solving a complex\nbilevel optimization problem. We introduce and rigorously define the trade-off\nbetween accurate modeling and optimization ease in meta-learning. At one end,\nclassic meta-learning algorithms account for the structure of meta-learning but\nsolve a complex optimization problem, while at the other end domain randomized\nsearch (otherwise known as joint training) ignores the structure of\nmeta-learning and solves a single level optimization problem. Taking MAML as\nthe representative meta-learning algorithm, we theoretically characterize the\ntrade-off for general non-convex risk functions as well as linear regression,\nfor which we are able to provide explicit bounds on the errors associated with\nmodeling and optimization. We also empirically study this trade-off for\nmeta-reinforcement learning benchmarks.\n', 'Provable Generalization of Overparameterized Meta-learning Trained with\n  SGD   Despite the superior empirical success of deep meta-learning, theoretical\nunderstanding of overparameterized meta-learning is still limited. This paper\nstudies the generalization of a widely used meta-learning approach,\nModel-Agnostic Meta-Learning (MAML), which aims to find a good initialization\nfor fast adaptation to new tasks. Under a mixed linear regression model, we\nanalyze the generalization properties of MAML trained with SGD in the\noverparameterized regime. We provide both upper and lower bounds for the excess\nrisk of MAML, which captures how SGD dynamics affect these generalization\nbounds. With such sharp characterizations, we further explore how various\nlearning parameters impact the generalization capability of overparameterized\nMAML, including explicitly identifying typical data and task distributions that\ncan achieve diminishing generalization error with overparameterization, and\ncharacterizing the impact of adaptation learning rate on both excess risk and\nthe early stopping time. Our theoretical findings are further validated by\nexperiments.\n', 'Transfer Meta-Learning: Information-Theoretic Bounds and Information\n  Meta-Risk Minimization   Meta-learning automatically infers an inductive bias by observing data from a\nnumber of related tasks. The inductive bias is encoded by hyperparameters that\ndetermine aspects of the model class or training algorithm, such as\ninitialization or learning rate. Meta-learning assumes that the learning tasks\nbelong to a task environment, and that tasks are drawn from the same task\nenvironment both during meta-training and meta-testing. This, however, may not\nhold true in practice. In this paper, we introduce the problem of transfer\nmeta-learning, in which tasks are drawn from a target task environment during\nmeta-testing that may differ from the source task environment observed during\nmeta-training. Novel information-theoretic upper bounds are obtained on the\ntransfer meta-generalization gap, which measures the difference between the\nmeta-training loss, available at the meta-learner, and the average loss on\nmeta-test data from a new, randomly selected, task in the target task\nenvironment. The first bound, on the average transfer meta-generalization gap,\ncaptures the meta-environment shift between source and target task environments\nvia the KL divergence between source and target data distributions. The second,\nPAC-Bayesian bound, and the third, single-draw bound, account for this shift\nvia the log-likelihood ratio between source and target task distributions.\nFurthermore, two transfer meta-learning solutions are introduced. For the\nfirst, termed Empirical Meta-Risk Minimization (EMRM), we derive bounds on the\naverage optimality gap. The second, referred to as Information Meta-Risk\nMinimization (IMRM), is obtained by minimizing the PAC-Bayesian bound. IMRM is\nshown via experiments to potentially outperform EMRM.\n']","[('learning meta learning', 0.733390212059021), ('meta learning', 0.7333576083183289), ('meta learning algorithms', 0.7052072882652283), ('agnostic meta learning', 0.6955862045288086), ('meta learning framework', 0.6745530962944031), ('meta reinforcement learning', 0.6730764508247375), ('learning meta', 0.6429286599159241), ('based meta learning', 0.6326009631156921), ('meta learned', 0.6283875703811646), ('meta learning maml', 0.5746688842773438)]"
785,785,40,785_order symmetric tensors_symmetric tensors_tensors symmetric_tensor symmetric,"['order symmetric tensors', 'symmetric tensors', 'tensors symmetric', 'tensor symmetric', 'symmetric tensor', 'order tensors', 'tensors', 'square tensor', 'tensor', 'tensors applications']","['Copositivity for 3rd order symmetric tensors and applications   The strict opositivity of 4th order symmetric tensor may apply to detect\nvacuum stability of general scalar potential. For finding analytical\nexpressions of (strict) opositivity of 4th order symmetric tensor, we may\nreduce its order to 3rd order to better deal with it. So, it is provided that\nseveral analytically sufficient conditions for the copositivity of 3th order 2\ndimensional (3 dimensional) symmetric tensors. Subsequently, applying these\nconclusions to 4th order tensors, the analytically sufficient conditions of\ncopositivity are proved for 4th order 2 dimensional and 3 dimensional symmetric\ntensors. Finally, we apply these results to present analytical vacuum stability\nconditions for vacuum stability for $\\mathbb{Z}_3$ scalar dark matter.\n', 'The analytic criterion of strict copositivity for a 4th-order\n  3-dimensional tensor   This paper focuses on the strict copositivity analysis of 4th-order\n3-dimensional symmetric tensors. A necessary and sufficient condition is\nprovided for the strict copositivity of a fourth-order symmetric tensor.\nSubsequently, building upon this conclusion, we discuss the strict copositivity\nof fourth-order three-dimensional symmetric tensors with its entries $\\pm 1,\n0$, and further build their necessary and sufficient conditions. Utilizing\nthese theorems, we can effectively verify the strict copositivity of a general\nfourth-order three-dimensional symmetric tensors.\n', 'Analytical expressions of copositivity for 4th order symmetric tensors\n  and applications   In particle physics, scalar potentials have to be bounded from below in order\nfor the physics to make sense. The precise expressions of checking lower bound\nof scalar potentials are essential, which is an analytical expression of\nchecking copositivity and positive definiteness of tensors given by such scalar\npotentials. Because the tensors given by general scalar potential are 4th order\nand symmetric, our work mainly focuses on finding precise expressions to test\ncopositivity and positive definiteness of 4th order tensors in this paper.\nFirst of all, an analytically sufficient and necessary condition of positive\ndefiniteness is provided for 4th order 2 dimensional symmetric tensors. For 4th\norder 3 dimensional symmetric tensors, we give two analytically sufficient\nconditions of (strictly) cpositivity by using proof technique of reducing\norders or dimensions of such a tensor. Furthermore, an analytically sufficient\nand necessary condition of copositivity is showed for 4th order 2 dimensional\nsymmetric tensors. We also give several distinctly analytically sufficient\nconditions of (strict) copositivity for 4th order 2 dimensional symmetric\ntensors. Finally, we apply these results to check lower bound of scalar\npotentials, and to present analytical vacuum stability conditions for\npotentials of two real scalar fields and the Higgs boson.\n']","[('order symmetric tensors', 0.7039493322372437), ('symmetric tensors', 0.668860137462616), ('tensors symmetric', 0.6672618985176086), ('tensor symmetric', 0.6605485081672668), ('symmetric tensor', 0.6477981805801392), ('order tensors', 0.6430254578590393), ('tensors', 0.5817714929580688), ('square tensor', 0.5692453384399414), ('tensor', 0.5586532354354858), ('tensors applications', 0.5487313866615295)]"
786,786,40,786_convex feasibility_alternating projections_computing projections_alternating projection,"['convex feasibility', 'alternating projections', 'computing projections', 'alternating projection', 'projection onto closed', 'convex cones', 'projections', 'convex sets', 'projections onto', 'projections two']","['Projecting onto intersections of halfspaces and hyperplanes   It is well-known that the sequence of iterations of the composition of\nprojections onto closed affine subspaces converges linearly to the projection\nonto the intersection of the affine subspaces when the sum of the corresponding\nlinear subspaces is closed. Inspired by this, in this work, we systematically\nstudy the relation between the projection onto intersection of halfspaces and\nhyperplanes, and the composition of projections onto halfspaces and\nhyperplanes. In addition, as by-products, we provide the Karush-Kuhn-Tucker\nconditions for characterizing the optimal solution of convex optimization with\nfinitely many equality and inequality constraints in Hilbert spaces and\nconstruct an explicit formula for the projection onto the intersection of\nhyperplane and halfspace.\n', 'Infeasibility and error bound imply finite convergence of alternating\n  projections   This paper combines two ingredients in order to get a rather surprising\nresult on one of the most studied, elegant and powerful tools for solving\nconvex feasibility problems, the method of alternating projections (MAP). Going\nback to names such as Kaczmarz and von Neumann, MAP has the ability to track a\npair of points realizing minimum distance between two given closed convex sets.\nUnfortunately, MAP may suffer from arbitrarily slow convergence, and sublinear\nrates are essentially only surpassed in the presence of some Lipschitzian error\nbound, which is our first ingredient. The second one is a seemingly unfavorable\nand unexpected condition, namely, infeasibility. For two non-intersecting\nclosed convex sets satisfying an error bound, we establish finite convergence\nof MAP. In particular, MAP converges in finitely many steps when applied to a\npolyhedron and a hyperplane in the case in which they have empty intersection.\nMoreover, the farther the target sets lie from each other, the fewer are the\niterations needed by MAP for finding a best approximation pair. Insightful\nexamples and further theoretical and algorithmic discussions accompany our\nresults, including the investigation of finite termination of other projection\nmethods.\n', 'A variational approach to the alternating projections method   The 2-sets convex feasibility problem aims at finding a point in the nonempty\nintersection of two closed convex sets $A$ and $B$ in a Hilbert space $X$. The\nmethod of alternating projections is the simplest iterative procedure for\nfinding a solution and it goes back to von Neumann. In the present paper, we\nstudy some stability properties for this method in the following sense: we\nconsider two sequences of sets, each of them converging, with respect to the\nAttouch-Wets variational convergence, respectively, to $A$ and $B$. Given a\nstarting point $a_0$, we consider the sequences of points obtained by\nprojecting on the ""perturbed"" sets, i.e., the sequences $\\{a_n\\}$ and $\\{b_n\\}$\ngiven by $b_n=P_{B_n}(a_{n-1})$ and $a_n=P_{A_n}(b_n)$. Under appropriate\ngeometrical and topological assumptions on the intersection of the limit sets,\nwe ensure that the sequences $\\{a_n\\}$ and $\\{b_n\\}$ converge in norm to a\npoint in the intersection of $A$ and $B$. In particular, we consider both when\nthe intersection $A\\cap B$ reduces to a singleton and when the interior of $A\n\\cap B$ is nonempty. Finally we consider the case in which the limit sets $A$\nand $B$ are subspaces.\n']","[('convex feasibility', 0.5852498412132263), ('alternating projections', 0.5832872986793518), ('computing projections', 0.5717172622680664), ('alternating projection', 0.5508841872215271), ('projection onto closed', 0.5152748823165894), ('convex cones', 0.489655077457428), ('projections', 0.48550474643707275), ('convex sets', 0.4654832184314728), ('projections onto', 0.45954328775405884), ('projections two', 0.453887403011322)]"
787,787,39,787_mobile edge computing_multiple access noma_edge computing mec_computation offloading,"['mobile edge computing', 'multiple access noma', 'edge computing mec', 'computation offloading', 'edge computing', 'mobile edge', 'aided mobile edge', 'multiple access tdma', 'orthogonal multiple access', 'access noma']","['An Application-Driven Non-Orthogonal Multiple Access Enabled Computation\n  Offloading Scheme   To cope with the unprecedented surge in demand for data computing for the\napplications, the promising concept of multi-access edge computing (MEC) has\nbeen proposed to enable the network edges to provide closer data processing for\nmobile devices (MDs). Since enormous workloads need to be migrated, and MDs\nalways remain resource-constrained, data offloading from devices to the MEC\nserver will inevitably require more efficient transmission designs. The\nintegration of nonorthogonal multiple access (NOMA) technique with MEC has been\nshown to provide applications with lower latency and higher energy efficiency.\nHowever, existing designs of this type have mainly focused on the transmission\ntechnique, which is still insufficient. To further advance offloading\nperformance, in this work, we propose an application-driven NOMA enabled\ncomputation offloading scheme by exploring the characteristics of applications,\nwhere the common data of the application is offloaded through multi-device\ncooperation. Under the premise of successfully offloading the common data, we\nformulate the problem as the maximization of individual offloading throughput,\nwhere the time allocation and power control are jointly optimized. By using the\nsuccessive convex approximation (SCA) method, the formulated problem can be\niteratively solved. Simulation results demonstrate the convergence of our\nmethod and the effectiveness of the proposed scheme.\n', ""Task Offloading Optimization in NOMA-Enabled Multi-hop Mobile Edge\n  Computing System Using Conflict Graph   Resource allocation is investigated for offloading computational-intensive\ntasks in multi-hop mobile edge computing (MEC) system. The envisioned system\nhas both the cooperative access points (AP) with the computing capability and\nthe MEC servers. A user-device (UD) therefore first uploads a computing task to\nthe nearest AP, and the AP can either locally process the received task or\noffload to MEC server. In order to utilize the radio resource blocks (RRBs) in\nthe APs efficiently, we exploit the non-orthogonal multiple access for\noffloading the tasks from the UDs to the AP(s). For the considered NOMA-enabled\nmulti-hop MEC computing system, our objective is to minimize both the latency\nand energy consumption of the system jointly. Towards this goal, a joint\noptimization problem is formulated by taking the offloading decision of the\nAPs, the scheduling among the UDs, RRBs, and APs, and UDs' transmit power\nallocation into account. To solve this problem efficiently, (i) a conflict\ngraph-based approach is devised that solves the scheduling among the UDs, APs,\nand RRBs, the transmit power control, and the APs' computation resource\nallocation jointly, and (ii) a low-complexity pruning graph-based approach is\nalso devised. The efficiency of the proposed graph-based approaches over\nseveral benchmark schemes is verified via extensive simulations.\n"", 'Computation Efficiency Maximization in Wireless-Powered Mobile Edge\n  Computing Networks   Energy-efficient computation is an inevitable trend for mobile edge computing\n(MEC) networks. Resource allocation strategies for maximizing the computation\nefficiency are critically important. In this paper, computation efficiency\nmaximization problems are formulated in wireless-powered MEC networks under\nboth partial and binary computation offloading modes. A practical non-linear\nenergy harvesting model is considered. Both time division multiple access\n(TDMA) and non-orthogonal multiple access (NOMA) are considered and evaluated\nfor offloading. The energy harvesting time, the local computing frequency, and\nthe offloading time and power are jointly optimized to maximize the computation\nefficiency under the max-min fairness criterion. Two iterative algorithms and\ntwo alternative optimization algorithms are respectively proposed to address\nthe non-convex problems formulated in this paper. Simulation results show that\nthe proposed resource allocation schemes outperform the benchmark schemes in\nterms of user fairness. Moreover, a tradeoff is elucidated between the\nachievable computation efficiency and the total number of computed bits.\nFurthermore, simulation results demonstrate that the partial computation\noffloading mode outperforms the binary computation offloading mode and NOMA\noutperforms TDMA in terms of computation efficiency.\n']","[('mobile edge computing', 0.5390795469284058), ('multiple access noma', 0.5377629995346069), ('edge computing mec', 0.5108727216720581), ('computation offloading', 0.4910818338394165), ('edge computing', 0.4836416244506836), ('mobile edge', 0.47950857877731323), ('aided mobile edge', 0.4483322203159332), ('multiple access tdma', 0.44766658544540405), ('orthogonal multiple access', 0.44704920053482056), ('access noma', 0.4452827274799347)]"
788,788,39,788_robust sparse_sparse mean_robust estimation_matrix estimation,"['robust sparse', 'sparse mean', 'robust estimation', 'matrix estimation', 'robust covariance', 'covariance estimation', 'mean estimation', 'robust mean', 'estimator covariance matrix', 'estimation via']","['List-Decodable Covariance Estimation   We give the first polynomial time algorithm for \\emph{list-decodable\ncovariance estimation}. For any $\\alpha > 0$, our algorithm takes input a\nsample $Y \\subseteq \\mathbb{R}^d$ of size $n\\geq d^{\\mathsf{poly}(1/\\alpha)}$\nobtained by adversarially corrupting an $(1-\\alpha)n$ points in an i.i.d.\nsample $X$ of size $n$ from the Gaussian distribution with unknown mean $\\mu_*$\nand covariance $\\Sigma_*$. In $n^{\\mathsf{poly}(1/\\alpha)}$ time, it outputs a\nconstant-size list of $k = k(\\alpha)= (1/\\alpha)^{\\mathsf{poly}(1/\\alpha)}$\ncandidate parameters that, with high probability, contains a\n$(\\hat{\\mu},\\hat{\\Sigma})$ such that the total variation distance\n$TV(\\mathcal{N}(\\mu_*,\\Sigma_*),\\mathcal{N}(\\hat{\\mu},\\hat{\\Sigma}))<1-O_{\\alpha}(1)$.\nThis is the statistically strongest notion of distance and implies\nmultiplicative spectral and relative Frobenius distance approximation for\nparameters with dimension independent error. Our algorithm works more generally\nfor $(1-\\alpha)$-corruptions of any distribution $D$ that possesses low-degree\nsum-of-squares certificates of two natural analytic properties: 1)\nanti-concentration of one-dimensional marginals and 2) hypercontractivity of\ndegree 2 polynomials.\n  Prior to our work, the only known results for estimating covariance in the\nlist-decodable setting were for the special cases of list-decodable linear\nregression and subspace recovery due to Karmarkar, Klivans, and Kothari (2019),\nRaghavendra and Yau (2019 and 2020) and Bakshi and Kothari (2020). These\nresults need superpolynomial time for obtaining any subconstant error in the\nunderlying dimension. Our result implies the first polynomial-time \\emph{exact}\nalgorithm for list-decodable linear regression and subspace recovery that\nallows, in particular, to obtain $2^{-\\mathsf{poly}(d)}$ error in\npolynomial-time. Our result also implies an improved algorithm for clustering\nnon-spherical mixtures.\n', 'List-Decodable Mean Estimation in Nearly-PCA Time   Traditionally, robust statistics has focused on designing estimators tolerant\nto a minority of contaminated data. Robust list-decodable learning focuses on\nthe more challenging regime where only a minority $\\frac 1 k$ fraction of the\ndataset is drawn from the distribution of interest, and no assumptions are made\non the remaining data. We study the fundamental task of list-decodable mean\nestimation in high dimensions. Our main result is a new list-decodable mean\nestimation algorithm for bounded covariance distributions with optimal sample\ncomplexity and error rate, running in nearly-PCA time. Assuming the ground\ntruth distribution on $\\mathbb{R}^d$ has bounded covariance, our algorithm\noutputs a list of $O(k)$ candidate means, one of which is within distance\n$O(\\sqrt{k})$ from the truth. Our algorithm runs in time $\\widetilde{O}(ndk)$\nfor all $k = O(\\sqrt{d}) \\cup \\Omega(d)$, where $n$ is the size of the dataset.\nWe also show that a variant of our algorithm has runtime $\\widetilde{O}(ndk)$\nfor all $k$, at the expense of an $O(\\sqrt{\\log k})$ factor in the recovery\nguarantee. This runtime matches up to logarithmic factors the cost of\nperforming a single $k$-PCA on the data, which is a natural bottleneck of known\nalgorithms for (very) special cases of our problem, such as clustering\nwell-separated mixtures. Prior to our work, the fastest list-decodable mean\nestimation algorithms had runtimes $\\widetilde{O}(n^2 d k^2)$ and\n$\\widetilde{O}(nd k^{\\ge 6})$.\n  Our approach builds on a novel soft downweighting method, $\\mathsf{SIFT}$,\nwhich is arguably the simplest known polynomial-time mean estimation technique\nin the list-decodable learning setting. To develop our fast algorithms, we\nboost the computational cost of $\\mathsf{SIFT}$ via a careful ""win-win-win""\nanalysis of an approximate Ky Fan matrix multiplicative weights procedure we\ndevelop, which we believe may be of independent interest.\n', 'List-Decodable Sparse Mean Estimation via Difference-of-Pairs Filtering   We study the problem of list-decodable sparse mean estimation. Specifically,\nfor a parameter $\\alpha \\in (0, 1/2)$, we are given $m$ points in\n$\\mathbb{R}^n$, $\\lfloor \\alpha m \\rfloor$ of which are i.i.d. samples from a\ndistribution $D$ with unknown $k$-sparse mean $\\mu$. No assumptions are made on\nthe remaining points, which form the majority of the dataset. The goal is to\nreturn a small list of candidates containing a vector $\\widehat \\mu$ such that\n$\\| \\widehat \\mu - \\mu \\|_2$ is small. Prior work had studied the problem of\nlist-decodable mean estimation in the dense setting. In this work, we develop a\nnovel, conceptually simpler technique for list-decodable mean estimation. As\nthe main application of our approach, we provide the first sample and\ncomputationally efficient algorithm for list-decodable sparse mean estimation.\nIn particular, for distributions with ""certifiably bounded"" $t$-th moments in\n$k$-sparse directions and sufficiently light tails, our algorithm achieves\nerror of $(1/\\alpha)^{O(1/t)}$ with sample complexity $m =\n(k\\log(n))^{O(t)}/\\alpha$ and running time $\\mathrm{poly}(mn^t)$. For the\nspecial case of Gaussian inliers, our algorithm achieves the optimal error\nguarantee of $\\Theta (\\sqrt{\\log(1/\\alpha)})$ with quasi-polynomial sample and\ncomputational complexity. We complement our upper bounds with nearly-matching\nstatistical query and low-degree polynomial testing lower bounds.\n']","[('robust sparse', 0.4992574155330658), ('sparse mean', 0.48466089367866516), ('robust estimation', 0.48175203800201416), ('matrix estimation', 0.4620966911315918), ('robust covariance', 0.4551910161972046), ('covariance estimation', 0.45143476128578186), ('mean estimation', 0.44057518243789673), ('robust mean', 0.4266723692417145), ('estimator covariance matrix', 0.41610071063041687), ('estimation via', 0.39550453424453735)]"
789,789,39,789_difference sets_partial difference sets_combinatorial structures_difference group,"['difference sets', 'partial difference sets', 'combinatorial structures', 'difference group', 'groups combinatorial', 'sets groups', 'difference families', 'nonabelian groups', 'studied combinatorial', 'new constructions']","['On central difference sets in Suzuki $p$-groups of type $A$   In this paper, when the order of $\\theta$ is even, we prove that there exists\nno central difference sets in $A_2(m,\\theta)$ and establish some non-existence\nresults of central partial difference sets in $A_p(m,\\theta)$ with $p>2$. When\nthe order of $\\theta$ is odd, we construct central difference sets in\n$A_2(m,\\theta)$. Furthermore, we give some reduced linking systems of\ndifference sets in $A_2(m,\\theta)$ by using the difference sets we constructed.\nIn the case $p>2$, we construct Latin square type central partial difference\nsets in $A_p(m,\\theta)$ by a similar method.\n', ""Combinatorial transfer: a new method for constructing infinite families\n  of nonabelian difference sets, partial difference sets, and relative\n  difference sets   For nearly a century, mathematicians have been developing techniques for\nconstructing abelian automorphism groups of combinatorial objects, and,\nconversely, constructing combinatorial objects from abelian groups. While\nabelian groups are a natural place to start, recent computational evidence\nstrongly indicates that the vast majority of transitive automorphism groups of\ncombinatorial objects are nonabelian. This observation is the guiding\nmotivation for this paper. We propose a new method for constructing nonabelian\nautomorphism groups of combinatorial objects, which could be called the\n\\textit{combinatorial transfer method}, and we demonstrate its power by finding\n(1) the first infinite families of nonabelian Denniston partial difference sets\n(including nonabelian Denniston PDSs of odd order), (2) the first infinite\nfamily of Spence difference sets in groups with a Sylow 3-subgroup that is\nnon-normal and not elementary abelian, (3) the first infinite families of\nMcFarland difference sets in groups with a Sylow $p$-subgroup that is\nnon-normal and is not elementary abelian, (4) new infinite families of partial\ndifference sets in nonabelian $p$-groups with large exponent, (5) an infinite\nfamily of semiregular relative difference sets whose forbidden subgroup is\nnonabelian, and (6) a converse to Dillon's Dihedral Trick in the PDS setting.\nWe hope this paper will lead to more techniques to explore this largely\nunexplored topic.\n"", 'Packings of partial difference sets   A packing of partial difference sets is a collection of disjoint partial\ndifference sets in a finite group $G$. This configuration has received\nconsiderable attention in design theory, finite geometry, coding theory, and\ngraph theory over many years, although often only implicitly. We consider\npackings of certain Latin square type partial difference sets in abelian groups\nhaving identical parameters, the size of the collection being either the\nmaximum possible or one smaller. We unify and extend numerous previous results\nin a common framework, recognizing that a particular subgroup reveals important\nstructural information about the packing. Identifying this subgroup allows us\nto formulate a recursive lifting construction of packings in abelian groups of\nincreasing exponent, as well as a product construction yielding packings in the\ndirect product of the starting groups. We also study packings of certain\nnegative Latin square type partial difference sets of maximum possible size in\nabelian groups, all but one of which have identical parameters, and show how to\nproduce such collections using packings of Latin square type partial difference\nsets.\n']","[('difference sets', 0.5488458871841431), ('partial difference sets', 0.5410149097442627), ('combinatorial structures', 0.5184060335159302), ('difference group', 0.4993216395378113), ('groups combinatorial', 0.47613728046417236), ('sets groups', 0.4689082205295563), ('difference families', 0.4611588716506958), ('nonabelian groups', 0.46076273918151855), ('studied combinatorial', 0.4419803321361542), ('new constructions', 0.42143845558166504)]"
790,790,39,790_fokker planck equations_kinetic fokker planck_planck equations_fokker planck,"['fokker planck equations', 'kinetic fokker planck', 'planck equations', 'fokker planck', 'kinetic transport equations', 'decay estimates', 'class fokker planck', 'kinetic theory', 'kinetic fokker', 'kinetic equations']","[""How to construct decay rates for kinetic Fokker--Planck equations?   We study time averages for the norm of solutions to kinetic Fokker--Planck\nequations associated with general Hamiltonians. We provide fully explicit and\nconstructive decay estimates for systems subject to a confining potential,\nallowing fat-tail, sub-exponential and (super-)exponential local equilibria,\nwhich also include the classic Maxwellian case. The key step in our estimates\nis a modified Poincar\\'e inequality, obtained via a Lions--Poincar\\'e\ninequality and an averaging lemma.\n"", 'Gradient estimates for nonlinear kinetic Fokker-Planck equations   In this work, we provide a comprehensive gradient regularity theory for a\nbroad class of nonlinear kinetic Fokker-Planck equations. We achieve this by\nestablishing precise pointwise estimates in terms of the data in the spirit of\nnonlinear potential theory, leading to fine gradient regularity results under\nborderline assumptions on the data. Notably, our gradient estimates are novel\nalready in the absence of forcing terms and even for linear kinetic\nFokker-Planck equations in divergence form.\n', 'Holder estimates for kinetic Fokker-Planck equations up to the boundary   We obtain local Holder continuity estimates up to the boundary for a kinetic\nFokker-Planck equation with rough coefficients, with the prescribed influx\nboundary condition. Our result extends some recent developments that\nincorporate De Giorgi methods to kinetic Fokker-Planck equations. We also\nobtain higher order asymptotic estimates near the incoming part of the\nboundary. In particular, when the equation has a zero boundary conditions and\nno source term, we prove that the solution vanishes at infinite order on the\nincoming part of the boundary.\n']","[('fokker planck equations', 0.7226725816726685), ('kinetic fokker planck', 0.658480703830719), ('planck equations', 0.5341504216194153), ('fokker planck', 0.5185826420783997), ('kinetic transport equations', 0.5150924921035767), ('decay estimates', 0.5076481103897095), ('class fokker planck', 0.49439510703086853), ('kinetic theory', 0.4830314517021179), ('kinetic fokker', 0.47921085357666016), ('kinetic equations', 0.47522541880607605)]"
791,791,39,791_yang baxter maps_yang baxter equations_yang baxter solutions_quantum yang baxter,"['yang baxter maps', 'yang baxter equations', 'yang baxter solutions', 'quantum yang baxter', 'baxter maps', 'solutions yang baxter', 'baxter equations', 'baxter solutions', 'yang baxter', 'quantum yang']","['Local Yang--Baxter correspondences and set-theoretical solutions to the\n  Zamolodchikov tetrahedron equation   We study tetrahedron maps, which are set-theoretical solutions to the\nZamolodchikov tetrahedron equation, and their matrix Lax representations\ndefined by the local Yang--Baxter equation.\n  Sergeev [S.M. Sergeev 1998 Lett. Math. Phys. 45, 113--119] presented\nclassification results on three-dimensional tetrahedron maps obtained from the\nlocal Yang--Baxter equation for a certain class of matrix-functions in the\nsituation when the equation possesses a unique solution which determines a\ntetrahedron map. In this paper, using correspondences arising from the local\nYang--Baxter equation for some simple $2\\times 2$ matrix-functions, we show\nthat there are (non-unique) solutions to the local Yang--Baxter equation which\ndefine tetrahedron maps that do not belong to the Sergeev list; this paves the\nway for a new, wider classification of tetrahedron maps. We present invariants\nfor the derived tetrahedron maps and prove Liouville integrability for some of\nthem.\n  Furthermore, using the approach of solving correspondences arising from the\nlocal Yang--Baxter equation, we obtain several new birational tetrahedron maps,\nincluding maps with matrix Lax representations on arbitrary groups, a\n$9$-dimensional map associated with a Darboux transformation for the derivative\nnonlinear Schr\\""odinger (NLS) equation, and a $9$-dimensional generalisation of\nthe $3$-dimensional Hirota map.\n', 'Tetrahedron maps, Yang-Baxter maps, and partial linearisations   We study tetrahedron maps, which are set-theoretical solutions to the\nZamolodchikov tetrahedron equation, and Yang-Baxter maps, which are\nset-theoretical solutions to the quantum Yang-Baxter equation.\n  In particular, we clarify the structure of the nonlinear algebraic relations\nwhich define linear (parametric) tetrahedron maps (with nonlinear dependence on\nparameters), and we present several transformations which allow one to obtain\nnew such maps from known ones. Furthermore, we prove that the differential of a\n(nonlinear) tetrahedron map on a manifold is a tetrahedron map as well. Similar\nresults on the differentials of Yang-Baxter and entwining Yang-Baxter maps are\nalso presented.\n  Using the obtained general results, we construct new examples of (parametric)\nYang-Baxter and tetrahedron maps. The considered examples include maps\nassociated with integrable systems and matrix groups. In particular, we obtain\na parametric family of new linear tetrahedron maps, which are linear\napproximations for the nonlinear tetrahedron map constructed by Dimakis and\nM\\""uller-Hoissen [arXiv:1708.05694] in a study of soliton solutions of vector\nKadomtsev-Petviashvili (KP) equations. Also, we present invariants for this\nnonlinear tetrahedron map.\n', 'Two-component Yang-Baxter maps and star-triangle relations   It is shown how Yang-Baxter maps may be directly obtained from classical\ncounterparts of the star-triangle relations and quantum Yang-Baxter equations.\nThis is based on reinterpreting the latter equation and its solutions which are\ngiven in terms of special functions, as a set-theoretical form of the\nYang-Baxter equation whose solutions are given by quadrirational Yang-Baxter\nmaps. The Yang-Baxter maps obtained through this approach are found to satisfy\ntwo different types of Yang-Baxter equations, one that is the usual equation\ninvolving a single map, and another equation that involves a pair of maps,\nwhich is a case of what is also known as an entwining Yang-Baxter equation.\nApart from the elliptic case, each of these Yang-Baxter maps are\nquadrirational, but only maps that solve the former type of Yang-Baxter\nequation are reversible. The Yang-Baxter maps are expressed in terms of\ntwo-component variables, and two-component parameters, and have a natural\nQRT-like composition of separate maps for each component. Through this\napproach, sixteen different Yang-Baxter maps are derived from known solutions\nof the classical star-triangle relations.\n']","[('yang baxter maps', 0.7577078342437744), ('yang baxter equations', 0.7072587609291077), ('yang baxter solutions', 0.6619189977645874), ('quantum yang baxter', 0.6529871821403503), ('baxter maps', 0.6402269601821899), ('solutions yang baxter', 0.6136659979820251), ('baxter equations', 0.5904319286346436), ('baxter solutions', 0.5422689914703369), ('yang baxter', 0.5055490732192993), ('quantum yang', 0.44673043489456177)]"
792,792,39,792_stochastic volatility models_stochastic volatility_volatility models_options pricing,"['stochastic volatility models', 'stochastic volatility', 'volatility models', 'options pricing', 'option pricing', 'option prices', 'european options', 'volatility', 'european option', 'black scholes']","['Some asymptotics for short maturity Asian options   Most of the existing methods for pricing Asian options are less efficient in\nthe limit of small maturities and small volatilities. In this paper, we use the\nlarge deviations theory for the analysis of short-maturity Asian options. We\npresent a local volatility model for the underlying market that incorporates a\njump term in addition to the drift and diffusion terms. We estimate the\nasymptotics for the out-of-the-money, in-the-money, and at-the-money\nshort-maturity Asian call and put options. Under appropriate assumptions, we\nshow that the asymptotics for out-of-the-money Asian call and put options are\ngoverned by rare events. For the at-the-money Asian options, the result is more\ninvolved and in that case, we find the upper and lower bounds of the\nasymptotics of the Asian option price.\n', 'Option Pricing with Stochastic Volatility, Equity Premium, and Interest\n  Rates   This paper presents a new model for options pricing. The Black-Scholes-Merton\n(BSM) model plays an important role in financial options pricing. However, the\nBSM model assumes that the risk-free interest rate, volatility, and equity\npremium are constant, which is unrealistic in the real market. To address this,\nour paper considers the time-varying characteristics of those parameters. Our\nmodel integrates elements of the BSM model, the Heston (1993) model for\nstochastic variance, the Vasicek model (1977) for stochastic interest rates,\nand the Campbell and Viceira model (1999, 2001) for stochastic equity premium.\nWe derive a linear second-order parabolic PDE and extend our model to encompass\nfixed-strike Asian options, yielding a new PDE. In the absence of closed-form\nsolutions for any options from our new model, we utilize finite difference\nmethods to approximate prices for European call and up-and-out barrier options,\nand outline the numerical implementation for fixed-strike Asian call options.\n', 'Subleading correction to the Asian options volatility in the\n  Black-Scholes model   The short maturity limit $T\\to 0$ for the implied volatility of an Asian\noption in the Black-Scholes model is determined by the large deviations\nproperty for the time-average of the geometric Brownian motion. In this note we\nderive the subleading $O(T)$ correction to this implied volatility, using an\nasymptotic expansion for the Hartman-Watson distribution. The result is used to\ncompute subleading corrections to Asian options prices in a small maturity\nexpansion, sharpening the leading order result obtained using large deviations\ntheory. We demonstrate good numerical agreement with precise benchmarks for\nAsian options pricing in the Black-Scholes model.\n']","[('stochastic volatility models', 0.6321930289268494), ('stochastic volatility', 0.5550374984741211), ('volatility models', 0.5240919589996338), ('options pricing', 0.5018121004104614), ('option pricing', 0.4857569634914398), ('option prices', 0.4641428589820862), ('european options', 0.4115113914012909), ('volatility', 0.4067750573158264), ('european option', 0.4050861895084381), ('black scholes', 0.39981335401535034)]"
793,793,39,793_bound hausdorff dimension_hausdorff dimension_compute hausdorff dimension_lower bound hausdorff,"['bound hausdorff dimension', 'hausdorff dimension', 'compute hausdorff dimension', 'lower bound hausdorff', 'bound hausdorff', 'hausdorff measure', 'dimension sets', 'measure hausdorff', 'infty hausdorff', 'cantor sets']","['Hausdorff dimension of Gauss--Cantor sets and two applications to\n  classical Lagrange and Markov spectra   This paper is dedicated to the study of two famous subsets of the real line,\nnamely Lagrange spectrum $L$ and Markov spectrum $M$. Our first result, Theorem\n2.1, provides a rigorous estimate on the smallest value $t_1$ such that the\nportion of the Markov spectrum $(-\\infty,t_1)\\cap M$ has Hausdorff dimension\n$1$. Our second result, Theorem 3.1, gives a new upper bound on the Hausdorff\ndimension of the set difference $M\\setminus L$.\n  Our method combines new facts about the structure of the classical spectra\ntogether with finer estimates on the Hausdorff dimension of Gauss--Cantor sets\nof continued fraction expansions whose entries satisfy appropriate\nrestrictions.\n', ""Hausdorff dimension of some subsets of the Lagrange and Markov spectra\n  near $3$   We study the sets $\\mathcal{L}$ and $\\mathcal{M}\\setminus\\mathcal{L}$ near\n$3$, where $\\mathcal{L}$ and $\\mathcal{M}$ are the classical Lagrange and\nMarkov spectra. More specifically, we construct a strictly decreasing sequence\n$\\{a_r\\}_{r\\in \\mathbb{N}}$ converging to $3$, such that for any $r$ one can\nfind a subset $\\mathcal{B}_r\\subset (a_{r+1},a_r)\\cap \\mathcal{L}^{'}$ with the\nproperty that the Hausdorff dimension of $((a_{r+1},a_r)\\cap\n\\mathcal{L})\\setminus \\mathcal{B}_r$ is less than the Hausdorff dimension of\n$\\mathcal{B}_r$ and for $t\\in \\mathcal{B}_r$ the sets of irrational numbers\nwith Lagrange value bounded by $t$ and exactly $t$ respectively, have the same\nHausdorff dimension. We also show that, as $t$ varies in $\\mathcal{B}_r$, this\nHausdorff dimension is a strictly increasing function. Finally, in relation to\n$\\mathcal{M}\\setminus \\mathcal{L}$, we find $C>0$ such that we can bound from\nabove the Hausdorff dimension of $(\\mathcal{M}\\setminus \\mathcal{L})\\cap\n(-\\infty,3+\\rho)$ by $\\frac{\\log (\\abs{\\log \\rho})-\\log (\\log(\\abs{\\log\n\\rho}))+C}{\\abs{\\log \\rho}}$ if $\\rho>0$ is small.\n"", ""The dimension of the set of $\\psi$-badly approximable points in all\n  ambient dimensions; on a question of Beresnevich and Velani   Let $\\psi:\\mathbb{N} \\to [0,\\infty)$, $\\psi(q)=q^{-(1+\\tau)}$ and let\n$\\psi$-badly approximable points be those vectors in $\\mathbb{R}^{d}$ that are\n$\\psi$-well approximable, but not $c\\psi$-well approximable for arbitrarily\nsmall constants $c>0$. We establish that the $\\psi$-badly approximable points\nhave the Hausdorff dimension of the $\\psi$-well approximable points, the\ndimension taking the value $(d+1)/(\\tau+1)$ familiar from theorems of\nBesicovitch and Jarn\\'ik. The method of proof is an entirely new take on the\nMass Transference Principle by Beresnevich and Velani (Annals, 2006); namely,\nwe use the colloquially named `delayed pruning' to construct a sufficiently\nlarge $\\liminf$ set and combine this with ideas inspired by the proof of the\nMass Transference Principle to find a large $\\limsup$ subset of the $\\liminf$\nset. Our results are a generalisation of some $1$-dimensional results due to\nBugeaud and Moreira (Acta Arith, 2011), but our method of proof is nothing\nalike.\n""]","[('bound hausdorff dimension', 0.6236544847488403), ('hausdorff dimension', 0.5988259315490723), ('compute hausdorff dimension', 0.517541229724884), ('lower bound hausdorff', 0.5128401517868042), ('bound hausdorff', 0.4858230948448181), ('hausdorff measure', 0.4854673445224762), ('dimension sets', 0.4799281358718872), ('measure hausdorff', 0.4560896158218384), ('infty hausdorff', 0.4511556327342987), ('cantor sets', 0.41627323627471924)]"
794,794,39,794_stochastic integrals_stochastic integration_stochastic integral_valued martingales,"['stochastic integrals', 'stochastic integration', 'stochastic integral', 'valued martingales', 'valued stochastic', 'martingale representation', 'semimartingales', 'stochastic calculus', 'continuous semimartingale', 'martingale properties']","[""Stochastic integration in Hilbert spaces with respect to cylindrical\n  martingale-valued measures   In this work we introduce a theory of stochastic integration for\noperator-valued integrands with respect to some classes of cylindrical\nmartingale-valued measures in Hilbert spaces. The integral is constructed via\nthe radonification of cylindrical martingales by a Hilbert-Schmidt operator\ntheorem and unifies several other theories of stochastic integration in Hilbert\nspaces. In particular, our theory covers the theory of stochastic integration\nwith respect to a Hilbert space valued L\\'{e}vy process (which is not required\nto satisfy any moment condition), with respect to a cylindrical L\\'{e}vy\nprocesses with (weak) second moments and with respect to a L\\'{e}vy-valued\nrandom martingale measures with finite second moment. As an application of our\ntheory of integration we prove existence and uniqueness of solutions for\nstochastic stochastic partial differential equations driven by multiplicative\ncylindrical martingale-valued measure noise with rather general coefficients.\n"", 'Vector-Valued Stochastic Integration With Respect to Semimartingales in\n  the Dual of Nuclear Space   In this work, we introduce a theory of stochastic integration for\noperator-valued processes with respect to semimartingales taking values in the\ndual of a nuclear space. These semimartingales are required to have the good\nintegrator property, which is a property that we explore in detail and provide\nseveral examples. Our construction of the stochastic integral uses a\nregularization argument for cylindrical semimartingales and the theory of\nreal-valued stochastic integration introduced by the author in a previous work\n[Electron. J. Probab., Volume 26, paper no. 147, 2021]. We show various\nproperties of the stochastic integral; in particular we study continuity of the\nintegral mapping for integrands and for integrators, we prove a Riemman\nrepresentation formula, and we introduce sufficient conditions for the\nstochastic integral to be a good integrator. Finally, we apply our theory to\nshow an extension of \\""{U}st\\""{u}nel\'s version of It\\^{o}\'s formula in the\nspaces of distributions and of tempered distributions.\n', ""Stochastic integration with respect to cylindrical semimartingales   In this work we introduce a theory of stochastic integration with respect to\ngeneral cylindrical semimartingales defined on a locally convex space $\\Phi$.\nOur construction of the stochastic integral is based on the theory of tensor\nproducts of topological vector spaces and the property of good integrators of\nreal-valued semimartingales. This theory is further developed in the case where\n$\\Phi$ is a complete, barrelled, nuclear space, where we obtain a complete\ndescription of the class of integrands as $\\Phi$-valued locally bounded and\nweakly predictable processes. Several other properties of the stochastic\nintegral are proven, including a Riemann representation, a stochastic\nintegration by parts formula and a stochastic Fubini theorem. Our theory is\nthen applied to provide sufficient and necessary conditions for existence and\nuniqueness of solutions to linear stochastic evolution equations driven by\nsemimartingale noise taking values in the strong dual $\\Phi'$ of $\\Phi$. In the\nlast part of this article we apply our theory to define stochastic integrals\nwith respect to a sequence of real-valued semimartingales.\n""]","[('stochastic integrals', 0.7027001976966858), ('stochastic integration', 0.6621023416519165), ('stochastic integral', 0.6326663494110107), ('valued martingales', 0.60347980260849), ('valued stochastic', 0.5999562740325928), ('martingale representation', 0.5842940807342529), ('semimartingales', 0.5830215811729431), ('stochastic calculus', 0.582632839679718), ('continuous semimartingale', 0.5824270248413086), ('martingale properties', 0.5595754981040955)]"
795,795,39,795_one phase stefan_free boundary regularity_phase stefan_stefan problems,"['one phase stefan', 'free boundary regularity', 'phase stefan', 'stefan problems', 'dimensional free boundary', 'neumann boundary condition', 'free boundary', 'boundary condition', 'neumann boundary', 'boundary problems']","['The similarity method and explicit solutions for the fractional space\n  one-phase Stefan problems   In this paper we obtain self-similarity solutions for a one-phase\none-dimensional fractional space one-phase Stefan problem in terms of the three\nparametric Mittag-Leffer function $E_{\\alpha,m;l}(z)$. We consider Dirichlet\nand Newmann conditions at the fixed face, involving Caputo fractional space\nderivatives of order $0 < \\alpha < 1$. We recover the solution for the\nclassical one-phase Stefan problem when the order of the Caputo derivatives\napproaches one.\n', 'Free boundary regularity for the inhomogeneous one-phase Stefan problem In this paper, we prove that flat free boundaries of solutions to inhomogeneous one-phase Stefan problem are $C^{1,\\alpha}$.', 'Perturbative estimates for the one-phase Stefan Problem   We provide perturbative estimates for the one-phase Stefan free boundary\nproblem and obtain the regularity of flat free boundaries via a linearization\ntechnique in the spirit of the elliptic counterpart established by the first\nauthor.\n']","[('one phase stefan', 0.609437882900238), ('free boundary regularity', 0.5377296209335327), ('phase stefan', 0.5368925929069519), ('stefan problems', 0.5110552310943604), ('dimensional free boundary', 0.4910997152328491), ('neumann boundary condition', 0.48251694440841675), ('free boundary', 0.48028239607810974), ('boundary condition', 0.47044306993484497), ('neumann boundary', 0.4596801698207855), ('boundary problems', 0.45580554008483887)]"
796,796,39,796_hermitian random matrices_hermitian random_random matrix theory_quantum chaos,"['hermitian random matrices', 'hermitian random', 'random matrix theory', 'quantum chaos', 'quantum chaotic', 'gaussian unitary ensemble', 'random matrices', 'open quantum systems', 'unitary ensemble', 'quantum systems']","['Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos   We introduce a complex-plane generalization of the consecutive level-spacing\ndistribution, used to distinguish regular from chaotic quantum spectra. Our\napproach features the distribution of complex-valued ratios between nearest-\nand next-to-nearest neighbor spacings. We show that this quantity can\nsuccessfully detect the chaotic or regular nature of complex-valued spectra.\nThis is done in two steps. First, we show that, if eigenvalues are\nuncorrelated, the distribution of complex spacing ratios is flat within the\nunit circle, whereas random matrices show a strong angular dependence in\naddition to the usual level repulsion. The universal fluctuations of Gaussian\nUnitary and Ginibre Unitary universality classes in the large-matrix-size limit\nare shown to be well described by Wigner-like surmises for small-size matrices\nwith eigenvalues on the circle and on the two-torus, respectively. To study the\nlatter case, we introduce the Toric Unitary Ensemble, characterized by a flat\njoint eigenvalue distribution on the two-torus. Second, we study different\nphysical situations where nonhermitian matrices arise: dissipative quantum\nsystems described by a Lindbladian, non-unitary quantum dynamics described by\nnonhermitian Hamiltonians, and classical stochastic processes. We show that\nknown integrable models have a flat distribution of complex spacing ratios\nwhereas generic cases, expected to be chaotic, conform to Random Matrix Theory\npredictions. Specifically, we were able to clearly distinguish chaotic from\nintegrable dynamics in boundary-driven dissipative spin-chain Liouvillians and\nin the classical asymmetric simple exclusion process and to differentiate\nlocalized from delocalized phases in a nonhermitian disordered many-body\nsystem.\n', 'Singular-Value Statistics of Non-Hermitian Random Matrices and Open\n  Quantum Systems   The spectral statistics of non-Hermitian random matrices are of importance as\na diagnostic tool for chaotic behavior in open quantum systems. Here, we\ninvestigate the statistical properties of singular values in non-Hermitian\nrandom matrices as an effective measure of quantifying dissipative quantum\nchaos. By means of Hermitization, we reveal the unique characteristics of the\nsingular-value statistics that distinguish them from the complex-eigenvalue\nstatistics, and establish the comprehensive classification of the\nsingular-value statistics for all the 38-fold symmetry classes of non-Hermitian\nrandom matrices. We also analytically derive the singular-value statistics of\nsmall random matrices, which well describe those of large random matrices in\nthe similar spirit to the Wigner surmise. Furthermore, we demonstrate that\nsingular values of open quantum many-body systems follow the random-matrix\nstatistics, thereby identifying chaos and nonintegrability in open quantum\nsystems. Our work elucidates that the singular-value statistics serve as a\nclear indicator of symmetry and lay a foundation for statistical physics of\nopen quantum systems.\n', ""Higher order spacing ratios in random matrix theory and complex quantum\n  systems   The distribution of the ratios of nearest neighbor level spacings has become\na popular indicator of spectral fluctuations in complex quantum systems like\ninteracting many-body localized and thermalization phases, quantum chaotic\nsystems, and also in atomic and nuclear physics. In contrast to the level\nspacing distribution, which requires the cumbersome and at times ambiguous\nunfolding procedure, the ratios of spacings do not require unfolding and are\neasier to compute. In this work, for the class of Wigner-Dyson random matrices\nwith nearest neighbor spacing ratios $r$ distributed as $P_{\\beta}(r)$ for the\nthree ensembles indexed by $\\beta=1,2, 4$, their $k-$th order spacing ratio\ndistributions are shown to be identical to $P_{\\beta'}(r)$, where $\\beta'$, an\ninteger, is a function of $\\beta$ and $k$. This result is shown for Gaussian\nand circular ensembles of random matrix theory and for several physical systems\nsuch as spin chains, chaotic billiards, Floquet systems and measured nuclear\nresonances.\n""]","[('hermitian random matrices', 0.6511217355728149), ('hermitian random', 0.5851519703865051), ('random matrix theory', 0.5845159292221069), ('quantum chaos', 0.575358510017395), ('quantum chaotic', 0.540156364440918), ('gaussian unitary ensemble', 0.5364809036254883), ('random matrices', 0.5322949886322021), ('open quantum systems', 0.4680732488632202), ('unitary ensemble', 0.46312153339385986), ('quantum systems', 0.4597020745277405)]"
797,797,39,797_nonlinear observers_adaptive observer_state observer_state observers,"['nonlinear observers', 'adaptive observer', 'state observer', 'state observers', 'observer design', 'based observer', 'observer designed', 'observer', 'observers', 'state estimation']","[""Sliding Mode Observers for Set-valued Lur'e Systems with Uncertainties\n  Beyond Observational Range   In this paper, we introduce a new sliding mode observer for Lur'e set-valued\ndynamical systems, particularly addressing challenges posed by uncertainties\nnot within the standard range of observation. Traditionally, most of\nLuenberger-like observers and sliding mode observer have been designed only for\nuncertainties in the range of observation. Central to our approach is the\ntreatment of the uncertainty term which we decompose into two components: the\nfirst part in the observation subspace and the second part in its complemented\nsubspace. We establish that when the second part converges to zero, an exact\nsliding mode observer for the system can be obtained. In scenarios where this\nconvergence does not occur, our methodology allows for the estimation of errors\nbetween the actual state and the observer state. This leads to a practical\ninterval estimation technique, valuable in situations where part of the\nuncertainty lies outside the observable range. Finally, we show that our\nobserver is also a T- observer as well as a strong H-infinity observer.\n"", 'On Convergence of the Iteratively Preconditioned Gradient-Descent (IPG)\n  Observer   This paper considers the observer design problem for discrete-time nonlinear\ndynamical systems with sampled measurement data. Earlier, the recently proposed\nIteratively Preconditioned Gradient-Descent (IPG) observer, a Newton-type\nobserver, has been empirically shown to have improved robustness against\nmeasurement noise than the prominent nonlinear observers, a property that other\nNewton-type observers lack. However, no theoretical guarantees on the\nconvergence of the IPG observer were provided. This paper presents a rigorous\nconvergence analysis of the IPG observer for a class of nonlinear systems in\ndeterministic settings, proving its local linear convergence to the actual\ntrajectory. Our assumptions are standard in the existing literature of\nNewton-type observers, and the analysis further confirms the relation of the\nIPG observer with the Newton observer, which was only hypothesized earlier.\n', ""Unknown Input Observer Design for Linear Time-Invariant Systems -- A\n  Unifying Framework   This paper presents a new observer design approach for linear time invariant\nmultivariable systems subject to unknown inputs. The design is based on a\ntransformation to the so-called special coordinate basis. This form reveals\nimportant system properties like invertability or the finite and infinite zero\nstructure. Depending on the system's strong observability properties, the\nspecial coordinate basis allows for a straightforward unknown input observer\ndesign utilizing linear or nonlinear observers design techniques. The chosen\nobserver design technique does not only depend on the system properties, but\nalso on the desired convergence behavior of the observer. Hence, the proposed\ndesign procedure can be seen as a unifying framework for unknown input observer\ndesign.\n""]","[('nonlinear observers', 0.6621866822242737), ('adaptive observer', 0.6564788818359375), ('state observer', 0.5927071571350098), ('state observers', 0.5893641710281372), ('observer design', 0.588331401348114), ('based observer', 0.583766758441925), ('observer designed', 0.5469974875450134), ('observer', 0.5310800671577454), ('observers', 0.4971785545349121), ('state estimation', 0.4414438307285309)]"
798,798,39,798_multiplicative brownian_driven fractional brownian_dyson brownian motion_dyson brownian,"['multiplicative brownian', 'driven fractional brownian', 'dyson brownian motion', 'dyson brownian', 'brownian', 'brown measure', 'brownian motion', 'limit brownian motion', 'spectral measure', 'spectral distributions']","['Brown Measure Support and the Free Multiplicative Brownian Motion   The free multiplicative Brownian motion $b_{t}$ is the large-$N$ limit of\nBrownian motion $B_t^N$ on the general linear group\n$\\mathrm{GL}(N;\\mathbb{C})$. We prove that the Brown measure for\n$b_{t}$---which is an analog of the empirical eigenvalue distribution for\nmatrices---is supported on the closure of a certain domain $\\Sigma_{t}$ in the\nplane. The domain $\\Sigma_t$ was introduced by Biane in the context of the\nlarge-$N$ limit of the Segal--Bargmann transform associated to\n$\\mathrm{GL}(N;\\mathbb{C})$.\n  We also consider a two-parameter version, $b_{s,t}$: the large-$N$ limit of a\nrelated family of diffusion processes on $\\mathrm{GL}(N;\\mathbb{C})$ introduced\nby the second author. We show that the Brown measure of $b_{s,t}$ is supported\non the closure of a certain planar domain $\\Sigma_{s,t}$, generalizing\n$\\Sigma_t$, introduced by Ho.\n  In the process, we introduce a new family of spectral domains related to any\noperator in a tracial von Neumann algebra: the {\\em $L^p_n$-spectrum} for\n$n\\in\\mathbb{N}$ and $p\\ge 1$, a subset of the ordinary spectrum defined\nrelative to potentially-unbounded inverses. We show that, in general, the\nsupport of the Brown measure of an operator is contained in its\n$L_2^2$-spectrum.\n', 'The Brown measure of the sum of a self-adjoint element and an imaginary\n  multiple of a semicircular element   We compute the Brown measure of $x_{0}+i\\sigma_{t}$, where $\\sigma_{t}$ is a\nfree semicircular Brownian motion and $x_{0}$ is a freely independent\nself-adjoint element that is not a multiple of the identity. The Brown measure\nis supported in the closure of a certain bounded region $\\Omega_{t}$ in the\nplane. In $\\Omega_{t},$ the Brown measure is absolutely continuous with respect\nto Lebesgue measure, with a density that is constant in the vertical direction.\nOur results refine and rigorize results of Janik, Nowak, Papp, Wambach, and\nZahed and of Jarosz and Nowak in the physics literature.\n  We also show that pushing forward the Brown measure of $x_{0}+i\\sigma_{t}$ by\na certain map $Q_{t}:\\Omega_{t}\\rightarrow\\mathbb{R}$ gives the distribution of\n$x_{0}+\\sigma_{t}.$ We also establish a similar result relating the Brown\nmeasure of $x_{0}+i\\sigma_{t}$ to the Brown measure of $x_{0}+c_{t}$, where\n$c_{t}$ is the free circular Brownian motion.\n', 'The Brown measure of the free multiplicative Brownian motion   The free multiplicative Brownian motion $b_{t}$ is the large-$N$ limit of the\nBrownian motion on $\\mathsf{GL}(N;\\mathbb{C}),$ in the sense of $\\ast\n$-distributions. The natural candidate for the large-$N$ limit of the empirical\ndistribution of eigenvalues is thus the Brown measure of $b_{t}$. In previous\nwork, the second and third authors showed that this Brown measure is supported\nin the closure of a region $\\Sigma_{t}$ that appeared work of Biane. In the\npresent paper, we compute the Brown measure completely. It has a continuous\ndensity $W_{t}$ on $\\bar{\\Sigma}_{t},$ which is strictly positive and real\nanalytic on $\\Sigma_{t}$. This density has a simple form in polar coordinates:\n\\[ W_{t}(r,\\theta)=\\frac{1}{r^{2}}w_{t}(\\theta), \\] where $w_{t}$ is an\nanalytic function determined by the geometry of the region $\\Sigma_{t}$.\n  We show also that the spectral measure of free unitary Brownian motion\n$u_{t}$ is a ""shadow"" of the Brown measure of $b_{t}$, precisely mirroring the\nrelationship between Wigner\'s semicircle law and Ginibre\'s circular law. We\ndevelop several new methods, based on stochastic differential equations and\nPDE, to prove these results.\n']","[('multiplicative brownian', 0.5869631767272949), ('driven fractional brownian', 0.5706032514572144), ('dyson brownian motion', 0.5631518959999084), ('dyson brownian', 0.5629837512969971), ('brownian', 0.528197169303894), ('brown measure', 0.49303123354911804), ('brownian motion', 0.4821547269821167), ('limit brownian motion', 0.48009687662124634), ('spectral measure', 0.4787842035293579), ('spectral distributions', 0.4515344202518463)]"
799,799,39,799_percolation random graphs_bootstrap percolation_percolation graph_percolation threshold,"['percolation random graphs', 'bootstrap percolation', 'percolation graph', 'percolation threshold', 'percolation process', 'percolation', 'percolation random', 'percolating', 'probability infection', 'hamming graph']","['Bootstrap percolation is local   Metastability thresholds lie at the heart of bootstrap percolation theory.\nYet proving precise lower bounds is notoriously hard. We show that for two of\nthe most classical models, two-neighbour and Frob\\""ose, upper bounds are sharp\nto essentially arbitrary precision, by linking them to their local\ncounterparts.\n  In Frob\\""ose bootstrap percolation, iteratively, any vertex of the square\nlattice that is the only healthy vertex of a $1\\times1$ square becomes infected\nand infections never heal. We prove that if vertices are initially infected\nindependently with probability $p\\to0$, then with high probability the origin\nbecomes infected after\n\\[\\exp\\left(\\frac{\\pi^2}{6p}-\\frac{\\pi\\sqrt{2+\\sqrt2}}{\\sqrt\np}+\\frac{O(\\log^2(1/p))}{\\sqrt[3]p}\\right)\\] time steps. We achieve this by\nproposing a new paradigmatic view on bootstrap percolation based on locality.\nNamely, we show that studying the Frob\\""ose model is equivalent in an extremely\nstrong sense to studying its local version. As a result, we completely bypass\nHolroyd\'s classical but technical hierarchy method, yielding the first term\nabove and systematically used throughout bootstrap percolation for the last two\ndecades. Instead, the proof features novel links to large deviation theory,\neigenvalue perturbations and others.\n  We also use the locality viewpoint to resolve the so-called bootstrap\npercolation paradox. Indeed, we propose and implement an exact (deterministic)\nalgorithm which exponentially outperforms previous Monte Carlo approaches. This\nallows us to clearly showcase and quantify the slow convergence we prove\nrigorously.\n  The same approach applies, with more extensive computations, to the\ntwo-neighbour model, in which vertices are infected when they have at least two\ninfected neighbours and do not recover. We expect it to be applicable to a\nwider range of models and correspondingly conclude with a number of open\nproblems.\n', 'Maximal Bootstrap Percolation Time on the Hypercube via Generalised\n  Snake-in-the-Box   In $r$-neighbour bootstrap percolation, vertices (sites) of a graph $G$ are\ninfected, round-by-round, if they have $r$ neighbours already infected. Once\ninfected, they remain infected. An initial set of infected sites is said to\npercolate if every site is eventually infected. We determine the maximal\npercolation time for $r$-neighbour bootstrap percolation on the hypercube for\nall $r \\geq 3$ as the dimension $d$ goes to infinity up to a logarithmic\nfactor. Surprisingly, it turns out to be $\\frac{2^d}{d}$, which is in great\ncontrast with the value for $r=2$, which is quadratic in $d$, as established by\nPrzykucki. Furthermore, we discover a link between this problem and a\ngeneralisation of the well-known Snake-in-the-Box problem.\n', 'Bootstrap Percolation, Connectivity, and Graph Distance   Bootstrap Percolation is a process defined on a graph which begins with an\ninitial set of infected vertices. In each subsequent round, an uninfected\nvertex becomes infected if it is adjacent to at least $r$ previously infected\nvertices. If an initially infected set of vertices, $A_0$, begins a process in\nwhich every vertex of the graph eventually becomes infected, then we say that\n$A_0$ percolates. In this paper we investigate bootstrap percolation as it\nrelates to graph distance and connectivity. We find a sufficient condition for\nthe existence of cardinality 2 percolating sets in diameter 2 graphs when $r =\n2$. We also investigate connections between connectivity and bootstrap\npercolation and lower and upper bounds on the number of rounds to percolation\nin terms of invariants related to graph distance.\n']","[('percolation random graphs', 0.730875551700592), ('bootstrap percolation', 0.7276892066001892), ('percolation graph', 0.6924669742584229), ('percolation threshold', 0.6397382616996765), ('percolation process', 0.6313961148262024), ('percolation', 0.6306858062744141), ('percolation random', 0.627113401889801), ('percolating', 0.5381994843482971), ('probability infection', 0.38627228140830994), ('hamming graph', 0.3734138011932373)]"
800,800,39,800_disturbance rejection_feedback controller_proposed control scheme_control uncertain,"['disturbance rejection', 'feedback controller', 'proposed control scheme', 'control uncertain', 'tracking control', 'quadratic tracking', 'control scheme', 'finite time stabilization', 'proposed control strategy', 'adaptive control']","['An Approach to Mismatched Disturbance Rejection Control for\n  Uncontrollable Systems   This study focuses on the problem of optimal mismatched disturbance rejection\ncontrol for uncontrollable linear discrete-time systems. In contrast to\nprevious studies, by introducing a quadratic performance index such that the\nregulated state can track a reference trajectory and minimize the effects of\ndisturbances, mismatched disturbance rejection control is transformed into a\nlinear quadratic tracking problem. The necessary and sufficient conditions for\nthe solvability of this problem over a finite horizon and a disturbance\nrejection controller are derived by solving a forward-backward difference\nequation. In the case of an infinite horizon, a sufficient condition for the\nstabilization of the system is obtained under the detectable condition. This\npaper details our novel approach to disturbance rejection. Four examples are\nprovided to demonstrate the effectiveness of the proposed method.\n', ""Output feedback control with prescribed performance via funnel\n  pre-compensator   We study output reference tracking of systems with high relative degree via\noutput feedback only; this is, tracking where the output derivatives are\nunknown. To this end, we prove that the conjunction of the funnel\npre-compensator with a minimum phase system of arbitrary relative degree yields\na system of the same relative degree which is minimum phase as well. The error\nbetween the original system's output and the pre-compensator's output evolves\nwithin a prescribed performance funnel; and moreover, the derivatives of the\nfunnel pre-compensator's output are known explicitly. Therefore, output\nreference tracking with prescribed transient behaviour of the tracking error is\npossible without knowledge of the derivatives of the original system's output;\nvia funnel control schemes for instance.\n"", 'An Approach to Mismatched Disturbance Rejection Control for\n  Continuous-Time Uncontrollable Systems   This paper focuses on optimal mismatched disturbance rejection control for\nlinear continuoustime uncontrollable systems. Different from previous studies,\nby introducing a new quadratic performance index to transform the mismatched\ndisturbance rejection control into a linear quadratic tracking problem, the\nregulated state can track a reference trajectory and minimize the influence of\ndisturbance. The necessary and sufficient conditions for the solvability and\nthe disturbance rejection controller are obtained by solving a forward-backward\ndifferential equation over a finite horizon. A sufficient condition for system\nstability is obtained over an infinite horizon under detectable condition. This\npaper details our novel approach for transforming disturbance rejection into a\nlinear quadratic tracking problem. The effectiveness of the proposed method is\nprovided with two examples to demonstrate.\n']","[('disturbance rejection', 0.5545666217803955), ('feedback controller', 0.49616703391075134), ('proposed control scheme', 0.4909287095069885), ('control uncertain', 0.47266390919685364), ('tracking control', 0.4676954746246338), ('quadratic tracking', 0.46726033091545105), ('control scheme', 0.46440380811691284), ('finite time stabilization', 0.46140849590301514), ('proposed control strategy', 0.45617786049842834), ('adaptive control', 0.4377909302711487)]"
801,801,39,801_mean field games_mean field game_mean field control_agent reinforcement learning,"['mean field games', 'mean field game', 'mean field control', 'agent reinforcement learning', 'reinforcement learning algorithms', 'learning mean field', 'reinforcement learning', 'reinforcement learning rl', 'reinforcement learning methods', 'multi agent reinforcement']","[""Unified continuous-time q-learning for mean-field game and mean-field\n  control problems   This paper studies the continuous-time q-learning in mean-field\njump-diffusion models when the population distribution is not directly\nobservable. We propose the integrated q-function in decoupled form (decoupled\nIq-function) from the representative agent's perspective and establish its\nmartingale characterization, which provides a unified policy evaluation rule\nfor both mean-field game (MFG) and mean-field control (MFC) problems. Moreover,\nwe consider the learning procedure where the representative agent updates the\npopulation distribution based on his own state values. Depending on the task to\nsolve the MFG or MFC problem, we can employ the decoupled Iq-function\ndifferently to characterize the mean-field equilibrium policy or the mean-field\noptimal policy respectively. Based on these theoretical findings, we devise a\nunified q-learning algorithm for both MFG and MFC problems by utilizing test\npolicies and the averaged martingale orthogonality condition. For several\nfinancial applications in the jump-diffusion setting, we obtain the exact\nparameterization of the decoupled Iq-functions and the value functions, and\nillustrate our q-learning algorithm with satisfactory performance.\n"", ""Reinforcement Learning for Mean Field Games, with Applications to\n  Economics   Mean field games (MFG) and mean field control problems (MFC) are frameworks\nto study Nash equilibria or social optima in games with a continuum of agents.\nThese problems can be used to approximate competitive or cooperative games with\na large finite number of agents and have found a broad range of applications,\nin particular in economics. In recent years, the question of learning in MFG\nand MFC has garnered interest, both as a way to compute solutions and as a way\nto model how large populations of learners converge to an equilibrium. Of\nparticular interest is the setting where the agents do not know the model,\nwhich leads to the development of reinforcement learning (RL) methods. After\nreviewing the literature on this topic, we present a two timescale approach\nwith RL for MFG and MFC, which relies on a unified Q-learning algorithm. The\nmain novelty of this method is to simultaneously update an action-value\nfunction and a distribution but with different rates, in a model-free fashion.\nDepending on the ratio of the two learning rates, the algorithm learns either\nthe MFG or the MFC solution. To illustrate this method, we apply it to a mean\nfield problem of accumulated consumption in finite horizon with HARA utility\nfunction, and to a trader's optimal liquidation problem.\n"", ""Unified Reinforcement Q-Learning for Mean Field Game and Control\n  Problems   We present a Reinforcement Learning (RL) algorithm to solve infinite horizon\nasymptotic Mean Field Game (MFG) and Mean Field Control (MFC) problems. Our\napproach can be described as a unified two-timescale Mean Field Q-learning: The\n\\emph{same} algorithm can learn either the MFG or the MFC solution by simply\ntuning the ratio of two learning parameters. The algorithm is in discrete time\nand space where the agent not only provides an action to the environment but\nalso a distribution of the state in order to take into account the mean field\nfeature of the problem. Importantly, we assume that the agent can not observe\nthe population's distribution and needs to estimate it in a model-free manner.\nThe asymptotic MFG and MFC problems are also presented in continuous time and\nspace, and compared with classical (non-asymptotic or stationary) MFG and MFC\nproblems. They lead to explicit solutions in the linear-quadratic (LQ) case\nthat are used as benchmarks for the results of our algorithm.\n""]","[('mean field games', 0.6109583377838135), ('mean field game', 0.6087005734443665), ('mean field control', 0.5949997305870056), ('agent reinforcement learning', 0.5787265300750732), ('reinforcement learning algorithms', 0.5505116581916809), ('learning mean field', 0.545162558555603), ('reinforcement learning', 0.5445219278335571), ('reinforcement learning rl', 0.5413822531700134), ('reinforcement learning methods', 0.5362403392791748), ('multi agent reinforcement', 0.5014034509658813)]"
802,802,39,802_quaternion matrices_quaternion based_quaternion valued_quaternion,"['quaternion matrices', 'quaternion based', 'quaternion valued', 'quaternion', 'quaternions', 'quaternionic', 'matrix completion', 'order quaternion', 'matrix factorization', 'tensor completion']","['Low-rank quaternion tensor completion for recovering color videos and\n  images   Low-rank quaternion tensor completion method, a novel approach to recovery\ncolor videos and images is proposed in this paper. We respectively reconstruct\na color image and a color video as a quaternion matrix (second-order tensor)\nand a third-order quaternion tensor by encoding the red, green, and blue\nchannel pixel values on the three imaginary parts of a quaternion. Different\nfrom some traditional models which treat color pixel as a scalar and represent\ncolor channels separately, whereas, during the quaternion-based reconstruction,\nit is significant that the inherent color structures of color images and color\nvideos can be completely preserved. Under the definition of Tucker rank, the\nglobal low-rank prior to quaternion tensor is encoded as the nuclear norm of\nunfolding quaternion matrices. Then, by applying the ADMM framework, we provide\nthe tensor completion algorithm for any order quaternion tensors, which\ntheoretically can be well used to recover missing entries of any\nmultidimensional data with color structures. Simulation results for color\nvideos and color images recovery show the superior performance and efficiency\nof the proposed method over some state-of-the-art existing ones.\n', 'Quaternion-based bilinear factor matrix norm minimization for color\n  image inpainting   As a new color image representation tool, quaternion has achieved excellent\nresults in the color image processing, because it treats the color image as a\nwhole rather than as a separate color space component, thus it can make full\nuse of the high correlation among RGB channels. Recently, low-rank quaternion\nmatrix completion (LRQMC) methods have proven very useful for color image\ninpainting. In this paper, we propose three novel LRQMC methods based on three\nquaternion-based bilinear factor (QBF) matrix norm minimization models.\nSpecifically, we define quaternion double Frobenius norm (Q-DFN), quaternion\ndouble nuclear norm (Q-DNN) and quaternion Frobenius/nuclear norm (Q-FNN), and\nthen show their relationship with quaternion-based matrix Schatten-p (Q-\nSchatten-p ) norm for certain p values. The proposed methods can avoid\ncomputing quaternion singular value decompositions (QSVD) for large quaternion\nmatrices, and thus can effectively reduce the calculation time compared with\nexisting (LRQMC) methods. The experimental results demonstrate the superior\nperformance of the proposed methods over some state-of-the-art low-rank\n(quaternion) matrix completion methods.\n', 'Low Rank Pure Quaternion Approximation for Pure Quaternion Matrices   Quaternion matrices are employed successfully in many color image processing\napplications. In particular, a pure quaternion matrix can be used to represent\nred, green and blue channels of color images. A low-rank approximation for a\npure quaternion matrix can be obtained by using the quaternion singular value\ndecomposition. However, this approximation is not optimal in the sense that the\nresulting low-rank approximation matrix may not be pure quaternion, i.e., the\nlow-rank matrix contains real component which is not useful for the\nrepresentation of a color image. The main contribution of this paper is to find\nan optimal rank-$r$ pure quaternion matrix approximation for a pure quaternion\nmatrix (a color image). Our idea is to use a projection on a low-rank\nquaternion matrix manifold and a projection on a quaternion matrix with zero\nreal component, and develop an alternating projections algorithm to find such\noptimal low-rank pure quaternion matrix approximation. The convergence of the\nprojection algorithm can be established by showing that the low-rank quaternion\nmatrix manifold and the zero real component quaternion matrix manifold has a\nnon-trivial intersection point. Numerical examples on synthetic pure quaternion\nmatrices and color images are presented to illustrate the projection algorithm\ncan find optimal low-rank pure quaternion approximation for pure quaternion\nmatrices or color images.\n']","[('quaternion matrices', 0.6087071299552917), ('quaternion based', 0.5716050267219543), ('quaternion valued', 0.536655843257904), ('quaternion', 0.5098075866699219), ('quaternions', 0.5028092861175537), ('quaternionic', 0.5027005076408386), ('matrix completion', 0.4993414580821991), ('order quaternion', 0.49830037355422974), ('matrix factorization', 0.44423437118530273), ('tensor completion', 0.42322659492492676)]"
803,803,39,803_euclidean traveling salesman_traveling salesman tsp_traveling salesman_travelling salesman,"['euclidean traveling salesman', 'traveling salesman tsp', 'traveling salesman', 'travelling salesman', 'combinatorial optimization', 'salesman problems', 'salesman tsp', 'approximation algorithms', 'heuristics', 'euclidean traveling']","['The Approximation Ratio of the $k$-Opt Heuristic for the Euclidean\n  Traveling Salesman Problem   The $k$-Opt heuristic is a simple improvement heuristic for the Traveling\nSalesman Problem. It starts with an arbitrary tour and then repeatedly replaces\n$k$ edges of the tour by $k$ other edges, as long as this yields a shorter\ntour. We will prove that for 2-dimensional Euclidean Traveling Salesman\nProblems with $n$ cities the approximation ratio of the $k$-Opt heuristic is\n$\\Theta(\\log n / \\log \\log n)$. This improves the upper bound of $O(\\log n)$\ngiven by Chandra, Karloff, and Tovey in 1999 and provides for the first time a\nnon-trivial lower bound for the case $k\\ge 3$. Our results not only hold for\nthe Euclidean norm but extend to arbitrary $p$-norms with $1 \\le p < \\infty$.\n', 'Hard to Solve Instances of the Euclidean Traveling Salesman Problem   The well known $4/3$ conjecture states that the integrality ratio of the\nsubtour LP is at most $4/3$ for metric Traveling Salesman instances. We present\na family of Euclidean Traveling Salesman instances for which we prove that the\nintegrality ratio of the subtour LP converges to $4/3$. These instances (using\nthe rounded Euclidean norm) turn out to be hard to solve exactly with Concorde,\nthe fastest existing exact TSP solver. For a 200 vertex instance from our\nfamily of Euclidean Traveling Salesman instances Concorde needs several days of\nCPU time. This is more than 1,000,000 times the runtime for a TSPLIB instance\nof similar size. Thus our new family of Euclidean Traveling Salesman instances\nmay serve as new benchmark instances for TSP algorithms.\n', 'The Approximation Ratio of the 2-Opt Heuristic for the Euclidean\n  Traveling Salesman Problem   The 2-Opt heuristic is a simple improvement heuristic for the Traveling\nSalesman Problem. It starts with an arbitrary tour and then repeatedly replaces\ntwo edges of the tour by two other edges, as long as this yields a shorter\ntour. We will prove that for Euclidean Traveling Salesman Problems with $n$\ncities the approximation ratio of the 2-Opt heuristic is $\\Theta(\\log n/ \\log\n\\log n)$. This improves the upper bound of $O(\\log n$) given by Chandra,\nKarloff, and Tovey [3] in 1999.\n']","[('euclidean traveling salesman', 0.6969768404960632), ('traveling salesman tsp', 0.5973251461982727), ('traveling salesman', 0.5735471844673157), ('travelling salesman', 0.5674342513084412), ('combinatorial optimization', 0.4996024966239929), ('salesman problems', 0.49602705240249634), ('salesman tsp', 0.48596981167793274), ('approximation algorithms', 0.48418277502059937), ('heuristics', 0.4250091016292572), ('euclidean traveling', 0.42038530111312866)]"
804,804,39,804_affine root system_root systems_generalized root_laced root systems,"['affine root system', 'root systems', 'generalized root', 'laced root systems', 'root system', 'affine root', 'root system rank', 'systems root', 'class root', 'roots root']","['Oriented matroid structures on rank 3 root systems   We show that, given a rank 3 affine root system $\\Phi$ with Weyl group $W$,\nthere is a unique oriented matroid structure on $\\Phi$ which is $W$-equivariant\nand restricts to the usual matroid structure on rank 2 subsystems. Such\noriented matroids were called oriented matroid root systems in Dyer-Wang\n(2021), and are known to be non-unique in higher rank. We also show uniqueness\nfor any finite root system or ""clean"" rank 3 root system (which conjecturally\nincludes all rank 3 root systems).\n', 'Classification of marked elliptic root systems with non-reduced affine\n  quotient   The class of root systems, called elliptic root systems, were introduced in\n1985 by K. Saito, for his studies on a normal surface singularity which\ncontains a regular elliptic curve in its minimal resolution. He also classified\nsuch root systems when they admit a reduced affine quotient, as root system. In\nthis note, we provide the classification of elliptic root systems that admit a\nnon-reduced affine quotient, thus complete the classification of such root\nsystems.\n', 'Generalized root systems   We generalize the notion of a root system by relaxing the conditions that\nensure that it is invariant under reflections and study the resulting\nstructures, which we call generalized root systems (GRSs for short). Since both\nKostant root systems and root systems of Lie superalgebras are examples of\nGRSs, studying GRSs provides a uniform axiomatic approach to studying both of\nthem. GRSs inherit many of the properties of root systems. In particular, every\nGRS defines a crystallographic hyperplane arrangement. We believe that GRSs\nprovide an intrinsic counterpart to finite Weyl groupoids and crystallographic\nhyperplane arrangements, extending the relationship between finite Weyl\ngroupoids and crystallographic hyperplane arrangements established by Cuntz. An\nimportant difference between GRSs and root systems is that GRSs may lack a\n(large enough) Weyl group. In order to compensate for this, we introduce the\nnotion of a virtual reflection, building on a construction of Penkov and\nSerganova in the context of root systems of Lie superalgebras.\n  The most significant new feature of GRSs is that, along with subsystems, one\ncan define quotient GRSs. Both Kostant root systems and root systems of Lie\nsuperalgebras are equivalent to quotients of root systems and all root systems\nare isomorphic to quotients of simply-laced root systems. We classify all rank\n2 GRSs and show that they are equivalent to quotients of root systems. Finally,\nwe discuss in detail quotients of root systems. In particular we provide all\nisomorphisms and equivalences among them. Our results on quotient of root\nsystems provide a different point of view on flag manifolds, reproving results\nof Alekseevsky and Graev.\n']","[('affine root system', 0.7263604998588562), ('root systems', 0.6486176252365112), ('generalized root', 0.5936269760131836), ('laced root systems', 0.5826570987701416), ('root system', 0.5687012672424316), ('affine root', 0.563869297504425), ('root system rank', 0.5453413128852844), ('systems root', 0.5155434608459473), ('class root', 0.4456108510494232), ('roots root', 0.43364620208740234)]"
805,805,38,805_constrained quadratic programs_constrained quadratic programming_quadratic programs qcqps_semidefinite programming sdp,"['constrained quadratic programs', 'constrained quadratic programming', 'quadratic programs qcqps', 'semidefinite programming sdp', 'semidefinite programming', 'semidefinite program sdp', 'constrained quadratic program', 'quadratic programming', 'convex relaxation', 'quadratic programs']","['Exactness in SDP relaxations of QCQPs: Theory and applications   Quadratically constrained quadratic programs (QCQPs) are a fundamental class\nof optimization problems. In a QCQP, we are asked to minimize a (possibly\nnonconvex) quadratic function subject to a number of (possibly nonconvex)\nquadratic constraints. Such problems arise naturally in many areas of\noperations research, computer science, and engineering. Although QCQPs are\nNP-hard to solve in general, they admit a natural convex relaxation via the\nstandard (Shor) semidefinite program (SDP) relaxation. In this tutorial, we\nwill study the SDP relaxation for general QCQPs, present various exactness\nconcepts related to this relaxation and discuss conditions guaranteeing such\nSDP exactness. In particular, we will define and examine three notions of SDP\nexactness: (i) objective value exactness -- the condition that the optimal\nvalue of the QCQP and the optimal value of its SDP relaxation coincide, (ii)\nconvex hull exactness -- the condition that the convex hull of the QCQP\nepigraph coincides with the (projected) SDP epigraph, and (iii) the rank-one\ngenerated (ROG) property -- the condition that a particular conic subset of the\npositive semidefinite matrices related to a given QCQP is generated by its\nrank-one matrices. Our analysis for objective value exactness and convex hull\nexactness stems from a geometric treatment of the projected SDP relaxation and\ncrucially considers how the objective function interacts with the constraints.\nThe ROG property complements these results by offering a sufficient condition\nfor both objective value exactness and convex hull exactness which is oblivious\nto the objective function. We will give a variety of sufficient conditions for\nthese exactness conditions and discuss settings where these sufficient\nconditions are additionally necessary. Throughout, we will highlight\nimplications of our results for a number of example applications.\n', 'Extending Exact SDP Relaxations of Quadratically Constrained Quadratic\n  Programs   The semidefinite (SDP) relaxation of a quadratically constrained quadratic\nprogram (QCQP) is called exact if it has a rank-$1$ optimal solution\ncorresponding to a QCQP optimal solution. Given an arbitrary QCQP whose SDP\nrelaxation is exact, this paper investigates incorporating additional quadratic\ninequality constraints while maintaining the exactness of the SDP relaxation of\nthe resulting QCQP. Three important classes of QCQPs with exact SDP relaxations\ninclude (a) those characterized by rank-one generated cones, (b) those by\nconvexity, and (c) those by the sign pattern of the data coefficient matrices.\nThese classes have been studied independently until now. By adding quadratic\ninequality constraints satisfying the proposed conditions to QCQPs in these\nclasses, we extend the exact SDP relaxation to broader classes of QCQPs.\nIllustrative QCQP instances are provided.\n', 'A Geometric View of SDP Exactness in QCQPs and its Applications   Quadratically constrained quadratic programs (QCQPs) are a highly expressive\nclass of nonconvex optimization problems. While QCQPs are NP-hard in general,\nthey admit a natural convex relaxation via the standard (Shor) semidefinite\nprogram (SDP) relaxation. Towards understanding when this relaxation is exact,\nwe study general QCQPs and their (projected) SDP relaxations. We present\nsufficient (and in some cases, also necessary) conditions for objective value\nexactness (the condition that the objective values of the QCQP and its SDP\nrelaxation coincide) and convex hull exactness (the condition that the convex\nhull of the QCQP epigraph coincides with the epigraph of its SDP relaxation).\nOur conditions for exactness are based on geometric properties of $\\Gamma$, the\ncone of convex Lagrange multipliers, and its relatives $\\Gamma_P$ and\n$\\Gamma^\\circ$. These tools form the basis of our main message: questions of\nexactness can be treated systematically whenever $\\Gamma$, $\\Gamma_P$, or\n$\\Gamma^\\circ$ is well-understood. As further evidence of this message, we\napply our tools to address questions of exactness for a prototypical QCQP\ninvolving a binary on-off constraint, quadratic matrix programs, the QCQP\nformulation of the partition problem, and random and semi-random QCQPs.\n']","[('constrained quadratic programs', 0.6838041543960571), ('constrained quadratic programming', 0.6634372472763062), ('quadratic programs qcqps', 0.6615853309631348), ('semidefinite programming sdp', 0.6531198620796204), ('semidefinite programming', 0.6357347369194031), ('semidefinite program sdp', 0.6150814294815063), ('constrained quadratic program', 0.6131013035774231), ('quadratic programming', 0.5874348878860474), ('convex relaxation', 0.582172155380249), ('quadratic programs', 0.5740121006965637)]"
806,806,38,806_nilpotent algebras_classification nilpotent_dimensional nilpotent_algebras classification,"['nilpotent algebras', 'classification nilpotent', 'dimensional nilpotent', 'algebras classification', 'leibniz algebras', 'complex algebras', 'jordan algebras', 'algebras dimensional', 'graded nilpotent', 'algebras dimension']","[""The algebraic and geometric classification of nilpotent weakly\n  associative and symmetric Leibniz algebras   This paper is devoted to the complete algebraic and geometric classification\nof complex $4$-dimensional nilpotent weakly associative, complex\n$4$-dimensional symmetric Leibniz algebras, and complex $5$-dimensional\nnilpotent symmetric Leibniz algebras. In particular, we proved that the variety\nof complex $4$-dimensional symmetric Leibniz algebras has no\nVergne--Grunewald--O'Halloran Property (there is an irreducible component\nformed by only nilpotent algebras), but on the other hand, it has Vergne\nProperty (there are no rigid nilpotent algebras).\n"", 'The algebraic and geometric classification of nilpotent Leibniz algebras   This paper is devoted to the complete algebraic and geometric classification\nof complex $5$-dimensional nilpotent Leibniz algebras. In particular, the\nvariety of complex $5$-dimensional nilpotent Leibniz algebras has dimension\n$24$ it has $10$ irreducible components (there is only one rigid algebra in\nthis variety).\n', 'The algebraic and geometric classification of nilpotent binary and mono\n  Leibniz algebras   This paper is devoted to the complete algebraic and geometric classification\nof complex $5$-dimensional nilpotent binary Leibniz and $4$-dimensional\nnilpotent mono Leibniz algebras. As a corollary, we have the complete algebraic\nand geometric classification of complex $4$-dimensional nilpotent algebras of\nnil-index $3$.\n']","[('nilpotent algebras', 0.7348846793174744), ('classification nilpotent', 0.6262397766113281), ('dimensional nilpotent', 0.6140158772468567), ('algebras classification', 0.5996413230895996), ('leibniz algebras', 0.5805349946022034), ('complex algebras', 0.577721118927002), ('jordan algebras', 0.5538329482078552), ('algebras dimensional', 0.5419551134109497), ('graded nilpotent', 0.5291234850883484), ('algebras dimension', 0.5278657674789429)]"
807,807,38,807_magnetohydrodynamic mhd equations_magnetohydrodynamics mhd equations_magnetohydrodynamics equations_magnetohydrodynamics mhd,"['magnetohydrodynamic mhd equations', 'magnetohydrodynamics mhd equations', 'magnetohydrodynamics equations', 'magnetohydrodynamics mhd', 'magnetohydrodynamic mhd', 'ideal magnetohydrodynamics', 'divergence free magnetic', 'magnetohydrodynamics', 'ideal mhd equations', 'magnetohydrodynamic']","[""Provably Positivity-Preserving Constrained Transport (PPCT) Second-Order\n  Scheme for Ideal Magnetohydrodynamics   This paper proposes and analyzes a robust and efficient second-order\npositivity-preserving constrained transport (PPCT) scheme for ideal\nmagnetohydrodynamics (MHD) on non-staggered Cartesian meshes. The PPCT scheme\nensures two critical physical constraints: a globally discrete divergence-free\n(DDF) condition on the magnetic field and the positivity of density and\npressure. The method is inspired by a novel splitting technique from [T.A. Dao,\nM. Nazarov and I. Tomas, J. Comput. Phys., 508:113009, 2024], which divides the\nMHD system into an Euler subsystem with steady magnetic fields and a magnetic\nsubsystem with steady density and internal energy. To achieve these\nstructure-preserving properties, the PPCT scheme combines a\npositivity-preserving (PP) finite volume method for the Euler subsystem with a\nfinite difference constrained transport (CT) method for the magnetic subsystem\nvia Strang splitting. The finite volume method employs a new PP limiter that\nretains second-order accuracy and enforces the positivity of density and\npressure, with rigorous proof provided using the geometric quasilinearization\n(GQL) approach [K. Wu and C.-W. Shu, SIAM Review, 65:1031-1073, 2023]. For the\nmagnetic subsystem, we develop an implicit finite difference CT method that\nconserves energy and maintains a globally DDF constraint. This nonlinear system\nis efficiently solved to machine precision using an iterative algorithm. Since\nthe CT method is unconditionally energy-stable and conserves steady density and\ninternal energy, the PPCT scheme requires only a mild CFL condition for the\nfinite volume method to ensure stability and the PP property. While the focus\nis on 2D cases for clarity, the extension to 3D is discussed. Several\nchallenging numerical experiments, including highly magnetized MHD jets with\nhigh Mach numbers, validate the PPCT scheme's accuracy, robustness, and high\nresolution.\n"", 'Structure-Preserving Oscillation-Eliminating Discontinuous Galerkin\n  Schemes for Ideal MHD Equations: Locally Divergence-Free and\n  Positivity-Preserving   Numerically simulating magnetohydrodynamics (MHD) poses notable challenges,\nincluding the suppression of spurious oscillations near discontinuities (e.g.,\nshocks) and preservation of essential physical structures (e.g., the\ndivergence-free constraint of magnetic field and the positivity of density and\npressure). This paper develops structure-preserving oscillation-eliminating\ndiscontinuous Galerkin (OEDG) schemes for ideal MHD. The schemes leverage a\nlocally divergence-free (LDF) oscillation-eliminating (OE) procedure to\nsuppress spurious oscillations while retaining the LDF property of magnetic\nfield and many desirable attributes of original DG schemes, such as\nconservation, local compactness, and optimal convergence rates. The OE\nprocedure is based on the solution operator of a novel damping equation, a\nlinear system of ordinary differential equations that are exactly solvable\nwithout any discretization. The OE procedure is performed after each\nRunge-Kutta stage and does not impact DG spatial discretization, facilitating\nits easy integration into existing DG codes as an independent module. Moreover,\nthis paper presents a rigorous positivity-preserving (PP) analysis of the LDF\nOEDG schemes on Cartesian meshes, utilizing the optimal convex decomposition\ntechnique and the geometric quasi-linearization (GQL) approach. Efficient PP\nLDF OEDG schemes are derived by incorporating appropriate discretization of\nGodunov-Powell source terms into only the discrete equations of cell averages,\nunder a condition achievable through a simple PP limiter. Several one- and\ntwo-dimensional MHD tests verify the accuracy, effectiveness, and robustness of\nthe proposed structure-preserving OEDG schemes.\n', 'Provably Positive High-Order Schemes for Ideal Magnetohydrodynamics:\n  Analysis on General Meshes   This paper proposes and analyzes arbitrarily high-order discontinuous\nGalerkin (DG) and finite volume methods which provably preserve the positivity\nof density and pressure for the ideal MHD on general meshes. Unified auxiliary\ntheories are built for rigorously analyzing the positivity-preserving (PP)\nproperty of MHD schemes with a HLL type flux on polytopal meshes in any space\ndimension. The main challenges overcome here include establishing relation\nbetween the PP property and discrete divergence of magnetic field on general\nmeshes, and estimating proper wave speeds in the HLL flux to ensure the PP\nproperty. In 1D case, we prove that the standard DG and finite volume methods\nwith the proposed HLL flux are PP, under condition accessible by a PP limiter.\nFor multidimensional conservative MHD system, standard DG methods with a PP\nlimiter are not PP in general, due to the effect of unavoidable\ndivergence-error. We construct provably PP high-order DG and finite volume\nschemes by proper discretization of symmetrizable MHD system, with two\ndivergence-controlling techniques: locally divergence-free elements and a\npenalty term. The former leads to zero divergence within each cell, while the\nlatter controls the divergence error across cell interfaces. Our analysis\nreveals that a coupling of them is important for positivity preservation, as\nthey exactly contribute the discrete divergence-terms absent in standard DG\nschemes but crucial for ensuring the PP property. Numerical tests confirm the\nPP property and the effectiveness of proposed PP schemes. Unlike conservative\nMHD system, the exact smooth solutions of symmetrizable MHD system are proved\nto retain the positivity even if the divergence-free condition is not\nsatisfied. Our analysis and findings further the understanding, at both\ndiscrete and continuous levels, of the relation between the PP property and the\ndivergence-free constraint.\n']","[('magnetohydrodynamic mhd equations', 0.5880771279335022), ('magnetohydrodynamics mhd equations', 0.581399142742157), ('magnetohydrodynamics equations', 0.5250998735427856), ('magnetohydrodynamics mhd', 0.497344434261322), ('magnetohydrodynamic mhd', 0.4829350709915161), ('ideal magnetohydrodynamics', 0.47176244854927063), ('divergence free magnetic', 0.4666568338871002), ('magnetohydrodynamics', 0.4415866732597351), ('ideal mhd equations', 0.4404841363430023), ('magnetohydrodynamic', 0.4168728291988373)]"
808,808,38,808_convex bodies_ball convex_convex body_symmetric convex body,"['convex bodies', 'ball convex', 'convex body', 'symmetric convex body', 'euclidean ball', 'illumination', 'ball space', 'number convex', 'hyperplanes', 'coverings']","['On a Gallai-type problem and illumination of spiky balls and cap bodies   We show that any finite family of pairwise intersecting balls in\n$\\mathbb{E}^n$ can be pierced by $(\\sqrt{3/2}+o(1))^n$ points improving the\npreviously known estimate of $(2+o(1))^n$. As a corollary, this implies that\nany $2$-illuminable spiky ball in $\\mathbb{E}^n$ can be illuminated by\n$(\\sqrt{3/2}+o(1))^n$ directions. For the illumination number of convex spiky\nballs, i.e., cap bodies, we show an upper bound in terms of the sizes of\ncertain related spherical codes and coverings. For large dimensions, this\nresults in an upper bound of $1.19851^n$, which can be compared with the\nprevious $(\\sqrt{2}+o(1))^n$ established only for the centrally symmetric cap\nbodies. We also prove the lower bounds of $(\\tfrac{2}{\\sqrt{3}}-o(1))^n$ for\nthe three problems above.\n', 'On the illumination of centrally symmetric cap bodies in small\n  dimensions   The illumination number $I(K)$ of a convex body $K$ in Euclidean space\n$\\mathbb{E}^d$ is the smallest number of directions that completely illuminate\nthe boundary of a convex body. A cap body $K_c$ of a ball is the convex hull of\na Euclidean ball and a countable set of points outside the ball under the\ncondition that each segment connecting two of these points intersects the ball.\nThe main results of this paper are the sharp estimates $I(K_c)\\leq6$ for\ncentrally symmetric cap bodies of a ball in $\\mathbb{E}^3$, and $I(K_c)\\leq 8$\nfor unconditionally symmetric cap bodies of a ball in $\\mathbb{E}^4$.\n', 'Illuminating spiky balls and cap bodies   The convex hull of a ball with an exterior point is called a spike (or cap).\nA union of finitely many spikes of a ball is called a spiky ball. If a spiky\nball is convex, then we call it a cap body. In this note we upper bound the\nillumination numbers of $2$-illuminable spiky balls as well as centrally\nsymmetric cap bodies. In particular, we prove the Illumination Conjecture for\ncentrally symmetric cap bodies in sufficiently large dimensions by showing that\nany $d$-dimensional centrally symmetric cap body can be illuminated by $<2^d$\ndirections in Euclidean $d$-space for all $d\\geq 20$. Furthermore, we\nstrengthen the latter result for $1$-unconditionally symmetric cap bodies.\n']","[('convex bodies', 0.5327029228210449), ('ball convex', 0.47576025128364563), ('convex body', 0.4579434394836426), ('symmetric convex body', 0.44936591386795044), ('euclidean ball', 0.44868674874305725), ('illumination', 0.39713701605796814), ('ball space', 0.3827623426914215), ('number convex', 0.3579086363315582), ('hyperplanes', 0.35124409198760986), ('coverings', 0.347615122795105)]"
809,809,38,809_gaussian random fields_gaussian fields_gaussian random field_gaussian free,"['gaussian random fields', 'gaussian fields', 'gaussian random field', 'gaussian free', 'isotropic gaussian', 'planar gaussian', 'gaussian free field', 'gaussian field', 'smooth gaussian', 'points gaussian']","['Complexity of Gaussian random fields with isotropic increments   We study the energy landscape of a model of a single particle on a random\npotential, that is, we investigate the topology of level sets of smooth random\nfields on $\\mathbb R^{N}$ of the form $X_N(x) +\\frac\\mu2 \\|x\\|^2,$ where\n$X_{N}$ is a Gaussian process with isotropic increments. We derive asymptotic\nformulas for the mean number of critical points with critical values in an open\nset as the dimension $N$ goes to infinity. In a companion paper, we provide the\nsame analysis for the number of critical points with a given index.\n', 'Landscape $k$-complexity of isotropic centered Gaussian fields   In large dimension, we study the asymptotic behavior of the mean number of\ncritical points with index $k$ below a level $u$ for an isotropic centered\nGaussian random field defined on a family of subsets of $\\mathbb{R}^d$\ndepending on $d$. We prove the existence of three regimes depending on the\nspeed of growth of the volume the parameter set. In the first regime the mean\nnumber of critical points decreases exponentially with the dimension. For the\nsecond regime, there exists a critical level $u_c$ such that the mean number of\ncritical points with index $k$ below a level $u$ with $u>u_c$ increases\nexponentially with the dimension $d$ independently of the index $k$ and\ndecreases exponentially with $d$ when $u<u_c$. In the third regime, there\nexists a layered structure depending on the level $u$ considered and on the\nindex $k$ of the critical points. This behavior is similar to the one\nencountered on the sphere by Auffinger et al. [5]. In the particular case of\nthe Bargmann-Fock field, only two regimes coexist.\n', 'Mean number and correlation function of critical points of isotropic\n  Gaussian fields and some results on GOE random matrices   Let $\\mathcal{X}= \\{X(t) : t \\in \\mathbb{R}^N \\} $ be an isotropic Gaussian\nrandom field with real values.In a first part we study the mean number of\ncritical points of $\\mathcal{X}$ with index $k$ using random matrices tools.We\nobtain an exact expression for the probability density of the $k$th eigenvalue\nof a $N$-GOE matrix.We deduce some exact expressions for the mean number of\ncritical points with a given index. In a second part we study attraction or\nrepulsion between these critical points. A measure is the correlation\nfunction.We prove attraction between critical points when $N>2$, neutrality for\n$N=2$ and repulsion for $N=1$.The attraction between critical points that\noccurs when the dimension is greater than two is due to critical points with\nadjacent indexes.A strong repulsion between maxima and minima is proved. The\ncorrelation function between maxima (or minima) depends on the dimension of the\nambient space.\n']","[('gaussian random fields', 0.6289830803871155), ('gaussian fields', 0.5930847525596619), ('gaussian random field', 0.578471839427948), ('gaussian free', 0.5563110709190369), ('isotropic gaussian', 0.5504617691040039), ('planar gaussian', 0.5472959876060486), ('gaussian free field', 0.5398500561714172), ('gaussian field', 0.5372248888015747), ('smooth gaussian', 0.49627774953842163), ('points gaussian', 0.494331032037735)]"
810,810,38,810_stochastic heat equations_nonlinear stochastic heat_stochastic heat_linear stochastic heat,"['stochastic heat equations', 'nonlinear stochastic heat', 'stochastic heat', 'linear stochastic heat', 'stochastic partial differential', 'stochastic partial', 'heat equations', 'gaussian noise white', 'heat partial_t', 'nonlinear stochastic']","['Small ball probabilities for the stochastic heat equation with colored\n  noise   We consider the stochastic heat equation on the 1-dimensional torus\n$\\mathbb{T}:=\\left[-1,1\\right]$ with periodic boundary conditions: $$\n\\partial_t u(t,x)=\\partial^2_x u(t,x)+\\sigma(t,x,u)\\dot{F}(t,x),\\quad x\\in\n\\mathbb{T},t\\in\\mathbb{R}_+, $$ where $\\dot{F}(t,x)$ is a generalized Gaussian\nnoise, which is white in time and colored in space. Assuming that $\\sigma$ is\nLipschitz in $u$ and uniformly bounded, we estimate small ball probabilities\nfor the solution $u$ when $u(0,x)\\equiv 0$.\n', 'Polarity of almost all points for systems of non-linear stochastic heat\n  equations in the critical dimension   We study vector-valued solutions $u(t,x)\\in\\mathbb{R}^d$ to systems of\nnonlinear stochastic heat equations with multiplicative noise:\n\\begin{equation*} \\frac{\\partial}{\\partial t} u(t,x)=\\frac{\\partial^2}{\\partial\nx^2} u(t,x)+\\sigma(u(t,x))\\dot{W}(t,x). \\end{equation*} Here $t\\geq 0$,\n$x\\in\\mathbb{R}$ and $\\dot{W}(t,x)$ is an $\\mathbb{R}^d$-valued space-time\nwhite noise. We say that a point $z\\in\\mathbb{R}^d$ is polar if\n\\begin{equation*} P\\{u(t,x)=z\\text{ for some $t>0$ and $x\\in\\mathbb{R}$}\\}=0.\n\\end{equation*} We show that in the critical dimension $d=6$, almost all points\nin $\\mathbb{R}^d$ are polar.\n', 'A regularity theory for stochastic generalized Burgers\' equation driven\n  by a multiplicative space-time white noise   We introduce the uniqueness, existence, $L_p$-regularity, and maximal\nH\\""older regularity of the solution to semilinear stochastic partial\ndifferential equation driven by a multiplicative space-time white noise: $$ u_t\n= au_{xx} + bu_{x} + cu + \\bar b|u|^\\lambda u_{x} + \\sigma(u)\\dot W,\\quad\n(t,x)\\in(0,\\infty)\\times\\mathbb{R}; \\quad u(0,\\cdot) = u_0, $$ where $\\lambda >\n0$. The function $\\sigma(u)$ is either bounded Lipschitz or super-linear in\n$u$. The noise $\\dot W$ is a space-time white noise. The coefficients $a,b,c$\ndepend on $(\\omega,t,x)$, and $\\bar b$ depends on $(\\omega,t)$. The\ncoefficients $a,b,c,\\bar{b}$ are uniformly bounded, and $a$ satisfies\nellipticity condition. The random initial data $u_0 = u_0(\\omega,x)$ is\nnonnegative.\n  We have the maximal H\\""older regularity by employing the H\\""older embedding\ntheorem. For example, if $\\lambda \\in(0,1]$ and $\\sigma(u)$ has Lipschitz\ncontinuity, linear growth, and boundedness in $u$, for $T<\\infty$ and\n$\\varepsilon>0$, $$u \\in C^{1/4 - \\varepsilon,1/2 -\n\\varepsilon}_{t,x}([0,T]\\times\\mathbb{R})\\quad(a.s.). $$ On the other hand, if\n$\\lambda\\in(0,1)$ and $\\sigma(u) = |u|^{1+\\lambda_0}$ with\n$\\lambda_0\\in[0,1/2)$, for $T<\\infty$ and $\\varepsilon>0$, $$u \\in\nC^{\\frac{1/2-(\\lambda -1/2) \\vee \\lambda_0}{2} - \\varepsilon,1/2-(\\lambda -1/2)\n\\vee \\lambda_0 - \\varepsilon}_{t,x}([0,T]\\times\\mathbb{R})\\quad (a.s.).$$ It\nshould be noted that if $\\sigma(u)$ is bounded Lipschitz in $u$, the H\\""older\nregularity of the solution is independent of $\\lambda$. However, if $\\sigma(u)$\nis super-linear in $u$, the H\\""older regularities of the solution are affected\nby nonlinearities, $\\lambda$ and $\\lambda_0.$\n']","[('stochastic heat equations', 0.6252840161323547), ('nonlinear stochastic heat', 0.5918475985527039), ('stochastic heat', 0.5527523159980774), ('linear stochastic heat', 0.5524232387542725), ('stochastic partial differential', 0.5125332474708557), ('stochastic partial', 0.49549686908721924), ('heat equations', 0.46382787823677063), ('gaussian noise white', 0.4563634693622589), ('heat partial_t', 0.44409236311912537), ('nonlinear stochastic', 0.43947941064834595)]"
811,811,38,811_arithmetic coding_length encoding_compression efficiency_compression performance,"['arithmetic coding', 'length encoding', 'compression efficiency', 'compression performance', 'universal compression', 'compression rates', 'lossless compression', 'text compression', 'compression ratio', 'compression']","[""Efficiency of ANS Entropy Encoders   Asymmetric Numeral Systems (ANS) is a class of entropy encoders that had an\nimmense impact on the data compression, substituting arithmetic and Huffman\ncoding. It was studied by different authors but the precise asymptotics of its\nredundancy (in relation to the entropy) was not completely understood. We\nobtain optimal bounds for the redundancy of the tabled ANS (tANS), the most\npopular ANS variant. Given a sequence $a_1,a_2,\\ldots,a_n$ of symbols from an\nalphabet $\\{0,1,\\ldots,\\sigma-1\\}$ such that each symbol $a$ occurs in it $f_a$\ntimes and $n=2^r$, the tANS encoder using Duda's ``precise initialization'' to\nfill tANS tables transforms this sequence into a bit string of the following\nlength (the frequencies are not included in the encoding):\n$\\sum\\limits_{a\\in[0..\\sigma)}f_a\\cdot\\log\\frac{n}{f_a}+O(\\sigma+r)$, where\n$O(\\sigma+r)$ can be bounded by $\\sigma\\log e+r$. The $r$-bit term is an\nartifact indispensable to ANS; the rest incurs a redundancy of\n$O(\\frac{\\sigma}{n})$ bits per symbol. We complement this by examples showing\nthat an $\\Omega(\\sigma+r)$ redundancy is necessary. We argue that similar\nexamples exist for most adequate initialization methods for tANS. Thus, we\nrefute Duda's conjecture that the redundancy is $O(\\frac{\\sigma}{n^2})$ bits\nper symbol. We also propose a variant of the range ANS (rANS), called rANS with\nfixed accuracy, parameterized by $k\\ge 1$. In this variant the integer\ndivision, which is unavoidable in rANS, is performed only when its result\nbelongs to $[2^k..2^{k+1})$. Therefore, the division can be computed by faster\nmethods provided $k$ is small. We bound the redundancy for our rANS variant by\n$\\frac{n}{2^k-1}\\log e+r$.\n"", 'Encoding and Decoding Algorithms of ANS Variants and Evaluation of Their\n  Average Code Lengths   Asymmetric Numeral Systems (ANS) proposed by Jarek Duda are high-performance\ndistortionless data compression schemes that can achieve almost the same\ncompression performance as arithmetic codes with less arithmetic operations\nthan arithmetic coding. The ANS is widely used in various practical systems\nlike Facebook, Apple, Google, Dropbox, Microsoft, and Pixar, due to their high\nperformance, but many researchers still lack much knowledge about the ANS. This\npaper thoroughly explains the encoding and decoding algorithms of the ANS, and\ntheoretically analyzes the average code length achievable by the ANS.\n', ""Compression Optimality of Asymmetric Numeral Systems   Compression also known as entropy coding has a rich and long history.\nHowever, a recent explosion of multimedia Internet applications (such as\nteleconferencing and video streaming for instance) renews an interest in fast\ncompression that also squeezes out as much redundancy as possible. In 2009\nJarek Duda invented his asymmetric numeral system (ANS). Apart from a beautiful\nmathematical structure, it is very efficient and offers compression with a very\nlow residual redundancy. ANS works well for any symbol source statistics.\nBesides, ANS has become a preferred compression algorithm in the IT industry.\nHowever, designing ANS instance requires a random selection of its symbol\nspread function. Consequently, each ANS instance offers compression with a\nslightly different compression rate.\n  The paper investigates compression optimality of ANS. It shows that ANS is\noptimal (i.e. the entropies of encoding and source are equal) for any symbol\nsources whose probability distribution is described by natural powers of 1/2.\nWe use Markov chains to calculate ANS state probabilities. This allows us to\ndetermine ANS compression rate precisely. We present two algorithms for finding\nANS instances with high compression rates. The first explores state probability\napproximations in order to choose ANS instances with better compression rates.\nThe second algorithm is a probabilistic one. It finds ANS instances, whose\ncompression rate can be made as close to the best rate as required. This is\ndone at the expense of the number $\\theta$ of internal random ``coin'' tosses.\nThe algorithm complexity is ${\\cal O}(\\theta L^3)$, where $L$ is the number of\nANS states. The complexity can be reduced to ${\\cal O}(\\theta L\\log{L})$ if we\nuse a fast matrix inversion. If the algorithm is implemented on quantum\ncomputer, its complexity becomes ${\\cal O}(\\theta (\\log{L})^3)$.\n""]","[('arithmetic coding', 0.5974803566932678), ('length encoding', 0.5890799164772034), ('compression efficiency', 0.5821693539619446), ('compression performance', 0.565659761428833), ('universal compression', 0.5568761825561523), ('compression rates', 0.5567502975463867), ('lossless compression', 0.5534306764602661), ('text compression', 0.5349521636962891), ('compression ratio', 0.52413010597229), ('compression', 0.5199114680290222)]"
812,812,38,812_viscous conservation_viscous conservation law_stability viscous_viscous burgers,"['viscous conservation', 'viscous conservation law', 'stability viscous', 'viscous burgers', 'dissipation viscous', 'stability shock', 'shock waves', 'asymptotic stability', 'one dimensional burgers', 'shock formation']","['$L^2$ decay for large perturbations of viscous shocks for multi-D\n  Burgers equation   We consider a planar viscous shock of moderate strength for a scalar viscous\nconservation law in multi-D. We consider a strictly convex flux, as a small\nperturbation of the Burgers flux, along the normal direction to the shock\nfront. However, for the transversal directions, we do not have any restrictions\non flux function. We first show the contraction property for any large\nperturbations in $L^2$ of the planar viscous shock. If the initial\n$L^2$-perturbation is also in $L^1$, the large perturbation converges to zero\nin $L^2$ as time goes to infinity with $t^{-1/4}$ decay rate. The contraction\nand decay estimates hold up to dynamical shift. For the results, we do not\nimpose any smallness conditions on the initial value. This result extends the\n1D case \\cite{Kang-V-1} by the first author and Vasseur to the\nmulti-dimensional case.\n', 'The inviscid limit of viscous Burgers at nondegenerate shock formation   We study the vanishing viscosity limit of the one-dimensional Burgers\nequation near nondegenerate shock formation. We develop a matched asymptotic\nexpansion that describes small-viscosity solutions to arbitrary order up to the\nmoment the first shock forms. The inner part of this expansion has a novel\nstructure based on a fractional spacetime Taylor series for the inviscid\nsolution. We obtain sharp vanishing viscosity rates in a variety of norms,\nincluding $L^\\infty$. Comparable prior results break down in the vicinity of\nshock formation. We partially fill this gap.\n', ""Viscous shock waves of Burgers equation with fast diffusion and\n  singularity   In this paper, we study the asymptotic stability of viscous shock waves for\nBurgers' equation with fast diffusion $u_t+f(u)_x=\\mu (u^m)_{xx}$ on\n$\\mathbb{R} \\times (0, +\\infty)$ when $0<m<1$. For the proposed constant states\n$u_->u_+=0$, the equation with fast diffusion\n$(u^m)_{xx}=m\\left(\\frac{u_x}{u^{1-m}}\\right)_x$ processes a strong singularity\nat $u_+=0$, which causes the stability study to be challenging. We observe\nthat, there exist two different types of viscous shocks, one is the\nnon-degenerate shock satisfying Lax's entropy condition with fast algebraic\ndecay to the singular state $u_+=0$, which causes much strong singularity to\nthe system in the form of $m\\left(\\frac{u_x}{u^{1-m}}\\right)_x$, and the other\nis the degenerate viscous shock with slow algebraic decay to $u_+=0$, which\nmakes less strong singularity to the system. In order to overcome the\nsingularity at $u_+=0$, we technically use the weighted energy method and\ndevelop a new strategy where the weights related to the shock waves are\ncarefully selected, while the chosen weights for the non-degenerate case are\nstronger than the degenerate case. Numerical simulations are also carried out\nin different cases to illustrate and validate our theoretical results. In\nparticular, we numerically approximate the solution for different value of\n$0<m<1$, and find that the shapes of shock waves become steeper when the\nsingularity $\\left(\\frac{u_x}{u^{1-m}}\\right)_x$ is stronger as $m\\rightarrow\n0$, which indicates that the effect of singular fast diffusion on the solution\nis essential.\n""]","[('viscous conservation', 0.5791534185409546), ('viscous conservation law', 0.5617442727088928), ('stability viscous', 0.5589849352836609), ('viscous burgers', 0.5520671606063843), ('dissipation viscous', 0.5422986149787903), ('stability shock', 0.5064477324485779), ('shock waves', 0.4774791896343231), ('asymptotic stability', 0.46614590287208557), ('one dimensional burgers', 0.4660547077655792), ('shock formation', 0.45773953199386597)]"
813,813,38,813_theory continued fractions_hausdorff dimension_continued fractions_also hausdorff dimension,"['theory continued fractions', 'hausdorff dimension', 'continued fractions', 'also hausdorff dimension', 'continued fraction expansions', 'measure hausdorff dimension', 'regular continued fraction', 'hausdorff dimension sets', 'determine hausdorff dimension', 'infty hausdorff']","['Metrical properties of the product of partial quotients with geometric\n  mean in continued fractions   The theory of uniform Diophantine approximation concerns the study of\nDirichlet improvable numbers and the metrical aspect of this theory leads to\nthe study of the product of consecutive partial quotients in continued\nfractions. It is known that the dimension of the set of Dirichlet\nnon-improvable numbers depends upon the number of partial quotients in the\nproduct string. However, one can see that the Hausdorff dimension is the same\nfor any number of consecutive partial quotients with a constant gap. This paper\nis aimed at a detailed analysis on how the Hausdorff dimension changes when\nthere is a linear gap in indices and the number of partial quotients in the\nproduct grows. More precisely, let $d\\in \\N_{\\ge 1}, t\\in\\Z_{\\geq 0}$ and\n$f(n)=dn+t$, we present the detailed Hausdorff dimension analysis of the\nset\\begin{equation*} E_{f}(\\psi):=\\left\\{x\\in [0, 1):\n\\sqrt[n]{a_{f(n)}(x)a_{2f(n)}(x)\\cdots a_{nf(n)}(x)}\\geq \\psi(n) \\ {\\rm for \\\ninfinitely \\ many} \\ n\\in \\N\\right\\}. \\end{equation*} It is seen that the\ndimension is larger if $d$ is larger and $t$ has no contribution to the\ndimension.\n', 'Dimensions of certain sets of continued fractions with non-decreasing\n  partial quotients   Let $[a_1(x),a_2(x),a_3(x),\\cdots]$ be the continued fraction expansion of\n$x\\in (0,1)$. This paper is concerned with certain sets of continued fractions\nwith non-decreasing partial quotients. As a main result, we obtain the\nHausdorff dimension of the set \\[\\left\\{x\\in(0,1): a_1(x)\\leq a_2(x)\\leq\n\\cdots,\\ \\limsup\\limits_{n\\to\\infty}\\frac{\\log a_n(x)}{\\psi(n)}=1\\right\\}\\] for\nany $\\psi:\\mathbb{N}\\rightarrow\\mathbb{R}^+$ satisfying $\\psi(n)\\to\\infty$ as\n$n\\to\\infty$.\n', ""Hausdorff dimension of sets with restricted, slowly growing partial\n  quotients in semi-regular continued fractions   We determine the Hausdorff dimension of sets of irrationals in $(0,1)$ whose\npartial quotients in semi-regular continued fractions obey certain restrictions\nand growth conditions. This result substantially generalizes that of the second\nauthor [Proc. Amer. Math. Soc. {\\bf 151} (2023), 3645--3653] and the solution\nof Hirst's conjecture [B.-W. Wang and J. Wu, Bull. London Math. Soc. {\\bf 40}\n(2008), 18--22], both previously obtained for the regular continued fraction.\nTo prove the result, we construct non-autonomous iterated function systems\nwell-adapted to the given restrictions and growth conditions on partial\nquotients, estimate the associated pressure functions, and then apply Bowen's\nformula.\n""]","[('theory continued fractions', 0.6083031296730042), ('hausdorff dimension', 0.5017163157463074), ('continued fractions', 0.49745887517929077), ('also hausdorff dimension', 0.49651774764060974), ('continued fraction expansions', 0.4955609142780304), ('measure hausdorff dimension', 0.4938754141330719), ('regular continued fraction', 0.4841129183769226), ('hausdorff dimension sets', 0.46614590287208557), ('determine hausdorff dimension', 0.4495154917240143), ('infty hausdorff', 0.4481724798679352)]"
814,814,38,814_conformal field theories_conformal field theory_holographically_holographic,"['conformal field theories', 'conformal field theory', 'holographically', 'holographic', 'quantum gravity', 'entanglement entropy', 'dimensional conformal', 'ads cft', 'holography', 'gauge theories']","['A proposal for 3d quantum gravity and its bulk factorization   Recent progress in AdS/CFT has provided a good understanding of how the bulk\nspacetime is encoded in the entanglement structure of the boundary CFT.\nHowever, little is known about how spacetime emerges directly from the bulk\nquantum theory. We address this question in an effective 3d quantum theory of\npure gravity, which describes the high temperature regime of a holographic CFT.\nThis theory can be viewed as a $q$-deformation and dimensional uplift of JT\ngravity. Using this model, we show that the Bekenstein-Hawking entropy of a\ntwo-sided black hole equals the bulk entanglement entropy of gravitational edge\nmodes. In the conventional Chern-Simons description, these black holes\ncorrespond to Wilson lines in representations of $\\PSL(2,\\mathbb{R})\\otimes\n\\PSL(2,\\mathbb{R}) $. We show that the correct calculation of gravitational\nentropy suggests we should interpret the bulk theory as an extended topological\nquantum field theory associated to the quantum semi-group\n$\\SL^+_{q}(2,\\mathbb{R})\\otimes \\SL^+_{q}(2,\\mathbb{R})$. Our calculation\nsuggests an effective description of bulk microstates in terms of collective,\nanyonic degrees of freedom whose entanglement leads to the emergence of the\nbulk spacetime.\n', 'Ryu-Takayanagi Formula for Multi-Boundary Black Holes from 2D Large-$\\textbf{$c$}$ CFT Ensemble We study a class of quantum states involving multiple entangled CFTs in AdS$_3$/CFT$_2$, associated with multi-boundary black hole geometries, and demonstrate that the Ryu-Takayanagi (RT) formula for entanglement entropy can be derived using only boundary CFT data. Approximating the OPE coefficients by their Gaussian moments within the 2D large-$c$ CFT ensemble, we show that both the norm of the states and the entanglement entropies associated with various bipartitions--reproducing the expected bulk dual results--can be computed purely from the CFT. All $\\textit{macroscopic geometric}$ structures arising from gravitational saddles emerge entirely from the universal statistical moments of the $\\textit{microscopic algebraic}$ CFT data, revealing a statistical-mechanical mechanism underlying semiclassical gravity. We establish a precise correspondence between the CFT norm, the Liouville partition function with ZZ boundary conditions, and the exact gravitational path integral over 3D multi-boundary black hole geometries. For entanglement entropy, each RT phase arises from a distinct leading-order Gaussian contraction, with phase transitions--analogous to replica wormholes--emerging naturally from varying dominant statistical patterns in the CFT ensemble. Our derivation elucidates how the general mechanism behind holographic entropy, namely a boundary replica direction that elongates and becomes contractible in the bulk dual, is encoded explicitly in the statistical structure of the CFT data.', 'Simulating Holographic Conformal Field Theories on Hyperbolic Lattices   We demonstrate how table-top settings combining hyperbolic lattices with\nnonlinear dynamics universally encode aspects of the\nbulk-boundary-correspondence between gravity in anti-de-Sitter (AdS) space and\nconformal field theory (CFT). Our concrete and broadly applicable holographic\ntoy model simulates gravitational self-interactions in the bulk and features an\nemergent CFT with nontrivial correlations on the boundary. We measure the CFT\ndata contained in the two- and three-point functions and clarify how a thermal\nCFT is simulated through an effective black hole geometry. As a concrete\nexample, we propose and simulate an experimentally feasible protocol to measure\nthe holographic CFT using electrical circuits.\n']","[('conformal field theories', 0.5728599429130554), ('conformal field theory', 0.5327429175376892), ('holographically', 0.49999570846557617), ('holographic', 0.49091997742652893), ('quantum gravity', 0.4707924425601959), ('entanglement entropy', 0.447909951210022), ('dimensional conformal', 0.44222623109817505), ('ads cft', 0.433245986700058), ('holography', 0.4308120608329773), ('gauge theories', 0.4171833395957947)]"
815,815,38,815_polynomials knots_polynomial knot_alexander polynomials_alexander polynomial,"['polynomials knots', 'polynomial knot', 'alexander polynomials', 'alexander polynomial', 'polynomials links', 'knot theory', 'polynomial link', 'knots links', 'singular knots', 'knot types']","['Signature Jumps and Alexander Polynomials for Links   We relate the jumps of the signature function of a link to the roots of its\nfirst nonzero higher Alexander polynomial.\n', ""Alexander and Jones Polynomials of weaving 3-braid links and Whitney\n  rank polynomials of Lucas lattice   We establish a relationship between the Jones polynomial of generalized\nweaving knots of type $W(3,n,m)$ and the Chebyshev polynomial of the first\nkind. Consequently, we prove that the coefficients of the Jones polynomial of\nweaving knots are basically the Whitney numbers of Lucas lattices. Furthermore,\nwe give an explicit formula for the Alexander polynomial of weaving knots\n$W(3,n)$ and we prove that it satisfies Fox's trapezoidal conjecture.\n"", 'Alexander polynomials of ribbon knots and virtual knots   We find that Alexander polynomial of a ribbon knot in $ \\mathbb{Z}HS^3 $ is\ndetermined by the intrinsic singularity information of its ribbon, and give a\nformula to calculate Alexander polynomial of a ribbon knot by that. We define\nhalf Alexander polynomial $ A_R (t) $, an invariant of oriented ribbons, and in\nfact the Alexander polynomial of the ribbon knot is $ A_R (t) A_R (t^{-1}) $.\nWe give two useful simplified formulas for half Alexander polynomial. We\ncharacterize completely the polynomials arising as half Alexander polynomials\nof ribbons. The above study unexpectedly leads us to discover new formulas for\nAlexander polynomial of general knots and virtual knots in terms of Gauss\ndiagrams.\n']","[('polynomials knots', 0.742454469203949), ('polynomial knot', 0.7310178279876709), ('alexander polynomials', 0.6866999268531799), ('alexander polynomial', 0.6662452816963196), ('polynomials links', 0.6374948620796204), ('knot theory', 0.6250966191291809), ('polynomial link', 0.6100858449935913), ('knots links', 0.556451678276062), ('singular knots', 0.5433096289634705), ('knot types', 0.53639155626297)]"
816,816,38,816_bent functions_constructions generalized_dual generalized_functions construction,"['bent functions', 'constructions generalized', 'dual generalized', 'functions construction', 'secondary constructions', 'regular generalized', 'f_1 ldots f_m', 'functions satisfying', 'functions mathbb _2', 'extended affine']","['Bent Partitions, Vectorial Dual-Bent Functions and Partial Difference\n  Sets   It is known that partial spreads is a class of bent partitions. In\n\\cite{AM2022Be,MP2021Be}, two classes of bent partitions whose forms are\nsimilar to partial spreads were presented. In \\cite{AKM2022Ge}, more bent\npartitions $\\Gamma_{1}, \\Gamma_{2}, \\Gamma_{1}^{\\bullet}, \\Gamma_{2}^{\\bullet},\n\\Theta_{1}, \\Theta_{2}$ were presented from (pre)semifields, including the bent\npartitions given in \\cite{AM2022Be,MP2021Be}. In this paper, we investigate the\nrelations between bent partitions and vectorial dual-bent functions. For any\nprime $p$, we show that one can generate certain bent partitions (called bent\npartitions satisfying Condition $\\mathcal{C}$) from certain vectorial dual-bent\nfunctions (called vectorial dual-bent functions satisfying Condition A). In\nparticular, when $p$ is an odd prime, we show that bent partitions satisfying\nCondition $\\mathcal{C}$ one-to-one correspond to vectorial dual-bent functions\nsatisfying Condition A. We give an alternative proof that $\\Gamma_{1},\n\\Gamma_{2}, \\Gamma_{1}^{\\bullet}, \\Gamma_{2}^{\\bullet}, \\Theta_{1}, \\Theta_{2}$\nare bent partitions. We present a secondary construction of vectorial dual-bent\nfunctions, which can be used to generate more bent partitions. We show that any\nternary weakly regular bent function $f: V_{n}^{(3)}\\rightarrow \\mathbb{F}_{3}$\n($n$ even) of $2$-form can generate a bent partition. When such $f$ is weakly\nregular but not regular, the generated bent partition by $f$ is not coming from\na normal bent partition, which answers an open problem proposed in\n\\cite{AM2022Be}. We give a sufficient condition on constructing partial\ndifference sets from bent partitions, and when $p$ is an odd prime, we provide\na characterization of bent partitions satisfying Condition $\\mathcal{C}$ in\nterms of partial difference sets.\n', 'On design-theoretic aspects of Boolean and vectorial bent functions   There are two construction methods of designs from $(n,m)$-bent functions,\nknown as translation and addition designs. In this paper we analyze, which\nequivalence relation for Boolean bent functions, i.e. $(n,1)$-bent functions,\nand vectorial bent functions, i.e. $(n,m)$-bent functions with $2\\le m\\le n/2$,\nis coarser: extended-affine equivalence or isomorphism of associated\ntranslation and addition designs. First, we observe that similar to the Boolean\nbent functions, extended-affine equivalence of vectorial $(n,m)$-bent functions\nand isomorphism of addition designs are the same concepts for all even $n$ and\n$m\\le n/2$. Further, we show that extended-affine inequivalent Boolean bent\nfunctions in $n$ variables, whose translation designs are isomorphic, exist for\nall $n\\ge6$. This implies, that isomorphism of translation designs for Boolean\nbent functions is a coarser equivalence relation than extended-affine\nequivalence. However, we do not observe the same phenomenon for vectorial bent\nfunctions in a small number of variables. We classify and enumerate all\nvectorial bent functions in six variables and show, that in contrast to the\nBoolean case, one cannot exhibit isomorphic translation designs from\nextended-affine inequivalent vectorial $(6,m)$-bent functions with $m\\in\\{ 2,3\n\\}$.\n', 'On the Dual of Generalized Bent Functions   In this paper, we study the dual of generalized bent functions $f:\nV_{n}\\rightarrow \\mathbb{Z}_{p^k}$ where $V_{n}$ is an $n$-dimensional vector\nspace over $\\mathbb{F}_{p}$ and $p$ is an odd prime, $k$ is a positive integer.\nIt is known that weakly regular generalized bent functions always appear in\npairs since the dual of a weakly regular generalized bent function is also a\nweakly regular generalized bent function. The dual of non-weakly regular\ngeneralized bent functions can be generalized bent or not generalized bent. By\ngeneralizing the construction of \\cite{Cesmelioglu5}, we obtain an explicit\nconstruction of generalized bent functions for which the dual can be\ngeneralized bent or not generalized bent. We show that the generalized indirect\nsum construction method given in \\cite{Wang} can provide a secondary\nconstruction of generalized bent functions for which the dual can be\ngeneralized bent or not generalized bent. By using the knowledge on ideal\ndecomposition in cyclotomic field, we prove that $f^{**}(x)=f(-x)$ if $f$ is a\ngeneralized bent function and its dual $f^{*}$ is also a generalized bent\nfunction. For any non-weakly regular generalized bent function $f$ which\nsatisfies that $f(x)=f(-x)$ and its dual $f^{*}$ is generalized bent, we give a\nproperty and as a consequence, we prove that there is no self-dual generalized\nbent function $f: V_{n}\\rightarrow \\mathbb{Z}_{p^k}$ if $p\\equiv 3 \\ (mod \\ 4)$\nand $n$ is odd. For $p \\equiv 1 \\ (mod \\ 4)$ or $p\\equiv 3 \\ (mod \\ 4)$ and $n$\nis even, we give a secondary construction of self-dual generalized bent\nfunctions. In the end, we characterize the relations between the generalized\nbentness of the dual of generalized bent functions and the bentness of the dual\nof bent functions, as well as the self-duality relations between generalized\nbent functions and bent functions by the decomposition of generalized bent\nfunctions.\n']","[('bent functions', 0.5913937091827393), ('constructions generalized', 0.44653013348579407), ('dual generalized', 0.4440990090370178), ('functions construction', 0.4125659167766571), ('secondary constructions', 0.4049614369869232), ('regular generalized', 0.3897120952606201), ('f_1 ldots f_m', 0.38616812229156494), ('functions satisfying', 0.3794037997722626), ('functions mathbb _2', 0.37712183594703674), ('extended affine', 0.3769530653953552)]"
817,817,38,817_harmonic mappings_inequalities harmonic_harmonic mapping_harmonic functions,"['harmonic mappings', 'inequalities harmonic', 'harmonic mapping', 'harmonic functions', 'quasiconformal harmonic', 'preserving harmonic', 'properties harmonic', 'sense preserving harmonic', 'fixed analytic', 'bohr radius']","[""Bohr's phenomenon for the classes of Quasi-subordination and\n  $K$-quasiregular harmonic mappings   In this paper, we investigate the Bohr radius for $K$-quasiregular\nsense-preserving harmonic mappings $f=h+\\overline{g}$ in the unit disk\n$\\mathbb{D}$ such that the translated analytic part $h(z)-h(0)$ is\nquasi-subordinate to some analytic function. The main aim of this article is to\nextend and to establish sharp versions of four recent theorems by Liu and\nPonnusamy \\cite{LP2019} and, in particular, we settle affirmatively the two\nconjectures proposed by them. Furthermore, we establish two refined versions of\nBohr's inequalities and determine the Bohr radius for the derivatives of\nanalytic functions associated with quasi-subordination.\n"", ""The Bohr's phenomenon for certain K-quasiconformal harmonic mappings   The primary objective of this paper is to establish several sharp versions of\nimproved Bohr inequalities, refined Bohr inequalities, and Bohr-Rogosinski\ninequalities for the class of $K$-quasiconformal sense-preserving harmonic\nmappings $f=h+\\overline{g}$ in the unit disk $\\Bbb{D}:=\\{z\\in\\mathbb{C}:\n|z|<1\\}$, where $f$ and $g$ are analytic functions in $\\mathbb{D}$.\n"", ""The Bohr's Phenomenon for the class of K-quasiconformal harmonic\n  mappings   The primary objective of this paper is to establish several sharp versions of\nimproved Bohr inequality, refined Bohr-type inequality, and refined\nBohr-Rogosinski inequality for the class of $K$-quasiconformal sense-preserving\nharmonic mappings $f=h+\\overline{g}$ in the unit disk $\\mathbb{D} :=\n\\{z\\in\\mathbb{C} : |z| < 1\\}$. In order to achieve these objectives, we employ\nthe non-negative quantity $S_\\rho(h)$ and the concept of replacing the initial\ncoefficients of the majorant series by the absolute values of the analytic\nfunction and its derivative, as well as other various settings. Moreover, we\nobtain the sharp Bohr-Rogosinski radius for harmonic mappings in the unit disk\nby replacing the bounding condition on the analytic function $h$ with the\nhalf-plane condition.\n""]","[('harmonic mappings', 0.5888442397117615), ('inequalities harmonic', 0.5567302107810974), ('harmonic mapping', 0.5519084334373474), ('harmonic functions', 0.47783467173576355), ('quasiconformal harmonic', 0.46581903100013733), ('preserving harmonic', 0.456931471824646), ('properties harmonic', 0.43288731575012207), ('sense preserving harmonic', 0.41049230098724365), ('fixed analytic', 0.38901954889297485), ('bohr radius', 0.38380223512649536)]"
818,818,38,818_kloosterman sums_sums kloosterman sums_sums kloosterman_sums applications,"['kloosterman sums', 'sums kloosterman sums', 'sums kloosterman', 'sums applications', 'sums modulo', 'coefficients modular forms', 'bounds sums', 'dedekind zeta functions', 'kloosterman', 'sums arithmetic']","['Sums of Kloosterman sums over square-free and smooth integers   Recently there has been a large number of works on bilinear sums with\nKloosterman sums and on sums of Kloosterman sums twisted by arithmetic\nfunctions. Motivated by these, we consider several related new questions about\nsums of Kloosterman sums parametrised by square-free and smooth integers.\n', 'Kloosterman sums do not correlate with periodic functions   We provide uniform bounds for sums of Kloosterman sums in all arithmetic\nprogressions. As a consequence, we find that Kloosterman sums do not correlate\nwith periodic functions.\n', 'Some applications of smooth bilinear forms with Kloosterman sums   We revisit a recent bound of I. Shparlinski and T. P. Zhang on bilinear forms\nwith Kloosterman sums, and prove an extension for correlation sums of\nKloosterman sums against Fourier coefficients of modular forms. We use these\nbounds to improve on earlier results on sums of Kloosterman sums along the\nprimes and on the error term of the fourth moment of Dirichlet $L$-functions.\n']","[('kloosterman sums', 0.8411476016044617), ('sums kloosterman sums', 0.8327558636665344), ('sums kloosterman', 0.7801035642623901), ('sums applications', 0.48771345615386963), ('sums modulo', 0.4809127748012543), ('coefficients modular forms', 0.46800696849823), ('bounds sums', 0.46034330129623413), ('dedekind zeta functions', 0.4539320170879364), ('kloosterman', 0.4483291804790497), ('sums arithmetic', 0.44556301832199097)]"
819,819,38,819_species reaction diffusion_predator prey system_asymptotic spreading_prey system,"['species reaction diffusion', 'predator prey system', 'asymptotic spreading', 'prey system', 'reaction diffusion', 'diffusion system', 'diffusion', 'dispersal', 'spreading speeds', 'diffusion case']","['Dynamics for a Ratio-dependent Prey-predator Model with Different Free\n  Boundaries   In this paper, we study the dynamics of the ratio-dependent type\nprey-predator model with different free boundaries. The two free boundaries,\ndetermined by prey and predator respectively, implying that they may intersect\neach other as time evolves, are used to describe the spreading of prey and\npredator. We mainly investigate the longtime behaviors of predator and prey.\nThen some sufficient conditions for spreading and vanishing are given. In\naddition, when spreading occurs, some estimates of asymptotic spreading speeds\nof u, v and asymptotic speeds of h, g are provided.\n', 'Asymptotic spreading of predator-prey populations in a shifting\n  environment   Inspired by recent studies associating shifting temperature conditions with\nchanges in the efficiency of predator species in converting their prey to\noffspring, we propose a predator-prey model of reaction-diffusion type to\nanalyze the consequence of such effects on the population dynamics and spread\nof species. In the model, the predator conversion efficiency is represented by\na spatially heterogeneous function depending on the variable $\\xi=x-c_1t$ for\nsome given $c_1>0$. Using the Hamilton-Jacobi approach, we provide explicit\nformulas for the spreading speed of the predator species. When the conversion\nfunction is monotone increasing, the spreading speed is determined in all cases\nand non-local pulling is possible. When the function is monotone decreasing, we\nprovide formulas for the spreading speed when the rate of shift of the\nconversion function is sufficiently fast or slow.\n', 'A Free Boundary Problem with a Stefan Condition for a Ratio-dependent\n  Predator-prey Model   In this paper we study a ratio-dependent predator-prey model with a free\nboundary causing by both prey and predator over a one dimensional habitat. We\nstudy the long time behaviors of the two species and prove a\nspreading-vanishing dichotomy, namely, as t goes to infinity, both prey and\npredator successfully spread to the whole space and survive in the new\nenvironment, or they spread within a bounded area and die out eventually. Then\nthe criteria governing spreading and vanishing are obtained. Finally, when\nspreading occurs, we provide some estimates to the asymptotic spreading speed\nof h(t).\n']","[('species reaction diffusion', 0.5940065383911133), ('predator prey system', 0.5658944845199585), ('asymptotic spreading', 0.5586237907409668), ('prey system', 0.5303263068199158), ('reaction diffusion', 0.5152600407600403), ('diffusion system', 0.5118148922920227), ('diffusion', 0.5048444867134094), ('dispersal', 0.5046676993370056), ('spreading speeds', 0.5007911324501038), ('diffusion case', 0.48694029450416565)]"
820,820,38,820_quiver gauge theories_supersymmetric gauge theories_gauge theories_corresponding toric,"['quiver gauge theories', 'supersymmetric gauge theories', 'gauge theories', 'corresponding toric', 'calabi yau threefolds', 'supersymmetric gauge', 'calabi yau folds', 'branes', 'structure moduli', 'yau threefolds']","['Generative AI for Brane Configurations and Coamoeba   We introduce a generative AI model to obtain Type IIB brane configurations\nthat realize toric phases of a family of 4d N=1 supersymmetric gauge theories.\nThese 4d N=1 quiver gauge theories are worldvolume theories of a D3-brane\nprobing a toric Calabi-Yau 3-fold. The Type IIB brane configurations are given\nby the coamoeba projection of the mirror curve associated with the toric\nCalabi-Yau 3-fold. The shape of the mirror curve and its coamoeba projection,\nas well as the corresponding Type IIB brane configuration and the toric phase\nof the 4d N=1 theory, all depend on the complex structure moduli parameterizing\nthe mirror curve. We train a generative AI model, a conditional variational\nautoencoder (CVAE), that takes a choice of complex structure moduli as input\nand generates the corresponding coamoeba. This enables us not only to obtain a\nhigh-resolution representation of the entire phase space for a family of 4d N=1\ntheories corresponding to the same toric Calabi-Yau 3-fold, but also to\ncontinuously track the movements of the mirror curve and the branes wrapping\nthe curve in the corresponding Type IIB brane configurations during phase\ntransitions associated with Seiberg duality.\n', '4d Crystal Melting, Toric Calabi-Yau 4-Folds and Brane Brick Models   We introduce a class of 4-dimensional crystal melting models that count the\nBPS bound state of branes on toric Calabi-Yau 4-folds. The crystalline\nstructure is determined by the brane brick model associated to the Calabi-Yau\n4-fold under consideration or, equivalently, its dual periodic quiver. The\ncrystals provide a discretized version of the underlying toric geometries. We\nintroduce various techniques to visualize crystals and their melting\nconfigurations, including 3-dimensional slicing and Hasse diagrams. We\nillustrate the construction with the D0-D8 system on $\\mathbb{C}^4$. Finally,\nwe outline how our proposal generalizes to arbitrary toric CY 4-folds and\ngeneral brane configurations.\n', ""Birational Transformations and 2d (0,2) Quiver Gauge Theories beyond\n  Toric Fano 3-folds   We show that a family of birational transformations that relate toric Fano\n3-folds defined by reflexive lattice polytopes can be identified with mass\ndeformations of corresponding 2d (0,2) supersymmetric quiver gauge theories.\nThese theories are realized by a Type IIA brane configuration known as brane\nbrick models. We further show that the same family of birational\ntransformations extends to more general toric Calabi-Yau 4-folds, including\nthose defined by non-reflexive toric diagrams. Under these birational\ntransformations, the mesonic moduli spaces of the associated abelian 2d (0,2)\nsupersymmetric gauge theories and brane brick models share the same number of\ngenerators and the same Hilbert series when refined only under the U(1)R\nsymmetry. Since these transformations categorize toric Calabi-Yau 4-folds and\ntheir corresponding 2d (0,2) supersymmetric gauge theories into non-trivial\nequivalence classes, we anticipate that our findings will pave the way for a\n`Minimal Model Program' for quiver gauge theories corresponding to toric\nCalabi-Yau manifolds.\n""]","[('quiver gauge theories', 0.5269792675971985), ('supersymmetric gauge theories', 0.5182130336761475), ('gauge theories', 0.5049285292625427), ('corresponding toric', 0.4572228491306305), ('calabi yau threefolds', 0.44697287678718567), ('supersymmetric gauge', 0.43034428358078003), ('calabi yau folds', 0.4284743368625641), ('branes', 0.4279279112815857), ('structure moduli', 0.4181090295314789), ('yau threefolds', 0.41428786516189575)]"
821,821,38,821_musical_compositions_chords_melody,"['musical', 'compositions', 'chords', 'melody', 'rhythmic', 'music', 'octave', 'patterns various', 'patterns', 'rhythm']","['The music box operad: Random generation of musical phrases from patterns   We introduce the notion of multi-patterns, a combinatorial abstraction of\npolyphonic musical phrases. The interest of this approach in encoding musical\nphrases lies in the fact that it becomes possible to compose multi-patterns in\norder to produce new ones. This composition is parameterized by a monoid\nstructure on the scale degrees. This embeds the set of the musical phrases into\nan algebraic framework since the set of the multi-patterns is endowed with the\nstructure of an operad. Operads are algebraic structures offering a\nformalization and an abstraction of the notion of operators and their\ncompositions. Seeing musical phrases as operators allows us to perform\ncomputations on phrases and admits applications in generative music. Indeed,\ngiven a set of initial multi-patterns, we propose various algorithms to\nrandomly generate a new and longer phrase emulating the style suggested by the\ninputted multi-patterns. The designed algorithms use types of grammars working\nwith operads and colored operads, known as bud generating systems.\n', 'General Theory of Music by Icosahedron 1: A bridge between ""artificial""\n  scales and ""natural"" scales, Duality between chromatic scale and Pythagorean\n  chain, and Golden Major Minor Self-Duality   Relations among various musical concepts are investigated through a new\nconcept, musical icosahedron that is the regular icosahedron each of whose\nvertices has one of 12 tones. First, we found that there exist four musical\nicosahedra that characterize the topology of the chromatic scale and one of the\nwhole tone scales, and have the hexagon-icosahedron symmetry (an operation of\nraising all the tones of a given scale by two semitones corresponds to a\nsymmetry transformation of the regular icosahedron): chromatic/whole tone\nmusical icosahedra. The major triads or the minor triads are set on the golden\ntriangles of these musical icosahedra. Also, various dualities between musical\nconcepts are shown by these musical icosahedra: the major triads/scales and the\nminor triads/scales, the major/minor triads and the fundamental triads for the\nhexatonic major/minor scales, the major/minor scales and the Gregorian modes.\nSecond, we proposed Pythagorean/whole tone musical icosahedra that characterize\nthe topology of the Pythagorean chain and one of the whole tone scales, and\nhave the hexagon-icosahedron symmetry. The Pythagorean chain (chromatic scale)\nin the chromatic (Pythagorean)/whole tone musical icosahedron is constructed by\n""middle"" lines of the regular icosahedron. While some golden triangles\ncorrespond to the major/minor triads in the chromatic/whole tone musical\nicosahedra, in the Pythagorean/whole tone musical icosahedra, some golden\ngnomons correspond to the minor/major triads. Third, we found four types of\nmusical icosahedra other than the chromatic/whole tone musical icosahedra and\nthe Pythagorean/whole tone musical icosahedra that have the hexagon-icosahedron\nsymmetry. All the major triads and minor triads are represented by the golden\ntriangles or the golden gnomons on each type. All of these musical icosahedra\nlead to generalizations of major/minor triads and scales.\n', 'Consonance in music -- the Pythagorean approach revisited   The Pythagorean school attributed consonance in music to simplicity of\nfrequency ratios between musical tones. In the last two centuries, the\nconsonance curves developed by Helmholtz, Plompt and Levelt shifted focus to\npsycho-acoustic considerations in perceiving consonances. The appearance of\npeaks of these curves at the ratios considered by the Pythagorean school, and\nwhich were a consequence of an attempt to understand the world by nice\nmathematical proportions, remained a curiosity. This paper addresses this\ncuriosity, by describing a mathematical model of musical sound, along with a\nmathematical definition of consonance. First, we define pure, complex and mixed\ntones as mathematical models of musical sound. By a sequence of numerical\nexperiments and analytic calculations, we show that continuous cosine\nsimilarity, abbreviated as cosim, applied to these models quantifies the\nelusive concept of consonance as a frequency ratio which gives a local maximum\nof the cosim function. We prove that these maxima occur at the ratios\nconsidered as consonant in classical music theory. Moreover, we provide a\nsimple explanation why the number of musical intervals considered as consonant\nby musicians is finite, but has been increasing over the centuries.\nSpecifically, our formulas show that the number of consonant intervals changes\nwith the depth of the tone (the number of harmonics present).\n']","[('musical', 0.5110500454902649), ('compositions', 0.4463975429534912), ('chords', 0.4400540292263031), ('melody', 0.4351009130477905), ('rhythmic', 0.4341777563095093), ('music', 0.4319624602794647), ('octave', 0.397250771522522), ('patterns various', 0.387391597032547), ('patterns', 0.38138139247894287), ('rhythm', 0.37970349192619324)]"
822,822,38,822_information theoretic bounds_generalization error bounds_generalization error bound_information bound,"['information theoretic bounds', 'generalization error bounds', 'generalization error bound', 'information bound', 'information theoretic generalization', 'generalization bounds', 'bounds generalization', 'generalisation bounds', 'upper bounds generalization', 'bounds generalization error']","['Generalization Bounds via Information Density and Conditional\n  Information Density   We present a general approach, based on exponential inequalities, to derive\nbounds on the generalization error of randomized learning algorithms. Using\nthis approach, we provide bounds on the average generalization error as well as\nbounds on its tail probability, for both the PAC-Bayesian and single-draw\nscenarios. Specifically, for the case of sub-Gaussian loss functions, we obtain\nnovel bounds that depend on the information density between the training data\nand the output hypothesis. When suitably weakened, these bounds recover many of\nthe information-theoretic bounds available in the literature. We also extend\nthe proposed exponential-inequality approach to the setting recently introduced\nby Steinke and Zakynthinou (2020), where the learning algorithm depends on a\nrandomly selected subset of the available training data. For this setup, we\npresent bounds for bounded loss functions in terms of the conditional\ninformation density between the output hypothesis and the random variable\ndetermining the subset choice, given all training data. Through our approach,\nwe recover the average generalization bound presented by Steinke and\nZakynthinou (2020) and extend it to the PAC-Bayesian and single-draw scenarios.\nFor the single-draw scenario, we also obtain novel bounds in terms of the\nconditional $\\alpha$-mutual information and the conditional maximal leakage.\n', 'Information-Theoretic Bounds on the Moments of the Generalization Error\n  of Learning Algorithms   Generalization error bounds are critical to understanding the performance of\nmachine learning models. In this work, building upon a new bound of the\nexpected value of an arbitrary function of the population and empirical risk of\na learning algorithm, we offer a more refined analysis of the generalization\nbehaviour of a machine learning models based on a characterization of (bounds)\nto their generalization error moments. We discuss how the proposed bounds --\nwhich also encompass new bounds to the expected generalization error -- relate\nto existing bounds in the literature. We also discuss how the proposed\ngeneralization error moment bounds can be used to construct new generalization\nerror high-probability bounds.\n', 'Information-theoretic Characterizations of Generalization Error for the\n  Gibbs Algorithm   Various approaches have been developed to upper bound the generalization\nerror of a supervised learning algorithm. However, existing bounds are often\nloose and even vacuous when evaluated in practice. As a result, they may fail\nto characterize the exact generalization ability of a learning algorithm. Our\nmain contributions are exact characterizations of the expected generalization\nerror of the well-known Gibbs algorithm (a.k.a. Gibbs posterior) using\ndifferent information measures, in particular, the symmetrized KL information\nbetween the input training samples and the output hypothesis. Our result can be\napplied to tighten existing expected generalization error and PAC-Bayesian\nbounds. Our information-theoretic approach is versatile, as it also\ncharacterizes the generalization error of the Gibbs algorithm with a\ndata-dependent regularizer and that of the Gibbs algorithm in the asymptotic\nregime, where it converges to the standard empirical risk minimization\nalgorithm. Of particular relevance, our results highlight the role the\nsymmetrized KL information plays in controlling the generalization error of the\nGibbs algorithm.\n']","[('information theoretic bounds', 0.7302963733673096), ('generalization error bounds', 0.7016656994819641), ('generalization error bound', 0.6865066289901733), ('information bound', 0.6617246866226196), ('information theoretic generalization', 0.645096480846405), ('generalization bounds', 0.6434037089347839), ('bounds generalization', 0.5885711908340454), ('generalisation bounds', 0.5568756461143494), ('upper bounds generalization', 0.5473809242248535), ('bounds generalization error', 0.5407301187515259)]"
823,823,38,823_fractional differential equations_differential equations fractional_numerical fractional_nonlinear fractional differential,"['fractional differential equations', 'differential equations fractional', 'numerical fractional', 'nonlinear fractional differential', 'variable order fractional', 'fractional differential', 'order fractional differential', 'fractional derivatives', 'nonlinear fractional', 'fractional derivative']","[""Efficient and fast predictor-corrector method for solving nonlinear\n  fractional differential equations with non-singular kernel   Efficient and fast predictor-corrector methods are proposed to deal with\nnonlinear Caputo-Fabrizio fractional differential equations, where\nCaputo-Fabrizio operator is a new proposed fractional derivative with a smooth\nkernel. The proposed methods achieve a uniform accuracy order with the\nsecond-order scheme for linear interpolation and the third-order scheme for\nquadratic interpolation. The convergence analysis is proved by using the\ndiscrete Gronwall's inequality. Furthermore, applying the recurrence relation\nof the memory term, it reduces CPU time executed the proposed methods. The\nproposed fast algorithm requires approximately $O(N)$ arithmetic operations\nwhile $O(N^2)$ is required in case of the regular predictor-corrector schemes,\nwhere $N$ is the total number of time step. The following numerical examples\ndemonstrate the accuracy of the proposed methods as well as the efficiency;\nnonlinear fractional differential equations, time-fraction sub-diffusion, and\ntime-fractional advection-diffusion equation. The theoretical convergence rates\nare also verified by numerical experiments.\n"", 'Numerical Investigation of the Fractional Oscillation Equations under\n  the Context of Variable Order Caputo Fractional Derivative via Fractional\n  Order Bernstein Wavelets   This article describes an approximation technique based on fractional order\nBernstein wavelets for the numerical simulations of fractional oscillation\nequations under variable order, and the fractional order Bernstein wavelets are\nderived by means of fractional Bernstein polynomials. The oscillation equation\ndescribes electrical circuits and exhibits a wide range of nonlinear dynamical\nbehaviors. The proposed variable order model is of current interest in a lot of\napplication areas in engineering and applied sciences. The purpose of this\nstudy is to analyze the behavior of the fractional force-free and forced\noscillation equations under the variable-order fractional operator. The basic\nidea behind using the approximation technique is that it converts the proposed\nmodel into non-linear algebraic equations with the help of collocation nodes\nfor easy computation. Different cases of the proposed model are examined under\nthe selected variable order parameters for the first time in order to show the\nprecision and performance of the mentioned scheme. The dynamic behavior and\nresults are presented via tables and graphs to ensure the validity of the\nmentioned scheme. Further, the behavior of the obtained solutions for the\nvariable order is also depicted. From the calculated results, it is observed\nthat the mentioned scheme is extremely simple and efficient for examining the\nbehavior of nonlinear random (constant or variable) order fractional models\noccurring in engineering and science.\n', 'Numerical Solution of Variable-Order Fractional Differential Equations\n  Using Bernoulli Polynomials   We introduce a new numerical method, based on Bernoulli polynomials, for\nsolving multiterm variable-order fractional differential equations. The\nvariable-order fractional derivative was considered in the Caputo sense, while\nthe Riemann--Liouville integral operator was used to give approximations for\nthe unknown function and its variable-order derivatives. An operational matrix\nof variable-order fractional integration was introduced for the Bernoulli\nfunctions. By assuming that the solution of the problem is sufficiently smooth,\nwe approximated a given order of its derivative using Bernoulli polynomials.\nThen, we used the introduced operational matrix to find some approximations for\nthe unknown function and its derivatives. Using these approximations and some\ncollocation points, the problem was reduced to the solution of a system of\nnonlinear algebraic equations. An error estimate is given for the approximate\nsolution obtained by the proposed method. Finally, five illustrative examples\nwere considered to demonstrate the applicability and high accuracy of the\nproposed technique, comparing our results with the ones obtained by existing\nmethods in the literature and making clear the novelty of the work. The\nnumerical results showed that the new method is efficient, giving high-accuracy\napproximate solutions even with a small number of basis functions and when the\nsolution to the problem is not infinitely differentiable, providing better\nresults and a smaller number of basis functions when compared to\nstate-of-the-art methods.\n']","[('fractional differential equations', 0.6833720803260803), ('differential equations fractional', 0.6735664010047913), ('numerical fractional', 0.6727715730667114), ('nonlinear fractional differential', 0.6359628438949585), ('variable order fractional', 0.61628258228302), ('fractional differential', 0.6097248792648315), ('order fractional differential', 0.6088844537734985), ('fractional derivatives', 0.6074806451797485), ('nonlinear fractional', 0.5972428321838379), ('fractional derivative', 0.5880559086799622)]"
824,824,38,824_ample line bundles_ample line bundle_seshadri constants_bundles surfaces,"['ample line bundles', 'ample line bundle', 'seshadri constants', 'bundles surfaces', 'seshadri constant', 'ample line', 'projective bundles', 'bundles complex projective', 'bundles projective', 'projective variety']","['Seshadri constants of parabolic vector bundles   Let $X$ be a complex projective variety, and let $E_{\\ast}$ be a parabolic\nvector bundle on $X$. We introduce the notion of \\textit{parabolic Seshadri\nconstants} of $E_{\\ast}$. It is shown that these constants are analogous to the\nclassical Seshadri constants of vector bundles, in particular, they have\nparallel definitions and properties. We prove a Seshadri criterion for\nparabolic ampleness of $E_{\\ast}$ in terms of parabolic Seshadri constants. We\nalso compute parabolic Seshadri constants for symmetric powers and tensor\nproducts of parabolic vector bundles.\n', 'Seshadri constants of curve configurations on surfaces   Let $X$ be a complex nonsingular projective surface and let $L$ be an ample\nline bundle on $X$. We study multi-point Seshadri constants of $L$ at singular\npoints of certain arrangements of curves on $X$. We pose some questions about\nsuch Seshadri constants and prove some results in the case of star arrangements\nof curves. We also study the configurational Seshadri constants for curve\narrangements on surfaces and compare them with the usual Seshadri constants. We\ngive several examples illustrating the properties that we study.\n', 'Seshadri constants on some blow-ups of projective spaces   Let $X^n_{r,s}$ denote the blow-up of $\\mathbb{P}^n$ along $r$ general lines\nand $s$ general points. In this paper, we focus on $l$-very ample line bundles\non $X^n_{0,s}$ and investigate their Seshadri constants with some restrictions\non $s$. Additionally, we compute the nef cone of $X^3_{r,0}$ for $r\\leq 6$ and\nstudy the Seshadri constants of some ample line bundles on it. We also examine\nthe Seshadri constants of some ample line bundles on $X^4_{r,0}$ ($r\\leq 7$)\nand $X^5_{r,0}$ ($r \\leq 5$).\n']","[('ample line bundles', 0.6942558288574219), ('ample line bundle', 0.6633613109588623), ('seshadri constants', 0.6153395175933838), ('bundles surfaces', 0.5808391571044922), ('seshadri constant', 0.5661035776138306), ('ample line', 0.5432190299034119), ('projective bundles', 0.5347114205360413), ('bundles complex projective', 0.5124968886375427), ('bundles projective', 0.5065297484397888), ('projective variety', 0.5026228427886963)]"
825,825,37,825_integer linear programs_integer programming solvers_integer linear programming_integer programming,"['integer linear programs', 'integer programming solvers', 'integer linear programming', 'integer programming', 'integer programs', 'branch cut', 'mixed integer programs', 'mixed integer programming', 'cutting plane methods', 'integer programming problems']","['Branching via Cutting Plane Selection: Improving Hybrid Branching   Cutting planes and branching are two of the most important algorithms for\nsolving mixed-integer linear programs. For both algorithms, disjunctions play\nan important role, being used both as branching candidates and as the\nfoundation for some cutting planes. We relate branching decisions and cutting\nplanes to each other through the underlying disjunctions that they are based\non, with a focus on Gomory mixed-integer cuts and their corresponding split\ndisjunctions. We show that selecting branching decisions based on quality\nmeasures of Gomory mixed-integer cuts leads to relatively small\nbranch-and-bound trees, and that the result improves when using cuts that more\naccurately represent the branching decisions. Finally, we show how the history\nof previously computed Gomory mixed-integer cuts can be used to improve the\nperformance of the state-of-the-art hybrid branching rule of SCIP. Our results\nshow a 4% decrease in solve time, and an 8% decrease in number of nodes over\naffected instances of MIPLIB 2017.\n', 'Structural Analysis of Branch-and-Cut and the Learnability of Gomory\n  Mixed Integer Cuts   The incorporation of cutting planes within the branch-and-bound algorithm,\nknown as branch-and-cut, forms the backbone of modern integer programming\nsolvers. These solvers are the foremost method for solving discrete\noptimization problems and thus have a vast array of applications in machine\nlearning, operations research, and many other fields. Choosing cutting planes\neffectively is a major research topic in the theory and practice of integer\nprogramming. We conduct a novel structural analysis of branch-and-cut that pins\ndown how every step of the algorithm is affected by changes in the parameters\ndefining the cutting planes added to the input integer program. Our main\napplication of this analysis is to derive sample complexity guarantees for\nusing machine learning to determine which cutting planes to apply during\nbranch-and-cut. These guarantees apply to infinite families of cutting planes,\nsuch as the family of Gomory mixed integer cuts, which are responsible for the\nmain breakthrough speedups of integer programming solvers. We exploit geometric\nand combinatorial structure of branch-and-cut in our analysis, which provides a\nkey missing piece for the recent generalization theory of branch-and-cut.\n', 'Learning Cut Generating Functions for Integer Programming   The branch-and-cut algorithm is the method of choice to solve large scale\ninteger programming problems in practice. A key ingredient of branch-and-cut is\nthe use of cutting planes which are derived constraints that reduce the search\nspace for an optimal solution. Selecting effective cutting planes to produce\nsmall branch-and-cut trees is a critical challenge in the branch-and-cut\nalgorithm. Recent advances have employed a data-driven approach to select\noptimal cutting planes from a parameterized family, aimed at reducing the\nbranch-and-bound tree size (in expectation) for a given distribution of integer\nprogramming instances. We extend this idea to the selection of the best cut\ngenerating function (CGF), which is a tool in the integer programming\nliterature for generating a wide variety of cutting planes that generalize the\nwell-known Gomory Mixed-Integer (GMI) cutting planes. We provide rigorous\nsample complexity bounds for the selection of an effective CGF from certain\nparameterized families that provably performs well for any specified\ndistribution on the problem instances. Our empirical results show that the\nselected CGF can outperform the GMI cuts for certain distributions.\nAdditionally, we explore the sample complexity of using neural networks for\ninstance-dependent CGF selection.\n']","[('integer linear programs', 0.5975319147109985), ('integer programming solvers', 0.5861156582832336), ('integer linear programming', 0.571590006351471), ('integer programming', 0.5555003881454468), ('integer programs', 0.5514081120491028), ('branch cut', 0.542662501335144), ('mixed integer programs', 0.538975179195404), ('mixed integer programming', 0.5308443307876587), ('cutting plane methods', 0.5272994637489319), ('integer programming problems', 0.50816810131073)]"
826,826,37,826_processes fractional_counting processes_compound poisson processes_poisson processes,"['processes fractional', 'counting processes', 'compound poisson processes', 'poisson processes', 'fractional poisson', 'homogeneous poisson process', 'fractional generalized', 'generalized fractional', 'compound poisson process', 'poisson process']","[""On the Multivariate Generalized Counting Process and its Time-Changed\n  Variants   In this paper, we study a multivariate version of the generalized counting\nprocess (GCP) and discuss its various time-changed variants. The time is\nchanged using random processes such as the stable subordinator, inverse stable\nsubordinator, and their composition, tempered stable subordinator, gamma\nsubordinator $etc.$ Several distributional properties that include the\nprobability generating function, probability mass function and their governing\ndifferential equations are obtained for these variants. It is shown that some\nof these time-changed processes are L\\'evy and for such processes we have\nderived the associated L\\'evy measure. The explicit expressions for the\ncovariance and codifference of the component processes for some of these\ntime-changed variants are obtained. An application of the multivariate\ngeneralized space fractional counting process to shock models is discussed.\n"", ""Generalized Counting Process: its Non-Homogeneous and Time-Changed\n  Versions   We introduce a non-homogeneous version of the generalized counting process\n(GCP), namely, the non-homogeneous generalized counting process (NGCP). We\ntime-change the NGCP by an independent inverse stable subordinator to obtain\nits fractional version, and call it as the non-homogeneous generalized\nfractional counting process (NGFCP). A generalization of the NGFCP is obtained\nby time-changing the NGCP with an independent inverse subordinator. We derive\nthe system of governing differential-integral equations for the marginal\ndistributions of the increments of NGCP, NGFCP and its generalization. Then, we\nconsider the GCP time-changed by a multistable subordinator and obtain its\nL\\'evy measure, associated Bern\\v{s}tein function and distribution of the first\npassage times. The GCP and its fractional version, that is, the generalized\nfractional counting process when time-changed by a L\\'evy subordinator are\nknown as the time-changed generalized counting process-I (TCGCP-I) and the\ntime-changed generalized fractional counting process-I (TCGFCP-I),\nrespectively. We obtain the distribution of first passage times and related\ngoverning equations for the TCGCP-I. An application of the TCGCP-I to ruin\ntheory is discussed. We obtain the conditional distribution of the $k$th order\nstatistic from a sample whose size is modelled by a particular case of\nTCGFCP-I, namely, the time fractional negative binomial process. Later, we\nconsider a fractional version of the TCGCP-I and obtain the system of\ndifferential equations that governs its state probabilities. Its mean,\nvariance, covariance, {\\it etc.} are obtained and using which its long-range\ndependence property is established. Some results for its two particular cases\nare obtained.\n"", ""Skellam and Time-Changed Variants of the Generalized Fractional Counting\n  Process   In this paper, we study a Skellam type variant of the generalized counting\nprocess (GCP), namely, the generalized Skellam process. Some of its\ndistributional properties such as the probability mass function, probability\ngenerating function, mean, variance and covariance are obtained. Its fractional\nversion, namely, the generalized fractional Skellam process (GFSP) is\nconsidered by time-changing it with an independent inverse stable subordinator.\nIt is observed that the GFSP is a Skellam type version of the generalized\nfractional counting process (GFCP) which is a fractional variant of the GCP. It\nis shown that the one-dimensional distributions of the GFSP are not infinitely\ndivisible. An integral representation for its state probabilities is obtained.\nWe establish its long-range dependence property by using its variance and\ncovariance structure. Also, we consider two time-changed versions of the GFCP.\nThese are obtained by time-changing the GFCP by an independent L\\'evy\nsubordinator and its inverse. Some particular cases of these time-changed\nprocesses are discussed by considering specific L\\'evy subordinators.\n""]","[('processes fractional', 0.5530916452407837), ('counting processes', 0.5369438529014587), ('compound poisson processes', 0.5162718892097473), ('poisson processes', 0.513875424861908), ('fractional poisson', 0.505128026008606), ('homogeneous poisson process', 0.503804624080658), ('fractional generalized', 0.48310601711273193), ('generalized fractional', 0.48230108618736267), ('compound poisson process', 0.47851985692977905), ('poisson process', 0.468360036611557)]"
827,827,37,827_almost periodic functions_almost periodicity_almost periodic_periodic functions,"['almost periodic functions', 'almost periodicity', 'almost periodic', 'periodic functions', 'periodic type', 'differential equations almost', 'compact almost', 'periodicity', 'differential equations banach', 'equations banach spaces']","[""Metrical almost periodicity and applications   In this paper, we analyze various classes of multi-dimensional almost\nperiodic type functions in general metric. The main classes of functions under\nour consideration are $({\\mathrm R}, {\\mathcal B},{\\mathcal P},L)$-multi-almost\nperiodic functions, $({\\mathrm R}_{X}, {\\mathcal B},{\\mathcal\nP},L)$-multi-almost periodic functions, Bohr $({\\mathcal B}, I',\\rho,{\\mathcal\nP})$-almost periodic functions and $({\\mathcal B}, I',\\rho,{\\mathcal\nP})$-uniformly recurrent functions. We clarify the main structural properties\nfor the introduced classes of almost periodic type functions and provide some\napplications of our results to the abstract Volterra integro-differential\nequations.\n"", 'Vector valued piecewise continuous almost automorphic functions and some\n  consequences   In the present work, for $\\mathbb{X}$ a Banach space, the notion of piecewise\ncontinuous $\\mathbb{Z}$-almost automorphic functions with values in finite\ndimensional spaces is extended to piecewise continuous $\\mathbb{Z}$-almost\nautomorphic functions with values in $\\mathbb{X}$. Several properties of this\nclass of functions are provided, in particular it is shown that if $\\mathbb{X}$\nis a Banach algebra, then this class of functions constitute also a Banach\nalgebra; furthermore, using the theory of $\\mathbb{Z}$-almost automorphic\nfunctions, a new characterization of compact almost automorphic functions is\ngiven. As consequences, with the help of $\\mathbb{Z}$-almost automorphic\nfunctions, it is presented a simple proof of the characterization of almost\nautomorphic sequences by compact almost automorphic functions; the method\npermits us to give explicit examples of compact almost automorphic functions\nwhich are not almost periodic. Also, using the theory developed here, it is\nshown that almost automorphic solutions of differential equations with\npiecewise constant argument are in fact compact almost automorphic. Finally, it\nis proved that the classical solution of the $1D$ heat equation with continuous\n$\\mathbb{Z}$-almost automorphic source is also continuous $\\mathbb{Z}$-almost\nautomorphic; furthermore, we comment applications to the existence and\nuniqueness of the asymptotically continuous $\\mathbb{Z}$-almost automorphic\nmild solution to abstract integro-differential equations with nonlocal initial\nconditions.\n', 'Multi-dimensional almost periodic type functions and applications   In this paper, we analyze multi-dimensional $({\\mathrm R}_{X},{\\mathcal\nB})$-almost periodic type functions and multi-dimensional Bohr ${\\mathcal\nB}$-almost periodic type functions. The main structural characterizations and\ncomposition principles for the introduced classes of almost periodic functions\nare established. Several applications of our abstract theoretical results to\nthe abstract Volterra integro-differential equations in Banach spaces are\nprovided, as well.\n']","[('almost periodic functions', 0.7599493265151978), ('almost periodicity', 0.6411191821098328), ('almost periodic', 0.5896925926208496), ('periodic functions', 0.5522801876068115), ('periodic type', 0.47229766845703125), ('differential equations almost', 0.47046446800231934), ('compact almost', 0.44765353202819824), ('periodicity', 0.4459526240825653), ('differential equations banach', 0.412659615278244), ('equations banach spaces', 0.39328768849372864)]"
828,828,37,828_martingale optimal transport_transport convex_martingale optimal_classical optimal transport,"['martingale optimal transport', 'transport convex', 'martingale optimal', 'classical optimal transport', 'optimal transport', 'weak martingale', 'optimal transport problems', 'semi martingale', 'martingale', 'martingales']","['A Multi-Marginal C-Convex Duality Theorem for Martingale Optimal\n  Transport   A convex duality result for martingale optimal transport problems with two\nmarginals was established in Beiglb\\""ock et al. (2013). In this paper we\nprovide a generalization of this result to the multi-period setting.\n', 'Existence of Bass martingales and the martingale Benamou$-$Brenier\n  problem in $\\mathbb{R}^{d}$   In classical optimal transport, the contributions of Benamou$-$Brenier and\nMcCann regarding the time-dependent version of the problem are cornerstones of\nthe field and form the basis for a variety of applications in other\nmathematical areas.\n  In this article, we characterize solutions to the martingale\nBenamou$-$Brenier problem as $\\textit{Bass martingales}$, i.e. transformations\nof Brownian motion through the gradient of a convex function. Our result is\nbased on a new (static) Brenier-type theorem for a particular weak martingale\noptimal transport problem. As in the classical case, the structure of the\nprimal optimizer is derived from its dual counterpart, whose derivation forms\nthe technical core of this article. A key challenge is that dual attainment is\na subtle issue in martingale optimal transport, where dual optimizers may fail\nto exist, even in highly regular settings.\n', 'Continuity of the martingale optimal transport problem on the real line   We show continuity of the martingale optimal transport optimisation problem\nas a functional of its marginals. This is achieved via an estimate on the\nprojection in the nested/causal Wasserstein distance of an arbitrary coupling\non to the set of martingale couplings with the same marginals. As a corollary\nwe obtain an independent proof of sufficiency of the monotonicity principle\nestablished in [Beiglboeck, M., & Juillet, N. (2016). On a problem of optimal\ntransport under marginal martingale constraints. Ann. Probab., 44 (2016), no.\n1, 42106] for cost functions of polynomial growth.\n']","[('martingale optimal transport', 0.7984417080879211), ('transport convex', 0.622685432434082), ('martingale optimal', 0.6197004318237305), ('classical optimal transport', 0.6162292957305908), ('optimal transport', 0.5892089605331421), ('weak martingale', 0.5707838535308838), ('optimal transport problems', 0.559744656085968), ('semi martingale', 0.5584511756896973), ('martingale', 0.5258181095123291), ('martingales', 0.516309916973114)]"
829,829,37,829_gibbs measure_gibbs measures_gibbsian_line ensembles,"['gibbs measure', 'gibbs measures', 'gibbsian', 'line ensembles', 'line ensemble', 'invariant gibbs', 'ensembles', 'gibbs', 'translation invariant gibbs', 'ensemble']","['Tightness of $(H, H^{RW})$-Gibbsian line ensembles   We develop a black-box theory, which can be used to show that a sequence of\nGibbsian line ensembles is tight, provided that the one-point marginals of the\nlowest labeled curves of the ensembles are tight and globally approximate an\ninverted parabola. Our theory is applicable under certain technical assumptions\non the nature of the Gibbs property and the underlying random walk measure. As\na particular application of our general framework we show that a certain\nsequence of Gibbsian line ensembles, which naturally arises in the log-gamma\npolymer, is tight in the ubiquitous KPZ class $1/3: 2/3$ scaling, and also that\nall subsequential limits satisfy the Brownian Gibbs property, introduced by\nCorwin and Hammond in (Invent. Math. 195, 441-508, 2014).\n  One of the core results proved in the paper, which underlies many of our\narguments, is the construction of a continuous grand monotone coupling of\nGibbsian line ensembles with respect to their boundary data (entrance and exit\nvalues, and bounding curves). Continuous means that the Gibbsian line ensemble\nmeasure varies continuously as one varies the boundary data, grand means that\nall uncountably many measures (one for each boundary data) are coupled to the\nsame probability space, and monotone means that raising the values of the\nboundary data likewise raises the associated measure. Our continuous grand\nmonotone coupling generalizes an analogous construction, which was recently\nimplemented by Barraquand, Corwin and Dimitrov in (arXiv:2101.03045), from line\nensembles with a single curve to ones with an arbitrary finite number of\ncurves.\n', 'Characterization of Brownian Gibbsian line ensembles   In this paper we show that a Brownian Gibbsian line ensemble is completely\ncharacterized by the finite-dimensional marginals of its top curve, i.e. the\nfinite-dimensional sets of the its top curve form a separating class. A\nparticular consequence of our result is that the Airy line ensemble is the\nunique Brownian Gibbsian line ensemble, whose top curve is the Airy$_2$\nprocess.\n', 'Convergence of the KPZ line ensemble   In this paper we study the KPZ line ensembles under the KPZ scaling. Based on\ntheir Gibbs property, we derive quantitative local fluctuation estimates for\nthe scaled KPZ line ensembles. This allows us to show that the family of scaled\nKPZ line ensembles is tight. Together with the recent progress in [QS20],\n[Vir], and [DM], the tightness result yields the conjectural convergence of the\nscaled KPZ line ensembles to the Airy line ensemble.\n']","[('gibbs measure', 0.5931271314620972), ('gibbs measures', 0.5899965167045593), ('gibbsian', 0.57442307472229), ('line ensembles', 0.5674813985824585), ('line ensemble', 0.5465589761734009), ('invariant gibbs', 0.5327063202857971), ('ensembles', 0.4767903685569763), ('gibbs', 0.4414360225200653), ('translation invariant gibbs', 0.4377387464046478), ('ensemble', 0.4136882722377777)]"
830,830,37,830__2 manifolds_manifolds category_manifolds mathbb_manifolds,"['_2 manifolds', 'manifolds category', 'manifolds mathbb', 'manifolds', 'duality bundles', 'principal bundles', 'manifolds degree', 'mathbb _2 graded', 'bundles', 'manifold']","[""Riemannian structures on $\\mathbb{Z}_2^n$-manifolds   Very loosely, $\\mathbb{Z}_2^n$-manifolds are `manifolds' with\n$\\mathbb{Z}_2^n$-graded coordinates and their sign rule is determined by the\nscalar product of their $\\mathbb{Z}_2^n$-degrees. A little more carefully, such\nobjects can be understood within a sheaf-theoretical framework, just as\nsupermanifolds can, but with subtle differences. In this paper, we examine the\nnotion of a Riemannian $\\mathbb{Z}_2^n$-manifold, i.e., a\n$\\mathbb{Z}_2^n$-manifold equipped with a Riemannian metric that may carry\nnon-zero $\\mathbb{Z}_2^n$-degree. We show that the basic notions and tenets of\nRiemannian geometry directly generalise to the setting of\n$\\mathbb{Z}_2^n$-geometry. For example, the Fundamental Theorem holds in this\nhigher graded setting. We point out the similarities and differences with\nRiemannian supergeometry.\n"", ""The Schwarz-Voronov Embedding of ${\\mathbb Z}_{2}^{n}$-Manifolds   Informally, ${\\mathbb Z}_2^n$-manifolds are 'manifolds' with ${\\mathbb\nZ}_2^n$-graded coordinates and a sign rule determined by the standard scalar\nproduct of their ${\\mathbb Z}_2^n$-degrees. Such manifolds can be understood in\na sheaf-theoretic framework, as supermanifolds can, but with significant\ndifferences, in particular in integration theory. In this paper, we reformulate\nthe notion of a ${\\mathbb Z}_2^n$-manifold within a categorical framework via\nthe functor of points. We show that it is sufficient to consider ${\\mathbb\nZ}_2^n$-points, i.e., trivial ${\\mathbb Z}_2^n$-manifolds for which the reduced\nmanifold is just a single point, as 'probes' when employing the functor of\npoints. This allows us to construct a fully faithful restricted Yoneda\nembedding of the category of ${\\mathbb Z}_2^n$-manifolds into a subcategory of\ncontravariant functors from the category of ${\\mathbb Z}_2^n$-points to a\ncategory of Fr\\'echet manifolds over algebras. We refer to this embedding as\nthe Schwarz-Voronov embedding. We further prove that the category of ${\\mathbb\nZ}_2^n$-manifolds is equivalent to the full subcategory of locally trivial\nfunctors in the preceding subcategory.\n"", ""Principal bundles in the category of $\\mathbb{Z}_2^n$-manifolds   We introduce and examine the notion of principal $\\mathbb{Z}_2^n$-bundles,\ni.e., principal bundles in the category of $\\mathbb{Z}_2^n$-manifolds. The\nlatter are higher graded extensions of supermanifolds in which a\n$\\mathbb{Z}_2^n$-grading replaces $\\mathbb{Z}_2$-grading. These extensions have\nopened up new areas of research of great interest in both physics and\nmathematics. In principle, the geometry of $\\mathbb{Z}_2^n$-manifolds is\nessentially different than that of supermanifolds, as for $n>1$ we have formal\nvariables of even parity, so local smooth functions are formal power series. On\nthe other hand, a full version of differential calculus is still valid. We show\nin this paper that the fundamental properties of classical principal bundles\ncan be generalised to the setting of this `higher graded' geometry, with\nproperly defined frame bundles of $\\mathbb{Z}_2^n$-vector bundles as canonical\nexamples. However, formulating these concepts and proving these results relies\non many technical upshots established in earlier papers. A comprehensive\nintroduction to $\\mathbb{Z}_2^n$-manifolds is therefore included together with\nbasic examples.\n""]","[('_2 manifolds', 0.578316867351532), ('manifolds category', 0.4453675448894501), ('manifolds mathbb', 0.4447784721851349), ('manifolds', 0.4427868127822876), ('duality bundles', 0.43518829345703125), ('principal bundles', 0.4063204526901245), ('manifolds degree', 0.40540388226509094), ('mathbb _2 graded', 0.387861430644989), ('bundles', 0.3831384778022766), ('manifold', 0.3817814886569977)]"
831,831,37,831_quantum optimal_optimal quantum_transport quantum_quantum transport,"['quantum optimal', 'optimal quantum', 'transport quantum', 'quantum transport', 'distance quantum', 'classical wasserstein distance', 'optimal transport', 'wasserstein distances', 'wasserstein distance order', 'wasserstein distance']","['Quantum Optimal Transport: Quantum Couplings and Many-Body Problems   This text is a set of lecture notes for a 4.5-hour course given at the\nErd\\""os Center (R\\\'enyi Institute, Budapest) during the Summer School ""Optimal\nTransport on Quantum Structures"" (September 19th-23rd, 2023). Lecture I\nintroduces the quantum analogue of the Wasserstein distance of exponent $2$\ndefined in [F. Golse, C. Mouhot, T. Paul: Comm. Math. Phys. 343 (2016),\n165-205], and in [F. Golse, T. Paul: Arch. Ration. Mech. Anal. 223 (2017)\n57-94]. Lecture II discusses various applications of this quantum analogue of\nthe Wasserstein distance of exponent $2$, while Lecture III discusses several\nof its most important properties, such as the triangle inequality, and the\nKantorovich duality in the quantum setting, together with some of their\nimplications.\n', 'Quantum Monge-Kantorovich problem and transport distance between density\n  matrices   A quantum version of the Monge--Kantorovich optimal transport problem is\nanalyzed. The transport cost is minimized over the set of all bipartite\ncoupling states $\\rho^{AB}$, such that both of its reduced density matrices\n$\\rho^A$ and $\\rho^B$ of dimension $N$ are fixed. We show that, selecting the\nquantum cost matrix to be proportional to the projector on the antisymmetric\nsubspace, the minimal transport cost leads to a semidistance between $\\rho^A$\nand $\\rho^B$, which is bounded from below by the rescaled Bures distance and\nfrom above by the root infidelity. In the single qubit case we provide a\nsemi-analytic expression for the optimal transport cost between any two states\nand prove that its square root satisfies the triangle inequality and yields an\nanalogue of the Wasserstein distance of order two on the set of density\nmatrices. We introduce an associated measure of proximity of quantum states,\ncalled SWAP-fidelity, and discuss its properties and applications in quantum\nmachine learning.\n', ""Quantum Optimal Transport   We analyze a quantum version of the Monge--Kantorovich optimal transport\nproblem. The quantum transport cost related to a Hermitian cost matrix $C$ is\nminimized over the set of all bipartite coupling states $\\rho^{AB}$ with fixed\nreduced density matrices $\\rho^A$ and $\\rho^B$ of size $m$ and $n$. The minimum\nquantum optimal transport cost $\\rT^Q_{C}(\\rho^A,\\rho^B)$ can be efficiently\ncomputed using semidefinite programming. In the case $m=n$ the cost $\\rT^Q_{C}$\ngives a semidistance if and only if $C$ is positive semidefinite and vanishes\nexactly on the subspace of symmetric matrices. Furthermore, if $C$ satisfies\nthe above conditions, then $\\sqrt{\\rT^Q_{C}}$ induces a quantum analogue of the\nWasserstein-2 distance. Taking the quantum cost matrix $C^Q$ to be the\nprojector on the antisymmetric subspace, we provide a semi-analytic expression\nfor $\\rT^Q_{C^Q}$ for any pair of single-qubit states and show that its square\nroot yields a transport distance on the Bloch ball. Numerical simulations\nsuggest that this property holds also in higher dimensions. Assuming that the\ncost matrix suffers decoherence and that the density matrices become diagonal,\nwe study the quantum-to-classical transition of the Earth mover's distance,\npropose a continuous family of interpolating distances, and demonstrate that\nthe quantum transport is cheaper than the classical one. Furthermore, we\nintroduce a related quantity -- the SWAP-fidelity -- and compare its properties\nwith the standard Uhlmann--Jozsa fidelity. We also discuss the quantum optimal\ntransport for general $d$-partite systems.\n""]","[('quantum optimal', 0.6613446474075317), ('optimal quantum', 0.6557084918022156), ('transport quantum', 0.6110038161277771), ('quantum transport', 0.6052839756011963), ('distance quantum', 0.585548460483551), ('classical wasserstein distance', 0.582494854927063), ('optimal transport', 0.5581166744232178), ('wasserstein distances', 0.5446065664291382), ('wasserstein distance order', 0.5419650077819824), ('wasserstein distance', 0.5286522507667542)]"
832,832,37,832_sweeping processes_optimality conditions local_conditions local minimizers_sweeping,"['sweeping processes', 'optimality conditions local', 'conditions local minimizers', 'sweeping', 'optimal control problems', 'existence optimal solutions', 'optimality conditions', 'optimal control', 'necessary optimality conditions', 'local minimizers']","[""A fixed-point approach to history-dependent sweeping processes   In this paper, we study the well-posedness of state-dependent and\nstate-independent sweeping processes driven by prox-regular sets and perturbed\nby a history-dependent operator. Our approach, based on an enhanced version of\nGronwall's lemma and fixed-point arguments, provides an efficient framework for\nanalyzing sweeping processes. In particular, our findings recover all existing\nresults for the class of Volterra sweeping processes and provide new insights\ninto history-dependent sweeping processes. Finally, we apply our theoretical\nresults to establish the well-posedness of a viscoelastic model with long\nmemory.\n"", 'On the Solution Existence for Prox-Regular Perturbed Sweeping Processes   In the setting adopted by Edmond and Thibault [Mathematical Programming 104\n(2005), 347--373], we study a class of perturbed sweeping processes. Under\nsuitable assumptions, we obtain two solution existence theorems for perturbed\nsweeping processes with the constraint sets being prox-regular sublevel sets.\nThe results are applied to analyzing the behavior of some concrete mechanical\nsweeping processes, which appear for the first time in this paper.\n', 'Discrete Approximations and Optimal Control of Nonsmooth Perturbed\n  Sweeping Processes   The main goal of this paper is developing the method of discrete\napproximations to derive necessary optimality conditions for a class of\nconstrained sweeping processes with nonsmooth perturbations. Optimal control\nproblems for sweeping processes have been recently recognized among the most\ninteresting and challenging problems in modern control theory for discontinuous\ndifferential inclusions with irregular dynamics and implicit state constrained,\nwhile deriving necessary optimality conditions for their local minimizers have\nbeen significantly based on the smoothness of controlled dynamic perturbations.\nTo overcome these difficulties, we use the method of discrete approximations\nand employ advanced tools of second-order variational analysis. This approach\nallows us to obtain new necessary optimality conditions for nonsmooth and\nnonconvex discrete-time problems of the sweeping type. Then we employ the\nobtained conditions and the strong convergence of discrete approximations to\nestablish novel results for original nonsmooth sweeping control problems that\ninclude extended Euler-Lagrange and maximization conditions for local\nminimizers. Finally, we present applications of the obtained results to solving\na controlled mobile robot model with a nonsmooth sweeping dynamics that is of\nsome practical interest.\n']","[('sweeping processes', 0.5368225574493408), ('optimality conditions local', 0.48289868235588074), ('conditions local minimizers', 0.43348780274391174), ('sweeping', 0.42519211769104004), ('optimal control problems', 0.42278003692626953), ('existence optimal solutions', 0.39528515934944153), ('optimality conditions', 0.3942686915397644), ('optimal control', 0.39362168312072754), ('necessary optimality conditions', 0.37905383110046387), ('local minimizers', 0.3777974843978882)]"
833,833,37,833_rectifiability_hausdorff measure_rectifiable_carnot groups,"['rectifiability', 'hausdorff measure', 'rectifiable', 'carnot groups', 'finite hausdorff measure', 'measure free', 'radon measure', 'carnot group', 'finite perimeter sets', 'carnot groups step']","['Characterizations of uniformly differentiable co-horizontal intrinsic\n  graphs in Carnot groups   In arbitrary Carnot groups we study intrinsic graphs of maps with horizontal\ntarget. These graphs are $C^1_H$ regular exactly when the map is uniformly\nintrinsically differentiable. Our first main result characterizes the uniformly\nintrinsic differentiability by means of H\\""older properties along the\nprojections of left-invariant vector fields on the graph. We strengthen the\nresult in step-2 Carnot groups for intrinsic real-valued maps by only requiring\nhorizontal regularity. We remark that such a refinement is not possible already\nin the easiest step-3 group. As a by-product of independent interest, in every\nCarnot group we prove an area-formula for uniformly intrinsically\ndifferentiable real-valued maps. We also explicitly write the area element in\nterms of the intrinsic derivatives of the map.\n', ""On rectifiable measures in Carnot groups: Marstrand-Mattila\n  rectifiability criterion   In this paper we continue the study of the notion of\n$\\mathscr{P}$-rectifiability in Carnot groups. We say that a Radon measure is\n$\\mathscr{P}_h$-rectifiable, for $h\\in\\mathbb N$, if it has positive $h$-lower\ndensity and finite $h$-upper density almost everywhere, and, at almost every\npoint, it admits a unique tangent measure up to multiples. In this paper we\nprove a Marstrand--Mattila rectifiability criterion in arbitrary Carnot groups\nfor $\\mathscr{P}$-rectifiable measures with tangent planes that admit a normal\ncomplementary subgroup. Namely, in this co-normal case, even if a priori the\ntangent planes at a point might not be the same at different scales, a\nposteriori the measure has a unique tangent almost everywhere.\n  Since every horizontal subgroup of a Carnot group has a normal complement,\nour criterion applies in the particular case in which the tangents are\none-dimensional horizontal subgroups. Hence, as an immediate consequence of our\nMarstrand--Mattila rectifiability criterion and a result of\nChousionis--Magnani--Tyson, we obtain the one-dimensional Preiss's theorem in\nthe first Heisenberg group $\\mathbb H^1$. More precisely, we show that a Radon\nmeasure $\\phi$ on $\\mathbb H^1$ with positive and finite one-density with\nrespect to the Koranyi distance is absolutely continuous with respect to the\none-dimensional Hausdorff measure $\\mathcal{H}^1$, and it is supported on a\none-rectifiable set in the sense of Federer, i.e., it is supported on the\ncountable union of the images of Lipschitz maps from $A\\subseteq \\mathbb R$ to\n$\\mathbb H^1$.\n"", 'On rectifiable measures in Carnot groups: representation   This paper deals with the theory of rectifiability in arbitrary Carnot\ngroups, and in particular with the study of the notion of\n$\\mathscr{P}$-rectifiable measure.\n  First, we show that in arbitrary Carnot groups the natural\n\\textit{infinitesimal} definition of rectifiabile measure, i.e., the definition\ngiven in terms of the existence of \\textit{flat} tangent measures, is\nequivalent to the global definition given in terms of coverings with\nintrinsically differentiable graphs, i.e., graphs with \\textit{flat} Hausdorff\ntangents. In general we do not have the latter equivalence if we ask the\ncovering to be made of intrinsically Lipschitz graphs.\n  Second, we show a geometric area formula for the centered Hausdorff measure\nrestricted to intrinsically differentiable graphs in arbitrary Carnot groups.\nThe latter formula extends and strengthens other area formulae obtained in the\nliterature in the context of Carnot groups.\n  As an application, our analysis allows us to prove the intrinsic\n$C^1$-rectifiability of almost all the preimages of a large class of Lipschitz\nfunctions between Carnot groups. In particular, from the latter result, we\nobtain that any geodesic sphere in a Carnot group equipped with an arbitrary\nleft-invariant homogeneous distance is intrinsic $C^1$-rectifiable.\n']","[('rectifiability', 0.46310490369796753), ('hausdorff measure', 0.4117579758167267), ('rectifiable', 0.4032873213291168), ('carnot groups', 0.3849169611930847), ('finite hausdorff measure', 0.3841039538383484), ('measure free', 0.3446478545665741), ('radon measure', 0.32874640822410583), ('carnot group', 0.32612308859825134), ('finite perimeter sets', 0.31051623821258545), ('carnot groups step', 0.3023214042186737)]"
834,834,37,834_stationary gaussian processes_gaussian processes_fractional brownian_stationary gaussian process,"['stationary gaussian processes', 'gaussian processes', 'fractional brownian', 'stationary gaussian process', 'gaussian random fields', 'gaussian process', 'stationary gaussian', 'tail asymptotics', 'martingale approximation', 'brownian']","['Asymptotic properties of maximum composite likelihood estimators for\n  max-stable Brown-Resnick random fields over a fixed-domain   Likelihood inference for max-stable random fields is in general impossible\nbecause their finite-dimensional probability density functions are unknown or\ncannot be computed efficiently. The weighted composite likelihood approach that\nutilizes lower dimensional marginal likelihoods (typically pairs or triples of\nsites that are not too distant) is rather favored. In this paper, we consider\nthe family of spatial max-stable Brown-Resnick random fields associated with\nisotropic fractional Brownian fields. We assume that the sites are given by\nonly one realization of a homogeneous Poisson point process restricted to\n$\\mathbf{C}=(-1/2,1/2]^{2}$ and that the random field is observed at these\nsites. As the intensity increases, we study the asymptotic properties of the\ncomposite likelihood estimators of the scale and Hurst parameters of the\nfractional Brownian fields using different weighting strategies: we exclude\neither pairs that are not edges of the Delaunay triangulation or triples that\nare not vertices of triangles.\n', 'Fixed-domain asymptotic properties of maximum composite likelihood\n  estimators for max-stable Brown-Resnick random fields   Likelihood inference for max-stable random fields is in general impossible\nbecause their finite-dimen\\-sional probability density functions are unknown or\ncannot be computed efficiently. The weighted composite likelihood approach that\nutilizes lower dimensional marginal likelihoods (typically pairs or triples of\nsites that are not too distant) is rather favored. In this paper, we consider\nthe family of spatial max-stable Brown-Resnick random fields associated with\nisotropic fractional Brownian fields. We assume that the sites are given by\nonly one realization of a homogeneous Poisson point process restricted to\n$\\mathbf{C}=(-1/2,1/2]^{2}$ and that the random field is observed at these\nsites. As the intensity increases, we study the asymptotic properties of the\ncomposite likelihood estimators of the scale and Hurst parameters of the\nfractional Brownian fields using different weighting strategies: we exclude\neither pairs that are not edges of the Delaunay triangulation or triples that\nare not vertices of triangles.\n', 'Sojourn times of Gaussian related random fields   This paper is concerned with the asymptotic analysis of sojourn times of\nrandom fields with continuous sample paths. Under a very general framework we\nshow that there is an interesting relationship between tail asymptotics of\nsojourn times and that of supremum. Moreover, we establish the uniform\ndouble-sum method to derive the tail asymptotics of sojourn times. In the\nliterature, based on the pioneering research of S. Berman the sojourn times\nhave been utilised to derive the tail asymptotics of supremum of Gaussian\nprocesses. In this paper we show that the opposite direction is even more\nfruitful, namely knowing the asymptotics of supremum o f random processes and\nfields (in particular Gaussian) it is possible to establish the asymptotics of\ntheir sojourn times. We illustrate our findings considering i) two dimensional\nGaussian random fields, ii) chi-process generated by stationary Gaussian\nprocesses and iii) stationary Gaussian queueing processes.\n']","[('stationary gaussian processes', 0.5711736679077148), ('gaussian processes', 0.5665500164031982), ('fractional brownian', 0.5508019924163818), ('stationary gaussian process', 0.5241097807884216), ('gaussian random fields', 0.5192617774009705), ('gaussian process', 0.5174086689949036), ('stationary gaussian', 0.44480109214782715), ('tail asymptotics', 0.43590351939201355), ('martingale approximation', 0.4248259663581848), ('brownian', 0.41878730058670044)]"
835,835,37,835_dirac operators_two dimensional dirac_dirac operator_approximation dirac,"['dirac operators', 'two dimensional dirac', 'dirac operator', 'approximation dirac', 'dimensional dirac', 'self adjoint dirac', 'operators delta', 'boundary integral operators', 'adjoint dirac', 'operator spectral properties']","['On two-dimensional Dirac operators with $\\delta$-shell interactions\n  supported on unbounded curves with straight ends   In this paper we study the self-adjointness and spectral properties of\ntwo-dimensional Dirac operators with electrostatic, Lorentz scalar, and\nanomalous magnetic $\\delta$-shell interactions with constant weights that are\nsupported on a smooth unbounded curve that is straight outside a compact set\nand whose ends are rays that are not parallel to each other. For all possible\ncombinations of interaction strengths we describe the self-adjoint realizations\nand compute their essential spectra. Moreover, we prove in different situations\nthe existence of geometrically induced discrete eigenvalues.\n', 'Approximation of Dirac operators with confining electrostatic and Lorentz scalar $\\delta$-shell potentials In this paper we study the approximation of Dirac operators with $\\delta$-shell potentials in the norm resolvent sense. In particular, we consider the approximation of Dirac operators with confining electrostatic and Lorentz scalar $\\delta$-shell potentials, where the support of the $\\delta$-shell potentials is impermeable to particles modelled by such Dirac operators.', 'General $\\delta$-shell interactions for the two-dimensional Dirac\n  operator: self-adjointness and approximation   In this work we consider the two-dimensional Dirac operator with general\nlocal singular interactions supported on a closed curve. A systematic study of\nthe interaction is performed by decomposing it into a linear combination of\nfour elementary interactions: electrostatic, Lorentz scalar, magnetic, and a\nfourth one which can be absorbed by using unitary transformations. We address\nthe self-adjointness and the spectral description of the underlying Dirac\noperator, and moreover we describe its approximation by Dirac operators with\nregular potentials.\n']","[('dirac operators', 0.6813990473747253), ('two dimensional dirac', 0.6582910418510437), ('dirac operator', 0.6470091342926025), ('approximation dirac', 0.601983368396759), ('dimensional dirac', 0.5575503706932068), ('self adjoint dirac', 0.5318484306335449), ('operators delta', 0.5122044682502747), ('boundary integral operators', 0.5028033256530762), ('adjoint dirac', 0.4985983669757843), ('operator spectral properties', 0.4951133131980896)]"
836,836,37,836_graph cardinality_graphs general_graph general_graph theory,"['graph cardinality', 'graphs general', 'graph general', 'graph theory', 'general position number', 'largest vertices', 'sets graphs', 'graphs', 'position graph', 'vertex']","[""The k-general d-position problem for graphs   A set of vertices of a graph is said to be in general position if no three\nvertices from the set lie on a common geodesic. Recently Klav\\v{z}ar, Rall and\nYero generalized this notion by defining a set of vertices to be in general\n$d$-position if no three vertices from the set lie on a common geodesic of\nlength at most $d$. We generalize this notion further by defining a set of\nvertices to be in $k$-general $d$-position if no $k$ vertices of the set lie on\na common geodesic of length at most $d$. The $k$-general $d$-position number of\na graph is the largest cardinality of a $k$-general $d$-position set. We\nprovide upper and lower bounds on the $k$-general $d$-position number of graphs\nin terms of the $k$-general $d$-position number of certain kinds of subgraphs.\nWe compute the $k$-general $d$-position number of finite paths and cycles.\nAlong the way we establish that the maximally even subsets of cycles, which\nwere introduced in Clough and Douthett's work on music theory, provide the\nlargest possible $k$-general $d$-position sets in $n$-cycles. We generalize\nKlav\\v{z}ar and Manuel's notion of monotone-geodesic labeling to that of\n$k$-monotone-geodesic labeling in order to calculate the $k$-general\n$d$-position number of the infinite two-dimensional grid. We also prove a\nformula for the $k$-general $d$-position number of certain thin finite grids,\nproviding a partial answer to a question asked by Klav\\v{z}ar, Rall and Yero.\n"", 'Lower General Position Sets in Graphs   A subset $S$ of vertices of a graph $G$ is a \\emph{general position set} if\nno shortest path in $G$ contains three or more vertices of $S$. In this paper,\nwe generalise a problem of M. Gardner to graph theory by introducing the\n\\emph{lower general position number} $\\gp ^-(G)$ of $G$, which is the number of\nvertices in a smallest maximal general position set of $G$. We show that ${\\rm\ngp}^-(G) = 2$ if and only if $G$ contains a universal line and determine this\nnumber for several classes of graphs, including Kneser graphs $K(n,2)$, line\ngraphs of complete graphs, and Cartesian and direct products of two complete\ngraphs. We also prove several realisation results involving the lower general\nposition number, the general position number and the geodetic number, and\ncompare it with the lower version of the monophonic position number. We provide\na sharp upper bound on the size of graphs with given lower general position\nnumber. Finally we demonstrate that the decision version of the lower general\nposition problem is NP-complete.\n', 'Variety of general position problems in graphs   Let $X$ be a vertex subset of a graph $G$. Then $u, v\\in V(G)$ are\n$X$-positionable if $V(P)\\cap X \\subseteq \\{u,v\\}$ holds for any shortest\n$u,v$-path $P$. If each two vertices from $X$ are $X$-positionable, then $X$ is\na general position set. The general position number of $G$ is the cardinality\nof a largest general position set of $G$ and has been already well\ninvestigated. In this paper a variety of general position problems is\nintroduced based on which natural pairs of vertices are required to be\n$X$-positionable. This yields the total (resp.\\ dual, outer) general position\nnumber. It is proved that the total general position sets coincide with sets of\nsimplicial vertices, and that the outer general position sets coincide with\nsets of mutually maximally distant vertices. It is shown that a general\nposition set is a dual general position set if and only if its complement is\nconvex. Several sufficient conditions are presented that guarantee that a given\ngraph has no dual general position set. The total general position number, the\nouter general position number, and the dual general position number of\narbitrary Cartesian products are determined.\n']","[('graph cardinality', 0.5464398264884949), ('graphs general', 0.5401037335395813), ('graph general', 0.5059970617294312), ('graph theory', 0.5043725967407227), ('general position number', 0.46510887145996094), ('largest vertices', 0.45923399925231934), ('sets graphs', 0.4536344110965729), ('graphs', 0.4513779878616333), ('position graph', 0.4479506015777588), ('vertex', 0.42357128858566284)]"
837,837,37,837_grassmann manifold_grassmann manifolds_grassmannian_grassmannians,"['grassmann manifold', 'grassmann manifolds', 'grassmannian', 'grassmannians', 'grassmann', 'manifold optimization', 'flag manifolds', 'flag manifold', 'orthogonal projections', 'orthogonal']","['Chordal Averaging on Flag Manifolds and Its Applications   This paper presents a new, provably-convergent algorithm for computing the\nflag-mean and flag-median of a set of points on a flag manifold under the\nchordal metric. The flag manifold is a mathematical space consisting of flags,\nwhich are sequences of nested subspaces of a vector space that increase in\ndimension. The flag manifold is a superset of a wide range of known matrix\nspaces, including Stiefel and Grassmanians, making it a general object that is\nuseful in a wide variety computer vision problems.\n  To tackle the challenge of computing first order flag statistics, we first\ntransform the problem into one that involves auxiliary variables constrained to\nthe Stiefel manifold. The Stiefel manifold is a space of orthogonal frames, and\nleveraging the numerical stability and efficiency of Stiefel-manifold\noptimization enables us to compute the flag-mean effectively. Through a series\nof experiments, we show the competence of our method in Grassmann and rotation\naveraging, as well as principal component analysis. We release our source code\nunder https://github.com/nmank/FlagAveraging.\n', 'Grassmann angles between real or complex subspaces   The Grassmann angle improves upon similar angles between subspaces that\nmeasure volume contraction in orthogonal projections. It works in real or\ncomplex spaces, with important differences, and is asymmetric, what makes it\nmore efficient when dimensions are distinct. It can be seen as an angle in\nGrassmann algebra, being related to its products and those of Clifford algebra,\nand gives the Fubini-Study metric on Grassmannians, an asymmetric metric on the\nfull Grassmannian, and Hausdorff distances between full sub-Grassmannians. We\ngive formulas for computing it in arbitrary bases, and identities for angles\nwith certain families of subspaces, some of which are linked to real and\ncomplex Pythagorean theorems for volumes and quantum probabilities. Unusual\nfeatures of the angle with an orthogonal complement, or the angle in complex\nspaces, are examined.\n', 'On the stability of POD Basis Interpolation via Grassmann Manifolds for\n  Parametric Model Order Reduction in Hyperelasticity   This work considers the stability of Proper Orthogonal Decomposition (POD)\nbasis interpolation on Grassmann manifolds for parametric Model Order Reduction\n(pMOR) in hyperelasticity. The article contribution is mainly about stability\nconditions, all defined from strong mathematical background. We show how the\nstability of interpolation can be lost if certain geometrical requirements are\nnot satisfied by making a concrete elucidation of the local character of\nlinearization. To this effect, we draw special attention to the Grassmannian\nExponential map and optimal injectivity condition of this map, related to the\ncut--locus of Grassmann manifolds. From this, explicit stability conditions are\nestablished and can be directly used to determine the loss of injectivity in\npractical pMOR applications. Another stability condition is formulated when\nincreasing the number p of mode, deduced from principal angles of subspaces of\ndifferent dimensions p. This stability condition helps to explain the\nnon-monotonic oscillatory behavior of the error-norm with respect to the number\nof POD modes, and on the contrary, the monotonic decrease of the error-norm in\nthe two benchmark numerical examples considered herein. Under this study, pMOR\nis applied in hyperelastic structures using a non-intrusive approach for\ninserting the interpolated spatial POD ROM basis in a commercial FEM code. The\naccuracy is assessed by \\emph{a posteriori} error norms defined using the ROM\nFEM solution and its high fidelity counterpart simulation. Numerical studies\nsuccessfully ascertained and highlighted the implication of stability\nconditions. The various stability conditions can be applied to a variety of\nother relevant problems involving parametrized ROMs generation based on POD\nbasis interpolation via Grassmann manifolds.\n']","[('grassmann manifold', 0.7162570953369141), ('grassmann manifolds', 0.7147751450538635), ('grassmannian', 0.6560882329940796), ('grassmannians', 0.6261492967605591), ('grassmann', 0.5774134397506714), ('manifold optimization', 0.49335789680480957), ('flag manifolds', 0.4922129809856415), ('flag manifold', 0.48312240839004517), ('orthogonal projections', 0.45373034477233887), ('orthogonal', 0.4259571433067322)]"
838,838,37,838_cubic hypersurfaces_cubic hypersurface_cubic surfaces_hypersurfaces finite,"['cubic hypersurfaces', 'cubic hypersurface', 'cubic surfaces', 'hypersurfaces finite', 'number rational points', 'affine hypersurfaces', 'hypersurfaces mathbb', 'rational curves', 'hypersurfaces', 'mathbb rational points']","['Complete intersections of cubic and quadric hypersurfaces over\n  $\\mathbb{F}_q(t)$   Using a two-dimensional version of the delta method, we establish an\nasymptotic formula for the number of rational points of bounded height on\nnon-singular complete intersections of cubic and quadric hypersurfaces of\ndimension at least $23$ over $\\mathbb{F}_q(t)$, provided\n$\\text{cha}(\\mathbb{F}_q)>3$. Under the same hypotheses, we also verify weak\napproximation.\n', 'How often does a cubic hypersurface have a rational point?   A cubic hypersurface in $\\mathbb{P}^n$ defined over $\\mathbb{Q}$ is given by\nthe vanishing locus of a cubic form $f$ in $n+1$ variables. It is conjectured\nthat when $n \\geq 4$, such cubic hypersurfaces satisfy the Hasse principle.\nThis is now known to hold on average due to recent work of Browning, Le Boudec,\nand Sawin. Using this result, we determine the proportion of cubic\nhypersurfaces in $\\mathbb{P}^n$, ordered by the height of $f$, with a rational\npoint for $n \\geq 4$ explicitly as a product over primes $p$ of rational\nfunctions in $p$. In particular, this proportion is equal to 1 for cubic\nhypersurfaces in $\\mathbb{P}^n$ for $n \\geq 9$; for $100\\%$ of cubic\nhypersurfaces, this recovers a celebrated result of Heath-Brown that\nnon-singular cubic forms in at least 10 variables have rational zeros. In the\n$n=3$ case, we give a precise conjecture for the proportion of cubic surfaces\nin $\\mathbb{P}^3$ with a rational point.\n', ""On a question of Davenport and diagonal cubic forms over\n  $\\mathbb{F}_q(t)$   Given a non-singular diagonal cubic hypersurface $X\\subset\\mathbb{P}^{n-1}$\nover $\\mathbb{F}_q(t)$ with $\\mathrm{char} (\\mathbb{F}_q)\\neq 3$, we show that\nthe number of rational points of height at most $|P|$ is\n$O(|P|^{3+\\varepsilon})$ for $n=6$ and $O(\\lvert P \\rvert^{2+\\varepsilon})$ for\n$n=4$. In fact, if $n=4$ and $\\mathrm{char}(\\mathbb{F}_q) >3$ we prove that the\nnumber of rational points away from any rational line contained in $X$ is\nbounded by $O(|P|^{3/2+\\varepsilon})$. From the result in $6$ variables we\ndeduce weak approximation for diagonal cubic hypersurfaces for $n\\geq 7$ over\n$\\mathbb{F}_q(t)$ when $\\mathrm{char}(\\mathbb{F}_q)>3$ and handle Waring's\nproblem for cubes in $7$ variables over $\\mathbb{F}_q(t)$ when\n$\\mathrm{char}(\\mathbb{F}_q)\\neq 3$. Our results answer a question of Davenport\nregarding the number of solutions of bounded height to $x_1^3+x_2^3+x_3^3 =\nx_4^3+x_5^3+x_6^3$ with $x_i \\in \\mathbb{F}_q[t]$.\n""]","[('cubic hypersurfaces', 0.5814400911331177), ('cubic hypersurface', 0.5312977433204651), ('cubic surfaces', 0.4984939396381378), ('hypersurfaces finite', 0.49228984117507935), ('number rational points', 0.4777739942073822), ('affine hypersurfaces', 0.4740527272224426), ('hypersurfaces mathbb', 0.47183695435523987), ('rational curves', 0.470309853553772), ('hypersurfaces', 0.4609532058238983), ('mathbb rational points', 0.45381537079811096)]"
839,839,37,839_sensor network localization_network localization_simultaneous localization_simultaneous localization mapping,"['sensor network localization', 'network localization', 'simultaneous localization', 'simultaneous localization mapping', 'sensor network', 'localization mapping', 'localization techniques', 'graph optimization', 'minimization methods', 'localization mapping slam']","['Non-convex potential games for finding global solutions to sensor\n  network localization   Sensor network localization (SNL) problems require determining the physical\ncoordinates of all sensors in a network. This process relies on the global\ncoordinates of anchors and the available measurements between non-anchor and\nanchor nodes. Attributed to the intrinsic non-convexity, obtaining a globally\noptimal solution to SNL is challenging, as well as implementing corresponding\nalgorithms. In this paper, we formulate a non-convex multi-player potential\ngame for a generic SNL problem to investigate the identification condition of\nthe global Nash equilibrium (NE) therein, where the global NE represents the\nglobal solution of SNL. We employ canonical duality theory to transform the\nnon-convex game into a complementary dual problem. Then we develop a\nconjugation-based algorithm to compute the stationary points of the\ncomplementary dual problem. On this basis, we show an identification condition\nof the global NE: the stationary point of the proposed algorithm satisfies a\nduality relation. Finally, simulation results are provided to validate the\neffectiveness of the theoretical results.\n', 'Angle-Based Sensor Network Localization   This paper studies angle-based sensor network localization (ASNL) in a plane,\nwhich is to determine locations of all sensors in a sensor network, given\nlocations of partial sensors (called anchors) and angle measurements obtained\nin the local coordinate frame of each sensor. Firstly it is shown that a\nframework with a non-degenerate bilateration ordering must be angle fixable,\nimplying that it can be uniquely determined by angles between edges up to\ntranslations, rotations, reflections and uniform scaling. Then ASNL is proved\nto have a unique solution if and only if the grounded framework is angle\nfixable and anchors are not all collinear. Subsequently, ASNL is solved in\ncentralized and distributed settings, respectively. The centralized ASNL is\nformulated as a rank-constrained semi-definite program (SDP) in either a\nnoise-free or a noisy scenario, with a decomposition approach proposed to deal\nwith large-scale ASNL. The distributed protocol for ASNL is designed based on\ninter-sensor communications. Graphical conditions for equivalence of the\nformulated rank-constrained SDP and a linear SDP, decomposition of the SDP, as\nwell as the effectiveness of the distributed protocol, are proposed,\nrespectively. Finally, simulation examples demonstrate our theoretical results.\n', 'A Multi-Player Potential Game Approach for Sensor Network Localization\n  with Noisy Measurements   Sensor network localization (SNL) is a challenging problem due to its\ninherent non-convexity and the effects of noise in inter-node ranging\nmeasurements and anchor node position. We formulate a non-convex SNL problem as\na multi-player non-convex potential game and investigate the existence and\nuniqueness of a Nash equilibrium (NE) in both the ideal setting without\nmeasurement noise and the practical setting with measurement noise. We first\nshow that the NE exists and is unique in the noiseless case, and corresponds to\nthe precise network localization. Then, we study the SNL for the case with\nerrors affecting the anchor node position and the inter-node distance\nmeasurements. Specifically, we establish that in case these errors are\nsufficiently small, the NE exists and is unique. It is shown that the NE is an\napproximate solution to the SNL problem, and that the position errors can be\nquantified accordingly. Based on these findings, we apply the results to case\nstudies involving only inter-node distance measurement errors and only anchor\nposition information inaccuracies.\n']","[('sensor network localization', 0.6032245755195618), ('network localization', 0.5631992220878601), ('simultaneous localization', 0.4764266908168793), ('simultaneous localization mapping', 0.43474963307380676), ('sensor network', 0.4319469928741455), ('localization mapping', 0.41084885597229004), ('localization techniques', 0.39209339022636414), ('graph optimization', 0.3851993978023529), ('minimization methods', 0.37969857454299927), ('localization mapping slam', 0.37870651483535767)]"
840,840,37,840_quantum contextuality_quantum theory_contextuality_quantum,"['quantum contextuality', 'quantum theory', 'contextuality', 'quantum', 'quantum mechanics', 'quantum information', 'pauli observables', 'computation quantum', 'quantum computation', 'role quantum']","['Coming full circle -- A unified framework for Kochen-Specker\n  contextuality   Contextuality is a key distinguishing feature between classical and quantum\nphysics. It expresses a fundamental obstruction to describing quantum theory\nusing classical concepts. In turn, when understood as a resource for quantum\ncomputation, it is expected to hold the key to quantum advantage. Yet, despite\nits long recognised importance in quantum foundations and, more recently, in\nquantum computation, the mathematics of contextuality has remained somewhat\nelusive - different frameworks address different aspects of the phenomenon, yet\ntheir precise relationship often is unclear. In fact, there is a glaring\ndiscrepancy already between the original notion of contextuality introduced by\nKochen and Specker on the one side [J. Math. Mech., 17, 59, (1967)], and the\nmodern approach of studying contextual correlations on the other [Rev. Mod.\nPhys., 94, 045007 (2022)].\n  In a companion paper [arXiv:2408.16764], we introduce the conceptually new\ntool called ``context connections\'\', which allows to cast and analyse\nKochen-Specker (KS) contextuality in new form. Here, we generalise this notion,\nand based on it prove a complete characterisation of KS contextuality for\nfinite-dimensional systems. To this end, we develop the framework of\n``observable algebras"". We show in detail how this framework subsumes the\nmarginal and graph-theoretic approaches to contextuality, and thus that it\noffers a unified perspective on KS contextuality. In particular, we establish\nthe precise relationships between the various notions of ``contextuality"" used\nin the respective settings, and in doing so, generalise a number of results on\nthe characterisation of the respective notions in the literature.\n', 'State-independent all-versus-nothing arguments   Contextuality is a key feature of quantum information that challenges\nclassical intuitions, providing the basis for constructing explicit proofs of\nquantum advantage. While a number of evidences of quantum advantage are based\non the contextuality argument, the definition of contextuality is different in\neach research, causing incoherence in the establishment of instant connection\nbetween their results. In this report, we review the mathematical structure of\nsheaf-theoretic contextuality and extend this framework to explain\nKochen-Specker type contextuality. We first cover the definitions in\ncontextuality with detailed examples. Then, we state the all-versus-nothing\n(AvN) argument and define a state-independent AvN class. It is shown that\nKochen-Specker type contextuality, or contextuality in a partial closure, can\nbe translated into this framework by the partial closure of observables under\nthe multiplication of commuting measurements. Finally, we compare each case of\ncontextuality in an operator-side view, where the strict hierarchy of\ncontextuality class in a state-side view seems to merge into the\nstate-independent AvN class together with the partial closure formalism.\nOverall, this report provides a unified interpretation of contextuality by\nintegrating Kochen-Specker type notions into the state-independent AvN\nargument. The results present novel insights into contextuality, which pave the\nway for a coherent approach to constructing proofs of quantum advantage.\n', 'An algebraic characterisation of Kochen-Specker contextuality   Contextuality is a key distinguishing feature between classical and quantum\nphysics. It expresses a fundamental obstruction to describing quantum theory\nusing classical concepts. In turn, understood as a resource for quantum\ncomputation, it is expected to hold the key to quantum advantage. Yet, despite\nits long recognised importance in quantum foundations and, more recently, in\nquantum computation, the structural essence of contextuality has remained\nsomewhat elusive - different frameworks address different aspects of the\nphenomenon, yet their precise relationship often remains unclear. This issue\nalready looms large at the level of the Bell-Kochen-Specker theorem: while\ntraditional proofs proceed by showing the nonexistence of valuations, the\nnotion of state-independent contextuality in the marginal approach allows to\nprove contextuality from seemingly weaker assumptions. In the light of this,\nand at the absence of a unified mathematical framework for Kochen-Specker\ncontextuality, the original algebraic approach has been widely abandoned, in\nfavour of the study of contextual correlations.\n  Here, we reinstate the algebraic perspective on contextuality. Concretely, by\nbuilding on the novel concept of context connections, we reformulate the\nalgebraic relations between observables originally postulated by Kochen and\nSpecker, and we explicitly demonstrate their consistency with the notion of\nstate-independent contextuality. In the present paper, we focus on the new\nconceptual ideas and discuss them in the concrete setting of spin-1\nobservables, specifically those in the example of [S. Yu and C.H. Oh, Phys.\nRev. Lett., 108, 030402 (2012)]; in a companion paper, we generalise these\nideas, obtain a complete characterisation of Kochen-Specker contextuality and\nprovide a detailed comparison with the related notions of contextuality in the\nmarginal and graph-theoretic approach.\n']","[('quantum contextuality', 0.795662522315979), ('quantum theory', 0.5234910845756531), ('contextuality', 0.4901110827922821), ('quantum', 0.4881291091442108), ('quantum mechanics', 0.48093870282173157), ('quantum information', 0.4801272749900818), ('pauli observables', 0.47161799669265747), ('computation quantum', 0.46940159797668457), ('quantum computation', 0.4680301249027252), ('role quantum', 0.46418601274490356)]"
841,841,36,841_convex feasibility problems_convex feasibility_approximate projections_douglas rachford splitting,"['convex feasibility problems', 'convex feasibility', 'approximate projections', 'douglas rachford splitting', 'alternating projections', 'convex cones', 'closed convex cones', 'feasible point', 'solving convex', 'polyhedral cones']","['Douglas--Rachford is the best projection method   We prove that the Douglas--Rachford method applied to two closed convex cones\nin the Euclidean plane converges in finitely many steps if and only if the set\nof fixed points of the Douglas--Rachford operator is nontrivial. We analyze\nthis special case using circle dynamics.\n  We also construct explicit examples for a broad family of projection methods\nfor which the set of fixed points of the relevant projection method operator is\nnontrivial, but the convergence is not finite. This three-parametric family is\nwell known in the projection method literature and includes both the\nDouglas--Rachford method and the classic method of alternating projections.\n  Even though our setting is fairly elementary, this work contributes in a new\nway to the body of theoretical research justifying the superior performance of\nthe Douglas--Rachford method compared to other techniques. Moreover, our result\nleads to a neat sufficient condition for finite convergence of the\nDouglas--Rachford method in the locally polyhedral case on the plane, unifying\nand expanding several special cases available in the literature.\n', 'On the Circumcentered-Reflection Method for the Convex Feasibility\n  Problem   The ancient concept of circumcenter has recently given birth to the\nCircumcentered-Reflection method (CRM). CRM was first employed to solve best\napproximation problems involving affine subspaces. In this setting, it was\nshown to outperform the most prestigious projection based schemes, namely, the\nDouglas-Rachford method (DRM) and the method of alternating projections (MAP).\nWe now prove convergence of CRM for finding a point in the intersection of a\nfinite number of closed convex sets. This striking result is derived under a\nsuitable product space reformulation in which a point in the intersection of a\nclosed convex set with an affine subspace is sought. It turns out that CRM\nskillfully tackles the reformulated problem. We also show that for a point in\nthe affine set the CRM iteration is always closer to the solution set than both\nthe MAP and DRM iterations. Our theoretical results and numerical experiments,\nshowing outstanding performance, establish CRM as a powerful tool for solving\ngeneral convex feasibility problems.\n', 'Circumcentering the Douglas--Rachford method   We introduce and study a geometric modification of the Douglas-Rach\\-ford\nmethod called the Circumcentered-Douglas-Rachford method. This method iterates\nby taking the intersection of bisectors of reflection steps for solving certain\nclasses of feasibility problems. The convergence analysis is established for\nbest approximation problems involving two (affine) subspaces and both our\ntheoretical and numerical results compare favorably to the original\nDouglas-Rachford method. Under suitable conditions, it is shown that the linear\nrate of convergence of the Circumcentered-Douglas-Rachford method is at least\nthe cosine of the Friedrichs angle between the (affine) subspaces, which is\nknown to be the sharp rate for the Douglas-Rachford method. We also present a\npreliminary discussion on the Circumcentered-Douglas-Rachford method applied to\nthe many set case and to examples featuring non-affine convex sets.\n']","[('convex feasibility problems', 0.5751667022705078), ('convex feasibility', 0.5364297032356262), ('approximate projections', 0.49789372086524963), ('douglas rachford splitting', 0.4948354661464691), ('alternating projections', 0.48661863803863525), ('convex cones', 0.4826848804950714), ('closed convex cones', 0.4695741534233093), ('feasible point', 0.44319748878479004), ('solving convex', 0.4029206335544586), ('polyhedral cones', 0.40009620785713196)]"
842,842,36,842_scattering amplitudes_scattering amplitude_string amplitudes_amplitudes also,"['scattering amplitudes', 'scattering amplitude', 'string amplitudes', 'amplitudes also', 'amplitudes', 'level scattering', 'mathcal super yang', 'scattering equations', 'scattering', 'feynman diagrams']","['Towards Positive Geometries of Massive Scalar field theories   Building on the prior work in [1] we locate a family of positive geometries\nin the kinematic space which are a specific class of convex realisations of the\nassociahedron. These realisations are obtained by scaling and translating the\nkinematic space associahedron discovered by by Arkani-Hamed, Bai, He and Yan\n(ABHY). We call the resulting polytopes, deformed realisations of the\nassociahedron. The deformed realisations shed new light on the CHY formula. One\nof the striking discoveries in [2] was the fact that the CHY scattering\nequations generate diffeomorphism between the (compactified) CHY moduli space\nand the ABHY associahedron. As we argue, the deformed realisation of the\nassociahedron can also be interpreted as an diffeomorphic image of the CHY\nmoduli space under scattering equations that we call deformed scattering\nequations. The canonical form in the kinematic space is thus once again the\npush-forward of the Parke-Taylor form . A natural off-shoot of our analysis is\nthe universality of the Parke-Taylor form as a CHY Integrand for a class of\n(tree-level and planar) multi-scalar field amplitudes. These ideas help us in\nproving the existence of positive geometries for certain specific multi-scalar\ninteractions. We prove that in a field theory with a massless and a massive\nbi-adjoint scalar fields which interact via cubic interaction, the tree-level\nS-matrix with massless external states and at most one massive propagator is a\nweighted sum over the canonical forms defined by certain deformed realisations\nof the associahedron. Finally, we show that these ideas admit an extension to\none-loop. In particular, the one loop S-matrix integrand with at most one\nmassive propagator is a weighted sum over canonical forms of a family of\ndeformed realisations of the type-D cluster polytope, discovered in [3,4].\n', 'Stringy Canonical Forms   Canonical forms of positive geometries play an important role in revealing\nhidden structures of scattering amplitudes, from amplituhedra to associahedra.\nIn this paper, we introduce ""stringy canonical forms"", which provide a natural\ndefinition and extension of canonical forms for general polytopes, deformed by\na parameter $\\alpha\'$. They are defined by real or complex integrals regulated\nwith polynomials with exponents, and are meromorphic functions of the\nexponents, sharing various properties of string amplitudes. As $\\alpha\' \\to 0$,\nthey reduce to the usual canonical form of a polytope given by the Minkowski\nsum of the Newton polytopes of the regulating polynomials, or equivalently the\nvolume of the dual of this polytope, naturally determined by tropical\nfunctions. At finite $\\alpha\'$, they have simple poles corresponding to the\nfacets of the polytope, with the residue on the pole given by the stringy\ncanonical form of the facet. There is the remarkable connection between the\n$\\alpha\' \\to 0$ limit of tree-level string amplitudes, and scattering equations\nthat appear when studying the $\\alpha\' \\to \\infty$ limit. We show that there is\na simple conceptual understanding of this phenomenon for any stringy canonical\nform: the saddle-point equations provide a diffeomorphism from the integration\ndomain to the interior of the polytope, and thus the canonical form can be\nobtained as a pushforward via summing over saddle points. When the stringy\ncanonical form is applied to the ABHY associahedron in kinematic space, it\nproduces the usual Koba-Nielsen string integral, giving a direct path from\nparticle to string amplitudes without an a priori reference to the string\nworldsheet. We also discuss a number of other examples, including stringy\ncanonical forms for finite-type cluster algebras (with type A for string\namplitudes), and other natural integrals over the positive Grassmannian.\n', 'Splitting CEGM Amplitudes   The CEGM formalism offers a general framework for scattering amplitudes,\nwhich rests on Grassmannians, moduli spaces and tropical geometry. The physical\nimplications of this generalization are still to be understood. Conventional\nwisdom says that key features of scattering amplitudes, like factorization at\ntheir poles into lower-point amplitudes, are associated to their singularities.\nThe factorization behavior of CEGM amplitudes at their poles is interesting but\ncomplicated. Recent developments have revealed important properties of standard\nparticle and string scattering amplitudes from factorizations, known as splits,\nthat happen away from poles. In this paper we introduce a kinematic subspace on\nwhich the CEGM amplitude splits into very simple rational functions. These\nfunctions, called simplex amplitudes, arise from stringy integrals for the\nmultivariate beta function, and also from restricting the biadjoint scalar\namplitude in quantum field theory to certain kinematic loci. Using split\nkinematics we also discover a specific class of zeros of the CEGM amplitude.\nOur construction rests on viewing positive moduli space as a product of\nsimplices, and it suggests a novel approach for deriving scattering amplitudes\nfrom tropical determinantal varieties.\n']","[('scattering amplitudes', 0.5389352440834045), ('scattering amplitude', 0.4802360236644745), ('string amplitudes', 0.450194388628006), ('amplitudes also', 0.4495597183704376), ('amplitudes', 0.4397905766963959), ('level scattering', 0.43572625517845154), ('mathcal super yang', 0.43058815598487854), ('scattering equations', 0.42954373359680176), ('scattering', 0.41986340284347534), ('feynman diagrams', 0.39855343103408813)]"
843,843,36,843_generalized absolute_absolute value_matrix equations_value matrix,"['generalized absolute', 'absolute value', 'matrix equations', 'value matrix', 'error bound linear', 'value equations', 'linear complementarity', 'system matrix', 'unique solvability', 'fixed point iteration']","['The error and perturbation bounds of the general absolute value\n  equations   To our knowledge, the error and perturbation bounds of the general absolute\nvalue equations are not discussed. In order to fill in this study gap, in this\npaper, by introducing a class of absolute value functions, we study the error\nand perturbation bounds of two types of the general absolute value equations\n(AVEs): $Ax-B|x|=b$ and $Ax-|Bx|=b$. Some useful error bounds and perturbation\nbounds of the above two types of absolute value equations are provided. Without\nlimiting the matrix type, some computable estimates for the above upper bounds\nare given. By applying the absolute value equations, a new approach for some\nexisting perturbation bounds of the linear complementarity problem (LCP) in\n(SIAM J. Optim., 18 (2007), pp. 1250-1265) is provided. Some numerical examples\nfor the AVEs from the LCP are given to show the feasibility of the perturbation\nbounds.\n', 'Characterization of Unique Solvability of Absolute Value Equations: An\n  Overview, Extensions, and Future Directions   This paper provides an overview of the necessary and sufficient conditions\nfor guaranteeing the unique solvability of absolute value equations. In\naddition to discussing the basic form of these equations, we also address\nseveral generalizations, including generalized absolute value equations and\nmatrix absolute value equations. Our survey encompasses known results as well\nas novel characterizations proposed in this study.\n', 'The Unique Solvability Conditions for the Generalized Absolute Value\n  Equations   This paper investigates the conditions that guarantee unique solvability and\nunsolvability for the generalized absolute value equations (GAVE) given by $Ax\n- B \\vert x \\vert = b$. Further, these conditions are also valid to determine\nthe unique solution of the generalized absolute value matrix equations (GAVME)\n$AX - B \\vert X \\vert =F$. Finally, certain aspects related to the solvability\nand unsolvability of the absolute value equations (AVE) have been deliberated\nupon.\n']","[('generalized absolute', 0.5231056213378906), ('absolute value', 0.4950660169124603), ('matrix equations', 0.41217324137687683), ('value matrix', 0.38316699862480164), ('error bound linear', 0.3625601530075073), ('value equations', 0.3582655191421509), ('linear complementarity', 0.3355121612548828), ('system matrix', 0.3312683701515198), ('unique solvability', 0.330329567193985), ('fixed point iteration', 0.32955628633499146)]"
844,844,36,844_reproduction_basic reproduction_sterile_biological control,"['reproduction', 'basic reproduction', 'sterile', 'biological control', 'fertility', 'insects', 'dispersal', 'extinction', 'control spread', 'species']","[""Modeling the impact of rainfall and temperature on sterile insect\n  control strategies in a Tropical environment   The sterile insect technique (SIT) is a biological control technique that can\nbe used either to eliminate or decay a wild mosquito population under a given\nthreshold to reduce the nuisance or the epidemiological risk. In this work, we\npropose a model using a differential system that takes into account the\nvariations of rainfall and temperature over time and study their impacts on\nsterile males releases strategies. Our model is as simple as possible to avoid\ncomplexity while being able to capture the temporal variations of an Aedes\nalbopictus mosquito population in a domain treated by SIT, located in\nR{\\'e}union island. The main objective is to determine what period of the year\nis the most suitable to start a SIT control to minimize the duration of massive\nreleases and the amount of sterile males to release, either to reduce the\nmosquito nuisance, or to reduce the epidemiological risk. Since sterilization\nis not 100% efficient, we also study the impact of different levels of residual\nfertility within the released sterile male population. Our study shows that\nrainfall plays a major role in the dynamics of the mosquito and the SIT\ncontrol, that the best period to start a massive SIT treatment lasts from July\nto December, that residual fertility has to be as small as possible, and that\nincreasing the size of the releases is not always necessarily interesting. We\nalso highlight the importance of combining SIT with mechanical control, i.e.\nthe removal of breeding sites, in particular when the initial mosquito\npopulation is large.\n"", ""Potential of the Sterile Insect Technique for Control of Deer Ticks,\n  $\\textit{Ixodes scapularis}$   The deer tick, $\\textit{Ixodes scapularis}$, is a vector for numerous human\ndiseases, including Lyme disease, anaplasmosis, and babesiosis. Concern is\nrising in the US and abroad as the population and range of this species grow\nand new diseases emerge. Herein I consider the potential for control of\n$\\textit{I. scapularis}$ using the Sterile Insect Technique (SIT), which acts\nby reducing net fertility through release of sterile males. I construct a\npopulation model with density-dependent and -independent growth, migration, and\nan Allee effect (decline of the population when it is small), and use this\nmodel to simulate sterile tick release in both single- and multi-patch\nframeworks. I test two key concerns with implementing $\\textit{I. scapularis}$\nSIT: that the ticks' lengthy life course could make control take too long and\nthat low migration might mean sterile males need thorough manual dispersal to\nall parts of the control area. Results suggest that typical $\\textit{I.\nscapularis}$ SIT programs will take about eight years, a prediction near the\nnormal range for the technique, but that thorough distribution of sterile ticks\nover the control area is indeed critical, increasing expense substantially by\nnecessitating aerial release. With particularly high rearing costs also\nexpected for $\\textit{I. scapularis}$, the latter finding suggests that\ncost-effectiveness improvements to aerial release may be a prerequisite to\n$\\textit{I. scapularis}$ SIT.\n"", 'About contamination by sterile females and residual male fertility on\n  the effectiveness of the sterile insect technique. Impact on disease vector\n  control and disease control   The sterile insect technique (SIT) is a technique to control pests and\nvectors of diseases by releasing mainly sterile males. Several challenges need\nto be solved before large-scale field application in order to guarantee its\nsuccess. In this paper we intend to focus on two important issues: residual\n(sterile) male fertility and contamination by sterile females. Indeed, sterile\nmales are never $100\\%$ sterile, that is there is always a small proportion,\n$\\varepsilon$, of fertile males (sperm of) within the sterile male population.\nAmong the sterile insects that are released, a certain proportion,\n$\\epsilon_F$, of them are sterile females due to imperfect mechanical\nsex-separation technique. This can be particularly problematic when arthropod\nviruses are circulating, because mosquito females, even sterile, are vectors of\ndiseases. In this work, we extend results studied separately in [4,7]. To study\nthe impact of both issues, we develop and study a\nSIT-entomological-epidemiological mathematical model, with application to\nDengue. In order to guarantee the success of SIT control, we recommend to solve\nin priority the issue of residual fertility, and, then, to decay the\ncontamination by sterile females as low as possible.\n']","[('reproduction', 0.45061028003692627), ('basic reproduction', 0.4424658715724945), ('sterile', 0.41343146562576294), ('biological control', 0.37965062260627747), ('fertility', 0.3780127465724945), ('insects', 0.37463057041168213), ('dispersal', 0.36919161677360535), ('extinction', 0.3586873412132263), ('control spread', 0.35014867782592773), ('species', 0.3202383518218994)]"
845,845,36,845_asymmetric exclusion process_asymmetric exclusion_asymmetric simple exclusion_tableaux combinatorics,"['asymmetric exclusion process', 'asymmetric exclusion', 'asymmetric simple exclusion', 'tableaux combinatorics', 'exclusion process asep', 'exclusion process', 'simple exclusion process', 'transition probabilities', 'tableaux', 'macdonald polynomials']","[""From multiline queues to Macdonald polynomials via the exclusion process   Recently James Martin introduced multiline queues, and used them to give a\ncombinatorial formula for the stationary distribution of the multispecies\nasymmetric simple exclusion exclusion process (ASEP) on a circle. The ASEP is a\nmodel of particles hopping on a one-dimensional lattice, which was introduced\naround 1970, and has been extensively studied in statistical mechanics,\nprobability, and combinatorics. In this article we give an independent proof of\nMartin's result, and we show that by introducing additional statistics on\nmultiline queues, we can use them to give a new combinatorial formula for both\nthe symmetric Macdonald polynomials P_{lambda}(x; q, t), and the nonsymmetric\nMacdonald polynomials E_{lambda}(x; q, t), where lambda is a partition. This\nformula is rather different from others that have appeared in the literature,\nsuch as the formulas due to Haglund, Haiman, and Loehr, the formula due to Ram\nand Yip, and the one due to Lenart. Our proof uses results of Cantini, de Gier,\nand Wheeler, who recently linked the multispecies ASEP on a circle to Macdonald\npolynomials.\n"", 'Introducing DASEP: the doubly asymmetric simple exclusion process   Research in combinatorics has often explored the asymmetric simple exclusion\nprocess (ASEP). The ASEP, inspired by examples from statistical mechanics,\ninvolves particles of various species moving around a lattice. With the\ntraditional ASEP particles of a given species can move but do not change\nspecies. In this paper a new combinatorial formalism, the DASEP (doubly\nasymmetric simple exclusion process), is explored. The DASEP is inspired by\nbiological processes where, unlike the ASEP, the particles can change from one\nspecies to another. The combinatorics of the DASEP on a one dimensional lattice\nare explored, including the associated generating function. The stationary\nprobabilities of the DASEP are explored, and results are proven relating these\nstationary probabilities to those of the simpler ASEP.\n', 'Cylindric rhombic tableaux and the two-species ASEP on a ring   The asymmetric simple exclusion exclusion process (ASEP) is a model of\nparticles hopping on a one-dimensional lattice of n sites. It was introduced\naround 1970, and since then has been extensively studied by researchers in\nstatistical mechanics, probability, and combinatorics. Recently the ASEP on a\nlattice with open boundaries has been linked to Koornwinder polynomials, and\nthe ASEP on a ring has been linked to Macdonald polynomials. In this article we\nstudy the two-species asymmetric simple exclusion process (ASEP) on a ring, in\nwhich two kinds of particles (""heavy"" and ""light""), as well as ""holes,"" can hop\nboth clockwise and counterclockwise (at rates 1 or t depending on the particle\ntypes) on a ring of n sites. We introduce some new tableaux on a cylinder\ncalled cylindric rhombic tableaux (CRT), and use them to give a formula for the\nstationary distribution of the two-species ASEP -- each probability is\nexpressed as a sum over all CRT of a fixed type. When lambda is a partition in\n{0,1,2}^n, we then give a formula for the nonsymmetric Macdonald polynomial\nE_{lambda} and the symmetric Macdonald polynomial P_{lambda} by refining our\ntableaux formulas for the stationary distribution.\n']","[('asymmetric exclusion process', 0.6240545511245728), ('asymmetric exclusion', 0.5281145572662354), ('asymmetric simple exclusion', 0.5013920068740845), ('tableaux combinatorics', 0.4865044951438904), ('exclusion process asep', 0.4683530926704407), ('exclusion process', 0.45676347613334656), ('simple exclusion process', 0.4357913136482239), ('transition probabilities', 0.43312913179397583), ('tableaux', 0.4056570529937744), ('macdonald polynomials', 0.4029928743839264)]"
846,846,36,846_cellular networks_cellular network_distribution signal interference_millimeter wave,"['cellular networks', 'cellular network', 'distribution signal interference', 'millimeter wave', 'downlink coverage', 'wireless networks', 'signal interference plus', 'mmwave', 'stochastic geometry framework', 'network performance']","['On the Deployment of Reconfigurable Intelligent Surfaces in the Presence\n  of Blockages   Wireless communications aided by reconfigurable intelligent surfaces (RISs)\nis a promising way to improve the coverage for cellular users. The controlled\nreflection of signals from RISs is especially useful in mm-wave/THz networks\nwhen the direct link between a cellular user and its serving base station (BS)\nis weak or unavailable due to blockages. However, the joint blockage of the\nuser-RIS and the user-BS links may significantly degrade the performance of\nRIS-aided transmissions. This paper aims to study the impact of joint blockages\non downlink performance. When RIS locations are coupled with BS locations,\nusing tools from stochastic geometry, we obtain an optimal placement of RISs to\neither minimize the joint blockage probability of the user-RIS and the user-BS\nlinks or maximize the downlink coverage probability. The results show that\ninstalling RISs near the cell edge of BSs usually provides optimal coverage.\nMoreover, deploying RISs on street intersections improves the coverage\nprobability. For users associated with BSs that are deployed sufficiently close\nto intersections, the intersection-mounted RISs offer a better coverage\nperformance as compared to BS-coupled RISs.\n', 'Uncoordinated Spectrum Sharing in Millimeter Wave Networks Using Carrier\n  Sensing   We propose using Carrier Sensing (CS) for distributed interference management\nin millimeter-wave (mmWave) cellular networks where spectrum is shared by\nmultiple operators that do not coordinate among themselves. In addition, even\nthe base station sites can be shared by the operators. We describe important\nchallenges in using traditional CS in this setting and propose enhanced CS\nprotocols to address these challenges. Using stochastic geometry, we develop a\ngeneral framework for downlink coverage probability analysis of our shared\nmmWave network in the presence of CS and derive the downlink coverage\nprobability expressions for several CS protocols. To the best of our knowledge,\nour work is the first to investigate and analyze (using stochastic geometry) CS\nfor mmWave networks with spectrum and BS sites shared among non-coordinating\noperators. We evaluate the downlink coverage probability of our shared mmWave\nnetwork using simulations as well as numerical examples based on our analysis.\nOur evaluations show that our proposed enhancements lead to an improvement in\ndownlink coverage probability, compared to the downlink coverage probability\nwith no CS, for higher values of signal-to-interference and noise ratio (SINR).\nInterestingly, our evaluations also reveal that for lower values of SINR, not\nusing any CS is the best strategy in terms of the downlink coverage\nprobability.\n', 'Spatio-Temporal Analysis of SINR Meta Distribution for mmWave\n  Heterogeneous Networks Under Geo/G/1 Queues   A fine-grained analysis of network performance is crucial for system design.\nIn this paper, we focus on the meta distribution of the\nsignal-to-interference-plus-noise-ratio (SINR) in the mmWave heterogeneous\nnetworks where the base stations (BS) in each tier are modeled as a Poisson\npoint process (PPP). By utilizing stochastic geometry and queueing theory, we\ncharacterize the spatial and temporal randomness while the special\ncharacteristics of mmWave communications, including different path loss laws\nfor line-of-sight and non-line-of-sight links and directional beamforming, are\nincorporated into the analysis. We derive the moments of the conditional\nsuccessful transmission probability (STP). By taking the temporal random\narrival of traffic into consideration, an equation is formulated to derive the\nmeta distribution and the meta distribution can be obtained in a recursive\nmanner. The numerical results reveal the impact of the key network parameters,\nsuch as the SINR threshold and the blockage parameter, on the network\nperformance.\n']","[('cellular networks', 0.4833184778690338), ('cellular network', 0.4797055423259735), ('distribution signal interference', 0.4707346260547638), ('millimeter wave', 0.4286413788795471), ('downlink coverage', 0.42601123452186584), ('wireless networks', 0.42502671480178833), ('signal interference plus', 0.40523138642311096), ('mmwave', 0.38934800028800964), ('stochastic geometry framework', 0.38550102710723877), ('network performance', 0.38183754682540894)]"
847,847,36,847_neural differential equations_differential equations neural_neural odes_neural ode,"['neural differential equations', 'differential equations neural', 'neural odes', 'neural ode', 'delay differential equations', 'neural differential', 'neural ordinary differential', 'equations neural', 'learning dynamical systems', 'delay differential']","['Neural Piecewise-Constant Delay Differential Equations   Continuous-depth neural networks, such as the Neural Ordinary Differential\nEquations (ODEs), have aroused a great deal of interest from the communities of\nmachine learning and data science in recent years, which bridge the connection\nbetween deep neural networks and dynamical systems. In this article, we\nintroduce a new sort of continuous-depth neural network, called the Neural\nPiecewise-Constant Delay Differential Equations (PCDDEs). Here, unlike the\nrecently proposed framework of the Neural Delay Differential Equations (DDEs),\nwe transform the single delay into the piecewise-constant delay(s). The Neural\nPCDDEs with such a transformation, on one hand, inherit the strength of\nuniversal approximating capability in Neural DDEs. On the other hand, the\nNeural PCDDEs, leveraging the contributions of the information from the\nmultiple previous time steps, further promote the modeling capability without\naugmenting the network dimension. With such a promotion, we show that the\nNeural PCDDEs do outperform the several existing continuous-depth neural\nframeworks on the one-dimensional piecewise-constant delay population dynamics\nand real-world datasets, including MNIST, CIFAR10, and SVHN.\n', 'Neural Delay Differential Equations: System Reconstruction and Image\n  Classification   Neural Ordinary Differential Equations (NODEs), a framework of\ncontinuous-depth neural networks, have been widely applied, showing exceptional\nefficacy in coping with representative datasets. Recently, an augmented\nframework has been developed to overcome some limitations that emerged in the\napplication of the original framework. In this paper, we propose a new class of\ncontinuous-depth neural networks with delay, named Neural Delay Differential\nEquations (NDDEs). To compute the corresponding gradients, we use the adjoint\nsensitivity method to obtain the delayed dynamics of the adjoint. Differential\nequations with delays are typically seen as dynamical systems of infinite\ndimension that possess more fruitful dynamics. Compared to NODEs, NDDEs have a\nstronger capacity of nonlinear representations. We use several illustrative\nexamples to demonstrate this outstanding capacity. Firstly, we successfully\nmodel the delayed dynamics where the trajectories in the lower-dimensional\nphase space could be mutually intersected and even chaotic in a model-free or\nmodel-based manner. Traditional NODEs, without any argumentation, are not\ndirectly applicable for such modeling. Secondly, we achieve lower loss and\nhigher accuracy not only for the data produced synthetically by complex models\nbut also for the CIFAR10, a well-known image dataset. Our results on the NDDEs\ndemonstrate that appropriately articulating the elements of dynamical systems\ninto the network design is truly beneficial in promoting network performance.\n', ""Neural Delay Differential Equations   Neural Ordinary Differential Equations (NODEs), a framework of\ncontinuous-depth neural networks, have been widely applied, showing exceptional\nefficacy in coping with some representative datasets. Recently, an augmented\nframework has been successfully developed for conquering some limitations\nemergent in application of the original framework. Here we propose a new class\nof continuous-depth neural networks with delay, named as Neural Delay\nDifferential Equations (NDDEs), and, for computing the corresponding gradients,\nwe use the adjoint sensitivity method to obtain the delayed dynamics of the\nadjoint. Since the differential equations with delays are usually seen as\ndynamical systems of infinite dimension possessing more fruitful dynamics, the\nNDDEs, compared to the NODEs, own a stronger capacity of nonlinear\nrepresentations. Indeed, we analytically validate that the NDDEs are of\nuniversal approximators, and further articulate an extension of the NDDEs,\nwhere the initial function of the NDDEs is supposed to satisfy ODEs. More\nimportantly, we use several illustrative examples to demonstrate the\noutstanding capacities of the NDDEs and the NDDEs with ODEs' initial value.\nSpecifically, (1) we successfully model the delayed dynamics where the\ntrajectories in the lower-dimensional phase space could be mutually\nintersected, while the traditional NODEs without any argumentation are not\ndirectly applicable for such modeling, and (2) we achieve lower loss and higher\naccuracy not only for the data produced synthetically by complex models but\nalso for the real-world image datasets, i.e., CIFAR10, MNIST, and SVHN. Our\nresults on the NDDEs reveal that appropriately articulating the elements of\ndynamical systems into the network design is truly beneficial to promoting the\nnetwork performance.\n""]","[('neural differential equations', 0.6878042817115784), ('differential equations neural', 0.6864447593688965), ('neural odes', 0.658686637878418), ('neural ode', 0.5766006112098694), ('delay differential equations', 0.5479114651679993), ('neural differential', 0.5386245846748352), ('neural ordinary differential', 0.5336825251579285), ('equations neural', 0.5151059627532959), ('learning dynamical systems', 0.5120455026626587), ('delay differential', 0.5060936212539673)]"
848,848,36,848_fractional diffusion equations_time fractional diffusion_fractional diffusion_diffusion time fractional,"['fractional diffusion equations', 'time fractional diffusion', 'fractional diffusion', 'diffusion time fractional', 'fractional differential equations', 'time fractional derivative', 'time fractional differential', 'fractional derivatives time', 'fractional sobolev', 'fractional boundary']","['Comparison principles for the time-fractional diffusion equations with\n  the Robin boundary conditions. Part II: Semilinear equations   In this paper, we deal with analysis of the initial-boundary value problems\nfor the semilinear time-fractional diffusion equations, while the case of the\nlinear equations was considered in the first part of the present work. These\nequations contain uniformly elliptic spatial differential operators of the\nsecond order and the Caputo type fractional derivative acting in the fractional\nSobolev spaces as well as a semilinear term that depends on the spatial\nvariable, the unknown function and its gradient. The boundary conditions are\nformulated in form of the homogeneous Neumann or Robin conditions. For these\nproblems, we first prove uniqueness and existence of their solutions. Under\nsome suitable conditions, we then show the non-negativity of the solutions and\nderive several comparison principles. We also apply the monotonicity method by\nupper and lower solutions to deduce some a priori estimates for solutions to\nthe initial-boundary value problems for the semilinear time-fractional\ndiffusion equations. Finally, we consider some initial-boundary value problems\nfor systems of the linear and semilinear time-fractional diffusion equations\nand prove non-negativity of their solutions under the suitable conditions.\n', 'Comparison principles for the linear and semiliniar time-fractional\n  diffusion equations with the Robin boundary condition   The main objective of this paper is analysis of the initial-boundary value\nproblems for the linear and semilinear time-fractional diffusion equations with\na uniformly elliptic spatial differential operator of the second order and the\nCaputo type fractional derivative acting in the fractional Sobolev spaces. The\nboundary conditions are formulated in form of the homogeneous Neumann or Robin\nconditions. First we deal with the uniqueness and existence of the solutions to\nthese initial-boundary value problems. Then we show a positivity property for\nthe solutions and derive the corresponding comparison principles. In the case\nof the semilinear time-fractional diffusion equation, we also apply the\nmonotonicity method by upper and lower solutions. As an application of our\nresults, we present some a priori estimates for solutions to the semilinear\ntime-fractional diffusion equations.\n', 'Comparison principles for the time-fractional diffusion equations with\n  the Robin boundary conditions. Part I: Linear equations   The main objective of this paper is analysis of the initial-boundary value\nproblems for the linear time-fractional diffusion equations with a uniformly\nelliptic spatial differential operator of the second order and the Caputo type\ntime-fractional derivative acting in the fractional Sobolev spaces. The\nboundary conditions are formulated in form of the homogeneous Neumann or Robin\nconditions. First we discuss the uniqueness and existence of solutions to these\ninitial-boundary value problems. Under some suitable conditions on the problem\ndata, we then prove positivity of the solutions. Based on these results,\nseveral comparison principles for the solutions to the initial-boundary value\nproblems for the linear time-fractional diffusion equations are derived.\n']","[('fractional diffusion equations', 0.7948797941207886), ('time fractional diffusion', 0.7639303207397461), ('fractional diffusion', 0.749822199344635), ('diffusion time fractional', 0.7310872673988342), ('fractional differential equations', 0.6351462006568909), ('time fractional derivative', 0.6294338703155518), ('time fractional differential', 0.6277259588241577), ('fractional derivatives time', 0.6052952408790588), ('fractional sobolev', 0.5983693599700928), ('fractional boundary', 0.5937053561210632)]"
849,849,36,849_near field communications_near field communication_large antenna arrays_near field channel,"['near field communications', 'near field communication', 'large antenna arrays', 'near field channel', 'antenna arrays', 'antenna array', 'field communications', 'near field propagation', 'large scale mimo', 'antennas']","['Enabling More Users to Benefit from Near-Field Communications: From\n  Linear to Circular Array   Massive multiple-input multiple-output (MIMO) for 5G is evolving into the\nextremely large-scale antenna array (ELAA) to increase the spectrum efficiency\nby orders of magnitude for 6G communications. ELAA introduces\nspherical-wave-based near-field communications, where channel capacity can be\nsignificantly improved for single-user and multi-user scenarios. Unfortunately,\nthe near-field region at large incidence/emergence angles is greatly reduced\nwith the widely studied uniform linear array (ULA). Thus, many randomly\ndistributed users may fail to benefit from near-field communications. In this\npaper, we leverage the rotational symmetry of uniform circular array (UCA) to\nprovide uniform and enlarged near-field regions at all angles, enabling more\nusers to benefit from near-field communications. Specifically, by exploiting\nthe geometrical relationship between UCA and users, the near-field beamforming\ntechnique for UCA is developed. Based on the analysis of near-field\nbeamforming, we reveal that UCA is able to provide a larger near-field region\nthan ULA in terms of the effective Rayleigh distance. Moreover, a\nconcentric-ring codebook is designed to realize efficient codebook-based\nbeamforming in the near-field region. In addition, we find out that UCA could\ngenerate orthogonal near-field beams along the same direction when the focal\npoint of the near-field beam is exactly the zeros of other beams, which has the\npotential to further improve spectrum efficiency in multi-user communications\ncompared with ULA. Simulation results are provided to verify the effectiveness\nof theoretical analysis and feasibility of UCA to enable more users to benefit\nfrom near-field communications by broadening the near-field region.\n', 'Near-Field Communications for Extremely Large-Scale MIMO: A Beamspace\n  Perspective   Extremely large-scale multiple-input multiple-output (XL-MIMO) is regarded as\none of the key techniques to enhance the performance of future wireless\ncommunications. Different from regular MIMO, the XL-MIMO shifts part of the\ncommunication region from the far field to the near field, where the\nspherical-wave channel model cannot be accurately approximated by the\ncommonly-adopted planar-wave channel model. As a result, the well-explored\nfar-field beamspace is unsuitable for near-field communications, thereby\nrequiring the exploration of specialized near-field beamspace. In this article,\nwe investigate the near-field communications for XL-MIMO from the perspective\nof beamspace. Given the spherical wavefront characteristics of the near-field\nchannels, we first map the antenna space to the near-field beamspace with the\nfractional Fourier transform. Then, we divide the near-field beamspace into\nthree parts, including high mainlobe, low mainlobe, and sidelobe, and provide a\ncomprehensive analysis of these components. Based on the analysis, we\ndemonstrate the advantages of the near-field beamspace over the existing\nmethods. Finally, we point out several applications of the near-field beamspace\nand highlight some potential directions for future study in the near-field\nbeamspace.\n', 'Near-Field Beam Management for Extremely Large-Scale Array\n  Communications   Extremely large-scale arrays (XL-arrays) have emerged as a promising\ntechnology to achieve super-high spectral efficiency and spatial resolution in\nfuture wireless systems. The large aperture of XL-arrays means that spherical\nrather than planar wavefronts must be considered, and a paradigm shift from\nfar-field to near-field communications is necessary. Unlike existing works that\nhave mainly considered far-field beam management, we study the new near-field\nbeam management for XL-arrays. We first provide an overview of near-field\ncommunications and introduce various applications of XL-arrays in both outdoor\nand indoor scenarios. Then, three typical near-field beam management methods\nfor XL-arrays are discussed: near-field beam training, beam tracking, and beam\nscheduling. We point out their main design issues and propose promising\nsolutions to address them. Moreover, other important directions in near-field\ncommunications are also highlighted to motivate future research.\n']","[('near field communications', 0.6753467321395874), ('near field communication', 0.6230868697166443), ('large antenna arrays', 0.6084859371185303), ('near field channel', 0.5795796513557434), ('antenna arrays', 0.577041506767273), ('antenna array', 0.546100914478302), ('field communications', 0.5328032374382019), ('near field propagation', 0.509162425994873), ('large scale mimo', 0.48772260546684265), ('antennas', 0.45848706364631653)]"
850,850,36,850_polytopes order_order polytopes_polytopes associated_polytopes lattice,"['polytopes order', 'order polytopes', 'polytopes associated', 'polytopes lattice', 'polytopes call', 'order polytope', 'polytopes provide', 'family polytopes', 'polytopes', 'polytopes give']","['Order and chain polytopes of maximal ranked posets   The order and chain polytopes, introduced by Richard P. Stanley, form a pair\nof Ehrhart equivalent polytopes associated to a given finite poset. A\nconjecture by Takayuki Hibi and Nan Li states that the $f$-vector of the chain\npolytope dominates the $f$-vector of the order polytope. In this paper we prove\na stronger form of that conjecture for a special class of posets. More\nprecisely, we show that the $f$-vectors increase monotonically over an\nadmissible family of chain-order polytopes for such posets.\n', 'Restricted Chain-Order Polytopes via Combinatorial Mutations   We study restricted chain-order polytopes associated to Young diagrams using\ncombinatorial mutations. These polytopes are obtained by intersecting\nchain-order polytopes with certain hyperplanes. The family of chain-order\npolytopes associated to a poset interpolate between the order and chain\npolytopes of the poset. Each such polytope retains properties of the order and\nchain polytope; for example its Ehrhart polynomial. For a fixed Young diagram,\nwe show that all restricted chain-order polytopes are related by a sequence of\ncombinatorial mutations. Since the property of giving rise to the period\ncollapse phenomenon is invariant under combinatorial mutations, we provide a\nlarge class of rational polytopes that give rise to period collapse.\n', '2-levelness of Marked Poset Polytopes and the Ehrhart polynomial   It is already known that order polytopes and chain polytopes are always\n2-level polytopes. In general, this is not true for marked order and marked\nchain polytopes. We study the geometry of marked order polytopes, marked chain\npolytopes, and marked chain-order polytopes, providing a comprehensive\ncharacterisation of 2-levelness for these polytopes. Furthermore, we present an\nexact formula for the Ehrhart polynomial of marked order polytopes. Because of\ntheir connection to marked chain and marked chain-order polytopes, this\npolynomial is also the Ehrhart polynomial of these polytopes.\n']","[('polytopes order', 0.6738540530204773), ('order polytopes', 0.6649059057235718), ('polytopes associated', 0.652653157711029), ('polytopes lattice', 0.6228883862495422), ('polytopes call', 0.6221135854721069), ('order polytope', 0.6205660104751587), ('polytopes provide', 0.6131784319877625), ('family polytopes', 0.6021848320960999), ('polytopes', 0.5999706983566284), ('polytopes give', 0.5936257839202881)]"
851,851,36,851_conjecture finite group_automorphism group_automorphisms finite_abelian group non,"['conjecture finite group', 'automorphism group', 'automorphisms finite', 'abelian group non', 'automorphism order', 'automorphisms', 'finite groups', 'non abelian subgroup', 'inner automorphisms', 'non abelian group']","['On the non-inner automorphism conjecture of finite $p$-groups   A long-standing conjecture asserts that every finite non-abelian $p$-group\nhas a non-inner automorphism of order $p$. In this paper, we settle the\nconjecture for a finite $p$-group ($p >2$) of nilpotency class $n$ with certain\nconditions.\n', 'On the conjecture of non-inner automorphisms of finite $p$-groups   Let $p$ be a prime number. A longstanding conjecture asserts that every\nfinite non-abelian $p$-group has a non-inner automorphism of order $p$. In this\npaper, we prove that if $G$ is an odd order finite non-abelian monolithic\n$p$-group such that every maximal subgroup of $G$ is non-abelian and $[Z(M), g]\n\\leq Z(G)$ for every maximal subgroup $M$ of $G$ and $g \\in G \\setminus M$.\nThen $G$ has a non-inner automorphism of order $p$ leaving the Frattini\nsubgroup $\\Phi(G)$ elementwise fixed.\n', 'On the conjecture of non-inner automorphisms of finite $p$-groups with a\n  non-trivial abelian direct factor   Let $p$ be a prime number. A longstanding conjecture asserts that every\nfinite non-abelian $p$-group has a non-inner automorphism of order $p$. In this\npaper, we prove that the conjecture is true when a finite non-abelian $p$-group\n$G$ has a non-trivial abelian direct factor. Moreover, we prove that the\nnon-inner automorphism is central and fixes $\\Phi(G)$ elementwise. As a\nconsequence, we prove that every group which is not purely non-abelian has a\nnon-inner central automorphism of order $p$ which fixes $\\Phi(G)$ elementwise.\n']","[('conjecture finite group', 0.6140662431716919), ('automorphism group', 0.5589466691017151), ('automorphisms finite', 0.5262341499328613), ('abelian group non', 0.5152857303619385), ('automorphism order', 0.5110601186752319), ('automorphisms', 0.5033126473426819), ('finite groups', 0.50248122215271), ('non abelian subgroup', 0.4892469048500061), ('inner automorphisms', 0.4863124191761017), ('non abelian group', 0.4840198755264282)]"
852,852,36,852_bayesian frequentist_frequentist inference_probabilistic inference_bayesian inference,"['bayesian frequentist', 'frequentist inference', 'probabilistic inference', 'bayesian inference', 'probabilistic uncertainty', 'frequentist confidence', 'prior information available', 'prior information', 'bayesian methods', 'inferences']","[""Valid and efficient imprecise-probabilistic inference with partial\n  priors, I. First results   Between Bayesian and frequentist inference, it's commonly believed that the\nformer is for cases where one has a prior and the latter is for cases where one\nhas no prior. But the prior/no-prior classification isn't exhaustive, and most\nreal-world applications fit somewhere in between these two extremes. That\nneither of the two dominant schools of thought are suited for these\napplications creates confusion and slows progress. A key observation here is\nthat ``no prior information'' actually means no prior distribution can be ruled\nout, so the classically-frequentist context is best characterized as every\nprior. From this perspective, it's now clear that there's an entire spectrum of\ncontexts depending on what, if any, partial prior information is available,\nwith Bayesian (one prior) and frequentist (every prior) on opposite extremes.\nThis paper ties the two frameworks together by formally treating those cases\nwhere only partial prior information is available using the theory of imprecise\nprobability. The end result is a unified framework of (imprecise-probabilistic)\nstatistical inference with a new validity condition that implies both\nfrequentist-style error rate control for derived procedures and Bayesian-style\ncoherence properties, relative to the given partial prior information. This new\ntheory contains both the Bayesian and frequentist frameworks as special cases,\nsince they're both valid in this new sense relative to their respective partial\npriors. Different constructions of these valid inferential models are\nconsidered, and compared based on their efficiency.\n"", 'Hypothesis testing and confidence sets: why Bayesian not frequentist,\n  and how to set a prior with a regulatory authority   We marshall the arguments for preferring Bayesian hypothesis testing and\nconfidence sets to frequentist ones. We define admissible solutions to\ninference problems, noting that Bayesian solutions are admissible. We give\nseven weaker common-sense criteria for solutions to inference problems, all\nfailed by these frequentist methods but satisfied by any admissible method. We\nnote that pseudo-Bayesian methods made by handicapping Bayesian methods to\nsatisfy criteria on type I error rate makes them frequentist not Bayesian in\nnature.\n  We give five examples showing the differences between Bayesian and\nfrequentist methods; the first requiring little calculus, the second showing in\nabstract what is wrong with these frequentist methods, the third to illustrate\ninformation conservation, the fourth to show that the same problems arise in\neveryday statistical problems, and the fifth to illustrate how on some\nreal-life inference problems Bayesian methods require less data than fixed\nsample-size (resp. pseudo-Bayesian) frequentist hypothesis testing by factors\nexceeding 3000 (resp 300) without recourse to informative priors.\n  To address the issue of different parties with opposing interests reaching\nagreement on a prior, we illustrate the beneficial effects of a Bayesian ""Let\nthe data decide"" policy both on results under a wide variety of conditions and\non motivation to reach a common prior by consent.\n  We show that in general the frequentist confidence level contains less\nrelevant Shannon information than the Bayesian posterior, and give an example\nwhere no deterministic frequentist critical regions give any relevant\ninformation even though the Bayesian posterior contains up to the maximum\npossible amount. In contrast use of the Bayesian prior allows construction of\nnon-deterministic critical regions for which the Bayesian posterior can be\nrecovered from the frequentist confidence.\n', ""Bridging Bayesian, frequentist and fiducial (BFF) inferences using\n  confidence distribution   Bayesian, frequentist and fiducial (BFF) inferences are much more congruous\nthan they have been perceived historically in the scientific community (cf.,\nReid and Cox 2015; Kass 2011; Efron 1998). Most practitioners are probably more\nfamiliar with the two dominant statistical inferential paradigms, Bayesian\ninference and frequentist inference. The third, lesser known fiducial inference\nparadigm was pioneered by R.A. Fisher in an attempt to define an inversion\nprocedure for inference as an alternative to Bayes' theorem. Although each\nparadigm has its own strengths and limitations subject to their different\nphilosophical underpinnings, this article intends to bridge these different\ninferential methodologies through the lenses of confidence distribution theory\nand Monte-Carlo simulation procedures. This article attempts to understand how\nthese three distinct paradigms, Bayesian, frequentist, and fiducial inference,\ncan be unified and compared on a foundational level, thereby increasing the\nrange of possible techniques available to both statistical theorists and\npractitioners across all fields.\n""]","[('bayesian frequentist', 0.6501197814941406), ('frequentist inference', 0.6034577488899231), ('probabilistic inference', 0.5909286737442017), ('bayesian inference', 0.5880758166313171), ('probabilistic uncertainty', 0.555558979511261), ('frequentist confidence', 0.5420785546302795), ('prior information available', 0.5405555367469788), ('prior information', 0.5403088331222534), ('bayesian methods', 0.5367285013198853), ('inferences', 0.5341140031814575)]"
853,853,36,853_robust optimization problems_adjustable robust optimization_robust optimization_optimization robust,"['robust optimization problems', 'adjustable robust optimization', 'robust optimization', 'optimization robust', 'stage robust optimization', 'uncertainty robust', 'robust combinatorial', 'uncertainty sets', 'robust optimization ro', 'budgeted uncertainty']","[""Data-Driven Robust Optimization Using Scenario-Induced Uncertainty Sets   Uncertainty sets are at the heart of robust optimization (RO) because they\nplay a key role in determining the RO models' tractability, robustness, and\nconservativeness. Different types of uncertainty sets have been proposed that\nmodel uncertainty from various perspectives. Among them, polyhedral uncertainty\nsets are widely used due to their simplicity and flexible structure to model\nthe underlying uncertainty. However, the conventional polyhedral uncertainty\nsets present certain disadvantages; some are too conservative while others lead\nto computationally expensive RO models. This paper proposes a systematic\napproach to develop data-driven polyhedral uncertainty sets that mitigate these\ndrawbacks. The proposed uncertainty sets are polytopes induced by a given set\nof scenarios, capture correlation information between uncertain parameters, and\nallow for direct trade-offs between tractability and conservativeness issue of\nconventional polyhedral uncertainty sets. To develop these uncertainty sets, we\nuse principal component analysis (PCA) to transform the correlated scenarios\ninto their uncorrelated principal components and to shrink the uncertainty\nspace dimensionality. Thus, decision-makers can use the number of the leading\nprincipal components as a tool to trade-off tractability, conservativeness, and\nrobustness of RO models. We quantify the quality of the lower bound of a static\nRO problem with a scenario-induced uncertainty set by deriving a theoretical\nbound on the optimality gap. Additionally, we derive probabilistic guarantees\nfor the performance of the proposed scenario-induced uncertainty sets by\ndeveloping explicit lower bounds on the number of scenarios. Finally, we\ndemonstrate the practical applicability of the proposed uncertainty sets to\ntrade-off tractability, robustness, and conservativeness by examining a range\nof knapsack and power grid problems.\n"", 'Two-Stage Robust Optimization Problems with Two-Stage Uncertainty   We consider two-stage robust optimization problems, which can be seen as\ngames between a decision maker and an adversary. After the decision maker fixes\npart of the solution, the adversary chooses a scenario from a specified\nuncertainty set. Afterwards, the decision maker can react to this scenario by\ncompleting the partial first-stage solution to a full solution.\n  We extend this classic setting by adding another adversary stage after the\nsecond decision-maker stage, which results in min-max-min-max problems, thus\npushing two-stage settings further towards more general multi-stage problems.\nWe focus on budgeted uncertainty sets and consider both the continuous and\ndiscrete case. For the former, we show that a wide range of robust\ncombinatorial optimization problems can be decomposed into polynomially many\nsubproblems, which can be solved in polynomial time for example in the case of\n(\\textsc{representative}) \\textsc{selection}. For the latter, we prove\nNP-hardness for a wide range of problems, but note that the special case where\nfirst- and second-stage adversarial costs are equal can remain solvable in\npolynomial time.\n', 'Robust Combinatorial Optimization with Locally Budgeted Uncertainty   Budgeted uncertainty sets have been established as a major influence on\nuncertainty modeling for robust optimization problems. A drawback of such sets\nis that the budget constraint only restricts the global amount of cost increase\nthat can be distributed by an adversary. Local restrictions, while being\nimportant for many applications, cannot be modeled this way.\n  We introduce new variant of budgeted uncertainty sets, called locally\nbudgeted uncertainty. In this setting, the uncertain parameters become\npartitioned, such that a classic budgeted uncertainty set applies to each\npartition, called region.\n  In a theoretical analysis, we show that the robust counterpart of such\nproblems for a constant number of regions remains solvable in polynomial time,\nif the underlying nominal problem can be solved in polynomial time as well. If\nthe number of regions is unbounded, we show that the robust selection problem\nremains solvable in polynomial time, while also providing hardness results for\nother combinatorial problems.\n  In computational experiments using both random and real-world data, we show\nthat using locally budgeted uncertainty sets can have considerable advantages\nover classic budgeted uncertainty sets.\n']","[('robust optimization problems', 0.6490518450737), ('adjustable robust optimization', 0.641147792339325), ('robust optimization', 0.6345692873001099), ('optimization robust', 0.6250478625297546), ('stage robust optimization', 0.596370279788971), ('uncertainty robust', 0.579542875289917), ('robust combinatorial', 0.5548133850097656), ('uncertainty sets', 0.5541571378707886), ('robust optimization ro', 0.5482817888259888), ('budgeted uncertainty', 0.5391970872879028)]"
854,854,36,854_cameras_camera_3d reconstruction_algebraic geometry,"['cameras', 'camera', '3d reconstruction', 'algebraic geometry', 'three projective', 'view geometry', 'projective', 'point pairs', '3d point', 'multiview']","['Line Multiview Varieties   We present an algebraic study of line correspondences for pinhole cameras, in\ncontrast to the thoroughly studied point correspondences. We define the line\nmultiview variety as the Zariski closure of the image of the map projecting\nlines in 3-space to tuples of image lines in 2-space. We prove that in the case\nof generic camera matrices the line multiview variety is a determinantal\nvariety and we provide a complete set-theoretic description for any camera\narrangement. We investigate basic properties of this variety such as dimension,\nsmoothness, and multidegree. Finally, we give experimental results for the\nEuclidean distance degree and robustness under noise for the triangulation of\nlines.\n', 'Order-One Rolling Shutter Cameras   Rolling shutter (RS) cameras dominate consumer and smartphone markets.\nSeveral methods for computing the absolute pose of RS cameras have appeared in\nthe last 20 years, but the relative pose problem has not been fully solved yet.\nWe provide a unified theory for the important class of order-one rolling\nshutter (RS$_1$) cameras. These cameras generalize the perspective projection\nto RS cameras, projecting a generic space point to exactly one image point via\na rational map. We introduce a new back-projection RS camera model,\ncharacterize RS$_1$ cameras, construct explicit parameterizations of such\ncameras, and determine the image of a space line. We classify all minimal\nproblems for solving the relative camera pose problem with linear RS$_1$\ncameras and discover new practical cases. Finally, we show how the theory can\nbe used to explain RS models previously used for absolute pose computation.\n', 'Projections of Curves and Conic Multiview Varieties   We present an algebraic study of the projection of plane curves and twisted\ncubics in space onto multiple images of pinhole cameras. The Zariski closure of\nthe image of the projection of conics is a conic multiview varieties. Extending\nprevious work for point and line multiview varieties, we use back-projected\ncones to describe these varieties. For two views, we provide the defining ideal\nof the multiview variety. For any number of views, we state when the simplest\npossible set-theoretic description is achieved based on the geometry of the\ncamera centers. Finally, we investigate the complexity of the associated\ntriangulation problem and conjecture the Euclidean distance degree for the\nconic multiview variety for two cameras.\n']","[('cameras', 0.5051169991493225), ('camera', 0.4797227680683136), ('3d reconstruction', 0.4584561288356781), ('algebraic geometry', 0.44866615533828735), ('three projective', 0.4475877583026886), ('view geometry', 0.4416312575340271), ('projective', 0.43087345361709595), ('point pairs', 0.4243539273738861), ('3d point', 0.42309650778770447), ('multiview', 0.422397255897522)]"
855,855,36,855_random matrices_random matrix products_random matrix_ergodic decomposition,"['random matrices', 'random matrix products', 'random matrix', 'ergodic decomposition', 'cokernels', 'gl _n mathbb', 'cokernel', 'haar random', 'universality random', 'random groups']","['Universality for cokernels of random matrix products   For random integer matrices $M_1,\\ldots,M_k \\in\n\\operatorname{Mat}_n(\\mathbb{Z})$ with independent entries, we study the\ndistribution of the cokernel $\\operatorname{cok}(M_1 \\cdots M_k)$ of their\nproduct. We show that this distribution converges to a universal one as $n \\to\n\\infty$ for a general class of matrix entry distributions, and more generally\nshow universal limits for the joint distribution of\n$\\operatorname{cok}(M_1),\\operatorname{cok}(M_1M_2),\\ldots,\\operatorname{cok}(M_1\n\\cdots M_k)$. Furthermore, we characterize the universal distributions arising\nas marginals of a natural generalization of the Cohen-Lenstra measure to\nsequences of abelian groups with maps between them, which weights sequences\ninversely proportionally to their number of automorphisms. The proofs develop\nan extension of the moment method of Wood to joint moments of multiple groups,\nand rely also on the connection to Hall-Littlewood polynomials and symmetric\nfunction identities. As a corollary we obtain an explicit universal\ndistribution for coranks of random matrix products over $\\mathbb{F}_p$ as the\nmatrix size tends to infinity.\n', 'The cokernel of a polynomial push-forward of a random integral matrix\n  with concentrated residue   We prove new statistical results about the distribution of the cokernel of a\nrandom integral matrix with a concentrated residue. Given a prime $p$ and a\npositive integer $n$, consider a random $n \\times n$ matrix $X_n$ over the ring\n$\\mathbb{Z}_p$ of $p$-adic integers whose entries are independent. Previously,\nWood showed that regardless of the distribution of $X_n$, as long as each entry\nof $X_n$ is not too concentrated on a single residue modulo $p$, the\ndistribution of the cokernel $\\mathrm{cok}(X_n)$ of $X_n$, up to isomorphism,\nweakly converges to the Cohen--Lenstra distribution, as $n \\rightarrow \\infty$.\nIn this paper, we consider the case when $X_n$ has a concentrated residue $A_n$\nso that $X_n = A_n + pB_n$, where $B_n$ is a random $n \\times n$ matrix over\n$\\mathbb{Z}_p$. We show that for every fixed $n$ and a non-constant monic\npolynomial $P(t) \\in \\mathbb{Z}_p[t]$, we can explicitly compute the\ndistribution of $\\mathrm{cok}(P(X_n))$ when $B_n$ is a Haar-random matrix.\nUsing this, we also show that for specific choices of $A_n$ a much wider class\nof random matrices $B_n$ gives the same distribution of $\\mathrm{cok}(P(X_n))$.\nFor the Haar-random $B_n$, we deduce our result from an interesting\nequidistribution result for matrices over $\\mathbb{Z}_p[t]/(P(t))$, which we\nprove by establishing a version of the Weierstrass preparation theorem for the\nnoncommutative ring $\\mathrm{M}_n(\\mathbb{Z}_p)$ of $n \\times n$ matrices over\n$\\mathbb{Z}_p$.\n', 'Joint distribution of the cokernels of random $p$-adic matrices   In this paper, we study the joint distribution of the cokernels of random\n$p$-adic matrices. Let $p$ be a prime and $P_1(t), \\cdots, P_l(t) \\in\n\\mathbb{Z}_p[t]$ be monic polynomials whose reductions modulo $p$ in\n$\\mathbb{F}_p[t]$ are distinct and irreducible. We determine the limit of the\njoint distribution of the cokernels $\\text{cok} (P_1(A)), \\cdots,\n\\text{cok}(P_l(A))$ for a random $n \\times n$ matrix $A$ over $\\mathbb{Z}_p$\nwith respect to Haar measure as $n \\rightarrow \\infty$. By applying the\nlinearization of a random matrix model, we also provide a conjecture which\ngeneralizes this result. Finally, we provide a sufficient condition that the\ncokernels $\\text{cok}(A)$ and $\\text{cok}(A+B_n)$ become independent as $n\n\\rightarrow \\infty$, where $B_n$ is a fixed $n \\times n$ matrix over\n$\\mathbb{Z}_p$ for each $n$ and $A$ is a random $n \\times n$ matrix over\n$\\mathbb{Z}_p$.\n']","[('random matrices', 0.5104414224624634), ('random matrix products', 0.48779526352882385), ('random matrix', 0.4302600622177124), ('ergodic decomposition', 0.34354808926582336), ('cokernels', 0.31667932868003845), ('gl _n mathbb', 0.3123876452445984), ('cokernel', 0.27762678265571594), ('haar random', 0.27451080083847046), ('universality random', 0.25900575518608093), ('random groups', 0.25868886709213257)]"
856,856,36,856_strongly regular graphs_regular graphs_regular graphs also_regular graphs graph,"['strongly regular graphs', 'regular graphs', 'regular graphs also', 'regular graphs graph', 'strongly regular graph', 'distance regular graphs', 'regular graph classical', 'regular graph', 'graphs distance regular', 'regular graph diameter']","['On the spectral gap and the automorphism group of distance-regular\n  graphs   We prove that a distance-regular graph with a dominant distance is a spectral\nexpander. The key ingredient of the proof is a new inequality on the\nintersection numbers. We use the spectral gap bound to study the structure of\nthe automorphism group.\n  The minimal degree of a permutation group $G$ is the minimum number of points\nnot fixed by non-identity elements of $G$. Lower bounds on the minimal degree\nhave strong structural consequences on $G$. In 2014 Babai proved that the\nautomorphism group of a strongly regular graph with $n$ vertices has minimal\ndegree $\\geq c n$, with known exceptions. Strongly regular graphs correspond to\ndistance-regular graphs of diameter 2. Babai conjectured that Hamming and\nJohnson graphs are the only primitive distance-regular graphs of diameter\n$d\\geq 3$ whose automorphism group has sublinear minimal degree. We confirm\nthis conjecture for non-geometric primitive distance-regular graphs of bounded\ndiameter. We also show if the primitivity assumption is removed, then only one\nadditional family of exceptions arises, the cocktail-party graphs. We settle\nthe geometric case in a companion paper.\n', 'The transformation of edge-regular and pseudo strongly regular graphs\n  under graph operations   The graph $G$ is said to be strongly regular with parameters\n$(n,k,\\lambda,\\mu)$ if the following conditions hold:\n  (1) each vertex has $k$ neighbours; (2) any two adjacent vertices of $G$ have\n$\\lambda$ common neighbours; (3) any two non-adjacent vertices of $G$ have\n$\\mu$ common neighbours.\n  In this paper we study two weaker notions of strongly regular graphs. A graph\nsatisfying the conditions $(1)$ and $(2)$ is called an edge-regular graph with\nparameters $(n,k,\\lambda)$. We call a graph satisfying the conditions $(1)$ and\n$(3)$ a pseudo strongly regular graph with parameters $(n,k,\\mu)$. In this\npaper we study the impact of various graph operations on edge regular graphs\nand pseudo strongly regular graphs.\n', ""On cores of distance-regular graphs   We look at the question of which distance-regular graphs are core-complete,\nmeaning they are isomorphic to their own core or have a complete core. We build\non Roberson's homomorphism matrix approach by which method he proved the\nCameron-Kazanidis conjecture that strongly regular graphs are core-complete. We\ndevelop the theory of the homomorphism matrix for distance-regular graphs of\ndiameter $d$.\n  We derive necessary conditions on the cosines of a distance-regular graph for\nit to admit an endomorphism into a subgraph of smaller diameter $e<d$. As a\nconsequence of these conditions, we show that if $X$ is a primitive\ndistance-regular graph where the subgraph induced by the set of vertices\nfurthest away from a vertex $v$ is connected, any retraction of $X$ onto a\ndiameter-$d$ subgraph must be an automorphism, which recovers Roberson's result\nfor strongly regular graphs as a special case for diameter $2$.\n  We illustrate the application of our necessary conditions through\ncomputational results. We find that no antipodal, non-bipartite\ndistance-regular graphs of diameter 3, with degree at most $50$ admits an\nendomorphism to a diameter 2 subgraph. We also give many examples of\nintersection arrays of primitive distance-regular graphs of diameter $3$ which\nare core-complete. Our methods include standard tools from the theory of\nassociation schemes, particularly the spectral idempotents.\n  Keywords: algebraic graph theory, distance-regular graphs, association\nschemes, graph homomorphisms\n""]","[('strongly regular graphs', 0.7588853240013123), ('regular graphs', 0.7515975832939148), ('regular graphs also', 0.738730788230896), ('regular graphs graph', 0.733223557472229), ('strongly regular graph', 0.7267165184020996), ('distance regular graphs', 0.710716187953949), ('regular graph classical', 0.7003134489059448), ('regular graph', 0.7001602053642273), ('graphs distance regular', 0.6990011930465698), ('regular graph diameter', 0.6631078124046326)]"
857,857,35,857_hopf bifurcations_hopf bifurcation_bifurcation stability_bifurcation theory,"['hopf bifurcations', 'hopf bifurcation', 'bifurcation stability', 'bifurcation theory', 'bifurcation analysis', 'bifurcations', 'bifurcation', 'bifurcation parameter', 'bifurcation periodic', 'bifurcation point']","['Stability and Hopf bifurcation analysis of a two state delay\n  differential equation modeling the human respiratory system   We study the two state model which describes the balance equation for carbon\ndioxide and oxygen. These are nonlinear parameter dependent and because of the\ntransport delay in the respiratory control system, they are modeled with delay\ndifferential equation. So, the dynamics of a two state one delay model are\ninvestigated. By choosing the delay as a parameter, the stability and Hopf\nbifurcation conditions are obtained. We notice that as the delay passes through\nits critical value, the positive equilibrium loses its stability and Hopf\nbifurcation occurs. The stable region of the system with delay against the\nother parameters and bifurcation diagrams are also plotted. The three\ndimensional stability chart of the two state model is constructed. We find that\nthe delay parameter has effect on the stability but not on the equilibrium\nstate. The explicit derivation of the direction of Hopf bifurcation and the\nstability of the bifurcation periodic solutions are determined with the help of\nnormal form theory and center manifold theorem to delay differential equations.\nFinally, some numerical example and simulations are carried out to confirm the\nanalytical findings. The numerical simulations verify the theoretical results.\n', ""Resonance phenomena in a scalar delay differential equation with two\n  state-dependent delays   We study a scalar DDE with two delayed feedback terms that depend linearly on\nthe state. The associated constant-delay DDE, obtained by freezing the state\ndependence, is linear and without recurrent dynamics. With state dependent\ndelay terms, on the other hand, the DDE shows very complicated dynamics. To\ninvestigate this, we perform a bifurcation analysis of the system and present\nits bifurcation diagram in the plane of the two feedback strengths. It is\norganized by Hopf-Hopf bifurcation points that give rise to curves of torus\nbifurcation and associated two-frequency dynamics in the form of invariant tori\nand resonance tongues. We numerically determine the type of the Hopf-Hopf\nbifurcation points by computing the normal form on the center manifold; this\nrequires the expansion of the functional defining the state-dependent DDE in a\npower series whose terms up to order three only contain constant delays. We\nimplemented this expansion and the computation of the normal form coefficients\nin Matlab using symbolic differentiation. Numerical continuation of the torus\nbifurcation curves confirms the correctness of our normal form calculations.\nMoreover, it enables us to compute the curves of torus bifurcations more\nglobally, and to find associated curves of saddle-node bifurcations of periodic\norbits that bound the resonance tongues. The tori themselves are computed and\nvisualized in a three-dimensional projection, as well as the planar trace of a\nsuitable Poincar\\'e section. In particular, we compute periodic orbits on\nlocked tori and their associated unstable manifolds. This allows us to study\ntransitions through resonance tongues and the breakup of a 1:4 locked torus.\nThe work presented here demonstrates that state dependence alone is capable of\ngenerating a wealth of dynamical phenomena.\n"", ""Bifurcations and Amplitude Death from Distributed Delays in Coupled\n  Landau-Stuart Oscillators and a Chaotic Parametrically Forced van der\n  Pol-Rayleigh System   Distributed delays modeled by 'weak generic kernels' are introduced in the\nwell-known coupled Landau-Stuart system, as well as a chaotic van der\nPol-Rayleigh system with parametric forcing. The systems are close via the\n'linear chain trick'. Linear stability analysis of the systems and conditions\nfor Hopf bifurcation which initiates oscillations are investigated, including\nderiving the normal form at bifurcation, and deducing the stability of the\nresulting limit cycle attractor. The value of the delay parameter $a=a_{Hopf}$\nat Hopf bifurcation picks out the onset of Amplitude Death(AD) in all three\nsystems, with oscillations at larger values (corresponding to weaker delay). In\nthe Landau-Stuart system, the Hopf-generated limit cycles for $a>a_{Hopf}$ turn\nout to be remarkably stable under very large variations of all other system\nparameters beyond the Hopf bifurcation point, and do not undergo further\nsymmetry breaking, cyclic-fold, flip, transcritical or Neimark-Sacker\nbifurcations. This is to be expected as the corresponding undelayed systems are\nrobust oscillators over wide ranges of their respective parameters. Numerical\nsimulations reveal strong distortion and rotation of the limit cycles in phase\nspace as the parameters are pushed far into the post-Hopf regime, and reveal\nother features, such as how the oscillation amplitudes and time periods of the\nphysical variables on the limit cycle attractor change as the delay and other\nparameters are varied. For the chaotic system, very strong delays may still\nlead to the cessation of oscillations and the onset of AD (even for relatively\nlarge values of the system forcing which tends to oppose this phenomenon).\nVarying of the other important system parameter, the parametric excitation,\nleads to a rich sequence of dynamical behaviors, with the bifurcations leading\nfrom one regime (or type of attractor) into the next being carefully tracked.\n""]","[('hopf bifurcations', 0.7381877899169922), ('hopf bifurcation', 0.7235720157623291), ('bifurcation stability', 0.6908185482025146), ('bifurcation theory', 0.6900513768196106), ('bifurcation analysis', 0.6619381308555603), ('bifurcations', 0.6595137119293213), ('bifurcation', 0.6525482535362244), ('bifurcation parameter', 0.6486790180206299), ('bifurcation periodic', 0.6230128407478333), ('bifurcation point', 0.6059619188308716)]"
858,858,35,858_locally nilpotent derivation_nilpotent derivations_locally nilpotent_nilpotent derivation,"['locally nilpotent derivation', 'nilpotent derivations', 'locally nilpotent', 'nilpotent derivation', 'polynomial algebras', 'azumaya algebras', 'algebraically closed', 'polynomial algebra', 'every derivation', 'frobenius kernel']","['A note on homogeneous rank $2$ locally nilpotent derivations on\n  $k[X,Y,Z]$   In this article we show that for every prime number $p$, any irreducible\nhomogeneous locally nilpotent derivations of rank $2$ and degree $p-2$ are\ntriangularizable. Further, we describe the structure of irreducible\nnon-triangularizable homogeneous locally nilpotent derivations of rank $2$ and\ndegree $pq-2$, where $p,q$ are prime numbers. Consequently, we give explicit\ndescriptions of the generators of the image ideals of certain homogeneous\nlocally nilpotent derivations of rank $2$.\n', 'The images of some simple derivations   In the paper, we study the relation between the images of polynomial\nderivations and their simplicity. We prove that the images of simple Shamsuddin\nderivations are not Mathieu-Zhao spaces. In addition, we also show that the\nimages of some simple derivations in dimension three are not Mathieu-Zhao\nspaces. Thus, we conjecture that the images of simple derivations in dimension\ngreater than one are not Mathieu-Zhao spaces. We also prove that locally\nnilpotent derivations are not simple in dimension greater than one.\n', 'On locally nilpotent derivations of polynomial algebra in three\n  variables   In this paper we investigate locally nilpotent derivations on the polynomial\nalgebra in three variables over a field of characteristic zero. We introduce an\niterating construction giving all locally nilpotent derivations of rank $2$.\nThis construction allows to get examples of non-triangularizable locally\nnilpotent derivations of rank $2$. We also show that the well-known example of\na locally nilpotent derivation of rank $3$, given by Freudenburg, is a member\nof a large family of new examples of rank $3$ locally nilpotent derivations.\nOur approach is based on considering all locally nilpotent derivations\ncommuting with a given one. We obtain a characterization of locally nilpotent\nderivations with a given rank in terms of sets of commuting locally nilpotent\nderivations.\n']","[('locally nilpotent derivation', 0.6706830263137817), ('nilpotent derivations', 0.5992475748062134), ('locally nilpotent', 0.5563688278198242), ('nilpotent derivation', 0.5186942219734192), ('polynomial algebras', 0.4540663957595825), ('azumaya algebras', 0.4516284167766571), ('algebraically closed', 0.4137737452983856), ('polynomial algebra', 0.3899637758731842), ('every derivation', 0.37752899527549744), ('frobenius kernel', 0.37416672706604004)]"
859,859,35,859_continuous assimilation_navier stokes equations_dimensional navier stokes_heat navier stokes,"['continuous assimilation', 'navier stokes equations', 'dimensional navier stokes', 'heat navier stokes', 'incompressible navier stokes', '2d navier stokes', 'navier stokes', 'stokes equations nse', 'methods navier', 'two dimensional navier']","['Continuous data assimilation for problems with limited regularity using\n  non-interpolant observables   Continuous data assimilation addresses time-dependent problems with unknown\ninitial conditions by incorporating observations of the solution into a nudging\nterm. For the prototypical heat equation with variable conductivity and the\nNeumann boundary condition, we consider data assimilation schemes with\nnon-interpolant observables unlike previous studies. These generalized nudging\nstrategies are notably useful for problems which possess limited or even no\nadditional regularity beyond the minimal framework. We demonstrate that a\nspatially discretized nudged solution converges exponentially fast in time to\nthe true solution with the rate guaranteed by the choice of the nudging\nstrategy independent of the discretization. Furthermore, the long-term discrete\nerror is optimal as it matches the estimates available for problems of limited\nregularity with known initial conditions. Three particular strategies --\nnudging by a conforming finite element subspace, nudging by piecewise constants\non the boundary mesh, and nudging by the mean value -- are explored numerically\nfor three test cases, including a problem with Dirac delta forcing and the\nKellogg problem with discontinuous conductivity.\n', 'Analysis of continuous data assimilation with large (or even infinite)\n  nudging parameters   This paper considers continuous data assimilation (CDA) in partial\ndifferential equation (PDE) discretizations where nudging parameters can be\ntaken arbitrarily large. We prove that long-time optimally accurate solutions\nare obtained for such parameters for the heat and Navier-Stokes equations\n(using implicit time stepping methods), with error bounds that do not grow as\nthe nudging parameter gets large. Existing theoretical results either prove\noptimal accuracy but with the error scaled by the nudging parameter, or\nsuboptimal accuracy that is independent of it. The key idea to the improved\nanalysis is to decompose the error based on a weighted inner product that\nincorporates the (symmetric by construction) nudging term, and prove that the\nprojection error from this weighted inner product is optimal and independent of\nthe nudging parameter. We apply the idea to BDF2 - finite element\ndiscretizations of the heat equation and Navier-Stokes equations to show that\nwith CDA, they will admit optimal long-time accurate solutions independent of\nthe nudging parameter, for nudging parameters large enough. Several numerical\ntests are given for the heat equation, fluid transport equation, Navier-Stokes,\nand Cahn-Hilliard that illustrate the theory.\n', 'On the Infinite-Nudging Limit of the Nudging Filter for Continuous Data\n  Assimilation   This article studies the intimate relationship between two filtering\nalgorithms for continuous data assimilation, the synchronization filter and the\nnudging filter, in the paradigmatic context of the two-dimensional (2D)\nNavier-Stokes equations (NSE) for incompressible fluids. In this setting, the\nnudging filter can formally be viewed as an affine perturbation of the 2D NSE.\nThus, in the degenerate limit of zero nudging parameter, the nudging filter\nconverges to the solution of the 2D NSE. However, when the nudging parameter of\nthe nudging filter is large, the perturbation becomes singular. It is shown\nthat in the singular limit of infinite nudging parameter, the nudging filter\nconverges to the synchronization filter. In establishing this result, the\narticle fills a notable gap in the literature surrounding these algorithms.\nNumerical experiments are then presented that confirm the theoretical results\nand probes the issue of selecting a nudging strategy in the presence of\nobservational noise. In this direction, an adaptive nudging strategy is\nproposed that leverages the insight gained from the relationship between the\nsynchronization filter and the nudging filter that produces measurable\nimprovement over the constant nudging strategy.\n']","[('continuous assimilation', 0.49643978476524353), ('navier stokes equations', 0.4588126242160797), ('dimensional navier stokes', 0.43621689081192017), ('heat navier stokes', 0.42870453000068665), ('incompressible navier stokes', 0.4188895523548126), ('2d navier stokes', 0.40688270330429077), ('navier stokes', 0.4055786430835724), ('stokes equations nse', 0.38261955976486206), ('methods navier', 0.36257076263427734), ('two dimensional navier', 0.3483145833015442)]"
860,860,35,860_spiking neurons_spiking activity_interacting neurons_spiking,"['spiking neurons', 'spiking activity', 'interacting neurons', 'spiking', 'propagation chaos', 'stochastic system', 'number neurons', 'neuron', 'neurons', 'neuronal']","['Conditional propagation of chaos for mean field systems of interacting\n  neurons   We study the stochastic system of interacting neurons introduced in De Masi\net al. (2015) and in Fournier and L\\""ocherbach (2016) in a diffusive scaling.\nThe system consists of $N$ neurons, each spiking randomly with rate depending\non its membrane potential. At its spiking time, the potential of the spiking\nneuron is reset to $0$ and all other neurons receive an additional amount of\npotential which is a centred random variable of order $ 1 / \\sqrt{N}.$ In\nbetween successive spikes, each neuron\'s potential follows a deterministic\nflow. We prove the convergence of the system, as $N \\to \\infty$, to a limit\nnonlinear jumping stochastic differential equation driven by Poisson random\nmeasure and an additional Brownian motion $W$ which is created by the central\nlimit theorem. This Brownian motion is underlying each particle\'s motion and\ninduces a common noise factor for all neurons in the limit system.\nConditionally on $W,$ the different neurons are independent in the limit\nsystem. This is the {\\it conditional propagation of chaos} property. We prove\nthe well-posedness of the limit equation by adapting the ideas of Graham (1992)\nto our frame. To prove the convergence in distribution of the finite system to\nthe limit system, we introduce a new martingale problem that is well suited for\nour framework. The uniqueness of the limit is deduced from the exchangeability\nof the underlying system.\n', 'Multiple Phase Transitions for an Infinite System of Spiking Neurons   We consider a stochastic model describing the spiking activity of a countable\nset of neurons spatially organized into a homogeneous tree of degree $d$, $d\n\\geq 2$; the degree of a neuron is just the number of connections it has.\nRoughly, the model is as follows. Each neuron is represented by its membrane\npotential, which takes non-negative integer values. Neurons spike at Poisson\nrate 1, provided they have strictly positive membrane potential. When a spike\noccurs, the potential of the spiking neuron changes to 0, and all neurons\nconnected to it receive a positive amount of potential. Moreover, between\nsuccessive spikes and without receiving any spiking inputs from other neurons,\neach neuron\'s potential behaves independently as a pure death process with\ndeath rate $\\gamma \\geq 0$. In this article, we show that if the number $d$ of\nconnections is large enough, then the process exhibits at least two phase\ntransitions depending on the choice of rate $\\gamma$: For large values of\n$\\gamma$, the neural spiking activity almost surely goes extinct; For small\nvalues of $\\gamma$, a fixed neuron spikes infinitely many times with a positive\nprobability, and for ""intermediate"" values of $\\gamma$, the system has a\npositive probability of always presenting spiking activity, but, individually,\neach neuron eventually stops spiking and remains at rest forever.\n', 'Metastability in a Stochastic System of Spiking Neurons with Leakage   We consider a finite system of interacting point processes with memory of\nvariable length modeling a finite but large network of spiking neurons with two\ndifferent leakage mechanisms. Associated to each neuron there are two point\nprocesses, describing its successive spiking and leakage times. For each\nneuron, the rate of the spiking point process is an exponential function of its\nmembrane potential, with the restriction that the rate takes the value 0 when\nthe membrane potential is 0. At each spiking time, the membrane potential of\nthe neuron resets to 0, and simultaneously, the membrane potentials of the\nother neurons increase by one unit. The leakage can be modeled in two different\nways. In the first way, at each occurrence time of the leakage point process\nassociated to a neuron, the membrane potential of that neuron is reset to 0,\nwith no effect on the other neurons. In the second way, if the membrane\npotential of the neuron is strictly positive, at each occurrence time of the\nleakage point process associated to that neuron, its membrane potential\ndecreases by one unit, with no effect on the other neurons. In both cases, the\nleakage point process of the neurons has constant rate. For both models, we\nprove that the system has a metastable behavior as the population size\ndiverges. This means that the time at which the system gets trapped by the list\nof null membrane potentials suitably re-scaled converges to a mean one\nexponential random time.\n']","[('spiking neurons', 0.6085858345031738), ('spiking activity', 0.4895102381706238), ('interacting neurons', 0.4890253245830536), ('spiking', 0.46771785616874695), ('propagation chaos', 0.4563632905483246), ('stochastic system', 0.4260545074939728), ('number neurons', 0.41531142592430115), ('neuron', 0.4144020080566406), ('neurons', 0.40971773862838745), ('neuronal', 0.4087769091129303)]"
861,861,35,861_uav aided_vehicle uav_uav_aerial vehicle uav,"['uav aided', 'vehicle uav', 'uav', 'aerial vehicle uav', 'aerial vehicles uavs', 'multi uav', 'vehicles uavs', 'deep reinforcement learning', 'unmanned aerial vehicles', 'unmanned aerial vehicle']","[""Trajectory Design for UAV-Based Internet-of-Things Data Collection: A\n  Deep Reinforcement Learning Approach   In this paper, we investigate an unmanned aerial vehicle (UAV)-assisted\nInternet-of-Things (IoT) system in a sophisticated three-dimensional (3D)\nenvironment, where the UAV's trajectory is optimized to efficiently collect\ndata from multiple IoT ground nodes. Unlike existing approaches focusing only\non a simplified two-dimensional scenario and the availability of perfect\nchannel state information (CSI), this paper considers a practical 3D urban\nenvironment with imperfect CSI, where the UAV's trajectory is designed to\nminimize data collection completion time subject to practical throughput and\nflight movement constraints. Specifically, inspired from the state-of-the-art\ndeep reinforcement learning approaches, we leverage the twin-delayed deep\ndeterministic policy gradient (TD3) to design the UAV's trajectory and present\na TD3-based trajectory design for completion time minimization (TD3-TDCTM)\nalgorithm. In particular, we set an additional information, i.e., the merged\npheromone, to represent the state information of UAV and environment as a\nreference of reward which facilitates the algorithm design. By taking the\nservice statuses of IoT nodes, the UAV's position, and the merged pheromone as\ninput, the proposed algorithm can continuously and adaptively learn how to\nadjust the UAV's movement strategy. By interacting with the external\nenvironment in the corresponding Markov decision process, the proposed\nalgorithm can achieve a near-optimal navigation strategy. Our simulation\nresults show the superiority of the proposed TD3-TDCTM algorithm over three\nconventional non-learning based baseline methods.\n"", 'Deep Reinforcement Learning for Fresh Data Collection in UAV-assisted\n  IoT Networks   Due to the flexibility and low operational cost, dispatching unmanned aerial\nvehicles (UAVs) to collect information from distributed sensors is expected to\nbe a promising solution in Internet of Things (IoT), especially for\ntime-critical applications. How to maintain the information freshness is a\nchallenging issue. In this paper, we investigate the fresh data collection\nproblem in UAV-assisted IoT networks. Particularly, the UAV flies towards the\nsensors to collect status update packets within a given duration while\nmaintaining a non-negative residual energy. We formulate a Markov Decision\nProcess (MDP) to find the optimal flight trajectory of the UAV and transmission\nscheduling of the sensors that minimizes the weighted sum of the age of\ninformation (AoI). A UAV-assisted data collection algorithm based on deep\nreinforcement learning (DRL) is further proposed to overcome the curse of\ndimensionality. Extensive simulation results demonstrate that the proposed\nDRL-based algorithm can significantly reduce the weighted sum of the AoI\ncompared to other baseline algorithms.\n', 'Decentralized Computation Offloading With Cooperative UAVs: Multi-Agent\n  Deep Reinforcement Learning Perspective   Limited computing resources of internet-of-things (IoT) nodes incur\nprohibitive latency in processing input data. This triggers new research\nopportunities toward task offloading systems where edge servers handle\nintensive computations of IoT devices. Deploying the computing servers at\nexisting base stations may not be sufficient to support IoT nodes operating in\na harsh environment. This requests mobile edge servers to be mounted on\nunmanned aerial vehicles (UAVs) that provide on-demand mobile edge computing\n(MEC) services. Time-varying offloading demands and mobility of UAVs need a\njoint design of the optimization variables for all time instances. Therefore,\nan online decision mechanism is essential for UAV-aided MEC networks. This\narticle presents an overview of recent deep reinforcement learning (DRL)\napproaches where decisions about UAVs and IoT nodes are taken in an online\nmanner. Specifically, joint optimization over task offloading, resource\nallocation, and UAV mobility is addressed from the DRL perspective. For the\ndecentralized implementation, a multi-agent DRL method is proposed where\nmultiple intelligent UAVs cooperatively determine their computations and\ncommunication policies without central coordination. Numerical results\ndemonstrate that the proposed decentralized learning strategy is superior to\nexisting DRL solutions. The proposed framework sheds light on the viability of\nthe decentralized DRL techniques in designing self-organizing IoT networks.\n']","[('uav aided', 0.5027276873588562), ('vehicle uav', 0.4943230152130127), ('uav', 0.49364832043647766), ('aerial vehicle uav', 0.4904625117778778), ('aerial vehicles uavs', 0.48410195112228394), ('multi uav', 0.4624636769294739), ('vehicles uavs', 0.4612608253955841), ('deep reinforcement learning', 0.4610154926776886), ('unmanned aerial vehicles', 0.451546847820282), ('unmanned aerial vehicle', 0.4466117322444916)]"
862,862,35,862_integer factorization_factorization algorithms_new factorization_factorization,"['integer factorization', 'factorization algorithms', 'new factorization', 'factorization', 'distinct prime factors', 'prime factors', 'factorization based', 'factorisation', 'factorization article', 'integer prime']","['Smooth Subsum Search: A heuristic for practical integer factorization   The two currently fastest general-purpose integer factorization algorithms\nare the Quadratic Sieve and the Number Field Sieve. Both techniques are used to\nfind so-called smooth values of certain polynomials, i.e., values that factor\ncompletely over a set of small primes (the factor base). As the names of the\nmethods suggest, a sieving procedure is used for the task of quickly\nidentifying smooth values among the candidates in a certain range. While the\nNumber Field Sieve is asymptotically faster, the Quadratic Sieve is still\nconsidered the most efficient factorization technique for numbers up to around\n100 digits. In this paper, we challenge the Quadratic Sieve by presenting a\nnovel approach based on representing smoothness candidates as sums that are\nalways divisible by several of the primes in the factor base. The resulting\nvalues are generally smaller than those considered in the Quadratic Sieve,\nincreasing the likelihood of them being smooth. Using the fastest\nimplementations of the Self-initializing Quadratic Sieve in Python as\nbenchmarks, a Python implementation of our approach runs consistently 5 to 7\ntimes faster for numbers with 45-100 digits, and around 10 times faster for\nnumbers with 30-40 digits. We discuss several avenues for further improvements\nand applications of the technique.\n', 'Expressing three consecutive integers as sums of three cubes   This paper is concerned with the problem of expressing three consecutive\nintegers as sums of three cubes. We give several parametric solutions of the\nproblem. We also give somewhat trivial solutions of five or seven consecutive\nintegers that can expressed as sums of three cubes. We conclude the paper with\nan open problem regarding four or more consecutive integers expressible as sums\nof three cubes.\n', ""The new Fermat-type factorization algorithm   Let n be any odd natural number other than a perfect square, in this article\nit is demonstrated that this new factorization algorithm is much more efficient\nthan the implementation technique [2,3 p.1470], described in this article, of\nthe Fermat's factorization algorithm [1 p.6,3 p.1470], implementation technique\nwhich I call the Fermat's factorization method (like the title, translated into\nEnglish, of the reference document [2] published in Italian) and which is,\namong the implementation techniques [1 pp.6-8,2,3 pp.1470-1471] of the Fermat's\nfactorization algorithm, the one with which a smaller iterations number occurs\nto identify the factors, trivial or non-trivial, of n (except for the\ncircumstance in which two factors, trivial or non-trivial, of n are so close to\neach other that they are identified at the 1st iteration with each of the\nimplementation techniques of the Fermat's factorization algorithm). In fact,\nthrough the way in which the Euler's function [4] is applied to the Fermat's\nfactorization method, we arrive at this new factorization algorithm with which\nwe obtain the certain reduction in the iterations number (except for the cases\nin which two factors of n are so close to each other that they are identified\nat the 1st iteration with the Fermat's factorization method) compared to the\niterations number that occurs with the Fermat's factorization method.\nFurthermore, in this article I represent the hypotheses field according to\nwhich it will eventually be possible to further reduce the iterations number.\nFinally and always in relation to this new factorization algorithm, in this\narticle I represent in detail the limit iterations number, which is smaller\nthan the iterations number that occurs to reach the condition x - y = 1 which\ncharacterizes the pair of trivial factors of n, beyond which it is no longer\npossible for pairs of non-trivial factors of n to occur.\n""]","[('integer factorization', 0.7351935505867004), ('factorization algorithms', 0.5979810357093811), ('new factorization', 0.5765489935874939), ('factorization', 0.5386195182800293), ('distinct prime factors', 0.5340776443481445), ('prime factors', 0.532925009727478), ('factorization based', 0.5236647725105286), ('factorisation', 0.504045844078064), ('factorization article', 0.4973035156726837), ('integer prime', 0.4861256778240204)]"
863,863,35,863_random tensors_random tensor_generalized tensor_tensors,"['random tensors', 'random tensor', 'generalized tensor', 'tensors', 'tensors product', 'tensor valued', 'product tensor', 'tensors work', 'new tensor', 'tensor']","['Generalized Hanson-Wright Inequality for Random Tensors   The Hanson-Wright inequality is an upper bound for tails of real quadratic\nforms in independent random variables. In this work, we extend the\nHanson-Wright inequality for the Ky Fan k-norm for the polynomial function of\nthe quadratic sum of random tensors under Einstein product. We decompose the\nquadratic tensors sum into the diagonal part and the coupling part. For the\ndiagonal part, we can apply the generalized tensor Chernoff bound directly.\nBut, for the coupling part, we have to apply decoupling method first, i.e.,\ndecoupling inequality to bound expressions with dependent random tensors with\nindependent random tensors, before applying generalized tensor Chernoff bound\nagain to get the the tail probability of the Ky Fan $k$-norm of the coupling\npart sum of independent random tensors. At the end, the generalized\nHanson-Wright inequality for the Ky Fan k-norm for the polynomial function of\nthe quadratic sum of random tensors can be obtained by the combination of the\nbound from the diagonal sum part and the bound from the coupling sum part.\n', ""General Tail Bounds for Random Tensors Summation: Majorization Approach   In recent years, tensors have been applied to different applications in\nscience and engineering fields. In order to establish theory about tail bounds\nof the tensors summation behavior, this work extends previous work by\nconsidering the tensors summation tail behavior of the top $k$-largest singular\nvalues of a function of the tensors summation, instead of the largest/smallest\nsingular value of the tensors summation directly (identity function) explored\nin Shih Yu's work: Convenient tail bounds for sums of random tensors.\nMajorization and antisymmetric tensor product tools are main techniques\nutilized to establish inequalities for unitarily norms of multivariate tensors.\nThe Laplace transform method is integrated with these inequalities for\nunitarily norms of multivariate tensors to give us tail bounds estimation for\nKy Fan $k$-norm for a function of the tensors summation. By restricting\ndifferent random tensor conditions, we obtain generalized tensor Chernoff and\nBernstein inequalities.\n"", 'Random Tensor Inequalities and Tail bounds for Bivariate Random Tensor\n  Means, Part II   This is Part II of our work about random tensor inequalities and tail bounds\nfor bivariate random tensor means. After reviewing basic facts about random\ntensors, we first consider tail bounds with more general connection functions.\nThen, a general Lie-Trotter formula for tensors is derived and this formula is\napplied to establish tail bounds for bivariate random tensor means involving\ntensor logarithm. All random tensors studied in our Part I work are assumed as\npositive definite (PD) random tensors, which are invertible tensors. In this\nPart II work, we generalize our tail bounds for bivariate random tensor means\nfrom positive definite (PD) random tensors to positive semidefinite (PSD)\nrandom tensors by defining Random Tensor Topology (RTT) and developing the\nlimitation method based on RTT. Finally, we apply our theory to establish tail\nbounds and L\\""owner ordering relationships for bivariate random tensor means\nbefore and after two tensor data processing methods: data fusion and linear\ntransform. %\n']","[('random tensors', 0.6872465014457703), ('random tensor', 0.6489404439926147), ('generalized tensor', 0.5325205326080322), ('tensors', 0.5033995509147644), ('tensors product', 0.5022736191749573), ('tensor valued', 0.4966261386871338), ('product tensor', 0.49100109934806824), ('tensors work', 0.48098960518836975), ('new tensor', 0.47273561358451843), ('tensor', 0.46595001220703125)]"
864,864,35,864_calabi yau manifolds_yau manifolds_calabi yau metrics_calabi yau metric,"['calabi yau manifolds', 'yau manifolds', 'calabi yau metrics', 'calabi yau metric', 'calabi yau hypersurfaces', 'ricci flat metrics', 'yau metrics', 'yau hypersurfaces', 'ricci flat metric', 'ricci flat']","['Calabi-Yau Metrics, Energy Functionals and Machine-Learning   We apply machine learning to the problem of finding numerical Calabi-Yau\nmetrics. We extend previous work on learning approximate Ricci-flat metrics\ncalculated using Donaldson\'s algorithm to the much more accurate ""optimal""\nmetrics of Headrick and Nassar. We show that machine learning is able to\npredict the K\\""ahler potential of a Calabi-Yau metric having seen only a small\nsample of training data.\n', 'Lectures on the Calabi-Yau Landscape   In these lecture notes, we survey the landscape of Calabi-Yau threefolds, and\nthe use of machine learning to explore it. We begin with the compact portion of\nthe landscape, focusing in particular on complete intersection Calabi-Yau\nvarieties (CICYs) and elliptic fibrations. Non-compact Calabi-Yau manifolds are\nmanifest in Type II superstring theories, they arise as representation\nvarieties of quivers, used to describe gauge theories in the bulk familiar four\ndimensions. Finally, given the huge amount of Calabi-Yau data, whether and how\nmachine learning can be applied to algebraic geometry and string landscape is\nalso discussed. These notes are directed to the beginning graduate student\ninterested in mathematics and in physics, and are based on lectures given by\nthe 2nd author at the 2019 PIMS Summer School on Algebraic Geometry in\nHigh-Energy Physics at the University of Saskatchewan.\n', 'Machine Learning Calabi-Yau Four-folds   Hodge numbers of Calabi-Yau manifolds depend non-trivially on the underlying\nmanifold data and they present an interesting challenge for machine learning.\nIn this letter we consider the data set of complete intersection Calabi-Yau\nfour-folds, a set of about 900,000 topological types, and study supervised\nlearning of the Hodge numbers h^1,1 and h^3,1 for these manifolds. We find that\nh^1,1 can be successfully learned (to 96% precision) by fully connected\nclassifier and regressor networks. While both types of networks fail for h^3,1,\nwe show that a more complicated two-branch network, combined with feature\nenhancement, can act as an efficient regressor (to 98% precision) for h^3,1, at\nleast for a subset of the data. This hints at the existence of an, as yet\nunknown, formula for Hodge numbers.\n']","[('calabi yau manifolds', 0.6880799531936646), ('yau manifolds', 0.6245985627174377), ('calabi yau metrics', 0.6150442957878113), ('calabi yau metric', 0.5764901638031006), ('calabi yau hypersurfaces', 0.5721253752708435), ('ricci flat metrics', 0.5421112179756165), ('yau metrics', 0.5380423069000244), ('yau hypersurfaces', 0.5330696702003479), ('ricci flat metric', 0.5096831917762756), ('ricci flat', 0.49664175510406494)]"
865,865,35,865_invariants braids_generalized braid_links invariants_braid groups,"['invariants braids', 'generalized braid', 'links invariants', 'braid groups', 'knot theory', 'braid arrangement', 'braid monoid', 'braids', 'braid group', 'knot groups']","['Tied pseudo links \\& Pseudo knotoids   In this paper we study the theory of {\\it pseudo knots}, which are knots with\nsome missing crossing information, and we introduce and study the theory of\n{\\it pseudo tied links} and the theory of {\\it pseudo knotoids}. In particular,\nwe first present a braiding algorithm for pseudo knots and we then introduce\nthe $L$-moves in that setting, with the use of which we formulate a sharpened\nversion of the analogue of the Markov theorem for pseudo braids. Then we\nintroduce and study the theory of {\\it tied pseudo links}, that generalize the\nnotion of tied links, and we exploit the relation between tied pseudo links and\ntied singular links. We first present an $L$-move braid equivalence for tied\nsingular braids. Then, we introduce the tied pseudo braid monoid and we\nformulate and prove analogues of the Alexander and Markov theorems for tied\npseudo links. Finally, we introduce and study the theory of {\\it pseudo\nknotoids}, that generalize the notion of knotoids. We present an isotopy\ntheorem for pseudo knotoids and we then pass to the level of braidoids. We\nfurther introduce and study the {\\it pseudo braidoids} by introducing the {\\it\npseudo} $L${\\it -moves} and by presenting the analogues of the Alexander and\nMarkov theorems for pseudo knotoids. We also discuss further research related\nto {\\it tied (multi)-knotoids and tied pseudo (multi)-knotoids}. The theory of\npseudo knots may serve as a strong tool in the study of DNA, while tied links\nhave potential use in other aspects of molecular biology.\n', 'Virtual singular braids and links   Virtual singular braids are generalizations of singular braids and virtual\nbraids. We define the virtual singular braid monoid via generators and\nrelations, and prove Alexander- and Markov-type theorems for virtual singular\nlinks. We also show that the virtual singular braid monoid has another\npresentation with fewer generators.\n', 'Pseudo links and singular links in the Solid Torus   In this paper we introduce and study the theories of pseudo links and\nsingular links in the Solid Torus, ST. Pseudo links are links with some missing\ncrossing information that naturally generalize the notion of knot diagrams, and\nthat have potential use in molecular biology, while singular links are links\nthat contain a finite number of self-intersections. We consider pseudo links\nand singular links in ST and we set up the appropriate topological theory in\norder to construct invariants for these types of links in ST. In particular, we\nformulate and prove the analogue of the Alexander theorem for pseudo links and\nfor singular links in ST. We then introduce the mixed pseudo braid monoid and\nthe mixed singular braid monoid, with the use of which, we formulate and prove\nthe analogue of the Markov theorem for pseudo links and for singular links in\nST. \\smallbreak Moreover, we introduce the pseudo Hecke algebra of type A,\n$P\\mathcal{H}_n$, the cyclotomic and generalized pseudo Hecke algebras of type\nB, $P\\mathcal{H}_{1, n}$, and discuss how the pseudo braid monoid (cor. the\nmixed pseudo braid monoid) can be represented by $P\\mathcal{H}_{n}$ (cor. by\n$P\\mathcal{H}_{1, n}$). This is the first step toward the construction of\nHOMFLYPT-type invariants for pseudo links in $S^3$ and in ST. We also introduce\nthe cyclotomic and generalized singular Hecke algebras of type B,\n$S\\mathcal{H}_{1, n}$, and we present two sets that we conjecture that they\nform linear bases for $S\\mathcal{H}_{1, n}$. Finally, we generalize the bracket\npolynomial for pseudo links in ST.\n']","[('invariants braids', 0.7368170619010925), ('generalized braid', 0.7104904055595398), ('links invariants', 0.6445035934448242), ('braid groups', 0.6372673511505127), ('knot theory', 0.6082072257995605), ('braid arrangement', 0.6025581359863281), ('braid monoid', 0.5963690876960754), ('braids', 0.5899666547775269), ('braid group', 0.583503782749176), ('knot groups', 0.5787588357925415)]"
866,866,35,866_seiberg witten equations_witten equations_moduli space solutions_seiberg witten,"['seiberg witten equations', 'witten equations', 'moduli space solutions', 'seiberg witten', 'manifold spin', 'compact ahler surface', 'ahler manifold', 'gauge theoretic', 'four manifolds', 'hyperk ahler manifold']","[""On the compactness problem for a family of generalized Seiberg-Witten\n  equations in dimension three   We prove an abstract compactness theorem for a family of generalized\nSeiberg-Witten equations in dimension three. This result recovers Taubes'\ncompactness theorem for stable flat\n$\\mathbf{P}\\mathrm{SL}_2(\\mathbf{C})$-connections as well as the compactness\ntheorem for Seiberg-Witten equations with multiple spinors. Furthermore, this\nresult implies a compactness theorem for the ADHM$_{1,2}$ Seiberg-Witten\nequation, which partially verifies a conjecture by Doan and Walpuski.\n"", 'The three-dimensional Seiberg-Witten equations for 3/2-spinors: a\n  compactness theorem   The Rarita-Schwinger-Seiberg-Witten (RS-SW) equations are defined similarly\nto the classical Seiberg-Witten equations, where a geometric non-Dirac-type\noperator replaces the Dirac operator called the Rarita-Schwinger operator. In\ndimension four, the RS-SW equation was first considered by the second-named\nauthor. The variational approach will also give us a three-dimensional version\nof the equations. The RS-SW equations share some features with the\nmultiple-spinor Seiberg-Witten equations, where the moduli space of solutions\ncould be non-compact. In this note, we prove a compactness theorem regarding\nthe moduli space of solutions of the RS-SW equations defined on 3-manifolds.\n', 'An abelian gauge-theoretic variant of the Seiberg-Witten equations for\n  multiple-spinors   We consider a variant of the Seiberg-Witten equations for multiple-spinors.\nThe moduli space of solutions to our generalized Seiberg-Witten equations in\nthe setting of K\\""ahler surfaces has a direct relation with ASD connections of\nholomorphic vector bundle. Also in K\\""ahler setting, we construct a numerical\ninvariant from the equations that detects a notion of $\\phi-$stability of\n$SU(n)-$holomorphic vector bundles where $\\phi$ is some prescribed non-trivial\nholomorphic section.\n']","[('seiberg witten equations', 0.7038481831550598), ('witten equations', 0.6313875317573547), ('moduli space solutions', 0.5021122694015503), ('seiberg witten', 0.46033430099487305), ('manifold spin', 0.4462065100669861), ('compact ahler surface', 0.4419660270214081), ('ahler manifold', 0.43744564056396484), ('gauge theoretic', 0.437347412109375), ('four manifolds', 0.4354695975780487), ('hyperk ahler manifold', 0.42768052220344543)]"
867,867,35,867_linear recurrence sequences_linear recurrences_sequence adic_order linear recurrence,"['linear recurrence sequences', 'linear recurrences', 'sequence adic', 'order linear recurrence', 'linear recurrence sequence', 'sequence zero', 'linear recurrence', 'validity conjecture', 'recurrence sequences', 'three conjectures']","['Completing the picture for the Skolem Problem on order-4 linear\n  recurrence sequences   For almost a century, the decidability of the Skolem Problem - that is, the\nproblem of finding whether a given linear recurrence sequence (LRS) has a zero\nterm - has remained open. A breakthrough in the 1980s established that the\nSkolem Problem is indeed decidable for algebraic LRS of order at most 3, and\nreal algebraic LRS of order at most 4. However, for general algebraic LRS of\norder 4 the question of decidability has remained open. Our main contribution\nin this paper is to prove decidability for this last case, i.e. we show that\nthe Skolem Problem is decidable for all algebraic LRS of order at most 4.\n', 'Skolem Problem for Linear Recurrence Sequences with 4 Dominant Roots\n  (after Mignotte, Shorey, Tijdeman, Vereshchagin and Bacik)   It is an exposition of the work of Mignotte, Shorey, Tijdeman, Vereshchagin\nand Bacik on decidability of the vanishing problem for linear recurrence\nsequences of order 4.\n', 'Skolem Meets Schanuel   The celebrated Skolem-Mahler-Lech Theorem states that the set of zeros of a\nlinear recurrence sequence is the union of a finite set and finitely many\narithmetic progressions. The corresponding computational question, the Skolem\nProblem, asks to determine whether a given linear recurrence sequence has a\nzero term. Although the Skolem-Mahler-Lech Theorem is almost 90 years old,\ndecidability of the Skolem Problem remains open. The main contribution of this\npaper is an algorithm to solve the Skolem Problem for simple linear recurrence\nsequences (those with simple characteristic roots). Whenever the algorithm\nterminates, it produces a stand-alone certificate that its output is correct --\na set of zeros together with a collection of witnesses that no further zeros\nexist. We give a proof that the algorithm always terminates assuming two\nclassical number-theoretic conjectures: the Skolem Conjecture (also known as\nthe Exponential Local-Global Principle) and the $p$-adic Schanuel Conjecture.\nPreliminary experiments with an implementation of this algorithm within the\ntool \\textsc{Skolem} point to the practical applicability of this method.\n']","[('linear recurrence sequences', 0.4570295512676239), ('linear recurrences', 0.41578614711761475), ('sequence adic', 0.414514422416687), ('order linear recurrence', 0.41332152485847473), ('linear recurrence sequence', 0.4054645001888275), ('sequence zero', 0.40543726086616516), ('linear recurrence', 0.3874317407608032), ('validity conjecture', 0.38049671053886414), ('recurrence sequences', 0.38010185956954956), ('three conjectures', 0.37299230694770813)]"
868,868,35,868_metrizable space_indecomposable continuum_compact metrizable space_compact metrizable spaces,"['metrizable space', 'indecomposable continuum', 'compact metrizable space', 'compact metrizable spaces', 'compact metrizable', 'continuum theory', 'continuum non', 'topological point', 'continuum', 'every hausdorff']","['Shore and Non-Block Points in Hausdorff Continua   We study the shore and non-block points of non-metric continua. We reduce the\nproblem of showing a continuum to have non-block points to that of showing an\nindecomposable continuum to have non-block points. As a corollary we prove that\nseparable continua have at least two non-block points -- and moreover are\nirreducible about their set of non-block points.\n', 'Some decomposable continua and Whitney levels of their hyperspaces   We introduce the new class of continua; $D^{**}$-$continua$. The classes of\nWilder continua and $D^{*}$-continua are strictly contained in the class of\n$D^{**}$-continua. Also, the class of $D$-continua is bigger than the class of\n$D^{**}$-continua. Using $D^{**}$-continua, we give the negative answer to a\nQuestion. Furthermore, we prove that being Wilder, being $D$, being $D^*$ and\nbeing $D^{**}$ are Whitney properties.\n', 'Some theorems on decomposable continua   We prove some theorems on decomposable continua. In particular, we prove; (i)\nthe property of being a Wilder continuum is not a Whitney reversible property,\n(ii) inverse limits of D**-continua with surjective monotone upper\nsemi-continuous bonding functions are D**, and (iii) there exists a\nD**-continuum which contains neither Wilder continua nor D*-continua. Also, we\nshow the existence of a Wilder continuum containing no D*-continua and a\nD*-continuum containing no Wilder continua.\n']","[('metrizable space', 0.5505200028419495), ('indecomposable continuum', 0.5503559112548828), ('compact metrizable space', 0.5389552712440491), ('compact metrizable spaces', 0.5345486402511597), ('compact metrizable', 0.5094238519668579), ('continuum theory', 0.4993707239627838), ('continuum non', 0.46571359038352966), ('topological point', 0.46039873361587524), ('continuum', 0.44043096899986267), ('every hausdorff', 0.4234609603881836)]"
869,869,35,869_riordan arrays_arrays_arrays also_arrays whose,"['riordan arrays', 'arrays', 'arrays also', 'arrays whose', 'riordan', 'array', 'arrays two', 'arrays multiple', 'lower triangular matrices', 'triangular matrices']","['Total Positivity of Quasi-Riordan Arrays   In this paper the total positivity of quasi-Riordan arrays is investigated\nwith use of the sequence characterization of quasi-Riordan arrays. Due to the\ncorrelation between quasi-Riordan arrays and Riordan arrays, this study is an\nin-depth discussion of the total positivity of Riordan arrays.\n', 'The Double Almost-Riordan Arrays and Their Sequence Characterization,\n  Compression, and Total Positivity   In this paper, we define double almost-Riordan arrays and find that the set\nof all double almost-Riordan arrays forms a group, called the double\nalmost-Riordan group. We also obtain the sequence characteristics of double\nalmost-Riordan arrays and give the production matrices for double\nalmost-Riordan arrays. We define the compression of double almost-Riordan\narrays and present their sequence characterization. Finally we give a\ncharacteristic for the total positivity of double Riordan arrays, by using\nwhich we discuss the total positivity for compressed double almost-Riordan\narrays.\n', ""On Sums, Derivatives, and Flips of Riordan Arrays   We study three operations on Riordan arrays. First, we investigate when the\nsum of Riordan arrays yields another Riordan array. We characterize the $A$-\nand $Z$-sequences of these sums of Riordan arrays, and also identify an analog\nfor $A$-sequences when the sum of Riordan arrays does not yield a Riordan\narray. In addition, we define the new operations `Der' and `Flip' on Riordan\narrays. We fully characterize the Riordan arrays resulting from these\noperations applied to the Appell and Lagrange subgroups of the Riordan group.\nFinally, we study the application of these operations to various known Riordan\narrays, generating many combinatorial identities in the process.\n""]","[('riordan arrays', 0.7912703156471252), ('arrays', 0.5395261645317078), ('arrays also', 0.531640350818634), ('arrays whose', 0.527302622795105), ('riordan', 0.46243157982826233), ('array', 0.4478292465209961), ('arrays two', 0.4455207586288452), ('arrays multiple', 0.42230311036109924), ('lower triangular matrices', 0.3781648874282837), ('triangular matrices', 0.34216850996017456)]"
870,870,35,870_bias optimal_optimal stopping_random order_optimal strategy,"['bias optimal', 'optimal stopping', 'random order', 'optimal strategy', 'optimal probability', 'optimal', 'uniformly random order', 'asymptotically optimal', 'optimal threshold', 'maximize probability']","['The secretary problem with non-uniform arrivals via a\n  left-to-right-minimum exponentially tilted distribution   We solve the secretary problem in the case that the ranked items arrive in a\nstatistically biased order rather than in uniformly random order. The bias is\ngiven by the left-to-right-minimum exponentially tilted distribution with\nparameter $q\\in(0,\\infty)$. That is, for $\\sigma\\in S_n$, $P_n(\\sigma)$ is\nproportional to $q^{\\text{LR}^{-}_n(\\sigma)}$, where the left-to-right minimum\nstatistic $\\text{LR}^-_n$ is defined by $$ \\text{LR}^{-}_n(\\sigma)=|\\{j\\in[n]:\n\\sigma_j=\\min\\{\\sigma_i:1\\le i\\le j\\}\\}|,\\ \\sigma\\in S_n. $$ For $q\\in(0,1)$,\nhigher ranked items tend to arrive earlier than in the case of the uniform\ndistribution, and for $q\\in(1,\\infty)$, they tend to arrive later. In the\nclassical problem, the asymptotically optimal strategy is to reject the first\n$M_n^*$ items, where $M_n^*\\sim\\frac ne$, and then to select the first item\nranked higher than any of the first $M_n^*$ items (if such an item exists).\nThis yields $e^{-1}$ as the limiting probability of success. With the above\nbias on arrivals, we calculate the asymptotic behavior of the optimal strategy\n$M_n^*$ and the corresponding limiting probability of success, for all regimes\nof $\\{q_n\\}_{n=1}^\\infty$. In particular, if the leading order asymptotic\nbehavior of $\\{q_n\\}_{n=1}^\\infty$ is at least $\\frac1{\\log n}$, and if also\nits order is no more than $o(n)$, then the limiting probability of success when\nusing an asymptotically optimal strategy is $e^{-1}$; otherwise, this limiting\nprobability of success is greater than $e^{-1}$. Also, the limiting fraction of\nnumbers, $\\lim_{n\\to\\infty}\\frac{M^*_n}n$, that are summarily rejected by an\nasymptotically optimal strategy lies in $(0,1)$ if and only if\n$\\lim_{n\\to\\infty}q_n\\in(0,\\infty)$.\n', 'The secretary problem with biased arrival order via a Mallows\n  distribution   We solve the secretary problem in the case that the ranked items arrive in a\nstatistically biased order rather than in uniformly random order. The bias is\ngiven by a Mallows distribution with parameter $q\\in(0,1)$, so that higher\nranked items tend to arrive later and lower ranked items tend to arrive sooner.\nIn the classical problem, the asymptotically optimal strategy is to reject the\nfirst $M_n^*$ items, where $M_n^*\\sim\\frac ne$, and then to select the first\nitem ranked higher than any of the first $M_n^*$ items (if such an item\nexists). This yields $\\frac1e$ as the limiting probability of success. The\nMallows distribution with parameter $q=1$ is the uniform distribution. For the\nregime $q_n=1-\\frac cn$, with $c>0$, the case of weak bias, the optimal\nstrategy occurs with $M_n^*\\sim\nn\\Big(\\frac1c\\log\\big(1+\\frac{e^c-1}e\\big)\\Big)$, with the limiting probability\nof success being $\\frac1e$. For the regime $q_n=1-\\frac c{n^\\alpha}$, with\n$c>0$ and $\\alpha\\in(0,1)$, the case of moderate bias, the optimal strategy\noccurs with $n-M_n\\sim\\frac{n^\\alpha}c$, with the limiting probability of\nsuccess being $\\frac1e$. For fixed $q\\in(0,1)$, the case of strong bias, the\noptimal strategy occurs with $M_n^*=n-L$ where $\\frac{L-1}L<q\\le \\frac L{L+1}$,\nwith limiting probability of success being $(1-q)q^{L-1}L>\\frac1e$.\n', ""The secretary problem with items arriving according to a random\n  permutation avoiding a pattern of length three   In the classical secretary problem, $n$ ranked items arrive one by one, and\neach item's rank relative to its predecessors is noted. The observer must\nselect or reject each item as it arrives, with the object of selecting the item\nof highest rank. For $M_n\\in\\{0,1,\\cdots, n-1\\}$, let $\\mathcal{S}(n,M_n)$\ndenote the strategy whereby the observer rejects the first $M_n$ items, and\nthen selects the first later-arriving item whose rank is higher than that of\nany of the first $M_n$ items (if such an item exists). If the ranked items\narrive in a uniformly random order, it is well-known that the limiting optimal\nprobability of success is $\\frac1e$, which occurs if $M_n\\sim\\frac ne$. It has\nbeen shown that when the ranked items arrive according to certain non-uniform\ndistributions on the set of permutations, $\\frac1e$ serves as a lower bound for\nthe optimal probability. There is a fundamental reason for this phenomenon. We\nconsider certain distributions for which that reason does not apply. We begin\nby noting a cooked-up class of distributions for which $\\mathcal{S}(n,M)$\nyields the lowest possible probability of success -- namely $\\frac1n$, for all\n$M$. We then consider the uniform distribution over all permutations avoiding a\nparticular pattern of length three. In the case of the pattern 231 or 132, for\nany choice of $M_n$, the strategy $\\mathcal{S}(n,M_n)$ yields the very same\nprobability of success; namely $\\frac{n+1}{2(2n-1)}$, which gives a limiting\nprobability of $\\frac14$. For the pattern 213, the optimal strategy is obtained\nfor $M\\in\\{0,1\\}$, also yielding a limiting probability of $\\frac14$. For the\npattern 123, the optimal strategy is obtained for $M=1$, yielding a limiting\nprobability of $\\frac34$. For the other two patterns, 312 and 321, an optimal\nstrategy will yield a limiting probability of at least $\\frac7{16}$.\n""]","[('bias optimal', 0.5013510584831238), ('optimal stopping', 0.498129278421402), ('random order', 0.49514874815940857), ('optimal strategy', 0.44308966398239136), ('optimal probability', 0.42870017886161804), ('optimal', 0.4267770051956177), ('uniformly random order', 0.4267115890979767), ('asymptotically optimal', 0.4254903495311737), ('optimal threshold', 0.40335720777511597), ('maximize probability', 0.3649649918079376)]"
871,871,35,871_quantum games_strategies quantum_quantum correlations_finite dimensional quantum,"['quantum games', 'strategies quantum', 'quantum correlations', 'finite dimensional quantum', 'quantum information theory', 'quantum', 'classical quantum', 'dimensional quantum', 'quantum versions', 'quantum models']","['Tracial embeddable strategies: Lifting MIP* tricks to MIPco   We prove that any two-party correlation in the commuting operator model can\nbe approximated using a tracial embeddable strategy, a class of strategy\ndefined on a finite tracial von Neumann algebra, which we define in this paper.\nUsing this characterization, we show that any approximately synchronous\ncorrelation can be approximated to the average of a collection of synchronous\ncorrelations in the commuting operator model. This generalizes the result from\nVidick [JMP 2022] which only applies to finite-dimensional quantum\ncorrelations. As a corollary, we show that the quantum tensor code test from Ji\net al. [FOCS 2022] follows the soundness property even under the general\ncommuting operator model.\n  Furthermore, we extend the state-dependent norm variant of the Gowers-Hatami\ntheorem to finite von Neumann algebras. Combined with the aforementioned\ncharacterization, this enables us to lift many known results about robust\nself-testing for non-local games to the commuting operator model, including a\nsample efficient finite-dimensional EPR testing for the commuting operator\nstrategies. We believe that, in addition to the contribution from this paper,\nthis class of strategies can be helpful for further understanding non-local\ngames in the infinite-dimensional setting.\n', 'Quantum no-signalling correlations and non-local games   We introduce and examine three subclasses of the family of quantum\nno-signalling (QNS) correlations introduced by Duan and Winter: quantum\ncommuting, quantum and local. We formalise the notion of a universal TRO of a\nblock operator isometry, define an operator system, universal for stochastic\noperator matrices, and realise it as a quotient of a matrix algebra. We\ndescribe the classes of QNS correlations in terms of states on the tensor\nproducts of two copies of the universal operator system, and specialise the\ncorrelation classes and their representations to classical-to-quantum\ncorrelations. We study various quantum versions of synchronous no-signalling\ncorrelations and show that they possess invariance properties for suitable sets\nof states. We introduce quantum non-local games as a generalisation of\nnon-local games. We define the operation of quantum game composition and show\nthat the perfect strategies belonging to a certain class are closed under\nchannel composition. We specialise to the case of graph colourings, where we\nexhibit quantum versions of the orthogonal rank of a graph as the optimal\noutput dimension for which perfect classical-to-quantum strategies of the graph\ncolouring game exist, as well as to non-commutative graph homomorphisms, where\nwe identify quantum versions of non-commutative graph homomorphisms introduced\nby Stahlke.\n', 'Synchronicity for quantum non-local games   We introduce concurrent quantum non-local games, quantum output mirror games\nand concurrent classical-to-quantum non-local games, as quantum versions of\nsynchronous non-local games, and provide tracial characterisations of their\nperfect strategies belonging to various correlation classes. We define\n*-algebras and C*-algebras of concurrent classical-to-quantum and concurrent\nquantum non-local games, and algebraic versions of the orthogonal rank of a\ngraph. We show that quantum homomorphisms of quantum graphs can be viewed as\nentanglement assisted classical homomorphisms of the graphs, and give\ndescriptions of the perfect quantum commuting and the perfect approximately\nquantum strategies for the quantum graph homomorphism game. We specialise the\nlatter results to the case where the inputs of the game are based on a\nclassical graph.\n']","[('quantum games', 0.6341736316680908), ('strategies quantum', 0.5391098260879517), ('quantum correlations', 0.5344950556755066), ('finite dimensional quantum', 0.4777568280696869), ('quantum information theory', 0.4673529267311096), ('quantum', 0.4575372338294983), ('classical quantum', 0.4497409462928772), ('dimensional quantum', 0.44111159443855286), ('quantum versions', 0.43983903527259827), ('quantum models', 0.4358258545398712)]"
872,872,35,872_districts_district_elections_representatives,"['districts', 'district', 'elections', 'representatives', 'graph partitions', 'election', 'sampling', 'states', 'census', 'bias']","['Sequential Monte Carlo for Sampling Balanced and Compact Redistricting\n  Plans   Random sampling of graph partitions under constraints has become a popular\ntool for evaluating legislative redistricting plans. Analysts detect partisan\ngerrymandering by comparing a proposed redistricting plan with an ensemble of\nsampled alternative plans. For successful application, sampling methods must\nscale to maps with a moderate or large number of districts, incorporate\nrealistic legal constraints, and accurately and efficiently sample from a\nselected target distribution. Unfortunately, most existing methods struggle in\nat least one of these areas. We present a new Sequential Monte Carlo (SMC)\nalgorithm that generates a sample of redistricting plans converging to a\nrealistic target distribution. Because it draws many plans in parallel, the SMC\nalgorithm can efficiently explore the relevant space of redistricting plans\nbetter than the existing Markov chain Monte Carlo (MCMC) algorithms that\ngenerate plans sequentially. Our algorithm can simultaneously incorporate\nseveral constraints commonly imposed in real-world redistricting problems,\nincluding equal population, compactness, and preservation of administrative\nboundaries. We validate the accuracy of the proposed algorithm by using a small\nmap where all redistricting plans can be enumerated. We then apply the SMC\nalgorithm to evaluate the partisan implications of several maps submitted by\nrelevant parties in a recent high-profile redistricting case in the state of\nPennsylvania. We find that the proposed algorithm converges faster and with\nfewer samples than a comparable MCMC algorithm. Open-source software is\navailable for implementing the proposed methodology.\n', 'Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting   We develop a Multi-Scale Merge-Split Markov chain on redistricting plans. The\nchain is designed to be usable as the proposal in a Markov Chain Monte Carlo\n(MCMC) algorithm. Sampling the space of plans amounts to dividing a graph into\na partition with a specified number of elements which each correspond to a\ndifferent district. The districts satisfy a collection of hard constraints and\nthe measure may be weighted with regard to a number of other criteria. The\nmulti-scale algorithm is similar to our previously developed Merge-Split\nproposal, however, this algorithm provides improved scaling properties and may\nalso be used to preserve nested communities of interest such as counties and\nprecincts. Both works use a proposal which extends the ReCom algorithm which\nleveraged spanning trees merge and split districts. In this work we extend the\nstate space so that each district is defined by a hierarchy of trees. In this\nsense, the proposal step in both algorithms can be seen as a ""Forest ReCom."" We\nalso expand the state space to include edges that link specified districts,\nwhich further improves the computational efficiency of our algorithm. The\ncollection of plans sampled by the MCMC algorithm can serve as a baseline\nagainst which a particular plan of interest is compared. If a given plan has\ndifferent racial or partisan qualities than what is typical of the collection\nof plans, the given plan may have been gerrymandered and is labeled as an\noutlier.\n', ""Irreducibility of Recombination Markov Chains in the Triangular Lattice   In the United States, regions are frequently divided into districts for the\npurpose of electing representatives. How the districts are drawn can affect\nwho's elected, and drawing districts to give an advantage to a certain group is\nknown as gerrymandering. It can be surprisingly difficult to detect\ngerrymandering, but one algorithmic method is to compare a current districting\nplan to a large number of randomly sampled plans to see whether it is an\noutlier. Recombination Markov chains are often used for this random sampling:\nrandomly choose two districts, consider their union, and split this union in a\nnew way. This works well in practice, but the theory behind it remains\nunderdeveloped. For example, it's not known if recombination Markov chains are\nirreducible, that is, if recombination moves suffice to move from any\ndistricting plan to any other.\n  Irreducibility of recombination Markov chains can be formulated as a graph\nproblem: for a graph $G$, is the space of all partitions of $G$ into $k$\nconnected subgraphs ($k$ districts) connected by recombination moves? We\nconsider three simply connected districts and district sizes $k_1\\pm 1$\nvertices, $k_2\\pm 1$ vertices, and $k3\\pm 1$ vertices. We prove for arbitrarily\nlarge triangular regions in the triangular lattice, recombination Markov chains\nare irreducible. This is the first proof of irreducibility under tight district\nsize constraints for recombination Markov chains beyond small or trivial\nexamples.\n""]","[('districts', 0.5123831033706665), ('district', 0.43627461791038513), ('elections', 0.4158461093902588), ('representatives', 0.34845438599586487), ('graph partitions', 0.3422524034976959), ('election', 0.33555009961128235), ('sampling', 0.330537348985672), ('states', 0.32750070095062256), ('census', 0.32730451226234436), ('bias', 0.3095661401748657)]"
873,873,35,873_stochastic volatility models_rough volatility_stochastic volatility_volatility models,"['stochastic volatility models', 'rough volatility', 'stochastic volatility', 'volatility models', 'rough stochastic', 'fractional brownian motion', 'fractional brownian', 'stochastic volterra', 'fractional stochastic', 'stochastic volterra equations']","[""Rough volatility: fact or artefact?   We investigate the statistical evidence for the use of `rough' fractional\nprocesses with Hurst exponent $H< 0.5$ for the modeling of volatility of\nfinancial assets, using a model-free approach. We introduce a non-parametric\nmethod for estimating the roughness of a function based on discrete sample,\nusing the concept of normalized $p$-th variation along a sequence of\npartitions. We investigate the finite sample performance of our estimator for\nmeasuring the roughness of sample paths of stochastic processes using detailed\nnumerical experiments based on sample paths of fractional Brownian motion and\nother fractional processes. We then apply this method to estimate the roughness\nof realized volatility signals based on high-frequency observations. Detailed\nnumerical experiments based on stochastic volatility models show that, even\nwhen the instantaneous volatility has diffusive dynamics with the same\nroughness as Brownian motion, the realized volatility exhibits rough behaviour\ncorresponding to a Hurst exponent significantly smaller than $0.5$. Comparison\nof roughness estimates for realized and instantaneous volatility in fractional\nvolatility models with different values of Hurst exponent shows that,\nirrespective of the roughness of the spot volatility process, realized\nvolatility always exhibits `rough' behaviour with an apparent Hurst index\n$\\hat{H}<0.5$. These results suggest that the origin of the roughness observed\nin realized volatility time-series lies in the microstructure noise rather than\nthe volatility process itself.\n"", 'Precise asymptotics: robust stochastic volatility models   We present a new methodology to analyze large classes of (classical and\nrough) stochastic volatility models, with special regard to short-time and\nsmall noise formulae for option prices. Our main tool is the theory of\nregularity structures, which we use in the form of [Bayer et al; A regularity\nstructure for rough volatility, 2017]. In essence, we implement a Laplace\nmethod on the space of models (in the sense of Hairer), which generalizes\nclassical works of Azencott and Ben Arous on path space and then Aida,\nInahama--Kawabi on rough path space. When applied to rough volatility models,\ne.g. in the setting of [Forde-Zhang, Asymptotics for rough stochastic\nvolatility models, 2017], one obtains precise asymptotic for European options\nwhich refine known large deviation asymptotics.\n', 'Short-time asymptotics for non self-similar stochastic volatility models   We provide a short-time large deviation principle (LDP) for stochastic\nvolatility models, where the volatility is expressed as a function of a\nVolterra process. This LDP does not require strict self-similarity assumptions\non the Volterra process. For this reason, we are able to apply such an LDP to\ntwo notable examples of non self-similar rough volatility models: models where\nthe volatility is given as a function of a log-modulated fractional Brownian\nmotion [Bayer et al., Log-modulated rough stochastic volatility models. SIAM J.\nFinanc. Math, 2021, 12(3), 1257-1284], and models where it is given as a\nfunction of a fractional Ornstein-Uhlenbeck (fOU) process [Gatheral et al.,\nVolatility is rough. Quant. Finance, 2018, 18(6), 933-949]. In both cases we\nderive consequences for short-maturity European option prices, implied\nvolatility surfaces and implied volatility skew. In the fOU case we also\ndiscuss moderate deviations pricing and simulation results.\n']","[('stochastic volatility models', 0.6967331767082214), ('rough volatility', 0.6664459705352783), ('stochastic volatility', 0.6115907430648804), ('volatility models', 0.6091417670249939), ('rough stochastic', 0.5581696629524231), ('fractional brownian motion', 0.5515158176422119), ('fractional brownian', 0.5451503396034241), ('stochastic volterra', 0.5408046245574951), ('fractional stochastic', 0.5278311371803284), ('stochastic volterra equations', 0.5095804929733276)]"
874,874,35,874_eulerian polynomials_eulerian polynomial_polynomials permutations_eulerian numbers,"['eulerian polynomials', 'eulerian polynomial', 'polynomials permutations', 'eulerian numbers', 'generalized stirling', 'gamma coefficients', 'stirling permutations', 'combinatorial theory', 'signed permutations', 'gamma positivity']","['Excedance-type polynomials and gamma-positivity   The object of this paper is to give a systematic treatment of excedance-type\npolynomials. We first give a sufficient condition for a sequence of polynomials\nto have alternatingly increasing property, and then we present a systematic\nstudy of the joint distribution of excedances, fixed points and cycles of\npermutations and derangements, signed or not, colored or not. Let $p\\in [0,1]$\nand $q\\in [0,1]$ be two given real numbers. We prove that the cyc q-Eulerian\npolynomials of permutations are bi-gamma-positive, and the fix and cyc\n(p,q)-Eulerian polynomials of permutations are alternatingly increasing, and so\nthey are unimodal with modes in the middle, where fix and cyc are the fixed\npoint and cycle statistics. When p=1 and q=1/2, we find a combinatorial\ninterpretation of the bi-gamma-coefficients of the (p,q)-Eulerian polynomials.\nWe then study excedance and flag excedance statistics of signed permutations\nand colored permutations. In particular, we establish the relationships between\nthe (p,q)-Eulerian polynomials and some multivariate Eulerian polynomials. Our\nresults unify and generalize a variety of recent results.\n', ""Colored Multiset Eulerian Polynomials   Colored multiset Eulerian polynomials are a common generalization of\nMacMahon's multiset Eulerian polynomials and the colored Eulerian polynomials,\nboth of which are known to satisfy well-studied distributional properties\nincluding real-rootedness, log-concavity and unimodality. The symmetric colored\nmultiset Eulerian polynomials are characterized and used to prove sufficient\nconditions for a colored multiset Eulerian polynomial to be self-interlacing.\nThe latter property implies the aforementioned distributional properties as\nwell as others, including the alternatingly increasing property and\nbi-$\\gamma$-positivity. To derive these results, multivariate generalizations\nof an identity due to MacMahon are deduced. The results are applied to a pair\nof questions, both previously studied in several special cases, that are seen\nto admit more general answers when framed in the context of colored multiset\nEulerian polynomials. The first question pertains to $s$-Eulerian polynomials,\nand the second to interpretations of $\\gamma$-coefficients.\n"", ""Gamma positivity of variations of $(\\alpha,t)$-Eulerian polynomials   In 1977 Carlitz and Scoville introduced the cycle $(\\alpha,t)$-Eulerian\npolynomials $A^{\\mathrm{cyc}}_n(x,y, t\\,|\\,\\alpha)$ by enumerating permutations\nwith respect to the number of excedances, drops, fixed points and cycles. In\nthis paper, we introduce a nine-variable generalization of the Eulerian\npolynomials $A_n(u_1,u_2,u_3,u_4, f, g, t\\,|\\,\\alpha, \\beta)$ in terms of\ndescent based statistics of permutations and prove a connection formula between\nthese two kinds of generalized Eulerian polynomials. By exploring the\nconnection formula, we derive plainly the exponential generating function of\nthe latter polynomials and various $\\gamma$-positive formulas for variants of\nEulerian polynomials. In particular, our results unify and strengthen the\nrecent results by Ji and Ji-Lin. In related work to the transition matrix\nbetween the Specht and web bases, Hwang, Jang and Oh recently introduced the\nweb permutations, which can be characterised by cycle Andr\\'e permutations. We\nshow that enumerating the latter permutations with respect to the number of\ndrops, fixed points and cycles gives rise to the normalised $\\gamma$-vectors of\nthe $(\\alpha,t)$-Eulerian polynomials. Our result generalizes and unifies\nseveral known results in the literature.\n""]","[('eulerian polynomials', 0.6653112173080444), ('eulerian polynomial', 0.5714169144630432), ('polynomials permutations', 0.5110957622528076), ('eulerian numbers', 0.4911266565322876), ('generalized stirling', 0.452603280544281), ('gamma coefficients', 0.4501361548900604), ('stirling permutations', 0.4477003216743469), ('combinatorial theory', 0.43432775139808655), ('signed permutations', 0.4268319606781006), ('gamma positivity', 0.4049991965293884)]"
875,875,35,875_elliptic calogero moser_dimensional yang mills_associative yang baxter_elliptic calogero,"['elliptic calogero moser', 'dimensional yang mills', 'associative yang baxter', 'elliptic calogero', 'lax matrices', 'lax matrix', 'spin calogero', 'commuting hamiltonians', 'calogero moser sutherland', 'quantum classical']","['Spin Calogero-Moser periodic chains and two dimensional Yang-Mills\n  theory with corners   Quantum Calogero-Moser spin system is a superintegable system with the\nspectrum of commuting Hamiltonians that can be described entirely in terms of\nrepresentation theory of corresponding simple Lie group. In this paper the\nunderlying Lie group G is a compact connected, simply connected simple Lie\ngroup. It has a natural generalization known as quantum Calogero-Moser spin\nchain. In the first part of the paper we show that quantum Calogero-Moser spin\nchain is a quantum superintegrable systems. Then we show that the Euclidean\nmulti-time propagator for this model can be written as a partition function of\na two-dimensional Yang-Mills theory on a cylinder. Then we argue that the\ntwo-dimensional Yang-Mills theory with Wilson loops with ""outer ends"" should be\nregarded as the theory on space times with non-removable corners. Partition\nfunctions of such theory satisfy non-stationary Calogero-Moser equations.\n', ""Gauge equivalence of 1+1 Calogero-Moser-Sutherland field theory and\n  higher rank trigonometric Landau-Lifshitz model   We consider the classical integrable 1+1 trigonometric ${\\rm gl}_N$\nLandau-Lifshitz models constructed by means of quantum $R$-matrices satisfying\nalso the associative Yang-Baxter equation. It is shown that 1+1 field analogue\nof the trigonometric Calogero-Moser-Sutherland model is gauge equivalent to the\nLandau-Lifshitz model, which arises from the Antonov-Hasegawa-Zabrodin\ntrigonometric non-standard $R$-matrix. The latter generalizes the Cherednik's\n7-vertex $R$-matrix in ${\\rm GL}_2$ case to the case of ${\\rm GL}_N$. Explicit\nchange of variables between the 1+1 models is obtained.\n"", 'Gauge equivalence between 1+1 rational Calogero-Moser field theory and\n  higher rank Landau-Lifshitz equation   In this paper we study 1+1 field generalization of the rational $N$-body\nCalogero-Moser model. We show that this model is gauge equivalent to some\nspecial higher rank matrix Landau-Lifshitz equation. The latter equation is\ndescribed in terms of ${\\rm GL}_N$ rational $R$-matrix, which turns into the\n11-vertex $R$-matrix in the $N=2$ case. The rational $R$-matrix satisfies the\nassociative Yang-Baxter equation, which underlies construction of the Lax pair\nfor the Zakharov-Shabat equation. The field analogue of the IRF-Vertex\ntransformation is proposed. It allows to compute explicit change of variables\nbetween the field Calogero-Moser model and the Landau-Lifshitz equation.\n']","[('elliptic calogero moser', 0.5391216278076172), ('dimensional yang mills', 0.4733425974845886), ('associative yang baxter', 0.4372892677783966), ('elliptic calogero', 0.4301605522632599), ('lax matrices', 0.419661283493042), ('lax matrix', 0.39098572731018066), ('spin calogero', 0.38898441195487976), ('commuting hamiltonians', 0.38730329275131226), ('calogero moser sutherland', 0.36786216497421265), ('quantum classical', 0.36777886748313904)]"
876,876,35,876_helly type theorems_convex sets mathbb_convex sets_compact convex sets,"['helly type theorems', 'convex sets mathbb', 'convex sets', 'compact convex sets', 'colorful helly', 'type theorems', 'helly type', 'theorems', 'compact convex', 'mathbb points']","['Helly-type theorems for separated $d$-intervals A separated $d$-interval is defined as a disjoint union of $d$ convex sets from the real line $\\mathbb R$. In this paper, we establish a series of Helly-type theorems for convexity spaces derived from separated $d$-intervals. Our results encompass the Radon number, Helly number, colorful Helly number, fractional Helly number, colorful fractional Helly theorem, $(p,q)$ theorem, and two kinds of colorful $(p,q)$ theorems for these convexity spaces. The primary tools employed in our proofs involve simplicial complexes and collapsibility.', ""A m\\'elange of diameter Helly-type theorems   A Helly-type theorem for diameter provides a bound on the diameter of the\nintersection of a finite family of convex sets in $\\mathbb{R}^d$ given some\ninformation on the diameter of the intersection of all sufficiently small\nsubfamilies. We prove fractional and colorful versions of a longstanding\nconjecture by B\\'ar\\'any, Katchalski, and Pach. We also show that a Minkowski\nnorm admits an exact Helly-type theorem for diameter if and only if its unit\nball is a polytope and prove a colorful version for those that do. Finally, we\nprove Helly-type theorems for the property of ``containing $k$ colinear integer\npoints.\n"", 'Helly numbers for Quantitative Helly-type results   We obtain three Helly-type results. First, we establish a Quantitative\nColorful Helly-type theorem with the optimal Helly number \\(2d\\) concerning the\ndiameter of the intersection of a family of convex bodies. Second, we prove a\nQuantitative Helly-type theorem with the optimal Helly number \\(2d+1\\) for the\npointwise minimum of logarithmically concave functions. Finally, we present a\ncolorful version of the latter result with Helly number (number of color\nclasses) \\(3d+1\\); however, we have no reason to believe that this bound is\nsharp.\n']","[('helly type theorems', 0.6884496212005615), ('convex sets mathbb', 0.47407394647598267), ('convex sets', 0.45779234170913696), ('compact convex sets', 0.432536780834198), ('colorful helly', 0.42147862911224365), ('type theorems', 0.396240770816803), ('helly type', 0.3936748504638672), ('theorems', 0.3746390640735626), ('compact convex', 0.36920976638793945), ('mathbb points', 0.35304397344589233)]"
877,877,35,877_classifiers_imbalanced classification_optimal classifier_classification performance,"['classifiers', 'imbalanced classification', 'optimal classifier', 'classification performance', 'classifier', 'binary classifier', 'classification', 'classification metrics', 'binary classification', 'multiclass classification']","['Approximation and generalization properties of the random projection\n  classification method   The generalization gap of a classifier is related to the complexity of the\nset of functions among which the classifier is chosen. We study a family of\nlow-complexity classifiers consisting of thresholding a random one-dimensional\nfeature. The feature is obtained by projecting the data on a random line after\nembedding it into a higher-dimensional space parametrized by monomials of order\nup to k. More specifically, the extended data is projected n-times and the best\nclassifier among those n, based on its performance on training data, is chosen.\nWe show that this type of classifier is extremely flexible as, given full\nknowledge of the class conditional densities, under mild conditions, the error\nof these classifiers would converge to the optimal (Bayes) error as k and n go\nto infinity. We also bound the generalization gap of the random classifiers. In\ngeneral, these bounds are better than those for any classifier with VC\ndimension greater than O(ln n). In particular, the bounds imply that, unless\nthe number of projections n is extremely large, the generalization gap of the\nrandom projection approach is significantly smaller than that of a linear\nclassifier in the extended space. Thus, for certain classification problems\n(e.g., those with a large Rashomon ratio), there is a potntially large gain in\ngeneralization properties by selecting parameters at random, rather than\nselecting the best one amongst the class.\n', 'Kernel-Free Universum Quadratic Surface Twin Support Vector Machines for\n  Imbalanced Data   Binary classification tasks with imbalanced classes pose significant\nchallenges in machine learning. Traditional classifiers often struggle to\naccurately capture the characteristics of the minority class, resulting in\nbiased models with subpar predictive performance. In this paper, we introduce a\nnovel approach to tackle this issue by leveraging Universum points to support\nthe minority class within quadratic twin support vector machine models. Unlike\ntraditional classifiers, our models utilize quadratic surfaces instead of\nhyperplanes for binary classification, providing greater flexibility in\nmodeling complex decision boundaries. By incorporating Universum points, our\napproach enhances classification accuracy and generalization performance on\nimbalanced datasets. We generated four artificial datasets to demonstrate the\nflexibility of the proposed methods. Additionally, we validated the\neffectiveness of our approach through empirical evaluations on benchmark\ndatasets, showing superior performance compared to conventional classifiers and\nexisting methods for imbalanced classification.\n', 'Optimal Binary Classification Beyond Accuracy   The vast majority of statistical theory on binary classification\ncharacterizes performance in terms of accuracy. However, accuracy is known in\nmany cases to poorly reflect the practical consequences of classification\nerror, most famously in imbalanced binary classification, where data are\ndominated by samples from one of two classes. The first part of this paper\nderives a novel generalization of the Bayes-optimal classifier from accuracy to\nany performance metric computed from the confusion matrix. Specifically, this\nresult (a) demonstrates that stochastic classifiers sometimes outperform the\nbest possible deterministic classifier and (b) removes an empirically\nunverifiable absolute continuity assumption that is poorly understood but\npervades existing results. We then demonstrate how to use this generalized\nBayes classifier to obtain regret bounds in terms of the error of estimating\nregression functions under uniform loss. Finally, we use these results to\ndevelop some of the first finite-sample statistical guarantees specific to\nimbalanced binary classification. Specifically, we demonstrate that optimal\nclassification performance depends on properties of class imbalance, such as a\nnovel notion called Uniform Class Imbalance, that have not previously been\nformalized. We further illustrate these contributions numerically in the case\nof $k$-nearest neighbor classification\n']","[('classifiers', 0.65556800365448), ('imbalanced classification', 0.649971067905426), ('optimal classifier', 0.6393368244171143), ('classification performance', 0.6219899654388428), ('classifier', 0.6217853426933289), ('binary classifier', 0.5848141312599182), ('classification', 0.5741498470306396), ('classification metrics', 0.5664893984794617), ('binary classification', 0.5589500665664673), ('multiclass classification', 0.5390069484710693)]"
878,878,35,878_functions variational_second order variational_variational properties_variational analysis,"['functions variational', 'second order variational', 'variational properties', 'variational analysis', 'strong variational', 'subdifferentials', 'subgradients', 'order variational analysis', 'variational', 'subdifferential']","['Generalized Twice Differentiability and Quadratic Bundles in\n  Second-Order Variational Analysis   In this paper, we investigate the concepts of generalized twice\ndifferentiability and quadratic bundles of nonsmooth functions that have been\nvery recently proposed by Rockafellar in the framework of second-order\nvariational analysis. These constructions, in contrast to second-order\nsubdifferentials, are defined in primal spaces. We develop new techniques to\nstudy generalized twice differentiability for a broad class of prox-regular\nfunctions, establish their novel characterizations. Subsequently, quadratic\nbundles of prox-regular functions are shown to be nonempty, which provides the\nground of potential applications in variational analysis and optimization.\n', 'On second-order variational analysis of variational convexity of\n  prox-regular functions   Variational convexity, together with ist strong counterpart, of\nextended-real-valued functions has been recently introduced by Rockafellar. In\nthis paper we present second-order characterizations of these properties, i.e.,\nconditions using first-order generalized derivatives of the subgradient\nmapping. Up to now, such characterizations are only known under the assumptions\nof prox-regularity and subdifferential continuity and in this paper we discard\nthe latter. To this aim we slightly modify the definitions of the generalized\nderivatives to be compatible with the $f$-attentive convergence appearing in\nthe definition of subgradients. We formulate our results in terms of both\ncoderivatives and subspace containing derivatives. We also give formulas for\nthe exact bound of variational convexity and study relations between\nvariational strong convexity, tilt-stable local minimizers and strong metric\nregularity of some truncation of the subgradient mapping.\n', 'Role of Subgradients in Variational Analysis of Polyhedral Functions   Understanding the role that subgradients play in various second-order\nvariational analysis constructions can help us uncover new properties of\nimportant classes of functions in variational analysis. Focusing mainly on the\nbehavior of the second subderivative and subgradient proto-derivative of\npolyhedral functions, functions with polyhedral epigraphs, we demonstrate that\nchoosing the underlying subgradient, utilized in the definitions of these\nconcepts, from the relative interior of the subdifferential of polyhedral\nfunctions ensures stronger second-order variational properties such as strict\ntwice epi-differentiability and strict subgradient proto-differentiability.\nThis allows us to characterize continuous differentiability of the proximal\nmapping and twice continuous differentiability of the Moreau envelope of\npolyhedral functions. We close the paper with proving the equivalence of metric\nregularity and strong metric regularity of a class of generalized equations at\ntheir nondegenerate solutions.\n']","[('functions variational', 0.6100277900695801), ('second order variational', 0.5711497664451599), ('variational properties', 0.5704344511032104), ('variational analysis', 0.5621951222419739), ('strong variational', 0.5192586183547974), ('subdifferentials', 0.5130957961082458), ('subgradients', 0.5114256143569946), ('order variational analysis', 0.5103057026863098), ('variational', 0.5044629573822021), ('subdifferential', 0.5009838938713074)]"
879,879,35,879_quaternion algebras_quaternion algebra_generalized quaternion_quaternions,"['quaternion algebras', 'quaternion algebra', 'generalized quaternion', 'quaternions', 'functions quaternionic', 'two quaternionic', 'quaternionic', 'quaternion', 'quaternions octonions', 'hilbert nullstellensatz']","['Quadratic formulas for split quaternions   Unlike the Hamilton quaternion algebra, the split-quaternions contain\nnontrivial zero divisors. In general speaking, it is hard to find the solutions\nof equations in algebras containing zero divisor. In this paper, we manage to\nderive explicit formulas for computing the roots of $x^{2}+bx+c=0$ in split\nquaternion algebra.\n', 'Zero sets and Nullstellensatz type theorems for slice regular\n  quaternionic polynomials   We study the vanishing sets of slice regular polynomials in several\nquaternionic variables. We obtain a geometric description of the vanishing sets\nin two variables, which leads to a new version of the Strong Hilbert\nNullstellensatz in the quaternionic setting.\n', 'A Strong Version of the Hilbert Nullstellensatz for slice regular\n  polynomials in several quaternionic variables   In this paper we prove a strong version of the Hilbert Nullstellensatz in the\nring $\\mathbb H[q_1,\\ldots,q_n]$ of slice regular polynomials in several\nquaternionic variables. Our proof deeply depends on a detailed analysis of the\ncommon zeros of slice regular polynomials which belong to an ideal in $\\mathbb\nH[q_1,\\ldots,q_n]$. This study motivates the introduction of a new notion of\nalgebraic set in the quaternionic setting, which allows us to define a\nZariski-type topology on $\\mathbb H^n$.\n']","[('quaternion algebras', 0.7446972727775574), ('quaternion algebra', 0.7313478589057922), ('generalized quaternion', 0.6859990954399109), ('quaternions', 0.6600795388221741), ('functions quaternionic', 0.6393894553184509), ('two quaternionic', 0.6234575510025024), ('quaternionic', 0.6135469675064087), ('quaternion', 0.609243631362915), ('quaternions octonions', 0.5921275019645691), ('hilbert nullstellensatz', 0.589907169342041)]"
880,880,35,880_ordinary differential equations_nonlinear odes_nonlinear differential equations_first order odes,"['ordinary differential equations', 'nonlinear odes', 'nonlinear differential equations', 'first order odes', 'odes', 'differential equations', 'order differential equations', 'second order nonlinear', 'order odes', 'differential equations short']","['New Solvable System OF 2 First-Order Nonlinearly-Coupled Ordinary\n  Differential Equations   In this short communication we introduce a rather simple autonomous system of\n2 nonlinearly-coupled first-order Ordinary Differential Equations (ODEs), whose\ninitial-values problem is explicitly solvable by algebraic operations. Its ODEs\nfeature 2 right-hand sides which are the ratios of 2 homogeneous polynomials of\nfirst degree divided by the same homogeneous polynomial of second degree. The\nmodel features only 4 arbitrary parameters. We also report its isochronous\nvariant featuring 4 nonlinearly-coupled first-order ODEs in 4 dependent\nvariables, featuring 9 arbitrary parameters.\n', 'Explicitly solvable systems of two autonomous first-order Ordinary\n  Differential Equations with homogeneous quadratic right-hand sides   After tersely reviewing the various meanings that can be given to the\nproperty of a system of nonlinear ODEs to be solvable, we identify a special\ncase of the system of two first-order ODEs with homogeneous quadratic\nright-hand sides which is explicitly solvable. It is identified by 2 explicit\nalgebraic constraints on the 6 a priori arbitrary parameters that characterize\nthis system. Simple extensions of this model to cases with nonhomogeneous\nquadratic right-hand sides are also identified, including isochronous cases.\n', 'Explicitly Solvable Systems of First-order Ordinary Differential\n  Equations with Polynomial Right-hand Sides, and Their Periodic Variants   In this Letter we identify special systems of (an arbitrary number) N of\nfirst-order Ordinary Differential Equations with homogeneous polynomials of\narbitrary degree M on their right-hand sides, which feature very simple\nexplicit solutions; as well as variants of these systems--with right-hand sides\nno more homogeneous--which feature periodic solutions. A novelty of these\nfindings is to consider special systems characterized by constraints involving\nboth their parameters and their initial data.\n']","[('ordinary differential equations', 0.6151768565177917), ('nonlinear odes', 0.6065258383750916), ('nonlinear differential equations', 0.588799774646759), ('first order odes', 0.5833553671836853), ('odes', 0.5353256464004517), ('differential equations', 0.534856915473938), ('order differential equations', 0.5310055017471313), ('second order nonlinear', 0.5306462645530701), ('order odes', 0.5298945307731628), ('differential equations short', 0.5292534828186035)]"
881,881,34,881_mean spectral_positive definite operators_positive definite matrices_two positive definite,"['mean spectral', 'positive definite operators', 'positive definite matrices', 'two positive definite', 'weighted geometric means', 'positive definite', 'spectral geometric', 'positive matrices', 'geometric mean', 'definite operators']","['Order Relations of the Wasserstein mean and the spectral geometric mean   On the space of positive definite matrices, several operator means are\npopular and have been studied extensively. In this paper, we investigate the\nnear order and the L\\""owner order relations on the curves defined by the\nWasserstein mean and the spectral geometric mean. We show that the near order\n$\\preceq $ is stronger than the eigenvalue entrywise order, and that\n$A\\natural_t B \\preceq A\\diamond_t B$ for $t\\in [0,1]$. We prove the\nmonotonicity properties of the curves originated from the Wasserstein mean and\nthe spectral geometric mean in terms of the near order. The L\\""owner order\nproperties of the Wasserstein mean and the spectral geometric mean are also\nexplored.\n', 'Operator Spectral Geometric Versus Geometric Mean   The main goal of this article is to present new inequalities for the spectral\ngeometric mean $A\\natural_t B$ of two positive definite operators $A, B$ on a\nHilbert space. The obtained results complement many known inequalities for the\ngeometric mean $A\\sharp_t B$. In particular, explicit comparisons between\n  $A\\natural_t B$ and $A\\sharp_t B$ are given, with applications towards\nAndo-type inequalities and Ando-Hiai inequalities for $A\\natural_t B$ and some\nother consequences.\n', 'Revisit on spectral geometric mean   In this paper we introduce the limit, unique solution of the nonlinear\nequations, geodesic property, tolerance relations and pinch on the spectral\ngeometric mean for two positive definite operators. We show that the spectral\ngeometric mean is a geodesic with respect to some semi-metric. We also prove\nthat the tolerance relation on determinant one matrices can be characterized by\nthe spectral geometric mean. Moreover, two positive tuples can be pinched by\nthe spectral geometric mean.\n']","[('mean spectral', 0.6250083446502686), ('positive definite operators', 0.61821049451828), ('positive definite matrices', 0.49613597989082336), ('two positive definite', 0.4835931658744812), ('weighted geometric means', 0.4751299321651459), ('positive definite', 0.46295949816703796), ('spectral geometric', 0.4627976417541504), ('positive matrices', 0.4481097161769867), ('geometric mean', 0.43695658445358276), ('definite operators', 0.4318891167640686)]"
882,882,34,882_vietoris rips complexes_rips complexes_vietoris rips_simplicial complexes,"['vietoris rips complexes', 'rips complexes', 'vietoris rips', 'simplicial complexes', 'homotopy types', 'homotopy equivalent', 'vietoris', 'persistent homology', 'homotopy type', 'homotopy equivalent wedge']","['Graphs and Their Vietoris-Rips Complexes Have the Same Pseudotopological\n  Weak Homotopy Type   In this document, we propose a bridge between the graphs and the geometric\nrealizations of their Vietoris Rips complexes, i.e. Graphs, with their\ncanonical \\v{C}ech closure structure, have the same homotopy type that the\nrealization of their Vietoris Rips complex.\n', 'Vietoris thickenings and complexes are weakly homotopy equivalent   Characterizing the homotopy types of the Vietoris--Rips complexes of a metric\nspace $X$ is in general a difficult problem. The Vietoris--Rips metric\nthickening, a metric space analogue of the Vietoris--Rips complex, was\nintroduced as a potentially more amenable object of study with several\nadvantageous properties, yet the relationship between its homotopy type and\nthat of the Vietoris--Rips complex was not fully understood. We show that for\nany metric space $X$ and threshold $r>0$, the natural bijection between the\n(open) Vietoris--Rips complex and Vietoris--Rips metric thickening is a weak\nhomotopy equivalence.\n', 'On $\\ell_p$-Vietoris-Rips complexes   We study the concepts of the $\\ell_p$-Vietoris-Rips simplicial set and the\n$\\ell_p$-Vietoris-Rips complex of a metric space, where $1\\leq p \\leq \\infty.$\nThis theory unifies two established theories: for $p=\\infty,$ this is the\nclassical theory of Vietoris-Rips complexes, and for $p=1,$ this corresponds to\nthe blurred magnitude homology theory. We prove several results that are known\nfor the Vietoris-Rips complex in the general case: (1) we prove a stability\ntheorem for the corresponding version of the persistent homology; (2) we show\nthat, for a compact Riemannian manifold and a sufficiently small scale\nparameter, all the ""$\\ell_p$-Vietoris-Rips spaces"" are homotopy equivalent to\nthe manifold; (3) we demonstrate that the $\\ell_p$-Vietoris-Rips spaces are\ninvariant (up to homotopy) under taking the metric completion. Additionally, we\nshow that the limit of the homology groups of the $\\ell_p$-Vietoris-Rips\nspaces, as the scale parameter tends to zero, does not depend on $p$; and that\nthe homology groups of the $\\ell_p$-Vietoris-Rips spaces commute with filtered\ncolimits of metric spaces.\n']","[('vietoris rips complexes', 0.7510043978691101), ('rips complexes', 0.6421032547950745), ('vietoris rips', 0.6196627020835876), ('simplicial complexes', 0.5028153657913208), ('homotopy types', 0.4985275864601135), ('homotopy equivalent', 0.48758938908576965), ('vietoris', 0.48175734281539917), ('persistent homology', 0.46940770745277405), ('homotopy type', 0.46085816621780396), ('homotopy equivalent wedge', 0.4591095745563507)]"
883,883,34,883_higgs bundles_higgs bundle_parabolic higgs_bundles,"['higgs bundles', 'higgs bundle', 'parabolic higgs', 'bundles', 'bundles rank', 'mathbb higgs', 'higgs', 'hermitian yang mills', 'vector bundles', 'hitchin moduli space']","[""On Hitchin's equations for cyclic G-Higgs bundles   We develop a Lie-theoretic perspective on Hitchin's equations for cyclic\n$G$-Higgs bundles, which we use to study analytic and geometric properties of\nharmonic maps. Among other things, we prove Dai-Li's conjecture on the\nmonotonicity of the energy density in the case of Coxeter cyclic $G$-Higgs\nbundles, for all $G$, and Dai-Li's negative curvature conjecture for Coxeter\ncyclic $G$-Higgs bundles, for all $G$ except those of type $\\mathrm{E}_7$ and\n$\\mathrm{E}_8.$\n"", ""On $2k$-Hitchin's equations and Higgs bundles: a survey   We study the $2k$-Hitchin equations introduced by Ward \\cite{Ward 2} from the\ngeometric viewpoint of Higgs bundles. After an introduction on Higgs bundles\nand $2k$-Hitchin's equations, we review some elementary facts on complex\ngeometry and Yang-Mills theory. Then we study some properties of holomorphic\nvector bundles and Higgs bundles and we review the Hermite-Yang-Mills equations\ntogether with two functionals related to such equations. Using some geometric\ntools we show that, as far as Higgs bundles is concern, $2k$-Hitchin's\nequations are reduced to a set of two equations. Finally, we introduce a\nfunctional closely related to $2k$-Hitchin's equations and we study some of its\nbasic properties.\n"", 'Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section   Given a tuple of holomorphic differentials on a Riemann surface, one can\ndefine a Higgs bundle in the Hitchin section and a natural symmetric pairing of\nthe Higgs bundle. We study whether a Higgs bundle of rank 3 in the Hitchin\nsection has a compatible harmonic metric when the spectral curve is a 2-sheeted\nbranched covering of the Riemann surface. In particular, we give a condition\nfor Higgs bundles in the Hitchin section on $\\mathbb{C}$ or $\\mathbb{C}^*$ to\nhave compatible harmonic metrics.\n']","[('higgs bundles', 0.6953840851783752), ('higgs bundle', 0.6885321736335754), ('parabolic higgs', 0.5713784098625183), ('bundles', 0.518015444278717), ('bundles rank', 0.5057990550994873), ('mathbb higgs', 0.4966871440410614), ('higgs', 0.4955984652042389), ('hermitian yang mills', 0.4916544258594513), ('vector bundles', 0.4828743636608124), ('hitchin moduli space', 0.461305171251297)]"
884,884,34,884_rogers ramanujan identities_ramanujan type identities_identities rogers ramanujan_ramanujan identities,"['rogers ramanujan identities', 'ramanujan type identities', 'identities rogers ramanujan', 'ramanujan identities', 'partition identities', 'gordon identities', 'integer partitions', 'rogers ramanujan type', 'ramanujan type', 'partitions']","[""Euler's partition theorem for all moduli and new companions to\n  Rogers-Ramanujan-Andrews-Gordon identities   In this paper, we give a conjecture, which generalises Euler's partition\ntheorem involving odd parts and different parts for all moduli. We prove this\nconjecture for two family partitions. We give $q$-difference equations for the\nrelated generating function if the moduli is three. We provide new companions\nto Rogers-Ramanujan-Andrews-Gordon identities under this conjecture.\n"", 'Looking for a new member of Gordon\'s identities   We give a commutative algebra viewpoint on Andrews recursive formula for the\npartitions appearing in ""Gordon\'s identities"", which are a generalization of\nRogers-Ramanujan identities. Using this approach and differential ideals we\nconjecture a family of partition identities which extend Gordon\'s identities.\nThis family is indexed by r >=2. We prove the conjecture for r=2 and r=3.\n', ""Euler's partition theorem for all moduli and new companions to\n  Rogers-Ramanujan-Andrews-Gordon identities   We generalise Euler's partition theorem involving odd parts and different\nparts for all moduli and provide new companions to Rogers-Ramanujan-\nAndrews-Gordon identities related to this theorem.\n""]","[('rogers ramanujan identities', 0.6591972708702087), ('ramanujan type identities', 0.6486073136329651), ('identities rogers ramanujan', 0.6305948495864868), ('ramanujan identities', 0.6237323880195618), ('partition identities', 0.6111161112785339), ('gordon identities', 0.5780544281005859), ('integer partitions', 0.49171602725982666), ('rogers ramanujan type', 0.45623427629470825), ('ramanujan type', 0.42715829610824585), ('partitions', 0.42117008566856384)]"
885,885,34,885_planar maps_general maps_associated generating functions_maps arbitrary,"['planar maps', 'general maps', 'associated generating functions', 'maps arbitrary', 'triangulations', 'combinatorial', 'planar bipartite', 'series maps', 'bipartite planar', 'quadrangulations']","['Spanning forests in regular planar maps   We address the enumeration of p-valent planar maps equipped with a spanning\nforest, with a weight z per face and a weight u per connected component of the\nforest. Equivalently, we count p-valent maps equipped with a spanning tree,\nwith a weight z per face and a weight \\mu:=u+1 per internally active edge, in\nthe sense of Tutte; or the (dual) p-angulations equipped with a recurrent\nsandpile configuration, with a weight z per vertex and a variable \\mu:=u+1 that\nkeeps track of the level of the configuration. This enumeration problem also\ncorresponds to the limit q -> 0 of the q-state Potts model on p-angulations.\nOur approach is purely combinatorial. The associated generating function,\ndenoted F(z,u), is expressed in terms of a pair of series defined implicitly by\na system involving doubly hypergeometric series. We derive from this system\nthat F(z,u) is differentially algebraic in z, that is, satisfies a differential\nequation in z with polynomial coefficients in z and u. This has recently been\nproved to hold for the more general Potts model on 3-valent maps, but via a\nmuch more involved and less combinatorial proof. For u >= -1, we study the\nsingularities of F(z,u) and the corresponding asymptotic behaviour of its n-th\ncoefficient. For u>0, we find the standard asymptotic behaviour of planar maps,\nwith a subexponential term in n^{-5/2}. At u=0 we witness a phase transition\nwith a term n^{-3}. When u\\in[-1,0), we obtain an extremely unusual behaviour\nin n^{-3}(\\ln n)^{-2}. To our knowledge, this is a new ""universality class"" for\nplanar maps.\n', 'Refined enumeration of planar Eulerian orientations   We address the enumeration of Eulerian orientations of 4-valent planar maps\naccording to three parameters: the number of vertices, the number of\nalternating vertices (having in/out/in/out incident edges), and the number of\nclockwise oriented faces. This is a refinement of the six vertex model studied\nby Kostov, then Zinn-Justin and Elvey Price, where one only considers the first\ntwo parameters. Via a bijection of Ambjorn and Budd, our problem is equivalent\nto the enumeration of Eulerian partial orientations of general planar maps,\ncounted by the number of edges, the number of undirected edges, and the number\nof vertices.\n  We first derive from combinatorial arguments a system of functional equations\ncharacterising the associated trivariate series $Q(t,\\omega,v)$. We then derive\nfrom this system a compact characterisation of this series. We use it to\ndetermine $Q(t,\\omega,v)$ in three two-parameter cases. The first two cases\ncorrespond to setting the variable $\\omega$ counting alternating vertices (or\nundirected edges after the AB bijection) to $0$ or $1$: when $\\omega=0$ we\ncount Eulerian orientations of general planar maps by edges and vertices, and\nwhen $\\omega=1$ we count Eulerian orientations of quartic maps by vertices and\nclockwise faces. The final forms of these two series, namely $Q(t,0, v)$ and\n$Q(t,1,v)$, refine those obtained by the authors in an earlier paper for $v=1$.\nThe third case that we solve, namely $v=1$ (but $\\omega$ arbitrary), is the\nstandard six-vertex model, for which we provide a new proof of the formula of\nElvey Price and Zinn-Justin involving Jacobi theta functions.\n  This new derivation remains purely in the world of formal power series, not\nrelying on complex analysis. Our results also use a more direct approach to\nsolving the functional equations, in contrast to the guess and check approaches\nused in previous work.\n', 'The generating function of planar Eulerian orientations   The enumeration of planar maps equipped with an Eulerian orientation has\nattracted attention in both combinatorics and theoretical physics since at\nleast 2000. The case of 4-valent maps is particularly interesting: these\norientations are in bijection with properly 3-coloured quadrangulations, while\nin physics they correspond to configurations of the ice model.\n  We solve both problems -- namely the enumeration of planar Eulerian\norientations and of 4-valent planar Eulerian orientations -- by expressing the\nassociated generating functions as the inverses (for the composition of series)\nof simple hypergeometric series. Using these expressions, we derive the\nasymptotic behaviour of the number of planar Eulerian orientations, thus\nproving earlier predictions of Kostov, Zinn-Justin, Elvey Price and Guttmann.\nThis behaviour, $\\mu^n /(n \\log n)^2$, prevents the associated generating\nfunctions from being D-finite. Still, these generating functions are\ndifferentially algebraic, as they satisfy non-linear differential equations of\norder $2$. Differential algebraicity has recently been proved for other map\nproblems, in particular for maps equipped with a Potts model.\n  Our solutions mix recursive and bijective ingredients. In particular, a\npreliminary bijection transforms our oriented maps into maps carrying a height\nfunction on their vertices. In the 4-valent case, we also observe an unexpected\nconnection with the enumeration of maps equipped with a spanning tree that is\ninternally inactive in the sense of Tutte. This connection remains to be\nexplained combinatorially.\n']","[('planar maps', 0.543308436870575), ('general maps', 0.41667312383651733), ('associated generating functions', 0.4014824628829956), ('maps arbitrary', 0.39719775319099426), ('triangulations', 0.38728341460227966), ('combinatorial', 0.38376039266586304), ('planar bipartite', 0.3695473372936249), ('series maps', 0.3655882477760315), ('bipartite planar', 0.36550378799438477), ('quadrangulations', 0.3640489876270294)]"
886,886,34,886_hopf galois extensions_hopf galois theory_hopf galois_galois structures,"['hopf galois extensions', 'hopf galois theory', 'hopf galois', 'galois structures', 'galois structure', 'galois correspondence', 'galois theory', 'galois extensions', 'extension galois', 'extension galois group']","['Minimal Hopf-Galois Structures on Separable Field Extensions   In Hopf-Galois theory, every $H$-Hopf-Galois structure on a field extension\n$K/k$ gives rise to an injective map $\\mathcal{F}$ from the set of $k$-sub-Hopf\nalgebras of $H$ into the intermediate fields of $K/k$. Recent papers on the\nfailure of the surjectivity of $\\mathcal{F}$ reveal that there exist many\nHopf-Galois structures for which there are many more subfields than sub-Hopf\nalgebras. This paper surveys and illustrates group-theoretical methods to\ndetermine $H$-Hopf-Galois structures on finite separable extensions in the\nextreme situation when $H$ has only two sub-Hopf algebras.\n', ""On $ \\rho $-conjugate Hopf-Galois structures   The Hopf-Galois structures admitted by a Galois extension of fields $ L/K $\nwith Galois group $ G $ correspond bijectively with certain subgroups of $\n\\mathrm{Perm}(G) $. We use a natural partition of the set of such subgroups to\nobtain a method for partitioning the set of corresponding Hopf-Galois\nstructures, which we term $ \\rho $-conjugation. We study properties of this\nconstruction, with particular emphasis on the Hopf-Galois analogue of the\nGalois correspondence, the connection with skew left braces, and applications\nto questions of integral module structure in extensions of local or global\nfields. In particular, we show that the number of distinct $ \\rho $-conjugates\nof a given Hopf-Galois structure is determined by the corresponding skew left\nbrace, and that if $ H, H' $ are Hopf algebras giving $ \\rho $-conjugate\nHopf-Galois structures on a Galois extension of local or global fields $ L/K $\nthen an ambiguous ideal $ \\mathfrak{B} $ of $ L $ is free over its associated\norder in $ H $ if and only if it is free over its associated order in $ H' $.\nWe exhibit a variety of examples arising from interactions with existing\nconstructions in the literature.\n"", 'Classification of the types for which every Hopf--Galois correspondence\n  is bijective   Let $L/K$ be any finite Galois extension with Galois group $G$. It is known\nby Chase and Sweedler that the Hopf--Galois correspondence is injective for\nevery Hopf--Galois structure on $L/K$, but it need not be bijective in general.\nHopf--Galois structures are known to be related to skew braces, and recently,\nthe first-named author and Trappeniers proposed a new version of this\nconnection with the property that the intermediate fields of $L/K$ in the image\nof the Hopf--Galois correspondence are in bijection with the left ideals of the\nassociated skew brace. As an application, they classified the groups $G$ for\nwhich the Hopf--Galois correspondence is bijective for every Hopf--Galois\nstructure on any $G$-Galois extension. In this paper, using a similar approach,\nwe shall classify the groups $N$ for which the Hopf--Galois correspondence is\nbijective for every Hopf--Galois structure of type $N$ on any Galois extension.\n']","[('hopf galois extensions', 0.7564377188682556), ('hopf galois theory', 0.7339462637901306), ('hopf galois', 0.7145284414291382), ('galois structures', 0.6926823258399963), ('galois structure', 0.6599507927894592), ('galois correspondence', 0.6564935445785522), ('galois theory', 0.6436945796012878), ('galois extensions', 0.6353241205215454), ('extension galois', 0.6249852776527405), ('extension galois group', 0.6163361072540283)]"
887,887,34,887_saddle node bifurcation_bifurcations critical_manifolds unstable_bifurcations,"['saddle node bifurcation', 'bifurcations critical', 'manifolds unstable', 'bifurcations', 'dimensional phase space', 'unstable manifolds', 'energy surfaces', 'phase space', 'bifurcation', 'stable unstable manifolds']","['Hamiltonian pitchfork bifurcation in transition across index-1 saddles   We study the effect of changes in the parameters of a two-dimensional\npotential energy surface on the phase space structures relevant for chemical\nreaction dynamics. The changes in the potential energy are representative of\nchemical reactions such as isomerization between two structural conformations\nor dissociation of a molecule with an intermediate. We present a two degrees of\nfreedom quartic Hamiltonian that shows pitchfork bifurcation when the\nparameters are varied and we derive the bifurcation criteria relating the\nparameters. Next, we describe the phase space structures - unstable periodic\norbits and their associated invariant manifolds, and phase space dividing\nsurfaces - for the systems that can show trajectories undergo reaction defined\nas crossing of a potential energy barrier. Finally, we quantify the reaction\ndynamics for these systems by obtaining the directional flux and gap time\ndistribution to illustrate the dependence on total energy and the coupling\nstrength between the two degrees of freedom.\n', 'Phase Space Analysis of the Dynamics on a Potential Energy Surface with\n  an Entrance Channel and Two Potential Wells   In this paper we unveil the geometrical template of phase space structures\nthat governs transport in a Hamiltonian system described by a potential energy\nsurface with an entrance/exit channel and two wells separated by an index-1\nsaddle. For the analysis of the nonlinear dynamics mechanisms, we apply the\nmethod of Lagrangian descriptors, a trajectory-based scalar diagnostic tool\nthat is capable of providing a detailed phase space tomography of the interplay\nbetween the invariant manifolds of the system. Our analysis reveals that, the\nstable and unstable manifolds of two families of unstable periodic orbits\n(UPOs) that exist in the regions of the wells are responsible for controlling\nthe access to the wells of trajectories that enter the system through the\nchannel. In fact, we demonstrate that the heteroclinic and homoclinic\nconnections that arise in the system between the manifolds of the families of\nUPOs characterize the branching ratio, a relevant quantity used to measure\nproduct distributions in chemical reaction dynamics.\n', 'The Phase Space Mechanism for Selectivity in a Symmetric Potential\n  Energy Surface with a Post-Transition-State Bifurcation   Chemical selectivity is a phenomenon displayed by potential energy surfaces\n(PES) that is relevant for many organic chemical reactions whose PES feature a\nvalley-ridge inflection point (VRI) in the region between two sequential\nindex-1 saddles. In this letter we describe the underlying dynamical phase\nspace mechanism that qualitatively determines the product distributions\nresulting from bifurcating reaction pathways. We show that selectivity is a\nconsequence of the heteroclinic and homoclinic connections established between\nthe invariant manifolds of the families of unstable periodic orbits (UPOs)\npresent in the system. The geometry of the homoclinic and heteroclininc\nconnections is determined using the technique of Lagrangian descriptors, a\ntrajectory-based scalar technique with the capability of unveiling the\ngeometrical template of phase space structures that characterizes transport.\n']","[('saddle node bifurcation', 0.5299614071846008), ('bifurcations critical', 0.49661189317703247), ('manifolds unstable', 0.47217655181884766), ('bifurcations', 0.470759779214859), ('dimensional phase space', 0.46930021047592163), ('unstable manifolds', 0.46737584471702576), ('energy surfaces', 0.4445095658302307), ('phase space', 0.4424746334552765), ('bifurcation', 0.43292590975761414), ('stable unstable manifolds', 0.431957870721817)]"
888,888,34,888_path planning_trajectory planning_collision avoidance_planning autonomous,"['path planning', 'trajectory planning', 'collision avoidance', 'planning autonomous', 'motion planning', 'automated driving', 'autonomous driving', 'autonomous vehicles', 'autonomous vehicle', 'self driving']","[""Risk in Stochastic and Robust Model Predictive Path-Following Control\n  for Vehicular Motion Planning   In automated driving, risk describes potential harm to passengers of an\nautonomous vehicle (AV) and other road users. Recent studies suggest that\nhuman-like driving behavior emerges from embedding risk in AV motion planning\nalgorithms. Additionally, providing evidence that risk is minimized during the\nAV operation is essential to vehicle safety certification. However, there has\nyet to be a consensus on how to define and operationalize risk in motion\nplanning or how to bound or minimize it during operation. In this paper, we\ndefine a stochastic risk measure and introduce it as a constraint into both\nrobust and stochastic nonlinear model predictive path-following controllers\n(RMPC and SMPC respectively). We compare the vehicle's behavior arising from\nemploying SMPC and RMPC with respect to safety and path-following performance.\nFurther, the implementation of an automated driving example is provided,\nshowcasing the effects of different risk tolerances and uncertainty growths in\npredictions of other road users for both cases. We find that the RMPC is\nsignificantly more conservative than the SMPC, while also displaying greater\nfollowing errors towards references. Further, the RMPCs behavior cannot be\nconsidered as human-like. Moreover, unlike SMPC, the RMPC cannot account for\ndifferent risk tolerances. The RMPC generates undesired driving behavior for\neven moderate uncertainties, which are handled better by the SMPC.\n"", 'Real Time Motion Planning Using Constrained Iterative Linear Quadratic\n  Regulator for On-Road Self-Driving   Collision avoidance is one of the most challenging tasks people need to\nconsider for developing the self-driving technology. In this paper we propose a\nnew spatiotemporal motion planning algorithm that efficiently solves a\nconstrained nonlinear optimal control problem using the iterative linear\nquadratic regulator (iLQR), which takes into account the uncertain driving\nbehaviors of the traffic vehicles and minimizes the collision risks between the\nself-driving vehicle (referred to as the ""ego"" vehicle) and the traffic\nvehicles such that the ego vehicle is able to maintain sufficiently large\ndistances to all the surrounding vehicles for achieving the desired collision\navoidance maneuver in traffic. To this end, we introduce the concept of the\n""collision polygon"" for computing the minimum distances between the ego vehicle\nand the traffic vehicles, and provide two different solutions for designing the\nconstraints of the motion planning problem by properly modeling the behaviors\nof the traffic vehicles in order to evaluate the collision risk. Finally, the\niLQR motion planning algorithm is validated in multiple real-time tasks for\ncollision avoidance using both a simulator and a level-3 autonomous driving\ntest platform.\n', 'Informed sampling-based trajectory planner for automated driving in\n  dynamic urban environments   The urban environment is amongst the most difficult domains for autonomous\nvehicles. The vehicle must be able to plan a safe route on challenging road\nlayouts, in the presence of various dynamic traffic participants such as\nvehicles, cyclists and pedestrians and in various environmental conditions. The\nchallenge remains to have motion planners that are computationally fast and\nthat account for future movements of other road users proactively. This paper\ndescribes an computationally efficient sampling-based trajectory planner for\nsafe and comfortable driving in urban environments. The planner improves the\nStable-Sparse-RRT algorithm by adding initial exploration branches to the\nsearch tree based on road layout information and reiterating the previous\nsolution. Furthermore, the trajectory planner accounts for the predicted motion\nof other traffic participants to allow for safe driving in urban traffic.\nSimulation studies show that the planner is capable of planning collision-free,\ncomfortable trajectories in several urban traffic scenarios. Adding the\ndomain-knowledge-based exploration branches increases the efficiency of\nexploration of highly interesting areas, thereby increasing the overall\nplanning performance.\n']","[('path planning', 0.5693362951278687), ('trajectory planning', 0.5599337220191956), ('collision avoidance', 0.5590195059776306), ('planning autonomous', 0.5546849370002747), ('motion planning', 0.5472506880760193), ('automated driving', 0.537945568561554), ('autonomous driving', 0.5117189288139343), ('autonomous vehicles', 0.49704229831695557), ('autonomous vehicle', 0.4952934980392456), ('self driving', 0.48876115679740906)]"
889,889,34,889_catalan numbers_hankel determinants_hankel matrices_related catalan,"['catalan numbers', 'hankel determinants', 'hankel matrices', 'related catalan', 'palindromic polynomials', 'catalan', 'determinants', 'jacobi polynomials', 'catalan triangle', 'hankel transform']","['Some experimental observations about Hankel determinants of convolution\n  powers of Catalan numbers   Computer experiments suggest some conjectures about Hankel determinants of\nconvolution powers of Catalan numbers. Unfortunately, for most of them I have\nno proofs. I would like to present them anyway hoping that someone finds them\ninteresting and can prove them.\n', 'Shifted Hankel determinants of Catalan numbers and related results   In this (partly expository) paper we give a short overview about the close\nrelationship between the sequence of Catalan numbers and Hankel determinants\nfrom the point of view of orthogonal polynomials and show that an analogous\nsituation exists for more general sequences.\n', 'Shifted Hankel determinants of Catalan numbers and related results II:\n  Backward shifts   By prepending zeros to a given sequence Hankel determinants of backward\nshifts of this sequence become meaningful. We obtain some results for the\nsequences of Catalan numbers and of some numbers and polynomials which are\nrelated to Catalan numbers and propose conjectures for sequences of convolution\npowers of Catalan numbers.\n']","[('catalan numbers', 0.6287076473236084), ('hankel determinants', 0.5999965071678162), ('hankel matrices', 0.5086867809295654), ('related catalan', 0.4404076039791107), ('palindromic polynomials', 0.434555321931839), ('catalan', 0.4264959692955017), ('determinants', 0.40453067421913147), ('jacobi polynomials', 0.39811816811561584), ('catalan triangle', 0.38732877373695374), ('hankel transform', 0.3865903615951538)]"
890,890,34,890_instanton moduli space_instanton moduli_rank bundles_sheaves projective,"['instanton moduli space', 'instanton moduli', 'rank bundles', 'sheaves projective', 'bundles projective', 'bundles associated', 'bundles', 'bundles fano', 'sheaves', 'bundles mathbb']","['Instanton bundles on $\\mathbb{P}^1\\times\\mathbb{F}_1$   In this paper we deal with a particular class of rank two vector bundles\n(\\emph{instanton} bundles) on the Fano threefold of index one $F:=\\mathbb{F}_1\n\\times \\mathbb{P}^1$. We show that every instanton bundle on $F$ can be\ndescribed as the cohomology of a monad whose terms are free sheaves.\nFurthermore we prove the existence of instanton bundles for any admissible\nsecond Chern class and we construct a nice component of the moduli space where\nthey sit. Finally we show that minimal instanton bundles (i.e. with the least\npossible degree of the second Chern class) are aCM and we describe their moduli\nspace.\n', 'Instanton sheaves on Fano threefolds   Generalizing the definitions originally presented by Kuznetsov and Faenzi, we\nstudy (possibly non locally free) instanton sheaves of arbitrary rank on Fano\nthreefolds. We classify rank 1 instanton sheaves and describe all curves whose\nstructure sheaves are rank 0 instanton sheaves. In addition, we show that every\nrank 2 instanton sheaf is an elementary transformation of a locally free\ninstanton sheaf along a rank 0 instanton sheaf. To complete the paper, we\ndescribe the moduli space of rank 2 instanton sheaves of charge 2 on a quadric\nthreefold $X$, and show that the full moduli space of rank 2 semistable sheaves\non $X$ with Chern classes $(c_1,c_2,c_3)=(-1,2,0)$ is connected and contains,\nbesides the instanton component, just one other irreducible component which is\nalso fully described.\n', 'On rank 3 instanton bundles on $\\mathbb{P}^3$   We investigate rank $3$ instanton vector bundles on $\\mathbb{P}^3$ of charge\n$n$ and its correspondence with rational curves of degree $n+3$. For $n=2$ we\npresent a correspondence between stable rank $3$ instanton bundles and stable\nrank $2$ reflexive linear sheaves of Chern classes $(c_1,c_2,c_3)=(-1,3,3)$ and\nwe use this correspondence to compute the dimension of the family of stable\nrank $3$ instanton bundles of charge $2$. Finally, we use the results above to\nprove that the moduli space of rank $3$ instanton bundles on $\\mathbb{P}^3$ of\ncharge $2$ coincides with the moduli space of rank $3$ stable locally free\nsheaves on $\\mathbb{P}^3$ of Chern classes $(c_1,c_2,c_3)=(0,2,0)$. This moduli\nspace is irreducible, has dimension 16 and its generic point corresponds to a\n\\textcolor{black}{generalized} t`Hooft instanton bundle.\n']","[('instanton moduli space', 0.6673495173454285), ('instanton moduli', 0.5851829051971436), ('rank bundles', 0.5699608325958252), ('sheaves projective', 0.5675225257873535), ('bundles projective', 0.5489687919616699), ('bundles associated', 0.5480837821960449), ('bundles', 0.5365243554115295), ('bundles fano', 0.5264997482299805), ('sheaves', 0.5153892040252686), ('bundles mathbb', 0.5078590512275696)]"
891,891,34,891_aronszajn trees_trees moreover_tree exists_subtrees,"['aronszajn trees', 'trees moreover', 'tree exists', 'subtrees', 'tree every', 'kappa weakly compact', 'tree contains', 'subtree', 'inaccessible cardinal', 'tree can']","[""Can You Take Komjath's Inaccessible Away?   In this paper we aim to compare Kurepa trees and Aronszajn trees. Moreover,\nwe analyze the affect of large cardinal assumptions on this comparison. Using\nthe the method of walks on ordinals, we will show it is consistent with ZFC\nthat there is a Kurepa tree and every Kurepa tree contains an Aronszajn\nsubtree, if there is an inaccessible cardinal. This is stronger than Komjath's\ntheorem that asserts the same consistency from two inaccessible cardinals.\nMoreover, we prove it is consistent with ZFC that there is a Kurepa tree $T$\nsuch that if $U \\subset T$ is a Kurepa tree with the inherited order from $T$,\nthen $U$ has an Aronszajn subtree. This theorem uses no large cardinal\nassumption. Our last theorem immediately implies the following: assume\n$\\textrm{MA}_{\\omega_2}$ holds and $\\omega_2$ is not a Mahlo cardinal in\n$\\textsc{L}$. Then there is a Kurepa tree with the property that every Kurepa\nsubset has an Aronszajn subtree. Our work entails proving a new lemma about\nTodorcevic's $\\rho$ function which might be useful in other contexts.\n"", ""The vanishing levels of a tree   We initiate the study of the spectrum $Vspec(\\kappa)$ of sets that can be\nrealized as the vanishing levels $V(T)$ of a normal $\\kappa$-tree $T$. The\nlatter is an invariant in the sense that if $T$ and $T'$ are club-isomorphic,\nthen the symmetric difference of $V(T)$ and $V(T')$ is nonstationary.\nAdditional features of this invariant imply that $Vspec(\\kappa)$ is closed\nunder finite unions and intersections.\n  The set $V(T)$ must be stationary for an homogeneous normal\n$\\kappa$-Aronszajn tree $T$, and if there exists a special $\\kappa$-Aronszajn\ntree, then there exists one $T$ that is homogeneous and satisfies $V(T)=\\kappa$\n(modulo clubs). It is consistent (from large cardinals) that there is an\n$\\aleph_2$-Souslin tree, and yet $V(T)$ is co-stationary for every\n$\\aleph_2$-tree $\\mathbf T$. Both $V(T)=\\emptyset$ and $V(T)=\\kappa$ (modulo\nclubs) are shown to be feasible using $\\kappa$-Souslin trees even at some large\ncardinal close to a weakly compact. It is also possible to have a family of\n$2^\\kappa$ many $\\kappa$-Souslin trees for which the corresponding family of\nvanishing levels forms an antichain modulo clubs.\n"", 'Some Results on Finitely Splitting Subtrees of Aronszajn Trees   For any $2 \\le n < \\omega$, we introduce a forcing poset using generalized\npromises which adds a normal $n$-splitting subtree to a $(\\ge \\! n)$-splitting\nnormal Aronszajn tree. Using this forcing poset, we prove several consistency\nresults concerning finitely splitting subtrees of Aronszajn trees. For example,\nit is consistent that there exists an infinitely splitting Suslin tree whose\ntopological square is not Lindel\\""{o}f, which solves an open problem due to\nMarun. For any $2 < n < \\omega$, it is consistent that every $(\\ge \\!\nn)$-splitting normal Aronszajn tree contains a normal $n$-splitting subtree,\nbut there exists a normal infinitely splitting Aronszajn tree which contains no\n$(< \\! n)$-splitting subtree. To show the latter consistency result, we prove a\nforcing iteration preservation theorem related to not adding new\nsmall-splitting subtrees of Aronszajn trees.\n']","[('aronszajn trees', 0.6553260087966919), ('trees moreover', 0.5505425333976746), ('tree exists', 0.5324656367301941), ('subtrees', 0.5035410523414612), ('tree every', 0.48236069083213806), ('kappa weakly compact', 0.4802878797054291), ('tree contains', 0.4697209596633911), ('subtree', 0.4696800410747528), ('inaccessible cardinal', 0.46077337861061096), ('tree can', 0.45485925674438477)]"
892,892,34,892_foundations mathematics_reverse mathematics_countability_higher order arithmetic,"['foundations mathematics', 'reverse mathematics', 'countability', 'higher order arithmetic', 'computability theory', 'higher order', 'axioms', 'basic theorems', 'mathematics', 'theorems']","['Countable sets versus sets that are countable in Reverse Mathematics   The program Reverse Mathematics (RM for short) seeks to identify the axioms\nnecessary to prove theorems of ordinary mathematics, usually working in the\nlanguage of second-order arithmetic $L_{2}$. A major theme in RM is therefore\nthe study of structures that are countable or can be approximated by countable\nsets. Now, countable sets are represented by sequences here, because the usual\nhigher-order definition of `countable set\'cannot be expressed in $L_{2}$.\nWorking in Kohlenbach\'s higher-order RM, we investigate various central\ntheorems, e.g. those due to K\\""onig, Ramsey, Bolzano, Weierstrass, and Borel,\nin their (often original) formulation involving the usual definition(s) of\n`countable set\' instead of `sequence\'. This study turns out to be closely\nrelated to the logical properties of the uncountably of $\\mathbb{R}$, recently\ndeveloped by the author and Dag Normann. Now, `being countable\' can be\nexpressed by the existence of an injection to $\\mathbb{N}$ (Kunen) or the\nexistence of a bijection to $\\mathbb{N}$ (Hrbacek-Jech). The former (and not\nthe latter) choice yields `explosive\' theorems, i.e. relatively weak statements\nthat become much stronger when combined with discontinuous functionals, even up\nto $\\Pi_2^1$-CA$_0$. Nonetheless, replacing `sequence\' by `countable set\'\nseriously reduces the first-order strength of these theorems, whatever the\nnotion of `set\' used. Finally, we obtain `splittings\' involving e.g. lemmas by\nK\\""onig and theorems from the RM zoo, showing that the latter are `a lot more\ntame\' when formulated with countable sets.\n', ""Plato and the foundations of mathematics   Plato is well-known in mathematics for the eponymous foundational philosophy\nPlatonism based on ideal objects. Plato's allegory of the cave provides a\npowerful visual illustration of the idea that we only have access to shadows or\nreflections of these ideal objects. An inquisitive mind might then wonder what\nthe current foundations of mathematics, like e.g. Reverse Mathematics and the\nassociated Goedel hierarchy, are reflections of. In this paper, we identify a\nhierarchy in higher-order arithmetic that maps to the Big Five of Reverse\nMathematics under the canonical embedding of higher-order into second-order\narithmetic. Conceptually pleasing, the latter mapping replaces uncountable\nobjects by countable 'codes', i.e. the very practise of formalising mathematics\nin second-order arithmetic. This higher-order hierarchy can be defined in\nHilbert-Bernays' Grundlagen, the spiritual ancestor of second-order arithmetic,\nwhile the associated embedding preserves equivalences. Also, in contrast to\nKohlenbach's hierarchy based on discontinuity, our hierarchy can be formulated\nin terms of (classically valid) continuity axioms from Brouwer's intuitionistic\nmathematics. Moreover, the higher-order counterpart of sequences is provided by\nnets, aka Moore-Smith sequences, while the gauge integral is the correct\ngeneralisation of the Riemann integral. For all these reasons, we baptise our\nhigher-order hierarchy the Plato hierarchy.\n"", ""On two recent extensions of the Big Five of Reverse Mathematics   The program Reverse Mathematics in the foundations of mathematics seeks to\nidentify the minimal axioms required to prove theorems of ordinary mathematics.\nOne always assumes the base theory, a logical system embodying computable\nmathematics. As it turns out, many (most?) theorems are either provable in said\nbase theory, or equivalent to one of four logical systems, collectively called\nthe Big Five. This paper provides an overview of two recent extensions of the\nBig Five, working in Kohlenbach's higher-order framework. On one hand, we\nobtain a large number of equivalences between the second-order Big Five and\nthird-order theorems of real analysis dealing with possibly discontinuous\nfunctions. On the other hand, we identify four new 'Big' systems, i.e. boasting\nmany equivalences over the base theory, namely the uncountability of the reals,\nthe Jordan decomposition theorem, the Baire category theorem, and Tao's pigeon\nhole principle for the Lebesgue measure. We discuss a connection to\nhyperarithmetical analysis, completing the picture.\n""]","[('foundations mathematics', 0.5361623167991638), ('reverse mathematics', 0.49052417278289795), ('countability', 0.48355644941329956), ('higher order arithmetic', 0.46881240606307983), ('computability theory', 0.45148634910583496), ('higher order', 0.4313370883464813), ('axioms', 0.4250846803188324), ('basic theorems', 0.420266330242157), ('mathematics', 0.40783917903900146), ('theorems', 0.40530091524124146)]"
893,893,34,893_holomorphic self maps_holomorphic maps_semigroups_continuous semigroup,"['holomorphic self maps', 'holomorphic maps', 'semigroups', 'continuous semigroup', 'holomorphic dynamics', 'semigroups positive', 'semigroup', 'semigroups finite', 'one parameter semigroups', 'parameter semigroups']","['Asymptotic upper bound for tangential speed of parabolic semigroups of\n  holomorphic self-maps in the unit disc   We show that the tangential speed of a parabolic semigroup of holomorphic\nself-maps in the unit disc is asymptotically bounded from above by (1/2)logt,\nproving a conjecture by Bracci. In order to show the proof we need a result of\n""asymptotical monotonicity"" of the tangential speed for proper pairs of\nparabolic semigroups with positive hyperbolic step.\n', 'On the rates of convergence of orbits in semigroups of holomorphic\n  functions   Let $(\\phi_t)$ be a continuous semigroup of holomorphic self-maps of the unit\ndisk $\\mathbb{D}$ with Denjoy-Wolff point $\\tau\\in\\overline{\\mathbb{D}}$. We\nstudy the rate of convergence of the forward orbits of $(\\phi_t)$ to the\nDenjoy-Wolff point by finding explicit bounds for the quantity\n$|\\phi_t(z)-\\tau|$, $z\\in\\overline{\\mathbb{D}}$, $t > 0$. We further discuss\nthe corresponding rate of convergence for the backward orbits of $(\\phi_t)$.\n', 'On the monotonicity of the speeds for semigroups of holomorphic\n  self-maps of the unit disk   We study semigroups $(\\phi_t)_{t\\geq 0}$ of holomorphic self-maps of the unit\ndisk with Denjoy-Wolff point on the boundary. We show that the orthogonal speed\nof such semigroups is a strictly increasing function. This answers a question\nraised by F. Bracci, D. Cordella, and M. Kourou, and implies a domain\nmonotonicity property for orthogonal speeds conjectured by Bracci. We give an\nexample of a semigroup such that its total speed is not eventually increasing.\nWe also provide another example of a semigroup having total speed of a certain\nasymptotic behavior, thus answering another question of Bracci.\n']","[('holomorphic self maps', 0.579740583896637), ('holomorphic maps', 0.5045037865638733), ('semigroups', 0.5028523802757263), ('continuous semigroup', 0.5019875764846802), ('holomorphic dynamics', 0.500378429889679), ('semigroups positive', 0.4989820122718811), ('semigroup', 0.4977840185165405), ('semigroups finite', 0.47521135210990906), ('one parameter semigroups', 0.4706098139286041), ('parameter semigroups', 0.46696776151657104)]"
894,894,34,894_randomness_algorithmic randomness_probabilistic_notion probability,"['randomness', 'algorithmic randomness', 'probabilistic', 'notion probability', 'probability theory', 'theoretic probability', 'probabilities infinite', 'probabilistic numerics', 'kolmogorov', 'classical probability']","[""Revisiting the Sleeping Beauty problem   The Sleeping Beauty problem is a probability riddle with no definite solution\nfor more than two decades and its solution is of great interest in many fields\nof knowledge. There are two main competing solutions to the problem: the halfer\napproach, and the thirder approach. The main reason for disagreement in the\nliterature is connected to the use of different probability spaces to represent\nthe same probabilistic riddle. In this work, we analyse the problem from a\nmathematical perspective, identifying probability distributions induced\ndirectly from the thought experiment's rules. The precise choices of\nprobability spaces provide both halfer and thirder solutions to the problem. To\ntry and decide on which approach to follow, a criterion involving the\ninformation available to Sleeping Beauty is proposed.\n"", 'The Sleeping Beauty Problem -- A Real-World Solution   The Sleeping Beauty Problem remains a paradoxical problem that penetrates\nmultiple disciplines that include probability theory, self-locating belief,\ndecision theory, cognitive science, the philosophy of mathematics and science.\nIt asks the credence of Sleeping Beauty on a coin toss being Heads in the\nexperiment that incites two main stances, that of the Halfers and Thirders.\nHere a real-world empirical approach numerically highlights breakdown between\nthese groups and considers the role of how a real-world application of such an\nexperiment with sleep induction by anesthesia and pharmacological amnesia\ninduction would affect the coin credence probability of Sleeping Beauty.\n', ""Stunned by Sleeping Beauty: How Prince Probability updates his forecast\n  upon their fateful encounter   The Sleeping Beauty problem is a puzzle in probability theory that has gained\nmuch attention since Elga's discussion of it [Elga, Adam, Analysis 60 (2),\np.143-147 (2000)]. Sleeping Beauty is put asleep, and a coin is tossed. If the\noutcome of the coin toss is Tails, Sleeping Beauty is woken up on Monday, put\nasleep again and woken up again on Tuesday (with no recollection of having\nwoken up on Monday). If the outcome is Heads, Sleeping Beauty is woken up on\nMonday only. Each time Sleeping Beauty is woken up, she is asked what her\nbelief is that the outcome was Heads. What should Sleeping Beauty reply? In\nliterature arguments have been given for both 1/3 and 1/2 as the correct\nanswer. In this short note we argue using simple Bayesian probability theory\nwhy 1/3 is the right answer, and not 1/2. Briefly, when Sleeping Beauty\nawakens, her being awake is nontrivial extra information that leads her to\nupdate her beliefs about Heads to 1/3. We strengthen our claim by considering\nan additional observer, Prince Probability, who may or may not meet Sleeping\nBeauty. If he meets Sleeping Beauty while she is awake, he lowers his credence\nin Heads to 1/3. We also briefly consider the credence in Heads of a Sleeping\nBeauty who knows that she is dreaming (and thus asleep).\n""]","[('randomness', 0.6261655688285828), ('algorithmic randomness', 0.6256295442581177), ('probabilistic', 0.5864083766937256), ('notion probability', 0.5617156028747559), ('probability theory', 0.550623893737793), ('theoretic probability', 0.5331303477287292), ('probabilities infinite', 0.4846588373184204), ('probabilistic numerics', 0.478938490152359), ('kolmogorov', 0.47314420342445374), ('classical probability', 0.45989370346069336)]"
895,895,34,895_insulin_glucose_diabetes_biophysical models,"['insulin', 'glucose', 'diabetes', 'biophysical models', 'metabolic', 'diabetic', 'metabolism', 'physiology', 'mathematical models', 'modelling']","['Low-Order Nonlinear Animal Model of Glucose Dynamics for a Bihormonal\n  Intraperitoneal Artificial Pancreas   Objective: The design of an Artificial Pancreas (AP) to regulate blood\nglucose levels requires reliable control methods. Model Predictive Control has\nemerged as a promising approach for glycemia control. However, model--based\ncontrol methods require computationally simple and identifiable mathematical\nmodels that represent glucose dynamics accurately, which is challenging due to\nthe complexity of glucose homeostasis. Methods: In this work, a simple model is\ndeduced to estimate blood glucose concentration in subjects with Type 1\nDiabetes Mellitus (T1DM). Novel features in the model are power--law kinetics\nfor intraperitoneal insulin absorption and a separate glucagon sensitivity\nstate. Profile likelihood and a method based on singular value decomposition of\nthe sensitivity matrix are carried out to assess parameter identifiability and\nguide a model reduction for improving the identification of parameters.\nResults: A reduced model with 10 parameters is obtained and calibrated, showing\ngood fit to experimental data from pigs where insulin and glucagon boluses were\ndelivered in the intraperitoneal cavity. Conclusion: A simple model with\npower--law kinetics can accurately represent glucose dynamics submitted to\nintraperitoneal insulin and glucagon injections. The reduced model was found to\nexhibit local practical as well as structural identifiability. Importance: The\nproposed model facilitates intraperitoneal bi-hormonal model-based closed-loop\ncontrol in animal trials.\n', ""Exploring Analytical Methods for Glucose-Sensitive Membranes in\n  Closed-Loop Insulin Delivery Using Akbar Ganji's Approach   The research explores a novel mathematical model for closed loop insulin\ndelivery systems, featuring a glucose sensitive membrane. It employs a\nsophisticated framework of nonlinear reaction diffusion equations and enzyme\nkinetics. Central to the study is the development of analytical solutions for\nthe glucose, gluconic acid, and oxygen concentrations, which are meticulously\nvalidated against simulation outcomes. This validation underscores the model's\naccuracy in capturing the complex dynamics inherent in such systems.\nAdditionally, the study leverages Akbar and Ganji's methodology to provide\napproximate solutions, enabling a comprehensive comparison with analytical\nresults and offering deeper insights into the system's behavior under varying\nparameters. By integrating both analytical and approximate approaches, the\nresearch not only enhances our understanding of biochemical processes but also\nlays the groundwork for refining closed-loop insulin delivery technology. The\nfindings promise to significantly improve the precision and efficacy of insulin\nadministration, crucial for managing glucose levels in diabetic patients more\neffectively. Furthermore, the study's implications extend beyond insulin\ndelivery, potentially informing the development of advanced biomedical systems\nwhere precise control and understanding of biochemical interactions are\nparamount. Ultimately, this work represents a significant contribution to both\ntheoretical biochemistry and practical medical applications, setting a\nfoundation for the next generation of closed-loop insulin delivery systems\ndesigned to better meet the complex metabolic needs of patients with diabetes.\n"", 'Sounding the metabolic orchestra: A delay dynamical systems perspective\n  on the glucose-insulin regulatory response to on-off glucose infusion   We investigate the consequences of periodic, on-off glucose infusion on the\nglucose-insulin regulatory system on the basis of a system-level mathematical\nmodel with two explicit time delays. Studying the effects of such infusion\nprotocols is mathematically challenging yet a promising direction for probing\nthe system response to infusion. We pay special attention to the interplay of\nthe infusion with intermediate-time-scale, ultradian oscillations that arise as\na results of the physiological response of glucose uptake and back-release into\nthe bloodstream. By using numerical solvers and numerical continuation\nsoftware, we investigate the response of the model to different infusion\npatterns, and explore how these patterns affect the overall levels of glucose\nand insulin, and can lead to entrainment. By doing so, we provide a road-map of\nsystem responses that can potentially help identify new test strategies for\ndetecting abnormal responses to glucose uptake.\n']","[('insulin', 0.5061264038085938), ('glucose', 0.46433985233306885), ('diabetes', 0.4513552784919739), ('biophysical models', 0.38627326488494873), ('metabolic', 0.3596697151660919), ('diabetic', 0.333356112241745), ('metabolism', 0.3049367070198059), ('physiology', 0.2980891466140747), ('mathematical models', 0.2900749742984772), ('modelling', 0.2878566086292267)]"
896,896,34,896_alternating sign matrices_alternating sign matrix_symmetric alternating_sign matrices,"['alternating sign matrices', 'alternating sign matrix', 'symmetric alternating', 'sign matrices', 'alternating sign', 'sign matrix', 'symmetric plane partitions', 'permutation matrices', 'number alternating', 'alternating']","['Characterizing Alternating Sign Triangles   Alternating sign triangles were introduced by Carroll and Speyer in relation\nto cube recurrence, by analogy to alternating sign matrices for octahedron\nrecurrence. Permutation triangles are the alternating sign triangles whose\nentries are either 0 or 1, by analogy with permutation matrices. In this paper,\nwe prove a simple characterization of permutation triangles, originally\nconjectured by Glick. We will also prove some properties of alternating sign\ntriangles.\n', 'Connectivity of Alternating Sign Triangle   Alternating sign triangles were introduced by Carroll and Speyer in relation\nto cube recurrence, by analogy to alternating sign matrices for octahedron\nrecurrence. In this paper, we prove the connectivity of alternating sign\ntriangles, which is analogous to the connectivity of alternating sign matrices.\n', 'Alternating Sign Pentagons and Magog Pentagons   Alternating sign triangles have been introduced by Ayyer, Behrend and Fischer\nin 2016 and it was proven that there is the same number of alternating sign\ntriangles with $n$ rows as there is of $n\\times n$ alternating sign matrices.\nLater on Fischer gave a refined enumeration of alternating sign triangles with\nrespect to a statistic $\\rho$, having the same distribution as the unique 1 in\nthe top row of an alternating sign matrix, by connecting alternating sign\ntriangles to $(0,n,n)$- Magog trapezoids. We introduce two more statistics\ncounting the all $0$-columns on the left and right in an alternating sign\ntriangle yielding objects we call alternating sign pentagons. We then show the\nequinumeracy of these alternating sign pentagons with Magog pentagons of a\ncertain shape taking into account the statistic $\\rho$. Furthermore we deduce a\ngenerating function of these alternating sign pentagons with respect to the\nstatistic $\\rho$ in terms of a Pfaffian and consider the implications of our\nnew results on some open conjectures.\n']","[('alternating sign matrices', 0.6642016172409058), ('alternating sign matrix', 0.6121138334274292), ('symmetric alternating', 0.559561014175415), ('sign matrices', 0.5014104247093201), ('alternating sign', 0.46553632616996765), ('sign matrix', 0.4550458788871765), ('symmetric plane partitions', 0.43390756845474243), ('permutation matrices', 0.42178231477737427), ('number alternating', 0.4165905714035034), ('alternating', 0.41340553760528564)]"
897,897,34,897_submodular optimization_submodular maximization_maximizing submodular_submodular functions,"['submodular optimization', 'submodular maximization', 'maximizing submodular', 'submodular functions', 'monotone submodular', 'submodularity', 'discrete optimization', 'submodular', 'supermodular functions', 'approximation algorithms']","['Randomized Algorithms for Monotone Submodular Function Maximization on\n  the Integer Lattice   Optimization problems with set submodular objective functions have many\nreal-world applications. In discrete scenarios, where the same item can be\nselected more than once, the domain is generalized from a 2-element set to a\nbounded integer lattice. In this work, we consider the problem of maximizing a\nmonotone submodular function on the bounded integer lattice subject to a\ncardinality constraint. In particular, we focus on maximizing DR-submodular\nfunctions, i.e., functions defined on the integer lattice that exhibit the\ndiminishing returns property. Given any epsilon > 0, we present a randomized\nalgorithm with probabilistic guarantees of O(1 - 1/e - epsilon) approximation,\nusing a framework inspired by a Stochastic Greedy algorithm developed for set\nsubmodular functions by Mirzasoleiman et al. We then show that, on synthetic\nDR-submodular functions, applying our proposed algorithm on the integer lattice\nis faster than the alternatives, including reducing a target problem to the set\ndomain and then applying the fastest known set submodular maximization\nalgorithm.\n', 'Concave Aspects of Submodular Functions   Submodular Functions are a special class of set functions, which generalize\nseveral information-theoretic quantities such as entropy and mutual information\n[1]. Submodular functions have subgradients and subdifferentials [2] and admit\npolynomial-time algorithms for minimization, both of which are fundamental\ncharacteristics of convex functions. Submodular functions also show signs\nsimilar to concavity. Submodular function maximization, though NP-hard, admits\nconstant-factor approximation guarantees, and concave functions composed with\nmodular functions are submodular. In this paper, we try to provide a more\ncomplete picture of the relationship between submodularity with concavity. We\ncharacterize the super-differentials and polyhedra associated with upper bounds\nand provide optimality conditions for submodular maximization using the-super\ndifferentials. This paper is a concise and shorter version of our longer\npreprint [3].\n', 'An Exact Cutting Plane Method for $k$-submodular Function Maximization   A natural and important generalization of submodularity -- $k$-submodularity\n-- applies to set functions with $k$ arguments and appears in a broad range of\napplications, such as infrastructure design, machine learning, and healthcare.\nIn this paper, we study maximization problems with $k$-submodular objective\nfunctions. We propose valid linear inequalities, namely the $k$-submodular\ninequalities, for the hypograph of any $k$-submodular function. This class of\ninequalities serves as a novel generalization of the well-known submodular\ninequalities. We show that maximizing a $k$-submodular function is equivalent\nto solving a mixed-integer linear program with exponentially many\n$k$-submodular inequalities. Using this representation in a delayed constraint\ngeneration framework, we design the first exact algorithm, that is not a\ncomplete enumeration method, to solve general $k$-submodular maximization\nproblems. Our computational experiments on the multi-type sensor placement\nproblems demonstrate the efficiency of our algorithm in constrained nonlinear\n$k$-submodular maximization problems for which no alternative compact\nmixed-integer linear formulations are available. The computational experiments\nshow that our algorithm significantly outperforms the only available exact\nsolution method -- exhaustive search. Problems that would require over 13 years\nto solve by exhaustive search can be solved within ten minutes using our\nmethod.\n']","[('submodular optimization', 0.7185033559799194), ('submodular maximization', 0.7114943265914917), ('maximizing submodular', 0.6689215302467346), ('submodular functions', 0.6183157563209534), ('monotone submodular', 0.5562781095504761), ('submodularity', 0.5442473888397217), ('discrete optimization', 0.5391342639923096), ('submodular', 0.5129538178443909), ('supermodular functions', 0.4894269108772278), ('approximation algorithms', 0.4465199410915375)]"
898,898,34,898_bin packing_packing problems_packing_bins,"['bin packing', 'packing problems', 'packing', 'bins', 'knapsack', 'number bins', 'integer linear programming', 'bin', 'integer programming', 'obtains optimal']","['Basic Analysis of Bin-Packing Heuristics   The bin-packing problem continues to remain relevant in numerous application\nareas. This technical report discusses the empirical performance of different\nbin-packing heuristics for certain test problems.\n', 'Open-end bin packing: new and old analysis approaches   We analyze a recently introduced concept, called the price of clustering, for\nvariants of bin packing called open-end bin packing problems (OEBP). Input\nitems have sizes, and they also belong to a certain number of types. The new\nconcept deals with the comparison of optimal solutions for the cases where\nitems of distinct types can and cannot be packed together, respectively. The\nproblem is related to greedy bin packing algorithms and to batched bin packing,\nand we discuss some of those concepts as well. We analyze max-OEBP, where a\npacked bin is valid if by excluding its largest item, the total size of items\nis below 1. For this variant, we study the case of general item sizes, and the\nparametric case with bounded item sizes, which shows the effect of small items.\nFinally, we briefly discuss min-OEBP, where a bin is valid if the total size of\nits items excluding the smallest item is below 1, which is known to be an\nentirely different problem.\n', 'Several methods of analysis for cardinality constrained bin packing   We consider a known variant of bin packing called {\\it cardinality\nconstrained bin packing}, also called {\\it bin packing with cardinality\nconstraints} (BPCC). In this problem, there is a parameter k\\geq 2, and items\nof rational sizes in [0,1] are to be packed into bins, such that no bin has\nmore than k items or total size larger than 1. The goal is to minimize the\nnumber of bins.\n  A recently introduced concept, called the price of clustering, deals with\ninputs that are presented in a way that they are split into clusters. Thus, an\nitem has two attributes which are its size and its cluster. The goal is to\nmeasure the relation between an optimal solution that cannot combine items of\ndifferent clusters into bins, and an optimal solution that can combine items of\ndifferent clusters arbitrarily. Usually the number of clusters may be large,\nwhile clusters are relatively small, though not trivially small. Such problems\nare related to greedy bin packing algorithms, and to batched bin packing, which\nis similar to the price of clustering, but there is a constant number of large\nclusters. We analyze the price of clustering for BPCC, including the parametric\ncase with bounded item sizes. We discuss several greedy algorithms for this\nproblem that were not studied in the past, and comment on batched bin packing.\n']","[('bin packing', 0.76375812292099), ('packing problems', 0.5924785733222961), ('packing', 0.5643397569656372), ('bins', 0.5490677356719971), ('knapsack', 0.5390535593032837), ('number bins', 0.5143036842346191), ('integer linear programming', 0.4968491196632385), ('bin', 0.47305768728256226), ('integer programming', 0.46769073605537415), ('obtains optimal', 0.4220038056373596)]"
899,899,34,899_boundary mean curvature_curvature equations_curvature conformal_conformal curvature,"['boundary mean curvature', 'curvature equations', 'curvature conformal', 'conformal curvature', 'prescribed scalar curvature', 'conformal laplacian', 'minimal boundary', 'curvatures', 'curvature metrics', 'constant curvature metrics']","['The Nirenberg problem on high dimensional half spheres: The effect of\n  pinching conditions   In this paper we study the Nirenberg problem on standard half spheres\n$(\\mathbb{S}^n_+,g), \\, n \\geq 5$, which consists of finding conformal metrics\nof prescribed scalar curvature and zero boundary mean curvature on the\nboundary. This problem amounts to solve the following boundary value problem\ninvolving the critical Sobolev exponent: \\begin{equation*} (\\mathcal{P}) \\quad\n\\begin{cases}\n  -\\D_{g} u \\, + \\, \\frac{n(n-2)}{4} u \\, = K \\, u^{\\frac{n+2}{n-2}},\\, u > 0 &\n\\mbox{in } \\mathbb{S}^n_+,\n  \\frac{\\partial u}{\\partial \\nu }\\, =\\, 0 & \\mbox{on } \\partial\n\\mathbb{S}^n_+. \\end{cases} \\end{equation*} where $K \\in C^3(\\mathbb{S}^n_+)$\nis a positive function.\n  This problem has a variational structure but the related Euler-Lagrange\nfunctional $J_K$ lacks compactness. Indeed it admits \\emph{critical points at\ninfinity}, which are \\emph{limits} of non compact orbits of the (negative)\ngradient flow. Through the construction of an appropriate \\emph{pseudogradient}\nin the \\emph{neighborhood at infinity}, we characterize these \\emph{critical\npoints at infinity}, associate to them an index, perform a \\emph{Morse type\nreduction} of the functional $J_K$ in their neighborhood and compute their\ncontribution to the difference of topology between the level sets of $J_K$,\nhence extending the full Morse theoretical approach to this \\emph{non compact\nvariational problem}. Such an approach is used to prove, under various pinching\nconditions, some existence results for $(\\mathcal{P})$ on half spheres of\ndimension $n \\geq 5$.\n', 'Non simple blow ups for the Nirenberg problem on half spheres   In this paper we study a Nirenberg type problem on standard half spheres\n$(\\mathbb{S}^n_+,g_0)$ consisting of finding conformal metrics of prescribed\nscalar curvature and zero boundary mean curvature on the boundary $\\partial\n\\mathbb{S}^n_+$. This problem amounts to solve the following boundary value\nproblem involving the critical Sobolev exponent: \\begin{equation*}\n(\\mathcal{P}) \\quad \\begin{cases}\n  -\\D_{g_0} u \\, + \\, \\frac{n(n-2)}{4} u \\, = K \\, u^{\\frac{n+2}{n-2}},\\, u > 0\n& \\mbox{in } \\mathbb{S}^n_+,\n  \\frac{\\partial u}{\\partial \\nu }\\, =\\, 0 & \\mbox{on } \\partial\n\\mathbb{S}^n_+. \\end{cases} \\end{equation*} where $K \\in C^2(\\mathbb{S}^n_+)$\nis a positive function.\n  We construct, under generic conditions on the function $K$, finite energy\nsolutions of a subcritical approximation of $(\\mathcal{P})$ on half spheres of\ndimension $n \\geq 5$, which exhibit multiple blow up of \\emph{cluster-type} at\nthe same boundary point. These solutions may have zero or non zero weak limit\nand may develop clusters at different boundary points. Such blow up phenomena\non half spheres drastically contrast with the case of the Nirenberg problem on\nspheres, where non simple blow up for finite energy subsolutions cannot occur\nand unveils an unexpected connection with vortex type problems arising in Euler\nequations in fluid dynamic and mean fields type equations in mathematical\nphysics.\n  We construct also, under suitable conditions on the restriction of $K$ on\n$\\partial \\mathbb{S}^n_+$, approximate solutions of arbitrarily large energy\nand Morse index\n', 'The Boundary Yamabe Problem, I: Minimal Boundary Case   We apply iteration schemes and perturbation methods to provide a complete\nsolution of the boundary Yamabe problem with minimal boundary scenario, or\nequivalently, the existence of a real, positive, smooth solution of $\n-\\frac{4(n -1)}{n - 2} \\Delta_{g} u + S_{g} u = \\lambda u^{\\frac{n+2}{n - 2}} $\nin $ M $, $ \\frac{\\partial u}{\\partial \\nu} + \\frac{n-2}{2} h_{g} u = 0 $ on $\n\\partial M $. Thus $ g $ is conformal to to the metric $ \\tilde{g} =\nu^{\\frac{4}{n -2}} g $ of constant scalar curvature $ \\lambda $ with minimal\nboundary. In contrast to the classical method of calculus of variations with\nassumptions on Weyl tensors and classification of types of points on $ \\partial\nM $, the boundary Yamabe problem is fully solved here in three cases classified\nby the sign of the first eigenvalue $ \\eta_{1} $ of the conformal Laplacian\nwith Robin condition. When $ \\eta_{1} < 0 $, a pair of global sub-solution and\nsuper-solution are constructed. When $ \\eta_{1} > 0 $, a perturbed boundary\nYamabe equation $ -\\frac{4(n -1)}{n - 2} \\Delta_{g} u_{\\beta} + \\left( S_{g} +\n\\beta \\right) u_{\\beta} = \\lambda_{\\beta} u_{\\beta}^{\\frac{n+2}{n - 2}} $ in $\nM $, $ \\frac{\\partial u_{\\beta}}{\\partial \\nu} + \\frac{n-2}{2} h_{g} u_{\\beta}\n= 0 $ on $ \\partial M $ is solved with $ \\beta < 0 $. The boundary Yamabe\nequation is then solved by taking $ \\beta \\rightarrow 0^{-} $. The signs of\nscalar curvature $ S_{g} $ and mean curvature $ h_{g} $ play important roles in\nthis existence result.\n']","[('boundary mean curvature', 0.5485285520553589), ('curvature equations', 0.5251739621162415), ('curvature conformal', 0.4792121946811676), ('conformal curvature', 0.4673365354537964), ('prescribed scalar curvature', 0.4619094729423523), ('conformal laplacian', 0.45255616307258606), ('minimal boundary', 0.43875402212142944), ('curvatures', 0.4382284879684448), ('curvature metrics', 0.43411439657211304), ('constant curvature metrics', 0.428213506937027)]"
900,900,34,900_polyhedral products_simplicial complexes_polyhedral product_associated simplicial complex,"['polyhedral products', 'simplicial complexes', 'polyhedral product', 'associated simplicial complex', 'simplicial complex', 'products spheres', 'product spheres', 'dimensional simplicial', 'polyhedral', 'properties polyhedral']","[""Connected sums of sphere products and minimally non-Golod complexes   We show that if the moment-angle complex $\\mathcal{Z}_K$ associated to a\nsimplicial complex $K$ is homotopy equivalent to a connected sum of sphere\nproducts with two spheres in each product, then $K$ decomposes as the\nsimplicial join of an $n$-simplex $\\Delta^n$ and a minimally non-Golod complex.\nIn particular, we prove that $K$ is minimally non-Golod for every moment-angle\ncomplex $\\mathcal{Z}_K$ homeomorphic to a connected sum of two-fold products of\nspheres, answering a question of Grbi\\'c, Panov, Theriault and Wu.\n"", 'The Goodwillie calculus of polyhedral products   We describe the Goodwillie calculus of polyhedral products in the case that\nthe fat wedge filtration on the associated real moment-angle complex is\ntrivial. We do this by analysing the behaviour on calculus of the Denham-Suciu\nfibre sequence, the Iriye-Kishimoto decomposition of the polyhedral product\nconstructed from a collection of pairs of cones and their bases, and the\nHilton-Milnor decomposition. As a corollary we show that the Goodwillie\ncalculus of these polyhedral products converges integrally and diverges in\n$v_h$-periodic homotopy unless the simplicial complex is a full simplex.\n', 'A unifying view toward polyhedral products through panel structures   A panel structure on a topological space is just a locally finite family of\nclosed subspaces. A space together with a panel structure is called a space\nwith faces. In this paper, we introduce a notion of polyhedral product over a\nspace with faces. This notion provides a unifying viewpoint on the\nconstructions of polyhedral products and generalized moment-angle complexes in\nvarious settings. We compute the stable decomposition of these spaces and use\nit to study their cohomology ring structures. Moreover, we can compute the\nequivariant cohomology ring of the moment-angle complex over a space with faces\nwith respect to the canonical torus action. The calculation leads to the notion\nof topological face ring of a space with faces, which generalizes the classical\nnotion of face ring (Stanley-Reisner ring) of a simplicial complex. We will see\nthat many known results in the study of polyhedral products and moment-angle\ncomplexes can be reinterpreted from our general theorems on the polyhedral\nproduct over a space with faces. Moreover, we can derive some new results via\nour approach in some settings.\n']","[('polyhedral products', 0.6044881343841553), ('simplicial complexes', 0.5793372988700867), ('polyhedral product', 0.5674896836280823), ('associated simplicial complex', 0.548419177532196), ('simplicial complex', 0.5464993715286255), ('products spheres', 0.5004393458366394), ('product spheres', 0.4883785843849182), ('dimensional simplicial', 0.4827151596546173), ('polyhedral', 0.45661863684654236), ('properties polyhedral', 0.45448487997055054)]"
901,901,34,901_local discontinuous galerkin_discontinuous galerkin_convection diffusion problems_discontinuous galerkin ldg,"['local discontinuous galerkin', 'discontinuous galerkin', 'convection diffusion problems', 'discontinuous galerkin ldg', 'convection diffusion equations', 'finite element methods', 'galerkin finite', 'convection diffusion', 'galerkin finite element', 'singular perturbation parameter']","['The local discontinuous Galerkin method for a singularly perturbed\n  convection-diffusion problem with characteristic and exponential layers   A singularly perturbed convection-diffusion problem,posed on the unit square\nin $\\mathbb{R}^2$, is studied; its solution has both exponential and\ncharacteristic boundary layers. The problem is solved numerically using the\nlocal discontinuous Galerkin (LDG) method on Shishkin meshes. Using\ntensor-product piecewise polynomials of degree at most $k>0$ in each variable,\nthe error between the LDG solution and the true solution is proved to converge,\nuniformly in the singular perturbation parameter, at a rate of $O((N^{-1}\\ln\nN)^{k+1/2})$ in an associated energy norm, where $N$ is the number of mesh\nintervals in each coordinate direction.(This is the first uniform convergence\nresult proved for the LDG method applied to a problem with characteristic\nboundary layers.) Furthermore, we prove that this order of convergence\nincreases to $O((N^{-1}\\ln N)^{k+1})$ when one measures the energy-norm\ndifference between the LDG solution and a local Gauss-Radau projection of the\ntrue solution into the finite element space.This uniform supercloseness\nproperty implies an optimal $L^2$ error estimate of order $(N^{-1}\\ln N)^{k+1}$\nfor our LDG method. Numerical experiments show the sharpness of our theoretical\nresults.\n', 'Supercloseness of the local discontinuous Galerkin method for a\n  singularly perturbed convection-diffusion problem   A singularly perturbed convection-diffusion problem posed on the unit square\nin $\\mathbb{R}^2$, whose solution has exponential boundary layers, is solved\nnumerically using the local discontinuous Galerkin (LDG) method with piecewise\npolynomials of degree at most $k>0$ on three families of layer-adapted meshes:\nShishkin-type, Bakhvalov-Shishkin-type and Bakhvalov-type.On Shishkin-type\nmeshes this method is known to be no greater than $O(N^{-(k+1/2)})$ accurate in\nthe energy norm induced by the bilinear form of the weak formulation, where $N$\nmesh intervals are used in each coordinate direction. (Note: all bounds in this\nabstract are uniform in the singular perturbation parameter and neglect\nlogarithmic factors that will appear in our detailed analysis.) A delicate\nargument is used in this paper to establish $O(N^{-(k+1)})$ energy-norm\nsuperconvergence on all three types of mesh for the difference between the LDG\nsolution and a local Gauss-Radau projection of the exact solution into the\nfinite element space. This supercloseness property implies a new $N^{-(k+1)}$\nbound for the $L^2$ error between the LDG solution on each type of mesh and the\nexact solution of the problem; this bound is optimal (up to logarithmic\nfactors). Numerical experiments confirm our theoretical results.\n', 'Supercloseness of the LDG method for a two-dimensional singularly\n  perturbed convection-diffusion problem on Bakhvalov-type mesh   In this paper, we focus on analyzing the supercloseness property of a\ntwo-dimensional singularly perturbed convection-diffusion problem with\nexponential boundary layers. The local discontinuous Galerkin (LDG) method with\npiecewise tensor-product polynomials of degree k is applied to Bakhvalov-type\nmesh. By developing special two-dimensional local Gauss-Radau projections and\nestablishing a novel interpolation, supercloseness of an optimal order k+1 can\nbe achieved on Bakhvalov-type mesh. It is crucial to highlight that this\nsupercloseness result is independent of the singular perturbation parameter.\n']","[('local discontinuous galerkin', 0.5476335287094116), ('discontinuous galerkin', 0.5454573035240173), ('convection diffusion problems', 0.5075286626815796), ('discontinuous galerkin ldg', 0.5054238438606262), ('convection diffusion equations', 0.4735681414604187), ('finite element methods', 0.45769307017326355), ('galerkin finite', 0.4430774450302124), ('convection diffusion', 0.4422050714492798), ('galerkin finite element', 0.4346274435520172), ('singular perturbation parameter', 0.4302905797958374)]"
902,902,34,902_processing unit gpu_gpu implementation_gpu accelerated_processing units gpus,"['processing unit gpu', 'gpu implementation', 'gpu accelerated', 'processing units gpus', 'gpu acceleration', 'cpu gpu', 'gpu', 'gpus', 'unit gpu', 'single gpu']","[""Automated Translation and Accelerated Solving of Differential Equations\n  on Multiple GPU Platforms   We demonstrate a high-performance vendor-agnostic method for massively\nparallel solving of ensembles of ordinary differential equations (ODEs) and\nstochastic differential equations (SDEs) on GPUs. The method is integrated with\na widely used differential equation solver library in a high-level language\n(Julia's DifferentialEquations.jl) and enables GPU acceleration without\nrequiring code changes by the user. Our approach achieves state-of-the-art\nperformance compared to hand-optimized CUDA-C++ kernels while performing\n20--100$\\times$ faster than the vectorizing map (vmap) approach implemented in\nJAX and PyTorch. Performance evaluation on NVIDIA, AMD, Intel, and Apple GPUs\ndemonstrates performance portability and vendor-agnosticism. We show\ncomposability with MPI to enable distributed multi-GPU workflows. The\nimplemented solvers are fully featured -- supporting event handling, automatic\ndifferentiation, and incorporation of datasets via the GPU's texture memory --\nallowing scientists to take advantage of GPU acceleration on all major current\narchitectures without changing their model code and without loss of\nperformance. We distribute the software as an open-source library\nhttps://github.com/SciML/DiffEqGPU.jl\n"", 'Multiple-GPU accelerated high-order gas-kinetic scheme for direct\n  numerical simulation of compressible turbulence   High-order gas-kinetic scheme (HGKS) has become a workable tool for the\ndirect numerical simulation (DNS) of turbulence. In this paper, to accelerate\nthe computation, HGKS is implemented with the graphical processing unit (GPU)\nusing the compute unified device architecture (CUDA). To conduct the much\nlarge-scale DNS of turbulence, HGKS also be further upgraded with multiple GPUs\nusing message passing interface (MPI) and CUDA architecture. The benchmark\ncases for compressible turbulence, including Taylor-Green vortex and turbulent\nchannel flows, are presented to assess the numerical performance of HGKS with\nNvidia TITAN RTX and Tesla V100 GPUs. For single-GPU computation, compared with\nthe parallel central processing unit (CPU) code running on the Intel Core\ni7-9700 with open multi-processing (OpenMP) directives, 7x speedup is achieved\nby TITAN RTX and 16x speedup is achieved by Tesla V100. For multiple-GPU\ncomputation, the computational time of parallel CPU code running on 1024 Intel\nXeon E5-2692 cores with MPI is approximately 3 times longer than that of GPU\ncode using 8 Tesla V100 GPUs with MPI and CUDA. Numerical results confirm the\nexcellent performance of multiple-GPU accelerated HGKS for large-scale DNS of\nturbulence. HGKS in GPU is also compiled with FP32 precision to evaluate the\neffect of number formats precision. Reasonably, compared to the computation\nwith FP64 precision, the efficiency is improved and the memory cost is reduced\nwith FP32 precision. For turbulent channel flows, difference in long-time\nstatistical turbulent quantities is acceptable between FP32 and FP64 precision\nsolutions. While the obvious discrepancy in instantaneous turbulent quantities\ncan be observed, which shows that FP32 precision is not safe for DNS in\ncompressible turbulence. The choice of precision should depended on the\nrequirement of accuracy and the available computational resources.\n', 'Multiple-GPU accelerated high-order gas-kinetic scheme on\n  three-dimensional unstructured meshes   Recently, successes have been achieved for the high-order gas-kinetic schemes\n(HGKS) on unstructured meshes for compressible flows. In this paper, to\naccelerate the computation, HGKS is implemented with the graphical processing\nunit (GPU) using the compute unified device architecture (CUDA). HGKS on\nunstructured meshes is a fully explicit scheme, and the acceleration framework\ncan be developed based on the cell-level parallelism. For single-GPU\ncomputation, the connectivity of geometric information is generated for the\nrequirement of data localization and independence. Based on such data\nstructure, the kernels and corresponding girds of CUDA are set. With the\none-to-one mapping between the indices of cells and CUDA threads, the\nsingle-GPU computation using CUDA can be implemented for HGKS. For multiple-GPU\ncomputation, the domain decomposition and data exchange need to be taken into\naccount. The domain is decomposed into subdomains by METIS, and the MPI\nprocesses are created for the control of each process and communication among\nGPUs. With reconstruction of connectivity and adding ghost cells, the main\nconfiguration of CUDA for single-GPU can be inherited by each GPU. The\nbenchmark cases for compressible flows, including accuracy test and flow\npassing through a sphere, are presented to assess the numerical performance of\nHGKS with Nvidia RTX A5000 and Tesla V100 GPUs. For single-GPU computation,\ncompared with the parallel central processing unit (CPU) code running on the\nIntel Xeon Gold 5120 CPU with open multi-processing (OpenMP) directives, 5x\nspeedup is achieved by RTX A5000 and 9x speedup is achieved by Tesla V100. For\nmultiple-GPU computation, HGKS code scales properly with the increasing number\nof GPU. Numerical results confirm the excellent performance of multiple-GPU\naccelerated HGKS on unstructured meshes.\n']","[('processing unit gpu', 0.6541945338249207), ('gpu implementation', 0.6372808218002319), ('gpu accelerated', 0.6323930621147156), ('processing units gpus', 0.6095854043960571), ('gpu acceleration', 0.5778697729110718), ('cpu gpu', 0.5773550868034363), ('gpu', 0.5620568990707397), ('gpus', 0.5471682548522949), ('unit gpu', 0.5315873622894287), ('single gpu', 0.5141654014587402)]"
903,903,34,903_nonlinear parabolic problems_global existence solutions_fully nonlinear parabolic_degenerate parabolic equations,"['nonlinear parabolic problems', 'global existence solutions', 'fully nonlinear parabolic', 'degenerate parabolic equations', 'nonlinear parabolic equations', 'nonlocal boundary condition', 'global time solutions', 'nonlinear parabolic', 'existence global time', 'existence solutions']","[""Smoothing effects and infinite time blowup for reaction-diffusion\n  equations: an approach via Sobolev and Poincar\\'e inequalities   We consider reaction-diffusion equations either posed on Riemannian manifolds\nor in the Euclidean weighted setting, with pow\\-er-type nonlinearity and slow\ndiffusion of porous medium time. We consider the particularly delicate case\n$p<m$ in problem (1.1), a case largely left open in [21] even when the initial\ndatum is smooth and compactly supported. We prove global existence for L$^m$\ndata, and a smoothing effect for the evolution, i.e. that solutions\ncorresponding to such data are bounded at all positive times with a\nquantitative bound on their L$^\\infty$ norm. As a consequence of this fact and\nof a result of [21], it follows that on Cartan-Hadamard manifolds with\ncurvature pinched between two strictly negative constants, solutions\ncorresponding to sufficiently large L$^m$ data give rise to solutions that blow\nup pointwise everywhere in infinite time, a fact that has no Euclidean\nanalogue. The methods of proof of the smoothing effect are functional analytic\nin character, as they depend solely on the validity of the Sobolev inequality\nand on the fact that the L$^2$ spectrum of $\\Delta$ on $M$ is bounded away from\nzero (namely on the validity of a Poincar\\'{e} inequality on $M$). As such,\nthey are applicable to different situations, among which we single out the case\nof (mass) weighted reaction-diffusion equation in the Euclidean setting. In\nthis latter setting, a modification of the methods of [37] allows to deal also,\nwith stronger results for large times, with the case of globally integrable\nweights.\n"", 'Global existence of solutions of initial-boundary value problem for\n  nonlocal parabolic equation with nonlocal boundary condition   We prove global existence and blow-up of solutions of initial-boundary value\nproblem for nonlinear nonlocal parabolic equation with nonlinear nonlocal\nboundary condition. Obtained results depend on the behavior of variable\ncoefficients for large values of time.\n', ""Global existence of solutions and smoothing effects for classes of\n  reaction-diffusion equations on manifolds   We consider the porous medium equation with a power-like reaction term, posed\non Riemannian manifolds. Under certain assumptions on $p$ and $m$ in (1.1), and\nfor small enough nonnegative initial data, we prove existence of global in time\nsolutions, provided that the Sobolev inequality holds on the manifold.\nFurthermore, when both the Sobolev and the Poincar\\'e inequality hold, similar\nresults hold under weaker assumptions on the forcing term. By the same\nfunctional analytic methods, we investigate global existence for solutions to\nthe porous medium equation with source term and variable density in ${\\mathbb\nR}^n$.\n""]","[('nonlinear parabolic problems', 0.6172946691513062), ('global existence solutions', 0.599277913570404), ('fully nonlinear parabolic', 0.5718051791191101), ('degenerate parabolic equations', 0.5675862431526184), ('nonlinear parabolic equations', 0.548007607460022), ('nonlocal boundary condition', 0.5462245345115662), ('global time solutions', 0.5339525938034058), ('nonlinear parabolic', 0.5339465737342834), ('existence global time', 0.5222745537757874), ('existence solutions', 0.5154241919517517)]"
904,904,34,904_vlasov poisson equations_vlasov poisson system_vlasov poisson_discontinuous galerkin,"['vlasov poisson equations', 'vlasov poisson system', 'vlasov poisson', 'discontinuous galerkin', 'particle methods', 'poisson equations', 'maxwell equations', 'dimensional vlasov', 'time discretizations', 'discretization']","['Energy conserving particle-in-cell methods for relativistic\n  Vlasov--Maxwell equations of laser-plasma interaction   Energy conserving particle-in-cell schemes are constructed for a class of\nreduced relativistic Vlasov--Maxwell equations of laser-plasma interaction.\nDiscrete Poisson equation is also satisfied by the numerical solution.\nSpecifically, distribution function is discretized using particle-in-cell\nmethod, discretization of electromagnetic fields is done using compatible\nfinite element method in the framework of finite element of exterior calculus,\nand time discretization used is based on discrete gradient method combined with\nPoisson splitting. Numerical experiments of parametric instability are done to\nvalidate the conservation properties and good long time behavior of the\nnumerical methods constructed.\n', 'Geometric particle-in-cell methods for Vlasov--Poisson equations with\n  Maxwell--Boltzmann electrons   In this paper, variational and Hamiltonian formulations of the\nVlasov--Poisson equations with Maxwell--Boltzmann electrons are introduced.\nStructure-preserving particle-in-cell methods are constructed by discretizing\nthe action integral and the Poisson bracket. We use the Hamiltonian splitting\nmethods and the discrete gradient methods for time discretizations to preserve\nthe geometric structure and energy, respectively. The global neutrality\ncondition is also conserved by the discretizations. The schemes are asymptotic\npreserving when taking the quasi-neutral limit, and the limiting schemes are\nstructure-preserving for the limiting model. Numerical experiments of finite\ngrid instability, Landau damping, and two-stream instability illustrate the\nbehavior of the proposed numerical methods.\n', ""Energy-conserving time propagation for a geometric particle-in-cell\n  Vlasov--Maxwell solver   This paper discusses energy-conserving time-discretizations for finite\nelement particle-in-cell discretizations of the Vlasov--Maxwell system. A\ngeometric spatially discrete system can be obtained using a standard\nparticle-in-cell discretization of the particle distribution and compatible\nfinite element spaces for the fields to discretize the Poisson bracket of the\nVlasov--Maxwell model (see Kraus et al., J Plasma Phys 83, 2017). In this\npaper, we derive energy-conserving time-discretizations based on the discrete\ngradient method applied to an antisymmetric splitting of the Poisson matrix.\nFirstly, we propose a semi-implicit method based on the average-vector-field\ndiscretization of the subsystems. Moreover, we devise an alternative discrete\ngradient that yields a time discretization that can additionally conserve\nGauss' law. Finally, we explain how substepping for fast species dynamics can\nbe incorporated.\n""]","[('vlasov poisson equations', 0.6499069333076477), ('vlasov poisson system', 0.616165280342102), ('vlasov poisson', 0.5115662217140198), ('discontinuous galerkin', 0.4342817962169647), ('particle methods', 0.43308863043785095), ('poisson equations', 0.41559940576553345), ('maxwell equations', 0.39828094840049744), ('dimensional vlasov', 0.3899233341217041), ('time discretizations', 0.38916438817977905), ('discretization', 0.36677777767181396)]"
905,905,33,905_quandles_quandle_invariants knots_quivers,"['quandles', 'quandle', 'invariants knots', 'quivers', 'quiver', 'link invariants', 'knot theory', 'knots links', 'virtual knots links', 'virtual knots']","['Quandle Coloring Quivers of (p, 2)-Torus Links   A quandle coloring quiver is a quiver structure, introduced by Karina Cho and\nSam Nelson, which is defined on the set of quandle colorings of an oriented\nknot or link by a finite quandle. We study quandle coloring quivers of (p,\n2)-torus knots and links with respect to dihedral quandles.\n', ""Quandle coloring quivers of links using dihedral quandles   K. Cho and S. Nelson introduced the notion of a quandle coloring quiver,\nwhich is a quiver-valued link invariant, and a quandle cocycle quiver which is\nan enhancement of the quandle coloring quiver by assigning to each vertex a\nweight computed using a quandle 2-cocycle. In this paper, we study quandle\ncoloring quivers using dihedral quandles and introduce the notions of a shadow\nquandle coloring quiver and a shadow quandle cocycle quiver, which are shadow\nversions of the quandle coloring quiver and the quandle cocycle quiver. We show\nthat, when we use a dihedral quandle of prime order, the quandle coloring\nquivers are equivalent to the quandle coloring numbers and when we use a\ndihedral quandle of prime order and Mochizuki's 3-cocycle, the shadow quandle\ncocycle quivers are equivalent to the shadow quandle cocycle invariants.\n"", 'Quandle Action Quivers   Quandle Coloring Quivers are directed graph-valued invariants of classical\nand virtual knots and links associated to finite quandles. Quandle action\nquivers are subquivers of the full quandle coloring quiver associated to\nquandle actions by elements of the coloring quandle. These quivers provide a\ncategorification of the quandle counting invariant associated to each element\nof the quandle. We obtain new polynomial invariants called quandle action\npolynomials from these quivers as decategorifications.\n']","[('quandles', 0.5714480876922607), ('quandle', 0.5554916262626648), ('invariants knots', 0.5332043766975403), ('quivers', 0.5324035882949829), ('quiver', 0.5041159987449646), ('link invariants', 0.4882783591747284), ('knot theory', 0.4747709035873413), ('knots links', 0.46231982111930847), ('virtual knots links', 0.4561510384082794), ('virtual knots', 0.42354828119277954)]"
906,906,33,906_frieze patterns_triangular lattices_polygons_tilings,"['frieze patterns', 'triangular lattices', 'polygons', 'tilings', 'triangulations', 'lattices', 'patterns', 'polygon', 'numbers edges', 'conway']","['Periodic Infinite Frieze Patterns of Type $\\Lambda_{p_1,\\ldots,p_n}$ and\n  Dissections on Annuli   Finite frieze patterns with entries in\n$\\mathbb{Z}[\\lambda_{p_1},\\ldots,\\lambda_{p_s}]$ where $\\{p_1,\\ldots,p_s\\}\n\\subseteq \\mathbb{Z}_{\\geq 3}$ and $\\lambda_p = 2 \\cos(\\pi/p)$ were shown to\nhave a connection to dissected polygons by Holm and Jorgensen. We extend their\nwork by studying the connection between infinite frieze patterns with such\nentries and dissections of annuli and once-punctured discs. We give an\nalgorithm to determine whether a frieze pattern with entries in\n$\\mathbb{Z}[\\lambda_{p_1},\\ldots,\\lambda_{p_s}]$, finite or infinite, comes\nfrom a dissected surface. We introduce quotient dissections as a realization\nfor some frieze patterns unrealizable by an ordinary dissection. We also\nintroduce two combinatorial interpretations for entries of frieze patterns from\ndissected surfaces. These interpretations are a generalization of matchings\nintroduced by Broline, Crowe, and Isaacs for finite frieze patterns over\n$\\mathbb{Z}$.\n', ""Frieze patterns with coefficients   Frieze patterns, as introduced by Coxeter in the 1970's, are closely related\nto cluster algebras without coefficients. A suitable generalization of frieze\npatterns, linked to cluster algebras with coefficients, has only briefly\nappeared in an unpublished manuscript by Propp. In this paper we study these\nfrieze patterns with coefficients systematically and prove various fundamental\nresults, generalizing classic results for frieze patterns. As a consequence we\nsee how frieze patterns with coefficients can be obtained from classic frieze\npatterns by cutting out subpolygons from the triangulated polygons associated\nto classic Conway-Coxeter frieze patterns. We address the question of which\nfrieze patterns with coefficients can be obtained in this way and solve this\nproblem completely for triangles. Finally, we prove a finiteness result for\nfrieze patterns with coefficients by showing that for a given boundary sequence\nthere are only finitely many (non-zero) frieze patterns with coefficients with\nentries in a discrete subset of the complex numbers.\n"", 'Frieze patterns over algebraic numbers   Conway and Coxeter have shown that frieze patterns over positive rational\nintegers are in bijection with triangulations of polygons. An investigation of\nfrieze patterns over other subsets of the complex numbers has recently been\ninitiated by Jorgensen and the first two authors. In this paper we first show\nthat a ring of algebraic numbers has finitely many units if and only if it is\nan order in a quadratic number field $\\mathbb{Q}(\\sqrt{d})$ where $d<0$. We\nconclude that these are exactly the rings of algebraic numbers over which there\nare finitely many non-zero frieze patterns for any given height. We then show\nthat apart from the cases $d\\in \\{-1,-2,-3,-7,-11\\}$ all non-zero frieze\npatterns over the rings of integers $\\mathcal{O}_d$ for $d<0$ have only\nintegral entries and hence are known as (twisted) Conway-Coxeter frieze\npatterns.\n']","[('frieze patterns', 0.6128072738647461), ('triangular lattices', 0.5068049430847168), ('polygons', 0.4665350019931793), ('tilings', 0.42154043912887573), ('triangulations', 0.4187176525592804), ('lattices', 0.4095604419708252), ('patterns', 0.39759698510169983), ('polygon', 0.39027830958366394), ('numbers edges', 0.3753938674926758), ('conway', 0.3711947202682495)]"
907,907,33,907_hardy rellich inequalities_hardy type inequalities_hardy type inequality_hardy inequalities,"['hardy rellich inequalities', 'hardy type inequalities', 'hardy type inequality', 'hardy inequalities', 'hardy inequality', 'rellich type inequalities', 'rellich inequalities', 'type inequality', 'discrete hardy', 'inequalities improved']","['On the improvements of Hardy and Copson inequalities   In this current work, we revisit the recent improvement of the discrete\nHardy\'s inequality in one dimension and establish an extended improved discrete\nHardy\'s inequality with its optimality. We also study one-dimensional discrete\nCopson\'s inequality (E.T. Copson, \\emph{Notes on a series of positive terms},\nJ. London Math. Soc., 2 (1927), 9-12.), and achieve an improvement of the same\nin a particular case. Further, we study some fundamental structures such as\ncompleteness, K\\""{o}the-Toeplitz duality, separability, etc. of the sequence\nspaces which originated from the improved discrete Hardy and Copson\ninequalities in one dimension.\n', ""On improvements of the Hardy, Copson and Rellich inequalities   Using a method of factorization and by introducing a generalized discrete\nDirichlet's Laplacian matrix $(-\\Delta_{\\Lambda})$, we establish an extended\nimproved discrete Hardy's inequality and Rellich inequality in one dimension.\nWe prove that the discrete Copson inequality (E.T. Copson, \\emph{Notes on a\nseries of positive terms}, J. London Math. Soc., 2 (1927), 9-12.) in\none-dimension admits an improvement. We also prove that the improved Copson's\nweights are optimal (in fact \\emph{critical}). It is shown that improvement of\nthe Knopp inequalities (Knopp in J. London Math. Soc. 3(1928), 205-211 and\n5(1930), 13-21) lies on improvement of the Rellich inequalities. Further, an\nimprovement of the generalized Hardy's inequality (Hardy in Messanger of Math.\n54(1925), 150-156) in a special case is obtained.\n"", 'Factorizations and Power Weighted Rellich and Hardy--Rellich-Type\n  Inequalities   We revisit and extend a variety of inequalities related to power weighted\nRellich and Hardy--Rellich inequalities, including an inequality due to\nSchmincke.\n']","[('hardy rellich inequalities', 0.8043079972267151), ('hardy type inequalities', 0.750302791595459), ('hardy type inequality', 0.7464979887008667), ('hardy inequalities', 0.737982451915741), ('hardy inequality', 0.698349118232727), ('rellich type inequalities', 0.6719292998313904), ('rellich inequalities', 0.6548618078231812), ('type inequality', 0.5692332983016968), ('discrete hardy', 0.5683411359786987), ('inequalities improved', 0.5401384234428406)]"
908,908,33,908_quadratic forms fields_quadratic forms field_quadratic forms also_quadratic forms,"['quadratic forms fields', 'quadratic forms field', 'quadratic forms also', 'quadratic forms', 'degenerate quadratic form', 'forms galois', 'bilinear forms', 'symmetric bilinear forms', 'forms characteristic', 'algebraic fields']","['Failure of the local-global principle for isotropy of quadratic forms\n  over function fields   We prove the failure of the local-global principle, with respect to discrete\nvaluations, for isotropy of quadratic forms over function fields of\ntranscendence degree at least 2 over algebraically closed fields. Our\nconstruction involves generalized Kummer varieties as well as a new\nnontriviality result for the unramified cohomology of products of elliptic\ncurves over discretely valued fields, which can be viewed as an arithmetic\nversion of a theorem of Gabber.\n', 'Linkage of Pfister forms over semi-global fields   We study linkage of $(d+1)$-fold quadratic Pfister forms over function fields\nin one variable over a henselian valued field of 2-cohomological dimension $d$.\nSpecifically, we characterise this property in terms of linkage of quadratic\nPfister forms over function fields over the residue field of the henselian\nvalued field; in full generality in characteristic different from 2, and for\nmost complete discretely valued fields in characteristic 2. As an application,\nwe obtain a proof that $(d+2)$-fold quadratic Pfister forms over function\nfields in one variable over a $d$-dimensional higher local field are linked.\n', 'Isotropy of quadratic forms over function fields in characteristic 2   We extend to characteristic two recent results about isotropy of quadratic\nforms over function fields. In particular, we provide a characterization of\nfunction fields not only of quadratic forms but also more generally of\npolynomials in several variables, over which a quadratic form becomes\nisotropic. As an application of these results, we obtain criteria for stable\nbirational equivalence of quadratic forms.\n']","[('quadratic forms fields', 0.7382510304450989), ('quadratic forms field', 0.6971456408500671), ('quadratic forms also', 0.6463741660118103), ('quadratic forms', 0.6144465804100037), ('degenerate quadratic form', 0.5729473829269409), ('forms galois', 0.5437169671058655), ('bilinear forms', 0.5351822972297668), ('symmetric bilinear forms', 0.5326343178749084), ('forms characteristic', 0.5111690759658813), ('algebraic fields', 0.506232738494873)]"
909,909,33,909_visibility graphs_graphs visibility_visibility graph_visibility,"['visibility graphs', 'graphs visibility', 'visibility graph', 'visibility', 'visible', 'graph invariants', 'graph subseteq', 'graphs', 'product graphs', 'two complete graphs']","['Mutual-visibility in strong products of graphs via total\n  mutual-visibility   Let $G$ be a graph and $X\\subseteq V(G)$. Then $X$ is a mutual-visibility set\nif each pair of vertices from $X$ is connected by a geodesic with no internal\nvertex in $X$. The mutual-visibility number $\\mu(G)$ of $G$ is the cardinality\nof a largest mutual-visibility set. In this paper, the mutual-visibility number\nof strong product graphs is investigated. As a tool for this, total\nmutual-visibility sets are introduced. Along the way, basic properties of such\nsets are presented. The (total) mutual-visibility number of strong products is\nbounded from below in two ways, and determined exactly for strong grids of\narbitrary dimension. Strong prisms are studied separately and a couple of tight\nbounds for their mutual-visibility number are given.\n', 'Visibility polynomials, dual visibility spectrum, and characterization\n  of total mutual-visibility sets   Mutual-visibility sets were motivated by visibility in distributed systems\nand social networks, and intertwine with several classical mathematical areas.\nMonotone properties of the variety of mutual-visibility sets, and restrictions\nof such sets to convex and isometric subgraphs are studied. Dual\nmutual-visibility sets are shown to be intrinsically different from other types\nof mutual-visibility sets. It is proved that for every finite subset $Z$ of\npositive integers there exists a graph $G$ that has a dual mutual-visibility\nset of size $i$ if and only if $i\\in Z\\cup \\{0\\}$, while for the other types of\nmutual-visibility such a set consists of consecutive integers. Visibility\npolynomials are introduced and their properties derived. As a surprise, every\npolynomial with nonnegative integer coefficients and with a constant term $1$\nis a dual visibility polynomial of some graph. Characterizations are given for\ntotal mutual-visibility sets, for graphs with total mutual-visibility number\n$1$, and for sets which are not total mutual-visibility sets, yet every proper\nsubset is such. Along the way an earlier result from the literature is\ncorrected.\n', 'Mutual Visibility in Graphs   Let $G=(V,E)$ be a graph and $P\\subseteq V$ a set of points. Two points are\nmutually visible if there is a shortest path between them without further\npoints. $P$ is a mutual-visibility set if its points are pairwise mutually\nvisible. The mutual-visibility number of $G$ is the size of any largest\nmutual-visibility set. In this paper we start the study about this new\ninvariant and the mutual-visibility sets in undirected graphs. We introduce the\nmutual-visibility problem which asks to find a mutual-visibility set with a\nsize larger than a given number. We show that this problem is NP-complete,\nwhereas, to check whether a given set of points is a mutual-visibility set is\nsolvable in polynomial time. Then we study mutual-visibility sets and\nmutual-visibility numbers on special classes of graphs, such as block graphs,\ntrees, grids, tori, complete bipartite graphs, cographs. We also provide some\nrelations of the mutual-visibility number of a graph with other invariants.\n']","[('visibility graphs', 0.7276226282119751), ('graphs visibility', 0.7055065631866455), ('visibility graph', 0.6947465538978577), ('visibility', 0.5187392234802246), ('visible', 0.4409797489643097), ('graph invariants', 0.4360645115375519), ('graph subseteq', 0.40528222918510437), ('graphs', 0.39500147104263306), ('product graphs', 0.3929908275604248), ('two complete graphs', 0.39217230677604675)]"
910,910,33,910_critical besov spaces_critical besov space_posedness strong solutions_besov space b_,"['critical besov spaces', 'critical besov space', 'posedness strong solutions', 'besov space b_', 'equations besov', 'besov spaces', 'besov space', 'besov spaces s_', 'initial besov', 'critical besov']","['Ill-posedness for the Cauchy problem of the modified Camassa-Holm\n  equation in $B^0_{\\infty,1}$   In this paper, we prove the norm inflation and get the ill-posedness for the\nmodified Camassa-Holm equation in $B_{\\infty,1}^0$. Therefore we completed all\nwell-posedness and ill-posedness problem for the modified Camassa-Holm equation\nin all critical spaces $B_{p,1}^\\frac{1}{p}$ with $p\\in[1,\\infty]$.\n', 'Sharp ill-posedness for the generalized Camassa-Holm equation in Besov\n  spaces   In this paper, we consider the Cauchy problem for the generalized\nCamassa-Holm equation that includes the Camassa-Holm as well as the Novikov\nequation on the line. We present a new and unified method to prove the sharp\nill-posedness for the generalized Camassa-Holm equation in $B^s_{p,\\infty}$\nwith $s>\\max\\{1+1/p, 3/2\\}$ and $1\\leq p\\leq\\infty$ in the sense that the\nsolution map to this equation starting from $u_0$ is discontinuous at $t = 0$\nin the metric of $B^s_{p,\\infty}$. Our results cover and improve the previous\nwork given in [J. Li, Y. Yu, W. Zhu, Ill-posedness for the Camassa-Holm and\nrelated equations in Besov spaces, J. Differential Equations, 306 (2022),\n403--417], solving an open problem left in [J. Li, Y. Yu, W. Zhu, Ill-posedness\nfor the Camassa-Holm and related equations in Besov spaces, J. Differential\nEquations, 306 (2022), 403--417].\n', 'Zero-filter limit issue for the Camassa-Holm equation in Besov spaces   In this paper, we focus on zero-filter limit problem for the Camassa-Holm\nequation in the more general Besov spaces. We prove that the solution of the\nCamassa-Holm equation converges strongly in $L^\\infty(0,T;B^s_{2,r}(\\R))$ to\nthe inviscid Burgers equation as the filter parameter $\\alpha$ tends to zero\nwith the given initial data $u_0\\in B^s_{2,r}(\\R)$. Moreover, we also show that\nthe zero-filter limit for the Camassa-Holm equation does not converges\nuniformly with respect to the initial data in $B^s_{2,r}(\\R)$.\n']","[('critical besov spaces', 0.5621662139892578), ('critical besov space', 0.5549679398536682), ('posedness strong solutions', 0.5539819598197937), ('besov space b_', 0.5319323539733887), ('equations besov', 0.5288012623786926), ('besov spaces', 0.5258694291114807), ('besov space', 0.5190336108207703), ('besov spaces s_', 0.4917283356189728), ('initial besov', 0.4635828733444214), ('critical besov', 0.45395511388778687)]"
911,911,33,911_satisfiability threshold_satisfiability_sat instances_random constraint satisfaction,"['satisfiability threshold', 'satisfiability', 'sat instances', 'random constraint satisfaction', 'satisfiable', 'sat formulas', 'sat sat', 'unsatisfiable', 'random constraint', 'sat']","['Polarised random k-SAT   In this paper we study a variation of the random $k$-SAT problem, called\npolarized random $k$-SAT. In this model there is a polarization parameter $p$,\nand in half of the clauses each variable occurs negated with probability $p$\nand pure otherwise, while in the other half the probabilities are interchanged.\nFor $p=1/2$ we get the classical random $k$-SAT model, and at the other extreme\nwe have the fully polarized model where $p=0$, or $1$. Here there are only two\ntypes of clauses: clauses where all $k$ variables occur pure, and clauses where\nall $k$ variables occur negated. That is, for $p=0$ we get an instance of\nrandom monotone $k$-SAT. We show that the threshold of satisfiability does not\ndecrease as $p$ moves away from $\\frac{1}{2}$ and thus that the satisfiability\nthreshold for polarized random $k$-SAT is an upper bound on the threshold for\nrandom $k$-SAT. In fact, we conjecture that asymptotically the two thresholds\ncoincide.\n', 'On the Regularity of Random 2-SAT and 3-SAT   We consider the random $k$-SAT problem with $n$ variables, $m=m(n)$ clauses,\nand clause density $\\alpha=\\lim_{n\\to\\infty}m/n$ for $k=2,3$. It is known that\nif $\\alpha$ is small enough, then the random $k$-SAT problem admits a solution\nwith high probability, which we interpret as the problem being\nunder-constrained. In this paper, we quantify exactly how under-constrained the\nrandom $k$-SAT problems are by determining their degrees of freedom, which we\ndefine as the threshold for the number of variables we can fix to an arbitrary\nvalue before the problem no longer is solvable with high probability. We show\nthat the random $2$-SAT and $3$-SAT problems have $n/m^{1/2}$ and $n/m^{1/3}$\ndegrees of freedom, respectively. Our main result is an explicit computation of\nthe corresponding threshold functions. Our result shows that the threshold\nfunction for the random $2$-SAT problem is regular, while it is non-regular for\nthe random $3$-SAT problem. By regular, we mean continuous and analytic on the\ninterior of its support. This result shows that the random $3$-SAT problem is\nmore sensitive to small changes in the clause density $\\alpha$ than the random\n$2$-SAT problem.\n', 'A Model of Random Industrial SAT   One of the most studied models of SAT is random SAT. In this model, instances\nare composed from clauses chosen uniformly randomly and independently of each\nother. This model may be unsatisfactory in that it fails to describe various\nfeatures of SAT instances, arising in real-world applications. Various\nmodifications have been suggested to define models of industrial SAT. Here, we\nfocus mainly on the aspect of community structure. Namely, here the set of\nvariables consists of a number of disjoint communities, and clauses tend to\nconsist of variables from the same community. Thus, we suggest a model of\nrandom industrial SAT, in which the central generalization with respect to\nrandom SAT is the additional community structure.\n  There has been a lot of work on the satisfiability threshold of random\n$k$-SAT, starting with the calculation of the threshold of $2$-SAT, up to the\nrecent result that the threshold exists for sufficiently large $k$.\n  In this paper, we endeavor to study the satisfiability threshold for the\nproposed model of random industrial SAT. Our main result is that the threshold\nin this model tends to be smaller than its counterpart for random SAT.\nMoreover, under some conditions, this threshold even vanishes.\n']","[('satisfiability threshold', 0.6441949009895325), ('satisfiability', 0.5492592453956604), ('sat instances', 0.5394642949104309), ('random constraint satisfaction', 0.5259527564048767), ('satisfiable', 0.5016604065895081), ('sat formulas', 0.4609568417072296), ('sat sat', 0.4554253816604614), ('unsatisfiable', 0.455414742231369), ('random constraint', 0.4431002736091614), ('sat', 0.4232189357280731)]"
912,912,33,912_fast fourier transforms_sparse fourier_fast fourier transform_fast fourier,"['fast fourier transforms', 'sparse fourier', 'fast fourier transform', 'fast fourier', 'dimensional periodic functions', 'fourier basis functions', 'fourier samples', 'functions wavelets', 'fourier basis', 'transform high dimensional']","['Fast and interpretable Support Vector Classification based on the\n  truncated ANOVA decomposition   Support Vector Machines (SVMs) are an important tool for performing\nclassification on scattered data, where one usually has to deal with many data\npoints in high-dimensional spaces. We propose solving SVMs in primal form using\nfeature maps based on trigonometric functions or wavelets. In small dimensional\nsettings the Fast Fourier Transform (FFT) and related methods are a powerful\ntool in order to deal with the considered basis functions. For growing\ndimensions the classical FFT-based methods become inefficient due to the curse\nof dimensionality. Therefore, we restrict ourselves to multivariate basis\nfunctions, each of which only depends on a small number of dimensions. This is\nmotivated by the well-known sparsity of effects and recent results regarding\nthe reconstruction of functions from scattered data in terms of truncated\nanalysis of variance (ANOVA) decompositions, which makes the resulting model\neven interpretable in terms of importance of the features as well as their\ncouplings. The usage of small superposition dimensions has the consequence that\nthe computational effort no longer grows exponentially but only polynomially\nwith respect to the dimension. In order to enforce sparsity regarding the basis\ncoefficients, we use the frequently applied $\\ell_2$-norm and, in addition,\n$\\ell_1$-norm regularization. The found classifying function, which is the\nlinear combination of basis functions, and its variance can then be analyzed in\nterms of the classical ANOVA decomposition of functions. Based on numerical\nexamples we show that we are able to recover the signum of a function that\nperfectly fits our model assumptions. Furthermore, we perform classification on\ndifferent artificial and real-world data sets. We obtain better results with\n$\\ell_1$-norm regularization, both in terms of accuracy and clarity of\ninterpretability.\n', 'Grouped Transformations and Regularization in High-Dimensional\n  Explainable ANOVA Approximation   In this paper we propose a tool for high-dimensional approximation based on\ntrigonometric polynomials where we allow only low-dimensional interactions of\nvariables. In a general high-dimensional setting, it is already possible to\ndeal with special sampling sets such as sparse grids or rank-1 lattices. This\nrequires black-box access to the function, i.e., the ability to evaluate it at\nany point. Here, we focus on scattered data points and grouped frequency index\nsets along the dimensions. From there we propose a fast matrix-vector\nmultiplication, the grouped Fourier transform, for high-dimensional grouped\nindex sets. Those transformations can be used in the application of the\npreviously introduced method of approximating functions with low superposition\ndimension based on the analysis of variance (ANOVA) decomposition where there\nis a one-to-one correspondence from the ANOVA terms to our proposed groups. The\nmethod is able to dynamically detected important sets of ANOVA terms in the\napproximation. In this paper, we consider the involved least-squares problem\nand add different forms of regularization: Classical Tikhonov-regularization,\nnamely, regularized least squares and the technique of group lasso, which\npromotes sparsity in the groups. As for the latter, there are no explicit\nsolution formulas which is why we applied the fast iterative\nshrinking-thresholding algorithm to obtain the minimizer. Moreover, we discuss\nthe possibility of incorporating smoothness information into the least-squares\nproblem. Numerical experiments in under-, overdetermined, and noisy settings\nindicate the applicability of our algorithms. While we consider periodic\nfunctions, the idea can be directly generalized to non-periodic functions as\nwell.\n', 'A Deterministic Algorithm for Constructing Multiple Rank-1 Lattices of\n  Near-Optimal Size   In this paper we present the first known deterministic algorithm for the\nconstruction of multiple rank-1 lattices for the approximation of periodic\nfunctions of many variables. The algorithm works by converting a potentially\nlarge reconstructing single rank-1 lattice for some $ d $-dimensional frequency\nset $ I \\subset [N]^d $ into a collection of much smaller rank-1 lattices which\nallow for accurate and efficient reconstruction of trigonometric polynomials\nwith coefficients in $ I $ (and, therefore, for the approximation of\nmultivariate periodic functions). The total number of sampling points in the\nresulting multiple rank-1 lattices is theoretically shown to be less than $\n\\mathcal{O}\\left( |I| \\log^{ 2 }(N |I|) \\right) $ with constants independent of\n$d$, and by performing one-dimensional fast Fourier transforms on samples of\ntrigonometric polynomials with Fourier support in $ I $ at these points, we\nobtain exact reconstruction of all Fourier coefficients in fewer than $\n\\mathcal{O}\\left(d\\,|I|\\log^4 (N|I|)\\right) $ total operations.\n  Additionally, we present a second multiple rank-1 lattice construction\nalgorithm which constructs lattices with even fewer sampling points at the cost\nof only being able to reconstruct exact trigonometric polynomials rather than\nhaving additional theoretical approximation. Both algorithms are tested\nnumerically and surpass the theoretical bounds. Notably, we observe that the\noversampling factors #samples$/|I|$ appear to grow only logarithmically in $\n|I| $ for the first algorithm and appear near-optimally bounded by four in the\nsecond algorithm.\n']","[('fast fourier transforms', 0.6151852011680603), ('sparse fourier', 0.6066457033157349), ('fast fourier transform', 0.5461965799331665), ('fast fourier', 0.5315749049186707), ('dimensional periodic functions', 0.47724393010139465), ('fourier basis functions', 0.47143062949180603), ('fourier samples', 0.46967294812202454), ('functions wavelets', 0.45403414964675903), ('fourier basis', 0.44373905658721924), ('transform high dimensional', 0.42296749353408813)]"
913,913,33,913_legendrian knots_legendrian embeddings_invariant legendrian_legendrian knot,"['legendrian knots', 'legendrian embeddings', 'invariant legendrian', 'legendrian knot', 'legendrian submanifolds', 'lagrangian tori', 'dimensional legendrian', 'lagrangian cobordisms', 'legendrian contact', 'monotone lagrangian tori']","['Legendrian loops and cluster modular groups   This work studies Legendrian loop actions on exact Lagrangian fillings of\nLegendrian links in $(\\R^3, \\xi_{\\st})$. By identifying the induced action of\nLegendrian loops as generators of cluster modular groups, we establish the\nexistence of faithful group actions on the exact Lagrangian fillings of several\nfamilies of Legendrian positive braid closures, including all positive torus\nlinks. In addition, we leverage a Nielsen-Thurston-like classification of\ncluster automorphisms to provide new combinatorial and algebraic tools for\nproving that a Legendrian loop action has infinite order.\n', 'Braid Loops with infinite monodromy on the Legendrian contact DGA   We present the first examples of elements in the fundamental group of the\nspace of Legendrian links in the standard contact 3-sphere whose action on the\nLegendrian contact DGA is of infinite order. This allows us to construct the\nfirst families of Legendrian links that can be shown to admit infinitely many\nLagrangian fillings by Floer-theoretic techniques. These families include the\nfirst known Legendrian links with infinitely many fillings that are not rainbow\nclosures of positive braids, and the smallest Legendrian link with infinitely\nmany fillings known to date. We discuss how to use our examples to construct\nother links with infinitely many fillings, in particular giving the first\nFloer-theoretic proof that Legendrian (n,m) torus links have infinitely many\nLagrangian fillings, if n is greater than 3 and m greater than 6, or\n(n,m)=(4,4),(4,5). In addition, for any given higher genus, we construct a\nWeinstein 4-manifold homotopic to the 2-sphere whose wrapped Fukaya category\ncan distinguish infinitely many exact closed Lagrangian surfaces of that genus.\nA key technical ingredient behind our results is a new combinatorial formula\nfor decomposable cobordism maps between Legendrian contact DGAs with integer\n(group ring) coefficients.\n', 'Augmentations, Fillings, and Clusters   We investigate positive braid Legendrian links via a Floer-theoretic approach\nand prove that their augmentation varieties are cluster K2 (aka. A-) varieties.\nUsing the exact Lagrangian cobordisms of Legendrian links in [EHK16], we prove\nthat a large family of exact Lagrangian fillings of positive braid Legendrian\nlinks correspond to cluster seeds of their augmentation varieties. We solve the\ninfinite-filling problem for positive braid Legendrian links; i.e., whenever a\npositive braid Legendrian link is not of type ADE, it admits infinitely many\nexact Lagrangian fillings up to Hamiltonian isotopy.\n']","[('legendrian knots', 0.6156506538391113), ('legendrian embeddings', 0.608025312423706), ('invariant legendrian', 0.5742624402046204), ('legendrian knot', 0.5675747394561768), ('legendrian submanifolds', 0.5654195547103882), ('lagrangian tori', 0.5069628953933716), ('dimensional legendrian', 0.4756809175014496), ('lagrangian cobordisms', 0.46037188172340393), ('legendrian contact', 0.4478614926338196), ('monotone lagrangian tori', 0.44673267006874084)]"
914,914,33,914_preconditioned matrix_preconditioning techniques_proposed preconditioner_preconditioning technique,"['preconditioned matrix', 'preconditioning techniques', 'proposed preconditioner', 'preconditioning technique', 'based preconditioners', 'based preconditioner', 'preconditioning', 'preconditioned system', 'new preconditioner', 'preconditioner']","['A single-sided all-at-once preconditioning for linear system from a\n  non-local evolutionary equation with weakly singular kernels   {In [X. L. Lin, M. K. Ng, and Y. Zhi. {\\it J. Comput. Phys.}, 434 (2021), pp.\n110221] and [Y. L. Zhao, J. Wu, X. M. Gu, and H. Li. {\\it Comput. Math. Appl.},\n148(2023), pp. 200--210]}, two-sided preconditioning techniques are proposed\nfor non-local evolutionary equations, which possesses (i) mesh-size independent\ntheoretical bound of condition number of the two-sided preconditioned matrix;\n(ii) small and stable iteration numbers in numerical tests. In this paper, we\nmodify the two-sided preconditioning by multiplying the left-sided and the\nright-sided preconditioners together as a single-sided preconditioner. Such a\nsingle-sided preconditioner essentially derives from approximating the spatial\nmatrix with a fast diagonalizable matrix and keeping the temporal matrix\nunchanged. Clearly, the matrix-vector multiplication of the single-sided\npreconditioning is faster to compute than that of the two-sided one, since the\nsingle-sided preconditioned matrix has a simpler structure. More importantly,\nwe show theoretically that the single-sided preconditioned generalized minimal\nresidual (GMRES) method has a convergence rate no worse than the two-sided\npreconditioned one. As a result, the one-sided preconditioned GMRES solver\nrequires less computational time than the two-sided preconditioned GMRES solver\nin total. Numerical results are reported to show the efficiency of the proposed\nsingle-sided preconditioning technique.\n', 'An optimal parallel-in-time preconditioner for parabolic optimal control\n  problems   In this work, we propose a novel diagonalization-based preconditioner for the\nall-at-once linear system arising from the optimal control problem of parabolic\nequations. The proposed preconditioner is constructed based on an\n$\\epsilon$-circulant modification to the rotated block diagonal (RBD)\npreconditioning technique, which can be efficiently diagonalized by fast\nFourier transforms in a parallel-in-time fashion. \\textcolor{black}{To our\nknowledge, this marks the first application of the $\\epsilon$-circulant\nmodification to RBD preconditioning. Before our work, the studies of PinT\npreconditioning techniques for the optimal control problem are mainly focused\non $\\epsilon$-circulant modification to Schur complement based preconditioners,\nwhich involves multiplication of forward and backward evolutionary processes\nand thus square the condition number. Compared with those Schur complement\nbased preconditioning techniques in the literature, the advantage of the\nproposed $\\epsilon$-circulant modified RBD preconditioning is that it does not\ninvolve the multiplication of forward and backward evolutionary processes. When\nthe generalized minimal residual method is deployed on the preconditioned\nsystem, we prove that when choosing $\\epsilon=\\mathcal{O}(\\sqrt{\\tau})$ with\n$\\tau$ being the temporal step-size , the convergence rate of the\npreconditioned GMRES solver is independent of the matrix size and the\nregularization parameter. Such restriction on $\\epsilon$ is more relax than the\nassumptions on $\\epsilon$ from other works related to $\\epsilon$-circulant\nbased preconditioning techniques for the optimal control problem. Numerical\nresults are provided to demonstrate the effectiveness of our proposed solvers.\n', 'A parallel-in-time two-sided preconditioning for all-at-once system from\n  a non-local evolutionary equation with weakly singular kernel   In this paper, we study a parallel-in-time (PinT) algorithm for all-at-once\nsystem from a non-local evolutionary equation with weakly singular kernel where\nthe temporal term involves a non-local convolution with a weakly singular\nkernel and the spatial term is the usual Laplacian operator with variable\ncoefficients. We propose to use a two-sided preconditioning technique for the\nall-at-once discretization of the equation. Our preconditioner is constructed\nby replacing the variable diffusion coefficients with a constant coefficient to\nobtain a constant-coefficient all-at-once matrix. We split a square root of the\nconstant Laplacian operator out of the constant-coefficient all-at-once matrix\nas a right preconditioner and take the remaining part as a left preconditioner,\nwhich constitutes our two-sided preconditioning. Exploiting the\ndiagonalizability of the constant-Laplacian matrix and the triangular Toeplitz\nstructure of the temporal discretization matrix, we obtain efficient\nrepresentations of inverses of the right and the left preconditioners, because\nof which the iterative solution can be fast updated in a PinT manner.\nTheoretically, the condition number of the two-sided preconditioned matrix is\nproven to be uniformly bounded by a constant independent of the matrix size. To\nthe best of our knowledge, for the non-local evolutionary equation with\nvariable coefficients, this is the first attempt to develop a PinT\npreconditioning technique that has fast and exact implementation and that the\ncorresponding preconditioned system has a uniformly bounded condition number.\nNumerical results are reported to confirm the efficiency of the proposed\ntwo-sided preconditioning technique.\n']","[('preconditioned matrix', 0.7141225337982178), ('preconditioning techniques', 0.650011420249939), ('proposed preconditioner', 0.6434935927391052), ('preconditioning technique', 0.643428385257721), ('based preconditioners', 0.6359004974365234), ('based preconditioner', 0.6317576766014099), ('preconditioning', 0.6085957884788513), ('preconditioned system', 0.5920698046684265), ('new preconditioner', 0.5674125552177429), ('preconditioner', 0.5605146884918213)]"
915,915,33,915_algebras hilbert_algebras associated_dimensional algebras_evolution operators,"['algebras hilbert', 'algebras associated', 'dimensional algebras', 'evolution operators', 'algebras corresponding', 'algebras generalize', 'associative algebras', 'algebras automorphism', 'algebra associated', 'operators evolution']","['On absolute nilpotent and idempotent elements of an evolution algebra\n  corresponding to permutations   We describe absolute nilpotent and some idempotent elements of an $n$-\ndimensional evolution algebra corresponding to two permutations and we\ndecompose such algebras to the direct sum of evolution algebras corresponding\nto cycles of the permutations.\n', 'Natural families in evolution algebras   In this paper we introduce the notion of evolution rank and give a\ndecomposition of an evolution algebra into its annihilator plus extending\nevolution subspaces having evolution rank one. This decomposition can be used\nto prove that in non-degenerate evolution algebras, any family of natural and\northogonal vectors can be extended to a natural basis. Central results are the\ncharacterization of those families of orthogonal linearly independent vectors\nwhich can be extended to a natural basis.\n  We also consider ideals in perfect evolution algebras and prove that they\ncoincide with the basic ideals.\n  Nilpotent elements of order three can be localized (in a perfect evolution\nalgebra over a field in which every element is a square) by merely looking at\nthe structure matrix: any vanishing principal minor provides one. Conversely,\nif a perfect evolution algebra over an arbitrary field has a nilpotent element\nof order three, then its structure matrix has a vanishing principal minor.\n  We finish by considering the adjoint evolution algebra and relating its\nproperties to the corresponding in the initial evolution algebra.\n', 'On Hilbert evolution algebras of a graph   Evolution algebras are a special class of non-associative algebras exhibiting\nconnections with different fields of Mathematics. Hilbert evolution algebras\ngeneralize the concept through a framework of Hilbert spaces. This allows to\ndeal with a wide class of infinite-dimensional spaces. In this work we study\nHilbert evolution algebras associated to a graph. Inspired in definitions of\nevolution algebras we define the Hilbert evolution algebra associated to a\ngiven graph and the Hilbert evolution algebra associated to the symmetric\nrandom walk on a graph. For a given graph, we provide conditions under which\nthese structures are or are not isomorphic. Our definitions and results extend\nto graphs with infinitely many vertices a similar theory developed for\nevolution algebras associated to finite graphs.\n']","[('algebras hilbert', 0.5644875168800354), ('algebras associated', 0.5273358225822449), ('dimensional algebras', 0.5245323777198792), ('evolution operators', 0.5240970849990845), ('algebras corresponding', 0.5043705105781555), ('algebras generalize', 0.4943321645259857), ('associative algebras', 0.4926125407218933), ('algebras automorphism', 0.49064934253692627), ('algebra associated', 0.4791824221611023), ('operators evolution', 0.4707283079624176)]"
916,916,33,916_pseudo anosov maps_pseudo anosov map_pseudo anosov homeomorphisms_anosov maps,"['pseudo anosov maps', 'pseudo anosov map', 'pseudo anosov homeomorphisms', 'anosov maps', 'anosov map', 'pseudo anosov mapping', 'pseudo anosov homeomorphism', 'anosov homeomorphisms', 'anosov mapping', 'pseudo anosovs']","[""Distinctness of two pseudo-Anosov maps   In 1981, Arnoux and Yoccoz gave the first examples of pseudo-Anosov maps with\nodd degree stretch factors. In 1985, D.~Fried deduced the existence of a\npseudo-Anosov map in genus three with the same stretch factor as the\nArnoux-Yoccoz example in that genus, and asked if these were the same. We show\nthat they are distinct. We do this by, in a sense, reversing Fried's\nconstruction; we show that the mapping torus of the pseudo-Anosov map induced\nby the Arnoux-Yoccoz map on the surface obtained by blowing-up its two\nsingularities has no cross section which is a torus with two points blown-up.\n"", 'Creating pseudo-Anosov Maps from Permutations and Matrices   We provide an integral combinatorial characterization of pseudo-Anosov maps\non closed oriented surfaces of genus g > 1. We show that an\norientation-preserving pseudo-Anosov homeomorphism with orientable foliations\nand fixing all critical trajectories can be encoded as a permutation of 2g+v-1\npositive integers, where v is the number of singular points of the foliations\n(disregarding multiplicity). We call such a permutations an ordered block\npermutation (OBP), and it satisfies an admissiblity condition. Conversely, we\nshow that a surface along with measured foliations (up to scaling) and the\npseudo-Anosov map can be uniquely constructed out of the data of an admissible\npermutation of 2g+v-1 positive integers. In particular, for closed surfaces, we\nconstruct every orientable foliation invariant under a pseudo-Anosov\nhomeomorphism.\n', ""Minimal pseudo-Anosov stretch factors on nonoriented surfaces   We determine the smallest stretch factor among pseudo-Anosov maps with an\norientable invariant foliation on the closed nonorientable surfaces of genus 4,\n5, 6, 7, 8, 10, 12, 14, 16, 18 and 20. We also determine the smallest stretch\nfactor of an orientation-reversing pseudo-Anosov map with orientable invariant\nfoliations on the closed orientable surfaces of genus 1, 3, 5, 7, 9 and 11. As\na byproduct, we obtain that the stretch factor of a pseudo-Anosov map on a\nnonorientable surface or an orientation-reversing pseudo-Anosov map on an\norientable surface does not have Galois conjugates on the unit circle. This\nshows that the techniques that were used to disprove Penner's conjecture on\norientable surfaces are ineffective in the nonorientable cases.\n""]","[('pseudo anosov maps', 0.7217448353767395), ('pseudo anosov map', 0.7090587615966797), ('pseudo anosov homeomorphisms', 0.6925562024116516), ('anosov maps', 0.676474392414093), ('anosov map', 0.6606243252754211), ('pseudo anosov mapping', 0.6594724655151367), ('pseudo anosov homeomorphism', 0.6585515141487122), ('anosov homeomorphisms', 0.6451596617698669), ('anosov mapping', 0.6229259967803955), ('pseudo anosovs', 0.6154019832611084)]"
917,917,33,917_brownian motion space_riemannian manifolds_riemannian manifold_compact riemannian,"['brownian motion space', 'riemannian manifolds', 'riemannian manifold', 'compact riemannian', 'sub riemannian manifolds', 'construction brownian motion', 'riemannian', 'sub riemannian', 'brownian motions', 'complete riemannian manifolds']","['Large deviations for Brownian motion in evolving Riemannian manifolds   We prove large deviations for $g(t)$-Brownian motion in a complete, evolving\nRiemannian manifold $M$ with respect to a collection $\\{g(t)\\}_{t\\in [0,1]}$ of\nRiemannian metrics, smoothly depending on $t$. We show how the large deviations\nare obtained from the large deviations of the (time-dependent) horizontal lift\nof $g(t)$-Brownian motion to the frame bundle $FM$ over $M$. The latter is\nproved by embedding the frame bundle into some Euclidean space and applying\nFreidlin-Wentzell theory for diffusions with time-dependent coefficients, where\nthe coefficients are jointly Lipschitz in space and time.\n', 'On the Onsager-Machlup functional for the Brownian motion on the\n  Heisenberg group   Onsager-Machlup functionals are used to describe the dynamics of a continuous\nstochastic process. For a stochastic process taking values in a Riemannian\nmanifold, they have been studied extensively. We describe the Onsager-Machlup\nfunctional with respect to the sup norm for a hypoelliptic Brownian motion on a\nHeisenberg group. Unlike in the Riemannian case we do not rely on the tools\nfrom differential geometry such as comparison theorems or curvature bounds as\nthese are not easily available in the sub-Riemannian setting. In addition, we\nstudy fine properties of trajectories of the hypoelliptic Brownian motion,\nincluding a new notion of horizontal continuous curves.\n', 'Cartan connections for stochastic developments on sub-Riemannian\n  manifolds   Analogous to the characterisation of Brownian motion on a Riemannian manifold\nas the development of Brownian motion on a Euclidean space, we construct\nsub-Riemannian diffusions on equinilpotentisable sub-Riemannian manifolds by\ndeveloping a canonical stochastic process arising as the lift of Brownian\nmotion to an associated model space. The notion of stochastic development we\nintroduce for equinilpotentisable sub-Riemannian manifolds uses Cartan\nconnections, which take the place of the Levi-Civita connection in Riemannian\ngeometry. We first derive a general expression for the generator of the\nstochastic process which is the stochastic development with respect to a Cartan\nconnection of the lift of Brownian motion to the model space. We further\nprovide a necessary and sufficient condition for the existence of a Cartan\nconnection which develops the canonical stochastic process to the\nsub-Riemannian diffusion associated with the sub-Laplacian defined with respect\nto the Popp volume. We illustrate the construction of a suitable Cartan\nconnection for free sub-Riemannian structures with two generators and we\ndiscuss an example where the condition is not satisfied.\n']","[('brownian motion space', 0.6238287091255188), ('riemannian manifolds', 0.5933550000190735), ('riemannian manifold', 0.5928724408149719), ('compact riemannian', 0.5726898312568665), ('sub riemannian manifolds', 0.5704908967018127), ('construction brownian motion', 0.5677075982093811), ('riemannian', 0.5659286975860596), ('sub riemannian', 0.5577514171600342), ('brownian motions', 0.5498576760292053), ('complete riemannian manifolds', 0.5410202741622925)]"
918,918,33,918_existence ground states_existence ground state_ground state energy_degenerate ground state,"['existence ground states', 'existence ground state', 'ground state energy', 'degenerate ground state', 'non relativistic quantum', 'renormalization', 'relativistic quantum', 'ground states', 'hamiltonian self adjoint', 'quantum field']","['Absence of Ground States in the Renormalized Massless\n  Translation-Invariant Nelson Model   We consider a model for a massive uncharged non-relativistic particle\ninteracting with a massless bosonic field, widely referred to as the Nelson\nmodel. It is well known, that an ultraviolet renormalized Hamilton operator\nexists in this case. Further, due to translation-invariance, it decomposes into\nfiber operators.\n  In this paper, we treat the renormalized fiber operators. We give a\ndescription of the operator and form domains and prove that the fiber operators\ndo not have a ground state. Our results hold for any non-zero coupling constant\nand arbitrary total momentum. Our proof for the absence of ground states is a\nnew generalization of methods recently applied to related models. A major\nenhancement we provide, is that the method can be applied to models with\ndegenerate ground state eigenspaces.\n', ""Quasi-classical Ground States. I. Linearly Coupled Pauli-Fierz\n  Hamiltonians   We consider a spinless, non-relativistic particle bound by an external\npotential and linearly coupled to a quantized radiation field. The energy\n$\\mathcal{E}(u,f)$ of product states of the form $u\\otimes \\Psi_f$, where $u$\nis a normalized state for the particle and $\\Psi_f$ is a coherent state in Fock\nspace for the field, gives the energy of a Klein-Gordon--Schr\\''odinger system.\nWe minimize the functional $\\mathcal{E}(u,f)$ on its natural energy space. We\nprove the existence and uniqueness of a ground state under general conditions\non the coupling function. In particular, neither an ultraviolet cutoff nor an\ninfrared cutoff is imposed. Our results establish the convergence in the\nultraviolet limit of both the ground state and ground state energy of the\nKlein-Gordon--Schr\\''odinger energy functional, and provide the second-order\nasymptotic expansion of the ground state energy at small coupling.\n"", ""Ground states and associated path measures in the renormalized Nelson\n  model   We prove the existence, uniqueness, and strict positivity of ground states of\nthe possibly massless renormalized Nelson operator under an infrared regularity\ncondition and for Kato decomposable electrostatic potentials fulfilling a\nbinding condition. If the infrared regularity condition is violated, then we\nshow non-existence of ground states of the massless renormalized Nelson\noperator with an arbitrary Kato decomposable potential. Furthermore, we prove\nthe existence, uniqueness, and strict positivity of ground states of the\nmassless renormalized Nelson operator in a non-Fock representation where the\ninfrared condition is unnecessary. Exponential and superexponential estimates\non the pointwise spatial decay and the decay with respect to the boson number\nfor elements of spectral subspaces below localization thresholds are provided.\nMoreover, some continuity properties of ground state eigenvectors are\ndiscussed. Byproducts of our analysis are a hypercontractivity bound for the\nsemigroup and a new remark on Nelson's operator theoretic renormalization\nprocedure. Finally, we construct path measures associated with ground states of\nthe renormalized Nelson operator. Their analysis entails improved boson number\ndecay estimates for ground state eigenvectors, as well as upper and lower\nbounds on the Gaussian localization with respect to the field variables in the\nground state. As our results on uniqueness, positivity, and path measures\nexploit the ergodicity of the semigroup, we restrict our attention to one\nmatter particle. All results are non-perturbative.\n""]","[('existence ground states', 0.546381413936615), ('existence ground state', 0.4905672073364258), ('ground state energy', 0.4613955020904541), ('degenerate ground state', 0.43325623869895935), ('non relativistic quantum', 0.4172428250312805), ('renormalization', 0.39250266551971436), ('relativistic quantum', 0.3871961832046509), ('ground states', 0.3869713544845581), ('hamiltonian self adjoint', 0.36993172764778137), ('quantum field', 0.3684034049510956)]"
919,919,33,919_quantum walks_time quantum walks_quantum walk_time quantum walk,"['quantum walks', 'time quantum walks', 'quantum walk', 'time quantum walk', 'dimensional quantum walk', 'quantum random walks', 'walk quantum', 'classical random walks', 'discrete time quantum', 'continuous time quantum']","[""Scaling limit of the time averaged distribution for continuous time\n  quantum walk and Szegedy's walk on the path   In this paper, we consider Szegedy's walk, a type of discrete time quantum\nwalk, and corresponding continuous time quantum walk related to the birth and\ndeath chain. We show that the scaling limit of time averaged distribution for\nthe continuous time quantum walk induces that of Szegedy's walk if there exists\nthe spectral gap on so-called the corresponding Jacobi matrix .\n"", 'Phase transition of a continuous-time quantum walk on the half line   Quantum walks are referred to as quantum analogs to random walks in\nmathematics. They have been studied as quantum algorithms in quantum\ninformation for quantum computers. There are two types of quantum walks. One is\nthe discrete-time quantum walk and the other is the continuous-time quantum\nwalk. We study a continuous-time quantum walk on the half line and challenge to\nfind a limit theorem for it in this paper. As a result, approximate behavior of\nthe quantum walker is revealed after the system of quantum walk gets updated in\nlong time.\n', 'A method of approximation of discrete Schr\\""odinger equation with the\n  normalized Laplacian by discrete-time quantum walk on graphs   We propose a class of continuous-time quantum walk models on graphs induced\nby a certain class of discrete-time quantum walk models with the parameter\n$\\epsilon\\in [0,1]$. Here the graph treated in this paper can be applied both\nfinite and infinite cases. The induced continuous-time quantum walk is an\nextended version of the (free) discrete-Schr\\""odinger equation driven by the\nnormalized Laplacian: the element of the weighted Hermitian takes not only a\nscalar value but also a matrix value depending on the underlying discrete-time\nquantum walk. We show that each discrete-time quantum walk with an appropriate\nsetting of the parameter $\\epsilon$ in the long time limit identifies with its\ninduced continuous-time quantum walk and give the running time for the\ndiscrete-time to approximate the induced continuous-time quantum walk with a\nsmall error $\\delta$. We also investigate the detailed spectral information on\nthe induced continuous-time quantum walk.\n']","[('quantum walks', 0.7983278632164001), ('time quantum walks', 0.7928012609481812), ('quantum walk', 0.7852914929389954), ('time quantum walk', 0.7806593179702759), ('dimensional quantum walk', 0.7754533290863037), ('quantum random walks', 0.7727766036987305), ('walk quantum', 0.7578362822532654), ('classical random walks', 0.6484670639038086), ('discrete time quantum', 0.6345421075820923), ('continuous time quantum', 0.5879243016242981)]"
920,920,33,920_density functional theory_electronic structure calculations_density functional_functional adaptive,"['density functional theory', 'electronic structure calculations', 'density functional', 'functional adaptive', 'theory dft', 'ground state density', 'approximations density', 'functional theory', 'electronic structure', 'structure calculations']","['Energy-Adaptive Riemannian Conjugate Gradient Method for Density\n  Functional Theory   This paper presents a novel Riemannian conjugate gradient method for the\nKohn-Sham energy minimization problem in density functional theory (DFT), with\na focus on non-metallic crystal systems. We introduce an energy-adaptive metric\nthat preconditions the Kohn-Sham model, significantly enhancing optimization\nefficiency. Additionally, a carefully designed shift strategy and several\nalgorithmic improvements make the implementation comparable in performance to\nhighly optimized self-consistent field iterations. The energy-adaptive\nRiemannian conjugate gradient method has a sound mathematical foundation,\nincluding stability and convergence, offering a reliable and efficient\nalternative for DFT-based electronic structure calculations in computational\nchemistry.\n', 'A posteriori error estimator for adaptive local basis functions to solve\n  Kohn-Sham density functional theory   Kohn-Sham density functional theory is one of the most widely used electronic\nstructure theories. The recently developed adaptive local basis functions form\nan accurate and systematically improvable basis set for solving Kohn-Sham\ndensity functional theory using discontinuous Galerkin methods, requiring a\nsmall number of basis functions per atom. In this paper we develop\nresidual-based a posteriori error estimates for the adaptive local basis\napproach, which can be used to guide non-uniform basis refinement for highly\ninhomogeneous systems such as surfaces and large molecules. The adaptive local\nbasis functions are non-polynomial basis functions, and standard a posteriori\nerror estimates for $hp$-refinement using polynomial basis functions do not\ndirectly apply. We generalize the error estimates for $hp$-refinement to\nnon-polynomial basis functions. We demonstrate the practical use of the a\nposteriori error estimator in performing three-dimensional Kohn-Sham density\nfunctional theory calculations for quasi-2D aluminum surfaces and a\nsingle-layer graphene oxide system in water.\n', 'Convergent and orthogonality preserving schemes for approximating the\n  Kohn-Sham orbitals   To obtain convergent numerical approximations without using any\northogonalization operations is of great importance in electronic structure\ncalculations. In this paper, we propose and analyze a class of iteration\nschemes for the discretized Kohn- Sham Density Functional Theory model, with\nwhich the iterative approximations are guaranteed to converge to the Kohn-Sham\norbitals exponentially without any orthogonalization as long as the initial\norbitals are orthogonal and the time step sizes are given properly. In\naddition, we present a feasible and efficient approach to get suitable time\nstep sizes and report some numerical experiments to validate our theory.\n']","[('density functional theory', 0.5518660545349121), ('electronic structure calculations', 0.4848962724208832), ('density functional', 0.46315112709999084), ('functional adaptive', 0.37310412526130676), ('theory dft', 0.37017205357551575), ('ground state density', 0.34623754024505615), ('approximations density', 0.34302666783332825), ('functional theory', 0.3273434340953827), ('electronic structure', 0.32178357243537903), ('structure calculations', 0.3154740035533905)]"
921,921,33,921_underdamped langevin dynamics_overdamped langevin dynamics_langevin dynamics_models langevin,"['underdamped langevin dynamics', 'overdamped langevin dynamics', 'langevin dynamics', 'models langevin', 'underdamped langevin', 'molecular dynamics simulations', 'overdamped langevin', 'langevin', 'stochastic dynamics', 'dynamics approximates']","['On the Numerical Stationary Distribution of Overdamped Langevin Equation\n  in Harmonic System   Efficient numerical algorithm for stochastic differential equation has been\nan important object in the research of statistical physics and mathematics for\na long time. In this paper we study the highly accurate numerical algorithm of\nthe overdamped Langevin equation. In particular, our interest is the behaviour\nof the numerical schemes for solving the overdamped Langevin equation in the\nharmonic system. Three algorithms are obtained for overdamped Langevin\nequation, from the large friction limit of the schemes for underdamped Langevin\ndynamics. We derive the explicit expression of the stationary distribution of\neach algorithm by analysing the discrete time trajectory, for both\none-dimensional and multi-dimensional cases. The accuracy of the stationary\ndistribution of each algorithm is illustrated by comparing to the exact\nBoltzmann distribution. Our results demonstrate that, the ""BAOA-limit""\nalgorithm generates the exact distribution for the harmonic system in the\ncanonical ensemble, within the stable regime of the time interval. The other\nalgorithms do not produce the exact distribution of the harmonic system.\n', ""Bottom-up transient time models in coarse-graining molecular systems   This work presents a systematic methodology for describing the transient\ndynamics of coarse-grained molecular systems inferred from all-atom simulated\ndata. We suggest Langevin-type dynamics where the coarse-grained interaction\npotential depends explicitly on time to efficiently approximate the transient\ncoarse-grained dynamics. We apply the path-space force matching approach at the\ntransient dynamics regime to learn the proposed model parameters. In\nparticular, we parameterize the coarse-grained potential both with respect to\nthe pair distance of the CG particles and the time, and we obtain an evolution\nmodel that is explicitly time-dependent. Moreover, we follow a data-driven\napproach to estimate the friction kernel, given by appropriate correlation\nfunctions directly from the underlying all-atom molecular dynamics simulations.\nTo explore and validate the proposed methodology we study a benchmark system of\na moving particle in a box. We examine the suggested model's effectiveness in\nterms of the system's correlation time and find that the model can approximate\nwell the transient time regime of the system, depending on the correlation time\nof the system. As a result, in the less correlated case, it can represent the\ndynamics for a longer time interval. We present an extensive study of our\napproach to a realistic high-dimensional water molecular system. Posing the\nwater system initially out of thermal equilibrium we collect trajectories of\nall-atom data for the, empirically estimated, transient time regime. Then, we\ninfer the suggested model and strengthen the model's validity by comparing it\nwith simplified Markovian models.\n"", 'Quantification of coarse-graining error in Langevin and overdamped\n  Langevin dynamics   In molecular dynamics and sampling of high dimensional Gibbs measures\ncoarse-graining is an important technique to reduce the dimensionality of the\nproblem. We will study and quantify the coarse-graining error between the\ncoarse-grained dynamics and an effective dynamics. The effective dynamics is a\nMarkov process on the coarse-grained state space obtained by a closure\nprocedure from the coarse-grained coefficients. We obtain error estimates both\nin relative entropy and Wasserstein distance, for both Langevin and overdamped\nLangevin dynamics. The approach allows for vectorial coarse-graining maps.\nHereby, the quality of the chosen coarse-graining is measured by certain\nfunctional inequalities encoding the scale separation of the Gibbs measure. The\nmethod is based on error estimates between solutions of (kinetic) Fokker-Planck\nequations in terms of large-deviation rate functionals.\n']","[('underdamped langevin dynamics', 0.7260658144950867), ('overdamped langevin dynamics', 0.7241560816764832), ('langevin dynamics', 0.7111495733261108), ('models langevin', 0.6112620830535889), ('underdamped langevin', 0.5400373339653015), ('molecular dynamics simulations', 0.5312791466712952), ('overdamped langevin', 0.5266219973564148), ('langevin', 0.47866368293762207), ('stochastic dynamics', 0.47718480229377747), ('dynamics approximates', 0.4759383201599121)]"
922,922,33,922_digraph vertex_digraphs digraph_connected digraph_digraph vertices,"['digraph vertex', 'digraphs digraph', 'connected digraph', 'digraph vertices', 'vertices digraph', 'digraph order', 'digraphs let', 'digraphs', 'pairwise vertex disjoint', 'every digraph']","['$3$-anti-circulant digraphs are $\\alpha$-diperfect and BE-diperfect   Let $D$ be a digraph. A subset $S$ of $V(D)$ is a stable set if every pair of\nvertices in $S$ is non-adjacent in $D$. A collection of disjoint paths\n$\\mathcal{P}$ of $D$ is a path partition of $V(D)$, if every vertex in $V(D)$\nis exactly on a path of $\\mathcal{P}$. We say that a stable set $S$ and a path\npartition $\\mathcal{P}$ are orthogonal if each path of $P$ contains exactly one\nvertex of $S$. A digraph $D$ satisfies the $\\alpha$-property if for every\nmaximum stable set $S$ of $D$, there exists a path partition $\\mathcal{P}$ such\nthat $S$ and $\\mathcal{P}$ are orthogonal. A digraph $D$ is $\\alpha$-diperfect\nif every induced subdigraph of $D$ satisfies the $\\alpha$-property. In 1982,\nClaude Berge proposed a characterization for $\\alpha$-diperfect digraphs in\nterms of forbidden anti-directed odd cycles. In 2018, Sambinelli, Silva and Lee\nproposed a similar conjecture. A digraph $D$ satisfies the Begin-End-property\nor BE-property if for every maximum stable set $S$ of $D$, there exists a path\npartition $\\mathcal{P}$ such that (i) $S$ and $\\mathcal{P}$ are orthogonal and\n(ii) for each path $P \\in \\mathcal{P}$, either the start or the end of $P$\nbelongs to $S$. A digraph $D$ is BE-diperfect if every induced subdigraph of\n$D$ satisfies the BE-property. Sambinelli, Silva and Lee proposed a\ncharacterization for BE-diperfect digraphs in terms of forbidden blocking odd\ncycles. In this paper, we verified both conjectures for $3$-anti-circulant\ndigraphs. We also present some structural results for $\\alpha$-diperfect and\nBE-diperfect digraphs.\n', ""Some results on Berge's conjecture and Begin-End conjecture   Let $D$ be a digraph. A subset $S$ of $V(D)$ is a stable set if every pair of\nvertices in $S$ is non-adjacent in $D$. A collection of disjoint paths\n$\\mathcal{P}$ of $D$ is a path partition of $V(D)$, if every vertex in $V(D)$\nis on a path of $\\mathcal{P}$. We say that a stable set $S$ and a path\npartition $\\mathcal{P}$ are orthogonal if each path of $P$ contains exactly one\nvertex of $S$. A digraph $D$ satisfies the $\\alpha$-property if for every\nmaximum stable set $S$ of $D$, there exists a path partition $\\mathcal{P}$ such\nthat $S$ and $\\mathcal{P}$ are orthogonal. A digraph $D$ is $\\alpha$-diperfect\nif every induced subdigraph of $D$ satisfies the $\\alpha$-property. In 1982,\nClaude Berge proposed a characterization of $\\alpha$-diperfect digraphs in\nterms of forbidden anti-directed odd cycles. In 2018, Sambinelli, Silva and Lee\nproposed a similar conjecture. A digraph $D$ satisfies the Begin-End-property\nor BE-property if for every maximum stable set $S$ of $D$, there exists a path\npartition $\\mathcal{P}$ such that (i) $S$ and $\\mathcal{P}$ are orthogonal and\n(ii) for each path $P \\in \\mathcal{P}$, either the start or the end of $P$ lies\nin $S$. A digraph $D$ is BE-diperfect if every induced subdigraph of $D$\nsatisfies the BE-property. Sambinelli, Silva and Lee proposed a\ncharacterization of BE-diperfect digraphs in terms of forbidden blocking odd\ncycles. In this paper, we show some structural results for $\\alpha$-diperfect\nand BE-diperfect digraphs. In particular, we show that in every minimal\ncounterexample $D$ to both conjectures, the size of a maximum stable set is\nsmaller than $\\vert V(D)\\vert /2$. As an application we use these results to\nprove both conjectures for arc-locally in-semicomplete and arc-locally\nout-semicomplete digraphs.\n"", 'A minimum semi-degree sufficient condition for one-to-many disjoint path\n  covers in semicomplete digraphs   Let $D$ be a digraph. We define the minimum semi-degree of $D$ as\n$\\delta^{0}(D) := \\min \\{\\delta^{+}(D), \\delta^{-}(D)\\}$. Let $k$ be a positive\ninteger, and let $S = \\{s\\}$ and $T = \\{t_{1}, \\dots ,t_{k}\\}$ be any two\ndisjoint subsets of $V(D)$. A set of $k$ internally disjoint paths joining\nsource set $S$ and sink set $T$ that cover all vertices $D$ are called a\none-to-many $k$-disjoint directed path cover ($k$-DDPC for short) of $D$. A\ndigraph $D$ is semicomplete if for every pair $x,y$ of vertices of it, there is\nat least one arc between $x$ and $y$.\n  In this paper, we prove that every semicomplete digraph $D$ of sufficiently\nlarge order $n$ with $\\delta^{0}(D) \\geq \\lceil (n+k-1)/2\\rceil$ has a\none-to-many $k$-DDPC joining any disjoint source set $S$ and sink set $T$,\nwhere $S = \\{s\\}, T = \\{t_{1}, \\dots, t_{k}\\}$.\n']","[('digraph vertex', 0.5633285641670227), ('digraphs digraph', 0.562437117099762), ('connected digraph', 0.559738039970398), ('digraph vertices', 0.5549574494361877), ('vertices digraph', 0.5451057553291321), ('digraph order', 0.5217708349227905), ('digraphs let', 0.5197505950927734), ('digraphs', 0.5162363648414612), ('pairwise vertex disjoint', 0.5077281594276428), ('every digraph', 0.49980688095092773)]"
923,923,33,923_branching random walks_branching random walk_branching random_random walk space,"['branching random walks', 'branching random walk', 'branching random', 'random walk space', 'branching processes', 'random walks', 'walk random environment', 'random walk', 'continuous time branching', 'branching process']","['A localisation phase transition for the catalytic branching random walk   We show the existence of a phase transition between a localisation and a\nnon-localisation regime for a branching random walk with a catalyst at the\norigin. More precisely, we consider a continuous-time branching random walk\nthat jumps at rate one, with simple random walk jumps on $\\mathbb Z^d$, and\nthat branches (with binary branching) at rate $\\lambda>0$ everywhere, except at\nthe origin, where it branches at rate $\\lambda_0>\\lambda$. We show that, if\n$\\lambda_0$ is large enough, then the occupation measure of the branching\nrandom walk localises (i.e. converges almost surely without spatial\nrenormalisation), whereas, if $\\lambda_0$ is close enough to $\\lambda$, then\nlocalisation cannot occur, at least not in a strong sense. The case $\\lambda =\n0$ (when branching only occurs at the origin) has been extensively studied in\nthe literature and a transition between localisation and non-localisation was\nalso exhibited in this case. Strikingly, the transition that we observe,\nconjecture, and partially prove in this paper occurs at the same threshold as\nin the case $\\lambda=0$.\n', ""Maximal displacement of a supercritical branching random walk in a\n  time-inhomogeneous random environment   The behavior of the maximal displacement of a supercritical branching random\nwalk has been a subject of intense studies for a long time. But only recently\nthe case of time-inhomogeneous branching has gained focus. The contribution of\nthis paper is to analyze a time-inhomogeneous model with two levels of\nrandomness. In the first step a sequence of branching laws is sampled\nindependently according to a distribution on the set of point measures' laws.\nConditionally on the realization of this sequence (called environment) we\ndefine a branching random walk and find the asymptotic behavior of its maximal\nparticle. It is of the form $V_n -\\varphi \\log n + o_\\mathbf{P}(\\log n)$, where\n$V_n$ is a function of the environment that behaves as a random walk and\n$\\varphi>0$ is a deterministic constant, which turns out to be bigger than the\nusual logarithmic correction of the homogeneous branching random walk.\n"", 'Large Deviations for the Right-Most Position of a Last Progeny Modified\n  Branching Random Walk   In this work, we consider a modification of the usual Branching Random Walk\n(BRW), where we give certain independent and identically distributed (i.i.d.)\ndisplacements to all the particles at the $n$-th generation, which may be\ndifferent from the driving increment distribution. This model was first\nintroduced by Bandyopadhyay and Ghosh (2021) and they termed it as Last Progeny\nModified Branching Random Walk (LPM-BRW). Under very minimal assumptions, we\nderive the large deviation principle (LDP) for the right-most position of a\nparticle in generation $n$. As a byproduct, we also complete the LDP for the\nclassical model, which complements the earlier work by Gantert and\nH\\""{o}felsauer (2018).\n']","[('branching random walks', 0.7729709148406982), ('branching random walk', 0.7716266512870789), ('branching random', 0.6259450912475586), ('random walk space', 0.6178810596466064), ('branching processes', 0.6149280071258545), ('random walks', 0.6128180623054504), ('walk random environment', 0.5629149675369263), ('random walk', 0.5628622174263), ('continuous time branching', 0.5600619912147522), ('branching process', 0.5590695142745972)]"
924,924,33,924_nonnegative matrix factorization_matrix factorization nmf_negative matrix factorization_matrix factorizations,"['nonnegative matrix factorization', 'matrix factorization nmf', 'negative matrix factorization', 'matrix factorizations', 'matrix factorization', 'factorization nmf', 'sparse nonnegative', 'nonnegative least squares', 'nonnegative matrix', 'nonnegative matrices']","['Sparse Separable Nonnegative Matrix Factorization   We propose a new variant of nonnegative matrix factorization (NMF), combining\nseparability and sparsity assumptions. Separability requires that the columns\nof the first NMF factor are equal to columns of the input matrix, while\nsparsity requires that the columns of the second NMF factor are sparse. We call\nthis variant sparse separable NMF (SSNMF), which we prove to be NP-complete, as\nopposed to separable NMF which can be solved in polynomial time. The main\nmotivation to consider this new model is to handle underdetermined blind source\nseparation problems, such as multispectral image unmixing. We introduce an\nalgorithm to solve SSNMF, based on the successive nonnegative projection\nalgorithm (SNPA, an effective algorithm for separable NMF), and an exact sparse\nnonnegative least squares solver. We prove that, in noiseless settings and\nunder mild assumptions, our algorithm recovers the true underlying sources.\nThis is illustrated by experiments on synthetic data sets and the unmixing of a\nmultispectral image.\n', 'Distributionally Robust and Multi-Objective Nonnegative Matrix\n  Factorization   Nonnegative matrix factorization (NMF) is a linear dimensionality reduction\ntechnique for analyzing nonnegative data. A key aspect of NMF is the choice of\nthe objective function that depends on the noise model (or statistics of the\nnoise) assumed on the data. In many applications, the noise model is unknown\nand difficult to estimate. In this paper, we define a multi-objective NMF\n(MO-NMF) problem, where several objectives are combined within the same NMF\nmodel. We propose to use Lagrange duality to judiciously optimize for a set of\nweights to be used within the framework of the weighted-sum approach, that is,\nwe minimize a single objective function which is a weighted sum of the all\nobjective functions. We design a simple algorithm based on multiplicative\nupdates to minimize this weighted sum. We show how this can be used to find\ndistributionally robust NMF (DR-NMF) solutions, that is, solutions that\nminimize the largest error among all objectives, using a dual approach solved\nvia a heuristic inspired from the Frank-Wolfe algorithm. We illustrate the\neffectiveness of this approach on synthetic, document and audio data sets. The\nresults show that DR-NMF is robust to our incognizance of the noise model of\nthe NMF problem.\n', 'Generalized Separable Nonnegative Matrix Factorization   Nonnegative matrix factorization (NMF) is a linear dimensionality technique\nfor nonnegative data with applications such as image analysis, text mining,\naudio source separation and hyperspectral unmixing. Given a data matrix $M$ and\na factorization rank $r$, NMF looks for a nonnegative matrix $W$ with $r$\ncolumns and a nonnegative matrix $H$ with $r$ rows such that $M \\approx WH$.\nNMF is NP-hard to solve in general. However, it can be computed efficiently\nunder the separability assumption which requires that the basis vectors appear\nas data points, that is, that there exists an index set $\\mathcal{K}$ such that\n$W = M(:,\\mathcal{K})$. In this paper, we generalize the separability\nassumption: We only require that for each rank-one factor $W(:,k)H(k,:)$ for\n$k=1,2,\\dots,r$, either $W(:,k) = M(:,j)$ for some $j$ or $H(k,:) = M(i,:)$ for\nsome $i$. We refer to the corresponding problem as generalized separable NMF\n(GS-NMF). We discuss some properties of GS-NMF and propose a convex\noptimization model which we solve using a fast gradient method. We also propose\na heuristic algorithm inspired by the successive projection algorithm. To\nverify the effectiveness of our methods, we compare them with several\nstate-of-the-art separable NMF algorithms on synthetic, document and image data\nsets.\n']","[('nonnegative matrix factorization', 0.7784861326217651), ('matrix factorization nmf', 0.665677547454834), ('negative matrix factorization', 0.6582097411155701), ('matrix factorizations', 0.6251937747001648), ('matrix factorization', 0.6173757910728455), ('factorization nmf', 0.5620045065879822), ('sparse nonnegative', 0.5560885071754456), ('nonnegative least squares', 0.528592050075531), ('nonnegative matrix', 0.5141505599021912), ('nonnegative matrices', 0.5137818455696106)]"
925,925,33,925_interacting particle systems_particle systems random_interacting particle system_graphons,"['interacting particle systems', 'particle systems random', 'interacting particle system', 'graphons', 'graphon', 'interacting particles', 'particle systems', 'particles tends infinity', 'random graphs', 'graph limit']","['Graphon mean field systems   We consider heterogeneously interacting diffusive particle systems and their\nlarge population limit. The interaction is of mean field type with weights\ncharacterized by an underlying graphon. A law of large numbers result is\nestablished as the system size increases and the underlying graphons converge.\nThe limit is given by a graphon mean field system consisting of independent but\nheterogeneous nonlinear diffusions whose probability distributions are fully\ncoupled. Well-posedness, continuity and stability of such systems are provided.\nWe also consider a not-so-dense analogue of the finite particle system,\nobtained by percolation with vanishing rates and suitable scaling of\ninteractions. A law of large numbers result is proved for the convergence of\nsuch systems to the corresponding graphon mean field system.\n', 'Graphon Particle Systems, Part I: Spatio-Temporal Approximation and Law\n  of Large Numbers   We study a class of graphon particle systems with time-varying random\ncoefficients. In a graphon particle system, the interactions among particles\nare characterized by the coupled mean field terms through an underlying graphon\nand the randomness of the coefficients comes from the stochastic processes\nassociated with the particle labels. By constructing two-level approximated\nsequences converging in 2-Wasserstein distance, we prove the existence and\nuniqueness of the solution to the system. Besides, by constructing two-level\napproximated functions converging to the graphon mean field terms, we establish\nthe law of large numbers, which reveals that if the number of particles tends\nto infinity and the discretization step tends to zero, then the discrete-time\ninteracting particle system over a large-scale network converges to the graphon\nparticle system. As a byproduct, we discover that the graphon particle system\ncan describe the limiting dynamics of the distributed stochastic gradient\ndescent algorithm over the large-scale network and prove that if the gradients\nof the local cost functions are Lipschitz continuous, then the graphon particle\nsystem can be regarded as the spatio-temporal approximation of the\ndiscrete-time distributed stochastic gradient descent algorithm as the number\nof network nodes tends to infinity and the algorithm step size tends to zero.\n', 'Non-parametric estimates for graphon mean-field particle systems   We consider the graphon mean-field system introduced in the work of\nBayraktar, Chakraborty, and Wu. It is the large-population limit of a\nheterogeneously interacting diffusive particle system, where the interaction is\nof mean-field type with weights characterized by an underlying graphon\nfunction. Through observation of continuous-time trajectories within the\nparticle system, we construct plug-in estimators of the particle density, the\ndrift coefficient, and thus the graphon interaction weights of the mean-field\nsystem. Our estimators for the density and drift are direct results of kernel\ninterpolation on the empirical data, and a deconvolution method leads to an\nestimator of the underlying graphon function. We show that, as the number of\nparticles increases, the graphon estimator converges to the true graphon\nfunction pointwisely, and as a consequence, in the cut metric. Besides, we\nconduct a minimax analysis within a particular class of particle systems to\njustify the pointwise optimality of the density and drift estimators.\n']","[('interacting particle systems', 0.5562077760696411), ('particle systems random', 0.527958869934082), ('interacting particle system', 0.5147179961204529), ('graphons', 0.4880158007144928), ('graphon', 0.4876387119293213), ('interacting particles', 0.4818522334098816), ('particle systems', 0.4699470102787018), ('particles tends infinity', 0.4534187614917755), ('random graphs', 0.4511101543903351), ('graph limit', 0.4418242275714874)]"
926,926,33,926_vertex models_yang baxter algebra_models vertex_baxter equations,"['vertex models', 'yang baxter algebra', 'models vertex', 'baxter equations', 'baxter algebra', 'yang baxter associated', 'solutions yang baxter', 'yang baxter', 'vertex can', 'integrable spin']","['Quantum inverse scattering for the 20-vertex model up to Dynkin\n  automorphism: crossing probabilities, 3D Poisson structure, triangular height\n  functions, weak integrability   We initiate a novel application of the quantum-inverse scattering method for\nthe 20-vertex model, building upon seminal work from Faddeev and Takhtajan on\nthe study of Hamiltonian systems, with applications to crossing probabilities,\n3D Poisson structure, triangular height functions, and integrability. In\ncomparison to a previous work of the author in late $2023$ which characterized\nintegrability of a Hamiltonian flow for the 6-vertex model from integrability\nof inhomogeneous limit shapes, formalized in a work of Keating, Reshetikhin and\nSridhar, notions similar to those of integrability can be realized for the\n20-vertex model by studying new classes of higher-dimensional L-operators. In\ncomparison to two-dimensional L-operators expressed in terms of Pauli basis\nelements, three-dimensional L-operators provided by Boos and colleagues have\nalgebraic, combinatorial, and geometric, qualities, all of which impact leading\norder approximations of correlations, products of L-operators, the transfer\nmatrix, and the quantum monodromy matrix in finite volume. In comparison to the\ninhomogeneous 6-vertex model, the 20-vertex model does not enjoy as strong of\nan integrability property through the existence of suitable action-angle\nvariables, which is of interest to further explore, possibly from information\non limit shapes given solutions to the three-dimensional Euler-Lagrange\nequations.\n', 'On the equivalence between n-state spin and vertex models on the square\n  lattice   In this paper we investigate a correspondence among spin and vertex models\nwith the same number of local states on the square lattice with toroidal\nboundary conditions. We argue that the partition functions of an arbitrary\n$n$-state spin model and of a certain specific $n$-state vertex model coincide\nfor finite lattice sizes. The equivalent vertex model has $n^3$ non-null\nBoltzmann weights and their relationship with the edge weights of the spin\nmodel is explicitly presented. In particular, the Ising model in a magnetic\nfield is mapped to an eight-vertex model whose weights configurations combine\nboth even and odd number of incoming and outcoming arrows at a vertex. We have\nstudied the Yang-Baxter algebra for such mixed eight-vertex model when the\nweights are invariant under arrows reversing. We find that while the Lax\noperator lie on the same elliptic curve of the even eight-vertex model the\nrespective $\\mathrm{R}$-matrix can not be presented in terms of the difference\nof two rapidities. We also argue that the spin-vertex equivalence may be used\nto imbed an integrable spin model in the realm of the quantum inverse\nscattering framework. As an example, we show how to determine the\n$\\mathrm{R}$-matrix of the 27-vertex model equivalent to a three-state spin\nmodel devised by Fateev and Zamolodchikov.\n', 'Approximability of Poisson structures for the 4-vertex model, and the\n  higher-spin XXX chain, and Yang-Baxter algebras   We implement the quantum inverse scattering method for the 4-vertex model. In\ncomparison to previous works of the author which examined the 6-vertex, and\n20-vertex, models, the 4-vertex model exhibits different characteristics,\nranging from L-operators expressed in terms of projectors and Pauli matrices to\nalgebraic and combinatorial properties, including Poisson structure and boxed\nplane partitions. With far fewer computations with an L-operator provided for\nthe 4-vertex model by Bogoliubov in 2007, in comparison to those for\nL-operators of the 6, and 20, vertex models, from lower order expansions of the\ntransfer matrix we derive a system of relations from the structure of operators\nthat can be leveraged for studying characteristics of the higher-spin XXX chain\nin the weak finite volume limit. In comparison to quantum inverse scattering\nmethods for the 6, and 20, vertex models which can be used to further study\nintegrability, and exact solvability, an adaptation of such an approach for the\n4-vertex model can be used to approximate, asymptotically in the weak finite\nvolume limit, sixteen brackets which generate the Poisson structure. From\nexplicit relations for operators of the 4-vertex transfer matrix, we conclude\nby discussing corresponding aspects of the Yang-Baxter algebra, which is\nclosely related to the operators obtained from products of L-operators for\napproximating the transfer, and quantum monodromy, matrices. The structure of\ncomputations from L-operators of the 4-vertex model directly transfers to\nL-operators of the higher-spin XXX chain, revealing a similar structure of\nanother Yang-Baxter algebra of interest.\n']","[('vertex models', 0.5471941828727722), ('yang baxter algebra', 0.5242162346839905), ('models vertex', 0.5077848434448242), ('baxter equations', 0.474685400724411), ('baxter algebra', 0.4717343747615814), ('yang baxter associated', 0.44250041246414185), ('solutions yang baxter', 0.43491649627685547), ('yang baxter', 0.42137736082077026), ('vertex can', 0.4134446680545807), ('integrable spin', 0.41273146867752075)]"
927,927,33,927_nash equilibrium_pure nash equilibria_nash equilibria_duopoly,"['nash equilibrium', 'pure nash equilibria', 'nash equilibria', 'duopoly', 'oligopoly', 'market equilibrium', 'monopoly', 'congestion games', 'congestion game', 'equilibrium']","['Equilibrium Computation in Resource Allocation Games   We study the equilibrium computation problem for two classical resource\nallocation games: atomic splittable congestion games and multimarket Cournot\noligopolies. For atomic splittable congestion games with singleton strategies\nand player-specific affine cost functions, we devise the first polynomial time\nalgorithm computing a pure Nash equilibrium. Our algorithm is combinatorial and\ncomputes the exact equilibrium assuming rational input. The idea is to compute\nan equilibrium for an associated integrally-splittable singleton congestion\ngame in which the players can only split their demands in integral multiples of\na common packet size. While integral games have been considered in the\nliterature before, no polynomial time algorithm computing an equilibrium was\nknown. Also for this class, we devise the first polynomial time algorithm and\nuse it as a building block for our main algorithm.\n  We then develop a polynomial time computable transformation mapping a\nmultimarket Cournot competition game with firm-specific affine price functions\nand quadratic costs to an associated atomic splittable congestion game as\ndescribed above. The transformation preserves equilibria in either games and,\nthus, leads -- via our first algorithm -- to a polynomial time algorithm\ncomputing Cournot equilibria. Finally, our analysis for integrally-splittable\ngames implies new bounds on the difference between real and integral Cournot\nequilibria. The bounds can be seen as a generalization of the recent bounds for\nsingle market oligopolies obtained by Todd [2016].\n', ""Ambiguity aversion as a route to randomness in a duopoly game   The global dynamics is investigated for a duopoly game where the perfect\nforesight hypothesis is relaxed and firms are worst-case maximizers.\nOverlooking the degree of product substitutability as well as the sensitivity\nof price to quantity, the unique and globally stable Cournot-Nash equilibrium\nof the complete-information duopoly game, loses stability when firms are not\naware if they are playing a duopoly game, as it is, or an oligopoly game with\nmore than two competitors. This finding resembles Theocharis' condition for the\nstability of the Cournot-Nash equilibrium in oligopolies without uncertainty.\nAs opposed to complete-information oligopoly games, coexisting attractors,\ndisconnected basins of attractions and chaotic dynamics emerge when the\nCournot-Nash equilibrium loses stability. This difference in the global\ndynamics is due to the nonlinearities introduced by the worst-case approach to\nuncertainty, which mirror in bimodal best-reply functions. Conducted with\ntechniques that require a symmetric setting of the game, the investigation of\nthe dynamics reveals that a chaotic regime prevents firms from being ambiguity\naverse, that is, firms are worst-case maximizers only in the\nquantity-expectation space. Therefore, chaotic dynamics are the result and at\nthe same time the source of profit uncertainty.\n"", 'Pure Nash Equilibria in Weighted Congestion Games with Complementarities\n  and Beyond   Congestion games offer a primary model in the study of pure Nash equilibria\nin non-cooperative games, and a number of generalized models have been proposed\nin the literature. One line of generalization includes weighted congestion\ngames, in which the cost of a resource is a function of the total weight of the\nplayers choosing that resource. Another line includes congestion games with\nmixed costs, in which the cost imposed on a player is a convex combination of\nthe total cost and the maximum cost of the resources in her strategy. This\nmodel is further generalized to that of congestion games with\ncomplementarities. For the above models, the existence of a pure Nash\nequilibrium is proved under some assumptions, including that the strategy space\nof each player is the base family of a matroid and that the cost functions have\na certain kind of monotonicity. In this paper, we deal with common\ngeneralizations of these two lines, namely weighted matroid congestion games\nwith complementarities, and its further generalization. Our main technical\ncontribution is a proof of the existence of pure Nash equilibria in these\ngeneralized models under a simplified assumption on the monotonicity, which\nprovide a common extension of the previous results. We also present some\nextensions on the existence of pure Nash equilibria in player-specific and\nweighted matroid congestion games with mixed costs.\n']","[('nash equilibrium', 0.6738358736038208), ('pure nash equilibria', 0.6381139159202576), ('nash equilibria', 0.6109659075737), ('duopoly', 0.5671519637107849), ('oligopoly', 0.5649636387825012), ('market equilibrium', 0.5443773865699768), ('monopoly', 0.5156446099281311), ('congestion games', 0.5116968750953674), ('congestion game', 0.5013328790664673), ('equilibrium', 0.47535440325737)]"
928,928,33,928_fano varieties_stability fano_fano hypersurfaces_fano variety,"['fano varieties', 'stability fano', 'fano hypersurfaces', 'fano variety', 'log fano pairs', 'log fano', 'fano pairs', 'smooth fano', 'algebraic stability', 'criterion stability']","['K\\""ahler-Ricci solitons on Fano threefolds with non-trivial moduli   We find Fano threefolds $X$ admitting K\\""ahler-Ricci solitons (KRS) with\nnon-trivial moduli, which are $\\mathbb{T}$-varieties of complexity two. More\nprecisely, we show that the weighted K-stability of $(X,\\xi_0)$ (where $\\xi_0$\nis the soliton candidate) is equivalent to certain GIT-stability. In\nparticular, this provides the first examples of strictly weighted K-semistable\nFano varieties. On the other hand, we generalize Koiso\'s theorem to the log\nFano setting. Indeed, we show that the K-stability of a log Fano pair\n$(V,\\Delta_V)$ is equivalent to the weighted K-stability of a cone $(Y,\n\\Delta_Y, \\xi_0)$ over it. This also leads to new examples of KRS Fano\nvarieties with non-trivial moduli and small automorphism groups. To achieve\nthese, we establish the weighted Abban-Zhuang estimate generalizing the work of\n\\cite{AZ22}, which gives a lower bound of the weighted stability threshold\n$\\delta^g_{\\mathbb{T}}(X,\\Delta)$. This is an effective way to check the\nweighted K-semistablity of a log Fano triple $(X,\\Delta,\\xi_0)$. This estimate\nis also useful in testing (weighted) K-polystability based on the work of\n\\cite{BLXZ23}.\n', 'Finite generation for valuations computing stability thresholds and\n  applications to K-stability   We prove that on any log Fano pair of dimension $n$ whose stability threshold\nis less than $\\frac{n+1}{n}$, any valuation computing the stability threshold\nhas a finitely generated associated graded ring. Together with earlier works,\nthis implies: (a) a log Fano pair is uniformly K-stable (resp. reduced\nuniformly K-stable) if and only if it is K-stable (resp. K-polystable); (b) the\nK-moduli spaces are proper and projective; and combining with the previously\nknown equivalence between the existence of K\\""ahler-Einstein metric and reduced\nuniform K-stability proved by the variational approach, (c) the\nYau-Tian-Donaldson conjecture holds for general (possibly singular) log Fano\npairs.\n', '$\\delta$-invariants of log Fano planes We compute the $\\delta$-invariant for pairs $(\\mathbb{P}^2, \\lambda C_d)$, where $C_d$ is a plane curve of degree $d \\leq 4$. These computations provide new examples of $K$-stable and $K$-semistable log Fano pairs, and contribute to the study of $K$-stability of log Fano varieties via the Abban-Zhuang method, which reduces higher-dimensional problems to the surface case.']","[('fano varieties', 0.6066615581512451), ('stability fano', 0.5659857988357544), ('fano hypersurfaces', 0.5384519696235657), ('fano variety', 0.5208280086517334), ('log fano pairs', 0.5082427263259888), ('log fano', 0.4493814706802368), ('fano pairs', 0.4466005563735962), ('smooth fano', 0.4393644630908966), ('algebraic stability', 0.4377620816230774), ('criterion stability', 0.42516228556632996)]"
929,929,33,929_alternating minimization_alternating direction multipliers_convex optimization_alternating direction multiplier,"['alternating minimization', 'alternating direction multipliers', 'convex optimization', 'alternating direction multiplier', 'convex optimization problems', 'linearized alternating direction', 'convex programming', 'linearized alternating', 'nonconvex optimization', 'proximal alternating direction']","['Alternating direction method of multipliers for convex programming: a\n  lift-and-permute scheme   A lift-and-permute scheme of alternating direction method of multipliers\n(ADMM) is proposed for linearly constrained convex programming. It contains not\nonly the newly developed balanced augmented Lagrangian method and its\ndual-primal variation, but also the proximal ADMM and Douglas-Rachford\nsplitting algorithm. It helps to propose accelerated algorithms with worst-case\n$O(1/k^2)$ convergence rates in the case that the objective function to be\nminimized is strongly convex.\n', ""Accelerated linearized alternating direction method of multipliers with\n  Nesterov extrapolation   The alternating direction method of multipliers (ADMM) has found widespread\nuse in solving separable convex optimization problems. In this paper, by\nemploying Nesterov extrapolation technique, we propose two families of\naccelerated linearized ADMMs for addressing two-block linearly constrained\nseparable convex optimization problems where each block of the objective\nfunction exhibits a ``nonsmooth'' + ``smooth'' composite structure. Our\nproposed accelerated linearized ADMMs extend two classical Nesterov\nacceleration methods designed for unconstrained composite optimization problems\nto linearly constrained problems. These methods are capable of achieving\nnon-ergodic convergence rates of $\\mathcal{O}(1/k^2)$, provided that one block\nof the objective function exhibits strong convexity and the gradients of smooth\nterms are Lipschitz continuous. We show that the proposed methods can reduce to\naccelerated linearized augmented Lagrangian methods (ALMs) for solving\none-block linearly constrained convex optimization problems. By choosing\ndifferent extrapolation parameters, we explore the relationship between the\nproposed methods and some existing accelerated methods. Numerical results are\npresented to validate the efficacy and reliability of the proposed algorithms.\n"", 'The global linear convergence rate of the proximal version of the\n  generalized alternating direction method of multipliers for separable convex\n  programming   To solve the separable convex optimization problem with linear constraints,\nEckstein and Bertsekas introduced the generalized alternating direction method\nof multipliers (in short, GADMM), which is an efficient and simple acceleration\nscheme of the aternating direction method of multipliers. Recently,\n\\textbf{Fang et. al} proposed the linearized version of generalized alternating\ndirection method of multipliers (in short, L-GADMM), where one of its\nsubproblems is approximated by a linearization strategy, and proved its\nworst-case $\\mathcal{O}(1/t)$ convergence rate measured by the iteration\ncomplexity in both ergodic and nonergodic senses. In this paper, we introduce\nthe doubly linearized version of generalized alternating direction method of\nmultipliers (in short, DL-GADMM), where both the $x$-subproblem and\n$y$-subproblem are approximated by linearization strategies. Based on the error\nbound approach, we establish the linear convergence rate of both L-GADMM and\nDL-GADMM for separable convex optimization problem that the subdifferentials of\nthe underlying functions are piecewise linear multifunctions. The results in\nthis paper extend, generalize and improve some known results in the literature.\n']","[('alternating minimization', 0.6283243298530579), ('alternating direction multipliers', 0.6005332469940186), ('convex optimization', 0.5592957139015198), ('alternating direction multiplier', 0.552680253982544), ('convex optimization problems', 0.5495433807373047), ('linearized alternating direction', 0.5450684428215027), ('convex programming', 0.5358703136444092), ('linearized alternating', 0.5206400752067566), ('nonconvex optimization', 0.5037586688995361), ('proximal alternating direction', 0.49635598063468933)]"
930,930,33,930_gapped quantum_quantum spin systems_quantum lattice systems_spectral gaps,"['gapped quantum', 'quantum spin systems', 'quantum lattice systems', 'spectral gaps', 'spectral gap', 'spin systems', 'gapped ground state', 'spin hamiltonians', 'topological quantum', 'quantum chains']","['Quasi-Locality Bounds for Quantum Lattice Systems. Part II.\n  Perturbations of Frustration-Free Spin Models with Gapped Ground States   We study the stability with respect to a broad class of perturbations of\ngapped ground state phases of quantum spin systems defined by frustration-free\nHamiltonians. The core result of this work is a proof using the\nBravyi-Hastings-Michalakis (BHM) strategy that under a condition of Local\nTopological Quantum Order, the bulk gap is stable under perturbations that\ndecay at long distances faster than a stretched exponential. Compared to\nprevious work we expand the class of frustration-free quantum spin models that\ncan be handled to include models with more general boundary conditions, and\nmodels with discrete symmetry breaking. Detailed estimates allow us to\nformulate sufficient conditions for the validity of positive lower bounds for\nthe gap that are uniform in the system size and that are explicit to some\ndegree. We provide a survey of the BHM strategy following the approach of\nMichalakis and Zwolak, with alterations introduced to accommodate more general\nthan just periodic boundary conditions and more general lattices. We express\nthe fundamental condition known as LTQO by means of the notion of\nindistinguishability radius, which we introduce. Using the uniform\nfinite-volume results we then proceed to study the thermodynamic limit. We\nfirst study the case of a unique limiting ground state and then also consider\nmodels with spontaneous breaking of a discrete symmetry. In the latter case,\nLTQO cannot hold for all local observables. However, for perturbations that\npreserve the symmetry, we show stability of the gap and the structure of the\nbroken symmetry phases. We prove that the GNS Hamiltonian associated with each\npure state has a non-zero spectral gap above the ground state.\n', 'Quantum Spin Systems   This work provides an overview of gapped quantum spin systems, including\nconcepts, techniques, properties, and results. The basic framework and objects\nof interest for quantum spin systems are introduced, and the main ideas behind\nmethods for proving spectral gaps for frustration-free models are outlined.\nAfter reviewing recent progress on several spectral gap conjectures, we discuss\nquasi-locality of the Heisenberg dynamics and its utility in proving properties\nof gapped quantum spin systems. Lieb-Robinson bounds have played a central role\nin establishing exponential decay of ground state correlations, an area law for\none-dimensional systems, a many-body adiabatic theorem, and spectral gap\nstability. They also aided in the development of the quasi-adiabatic\ncontinuation, which is a useful for investigating gapped ground state phases,\nboth of which are also discussed.\n', 'Local stability of ground states in locally gapped and weakly\n  interacting quantum spin systems   Based on a result by Yarotsky (J. Stat. Phys. 118, 2005), we prove that\nlocalized but otherwise arbitrary perturbations of weakly interacting quantum\nspin systems with uniformly gapped on-site terms change the ground state of\nsuch a system only locally, even if they close the spectral gap. We call this a\nstrong version of the local perturbations perturb locally (LPPL) principle\nwhich is known to hold for much more general gapped systems, but only for\nperturbations that do not close the spectral gap of the Hamiltonian. We also\nextend this strong LPPL-principle to Hamiltonians that have the appropriate\nstructure of gapped on-site terms and weak interactions only locally in some\nregion of space.\n  While our results are technically corollaries to a theorem of Yarotsky, we\nexpect that the paradigm of systems with a locally gapped ground state that is\ncompletely insensitive to the form of the Hamiltonian elsewhere extends to\nother situations and has important physical consequences.\n']","[('gapped quantum', 0.6268677115440369), ('quantum spin systems', 0.5935460329055786), ('quantum lattice systems', 0.5608203411102295), ('spectral gaps', 0.5358720421791077), ('spectral gap', 0.5233171582221985), ('spin systems', 0.5129846930503845), ('gapped ground state', 0.5115890502929688), ('spin hamiltonians', 0.49985072016716003), ('topological quantum', 0.4976270794868469), ('quantum chains', 0.4750666618347168)]"
931,931,33,931_binary sequences_binary sequence_symmetric sequences_automatic sequences,"['binary sequences', 'binary sequence', 'symmetric sequences', 'automatic sequences', 'sequences length', 'sequences large', 'sequences high', 'symmetric binary', 'sequences odd', 'autocorrelations']","['Computational Searching of Long Skew-symmetric Binary Sequences with\n  High Merit Factors   In this paper, we present a computational search for best-known merit factors\nof longer binary sequences with an odd length. Finding low autocorrelation\nbinary sequences with optimal or suboptimal merit factors is a very difficult\noptimization problem. An improved version of the heuristic algorithm is\npresented and tackled to search for aperiodic binary sequences with good\nautocorrelation properties. High-performance computations with the execution of\nour stochastic algorithm to search skew-symmetric binary sequences with high\nmerit factors. After experimental work, as results, we present new binary\nsequences with odd lengths between 201 and 303 that are skew-symmetric and have\nthe merit factor $F$ greater than 8.5. Moreover, an example of a binary\nsequence having $F > 8$ has been found for all odd lengths between 201 and 303.\nThe longest binary sequence with $F > 9$ found to date is of length 255.\n', 'Arithmetic autocorrelation distribution of binary $m$-sequences   Binary $m$-sequences are ones with the largest period $n=2^m-1$ among the\nbinary sequences produced by linear shift registers with length $m$. They have\na wide range of applications in communication since they have several desirable\npseudorandomness such as balance, uniform pattern distribution and ideal\n(classical) autocorrelation. In his reseach on arithmetic codes, Mandelbaum\n\\cite{9Mand} introduces a 2-adic version of classical autocorrelation of binary\nsequences, called arithmetic autocorrelation. Later, Goresky and Klapper\n\\cite{3G1,4G2,5G3,6G4} generalize this notion to nonbinary case and develop\nseveral properties of arithmetic autocorrelation related to linear shift\nregisters with carry. Recently, Z. Chen et al. \\cite{1C1} show an upper bound\non arithmetic autocorrelation of binary $m$-sequences and raise a conjecture on\nabsolute value distribution on arithmetic autocorrelation of binary\n$m$-sequences.\n', ""Linear Complexity of Binary Interleaved Sequences of Period 4n   Binary periodic sequences with good autocorrelation property have many\napplications in many aspects of communication. In past decades many series of\nsuch binary sequences have been constructed. In the application of\ncryptography, such binary sequences are required to have larger linear\ncomplexity. Tang and Ding \\cite{X. Tang} presented a method to construct a\nseries of binary sequences with period 4$n$ having optimal autocorrelation.\nSuch sequences are interleaved by two arbitrary binary sequences with period\n$n\\equiv 3\\pmod 4$ and ideal autocorrelation. In this paper we present a\ngeneral formula on the linear complexity of such interleaved sequences.\nParticularly, we show that the linear complexity of such sequences with period\n4$n$ is not bigger than $2n+2$. Interleaving by several types of known binary\nsequences with ideal autocorrelation ($m$-sequences, Legendre, twin-prime and\nHall's sequences), we present many series of such sequences having the maximum\nvalue $2n+2$ of linear complexity which gives an answer of a problem raised by\nN. Li and X. Tang \\cite{N. Li}. Finally, in the conclusion section we show that\nit can be seen easily that the 2-adic complexity of all such interleaved\nsequences reaches the maximum value $\\log_{2}(2^{4n}-1)$.\n""]","[('binary sequences', 0.5763679146766663), ('binary sequence', 0.5167942643165588), ('symmetric sequences', 0.47733110189437866), ('automatic sequences', 0.47104722261428833), ('sequences length', 0.46473920345306396), ('sequences large', 0.45295101404190063), ('sequences high', 0.43920624256134033), ('symmetric binary', 0.43564218282699585), ('sequences odd', 0.4315601885318756), ('autocorrelations', 0.4278120696544647)]"
932,932,33,932_heegaard splittings_heegaard splitting_heegaard genus_heegaard,"['heegaard splittings', 'heegaard splitting', 'heegaard genus', 'heegaard', 'seifert manifold', 'seifert fibered spaces', 'genus three', 'orientable manifold', 'closed orientable manifold', 'genus two']","['Finite presentations of the mapping class groups of once-stabilized\n  Heegaard splittings   Let $g \\ge 2$ and assume that we are given a genus $g$ Heegaard splitting of\na closed orientable $3$-manifold with the distance greater than $2g+2$. We\nprove that the mapping class group of the once-stabilization of such a Heegaard\nsplitting is finitely presented.\n', 'On the weak reducing pairs in critical Heegaard splitting   A weak reducing pair in a Heegaard splitting M = V \\cup_S W is a pair of\ndisjoint essential disks D \\in V and E \\in W. The weakly reducible Heegaard\nsplitting contains at least one weak reducing pair. Critical Heegaard splitting\nis a special case of weakly reducible Heegaard splitting which contains at\nleast two weak reducing pairs satisfying some special conditions. In this\npaper, we discuss the properties of weak reducing pairs in a critical Heegaard\nsplitting and give a necessary condition for Heegaard surface to be critical.\n', 'Genus 2 Goeritz Equivalence in $S^3$   The Goeritz group of a genus $g$ Heegaard splitting of a 3-manifold is the\ngroup of isotopy classes of orientation-preserving automorphisms of the\nmanifold that preserve the Heegaard splitting. In the context of the standard\ngenus 2 Heegaard splitting of $S^3$, we introduce the concept of Goeritz\nequivalence of curves, present two algebraic obstructions to Goeritz\nequivalence of simple closed curves that are straightforward to compute, and\nprovide families of examples demonstrating how these obstructions may be used.\n']","[('heegaard splittings', 0.8089955449104309), ('heegaard splitting', 0.7822936177253723), ('heegaard genus', 0.711970329284668), ('heegaard', 0.6125331521034241), ('seifert manifold', 0.5376759767532349), ('seifert fibered spaces', 0.4663276970386505), ('genus three', 0.41766881942749023), ('orientable manifold', 0.4159947335720062), ('closed orientable manifold', 0.40687036514282227), ('genus two', 0.3946378231048584)]"
933,933,32,933_sobolev type inequality_hardy sobolev inequality_sobolev inequality_nirenberg inequality,"['sobolev type inequality', 'hardy sobolev inequality', 'sobolev inequality', 'nirenberg inequality', 'kohn nirenberg inequality', 'positive radially symmetric', 'hardy sobolev', 'radially symmetric', 'sobolev type', 'sobolev']","['Symmetry breaking of extremals for the high order\n  Caffarelli-Kohn-Nirenberg type inequalities: the singular case   Let us consider the following Caffarelli-Kohn-Nirenberg type inequality\n\\begin{equation}\\label{nsckn} \\int_{\\mathbb{R}^N}|x|^{-\\beta}|\\mathrm{div}\n(|x|^{\\alpha}\\nabla u)|^2 \\mathrm{d}x \\geq\n\\mathcal{S}\\left(\\int_{\\mathbb{R}^N}|x|^{\\gamma} |u|^{2^{**}_{\\alpha,\\beta}}\n\\mathrm{d}x\\right)^{\\frac{2}{2^{**}_{\\alpha,\\beta}}}, \\quad \\mbox{for all}\\quad\nu\\in C^\\infty_0(\\mathbb{R}^N\\setminus\\{0\\}), \\end{equation} for some\n$\\mathcal{S}=\\mathcal{S}(N,\\alpha,\\beta)>0$, where $N\\geq 5$, $\\alpha>2-N$,\n$\\frac{N-4}{N-2}\\alpha-4 \\leq \\beta\\leq\\alpha -2$ and \\begin{align*}\n2^{**}_{\\alpha,\\beta}:=\\frac{2(N+\\gamma)}{N+2\\alpha-\\beta-4} \\quad\n\\mbox{with}\\quad (N+\\beta)(N+\\gamma)=(N+2\\alpha-\\beta-4)^2. \\end{align*} A\ncrucial element is that the functional\n$\\int_{\\mathbb{R}^N}|x|^{-\\beta}|\\mathrm{div} (|x|^{\\alpha}\\nabla u)|^2\n\\mathrm{d}x$ is equivalent to $\\int_{\\mathbb{R}^N}|x|^{2\\alpha-\\beta}|\\Delta\nu|^2 \\mathrm{d}x$. Firstly, we obtain a symmetry result (with partial\ntranslation invariant) when $\\alpha=0$ and $\\beta=-4$, then existence and\nnon-existence of extremal functions for the best constant $\\mathcal{S}$ in\n\\eqref{nsckn} under different conditions are completely given. Moreover, by a\nresult of linearized problem related to radial solution of \\eqref{Pwhs0}, we\nobtain a symmetry breaking conclusion: when $\\alpha>0$ and\n$\\frac{N-4}{N-2}\\alpha-4<\\beta<\\beta_{\\mathrm{FS}}(\\alpha)$ where\n$\\beta_{\\mathrm{FS}}(\\alpha):= N+2\\alpha-4-\\sqrt{(N-2+\\alpha)^2+4(N-1)}$, the\nextremal functions for $\\mathcal{S}$ are nonradial. Finally, we give a partial\nsymmetry result when $\\beta=\\frac{N-4}{N-2}\\alpha-4$ and $2-N<\\alpha<0$, and we\nalso study the stability of extremal functions.\n', ""Symmetry and symmetry breaking for the fractional\n  Caffarelli-Kohn-Nirenberg inequality   In this paper, we will consider the fractional Caffarelli-Kohn-Nirenberg\ninequality \\begin{equation*} {\\Lambda} \\left(\\int_{\\mathbb\nR^n}\\frac{|u(x)|^{p}}{|x|^{{\\beta} {p}}}\\,dx\\right)^{\\frac{2}{p}}\\leq\n\\int_{\\mathbb R^n}\\int_{\\mathbb\nR^n}\\frac{(u(x)-u(y))^2}{|x-y|^{n+2\\gamma}|x|^{{\\alpha}}|y|^{{\\alpha}}}\\,dy\\,dx\n\\end{equation*} where $\\gamma\\in(0,1)$, $n\\geq 2$, and $\\alpha,\\beta\\in\\mathbb\nR$ satisfy \\begin{equation*} \\alpha\\leq \\beta\\leq \\alpha+\\gamma, \\\n-2\\gamma<\\alpha<\\frac{n-2\\gamma}{2}, \\end{equation*} and the exponent $p$ is\nchosen to be \\begin{equation*} p=\\frac{2n}{n-2\\gamma+2(\\beta-\\alpha)},\n\\end{equation*} such that the inequality is invariant under scaling. We first\nstudy the existence and nonexistence of extremal solutions. Our next goal is to\nshow some results on the symmetry and symmetry breaking region for the\nminimizers; these suggest the existence of a Felli-Schneider type curve\nseparating both regions but, surprisingly, we find a novel behavior as\n$\\alpha\\to -2\\gamma$. The main idea in the proofs, as in the classical case, is\nto reformulate the fractional Caffarelli-Kohn-Nirenberg inequality in\ncylindrical variables. Then, in order to find the radially symmetric solutions\nwe need to solve a non-local ODE.\n  For this equation we also get uniqueness of minimizers in the radial symmetry\nclass; indeed, we show that the unique continuation argument of Frank-Lenzmann\n(Acta'13) can be applied to more general operators with good spectral\nproperties. We provide, in addition, a completely new proof of non-degeneracy\nwhich works for all critical points. It is based on the variation of constants\napproach and the non-local Wronskian of\nAo-Chan-DelaTorre-Fontelos-Gonz\\'alez-Wei (Duke'19).\n"", ""Stability of Caffarelli-Kohn-Nirenberg inequality   In this paper, we consider the Caffarelli-Kohn-Nirenberg (CKN) inequality:\n\\begin{eqnarray*} \\bigg(\\int_{{\\mathbb\nR}^N}|x|^{-b(p+1)}|u|^{p+1}dx\\bigg)^{\\frac{2}{p+1}}\\leq C_{a,b,N}\\int_{{\\mathbb\nR}^N}|x|^{-2a}|\\nabla u|^2dx \\end{eqnarray*} where $N\\geq3$, $a<\\frac{N-2}{2}$,\n$a\\leq b\\leq a+1$ and $p=\\frac{N+2(1+a-b)}{N-2(1+a-b)}$. It is well-known that\nup to dilations $\\tau^{\\frac{N-2}{2}-a}u(\\tau x)$ and scalar multiplications\n$Cu(x)$, the CKN inequality has a unique extremal function $W(x)$ which is\npositive and radially symmetric in the parameter region $b_{FS}(a)\\leq b<a+1$\nwith $a<0$ and $a\\leq b<a+1$ with $a\\geq0$ and $a+b>0$, where $b_{FS}(a)$ is\nthe Felli-Schneider curve. We prove that in the above parameter region the\nfollowing stabilities hold: \\begin{enumerate} \\item[$(1)$] \\quad stability of\nCKN inequality in the functional inequality setting $$dist_{D^{1,2}_{a}}^2(u,\n\\mathcal{Z})\\lesssim\\|u\\|^2_{D^{1,2}_a({\\mathbb\nR}^N)}-C_{a,b,N}^{-1}\\|u\\|^2_{L^{p+1}(|x|^{-b(p+1)},{\\mathbb R}^N)}$$ where\n$\\mathcal{Z}= \\{ c W_\\tau\\mid c\\in\\bbr\\backslash\\{0\\}, \\tau>0\\}$;\n\\item[$(2)$]\\quad stability of CKN inequality in the critical point setting (in\nthe class of nonnegative functions) \\begin{eqnarray*} dist_{D_a^{1,2}}(u,\n\\mathcal{Z}_0^\\nu)\\lesssim\\left\\{\\aligned &\\Gamma(u),\\quad p>2\\text{ or\n}\\nu=1,\\\\ &\\Gamma(u)|\\log\\Gamma(u)|^{\\frac12},\\quad p=2\\text{ and }\\nu\\geq2,\\\\\n&\\Gamma(u)^{\\frac{p}{2}},\\quad 1<p<2\\text{ and }\\nu\\geq2, \\endaligned\\right.\n\\end{eqnarray*} where $\\Gamma (u)=\\|div(|x|^{-a}\\nabla\nu)+|x|^{-b(p+1)}|u|^{p-1}u\\|_{(D^{1,2}_a)^{'}}$ and\n$$\\mathcal{Z}_0^\\nu=\\{(W_{\\tau_1},W_{\\tau_2},\\cdots,W_{\\tau_\\nu})\\mid\n\\tau_i>0\\}.$$\n""]","[('sobolev type inequality', 0.4964633285999298), ('hardy sobolev inequality', 0.47779738903045654), ('sobolev inequality', 0.4769239127635956), ('nirenberg inequality', 0.4708486795425415), ('kohn nirenberg inequality', 0.4691905975341797), ('positive radially symmetric', 0.3811880052089691), ('hardy sobolev', 0.35020849108695984), ('radially symmetric', 0.3253561556339264), ('sobolev type', 0.3239899277687073), ('sobolev', 0.3098953068256378)]"
934,934,32,934_logarithmic sobolev inequality_log sobolev inequality_logarithmic sobolev inequalities_log sobolev inequalities,"['logarithmic sobolev inequality', 'log sobolev inequality', 'logarithmic sobolev inequalities', 'log sobolev inequalities', 'entropy inequality', 'sobolev inequality', 'sobolev inequalities', 'entropy inequalities', 'log concave measures', 'concentration inequality']","[""Logarithmic Sobolev inequalities for Dunkl operators with applications\n  to functional inequalities for singular Boltzmann-Gibbs measures   In this paper we study several inequalities of log-Sobolev type for Dunkl\noperators. After proving an equivalent of the classical inequality for the\nusual Dunkl measure $\\mu_k$, we also study a number of inequalities for\nprobability measures of Boltzmann type of the form $e^{-|x|^p} d\\mu_k$. These\nare obtained using the method of $U$-bounds. Poincar\\'e inequalities are\nobtained as consequences of the log-Sobolev inequality. The connection between\nPoincar\\'e and log-Sobolev inequalities is further examined, obtaining in\nparticular tight log-Sobolev inequalities. Finally, we study application to\nexponential integrability and to functional inequalities for a class of\nsingular Boltzmann-Gibbs measures.\n"", ""Instability results for the logarithmic Sobolev inequality and its\n  application to related inequalities   We show that there are no general stability results for the logarithmic\nSobolev inequality in terms of the Wasserstein distances and $L^{p}(d\\gamma)$\ndistance for $p>1$. To this end, we construct a sequence of centered\nprobability measures such that the deficit of the logarithmic Sobolev\ninequality converges to zero but the relative entropy and the moments do not,\nwhich leads to instability for the logarithmic Sobolev inequality. As an\napplication, we prove instability results for Talagrand's transportation\ninequality and the Beckner--Hirschman inequality.\n"", 'Stability of the logarithmic Sobolev inequality via the F\\""ollmer\n  Process   We study the stability and instability of the Gaussian logarithmic Sobolev\ninequality, in terms of covariance, Wasserstein distance and Fisher\ninformation, addressing several open questions in the literature. We first\nestablish an improved logarithmic Sobolev inequality which is at the same time\nscale invariant and dimension free. As a corollary, we show that if the\ncovariance of the measure is bounded by the identity, one may obtain a sharp\nand dimension-free stability bound in terms of the Fisher information matrix.\nWe then investigate under what conditions stability estimates control the\ncovariance, and when such control is impossible. For the class of measures\nwhose covariance matrix is dominated by the identity, we obtain optimal\ndimension-free stability bounds which show that the deficit in the logarithmic\nSobolev inequality is minimized by Gaussian measures, under a fixed covariance\nconstraint. On the other hand, we construct examples showing that without the\nboundedness of the covariance, the inequality is not stable. Finally, we study\nstability in terms of the Wasserstein distance, and show that even for the\nclass of measures with a bounded covariance matrix, it is hopeless to obtain a\ndimension-free stability result. The counterexamples provided motivate us to\nput forth a new notion of stability, in terms of proximity to mixtures of the\nGaussian distribution. We prove new estimates (some dimension-free) based on\nthis notion. These estimates are strictly stronger than some of the existing\nstability results in terms of the Wasserstein metric. Our proof techniques rely\nheavily on stochastic methods.\n']","[('logarithmic sobolev inequality', 0.6567496657371521), ('log sobolev inequality', 0.6533122658729553), ('logarithmic sobolev inequalities', 0.6493963599205017), ('log sobolev inequalities', 0.6440371870994568), ('entropy inequality', 0.6011341214179993), ('sobolev inequality', 0.5708683729171753), ('sobolev inequalities', 0.5671609044075012), ('entropy inequalities', 0.5624983906745911), ('log concave measures', 0.562480628490448), ('concentration inequality', 0.5268920063972473)]"
935,935,32,935_graph simplicial complex_complexes graphs_independence complexes_simplicial complex,"['graph simplicial complex', 'complexes graphs', 'independence complexes', 'simplicial complex', 'simplicial complex whose', 'graphs homotopy', 'graph simplicial', 'matching complexes', 'complexes', 'complexes associated']","['On the Homotopy Type of the Polyhedral Join over the Independence\n  Complex of a Forest   We consider a certain class of simplicial complexes which includes the\nindependence complexes of forests. We show that if a simplicial complex $K$\nbelongs to this class, then the polyhedral join\n$\\mathcal{Z}^*_{K}(\\underline{X}, \\emptyset)$ is homotopy equivalent to a wedge\nsum of CW complexes of the form $\\Sigma^r X_{i_1} * X_{i_2} * \\cdots *\nX_{i_k}$, where $\\underline{X}$ is a family $\\{X_i\\}_{i \\in V(K)}$ of CW\ncomplexes and $\\Sigma$ denotes the unreduced suspension. This result is applied\nto study the homotopy type of the independence complex of the lexicographic\nproduct $G[H]$ of a graph $H$ over a forest $G$. We denote by $L_m$ a tree on\n$m$ vertices with no branches. We show that the geometric realization of the\nindependence complex of $L_m [H]$ is homotopy equivalent to a wedge sum of\nspheres if $m \\neq 2,3$ and the geometric realization of the independence\ncomplex of $H$ is homotopy equivalent to a wedge sum of same dimensional\nspheres.\n', 'Matching complexes of $\\bf 3 \\times n$ grid graphs   The matching complex of a graph $G$ is a simplicial complex whose simplices\nare matchings in $G$. In the last few years the matching complexes of grid\ngraphs have gained much attention among the topological combinatorists. In\n2017, Braun and Hough obtained homological results related to the matching\ncomplexes of $2 \\times n$ grid graphs. Further in 2019, Matsushita showed that\nthe matching complexes of $2 \\times n$ grid graphs are homotopy equivalent to a\nwedge of spheres. In this article we prove that the matching complexes of\n$3\\times n$ grid graphs are homotopy equivalent to a wedge of spheres. We also\ngive the comprehensive list of the dimensions of spheres appearing in the\nwedge.\n', 'The topology of independence complexes of square grids   The independence complex of a graph G is a simplicial complex whose simplices\nare the independent sets in G. In the last couple of decades, the independence\ncomplexes of square grids (with various boundary conditions) have gained much\nattention because of their connections with the hard square model from\nstatistical physics. In this article, we prove that if G is an $m\\times n$ grid\nwith open or cylindrical boundary condition then its independence complex is\nhomotopy equivalent to a wedge of spheres. A part of this result settles a\nconjecture of Iriye.\n']","[('graph simplicial complex', 0.6530396938323975), ('complexes graphs', 0.6488934755325317), ('independence complexes', 0.5992608070373535), ('simplicial complex', 0.5990431904792786), ('simplicial complex whose', 0.5971105098724365), ('graphs homotopy', 0.5916998982429504), ('graph simplicial', 0.5626470446586609), ('matching complexes', 0.5458251237869263), ('complexes', 0.5221084952354431), ('complexes associated', 0.5217562913894653)]"
936,936,32,936_splines defined_spline spaces_spline space_spline functions,"['splines defined', 'spline spaces', 'spline space', 'spline functions', 'spline basis', 'smooth splines', 'splines', 'hierarchical splines', 'splines used', 'rational splines']","['An algebraic framework for geometrically continuous splines   Geometrically continuous splines are piecewise polynomial functions defined\non a collection of patches which are stitched together through transition maps.\nThey are called $G^{r}$-splines if, after composition with the transition maps,\nthey are continuously differentiable functions to order $r$ on each pair of\npatches with stitched boundaries. This type of splines has been used to\nrepresent smooth shapes with complex topology for which (parametric) spline\nfunctions on fixed partitions are not sufficient. In this article, we develop\nnew algebraic tools to analyze $G^r$-spline spaces. We define $G^{r}$-domains\nand transition maps using an algebraic approach, and establish an algebraic\ncriterion to determine whether a piecewise function is $G^r$-continuous on the\ngiven domain. In the proposed framework, we construct a chain complex whose top\nhomology is isomorphic to the $G^{r}$-spline space. This complex generalizes\nBillera-Schenck-Stillman homological complex used to study parametric splines.\nAdditionally, we show how previous constructions of $G^r$-splines fit into this\nnew algebraic framework, and present an algorithm to construct a bases for\n$G^r$-spline spaces. We illustrate how our algebraic approach works with\nconcrete examples, and prove a dimension formula for the $G^r$-spline space in\nterms of invariants to the chain complex. In some special cases, explicit\ndimension formulas in terms of the degree of splines are also given.\n', 'Linear dependence of bivariate Minimal Support and Locally Refined\n  B-splines over LR-meshes   The focus on locally refined spline spaces has grown rapidly in recent years\ndue to the need in Isogeoemtric analysis (IgA) of spline spaces with local\nadaptivity: a property not offered by the strict regular structure of tensor\nproduct B-spline spaces. However, this flexibility sometimes results in\ncollections of B-splines spanning the space that are not linearly independent.\nIn this paper we address the minimal number of B-splines that can form a linear\ndependence relation for Minimal Support B-splines (MS B-splines) and for\nLocally Refinable B-splines (LR B-splines) on LR-meshes. We show that the\nminimal number is six for MS B-splines, and eight for LR B-splines. The risk of\nlinear dependency is consequently significantly higher for MS B-splines than\nfor LR B-splines. Further results are established to help detecting collections\nof B-splines that are linearly independent.\n', 'Counting the dimension of splines of mixed smoothness: A general recipe,\n  and its application to meshes of arbitrary topologies   In this paper we study the dimension of bivariate polynomial splines of mixed\nsmoothness on polygonal meshes. Here, ""mixed smoothness"" refers to the choice\nof different orders of smoothness across different edges of the mesh. To study\nthe dimension of spaces of such splines, we use tools from Homological Algebra.\nThese tools were first applied to the study of splines by Billera (1988). Using\nthem, estimation of the spline space dimension amounts to the study of the\ngeneralized Billera-Schenck-Stillman complex for the spline space. In\nparticular, when the homology in positions one and zero of this complex are\ntrivial, the dimension of the spline space can be computed combinatorially. We\ncall such spline spaces ""lower-acyclic."" In this paper, starting from a spline\nspace which is lower-acyclic, we present sufficient conditions that ensure that\nthe same will be true for the spline space obtained after relaxing the\nsmoothness requirements across a subset of the mesh edges. This general recipe\nis applied in a specific setting: meshes of arbitrary topologies. We show how\nour results can be used to compute the dimensions of spline spaces on\ntriangulations, polygonal meshes, and T-meshes with holes.\n']","[('splines defined', 0.7314746379852295), ('spline spaces', 0.7184091806411743), ('spline space', 0.7114237546920776), ('spline functions', 0.6948376893997192), ('spline basis', 0.687195360660553), ('smooth splines', 0.6828991174697876), ('splines', 0.6774836778640747), ('hierarchical splines', 0.6682880520820618), ('splines used', 0.6606513261795044), ('rational splines', 0.6531916856765747)]"
937,937,32,937_nilpotent lie groups_lie groups_dimensional lie groups_lie group,"['nilpotent lie groups', 'lie groups', 'dimensional lie groups', 'lie group', 'connected lie groups', 'linear control systems', 'invariant control', 'control affine systems', 'control sets', 'linear control']","['Weak condition for the existence of control sets with a nonempty\n  interior of linear control systems on nilpotent groups   In this paper, we show that for a linear control system on a nilpotent Lie\ngroup, the Lie algebra rank condition is enough to assure the existence of a\ncontrol set with a nonempty interior, as soon as the set of singularities of\nthe drift is compact. Moreover, this control set is unique and contains the\nsingularities of the drift in its closure.\n', 'One-input linear control systems on the homogeneous spaces of the\n  Heisenberg group -- The singular case   The controllability issue of control-affine systems on smooth manifolds is\none of the main problems in the theory, and it is recently known [Jouan P.\nEquivalence of control systems with linear systems on Lie groups and\nhomogeneous spaces. ESAIM: Control Optim. Calc. Var. 2010, 16, 956-973] that it\nmight be connected to that of a particular class of systems called linear\ncontrol systems on (a homogeneous manifold of) a Lie group. Note that it may\nbecome very complicated to establish the controllability property of systems\nevolving on homogeneous spaces of Lie groups whose dynamics are induced by\nthose of systems in the Lie group under consideration. In fact, even in\nlow-dimensional certain homogeneous spaces, this is quite a challenging task,\nand for this reason, we have classified in [Da Silva, A., Kizil, E., Duman, O.\nLinear Control Systems on Homogeneous Spaces of the Heisenberg Group. J. Dyn.\nControl Syst. 2023, 29, 2065-2086] as a first goal all linear control systems\non the homogeneous spaces of the 3-dimensional Heisenberg group $\\mathbb{H}$\nthrough its closed subgroups $L$ and, in particular, the controllability and\nthe control sets have been studied for one of the homogeneous spaces\n$L\\setminus \\mathbb{H}$.\n  In this paper, we study the controllability and control sets of the induced\nlinear control systems in the homogeneous spaces left. In particular, we focus\non the singularity of the induced drift vector fields that results in many\ncases and subcases to reveal control sets after quite a technical analysis. We\ngive some nice illustrations to better understand what is going on\ngeometrically.\n', 'Control sets of one-input linear control systems on solvable,\n  nonnilpotent 3D Lie groups   In this article, we completely describe the control sets of one-input linear\ncontrol systems on solvable, nonnilpotent 3D Lie groups. We show that, if the\nrestriction of the associate derivation to the nilradical is nontrivial, the\nLie algebra rank condition is enough to assure the existence of a control set\nwith a nonempty interior. Moreover, such a control set is unique and, up to\nconjugations, given as a cylinder of the state space. On the other hand, if\nsuch a restriction is trivial, one can obtain an infinite number of control\nsets with empty interiors or even controllability, depending on the group\nconsidered.\n']","[('nilpotent lie groups', 0.5913504958152771), ('lie groups', 0.5869743824005127), ('dimensional lie groups', 0.5796324014663696), ('lie group', 0.5670908093452454), ('connected lie groups', 0.5320622324943542), ('linear control systems', 0.5233091711997986), ('invariant control', 0.5091637372970581), ('control affine systems', 0.5031331777572632), ('control sets', 0.48796382546424866), ('linear control', 0.47860726714134216)]"
938,938,32,938_shifted tableaux_semistandard young tableaux_crystal operators_crystal structures,"['shifted tableaux', 'semistandard young tableaux', 'crystal operators', 'crystal structures', 'young tableaux', 'tableaux', 'crystal structure', 'crystals', 'crystal graph', 'crystal']","['A shifted Berenstein-Kirillov group and the cactus group   The Bender-Knuth involutions on semistandard Young tableaux are known to\ncoincide with the tableau switching on horizontal border strips of two adjacent\nletters, together with the swapping of those letters. Motivated by this\ncoincidence and using the shifted tableau switching due to Choi, Nam and Oh\n(2019), we consider a shifted version of the Bender-Knuth involutions and\ndefine a shifted version of the Berenstein-Kirillov group (1995). Similarly to\nthe classical case, the shifted version of the Berenstein-Kirillov group also\nacts on the straight-shaped shifted tableau crystals introduced by Gillespie,\nLevinson and Purbhoo (2020), via partial Sch\\""utzenberger involutions, thus\ncoinciding with the action of the cactus group on the same crystal, due to the\nauthor. Following the works of Halacheva (2016, 2020), and Chmutov, Glick and\nPylyavskyy (2020), on the relation between the actions of the\nBerenstein-Kirillov group and the cactus group on a crystal of straight-shaped\nYoung tableaux, we also show that the shifted Berenstein-Kirillov group is\nisomorphic to a quotient of the cactus group. Not all the known relations that\nhold in the classic Berenstein-Kirillov group need to be satisfied by the\nshifted Bender-Knuth involutions, but the ones implying the relations of the\ncactus group are verified. Hence, we have an alternative presentation for the\ncactus group in terms of the shifted Bender-Knuth involutions. We also use the\nshifted growth diagrams due to Thomas and Yong (2016) to provide an alternative\nproof concerning the mentioned cactus group action.\n', 'An action of the cactus group on shifted tableau crystals   Recently, Gillespie, Levinson and Purbhoo introduced a crystal-like structure\nfor shifted tableaux, called the shifted tableau crystal. We introduce a\nshifted analogue of the crystal reflection operators, which coincides with the\nrestriction of the shifted Sch\\""utzenberger involution to any primed interval\nof two adjacent letters. Unlike type $A$ Young tableau crystals, these\noperators do not realize an action of the symmetric group on the shifted\ntableau crystal because braid relations do not hold. We exhibit a natural\ninternal action of the cactus group, realized by restrictions of the shifted\nSch\\""utzenberger involution on primed intervals of the underlying crystal\nalphabet.\n', 'An action of the cactus group of shifted tableau crystals   Recently, Gillespie, Levinson and Purbhoo introduced a crystal-like structure\nfor shifted tableaux, called the shifted tableau crystal. We introduce, on this\nstructure, a shifted version of the crystal reflection operators, which\ncoincide with the restrictions of the shifted Sch\\""utzenberger involution to\nany primed interval of two adjacent letters. Unlike type $A$ Young tableau\ncrystals, these operators do not realize an action of the symmetric group on\nthe shifted tableau crystal since the braid relations do not need to hold.\nFollowing a similar approach as Halacheva, we exhibit a natural internal action\nof the cactus group on this crystal, realized by the restrictions of the\nshifted Sch\\""utzenberger involution to all primed intervals of the underlying\ncrystal alphabet, containing, in particular, the aforesaid action of the\nshifted crystal reflection operator analogues.\n']","[('shifted tableaux', 0.5817694664001465), ('semistandard young tableaux', 0.571567714214325), ('crystal operators', 0.5259206891059875), ('crystal structures', 0.520947277545929), ('young tableaux', 0.5146346092224121), ('tableaux', 0.5115557312965393), ('crystal structure', 0.4958871901035309), ('crystals', 0.47904932498931885), ('crystal graph', 0.46571117639541626), ('crystal', 0.43604257702827454)]"
939,939,32,939_supply chain network_supply chain logistics_supply chain management_chain logistics,"['supply chain network', 'supply chain logistics', 'supply chain management', 'chain logistics', 'supply chain', 'supply chains', 'production inventory', 'chain management', 'linear programming', 'logistics']","['Sustainable Closed-loop supply chain under uncertainty   With the fast change of information and communication technologies and global\neconomics manufacturing industry faces the challenges in both market and supply\nsides. The challenges in the market include short product life cycle, demand\nuncertainty, and product delivery. Accordingly, supply challenges are the\ndramatic increase of flexibility in productions and complexity in the supply\nchain, which result from the changes in the industry and rapid development of\nICPT (Information, Communication, and Production Technologies). In this study,\nwe consider a supply chain converged with ICPT, called Smart Manufacturing\nSupply Chain (SMSC). By investigating the attributes of SMSC, we identify the\nfunctional and structural characteristics of SMSC. Tactical supply planning in\nSMSC recognizes the ability of a pseudo real-time decision-making constrained\nby the planning horizon. In order to take advantages of SMSC a multi-objective\nmulti-period mixed integer non-linear programming for closed-loop supply chain\nnetwork design is presented. This model aims to minimizing overall costs\nenvironment effects and lead time. To solve the proposed model, considering\nuncertainties in the problem, the improved epsilon-constraint approach was\nadopted to transform the multi-objective model into a single-objective one.\nThen, the Lagrange relaxation method was employed for an effective\nproblem-solving. In the following a case study in the real world was proposed\nto evaluate the models performance. Finally a sensitivity analysis was carried\nout to investigate the effects of important parameters on the optimal solution.\n', ""Traceability Technology Adoption in Supply Chain Networks   Modern traceability technologies promise to improve supply chain management\nby simplifying recalls, increasing visibility, or verifying sustainable\nsupplier practices. Initiatives leading the implementation of traceability\ntechnologies must choose the least-costly set of firms - or seed set - to\ntarget for early adoption. Choosing this seed set is challenging because firms\nare part of supply chains interlinked in complex networks, yielding an inherent\nsupply chain effect: benefits obtained from traceability are conditional on\ntechnology adoption by a subset of firms in a product's supply chain. We prove\nthat the problem of selecting the least-costly seed set in a supply chain\nnetwork is hard to solve and even approximate within a polylogarithmic factor.\nNevertheless, we provide a novel linear programming-based algorithm to identify\nthe least-costly seed set. The algorithm is fixed-parameter tractable in the\nsupply chain network's treewidth, which we show to be low in real-world supply\nchain networks. The algorithm also enables us to derive easily-computable\nbounds on the cost of selecting an optimal seed set. Finally, we leverage our\nalgorithms to conduct large-scale numerical experiments that provide insights\ninto how the supply chain network structure influences diffusion. These\ninsights can help managers optimize their technology diffusion strategy.\n"", 'An Integrated Supply Chain Network Design for Advanced Air Mobility\n  Aircraft Manufacturing Using Stochastic Optimization   Electric vertical takeoff and landing (eVTOL) aircraft manufacturers await\nnumerous pre-orders for eVTOLs and expect demand for such advanced air mobility\n(AAM) aircraft to rise dramatically soon. However, eVTOL manufacturers (EMs)\ncannot commence mass production of commercial eVTOLs due to a lack of supply\nchain planning for eVTOL manufacturing. The eVTOL supply chain differs from\ntraditional ones due to stringent quality standards and limited suppliers for\neVTOL parts, shortages in skilled labor and machinery, and contract\nrenegotiations with major aerospace suppliers. The emerging AAM aircraft market\nintroduces uncertainties in supplier pricing and capacities, eVTOL\nmanufacturing costs, and eVTOL demand, further compounding the supply chain\nplanning challenges for EMs. Despite this critical need, no study has been\nconducted to develop a comprehensive supply chain planning model for EMs. To\naddress this research gap, we propose a stochastic optimization model for\nintegrated supply chain planning of EMs while maximizing their operating\nprofits under the abovementioned uncertainties. We conduct various numerical\ncases to analyze the impact of 1) endogenous eVTOL demand influenced by the\nquality of eVTOLs, 2) supply chain disruptions caused by geopolitical conflicts\nand resource scarcity, and 3) high-volume eVTOL demand similar to that\nexperienced by automotive manufacturers, on EM supply chain planning. The\nresults indicate that our proposed model is adaptable in all cases and\noutperforms established benchmark stochastic models. The findings suggest that\nEMs can commence mass eVTOL production with our model, enabling them to make\noptimal decisions and profits even under potential disruptions.\n']","[('supply chain network', 0.6000398993492126), ('supply chain logistics', 0.5969390273094177), ('supply chain management', 0.5684158802032471), ('chain logistics', 0.5622338056564331), ('supply chain', 0.5492167472839355), ('supply chains', 0.5487352609634399), ('production inventory', 0.4794118106365204), ('chain management', 0.457915335893631), ('linear programming', 0.45575639605522156), ('logistics', 0.43868690729141235)]"
940,940,32,940_canard cycles_hopf bifurcation_saddle node bifurcation_bifurcations,"['canard cycles', 'hopf bifurcation', 'saddle node bifurcation', 'bifurcations', 'singularly perturbed', 'bifurcation', 'neimark sacker bifurcation', 'bifurcation analysis', 'bifurcation diagrams', 'singular perturbation theory']","['Saddle-node canard cycles in planar piecewise linear differential\n  systems   By applying a singular perturbation approach, canard limit cycles exhibited\nby a general family of singularly perturbed planar piecewise linear (PWL)\ndifferential systems are analyzed. The performed study involves both hyperbolic\nand non-hyperbolic canard limit cycles appearing after both a supercritical and\na subcritical Hopf bifurcation.\n  The obtained results are completely comparable with those obtained for smooth\nvector fields. In some sense, the manuscript can be understood as an extension\ntowards the PWL framework of the results obtained for smooth systems by Krupa\nand Szmolyan [18]. In addition, some novel slow-fast behaviors are obtained. In\nparticular, in the supercritical case, and under suitable conditions, it is\nproved that the limit cycles are organized along a curve exhibiting two folds.\nEach of these folds corresponds to a saddle-node bifurcation of canard limit\ncycles, one involving headless canard cycles, whereas the other involving\ncanard cycles with head. This configuration allows the coexistence of three\ncanard limit cycles.\n', 'Controlling Canard Cycles   Canard cycles are periodic orbits that appear as special solutions of\nfast-slow systems (or singularly perturbed Ordinary Differential Equations). It\nis well known that canard cycles are difficult to detect, hard to reproduce\nnumerically, and that they are sensible to exponentially small changes in\nparameters. In this paper we combine techniques from geometric singular\nperturbation theory, the blow-up method, and control theory, to design\ncontrollers that stabilize canard cycles of planar fast-slow systems with a\nfolded critical manifold. As an application, we propose a controller that\nproduces stable mixed-mode oscillations in the van der Pol oscillator.\n', ""The dud canard: Existence of strong canard cycles in $\\mathbb R^3$   In this paper, we provide a rigorous description of the birth of canard limit\ncycles in slow-fast systems in $\\mathbb R^3$ through the folded saddle-node of\ntype II and the singular Hopf bifurcation. In particular, we prove -- in the\nanalytic case only -- that for all $0<\\epsilon\\ll 1$ there is a family of\nperiodic orbits, born in the (singular) Hopf bifurcation and extending to\n$\\mathcal O(1)$ cycles that follow the strong canard of the folded saddle-node.\nOur results can be seen as an extension of the canard explosion in $\\mathbb\nR^2$, but in contrast to the planar case, the family of periodic orbits in\n$\\mathbb R^3$ is not explosive. For this reason, we have chosen to call the\nphenomena in $\\mathbb R^3$, the ``dud canard''. The main difficulty of the\nproof lies in connecting the Hopf cycles with the canard cycles, since these\nare described in different scalings. As in $\\mathbb R^2$, we use blowup to\novercome this, but we also have to compensate for the lack of uniformity near\nthe Hopf bifurcation, due to its singular nature; it is a zero-Hopf bifurcation\nin the limit $\\epsilon=0$. In the present paper, we do so by imposing\nanalyticity of the vector-field. This allows us to prove existence of an\ninvariant slow manifold, that is not normally hyperbolic.\n""]","[('canard cycles', 0.5774410963058472), ('hopf bifurcation', 0.5758876800537109), ('saddle node bifurcation', 0.5350374579429626), ('bifurcations', 0.527237057685852), ('singularly perturbed', 0.5122913122177124), ('bifurcation', 0.5069405436515808), ('neimark sacker bifurcation', 0.5028155446052551), ('bifurcation analysis', 0.4978809356689453), ('bifurcation diagrams', 0.49653375148773193), ('singular perturbation theory', 0.49164527654647827)]"
941,941,32,941_symplectic capacities_symplectic capacity_symplectic embeddings_symplectic embedding,"['symplectic capacities', 'symplectic capacity', 'symplectic embeddings', 'symplectic embedding', 'dimensional symplectic', 'symplectic manifolds', 'equivariant symplectic', 'symplectic manifold', 'symplectic homology', 'standard symplectic']","['Characterizing symplectic capacities on ellipsoids   It is a long-standing conjecture that all symplectic capacities which are\nequal to the Gromov width for ellipsoids coincide on a class of convex domains\nin $\\mathbb{R}^{2n}$. It is known that they coincide for monotone toric domains\nin all dimensions. In this paper, we study whether requiring a capacity to be\nequal to the $k^{th}$ Ekeland-Hofer capacity for all ellipsoids can\ncharacterize it on a class of domains. We prove that for $k=n=2$, this holds\nfor convex toric domains, but not for all monotone toric domains. We also prove\nthat for $k=n\\ge 3$, this does not hold even for convex toric domains.\n', 'Examples around the strong Viterbo conjecture   A strong version of a conjecture of Viterbo asserts that all normalized\nsymplectic capacities agree on convex domains. We review known results showing\nthat certain specific normalized symplectic capacities agree on convex domains.\nWe also review why all normalized symplectic capacities agree on\n$S^1$-invariant convex domains. We introduce a new class of examples called\n""monotone toric domains"", which are not necessarily convex, and which include\nall dynamically convex toric domains in four dimensions. We prove that for\nmonotone toric domains in four dimensions, all normalized symplectic capacities\nagree. For monotone toric domains in arbitrary dimension, we prove that the\nGromov width agrees with the first equivariant capacity. We also study a family\nof examples of non-monotone toric domains and determine when the conclusion of\nthe strong Viterbo conjecture holds for these examples. Along the way we\ncompute the cylindrical capacity of a large class of ""weakly convex toric\ndomains"" in four dimensions.\n', 'Equivariant symplectic homology, linearized contact homology and the\n  Lagrangian capacity   We establish computational results concerning the Lagrangian capacity from\n""Cieliebak and Mohnke - Punctured holomorphic curves and Lagrangian\nembeddings"". More precisely, we show that the Lagrangian capacity of a\n4-dimensional convex toric domain is equal to its diagonal. The proof involves\ncomparisons between the Lagrangian capacity, the McDuff-Siegel capacities from\n""McDuff and Siegel - Symplectic capacities, unperturbed curves, and convex\ntoric domains"", and the Gutt-Hutchings capacities from ""Gutt and Hutchings -\nSymplectic capacities from positive S1-equivariant symplectic homology"".\nWorking under the assumption that there is a suitable virtual perturbation\nscheme which defines the curve counts of linearized contact homology, we extend\nthe previous result to toric domains which are convex or concave and of any\ndimension. For this, we use the higher symplectic capacities from ""Siegel -\nHigher symplectic capacities"". The key step is showing that moduli spaces of\nasymptotically cylindrical holomorphic curves in ellipsoids are transversely\ncut out.\n']","[('symplectic capacities', 0.7628048062324524), ('symplectic capacity', 0.692393958568573), ('symplectic embeddings', 0.5959053635597229), ('symplectic embedding', 0.5673425793647766), ('dimensional symplectic', 0.567064106464386), ('symplectic manifolds', 0.5617631673812866), ('equivariant symplectic', 0.5479220747947693), ('symplectic manifold', 0.5306453108787537), ('symplectic homology', 0.5268083214759827), ('standard symplectic', 0.5232105255126953)]"
942,942,32,942_roots cubic_real roots_roots real_cubic equations,"['roots cubic', 'real roots', 'roots real', 'cubic equations', 'real roots real', 'roots', 'quartic polynomial', 'roots lie', 'cubic polynomial', 'real root']","['A Method for Locating the Real Roots of the Symbolic Quintic Equation\n  Using Quadratic Equations   A method is proposed with which the locations of the roots of the monic\nsymbolic quintic polynomial $x^5 + a_4 x^4 + a_3 x^3 + a_2 x^2 + a_1 x + a_0$\ncan be determined using the roots of two resolvent quadratic polynomials:\n$q_1(x) = x^2 + a_4 x + a_3$ and $q_2(x) = a_2 x^2 + a_1 x + a_0$, whose\ncoefficients are exactly those of the quintic polynomial. The different cases\ndepend on the coefficients of $q_1(x)$ and $q_2(x)$ and on some specific\nrelationships between them. The method is illustrated with the full analysis of\none of the possible cases. Some of the roots of the symbolic quintic equation\nfor this case have their isolation intervals determined and, as this cannot be\ndone for all roots with the help of quadratic equations only, finite intervals\ncontaining 1 or 3 roots, or 0 or 2 roots, or, rarely, 0, or 2, or 4 roots of\nthe quintic are identified. Knowing the stationary points of the quintic\npolynomial, lifts the latter indeterminacy and allows one to find the isolation\ninterval of each of the roots of the quintic. Separately, using the complete\nroot classification of the quintic, one can also lift this indeterminacy. The\nmethod also allows to see how variation of the individual coefficients of the\nquintic affect its roots. No root finding iterations or any numerical\napproximations are used and no equations of degree higher than 2 are solved.\n', 'Classification of the Real Roots of the Quartic Equation and their\n  Pythagorean Tunes   Presented is a two-tier analysis of the location of the real roots of the\ngeneral quartic equation $x^4 + ax^3 + bx^2 + cx + d = 0$ with real\ncoefficients and the classification of the roots in terms of $a$, $b$, $c$, and\n$d$, without using any numerical approximations. Associated with the general\nquartic, there is a number of subsidiary quadratic equations (resolvent\nquadratic equations) whose roots allow this systematization as well as the\ndetermination of the bounds of the individual roots of the quartic. In many\ncases the root isolation intervals are found. The second tier of the analysis\nuses two subsidiary cubic equations (auxiliary cubic equations) and solving\nthese, together with some of the resolvent quadratic equations, allows the full\nclassification of the roots of the general quartic and also the determination\nof the isolation interval of each root. These isolation intervals involve the\nstationary points of the quartic (among others) and, by solving some of the\nresolvent quadratic equations, the isolation intervals of the stationary points\nof the quartic are also determined. Each possible case has been carefully\nstudied and illustrated with a detailed figure containing a description of its\nspecific characteristics, analysis based on solving cubic equations and\nanalysis based on solving quadratic equations only. As the analysis of the\nroots of the quartic equation is done by studying the intersection points of\nthe ""sub-quartic"" $x^4 + ax^3 + bx^2$ with a set of suitable parallel lines, a\nbeautiful Pythagorean analogy can be found between these intersection points\nand the set of parallel lines on one hand and the musical notes and the staves\nrepresenting different musical pitches on the other: each particular case of\nthe quartic equation has its own short tune.\n', 'Isolation Intervals of the Real Roots of the Parametric Cubic Equation\n  and Improved Complete Root Classification   The isolation intervals of the real roots of the real symbolic monic cubic\npolynomial $p(x) = x^3 + a x^2 + b x + c\\,\\,$ are found in terms of simple\nfunctions of the coefficients of the polynomial (such as: $-a$, $-a/3$, $-c/b$,\n$\\pm \\sqrt{-b}$, when $b$ is negative), and the roots of some auxiliary\nquadratic equations whose coefficients are also simple functions of the\ncoefficients of the cubic. All possible cases are presented with clear and very\ndetailed diagrams. It is very easy to identify which of these diagrams is the\nrelevant one for any given cubic equation and to read from it the isolation\nintervals of the real roots of the equation. A much-improved complete root\nclassification, addressing the signs (together with giving the isolation\nintervals) of the individual roots, is also presented. No numerical\napproximations or root finding techniques are used. Instead of considering the\ndiscriminant of the cubic, criterion for the existence of a single real root or\nthree real roots is found as conditions on the coefficients of the cubic,\nresulting from the roots of the auxiliary quadratic equations. It is also shown\nthat, if a cubic equation has three real roots, then these lie in an interval\n$I$ such that $\\sqrt{3}\\sqrt{a^2/3 - b} \\le I \\le 2 \\sqrt{a^2/3 - b}$,\nindependent of $c$. A detailed algorithm for applying the method for isolation\nof the roots of the cubic is also given and it is illustrated through examples,\nincluding the full mathematical analysis of the cubic equation associated with\nthe Rayleigh elastic waves and finding the isolation intervals of its real\nroots.\n']","[('roots cubic', 0.650597095489502), ('real roots', 0.5740432143211365), ('roots real', 0.5626543760299683), ('cubic equations', 0.5587776899337769), ('real roots real', 0.5242685675621033), ('roots', 0.5161629319190979), ('quartic polynomial', 0.5118095874786377), ('roots lie', 0.49903321266174316), ('cubic polynomial', 0.485409677028656), ('real root', 0.48111191391944885)]"
943,943,32,943_finitely additive measures_additive measures_measure theory_measures,"['finitely additive measures', 'additive measures', 'measure theory', 'measures', 'valued measure', 'measure space', 'borel measure', 'probability measures', 'measure defined', 'measurable space']","[""Measure and integration on Boolean algebras of regular open subsets in a\n  topological space   The regular open subsets of a topological space form a Boolean algebra, where\nthe `join' of two regular open sets is the interior of the closure of their\nunion. A `credence' is a finitely additive probability measure on this Boolean\nalgebra, or on one of its subalgebras. We develop a theory of integration for\nsuch credences. We then explain the relationship between credences, residual\ncharges, and Borel probability measures. We show that a credence can be\nrepresented by a normal Borel measure, augmented with a `liminal structure',\nwhich specifies how two or more regular open sets share the probability mass of\ntheir common boundary. In particular, a credence on a locally compact Hausdorff\nspace can be represented by a normal Borel measure and a liminal structure on\nthe Stone-\\v{C}ech compactification of that space. We also show how credences\ncan be represented by Borel measures on the Stone space of the underlying\nBoolean algebra of regular open sets. Finally, we show that these constructions\nare functorial.\n"", 'Minimally generated Boolean algebras and the Nikodym property   A Boolean algebra $\\mathcal A$ has the Nikodym property if every pointwise\nbounded sequence of bounded finitely additive measures on $\\mathcal A$ is\nuniformly bounded. Assuming the Diamond Principle $\\Diamond$, we will construct\nan example of a minimally generated Boolean algebra $\\mathcal A$ with the\nNikodym property. The Stone space of such an algebra must necessarily be an\nEfimov space. The converse is, however, not true - again under $\\Diamond$ we\nwill provide an example of a minimally generated Boolean algebra whose Stone\nspace is Efimov but which does not have the Nikodym property. The results have\ninteresting measure-theoretic and topological consequences.\n', 'Finitely additive measures on Boolean algebras   In this article, we conduct a detailed study of \\emph{finitely additive\nmeasures} (fams) in the context of Boolean algebras, focusing on three specific\ntopics: freeness and approximation, existence and extension criteria, and\nintegration theory. In the first topic, we present a classification of\n\\emph{free} finitely additive measures, that is, those for which the measure of\nfinite sets is zero, in terms of approximation to uniform probability measures.\nThis inspires a weaker version of this notion, which we call the \\emph{uniform\napproximation property}, characterized in terms of freeness and another\nwell-determined type of fams we call \\emph{uniformly supported}. In the second\ntopic, we study criteria for existence and extension of finitely additive\nmeasures for Boolean algebras, offering a relatively short proof of the\n\\emph{compatibility theorem} for fams.\n  Finally, we study a Riemann-type integration theory on fields of sets with\nrespect to finitely additive measures, allowing us to extend and generalize\nsome classical concepts and results from real analysis, such as Riemann\nintegration over rectangles in $\\mathbb{R}^{n}$ and the Jordan measure. We also\ngeneralize the extension criteria for fams allowing desired values of integrals\nof a given set of functions. At the end, we explore the connection between\nintegration in fields of sets and the Lebesgue integration in the Stone space\nof the corresponding field, where we establish a characterization of\nintegrability in the sense of the Lebesgue-Vitali theorem, which follows as a\nconsequence of our results.\n']","[('finitely additive measures', 0.6660559773445129), ('additive measures', 0.612034797668457), ('measure theory', 0.5467572808265686), ('measures', 0.5380554795265198), ('valued measure', 0.5343393683433533), ('measure space', 0.5230980515480042), ('borel measure', 0.5118647813796997), ('probability measures', 0.5037311911582947), ('measure defined', 0.49759170413017273), ('measurable space', 0.494772344827652)]"
944,944,32,944_decoding algorithms_reed muller codes_iterative decoding_decoding performance,"['decoding algorithms', 'reed muller codes', 'iterative decoding', 'decoding performance', 'decoders', 'decoding', 'proposed decoder', 'muller rm codes', 'hard decision decoding', 'muller codes']","['Recursive/Iterative unique Projection-Aggregation of RM codes   We describe recursive unique projection-aggregation (RUPA) decoding and\niterative unique projection-aggregation (IUPA) decoding of Reed-Muller (RM)\ncodes, which remove non-unique projections from the recursive\nprojection-aggregation (RPA) and iterative projection-aggregation (IPA)\nalgorithms respectively. We show that these algorithms have competitive\nerror-correcting performance while requiring up to 95% projections less than\nthe baseline RPA algorithm.\n', 'Reed-Muller Subcodes: Machine Learning-Aided Design of Efficient Soft\n  Recursive Decoding   Reed-Muller (RM) codes are conjectured to achieve the capacity of any\nbinary-input memoryless symmetric (BMS) channel, and are observed to have a\ncomparable performance to that of random codes in terms of scaling laws. On the\nnegative side, RM codes lack efficient decoders with performance close to that\nof a maximum likelihood decoder for general parameters. Also, they only admit\ncertain discrete sets of rates. In this paper, we focus on subcodes of RM codes\nwith flexible rates that can take any code dimension from 1 to n, where n is\nthe blocklength. We first extend the recursive projection-aggregation (RPA)\nalgorithm proposed recently by Ye and Abbe for decoding RM codes. To lower the\ncomplexity of our decoding algorithm, referred to as subRPA in this paper, we\ninvestigate different ways for pruning the projections. We then derive the\nsoft-decision based version of our algorithm, called soft-subRPA, that is shown\nto improve upon the performance of subRPA. Furthermore, it enables training a\nmachine learning (ML) model to search for \\textit{good} sets of projections in\nthe sense of minimizing the decoding error rate. Training our ML model enables\nachieving very close to the performance of full-projection decoding with a\nsignificantly reduced number of projections. For instance, our simulation\nresults on a (64,14) RM subcode show almost identical performance for\nfull-projection decoding and pruned-projection decoding with 15 projections\npicked via training our ML model. This is equivalent to lowering the complexity\nby a factor of more than 4 without sacrificing the decoding performance.\n', 'Machine Learning-Aided Efficient Decoding of Reed-Muller Subcodes   Reed-Muller (RM) codes achieve the capacity of general binary-input\nmemoryless symmetric channels and are conjectured to have a comparable\nperformance to that of random codes in terms of scaling laws. However, such\nresults are established assuming maximum-likelihood decoders for general code\nparameters. Also, RM codes only admit limited sets of rates. Efficient decoders\nsuch as successive cancellation list (SCL) decoder and recently-introduced\nrecursive projection-aggregation (RPA) decoders are available for RM codes at\nfinite lengths. In this paper, we focus on subcodes of RM codes with flexible\nrates. We first extend the RPA decoding algorithm to RM subcodes. To lower the\ncomplexity of our decoding algorithm, referred to as subRPA, we investigate\ndifferent approaches to prune the projections. Next, we derive the\nsoft-decision based version of our algorithm, called soft-subRPA, that not only\nimproves upon the performance of subRPA but also enables a differentiable\ndecoding algorithm. Building upon the soft-subRPA algorithm, we then provide a\nframework for training a machine learning (ML) model to search for\n\\textit{good} sets of projections that minimize the decoding error rate.\nTraining our ML model enables achieving very close to the performance of\nfull-projection decoding with a significantly smaller number of projections. We\nalso show that the choice of the projections in decoding RM subcodes matters\nsignificantly, and our ML-aided projection pruning scheme is able to find a\n\\textit{good} selection, i.e., with negligible performance degradation compared\nto the full-projection case, given a reasonable number of projections.\n']","[('decoding algorithms', 0.6446646451950073), ('reed muller codes', 0.6373131275177002), ('iterative decoding', 0.6269320249557495), ('decoding performance', 0.6173188090324402), ('decoders', 0.5871022939682007), ('decoding', 0.5865605473518372), ('proposed decoder', 0.5761395692825317), ('muller rm codes', 0.5759763121604919), ('hard decision decoding', 0.5672663450241089), ('muller codes', 0.5568856596946716)]"
945,945,32,945_multi criteria decision_criteria decision making_criteria selection_criteria decision,"['multi criteria decision', 'criteria decision making', 'criteria selection', 'criteria decision', 'multi criteria', 'multiple criteria', 'fuzzy sets', 'fuzzy logic', 'type fuzzy', 'decision maker']","['Preference Disaggregation Analysis with Criteria Selection in a Regularization Framework Limited by cognitive abilities, decision-makers (DMs) may struggle to evaluate decision alternatives based on all criteria in multiple criteria decision-making problems. This paper proposes an embedded criteria selection method derived from preference disaggregation technique and regularization theory. The method aims to infer the criteria and value functions used by the DM to evaluate decision alternatives. It measures the quality of criteria subsets by investigating both the empirical error (fitting ability of value functions to preference information) and generalization error (complexity of value functions). Unlike existing approaches that consider only the deviation from linearity as a measure of complexity, we argue that the number of marginal value functions also affects complexity. To address this, we use 0-1 variables to indicate whether a criterion is selected in the value function or not, and construct a criteria selection model with the trade-off between empirical and generalization errors as the objective function. If the criteria are sufficiently discriminative, we identify all supporting criteria sets that can restore preference information without unnecessary criteria. We further analyze the likelihood of criteria being selected by the DM. Finally, the effectiveness of the proposed method is demonstrated by applying it to an example of the green supplier selection problem.', ""Building Interval Type-2 Fuzzy Membership Function: A Deck of Cards\n  based Co-constructive Approach   Since its inception, Fuzzy Set has been widely used to handle uncertainty and\nimprecision in decision-making. However, conventional fuzzy sets, often\nreferred to as type-1 fuzzy sets (T1FSs) have limitations in capturing higher\nlevels of uncertainty, particularly when decision-makers (DMs) express\nhesitation or ambiguity in membership degree. To address this, Interval Type-2\nFuzzy Sets (IT2FSs) have been introduced by incorporating uncertainty in\nmembership degree allocation, which enhanced flexibility in modelling\nsubjective judgments. Despite their advantages, existing IT2FS construction\nmethods often lack active involvement from DMs and that limits the\ninterpretability and effectiveness of decision models. This study proposes a\nsocio-technical co-constructive approach for developing IT2FS models of\nlinguistic terms by facilitating the active involvement of DMs in preference\nelicitation and its application in multicriteria decision-making (MCDM)\nproblems. Our methodology is structured in two phases. The first phase involves\nan interactive process between the DM and the decision analyst, in which a\nmodified version of Deck-of-Cards (DoC) method is proposed to construct T1FS\nmembership functions on a ratio scale. We then extend this method to\nincorporate ambiguity in subjective judgment and that resulted in an IT2FS\nmodel that better captures uncertainty in DM's linguistic assessments. The\nsecond phase formalizes the constructed IT2FS model for application in MCDM by\ndefining an appropriate mathematical representation of such information,\naggregation rules, and an admissible ordering principle. The proposed framework\nenhances the reliability and effectiveness of fuzzy decision-making not only by\naccurately representing DM's personalized semantics of linguistic information.\n"", 'Double Fuzzy Probabilistic Interval Linguistic Term Set and a Dynamic\n  Fuzzy Decision Making Model based on Markov Process with tts Application in\n  Multiple Criteria Group Decision Making   The probabilistic linguistic term has been proposed to deal with probability\ndistributions in provided linguistic evaluations. However, because it has some\nfundamental defects, it is often difficult for decision-makers to get\nreasonable information of linguistic evaluations for group decision making. In\naddition, weight information plays a significant role in dynamic information\nfusion and decision making process. However, there are few research methods to\ndetermine the dynamic attribute weight with time. In this paper, I propose the\nconcept of double fuzzy probability interval linguistic term set (DFPILTS).\nFirstly, fuzzy semantic integration, DFPILTS definition, its preference\nrelationship, some basic algorithms and aggregation operators are defined.\nThen, a fuzzy linguistic Markov matrix with its network is developed. Then, a\nweight determination method based on distance measure and information entropy\nto reducing the inconsistency of DFPILPR and obtain collective priority vector\nbased on group consensus is developed. Finally, an aggregation-based approach\nis developed, and an optimal investment case from a financial risk is used to\nillustrate the application of DFPILTS and decision method in multi-criteria\ndecision making.\n']","[('multi criteria decision', 0.6084718704223633), ('criteria decision making', 0.5830914378166199), ('criteria selection', 0.5819900631904602), ('criteria decision', 0.5629045367240906), ('multi criteria', 0.5128836631774902), ('multiple criteria', 0.5014164447784424), ('fuzzy sets', 0.4595676064491272), ('fuzzy logic', 0.44720178842544556), ('type fuzzy', 0.4356353282928467), ('decision maker', 0.43047812581062317)]"
946,946,32,946_crowd dynamics_crowd motion_crowding_pedestrians,"['crowd dynamics', 'crowd motion', 'crowding', 'pedestrians', 'crowds', 'epidemics', 'dynamics', 'disease spreading', 'simulations', 'crowd']","['Disease contagion models coupled to crowd motion and mesh-free\n  simulation   Modeling and simulation of disease spreading in pedestrian crowds has been\nrecently become a topic of increasing relevance. In this paper, we consider the\ninfluence of the crowd motion in a complex dynamical environment on the course\nof infection of the pedestrians. To model the pedestrian dynamics we consider a\nkinetic equation for multi-group pedestrian flow based on a social force model\ncoupled with an Eikonal equation. This model is coupled with a non-local SEIS\ncontagion model for disease spread, where besides the description of local\ncontacts also the influence of contact times has been modelled. Hydrodynamic\napproximations of the coupled system are derived. Finally, simulations of the\nhydrodynamic model are carried out using a mesh-free particle method. Different\nnumerical test cases are investigated including uni- and bi-directional flow in\na passage with and without obstacles.\n', 'A kinetic theory approach to model crowd dynamics with disease contagion   We present some ideas on how to extend a kinetic type model for crowd\ndynamics to account for an infectious disease spreading. We focus on a medium\nsize crowd occupying a confined environment where the disease is easily spread.\nThe kinetic theory approach we choose uses tools of game theory to model the\ninteractions of a person with the surrounding people and the environment and it\nfeatures a parameter to represent the level of stress. It is known that people\nchoose different walking strategies when subjected to fear or stressful\nsituations. To demonstrate that our model for crowd dynamics could be used to\nreproduce realistic scenarios, we simulate passengers in one terminal of Hobby\nAirport in Houston. In order to model disease spreading in a walking crowd, we\nintroduce a variable that denotes the level of exposure to people spreading the\ndisease. In addition, we introduce a parameter that describes the contagion\ninteraction strength and a kernel function that is a decreasing function of the\ndistance between a person and a spreading individual. We test our contagion\nmodel on a problem involving a small crowd walking through a corridor.\n', 'Coupling kinetic theory approaches for pedestrian dynamics and disease\n  contagion in a confined environment   The goal of this work is to study an infectious disease spreading in a medium\nsize population occupying a confined environment. For this purpose, we consider\na kinetic theory approach to model crowd dynamics in bounded domains and couple\nit to a kinetic equation to model contagion. The interactions of a person with\nother pedestrians and the environment are modeled by using tools of game\ntheory. The pedestrian dynamics model allows to weight between two competing\nbehaviors: the search for less congested areas and the tendency to follow the\nstream unconsciously in a panic situation. Each person in the system has a\ncontagion level that is affected by their neighborhood. For the numerical\nsolution of the coupled problem, we propose a numerical algorithm that at every\ntime step solves one crowd dynamics problem and one contagion problem, i.e.\nwith no subiterations between the two. We test our coupled model on a problem\ninvolving a small crowd walking through a corridor.\n']","[('crowd dynamics', 0.6627461314201355), ('crowd motion', 0.5872097015380859), ('crowding', 0.48322194814682007), ('pedestrians', 0.4717000126838684), ('crowds', 0.45665448904037476), ('epidemics', 0.4348943829536438), ('dynamics', 0.415276437997818), ('disease spreading', 0.414559543132782), ('simulations', 0.4082956612110138), ('crowd', 0.4077482521533966)]"
947,947,32,947_holonomic modules_riemann hilbert correspondence_mathcal modules_modules fourier,"['holonomic modules', 'riemann hilbert correspondence', 'mathcal modules', 'modules fourier', 'modules complex', 'hilbert correspondence', 'modules smooth', 'modules characteristic', 'holonomic', 'sheafification']","['On a topological counterpart of regularization for holonomic D-modules   On a complex manifold, the embedding of the category of regular holonomic\nD-modules into that of holonomic D-modules has a left quasi-inverse functor\n$\\mathcal{M}\\mapsto\\mathcal{M}_{\\mathrm{reg}}$, called regularization. Recall\nthat $\\mathcal{M}_{\\mathrm{reg}}$ is reconstructed from the de Rham complex of\n$\\mathcal{M}$ by the regular Riemann-Hilbert correspondence. Similarly, on a\ntopological space, the embedding of sheaves into enhanced ind-sheaves has a\nleft quasi-inverse functor, called here sheafification. Regularization and\nsheafification are intertwined by the irregular Riemann-Hilbert correspondence.\nHere, we study some of their properties. In particular, we provide a germ\nformula for the sheafification of enhanced specialization and\nmicrolocalization.\n', 'On characteristic cycles of irregular holonomic D-modules   Based on the recent progress in the irregular Riemann-Hilbert correspondence\nfor holonomic D-modules, we show that the characteristic cycles of some\nstandard irregular holonomic D-modules can be expressed as in the classical\ntheorem of Ginsburg. For this purpose, we first prove a formula for the\nenhanced solution complexes of holonomic D-modules having a quasi-normal form,\nvia which, to our surprise, their solution complexes can be calculated more\neasily by topological methods. In the formulation and the proof of our main\ntheorems, not necessarily homogeneous Lagrangian cycles that we call irregular\ncharacteristic cycles will play a crucial role.\n', ""Note on Relation between Enhanced Ind-Sheaves and Enhanced Subanalytic\n  Sheaves   In this paper, we will explain a relation between [Thm. 9.5.3, Andrea\nD'Agnolo and Masaki Kashiwara, Riemann-Hilbert correspondence for holonomic\nD-modules, 2016] and [Thm. 6.3, Masaki Kashiwara, Riemann-Hilbert\ncorrespondence for irregular holonomic D-modules]. For this purpose, we will\nalso explain a relation between enhanced ind-sheaves and enhanced subanalytic\nsheaves.\n""]","[('holonomic modules', 0.6629284620285034), ('riemann hilbert correspondence', 0.5186482071876526), ('mathcal modules', 0.4932386875152588), ('modules fourier', 0.476608008146286), ('modules complex', 0.4744735062122345), ('hilbert correspondence', 0.46494030952453613), ('modules smooth', 0.45433545112609863), ('modules characteristic', 0.4270767271518707), ('holonomic', 0.4253585934638977), ('sheafification', 0.41063186526298523)]"
948,948,32,948_acoustic waveguide_waveguide_waveguides_wave propagation,"['acoustic waveguide', 'waveguide', 'waveguides', 'wave propagation', 'wave scattering', 'propagation elastic', 'acoustic scattering', 'acoustic waves', 'scattering problems', 'waves']","['Layer stripping approach to reconstruct shape defects in waveguides\n  using locally resonant frequencies   This article present a new method to reconstruct slowly varying width defects\nin 2D waveguides using one-side section measurements at locally resonant\nfrequencies. At these frequencies, locally resonant modes propagate in the\nwaveguide up to a ""cut-off"" position. In this particular point, the local width\nof the waveguide can be recovered. Given multi-frequency measurements taken on\na section of the waveguide, we perform an efficient layer stripping approach to\nrecover shape variations slice by slice. It provides an L infinite-stable\nmethod to reconstruct the width of a slowly monotonous varying waveguide. We\nvalidate this method on numerical data and discuss its limits.\n', 'Reconstruction of smooth shape defects in waveguides using locally\n  resonant frequencies   This article aims to present a new method to reconstruct slowly varying width\ndefects in 2D waveguides using locally resonant frequencies. At these\nfrequencies, locally resonant modes propagate in the waveguide under the form\nof Airy functions depending on a parameter called the locally resonant point.\nIn this particular point, the local width of the waveguide is known and its\nlocation can be recovered from boundary measurements of the wavefield. Using\nthe same process for different frequencies, we produce a good approximation of\nthe width in all the waveguide. Given multi-frequency measurements taken at the\nsurface of the waveguide, we provide a L \\infty-stable explicit method to\nreconstruct the width of the waveguide. We finally validate our method on\nnumerical data, and we discuss its applications and limits.\n', 'Small defects reconstruction in waveguides from multifrequency one-side\n  scattering data   Localization and reconstruction of small defects in acoustic or\nelectromagnetic waveguides is of crucial interest in nondestructive evaluation\nof structures. The aim of this work is to present a new multi-frequency\ninversion method to reconstruct small defects in a 2D waveguide. Given one-side\nmulti-frequency wave field measurements of propagating modes, we use a Born\napproximation to provide a L2-stable reconstruction of three types of defects:\na local perturbation inside the waveguide, a bending of the waveguide, and a\nlocalized defect in the geometry of the waveguide. This method is based on a\nmode-by-mode spacial Fourier inversion from the available partial data in the\nFourier domain. Indeed, in the available data, some high and low spatial\nfrequency information on the defect are missing. We overcome this issue using\nboth a compact support hypothesis and a minimal smoothness hypothesis on the\ndefects. We also provide a suitable numerical method for efficient\nreconstruction of such defects and we discuss its applications and limits.\n']","[('acoustic waveguide', 0.5289669036865234), ('waveguide', 0.5070871114730835), ('waveguides', 0.4788213074207306), ('wave propagation', 0.4706990122795105), ('wave scattering', 0.4443994164466858), ('propagation elastic', 0.4121001064777374), ('acoustic scattering', 0.3808690011501312), ('acoustic waves', 0.3604860007762909), ('scattering problems', 0.3398650884628296), ('waves', 0.32529503107070923)]"
949,949,32,949_del pezzo fibrations_pezzo fibrations_del pezzo surfaces_pezzo surfaces,"['del pezzo fibrations', 'pezzo fibrations', 'del pezzo surfaces', 'pezzo surfaces', 'pezzo surfaces degree', 'del pezzo surface', 'pezzo surface', 'singular del pezzo', 'surfaces picard rank', 'fibrations']","['Classification of del Pezzo surfaces of rank one. I. Height 1 and 2. II.\n  Descendants with elliptic boundaries   This is the first article in a series aimed at classifying normal del Pezzo\nsurfaces of Picard rank one over algebraically closed fields of arbitrary\ncharacteristic up to an isomorphism. Our guiding invariant is the height of a\ndel Pezzo surface, defined as the minimal intersection number of the\nexceptional divisor of the minimal resolution and a fiber of some\n$\\mathbb{P}^1$-fibration. The geometry of del Pezzo surfaces gets more\nconstrained as the height grows; in characteristic $0$ no example of height\nbigger than $4$ is known.\n  In this article, we classify del Pezzo surfaces of Picard rank one and height\nat most $2$; in particular we describe the non-log terminal ones. We also\ndescribe a natural class of del Pezzo surfaces which have descendants with\nelliptic boundary, i.e. whose minimal resolution has a birational morphism onto\na canonical del Pezzo surface of rank one mapping the exceptional divisor to an\nanti-canonical curve.\n', 'Birational rigidity of orbifold degree 2 del Pezzo fibrations   Varieties fibered into del Pezzo surfaces form a class of possible outputs of\nthe minimal model program. It is known that del Pezzo fibrations of degrees $1$\nand $2$ over the projective line with smooth total space satisfying the\nso-called $K^2$-condition are birationally rigid: their Mori fibre space\nstructure is unique. This implies that they are not birational to any Fano\nvarieties, conic bundles or other del Pezzo fibrations. In particular, they are\nirrational. The families of del Pezzo fibrations with smooth total space of\ndegree $2$ are rather special, as for ""most"" families a general del Pezzo\nfibration has the simplest orbifold singularities. We prove that orbifold del\nPezzo fibrations of degree $2$ over the projective line satisfying explicit\ngenerality conditions as well as a generalised $K^2$-condition are birationally\nrigid.\n', 'Geometry of 3-dimensional del Pezzo fibrations in positive\n  characteristic   We survey some of the recent works on the geometry of del Pezzo surfaces over\nimperfect fields, with applications to 3-dimensional del Pezzo fibrations in\npositive characteristic. We place particular emphasis on cases where the\ngeneral fibres of the fibrations are not smooth\n']","[('del pezzo fibrations', 0.7756108641624451), ('pezzo fibrations', 0.7479931116104126), ('del pezzo surfaces', 0.7291257977485657), ('pezzo surfaces', 0.710976243019104), ('pezzo surfaces degree', 0.6835670471191406), ('del pezzo surface', 0.6522921323776245), ('pezzo surface', 0.6385301947593689), ('singular del pezzo', 0.5434070229530334), ('surfaces picard rank', 0.5091076493263245), ('fibrations', 0.49855470657348633)]"
950,950,32,950_temperley lieb algebras_temperley lieb algebra_lieb algebras_lieb algebra,"['temperley lieb algebras', 'temperley lieb algebra', 'lieb algebras', 'lieb algebra', 'algebra representation theory', 'temperley lieb', 'boundary temperley lieb', 'schur weyl duality', 'hecke algebra', 'algebras type']","['Projectors in the Virtual Temperley-Lieb Algebra   We present a method of defining projectors in the virtual Temperley-Lieb\nalgebra, that generalizes the Jones-Wenzl projectors in Temperley-Lieb algebra.\nWe show that the projectors have similar properties with the Jones-Wenzl\nprojectors, and contain an extra property which is associated with the virtual\ngenerator elements, that is, the product of a projector with a virtual\ngenerator is unchanged. We also show the uniqueness of the projector $f_n$ in\nterms of its axiomatic properties in the virtual Temperley-Lieba algebra\n$VTL_n(d)$. Finally, we find the coefficients of $f_n$ and give an explicit\nformula for the projector $f_n$.\n', 'Generalised Temperley-Lieb algebras of type $G(r,1,n)$   In this paper, we define a quotient of the cyclotomic Hecke algebra of type\n$G(r,1,n)$ as a generalisation of the Temperley-Lieb algebras of type $A$ and\n$B$. We establish a graded cellular structure for the generalised\nTemperley-Lieb algebra and, using the technology of $KLR$ algebras, determine\nthe corresponding decomposition matrix.\n', 'Limits of traces of Temperley-Lieb algebras   We review the classification of positive extremal traces on the generic\ninfinite Temperley-Lieb algebra, and then extend the classification to the\nnon-semisimple root of unity case. As a result, we obtain Hilbert space\nstructures on the full infinite Temperley-Lieb algebra at roots of unity.\n']","[('temperley lieb algebras', 0.8891578912734985), ('temperley lieb algebra', 0.85513836145401), ('lieb algebras', 0.7489392161369324), ('lieb algebra', 0.7016545534133911), ('algebra representation theory', 0.561726450920105), ('temperley lieb', 0.5410689115524292), ('boundary temperley lieb', 0.5063034296035767), ('schur weyl duality', 0.49621862173080444), ('hecke algebra', 0.46414557099342346), ('algebras type', 0.45806246995925903)]"
951,951,32,951_monomial curves_arithmetically cohen macaulay_graded polynomial ring_macaulay type,"['monomial curves', 'arithmetically cohen macaulay', 'graded polynomial ring', 'macaulay type', 'cohen macaulay type', 'standard graded polynomial', 'curves affine', 'projective closure', 'castelnuovo mumford regularity', 'cohen macaulay gorenstein']","['On the Betti numbers of the tangent cones for Gorenstein Monomial Curves   The aim of the article is to study the Betti numbers of the tangent cone of\nGorenstein monomial curves in affine 4-space. If $C_S$ is a non-complete\nintersection Gorenstein monomial curve whose tangent cone is Cohen-Macaulay, we\nshow that the possible Betti sequences are (1,5,5,1), (1,5,6,2) and (1,6,8,3).\n', 'On the reduction numbers and the Castelnuovo-Mumford regularity of\n  projective monomial curves   This paper gives explicit formulas for the reduction number and the\nCastelnuovo-Mumford regularity of projective monomial curves.\n', 'Buchsbaumness and Castelnuovo-Mumford regularity of non-smooth monomial\n  curves   Projective monomial curves correspond to rings generated by monomials of the\nsame degree in two variables. Such rings always have finite Macaulayfication.\nWe show how to characterize the Buchsbaumness and the Castelnuovo-Mumford\nregularity of these rings by means of their finite Macaulayfication, and we use\nthis method to study the Buchsbaumness and to estimate the Castelnuovo-Mumford\nregularity of large classes of non-smooth monomial curves in terms of the given\nmonomials.\n']","[('monomial curves', 0.6722620129585266), ('arithmetically cohen macaulay', 0.553834855556488), ('graded polynomial ring', 0.5284935832023621), ('macaulay type', 0.5219807028770447), ('cohen macaulay type', 0.5171509981155396), ('standard graded polynomial', 0.49181222915649414), ('curves affine', 0.4850129187107086), ('projective closure', 0.470691442489624), ('castelnuovo mumford regularity', 0.46514183282852173), ('cohen macaulay gorenstein', 0.4621325731277466)]"
952,952,32,952_symmetric polytopes_regular polytopes_regular polytope_polytopes whose,"['symmetric polytopes', 'regular polytopes', 'regular polytope', 'polytopes whose', 'polytopes every', 'polytopes type', 'polytope associated', 'polytopes', 'polytope polytope', 'polytopes order']","['Regular 3-polytopes of type $\\{n,n\\}$ For each integer \\( n \\geq 3 \\), we construct a self-dual regular 3-polytope \\( \\mathcal{P} \\) of type \\( \\{n, n\\} \\) with \\( 2^n n \\) flags, resolving two foundamental open questions on the existence of regular polytopes with certain Schl\\""afli types. The automorphism group \\( \\operatorname{Aut}(\\mathcal{P}) \\) is explicitly realized as the semidirect product \\( \\mathbb{F}_2^{n-1} \\rtimes D_{2n} \\), where \\( D_{2n} \\) is the dihedral group of order \\( 2n \\), with a complete presentation for \\( \\operatorname{Aut}(\\mathcal{P}) \\) is provided. This advances the systematic construction of regular polytopes with prescribed symmetries.', 'On the Schl\\""afli symbol of chiral extensions of polytopes   Given an abstract $n$-polytope $\\mathcal{K}$, an abstract $(n+1)$-polytope\n$\\mathcal{P}$ is an extension of $\\mathcal{K}$ if all the facets of\n$\\mathcal{P}$ are isomorphic to $\\mathcal{K}$. A chiral polytope is a polytope\nwith maximal rotational symmetry that does not admit any reflections. If\n$\\mathcal{P}$ is a chiral extension of $\\mathcal{K}$, then all but the last\nentry of the Schl\\""afli symbol of $\\mathcal{P}$ are determined. In this paper\nwe introduce some constructions of chiral extensions $\\mathcal{P}$ of certain\nchiral polytopes in such a way that the last entry of the Schl\\""afli symbol of\n$\\mathcal{P}$ is arbitrarily large.\n', 'Regular $3$-polytopes of order $2^np$   In [Problems on polytopes, their groups, and realizations, Periodica Math.\nHungarica 53 (2006) 231-255] Schulte and Weiss proposed the following problem:\n{\\em Characterize regular polytopes of orders $2^np$ for $n$ a positive integer\nand $p$ an odd prime}. In this paper, we first prove that if a $3$-polytope of\norder $2^np$ has Schl\\""afli type $\\{k_1, k_2\\}$, then $p \\mid k_1$ or $p \\mid\nk_2$. This leads to two classes, up to duality, for the Schl\\""afli type, namely\nType (1) where $k_1=2^sp$ and $k_2=2^t$ and Type (2) where $k_1=2^sp$ and\n$k_2=2^tp$. We then show that there exists a regular $3$-polytope of order\n$2^np$ with Type (1) when $s\\geq 2$, $t\\geq 2$ and $n\\geq s+t+1$ coming from a\ngeneral construction of regular $3$-polytopes of order $2^n\\ell_1\\ell_2$ with\nSchl\\""afli type $\\{2^s\\ell_1,2^t\\ell_2\\}$ where both $\\ell_1$ and $\\ell_2$ are\nodd. Furthermore, for $p=3$ and $n \\geq 7$, we show that there exists a regular\n3-polytope of order $3\\cdot2^n$ with type $\\{6,2^s\\}$ if and only if $2\\leq s\n\\leq n-2$ and $s \\neq n-3$. For Type (2), we prove that there exists a regular\n$3$-polytope of order $2^n\\cdot 3$ with Schl\\""afli type $\\{6, 6\\}$ when $n \\ge\n5$ coming from a general construction of regular $3$-polytopes of Schl\\""afli\ntype $\\{6,6\\}$ with orders $192m^3$, $384m^3$ or $768m^3$, for any positive\ninteger $m$.\n']","[('symmetric polytopes', 0.6735952496528625), ('regular polytopes', 0.6712474822998047), ('regular polytope', 0.6385337114334106), ('polytopes whose', 0.611153781414032), ('polytopes every', 0.6071261763572693), ('polytopes type', 0.6046927571296692), ('polytope associated', 0.599308431148529), ('polytopes', 0.5819530487060547), ('polytope polytope', 0.5750942230224609), ('polytopes order', 0.5670884251594543)]"
953,953,32,953_positive linear systems_lyapunov functions_linear time invariant_linear dynamical system,"['positive linear systems', 'lyapunov functions', 'linear time invariant', 'linear dynamical system', 'dynamical systems', 'quadratic lyapunov', 'positive systems', 'linear systems', 'lyapunov', 'linear dynamical']","['A sufficient condition for $k$-contraction of the series connection of\n  two systems   The flow of contracting systems contracts 1-dimensional parallelotopes, i.e.,\nline segments, at an exponential rate. One reason for the usefulness of\ncontracting systems is that many interconnections of contracting sub-systems\nyield an overall contracting system.\n  A generalization of contracting systems is $k$-contracting systems, where\n$k\\in\\{1,\\dots,n\\}$. The flow of such systems contracts the volume of\n$k$-dimensional parallelotopes at an exponential rate, and in particular they\nreduce to contracting systems when $k=1$. It was shown by Muldowney and Li that\ntime-invariant $2$-contracting systems have a well-ordered asymptotic\nbehaviour: all bounded trajectories converge to the set of equilibria.\n  Here, we derive a sufficient condition guaranteeing that the system obtained\nfrom the series interconnection of two sub-systems is $k$-contracting. This is\nbased on a new formula for the $k$th multiplicative and additive compounds of a\nblock-diagonal matrix, which may be of independent interest. As an application,\nwe find conditions guaranteeing that $2$-contracting systems with an\nexponentially decaying input retain the well-ordered behaviour of\ntime-invariant 2-contracting systems.\n', 'Diagonal Stability of Discrete-time $k$-Positive linear Systems with\n  Applications to Nonlinear Systems   A linear dynamical system is called $k$-positive if its dynamics maps the set\nof vectors with up to $k-1$ sign variations to itself. For $k=1$, this reduces\nto the important class of positive linear systems. Since stable positive linear\ntime-invariant (LTI) systems always admit a diagonal quadratic Lyapunov\nfunction, i.e. they are diagonally stable, we may expect that this holds also\nfor stable $k$-positive systems. We show that, in general, this is not the case\nboth in the continuous-time (CT) and discrete-time (DT) case. We then focus on\nDT $k$-positive linear systems and introduce the new notion of DT $k$-diagonal\nstability. It is shown that this is a necessary condition for standard DT\ndiagonal stability. We demonstrate an application of this new notion to the\nanalysis of a class of DT nonlinear systems.\n', 'k-Contraction: Theory and Applications   A dynamical system is called contractive if any two solutions approach one\nanother at an exponential rate. More precisely, the dynamics contracts lines at\nan exponential rate. This property implies highly ordered asymptotic behavior\nincluding entrainment to time-varying periodic vector fields and, in\nparticular, global asymptotic stability for time-invariant vector fields.\nContraction theory has found numerous applications in systems and control\ntheory because there exist easy to verify sufficient conditions, based on\nmatrix measures, guaranteeing contraction.\n  Here, we provide a geometric generalization of contraction theory called\nk-order contraction. A dynamical system is called k-order contractive if the\ndynamics contracts k-parallelotopes at an exponential rate. For k=1 this\nreduces to standard contraction.\n  We describe easy to verify sufficient conditions for k-order contractivity\nbased on matrix measures and the kth additive compound of the Jacobian of the\nvector field. We also describe applications of the seminal work of Muldowney\nand Li, that can be interpreted in the framework of 2-order contraction, to\nsystems and control theory.\n']","[('positive linear systems', 0.609785258769989), ('lyapunov functions', 0.5148659348487854), ('linear time invariant', 0.5051037073135376), ('linear dynamical system', 0.49416130781173706), ('dynamical systems', 0.4936867356300354), ('quadratic lyapunov', 0.48495689034461975), ('positive systems', 0.4802507162094116), ('linear systems', 0.4767690896987915), ('lyapunov', 0.4748096764087677), ('linear dynamical', 0.4731563627719879)]"
954,954,31,954_active learning_learning active_based active learning_efficient active,"['active learning', 'learning active', 'based active learning', 'efficient active', 'semi supervised', 'learning scheme', 'weakly supervised', 'semi supervised classification', 'learning models', 'learning classification']","['MALADY: Multiclass Active Learning with Auction Dynamics on Graphs   Active learning enhances the performance of machine learning methods,\nparticularly in semi-supervised cases, by judiciously selecting a limited\nnumber of unlabeled data points for labeling, with the goal of improving the\nperformance of an underlying classifier. In this work, we introduce the\nMulticlass Active Learning with Auction Dynamics on Graphs (MALADY) framework\nwhich leverages the auction dynamics algorithm on similarity graphs for\nefficient active learning. In particular, we generalize the auction dynamics\nalgorithm on similarity graphs for semi-supervised learning in [24] to\nincorporate a more general optimization functional. Moreover, we introduce a\nnovel active learning acquisition function that uses the dual variable of the\nauction algorithm to measure the uncertainty in the classifier to prioritize\nqueries near the decision boundaries between different classes. Lastly, using\nexperiments on classification tasks, we evaluate the performance of our\nproposed method and show that it exceeds that of comparison algorithms.\n', 'Pool-Based Active Learning with Proper Topological Regions   Machine learning methods usually rely on large sample size to have good\nperformance, while it is difficult to provide labeled set in many applications.\nPool-based active learning methods are there to detect, among a set of\nunlabeled data, the ones that are the most relevant for the training. We\npropose in this paper a meta-approach for pool-based active learning strategies\nin the context of multi-class classification tasks based on Proper Topological\nRegions. PTR, based on topological data analysis (TDA), are relevant regions\nused to sample cold-start points or within the active learning scheme. The\nproposed method is illustrated empirically on various benchmark datasets, being\ncompetitive to the classical methods from the literature.\n', 'Active Learning of Deep Neural Networks via Gradient-Free Cutting Planes   Active learning methods aim to improve sample complexity in machine learning.\nIn this work, we investigate an active learning scheme via a novel\ngradient-free cutting-plane training method for ReLU networks of arbitrary\ndepth and develop a convergence theory. We demonstrate, for the first time,\nthat cutting-plane algorithms, traditionally used in linear models, can be\nextended to deep neural networks despite their nonconvexity and nonlinear\ndecision boundaries. Moreover, this training method induces the first deep\nactive learning scheme known to achieve convergence guarantees, revealing a\ngeometric contraction rate of the feasible set. We exemplify the effectiveness\nof our proposed active learning method against popular deep active learning\nbaselines via both synthetic data experiments and sentimental classification\ntask on real datasets.\n']","[('active learning', 0.7534881234169006), ('learning active', 0.6950762271881104), ('based active learning', 0.6677145957946777), ('efficient active', 0.5171154737472534), ('semi supervised', 0.5074621438980103), ('learning scheme', 0.5001581907272339), ('weakly supervised', 0.49261710047721863), ('semi supervised classification', 0.4805299639701843), ('learning models', 0.473296195268631), ('learning classification', 0.4713367521762848)]"
955,955,31,955_equiangular lines_spherical designs_equiangular_designs obtained,"['equiangular lines', 'spherical designs', 'equiangular', 'designs obtained', 'designs finite', 'construction spherical', 'triangular', 'lines dimension', 'complex designs', 'dimension 18']","['Enumeration of sets of equiangular lines with common angle\n  $\\arccos(1/3)$   In 2018, Sz\\""{o}ll\\H{o}si and \\""{O}sterg\\r{a}rd enumerated some sets of\nequiangular lines with common angle $\\arccos(1/3)$ with a computer.\nFurthermore, they verified that the numbers $\\omega(n)$ of sets of $n$\nequiangular lines with common angle $\\arccos(1/3)$ in dimension $7$ are almost\nsymmetric around $n=14$. In this paper, we construct the other sets of\nequiangular lines with common angle $\\arccos(1/3)$ from root lattices of type\n$A$ or $D$ with the aid of switching roots. In addition, we prove that the\nnumbers $\\omega(n)$ are almost symmetric without a computer.\n', 'Sets of equiangular lines in dimension $18$ constructed from $A_9 \\oplus\n  A_9 \\oplus A_1$   In 2023, Greaves et~al.\\ constructed several sets of 57 equiangular lines in\ndimension 18. Using the concept of switching root introduced by Cao et~al.\\ in\n2021, these sets of equiangular lines are embedded in a lattice of rank 19\nspanned by norm 3 vectors together with a switching root. We characterize this\nlattice as an overlattice of the root lattice $A_9\\oplus A_9\\oplus A_1$, and\nshow that there are at least $246896$ sets of 57 equiangular lines in dimension\n$18$ arising in this way, up to isometry. Additionally, we prove that all of\nthese sets of equiangular lines are strongly maximal. Here, a set of\nequiangular lines is said to be strongly maximal if there is no set of\nequiangular lines properly containing it even if the dimension of the\nunderlying space is increased. Among these sets, there are ones with only six\ndistinct Seidel eigenvalues.\n', 'The Lemmens-Seidel conjecture for base size $5$   In 2020, Lin and Yu claimed to prove the so-called Lemmens-Seidel conjecture\nfor base size $5$. However, their proof has a gap, and in fact, some set of\nequiangular lines found by Greaves et al. in 2021 is a counterexample to one of\ntheir claims. In this paper, we give a proof of the conjecture for base size\n$5$. Also, we answer in the negative a question of Greaves et al. in 2021\nwhether some sets of $57$ equiangular lines with common angle $\\arccos(1/5)$ in\ndimension $18$ are contained in a unique set of $276$ equiangular lines with\ncommon angle $\\arccos(1/5)$ in dimension $23$. In addition, we answer in the\nnegative a question of Cao et al. in 2021 whether a strongly maximal set of\nequiangular lines with common angle $\\arccos(1/5)$ exists except the set of\n$276$ equiangular lines with common angle $\\arccos(1/5)$ in dimension $23$.\n']","[('equiangular lines', 0.5792405605316162), ('spherical designs', 0.5345312356948853), ('equiangular', 0.48705703020095825), ('designs obtained', 0.4239487051963806), ('designs finite', 0.39905300736427307), ('construction spherical', 0.3911353051662445), ('triangular', 0.37756478786468506), ('lines dimension', 0.37231728434562683), ('complex designs', 0.36045584082603455), ('dimension 18', 0.35585305094718933)]"
956,956,31,956_noncommutative quantum_quantum mechanics qm_quantum mechanics_quantum mechanical,"['noncommutative quantum', 'quantum mechanics qm', 'quantum mechanics', 'quantum mechanical', 'quantum theory', 'quantum', 'picture quantum', 'classical phase space', 'quantum operator', 'classical hamiltonian']","['On the Operator Origins of Classical and Quantum Wave Functions   We investigate operator algebraic origins of the classical Koopman-von\nNeumann wave function $\\psi_{KvN}$ as well as the quantum mechanical one\n$\\psi_{QM}$. We introduce a formalism of Operator Mechanics (OM) based on a\nnoncommutative Poisson, symplectic and noncommutative differential structures.\nOM serves as a pre-quantum algebra from which algebraic structures relevant to\nreal-world classical and quantum mechanics follow. In particular, $\\psi_{KvN}$\nand $\\psi_{QM}$ are both consequences of this pre-quantum formalism. No a\npriori Hilbert space is needed. OM admits an algebraic notion of operator\nexpectation values without invoking states. A phase space bundle ${\\cal E}$\nfollows from this. $\\psi_{KvN}$ and $\\psi_{QM}$ are shown to be sections in\n${\\cal E}$. The difference between $\\psi_{KvN}$ and $\\psi_{QM}$ originates from\na quantization map interpreted as ""twisting"" of sections over ${\\cal E}$. We\nalso show that the Schr\\""{o}dinger equation is obtained from the Koopman-von\nNeumann equation. What this suggests is that neither the Schr\\""{o}dinger\nequation nor the quantum wave function are fundamental structures. Rather, they\nboth originate from a pre-quantum operator algebra. Finally, we comment on how\nentanglement between these operators suggests emergence of space; and possible\nextensions of this formalism to field theories.\n', 'Classical Systems in Quantum Mechanics   If we admit that quantum mechanics (QM) is universal theory, then QM should\ncontain also some description of classical mechanical systems. The presented\ntext contains description of two different ways how the mathematical\ndescription of kinematics and dynamics of classical systems emerges from the\nmathematical formalism of QM. The first of these ways is to obtain an\nequivalent description of QM (with finite number of degrees of freedom) as a\nclassical Hamiltonian field theory and afterwards restrict it in dependence of\nspecific classical system to obtain the classical Hamiltonian mechanics of that\nfinite system. The second way is transition to QM of systems with infinite\nnumber of degrees of freedom - i.e. of macroscopic systems - and extract from\nit classical mechanics (with finite number of degrees of freedom) of\nmacroscopic variables of this quantum system. The last chapter contains some\nconsiderations concerning the ""measurement problem in QM"", in which a measured\nquantum ""microsystem"" has to be dynamically connected with changes of classical\nstates of a macroscopic quantum (sub-)system - the measuring device. Several\nmodels of this process are presented.\n', ""On the entanglement of co-ordinate and momentum degrees of freedom in\n  noncommutative space   In this paper, we investigate the quantum entanglement induced by phase-space\nnoncommutativity. Both the position-position and momentum-momentum\nnoncommutativity are incorporated to study the entanglement properties of\ncoordinate and momentum degrees of freedom under the shade of oscillators in\nnoncommutative space. Exact solutions for the systems are obtained after the\nmodel is re-expressed in terms of canonical variables, by performing a\nparticular Bopp's shift to the noncommuting degrees of freedom. It is shown\nthat the bipartite Gaussian state for an isotropic oscillator is always\nseparable. To extend our study for the time-dependent system, we allow\narbitrary time dependency on parameters. The time-dependent isotropic\noscillator is solved with the Lewis-Riesenfeld invariant method. It turns out\nthat even for arbitrary time-dependent scenarios, the separability property\ndoes not alter. We extend our study to the anisotropic oscillator, which\nprovides an entangled state even for time-independent parameters. The Wigner\nquasi-probability distribution is constructed for a bipartite Gaussian state.\nThe noise matrix (covariance matrix) is explicitly studied with the help of\nWigner distribution. Simon's separability criterion (generalized\nPeres-Horodecki criterion) has been employed to find the unique function of the\n(mass and frequency) parameters, for which the bipartite states are separable.\nIn particular, we show that the mere inclusion of non-commutativity of\nphase-space is not sufficient to generate the entanglement, rather anisotropy\nis important at the same footing.\n""]","[('noncommutative quantum', 0.6510017514228821), ('quantum mechanics qm', 0.6113571524620056), ('quantum mechanics', 0.5860567688941956), ('quantum mechanical', 0.5838152170181274), ('quantum theory', 0.5773310661315918), ('quantum', 0.547139048576355), ('picture quantum', 0.5245262980461121), ('classical phase space', 0.5179911851882935), ('quantum operator', 0.487680047750473), ('classical hamiltonian', 0.4791337847709656)]"
957,957,31,957_algebras superalgebras_jordan algebras_lie superalgebras_jordan algebra,"['algebras superalgebras', 'jordan algebras', 'lie superalgebras', 'jordan algebra', 'classical lie superalgebras', 'superalgebras', 'superalgebras describe', 'superalgebra mathcal', 'lie superalgebra', 'superalgebra']","['$\\delta$-superderivations of KKM Double   We described $\\delta$-derivations and $\\delta$-superderivations of simple\nJordan superalgebra <<KKM Double>> (also known as superalgebra of Jordan\nbrackets) and unital simple finite-dimensional Jordan superalgebras over\nalgebraic closed fields with characteristic $p\\neq2$. As a consequence, we\nreceived relationship between non-trivial $\\delta$-derivations and specialty of\nsimple superalgebra <<KKM Double>>. We constructed new examples of non-trivial\n1/2-derivations of Jordan superalgebras of vector type.\n', '$\\delta$-derivations of simple Jordan algebras and superalgebras   We describe non-trivial $\\delta$-derivations of semisimple finite-dimensional\nJordan algebras over an algebraically closed field of characteristic not 2, and\nof simple finite-dimensional Jordan superalgebras over an algebraically closed\nfield of characteristic 0. For these classes of algebras and superalgebras,\nnon-zero $\\delta$-derivations are shown to be missing for $\\delta\\neq\n0,{1}{2},1$, and we give a complete account of ${1}{2}$-derivations.\n', '$\\delta$-superderivations of simple finite-dimensional Jordan and Lie\n  superalgebras   We introduce the concept of a $\\delta$-superderivation of a superalgebra.\n$\\delta$-Derivations of Cartan-type Lie superalgebras are treated, as well as\n$\\delta$-superderivations of simple finite-dimensional Lie superalgebras and\nJordan superalgebras over an algebraically closed field of characteristic 0. We\ngive a complete description of $\\{1}{2}$-derivations for Cartan-type Lie\nsuperalgebras. It is proved that nontrivial $\\delta$-(super)derivations are\nmissing on the given classes of superalgebras, and as a consequence,\n$\\delta$-superderivations are shown to be trivial on simple finite-dimensional\nnoncommutative Jordan superalgebras of degree at least 2 over an algebraically\nclosed field of characteristic 0. Also we consider $\\delta$-derivations of\nunital flexible and semisimple finite-dimensional Jordan algebras over a field\nof characteristic not 2.\n']","[('algebras superalgebras', 0.6902502775192261), ('jordan algebras', 0.6685943007469177), ('lie superalgebras', 0.639311671257019), ('jordan algebra', 0.6339477896690369), ('classical lie superalgebras', 0.627194344997406), ('superalgebras', 0.625762403011322), ('superalgebras describe', 0.623564600944519), ('superalgebra mathcal', 0.5969419479370117), ('lie superalgebra', 0.5825867652893066), ('superalgebra', 0.5452232956886292)]"
958,958,31,958_chromatic number_chromatic number denoted_graphs chi__chromatic,"['chromatic number', 'chromatic number denoted', 'graphs chi_', 'chromatic', 'graph bijection', 'graphs local', 'vertex coloring', 'graph local', 'graphs regular graphs', 'regular graphs']","[""On local antimagic chromatic number of lexicographic product graphs   Let $G = (V,E)$ be a connected simple graph of order $p$ and size $q$. A\ngraph $G$ is called local antimagic if $G$ admits a local antimagic labeling. A\nbijection $f : E \\to \\{1,2,\\ldots,q\\}$ is called a local antimagic labeling of\n$G$ if for any two adjacent vertices $u$ and $v$, we have $f^+(u) \\ne f^+(v)$,\nwhere $f^+(u) = \\sum_{e\\in E(u)} f(e)$, and $E(u)$ is the set of edges incident\nto $u$. Thus, any local antimagic labeling induces a proper vertex coloring of\n$G$ if vertex $v$ is assigned the color $f^+(v)$. The local antimagic chromatic\nnumber, denoted $\\chi_{la}(G)$, is the minimum number of induced colors taken\nover local antimagic labeling of $G$. Let $G$ and $H$ be two vertex disjoint\ngraphs. The {\\it lexicographic product} of $G$ and $H$, denoted $G[H]$, is the\ngraph with vertex set $V(G) \\times V(H)$, and $(u,u')$ is adjacent to $(v,v')$\nin $G[H]$ if $(u,v)\\in E(G)$ or if $u=v$ and $u'v'\\in E(H)$. In this paper, we\nobtained sharp upper bound of $\\chi_{la}(G[O_n])$ where $O_n$ is a null graph\nof order $n\\ge 1$. Sufficient conditions for even regular bipartite and\ntripartite graphs $G$ to have $\\chi_{la}(G)=3$ are also obtained. Consequently,\nwe successfully determined the local antimagic chromatic number of infinitely\nmany (connected and disconnected) regular graphs that partially support the\nexistence of $r$-regular graph $G$ of order $p$ such that (i)\n$\\chi_{la}(G)=\\chi(G)=k$, and (ii) $\\chi_{la}(G)=\\chi(G)+1=k$ for each possible\n$r,p,k$.\n"", 'On local antimagic chromatic number of cycle-related join graphs   An edge labeling of a connected graph $G = (V, E)$ is said to be local\nantimagic if it is a bijection $f:E \\to\\{1,\\ldots ,|E|\\}$ such that for any\npair of adjacent vertices $x$ and $y$, $f^+(x)\\not= f^+(y)$, where the induced\nvertex label $f^+(x)= \\sum f(e)$, with $e$ ranging over all the edges incident\nto $x$. The local antimagic chromatic number of $G$, denoted by $\\chi_{la}(G)$,\nis the minimum number of distinct induced vertex labels over all local\nantimagic labelings of $G$. In this paper, several sufficient conditions for\n$\\chi_{la}(H)\\le \\chi_{la}(G)$ are obtained, where $H$ is obtained from $G$\nwith a certain edge deleted or added. We then determined the exact value of the\nlocal antimagic chromatic number of many cycle related join graphs.\n', 'Complete characterization of s-bridge graphs with local antimagic\n  chromatic number 2   An edge labeling of a connected graph $G = (V, E)$ is said to be local\nantimagic if it is a bijection $f:E \\to\\{1,\\ldots ,|E|\\}$ such that for any\npair of adjacent vertices $x$ and $y$, $f^+(x)\\not= f^+(y)$, where the induced\nvertex label $f^+(x)= \\sum f(e)$, with $e$ ranging over all the edges incident\nto $x$. The local antimagic chromatic number of $G$, denoted by $\\chi_{la}(G)$,\nis the minimum number of distinct induced vertex labels over all local\nantimagic labelings of $G$. In this paper, we characterize $s$-bridge graphs\nwith local antimagic chromatic number 2.\n']","[('chromatic number', 0.5568638443946838), ('chromatic number denoted', 0.5166552662849426), ('graphs chi_', 0.4825316071510315), ('chromatic', 0.4724532663822174), ('graph bijection', 0.4684683382511139), ('graphs local', 0.4615975022315979), ('vertex coloring', 0.4531300961971283), ('graph local', 0.4433104991912842), ('graphs regular graphs', 0.4111707806587219), ('regular graphs', 0.4050125181674957)]"
959,959,31,959_sphere packings_circle packings_sphere packing_circle packing,"['sphere packings', 'circle packings', 'sphere packing', 'circle packing', 'packings', 'apollonian', 'ball packings', 'packing density', 'packing', 'packing densities']","['Links in orthoplicial Apollonian packings   In this paper, we establish a connection between Apollonian packings and knot\ntheory. We introduce new representations of links realized in the tangency\ngraph of the regular crystallographic sphere packings. Particularly, we prove\nthat any algebraic link can be realized in the cubic section of the\northoplicial Apollonian packing. We use these representations to improve the\nupper bound on the ball number of an infinite family of alternating algebraic\nlinks. Furthermore, the later allow us to reinterpret the correspondence of\nrational tangles and rational numbers and to reveal geometrically primitive\nsolutions for the Diophantine equation $x^4 + y^4 + z^4 = 2t^2$.\n', 'Apollonian Packings and Kac-Moody Root Systems   We study Apollonian circle packings in relation to a certain rank 4\nindefinite Kac-Moody root system $\\Phi$. We introduce the generating function\n$Z(\\mathbf{s})$ of a packing, an exponential series in four variables with an\nApollonian symmetry group, which relates to Weyl-Kac characters of $\\Phi$. By\nexploiting the presence of affine and Lorentzian hyperbolic root subsystems of\n$\\Phi$, with automorphic Weyl denominators, we express $Z(\\mathbf{s})$ in terms\nof Jacobi theta functions and the Siegel modular form $\\Delta_5$. We also show\nthat the domain of convergence of $Z(\\mathbf{s})$ is the Tits cone of $\\Phi$,\nand discover that this domain inherits the intricate geometric structure of\nApollonian packings.\n', 'Enriques surfaces and an Apollonian packing in eight dimensions   We call a packing of hyperspheres in $n$ dimensions an Apollonian sphere\npacking if the spheres intersect tangentially or not at all; they fill the\n$n$-dimensional space; and every sphere in the packing is a member of a cluster\nof $n+2$ mutually tangent spheres (and a few more properties described herein).\nIn this paper, we describe an Apollonian packing in eight dimensions that\nnaturally arises from the study of generic nodal Enriques surfaces. The $E_7$,\n$E_8$ and Reye lattices play roles. We use the packing to generate an\nApollonian packing in nine dimensions, and a cross section in seven dimensions\nthat is weakly Apollonian. Maxwell described all three packings but seemed\nunaware that they are Apollonian. The packings in seven and eight dimensions\nare different than those found in an earlier paper. In passing, we give a\nsufficient condition for a Coxeter graph to generate mutually tangent spheres,\nand use this to identify an Apollonian sphere packing in three dimensions that\nis not the Soddy sphere packing.\n']","[('sphere packings', 0.6527810096740723), ('circle packings', 0.6239981055259705), ('sphere packing', 0.5998882055282593), ('circle packing', 0.5713627934455872), ('packings', 0.4329804480075836), ('apollonian', 0.4287947714328766), ('ball packings', 0.421316534280777), ('packing density', 0.41133585572242737), ('packing', 0.4040662348270416), ('packing densities', 0.3894721567630768)]"
960,960,31,960_energy stable numerical_energy stable schemes_auxiliary variable sav_numerical schemes,"['energy stable numerical', 'energy stable schemes', 'auxiliary variable sav', 'numerical schemes', 'numerical methods numerical', 'energy quadratization', 'gradient flows', 'gradient flow', 'energy stability', 'variable sav']","['The generalized scalar auxiliary variable approach (G-SAV) for gradient\n  flows   We establish a general framework for developing, efficient energy stable\nnumerical schemes for gradient flows and develop three classes of generalized\nscalar auxiliary variable approaches (G-SAV). Numerical schemes based on the\nG-SAV approaches are as efficient as the original SAV schemes\n\\cite{SXY19,cheng2018multiple} for gradient flows, i.e., only require solving\nlinear equations with constant coefficients at each time step, can be\nunconditionally energy stable. But G-SAV approaches remove the definition\nrestriction that auxiliary variables can only be square root function. The\ndefinition form of auxiliary variable is applicable to any reversible function\nfor G-SAV approaches . Ample numerical results for phase field models are\npresented to validate the effectiveness and accuracy of the proposed G-SAV\nnumerical schemes.\n', 'A novel energy-optimal scalar auxiliary variable (EOP-SAV) approach for\n  gradient flows   In recent years, the scalar auxiliary variable (SAV) approach has become very\npopular and hot in the design of linear, high-order and unconditional energy\nstable schemes of gradient flow models. However, the nature of SAV-based\nnumerical schemes preserving modified energy dissipation limits its wider\napplication. A relaxation technique to correct the modified energy for the\nbaseline SAV method (RSAV) was proposed by Zhao et al. and Shen et al.. The\nRSAV approach is unconditionally energy stable with respect to a modified\nenergy that is closer to the original free energy, and provides a much improved\naccuracy when compared with the SAV approach. In this paper, inspired by the\nRSAV approach, we propose a novel technique to correct the modified energy of\nthe SAV approach, which can be proved to be an optimal energy approximation. We\nconstruct new high-order implicit-explicit schemes based on the proposed\nenergy-optimal SAV (EOP-SAV) approach. The constructed EOP-SAV schemes not only\nprovide an improved accuracy but also simplify calculation, and can be viewed\nas the optimal relaxation. We also prove that the numerical schemes based on\nthe EOP-SAV approach are unconditionally energy stable. Compared with the RSAV\napproach, the proposed EOP-SAV approach does not need introduce any relaxed\nfactors and can share the similar procedure for error estimates. Several\ninteresting numerical examples have been presented to demonstrate the accuracy\nand effectiveness of the proposed methods.\n', 'Highly efficient exponential scalar auxiliary variable approaches with\n  relaxation (RE-SAV) for gradient flows   For the past few years, scalar auxiliary variable (SAV) and SAV-type\napproaches became very hot and efficient methods to simulate various gradient\nflows. Inspired by the new SAV approach in \\cite{huang2020highly}, we propose a\nnovel technique to construct a new exponential scalar auxiliary variable\n(E-SAV) approach to construct high-order numerical energy stable schemes for\ngradient flows. To improve its accuracy and consistency noticeably, we propose\nan E-SAV approach with relaxation, which we named the relaxed E-SAV (RE-SAV)\nmethod for gradient flows. The RE-SAV approach preserves all the advantages of\nthe traditional SAV approach. In addition, we do not need any the\nbounded-from-below assumptions for the free energy potential or nonlinear term.\nBesides, the first-order, second-order and higher-order unconditionally energy\nstable time-stepping schemes are easy to construct. Several numerical examples\nare provided to demonstrate the improved efficiency and accuracy of the\nproposed method.\n']","[('energy stable numerical', 0.5653195381164551), ('energy stable schemes', 0.5396496653556824), ('auxiliary variable sav', 0.4492585062980652), ('numerical schemes', 0.4473704695701599), ('numerical methods numerical', 0.4035933315753937), ('energy quadratization', 0.39919576048851013), ('gradient flows', 0.39833757281303406), ('gradient flow', 0.38552457094192505), ('energy stability', 0.37919098138809204), ('variable sav', 0.3769918382167816)]"
961,961,31,961_quantum state tomography_quantum measurement_quantum tomography_quantum phase estimation,"['quantum state tomography', 'quantum measurement', 'quantum tomography', 'quantum phase estimation', 'quantum metrology', 'quantum sensing', 'information quantum', 'quantum state', 'quantum states', 'quantum']","[""The gap persistence theorem for quantum multiparameter estimation   One key aspect of quantum metrology, measurement incompatibility, is evident\nonly through the simultaneous estimation of multiple parameters. The symmetric\nlogarithmic derivative Cram\\'er-Rao bound (SLDCRB), gives the attainable\nprecision, if the optimal measurements for estimating each individual parameter\ncommute. When the optimal measurements do not commute, the SLDCRB is not\nnecessarily attainable. In this regard, the Holevo Cram\\'er-Rao bound (HCRB)\nplays a fundamental role, providing the ultimate attainable precisions when one\nallows simultaneous measurements on infinitely many copies of a quantum state.\nFor practical purposes, the Nagaoka Cram\\'er-Rao bound (NCRB) is more relevant,\napplying when restricted to measuring quantum states individually. The\ninterplay between these three bounds dictates how rapidly the ultimate\nmetrological precisions can be approached through collective measurements on\nfinite copies of the probe state. We first consider two parameter estimation\nand prove that if the HCRB cannot be saturated with a single copy of the probe\nstate, then it cannot be saturated for any finite number of copies of the probe\nstate. With this, we show that it is impossible to saturate the HCRB for\nseveral physically motivated problems. For estimating any number of parameters,\nwe provide necessary and sufficient conditions for the attainability of the\nSLDCRB with separable measurements. We further prove that if the SLDCRB cannot\nbe reached with a single copy of the probe state, it cannot be reached with\ncollective measurements on any finite number of copies of the probe state.\nThese results together provide necessary and sufficient conditions for the\nattainability of the SLDCRB for any finite number of copies of the probe state.\nThis solves a significant generalisation of one of the five problems recently\nhighlighted by [P.Horodecki et al, Phys. Rev. X Quantum 3, 010101 (2022)].\n"", 'Quantum enhanced metrology of Hamiltonian parameters beyond the\n  Cram\\`er-Rao bound   This is a tutorial aimed at illustrating some recent developments in quantum\nparameter estimation beyond the Cram\\`er-Rao bound, as well as their\napplications in quantum metrology. Our starting point is the observation that\nthere are situations in classical and quantum metrology where the unknown\nparameter of interest, besides determining the state of the probe, is also\ninfluencing the operation of the measuring devices, e.g. the range of possible\noutcomes. In those cases, non-regular statistical models may appear, for which\nthe Cram\\`er-Rao theorem does not hold. In turn, the achievable precision may\nexceed the Cram\\`er-Rao bound, opening new avenues for enhanced metrology. We\nfocus on quantum estimation of Hamiltonian parameters and show that an\nachievable bound to precision (beyond the Cram\\`er-Rao) may be obtained in a\nclosed form for the class of so-called controlled energy measurements. Examples\nof applications of the new bound to various estimation problems in quantum\nmetrology are worked out in some details.\n', 'Quantum state tomography for qutrits subject to laser cooling   In this article we propose a dynamic quantum state tomography model for\nqutrits subject to laser cooling. We prove that one can reduce the number of\ndistinct measurement setups required for state reconstruction by employing the\nstroboscopic approach. The results are in line with current advances in quantum\ntomography where there is a strong tendency to investigate the optimal criteria\nfor state reconstruction. We believe that the stroboscopic approach can be\nconsidered an efficient tool for density matrix identification since it allows\nto determine the minimal number of distinct observables needed for quantum\nstate tomography.\n']","[('quantum state tomography', 0.7581177949905396), ('quantum measurement', 0.7458701729774475), ('quantum tomography', 0.7145746946334839), ('quantum phase estimation', 0.6798431277275085), ('quantum metrology', 0.6567211747169495), ('quantum sensing', 0.6220380067825317), ('information quantum', 0.6014671325683594), ('quantum state', 0.6004229187965393), ('quantum states', 0.5920040607452393), ('quantum', 0.5880274772644043)]"
962,962,31,962_dimensional associative algebras_commutative algebras_associative algebras_nonassociative algebras,"['dimensional associative algebras', 'commutative algebras', 'associative algebras', 'nonassociative algebras', 'filiform associative algebras', 'non associative algebra', 'algebras characterized', 'dimensional algebras', 'commutative algebra', 'algebras analogue']","['A classification of 2-dimensional endo-commutative straight algebras of\n  type II_1   In this paper, we present a complete classification of 2-dimensional\nendo-commutative straight algebras of type II$_1$ over any field. An\nendo-commutative algebra is a non-associative algebra in which the square\nmapping preserves multiplication. A 2-dimensional straight algebra satisfies\nthe condition that there exists an element $x$ such that $x$ and $x^2$ are\nlinearly independent. The term type II$_1$ denotes a distinguishing\ncharacteristic of its structure matrix, which has rank 2. We provide\nmultiplication tables for these algebras, listing them up to isomorphism.\n', 'A classification of 2-dimensional endo-commutative straight algebras of\n  rank 1 over a non-trivial field   An endo-commutative algebra is a nonassociative algebra in which the square\nmapping preserves multiplication. In this paper, we give a complete\nclassification of 2-dimensional endo-commutative straight algebras of rank one\nover an arbitrary non-trivial field, where a straight algebra of dimension 2\nsatisfies the condition that there exists an element $x$ such that $x$ and\n$x^2$ are linearly independent. We list all multiplication tables of the\nalgebras up to isomorphism.\n', 'A Classification of 2-dimensional endo-commutative straight algebras of\n  type I   In this paper, we provide a complete classification of 2-dimensional\nendo-commutative straight algebras of type I over any field. An\nendo-commutative algebra is a non-associative algebra in which the square\nmapping preserves multiplication. Type I denotes a distinguishing\ncharacteristic of its structure matrix of rank 2. We list all multiplication\ntables of these algebras up to isomorphism.\n']","[('dimensional associative algebras', 0.6752982139587402), ('commutative algebras', 0.6537922620773315), ('associative algebras', 0.6527001261711121), ('nonassociative algebras', 0.6349883079528809), ('filiform associative algebras', 0.6203522682189941), ('non associative algebra', 0.6095312237739563), ('algebras characterized', 0.6068878769874573), ('dimensional algebras', 0.6050779223442078), ('commutative algebra', 0.6027930378913879), ('algebras analogue', 0.5969089865684509)]"
963,963,31,963_decoding strategies_game information_nash equilibrium_asymmetric information,"['decoding strategies', 'game information', 'nash equilibrium', 'asymmetric information', 'game theoretical', 'nash equilibria', 'stochastic dynamic games', 'private information', 'information decoder', 'information bottleneck']","[""Maximizing Social Welfare and Agreement via Information Design in\n  Linear-Quadratic-Gaussian Games   We consider linear-quadratic Gaussian (LQG) games in which players have\nquadratic payoffs that depend on the players' actions and an unknown\npayoff-relevant state, and signals on the state that follow a Gaussian\ndistribution conditional on the state realization. An information designer\ndecides the fidelity of information revealed to the players in order to\nmaximize the social welfare of the players or reduce the disagreement among\nplayers' actions. Leveraging the semi-definiteness of the information design\nproblem, we derive analytical solutions for these objectives under specific LQG\ngames. We show that full information disclosure maximizes social welfare when\nthere is a common payoff-relevant state, when there is strategic\nsubstitutability in the actions of players, or when the signals are public.\nNumerical results show that as strategic substitution increases, the value of\nthe information disclosure increases. When the objective is to induce\nconformity among players' actions, hiding information is optimal. Lastly, we\nconsider the information design objective that is a weighted combination of\nsocial welfare and cohesiveness of players' actions. We obtain an interval for\nthe weights where full information disclosure is optimal under public signals\nfor games with strategic substitutability. Numerical solutions show that the\nactual interval where full information disclosure is optimal gets close to the\nanalytical interval obtained as substitution increases.\n"", ""Learning How to Strategically Disclose Information   Strategic information disclosure, in its simplest form, considers a game\nbetween an information provider (sender) who has access to some private\ninformation that an information receiver is interested in. While the receiver\ntakes an action that affects the utilities of both players, the sender can\ndesign information (or modify beliefs) of the receiver through signal\ncommitment, hence posing a Stackelberg game. However, obtaining a Stackelberg\nequilibrium for this game traditionally requires the sender to have access to\nthe receiver's objective. In this work, we consider an online version of\ninformation design where a sender interacts with a receiver of an unknown type\nwho is adversarially chosen at each round. Restricting attention to Gaussian\nprior and quadratic costs for the sender and the receiver, we show that\n$\\mathcal{O}(\\sqrt{T})$ regret is achievable with full information feedback,\nwhere $T$ is the total number of interactions between the sender and the\nreceiver. Further, we propose a novel parametrization that allows the sender to\nachieve $\\mathcal{O}(\\sqrt{T})$ regret for a general convex utility function.\nWe then consider the Bayesian Persuasion problem with an additional cost term\nin the objective function, which penalizes signaling policies that are more\ninformative and obtain $\\mathcal{O}(\\log(T))$ regret. Finally, we establish a\nsublinear regret bound for the partial information feedback setting and provide\nsimulations to support our theoretical results.\n"", ""Strategic information transmission with sender's approval   We consider a sender-receiver game with an outside option for the sender.\nAfter the cheap talk phase, the receiver makes a proposal to the sender, which\nthe latter can reject. We study situations in which the sender's approval is\ncrucial to the receiver.We show that a partitional, (perfect Bayesian Nash)\nequilibrium exists if the sender has only two types or if the receiver's\npreferences over decisions do not depend on the type of the sender as long as\nthe latter participates. The result does not extend: we construct a\ncounter-example (with three types for the sender and type-dependent affine\nutility functions) in which there is no mixed equilibrium. In the three type\ncase, we provide a full characterization of (possibly mediated) equilibria.\n""]","[('decoding strategies', 0.5071766376495361), ('game information', 0.48557156324386597), ('nash equilibrium', 0.46164649724960327), ('asymmetric information', 0.44876953959465027), ('game theoretical', 0.4361076354980469), ('nash equilibria', 0.4298306703567505), ('stochastic dynamic games', 0.4276374280452728), ('private information', 0.4175263047218323), ('information decoder', 0.4029712975025177), ('information bottleneck', 0.3897211253643036)]"
964,964,31,964_identifiability analysis_parameter identifiability_identifiable parameters_identifiability,"['identifiability analysis', 'parameter identifiability', 'identifiable parameters', 'identifiability', 'identifiability issues', 'global identifiability', 'structural identifiability', 'ode models', 'differential models', 'ode systems']","['Multi-experiment parameter identifiability of ODEs and model theory   Structural identifiability is a property of an ODE model with parameters that\nallows for the parameters to be determined from continuous noise-free data.\nThis is a natural prerequisite for practical identifiability. Conducting\nmultiple independent experiments could make more parameters or functions of\nparameters identifiable, which is a desirable property to have. How many\nexperiments are sufficient? In the present paper, we provide an algorithm to\ndetermine the exact number of experiments for multi-experiment local\nidentifiability and obtain an upper bound that is off at most by one for the\nnumber of experiments for multi-experiment global identifiability.\n  Interestingly, the main theoretical ingredient of the algorithm has been\ndiscovered and proved using model theory (in the sense of mathematical logic).\nWe hope that this unexpected connection will stimulate interactions between\napplied algebra and model theory, and we provide a short introduction to model\ntheory in the context of parameter identifiability. As another related\napplication of model theory in this area, we construct a nonlinear ODE system\nwith one output such that single-experiment and multiple-experiment\nidentifiability are different for the system. This contrasts with recent\nresults about single-output linear systems.\n  We also present a Monte Carlo randomized version of the algorithm with a\npolynomial arithmetic complexity. Implementation of the algorithm is provided\nand its performance is demonstrated on several examples. The source code is\navailable at https://github.com/pogudingleb/ExperimentsBound.\n', 'Parameter identifiability and input-output equations   Structural parameter identifiability is a property of a differential model\nwith parameters that allows for the parameters to be determined from the model\nequations in the absence of noise. One of the standard approaches to assessing\nthis problem is via input-output equations and, in particular, characteristic\nsets of differential ideals. The precise relation between identifiability and\ninput-output identifiability is subtle. The goal of this note is to clarify\nthis relation. The main results are:\n  1) identifiability implies input-output identifiability;\n  2) these notions coincide if the model does not have rational first\nintegrals;\n  3) the field of input-output identifiable functions is generated by the\ncoefficients of a ""minimal"" characteristic set of the corresponding\ndifferential ideal.\n  We expect that some of these facts may be known to the experts in the area,\nbut we are not aware of any articles in which these facts are stated precisely\nand rigorously proved.\n', 'Input-output equations and identifiability of linear ODE models   Structural identifiability is a property of a differential model with\nparameters that allows for the parameters to be determined from the model\nequations in the absence of noise. The method of input-output equations is one\nmethod for verifying structural identifiability. This method stands out in its\nimportance because the additional insights it provides can be used to analyze\nand improve models. However, its complete theoretical grounds and applicability\nare still to be established. A subtlety and key for this method to work\ncorrectly is knowing whether the coefficients of these equations are\nidentifiable.\n  In this paper, to address this, we prove identifiability of the coefficients\nof input-output equations for types of differential models that often appear in\npractice, such as linear models with one output and linear compartment models\nin which, from each compartment, one can reach either a leak or an input. This\nshows that checking identifiability via input-output equations for these models\nis legitimate and, as we prove, that the field of identifiable functions is\ngenerated by the coefficients of the input-output equations. Finally, we\nexploit a connection between input-output equations and the transfer function\nmatrix to show that, for a linear compartment model with an input and strongly\nconnected graph, the field of all identifiable functions is generated by the\ncoefficients of the transfer function matrix even if the initial conditions are\ngeneric.\n']","[('identifiability analysis', 0.6371659636497498), ('parameter identifiability', 0.6238663196563721), ('identifiable parameters', 0.6093084812164307), ('identifiability', 0.601864218711853), ('identifiability issues', 0.5848947167396545), ('global identifiability', 0.5848144292831421), ('structural identifiability', 0.5687943696975708), ('ode models', 0.558402955532074), ('differential models', 0.4822334051132202), ('ode systems', 0.47038978338241577)]"
965,965,31,965_generalized tur problems_graphs generalized_complete bipartite graphs_free graph vertices,"['generalized tur problems', 'graphs generalized', 'complete bipartite graphs', 'free graph vertices', 'extremal graphs', 'bounded matching', 'free graph', 'bounded matching number', 'bipartite graphs', 'vertex free']","[""On generalized Tur\\'an problems with bounded matching number   Given a graph $H$ and a family of graphs $\\mathcal{F}$, the generalized\nTur\\'an number $\\mathrm{ex}(n,H,\\mathcal{F})$ is the maximum number of copies\nof $H$ in an $n$-vertex graphs that do not contain any member of $\\mathcal{F}$\nas a subgraph. Recently there has been interest in studying the case\n$\\mathcal{F}=\\{F,M_{s+1}\\}$ for arbitrary $F$ and $H=K_r$. We extend these\ninvestigations to the case $H$ is arbitrary as well.\n"", ""On generalized Tur\\'an problems with bounded matching number   The generalized Tur\\'an number $\\mathrm{ex}(n, H, \\mathcal{F})$ is defined as\nthe maximum number of copies of a graph $H$ in an $n$-vertex graph that does\nnot contain any graph $F \\in \\mathcal{F}$. Alon and Frankl initiated the study\nof Tur\\'an problems with a bounded matching number.In this paper, we establish\nstability results for generalized Tur\\'an problems with bounded matching\nnumber.Using the stability results, we provide exact values of\n$\\ex(n,K_r,\\{F,M_{s+1}\\})$ for $F$ being any non-bipartite graph or a path on\n$k$ vertices.\n"", ""On generalized Tur{\\'a}n problems with bounded matching number and\n  circumference   Let \\( \\mathcal{F} \\) be a family of graphs. The generalized Tur\\'an number\n\\( \\operatorname{ex}(n, K_r, \\mathcal{F}) \\) is the maximum number of $K_r$ in\nan \\( n \\)-vertex graph that does not contain any member of \\( \\mathcal{F} \\)\nas a subgraph. Recently, Alon and Frankl initiated the study of Tur\\'an\nproblems with bounded matching number. In this paper, we determine the\ngeneralized Tur\\'an number of \\( C_{\\geq k} \\) with bounded matching number.\n""]","[('generalized tur problems', 0.5836183428764343), ('graphs generalized', 0.5680796504020691), ('complete bipartite graphs', 0.5328994393348694), ('free graph vertices', 0.5141817331314087), ('extremal graphs', 0.5139228105545044), ('bounded matching', 0.4893975853919983), ('free graph', 0.48424673080444336), ('bounded matching number', 0.48093950748443604), ('bipartite graphs', 0.4757471978664398), ('vertex free', 0.47069114446640015)]"
966,966,31,966_rate distortion theory_rate distortion_lossy source coding_distortion rate,"['rate distortion theory', 'rate distortion', 'lossy source coding', 'distortion rate', 'distortion theory', 'distortion measure', 'distortion constraint', 'coding rate', 'encoder decoder', 'squared error distortion']","['Rate-Distortion-Perception Tradeoff Based on the\n  Conditional-Distribution Perception Measure   This paper studies the rate-distortion-perception (RDP) tradeoff for a\nmemoryless source model in the asymptotic limit of large block-lengths. The\nperception measure is based on a divergence between the distributions of the\nsource and reconstruction sequences \\emph{conditioned} on the encoder output,\nfirst proposed by Mentzer et al. We consider the case when there is no shared\nrandomness between the encoder and the decoder and derive a single-letter\ncharacterization of the RDP function for the case of discrete memoryless\nsources. This is in contrast to the marginal-distribution metric case\n(introduced by Blau and Michaeli), whose RDP characterization remains open when\nthere is no shared randomness. The achievability scheme is based on lossy\nsource coding with a posterior reference map. For the case of continuous valued\nsources under the squared error distortion measure and the squared quadratic\nWasserstein perception measure, we also derive a single-letter characterization\nand show that the decoder can be restricted to a noise-adding mechanism.\nInterestingly, the RDP function characterized for the case of zero perception\nloss coincides with that of the marginal metric, and further zero perception\nloss can be achieved with a 3-dB penalty in minimum distortion. Finally we\nspecialize to the case of Gaussian sources, and derive the RDP function for\nGaussian vector case and propose a reverse water-filling type solution. We also\npartially characterize the RDP function for a mixture of Gaussian vector\nsources.\n', ""Rate-Distortion-Perception Function of Bernoulli Vector Sources   In this paper, we consider the rate-distortion-perception (RDP) trade-off for\nthe lossy compression of a Bernoulli vector source, which is a finite\ncollection of independent binary random variables. The RDP function quantifies\nin a way the efficient compression of a source when we impose a distortion\nconstraint that limits the dissimilarity between the source and the\nreconstruction and a perception constraint that restricts the distributional\ndiscrepancy of the source and the reconstruction. In this work, we obtain an\nexact characterization of the RDP function of a Bernoulli vector source with\nthe Hamming distortion function and a single-letter perception function that\nmeasures the closeness of the distributions of the components of the source.\nThe solution can be described by partitioning the set of distortion and\nperception levels $(D,P)$ into three regions, where in each region the optimal\ndistortion and perception levels we allot to the components have a similar\nnature. Finally, we introduce the RDP function for graph sources and apply our\nresult to the Erd\\H{o}s-R\\'enyi graph model.\n"", ""On the Rate-Distortion-Perception Function   Rate-distortion-perception theory generalizes Shannon's rate-distortion\ntheory by introducing a constraint on the perceptual quality of the output. The\nperception constraint complements the conventional distortion constraint and\naims to enforce distribution-level consistencies. In this new theory, the\ninformation-theoretic limit is characterized by the rate-distortion-perception\nfunction. Although a coding theorem for the rate-distortion-perception function\nhas recently been established, the fundamental nature of the optimal coding\nschemes remains unclear, especially regarding the role of randomness in\nencoding and decoding. It is shown in the present work that except for certain\nextreme cases, the rate-distortion-perception function is achievable by\ndeterministic codes. This paper also clarifies the subtle differences between\ntwo notions of perfect perceptual quality and explores some alternative\nformulations of the perception constraint.\n""]","[('rate distortion theory', 0.6326698660850525), ('rate distortion', 0.5491423606872559), ('lossy source coding', 0.5445928573608398), ('distortion rate', 0.4968271851539612), ('distortion theory', 0.48080119490623474), ('distortion measure', 0.4766994118690491), ('distortion constraint', 0.45753592252731323), ('coding rate', 0.44578519463539124), ('encoder decoder', 0.4454071521759033), ('squared error distortion', 0.4432038366794586)]"
967,967,31,967_goodness fit tests_goodness fit testing_tests goodness fit_goodness fit test,"['goodness fit tests', 'goodness fit testing', 'tests goodness fit', 'goodness fit test', 'tests goodness', 'distributions test statistics', 'statistic testing', 'fit tests', 'distribution test statistic', 'goodness fit']","['A new set of tools for goodness-of-fit validation   We introduce two new tools to assess the validity of statistical\ndistributions. These tools are based on components derived from a new\nstatistical quantity, the $comparison$ $curve$. The first tool is a graphical\nrepresentation of these components on a $bar$ $plot$ (B plot), which can\nprovide a detailed appraisal of the validity of the statistical model, in\nparticular when supplemented by acceptance regions related to the model. The\nknowledge gained from this representation can sometimes suggest an existing\n$goodness$-$of$-$fit$ test to supplement this visual assessment with a control\nof the type I error. Otherwise, an adaptive test may be preferable and the\nsecond tool is the combination of these components to produce a powerful\n$\\chi^2$-type goodness-of-fit test. Because the number of these components can\nbe large, we introduce a new selection rule to decide, in a data driven\nfashion, on their proper number to take into consideration. In a simulation,\nour goodness-of-fit tests are seen to be powerwise competitive with the best\nsolutions that have been recommended in the context of a fully specified model\nas well as when some parameters must be estimated. Practical examples show how\nto use these tools to derive principled information about where the model\ndeparts from the data.\n', 'Conditional Goodness-of-Fit Tests for Discrete Distributions   In this paper, we address the problem of testing goodness-of-fit for discrete\ndistributions, where we focus on the geometric distribution. We define new\nlikelihood-based goodness-of-fit tests using the beta-geometric distribution\nand the type I discrete Weibull distribution as alternative distributions. The\ntests are compared in a simulation study, where also the classical\ngoodness-of-fit tests are considered for comparison. Throughout the paper we\nconsider conditional testing given a minimal sufficient statistic under the\nnull hypothesis, which enables the calculation of exact p-values. For this\npurpose, a new method is developed for drawing conditional samples from the\ngeometric distribution and the negative binomial distribution. We also explain\nbriefly how the conditional approach can be modified for the binomial, negative\nbinomial and Poisson distributions. It is finally noted that the simulation\nmethod may be extended to other discrete distributions having the same\nsufficient statistic, by using the Metropolis-Hastings algorithm.\n', 'Bahadur efficiency for certain goodness--of--fit tests based on the\n  empirical characteristic function   We study the Bahadur efficiency of several weighted L2--type\ngoodness--of--fit tests based on the empirical characteristic function. The\nmethods considered are for normality and exponentiality testing, and for\ntesting goodness--of--fit to the logistic distribution. Our results are helpful\nin deciding which specific test a potential practitioner should apply. For the\ncelebrated BHEP and energy tests for normality we obtain novel efficiency\nresults, with some of them in the multivariate case, while in the case of the\nlogistic distribution this is the first time that efficiencies are computed for\nany composite goodness--of--fit test.\n']","[('goodness fit tests', 0.7061587572097778), ('goodness fit testing', 0.6981202363967896), ('tests goodness fit', 0.671575665473938), ('goodness fit test', 0.6534883379936218), ('tests goodness', 0.582870364189148), ('distributions test statistics', 0.5261560082435608), ('statistic testing', 0.5208079814910889), ('fit tests', 0.5096961855888367), ('distribution test statistic', 0.5096074938774109), ('goodness fit', 0.49935227632522583)]"
968,968,31,968_geometric optics_scattering models_ray tracing_propagation optical,"['geometric optics', 'scattering models', 'ray tracing', 'propagation optical', 'prolate spheroidal', 'wave functions', 'diffraction', 'optics', 'reflecting surface', 'gaussian surface']","['Bridging Statistical Scattering and Aberration Theory: Ray Deflection\n  Function -- II: Numerical Validation   This paper presents a comprehensive experimental validation of a recently\ndeveloped Ray Deflection Function (RDF) approach, which offers a new framework\nfor modeling surface roughness effects in optical systems. Through detailed\ngeometrical ray tracing simulations, we demonstrate that the RDF methodology\nsuccessfully bridges two traditionally separate domains: statistical scattering\nmodels and deterministic aberration analysis. We implement and compare the two\napproaches for modeling a parabolic mirror with surface imperfections with\nthree cases: (1) an ideal parabolic mirror baseline, (2) the conventional\nHarvey-Shack (HS) statistical scattering theory applied to ray perturbations,\nand (3) the newly proposed aberration term method based on the RDF theory. Our\nresults confirm the statistical equivalence between the HS approach and the\nRDF-based aberration term method, with both producing close near-focal-plane\ndistributions and focal volume characteristics. By establishing this\nequivalence, we validate that surface roughness effects can be accurately\nrepresented as deterministic aberration terms while maintaining fidelity to\nestablished statistical scattering models.\n', 'Bridging Statistical Scattering and Aberration Theory: Ray Deflection\n  Function -- I: Theoretical Framework   This paper introduces a new conceptual framework that recasts surface\nroughness effects as a ""ray deflection function"" (RDF) which can be\nstatistically represented through a modified Zernike-Fourier hybrid approach\nthat directly connects the PSD with statistical aberration coefficients through\nspectral overlap integration. By establishing a direct mathematical\nrelationship between the power spectral density (PSD) of surface imperfections\nand the statistical distribution of aberration coefficients, we develop a\nformalism that bridges known probabilistic scattering theory with deterministic\naberration analysis. This transformation allows surface roughness to be\nseamlessly integrated with other optical aberrations by expressing its effects\nthrough equivalent modifications to the ideal mirror shape. This framework\nprovides computational advantages for ray-tracing simulations while maintaining\nstatistical fidelity to established scattering models, particularly for\npredicting the three-dimensional structure of imperfect focal bodies in optical\nsystems.\n', 'On the numerical evaluation of the prolate spheroidal wave functions of\n  order zero   We describe a method for the numerical evaluation of the angular prolate\nspheroidal wave functions of the first kind of order zero. It is based on the\nobservation that underlies the WKB method, namely that many second order\ndifferential equations admit solutions whose logarithms can be represented much\nmore efficiently than the solutions themselves. However, rather than exploiting\nthis fact to construct asymptotic expansions of the prolate spheroidal wave\nfunctions, our algorithm operates by numerically solving the Riccati equation\nsatisfied by their logarithms. Its running time grows much more slowly with\nbandlimit and characteristic exponent than standard algorithms. We illustrate\nthis and other properties of our algorithm with numerical experiments.\n']","[('geometric optics', 0.515070378780365), ('scattering models', 0.4628428816795349), ('ray tracing', 0.4304501414299011), ('propagation optical', 0.4170575439929962), ('prolate spheroidal', 0.41579681634902954), ('wave functions', 0.39597612619400024), ('diffraction', 0.39426422119140625), ('optics', 0.3895331919193268), ('reflecting surface', 0.38882723450660706), ('gaussian surface', 0.3884057402610779)]"
969,969,31,969_finite poset_maximal chains_minuscule posets_noncommutative,"['finite poset', 'maximal chains', 'minuscule posets', 'noncommutative', 'combinatorial properties', 'number maximal chains', 'lattices', 'partition posets', 'lattice', 'fibonacci lattice']","[""Birational Rowmotion and the Octahedron Recurrence   We use the octahedron recurrence to give a simplified statement and proof of\na formula for iterated birational rowmotion on a product of two chains, first\ndescribed by Musiker and Roby. Using this, we show that weights of certain\nchains in rectangles shift in a predictable way under the action of rowmotion.\nWe then define generalized Stanley-Thomas words whose cyclic rotation uniquely\ndetermines birational rowmotion on the product of two chains. We also discuss\nthe relationship between rowmotion and birational RSK and give a birational\nanalogue of Greene's theorem in this setting.\n"", 'Birational rowmotion on a rectangle over a noncommutative ring   We extend the periodicity of birational rowmotion for rectangular posets to\nthe case when the base field is replaced by a noncommutative ring (under\nappropriate conditions). This resolves a conjecture from 2014. The proof uses a\nnovel approach and is fully self-contained.\n  Consider labellings of a finite poset $P$ by $\\left|P\\right| + 2$ elements of\na ring $\\mathbb{K}$: one label associated with each poset element and two\nconstant labels for the added top and bottom elements in $\\hat{P}$. *Birational\nrowmotion* is a partial map on such labellings. It was originally defined by\nEinstein and Propp for $\\mathbb{K}=\\mathbb{R}$ as a lifting (via\ndetropicalization) of *piecewise-linear rowmotion*, a map on the order polytope\n$\\mathcal{O}(P) := \\{\\text{order-preserving } f: P \\to[0,1]\\}$. The latter, in\nturn, extends the well-studied rowmotion map on the set of order ideals (or\nmore properly, the set of order filters) of $P$, which correspond to the\nvertices of $\\mathcal{O}(P)$. Dynamical properties of these combinatorial maps\nsometimes (but not always) extend to the birational level, while results proven\nat the birational level always imply their combinatorial counterparts. Allowing\n$\\mathbb{K}$ to be noncommutative, we generalize the birational level even\nfurther, and some properties are in fact lost at this step.\n  In 2014, the authors gave the first proof of periodicity for birational\nrowmotion on rectangular posets (when $P$ is a product of two chains) for\n$\\mathbb{K}$ a field, and conjectured that it survives (in an appropriately\ntwisted form) in the noncommutative case. In this paper, we prove this\nnoncommutative periodicity and a concomitant antipodal reciprocity formula. We\nend with some conjectures about periodicity for other posets, and the question\nof whether our results can be extended to (noncommutative) semirings.\n', 'Birational rowmotion and coxeter-motion on minuscule posets   Birational rowmotion is a discrete dynamical system on the set of all\npositive real-valued functions on a finite poset, which is a birational lift of\ncombinatorial rowmotion on order ideals. It is known that combinatorial\nrowmotion for a minuscule poset has order equal to the Coxeter number, and\nexhibits the file homomesy phenomenon for refined order ideal cardinality\nstatistic. In this paper we generalize these results to the birational setting.\nMoreover, as a generalization of birational promotion on a product of two\nchains, we introduce birational Coxeter-motion on minuscule posets, and prove\nthat it enjoys periodicity and file homomesy.\n']","[('finite poset', 0.5090373158454895), ('maximal chains', 0.4172791838645935), ('minuscule posets', 0.4136916399002075), ('noncommutative', 0.413040429353714), ('combinatorial properties', 0.3946419358253479), ('number maximal chains', 0.38743311166763306), ('lattices', 0.3817006051540375), ('partition posets', 0.3598543703556061), ('lattice', 0.3588023781776428), ('fibonacci lattice', 0.33851444721221924)]"
970,970,31,970_stochastic search_random search_search processes_optimal search,"['stochastic search', 'random search', 'search processes', 'optimal search', 'stochastic resetting', 'stochastic', 'search process', 'search strategy', 'stochastic simulations', 'passage time fpt']","['Extreme hitting probabilities for diffusion   A variety of systems in physics, chemistry, biology, and psychology are\nmodeled in terms of diffusing ""searchers"" looking for ""targets."" Examples range\nfrom gene regulation, to cell sensing, to human decision-making. A commonly\nstudied statistic in these models is the so-called hitting probability for each\ntarget, which is the probability that a given single searcher finds that\nparticular target. However, the decisive event in many systems is not the\narrival of a given single searcher to a target, but rather the arrival of the\nfastest searcher to a target out of many searchers. In this paper, we study the\nprobability that the fastest diffusive searcher hits a given target in the many\nsearcher limit, which we call the extreme hitting probability. We first prove\nan upper bound for the decay of the probability that the searcher finds a\ntarget other than the closest target. This upper bound applies in very general\nsettings and depends only on the relative distances to the targets.\nFurthermore, we find the exact asymptotics of the extreme hitting probabilities\nin terms of the short-time distribution of when a single searcher hits a\ntarget. These results show that the fastest searcher always hits the closest\ntarget in the many searcher limit. While this fact is intuitive in light of\nrecent results on the time it takes the fastest searcher to find a target, our\nresults give rigorous, quantitative estimates for the extreme hitting\nprobabilities. We illustrate our results in several examples and numerical\nsimulations.\n', 'A probabilistic approach to extreme statistics of Brownian escape times\n  in dimensions 1, 2, and 3   First passage time (FPT) theory is often used to estimate timescales in\ncellular and molecular biology. While the overwhelming majority of studies have\nfocused on the time it takes a given single Brownian searcher to reach a\ntarget, cellular processes are instead often triggered by the arrival of the\nfirst molecule out of many molecules. In these scenarios, the more relevant\ntimescale is the FPT of the first Brownian searcher to reach a target from a\nlarge group of independent and identical Brownian searchers. Though the\nsearchers are identically distributed, one searcher will reach the target\nbefore the others and will thus have the fastest FPT. This fastest FPT depends\non extremely rare events and its mean can be orders of magnitude faster than\nthe mean FPT of a given single searcher. In this paper, we use rigorous\nprobabilistic methods to study this fastest FPT. We determine the asymptotic\nbehavior of all the moments of this fastest FPT in the limit of many searchers\nin a general class of two- and three-dimensional domains. We establish these\nresults by proving that the fastest searcher takes an almost direct path to the\ntarget.\n', 'Competition of many searchers   First passage times (FPTs) are often used to study timescales in physical,\nchemical, and biological processes. FPTs generically describe the time it takes\na random ""searcher"" to find a ""target."" In many systems, the important\ntimescale is not the time it takes a single searcher to find a target, but\nrather the time it takes the fastest searcher out of many searchers to find a\ntarget. Such fastest FPTs or extreme FPTs result from many searchers competing\nto find the target and differ markedly from FPTs of single searchers. In this\nchapter, we review recent results on fastest FPTs. We show how fastest FPTs\ndepend on the mode of stochastic search (including search by diffusion,\nsubdiffusion, superdiffusion, and discrete jumps), the initial searcher\ndistribution, and properties of the spatial domain.\n']","[('stochastic search', 0.6594160199165344), ('random search', 0.5229260921478271), ('search processes', 0.5173678994178772), ('optimal search', 0.5125622749328613), ('stochastic resetting', 0.4936704933643341), ('stochastic', 0.47326335310935974), ('search process', 0.4557080864906311), ('search strategy', 0.4356432557106018), ('stochastic simulations', 0.4337444007396698), ('passage time fpt', 0.43220651149749756)]"
971,971,31,971_meromorphic maps_hypersurfaces projective_meromorphic_holomorphic mappings,"['meromorphic maps', 'hypersurfaces projective', 'meromorphic', 'holomorphic mappings', 'family hypersurfaces', 'holomorphic maps', 'hypersurfaces', 'hler manifolds', 'projective varieties', 'projective variety']","['Degeneracy theorems for meromorphic mappings of a complete K\\""{a}hler\n  manifold sharing hyperplanes in a projective space   Let $M$ be a complete K\\""{a}hler manifold, whose universal covering is\nbiholomorphic to a ball $\\mathbb B^m(R_0)$ in $\\mathbb C^m$ ($0<R_0\\le\n+\\infty$). In this article, we will show that if three meromorphic mappings\n$f^1,f^2,f^3$ of $M$ into $\\mathbb P^n(\\mathbb C)\\ (n\\ge 2)$ satisfying the\ncondition $(C_\\rho)$ and sharing $q\\ (q> C+\\rho K)$ hyperplanes in general\nposition regardless of multiplicity with certain positive constants $K$ and $C\n<2n$ (explicitly estimated), then there are some algebraic relation between\nthem. A degeneracy theorem for $k\\ (2\\le k\\le n+1)$ meromorphic mappings\nsharing hyperplanes is also given. Our result generalize the previous result in\nthe case where the mappings from $\\mathbb C^m$ into $\\mathbb P^n(\\mathbb C)$.\n', 'Meromorphic mappings of a complete connected K\\""{a}hler manifold into a\n  projective space sharing hyperplanes   Let $M$ be a complete K\\""{a}hler manifold, whose universal covering is\nbiholomorphic to a ball $\\mathbb B^m(R_0)$ in $\\mathbb C^m$ ($0<R_0\\le\n+\\infty$). In this article, we will show that if three meromorphic mappings\n$f^1,f^2,f^3$ of $M$ into $\\mathbb P^n(\\mathbb C)\\ (n\\ge 2)$ satisfying the\ncondition $(C_\\rho)$ and sharing $q\\ (q> 2n+1+\\alpha+\\rho K)$ hyperplanes in\ngeneral position regardless of multiplicity with certain positive constants $K$\nand $\\alpha <1$ (explicitly estimated), then $f^1=f^2$ or $f^2=f^3$ or\n$f^3=f^1$. Moreover, if the above three mappings share the hyperplanes with\nmutiplicity counted to level $n+1$ then $f^1=f^2=f^3.$ Our results generalize\nthe finiteness and uniqueness theorems for meromorphic mappings of $\\mathbb\nC^m$ into $\\mathbb P^n(\\mathbb C)$ sharing $2n+2$ hyperplanes in general\nposition with truncated multiplicity.\n', 'Generalizations of degeneracy second main theorem and Schmidt\'s subspace\n  theorem   In this paper, by introducing the notion of ""\\textit{distributive constant}""\nof a family of hypersurfaces with respect to a projective variety, we prove a\nsecond main theorem in Nevanlinna theory for meromorphic mappings with\narbitrary families of hypersurfaces in projective varieties. Our second main\ntheorem generalizes and improves previous results for meromorphic mappings with\nhypersurfaces, in particular for algebraically degenerate mappings and for the\nfamilies of hypersurfaces in subgeneral position. The analogous results for the\nholomorphic curves with finite growth index from a complex disc into a project\nvariety, and for meromorphic mappings on a complete K\\""{a}hler manifold are\nalso given. For the last aim, we will prove a Schmidt\'s subspace theorem for an\narbitrary families of homogeneous polynomials, which is the counterpart in\nNumber theory of our second main theorem. Our these results are generalizations\nand improvements of all previous results.\n']","[('meromorphic maps', 0.6405160427093506), ('hypersurfaces projective', 0.6265811324119568), ('meromorphic', 0.5573965311050415), ('holomorphic mappings', 0.5398101210594177), ('family hypersurfaces', 0.5353900790214539), ('holomorphic maps', 0.5352028608322144), ('hypersurfaces', 0.5265929698944092), ('hler manifolds', 0.5167006850242615), ('projective varieties', 0.5049495697021484), ('projective variety', 0.4995746314525604)]"
972,972,31,972_type concentration inequalities_anti concentration inequalities_concentration inequalities_bound probability random,"['type concentration inequalities', 'anti concentration inequalities', 'concentration inequalities', 'bound probability random', 'berry esseen bound', 'variance bounds', 'bound probability', 'berry esseen bounds', 'tail bound', 'unimodal distributions']","['Dual Induction CLT for High-dimensional m-dependent Data   We derive novel and sharp high-dimensional Berry--Esseen bounds for the sum\nof $m$-dependent random vectors over the class of hyper-rectangles exhibiting\nonly a poly-logarithmic dependence in the dimension. Our results hold under\nminimal assumptions, such as non-degenerate covariances and finite third\nmoments, and yield a sample complexity of order $\\sqrt{m/n}$, aside from\nlogarithmic terms, matching the optimal rates established in the univariate\ncase. When specialized to the sums of independent non-degenerate random\nvectors, we obtain sharp rates under the weakest possible conditions. On the\ntechnical side, we develop an inductive relationship between anti-concentration\ninequalities and Berry--Esseen bounds, inspired by the classical Lindeberg\nswapping method and the concentration inequality approach for dependent data,\nthat may be of independent interest.\n', 'High-dimensional Berry-Esseen Bound for $m$-Dependent Random Samples   In this work, we provide a $(n/m)^{-1/2}$-rate finite sample Berry-Esseen\nbound for $m$-dependent high-dimensional random vectors over the class of\nhyper-rectangles. This bound imposes minimal assumptions on the random vectors\nsuch as nondegenerate covariances and finite third moments. The proof uses\ninductive relationships between anti-concentration inequalities and\nBerry--Esseen bounds, which are inspired by the telescoping method of Chen and\nShao (2004) and the recursion method of Kuchibhotla and Rinaldo (2020).\nPerforming a dual induction based on the relationships, we obtain tight\nBerry-Esseen bounds for dependent samples.\n', ""A Markovian Gau\\ss \\, Inequality for Asymmetric Deviations from the Mode\n  of Symmetric Unimodal Distributions   For a random variable with a unimodal distribution and finite second moment\nGau\\ss \\, (1823) proved a sharp bound on the probability of the random variable\nto be outside a symmetric interval around its mode. An alternative proof for it\nis given based on Khintchine's representation of unimodal random variables.\nAnalogously, a sharp inequality is proved for the slightly broader class of\nunimodal distributions with finite first absolute moment, which might be called\na Markovian Gau\\ss\\ inequality. For symmetric unimodal distributions with\nfinite second moment Semenikhin (2019) generalized Gau\\ss's inequality to\narbitrary intervals. For the class of symmetric unimodal distributions with\nfinite first absolute moment we construct a Markovian version of it. Related\ninequalities of Volkov (1969) and Sellke and Sellke (1997) will be discussed as\nwell.\n""]","[('type concentration inequalities', 0.5363244414329529), ('anti concentration inequalities', 0.5255422592163086), ('concentration inequalities', 0.5083290338516235), ('bound probability random', 0.4858767092227936), ('berry esseen bound', 0.4767659306526184), ('variance bounds', 0.4709569811820984), ('bound probability', 0.45871418714523315), ('berry esseen bounds', 0.44291651248931885), ('tail bound', 0.4315601587295532), ('unimodal distributions', 0.4236167371273041)]"
973,973,31,973_logarithmic sobolev inequalities_hardy rellich inequalities_log sobolev inequalities_logarithmic sobolev inequality,"['logarithmic sobolev inequalities', 'hardy rellich inequalities', 'log sobolev inequalities', 'logarithmic sobolev inequality', 'log sobolev inequality', 'hardy type inequalities', 'sobolev inequalities', 'homogeneous lie groups', 'sobolev inequality', 'hardy inequalities']","['Logarithmic Sobolev inequalities on non-isotropic Heisenberg groups   We study logarithmic Sobolev inequalities with respect to a heat kernel\nmeasure on finite-dimensional and infinite-dimensional Heisenberg groups. Such\na group is the simplest non-trivial example of a sub-Riemannian manifold. First\nwe consider logarithmic Sobolev inequalities on non-isotropic Heisenberg\ngroups. These inequalities are considered with respect to the hypoelliptic heat\nkernel measure, and we show that the logarithmic Sobolev constants can be\nchosen to be independent of the dimension of the underlying space. In this\nsetting, a natural Laplacian is not an elliptic but a hypoelliptic operator.\nThe argument relies on comparing logarithmic Sobolev constants for the\nthree-dimensional non-isotropic and isotropic Heisenberg groups, and\ntensorization of logarithmic Sobolev inequalities in the sub-Riemannian\nsetting. Furthermore, we apply these results in an infinite-dimensional setting\nand prove a logarithmic Sobolev inequality on an infinite-dimensional\nHeisenberg group modelled on an abstract Wiener space.\n', 'Logarithmic Sobolev-type inequalities on Lie groups   In this paper we show a number of logarithmic inequalities on several classes\nof Lie groups: log-Sobolev inequalities on general Lie groups, log-Sobolev\n(weighted and unweighted), log-Gagliardo-Nirenberg and\nlog-Caffarelli-Kohn-Nirenberg inequalities on graded Lie groups. Furthermore,\non stratified groups, we show that one of the obtained inequalities is\nequivalent to a Gross-type log-Sobolev inequality with the horizontal gradient.\nAs a result, we obtain the Gross log-Sobolev inequality on general stratified\ngroups but, {\\bf very interestingly}, with the Gaussian measure on the first\nstratum of the group. Moreover, our methods also yield weighted versions of the\nGross log-Sobolev inequality. In particular, we also obtain new weighted\nGross-type log-Sobolev inequalities on $\\mathbb R^n$ for arbitrary choices of\nhomogeneous quasi-norms. As another consequence we derive the Nash inequalities\non graded groups and an example application to the decay rate for the heat\nequations for sub-Laplacians on stratified groups. We also obtain weighted\nversions of log-Sobolev and Nash inequalities for general Lie groups.\n', ""Logarithmic Hardy-Rellich inequalities on Lie groups   In this paper we obtain logarithmic Hardy and Rellich inequalities on general\nLie groups. In the case of graded groups, we also show their refinements using\nthe homogeneous Sobolev norms. In fact, we derive a family of weighted\nlogarithmic Hardy-Rellich inequalities, for which logarithmic Hardy and Rellich\ninequalities are special cases. As a consequence of these inequalities, we also\nderive a Gross type logarithmic Hardy inequality on general stratified groups.\nAn interesting feature of such estimate is that we consider the measure which\nis Gaussian only on the first stratum of the group. Such choice of the measure\nis natural in view of the known Gross type logarithmic Sobolev inequalities on\nstratified groups. The obtained results are new already in the setting of the\nEuclidean space $\\mathbb R^n.$ Finally, we also present a simple argument for\ngetting a logarithmic Poincar\\'e inequality, as well as the logarithmic Hardy\ninequality for the fractional $p$-sub-Laplacian on homogeneous groups.\n""]","[('logarithmic sobolev inequalities', 0.5481213927268982), ('hardy rellich inequalities', 0.5362337827682495), ('log sobolev inequalities', 0.5361361503601074), ('logarithmic sobolev inequality', 0.5286878347396851), ('log sobolev inequality', 0.5254811644554138), ('hardy type inequalities', 0.5240535736083984), ('sobolev inequalities', 0.513999879360199), ('homogeneous lie groups', 0.5111414790153503), ('sobolev inequality', 0.492538720369339), ('hardy inequalities', 0.48183342814445496)]"
974,974,31,974_abelian sandpile_sandpile models_sandpiles_sandpile,"['abelian sandpile', 'sandpile models', 'sandpiles', 'sandpile', 'sandpile group', 'fractal graphs', 'infinite graphs', 'random configurations', 'sierpinski gasket', 'sand']","['Abelian sandpiles on Sierpinski gasket graphs   The aim of the current work is to investigate structural properties of the\nsandpile group of a special class of self-similar graphs. More precisely, we\nconsider Abelian sandpiles on Sierpinski gasket graphs and for the choice of\nnormal boundary conditions, we give a characterization of the identity element\nand a recursive description of the sandpile group. Finally, we consider Abelian\nsandpile Markov chains on the aforementioned graphs and we improve the existing\nbounds on the speed of convergence to stationarity.\n', ""Abelian and stochastic sandpile models on complete bipartite graphs   In the sandpile model, vertices of a graph are allocated grains of sand. At\neach unit of time, a grain is added to a randomly chosen vertex. If that causes\nits number of grains to exceed its degree, that vertex is called unstable, and\ntopples. In the Abelian sandpile model (ASM), topplings are deterministic,\nwhereas in the stochastic sandpile model (SSM) they are random. We study the\nASM and SSM on complete bipartite graphs. For the SSM, we provide a stochastic\nversion of Dhar's burning algorithm to check if a given (stable) configuration\nis recurrent or not, with linear complexity. We also exhibit a bijection\nbetween sorted recurrent configurations and pairs of compatible Ferrers\ndiagrams. We then provide a similar bijection for the ASM, and also interpret\nits recurrent configurations in terms of labelled Motzkin paths.\n"", 'Laplacian growth & sandpiles on the Sierpinski gasket: limit shape\n  universality and exact solutions   We establish quantitative spherical shape theorems for rotor-router\naggregation and abelian sandpile growth on the graphical Sierpinski gasket\n($SG$) when particles are launched from the corner vertex.\n  In particular, the abelian sandpile growth problem is exactly solved via a\nrecursive construction of self-similar sandpile tiles. We show that sandpile\ngrowth and patterns exhibit a $(2\\cdot 3^n)$-periodicity as a function of the\ninitial mass. Moreover, the cluster explodes---increments by more than 1 in\nradius---at periodic intervals, a phenomenon not seen on $\\mathbb{Z}^d$ or\ntrees. We explicitly characterize all the radial jumps, and use the renewal\ntheorem to prove the scaling limit of the cluster radius, which satisfies a\npower law modulated by log-periodic oscillations. In the course of our proofs\nwe also establish structural identities of the sandpile groups of subgraphs of\n$SG$ with two different boundary conditions, notably the corresponding identity\nelements conjectured by Fairchild, Haim, Setra, Strichartz, and Westura.\n  Our main theorems, in conjunction with recent results of Chen, Huss,\nSava-Huss, and Teplyaev, establish $SG$ as a positive example of a state space\nwhich exhibits ""limit shape universality,"" in the sense of Levine and Peres,\namong the four Laplacian growth models: divisible sandpiles, abelian sandpiles,\nrotor-router aggregation, and internal diffusion-limited aggregation (IDLA). We\nconclude the paper with conjectures about radial fluctuations in IDLA on $SG$,\npossible extensions of limit shape universality to other state spaces, and\nrelated open problems.\n']","[('abelian sandpile', 0.6161588430404663), ('sandpile models', 0.5811890363693237), ('sandpiles', 0.5647500157356262), ('sandpile', 0.5233750939369202), ('sandpile group', 0.4892055094242096), ('fractal graphs', 0.42659351229667664), ('infinite graphs', 0.4060441851615906), ('random configurations', 0.3947674334049225), ('sierpinski gasket', 0.36914482712745667), ('sand', 0.3511253297328949)]"
975,975,31,975_quiver varieties_nakajima quiver varieties_quiver variety_mckay quiver,"['quiver varieties', 'nakajima quiver varieties', 'quiver variety', 'mckay quiver', 'nakajima quiver', 'crepant resolutions', 'quiver', 'case quiver', 'cyclic quotient singularities', 'quotient varieties']","['Nonprojective crepant resolutions of quiver varieties In this paper, we construct a large class of examples of proper, nonprojective crepant resolutions of singularities for Nakajima quiver varieties. These include four and six dimensional examples and examples with $Q$ containing only three vertices. There are two main techniques: by taking a locally projective resolution of a projective partial resolution as in our previous work arXiv:2311.07539, and more generally by taking quotients of open subsets of representation space which are not stable loci, related to Arzhantsev--Derental--Hausen--Laface\'s construction in the setting of Cox rings. By the latter method we exhibit a proper crepant resolution that does not factor through a projective partial resolution. Most of our quiver settings involve one-dimensional vector spaces, hence the resolutions are toric hyperk\\""ahler, which were studied from a different point of view in Arbo and Proudfoot arXiv:1511.09138.\n  This builds on the classification of projective crepant resolutions of a large class of quiver varieties in arXiv:2212.09623 and the classification of proper crepant resolutions for the hyperpolygon quiver varieties in arXiv:2406.04117.', ""Walls for $G$-Hilb via Reid's Recipe   The three-dimensional McKay correspondence seeks to relate the geometry of\ncrepant resolutions of Gorenstein $3$-fold quotient singularities\n$\\mathbb{A}^3/G$ with the representation theory of the group $G$. The first\ncrepant resolution studied in depth was the $G$-Hilbert scheme\n$G\\text{-Hilb}\\,\\mathbb{A}^3$, which is also a moduli space of $\\theta$-stable\nrepresentations of the McKay quiver associated to $G$. As the stability\nparameter $\\theta$ varies, we obtain many other crepant resolutions. In this\npaper we focus on the case where $G$ is abelian, and compute explicit\ninequalities for the chamber of the stability space defining\n$G\\text{-Hilb}\\,\\mathbb{A}^3$ in terms of a marking of exceptional subvarieties\nof $G\\text{-Hilb}\\,\\mathbb{A}^3$ called Reid's recipe. We further show which of\nthese inequalities define walls. This procedure depends only on the\ncombinatorics of the exceptional fibre and has applications to the birational\ngeometry of other crepant resolutions.\n"", 'All crepant resolutions of hyperpolygon spaces via their Cox rings   We construct and enumerate all crepant resolutions of hyperpolygon spaces, a\nfamily of conical symplectic singularities arising as Nakajima quiver varieties\nassociated to a star-shaped quiver. We provide an explicit presentation of the\nCox ring of any such crepant resolution. Using techniques developed by\nArzhantsev-Derenthal-Hausen-Laface we construct all crepant resolutions of the\nhyperpolygon spaces, including those which are not projective over the\nsingularity. We find that the number of crepant resolutions equals the\nHo\\c{s}ten-Morris numbers. In proving these results, we obtain a description of\nall complete geometric quotients associated to the classical GIT problem\nconstructing moduli spaces of ordered points on the projective line. These\nmoduli spaces appear as the Lagrangian subvarieties of crepant resolutions of\nhyperpolygon spaces fixed under the conical action.\n']","[('quiver varieties', 0.6029675602912903), ('nakajima quiver varieties', 0.5940778255462646), ('quiver variety', 0.571970522403717), ('mckay quiver', 0.49803707003593445), ('nakajima quiver', 0.4885208308696747), ('crepant resolutions', 0.4611049294471741), ('quiver', 0.46091100573539734), ('case quiver', 0.4537125825881958), ('cyclic quotient singularities', 0.4218728840351105), ('quotient varieties', 0.41109806299209595)]"
976,976,31,976_robust spectral_stationary stochastic_stationary sequences_stochastic sequence,"['robust spectral', 'stationary stochastic', 'stationary sequences', 'stochastic sequence', 'error spectral', 'optimal estimates', 'robust estimation', 'spectral densities', 'optimal estimation', 'autoregressive']","['Robust filtering of sequences with periodically stationary\n  multiplicative seasonal increments   We study stochastic sequences $\\xi(k)$ with periodically stationary\ngeneralized multiple increments of fractional order which combines\ncyclostationary, multi-seasonal, integrated and fractionally integrated\npatterns. We solve the filtering problem for linear functionals constructed\nfrom unobserved values of a stochastic sequence $\\xi(k)$ based on observations\nwith the periodically stationary noise sequence. For sequences with known\nmatrices of spectral densities, we obtain formulas for calculating values of\nthe mean square errors and the spectral characteristics of the optimal\nestimates of the functionals. Formulas that determine the least favorable\nspectral densities and minimax (robust) spectral characteristics of the optimal\nlinear estimates of the functionals are proposed in the case where spectral\ndensities of sequences are not exactly known while some sets of admissible\nspectral densities are given.\n', 'Minimax-robust estimation problems for sequences with periodically\n  stationary increments observed with noise   The problem of optimal estimation of linear functionals constructed from the\nunobserved values of a stochastic sequence with periodically stationary\nincrements based on observations of the sequence with stationary noise is\nconsidered. For sequences with known spectral densities, we obtain formulas for\ncalculating values of the mean square errors and the spectral characteristics\nof the optimal estimates of the functionals. Formulas that determine the least\nfavorable spectral densities and the minimax-robust spectral characteristics of\nthe optimal linear estimates of functionals are proposed in the case where\nspectral densities of the sequence are not exactly known while some sets of\nadmissible spectral densities are specified.\n', 'Minimax-robust forecasting of sequences with periodically stationary\n  long memory multiple seasonal increments   We introduce stochastic sequences $\\zeta(k)$ with periodically stationary\ngeneralized multiple increments of fractional order which combines\ncyclostationary, multi-seasonal, integrated and fractionally integrated\npatterns. We solve the problem of optimal estimation of linear functionals\nconstructed from unobserved values of stochastic sequences $\\zeta(k)$ based on\ntheir observations at points $ k<0$. For sequences with known spectral\ndensities, we obtain formulas for calculating values of the mean square errors\nand the spectral characteristics of the optimal estimates of functionals.\nFormulas that determine the least favorable spectral densities and minimax\n(robust) spectral characteristics of the optimal linear estimates of\nfunctionals are proposed in the case where spectral densities of sequences are\nnot exactly known while some sets of admissible spectral densities are given.\n']","[('robust spectral', 0.5314542055130005), ('stationary stochastic', 0.47243747115135193), ('stationary sequences', 0.46786579489707947), ('stochastic sequence', 0.46210241317749023), ('error spectral', 0.440523624420166), ('optimal estimates', 0.4206095337867737), ('robust estimation', 0.4162653088569641), ('spectral densities', 0.41501423716545105), ('optimal estimation', 0.413959801197052), ('autoregressive', 0.3934684693813324)]"
977,977,31,977_cluster categories_cluster tilting subcategories_cluster tilting subcategory_cluster category,"['cluster categories', 'cluster tilting subcategories', 'cluster tilting subcategory', 'cluster category', 'triangulated categories', 'triangulated category', 'cluster algebras', 'type cluster', 'cluster tilting objects', 'cluster structures']","['Completions of discrete cluster categories of type $\\mathbb{A}$   We complete the discrete cluster categories of type $\\mathbb{A}$ as defined\nby Igusa and Todorov, by embedding such a discrete cluster category inside a\nlarger one, and then taking a certain Verdier quotient. The resulting category\nis a Hom-finite Krull-Schmidt triangulated category containing the discrete\ncluster category as a full subcategory. The objects and Hom-spaces in this new\ncategory can be described geometrically, even though the category is not\n$2$-Calabi-Yau and Ext-spaces are not always symmetric. We describe all\ncluster-tilting subcategories. Given such a subcategory, we define a cluster\ncharacter that takes values in a ring with infinitely many indeterminates. Our\ncluster character is new in that it takes into account infinite dimensional\nsub-representations of infinite dimensional ones. We show that it satisfies the\nmultiplication formula and also the exchange formula, provided that the objects\nbeing exchanged satisfy some local Calabi-Yau conditions.\n', 'Cluster categories for completed infinity-gons I: Categorifying\n  triangulations   Paquette and Y{\\i}ld{\\i}r{\\i}m recently introduced triangulated categories of\narcs in completed infinity-gons, which are discs with an infinite closed set of\nmarked points on their boundary. These categories have many features in common\nwith the cluster categories associated to discs with different sets of marked\npoints. In particular, they have (weak) cluster-tilting subcategories, which\nPaquette and Y{\\i}ld{\\i}r{\\i}m show are in bijection with very special\ntriangulations of the disc. This is in contrast to Igusa and Todorov\'s earlier\nwork in the uncompleted case, in which every triangulation corresponds to a\nweak cluster-tilting subcategory.\n  In this paper, we replace the triangulated structure of Paquette and\nY{\\i}ld{\\i}r{\\i}m\'s category by an extriangulated substructure and prove that,\nwith this structure, the weak cluster-tilting subcategories are once again in\nbijection with triangulations. We further show that functorial finiteness of a\nweak cluster-tilting subcategory is equivalent to a very mild condition on the\ntriangulation, which also appears in \\c{C}anak\\c{c}{\\i} and Felikson\'s study of\ninfinite rank cluster algebras from Teichm\\""uller theory. By comparison with\nthe combinatorics of triangulations, we are also able to characterise when weak\ncluster-tilting subcategories can be mutated in this new extriangulated\ncategory.\n', ""Progress on Infinite Cluster Categories Related to Triangulations of the\n  (Punctured) Disk   In this mostly expository paper, we present recent progress on infinite\n(weak) cluster categories that are related to triangulations of the disk, with\nand without a puncture. First we recall the notion of a cluster category. Then\nwe move to the infinite setting and survey recent work on infinite cluster\ncategories of types $\\mathbb{A}$ and $\\mathbb{D}$. We conclude with our\ncontributions, two infinite families of infinite (weak) cluster categories of\ntype $\\mathbb{D}$. We first present a discrete, infinite version of Schiffler's\ncombinatorial model of the punctured disk with marked points. We then produce\neach (weak) cluster category starting with representations of thread quivers,\ntaking the derived category, and then taking the appropriate orbit category. We\nshow that the combinatorics in the (weak) cluster categories match with the\ncorresponding combinatorics of the punctured disk with countably-many marked\npoints. We also state two conjectures concerning weak cluster structures inside\nour (weak) cluster categories.\n""]","[('cluster categories', 0.7241160273551941), ('cluster tilting subcategories', 0.707984447479248), ('cluster tilting subcategory', 0.6926708817481995), ('cluster category', 0.6903305649757385), ('triangulated categories', 0.6304701566696167), ('triangulated category', 0.6008027195930481), ('cluster algebras', 0.581902027130127), ('type cluster', 0.5803968906402588), ('cluster tilting objects', 0.5680981874465942), ('cluster structures', 0.567891001701355)]"
978,978,31,978_encoders decoders_codes deep_channel coding_encoders,"['encoders decoders', 'codes deep', 'channel coding', 'encoders', 'encoder decoder', 'codes channels', 'encoder', 'autoencoders', 'channel codes', 'decoders']","['Robust Non-Linear Feedback Coding via Power-Constrained Deep Learning   The design of codes for feedback-enabled communications has been a\nlong-standing open problem. Recent research on non-linear, deep learning-based\ncoding schemes have demonstrated significant improvements in communication\nreliability over linear codes, but are still vulnerable to the presence of\nforward and feedback noise over the channel. In this paper, we develop a new\nfamily of non-linear feedback codes that greatly enhance robustness to channel\nnoise. Our autoencoder-based architecture is designed to learn codes based on\nconsecutive blocks of bits, which obtains de-noising advantages over bit-by-bit\nprocessing to help overcome the physical separation between the encoder and\ndecoder over a noisy channel. Moreover, we develop a power control layer at the\nencoder to explicitly incorporate hardware constraints into the learning\noptimization, and prove that the resulting average power constraint is\nsatisfied asymptotically. Numerical experiments demonstrate that our scheme\noutperforms state-of-the-art feedback codes by wide margins over practical\nforward and feedback noise regimes, and provide information-theoretic insights\non the behavior of our non-linear codes. Moreover, we observe that, in a long\nblocklength regime, canonical error correction codes are still preferable to\nfeedback codes when the feedback noise becomes high.\n', 'ProductAE: Towards Training Larger Channel Codes based on Neural Product\n  Codes   There have been significant research activities in recent years to automate\nthe design of channel encoders and decoders via deep learning. Due the\ndimensionality challenge in channel coding, it is prohibitively complex to\ndesign and train relatively large neural channel codes via deep learning\ntechniques. Consequently, most of the results in the literature are limited to\nrelatively short codes having less than 100 information bits. In this paper, we\nconstruct ProductAEs, a computationally efficient family of deep-learning\ndriven (encoder, decoder) pairs, that aim at enabling the training of\nrelatively large channel codes (both encoders and decoders) with a manageable\ntraining complexity. We build upon the ideas from classical product codes, and\npropose constructing large neural codes using smaller code components. More\nspecifically, instead of directly training the encoder and decoder for a large\nneural code of dimension $k$ and blocklength $n$, we provide a framework that\nrequires training neural encoders and decoders for the code parameters\n$(n_1,k_1)$ and $(n_2,k_2)$ such that $n_1 n_2=n$ and $k_1 k_2=k$. Our training\nresults show significant gains, over all ranges of signal-to-noise ratio (SNR),\nfor a code of parameters $(225,100)$ and a moderate-length code of parameters\n$(441,196)$, over polar codes under successive cancellation (SC) decoder.\nMoreover, our results demonstrate meaningful gains over Turbo Autoencoder\n(TurboAE) and state-of-the-art classical codes. This is the first work to\ndesign product autoencoders and a pioneering work on training large channel\ncodes.\n', 'DRF Codes: Deep SNR-Robust Feedback Codes   We present a new deep-neural-network (DNN) based error correction code for\nfading channels with output feedback, called deep SNR-robust feedback (DRF)\ncode. At the encoder, parity symbols are generated by a long short term memory\n(LSTM) network based on the message as well as the past forward channel outputs\nobserved by the transmitter in a noisy fashion. The decoder uses a\nbi-directional LSTM architecture along with a signal to noise ratio (SNR)-aware\nattention NN to decode the message. The proposed code overcomes two major\nshortcomings of the previously proposed DNN-based codes over channels with\npassive output feedback: (i) the SNR-aware attention mechanism at the decoder\nenables reliable application of the same trained NN over a wide range of SNR\nvalues; (ii) curriculum training with batch-size scheduling is used to speed up\nand stabilize training while improving the SNR-robustness of the resulting\ncode. We show that the DRF codes significantly outperform state-of-the-art in\nterms of both the SNR-robustness and the error rate in additive white Gaussian\nnoise (AWGN) channel with feedback. In fading channels with perfect phase\ncompensation at the receiver, DRF codes learn to efficiently exploit knowledge\nof the instantaneous fading amplitude (which is available to the encoder\nthrough feedback) to reduce the overhead and complexity associated with channel\nestimation at the decoder. Finally, we show the effectiveness of DRF codes in\nmulticast channels with feedback, where linear feedback codes are known to be\nstrictly suboptimal.\n']","[('encoders decoders', 0.5944767594337463), ('codes deep', 0.5759016275405884), ('channel coding', 0.5702858567237854), ('encoders', 0.5603774785995483), ('encoder decoder', 0.5598193407058716), ('codes channels', 0.5558379888534546), ('encoder', 0.5550918579101562), ('autoencoders', 0.5536866188049316), ('channel codes', 0.5350778102874756), ('decoders', 0.524314284324646)]"
979,979,31,979_subharmonic functions_subharmonic_hessian type_hessian type equations,"['subharmonic functions', 'subharmonic', 'hessian type', 'hessian type equations', 'hessian operators', 'complex hessian', 'respect hessian', 'complex hessian equations', 'sobolev type', 'moser trudinger type']","['Weighted energy class of $m$-subharmonic functions   In this paper, we introduce the class $\\mathcal{E}_{m,F}(\\Omega)$ and solve\ncomplex $m$-Hessian equations in the class $\\mathcal{E}_{m,F}(\\Omega)$.\nAfterthat, we study subextension in the class $\\mathcal{E}_{m,F}(\\Omega)$ with\nthe weighted Hessian measure of subextension unchanged. This is an extensive\nversion of the result in [24] in the case when the smaller domain is relatively\ncompact inside the large one.\n', 'Subextension and approximation of $m$-subharmonic functions with given\n  boundary values   In this paper we establish a result on subextension of $m$-subharmonic\nfunctions in the class $\\mathcal{F}_m(\\Omega,f)$ without changing the hessian\nmeasures. As application, we approximate a $m$-subharmonic function with given\nboudary value by an increasing sequence of $m$-subharmonic functions defined on\nlarger domains.\n', 'Kiselman Minimum Principle and Rooftop Envelopes in Complex Hessian\n  Equations   We initiate the study of $m$-subharmonic functions with respect to a\nsemipositive $(1,1)$-form in Euclidean domains, providing a significant element\nin understanding geodesics within the context of complex Hessian equations.\nBased on the foundational Perron envelope construction, we prove a\ndecomposition of $m$-subharmonic solutions, and a general comparison principle\nthat effectively manages singular Hessian measures. Additionally, we establish\na rooftop equality and an analogue of the Kiselman minimum principle, which are\ncrucial ingredients in establishing a criterion for geodesic connectivity among\n$m$-subharmonic functions, expressed in terms of their asymptotic envelopes.\n']","[('subharmonic functions', 0.7201507687568665), ('subharmonic', 0.5269210338592529), ('hessian type', 0.4480185806751251), ('hessian type equations', 0.4478827714920044), ('hessian operators', 0.4373939633369446), ('complex hessian', 0.4190290570259094), ('respect hessian', 0.41860175132751465), ('complex hessian equations', 0.41836056113243103), ('sobolev type', 0.40349018573760986), ('moser trudinger type', 0.39940011501312256)]"
980,980,31,980_reinsurance_insurance_optimal investment_insurer,"['reinsurance', 'insurance', 'optimal investment', 'insurer', 'risk aversion', 'insured', 'insurance company', 'risk free asset', 'risk process', 'robust optimal']","[""Dynamic Reinsurance in Discrete Time Minimizing the Insurer's Cost of\n  Capital   In the classical static optimal reinsurance problem, the cost of capital for\nthe insurer's risk exposure determined by a monetary risk measure is minimized\nover the class of reinsurance treaties represented by increasing Lipschitz\nretained loss functions. In this paper, we consider a dynamic extension of this\nreinsurance problem in discrete time which can be viewed as a risk-sensitive\nMarkov Decision Process. The model allows for both insurance claims and premium\nincome to be stochastic and operates with general risk measures and premium\nprinciples. We derive the Bellman equation and show the existence of a\nMarkovian optimal reinsurance policy. Under an infinite planning horizon, the\nmodel is shown to be contractive and the optimal reinsurance policy to be\nstationary. The results are illustrated with examples where the optimal policy\ncan be determined explicitly.\n"", ""A Stackelberg reinsurance-investment game under $\\alpha$-maxmin\n  mean-variance criterion and stochastic volatility   This paper investigates a Stackelberg game between an insurer and a reinsurer\nunder the $\\alpha$-maxmin mean-variance criterion. The insurer can purchase\nper-loss reinsurance from the reinsurer. With the insurer's feedback\nreinsurance strategy, the reinsurer optimizes the reinsurance premium in the\nStackelberg game. The financial market consists of cash and stock with Heston's\nstochastic volatility. Both the insurer and reinsurer maximize their respective\n$\\alpha$-maxmin mean-variance preferences in the market. The criterion is\ntime-inconsistent and we derive the equilibrium strategies by the extended\nHamilton-Jacobi-Bellman equations. Similar to the non-robust case in Li and\nYoung (2022), excess-of-loss reinsurance is the optimal form of reinsurance\nstrategy for the insurer. The equilibrium investment strategy is determined by\na system of Riccati differential equations. Besides, the equations determining\nthe equilibrium reinsurance strategy and reinsurance premium rate are given\nsemi-explicitly, which is simplified to an algebraic equation in a specific\nexample. Numerical examples illustrate that the game between the insurer and\nreinsurer makes the insurance more radical when the agents become more\nambiguity aversion or risk aversion. Furthermore, the level of ambiguity,\nambiguity attitude, and risk attitude of the insurer (reinsurer) have similar\neffects on the equilibrium reinsurance strategy, reinsurance premium, and\ninvestment strategy.\n"", 'Optimal per-loss reinsurance and investment to minimize the probability\n  of drawdown   In this paper, we study an optimal reinsurance-investment problem in a risk\nmodel with two dependent classes of insurance business, where the two claim\nnumber processes are correlated through a common shock component. We assume\nthat the insurer can purchase per-loss reinsurance for each line of business\nand invest its surplus in a financial market consisting of a risk-free asset\nand a risky asset. Under the criterion of minimizing the probability of\ndrawdown, the closed-form expressions of the optimal reinsurance-investment\nstrategy and the corresponding value function are obtained. We show that the\noptimal reinsurance strategy is in the form of pure excess-of-loss reinsurance\nstrategy under the expected value principle, and under the variance premium\nprinciple, the optimal reinsurance strategy is in the form of pure quota-share\nreinsurance. Furthermore, we extend our model to the case where the insurance\ncompany involves $n$ $(n\\geq3)$ dependent classes of insurance business and the\noptimal results are derived explicitly as well.\n']","[('reinsurance', 0.6520408987998962), ('insurance', 0.48776960372924805), ('optimal investment', 0.4673740267753601), ('insurer', 0.46040427684783936), ('risk aversion', 0.44403403997421265), ('insured', 0.42807093262672424), ('insurance company', 0.4124893546104431), ('risk free asset', 0.3972354829311371), ('risk process', 0.39406493306159973), ('robust optimal', 0.3929358422756195)]"
981,981,31,981_effective viscosity_viscosity_particles fluid_newtonian fluid,"['effective viscosity', 'viscosity', 'particles fluid', 'newtonian fluid', 'rigid particles', 'viscous', 'hydrodynamic interactions', 'stokes flows', 'particle density', 'hydrodynamic']","[""The Influence of Einstein's Effective Viscosity on Sedimentation at Very\n  Small Particle Volume Fraction   We investigate the sedimentation of identical inertialess spherical particles\nin a Stokes fluid in the limit of many small particles. It is known that the\npresence of the particles leads to an increase of the effective viscosity of\nthe suspension. By Einstein's formula this effect is of the order of the\nparticle volume fraction $\\phi$. The disturbance of the fluid flow responsible\nfor this increase of viscosity is very singular (like $|x|^{-2}$).\nNevertheless, for well-prepared initial configurations and $\\phi\\to 0$, we show\nthat the microscopic dynamics is approximated to order $\\phi^2 |\\log \\phi|$ by\na macroscopic coupled transport-Stokes system with an effective viscosity\naccording to Einstein's formula. We provide quantitative estimates both for\nconvergence of the densities in the $p$-Wasserstein distance for all $p$ and\nfor the fluid velocity in Lebesgue spaces in terms of the $p$-Wasserstein\ndistance of the initial data. Our proof is based on approximations through the\nmethod of reflections and on a generalization of a classical result on\nconvergence to mean-field limits in the infinite Wasserstein metric by Hauray.\n"", ""On Einstein's effective viscosity formula   In his PhD thesis, Einstein derived an explicit first-order expansion for the\neffective viscosity of a Stokes fluid with a suspension of small rigid\nparticles at low density. His formal derivation relied on two implicit\nassumptions: (i) there is a scale separation between the size of the particles\nand the observation scale; and (ii) at first order, dilute particles do not\ninteract with one another. In mathematical terms, the first assumption amounts\nto the validity of a homogenization result defining the effective viscosity\ntensor, which is now well understood. Next, the second assumption allowed\nEinstein to approximate this effective viscosity at low density by considering\nparticles as being isolated. The rigorous justification is, in fact, quite\nsubtle as the effective viscosity is a nonlinear nonlocal function of the\nensemble of particles and as hydrodynamic interactions have borderline\nintegrability. In the present memoir, we establish Einstein's effective\nviscosity formula in the most general setting. In addition, we pursue the\nlow-density expansion to arbitrary order in form of a cluster expansion, where\nthe summation of hydrodynamic interactions crucially requires suitable\nrenormalizations. In particular, we justify a celebrated result by Batchelor\nand Green on the second-order correction and we explicitly describe all\nhigher-order renormalizations for the first time. In some specific settings, we\nfurther address the summability of the whole cluster expansion. Our approach\nrelies on a combination of combinatorial arguments, variational analysis,\nelliptic regularity, probability theory, and diagrammatic integration methods.\n"", ""Effective viscosity of semi-dilute suspensions   This review is devoted to the large-scale rheology of suspensions of rigid\nparticles in Stokes fluid. After describing recent results on the definition of\nthe effective viscosity of such systems in the framework of homogenization\ntheory, we turn to our new results on the asymptotic expansion of the effective\nviscosity in the dilute regime. This includes an optimal proof of Einstein's\nviscosity formula for the first-order expansion, as well as the continuation of\nthis expansion to higher orders. The essential difficulty originates in the\nlong-range nature of hydrodynamic interactions: suitable renormalizations are\nneeded and are captured by means of diagrammatic expansions.\n""]","[('effective viscosity', 0.6173198223114014), ('viscosity', 0.5605691075325012), ('particles fluid', 0.511942982673645), ('newtonian fluid', 0.49437418580055237), ('rigid particles', 0.49420860409736633), ('viscous', 0.4693942070007324), ('hydrodynamic interactions', 0.4432953894138336), ('stokes flows', 0.4376283884048462), ('particle density', 0.41187000274658203), ('hydrodynamic', 0.4070284962654114)]"
982,982,31,982_causal discovery_inferring causal_causal models_causal relationships,"['causal discovery', 'inferring causal', 'causal models', 'causal relationships', 'causal graphs', 'causal inference', 'underlying causal', 'causal relations', 'causal', 'causal structure']","['Causal Inference on Process Graphs, Part II: Causal Structure and Effect\n  Identification   A structural vector autoregressive (SVAR) process is a linear causal model\nfor variables that evolve over a discrete set of time points and between which\nthere may be lagged and instantaneous effects. The qualitative causal structure\nof an SVAR process can be represented by its finite and directed process graph,\nin which a directed link connects two processes whenever there is a lagged or\ninstantaneous effect between them. At the process graph level, the causal\nstructure of SVAR processes is compactly parameterised in the frequency domain.\nIn this paper, we consider the problem of causal discovery and causal effect\nestimation from the spectral density, the frequency domain analogue of the auto\ncovariance, of the SVAR process. Causal discovery concerns the recovery of the\nprocess graph and causal effect estimation concerns the identification and\nestimation of causal effects in the frequency domain.\n  We show that information about the process graph, in terms of $d$- and\n$t$-separation statements, can be identified by verifying algebraic constraints\non the spectral density. Furthermore, we introduce a notion of rational\nidentifiability for frequency causal effects that may be confounded by\nexogenous latent processes, and show that the recent graphical latent factor\nhalf-trek criterion can be used on the process graph to assess whether a given\n(confounded) effect can be identified by rational operations on the entries of\nthe spectral density.\n', ""Reconstructing regime-dependent causal relationships from observational\n  time series   Inferring causal relations from observational time series data is a key\nproblem across science and engineering whenever experimental interventions are\ninfeasible or unethical. Increasing data availability over the past decades has\nspurred the development of a plethora of causal discovery methods, each\naddressing particular challenges of this difficult task. In this paper we focus\non an important challenge that is at the core of time series causal discovery:\nregime-dependent causal relations. Often dynamical systems feature transitions\ndepending on some, often persistent, unobserved background regime, and\ndifferent regimes may exhibit different causal relations. Here, we assume a\npersistent and discrete regime variable leading to a finite number of regimes\nwithin which we may assume stationary causal relations. To detect\nregime-dependent causal relations, we combine the conditional\nindependence-based PCMCI method with a regime learning optimisation approach.\nPCMCI allows for linear and nonlinear, high-dimensional time series causal\ndiscovery. Our method, Regime-PCMCI, is evaluated on a number of numerical\nexperiments demonstrating that it can distinguish regimes with different causal\ndirections, time lags, effects and sign of causal links, as well as changes in\nthe variables' autocorrelation. Further, Regime-PCMCI is employed to\nobservations of El Ni\\~no Southern Oscillation and Indian rainfall,\ndemonstrating skill also in real-world datasets.\n"", 'Granger Causality in Extremes   We introduce a rigorous mathematical framework for Granger causality in\nextremes, designed to identify causal links from extreme events in time series.\nGranger causality plays a pivotal role in uncovering directional relationships\namong time-varying variables. While this notion gains heightened importance\nduring extreme and highly volatile periods, state-of-the-art methods primarily\nfocus on causality within the body of the distribution, often overlooking\ncausal mechanisms that manifest only during extreme events. Our framework is\ndesigned to infer causality mainly from extreme events by leveraging the causal\ntail coefficient. We establish equivalences between causality in extremes and\nother causal concepts, including (classical) Granger causality, Sims causality,\nand structural causality. We prove other key properties of Granger causality in\nextremes and show that the framework is especially helpful under the presence\nof hidden confounders. We also propose a novel inference method for detecting\nthe presence of Granger causality in extremes from data. Our method is\nmodel-free, can handle non-linear and high-dimensional time series, outperforms\ncurrent state-of-the-art methods in all considered setups, both in performance\nand speed, and was found to uncover coherent effects when applied to financial\nand extreme weather observations.\n']","[('causal discovery', 0.6168652176856995), ('inferring causal', 0.5877993702888489), ('causal models', 0.5549649596214294), ('causal relationships', 0.5330212116241455), ('causal graphs', 0.5301951766014099), ('causal inference', 0.5212035775184631), ('underlying causal', 0.518728494644165), ('causal relations', 0.5184903144836426), ('causal', 0.5152960419654846), ('causal structure', 0.5137273669242859)]"
983,983,31,983_quantum coherence_quantum resource_quantum resources_resources quantum,"['quantum coherence', 'quantum resource', 'quantum resources', 'resources quantum', 'coherence', 'quantum states', 'theory quantum', 'quantum', 'quantum state', 'quantum channel']","['Dynamical Resource Theory of Quantum Coherence   Decoherence is all around us. Every quantum system that interacts with the\nenvironment is doomed to decohere. The preservation of quantum coherence is one\nof the major challenges faced in quantum technologies, but its use as a\nresource is very promising and can lead to various operational advantages, for\nexample in quantum algorithms. Hence, much work has been devoted in recent\nyears to quantify the coherence present in a system. In the present paper, we\nformulate the quantum resource theory of dynamical coherence. The underlying\nphysical principle we follow is that the free dynamical objects are those that\ncannot preserve or distribute coherence. This leads us to identify classical\nchannels as the free elements in this theory. Consequently, even the quantum\nidentity channel is not free as all physical systems undergo decoherence and\nhence, the preservation of coherence should be considered a resource. In our\nwork, we introduce four different types of free superchannels (analogous to\nMIO, DIO, IO, and SIO) and discuss in detail two of them, namely,\ndephasing-covariant incoherent superchannels (DISC), maximally incoherent\nsuperchannels (MISC). The latter consists of all superchannels that do not\ngenerate non-classical channels from classical ones. We quantify dynamical\ncoherence using channel-divergence-based monotones for MISC and DISC. We show\nthat some of these monotones have operational interpretations as the exact, the\napproximate, and the liberal coherence cost of a quantum channel. Moreover, we\nprove that the liberal asymptotic cost of a channel is equal to a new type of\nregularized relative entropy. Finally, we show that the conversion distance\nbetween two channels under MISC and DISC can be computed using a semi-definite\nprogram (SDP).\n', ""Completing the Grand Tour of asymptotic quantum coherence manipulation   We compute on all quantum states several measures that characterise\nasymptotic quantum coherence manipulation under restricted classes of\noperations. We focus on the distillable coherence, i.e. the maximum rate of\nproduction of approximate pure bits of coherence starting from independent\ncopies of an input state $\\rho$, and on the coherence cost, i.e. the minimum\nrate of consumption of pure coherence bits that is needed to generate many\ncopies of $\\rho$ with vanishing error. We obtain the first closed-form\nexpression for the distillable coherence under strictly incoherent operations\n(SIO), proving that it coincides with that obtained via physically incoherent\noperations (PIO). This shows that SIO and PIO are equally weak at distilling\ncoherence, sheds light on the recently discovered phenomenon of generic bound\ncoherence, and provides us with an explicit optimal distillation protocol that\nis amenable to practical implementations. We give a single-letter formula for\nthe coherence cost under PIO, showing that it is finite on a set of states with\nnonzero volume. Since PIO can be realised in a laboratory with incoherent\nancillae, unitaries, and measurements, our result puts fundamental limitations\non coherence manipulation in an experimentally relevant setting. We find\nexamples of 'abyssally bound' states with vanishing PIO distillable coherence\nyet infinite PIO coherence cost. Our findings complete the picture of\nasymptotic coherence manipulation under all the main classes of incoherent\noperations.\n"", 'One-Shot Coherence Distillation: Towards Completing the Picture   The resource framework of quantum coherence was introduced by Baumgratz,\nCramer and Plenio [PRL 113, 140401 (2014)] and further developed by Winter and\nYang [PRL 116, 120404 (2016)]. We consider the one-shot problem of distilling\npure coherence from a single instance of a given resource state. Specifically,\nwe determine the distillable coherence with a given fidelity under incoherent\noperations (IO) through a generalisation of the Winter-Yang protocol. This is\ncompared to the distillable coherence under maximal incoherent operations (MIO)\nand dephasing-covariant incoherent operations (DIO), which can be cast as a\nsemidefinite programme, that has been presented previously by Regula et al.\n[PRL 121, 010401 (2018)]. Our results are given in terms of a smoothed\nmin-relative entropy distance from the incoherent set of states, and a variant\nof the hypothesis-testing relative entropy distance, respectively. The one-shot\ndistillable coherence is also related to one-shot randomness extraction.\n  Moreover, from the one-shot formulas under IO, MIO, DIO, we can recover the\noptimal distillable rate in the many-copy asymptotics, yielding the relative\nentropy of coherence. These results can be compared with previous work by some\nof the present authors [Zhao et al., PRL 120, 070403 (2018)] on one-shot\ncoherence formation under IO, MIO, DIO and also SIO. This shows that the amount\nof distillable coherence is essentially the same for IO, DIO, and MIO, despite\nthe fact that the three classes of operations are very different. We also\nrelate the distillable coherence under strictly incoherent operations (SIO) to\na constrained hypothesis testing problem and explicitly show the existence of\nbound coherence under SIO in the asymptotic regime.\n']","[('quantum coherence', 0.7470125555992126), ('quantum resource', 0.6043581962585449), ('quantum resources', 0.5695579648017883), ('resources quantum', 0.5428192019462585), ('coherence', 0.5352503061294556), ('quantum states', 0.5166104435920715), ('theory quantum', 0.5144360065460205), ('quantum', 0.5053620934486389), ('quantum state', 0.5042423605918884), ('quantum channel', 0.48828622698783875)]"
984,984,30,984_kalman filters_kalman filter_extended kalman filter_kalman filter ekf,"['kalman filters', 'kalman filter', 'extended kalman filter', 'kalman filter ekf', 'unscented kalman filter', 'unscented kalman', 'extended kalman', 'inertial frame', 'nonlinear observer', 'nonlinear observers']","['Guaranteed Performance of Nonlinear Pose Filter on SE(3)   This paper presents a novel nonlinear pose filter evolved directly on the\nSpecial Euclidean Group SE(3) with guaranteed characteristics of transient and\nsteady-state performance. The above-mention characteristics can be achieved by\ntrapping the position error and the error of the normalized Euclidean distance\nof the attitude in a given large set and guiding them to converge\nsystematically to a small given set. The error vector is proven to approach the\norigin asymptotically from almost any initial condition. The proposed filter is\nable to provide a reliable pose estimate with remarkable convergence properties\nsuch that it can be fitted with measurements obtained from low-cost measurement\nunits. Simulation results demonstrate high convergence capabilities and\nrobustness considering large error in initialization and high level of\nuncertainties in measurements. Keywords: Pose, estimator, observer, attitude,\nposition, estimate, special orthogonal group, special Euclidean group,\nprescribed performance, steady-state, transient response, homogeneous\ntransformation matrix, complimentary filter, mapping, Parameterization,\nRepresentation, Robust, stability, uncertain, Gaussian, noise, vectorial\nmeasurement, vector measurement, translational velocity, angular velocity,\nsingular value decomposition, rotational matrix, identity, deterministic,\ncomparison, inertial frame, rigid body, three dimensional, 3D, space, Lie\ngroup, projection, landmark, feature, gyroscope, micro electromechanical\nsystems, Inertial measurement units, sensor, IMUs, Fixed, moving, orientation,\nRoll, Pitch, Yaw, SVD, UAVs, QUAV, unmanned, underwater vehicle, robot, robotic\nSystem, spacecraft, quadrotor, quadcopter, overview, autonomous, xyz, axis,\nSO(3), SE(3).\n', 'Nonlinear Stochastic Attitude Filters on the Special Orthogonal Group 3:\n  Ito and Stratonovich   Two nonlinear stochastic complimentary filters are developed on SO(3). They\nguarantee that errors in the Rodriguez vector and estimates are semi-globally\nuniformly ultimately bounded in mean square, and they converge to a small\nneighborhood of the origin. Simulation results are presented to illustrate the\neffectiveness of the proposed filters considering high level of uncertainties\nin angular velocity as well as body-frame vector measurements. Keywords:\nAttitude estimate, Attitude estimator, Attitude observer, Attitude filter,\nNonlinear stochastic filter, stochastic differential equations, Brownian motion\nprocess, Ito, Stratonovich, Wong Zakai, Rodriguez vector, unit-quaternion,\nspecial orthogonal group 3, Euclidean, Euler angles, Angle-axis, Mapping,\nParameterization, Representation, Robust, Invariant, Kalman Filter, Extended\nKalman Filter, Multiplicative Extended Kalman Filter, Unscented Kalman Filter,\nParticle Filter, KF, EKF, MEKF, IEKF, first, second, Partial derivative,\noperator, probability, small, error, dynamics, kinematics, equilibrium,\nasymptotic, covariance, mean square, expected value, zero, unknown,\ntime-varying, global, semi-global, stable, stability, uncertain, white noise,\nGaussian noise, colored noise, bias, vectorial, vector measurement, angular\nvelocity, singular value decomposition, bounded, rotational matrix, identity,\ndeterministic, orientation, body frame, comparison, inertial frame, rigid body,\nthree dimensional, 3D, space, Attitude Control, Lie algebra, Lie group,\nprojection, Gyroscope, Inertial measurement units, micro electromechanical\nsystems, sensor, IMUs, MEMS, Roll, Pitch, Yaw, UAVs, QUAV, SVD, Fixed, Moving,\nVehicles, Robot, Robotic System, Spacecraft, submarine, Underwater vehicle,\nProblem, advantage, integral, integration, passive complementary filter,\nDisadvantage, autonomous, Review, Overview, Survey, comparative study, pose,\nSDEs, SE(3), SO(3).\n', 'Nonlinear Pose Filters on the Special Euclidean Group SE(3) with\n  Guaranteed Transient and Steady-state Performance   Two novel nonlinear pose (i.e, attitude and position) filters developed\ndirectly on the Special Euclidean Group SE(3)able to guarantee prescribed\ncharacteristics of transient and steady-state performance are proposed. The\nposition error and normalized Euclidean distance of attitude error are trapped\nto arbitrarily start within a given large set and converge systematically and\nasymptotically to the origin from almost any initial condition. The transient\nerror is guaranteed not to exceed a prescribed value while the steady-state\nerror is bounded by a predefined small value. The first pose filter operates\nbased on a set of vectorial measurements coupled with a group of velocity\nvectors and requires preliminary pose reconstruction. The second filter, on the\ncontrary, is able to perform its function using a set of vectorial measurements\nand a group of velocity vectors directly. Both proposed filters provide\nreasonable pose estimates with superior convergence properties while being able\nto use measurements obtained from low-cost inertial measurement, landmark\nmeasurement, and velocity measurement units. Simulation results demonstrate\neffectiveness and robustness of the proposed filters considering large error in\ninitialization and high level of uncertainties in velocity vectors as well as\nin the set of vector measurements. Attitude, position, pose estimation,\nnonlinear observer, estimate, special orthogonal group, special Euclidean\ngroup, SO(3), SE(3), prescribed performance function, transient, steady-state\nerror, transformed error, Landmark, feature measurement, PPF, IMU, Lie algebra,\nLie group, projection, Gyroscope, Inertial measurement units, rigid body, micro\nelectromechanical systems, sensor, IMUs, MEMS, Roll, Pitch, Yaw, UAVs, QUAV,\nSVD, Fixed, Moving, Vehicles, Robot, Robotic System, Spacecraft, submarine,\nUnderwater vehicle.\n']","[('kalman filters', 0.5765407085418701), ('kalman filter', 0.5599594712257385), ('extended kalman filter', 0.537532389163971), ('kalman filter ekf', 0.520851731300354), ('unscented kalman filter', 0.5173472762107849), ('unscented kalman', 0.4662928879261017), ('extended kalman', 0.4625481069087982), ('inertial frame', 0.4267325699329376), ('nonlinear observer', 0.41805416345596313), ('nonlinear observers', 0.41410475969314575)]"
985,985,30,985_quadratic optimal control_stochastic riccati_stochastic linear quadratic_linear quadratic stochastic,"['quadratic optimal control', 'stochastic riccati', 'stochastic linear quadratic', 'linear quadratic stochastic', 'backward stochastic differential', 'optimal control forward', 'optimal control problems', 'linear stochastic differential', 'stochastic differential equations', 'stochastic optimal']","['General Indefinite Backward Stochastic Linear-Quadratic Optimal Control\n  Problems   A general backward stochastic linear-quadratic optimal control problem is\nstudied, in which both the state equation and the cost functional contain the\nnonhomogeneous terms. The main feature of the problem is that the weighting\nmatrices in the cost functional are allowed to be indefinite and cross-product\nterms in the control and the state processes are present. Necessary and\nsufficient conditions for the solvability of the problem are obtained, and a\ncharacterization of the optimal control in terms of forward-backward stochastic\ndifferential equations is derived. By a Riccati equation approach, a general\nprocedure for constructing optimal controls is developed and the value function\nis obtained explicitly.\n', 'Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control\n  Problems with Poisson Jumps   This paper is concerned with the stochastic linear-quadratic optimal control\nproblem with Poisson jumps. The coefficients in the state equation and the\nweighting matrices in the cost functional are all deterministic but are allowed\nindefinite. The notion of closed-loop strategies is introduced, and the optimal\nclosed-loop strategy is characterized by a Riccati integral-differential\nequation and a backward stochastic differential equation with Poisson jumps.\n', 'Open-loop and closed-loop solvabilities for discrete-time mean-field\n  stochastic linear quadratic optimal control problems   This paper discusses the discrete-time mean-field stochastic linear quadratic\noptimal control problems, whose weighting matrices in the cost functional are\nnot assumed to be definite. The open-loop solvability is characterized by the\nexistence of the solution to a mean-field forward-backward stochastic\ndifference equations with a convexity condition and a stationary condition. The\nclosed-loop solvability is presented by virtue of the existences of the regular\nsolution to the generalized Riccati equations and the solution to the linear\nrecursive equation, which is also shown by the uniform convexity of the cost\nfunctional. Moreover, based on a family of uniformly convex cost functionals,\nthe finiteness of the problem is characterized. Also, it turns out that a\nminimizing sequence, whose convergence is equivalent to the open-loop\nsolvability of the problem. Finally, some examples are given to illustrate the\ntheory developed.\n']","[('quadratic optimal control', 0.6009861826896667), ('stochastic riccati', 0.5879852175712585), ('stochastic linear quadratic', 0.5843642354011536), ('linear quadratic stochastic', 0.5751850008964539), ('backward stochastic differential', 0.564659595489502), ('optimal control forward', 0.5543762445449829), ('optimal control problems', 0.5537005066871643), ('linear stochastic differential', 0.5498611330986023), ('stochastic differential equations', 0.5497848391532898), ('stochastic optimal', 0.539436399936676)]"
986,986,30,986_secret sharing schemes_secret sharing scheme_secret sharing_shamir secret sharing,"['secret sharing schemes', 'secret sharing scheme', 'secret sharing', 'shamir secret sharing', 'shares secret', 'sharing scheme', 'sharing schemes', 'ramp secret sharing', 'secret among', 'information secret']","['On Ideal Secret-Sharing Schemes for $k$-homogeneous access structures   A $k$-uniform hypergraph is a hypergraph where each $k$-hyperedge has exactly\n$k$ vertices. A $k$-homogeneous access structure is represented by a\n$k$-uniform hypergraph $\\mathcal{H}$, in which the participants correspond to\nthe vertices of hypergraph $\\mathcal{H}$. A set of vertices can reconstruct the\nsecret value from their shares if they are connected by a $k$-hyperedge, while\na set of non-adjacent vertices does not obtain any information about the\nsecret. One parameter for measuring the efficiency of a secret sharing scheme\nis the information rate, defined as the ratio between the length of the secret\nand the maximum length of the shares given to the participants. Secret sharing\nschemes with an information rate equal to one are called ideal secret sharing\nschemes. An access structure is considered ideal if an ideal secret sharing\nscheme can realize it. Characterizing ideal access structures is one of the\nimportant problems in secret sharing schemes. The characterization of ideal\naccess structures has been studied by many authors~\\cite{BD, CT,JZB,\nFP1,FP2,DS1,TD}. In this paper, we characterize ideal $k$-homogeneous access\nstructures using the independent sequence method. In particular, we prove that\nthe reduced access structure of $\\Gamma$ is an $(k, n)$-threshold access\nstructure when the optimal information rate of $\\Gamma$ is larger than\n$\\frac{k-1}{k}$, where $\\Gamma$ is a $k$-homogeneous access structure\nsatisfying specific criteria.\n', 'Ideal Secret Sharing Schemes: Combinatorial Characterizations, Certain\n  Access Structures, and Related Geometric Problems   An ideal secret sharing scheme is a method of sharing a secret key in some\nkey space among a finite set of participants in such a way that only the\nauthorized subsets of participants can reconstruct the secret key from their\nshares which are of the same length as that of the secret key. The set of all\nauthorized subsets of participants is the access structure of the secret\nsharing scheme. In this paper, we derive several properties and restate the\ncombinatorial characterization of an ideal secret sharing scheme in\nBrickell-Stinson model in terms of orthogonality of its representative array.\nWe propose two practical models, namely the parallel and hierarchical models,\nfor access structures, and then, by the restated characterization, we discuss\nsufficient conditions on finite geometries for ideal secret sharing schemes to\nrealize these access structure models. Several series of ideal secret sharing\nschemes realizing special parallel or hierarchical access structure model are\nconstructed from finite projective planes.\n', 'Secret Sharing for Generic Theoretic Cryptography   Sharing a secret efficiently amongst a group of participants is not easy\nsince there is always an adversary / eavesdropper trying to retrieve the\nsecret. In secret sharing schemes, every participant is given a unique share.\nWhen the desired group of participants come together and provide their shares,\nthe secret is obtained. For other combinations of shares, a garbage value is\nreturned. A threshold secret sharing scheme was proposed by Shamir and Blakley\nindependently. In this (n,t) threshold secret sharing scheme, the secret can be\nobtained when at least t out of n participants contribute their shares. This\npaper proposes a novel algorithm to reveal the secret only to the subsets of\nparticipants belonging to the access structure. This scheme implements totally\ngeneralized ideal secret sharing. Unlike threshold secret sharing schemes, this\nscheme reveals the secret only to the authorized sets of participants, not any\narbitrary set of users with cardinality more than or equal to t. Since any\naccess structure can be realized with this scheme, this scheme can be exploited\nto implement various access priorities and access control mechanisms. A major\nadvantage of this scheme over the existing ones is that the shares being\ndistributed to the participants is totally independent of the secret being\nshared. Hence, no restrictions are imposed on the scheme and it finds a wider\nuse in real world applications.\n']","[('secret sharing schemes', 0.804269552230835), ('secret sharing scheme', 0.7658504247665405), ('secret sharing', 0.712887704372406), ('shamir secret sharing', 0.6521356105804443), ('shares secret', 0.6323530673980713), ('sharing scheme', 0.6192446947097778), ('sharing schemes', 0.6067348718643188), ('ramp secret sharing', 0.601652979850769), ('secret among', 0.5198654532432556), ('information secret', 0.5106817483901978)]"
987,987,30,987_cooperative game theory_coalition game_cooperative games_cooperative game,"['cooperative game theory', 'coalition game', 'cooperative games', 'cooperative game', 'coalition formation', 'game theory', 'coalitions', 'coalitional', 'coalition', 'cooperative']","['Cooperative Ressource Sharing With Adamant Player   Cooperative game theory deals with systems where players want to cooperate to\nimprove their payoffs. But players may choose coalitions in a non-cooperative\nmanner, leading to a coalition-formation game. We consider such a game with\nseveral players (willing to cooperate) and an adamant player (unwilling to\ncooperate) involved in resource-sharing. Here, the strategy of a player is the\nset of players with whom it wants to form a coalition. Given a strategy\nprofile, an appropriate partition of coalitions is formed; players in each\ncoalition maximize their collective utilities leading to a non-cooperative\nresource-sharing game among the coalitions, the utilities at the resulting\nequilibrium are shared via Shapley-value; these shares define the utilities of\nplayers for the given strategy profile in coalition-formation game. We also\nconsider the utilitarian solution to derive the price of anarchy (PoA). We\nconsidered a case with symmetric players and an adamant player; wherein we\nobserved that players prefer to stay alone at Nash equilibrium when the number\nof players (n) is more than 4. In contrast, in the majority of the cases, the\nutilitarian partition is grand coalition. Interestingly the PoA is smaller with\nan adamant player of intermediate strength. Further, PoA grows like O(n).\n', 'A Hodge theoretic extension of Shapley axioms   Lloyd S. Shapley \\cite{Shapley1953a, Shapley1953} introduced a set of axioms\nin 1953, now called the {\\em Shapley axioms}, and showed that the axioms\ncharacterize a natural allocation among the players who are in grand coalition\nof a {\\em cooperative game}. Recently, \\citet{StTe2019} showed that a\ncooperative game can be decomposed into a sum of {\\em component games}, one for\neach player, whose value at the grand coalition coincides with the {\\em Shapley\nvalue}. The component games are defined by the solutions to the naturally\ndefined system of least squares linear equations via the framework of the {\\em\nHodge decomposition} on the hypercube graph.\n  In this paper we propose a new set of axioms which characterizes the\ncomponent games. Furthermore, we realize them through an intriguing stochastic\npath integral driven by a canonical Markov chain. The integrals are natural\nrepresentation for the expected total contribution made by the players for each\ncoalition, and hence can be viewed as their fair share. This allows us to\ninterpret the component game values for each coalition also as a valid measure\nof fair allocation among the players in the coalition. Our axioms may be viewed\nas a completion of Shapley axioms in view of this characterization of the\nHodge-theoretic component games, and moreover, the stochastic path integral\nrepresentation of the component games may be viewed as an extension of the {\\em\nShapley formula}.\n', ""Cooperative networks and Hodge-Shapley value   Lloyd Shapley's cooperative value allocation theory stands as a central\nconcept in game theory, extensively utilized across various domains to\ndistribute resources, evaluate individual contributions, and ensure fairness.\nThe Shapley value formula and his four axioms that characterize it form the\nfoundation of the theory.\n  Traditionally, the Shapley value is assigned under the assumption that all\nplayers in a cooperative game will ultimately form the grand coalition. In this\npaper, we reinterpret the Shapley value as an expectation of a certain\nstochastic path integral, with each path representing a general coalition\nformation process. As a result, the value allocation is naturally extended to\nall partial coalition states. In addition, we provide a set of five properties\nthat extend the Shapley axioms and characterize the stochastic path integral.\nFinally, by integrating Hodge calculus, stochastic processes, and path\nintegration of edge flows on graphs, we expand the cooperative value allocation\ntheory beyond the standard coalition game structure to encompass a broader\nrange of cooperative network configurations.\n""]","[('cooperative game theory', 0.656927227973938), ('coalition game', 0.6541196703910828), ('cooperative games', 0.6132755279541016), ('cooperative game', 0.5836618542671204), ('coalition formation', 0.5751060843467712), ('game theory', 0.5548329949378967), ('coalitions', 0.5503440499305725), ('coalitional', 0.5421687364578247), ('coalition', 0.5260298252105713), ('cooperative', 0.4786709249019623)]"
988,988,30,988_optimal quantization_quantization dimensions_quantization_quantization errors,"['optimal quantization', 'quantization dimensions', 'quantization', 'quantization errors', 'distributions optimal', 'quantization error', 'vector quantization', 'optimal means', 'quantizers', 'discrete distributions']","['Optimal quantization for piecewise uniform distributions   Quantization for a probability distribution refers to the idea of estimating\na given probability by a discrete probability supported by a finite number of\npoints. In this paper, firstly a general approach to this process is outlined\nusing independent random variables and ergodic maps; these give asymptotically\nthe optimal sets of $n$-means and the $n$th quantization errors for all\npositive integers $n$. Secondly two piecewise uniform distributions are\nconsidered on $\\mathbb R$: one with infinite number of pieces and one with\nfinite number of pieces. For these two probability measures, we describe the\noptimal sets of $n$-means and the $n$th quantization errors for all $n\\in\n\\mathbb N$. It is seen that for a uniform distribution with infinite number of\npieces to determine the optimal sets of $n$-means for $n\\geq 2$ one needs to\nknow an optimal set of $(n-1)$-means, but for a uniform distribution with\nfinite number of pieces one can directly determine the optimal sets of\n$n$-means and the $n$th quantization errors for all $n\\in \\mathbb N$.\n', 'Constrained quantization for a uniform distribution   Constrained quantization for a Borel probability measure refers to the idea\nof estimating a given probability by a discrete probability with a finite\nnumber of supporting points lying on a specific set. The specific set is known\nas the constraint of the constrained quantization. A quantization without a\nconstraint is known as an unconstrained quantization, which traditionally in\nthe literature is known as quantization. Constrained quantization has recently\nbeen introduced by Pandey and Roychowdhury. In this paper, for a uniform\ndistribution with support lying on a side of an equilateral triangle, and the\nconstraint as the union of the other two sides, we obtain the optimal sets of\n$n$-points and the $n$th constrained quantization errors for all positive\nintegers $n$. We also calculate the constrained quantization dimension and the\nconstrained quantization coefficient.\n', 'Quantization for uniform distributions on hexagonal, semicircular, and\n  elliptical curves   In this paper, first we have defined a uniform distribution on the boundary\nof a regular hexagon, and then investigated the optimal sets of $n$-means and\nthe $n$th quantization errors for all positive integers $n$. We give an exact\nformula to determine them, if $n$ is of the form $n=6k$ for some positive\ninteger $k$. We further calculate the quantization dimension, the quantization\ncoefficient, and show that the quantization dimension is equal to the dimension\nof the object, and the quantization coefficient exists as a finite positive\nnumber. Then, we define a mixture of two uniform distributions on the boundary\nof a semicircular disc, and obtain a sequence and an algorithm, with the help\nof which we determine the optimal sets of $n$-means and the $n$th quantization\nerrors for all positive integers $n$ with respect to the mixed distribution.\nFinally, for a uniform distribution defined on an elliptical curve, we\ninvestigate the optimal sets of $n$-means and the $n$th quantization errors for\nall positive integers $n$.\n']","[('optimal quantization', 0.6625769138336182), ('quantization dimensions', 0.5538992285728455), ('quantization', 0.5515447854995728), ('quantization errors', 0.5141671299934387), ('distributions optimal', 0.5034411549568176), ('quantization error', 0.48103803396224976), ('vector quantization', 0.4765990674495697), ('optimal means', 0.44533610343933105), ('quantizers', 0.44213709235191345), ('discrete distributions', 0.4202830493450165)]"
989,989,30,989_multiple polylogarithms_polylogarithms_polylogarithmic_polylogarithm,"['multiple polylogarithms', 'polylogarithms', 'polylogarithmic', 'polylogarithm', 'conjecture weight', 'functions ramanujan', 'theory elliptic functions', 'theory elliptic', 'elliptic theory', 'hypergeometric identities']","['Analytic continuation of Kochubei multiple polylogarithms and its\n  applications   In the present paper, we propose an analytic continuation of Kochubei\nmultiple polylogarithms using the techniques developed by Furusho. Moreover, we\nproduce a family of linear relations and a linear independence result for\nvalues of our analytically continued Kochubei polylogarithms at algebraic\nelements from a cohomological aspect.\n', 'Cluster Polylogarithms I: Quadrangular Polylogarithms   We suggest a definition of cluster polylogarithms on an arbitrary cluster\nvariety and classify them in type $A$. We find functional equations for\nmultiple polylogarithms which generalize equations discovered by Abel, Kummer,\nand Goncharov to an arbitrary weight. As an application, we prove a part of the\nGoncharov depth conjecture in weight six.\n', 'Multiple polylogarithms and the Steinberg module   We establish a connection between multiple polylogarithms on a torus and the\nSteinberg module of $\\mathbb{Q}$, and show that multiple polylogarithms of\ndepth $d$ and weight $n$ can be expressed via a single function\n$\\mathrm{Li}_{n-d+1,1,\\dots,1}(x_1,x_2,\\dots,x_d)$. Using this connection, we\ngive a simple proof of the Bykovski\\u{\\i} theorem, explain the duality between\nmultiple polylogarithms and iterated integrals, and provide a polylogarithmic\ninterpretation of the conjectures of Rognes and Church-Farb-Putman.\n']","[('multiple polylogarithms', 0.6836611032485962), ('polylogarithms', 0.6802675127983093), ('polylogarithmic', 0.6452784538269043), ('polylogarithm', 0.6324136257171631), ('conjecture weight', 0.370652437210083), ('functions ramanujan', 0.35362350940704346), ('theory elliptic functions', 0.33689653873443604), ('theory elliptic', 0.3235352039337158), ('elliptic theory', 0.3190663158893585), ('hypergeometric identities', 0.3149052560329437)]"
990,990,30,990_dimer models_planar graphs_invariant gibbs measures_invariant gibbs,"['dimer models', 'planar graphs', 'invariant gibbs measures', 'invariant gibbs', 'dimers', 'square lattice', 'gibbs measures', 'dimer', 'lattice', 'free boundary']","[""Two dimensional dimers beyond planarity   We consider a generalisation of the double dimer model which includes several\nmodels of interest, such as the monomer double dimer model, the dimer model,\nthe Spin O(N) model, and it is related to the loop O(N) model. We prove that on\ntwo-dimension like graphs (such as slabs), both the correlation function and\nthe probability that a loop visits two vertices converge to zero as the\ndistance between such vertices gets large. Our analysis is by introducing a new\n(complex) spin representation for all models belonging to this class, and by\nderiving a new proof of the Mermin-Wagner theorem which does not require the\npositivity of the Gibbs measure. Even for the well studied dimer and double\ndimer model our results are new since - not relying on solvability and\nKasteleyn's theorem - they hold beyond the framework of planar graphs.\n"", 'Asymptotics of pure dimer coverings on rail-yard graphs   We study asymptotic limit of random pure dimer coverings on rail yardgraphs\nwhen the mesh sizes of the graphs go to 0. Each pure dimer covering\ncorrespondsto a sequence of interlacing partitions starting with an empty\npartition and ending inan empty partition. Under the assumption that the\nprobability of each dimer covering isproportional to the product of weights of\npresent edges, we obtain the limit shape (Law ofLarge Numbers) of the rescaled\nheight function and the convergence of unrescaled heightfluctuation to a\ndiffeomorphic image of Gaussian Free Field (Central Limit Theorem); an-swering\na question in [6]. Applications include the limit shape and height fluctuations\nforpure steep tilings ([8]) and pyramid partitions ([20, 35, 36, 37]). The\ntechnique to obtainthese results is to analyze a class of Mcdonald processes\nwhich involve dual partitions as well.\n', 'Asymptotics of dimer coverings on free boundary rail-yard graphs   Rail-yard graphs are a general class of graphs introduced in \\cite{bbccr} on\nwhich the random dimer coverings form Schur processes. We study asymptotic\nlimits of random dimer coverings on rail yard graphs with free boundary\nconditions on both the left boundary and the right boundary (double-sided free\nboundary) when the mesh sizes of the graphs go to 0. Each dimer covering\ncorresponds to a sequence of interlacing partitions starting with an arbitrary\npartition and ending in an arbitrary partition. Under the assumption that the\nprobability of each dimer covering is proportional to the product of weights of\npresent edges, we obtain the moment formula for the height function which\nincludes an infinite product. By passing down to the scaling limit, we compute\nthe limit shape (law of large numbers) of the rescaled height functions and\nprove the convergence of unrescaled height fluctuations to a diffeomorphic\nimage of the restriction of the 0-boundary Gaussian free field (central limit\ntheorem) on the upper half plane to a subset. Applications include the limit\nshape and height fluctuations for free boundary steep tilings as proposed in\n\\cite{BCC17}. The technique to obtain these results is to analyze a class of\nMacdonald processes with dual specializations, subject to further complexities\narising from the infinite product in the moment formula.\n  We also obtain a new algorithm to sample double-sided free boundary dimer\ncoverings on rail-yard graphs, which fulfills an open problem in\n\\cite{bbbccv14}.\n']","[('dimer models', 0.5172243714332581), ('planar graphs', 0.4750208854675293), ('invariant gibbs measures', 0.4004443883895874), ('invariant gibbs', 0.3890734016895294), ('dimers', 0.3839718997478485), ('square lattice', 0.3783273994922638), ('gibbs measures', 0.3633592426776886), ('dimer', 0.3592340350151062), ('lattice', 0.3562472462654114), ('free boundary', 0.3552702069282532)]"
991,991,30,991_rankin selberg integrals_rankin selberg functions_values rankin selberg_rankin selberg,"['rankin selberg integrals', 'rankin selberg functions', 'values rankin selberg', 'rankin selberg', 'selberg integrals', 'selberg functions', 'selberg integral', 'automorphic representations gl', 'representations gl', 'cuspidal automorphic representations']","[""Product of Rankin-Selberg convolutions and a new proof of Jacquet's\n  local converse conjecture   In this article, we construct a family of integrals which represent the\nproduct of Rankin-Selberg $L$-functions of $\\mathrm{GL}_{l}\\times\n\\mathrm{GL}_m$ and of $\\mathrm{GL}_{l}\\times \\mathrm{GL}_n $ when $m+n<l$. When\n$n=0$, these integrals are those defined by Jacquet--Piatetski-Shapiro--Shalika\nup to a shift. In this sense, these new integrals generalize\nJacquet--Piatetski-Shapiro--Shalika's Rankin-Selberg convolution integrals. We\nstudy basic properties of these integrals. In particular, we define local gamma\nfactors using this new family of integrals. As an application, we obtain a new\nproof of Jacquet's local converse conjecture using these new integrals.\n"", ""Uniform Integrality of critical values of the Rankin-Selberg\n  $L$-function for ${\\rm GL}_{n}\\times {\\rm GL}_{n-1}$   After introducing the notion of uniform integrality of critical values of the\nRankin-Selberg $L$-functions for $\\mathrm{GL}_{n}\\times \\mathrm{GL}_{n-1}$, we\nstudy it when the base field is totally imaginary. For this purpose, we adopt\nspecific models of highest weight representations of the general linear groups,\nconstruct the Eichler-Shimura classes for $\\mathrm{GL}_{n}$ and\n$\\mathrm{GL}_{n-1}$ in an explicit manner, and then evaluate the cohomological\ncup product of them, by making the best use of Gel'fand-Tsetlin basis.\n"", ""Rankin-Selberg convolutions for $\\mathrm{GL}(n)\\times \\mathrm{GL}(n)$\n  and $\\mathrm{GL}(n)\\times \\mathrm{GL}(n-1)$ for principal series\n  representations   Let $\\mathsf k$ be a local field. Let $I_\\nu$ and $I_{\\nu'}$ be smooth\nprincipal series representations of $\\mathrm{GL}_n(\\mathsf k)$ and\n$\\mathrm{GL}_{n-1}(\\mathsf k)$ respectively. The Rankin-Selberg integrals yield\na continuous bilinear map $I_\\nu\\times I_{\\nu'}\\rightarrow \\mathbb C$ with a\ncertain invariance property. We study integrals over a certain open orbit that\nalso yield a continuous bilinear map $I_\\nu\\times I_{\\nu'}\\rightarrow \\mathbb\nC$ with the same invariance property, and show that these integrals equal the\nRankin-Selberg integrals up to an explicit constant. Similar results are also\nobtained for Rankin-Selberg integrals for $\\mathrm{GL}_n(\\mathsf k)\\times\n\\mathrm{GL}_n(\\mathsf k)$.\n""]","[('rankin selberg integrals', 0.7653495073318481), ('rankin selberg functions', 0.750872790813446), ('values rankin selberg', 0.6369825601577759), ('rankin selberg', 0.6300938725471497), ('selberg integrals', 0.6276842355728149), ('selberg functions', 0.6048373579978943), ('selberg integral', 0.5444051623344421), ('automorphic representations gl', 0.49370336532592773), ('representations gl', 0.4662596881389618), ('cuspidal automorphic representations', 0.4341021180152893)]"
992,992,30,992_conditional mutual information_mutual information_mutual information conditional_generalized mutual information,"['conditional mutual information', 'mutual information', 'mutual information conditional', 'generalized mutual information', 'based mutual information', 'mutual information mi', 'mutual information cmi', 'information estimation', 'shannon mutual information', 'information theoretic']","['On Study of Mutual Information and its Estimation Methods   The presence of mutual information in the research of deep learning has grown\nsignificantly. It has been proven that mutual information can be a good\nobjective function to build a robust deep learning model. Most of the\nresearches utilize estimation methods to approximate the true mutual\ninformation. This technical report delivers an extensive study about\ndefinitions as well as properties of mutual information. This article then\ndelivers some reviews and current drawbacks of mutual information estimation\nmethods afterward.\n', 'Diffeomorphic Information Neural Estimation   Mutual Information (MI) and Conditional Mutual Information (CMI) are\nmulti-purpose tools from information theory that are able to naturally measure\nthe statistical dependencies between random variables, thus they are usually of\ncentral interest in several statistical and machine learning tasks, such as\nconditional independence testing and representation learning. However,\nestimating CMI, or even MI, is infamously challenging due the intractable\nformulation. In this study, we introduce DINE (Diffeomorphic Information Neural\nEstimator)-a novel approach for estimating CMI of continuous random variables,\ninspired by the invariance of CMI over diffeomorphic maps. We show that the\nvariables of interest can be replaced with appropriate surrogates that follow\nsimpler distributions, allowing the CMI to be efficiently evaluated via\nanalytical solutions. Additionally, we demonstrate the quality of the proposed\nestimator in comparison with state-of-the-arts in three important tasks,\nincluding estimating MI, CMI, as well as its application in conditional\nindependence testing. The empirical evaluations show that DINE consistently\noutperforms competitors in all tasks and is able to adapt very well to complex\nand high-dimensional relationships.\n', 'Neural Estimators for Conditional Mutual Information Using Nearest\n  Neighbors Sampling   The estimation of mutual information (MI) or conditional mutual information\n(CMI) from a set of samples is a long-standing problem. A recent line of work\nin this area has leveraged the approximation power of artificial neural\nnetworks and has shown improvements over conventional methods. One important\nchallenge in this new approach is the need to obtain, given the original\ndataset, a different set where the samples are distributed according to a\nspecific product density function. This is particularly challenging when\nestimating CMI.\n  In this paper, we introduce a new technique, based on k nearest neighbors\n(k-NN), to perform the resampling and derive high-confidence concentration\nbounds for the sample average. Then the technique is employed to train a neural\nnetwork classifier and the CMI is estimated accordingly. We propose three\nestimators using this technique and prove their consistency, make a comparison\nbetween them and similar approaches in the literature, and experimentally show\nimprovements in estimating the CMI in terms of accuracy and variance of the\nestimators.\n']","[('conditional mutual information', 0.659198522567749), ('mutual information', 0.6472488045692444), ('mutual information conditional', 0.6431812644004822), ('generalized mutual information', 0.6298277378082275), ('based mutual information', 0.6211224794387817), ('mutual information mi', 0.6198923587799072), ('mutual information cmi', 0.5757502317428589), ('information estimation', 0.563378095626831), ('shannon mutual information', 0.5559911131858826), ('information theoretic', 0.46053776144981384)]"
993,993,30,993_poisson voronoi tessellation_voronoi tessellations_voronoi tessellation_tessellations,"['poisson voronoi tessellation', 'voronoi tessellations', 'voronoi tessellation', 'tessellations', 'tessellation', 'poisson voronoi', 'voronoi cells', 'high dimensional poisson', 'dimensional poisson', 'poisson point process']","['Random Tessellations -- An Overview of Models   Random tessellations are a prominent class of models in stochastic geometry.\nIn this chapter, we give an overview of mechanisms that have been used to\nformulate random tessellation models. First, the notion of a random\ntessellation and basic geometric characteristics of random tessellations are\nintroduced. Then, several model classes are presented. This includes, but is\nnot limited to, Voronoi tessellations and their weighted generalizations,\nhyperplane tessellations, and STIT tessellations. Simulation of the\ntessellation models and approaches for model fitting are also discussed.\n', ""The $\\beta$-Delaunay tessellation II: The Gaussian limit tessellation   We study the weak convergence of $\\beta$- and $\\beta'$-Delaunay tessellations\nin $\\mathbb{R}^{d-1}$ that were introduced in part I of this paper, as\n$\\beta\\to\\infty$. The limiting stationary simplicial random tessellation, which\nis called the Gaussian-Delaunay tessellation, is characterized in terms of a\nspace-time paraboloid hull process in $\\mathbb{R}^{d-1}\\times\\mathbb{R}$. The\nlatter object has previously appeared in the analysis of the number of shocks\nin the solution of the inviscid Burgers' equation and the description of the\nlocal asymptotic geometry of Gaussian random polytopes. In this paper it is\nused to define a new stationary random simplicial tessellation in\n$\\mathbb{R}^{d-1}$. As for the $\\beta$- and $\\beta'$-Delaunay tessellation, the\ndistribution of volume-power weighted typical cells in the Gaussian-Delaunay\ntessellation is explicitly identified, establishing thereby a new bridge to\nGaussian random simplices. Also major geometric characteristics of these cells\nsuch as volume moments, expected angle sums and also the cell intensities of\nthe Gaussian-Delaunay tessellation are investigated.\n"", 'Sectional Voronoi tessellations: Characterization and high-dimensional\n  limits   The intersections of beta-Voronoi, beta-prime-Voronoi and Gaussian-Voronoi\ntessellations in $\\mathbb{R}^d$ with $\\ell$-dimensional affine subspaces,\n$1\\leq \\ell\\leq d-1$, are shown to be random tessellations of the same type but\nwith different model parameters. In particular, the intersection of a classical\nPoisson-Voronoi tessellation with an affine subspace is shown to have the same\ndistribution as a certain beta-Voronoi tessellation. The geometric properties\nof the typical cell and, more generally, typical $k$-faces, of the sectional\nPoisson-Voronoi tessellation are studied in detail. It is proved that in high\ndimensions, that is as $d\\to\\infty$, the intersection of the $d$-dimensional\nPoison-Voronoi tessellation with an affine subspace of fixed dimension $\\ell$\nconverges to the $\\ell$-dimensional Gaussian-Voronoi tessellation.\n']","[('poisson voronoi tessellation', 0.7740241885185242), ('voronoi tessellations', 0.7609696388244629), ('voronoi tessellation', 0.7417832016944885), ('tessellations', 0.6964949369430542), ('tessellation', 0.6618200540542603), ('poisson voronoi', 0.5484489798545837), ('voronoi cells', 0.5379312634468079), ('high dimensional poisson', 0.5351865887641907), ('dimensional poisson', 0.504645824432373), ('poisson point process', 0.43869128823280334)]"
994,994,30,994_projective hypersurfaces_hypersurfaces weighted projective_weighted projective space_points projective space,"['projective hypersurfaces', 'hypersurfaces weighted projective', 'weighted projective space', 'points projective space', 'projective space', 'projective varieties', 'points projective', 'cubic hypersurfaces', 'weighted projective', 'hypersurfaces degree']","['A Cayley-Bacharach theorem for points in $\\mathbb{P}^n$   We prove a Cayley-Bacharach-type theorem for points in projective space\n$\\mathbb{P}^n$ that lie on a complete intersection of $n$ hypersurfaces. This\nis made possible by new bounds on the growth of the Hilbert function of almost\ncomplete intersections.\n', 'Geometry of Points Satisfying Cayley-Bacharach Conditions and\n  Applications   In this paper, we study the geometry of points in complex projective space\nthat satisfy the Cayley-Bacharach condition with respect to the complete linear\nsystem of hypersurfaces of given degree. In particular, we improve a result by\nLopez and Pirola and we show that, if $k\\geq 1$ and $\\Gamma\n=\\{P_1,\\dots,P_d\\}\\subset \\mathbb{P}^n$ is a set of distinct points satisfying\nthe Cayley-Bacharach condition with respect to\n$|\\mathcal{O}_{\\mathbb{P}^n}(k)|$, with $d\\leq h(k-h+3)-1$ and $3\\leq h\\leq 5$,\nthen $\\Gamma$ lies on a curve of degree $h-1$. Then we apply this result to the\nstudy of linear series on curves on smooth surfaces in $\\mathbb{P}^3$.\nMoreover, we discuss correspondences with null trace on smooth hypersurfaces of\n$\\mathbb{P}^n$ and on codimension $2$ complete intersections.\n', 'A Cayley-Bacharach theorem and plane configurations   In this paper, we examine linear conditions on finite sets of points in\nprojective space implied by the Cayley-Bacharach condition. In particular, by\nbounding the number of points satisfying the Cayley-Bacharach condition, we\nforce them to lie on unions of low-dimensional linear spaces. These results are\nmotivated by investigations into degrees of irrationality of complete\nintersections, which are controlled by minimum-degree rational maps to\nprojective space. As an application of our main theorem, we describe the fibers\nof such maps for certain complete intersections of codimension two.\n']","[('projective hypersurfaces', 0.6567375063896179), ('hypersurfaces weighted projective', 0.6550244092941284), ('weighted projective space', 0.6253838539123535), ('points projective space', 0.5990353226661682), ('projective space', 0.5943700671195984), ('projective varieties', 0.5635525584220886), ('points projective', 0.5467831492424011), ('cubic hypersurfaces', 0.538249135017395), ('weighted projective', 0.5364380478858948), ('hypersurfaces degree', 0.534224271774292)]"
995,995,30,995_hypergroups_absorbing primary_lattice irreducible_krasner,"['hypergroups', 'absorbing primary', 'lattice irreducible', 'krasner', 'generalization prime', 'class algebraic', 'primary', 'classical prime', 'moreover notions', 'absorbing prime']","['Classes of F-hyperideals of a Krasner F^{(m,n)}-hyperring   Krasner F^{(m,n)}-hyperring were introduced and investigated by Farshi and\nDavvaz. In this paper, our purpose is to define and characterize three classes\nof F-hyperideals in a Krasner F^{(m,n)}-hyperring, namely, prime F-hyperideals,\nmaximal F-hyperideals and primary F-hyperideals.\n', 'wsq-primary hyperideals of a Krasner (m,n)-hyperring   In this paper we aim to introduce some hyperideals such as q-primary,\n(k,n)-absorbing q-primary, sq-primary, wsq-primary hyperideals.\n', '$\\phi$-$\\delta$-$S$-primary hyperideals   Among many generalizations of primary hyperideals, weakly $n$-ary primary\nhyperideals and $n$-ary $S$-primary hyperideals have been studied recently. Let\n$S$ be an $n$-ary multiplicative set of a commutative Krasner $(m,n)$-hyperring\n$K$ and, $\\phi$ and $\\delta$ be reduction and expansion functions of\nhyperideals of $K$, respectively. The purpose of this paper is to introduce\n$n$-ary $\\phi$-$\\delta$-$S$-primary hyperideals which serve as an extension of\n$S$-primary hyperideals with the help of $\\phi$ and $\\delta$. We present some\nmain results and examples explaining the sructure of this concept. We examine\nthe relations of $n$-ary $S$-primary hyperideals with other classes of\nhyperideals and give some ways to connect them. Moreover, we give some\ncharacterizations of this notion on direct product of commutative Krasner $(m,\nn)$-hyperrings.\n']","[('hypergroups', 0.3832211494445801), ('absorbing primary', 0.34837740659713745), ('lattice irreducible', 0.30660247802734375), ('krasner', 0.2887164056301117), ('generalization prime', 0.2649464011192322), ('class algebraic', 0.2627009153366089), ('primary', 0.24405798316001892), ('classical prime', 0.2426580786705017), ('moreover notions', 0.23691613972187042), ('absorbing prime', 0.23424015939235687)]"
996,996,30,996_landau vortices_ferromagnetic_magnetization_micromagnetics,"['landau vortices', 'ferromagnetic', 'magnetization', 'micromagnetics', 'magnetic field', 'external magnetic field', 'magnetic', 'dzyaloshinskii moriya interaction', 'external magnetic', 'constant external magnetic']","['Traveling antiferromagnetic domain walls in a magnetic field   We consider an antiferromagnet in one space dimension with easy-axis\nanisotropy in a perpendicular magnetic field. We study propagating domain wall\nsolutions that can have a velocity up to a maximum $v_c$. The width of the\ndomain wall is a non-monotonic function of the velocity and it diverges to\ninfinity at $v_c$. Both features are in contrast to the case of the Lorentz\ninvariant model in the absence of the field. We further study the modification\nof the wall profile when a Dzyaloshinskii-Moriya interaction is added. Finally,\nwe present a propagating spiral expected to form when the system is forced at a\nvelocity higher than the maximum velocity for domain walls and we give\nnumerical results for the effect of the Dzyaloshinskii-Moriya interaction.\n', 'Asymptotic stability of 2-domain walls for the Landau-Lifshitz-Gilbert\n  equation in a nanowire with Dzyaloshinskii-Moriya interaction   We consider a ferromagnetic nanowire, with an energy functional $E$ with\neasy-axis in the direction $e_1$, and which takes into account the\nDzyaloshinskii-Moriya interaction. We consider configurations of the\nmagnetization which are perturbations of two well separated domain wall, and\nstudy their evolution under the Landau-Lifshitz-Gilbert flow associated to E.\nOur main result is that, if the two walls have opposite speed, these\nconfigurations are asymptotically stable, up to gauges intrinsic to the\ninvariances of the energy $E$. Our analysis builds on the framework developed\nin [4], taking advantage that it is amenable to space localisation.\n', 'Asymptotic stability of precessing domain walls for the\n  Landau-Lifshitz-Gilbert equation in a nanowire with Dzyaloshinskii-Moriya\n  interaction   We consider a ferromagnetic nanowire and we focus on an asymptotic regime\nwhere the Dzyaloshinskii-Moriya interaction is taken into account. First we\nprove a dimension reduction result via $\\Gamma$-convergence that determines a\nlimit functional $E$ defined for maps $m:\\mathbb{R}\\to \\mathbb{S}^2$ in the\ndirection $e_1$ of the nanowire. The energy functional $E$ is invariant under\ntranslations in $e_1$ and rotations about the axis $e_1$. We fully classify the\ncritical points of finite energy $E$ when a transition between $-e_1$ and $e_1$\nis imposed; these transition layers are called (static) domain walls. The\nevolution of a domain wall by the Landau-Lifshitz-Gilbert equation associated\nto $E$ under the effect of an applied magnetic field $h(t)e_1$ depending on the\ntime variable $t$ gives rise to the so-called precessing domain wall. Our main\nresult proves the asymptotic stability of precessing domain walls for small $h$\nin $L^\\infty([0, +\\infty))$ and small $H^1(\\mathbb{R})$ perturbations of the\nstatic domain wall, up to a gauge which is intrinsic to invariances of the\nfunctional $E$.\n']","[('landau vortices', 0.5203145146369934), ('ferromagnetic', 0.4720430076122284), ('magnetization', 0.4554392397403717), ('micromagnetics', 0.42755505442619324), ('magnetic field', 0.4023347496986389), ('external magnetic field', 0.3991144299507141), ('magnetic', 0.3984559178352356), ('dzyaloshinskii moriya interaction', 0.39292046427726746), ('external magnetic', 0.38831108808517456), ('constant external magnetic', 0.38806065917015076)]"
997,997,30,997_heyting algebras_heyting algebra_dualities_distributive lattices,"['heyting algebras', 'heyting algebra', 'dualities', 'distributive lattices', 'algebras respectively', 'topological duality', 'bounded distributive lattices', 'duality characterize', 'spaces dual', 'duality generalizes']","['Heyting frames and Esakia duality   We introduce the category of Heyting frames and show that it is equivalent to\nthe category of Heyting algebras and dually equivalent to the category of\nEsakia spaces. This provides a frame-theoretic perspective on Esakia duality\nfor Heyting algebras. We also generalize these results to the setting of\nBrouwerian algebras and Brouwerian semilattices by introducing the\ncorresponding categories of Brouwerian frames and extending the above\nequivalences and dual equivalences. This provides a frame-theoretic perspective\non generalized Esakia duality for Brouwerian algebras and Brouwerian\nsemilattices.\n', 'Esakia Duals of Regular Heyting Algebras   We investigate in this article regular Heyting algebras by means of Esakia\nduality. In particular, we give a characterisation of Esakia spaces dual to\nregular Heyting algebras and we show that there are continuum-many varieties of\nHeyting algebras generated by regular Heyting algebras. We also study several\nlogical applications of these classes of objects and we use them to provide\nnovel topological completeness theorems for inquisitive logic,\n$\\mathtt{DNA}$-logics and dependence logic.\n', 'Colimits of Heyting Algebras through Esakia Duality   In this note we generalize the construction, due to Ghilardi, of the free\nHeyting algebra generated by a finite distributive lattice, to the case of\narbitrary distributive lattices. Categorically, this provides an explicit\nconstruction of a left adjoint to the inclusion of Heyting algebras in the\ncategory of distributive lattices This is shown to have several applications,\nboth old and new, in the study of Heyting algebras: (1) it allows a more\nconcrete description of colimits of Heyting algebras, as well as, via duality\ntheory, limits of Esakia spaces, by knowing their description over distributive\nlattices and Priestley spaces; (2) It allows a direct proof of the amalgamation\nproperty for Heyting algebras, and of related facts; (3) it allows a proof of\nthe fact that the category of Heyting algebras is co-distributive. We also\nstudy some generalizations and variations of this construction to different\nsettings. First, we analyse some subvarieties of Heyting algebras -- such as\nBoolean algebras, $\\mathsf{KC}$ and $\\mathsf{LC}$ algebras, and show how the\nconstruction can be adapted to this setting. Second, we study the relationship\nbetween the category of image-finite posets with p-morphisms and the category\nof posets with monotone maps, showing that a variation of the above ideas\nprovides us with an appropriate general idea.\n']","[('heyting algebras', 0.5916695594787598), ('heyting algebra', 0.47104886174201965), ('dualities', 0.4649650752544403), ('distributive lattices', 0.4562680125236511), ('algebras respectively', 0.4475741982460022), ('topological duality', 0.44580379128456116), ('bounded distributive lattices', 0.4414769113063812), ('duality characterize', 0.435202956199646), ('spaces dual', 0.4333183765411377), ('duality generalizes', 0.431744247674942)]"
998,998,30,998_veronese varieties_secant varieties_secant variety_segre varieties,"['veronese varieties', 'secant varieties', 'secant variety', 'segre varieties', 'varieties segre', 'variety dimension', 'projective varieties', 'varieties', 'segre variety', 'varieties projective']","['Secant varieties of Segre-Veronese varieties\n  $\\mathbb{P}^m\\times\\mathbb{P}^n$ embedded by $\\mathcal{O}(1,2)$ are\n  non-defective for $n\\gg m^3$, $m\\geq3$   We prove that for any $m\\geq3$, $n\\gg m^3$, all secant varieties of the\nSegre-Veronese variety $\\mathbb{P}^m\\times\\mathbb{P}^n$ have the expected\ndimension. This was already proved by Abo and Brambilla in the subabundant\ncase, hence we focus on the superabundant case. We generalize an approach due\nto Brambilla and Ottaviani into a construction we call the inductant. With\nthis, the proof of non-defectivity reduces to checking a finite collection of\nbase cases, which we verify using a computer-assisted proof.\n', 'Nondefectivity of invariant secant varieties   We show that a large class of secant varieties is nondefective. In\nparticular, we positively resolve most cases of the Baur-Draisma-de Graaf\nconjecture on Grassmannian secants in large dimensions. Our result improves the\nknown bounds on nondefectivity for various other secant varieties, including\nChow varieties, Segre-Veronese varieties and Gaussian moment varieties. We also\ngive bounds for identifiability and the generic ranks.\n', 'On secant defectiveness and identifiability of Segre-Veronese varieties   We give an almost asymptotically sharp bound for the non secant defectiveness\nand identifiability of Segre-Veronese varieties. We also provide new examples\nof defective Segre-Veronese varieties.\n']","[('veronese varieties', 0.7172518372535706), ('secant varieties', 0.7026985287666321), ('secant variety', 0.6447944641113281), ('segre varieties', 0.5969619154930115), ('varieties segre', 0.5705589056015015), ('variety dimension', 0.550108790397644), ('projective varieties', 0.524725079536438), ('varieties', 0.5158067345619202), ('segre variety', 0.5078046321868896), ('varieties projective', 0.5039479732513428)]"
999,999,30,999_puzzles_grids_tiles_cubes,"['puzzles', 'grids', 'tiles', 'cubes', 'hexagonal', 'distinct configurations', 'scrambling', 'grid', 'dimensional cube', 'sudoku']","[""Sliding Block Puzzles with a Twist: On Segerman's 15+4 Puzzle   Segerman's 15+4 puzzle is a hinged version of the classic 15-puzzle, in which\nthe tiles rotate as they slide around. In 1974, Wilson classified the groups of\nsolutions to sliding block puzzles. We generalize Wilson's result to puzzles\nlike the 15+4 puzzle, where the tiles can rotate, and the sets of solutions are\nsubgroups of the generalized symmetric groups. Aside from two exceptional\ncases, we see that the group of solutions to such a puzzle is always either the\nentire generalized symmetric group or one of two special subgroups of index\ntwo.\n"", 'Mathematical Definition and Systematization of Puzzle Rules   While logic puzzles have engaged individuals through problem-solving and\ncritical thinking, the creation of new puzzle rules has largely relied on\nad-hoc processes. Pencil puzzles, such as Slitherlink and Sudoku, represent a\nprominent subset of these games, celebrated for their intellectual challenges\nrooted in combinatorial logic and spatial reasoning. Despite extensive research\ninto solving techniques and automated problem generation, a unified framework\nfor systematic and scalable rule design has been lacking. Here, we introduce a\nmathematical framework for defining and systematizing pencil puzzle rules. This\nframework formalizes grid elements, their positional relationships, and\niterative composition operations, allowing for the incremental construction of\nstructures that form the basis of puzzle rules. Furthermore, we establish a\nformal method to describe constraints and domains for each structure, ensuring\nsolvability and coherence. Applying this framework, we successfully formalized\nthe rules of well-known Nikoli puzzles, including Slitherlink and Sudoku,\ndemonstrating the formal representation of a significant portion (approximately\none-fourth) of existing puzzles. These results validate the potential of the\nframework to systematize and innovate puzzle rule design, establishing a\npathway to automated rule generation. By providing a mathematical foundation\nfor puzzle rule creation, this framework opens avenues for computers,\npotentially enhanced by AI, to design novel puzzle rules tailored to player\npreferences, expanding the scope of puzzle diversity. Beyond its direct\napplication to pencil puzzles, this work illustrates how mathematical\nframeworks can bridge recreational mathematics and algorithmic design, offering\ntools for broader exploration in logic-based systems, with potential\napplications in educational game design, personalized learning, and\ncomputational creativity.\n', 'Parity Property of Hexagonal Sliding Puzzles   We study the puzzle graphs of hexagonal sliding puzzles of various shapes and\nwith various numbers of holes. The puzzle graph is a combinatorial model which\ncaptures the solvability and the complexity of sequential mechanical puzzles.\nQuestions relating to the puzzle graph have been previously studied and\nresolved for the 15 Puzzle which is the most famous, and unsolvable, square\nsliding puzzle of all time. It is known that for square puzzles such as the 15\nPuzzle, solvability depends on a parity property that splits the puzzle graph\ninto two components. In the case of hexagonal sliding puzzles, we get more\ninteresting parity properties that depend on the shape of the boards and on the\nmissing tiles or holes on the board. We show that for large-enough hexagonal,\ntriangular, or parallelogram-shaped boards with hexagonal tiles, all puzzles\nwith three or more holes are solvable. For puzzles with two or more holes, we\ngive a solvability criterion involving both a parity property and the placement\nof tiles in tight corners of the board. The puzzle graph is a discrete model\nfor the configuration space of hard tiles (hexagons or squares) moving on\ndifferent tessellation-based domains. Understanding the combinatorics of the\npuzzle graph could lead to understanding some aspects of the topology of these\nconfiguration spaces.\n']","[('puzzles', 0.5984258055686951), ('grids', 0.46819162368774414), ('tiles', 0.45553916692733765), ('cubes', 0.4213009476661682), ('hexagonal', 0.41478231549263), ('distinct configurations', 0.4142628610134125), ('scrambling', 0.39850565791130066), ('grid', 0.3873836100101471), ('dimensional cube', 0.3855922520160675), ('sudoku', 0.38272371888160706)]"
1000,1000,30,1000_homology group coefficients_torelli groups_homology group_integral homology group,"['homology group coefficients', 'torelli groups', 'homology group', 'integral homology group', 'first homology group', 'torelli group', 'homology', 'top homology', 'rational homology', 'group genus']","['The Johnson homomorphism and its kernel   We give a new proof of a celebrated theorem of Dennis Johnson that asserts\nthat the kernel of the Johnson homomorphism on the Torelli subgroup of the\nmapping class group is generated by separating twists. In fact, we prove a more\ngeneral result that also applies to ""subsurface Torelli groups"". Using this, we\nextend Johnson\'s calculation of the rational abelianization of the Torelli\ngroup not only to the subsurface Torelli groups, but also to finite-index\nsubgroups of the Torelli group that contain the kernel of the Johnson\nhomomorphism.\n', ""Torelli group, Johnson kernel and invariants of homology spheres   In the late 1980's, it was shown that the Casson invariant appears in the\ndifference between the two filtrations of the Torelli group: the lower central\nseries and the Johnson filtration, and that its core part was identified with\nthe secondary characteristic class $d_1$ associated with the fact that the\nfirst $\\mathrm{MMM}$ class vanishes on the Torelli group (however it turned out\nthat Johnson proved the former part highly likely prior to the above, see\nRemark 1.1). This secondary class $d_1$ is a rational generator of\n$H^1(\\mathcal{K}_g;\\mathbb{Z})^{\\mathcal{M}_g}\\cong\\mathbb{Z}$ where\n$\\mathcal{K}_g$ denotes the Johnson subgroup of the mapping class group\n$\\mathcal{M}_g$. Hain proved, as a particular case of his fundamental result,\nthat this is the only difference in degree $2$. In this paper, we prove that no\nother invariant than the above gives rise to new rational difference between\nthe two filtrations up to degree $6$. We apply this to determine\n$H_1(\\mathcal{K}_g;\\mathbb{Q})$ explicitly by computing the description given\nby Dimca, Hain and Papadima. We also show that any finite type rational\ninvariant of homology $3$-spheres of degrees up to $6$, including the second\nand the third Ohtsuki invariants, can be expressed by $d_1$ and lifts of\nJohnson homomorphisms.\n"", 'On the top homology group of Johnson kernel   The action of the mapping class group $\\mathrm{Mod}_g$ of an oriented surface\n$\\Sigma_g$ on the lower central series of $\\pi_1(\\Sigma_g)$ defines the\ndescending filtration in $\\mathrm{Mod}_g$ called the Johnson filtration. The\nfirst two terms of it are the Torelli group $\\mathcal{I}_g$ and the Johnson\nkernel $\\mathcal{K}_g$. By a fundamental result of Johnson (1985),\n$\\mathcal{K}_g$ is the subgroup of $\\mathrm{Mod}_g$ generated by all Dehn\ntwists about separating curves. In 2007, Bestvina, Bux, and Margalit showed the\ngroup $\\mathcal{K}_g$ has cohomological dimension $2g-3$. We prove that the top\nhomology group $H_{2g-3}(\\mathcal{K}_g)$ is not finitely generated. In fact, we\nshow that it contains a free abelian subgroup of infinite rank, hence, the\nvector space $H_{2g-3}(\\mathcal{K}_g,\\mathbb{Q})$ is infinite-dimensional.\nMoreover, we prove that $H_{2g-3}(\\mathcal{K}_g,\\mathbb{Q})$ is not finitely\ngenerated as a module over the group ring $\\mathbb{Q}[\\mathcal{I}_g]$.\n']","[('homology group coefficients', 0.606616735458374), ('torelli groups', 0.6038641333580017), ('homology group', 0.6015375256538391), ('integral homology group', 0.5984874367713928), ('first homology group', 0.5569496154785156), ('torelli group', 0.5459171533584595), ('homology', 0.5051299333572388), ('top homology', 0.5042839646339417), ('rational homology', 0.5019770860671997), ('group genus', 0.4935305714607239)]"
1001,1001,30,1001_bilayer graphene_graphene_dirac fermions_quantum electrodynamics,"['bilayer graphene', 'graphene', 'dirac fermions', 'quantum electrodynamics', 'two dimensional dirac', 'supersymmetric quantum', 'supersymmetric quantum mechanics', 'bilayer', 'quantum mechanics', 'condensed matter physics']","['Electron in bilayer graphene with magnetic fields leading to shape\n  invariant potentials   The quantum behavior of electrons in bilayer graphene with applied magnetic\nfields is addressed. By using second-order supersymmetric quantum mechanics the\nproblem is transformed into two intertwined one dimensional stationary\nSchr\\""odinger equations whose potentials are required to be shape invariant.\nAnalytical solutions for the energy bound states are obtained for several\nmagnetic fields. The associated spectrum is analyzed, and the probability and\ncurrent densities are determined.\n', 'Confluent supersymmetric algorithm for bilayer graphene   External magnetic field profiles leading to equidistant and partially\nequidistant bilayer graphene spectra within the tight-binding model are\nobtained. This is achieved by implementing the integral and differential\nversions of the second-order confluent algorithm to the harmonic oscillator for\narbitrary real factorization energies. Additionally, new Barut-Girardello and\nGilmore-Perelomov coherent states for bilayer graphene are derived, for both\ndiagonal and non-diagonal ladder operators. Their time evolution is analyzed,\nfinding temporal stability and cyclic evolution in some cases. This fact is\ncontrasted with the non-cyclic evolution of bilayer graphene coherent states\nobtained when using two different factorization energies. Likewise, the\ngeometric phase and uncertainty product of the quadratures for the previously\nobtained coherent states are studied.\n', 'Bilayer graphene coherent states   In this paper we consider the interaction of electrons in bilayer graphene\nwith a constant homogeneous magnetic field which is orthogonal to the bilayer\nsurface. Departing from the energy eigenstates of the effective Hamiltonian,\nthe corresponding coherent states will be constructed. For doing this, first we\nwill determine appropriate creation and annihilation operators in order to\nsubsequently derive the coherent states as eigenstates of the annihilation\noperator with complex eigenvalue. Then, we will calculate some physical\nquantities, as the Heisenberg uncertainty relation, the probabilities and\ncurrent density as well as the mean energy value. Finally, we will explore the\ntime evolution for these states and we will compare it with the corresponding\nevolution for monolayer graphene coherent states.\n']","[('bilayer graphene', 0.731662929058075), ('graphene', 0.6096180081367493), ('dirac fermions', 0.380149245262146), ('quantum electrodynamics', 0.3770460784435272), ('two dimensional dirac', 0.36941108107566833), ('supersymmetric quantum', 0.367309033870697), ('supersymmetric quantum mechanics', 0.36510559916496277), ('bilayer', 0.3465995192527771), ('quantum mechanics', 0.32098743319511414), ('condensed matter physics', 0.31787756085395813)]"
1002,1002,30,1002_spiking neurons_networks spiking neurons_networks spiking_chaotic dynamics,"['spiking neurons', 'networks spiking neurons', 'networks spiking', 'chaotic dynamics', 'spiking', 'oscillations', 'bursting', 'bifurcation', 'chaos solitons', 'excitable systems']","['Towards a new classification of bursting patterns: review & extensions   The mathematical classification of complex bursting oscillations in\nmultiscale excitable systems, seen for example in physics and neuroscience, has\nbeen the subject of active enquiry since the early 1980s. This classification\nproblem is fundamental as it also establishes analytical and numerical\nfoundations for studying complex temporal behaviours in multiple timescale\nmodels. This manuscript begins by reviewing the seminal works of Rinzel and\nIzhikevich in classifying bursting patterns of excitable cell models. Moreover,\nwe recall an alternative, yet complementary, mathematical classification\napproach by Golubitsky, which together with the Rinzel-Izhikevich proposals\nprovide the state-of-the-art foundations to the classification problem.\nUnexpectedly, while keeping within the Rinzel-Izhikevich framework, we find\nnovel cases of bursting mechanisms not considered before. Moving beyond the\nstate-of-the-art, we identify novel bursting mechanisms that fall outside the\ncurrent classifications. This leads us towards a new classification, which\nrequires the analysis of both the fast and the slow subsystems of an underlying\nslow-fast model. This new classification allows the dynamical dissection of a\nlarger class of bursters. To substantiate this, we add a new class of bursters\nwith at least two slow variables, which we denote folded-node bursters, to\nconvey the idea that the bursts are initiated or annihilated via a folded-node\nsingularity. In fact, there are two main families of folded-node bursters,\ndepending upon the phase of the bursting cycle during which folded-node\ndynamics occurs. If it occurs during the silent phase, we obtain the classical\nfolded-node bursting (or simply folded-node bursting). If it occurs during the\nactive phase, we have cyclic folded-node bursting. We classify both families\nand give examples of minimal systems displaying these novel types of bursting\nbehaviour.\n', ""Hyperchaos and complex dynamical regimes in $N$-dimensional neuron\n  lattices   We study the dynamics of $N$-dimensional lattices of nonchaotic Rulkov\nneurons coupled with a flow of electrical current. We consider both\nnearest-neighbor and next-nearest-neighbor couplings, homogeneous and\nheterogeneous neurons, and small and large lattices over a wide range of\nelectrical coupling strengths. As the coupling strength is varied, the neurons\nexhibit a number of complex dynamical regimes, including unsynchronized chaotic\nspiking, local quasi-bursting, synchronized chaotic bursting, and synchronized\nhyperchaos. For lattices in higher spatial dimensions, we discover dynamical\neffects arising from the ``destructive interference'' of many connected neurons\nand miniature ``phase transitions'' from coordinated spiking threshold\ncrossings. In large two- and three-dimensional neuron lattices, we observe\nemergent dynamics such as local synchronization, quasi-synchronization, and lag\nsynchronization. These results illustrate the rich dynamics that emerge from\ncoupled neurons in multiple spatial dimensions, highlighting how\ndimensionality, connectivity, and heterogeneity critically shape the collective\nbehavior of neuronal systems.\n"", 'The role of resonator neuron in the dynamics of two coupled integrator\n  and resonator neurons of different types of excitability   In this manuscript, a silent resonator neuron is coupled with a spiking\nintegrator neuron through the gap junction, when the coupled neurons are of\ndifferent types of excitability and none of the coupled neurons exhibit mixed\nmode oscillations and bursting oscillations intrinsically. By using dynamical\nsystems theory (e.g. the bifurcation theory), all the observed oscillation\npatterns and the transition mechanisms between them are investigated, when one\nof the coupling strengths is fixed and the other is varied. It is noticeable\nthat, there is an interval in the parameter space, for the parameter values\nwithin which the coupled system is multi-stable. This multistability\ncorresponds to the coexistence of mixed mode oscillations, bursting\noscillations and subthreshold oscillations of the resonator neuron. In\naddition, some interval in the parameter space is introduced such that, for the\nvalues of the coupling strength within which the resonator neuron is in tonic\nspiking mode, while for the values of the coupling strength outside which the\nresonator neuron exhibits subthreshold oscillations. It is also verified that\nthe final synchronization of the coupled neurons actually corresponds to the\nsynchronization of tonic spiking oscillations of the integrator neuron and\none-bursting oscillations of the resonator neuron.\n']","[('spiking neurons', 0.6097806692123413), ('networks spiking neurons', 0.6060200929641724), ('networks spiking', 0.5524938106536865), ('chaotic dynamics', 0.5149201154708862), ('spiking', 0.4905618727207184), ('oscillations', 0.4876546263694763), ('bursting', 0.48298197984695435), ('bifurcation', 0.4705551862716675), ('chaos solitons', 0.4646303057670593), ('excitable systems', 0.45507559180259705)]"
1003,1003,30,1003_dispersal rates_dispersal rate_random dispersal_dispersal,"['dispersal rates', 'dispersal rate', 'random dispersal', 'dispersal', 'population dynamics', 'populations time', 'persistence extinction', 'population models', 'diffusion rates', 'metapopulation']","['On a population model in discrete periodic habitat. I. spreading speed\n  and optimal dispersal strategy   Starting from an age-structured diffusive population growth law for single\nspecies in a discrete and periodic habitat, we formulate a stage structured\npopulation model with spatially periodic dispersal, mortality and recruitment.\nWith a KPP type setting, after establishing the fundamental solution of a\ndiscretized heat equation with spatially periodic dispersal, we apply some\nrecently developed dynamical system theories to obtain the existence of the\nspreading speed and its coincidence with the minimal speed of pulsating waves,\nas well as the variational characterization of the speed, by which we further\nanalyze how the habitat periodicity influences the speed. In particular, there\nis a unique optimal dispersal strategy to maximize the speed.\n', 'Effects of nonlocal dispersal strategies and heterogeneous environment\n  on total population   In this paper, we consider the following single species model with nonlocal\ndispersal strategy $$ d\\mathcal {L} [\\theta] (x,t) + \\theta(x,t) [m(x)-\n\\theta(x,t)]=0 , $$ where $\\mathcal {L}$ denotes the nonlocal diffusion\noperator, and investigate how the dispersal rate of the species and the\ndistribution of resources affect the total population. First, we show that the\nupper bound for the ratio between total population and total resource is\n$C\\sqrt{d}$. Moreover, examples are constructed to indicate that this upper\nbound is optimal. Secondly, for a type of simplified nonlocal diffusion\noperator, we prove that if $ \\frac{\\sup m}{\\inf m}<\\frac{\\sqrt{5}+1}{2}$, the\ntotal population as a function of dispersal rate $d$ admits exactly one local\nmaximum point in $\\displaystyle (\\inf m, \\sup m)$. These results reveal\nessential discrepancies between local and nonlocal dispersal strategies.\n', 'Dispersal-induced growth or decay in a time-periodic environment   This paper is a follow-up to a previous work where we considered populations\nwith time-varying growth rates living in patches and irreducible migration\nmatrix between the patches. Each population, when isolated, would become\nextinct. Dispersal-induced growth (DIG) occurs when the populations are able to\npersist and grow exponentially when dispersal among the populations is present.\nWe provide a mathematical analysis of this phenomenon, in the context of a\ndeterministic model with periodic variation of growth rates and migration. The\nmigration matrix can be reducible, so that the results apply in the case,\nimportant for applications, where there is migration in one direction in one\nseason and in the other direction in another season. We also consider\ndispersal-induced decay (DID), where each population, when isolated, grows\nexponentially, while populations die out when dispersal between populations is\npresent.\n']","[('dispersal rates', 0.7541925311088562), ('dispersal rate', 0.7434231638908386), ('random dispersal', 0.7159550786018372), ('dispersal', 0.691733717918396), ('population dynamics', 0.5963284969329834), ('populations time', 0.5904368758201599), ('persistence extinction', 0.5288154482841492), ('population models', 0.5240499377250671), ('diffusion rates', 0.47165507078170776), ('metapopulation', 0.4458658993244171)]"
1004,1004,30,1004_gushel mukai fourfolds_mukai fourfolds_moduli spaces stable_moduli spaces,"['gushel mukai fourfolds', 'mukai fourfolds', 'moduli spaces stable', 'moduli spaces', 'gushel mukai', 'k3 surfaces', 'moduli spaces bridgeland', 'conjecture kuznetsov', 'moduli spaces sheaves', 'moduli spaces semistable']","['Stability conditions and moduli spaces for Kuznetsov components of\n  Gushel-Mukai varieties   We prove the existence of Bridgeland stability conditions on the Kuznetsov\ncomponents of Gushel-Mukai varieties, and describe the structure of moduli\nspaces of Bridgeland semistable objects in these categories in the\neven-dimensional case. As applications, we construct a new infinite series of\nunirational locally complete families of polarized hyperk\\""{a}hler varieties of\nK3 type, and characterize Hodge-theoretically when the Kuznetsov component of\nan even-dimensional Gushel-Mukai variety is equivalent to the derived category\nof a K3 surface.\n', 'Stability conditions on Kuznetsov components of Gushel-Mukai threefolds\n  and Serre functor   We show that the stability conditions on the Kuznetsov component of a\nGushel-Mukai threefold, constructed by Bayer, Lahoz, Macr\\`i and Stellari, are\npreserved by the Serre functor, up to the action of the universal cover of\n$\\text{GL}^+_2(\\mathbb{R})$. As application, we construct stability conditions\non the Kuznetsov component of special Gushel-Mukai fourfolds.\n', 'Conics on Gushel-Mukai fourfolds, EPW sextics and Bridgeland moduli\n  spaces   We identify the double dual EPW sextic $\\widetilde{Y}_{A^{\\perp}}$ and the\ndouble EPW sextic $\\widetilde{Y}_A$, associated with a very general\nGushel-Mukai fourfold $X$, with the Bridgeland moduli spaces of stable objects\nof character $\\Lambda_1$ and $\\Lambda_2$ in the Kuznetsov component\n$\\mathcal{K}u(X)$. This provides an affirmative answer to a question of\nPerry-Pertusi-Zhao. As an application, we prove a conjecture of Kuznetsov-Perry\nfor very general Gushel-Mukai fourfolds.\n']","[('gushel mukai fourfolds', 0.6928907632827759), ('mukai fourfolds', 0.6244790554046631), ('moduli spaces stable', 0.5515481233596802), ('moduli spaces', 0.5023621320724487), ('gushel mukai', 0.5003648400306702), ('k3 surfaces', 0.4864964187145233), ('moduli spaces bridgeland', 0.45596185326576233), ('conjecture kuznetsov', 0.4433958828449249), ('moduli spaces sheaves', 0.4363171458244324), ('moduli spaces semistable', 0.4130195677280426)]"
1005,1005,30,1005_parallel sgd_stochastic gradient descent_distributed stochastic optimization_efficient asynchronous,"['parallel sgd', 'stochastic gradient descent', 'distributed stochastic optimization', 'efficient asynchronous', 'asynchronous parallel', 'sgd methods', 'distributed optimization', 'convergence asynchronous', 'distributed asynchronous', 'asynchronous stochastic']","[""On the Convergence Analysis of Asynchronous SGD for Solving Consistent\n  Linear Systems   In the realm of big data and machine learning, data-parallel, distributed\nstochastic algorithms have drawn significant attention in the present\ndays.~While the synchronous versions of these algorithms are well understood in\nterms of their convergence, the convergence analyses of their asynchronous\ncounterparts are not widely studied. In this paper, we propose and analyze a\n{\\it distributed, asynchronous parallel} SGD in light of solving an arbitrary\nconsistent linear system by reformulating the system into a stochastic\noptimization problem as studied by Richt\\'{a}rik and Tak\\'{a}\\~{c} in [35]. We\ncompare the convergence rates of our asynchronous SGD algorithm with the\nsynchronous parallel algorithm proposed by Richt\\'{a}rik and Tak\\'{a}\\v{c} in\n[35] under different choices of the hyperparameters---the stepsize, the damping\nfactor, the number of processors, and the delay factor. We show that our\nasynchronous parallel SGD algorithm also enjoys a global linear convergence\nrate, similar to the {\\em basic} method and the synchronous parallel method in\n[35] for solving any arbitrary consistent linear system via stochastic\nreformulation. We also show that our asynchronous parallel SGD improves upon\nthe {\\em basic} method with a better convergence rate when the number of\nprocessors is larger than four. We further show that this asynchronous approach\nperforms asymptotically better than its synchronous counterpart for certain\nlinear systems. Moreover, for certain linear systems, we compute the minimum\nnumber of processors required for which our asynchronous parallel SGD is\nbetter, and find that this number can be as low as two for some ill-conditioned\nproblems.\n"", ""Ringmaster ASGD: The First Asynchronous SGD with Optimal Time Complexity Asynchronous Stochastic Gradient Descent (Asynchronous SGD) is a cornerstone method for parallelizing learning in distributed machine learning. However, its performance suffers under arbitrarily heterogeneous computation times across workers, leading to suboptimal time complexity and inefficiency as the number of workers scales. While several Asynchronous SGD variants have been proposed, recent findings by Tyurin & Richt\\'arik (NeurIPS 2023) reveal that none achieve optimal time complexity, leaving a significant gap in the literature. In this paper, we propose Ringmaster ASGD, a novel Asynchronous SGD method designed to address these limitations and tame the inherent challenges of Asynchronous SGD. We establish, through rigorous theoretical analysis, that Ringmaster ASGD achieves optimal time complexity under arbitrarily heterogeneous and dynamically fluctuating worker computation times. This makes it the first Asynchronous SGD method to meet the theoretical lower bounds for time complexity in such scenarios."", 'Second-Order Convergence of Asynchronous Parallel Stochastic Gradient\n  Descent: When Is the Linear Speedup Achieved?   In machine learning, asynchronous parallel stochastic gradient descent\n(APSGD) is broadly used to speed up the training process through multi-workers.\nMeanwhile, the time delay of stale gradients in asynchronous algorithms is\ngenerally proportional to the total number of workers, which brings additional\ndeviation from the accurate gradient due to using delayed gradients. This may\nhave a negative influence on the convergence of the algorithm. One may ask: How\nmany workers can we use at most to achieve a good convergence and the linear\nspeedup?\n  In this paper, we consider the second-order convergence of asynchronous\nalgorithms in non-convex optimization. We investigate the behaviors of APSGD\nwith consistent read near strictly saddle points and provide a theoretical\nguarantee that if the total number of workers is bounded by\n$\\widetilde{O}(K^{1/3}M^{-1/3})$ ($K$ is the total steps and $M$ is the\nmini-batch size), APSGD will converge to good stationary points ($||\\nabla\nf(x)||\\leq \\epsilon, \\nabla^2 f(x)\\succeq -\\sqrt{\\epsilon}\\bm{I},\n\\epsilon^2\\leq O(\\sqrt{\\frac{1}{MK}}) $) and the linear speedup is achieved.\nOur works give the first theoretical guarantee on the second-order convergence\nfor asynchronous algorithms. The technique we provide can be generalized to\nanalyze other types of asynchronous algorithms to understand the behaviors of\nasynchronous algorithms in distributed asynchronous parallel training.\n']","[('parallel sgd', 0.644711434841156), ('stochastic gradient descent', 0.6413599848747253), ('distributed stochastic optimization', 0.6224789023399353), ('efficient asynchronous', 0.600088894367218), ('asynchronous parallel', 0.5857590436935425), ('sgd methods', 0.5765288472175598), ('distributed optimization', 0.5698694586753845), ('convergence asynchronous', 0.5620310306549072), ('distributed asynchronous', 0.560883641242981), ('asynchronous stochastic', 0.5472971200942993)]"
1006,1006,30,1006_sobolev maps_sobolev mappings_sobolev mapping_sobolev extension,"['sobolev maps', 'sobolev mappings', 'sobolev mapping', 'sobolev extension', 'sobolev spaces', 'sobolev space', 'mathcal sobolev', 'sobolev estimate', 'fractional sobolev', 'sobolev']","['Lifting of fractional Sobolev mappings to noncompact covering space   Given compact Riemannian manifolds $\\mathcal{M}$ and $\\mathcal{N}$, a\nRiemannian covering $\\pi : \\smash{\\widetilde{\\mathcal{N}}} \\to \\mathcal{N}$ by\na noncompact covering space $\\smash{\\widetilde{\\mathcal{N}}}$, $1 < p < \\infty$\nand $0 < s < 1$, the space of liftings of fractional Sobolev maps in\n$\\smash{\\dot{W}^{s, p}} (\\mathcal{M}, \\mathcal{N})$ is characterized when $sp >\n1$ and an optimal nonlinear fractional Sobolev estimate is obtained when\nmoreover $sp \\ge \\dim \\mathcal{M}$. A nonlinear characterization of the sum of\nspaces $\\smash{\\dot{W}^{s, p}} (\\mathcal{M}, \\mathbb{R}) + \\smash{\\dot{W}^{1,\nsp}} (\\mathcal{M}, \\mathbb{R})$ is also provided.\n', 'The extension of traces for Sobolev mappings between manifolds   The compact Riemannian manifolds $\\mathcal{M}$ and $\\mathcal{N}$ for which\nthe trace operator from the first-order Sobolev space of mappings\n$\\smash{\\dot{W}}^{1, p} (\\mathcal{M}, \\mathcal{N})$ to the fractional\nSobolev-Slobodecki\\u{\\i} space $\\smash{\\smash{\\dot{W}}^{1 - 1/p, p}} (\\partial\n\\mathcal{M}, \\mathcal{N})$ is surjective when $1 < p < \\dim \\mathcal{M}$ are\ncharacterised. The traces are extended using a new construction which can be\ncarried out assuming the absence of the known topological and analytical\nobstructions. When $p \\ge \\dim \\mathcal{M}$ the same construction provides a\nSobolev extension with linear estimates for maps that have a continuous\nextension, provided that there are no known analytical obstructions to such a\ncontrol.\n', 'Lifting in compact covering spaces for fractional Sobolev mappings   Let $\\pi : \\widetilde{\\mathcal{N}} \\to \\mathcal{N}$ be a Riemannian covering,\nwith $\\mathcal{N}$, $\\widetilde{\\mathcal{N}}$ smooth compact connected\nRiemannian manifolds. If $\\mathcal{M}$ is an $m$-dimensional compact\nsimply-connected Riemannian manifold, $0<s<1$ and $2 \\le sp< m$, we prove that\nevery mapping $u \\in W^{s, p} (\\mathcal{M}, \\mathcal{N})$ has a lifting in\n$W^{s,p}$, i.e., we have $u = \\pi \\, \\circ \\, \\widetilde{u}$ for some mapping\n$\\widetilde{u} \\in W^{s, p} (\\mathcal{M}, \\widetilde{\\mathcal{N}})$. Combined\nwith previous contributions of Bourgain, Brezis and Mironescu and Bethuel and\nChiron, our result \\emph{settles completely} the question of the lifting in\nSobolev spaces over covering spaces. The proof relies on an a priori estimate\nof the oscillations of $W^{s,p}$ maps with $0<s<1$ and $sp>1$, in dimension\n$1$. Our argument also leads to the existence of a lifting when $0<s<1$ and\n$1<sp<2\\le m$, provided there is no topological obstruction on $u$, i.e., $u =\n\\pi \\, \\circ \\, \\widetilde{u}$ holds in this range provided $u$ is in the\nstrong closure of $C^\\infty({\\mathcal{M}}, \\mathcal{N})$. However, when\n$0<s<1$, $sp = 1$ and $m\\ge 2$, we show that an (analytical) obstruction still\narises, even in absence of topological obstructions. More specifically, we\nconstruct some map $u\\in W^{s,p}(\\mathcal{M},\\mathcal{N})$ in the strong\nclosure of $C^\\infty({\\mathcal{M}}, \\mathcal{N})$, such that $u = \\pi \\, \\circ\n\\, \\widetilde{u}$ does not hold for any $\\widetilde{u} \\in W^{s, p}\n({\\mathcal{M}}, \\widetilde{\\mathcal{N}} )$.\n']","[('sobolev maps', 0.6234738826751709), ('sobolev mappings', 0.5998948812484741), ('sobolev mapping', 0.5634405016899109), ('sobolev extension', 0.5621861219406128), ('sobolev spaces', 0.540526270866394), ('sobolev space', 0.5368064641952515), ('mathcal sobolev', 0.5325072407722473), ('sobolev estimate', 0.5308488607406616), ('fractional sobolev', 0.507744550704956), ('sobolev', 0.46106967329978943)]"
1007,1007,30,1007_discrete conformal_combinatorial curvature_conformal structures_discrete curvature,"['discrete conformal', 'combinatorial curvature', 'conformal structures', 'discrete curvature', 'curvature discrete', 'conformal theory', 'polyhedral surfaces', 'conformal maps', 'conformal', 'curvatures']","[""Parameterized combinatorial curvatures and parameterized combinatorial\n  curvature flows for discrete conformal structures on polyhedral surfaces   Discrete conformal structure on polyhedral surfaces is a discrete analogue of\nthe smooth conformal structure on surfaces that assigns discrete metrics by\nscalar functions defined on vertices. In this paper, we introduce combinatorial\n$\\alpha$-curvature for discrete conformal structures on polyhedral surfaces,\nwhich is a parameterized generalization of the classical combinatorial\ncurvature. Then we prove the local and global rigidity of combinatorial\n$\\alpha$-curvature with respect to discrete conformal structures on polyhedral\nsurfaces, which confirms parameterized Glickenstein rigidity conjecture. To\nstudy the Yamabe problem for combinatorial $\\alpha$-curvature, we introduce\ncombinatorial $\\alpha$-Ricci flow for discrete conformal structures on\npolyhedral surfaces, which is a generalization of Chow-Luo's combinatorial\nRicci flow for Thurston's circle packings and Luo's combinatorial Yamabe flow\nfor vertex scaling on polyhedral surfaces. To handle the potential\nsingularities of the combinatorial $\\alpha$-Ricci flow, we extend the flow\nthrough the singularities by extending the inner angles in triangles by\nconstants. Under the existence of a discrete conformal structure with\nprescribed combinatorial curvature, the solution of extended combinatorial\n$\\alpha$-Ricci flow is proved to exist for all time and converge exponentially\nfast for any initial value. This confirms a parameterized generalization of\nanother conjecture of Glickenstein on the convergence of combinatorial Ricci\nflow, gives an almost equivalent characterization of the solvability of Yamabe\nproblem for combinatorial $\\alpha$-curvature in terms of combinatorial\n$\\alpha$-Ricci flow and provides an effective algorithm for finding discrete\nconformal structures with prescribed combinatorial $\\alpha$-curvatures.\n"", ""A new class of discrete conformal structures on surfaces with boundary   We introduce a new class of discrete conformal structures on surfaces with\nboundary, which have nice interpolations in 3-dimensional hyperbolic geometry.\nThen we prove the global rigidity of the new discrete conformal structures\nusing variational principles, which is a complement of Guo-Luo's rigidity of\nthe discrete conformal structures and Guo's rigidity of vertex scaling on\nsurface with boundary. As a result, new convexities of the volume of\ngeneralized hyperbolic pyramids with right-angled hyperbolic hexagonal bases\nare obtained. Motivated by Chow-Luo's combinatorial Ricci flow and Luo's\ncombinatorial Yamabe flow on closed surfaces, we further introduce\ncombinatorial Ricci flow and combinatorial Calabi flows to deform the new\ndiscrete conformal structures on surfaces with boundary. The basic properties\nof these combinatorial curvature flows are established. These combinatorial\ncurvature flows provide effective algorithms for constructing hyperbolic\nmetrics on surfaces with totally geodesic boundary components of prescribed\nlengths.\n"", ""Deformation of discrete conformal structures on surfaces   Glickenstein introduced the discrete conformal structures on polyhedral\nsurfaces in an axiomatic approach from Riemannian geometry perspective. It\nincludes Thurston's circle packings, Bowers-Stephenson's inversive distance\ncircle packings and Luo's vertex scalings as special cases. In this paper, we\nstudy the deformation of Glickenstein's discrete conformal structures by\ncombinatorial curvature flows. The combinatorial Ricci flow for Glickenstein's\ndiscrete conformal structures on triangulated surfaces is a generalization of\nChow-Luo's combinatorial Ricci flow for Thurston's circle packings and Luo's\ncombinatorial Yamabe flow for vertex scalings. We prove that the solution of\nthe combinatorial Ricci flow for Glickenstein's discrete conformal structures\non triangulated surfaces can be uniquely extended. Furthermore, under some\nnecessary conditions, we prove that the solution of the extended combinatorial\nRicci flow on a triangulated surface exists for all time and converges\nexponentially fast for any initial value. We further introduce the\ncombinatorial Calabi flow for Glickenstein's discrete conformal structures on\ntriangulated surfaces and study the basic properties of the flow. These\ncombinatorial curvature flows provide effective algorithms for finding\npiecewise constant curvature metrics on surfaces with prescribed combinatorial\ncurvatures.\n""]","[('discrete conformal', 0.6566406488418579), ('combinatorial curvature', 0.6124364137649536), ('conformal structures', 0.55103600025177), ('discrete curvature', 0.5229849815368652), ('curvature discrete', 0.5106435418128967), ('conformal theory', 0.5098094940185547), ('polyhedral surfaces', 0.509168803691864), ('conformal maps', 0.5037034749984741), ('conformal', 0.5029751062393188), ('curvatures', 0.4886622726917267)]"
1008,1008,30,1008_numbers normal_normal numbers_base expansion_cantor,"['numbers normal', 'normal numbers', 'base expansion', 'cantor', 'number normal', 'expansion base', '0_3 complete', 'normality', 'numeration systems', 'expansions real']","['Some complexity results in the theory of normal numbers   Let $\\mathscr{N}(b)$ be the set of real numbers which are normal to base $b$.\nA well-known result of H. Ki and T. Linton is that $\\mathscr{N}(b)$ is\n$\\boldsymbol{\\Pi}^0_3$-complete. We show that the set $\\mathscr{N}(b)$ of reals\nwhich preserve $\\mathscr{N}(b)$ under addition is also\n$\\boldsymbol{\\Pi}^0_3$-complete. We use the characteriztion of $\\mathscr{N}(b)$\ngiven by G. Rauzy in terms of an entropy-like quantity called the noise. It\nfollows from our results that no further characteriztion theorems could result\nin a still better bound on the complexity of $\\mathscr{N}(b)$. We compute the\nexact descriptive complexity of other naturally occurring sets associated with\nnoise. One of these is complete at the $\\boldsymbol{\\Pi}^0_4$ level. Finally,\nwe get upper and lower bounds on the Hausdorff dimension of the level sets\nassociated with the noise.\n', 'On the Borel complexity of continued fraction normal, absolutely\n  abnormal numbers   We show that normality for continued fractions expansions and normality for\nbase-$b$ expansions are maximally logically separate. In particular, the set of\nnumbers that are normal with respect to the continued fraction expansion but\nnot base-$b$ normal for a fixed $b\\ge 2$ is\n$D_2(\\boldsymbol{\\Pi}_3^0)$-complete. Moreover, the set of numbers that are\nnormal with respect to the continued fraction expansion but not normal to\n\\emph{any} base-$b$ expansion is $D_2(\\boldsymbol{\\Pi}_3^0)$-hard, confirming\nthe existence of uncountably many such numbers, which was previously only known\nassuming the generalized Riemann hypothesis.\n  By varying the method of proof we are also able to show that the set of\nbase-$2$ normal, base-$3$ non-normal numbers is also\n$D_2(\\boldsymbol{\\Pi}_3^0)$-complete. We also prove an auxiliary result on the\nnormality properties of the continued fraction expansions of fractions with a\nfixed denominator.\n', 'Descriptive complexity in Cantor series   A Cantor series expansion for a real number $x$ with respect to a basic\nsequence $Q=(q_1,q_2,\\dots)$, where $q_i \\geq 2$, is a representation of the\nform $x=a_0 + \\sum_{i=1}^\\infty \\frac{a_i}{q_1q_2\\cdots q_i}$ where $0 \\leq\na_i<q_i$. These generalize ordinary base $b$ expansions where $q_i=b$. Ki and\nLinton showed that for ordinary base $b$ expansions the set of normal numbers\nis a $\\boldsymbol{\\Pi}^0_3$-complete set, establishing the exact complexity of\nthis set. In the case of Cantor series there are three natural notions of\nnormality: normality, ratio normality,and distribution normality (these notions\nare equivalent for base $b$ expansions). We show that for any $Q$ the set\n$\\mathscr{DN}(Q)$ of distribution normal number is\n$\\boldsymbol{\\Pi}^0_3$-complete, and if $Q$ is $1$-divergent (i.e.,\n$\\sum_{i=1}^\\infty \\frac{1}{q_i}$ diverges) then the sets $\\mathscr{N}(Q)$ and\n$\\mathscr{RN}(Q)$ of normal and ratio normal numbers are\n$\\boldsymbol{\\Pi}^0_3$-complete. We further show that all five non-trivial\ndifferences of these sets are $D_2(\\boldsymbol{\\Pi}^0_3)$-complete if $\\lim_i\nq_i=\\infty$ and $Q$ is $1$-divergent (the trivial case is\n$\\mathscr{N}(Q)\\setminus \\mathscr{RN}(Q)=\\emptyset$). This shows that except\nfor the containment $\\mathscr{N}(Q)\\subseteq \\mathscr{RN}(Q)$, these three\nnotions are as independent as possible.\n']","[('numbers normal', 0.4080604314804077), ('normal numbers', 0.40796515345573425), ('base expansion', 0.40688419342041016), ('cantor', 0.3866029977798462), ('number normal', 0.3830074369907379), ('expansion base', 0.37618887424468994), ('0_3 complete', 0.35117101669311523), ('normality', 0.34763962030410767), ('numeration systems', 0.33686017990112305), ('expansions real', 0.33323419094085693)]"
1009,1009,30,1009_modular varieties_modular variety_varieties algebras_characterization congruence,"['modular varieties', 'modular variety', 'varieties algebras', 'characterization congruence', 'algebras varieties', 'varieties varieties', 'varieties provide', 'varieties', 'class varieties', 'congruence lattices']","['Abelian congruences and similarity in varieties with a weak difference\n  term   This is the first of three papers motivated by the author\'s desire to\nunderstand and explain ""algebraically"" one aspect of Dmitriy Zhuk\'s proof of\nthe CSP Dichotomy Theorem. In this paper we study abelian congruences in\nvarieties having a weak difference term. Each class of the congruence supports\nan abelian group structure; if the congruence is minimal, each class supports\nthe structure of a vector space over a division ring determined by the\ncongruence. A construction due to J. Hagemann, C. Herrmann and R. Freese in the\ncongruence modular setting extends to varieties with a weak difference term,\nand provides a ""universal domain"" for the abelian groups or vector spaces that\narise from the classes of the congruence within a single class of the\nannihilator of the congruence. The construction also supports an extension of\nFreese\'s similarity relation (between subdirectly irreducible algebras) from\nthe congruence modular setting to varieties with a weak difference term.\n', 'Another characterization of congruence distributive varieties   We provide a Maltsev characterization of congruence distributive varieties by\nshowing that a variety $\\mathcal {V}$ is congruence distributive if and only if\nthe congruence identity $\\alpha \\cap (\\beta \\circ \\gamma \\circ \\beta )\n\\subseteq \\alpha \\beta \\circ \\gamma \\circ \\alpha \\beta \\circ \\gamma \\dots $\n($k$ factors) holds in $\\mathcal {V}$, for some natural number $k$.\n', ""Day's Theorem is sharp for $n$ even   We solve some problems about relative lengths of Maltsev conditions, in\nparticular, we give an affirmative answer to a classical problem raised by A.\nDay more than fifty years ago.\n  In detail, both congruence distributive and congruence modular varieties\nadmit Maltsev characterizations by means of the existence of a finite but\nvariable number of appropriate terms. A. Day showed that from J\\'onsson terms\n$t_0, \\dots, t_n$ witnessing congruence distributivity it is possible to\nconstruct terms $u_0, \\dots, u _{2n-1} $ witnessing congruence modularity. We\nshow that Day's result about the number of such terms is sharp when $n$ is\neven.\n  We also deal with other kinds of terms, such as alvin, Gumm, Pixley,\ndirected, specular, mixed and defective. All the results hold when restricted\nto locally finite varieties. We introduce some families of congruence\ndistributive varieties and characterize many congruence identities they\nsatisfy.\n""]","[('modular varieties', 0.7177512645721436), ('modular variety', 0.6666933298110962), ('varieties algebras', 0.5944744944572449), ('characterization congruence', 0.5804789662361145), ('algebras varieties', 0.5753005743026733), ('varieties varieties', 0.5469784736633301), ('varieties provide', 0.5166495442390442), ('varieties', 0.5105255246162415), ('class varieties', 0.5091020464897156), ('congruence lattices', 0.480524480342865)]"
1010,1010,30,1010_representations quivers_quiver representations_quiver representation_representations quiver,"['representations quivers', 'quiver representations', 'quiver representation', 'representations quiver', 'quivers type', 'quiver type', 'acyclic quivers', 'quivers', 'acyclic quiver', 'quiver']","[""Gabriel's Theorem for Locally Finite-Dimensional Representations of\n  Infinite Quivers   We prove a version of Gabriel's theorem for locally finite-dimensional\nrepresentations of infinite quivers. Specifically, we show that if $\\Omega$ is\nany connected quiver, the category of locally finite-dimensional\nrepresentations of $\\Omega$ has unique representation type (meaning no two\nindecomposable representations have the same dimension vector) if and only if\nthe underlying graph of $\\Omega$ is a generalized ADE Dynkin diagram (i.e. one\nof $A_n, D_n, E_6, E_7, E_8, A_{\\infty}, A_{\\infty , \\infty}$ or $D_\\infty$).\nThis result is companion to earlier work of the authors generalizing Gabriel's\ntheorem to infinite quivers with different conditions.\n"", 'On the Combinatorics of $\\mathbb{F}_1$-Representations of Pseudotree\n  Quivers   We investigate quiver representations over $\\mathbb{F}_1$. Coefficient\nquivers are combinatorial gadgets equivalent to $\\mathbb{F}_1$-representations\nof quivers. We focus on the case when the quiver $Q$ is a pseudotree. For such\nquivers, we first use the notion of coefficient quivers to provide a complete\nclassification of asymptotic behaviors of indecomposable representations over\n$\\mathbb{F}_1$. Then, we prove some fundamental structural results about the\nLie algebras associated to pseudotrees. Finally, we construct examples of\n$\\mathbb{F}_1$-representations $M$ of a quiver $Q$ by using coverings, under\nwhich the Euler characteristics of the quiver Grassmannians\n$\\textrm{Gr}^Q_{\\underline{d}}(M)$ can be computed in a purely combinatorial\nway.\n', 'Maximal rigid representations of continuous quivers of type $A$   Bongartz and Gabriel gave a classification of maximal rigid representations\nfor quivers of type $A$ with linear orientation and counted the number of\nisomorphism classes. In this paper, we give a formula on the number of\nisomorphism classes of a kind of maximal rigid representations for continuous\nquivers of type $A$ introduced by Igusa, Rock and Todorov.\n']","[('representations quivers', 0.7767496705055237), ('quiver representations', 0.7707962989807129), ('quiver representation', 0.7487915754318237), ('representations quiver', 0.7368337512016296), ('quivers type', 0.6900571584701538), ('quiver type', 0.6674903035163879), ('acyclic quivers', 0.6409803032875061), ('quivers', 0.6059588193893433), ('acyclic quiver', 0.5823606252670288), ('quiver', 0.5783923864364624)]"
1011,1011,30,1011_symmetric tensor fields_tensor fields_ray transforms_symmetric tensor field,"['symmetric tensor fields', 'tensor fields', 'ray transforms', 'symmetric tensor field', 'ray transform', 'tensor field', 'symmetric tensors', 'symmetric tensor', 'transform recover', 'higher order tensor']","['Reconstruction of a vector field and a symmetric $2$-tensor field from\n  the moment ray transforms in $\\mathbb{R}^2$   We present a technique for recovering a vector field and a symmetric\n$2$-tensor field, both real-valued and compactly supported in some strictly\nconvex bounded domain with smooth boundary in the Euclidean plane, from the sum\nof their attenuated moment ray transforms. In addition, we provide a stability\nestimate for recovering both the vector field and the symmetric $2$-tensor\nfield from the aforementioned ray transform.\n', ""Inversion of a restricted transverse ray transform with sources on a\n  curve   In this paper, a restricted transverse ray transform acting on vector and\nsymmetric $m$-tensor fields is studied. We developed inversion algorithms using\nrestricted transverse ray transform data to recover symmetric $m$-tensor fields\nin $\\mathbb{R}^3$ and vector fields in $\\mathbb{R}^n$. We restrict the\ntransverse ray transform to all lines going through a fixed curve $\\gamma$ that\nsatisfies the Kirillov-Tuy condition. We show that the known restricted data\ncan be used to reconstruct a specific weighted Radon transform of the unknown\nvector/tensor field's components, which we then use to explicitly recover the\nunknown field.\n"", 'Microlocal inversion of a 3-dimensional restricted transverse ray\n  transform of symmetric $m$-tensor fields   We study the problem of inverting a restricted transverse ray transform to\nrecover a symmetric $m$-tensor field in $\\mathbb{R}^3$ using microlocal\nanalysis techniques. More precisely, we prove that a symmetric $m$-tensor field\ncan be recovered up to a known singular term and a smoothing term if its\ntransverse ray transform is known along all lines intersecting a fixed smooth\ncurve satisfying the Kirillov-Tuy condition.\n']","[('symmetric tensor fields', 0.6146358251571655), ('tensor fields', 0.5975124835968018), ('ray transforms', 0.5942685604095459), ('symmetric tensor field', 0.5913277864456177), ('ray transform', 0.572874903678894), ('tensor field', 0.5499697923660278), ('symmetric tensors', 0.5215033888816833), ('symmetric tensor', 0.5162317752838135), ('transform recover', 0.4990769922733307), ('higher order tensor', 0.4852210283279419)]"
1012,1012,30,1012_subgroups sl_discrete subgroups_discrete subgroup_fuchsian groups,"['subgroups sl', 'discrete subgroups', 'discrete subgroup', 'fuchsian groups', 'lie groups', 'special linear groups', 'rank lie groups', 'simple lie groups', 'semisimple lie groups', 'solvable groups']","['On regular subgroups of $\\mathsf{SL}_3(\\mathbb{R})$   Motivated by a question of M. Kapovich, we show that the $\\mathbb{Z}^2$\nsubgroups of $\\mathsf{SL}_3(\\mathbb{R})$ that are regular in the language of\nKapovich--Leeb--Porti, or divergent in the sense of Guichard--Wienhard, are\nprecisely the lattices in minimal horospherical subgroups. This rules out any\nrelative Anosov subgroups of $\\mathsf{SL}_3(\\mathbb{R})$ that are not in fact\nGromov-hyperbolic. By work of Oh, it also follows that a Zariski-dense discrete\nsubgroup $\\Gamma$ of $\\mathsf{SL}_3(\\mathbb{R})$ contains a regular\n$\\mathbb{Z}^2$ if and only if $\\Gamma$ is commensurable to a conjugate of\n$\\mathsf{SL}_3(\\mathbb{Z})$. In particular, a Zariski-dense regular subgroup of\n$\\mathsf{SL}_3(\\mathbb{R})$ contains no $\\mathbb{Z}^2$ subgroups.\n', 'Remarks on discrete subgroups with full limit sets in higher rank Lie\n  groups   We show that real semi-simple Lie groups of higher rank contain (infinitely\ngenerated) discrete subgroups with full limit sets in the corresponding\nFurstenberg boundaries. Additionally, we provide criteria under which discrete\nsubgroups of $G = \\operatorname{SL}(3,\\mathbb{R})$ must have a full limit set\nin the Furstenberg boundary of $G$.\n  In the appendix, we show the the existence of Zariski-dense discrete\nsubgroups $\\Gamma$ of $\\operatorname{SL}(n,\\mathbb{R})$, where $n\\ge 3$, such\nthat the Jordan projection of some loxodromic element $\\gamma \\in\\Gamma$ lies\non the boundary of the limit cone of $\\Gamma$.\n', 'Discrete subgroups of semisimple Lie groups, beyond lattices   Discrete subgroups of SL(2,R) are well understood, and classified by the\ngeometry of the corresponding hyperbolic surfaces. Discrete subgroups of\nhigher-rank semisimple Lie groups, such as SL(n,R) for n>2, remain more\nmysterious. While lattices in this setting are rigid, there also exist more\nflexible, ""thinner"" discrete subgroups, which may have large and interesting\ndeformation spaces, giving rise in particular to so-called higher Teichm\\""uller\ntheory. We survey recent progress in constructing and understanding such\ndiscrete subgroups from a geometric and dynamical viewpoint.\n']","[('subgroups sl', 0.6483340859413147), ('discrete subgroups', 0.5589357614517212), ('discrete subgroup', 0.5538368225097656), ('fuchsian groups', 0.5510193109512329), ('lie groups', 0.5443325638771057), ('special linear groups', 0.5238233208656311), ('rank lie groups', 0.5071026682853699), ('simple lie groups', 0.5048326849937439), ('semisimple lie groups', 0.48942458629608154), ('solvable groups', 0.4766028821468353)]"
1013,1013,30,1013_symmetric grothendieck polynomials_grothendieck polynomials_grothendieck functions_polynomials dual,"['symmetric grothendieck polynomials', 'grothendieck polynomials', 'grothendieck functions', 'polynomials dual', 'schur polynomials', 'stable grothendieck', 'schubert polynomials', 'canonical grothendieck', 'polynomials skew', 'macdonald polynomials']","['Refined canonical stable Grothendieck polynomials and their duals, Part\n  1   In this paper we introduce refined canonical stable Grothendieck polynomials\nand their duals with two infinite sequences of parameters. These polynomials\nunify several generalizations of Grothendieck polynomials including canonical\nstable Grothendieck polynomials due to Yeliussizov, refined Grothendieck\npolynomials due to Chan and Pflueger, and refined dual Grothendieck polynomials\ndue to Galashin, Liu, and Grinberg. We give Jacobi--Trudi-like formulas,\ncombinatorial models, Schur expansions, Schur positivity, and dualities of\nthese polynomials.\n', 'Key expansion of the flagged refined skew stable Grothendieck polynomial   The flagged refined stable Grothendieck polynomials of skew shapes generalize\nseveral polynomials like stable Grothendieck polynomials, flagged skew Schur\npolynomials. In this paper, we provide a combinatorial expansion of the flagged\nrefined skew stable Grothendieck polynomial in terms of key polynomials. We\npresent this expansion by imposing a Demazure crystal structure on the set of\nflagged semi-standard set-valued tableaux of a given skew shape and a flag. We\nalso provide expansions of the row-refined stable Grothendieck polynomials and\nrefined dual stable Grothendieck polynomials in terms of stable Grothendieck\npolynomials $G_{\\lambda}$ and in terms of dual stable Grothendieck polynomials\n$g_{\\lambda}$.\n', 'Jacobi--Trudi formulas for flagged refined dual stable Grothendieck\n  polynomials   Recently Galashin, Grinberg, and Liu introduced the refined dual stable\nGrothendieck polynomials, which are symmetric functions in $x=(x_1,x_2,\\dots)$\nwith additional parameters $t=(t_1,t_2,\\dots)$. The refined dual stable\nGrothendieck polynomials are defined as a generating function for reverse plane\npartitions of a given shape. They interpolate between Schur functions and dual\nstable Grothendieck polynomials introduced by Lam and Pylyavskyy in 2007.\nFlagged refined dual stable Grothendieck polynomials are a more refined version\nof refined dual stable Grothendieck polynomials, where lower and upper bounds\nare given for the entries of each row or column. In this paper\nJacobi--Trudi-type formulas for flagged refined dual stable Grothendieck\npolynomials are proved using plethystic substitution. This resolves a\nconjecture of Grinberg and generalizes a result by Iwao and\nAmanov--Yeliussizov.\n']","[('symmetric grothendieck polynomials', 0.7244040369987488), ('grothendieck polynomials', 0.6880666613578796), ('grothendieck functions', 0.5835991501808167), ('polynomials dual', 0.565194845199585), ('schur polynomials', 0.5402930974960327), ('stable grothendieck', 0.5264173746109009), ('schubert polynomials', 0.48309755325317383), ('canonical grothendieck', 0.47577059268951416), ('polynomials skew', 0.4688166379928589), ('macdonald polynomials', 0.46734562516212463)]"
1014,1014,30,1014_connectivity graph_edge connectivity_connected subgraph_connected graph,"['connectivity graph', 'edge connectivity', 'connected subgraph', 'connected graph', 'edge connected', 'edge disjoint paths', 'edge disjoint', 'connectivity', 'subgraphs', 'group graphs']","['Menger-type connectivity of line graphs of faulty hypercubes   A connected graph $G$ is called strongly Menger edge connected if $G$ has\nmin\\{deg$_G(x)$, deg$_G(y)$\\} edge-disjoint paths between any two distinct\nvertices $x$ and $y$ in $G$. In this paper, we consider two types of strongly\nMenger edge connectivity of the line graphs of $n$-dimensional hypercube-like\nnetworks with faulty edges, namely the $m$-edge-fault-tolerant and\n$m$-conditional edge-fault-tolerant strongly Menger edge connectivity. We show\nthat the line graph of any $n$-dimensional hypercube-like network is\n$(2n-4)$-edge-fault-tolerant strongly Menger edge connected for $n\\geq 3$ and\n$(4n-10)$-conditional edge-fault-tolerant strongly Menger edge connected for\n$n\\geq 4$. The two bounds for the maximum number of faulty edges are best\npossible.\n', 'Edge-fault-tolerant strong Menger edge connectivity of bubble-sort star\n  graphs   The connectivity and edge connectivity of interconnection network determine\nthe fault tolerance of the network. An interconnection network is usually\nviewed as a connected graph, where vertex corresponds processor and edge\ncorresponds link between two distinct processors. Given a connected graph $G$\nwith vertex set $V(G)$ and edge set $E(G)$, if for any two distinct vertices\n$u,v\\in V(G)$, there exist $\\min\\{d_G(u),d_G(v)\\}$ edge-disjoint paths between\n$u$ and $v$, then $G$ is strongly Menger edge connected. Let $m$ be an integer\nwith $m\\geq1$. If $G-F_e$ remains strongly Menger edge connected for any\n$F_e\\subseteq E(G)$ with $|F_e|\\leq m$, then $G$ is $m$-edge-fault-tolerant\nstrongly Menger edge connected. If $G-F_e$ is strongly Menger edge connected\nfor any $F_e\\subseteq E(G)$ with $|F_e|\\leq m$ and $\\delta(G-F_e)\\geq2$, then\n$G$ is $m$-conditional edge-fault-tolerant strongly Menger edge connected. In\nthis paper, we consider the $n$-dimensional bubble-sort star graph $BS_n$. We\nshow that $BS_n$ is $(2n-5)$-edge-fault-tolerant strongly Menger edge connected\nfor $n\\geq3$ and $(6n-17)$-conditional edge-fault-tolerant strongly Menger edge\nconnected for $n\\geq4$. Moreover, we give some examples to show that our\nresults are optimal.\n', ""Structure fault diameter of hypercubes   Structure connectivity and substructure connectivity are innovative\nindicators for assessing network reliability and fault tolerance. Similarly,\nfault diameter evaluates fault tolerance and transmission delays in networks.\nThis paper extends the concept of fault diameter by introducing two new\nvariants: structure fault diameter and substructure fault diameter, derived\nfrom structure connectivity and substructure connectivity respectively. For a\nconnected graph $G$ with $W$-structure connectivity $\\kappa(G;W)$ or\n$W$-substructure connectivity $\\kappa^s(G;W)$, the $W$-structure fault diameter\n$D_f(G;W)$ and $W$-substructure fault diameter $D_f^s(G;W)$ are defined as the\nmaximum diameter of any subgraph of $G$ resulting from removing fewer than\n$\\kappa(G;W)-1$ $W$-structures or $\\kappa^s(G;W)-1$ $W$-substructures. For the\n$n$-dimensional hypercube $Q_n$ with $n \\geq 3$ and $1 \\leq m \\leq n - 2$, we\ndetermine both $D_f(Q_n;Q_m)$ and $D_f^s(Q_n;Q_1)$. These findings generalize\nexisting results for the diameter and fault diameter of $Q_n$, providing a\nbroader understanding of the hypercube's structural properties under fault\nconditions.\n""]","[('connectivity graph', 0.5835943818092346), ('edge connectivity', 0.5447140336036682), ('connected subgraph', 0.536880373954773), ('connected graph', 0.5122745633125305), ('edge connected', 0.4811688959598541), ('edge disjoint paths', 0.45480209589004517), ('edge disjoint', 0.45213744044303894), ('connectivity', 0.4493074119091034), ('subgraphs', 0.4408421218395233), ('group graphs', 0.4141349196434021)]"
1015,1015,29,1015_riccati equations_equations riccati_matrix riccati_systems riccati,"['riccati equations', 'equations riccati', 'matrix riccati', 'systems riccati', 'oscillation', 'second order linear', 'quadratic dynamical', 'new oscillation', 'ordinary differential equations', 'riccati']","[""Oscillation and non oscillation criteria for linear nonhomogeneous\n  systems of two first-order ordinary differential equations   The Riccati equation method is used to establish an oscillatory and a non\noscillatory criteria for nonhomogeneous linear systems of two first-order\nordinary differential equations. It is shown that the obtained oscillatory\ncriterion is a generalization of J. S. W. Wong's oscillatory criterion.\n"", 'Oscillation, suboscillation and nonoscillation criteria for linear\n  systems of ordinary differential equations   The Riccati equation method and an approach of the use of unknown factors is\nused to establish oscillation, suboscillation and nonoscillation criteria for\nlinear systems of ordinary differential equations. A necessary condition for\nLyapunov (asymptotic) stability for these systems is obtained.\n', 'Oscillation and interval oscillation criteria for linear matrix\n  Hamiltonian systems   We use the Riccati equation method with other ones to establish new\noscillation and interval oscillation criteria for linear matrix Hamiltonian\nsystems. We investigate the oscillation problem for linear matrix Hamiltonian\nsystems in a new direction, which is to break the positive definiteness\ncondition, imposed on one of the coefficients of the system.\n']","[('riccati equations', 0.6151747107505798), ('equations riccati', 0.5721431374549866), ('matrix riccati', 0.5206673741340637), ('systems riccati', 0.5043967962265015), ('oscillation', 0.4271211624145508), ('second order linear', 0.4177374839782715), ('quadratic dynamical', 0.4011271297931671), ('new oscillation', 0.4000747799873352), ('ordinary differential equations', 0.3990783989429474), ('riccati', 0.3950304687023163)]"
1016,1016,29,1016_spectral theorems_nonautonomous systems_spectrums_exponential dichotomy,"['spectral theorems', 'nonautonomous systems', 'spectrums', 'exponential dichotomy', 'spectrum', 'spectra', 'spectrum based', 'nonhyperbolic', 'monotone systems', 'characterization mu']","['Nonuniform $\\mu$-dichotomy spectrum and kinematic similarity   For linear nonautonomous differential equations we introduce a new family of\nspectrums defined with general nonuniform dichotomies: for a given growth rate\n$\\mu$ in a large family of growth rates, we consider a notion of spectrum,\nnamed nonuniform $\\mu$-dichotomy spectrum. This family of spectrums contain the\nnonuniform dichotomy spectrum as the very particular case of exponential growth\nrates. For each growth rate $\\mu$, we describe all possible forms of the\nnonuniform $\\mu$-dichotomy spectrum, relate its connected components with\nadapted notions of Lyapunov exponents, and use it to obtain a reducibility\nresult for nonautonomous linear differential equations. We also give an\nillustrative examples where the spectrum is obtained, including a situation\nwhere a normal form is obtained for polynomial behavior.\n', 'Dichotomies uniform on subspaces and formulas for dichotomy spectra   In this note we introduce a notion of dichotomy which generalizes the\nclassical concept of exponential dichotomy and the recent notion of Bohl\ndichotomy. A key attribute is the discussion of the sets of subspaces of the\nstate space on which the dichotomy estimates are uniform. Two main results are\na dichotomy spectral theorem based on our notion of dichotomy which is uniform\non subspaces and a formula for the dichotomy spectral intervals which is new\nfor the Bohl dichotomy spectrum as well as for the classical exponential\ndichotomy spectrum.\n', 'Discrete $\\mu$-dichotomy spectrum: beyond uniformity and new insights   We develop spectral theorems for nonautonomous linear difference systems,\nconsidering different types of $\\mu$-dichotomies, both uniform and nonuniform.\nIn the nonuniform case, intriguing scenarios emerge -- that have been employed\nbut whose consequences have not been thoroughly explored -- which surprisingly\nexhibit unconventional behavior. These particular cases motivate us to\nintroduce two novel properties of nonautonomous systems (even in the\ncontinuous-time framework), which appear to have been overlooked in the\nexisting literature. Additionally, we introduce a new conceptualization of a\nnonuniform $\\mu$-dichotomy spectrum, which lies between the traditional\nnonuniform $\\mu$-dichotomy spectrum and the slow nonuniform $\\mu$-dichotomy\nspectrum. Moreover, and this is particularly noteworthy, we propose a\nconjecture that enables the derivation of spectral theorems in this new\nsetting. Finally, contrary to what has been believed in recent years, through\nthe lens of optimal ratio maps, we show that the nonuniform exponential\ndichotomy spectrum is not preserved between systems that are weakly\nkinematically similar.\n']","[('spectral theorems', 0.5417797565460205), ('nonautonomous systems', 0.5088802576065063), ('spectrums', 0.48279839754104614), ('exponential dichotomy', 0.46366894245147705), ('spectrum', 0.4607853591442108), ('spectra', 0.39063894748687744), ('spectrum based', 0.3784921169281006), ('nonhyperbolic', 0.3718821406364441), ('monotone systems', 0.36855053901672363), ('characterization mu', 0.34228432178497314)]"
1017,1017,29,1017_sparse bayesian learning_inference sparse_sparse bayesian_shrinkage priors,"['sparse bayesian learning', 'inference sparse', 'sparse bayesian', 'shrinkage priors', 'shrinkage prior', 'sparse regression', 'inference high dimensional', 'lasso', 'sparse high dimensional', 'prior distributions']","['Empirical Bayes inference in sparse high-dimensional generalized linear\n  models   High-dimensional linear models have been widely studied, but the developments\nin high-dimensional generalized linear models, or GLMs, have been slower. In\nthis paper, we propose an empirical or data-driven prior leading to an\nempirical Bayes posterior distribution which can be used for estimation of and\ninference on the coefficient vector in a high-dimensional GLM, as well as for\nvariable selection. We prove that our proposed posterior concentrates around\nthe true/sparse coefficient vector at the optimal rate, provide conditions\nunder which the posterior can achieve variable selection consistency, and prove\na Bernstein--von Mises theorem that implies asymptotically valid uncertainty\nquantification. Computation of the proposed empirical Bayes posterior is simple\nand efficient, and is shown to perform well in simulations compared to existing\nBayesian and non-Bayesian methods in terms of estimation and variable\nselection.\n', 'Fast Exact Bayesian Inference for Sparse Signals in the Normal Sequence\n  Model   We consider exact algorithms for Bayesian inference with model selection\npriors (including spike-and-slab priors) in the sparse normal sequence model.\nBecause the best existing exact algorithm becomes numerically unstable for\nsample sizes over n=500, there has been much attention for alternative\napproaches like approximate algorithms (Gibbs sampling, variational Bayes,\netc.), shrinkage priors (e.g. the Horseshoe prior and the Spike-and-Slab LASSO)\nor empirical Bayesian methods. However, by introducing algorithmic ideas from\nonline sequential prediction, we show that exact calculations are feasible for\nmuch larger sample sizes: for general model selection priors we reach n=25000,\nand for certain spike-and-slab priors we can easily reach n=100000. We further\nprove a de Finetti-like result for finite sample sizes that characterizes\nexactly which model selection priors can be expressed as spike-and-slab priors.\nThe computational speed and numerical accuracy of the proposed methods are\ndemonstrated in experiments on simulated data, on a differential gene\nexpression data set, and to compare the effect of multiple hyper-parameter\nsettings in the beta-binomial prior. In our experimental evaluation we compute\nguaranteed bounds on the numerical accuracy of all new algorithms, which shows\nthat the proposed methods are numerically reliable whereas an alternative based\non long division is not.\n', 'Nearly optimal Bayesian Shrinkage for High Dimensional Regression   During the past decade, shrinkage priors have received much attention in\nBayesian analysis of high-dimensional data. This paper establishes the\nposterior consistency for high-dimensional linear regression with a class of\nshrinkage priors, which has a heavy and flat tail and allocates a sufficiently\nlarge probability mass in a very small neighborhood of zero. While enjoying its\nefficiency in posterior simulations, the shrinkage prior can lead to a nearly\noptimal posterior contraction rate and variable selection consistency as the\nspike-and-slab prior. Our numerical results show that under the posterior\nconsistency, Bayesian methods can yield much better results in variable\nselection than the regularization methods such as Lasso and SCAD. This paper\nalso establishes a Bernstein von-Mises type result, which leads to a convenient\nway of uncertainty quantification for regression coefficient estimates.\n']","[('sparse bayesian learning', 0.6473654508590698), ('inference sparse', 0.6429460048675537), ('sparse bayesian', 0.6289765238761902), ('shrinkage priors', 0.5974419713020325), ('shrinkage prior', 0.5688988566398621), ('sparse regression', 0.5659733414649963), ('inference high dimensional', 0.5017656087875366), ('lasso', 0.49957039952278137), ('sparse high dimensional', 0.48362022638320923), ('prior distributions', 0.45669373869895935)]"
1018,1018,29,1018_dimensional integrable systems_integrable systems_integrable evolution equations_integrable equations,"['dimensional integrable systems', 'integrable systems', 'integrable evolution equations', 'integrable equations', 'davey stewartson system', 'integrable dimensional', 'integrable evolution', 'dimensional integrable', 'integrability conditions', 'construct integrable']","['Integrable (3+1)-dimensional generalization for dispersionless\n  Davey--Stewartson system   This paper introduces a (3+1)-dimensional dispersionless integrable system,\nutilizing a Lax pair involving contact vector fields, in alignment with\nmethodologies presented by A. Sergyeyev in 2018. Significantly, it is shown\nthat the proposed system serves as an integrable (3+1)-dimensional\ngeneralization of the well-studied (2+1)-dimensional dispersionless\nDavey-Stewartson system. This way, an interesting new example on integrability\nin higher dimensions is presented, with potential applications in modern\nmathematical physics. The work lays the foundation for future research into\nsymmetries, conservation laws, and Hamiltonian structures, offering avenues for\nfurther exploration.\n', 'Integrable semi-discretizations of the Davey-Stewartson system and a\n  $(2+1)$-dimensional Yajima-Oikawa system. II   This is a continuation of our previous paper arXiv:1904.07924, which is\ndevoted to the construction of integrable semi-discretizations of the\nDavey-Stewartson system and a $(2+1)$-dimensional Yajima-Oikawa system; in this\nseries of papers, we refer to a discretization of one of the two spatial\nvariables as a semi-discretization. In this paper, we construct an integrable\nsemi-discrete Davey-Stewartson system, which is essentially different from the\nsemi-discrete Davey-Stewartson system proposed in the previous paper\narXiv:1904.07924. We first obtain integrable semi-discretizations of the two\nelementary flows that compose the Davey-Stewartson system by constructing their\nLax-pair representations and show that these two elementary flows commute as in\nthe continuous case. Then, we consider a linear combination of the two\nelementary flows to obtain a new integrable semi-discretization of the\nDavey-Stewartson system. Using a linear transformation of the continuous\nindependent variables, one of the two elementary Davey-Stewartson flows can be\nidentified with an integrable semi-discretization of the $(2+1)$-dimensional\nYajima-Oikawa system proposed in\nhttps://link.aps.org/doi/10.1103/PhysRevE.91.062902 .\n', 'Integrable semi-discretizations of the Davey-Stewartson system and a\n  $(2+1)$-dimensional Yajima-Oikawa system. I   The integrable Davey-Stewartson system is a linear combination of the two\nelementary flows that commute: $\\mathrm{i} q_{t_1} + q_{xx} +\n2q\\partial_y^{-1}\\partial_x (|q|^2) =0$ and $\\mathrm{i} q_{t_2} + q_{yy} +\n2q\\partial_x^{-1}\\partial_y (|q|^2) =0$. In the literature, each elementary\nDavey-Stewartson flow is often called the Fokas system because it was studied\nby Fokas in the early 1990s. In fact, the integrability of the Davey-Stewartson\nsystem dates back to the work of Ablowitz and Haberman in 1975; the elementary\nDavey-Stewartson flows, as well as another integrable $(2+1)$-dimensional\nnonlinear Schr\\""odinger equation $\\mathrm{i} q_{t} + q_{xy} + 2\nq\\partial_y^{-1}\\partial_x (|q|^2) =0$ proposed by Calogero and Degasperis in\n1976, appeared explicitly in Zakharov\'s article published in 1980. By applying\na linear change of the independent variables, an elementary Davey-Stewartson\nflow can be identified with a $(2+1)$-dimensional generalization of the\nintegrable long wave-short wave interaction model, called the Yajima-Oikawa\nsystem: $\\mathrm{i} q_{t} + q_{xx} + u q=0$, $u_t + c u_y = 2(|q|^2)_x$. In\nthis paper, we propose a new integrable semi-discretization (discretization of\none of the two spatial variables, say $x$) of the Davey-Stewartson system by\nconstructing its Lax-pair representation; the two elementary flows in the\nsemi-discrete case indeed commute. By applying a linear change of the\ncontinuous independent variables to an elementary flow, we also obtain an\nintegrable semi-discretization of the $(2+1)$-dimensional Yajima-Oikawa system.\n']","[('dimensional integrable systems', 0.7167471051216125), ('integrable systems', 0.6849853992462158), ('integrable evolution equations', 0.5898433327674866), ('integrable equations', 0.5714796185493469), ('davey stewartson system', 0.5218266248703003), ('integrable dimensional', 0.5078445076942444), ('integrable evolution', 0.5059040188789368), ('dimensional integrable', 0.4908086955547333), ('integrability conditions', 0.4534755051136017), ('construct integrable', 0.43639782071113586)]"
1019,1019,29,1019_kernel density estimators_kernel density estimator_kernel estimators_kernel density,"['kernel density estimators', 'kernel density estimator', 'kernel estimators', 'kernel density', 'kernel smoothing', 'density estimators', 'kernel regression', 'bandwidth kernel', 'density estimation', 'estimation density']","['Kernel density estimation with polyspherical data and its applications   A kernel density estimator for data on the polysphere\n$\\mathbb{S}^{d_1}\\times\\cdots\\times\\mathbb{S}^{d_r}$, with\n$r,d_1,\\ldots,d_r\\geq 1$, is presented in this paper. We derive the main\nasymptotic properties of the estimator, including mean square error, normality,\nand optimal bandwidths. We address the kernel theory of the estimator beyond\nthe von Mises-Fisher kernel, introducing new kernels that are more efficient\nand investigating normalizing constants, moments, and sampling methods thereof.\nPlug-in and cross-validated bandwidth selectors are also obtained. As a\nspin-off of the kernel density estimator, we propose a nonparametric $k$-sample\ntest based on the Jensen-Shannon divergence. Numerical experiments illuminate\nthe asymptotic theory of the kernel density estimator and demonstrate the\nsuperior performance of the $k$-sample test with respect to parametric\nalternatives in certain scenarios. Our smoothing methodology is applied to the\nanalysis of the morphology of a sample of hippocampi of infants embedded on the\nhigh-dimensional polysphere $(\\mathbb{S}^2)^{168}$ via skeletal representations\n($s$-reps).\n', 'Effects of associated kernels in nonparametric multiple regressions   Associated kernels have been introduced to improve the classical continuous\nkernels for smoothing any functional on several kinds of supports such as\nbounded continuous and discrete sets. This work deals with the effects of\ncombined associated kernels on nonparametric multiple regression functions.\nUsing the Nadaraya-Watson estimator with optimal bandwidth matrices selected by\ncross-validation procedure, different behaviours of multiple regression\nestimations are pointed out according the type of multivariate associated\nkernels with correlation or not. Through simulation studies, there are no\neffect of correlation structures for the continuous regression functions and\nalso for the associated continuous kernels; however, there exist really effects\nof the choice of multivariate associated kernels following the support of the\nmultiple regression functions bounded continuous or discrete. Applications are\nmade on two real datasets.\n', 'On multivariate associated kernels for smoothing general density\n  functions   Multivariate associated kernel estimators, which depend on both target point\nand bandwidth matrix, are appropriate for partially or totally bounded\ndistributions and generalize the classical ones as Gaussian. Previous studies\non multivariate associated kernels have been restricted to product of\nunivariate associated kernels, also considered having diagonal bandwidth\nmatrices. However, it is shown in classical cases that for certain forms of\ntarget density such as multimodal, the use of full bandwidth matrices offers\nthe potential for significantly improved density estimation. In this paper,\ngeneral associated kernel estimators with correlation structure are introduced.\nProperties of these estimators are presented; in particular, the boundary bias\nis investigated. Then, the generalized bivariate beta kernels are handled with\nmore details. The associated kernel with a correlation structure is built with\na variant of the mode-dispersion method and two families of bandwidth matrices\nare discussed under the criterion of cross-validation. Several simulation\nstudies are done. In the particular situation of bivariate beta kernels, it is\ntherefore pointed out the very good performance of associated kernel estimators\nwith correlation structure compared to the diagonal case. Finally, an\nillustration on real dataset of paired rates in a framework of political\nelections is presented.\n']","[('kernel density estimators', 0.7446189522743225), ('kernel density estimator', 0.700221061706543), ('kernel estimators', 0.6114453673362732), ('kernel density', 0.594190776348114), ('kernel smoothing', 0.5894304513931274), ('density estimators', 0.5486226677894592), ('kernel regression', 0.5454908013343811), ('bandwidth kernel', 0.545490026473999), ('density estimation', 0.5426114201545715), ('estimation density', 0.5101988911628723)]"
1020,1020,29,1020_radial basis interpolation_radial basis rbf_basis rbf interpolation_radial basis functions,"['radial basis interpolation', 'radial basis rbf', 'basis rbf interpolation', 'radial basis functions', 'based radial basis', 'supported radial basis', 'rbf interpolation', 'radial basis', 'basis functions rbfs', 'radial kernel']","['Learning a robust shape parameter for RBF approximation   Radial basis functions (RBFs) play an important role in function\ninterpolation, in particular in an arbitrary set of interpolation nodes. The\naccuracy of the interpolation depends on a parameter called the shape\nparameter. There are many approaches in literature on how to appropriately\nchoose it as to increase the accuracy of interpolation while avoiding\ninstability issues. However, finding the optimal shape parameter value in\ngeneral remains a challenge. In this work, we present a novel approach to\ndetermine the shape parameter in RBFs. First, we construct an optimisation\nproblem to obtain a shape parameter that leads to an interpolation matrix with\nbounded condition number, then, we introduce a data-driven method that controls\nthe condition of the interpolation matrix to avoid numerically unstable\ninterpolations, while keeping a very good accuracy. In addition, a fall-back\nprocedure is proposed to enforce a strict upper bound on the condition number,\nas well as a learning strategy to improve the performance of the data-driven\nmethod by learning from previously run simulations. We present numerical test\ncases to assess the performance of the proposed methods in interpolation tasks\nand in a RBF based finite difference (RBF-FD) method, in one and two-space\ndimensions.\n', 'Towards stability of radial basis function based cubature formulas   Cubature formulas (CFs) based on radial basis functions (RBFs) have become an\nimportant tool for multivariate numerical integration of scattered data.\nAlthough numerous works have been published on such RBF-CFs, their stability\ntheory can still be considered as underdeveloped. Here, we strive to pave the\nway towards a more mature stability theory for RBF-CFs. In particular, we prove\nstability for RBF-CFs based on compactly supported RBFs under certain\nconditions on the shape parameter and the data points. Moreover, it is shown\nthat asymptotic stability of many RBF-CFs is independent of polynomial terms,\nwhich are often included in RBF approximations. While our findings provide some\nnovel conditions for stability of RBF-CFs, the present work also demonstrates\nthat there are still many gaps to fill in future investigations.\n', 'Towards stability results for global radial basis function based\n  quadrature formulas   Quadrature formulas (QFs) based on radial basis functions (RBFs) have become\nan essential tool for multivariate numerical integration of scattered data.\nAlthough numerous works have been published on RBF-QFs, their stability theory\ncan still be considered as underdeveloped. Here, we strive to pave the way\ntowards a more mature stability theory for global and function-independent\nRBF-QFs. In particular, we prove stability of these for compactly supported\nRBFs under certain conditions on the shape parameter and the data points. As an\nalternative to changing the shape parameter, we demonstrate how the\nleast-squares approach can be used to construct stable RBF-QFs by allowing the\nnumber of data points used for numerical integration to be larger than the\nnumber of centers used to generate the RBF approximation space. Moreover, it is\nshown that asymptotic stability of many global RBF-QFs is independent of\npolynomial terms, which are often included in RBF approximations. While our\nfindings provide some novel conditions for stability of global RBF-QFs, the\npresent work also demonstrates that there are still many gaps to fill in future\ninvestigations.\n']","[('radial basis interpolation', 0.7227950096130371), ('radial basis rbf', 0.6759709119796753), ('basis rbf interpolation', 0.663439929485321), ('radial basis functions', 0.6606729626655579), ('based radial basis', 0.6550300717353821), ('supported radial basis', 0.6302721500396729), ('rbf interpolation', 0.6235352158546448), ('radial basis', 0.5931420922279358), ('basis functions rbfs', 0.5602743625640869), ('radial kernel', 0.5055093765258789)]"
1021,1021,29,1021_steenrod algebra_generators degree_graded polynomial_mathbb f_2,"['steenrod algebra', 'generators degree', 'graded polynomial', 'mathbb f_2', 'f_2 f_2', 'polynomial algebra', 'invariant classes', 'f_2 two', 'mathbb otimes', 'minimal generators']","[""An application of the hit problem to the algebraic transfer Let $P_k$ be the polynomial algebra $\\mathbb F_2[x_1,x_2,\\ldots ,x_k]$ over the field $\\mathbb F_2$ with two elements, in $k$ variables $x_1, x_2, \\ldots , x_k$, each variable of degree 1. Denote by $GL_k$ the general linear group over $\\mathbb F_2$ which regularly acts on $P_k$. The algebra $P_k$ is a module over the mod-2 Steenrod algebra $\\mathcal A$. In 1989, Singer [22] defined the $k$-th homological algebraic transfer, which is a homomorphism $$\\varphi_k=(\\varphi_k)_m :{\\rm Tor}^{\\mathcal A}_{k,k+m} (\\mathbb F_2,\\mathbb F_2) \\to (\\mathbb F_2\\otimes_{\\mathcal A}P_k)_m^{GL_k}$$ from the homological group of the mod-2 Steenrod algebra $\\mbox{Tor}^{\\mathcal A}_{k,k+m} (\\mathbb F_2,\\mathbb F_2)$ to the subspace $(\\mathbb F_2\\otimes_{\\mathcal A}P_k)_m^{GL_k}$ of $\\mathbb F_2{\\otimes}_{\\mathcal A}P_k$ consisting of all the $GL_k$-invariant classes of degree $m$. In general, the transfer $\\varphi_k$ is not a monomorphism and Singer made a conjecture that $\\varphi_k$ is an epimorphism for any $k \\geqslant 0$. The conjecture is studied by many authors. It is true for $k \\leqslant 3$ but unknown for $k \\geqslant 4$.\n  In this paper, by using the results of the Peterson hit problem for the polynomial algebra in four variables, we prove that Singer's conjecture for the fourth algebraic transfer is true in the families of generic degrees $d_{s,t} = 2^{s+t}+2^s-3$ and $n_{s,t}=2^{s+t}+2^s-2$ with $s,\\, t$ positive integers. Our results also show that many of the results in Ph\\'uc [16,17,18] are seriously false. The proofs of the results in Ph\\'uc's works are only provided for a few special cases but they are false and incomplete."", 'On the determination of the Singer transfer   Let $P_k$ be the graded polynomial algebra $\\mathbb F_2[x_1,x_2,\\ldots ,x_k]$\nwith the degree of each generator $x_i$ being 1, where $\\mathbb F_2$ denote the\nprime field of two elements, and let $GL_k$ be the general linear group over\n$\\mathbb F_2$ which acts regularly on $P_k$. We study the algebraic transfer\nconstructed by Singer using the technique of the Peterson hit problem. This\ntransfer is a homomorphism from the homology of the mod-2 Steenrod algebra\n$\\mathcal A$, $\\text{Tor}^{\\mathcal A}_{k,k+d} (\\mathbb F_2,\\mathbb F_2)$, to\nthe subspace of $\\mathbb F_2{\\otimes}_{\\mathcal A}P_k$ consisting of all the\n$GL_k$-invariant classes of degree $d$. In this paper, by using the results on\nthe Peterson hit problem we present the proof of the fact that the Singer\nalgebraic transfer is an isomorphism for $k \\leqslant 3$. We also explicitly\ndetermine the fourth Singer algebraic transfer in some degrees.\n', ""Determination of the fifth Singer algebraic transfer in some degrees   Let $P_k$ be the graded polynomial algebra $\\mathbb F_2[x_1,x_2,\\ldots ,x_k]$\nover the prime field $\\mathbb F_2$ with two elements and the degree of each\nvariable $x_i$ being 1, and let $GL_k$ be the general linear group over\n$\\mathbb F_2$ which acts on $P_k$ as the usual manner. The algebra $P_k$ is\nconsidered as a module over the mod-2 Steenrod algebra $\\mathcal A$. In 1989,\nSinger [22] defined the $k$-th homological algebraic transfer, which is a\nhomomorphism $$\\varphi_k :{\\rm Tor}^{\\mathcal A}_{k,k+d} (\\mathbb F_2,\\mathbb\nF_2) \\to (\\mathbb F_2\\otimes_{\\mathcal A}P_k)_d^{GL_k}$$ from the homological\ngroup of the mod-2 Steenrod algebra $\\mbox{Tor}^{\\mathcal A}_{k,k+d} (\\mathbb\nF_2,\\mathbb F_2)$ to the subspace $(\\mathbb F_2\\otimes_{\\mathcal\nA}P_k)_d^{GL_k}$ of $\\mathbb F_2{\\otimes}_{\\mathcal A}P_k$ consisting of all\nthe $GL_k$-invariant classes of degree $d$.\n  In this paper, by using the results of the Peterson hit problem we present\nthe proof of the fact that the Singer algebraic transfer of rank five is an\nisomorphism in the internal degrees $d= 20$ and $d = 30$. Our result refutes\nthe proof for the case of $d=20$ in Ph\\'uc [17].\n""]","[('steenrod algebra', 0.4676123559474945), ('generators degree', 0.3735211193561554), ('graded polynomial', 0.36324426531791687), ('mathbb f_2', 0.3484407961368561), ('f_2 f_2', 0.33833858370780945), ('polynomial algebra', 0.3242871165275574), ('invariant classes', 0.32176873087882996), ('f_2 two', 0.31929272413253784), ('mathbb otimes', 0.3186616003513336), ('minimal generators', 0.3164753019809723)]"
1022,1022,29,1022_quasi interpolation_interpolation algorithms_interpolation schemes_adaptive interpolation,"['quasi interpolation', 'interpolation algorithms', 'interpolation schemes', 'adaptive interpolation', 'interpolation methods', 'empirical interpolation methods', 'sparse approximations', 'empirical interpolation', 'interpolation scheme', 'high dimensional approximation']","[""High-order quasi-interpolation with generalized Gaussian kernels\n  restricted over tori   The paper proposes a novel and efficient quasi-interpolation scheme with high\napproximation order for periodic function approximation over tori. The\nresulting quasi-interpolation takes the form of Schoenberg's tensor-product\ngeneralized Gaussian kernels restricted over circles. Notably, theoretical\nanalysis shows that it achieves the highest approximation order equal to the\norder of the generalized Strang-Fix condition satisfied by the generalized\nGaussian kernels. This is in sharp contrast to classical quasi-interpolation\ncounterparts, which often provide much lower approximation orders than those\ndictated by the generalized Strang-Fix conditions satisfied by the kernels.\nFurthermore, we construct a sparse grid counterpart for high-dimensional\nperiodic function approximation to alleviate the curse of dimensionality.\nNumerical simulations provided at the end of the paper demonstrate that our\nquasi-interpolation scheme is simple and computationally efficient.\n"", 'Quasi-interpolation for high-dimensional function approximation   The paper proposes a general quasi-interpolation scheme for high-dimensional\nfunction approximation. To facilitate error analysis, we view our\nquasi-interpolation as a two-step procedure. In the first step, we approximate\na target function by a purpose-built convolution operator (with an error term\nreferred to as convolution error). In the second step, we discretize the\nunderlying convolution operator using certain quadrature rules at the given\nsampling data sites (with an error term called discretization error). The final\napproximation error is obtained as an optimally balanced sum of these two\nerrors, which in turn views our quasi-interpolation as a regularization\ntechnique that balances convolution error and discretization error. As a\nconcrete example, we construct a sparse grid quasi-interpolation scheme for\nhigh-dimensional function approximation. Both theoretical analysis and\nnumerical implementations provide evidence that our quasi-interpolation scheme\nis robust and capable of mitigating the curse of dimensionality for\napproximating high-dimensional functions.\n', 'On multiscale quasi-interpolation of scattered scalar- and\n  manifold-valued functions   We address the problem of approximating an unknown function from its discrete\nsamples given at arbitrarily scattered sites. This problem is essential in\nnumerical sciences, where modern applications also highlight the need for a\nsolution to the case of functions with manifold values. In this paper, we\nintroduce and analyze a combination of kernel-based quasi-interpolation and\nmultiscale approximations for both scalar- and manifold-valued functions. While\nquasi-interpolation provides a powerful tool for approximation problems if the\ndata is defined on infinite grids, the situation is more complicated when it\ncomes to scattered data. Here, higher-order quasi-interpolation schemes either\nrequire derivative information or become numerically unstable. Hence, this\npaper principally studies the improvement achieved by combining\nquasi-interpolation with a multiscale technique. The main contributions of this\npaper are as follows. First, we introduce the multiscale quasi-interpolation\ntechnique for scalar-valued functions. Second, we show how this technique can\nbe carried over using moving least-squares operators to the manifold-valued\nsetting. Third, we give a mathematical proof that converging\nquasi-interpolation will also lead to converging multiscale\nquasi-interpolation. Fourth, we provide ample numerical evidence that\nmultiscale quasi-interpolation has superior convergence to quasi-interpolation.\nIn addition, we will provide examples showing that the multiscale\nquasi-interpolation approach offers a powerful tool for many data analysis\ntasks, such as denoising and anomaly detection. It is especially attractive for\ncases of massive data points and high dimensionality.\n']","[('quasi interpolation', 0.6738637089729309), ('interpolation algorithms', 0.6409289836883545), ('interpolation schemes', 0.624682605266571), ('adaptive interpolation', 0.6209707856178284), ('interpolation methods', 0.6188787817955017), ('empirical interpolation methods', 0.6148808002471924), ('sparse approximations', 0.603548526763916), ('empirical interpolation', 0.602173924446106), ('interpolation scheme', 0.598504900932312), ('high dimensional approximation', 0.588201642036438)]"
1023,1023,29,1023_combinatorial characterizations_closed graph classes_hereditary graph class_classes graphs,"['combinatorial characterizations', 'closed graph classes', 'hereditary graph class', 'classes graphs', 'graph classes', 'class graphs', 'monadic', 'graphs bounded', 'hereditary graph', 'ordered graphs']","['Twin-width V: linear minors, modular counting, and matrix multiplication   We continue developing the theory around the twin-width of totally ordered\nbinary structures, initiated in the previous paper of the series. We first\nintroduce the notion of parity and linear minors of a matrix, which consists of\niteratively replacing consecutive rows or consecutive columns with a linear\ncombination of them. We show that a matrix class has bounded twin-width if and\nonly if its linear-minor closure does not contain all matrices. We observe that\nthe fixed-parameter tractable algorithm for first-order model checking on\nstructures given with an $O(1)$-sequence (certificate of bounded twin-width)\nand the fact that first-order transductions of bounded twin-width classes have\nbounded twin-width, both established in Twin-width I, extend to first-order\nlogic with modular counting quantifiers. We make explicit a win-win argument\nobtained as a by-product of Twin-width IV, and somewhat similar to\nbidimensionality, that we call rank-bidimensionality. Armed with the\nabove-mentioned extension to modular counting, we show that the twin-width of\nthe product of two conformal matrices $A, B$ over a finite field is bounded by\na function of the twin-width of $A$, of $B$, and of the size of the field.\nFurthermore, if $A$ and $B$ are $n \\times n$ matrices of twin-width $d$ over\n$\\mathbb F_q$, we show that $AB$ can be computed in time $O_{d,q}(n^2 \\log n)$.\nWe finally present an ad hoc algorithm to efficiently multiply two matrices of\nbounded twin-width, with a single-exponential dependence in the twin-width\nbound: If the inputs are given in a compact tree-like form, called\ntwin-decomposition (of width $d$), then two $n \\times n$ matrices $A, B$ over\n$\\mathbb F_2$, a twin-decomposition of $AB$ with width $2^{d+o(d)}$ can be\ncomputed in time $4^{d+o(d)}n$ (resp. $4^{d+o(d)}n^{1+\\varepsilon}$), and\nentries queried in doubly-logarithmic (resp. constant) time.\n', 'First-Order Model Checking on Monadically Stable Graph Classes   A graph class $\\mathscr{C}$ is called monadically stable if one cannot\ninterpret, in first-order logic, arbitrary large linear orders in colored\ngraphs from $\\mathscr{C}$. We prove that the model checking problem for\nfirst-order logic is fixed-parameter tractable on every monadically stable\ngraph class. This extends the results of [Grohe, Kreutzer, and Siebertz; J. ACM\n\'17] for nowhere dense classes and of [Dreier, M\\""ahlmann, and Siebertz; STOC\n\'23] for structurally nowhere dense classes to all monadically stable classes.\n  As a complementary hardness result, we prove that for every hereditary graph\nclass $\\mathscr{C}$ that is edge-stable (excludes some half-graph as a\nsemi-induced subgraph) but not monadically stable, first-order model checking\nis $\\mathrm{AW}[*]$-hard on $\\mathscr{C}$, and $\\mathrm{W}[1]$-hard when\nrestricted to existential sentences. This confirms, in the special case of\nedge-stable classes, an on-going conjecture that the notion of monadic NIP\ndelimits the tractability of first-order model checking on hereditary classes\nof graphs.\n  For our tractability result, we first prove that monadically stable graph\nclasses have almost linear neighborhood complexity. Using this, we construct\nsparse neighborhood covers for monadically stable classes, which provides the\nmissing ingredient for the algorithm of [Dreier, M\\""ahlmann, and Siebertz; STOC\n\'23]. The key component of this construction is the usage of orders with low\ncrossing number [Welzl; SoCG \'88], a tool from the area of range queries.\n  For our hardness result, we prove a new characterization of monadically\nstable graph classes in terms of forbidden induced subgraphs. We then use this\ncharacterization to show that in hereditary classes that are edge-stable but\nnot monadically stable, one can effectively interpret the class of all graphs\nusing only existential formulas.\n', 'Flip-Breakability: A Combinatorial Dichotomy for Monadically Dependent\n  Graph Classes   A conjecture in algorithmic model theory predicts that the model-checking\nproblem for first-order logic is fixed-parameter tractable on a hereditary\ngraph class if and only if the class is monadically dependent. Originating in\nmodel theory, this notion is defined in terms of logic, and encompasses nowhere\ndense classes, monadically stable classes, and classes of bounded twin-width.\nWorking towards this conjecture, we provide the first two combinatorial\ncharacterizations of monadically dependent graph classes. This yields the\nfollowing dichotomy.\n  On the structure side, we characterize monadic dependence by a\nRamsey-theoretic property called flip-breakability. This notion generalizes the\nnotions of uniform quasi-wideness, flip-flatness, and bounded grid rank, which\ncharacterize nowhere denseness, monadic stability, and bounded twin-width,\nrespectively, and played a key role in their respective model checking\nalgorithms. Natural restrictions of flip-breakability additionally characterize\nbounded treewidth and cliquewidth and bounded treedepth and shrubdepth.\n  On the non-structure side, we characterize monadic dependence by explicitly\nlisting few families of forbidden induced subgraphs. This result is analogous\nto the characterization of nowhere denseness via forbidden subdivided cliques,\nand allows us to resolve one half of the motivating conjecture: First-order\nmodel checking is AW[$*$]-hard on every hereditary graph class that is\nmonadically independent. The result moreover implies that hereditary graph\nclasses which are small, have almost bounded twin-width, or have almost bounded\nflip-width, are monadically dependent.\n  Lastly, we lift our result to also obtain a combinatorial dichotomy in the\nmore general setting of monadically dependent classes of binary structures.\n']","[('combinatorial characterizations', 0.5412242412567139), ('closed graph classes', 0.5081933736801147), ('hereditary graph class', 0.49018269777297974), ('classes graphs', 0.4580857753753662), ('graph classes', 0.4546452462673187), ('class graphs', 0.4545958340167999), ('monadic', 0.4445466995239258), ('graphs bounded', 0.42220738530158997), ('hereditary graph', 0.41411831974983215), ('ordered graphs', 0.40387189388275146)]"
1024,1024,29,1024_graphs representation_graphs represented_graph can_representability,"['graphs representation', 'graphs represented', 'graph can', 'representability', 'graph universal', 'graphs', 'graphs introduced', 'whether every graph', 'graph semi', 'comparability graphs']","[""On the Existence of Word-representable Line Graphs of\n  Non-word-representable Graphs   An open question in the theory of word-representable graphs for the past\ndecade has been whether the line graph of a non-word-representable graph is\nalways non-word-representable. By formulating an appropriate optimization\nproblem for the decision problem of 3-semi-transitive graphs, we show that the\nline graph of a non-word-representable graph can be word-representable. Using\nIBM's CPLEX solver, we demonstrate for several known word-representable and\nnon-word-representable graphs that the line graph of a graph is\n3-semi-transitive when there is a solution to the optimization problem. This\nresults in an example where the line graph of a non-word-representable graph is\nboth 3-semi-transitive and semi-transitive and thus is word-representable.\n"", 'Word-representability of co-bipartite graph   A graph $G = (V, E)$ is word-representable, if there exists a word $w$ over\nthe alphabet $V$ such that for letters $\\{x,y\\}\\in V$, $x$ and $y$ alternate in\n$w$ if and only if $xy \\in E$. A graph is co-bipartite if its complement is a\nbipartite graph. Therefore, the vertex set of a co-bipartite graph can be\npartitioned into two disjoint cliques.\n  The concept of word-representability for co-bipartite graphs has not yet been\nfully studied. In the book Words and Graphs written by Sergey Kitaev and Vadim\nLozin, examples of co-bipartite graphs that are not word-representable are\nprovided. The authors have stated that it remains an open problem to\ncharacterize word-representable co-bipartite graphs. It is known that taking\nthe complement of word-representable graphs does not preserve their\nword-representability. In this paper, we first identify certain classes of\nbipartite graphs for which word-representation is preserved after the\ncomplement operation. We found that the complement of the path graphs, even\ncycle graphs and generalized crown graphs are also word-representable. Next, we\naim to find word-representable co-bipartite graphs in which the size of one\nclique partition is fixed while the other one can vary. We studied the\nword-representability of co-bipartite graphs where the sizes of one clique\npartition are $2$ and $3$. We found that any co-bipartite graphs where the size\nof the one clique partition is $2$ are word-representable. Also, when the size\nof the one clique partition is $3$, we found certain co-bipartite graphs are\nword-representable. Additionally, for word-representable graphs, it has been\nestablished that a graph is word-representable if and only if it can be\noriented in a specific manner, known as semi-transitive orientation. We provide\nthe necessary and sufficient conditions for a co-bipartite graph to have a\nsemi-transitive orientation.\n', 'p-complete square-free Word-representation of Word-representable Graphs   A graph $G = (V,E)$ is word-representable, if there exists a word $w$ over\nthe alphabet $V$ such that for letters ${x,y} \\in V$ , $x$ and $y$ alternate in\n$w$ if and only if $xy$ is an edge in the graph $G$. In this paper, we\nintroduce the concept of $p$-complete square-free word-representable graph\n$G(V,E)$. A word $w$ defined over alphabet $V$ is called $p$-complete\nsquare-free word if there does not exist any subset $S\\subseteq \\Sigma$ such\nthat the word $w_{S}$ contains a square $XX$ where $|X| \\ge p$ and $1\\le p \\le\n|w|/2$. A word-representable graph is considered $p$-complete square-free\nword-representable if there exists a $p$-complete square-free word-representant\nof that graph. This pattern is significant as it proves the existence of\npatterns that do not depend on graph labelling and cannot be avoided by certain\nclasses of word-representable graphs. The class of word-representable graphs\nincludes both $p$-complete square-free word-representable graphs and\nnon-$p$-complete square-free word-representable graphs. Additionally, this\nconcept generalises the square pattern found in the words. A word-representable\ngraph is $p$-complete square-free uniform word-representable if its\n$p$-complete square-free word-representant is a uniform word. We analyse the\nproperties of $p$-complete square-free uniform words and find that the graphs\nrepresented by these words avoid having $K_p$ (the complete graph on $p$\nvertices) as an induced subgraph. We provide classifications for small values\nof $p$: for $p=1$, only complete graphs and for $p=2$, only complete and\nedgeless graphs satisfy the condition. We find that $K_3$-free circle graphs\nare 3-complete square-free uniform word-representable. Furthermore, we\nestablish that only graphs with representation number at most 3 can be\n3-complete square-free uniform word-representable and provide a constructive\nmethod to generate such graphs.\n']","[('graphs representation', 0.6004917621612549), ('graphs represented', 0.5611128211021423), ('graph can', 0.5004928708076477), ('representability', 0.4925727844238281), ('graph universal', 0.48836222290992737), ('graphs', 0.4859306216239929), ('graphs introduced', 0.4752061367034912), ('whether every graph', 0.4750598669052124), ('graph semi', 0.47152626514434814), ('comparability graphs', 0.4712688624858856)]"
1025,1025,29,1025_stratified spaces_stratified space_spaces stratified_homotopy theory,"['stratified spaces', 'stratified space', 'spaces stratified', 'homotopy theory', 'homotopy theories', 'homotopy type theory', 'equivalent homotopy', 'theory stratified', 'spaces homotopy', 'homotopy']","[""On the homotopy theory of stratified spaces   Let $P$ be a poset. We define a new homotopy theory of suitably nice\n$P$-stratified topological spaces with equivalences on strata and links\ninverted. We show that the exit-path construction of MacPherson, Treumann, and\nLurie defines an equivalence from our homotopy theory of $P$-stratified\ntopological spaces to the $\\infty$-category of $\\infty$-categories with a\nconservative functor to $P$. This proves a stratified form of Grothendieck's\nhomotopy hypothesis, verifying a conjecture of Ayala-Francis-Rozenblyum. Our\nhomotopy theory of stratified spaces has the added benefit of capturing all\nexamples of geometric interest: conically stratified spaces fit into our\ntheory, and the Ayala-Francis-Tanaka-Rozenblyum homotopy theory of conically\nsmooth stratified spaces embeds into ours.\n"", ""Presenting the topological stratified homotopy hypothesis   This article is concerned with three different homotopy theories of\nstratified spaces: The one defined by Douteau and Henriques, the one defined by\nHaine, and the one defined by Nand-Lal. One of the central questions concerning\nthese theories has been how precisely they connect with geometric and\ntopological examples of stratified spaces, such as piecewise linear\npseudomanifolds, Whitney stratified spaces, or more recently Ayala, Francis and\nTanaka's conically smooth stratified spaces. More precisely, so far, it has\nbeen an open question whether there exist (semi-)model structures on stratified\ntopological spaces that present these theories, in which such relevant examples\nof stratified spaces are bifibrant. Here, we prove an affirmative answer to\nthis question. As a consequence, we obtain a model categorical interpretation\nof a stratified homotopy hypothesis. Specifically, we show that Lurie's\nstratified singular simplicial set functor induces a Quillen equivalence\nbetween the semimodel category of stratified topological spaces presenting\nNand-Lal's homotopy theory of stratified spaces and the left Bousfield\nlocalization of the Joyal model structure that corresponds to such\n$\\infty$-categories in which every endomorphism is an isomorphism. We then\nperform a detailed investigation of bifibrant objects in these model structures\nof stratified spaces, proving a series of detection criteria and illuminating\nthe relationship to Quinn's homotopically stratified spaces.\n"", ""A Simplicial Approach to Stratified Homotopy Theory   In this article we consider the homotopy theory of stratified spaces through\na simplicial point of view. We first consider a model category of filtered\nsimplicial sets over some fixed poset $P$, and show that it is a simplicial\ncombinatorial model category. We then define a generalization of the homotopy\ngroups for any fibrant filtered simplicial set $X$ : the filtered homotopy\ngroups $s\\pi_n(X)$. They are diagrams of groups built from the homotopy groups\nof the different pieces of $X$. We then show that the weak equivalences are\nexactly the morphisms that induce isomorphisms on those filtered homotopy\ngroups.\n  Then, using filtered versions of the topological realisation of a simplicial\nset and of the simplicial set of singular simplices, we transfer those results\nto a category whose objects are topological spaces stratified over $P$. In\nparticular, we get a stratified version of Whitehead's theorem. Specializing to\nthe case of conically stratified spaces, a wide class of topological stratified\nspaces, we recover a theorem of Miller saying that to understand the homotopy\ntype of conically stratified spaces, one only has to understand the homotopy\ntype of strata and holinks. We then provide a family of examples of conically\nstratified spaces and of computations of their filtered homotopy groups.\n""]","[('stratified spaces', 0.7022066712379456), ('stratified space', 0.6375291347503662), ('spaces stratified', 0.6347542405128479), ('homotopy theory', 0.6242014765739441), ('homotopy theories', 0.6227733492851257), ('homotopy type theory', 0.5981706380844116), ('equivalent homotopy', 0.5898247957229614), ('theory stratified', 0.5769233107566833), ('spaces homotopy', 0.563904881477356), ('homotopy', 0.5583460927009583)]"
1026,1026,29,1026_galois groups_galois group_galois group field_galois,"['galois groups', 'galois group', 'galois group field', 'galois', 'galois representations', 'galois group acts', 'absolute galois group', 'action galois', 'absolute galois', 'monodromy groups']","['The arithmetic basilica: a quadratic PCF arboreal Galois group   The arboreal Galois group of a polynomial $f$ over a field $K$ encodes the\naction of Galois on the iterated preimages of a root point $x_0\\in K$,\nanalogous to the action of Galois on the $\\ell$-power torsion of an abelian\nvariety. We compute the arboreal Galois group of the postcritically finite\npolynomial $f(z) = z^2 - 1$ when the field $K$ and root point $x_0$ satisfy a\nsimple condition. We call the resulting group the arithmetic basilica group\nbecause of its relation to the basilica group associated with the complex\ndynamics of $f$. For $K=\\mathbb{Q}$, our condition holds for infinitely many\nchoices of $x_0$.\n', ""Constraining images of quadratic arboreal representations   In this paper, we prove several results on finitely generated dynamical\nGalois groups attached to quadratic polynomials. First we show that, over\nglobal fields, quadratic post-critically finite polynomials are precisely those\nhaving an arboreal representation whose image is topologically finitely\ngenerated. To obtain this result, we also prove the quadratic case of Hindes'\nconjecture on dynamical non-isotriviality. Next, we give two applications of\nthis result. On the one hand, we prove that quadratic polynomials over global\nfields with abelian dynamical Galois group are necessarily post-critically\nfinite, and we combine our results with local class field theory to classify\nquadratic pairs over $\\mathbb Q$ with abelian dynamical Galois group, improving\non recent results of Andrews and Petsche. On the other hand we show that\nseveral infinite families of subgroups of the automorphism group of the\ninfinite binary tree cannot appear as images of arboreal representations of\nquadratic polynomials over number fields, yielding unconditional evidence\ntowards Jones' finite index conjecture.\n"", 'A Unique Chief Series in the arboreal Galois Group of Belyi Maps   We give a complete description of the normal subgroups of arboreal Galois\ngroups of Belyi maps. The normal groups form a unique chief series. We also\ncarefully compute the discriminate of the iterate of a polynomial minus an\nalgebraic number, which allows us to predict when a such discriminate is a\nperfect square in the base field or intermediate field for a postcritically\nfinite polynomials (PCF). As a consequence we are able to find another PCF\ncubic polynomial that has the same arboreal Galois group as the one of Belyi\nmaps.\n']","[('galois groups', 0.6399621367454529), ('galois group', 0.6143530607223511), ('galois group field', 0.5701354146003723), ('galois', 0.5650089383125305), ('galois representations', 0.5452110171318054), ('galois group acts', 0.5352033376693726), ('absolute galois group', 0.5253764986991882), ('action galois', 0.5081173777580261), ('absolute galois', 0.49658724665641785), ('monodromy groups', 0.44401657581329346)]"
1027,1027,29,1027_latency communication urllc_low latency communication_latency communication_repeat request harq,"['latency communication urllc', 'low latency communication', 'latency communication', 'repeat request harq', 'ultra reliable communications', 'harq incremental redundancy', 'incremental redundancy harq', 'ultra reliable communication', 'redundancy harq ir', 'reliable low latency']","['Outage Performance of Cross-Packet HARQ   As opposed to hybrid automatic repeat request with incremental redundancy\n(HARQ-IR) that all the resources are occupied to resend the redundant\ninformation, cross-packet HARQ (XP-HARQ) allows the introduction of new\ninformation into retransmissions to substantially exploit the remaining\nresources. This letter provides a profound investigation into the outage\nperformance of XP-HARQ. In particular, the exact outage expression of XP-HARQ\nis derived if the maximum number of transmissions is two, and tight outage\nbounds are obtained for more than two transmissions. Moreover, the asymptotic\noutage analysis of XP-HARQ in the high signal-to-noise ratio (SNR) regime is\ncarried out not only to simplify the outage expression, but also to show that\nfull time diversity is achievable by XP-HARQ. The simulation results are\neventually presented for verifications.\n', 'HARQ in Full-Duplex Relay-Assisted Transmissions for URLLC   The Release 16 completion unlocks the road to an exciting phase pertain to\nthe sixth generation (6G) era. Meanwhile, to sustain far-reaching applications\nwith unprecedented challenges in terms of latency and reliability, much\ninterest is already getting intensified toward physical layer specifications of\n6G. In support of this vision, this work exhibits the forward-looking\nperception of full-duplex (FD) cooperative relaying in support of upcoming\ngenerations and adopts as a mean concern the critical contribution of hybrid\nautomatic repeat request (HARQ) mechanism to ultra-reliable and low-latency\ncommunication (URLLC). Indeed, the HARQ roundtrip time (RTT) is known to\ninclude basic physical delays that may cause the HARQ abandonment for the 1 ms\nlatency use case of URLLC. Taking up these challenges, this article proposes a\nhybrid FD amplify-and-forward (AF)-selective decode-and-forward (SDF)\nrelay-based system for URLLC. Over this build system, two HARQ procedures\nwithin which the HARQ RTT is shortened, are suggested to face latency and\nreliability issues, namely, the conventional and the enhanced HARQ procedures.\nWe develop then an analytical framework of this relay based HARQ system within\nits different procedures. Finally, using Monte-Carlo simulations, we confirm\nthe theoretical results and compare the proposed relay-assisted HARQ procedures\nto the source-to-destination (S2D) HARQ-based system where no relay assists the\ncommunication between the source and the destination.\n', 'Analysis and Optimization of HARQ for URLLC   In this paper, we investigate the effectiveness of the hybrid automatic\nrepeat request (HARQ) technique in providing high-reliability and low-latency\nin the finite blocklength (FBL) regime in a single user uplink scenario. We\ncharacterize the packet error rate (PER), throughput, and delay performance of\nchase combining HARQ (CC-HARQ) and incremental redundancy HARQ (IR-HARQ) in\nAWGN and Rayleigh fading channel with $m$ retransmissions. Furthermore, we\nconsider a quasi-static fading channel model, which is more accurate than the\nover-simplified i.i.d. block fading or same channel assumption over consecutive\npackets. We use finite state Markov model under the FBL regime to model\ncorrelative fading. Numerical results present interesting insight into the\nreliability-latency trade-off of HARQ. Furthermore, we formulate an\noptimization problem to maximize the throughput performance of IR-HARQ by\nreducing excessive retransmission overhead for a target packet error\nperformance under different SNRs, Doppler frequencies, and rate regimes.\n']","[('latency communication urllc', 0.5788834095001221), ('low latency communication', 0.5167100429534912), ('latency communication', 0.5155816078186035), ('repeat request harq', 0.5154908895492554), ('ultra reliable communications', 0.5120850801467896), ('harq incremental redundancy', 0.5041979551315308), ('incremental redundancy harq', 0.49833911657333374), ('ultra reliable communication', 0.48139432072639465), ('redundancy harq ir', 0.4757896661758423), ('reliable low latency', 0.46667614579200745)]"
1028,1028,29,1028_distributed storage_distributed storage systems_distributed storage system_storage nodes,"['distributed storage', 'distributed storage systems', 'distributed storage system', 'storage nodes', 'coded storage', 'coded distributed', 'storage systems', 'storage network', 'replication', 'distributed']","[""Coded Data Rebalancing: Fundamental Limits and Constructions   Distributed databases often suffer unequal distribution of data among storage\nnodes, which is known as `data skew'. Data skew arises from a number of causes\nsuch as removal of existing storage nodes and addition of new empty nodes to\nthe database. Data skew leads to performance degradations and\n\\textcolor{black}{thus} necessitates `rebalancing' at regular intervals to\nreduce the amount of skew. We define an $r$-balanced distributed database as a\ndistributed database in which the storage across the nodes has uniform size,\nand each bit of the data is replicated in $r$ distinct storage nodes. We\nconsider the problem of designing such balanced databases along with associated\nrebalancing schemes which maintain the $r$-balanced property under node removal\nand addition operations. We present a class of $r$-balanced databases\n(parameterized by the number of storage nodes) which have the property of\nstructural invariance, i.e., the databases designed for different number of\nstorage nodes have the same essential structure. For this class of $r$-balanced\ndatabases, we present rebalancing schemes which use coded transmissions between\nstorage nodes, and characterize their communication loads under node addition\nand removal. We show that the communication cost incurred to rebalance our\ndistributed database for node addition and removal is optimal, i.e., it\nachieves the minimum possible cost among all possible balanced distributed\ndatabases and rebalancing schemes.\n"", 'Modeling and Optimization of Latency in Erasure-coded Storage Systems   As consumers are increasingly engaged in social networking and E-commerce\nactivities, businesses grow to rely on Big Data analytics for intelligence, and\ntraditional IT infrastructures continue to migrate to the cloud and edge, these\ntrends cause distributed data storage demand to rise at an unprecedented speed.\nErasure coding has seen itself quickly emerged as a promising technique to\nreduce storage cost while providing similar reliability as replicated systems,\nwidely adopted by companies like Facebook, Microsoft and Google. However, it\nalso brings new challenges in characterizing and optimizing the access latency\nwhen erasure codes are used in distributed storage. The aim of this monograph\nis to provide a review of recent progress (both theoretical and practical) on\nsystems that employ erasure codes for distributed storage.\n  In this monograph, we will first identify the key challenges and taxonomy of\nthe research problems and then give an overview of different approaches that\nhave been developed to quantify and model latency of erasure-coded storage.\nThis includes recent work leveraging MDS-Reservation, Fork-Join, Probabilistic,\nand Delayed-Relaunch scheduling policies, as well as their applications to\ncharacterize access latency (e.g., mean, tail, asymptotic latency) of\nerasure-coded distributed storage systems. We will also extend the problem to\nthe case when users are streaming videos from erasure-coded distributed storage\nsystems. Next, we bridge the gap between theory and practice, and discuss\nlessons learned from prototype implementation. In particular, we will discuss\nexemplary implementations of erasure-coded storage, illuminate key design\ndegrees of freedom and tradeoffs, and summarize remaining challenges in\nreal-world storage systems such as in content delivery and caching. Open\nproblems for future research are discussed at the end of each chapter.\n', 'Coded Data Rebalancing for Distributed Data Storage Systems with Cyclic\n  Storage   We consider replication-based distributed storage systems in which each node\nstores the same quantum of data and each data bit stored has the same\nreplication factor across the nodes. Such systems are referred to as balanced\ndistributed databases. When existing nodes leave or new nodes are added to this\nsystem, the balanced nature of the database is lost, either due to the\nreduction in the replication factor, or the non-uniformity of the storage at\nthe nodes. This triggers a rebalancing algorithm, that exchanges data between\nthe nodes so that the balance of the database is reinstated. The goal is then\nto design rebalancing schemes with minimal communication load. In a recent work\nby Krishnan et al., coded transmissions were used to rebalance a carefully\ndesigned distributed database from a node removal or addition. These coded\nrebalancing schemes have optimal communication load, however, require the\nfile-size to be at least exponential in the system parameters. In this work, we\nconsider a cyclic balanced database (where data is cyclically placed in the\nsystem nodes) and present coded rebalancing schemes for node removal and\naddition in such a database. These databases (and the associated rebalancing\nschemes) require the file-size to be only cubic in the number of nodes in the\nsystem. We bound the advantage of our node removal rebalancing scheme over the\nuncoded scheme, and show that our scheme has a smaller communication load. In\nthe node addition scenario, the rebalancing scheme presented is a simple\nuncoded scheme, which we show has optimal load. Finally, we derive a lower\nbound for the single node-removal rebalancing for the specific choice of data\nplacements specified by our achievable rebalancing schemes, and show that our\nachievable rebalancing loads are within a multiplicative gap from the lower\nbound obtained.\n']","[('distributed storage', 0.6698455810546875), ('distributed storage systems', 0.6336469650268555), ('distributed storage system', 0.6199200749397278), ('storage nodes', 0.5853592157363892), ('coded storage', 0.5677309036254883), ('coded distributed', 0.5359740853309631), ('storage systems', 0.5073490142822266), ('storage network', 0.4975948631763458), ('replication', 0.4974468946456909), ('distributed', 0.4833756685256958)]"
1029,1029,29,1029_turing instability_turing patterns_reaction diffusion systems_turing,"['turing instability', 'turing patterns', 'reaction diffusion systems', 'turing', 'stable steady states', 'reaction diffusion models', 'stable steady state', 'diffusion systems', 'bifurcation', 'numerical bifurcation']","['Turing pattern or system heterogeneity? A numerical continuation\n  approach to assessing the role of Turing instabilities in heterogeneous\n  reaction-diffusion systems   Turing patterns in reaction-diffusion (RD) systems have classically been\nstudied only in RD systems which do not explicitly depend on independent\nvariables such as space. In practise, many systems for which Turing patterning\nis important are not homogeneous with ideal boundary conditions. In\nheterogeneous systems with stable steady states, the steady states are also\nnecessarily heterogeneous which is problematic for applying the classical\nanalysis. Whilst there has been some work done to extend Turing analysis to\nsome heterogeneous systems, for many systems it is still difficult to determine\nif a stable patterned state is driven purely by system heterogeneity or if a\nTuring instability is playing a role. In this work, we try to define a\nframework which uses numerical continuation to map heterogeneous RD systems\nonto a sensible nearby homogeneous system. This framework may be used for\ndiscussing the role of Turing instabilities in establishing patterns in\nheterogeneous RD systems. We study the Schnakenberg and Gierer-Meinhardt models\nwith spatially heterogeneous production as test problems. It is shown that for\nsufficiently large system heterogeneity (large amplitude spatial variations in\nmorphogen production) it is possible that Turing-patterned and base states\nbecome coincident and therefore impossible to distinguish. Other exotic\nbehaviour is also shown to be possible. We also study a novel scenario in which\nmorphogen is produced locally at levels that could support Turing patterning\nbut on intervals/patches which are on the scale of classical critical domain\nlengths. Without classical domain boundaries, Turing patterns are allowed to\nbleed through; an effect noted by other authors. In this case, this phenomena\neffectively changes the critical domain length. Indeed, we even note that this\nphenomena may also effectively couple local patches together and drive\ninstability in this way.\n', 'Turing instability and Turing-Hopf bifurcation in diffusive Schnakenberg\n  systems with gene expression time delay   For delayed reaction-diffusion Schnakenberg systems with Neumann boundary\nconditions, critical conditions for Turing instability are derived, which are\nnecessary and sufficient. And existence conditions for Turing, Hopf and\nTuring-Hopf bifurcations are established. Normal forms truncated to order 3 at\nTuring-Hopf singularity of codimension 2, are derived. By investigating\nTuring-Hopf bifurcation, the parameter regions for the stability of a periodic\nsolution, a pair of spatially inhomogeneous steady states and a pair of\nspatially inhomogeneous periodic solutions, are derived in $(\\tau,\\varepsilon)$\nparameter plane ($\\tau$ for time delay, $\\varepsilon$ for diffusion rate). It\nis revealed that joint effects of diffusion and delay can lead to the\noccurrence of mixed spatial and temporal patterns. Moreover, it is also\ndemonstrated that various spatially inhomogeneous patterns with different\nspatial frequencies can be achieved via changing the diffusion rate. And, the\nphenomenon that time delay may induce a failure of Turing instability observed\nby Gaffney and Monk (2006) are theoretically explained.\n', ""The role of spatial dimension in the emergence of localised radial\n  patterns from a Turing instability   The emergence of localised radial patterns from a Turing instability has been\nwell studied in two and three dimensional settings and predicted for higher\nspatial dimensions. We prove the existence of localised $(n+1)$-dimensional\nradial patterns in general two-component reaction-diffusion systems near a\nTuring instability, where $n>0$ is taken to be a continuous parameter. We\ndetermine explicit dependence of each pattern's radial profile on the dimension\n$n$ through the introduction of $(n+1)$-dimensional Bessel functions, revealing\na deep connection between the formation of localised radial patterns in\ndifferent spatial dimensions.\n""]","[('turing instability', 0.6855348348617554), ('turing patterns', 0.5989254713058472), ('reaction diffusion systems', 0.5111508369445801), ('turing', 0.4994262456893921), ('stable steady states', 0.477181077003479), ('reaction diffusion models', 0.4756838083267212), ('stable steady state', 0.45967987179756165), ('diffusion systems', 0.4558744728565216), ('bifurcation', 0.44914767146110535), ('numerical bifurcation', 0.4419858455657959)]"
1030,1030,29,1030_morse boundary_hyperbolic spaces_boundary group_hyperbolic space,"['morse boundary', 'hyperbolic spaces', 'boundary group', 'hyperbolic space', 'gromov boundary', 'cat spaces', 'boundary hyperbolic', 'quasi geodesic', 'hyperbolic groups', 'quasi geodesics']","['Topological and Dynamic Properties of the Sublinearly Morse Boundary and\n  the Quasi-Redirecting Boundary   Sublinearly Morse boundaries of proper geodesic spaces are introduced by\nQing, Rafi and Tiozzo. Expanding on this work, Qing and Rafi recently developed\nthe quasi-redirecting boundary, denoted $\\partial G$, to include all directions\nof metric spaces at infinity. Both boundaries are topological spaces that\nconsist of equivalence classes of quasi-geodesic rays and are\nquasi-isometrically invariant. In this paper, we study these boundaries when\nthe space is equipped with a geometric group action. In particular, we show\nthat $G$ acts minimally on $\\partial_\\kappa G$ and that contracting elements of\nG induces a weak north-south dynamic on $\\partial_\\kappa G$. We also prove,\nwhen $\\partial G$ exists and $|\\partial_\\kappa G|\\geq3$, $G$ acts minimally on\n$\\partial G$ and $\\partial G$ is a second countable topological space. The last\nsection concerns the restriction to proper CAT(0) spaces and finite dimensional\n\\CAT cube complexes. We show that when $G$ acts geometrically on a finite\ndimensional CAT(0) cube complex (whose QR boundary is assumed to exist), then a\nnontrivial QR boundary implies the existence of a Morse element in $G$. Lastly,\nwe show that if $X$ is a proper cocompact CAT(0) space, then $\\partial G$ is a\nvisibility space.\n', 'Curtain Characterization of Sublinearly Morse Geodesics in CAT(0) Spaces   We show that the sublinear Morse boundary of every CAT(0) space continuously\ninjects into the Gromov boundary of a hyperbolic space, which was not\npreviously known even for all CAT(0) cube complexes. Our work utilizes the\ncurtain machinery introduced by Petyt-Spriano-Zalloum. Curtains are more\ngeneral combinatorial analogues of hyperplanes in cube complexes, and we\ndevelop multiple curtain characterizations of the sublinear Morse property\nalong the way. Our results answer multiple questions of Petyt-Spriano-Zalloum.\n', 'Geometry and dynamics on sublinearly Morse boundaries of CAT(0) groups   Given a sublinear function $\\kappa$, $\\kappa$-Morse boundaries $\\pka X$ of\nproper \\CAT spaces are introduced by Qing, Rafi and Tiozzo. It is a topological\nspace that consists of a large set of quasi-geodesic rays and it is\nquasi-isometrically invariant and metrizable.\n  In this paper, we study the sublinearly Morse boundaries with the assumption\nthat there is a proper cocompact action of a group $G$ on the \\CAT space in\nquestion. We show that $G$ acts minimally on $\\pka G$ and that contracting\nelements of $G$ induces a weak north-south dynamic on $\\pka G$. Furthermore, we\nshow that a homeomorphism $f \\from \\pka G \\to \\pka G\'$ comes from a\nquasi-isometry if and only if $f$ is successively quasi-m{\\""o}bius and stable.\nLastly, we characterize exactly when the sublinearly Morse boundary of a \\CAT\nspace is compact.\n']","[('morse boundary', 0.5713990926742554), ('hyperbolic spaces', 0.5305982232093811), ('boundary group', 0.5235651135444641), ('hyperbolic space', 0.491107702255249), ('gromov boundary', 0.48264744877815247), ('cat spaces', 0.46001487970352173), ('boundary hyperbolic', 0.45914727449417114), ('quasi geodesic', 0.4581272304058075), ('hyperbolic groups', 0.4574717879295349), ('quasi geodesics', 0.4563245177268982)]"
1031,1031,29,1031_quantum systems_quantum circuits_fermionic quantum field_quantum,"['quantum systems', 'quantum circuits', 'fermionic quantum field', 'quantum', 'entanglement entropy', 'quantum field theory', 'unitary transformations', 'von neumann entropy', 'abelian symmetries', 'correlation functions quantum']","['Qudit circuits with SU(d) symmetry: Locality imposes additional\n  conservation laws   Local symmetric quantum circuits provide a simple framework to study the\ndynamics and phases of complex quantum systems with conserved charges. However,\nsome of their basic properties have not yet been understood. Recently, it has\nbeen shown that such quantum circuits only generate a restricted subset of\nsymmetric unitary transformations [I. Marvian, Nature Physics, 2022]. In this\npaper, we consider circuits with 2-local SU(d)-invariant unitaries acting on\nqudits, i.e., d-dimensional quantum systems. Our results reveal a significant\ndistinction between the cases of d = 2 and d>2. For qubits with SU(2) symmetry,\narbitrary global rotationally-invariant unitaries can be generated with 2-local\nones, up to relative phases between the subspaces corresponding to inequivalent\nirreducible representations (irreps) of the symmetry, i.e., sectors with\ndifferent angular momenta. On the other hand, for d>2, in addition to similar\nconstraints on the relative phases between the irreps, locality also restricts\nthe generated unitaries inside these conserved subspaces. These constraints\nimpose conservation laws that hold for dynamics under 2-local SU(d)-invariant\nunitaries, but are violated under general SU(d)-invariant unitaries. Based on\nthis result, we show that the distribution of unitaries generated by random\n2-local SU(d)-invariant unitaries does not converge to the Haar measure over\nthe group of all SU(d)-invariant unitaries, and in fact, for d>2, is not even a\n2-design for the Haar distribution.\n', 'A framework for semi-universality: Semi-universality of 3-qudit\n  SU(d)-invariant gates   Quantum circuits with symmetry-respecting gates have attracted broad interest\nin quantum information science. While recent work has developed a theory for\ncircuits with Abelian symmetries, revealing important distinctions between\nAbelian and non-Abelian cases, a comprehensive framework for non-Abelian\nsymmetries has been lacking. In this work, we develop novel techniques and a\npowerful framework that is particularly useful for understanding circuits with\nnon-Abelian symmetries. Using this framework we settle an open question on\nquantum circuits with SU(d) symmetry. We show that 3-qudit SU(d)-invariant\ngates are semi-universal, i.e., generate all SU(d)-invariant unitaries, up to\ncertain constraints on the relative phases between sectors with inequivalent\nrepresentation of symmetry. Furthermore, we prove that these gates achieve full\nuniversality when supplemented with 3 ancilla qudits. Interestingly, we find\nthat studying circuits with 3-qudit gates is also useful for a better\nunderstanding of circuits with 2-qudit gates. In particular, we establish that\neven though 2-qudit SU(d)-invariant gates are not themselves semi-universal,\nthey become universal with at most 11 ancilla qudits. Additionally, we\ninvestigate the statistical properties of circuits composed of random\nSU(d)-invariant gates. Our findings reveal that while circuits with 2-qudit\ngates do not form a 2-design for the Haar measure over SU(d)-invariant\nunitaries, circuits with 3-qudit gates generate a t-design, with t that is\nquadratic in the number of qudits.\n', 'Theory of Quantum Circuits with Abelian Symmetries   Quantum circuits with gates (local unitaries) respecting a global symmetry\nhave broad applications in quantum information science and related fields, such\nas condensed matter theory and quantum thermodynamics. However, despite their\nwidespread use, fundamental properties of such circuits are not\nwell-understood. Recently, it was found that generic unitaries respecting a\nglobal symmetry cannot be realized, even approximately, using gates that\nrespect the same symmetry. This observation raises important open questions:\nWhat unitary transformations can be realized with k-local gates that respect a\nglobal symmetry? In other words, in the presence of a global symmetry, how does\nthe locality of interactions constrain the possible time evolution of a\ncomposite system? In this work, we address these questions for the case of\nAbelian (commutative) symmetries and develop constructive methods for\nsynthesizing circuits with such symmetries. Remarkably, as a corollary, we find\nthat, while the locality of interactions still imposes additional constraints\non realizable unitaries, certain restrictions observed in the case of\nnon-Abelian symmetries do not apply to circuits with Abelian symmetries. For\ninstance, in circuits with a general non-Abelian symmetry such as SU($d$), the\nunitary realized in a subspace with one irreducible representation (charge) of\nthe symmetry dictates the realized unitaries in multiple other sectors with\ninequivalent representations of the symmetry. Furthermore, in certain sectors,\nrather than all unitaries respecting the symmetry, the realizable unitaries are\nthe symplectic or orthogonal subgroups of this group. We prove that none of\nthese restrictions appears in the case of Abelian symmetries. This result\nsuggests that global non-Abelian symmetries may affect the thermalization of\nquantum systems in ways not possible under Abelian symmetries.\n']","[('quantum systems', 0.4986848533153534), ('quantum circuits', 0.4800262749195099), ('fermionic quantum field', 0.44065776467323303), ('quantum', 0.4249594807624817), ('entanglement entropy', 0.42492297291755676), ('quantum field theory', 0.4226353168487549), ('unitary transformations', 0.4149399697780609), ('von neumann entropy', 0.4136379361152649), ('abelian symmetries', 0.4087428152561188), ('correlation functions quantum', 0.4075755476951599)]"
1032,1032,29,1032_vortex solutions_vortex equations_vortex dynamics_landau vortices,"['vortex solutions', 'vortex equations', 'vortex dynamics', 'landau vortices', 'vortex', 'vortex lines', 'chern simons higgs', 'vortices two', 'vortices', 'gauge field theory']","['Analytic Approach for Computation of Topological Number of Integrable\n  Vortex on Torus   An analytic method to calculate the vortex number on a torus is constructed,\nfocusing on analytic vortex solutions to the Chern-Simons-Higgs theory, whose\ngoverning equation is the so-called Jackiw-Pi equation. The equation is one of\nthe integrable vortex equations and is reduced to Liouville\'s equation. The\nrequirement of continuity of the Higgs field strongly restricts the\ncharacteristics and the fundamental domain of the vortices. Also considered are\nthe decompactification limits of the vortices on a torus, in which ""flux loss""\nphenomena occasionally occur.\n', ""Bogomol'nyi Equations and Coexistence of Vortices and Antivortices in\n  Generalized Abelian Higgs Theories   We derive the Bogomol'nyi equations in generalized Abelian Higgs theories\nwhich allow the coexistence of vortices and antivortices over a compact Riemann\nsurface or the full plane. In the compact surface situation, we obtain a\nnecessary and sufficient condition for the existence of a unique solution\ndescribing a system of coexisting vortices and antivortices. In the full-plane\nsituation, we prove the existence of a unique solution representing an\narbitrary distribution of vortices and antivortices and obtain sharp asymptotic\nbehavior of the solution near infinity. These solutions carry quantized\nmagnetic fluxes and energies explicitly expressed in terms of the numbers of\nvortices and antivortices topologically characterized by the first Chern and\nThom classes.\n"", 'Nineteen vortex equations and integrability   The class of five integrable vortex equations discussed recently by Manton is\nextended so it includes the relativistic BPS Chern-Simons vortices, yielding a\ntotal of nineteen vortex equations. Not all the nineteen vortex equations are\nintegrable, but four new integrable equations are discovered and we generalize\nthem to infinitely many sets of four integrable vortex equations, with each set\ndenoted by its integer order $n$. Their integrability is similar to the known\ncases, but give rise to different (generalized) Baptista geometries, where the\nBaptista metric is a conformal rescaling of the background metric by the Higgs\nfield. In particular, the Baptista manifolds have conical singularities. Where\nthe Jackiw-Pi, Taubes, Popov and Ambj{\\o}rn-Olesen vortices have conical\ndeficits of $2\\pi$ at each vortex zero in their Baptista manifolds, the\nhigher-order generalizations of these equations are also integrable with larger\nconstant curvatures and a $2\\pi n$ conical deficit at each vortex zero. We then\ngeneralize a superposition law, known for Taubes vortices of how to add\nvortices to a known solution, to all the integrable vortex equations. We find\nthat although the Taubes and the Popov equations relate to themselves, the\nAmbj{\\o}rn-Olesen and Jackiw-Pi vortices are added by using the Baptista metric\nand the Popov equation. Finally, we find many further relations between vortex\nequations, e.g. we find that the Chern-Simons vortices can be interpreted as\nTaubes vortices on the Baptista manifold of their own solution.\n']","[('vortex solutions', 0.6289128065109253), ('vortex equations', 0.5992940068244934), ('vortex dynamics', 0.5585494637489319), ('landau vortices', 0.5140738487243652), ('vortex', 0.5058795809745789), ('vortex lines', 0.4820218086242676), ('chern simons higgs', 0.4806605279445648), ('vortices two', 0.47906213998794556), ('vortices', 0.47254133224487305), ('gauge field theory', 0.45781445503234863)]"
1033,1033,29,1033_monotone boolean functions_boolean functions_functions counting_monotone boolean,"['monotone boolean functions', 'boolean functions', 'functions counting', 'monotone boolean', 'functions boolean', 'functions enumeration', 'boolean degree', 'boolean', 'pseudo boolean', 'discrete functions']","['Counting self-dual monotone Boolean functions   Let $D_n$ denote the set of monotone Boolean functions with $n$ variables.\nElements of $D_n$ can be represented as strings of bits of length $2^n$. Two\nelements of $D_0$ are represented as 0 and 1 and any element $g\\in D_n$, with\n$n>0$, is represented as a concatenation $g_0\\cdot g_1$, where $g_0, g_1\\in\nD_{n-1}$ and $g_0\\le g_1$. For each $x\\in D_n$, we have dual $x^*\\in D_n $\nwhich is obtained by reversing and negating all bits. An element $x\\in D_n$ is\nself-dual if $x=x^*$. Let $\\lambda_n$ denote the cardinality of the set of all\nself-dual monotone Boolean functions of $n$ variables. The value $\\lambda_n$ is\nalso known as the $n$-th Hosten-Morris number. In this paper, we derive several\nalgorithms for counting self-dual monotone Boolean functions and confirm the\nknown result that $\\lambda_9$ equals 423,295,099,074,735,261,880.\n', 'Fixes of permutations acting on monotone Boolean functions   We present a few algorithms and methods to count fixes of permutations acting\non monotone Boolean functions. Some of these methods was used by Pawelski\n\\cite{P} to compute the number of inequivalent monotone Boolean functions with\n8 variables.\n', ""On the number of inequivalent monotone Boolean functions of 8 variables   In this paper, the author presents algorithms that allow determining the\nnumber of fixed points in permutations of a set of monotone Boolean functions.\nThen, using Burnside's lemma, the author determines the number of inequivalent\nmonotone Boolean functions of 8 variables. The number obtained is\n1,392,195,548,889,993,358.\n""]","[('monotone boolean functions', 0.6673208475112915), ('boolean functions', 0.6115933656692505), ('functions counting', 0.5860558748245239), ('monotone boolean', 0.5566320419311523), ('functions boolean', 0.5454071164131165), ('functions enumeration', 0.4938451051712036), ('boolean degree', 0.46987971663475037), ('boolean', 0.4456627368927002), ('pseudo boolean', 0.4264973998069763), ('discrete functions', 0.4191090166568756)]"
1034,1034,29,1034_quantum codes_codes quantum_quantum code_stabilizer codes,"['quantum codes', 'codes quantum', 'quantum code', 'stabilizer codes', 'classical codes', 'quantum stabilizer', 'stabilizer quantum', 'constacyclic codes', 'codes defined', 'linear codes']","['A Symbol-Pair Decoder for CSS Codes   The relation between stabilizer codes and binary codes provided by Gottesman\nand Calderbank et al. is a celebrated result, as it allows the lifting of\nclassical codes to quantum codes. An equivalent way to state this result is\nthat the work allows us to lift decoders for classical codes over the Hamming\nmetric to decoders for stabilizer quantum codes. A natural question to\nconsider: Can we do something similar with decoders for classical codes\nconsidered over other metrics? i.e., Can we lift decoders for classical codes\nover other metrics to obtain decoders for stabilizer quantum codes? In our\ncurrent work, we answer this question in the affirmative by considering\nclassical codes over the symbol-pair metric. In particular, we present a\nrelation between the symplectic weight and the symbol-pair weight and use it to\nimprove the error correction capability of CSS-codes (a well-studied class of\nstabilizer codes) obtained from cyclic codes.\n', 'MDS Entanglement-Assisted Quantum Codes of Arbitrary Lengths and\n  Arbitrary Distances   Quantum error correction is fundamentally important for quantum information\nprocessing and computation. Quantum error correction codes have been studied\nand constructed since the pioneering papers of Shor and Steane. Optimal (called\nMDS) $q$-qubit quantum codes attaining the quantum Singleton bound were\nconstructed for very restricted lengths $n \\leq q^2+1$. Entanglement-assisted\nquantum error correction (EAQEC) code was proposed to use the pre-shared\nmaximally entangled state for the enhancing of error correction capability.\nRecently there have been a lot of constructions of MDS EAQEC codes attaining\nthe quantum Singleton bound for very restricted lengths. In this paper we\nconstruct such MDS EAQEC $[[n, k, d, c]]_q$ codes for arbitrary $n$ satisfying\n$n \\leq q^2+1$ and arbitrary distance $d\\leq \\frac{n+2}{2}$. It is proved that\nfor any given length $n$ satisfying $O(q^2)=n \\leq q^2+1$ and any given\ndistance $d$ satisfying $ O(q^2)=d \\leq \\frac{n+2}{2}$, there exist at least\n$O(q^2)$ MDS EAQEC $[[n, k, d, c]]_q$ codes with different $c$ parameters. Our\nresults show that there are much more MDS entanglement-assisted quantum codes\nthan MDS quantum codes without consumption of the maximally entangled state.\nThis is natural from the physical point of view. Our method can also be applied\nto construct MDS entanglement-assisted quantum codes from the generalized MDS\ntwisted Reed-Solomon codes.\n', 'Quotient Space Quantum Codes   Additive codes and some nonadditive codes use the single and multiple\ninvariant subspaces of the stabilizer G, respectively, to construct quantum\ncodes, so the selection of the invariant subspaces is a key problem. In this\npaper, I provide the necessary and sufficient conditions for this problem and,\nestablish the quotient space codes to construct quantum codes. These new codes\nunify additive codes and codeword stabilized codes and can transmit classical\ncodewords. Actually, I give an alternative approach to constructing union\nstabilizer codes, which is different from that of Markus Grassl and Martin\nRoetteler, and which is easier to deal with degenerate codes. I also present\nnew bounds for quantum codes and provide a simple proof of the quantum\nSingleton bound. The quotient space approach provides a concise and clear\nmathematical framework for the study of quantum error-correcting codes.\n']","[('quantum codes', 0.7710354328155518), ('codes quantum', 0.7701281905174255), ('quantum code', 0.7054678201675415), ('stabilizer codes', 0.6378660202026367), ('classical codes', 0.6326882839202881), ('quantum stabilizer', 0.567755937576294), ('stabilizer quantum', 0.5420401096343994), ('constacyclic codes', 0.5122016668319702), ('codes defined', 0.5028871297836304), ('linear codes', 0.501413881778717)]"
1035,1035,29,1035_matrix integrals_schur functions_superintegrability_schur polynomials,"['matrix integrals', 'schur functions', 'superintegrability', 'schur polynomials', 'super integrability', 'superintegrable', 'matrix models', 'gaussian measures', 'gaussian matrix', 'schur']","['Superintegrability of the Wilson family of matrix models and moments of\n  multivariable orthogonal polynomials   We present new examples of superintegrable matrix/eigenvalue models. These\nexamples arise as a result of the exploration of the relationship between the\ntheory of superintegrability and multivariate orthogonal polynomials. The new\nsuperintegrable examples are built upon the multivariate generalizations of the\nMeixner-Pollaczek and Wilson polynomials and their respective measures. From\nthe perspective of multivariate orthogonal polynomials in this work we propose\nexpressions for (generalized) moments of the respective multi-variable\nmeasures. From the perspective of superintegrability we uncover a couple of new\nphenomena such as the deviation from Schur polynomials as the superintegrable\nbasis without any deformation and new combinatorial structures appearing in the\nanswers.\n', 'Superintegrability of Kontsevich matrix model   Many eigenvalue matrix models possess a peculiar basis of observables which\nhave explicitly calculable averages. This explicit calculability is a stronger\nfeature than ordinary integrability, just like the cases of quadratic and\nCoulomb potentials are distinguished among other central potentials, and we\ncall it superintegrability. Aa a peculiarity of matrix models, the relevant\nbasis is formed by the Schur polynomials (characters) and their\ngeneralizations, and superintegrability looks like a property\n$<character>\\,\\sim character$. This is already known to happen in the most\nimportant cases of Hermitian, unitary, and complex matrix models. Here we add\ntwo more examples of principal importance, where the model depends on external\nfields: a special version of the complex model and the cubic Kontsevich model.\nIn the former case, straightforward is a generalization to the complex tensor\nmodel. In the latter case, the relevant characters are the celebrated $Q$ Schur\nfunctions appearing in the description of spin Hurwitz numbers and other\nrelated contexts.\n', 'Superintegrability of the monomial Uglov matrix model   In this paper we propose a resolution to the problem of $\\beta$-deforming the\nnon-Gaussian monomial matrix models. The naive guess of substituting Schur\npolynomials with Jack polynomials does not work in that case, therefore, we are\nforced to look for another basis for superintegrability. We find that the\nrelevant symmetric functions are given by Uglov polynomials, and that the\nintegration measure should also be deformed. The measure appears to be related\nto the Uglov limit as well, when the quantum parameters $(q,t)$ go to a root of\nunity. The degree of the root must be equal to the degree of the potential. One\ncannot derive these results directly, for example, by studying Virasoro\nconstraints. Instead, we use the recently developed techniques of $W$-operators\nto arrive at the root of unity limit. From the perspective of matrix models\nthis new example demonstrates that even with a rather nontrivial integration\nmeasure one can find a superintegrability basis by studying the hidden symmetry\nof the moduli space of deformations.\n']","[('matrix integrals', 0.5297310948371887), ('schur functions', 0.5210608839988708), ('superintegrability', 0.5205237865447998), ('schur polynomials', 0.5166046619415283), ('super integrability', 0.5090839862823486), ('superintegrable', 0.4643768072128296), ('matrix models', 0.3860208988189697), ('gaussian measures', 0.34924137592315674), ('gaussian matrix', 0.34233224391937256), ('schur', 0.3395567238330841)]"
1036,1036,29,1036_systems hamilton jacobi_convex hamiltonians_hamilton jacobi equations_dependent hamilton jacobi,"['systems hamilton jacobi', 'convex hamiltonians', 'hamilton jacobi equations', 'dependent hamilton jacobi', 'stationary hamilton jacobi', 'solutions hamilton jacobi', 'system hamilton jacobi', 'convex hamiltonian', 'viscosity solutions hamilton', 'hamiltonian gradient']","[""The vanishing discount problem for monotone systems of Hamilton-Jacobi\n  equations. Part 2: Nonlinear coupling   We study the vanishing discount problem for a nonlinear monotone system of\nHamilton-Jacobi equations. This continues the first author's investigation on\nthe vanishing discount problem for a monotone system of Hamilton-Jacobi\nequations. As in Part 1, we introduce by the convex duality Mather measures and\ntheir analogues for the system, which we call respectively Mather and\nGreen-Poisson measures, and prove a convergence theorem for the vanishing\ndiscount problem. Moreover, we establish an existence result for the ergodic\nproblem.\n"", 'The vanishing discount problem for monotone systems of Hamilton-Jacobi\n  equations: a counterexample to the full convergence   In recent years there has been intense interest in the vanishing discount\nproblem for Hamilton-Jacobi equations. In the case of the scalar equation, B.\nZiliotto has recently given an example of the Hamilton-Jacobi equation having\nnon-convex Hamiltonian in the gradient variable, for which the full convergence\nof the solutions does not hold as the discount factor tends to zero. We give\nhere an explicit example of nonlinear monotone systems of Hamilton-Jacobi\nequations having convex Hamiltonians in the gradient variable, for which the\nfull convergence of the solutions fails as the discount factor goes to zero.\n', 'An example in the vanishing discount problem for monotone systems of\n  Hamilton-Jacobi equations   In recent years, there have been many contributions to the vanishing discount\nproblem for Hamilton-Jacobi equations. In the case of the scalar equation, B.\nZiliotto [Convergence of the solutions of the discounted Hamilton-Jacobi\nequation: a counterexample. J. Math. Pures Appl. (9) 128 (2019), 330-338] has\nshown an example of the Hamilton-Jacobi equation having non-convex Hamiltonian\nin the gradient variable, for which the full convergence of the solutions does\nnot hold as the discount factor tends to zero. We give an example of the\nnonlinear monotone system of Hamilton-Jacobi equations having convex\nHamiltonians in the gradient variable, for which the whole family convergence\nof the solutions does not hold.\n']","[('systems hamilton jacobi', 0.5923606157302856), ('convex hamiltonians', 0.590701699256897), ('hamilton jacobi equations', 0.5843735337257385), ('dependent hamilton jacobi', 0.5838894248008728), ('stationary hamilton jacobi', 0.5819247364997864), ('solutions hamilton jacobi', 0.5764891505241394), ('system hamilton jacobi', 0.576463520526886), ('convex hamiltonian', 0.5510275959968567), ('viscosity solutions hamilton', 0.5147202610969543), ('hamiltonian gradient', 0.5052335262298584)]"
1037,1037,29,1037_mathematical reasoning_mathematical arguments_mathematical knowledge_mathematical proofs,"['mathematical reasoning', 'mathematical arguments', 'mathematical knowledge', 'mathematical proofs', 'mathematical practice', 'proof assistants', 'mathematicians', 'proof assistant', 'mathematics', 'automated proof']","['Waterproof: Educational Software for Learning How to Write Mathematical\n  Proofs   In order to help students learn how to write mathematical proofs, we adapt\nthe Coq proof assistant into an educational tool we call Waterproof. Like with\nother interactive theorem provers, students write out their proofs inside the\nsoftware using a specific syntax, and the software provides feedback on the\nlogical validity of each step. Waterproof consists of two components: a custom\nproof language that allows formal, machine-verified proofs to be written in a\nstyle that closely resembles handwritten proofs, and a custom editor that\nallows these proofs to be combined with formatted text to improve readability.\nThe editor can be used for Coq documents in general, but also offers special\nfeatures designed for use in education. Student input, for example, can be\nlimited to specific parts of the document to prevent exercises from being\naccidentally deleted. Waterproof has been used to supplement teaching the\nAnalysis 1 course at Eindhoven University of Technology (TU/e) for the last\nfour years. Students started using the specific formulations of proof steps\nfrom the custom proof language in their handwritten proofs; the explicit\nphrasing of these sentences helped to clarify the logical structure of their\narguments.\n', ""Dialogue Types, Argumentation Schemes, and Mathematical Practice:\n  Douglas Walton and Mathematics   Douglas Walton's multitudinous contributions to the study of argumentation\nseldom, if ever, directly engage with argumentation in mathematics.\nNonetheless, several of the innovations with which he is most closely\nassociated lend themselves to improving our understanding of mathematical\narguments. I concentrate on two such innovations: dialogue types ({\\S}1) and\nargumentation schemes ({\\S}2). I argue that both devices are much more\napplicable to mathematical reasoning than may be commonly supposed.\n"", ""Argumentation in Mathematical Practice   Formal logic has often been seen as uniquely placed to analyze mathematical\nargumentation. While formal logic is certainly necessary for a complete\nunderstanding of mathematical practice, it is not sufficient. Important aspects\nof mathematical reasoning closely resemble patterns of reasoning in\nnonmathematical domains. Hence the tools developed to understand informal\nreasoning, collectively known as argumentation theory, are also applicable to\nmuch mathematical argumentation. This chapter investigates some of the details\nof that application. Consideration is given to the many contrasting meanings of\nthe word ``argument''; to some of the specific argumentation-theoretic tools\nthat have been applied to mathematics, notably Toulmin layouts and\nargumentation schemes; to some of the different ways that argumentation is\nimplicated in mathematical practices; and to the social aspects of mathematical\nargumentation.\n""]","[('mathematical reasoning', 0.6800298094749451), ('mathematical arguments', 0.6411731243133545), ('mathematical knowledge', 0.5510209202766418), ('mathematical proofs', 0.5381566882133484), ('mathematical practice', 0.5325886607170105), ('proof assistants', 0.5150778889656067), ('mathematicians', 0.49849405884742737), ('proof assistant', 0.49799227714538574), ('mathematics', 0.49690285325050354), ('automated proof', 0.49540361762046814)]"
1038,1038,29,1038_harmonic maps riemannian_harmonic maps_harmonic map_harmonic map flow,"['harmonic maps riemannian', 'harmonic maps', 'harmonic map', 'harmonic map flow', 'maps riemannian manifolds', 'maps riemannian', 'biharmonic maps', 'riemannian manifolds', 'riemannian manifold', 'maps hyperbolic']","['On stability of subelliptic harmonic maps with potential   In this paper, we investigate the stability problem of subelliptic harmonic\nmaps with potential. First, we derive the first and second variation formulas\nfor subelliptic harmonic maps with potential. As a result, it is proved that a\nsubelliptic harmonic map with potential is stable if the target manifold has\nnonpositive curvature and the Hessian of the potential is nonpositive definite.\nWe also give Leung type results which involve the instability of subelliptic\nharmonic maps with potential when the target manifold is a sphere of dimension\n$\\geq 3$.\n', 'On stability of exponentially subelliptic harmonic maps   In this paper, we study the stability problem of exponentially subelliptic\nharmonic maps from sub-Riemannian manifolds to Riemannian manifolds. We derive\nthe rst and second variation formulas for exponentially subelliptic harmonic\nmaps, and apply these formulas to prove that if the target manifold has\nnonpositive curvature, the exponentially subelliptic harmonic map is stable.\nFurther, we obtain the instability of exponentially subelliptic harmonic maps\nwhen the target manifold is a sphere.\n', 'The geometry of $\\Phi_{(3)}$-harmonic maps   In this paper, we motivate and extend the study of harmonic maps or\n$\\Phi_{(1)}$-harmonic maps (cf [15], Remark 1.3 (iii)), $\\Phi$-harmonic maps or\n$\\Phi_{(2)}$-harmonic maps (cf. [24], Remark 1.3 (v)), and explore geometric\nproperties of $\\Phi_{(3)}$-harmonic maps by unified geometric analytic methods.\nWe define the notion of $\\Phi_{(3)}$-harmonic maps and obtain the first\nvariation formula and the second variation formula of the $\\Phi_{(3)}$-energy\nfunctional $E_{\\Phi_{(3)}}$. By using a stress-energy tensor, the\n$\\Phi_{(3)}$-conservation law, a monotonicity formula, and the asymptotic\nassumption of maps at infinity, we prove Liouville type results for\n$\\Phi_{(3)}$-harmonic maps. We introduce the notion of\n$\\Phi_{(3)}$-Superstrongly Unstable ($\\Phi_{(3)}$-SSU) manifold and provide\nmany interesting examples. By using an extrinsic average variational method in\nthe calculus of variations (cf. [51, 49]), we find $\\Phi_{(3)}$-SSU manifold\nand prove that for $i=1,2,3$, every compact $\\Phi_{(i)}$-$\\operatorname{SSU}$\nmanifold is $\\Phi_{(i)}$-$\\operatorname{SU}$, and hence is\n$\\Phi_{(i)}$-$\\operatorname{U}$ (cf. Theorem 9.3). As consequences, we obtain\ntopological vanishing theorems and sphere theorems by employing a\n$\\Phi_{(3)}$-harmoic map as a catalyst. This is in contrast to the approaches\nof utilizing a geodesic ([45]), minimal surface, stable rectifiable current\n([34, 29, 50]), $p$-harmonic map (cf. [53]), etc., as catalysts. These\nmysterious phenomena are analogs of harmonic maps or $\\Phi_{(1)}$-harmonic\nmaps, $p$-harmonic maps, $\\Phi_{S}$-harmonic maps, $\\Phi_{S,p}$-harmonic maps,\n$\\Phi_{(2)}$-harmonic maps, etc., (cf. [21, 40, 42, 41, 12, 13]).\n']","[('harmonic maps riemannian', 0.7702906727790833), ('harmonic maps', 0.7521147131919861), ('harmonic map', 0.703946590423584), ('harmonic map flow', 0.6491484642028809), ('maps riemannian manifolds', 0.6247592568397522), ('maps riemannian', 0.5946387648582458), ('biharmonic maps', 0.5858522057533264), ('riemannian manifolds', 0.5542789697647095), ('riemannian manifold', 0.5395309925079346), ('maps hyperbolic', 0.5134178400039673)]"
1039,1039,29,1039_flow conjecture_nowhere zero flows_nowhere zero flow_zero flows,"['flow conjecture', 'nowhere zero flows', 'nowhere zero flow', 'zero flows', 'conjecture edge', 'zero flow', 'graph admits', 'signed graphs', 'planar graphs', 'edge connected graphs']","[""Tutte's $3$-Flow Conjecture in $3$-tree-connected graphs   Tutte's $3$-flow conjecture says that every $4$-edge-connected graph admits a\nnowhere-zero $3$-flow. Kochol (2001) showed that it is enough to prove this\nconjecture for $5$-edge-connected graphs. Former, Jaeger, Linial, Payan, and\nTarsi (1992) conjectured that every $5$-edge-connected graph is $Z_3$-connected\nand so it admits a nowhere-zero $3$-flow. In this note, we show that if the\nsecond conjecture would be true, then every $3$-tree-connected graph must also\nbe $Z_3$-connected and so Tutte's $3$-flow conjecture can be extended to this\nfamily of graphs.\n"", 'Flow modules and nowhere-zero flows   Let $\\Gamma$ be a graph, $A$ an abelian group, $\\mathcal{D}$ a given\norientation of $\\Gamma$ and $R$ a unital subring of the endomorphism ring of\n$A$. It is shown that the set of all maps $\\varphi$ from $E(\\Gamma)$ to $A$\nsuch that $(\\mathcal{D},\\varphi)$ is an $A$-flow forms a left $R$-module. Let\n$\\Gamma$ be a union of two subgraphs $\\Gamma_{1}$ and $\\Gamma_{2}$, and $p^n$ a\nprime power. It is proved that $\\Gamma$ admits a nowhere-zero $p^n$-flow if\n$\\Gamma_{1}$ and $\\Gamma_{2}$ have at most $p^n-2$ common edges and both have\nnowhere-zero $p^n$-flows. More important, it is proved that $\\Gamma$ admits a\nnowhere-zero $4$-flow if $\\Gamma_{1}$ and $\\Gamma_{2}$ both have nowhere-zero\n$4$-flows and their common edges induce a connected subgraph of $\\Gamma$ of\nsize at most $3$. This covers a result of Catlin that a graph admits a\nnowhere-zero $4$-flow if it is a union of a $4$-cycle and a subgraph admiting a\nnowhere-zero $4$-flow.\n', 'An 8-flow theorem for signed graphs   We prove that a signed graph admits a nowhere-zero $8$-flow provided that it\nis flow-admissible and the underlying graph admits a nowhere-zero $4$-flow.\nWhen combined with the 4-color theorem, this implies that every flow-admissible\nbridgeless planar signed graph admits a nowhere-zero $8$-flow. Our result\nimproves and generalizes previous results of Li et al. (European J. Combin. 108\n(2023), 103627), which state that every flow-admissible signed\n$3$-edge-colorable cubic graph admits a nowhere-zero $10$-flow, and that every\nflow-admissible signed hamiltonian graph admits a nowhere-zero $8$-flow.\n']","[('flow conjecture', 0.6223597526550293), ('nowhere zero flows', 0.5553855299949646), ('nowhere zero flow', 0.5414736866950989), ('zero flows', 0.5096631646156311), ('conjecture edge', 0.5091850161552429), ('zero flow', 0.4910575747489929), ('graph admits', 0.4861889183521271), ('signed graphs', 0.4616298973560333), ('planar graphs', 0.4608856737613678), ('edge connected graphs', 0.4390127956867218)]"
1040,1040,29,1040_cluster algebras_upper cluster algebras_rank cluster algebras_algebras cluster,"['cluster algebras', 'upper cluster algebras', 'rank cluster algebras', 'algebras cluster', 'cluster algebra', 'quantum cluster', 'quantum affine algebras', 'generalized quantum', 'algebras associated', 'algebras arising']","[""On $F$-Polynomials for Generalized Quantum Cluster Algebras and Gupta's\n  Formula   We show the polynomial property of $F$-polynomials for generalized quantum\ncluster algebras and obtain the associated separation formulas under a mild\ncondition. Along the way, we obtain Gupta's formulas of $F$-polynomials for\ngeneralized quantum cluster algebras. These formulas specialize to Gupta's\nformulas for quantum cluster algebras and cluster algebras respectively.\nFinally, a generalization of Gupta's formula has also been discussed in the\nsetting of generalized cluster algebras.\n"", 'Quantum cluster variables via canonical submodules   We study quantum cluster algebras from marked surfaces without punctures. We\nexpress the quantum cluster variables in terms of the canonical submodules. As\na byproduct, we obtain the positivity for this class of quantum cluster\nalgebra.\n', 'On the acyclic quantum cluster algebras with principal coefficients   In this paper, we focus on a new lower bound quantum cluster algebra which is\ngenerated by the initial quantum cluster variables and the quantum projective\ncluster variables of an acyclic quantum cluster algebra with principal\ncoefficients. We show that the new lower bound quantum cluster algebra\ncoincides with the corresponding acyclic quantum cluster algebra. Moreover, we\nestablish a class of formulas between these generators, and obtain the dual PBW\nbasis of this algebra.\n']","[('cluster algebras', 0.7145675420761108), ('upper cluster algebras', 0.6942152976989746), ('rank cluster algebras', 0.666377067565918), ('algebras cluster', 0.6605444550514221), ('cluster algebra', 0.6528062224388123), ('quantum cluster', 0.6385898590087891), ('quantum affine algebras', 0.6151666045188904), ('generalized quantum', 0.5049594640731812), ('algebras associated', 0.4946992099285126), ('algebras arising', 0.4689929485321045)]"
1041,1041,29,1041_spiking neurons_networks spiking neurons_networks spiking_spiking activity,"['spiking neurons', 'networks spiking neurons', 'networks spiking', 'spiking activity', 'synaptic plasticity', 'neuronal network', 'spiking', 'synapses', 'neuronal networks', 'neuron']","['Spiking hierarchy in an adaptive exponential integrate-and-fire network\n  synchronization   Neuronal network synchronization has received wide interests. Network\nconnection structure is known to play a key role in its synchronization. In the\npresent manuscript, we study the influence of initial membrane potentials\ntogether with network topology on bursting synchronization, in particular the\nsequential spiking order in stabilized inter bursts. We find a hierarchical\nphenomenon on spiking order. We grade neurons into different layers: primary\nneurons are those initiate the spike and lower-layer neurons are then\ndetermined via network connections successively. This constructs a directed\ngraph to indicate spiking propagation among different layers of neurons.\nNeurons in upper layers spike earlier than those in lower layers. More\ninterestingly, we find that among the same layer, neuron spiking order is\nmainly associated with stimuli they receive from upper layer via network\nconnections; more stimuli leads to earlier spiking. Furthermore, we find that\nwith effectively the same stimuli from upper layer, neurons with less\nconnections spike earlier.\n', 'Exact analysis of the subthreshold variability for conductance-based\n  neuronal models with synchronous synaptic inputs   The spiking activity of neocortical neurons exhibits a striking level of\nvariability, even when these networks are driven by identical stimuli. The\napproximately Poisson firing of neurons has led to the hypothesis that these\nneural networks operate in the asynchronous state. In the asynchronous state\nneurons fire independently from one another, so that the probability that a\nneuron experience synchronous synaptic inputs is exceedingly low. While the\nmodels of asynchronous neurons lead to observed spiking variability, it is not\nclear whether the asynchronous state can also account for the level of\nsubthreshold membrane potential variability. We propose a new analytical\nframework to rigorously quantify the subthreshold variability of a single\nconductance-based neuron in response to synaptic inputs with prescribed degrees\nof synchrony. Technically we leverage the theory of exchangeability to model\ninput synchrony via jump-process-based synaptic drives; we then perform a\nmoment analysis of the stationary response of a neuronal model with all-or-none\nconductances that neglects post-spiking reset. As a result, we produce exact,\ninterpretable closed forms for the first two stationary moments of the membrane\nvoltage, with explicit dependence on the input synaptic numbers, strengths, and\nsynchrony. For biophysically relevant parameters, we find that the asynchronous\nregime only yields realistic subthreshold variability (voltage variance $\\simeq\n4-9\\mathrm{mV^2}$) when driven by a restricted number of large synapses,\ncompatible with strong thalamic drive. By contrast, we find that achieving\nrealistic subthreshold variability with dense cortico-cortical inputs requires\nincluding weak but nonzero input synchrony, consistent with measured pairwise\nspiking correlations.\n', ""Firing rate distributions in plastic networks of spiking neurons   In recurrent networks of leaky integrate-and-fire (LIF) neurons, mean-field\ntheory has proven successful in describing various statistical properties of\nneuronal activity at equilibrium, such as firing rate distributions. Mean-field\ntheory has been applied to networks in which either the synaptic weights are\nhomogeneous across synapses and the number of incoming connections of\nindividual neurons is heterogeneous, or vice versa. Here we extend the previous\nmean-field formalisms to treat networks in which these two sources of\nstructural heterogeneity occur simultaneously, including networks whose\nsynapses are subject to plastic, activity-dependent modulation. The plasticity\nin our model is mediated by the introduction of one spike trace per neuron: a\nchemical signal that is released every time the neuron emits a spike and which\nis degraded over time. The temporal evolution of the trace is controlled by its\ndegradation rate $r_p$ and by the neuron's underlying firing rate $\\nu$. When\nthe ratio $\\alpha=\\nu / r_p$ tends to infinity, the trace can be rescaled to be\na reliable estimation of the neuron's firing rate. In this regime, the value of\nany synaptic weight at equilibrium is a function of the pre- and post-synaptic\nfiring rates, and this relation can be used in the mean-field formalism. The\nsolution to the mean-field equations specifies the firing rate and synaptic\nweight distributions at equilibrium. These equations are exact in the limit of\nreliable traces but they already provide accurate results when the degradation\nrate lies within a reasonable range, as we show by comparison with simulations\nof the full neuronal dynamics in networks composed of excitatory and inhibitory\nLIF neurons. Overall, this work offers a way to explore and better understand\nthe way in which plasticity shapes both activity and structure in neuronal\nnetworks.\n""]","[('spiking neurons', 0.7121952772140503), ('networks spiking neurons', 0.7055887579917908), ('networks spiking', 0.6562016010284424), ('spiking activity', 0.5953118205070496), ('synaptic plasticity', 0.5859814882278442), ('neuronal network', 0.5667393207550049), ('spiking', 0.5628523826599121), ('synapses', 0.5490636229515076), ('neuronal networks', 0.5414454340934753), ('neuron', 0.5300565958023071)]"
1042,1042,29,1042_toroidal domains_toroidal geometry_magnetic fields_flux surfaces,"['toroidal domains', 'toroidal geometry', 'magnetic fields', 'flux surfaces', 'magnetic field', 'magnetohydrodynamics', 'magnetohydrodynamic', 'magnetized plasmas', 'divergence free fields', 'magnetic confinement']","['Introduction to Field Line Helicity   Field line helicity measures the net linking of magnetic flux with a single\nmagnetic field line. It offers a finer topological description than the usual\nglobal magnetic helicity integral, while still being invariant in an ideal\nevolution unless there is a flux of helicity through the domain boundary. In\nthis chapter, we explore how to appropriately define field line helicity in\ndifferent volumes in a way that preserves a meaningful topological\ninterpretation. We also review the time evolution of field line helicity under\nboth boundary motions and magnetic reconnection.\n', 'Asymptotic windings, surface helicity and their applications in plasma\n  physics   In [J. Cantarella, J. Parsley, J. Geom. Phys. 60:1127 (2010)] Cantarella and\nParsley introduced the notion of submanifold helicity. In the present paper we\ninvestigate properties of surface helicity and in particular answer two open\nquestions posed in the aforementioned work: (i) We give a precise\nmathematically rigorous physical interpretation of surface helicity in terms of\nlinking of distinct field lines. (ii) We prove that surface helicity is\nnon-trivial if and only if the underlying surface has non-trivial topology\n(i.e. at least one hole).\n  We then focus on toroidal surfaces which are of relevance in plasma physics\nand express surface helicity in terms of average poloidal and toroidal windings\nof the individual field lines of the underlying vector field which enables us\nto provide a connection between surface helicity and rotational transform.\nFurther, we show how some of our results may be utilised in the context of coil\ndesigns for plasma fusion confinement devices in order to obtain coil\nconfigurations of particular ""simple"" shape.\n  Lastly, we consider the problem of optimising surface helicity among toroidal\nsurfaces of fixed area and show that toroidal surfaces admitting a symmetry\nconstitute global minimisers.\n', 'Quasisymmetric magnetic fields in asymmetric toroidal domains   We explore the existence of quasisymmetric magnetic fields in asymmetric\ntoroidal domains. These vector fields can be identified with a class of\nmagnetohydrodynamic equilibria in the presence of pressure anisotropy. First,\nusing Clebsch potentials, we derive a system of two coupled nonlinear first\norder partial differential equations expressing a family of quasisymmetric\nmagnetic fields in bounded domains. In regions where flux surfaces and surfaces\nof constant field strength are not tangential, this system can be further\nreduced to a single degenerate nonlinear second order partial differential\nequation with externally assigned initial data. Then, we exhibit regular\nquasisymmetric vector fields which correspond to local solutions of anisotropic\nmagnetohydrodynamics in asymmetric toroidal domains such that tangential\nboundary conditions are fulfilled on a portion of the bounding surface. The\nproblems of boundary shape and locality are also discussed. We find that\nsymmetric magnetic fields can be fitted into asymmetric domains, and that the\nmathematical difficulty encountered in the derivation of global quasisymmetric\nmagnetic fields lies in the topological obstruction toward global extension\naffecting local solutions of the governing nonlinear first order partial\ndifferential equations.\n']","[('toroidal domains', 0.5557273030281067), ('toroidal geometry', 0.5485830903053284), ('magnetic fields', 0.5471130013465881), ('flux surfaces', 0.5088222622871399), ('magnetic field', 0.49055707454681396), ('magnetohydrodynamics', 0.4571608901023865), ('magnetohydrodynamic', 0.45499464869499207), ('magnetized plasmas', 0.43246859312057495), ('divergence free fields', 0.4284219741821289), ('magnetic confinement', 0.42710569500923157)]"
1043,1043,29,1043_conley index theory_morse theory_conley index_dynamical systems,"['conley index theory', 'morse theory', 'conley index', 'dynamical systems', 'infinite dimensional dynamical', 'invariant sets', 'connection matrices', 'homological', 'dynamical', 'isolated invariant']","['Conley-Morse-Forman theory for generalized combinatorial multivector\n  fields on finite topological spaces   We generalize and extend the Conley-Morse-Forman theory for combinatorial\nmultivector fields introduced in \\cite{Mr2017}. The generalization consists in\ndropping the restrictive assumption in \\cite{Mr2017} that every multivector has\na unique maximal element. The extension is from the setting of Lefschetz\ncomplexes to the more general situation of finite topological spaces. We define\nisolated invariant sets, isolating neighbourhoods, Conley index and Morse\ndecompositions. We also establish the additivity property of the Conley index\nand the Morse inequalities.\n', 'Persistence of the Conley Index in Combinatorial Dynamical Systems   A combinatorial framework for dynamical systems provides an avenue for\nconnecting classical dynamics with data-oriented, algorithmic methods.\nCombinatorial vector fields introduced by Forman and their recent\ngeneralization to multivector fields have provided a starting point for\nbuilding such a connection. In this work, we strengthen this relationship by\nplacing the Conley index in the persistent homology setting. Conley indices are\nhomological features associated with so-called isolated invariant sets, so a\nchange in the Conley index is a response to perturbation in an underlying\nmultivector field. We show how one can use zigzag persistence to summarize\nchanges to the Conley index, and we develop techniques to capture such changes\nin the presence of noise. We conclude by developing an algorithm to track\nfeatures in a changing multivector field.\n', 'Persistence of Conley-Morse Graphs in Combinatorial Dynamical Systems   Multivector fields provide an avenue for studying continuous dynamical\nsystems in a combinatorial framework. There are currently two approaches in the\nliterature which use persistent homology to capture changes in combinatorial\ndynamical systems. The first captures changes in the Conley index, while the\nsecond captures changes in the Morse decomposition. However, such approaches\nhave limitations. The former approach only describes how the Conley index\nchanges across a selected isolated invariant set though the dynamics can be\nmuch more complicated than the behavior of a single isolated invariant set.\nLikewise, considering a Morse decomposition omits much information about the\nindividual Morse sets. In this paper, we propose a method to summarize changes\nin combinatorial dynamical systems by capturing changes in the so-called\nConley-Morse graphs. A Conley-Morse graph contains information about both the\nstructure of a selected Morse decomposition and about the Conley index at each\nMorse set in the decomposition. Hence, our method summarizes the changing\nstructure of a sequence of dynamical systems at a finer granularity than\nprevious approaches.\n']","[('conley index theory', 0.6061057448387146), ('morse theory', 0.48411864042282104), ('conley index', 0.48165926337242126), ('dynamical systems', 0.43573877215385437), ('infinite dimensional dynamical', 0.4177066385746002), ('invariant sets', 0.4154893457889557), ('connection matrices', 0.41214802861213684), ('homological', 0.3971657454967499), ('dynamical', 0.39501330256462097), ('isolated invariant', 0.3950035572052002)]"
1044,1044,29,1044_factorial moments_standard poisson_poisson_compound poisson,"['factorial moments', 'standard poisson', 'poisson', 'compound poisson', 'poisson distribution', 'distribution poisson', 'probability mass pmf', 'mass pmf', 'central moments', 'moments standard']","['Factorial moments of the Poisson distribution of order $k$   The factorial moments of the standard Poisson distribution are well known.\nThe present note presents an explicit combinatorial sum for the factorial\nmoments of the Poisson distribution of order $k$. Unlike the standard Poisson\ndistribution (the case $k=1$), for $k>1$ the structure of the factorial moments\nis much more complicated. Some properties of the factorial moments of the\nPoisson distribution of order $k$ are elucidated in this note.\n', ""Structure of the probability mass function of the Poisson distribution\n  of order $k$   The Poisson distribution of order $k$ is a special case of a compound Poisson\ndistribution. For $k=1$ it is the standard Poisson distribution. Although its\nprobability mass function (pmf) is known, what is lacking is a $visual$\ninterpretation, which a sum over terms with factorial denominators does not\nsupply. Unlike the standard Poisson distribution, the Poisson distribution of\norder $k$ can display a maximum of $four$ peaks simultaneously, as a function\nof two parameters: the order $k$ and the rate parameter $\\lambda$. This note\ncharacterizes the shape of the pmf of the Poisson distribution of order $k$.\nThe pmf can be partitioned into a single point at $n=0$, an increasing sequence\nfor $n \\in [1,k]$ and a mountain range for $n>k$ (explained in the text). The\n``parameter space'' of the pmf is mapped out and the significance of each\ndomain is explained, in particular the change in behavior of the pmf as a\ndomain boundary is crossed. A simple analogy (admittedly unrelated) is that of\nthe discriminant of a quadratic with real coefficients: its domains\ncharacterize the nature of the roots (real or complex), and the domain boundary\nsignifies the presence of a repeated root. Something similar happens with the\npmf of the Poisson distribution of order $k$. As an application, this note\nexplains the mode structure of the Poisson distribution of order $k$.\nImprovements to various inequalities are also derived (sharper bounds, etc.).\nNew conjectured upper and lower bounds for the median and the mode are also\nproposed.\n"", 'Moments of the Poisson distribution of order $k$   The factorial moments of the standard Poisson distribution are well known and\nare simple, but the raw moments are considered to be more complicated (Touchard\npolynomials). The present note presents a recurrence relation and an explicit\ncombinatorial sum for the raw moments of the Poisson distribution of order $k$.\nUnlike the standard Poisson distribution (the case $k=1$), for $k>1$ the\nstructure of the raw and factorial moments have many similarities and the raw\nmoments are not more complicated (formally, at least) than the factorial\nmoments. We remark briefly on the central moments (i.e.~moments centered on the\nmean) of the Poisson distribution of order $k$.\n']","[('factorial moments', 0.5747559070587158), ('standard poisson', 0.53596031665802), ('poisson', 0.511891782283783), ('compound poisson', 0.503145694732666), ('poisson distribution', 0.4877125918865204), ('distribution poisson', 0.4836605489253998), ('probability mass pmf', 0.4337342083454132), ('mass pmf', 0.42409756779670715), ('central moments', 0.3861091732978821), ('moments standard', 0.38360440731048584)]"
1045,1045,29,1045_tilings_tilings two_quadrilaterals_pentagonal,"['tilings', 'tilings two', 'quadrilaterals', 'pentagonal', 'pentagons', 'tiling problems', 'tiling', 'polygons', 'triangular prism', 'quadrilateral']","['Tilings of the sphere by congruent pentagons IV: Edge combination $a^4b$\n  with general angles   We classify edge-to-edge tilings of the sphere by congruent pentagons with\nthe edge combination $a^4b$ and with any irrational angle in degree: they are\nthree $1$-parameter families of pentagonal subdivisions of the Platonic solids,\nwith $12, 24$ and $60$ tiles; and a sequence of $1$-parameter families of\npentagons admitting non-symmetric $3$-layer earth map tilings together with\ntheir various rearrangements under extra conditions. Their parameter moduli and\ngeometric data are all computed in both exact and numerical form. The total\nnumbers of different tilings for any fixed such pentagon are counted\nexplicitly. As a byproduct, the degenerate pentagons produce naturally many new\nnon-edge-to-edge quadrilateral tilings. A sequel of this paper will handle\n$a^4b$-pentagons with all angles being rational in degree by solving some\ntrigonometric Diophantine equations, to complete our full classification of\nedge-to-edge tilings of the sphere by congruent pentagons.\n', 'Tilings of the Sphere by Congruent Pentagons IV: Edge Combination $a^4b$   We classify edge-to-edge tilings of the sphere by congruent almost\nequilateral pentagons, in which four edges have the same length. Together with\nour earlier classifications of edge-to-edge tilings of the sphere by congruent\nequilateral pentagons of other types, and our classification of edge-to-edge\ntilings of the sphere by congruent quadrilaterals or triangles, we complete the\nclassification of edge-to-edge tilings of the sphere by congruent polygons.\n', 'Tilings of the Sphere by Congruent Quadrilaterals or Triangles   We completely classify edge-to-edge tilings of the sphere by congruent\nquadrilaterals. As part of the classification, we also present a modern version\nof the classification of edge-to-edge tilings of the sphere by congruent\ntriangles. Together with our series of papers that classifies edge-to-edge\ntilings of the sphere by congruent pentagons, we complete the classification of\nedge-to-edge tilings of the sphere by congruent polygons.\n']","[('tilings', 0.5731428861618042), ('tilings two', 0.5452471375465393), ('quadrilaterals', 0.5168805718421936), ('pentagonal', 0.5053632259368896), ('pentagons', 0.5031503438949585), ('tiling problems', 0.49779966473579407), ('tiling', 0.4820748269557953), ('polygons', 0.47259560227394104), ('triangular prism', 0.4601372182369232), ('quadrilateral', 0.455324649810791)]"
1046,1046,29,1046_graphs finite fields_paley graphs_maximal cliques_maximum cliques,"['graphs finite fields', 'paley graphs', 'maximal cliques', 'maximum cliques', 'cliques generalized', 'cayley graphs finite', 'ramanujan graphs', 'graphs finite', 'paley graph', 'regular cayley graphs']","['Distribution of power residues over shifted subfields and maximal\n  cliques in generalized Paley graphs   We derive an asymptotic formula for the number of solutions in a given\nsubfield to certain system of equations over finite fields. As an application,\nwe construct new families of maximal cliques in generalized Paley graphs. Given\nintegers $d\\ge2$ and $q \\equiv 1 \\pmod d$, we show that for each positive\ninteger $m$ such that $\\operatorname{rad}(m) \\mid \\operatorname{rad}(d)$, there\nare maximal cliques of size approximately $q/m$ in the $d$-Paley graph defined\non $\\mathbb{F}_{q^d}$. We also confirm a conjecture of Goryainov, Shalaginov,\nand the second author on the maximality of certain cliques in generalized Paley\ngraphs, as well as an analogous conjecture of Goryainov for Peisert graphs.\n', 'The subspace structure of maximum cliques in pseudo-Paley graphs from\n  unions of cyclotomic classes   Blokhuis showed that all maximum cliques in Paley graphs of square order have\na subfield structure. Recently, it has been shown that in Peisert-type graphs,\nall maximum cliques are affine subspaces, and yet some maximum cliques do not\narise from a subfield. In this paper, we investigate the existence of a clique\nof size $\\sqrt{q}$ with a subspace structure in pseudo-Paley graphs of order\n$q$ from unions of semi-primitive cyclotomic classes. We show that such a\nclique must have an equal contribution from each cyclotomic class and that most\nsuch pseudo-Paley graphs do not admit such cliques, suggesting that the\nDelsarte bound $\\sqrt{q}$ on the clique number can be improved in general. We\nalso prove that generalized Peisert graphs are not isomorphic to Paley graphs\nor Peisert graphs, confirming a conjecture of Mullin.\n', 'Gauss sums and the maximum cliques in generalized Paley graphs of square\n  order   Let $GP(q,d)$ be the $d$-Paley graph defined on the finite field\n$\\mathbb{F}_q$. It is notoriously difficult to improve the trivial upper bound\n$\\sqrt{q}$ on the clique number of $GP(q,d)$. In this paper, we investigate the\nconnection between Gauss sums over a finite field and the maximum cliques of\ntheir corresponding generalized Paley graphs. We show that the trivial upper\nbound on the clique number of $GP(q,d)$ is tight if and only if $d \\mid\n(\\sqrt{q}+1)$, which strengthens the previous related results by\nBroere-D\\""oman-Ridley and Schneider-Silva. We also obtain a new simple proof of\nStickelberger\'s theorem on evaluating semi-primitive Gauss sums.\n']","[('graphs finite fields', 0.5796284675598145), ('paley graphs', 0.5487614274024963), ('maximal cliques', 0.5057236552238464), ('maximum cliques', 0.48569267988204956), ('cliques generalized', 0.4818975329399109), ('cayley graphs finite', 0.47951167821884155), ('ramanujan graphs', 0.4789928197860718), ('graphs finite', 0.4620261788368225), ('paley graph', 0.4523470103740692), ('regular cayley graphs', 0.44291624426841736)]"
1047,1047,29,1047_computable structure theory_computable structure_turing degrees_computably enumerable,"['computable structure theory', 'computable structure', 'turing degrees', 'computably enumerable', 'turing degree', 'partial computable', 'countable structure', 'computable', 'categorical structure', 'structures notions']","['Isomorphism Spectra and Computably Composite Structures   Adapting a result of Bazhenov, Kalimullin, and Yamaleev, we show that if a\nTuring degree $\\textbf{d}$ is the degree of categoricity of a computable\nstructure $\\mathcal{M}$ and is not the strong degree of categoricity of any\ncomputable structure, then $\\mathcal{M}$ has a pair of computable copies whose\nisomorphism spectrum is not finitely generated. Motivated by this result, we\nintroduce a class of computable structures called computably composite\nstructures with the property that the isomorphisms between arbitrary computable\ncopies of these structures are exactly the unions of isomorphisms between the\ncomputable copies of their components. We use this to show that any computable\nunion of isomorphism spectra is also an isomorphism spectrum. In particular,\nthis gives examples of isomorphism spectra that are not finitely generated.\n', 'Degrees of bi-embeddable categoricity   We investigate the complexity of embeddings between bi-embeddable structures.\nIn analogy with categoricity spectra, we define the bi-embeddable categoricity\nspectrum of a structure $\\mathcal A$ as the family of Turing degrees that\ncompute embeddings between any computable bi-embeddable copies of $\\mathcal A$;\nthe degree of bi-embeddable categoricity of $\\mathcal A$ is the least degree in\nthis spectrum (if it exists). We extend many known results about categoricity\nspectra to the case of bi-embeddability. In particular, we exhibit structures\nwithout degree of bi-embeddable categoricity, and we show that every degree\nd.c.e. above $\\mathbf{0}^{(\\alpha)}$ for $\\alpha$ a computable successor\nordinal and $\\mathbf{0}^{(\\lambda)}$ for $\\lambda$ a computable limit ordinal\nis a degree of bi-embeddable categoricity. We also give examples of families of\ndegrees that are not bi-embeddable categoricity spectra.\n', 'Notes on degrees of relative computable categoricity   We are studying the degrees in which a computable structure is relatively\ncomputably categoricity, i.e., computably categorcial among all non-computable\ncopies of the structure. Unlike the degrees of computable categoricity we can\nbound the possible degrees of relative computable categoricity by the oracle\n0"". In the case of rigid structures the bound is in fact 0\'. These estimations\nare precise, in particular we can build a computable structure which is\nrelatively computably categorical only in the degrees above 0"".\n']","[('computable structure theory', 0.6539012789726257), ('computable structure', 0.6131759881973267), ('turing degrees', 0.5422030687332153), ('computably enumerable', 0.5227410793304443), ('turing degree', 0.5124064683914185), ('partial computable', 0.5071233510971069), ('countable structure', 0.49951180815696716), ('computable', 0.4681735336780548), ('categorical structure', 0.4674910604953766), ('structures notions', 0.4670960605144501)]"
1048,1048,28,1048_homotopy types_homotopy type_homotopy decomposition_complexes homotopy,"['homotopy types', 'homotopy type', 'homotopy decomposition', 'complexes homotopy', 'homotopy groups spheres', 'homotopy groups', 'homotopy theory', 'homotopy theoretic', 'stable homotopy groups', 'determine homotopy']","['The homotopy decomposition of the suspension of a non-simply-connected\n  $5$-manifold   In this paper we determine the homotopy types of the reduced suspension space\nof certain connected orientable closed smooth $5$-manifolds. As applications,\nwe compute the reduced $K$-groups of $M$ and show that the suspension map\nbetween the third cohomotopy set $\\pi^3(M)$ and the fourth cohomotopy set\n$\\pi^4(\\Sigma M)$ is a bijection.\n', ""Suspension Homotopy of $(n-1)$-connected $(2n+2)$-dimensional\n  Poincar\\'{e} Duality Complexes   We study the homotopy decompositions of the suspension $\\Sigma M$ of an\n$(n-1)$-connected $(2n+2)$ dimensional Poincar\\'{e} duality complex $M$, $n\\geq\n2$. In particular, we completely determine the homotopy types of $\\Sigma M$ of\na simply-connected orientable closed (smooth) $6$-manifold $M$, whose integral\nhomology groups can have $2$-torsion. If $3\\leq n\\leq 5$, we obtain homotopy\ndecompositions of $\\Sigma M$ after localization away from $2$.\n"", ""Suspension splittings of 5-dimensional Poincar\\'{e} duality complexes\n  and their applications   Let $X$ be a connected, orientable, 5-dimensional Poincar\\'{e} duality\ncomplex with torsion-free $H_1(X;\\mathbb{Z})$. We show that $\\Sigma X$ is\nhomotopy equivalent to a wedge of recognisable spaces and study to what extent\nits homotopy type is determined by algebraic data. These results are then used\nto compute the unstable cohomotopy groups $\\pi^3(X)$ and\n$\\pi^3(X;\\mathbb{Z}/k)$ as well as give partial information about the\ncohomotopy set $\\pi^2(X)$.\n""]","[('homotopy types', 0.5785830020904541), ('homotopy type', 0.5673387050628662), ('homotopy decomposition', 0.5645865797996521), ('complexes homotopy', 0.557564914226532), ('homotopy groups spheres', 0.5467188954353333), ('homotopy groups', 0.5426166653633118), ('homotopy theory', 0.5257276296615601), ('homotopy theoretic', 0.5205172300338745), ('stable homotopy groups', 0.5179987549781799), ('determine homotopy', 0.49714046716690063)]"
1049,1049,28,1049_sample complexity lower_sample complexity_distribution testing_complexity lower bound,"['sample complexity lower', 'sample complexity', 'distribution testing', 'complexity lower bound', 'query complexity', 'conditional sampling', 'high dimensional distributions', 'complexity lower', 'complexity tilde', 'testing high dimensional']","['On Distribution Testing in the Conditional Sampling Model   Recently, there has been significant work studying distribution testing under\nthe Conditional Sampling model. In this model, a query specifies a subset $S$\nof the domain, and the output received is a sample drawn from the distribution\nconditioned on being in $S$. In this paper, we improve query complexity bounds\nfor several classic distribution testing problems in this model.\n  First, we prove that tolerant uniformity testing in the conditional sampling\nmodel can be solved using $\\tilde{O}(\\varepsilon^{-2})$ queries, which is\noptimal and improves upon the $\\tilde{O}(\\varepsilon^{-20})$-query algorithm of\nCanonne et al. [CRS15]. This bound even holds under a restricted version of the\nconditional sampling model called the Pair Conditional Sampling model. Next, we\nprove that tolerant identity testing in the conditional sampling model can be\nsolved in $\\tilde{O}(\\varepsilon^{-4})$ queries, which is the first known bound\nindependent of the support size of the distribution for this problem. Next, we\nuse our algorithm for tolerant uniformity testing to get an\n$\\tilde{O}(\\varepsilon^{-4})$-query algorithm for monotonicity testing in the\nconditional sampling model, improving on the\n$\\tilde{O}(\\varepsilon^{-22})$-query algorithm of Canonne [Can15]. Finally, we\nstudy (non-tolerant) identity testing under the pair conditional sampling\nmodel, and provide a tight bound of $\\tilde{\\Theta}(\\sqrt{\\log N} \\cdot\n\\varepsilon^{-2})$ for the query complexity, where the domain of the\ndistribution has size $N$. This improves upon both the known upper and lower\nbounds in [CRS15].\n', 'Tolerant Testing of High-Dimensional Samplers with Subcube Conditioning   We study the tolerant testing problem for high-dimensional samplers. Given as\ninput two samplers $\\mathcal{P}$ and $\\mathcal{Q}$ over the $n$-dimensional\nspace $\\{0,1\\}^n$, and two parameters $\\varepsilon_2 > \\varepsilon_1$, the goal\nof tolerant testing is to test whether the distributions generated by\n$\\mathcal{P}$ and $\\mathcal{Q}$ are $\\varepsilon_1$-close or\n$\\varepsilon_2$-far. Since exponential lower bounds (in $n$) are known for the\nproblem in the standard sampling model, research has focused on models where\none can draw \\textit{conditional} samples.\n  Among these models, \\textit{subcube conditioning} ($\\mathsf{SUBCOND}$), which\nallows conditioning on arbitrary subcubes of the domain, holds the promise of\nwidespread adoption in practice owing to its ability to capture the natural\nbehavior of samplers in constrained domains. To translate the promise into\npractice, we need to overcome two crucial roadblocks for tests based on\n$\\mathsf{SUBCOND}$: the prohibitively large number of queries\n($\\tilde{\\mathcal{O}}(n^5/\\varepsilon_2^5)$) and limitation to non-tolerant\ntesting (i.e., $\\varepsilon_1 = 0$).\n  The primary contribution of this work is to overcome the above challenges: we\ndesign a new tolerant testing methodology (i.e., $\\varepsilon_1 \\geq 0$) that\nallows us to significantly improve the upper bound to\n$\\tilde{\\mathcal{O}}(n^3/(\\varepsilon_2-\\varepsilon_1)^5)$.\n', 'Monotonicity Testing of High-Dimensional Distributions with Subcube\n  Conditioning   We study monotonicity testing of high-dimensional distributions on\n$\\{-1,1\\}^n$ in the model of subcube conditioning, suggested and studied by\nCanonne, Ron, and Servedio~\\cite{CRS15} and Bhattacharyya and\nChakraborty~\\cite{BC18}. Previous work shows that the \\emph{sample complexity}\nof monotonicity testing must be exponential in $n$ (Rubinfeld,\nVasilian~\\cite{RV20}, and Aliakbarpour, Gouleakis, Peebles, Rubinfeld,\nYodpinyanee~\\cite{AGPRY19}). We show that the subcube \\emph{query complexity}\nis $\\tilde{\\Theta}(n/\\varepsilon^2)$, by proving nearly matching upper and\nlower bounds. Our work is the first to use directed isoperimetric inequalities\n(developed for function monotonicity testing) for analyzing a distribution\ntesting algorithm. Along the way, we generalize an inequality of Khot, Minzer,\nand Safra~\\cite{KMS18} to real-valued functions on $\\{-1,1\\}^n$.\n  We also study uniformity testing of distributions that are promised to be\nmonotone, a problem introduced by Rubinfeld, Servedio~\\cite{RS09} , using\nsubcube conditioning. We show that the query complexity is\n$\\tilde{\\Theta}(\\sqrt{n}/\\varepsilon^2)$. Our work proves the lower bound,\nwhich matches (up to poly-logarithmic factors) the uniformity testing upper\nbound for general distributions (Canonne, Chen, Kamath, Levi,\nWaingarten~\\cite{CCKLW21}). Hence, we show that monotonicity does not help,\nbeyond logarithmic factors, in testing uniformity of distributions with subcube\nconditional queries.\n']","[('sample complexity lower', 0.5316011905670166), ('sample complexity', 0.5020689964294434), ('distribution testing', 0.4443877935409546), ('complexity lower bound', 0.4312306046485901), ('query complexity', 0.3935979902744293), ('conditional sampling', 0.3893170654773712), ('high dimensional distributions', 0.3867551386356354), ('complexity lower', 0.3733401596546173), ('complexity tilde', 0.3719182312488556), ('testing high dimensional', 0.36572250723838806)]"
1050,1050,28,1050_zeta functions associated_local zeta functions_zeta functions also_representation zeta,"['zeta functions associated', 'local zeta functions', 'zeta functions also', 'representation zeta', 'zeta functions', 'local zeta', 'virtually nilpotent groups', 'virtually nilpotent group', 'class nilpotent groups', 'free nilpotent groups']","['Ideal zeta functions associated to a family of class-2-nilpotent Lie\n  rings   We produce explicit formulae for various ideal zeta functions associated to\nthe members of an infinite family of class-$2$-nilpotent Lie rings, introduced\nin [1], in terms of Igusa functions. As corollaries we obtain information about\nanalytic properties of global ideal zeta functions, local functional equations,\ntopological, reduced, and graded ideal zeta functions, as well as\nrepresentation zeta functions for the unipotent group schemes associated to the\nLie rings in question.\n', 'Bivariate representation and conjugacy class zeta functions associated\n  to unipotent group schemes, I: Arithmetic properties   This is the first of two papers in which we introduce and study two bivariate\nzeta functions associated to unipotent group schemes over rings of integers of\nnumber fields. One of these zeta functions encodes the numbers of isomorphism\nclasses of irreducible complex representations of finite dimensions of\ncongruence quotients of the associated group and the other one encodes the\nnumbers of conjugacy classes of each size of such quotients. In this paper, we\nshow that these zeta functions satisfy Euler factorizations and almost all of\ntheir Euler factors are rational and satisfy functional equations. Moreover, we\nshow that such bivariate zeta functions specialize to (univariate) class number\nzeta functions. In case of nilpotency class 2, bivariate representation zeta\nfunctions also specialize to (univariate) twist representation zeta functions.\n', ""On pro-isomorphic zeta functions of $D^*$-groups of even Hirsch length   The pro-isomorphic zeta function of a finitely generated nilpotent group is a\nDirichlet generating series that enumerates all finite-index subgroups whose\nprofinite completion is isomorphic to that of the ambient group. We study the\npro-isomorphic zeta functions of $\\mathbb{Q}$-indecomposable $D^*$-groups of\neven Hirsch length. These groups are building blocks of finitely generated\nclass-two nilpotent groups with rank-two centre, up to commensurability. Due to\na classification by Grunewald and Segal, they are parameterised by primary\npolynomials whose companion matrices define commutator relations for an\nexplicit presentation. For Grunewald-Segal representatives of even Hirsch\nlength of type $f(t)=t^m$, we give a complete description of the algebraic\nautomorphism groups of associated Lie lattices. Utilising the automorphism\ngroups, we determine the local pro-isomorphic zeta functions of groups\nassociated to $t^2$ and $t^3$. In both cases, the local zeta functions are\nuniform in the prime $p$ and satisfy functional equations. The functional\nequations for these groups, not predicted by the currently available theory,\nprompt us to formulate a conjecture which prescribes, in particular,\ninformation about the symmetry factor appearing in local functional equations\nfor pro-isomorphic zeta functions of nilpotent groups. Our description of the\nlocal zeta functions also yields information about the analytic properties of\nthe corresponding global pro-isomorphic zeta functions. Some of our results for\nthe $D^*$-groups associated to $t^2$ and $t^3$ generalise to two infinite\nfamilies of class-two nilpotent groups that result naturally from the initial\ngroups via `base extensions'.\n""]","[('zeta functions associated', 0.6153010725975037), ('local zeta functions', 0.5993598103523254), ('zeta functions also', 0.5315364003181458), ('representation zeta', 0.5275774002075195), ('zeta functions', 0.509505569934845), ('local zeta', 0.49231061339378357), ('virtually nilpotent groups', 0.4862527549266815), ('virtually nilpotent group', 0.4794516861438751), ('class nilpotent groups', 0.47618168592453003), ('free nilpotent groups', 0.47286200523376465)]"
1051,1051,28,1051_random regular graphs_random regular graph_eigenvalues random_edge eigenvalues,"['random regular graphs', 'random regular graph', 'eigenvalues random', 'edge eigenvalues', 'eigenvalue random', 'extreme eigenvalues', 'regular graphs', 'regular hypergraphs', 'spectral behavior', 'regular graphs vertices']","['Spectrum of Random $d$-regular Graphs Up to the Edge   Consider the normalized adjacency matrices of random $d$-regular graphs on\n$N$ vertices with fixed degree $d\\geq3$. We prove that, with probability\n$1-N^{-1+{\\varepsilon}}$ for any ${\\varepsilon} >0$, the following two\nproperties hold as $N \\to \\infty$ provided that $d\\geq3$: (i) The eigenvalues\nare close to the classical eigenvalue locations given by the Kesten-McKay\ndistribution. In particular, the extremal eigenvalues are concentrated with\npolynomial error bound in $N$, i.e. $\\lambda_2, |\\lambda_N|\\leq 2+N^{-c}$. (ii)\nAll eigenvectors of random $d$-regular graphs are completely delocalized.\n', 'Ramanujan Property and Edge Universality of Random Regular Graphs   We consider the normalized adjacency matrix of a random $d$-regular graph on\n$N$ vertices with any fixed degree $d\\geq 3$ and denote its eigenvalues as\n$\\lambda_1=d/\\sqrt{d-1}\\geq \\lambda_2\\geq\\lambda_3\\cdots\\geq \\lambda_N$. We\nestablish the following two results as $N\\rightarrow \\infty$. (i) With high\nprobability, all eigenvalues are optimally rigid, up to an additional $N^{{\\rm\no}(1)}$ factor. Specifically, the fluctuations of bulk eigenvalues are bounded\nby $N^{-1+{\\rm o}(1)}$, and the fluctuations of edge eigenvalues are bounded by\n$N^{-2/3+{\\rm o}(1)}$. (ii) Edge universality holds for random $d$-regular\ngraphs. That is, the distributions of $\\lambda_2$ and $-\\lambda_N$ converge to\nthe Tracy-Widom$_1$ distribution associated with the Gaussian Orthogonal\nEnsemble. As a consequence, for sufficiently large $N$, approximately $69\\%$ of\n$d$-regular graphs on $N$ vertices are Ramanujan, meaning\n$\\max\\{\\lambda_2,|\\lambda_N|\\}\\leq 2$.\n', ""Edge rigidity and universality of random regular graphs of intermediate\n  degree   For random $d$-regular graphs on $N$ vertices with $1 \\ll d \\ll N^{2/3}$, we\ndevelop a $d^{-1/2}$ expansion of the local eigenvalue distribution about the\nKesten-McKay law up to order $d^{-3}$. This result is valid up to the edge of\nthe spectrum. It implies that the eigenvalues of such random regular graphs are\nmore rigid than those of Erd\\H{o}s-R\\'enyi graphs of the same average degree.\nAs a first application, for $1 \\ll d \\ll N^{2/3}$, we show that all nontrivial\neigenvalues of the adjacency matrix are with very high probability bounded in\nabsolute value by $(2 + o(1)) \\sqrt{d - 1}$. As a second application, for\n$N^{2/9} \\ll d \\ll N^{1/3}$, we prove that the extremal eigenvalues are\nconcentrated at scale $N^{-2/3}$ and their fluctuations are governed by\nTracy-Widom statistics. Thus, in the same regime of $d$, $52\\%$ of all\n$d$-regular graphs have second-largest eigenvalue strictly less than $2 \\sqrt{d\n- 1}$.\n""]","[('random regular graphs', 0.5872927308082581), ('random regular graph', 0.5349627137184143), ('eigenvalues random', 0.5260189771652222), ('edge eigenvalues', 0.49166402220726013), ('eigenvalue random', 0.48967549204826355), ('extreme eigenvalues', 0.45121100544929504), ('regular graphs', 0.4510742723941803), ('regular hypergraphs', 0.4446193277835846), ('spectral behavior', 0.44376319646835327), ('regular graphs vertices', 0.4393940269947052)]"
1052,1052,28,1052_extensive form games_finite games_game theoretic_game theory,"['extensive form games', 'finite games', 'game theoretic', 'game theory', 'form games', 'non cooperative games', 'cooperative games', 'strategy sets', 'sequence games', 'games strategic']","['Polytope-form games and Index/Degree Theories for Extensive-form games   We present an index theory of equilibria for extensive form games. This\nrequires developing an index theory for games where the strategy sets of\nplayers are general polytopes and their payoff functions are multiaffine in the\nproduct of these polytopes. Such polytopes arise from identifying\n(topologically) equivalent mixed strategies of a normal form game.\n', ""The Category of Node-and-Choice Extensive-Form Games   This paper develops the category $\\mathbf{NCG}$. Its objects are\nnode-and-choice games, which include essentially all extensive-form games. Its\nmorphisms allow arbitrary transformations of a game's nodes, choices, and\nplayers, as well as monotonic transformations of the utility functions of the\ngame's players. Among the morphisms are subgame inclusions. Several\ncharacterizations and numerous properties of the isomorphisms are derived. For\nexample, it is shown that isomorphisms preserve the game-theoretic concepts of\nno-absentmindedness, perfect-information, and (pure-strategy) Nash-equilibrium.\nFinally, full subcategories are defined for choice-sequence games and\nchoice-set games, and relationships among these two subcategories and\n$\\mathbf{NCG}$ itself are expressed and derived via isomorphic inclusions and\nequivalences.\n"", ""A Category for Extensive-Form Games   This paper introduces Gm, which is a category for extensive-form games. It\nalso provides some applications.\n  The category's objects are games, which are understood to be sets of nodes\nwhich have been endowed with edges, information sets, actions, players, and\nutility functions. Its arrows are functions from source nodes to target nodes\nthat preserve the additional structure. For instance, a game's information-set\ncollection is newly regarded as a topological basis for the game's\ndecision-node set, and thus a morphism's continuity serves to preserve\ninformation sets. Given these definitions, a game monomorphism is characterized\nby the property of not mapping two source runs (plays) to the same target run.\nFurther, a game isomorphism is characterized as a bijection whose restriction\nto decision nodes is a homeomorphism, whose induced player transformation is\ninjective, and which strictly preserves the ordinal content of the utility\nfunctions.\n  The category is then applied to some game-theoretic concepts beyond the\ndefinition of a game. A Selten subgame is characterized as a special kind of\ncategorical subgame, and game isomorphisms are shown to preserve strategy sets,\nNash equilibria, Selten subgames, subgame-perfect equilibria,\nperfect-information, and no-absentmindedness. Further, it is shown that the\nfull subcategory for distinguished-action sequence games is essentially wide in\nthe category of all games, and that the full subcategory of action-set games is\nessentially wide in the full subcategory for games with no-absentmindedness.\n""]","[('extensive form games', 0.6741420030593872), ('finite games', 0.65621018409729), ('game theoretic', 0.6177345514297485), ('game theory', 0.6107637882232666), ('form games', 0.6084689497947693), ('non cooperative games', 0.5598866939544678), ('cooperative games', 0.55312180519104), ('strategy sets', 0.550670862197876), ('sequence games', 0.5397950410842896), ('games strategic', 0.5208937525749207)]"
1053,1053,28,1053_chromatic numbers_chromatic number_minimum number colors_chromatic,"['chromatic numbers', 'chromatic number', 'minimum number colors', 'chromatic', 'finite colouring', 'distance graphs', 'graphs plane', 'number colors', 'number colors needed', 'coloring']","['Constructing 5-chromatic unit distance graphs embedded in the Euclidean\n  plane and two-dimensional spheres   This paper is devoted to the development of algorithms for finding unit\ndistance graphs with chromatic number greater than 4, embedded in a\ntwo-dimensional sphere or plane. Such graphs provide a lower bound for the\nNelson-Hadwiger problem on the chromatic number of the plane and its\ngeneralizations to the case of the sphere. A series of 5-chromatic unit\ndistance graphs on 64513 vertices embedded into the plane is constructed.\nUnlike previously known examples, these graphs do not contain the Moser spindle\nas a subgraph. The construction of 5-chromatic graphs embedded in a sphere at\ntwo values of the radius is given. Namely, the 5-chromatic unit distance graph\non 372 vertices embedded into the circumsphere of an icosahedron with a unit\nedge length, and the 5-chromatic graph on 972 vertices embedded into the\ncircumsphere of a great icosahedron are constructed.\n', 'Note on the chromatic number of Minkowski planes: the regular polygon\n  case   The famous Hadwiger-Nelson problem asks for the minimum number of colors\nneeded to color the points of the Euclidean plane so that no two points unit\ndistance apart are assigned the same color. In this note we consider a variant\nof the problem in Minkowski metric planes, where the unit circle is a regular\npolygon of even and at most 22 vertices. We present a simple lattice-sublattice\ncoloring scheme that uses 6 colors, proving that the chromatic number of the\nMinkowski planes above are at most 6. This result is new for regular polygons\nhaving more than 8 vertices.\n', 'A 5-chromatic same-distance graph in the hyperbolic plane   The chromatic number of the plane problem asks for the minimum number of\ncolors so that each point of the plane can be assigned a single color with the\nproperty that no two points unit-distance apart are identically colored. It is\nnow known that the answer is 5, 6, or 7.\n  Here we consider the problem in the context of the hyperbolic plane. We prove\nthat there exists a distance $d\\approx 1.375033509$ so that every 4-coloring of\nthe hyperbolic plane contains two points distance $d$ apart, which are\nidentically colored.\n']","[('chromatic numbers', 0.6552742719650269), ('chromatic number', 0.6509841084480286), ('minimum number colors', 0.5622521042823792), ('chromatic', 0.5486813187599182), ('finite colouring', 0.5323753952980042), ('distance graphs', 0.4779326021671295), ('graphs plane', 0.45903927087783813), ('number colors', 0.45871829986572266), ('number colors needed', 0.45383650064468384), ('coloring', 0.45325934886932373)]"
1054,1054,28,1054_solutions yang baxter_theoretic yang baxter_quantum yang baxter_skew braces,"['solutions yang baxter', 'theoretic yang baxter', 'quantum yang baxter', 'skew braces', 'skew brace', 'yang baxter associated', 'structure skew', 'theory skew', 'yang baxter', 'solutions yang']","['Skew left braces and 2-reductive solutions of the Yang-Baxter equation   We study 2-reductive non-involutive non-degenerate set-theoretic solutions of\nthe Yang-Baxter equation. We give a combinatorial construction of any such\nsolution of any (even infinite) size. We also prove that solutions associated\nto a skew left brace are 2-reductive if and only if the skew left brace is\nnilpotent of class 2. Moreover, all such skew left braces are actually bi-skew\nleft braces. We focus on these structures and we give several equivalent\nproperties characterizing solutions associated to bi-skew left braces.\n', 'Soluble skew left braces and soluble solutions of the Yang-Baxter\n  equation   The study of non-degenerate set-theoretic solutions of the Yang-Baxter\nequation calls for a deep understanding of the algebraic structure of a skew\nleft brace. In this paper, the skew brace theoretical property of solubility is\nintroduced and studied. It leads naturally to the notion of solubility of\nsolutions of the Yang-Baxter equation. It turns out that soluble non-degenerate\nset-theoretic solutions are characterised by soluble skew left braces. The rich\nideal structure of soluble skew left braces is also shown. A worked example\nshowing the relevance of the brace theoretical property of solubility is also\npresented.\n', 'Radical and weight of skew braces and their applications to structure\n  groups of solutions of the Yang-Baxter equation   We define the radical and weight of a skew left brace and provide some basic\nproperties of these notions. In particular, we obtain a Wedderburn type\ndecomposition for Artinian skew left braces. Furthermore, we prove analogues of\na theorem of Wiegold, a theorem of Schur and its converse in the context of\nskew left braces. Finally, we apply these results to detect torsion in the\nstructure group of a finite bijective non-degenerate set-theoretic solution of\nthe Yang-Baxter equation.\n']","[('solutions yang baxter', 0.596315324306488), ('theoretic yang baxter', 0.5631400346755981), ('quantum yang baxter', 0.5561410188674927), ('skew braces', 0.5469743013381958), ('skew brace', 0.5154340863227844), ('yang baxter associated', 0.4721335470676422), ('structure skew', 0.4596277177333832), ('theory skew', 0.44159674644470215), ('yang baxter', 0.4360617995262146), ('solutions yang', 0.4355686604976654)]"
1055,1055,28,1055_local controllability_controllability properties_approximate controllability_global controllability,"['local controllability', 'controllability properties', 'approximate controllability', 'global controllability', 'control affine systems', 'controllability', 'affine control systems', 'minimal controllability', 'controllability class', 'control affine system']","[""Strong chain control sets and affine control systems   For control-affine systems on non-compact manifolds, the notion of strong\nchain control sets is introduced and related to the strong chain transitivity\nof the associated control flows. Affine control systems on R^n are embedded\ninto bilinear control systems in an extended state space and it is shown that\nthey are topologically conjugate to the induced system on the northern\nhemisphere of the Poincar\\'e sphere. This preserves strong chain control sets.\nFurther chain controllability properties on spheres are analyzed\n"", ""On the Local Controllability of a Class of Quadratic Systems   The local controllability of a rich class of affine nonlinear control systems\nwith nonhomogeneous quadratic drift and constant control vector fields is\nanalyzed. The interest in this particular class of systems stems from the\nubiquity in science and engineering of some of its notable representatives,\nnamely the Sprott system, the Lorenz system and the rigid body among others. A\nnecessary and sufficient condition for strong accessibility reminiscent of the\nKalman rank condition is derived, and it generalizes Crouch's condition for the\nrigid body. This condition is in general not sufficient to infer small-time\nlocal controllability. However, under some additional mild assumptions local\ncontrollability is established. In particular for the Sprott and Lorenz\nsystems, sharp conditions for small-time local controllability are obtained in\nthe single-input case.\n"", 'Quadratic obstructions to small-time local controllability for\n  multi-input systems   We present a necessary condition for the small-time local controllability of\nmulti-input control-affine systems on $R^d$ . This condition is formulated on\nthe vectors of $R^d$ resulting from the evaluation at zero of the Lie brackets\nof the vector fields: it involves both their direction and their amplitude. The\nproof is an adaptation to the multi-input case of a general method introduced\nby Beauchard and Marbach in the single-input case. It relies on a Magnus-type\nrepresentation formula: the state is approximated by a linear combination of\nthe evaluation at zero of the Lie brackets of the vector fields, whose\ncoefficients are functionals of the time and the controls. Finally,\nobstructions to small-time local controllability result from interpolation\ninequalities.\n']","[('local controllability', 0.7331624031066895), ('controllability properties', 0.6774216890335083), ('approximate controllability', 0.6756928563117981), ('global controllability', 0.6619365215301514), ('control affine systems', 0.647200345993042), ('controllability', 0.6441622376441956), ('affine control systems', 0.6265795826911926), ('minimal controllability', 0.622997522354126), ('controllability class', 0.620944082736969), ('control affine system', 0.5937281847000122)]"
1056,1056,28,1056_distributed optimization_distributed learning_robust distributed_byzantine attacks,"['distributed optimization', 'distributed learning', 'robust distributed', 'byzantine attacks', 'distributed training', 'resilient distributed', 'byzantine resilient', 'stochastic gradient descent', 'byzantine', 'federated learning']","['ByRDiE: Byzantine-resilient distributed coordinate descent for\n  decentralized learning   Distributed machine learning algorithms enable learning of models from\ndatasets that are distributed over a network without gathering the data at a\ncentralized location. While efficient distributed algorithms have been\ndeveloped under the assumption of faultless networks, failures that can render\nthese algorithms nonfunctional occur frequently in the real world. This paper\nfocuses on the problem of Byzantine failures, which are the hardest to\nsafeguard against in distributed algorithms. While Byzantine fault tolerance\nhas a rich history, existing work does not translate into efficient and\npractical algorithms for high-dimensional learning in fully distributed (also\nknown as decentralized) settings. In this paper, an algorithm termed\nByzantine-resilient distributed coordinate descent (ByRDiE) is developed and\nanalyzed that enables distributed learning in the presence of Byzantine\nfailures. Theoretical analysis (convex settings) and numerical experiments\n(convex and nonconvex settings) highlight its usefulness for high-dimensional\ndistributed learning in the presence of Byzantine failures.\n', ""Stochastic Alternating Direction Method of Multipliers for\n  Byzantine-Robust Distributed Learning   This paper aims to solve a distributed learning problem under Byzantine\nattacks. In the underlying distributed system, a number of unknown but\nmalicious workers (termed as Byzantine workers) can send arbitrary messages to\nthe master and bias the learning process, due to data corruptions, computation\nerrors or malicious attacks. Prior work has considered a total variation (TV)\nnorm-penalized approximation formulation to handle the Byzantine attacks, where\nthe TV norm penalty forces the regular workers' local variables to be close,\nand meanwhile, tolerates the outliers sent by the Byzantine workers. To solve\nthe TV norm-penalized approximation formulation, we propose a Byzantine-robust\nstochastic alternating direction method of multipliers (ADMM) that fully\nutilizes the separable problem structure. Theoretically, we prove that the\nproposed method converges to a bounded neighborhood of the optimal solution at\na rate of O(1/k) under mild assumptions, where k is the number of iterations\nand the size of neighborhood is determined by the number of Byzantine workers.\nNumerical experiments on the MNIST and COVERTYPE datasets demonstrate the\neffectiveness of the proposed method to various Byzantine attacks.\n"", 'Byzantine-Robust Decentralized Stochastic Optimization over Static and\n  Time-Varying Networks   In this paper, we consider the Byzantine-robust stochastic optimization\nproblem defined over decentralized static and time-varying networks, where the\nagents collaboratively minimize the summation of expectations of stochastic\nlocal cost functions, but some of the agents are unreliable due to data\ncorruptions, equipment failures or cyber-attacks. The unreliable agents, which\nare called as Byzantine agents thereafter, can send faulty values to their\nneighbors and bias the optimization process. Our key idea to handle the\nByzantine attacks is to formulate a total variation (TV) norm-penalized\napproximation of the Byzantine-free problem, where the penalty term forces the\nlocal models of regular agents to be close, but also allows the existence of\noutliers from the Byzantine agents. A stochastic subgradient method is applied\nto solve the penalized problem. We prove that the proposed method reaches a\nneighborhood of the Byzantine-free optimal solution, and the size of\nneighborhood is determined by the number of Byzantine agents and the network\ntopology. Numerical experiments corroborate the theoretical analysis, as well\nas demonstrate the robustness of the proposed method to Byzantine attacks and\nits superior performance comparing to existing methods.\n']","[('distributed optimization', 0.5974067449569702), ('distributed learning', 0.5588486194610596), ('robust distributed', 0.5502188801765442), ('byzantine attacks', 0.5411455035209656), ('distributed training', 0.5402792096138), ('resilient distributed', 0.5027978420257568), ('byzantine resilient', 0.49102121591567993), ('stochastic gradient descent', 0.47420111298561096), ('byzantine', 0.46015575528144836), ('federated learning', 0.4498598575592041)]"
1057,1057,28,1057_bivariate polynomials_polynomial systems_bivariate polynomial_systems polynomial equations,"['bivariate polynomials', 'polynomial systems', 'bivariate polynomial', 'systems polynomial equations', 'univariate polynomials', 'systems polynomial', 'system polynomial equations', 'determinantal formulas', 'two polynomials', 'polynomial equations']","['Koszul-type determinantal formulas for families of mixed multilinear\n  systems   Effective computation of resultants is a central problem in elimination\ntheory and polynomial system solving. Commonly, we compute the resultant as a\nquotient of determinants of matrices and we say that there exists a\ndeterminantal formula when we can express it as a determinant of a matrix whose\nelements are the coefficients of the input polynomials. We study the resultant\nin the context of mixed multilinear polynomial systems, that is multilinear\nsystems with polynomials having different supports, on which determinantal\nformulas were not known. We construct determinantal formulas for two kind of\nmultilinear systems related to the Multiparameter Eigenvalue Problem (MEP):\nfirst, when the polynomials agree in all but one block of variables; second,\nwhen the polynomials are bilinear with different supports, related to a\nbipartite graph. We use the Weyman complex to construct Koszul-type\ndeterminantal formulas that generalize Sylvester-type formulas. We can use the\nmatrices associated to these formulas to solve square systems without computing\nthe resultant. The combination of the resultant matrices with the eigenvalue\nand eigenvector criterion for polynomial systems leads to a new approach for\nsolving MEP.\n', 'Roots of bivariate polynomial systems via determinantal representations   We give two determinantal representations for a bivariate polynomial. They\nmay be used to compute the zeros of a system of two of these polynomials via\nthe eigenvalues of a two-parameter eigenvalue problem. The first determinantal\nrepresentation is suitable for polynomials with scalar or matrix coefficients,\nand consists of matrices with asymptotic order $n^2/4$, where $n$ is the degree\nof the polynomial. The second representation is useful for scalar polynomials\nand has asymptotic order $n^2/6$. The resulting method to compute the roots of\na system of two bivariate polynomials is competitive with some existing methods\nfor polynomials up to degree 10, as well as for polynomials with a small number\nof terms.\n', ""Differentiation of resultants and common roots of pairs of polynomials   The well-known mathematical instrument for detection common roots for pairs\nof polynomials and multiple roots of polynomials are resultants and\ndiscriminants. For a pair of polynomials $f$ and $g$ their resultant $R(f,g)$\nis a function of their coefficients. Zeros of resultant $R(f,g)$ correspond to\nthe families of coefficients of $f$ and $g$ such that $f$ and $g$ have a common\nroot. Herewith the calculation of this common root is a separate problem.\n  The principal results on calculation of a unique common root of two\npolynomials and also about calculating a unique root of multiplicity 2 of a\npolynomial in terms of the first order partial derivatives of resultants and\ndiscriminants are given in the monograph by I.M. Gelfand, M.M. Kapranov, A.V.\nZelevinsky [1, Ch. 3, Ch. 12]. A significant development of the ideas of this\nbook in the direction of searching for formulas for multiple roots of\npolynomials is presented in the paper by I.A. Antipova, E.N. Mikhalkin, A.K.\nTsikh [2]. The key result of this article is [2, Theorem 1] where the\nexpression for a unique root of multiplicity $s \\geq 3$ in terms of the first\norder partial derivatives of resultant of the polynomial and it's derivative of\norder $s-1$.\n  In the present article the explicit formulas for higher derivatives of\nresultants of pairs of polynomials possessing common roots are obtained. On\nthis basis a series of results that differ in ideas from [2, Theorem 1] linking\nhigher derivatives of resultants and common multiple roots are proven. In\naddition the results obtained are applied for a new transparent proof of a\nrefinement of [2, Theorem 1].\n""]","[('bivariate polynomials', 0.6129692792892456), ('polynomial systems', 0.5983166098594666), ('bivariate polynomial', 0.5616021752357483), ('systems polynomial equations', 0.5489119291305542), ('univariate polynomials', 0.5461190342903137), ('systems polynomial', 0.5360000729560852), ('system polynomial equations', 0.535635232925415), ('determinantal formulas', 0.5204514861106873), ('two polynomials', 0.48750051856040955), ('polynomial equations', 0.4808642268180847)]"
1058,1058,28,1058_tensor triangulated category_triangulated categories_triangulated category mathcal_triangulated category,"['tensor triangulated category', 'triangulated categories', 'triangulated category mathcal', 'triangulated category', 'categories noetherian', 'tensor triangulated', 'balmer spectrum', 'hopf algebras', 'derived categories', 'stable module categories']","['Triangular spectra and their applications to derived categories of\n  noetherian schemes   For a triangulated category $\\mathcal{T}$, Matsui recently introduced a\ntopological space $\\mathrm{Spec}_\\triangle(\\mathcal{T})$ which we call the\ntriangular spectrum of $\\mathcal{T}$ as an analog of the Balmer spectrum\nintroduced by Balmer for a tensor triangulated category. In the present paper,\nwe use the triangular spectrum to reconstruct a noetherian scheme $X$ from its\nperfect derived category $\\mathrm{D^{pf}}(X)$. As an application, we give an\nalternative proof of the Bondal-Orlov-Ballard reconstruction theorem. Moreover,\nwe define the structure sheaf on $\\mathrm{Spec}_\\triangle(\\mathcal{T})$ and\ncompare the triangular spectrum and the Balmer spectrum as ringed spaces.\n', 'A conjecture on the composition of localizations on a stratified tensor\n  triangulated category   We study the composition of Bousfield localizations on a tensor triangulated\ncategory stratified via the Balmer-Favi support and with noetherian Balmer\nspectrum. Our aim is to provide reductions via purely axiomatic arguments,\nallowing us general applications to concrete categories examined in\nmathematical practice. We propose a conjecture which states that the behaviour\nof the composition of the localizations depends on the chains of inclusions of\nthe Balmer primes indexing said localizations. We prove this conjecture in the\ncase of finite or low dimensional Balmer spectra.\n', 'Noncommutative tensor triangulated categories and coherent frames   We develop a point-free approach for constructing the\nNakano-Vashaw-Yakimov-Balmer spectrum of a noncommutative tensor triangulated\ncategory under some mild assumptions. In particular, we provide a conceptual\nway of classifying radical thick tensor ideals of a noncommutative tensor\ntriangulated category using frame theoretic methods, recovering the universal\nsupport data in the process. We further show that there is a homeomorphism\nbetween the spectral space of radical thick tensor ideals of a noncommutative\ntensor triangulated category and the collection of open subsets of its spectrum\nin the Hochster dual topology.\n']","[('tensor triangulated category', 0.6373230814933777), ('triangulated categories', 0.566986083984375), ('triangulated category mathcal', 0.5613608360290527), ('triangulated category', 0.5251580476760864), ('categories noetherian', 0.5065099000930786), ('tensor triangulated', 0.48876339197158813), ('balmer spectrum', 0.4803529977798462), ('hopf algebras', 0.4299033284187317), ('derived categories', 0.42956313490867615), ('stable module categories', 0.4244145452976227)]"
1059,1059,28,1059_graded algebra_algebra graded_graded commutative_jordan algebra,"['graded algebra', 'algebra graded', 'graded commutative', 'jordan algebra', 'graded polynomial', 'basis graded', 'gradings algebra', 'compute graded', 'group graded', 'mathbb _2 graded']","['On graded identities of block-triangular matrices with the grading of Di\n  Vincenzo-Vasilovsky   The algebra of $n\\times n$ matrices over a field $F$ has a natural\n$\\mathbb{Z}_n$-grading. Its graded identities have been described by Vasilovsky\nwho extended a previous work of Di Vincenzo for the algebra of $2\\times 2$\nmatrices. In this paper we study the graded identities of block-triangular\nmatrices with the grading inherited by the grading of $M_n(F)$. We show that\nits graded identities follow from the graded identities of $M_n(F)$ and from\nits monomial identities of degree up to $2n-2$. In the case of blocks of sizes\n$n-1$ and 1, we give a complete description of its monomial identities, and\nexhibit a minimal basis for its $T_{\\mathbb{Z}_n}$-ideal.\n', 'On star-homogeneous-graded polynomial identities of upper triangular\n  matrices over an arbitrary field   We study the graded polynomial identities with a homogeneous involution on\nthe algebra of upper triangular matrices endowed with a fine group grading. We\ncompute their polynomial identities and a basis of the relatively free algebra,\nconsidering an arbitrary base field. We obtain the asymptotic behaviour of the\ncodimension sequence when the characteristic of the base field is zero. As a\nconsequence, we compute the exponent and the second exponent of the same\nalgebra endowed with any group grading and any homogeneous involution.\n', 'Graded polynomial identities of the infinite-dimensional upper\n  triangular matrices over an arbitrary field   We compute the graded polynomial identities of the infinite dimensional upper\ntriangular matrix algebra over an arbitrary field. If the grading group is\nfinite, we prove that the set of graded polynomial identities admits a finite\nbasis. We find conditions under which a grading on such an algebra satisfies a\nnontrivial graded polynomial identity. Finally, we provide examples showing\nthat two nonisomorphic gradings can have the same set of graded polynomial\nidentities.\n']","[('graded algebra', 0.6595044136047363), ('algebra graded', 0.5971135497093201), ('graded commutative', 0.5963289141654968), ('jordan algebra', 0.5707544684410095), ('graded polynomial', 0.5633982419967651), ('basis graded', 0.5568414926528931), ('gradings algebra', 0.5443967580795288), ('compute graded', 0.5176317095756531), ('group graded', 0.5168024897575378), ('mathbb _2 graded', 0.5077900290489197)]"
1060,1060,28,1060_brill noether varieties_brill noether theory_brill noether loci_noether varieties,"['brill noether varieties', 'brill noether theory', 'brill noether loci', 'noether varieties', 'noether loci', 'brill noether', 'general curve genus', 'curve genus', 'noether theory', 'prym varieties']","['Brill-Noether loci   Brill-Noether loci ${\\mathcal M}^r_{g,d}$ are those subsets of the moduli\nspace ${\\mathcal M}_g$ determined by the existence of a linear series of degree\n$d$ and dimension $r$. By looking at non-singular curves in a neighborhood of a\nspecial chain of elliptic curves, we provide a new proof of the non-emptiness\nof the Brill-Noether loci when the expected codimension satisfies $-g+r+1\\le\n\\rho(g,r,d)\\le 0$ and prove that for a generic point of a component of this\nlocus, the Petri map is onto. As an application, we show that Brill-Noether\nloci of the same codimension are distinct when the codimension is not too\nlarge, substantially generalizing the known result in codimensions 1 and 2. We\nalso provide a new technique for checking that Brill-Noether loci are not\nincluded in each other.\n', 'Maximal Brill--Noether loci via the gonality stratification   We study the restriction of Brill-Noether loci to the gonality stratification\nof the moduli space of curves of fixed genus. As an application, we give new\nproofs that Brill-Noether loci with $\\rho=-1$ have distinct support, and for\nfixed $r$ give lower bounds on when one direction of the non-containments of\nthe Maximal Brill-Noether Loci Conjecture hold for Brill-Noether loci of rank\n$r$ linear systems. Using these techniques, we also show that Brill-Noether\nloci corresponding to rank $2$ linear systems are maximal as soon as $g\\ge 28$\nand prove the Maximal Brill-Noether Loci Conjecture for $g=20$.\n', 'Maximal Brill-Noether loci via degenerations and double covers   Using limit linear series on chains of curves, we show that closures of\ncertain Brill--Noether loci contain a product of pointed Brill--Noether loci of\nsmall codimension. As a result, we obtain new non-containments of\nBrill--Noether loci, in particular that all dimensionally expected\nnon-containments hold for expected maximal Brill--Noether loci. Using these\ndegenerations, we also give a new proof that Brill--Noether loci with expected\ncodimension $-\\rho\\leq \\lceil g/2\\rceil$ have a component of the expected\ndimension. Additionally, we obtain new non-containments of Brill--Noether loci\nby considering the locus of the source curves of unramified double covers.\n']","[('brill noether varieties', 0.6119260191917419), ('brill noether theory', 0.5701161026954651), ('brill noether loci', 0.5291917324066162), ('noether varieties', 0.5067983865737915), ('noether loci', 0.4867710769176483), ('brill noether', 0.454494833946228), ('general curve genus', 0.43593382835388184), ('curve genus', 0.4235462248325348), ('noether theory', 0.42030689120292664), ('prym varieties', 0.4138125777244568)]"
1061,1061,28,1061_reinforcement learning deep_deep reinforcement learning_informed deep learning_reinforcement learning drl,"['reinforcement learning deep', 'deep reinforcement learning', 'informed deep learning', 'reinforcement learning drl', 'neural odes', 'deep neural network', 'functions deep neural', 'deep neural', 'physics informed deep', 'approximation lyapunov']","['Overcoming the curse of dimensionality for approximating Lyapunov\n  functions with deep neural networks under a small-gain condition   We propose a deep neural network architecture for storing approximate\nLyapunov functions of systems of ordinary differential equations. Under a\nsmall-gain condition on the system, the number of neurons needed for an\napproximation of a Lyapunov function with fixed accuracy grows only\npolynomially in the state dimension, i.e., the proposed approach is able to\novercome the curse of dimensionality.\n', 'SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning   Deep reinforcement learning (DRL) has shown significant promise for\nuncovering sophisticated control policies that interact in environments with\ncomplicated dynamics, such as stabilizing the magnetohydrodynamics of a tokamak\nfusion reactor or minimizing the drag force exerted on an object in a fluid\nflow. However, these algorithms require an abundance of training examples and\nmay become prohibitively expensive for many applications. In addition, the\nreliance on deep neural networks often results in an uninterpretable, black-box\npolicy that may be too computationally expensive to use with certain embedded\nsystems. Recent advances in sparse dictionary learning, such as the sparse\nidentification of nonlinear dynamics (SINDy), have shown promise for creating\nefficient and interpretable data-driven models in the low-data regime. In this\nwork we introduce SINDy-RL, a unifying framework for combining SINDy and DRL to\ncreate efficient, interpretable, and trustworthy representations of the\ndynamics model, reward function, and control policy. We demonstrate the\neffectiveness of our approaches on benchmark control environments and\nchallenging fluids problems. SINDy-RL achieves comparable performance to\nstate-of-the-art DRL algorithms using significantly fewer interactions in the\nenvironment and results in an interpretable control policy orders of magnitude\nsmaller than a deep neural network policy.\n', 'Computing Lyapunov functions using deep neural networks   We propose a deep neural network architecture and a training algorithm for\ncomputing approximate Lyapunov functions of systems of nonlinear ordinary\ndifferential equations. Under the assumption that the system admits a\ncompositional Lyapunov function, we prove that the number of neurons needed for\nan approximation of a Lyapunov function with fixed accuracy grows only\npolynomially in the state dimension, i.e., the proposed approach is able to\novercome the curse of dimensionality. We show that nonlinear systems satisfying\na small-gain condition admit compositional Lyapunov functions. Numerical\nexamples in up to ten space dimensions illustrate the performance of the\ntraining scheme.\n']","[('reinforcement learning deep', 0.5718962550163269), ('deep reinforcement learning', 0.5319191813468933), ('informed deep learning', 0.5241191387176514), ('reinforcement learning drl', 0.4622640013694763), ('neural odes', 0.4591330289840698), ('deep neural network', 0.4590255320072174), ('functions deep neural', 0.450629860162735), ('deep neural', 0.44887879490852356), ('physics informed deep', 0.4469181001186371), ('approximation lyapunov', 0.4274764955043793)]"
1062,1062,28,1062_isomonodromic deformations_isomonodromic deformation_spectral invariants_meromorphic connections,"['isomonodromic deformations', 'isomonodromic deformation', 'spectral invariants', 'meromorphic connections', 'associated spectral curve', 'riemann sphere', 'frobenius manifolds', 'isomonodromic', 'symplectic', 'frobenius manifold']","[""Hamiltonian structure of rational isomonodromic deformation systems   The Hamiltonian approach to isomonodromic deformation systems is extended to\ninclude generic rational covariant derivative operators on the Riemann sphere\nwith irregular singularities of arbitrary Poincar\\'e rank. The space of\nrational connections with given pole degrees carries a natural Poisson\nstructure corresponding to the standard classical rational R-matrix structure\non the dual space $L^*gl(r)$ of the loop algebra $Lgl(r)$. Nonautonomous\nisomonodromic counterparts of the isospectral systems generated by spectral\ninvariants are obtained by identifying the deformation parameters as Casimir\nfunctions on the phase space. These are shown to coincide with the higher\nBirkhoff invariants determining the local asymptotics near to irregular\nsingular points, together with the pole loci. Infinitesimal isomonodromic\ndeformations are shown to be generated by the sum of the Hamiltonian vector\nfield and an explicit derivative vector field that is transversal to the\nsymplectic foliation. The Casimir elements serve as coordinates complementing\nthose along the symplectic leaves, extended by the exponents of formal\nmonodromy, defining a local symplectomorphism between them. The explicit\nderivative vector fields preserve the Poisson structure and define a flat\ntransversal connection, spanning an integrable distribution whose leaves,\nlocally, may be identified as the orbits of a free abelian group. The\nprojection of the infinitesimal isomonodromic deformations vector fields to the\nquotient manifold under this action gives the commuting Hamiltonian vector\nfields corresponding to the spectral invariants dual to the Birkhoff invariants\nand the pole loci.\n"", 'Description of generalized isomonodromic deformations of rank two linear\n  differential equations using apparent singularities   In this paper, we consider the generalized isomonodromic deformations of rank\ntwo irregular connections on the Riemann sphere. We introduce Darboux\ncoordinates on the parameter space of a family of rank two irregular\nconnections by apparent singularities. By the Darboux coordinates, we describe\nthe generalized isomonodromic deformations as Hamiltonian systems.\n', ""Hamiltonian representation of isomonodromic deformations of general\n  rational connections on $\\mathfrak{gl}_2(\\mathbb{C})$   In this paper, we study and build the Hamiltonian system attached to any\n$\\mathfrak{gl}_2(\\mathbb{C})$ meromorphic connection with arbitrary number of\nnon-ramified poles of arbitrary degrees. In particular, we propose the Lax\npairs and Hamiltonian evolutions expressed in terms of irregular times and\nmonodromies associated to the poles as well as $g$ Darboux coordinates defined\nas the apparent singularities arising in the oper gauge. Moreover, we also\nprovide a reduction of the isomonodromic deformations to a subset of $g$\nnon-trivial isomonodromic deformations. This reduction is equivalent to a map\nreducing the set of irregular times to only $g$ non-trivial isomonodromic\ntimes. We apply our construction to all cases where the associated spectral\ncurve has genus 1 and recover the standard Painlev\\'{e} equations. We finally\nmake the connection with the topological recursion and the quantization of\nclassical spectral curve from this perspective.\n""]","[('isomonodromic deformations', 0.6484098434448242), ('isomonodromic deformation', 0.6071842908859253), ('spectral invariants', 0.47209206223487854), ('meromorphic connections', 0.4651486873626709), ('associated spectral curve', 0.4350712299346924), ('riemann sphere', 0.42855173349380493), ('frobenius manifolds', 0.42697954177856445), ('isomonodromic', 0.4201521575450897), ('symplectic', 0.4147988259792328), ('frobenius manifold', 0.4113007187843323)]"
1063,1063,28,1063_cluster tilting subcategories_cluster tilting subcategory_tilting subcategories_tilting subcategory mathcal,"['cluster tilting subcategories', 'cluster tilting subcategory', 'tilting subcategories', 'tilting subcategory mathcal', 'tilting subcategory', 'cluster tilting objects', 'subcategories abelian', 'mathcal cluster tilting', 'rigid subcategory', 'cluster tilting']","['$n$-cluster tilting subcategories of representation-directed algebras   We give a characterization of $n$-cluster tilting subcategories of\nrepresentation-directed algebras based on the $n$-Auslander-Reiten\ntranslations. As an application we classify acyclic Nakayama algebras with\nhomogeneous relations which admit an $n$-cluster tilting subcategory. Finally,\nwe classify Nakayama algebras of global dimension $d<\\infty$ which admit a\n$d$-cluster tilting subcategory.\n', 'Abelian categories arising from cluster tilting subcategories   For a triangulated category T, if C is a cluster-tilting subcategory of T,\nthen the quotient category T\\C is an abelian category. Under certain\nconditions, the converse also holds. This is an very important result of\ncluster-tilting theory, due to Koenig-Zhu and Beligiannis.\n  Now let B be a suitable extriangulated category, which is a simultaneous\ngeneralization of triangulated categories and exact categories. We introduce\nthe notion of pre-cluster tilting subcategory C of B, which is a generalization\nof cluster tilting subcategory. We show that C is cluster tilting if and only\nif B/C is abelian.\n', '$d\\mathbb{Z}$-cluster tilting subcategories of singularity categories   For an exact category $\\mathcal{E}$ with enough projectives and with a\n$d\\mathbb{Z}$-cluster tilting subcategory, we show that the singularity\ncategory of $\\mathcal{E}$ admits a $d\\mathbb{Z}$-cluster tilting subcategory.\nTo do this we introduce cluster tilting subcategories of left triangulated\ncategories, and we show that there is a correspondence between cluster tilting\nsubcategories of $\\mathcal{E}$ and $\\underline{\\mathcal{E}}$. We also deduce\nthat the Gorenstein projectives of $\\mathcal{E}$ admit a $d\\mathbb{Z}$-cluster\ntilting subcategory under some assumptions. Finally, we compute the\n$d\\mathbb{Z}$-cluster tilting subcategory of the singularity category for a\nfinite-dimensional algebra which is not Iwanaga-Gorenstein.\n']","[('cluster tilting subcategories', 0.8029404282569885), ('cluster tilting subcategory', 0.7985068559646606), ('tilting subcategories', 0.682487428188324), ('tilting subcategory mathcal', 0.6695294380187988), ('tilting subcategory', 0.6683171987533569), ('cluster tilting objects', 0.5878547430038452), ('subcategories abelian', 0.5824546217918396), ('mathcal cluster tilting', 0.5726607441902161), ('rigid subcategory', 0.5576331615447998), ('cluster tilting', 0.5558905005455017)]"
1064,1064,28,1064_jointly gaussian_gaussian sources_correlated gaussian_gaussian source,"['jointly gaussian', 'gaussian sources', 'correlated gaussian', 'gaussian source', 'gaussian random variables', 'multivariate gaussian', 'channel distributions', 'lossy source coding', 'correlated sources', 'rate distortion functions']","['Characterization of the Gray-Wyner Rate Region for Multivariate Gaussian\n  Sources: Optimality of Gaussian Auxiliary RV   Examined in this paper, is the Gray and Wyner achievable lossy rate region\nfor a tuple of correlated multivariate Gaussian random variables (RVs) $X_1 :\n\\Omega \\rightarrow {\\mathbb R}^{p_1}$ and $X_2 : \\Omega \\rightarrow {\\mathbb\nR}^{p_2}$ with respect to square-error distortions at the two decoders. It is\nshown that among all joint distributions induced by a triple of RVs $(X_1,X_2,\nW)$, such that $W : \\Omega \\rightarrow {\\mathbb W} $ is the auxiliary RV taking\ncontinuous, countable, or finite values, the Gray and Wyner achievable rate\nregion is characterized by jointly Gaussian RVs $(X_1,X_2, W)$ such that $W $\nis an $n$-dimensional Gaussian RV. It then follows that the achievable rate\nregion is parametrized by the three conditional covariances $Q_{X_1,X_2|W},\nQ_{X_1|W}, Q_{X_2|W}$ of the jointly Gaussian RVs. Furthermore, if the RV $W$\nmakes $X_1$ and $X_2$ conditionally independent, then the corresponding subset\nof the achievable rate region, is simpler, and parametrized by only the two\nconditional covariances $Q_{X_1|W}, Q_{X_2|W}$. The paper also includes the\ncharacterization of the Pangloss plane of the Gray-Wyner rate region along with\nthe characterizations of the corresponding rate distortion functions, their\ntest-channel distributions, and structural properties of the realizations which\ninduce these distributions.\n', ""Computing the Rate-Distortion Function of Gray-Wyner System   In this paper, the rate-distortion theory of the Gray-Wyner lossy source\ncoding system is investigated. For the case of jointly Gaussian distributed\nsources, we establish an expression for the rate-distortion function under the\nconstraint of quadratic distortion. Using the proposed rate-distortion\nfunction, any corner point on the rate-distortion region can be conveniently\ncalculated. We take Wyner's common information as an example and provide a\ngeneral and simple method to solve this problem. Through the analysis of the\nrate-distortion function, the rate on each layer and covariance matrix of\nauxiliary random variables and the sources are also presented in this paper.\n"", ""Characterization of Conditional Independence and Weak Realizations of\n  Multivariate Gaussian Random Variables: Applications to Networks   The Gray and Wyner lossy source coding for a simple network for sources that\ngenerate a tuple of jointly Gaussian random variables (RVs) $X_1 : \\Omega\n\\rightarrow {\\mathbb R}^{p_1}$ and $X_2 : \\Omega \\rightarrow {\\mathbb\nR}^{p_2}$, with respect to square-error distortion at the two decoders is\nre-examined using (1) Hotelling's geometric approach of Gaussian RVs-the\ncanonical variable form, and (2) van Putten's and van Schuppen's\nparametrization of joint distributions ${\\bf P}_{X_1, X_2, W}$ by Gaussian RVs\n$W : \\Omega \\rightarrow {\\mathbb R}^n $ which make $(X_1,X_2)$ conditionally\nindependent, and the weak stochastic realization of $(X_1, X_2)$. Item (2) is\nused to parametrize the lossy rate region of the Gray and Wyner source coding\nproblem for joint decoding with mean-square error distortions ${\\bf\nE}\\big\\{||X_i-\\hat{X}_i||_{{\\mathbb R}^{p_i}}^2 \\big\\}\\leq \\Delta_i \\in\n[0,\\infty], i=1,2$, by the covariance matrix of RV $W$. From this then follows\nWyner's common information $C_W(X_1,X_2)$ (information definition) is achieved\nby $W$ with identity covariance matrix, while a formula for Wyner's lossy\ncommon information (operational definition) is derived, given by\n$C_{WL}(X_1,X_2)=C_W(X_1,X_2)\n  = \\frac{1}{2} \\sum_{j=1}^n\n  \\ln\n  \\left(\n  \\frac{1+d_j}{1-d_j}\n  \\right),$ for the distortion region $ 0\\leq \\Delta_1 \\leq\n\\sum_{j=1}^n(1-d_j)$, $0\\leq \\Delta_2 \\leq \\sum_{j=1}^n(1-d_j)$, and where $1 >\nd_1 \\geq d_2 \\geq \\ldots \\geq d_n>0$ in $(0,1)$ are {\\em the canonical\ncorrelation coefficients} computed from the canonical variable form of the\ntuple $(X_1, X_2)$. The methods are of fundamental importance to other problems\nof multi-user communication, where conditional independence is imposed as a\nconstraint.\n""]","[('jointly gaussian', 0.5768645405769348), ('gaussian sources', 0.5316325426101685), ('correlated gaussian', 0.5224220156669617), ('gaussian source', 0.5134734511375427), ('gaussian random variables', 0.5091824531555176), ('multivariate gaussian', 0.5065833330154419), ('channel distributions', 0.5034201741218567), ('lossy source coding', 0.4928034543991089), ('correlated sources', 0.433505117893219), ('rate distortion functions', 0.4201963543891907)]"
1065,1065,28,1065_topological strings_topological string free_topological string_topological string partition,"['topological strings', 'topological string free', 'topological string', 'topological string partition', 'string theory', 'calabi yau manifolds', 'calabi yau threefolds', 'calabi yau fourfolds', 'donaldson thomas invariants', 'yau manifolds']","['Non-perturbative topological string theory on compact Calabi-Yau 3-folds   We obtain analytic and numerical results for the non-perturbative amplitudes\nof topological string theory on arbitrary, compact Calabi-Yau manifolds. Our\napproach is based on the theory of resurgence and extends previous special\nresults to the more general case. In particular, we obtain explicit\ntrans-series solutions of the holomorphic anomaly equations. Our results\npredict the all orders, large genus asymptotics of the topological string free\nenergies, which we test in detail against high genus perturbative series\nobtained recently in the compact case. We also provide additional evidence that\nthe Stokes constants appearing in the resurgent structure are closely related\nto integer BPS invariants.\n', 'Non-perturbative topological strings from resurgence   The partition function of topological string theory on any family of\nCalabi-Yau threefolds is defined perturbatively as an asymptotic series in the\ntopological string coupling and encodes, in a holomorphic limit, higher genus\nGromov-Witten as well as Gopakumar-Vafa invariants. We prove that the partition\nfunction of topological strings of any CY in this limit can be written as a\nproduct, where each factor is given by the partition function of the resolved\nconifold with shifted arguments, raised to the power of certain sheaf\ninvariants. We use this result to put forward an expression for the\nnon-perturbative topological string partition function in this limit, as a\nproduct over analytic functions in the topological string coupling which\ncorrespond to the Borel sums for the resolved conifold found previously. The\nnon-perturbative corrections to the partition function are identified with\nStokes jumps of a Borel summation. They depend only on genus zero GV invariants\nand can be expressed entirely in terms of a single function which is introduced\nas a deformation of the prepotential.\n', 'Intrinsic non-perturbative topological strings   We study difference equations which are obtained from the asymptotic\nexpansion of topological string theory on the deformed and the resolved\nconifold geometries as well as for topological string theory on arbitrary\nfamilies of Calabi-Yau manifolds near generic singularities at finite distance\nin the moduli space. Analytic solutions in the topological string coupling to\nthese equations are found. The solutions are given by known special functions\nand can be used to extract the strong coupling expansion as well as the\nnon-perturbative content. The strong coupling expansions show the\ncharacteristics of D-brane and NS5-brane contributions, this is illustrated for\nthe quintic Calabi-Yau threefold. For the resolved conifold, an expression\ninvolving both the Gopakumar-Vafa resummation as well as the refined\ntopological string in the Nekrasov-Shatashvili limit is obtained and compared\nto expected results in the literature. Furthermore, a precise relation between\nthe non-perturbative partition function of topological strings and the\ngenerating function of non-commutative Donaldson-Thomas invariants is given.\nMoreover, the expansion of the topological string on the resolved conifold near\nits singular small volume locus is studied. Exact expressions for the leading\nsingular term as well as the regular terms in this expansion are provided and\nproved. The constant term of this expansion turns out to be the known\nGromov-Witten constant map contribution.\n']","[('topological strings', 0.6597720384597778), ('topological string free', 0.6473725438117981), ('topological string', 0.6397039294242859), ('topological string partition', 0.6387895941734314), ('string theory', 0.5658986568450928), ('calabi yau manifolds', 0.5274856090545654), ('calabi yau threefolds', 0.47791555523872375), ('calabi yau fourfolds', 0.4698391556739807), ('donaldson thomas invariants', 0.45215120911598206), ('yau manifolds', 0.4458655118942261)]"
1066,1066,28,1066_integers sum__nonnegative integer coefficients_positive integers a_1_integers a_1,"['integers sum_', 'nonnegative integer coefficients', 'positive integers a_1', 'integers a_1', 'integers a_1 a_2', 'integer coefficients', 'arithmetic progressions', 'a_1 a_2 ldots', 'integer generalized', 'generalized frobenius']","['Sylvester sums on the Frobenius set in arithmetic progression   Let $a_1,a_2,\\dots,a_k$ be positive integers with\n$\\gcd(a_1,a_2,\\dots,a_k)=1$. The concept of the weighted sum $\\sum_{n\\in{\\rm\nNR}}\\lambda^{n}$ is introduced in \\cite{KZ0,KZ}, where ${\\rm NR}={\\rm\nNR}(a_1,a_2,\\dots,a_k)$ denotes the set of positive integers nonrepresentable\nin terms of $a_1,a_2,\\dots,a_k$. When $\\lambda=1$, such a sum is often called\nSylvester sum. The main purpose of this paper is to give explicit expressions\nof the Sylvester sum ($\\lambda=1$) and the weighed sum ($\\lambda\\ne 1$), where\n$a_1,a_2,\\dots,a_k$ forms arithmetic progressions. As applications, various\nother cases are also considered, including weighted sums, almost arithmetic\nsequences, arithmetic sequences with an additional term, and geometric-like\nsequences. Several examples illustrate and confirm our results.\n', 'Sylvester power and weighted sums on the Frobenius set in arithmetic\n  progression   Let $a_1,a_2,\\dots,a_k$ be positive integers with\n$\\gcd(a_1,a_2,\\dots,a_k)=1$. Frobenius number is the largest positive integer\nthat is NOT representable in terms of $a_1,a_2,\\dots,a_k$. When $k\\ge 3$, there\nis no explicit formula in general, but some formulae may exist for special\nsequences $a_1,a_2,\\dots,a_k$, including, those forming arithmetic progressions\nand their modifications. In this paper, we give formulae for the power and\nweighted sum of nonrepresentable positive integers. As applications, we show\nexplicit expressions of these sums for $a_1,a_2,\\dots,a_k$ forming arithmetic\nprogressions.\n', 'Sylvester sums on the Frobenius set in arithmetic progression with\n  initial gaps   Let $a_1,a_2,\\dots,a_k$ be positive integers with\n$\\gcd(a_1,a_2,\\dots,a_k)=1$. Frobenius number is the largest positive integer\nthat is NOT representable in terms of $a_1,a_2,\\dots,a_k$. When $k\\ge 3$, there\nis no explicit formula in general, but some formulae may exist for special\nsequences $a_1,a_2,\\dots,a_k$, including, those forming arithmetic progressions\nand their modifications. In this paper we give explicit formulae for the sum of\nnonrepresentable positive integers (Sylvester sum) as well as Frobenius numbers\nand the number of nonrepresentable positive integers (Sylverster number) for\n$a_1,a_2,\\dots,a_k$ forming arithmetic progressions with initial gaps.\n']","[('integers sum_', 0.48951300978660583), ('nonnegative integer coefficients', 0.48801910877227783), ('positive integers a_1', 0.4863245189189911), ('integers a_1', 0.4851168692111969), ('integers a_1 a_2', 0.4784354269504547), ('integer coefficients', 0.46537384390830994), ('arithmetic progressions', 0.4624992311000824), ('a_1 a_2 ldots', 0.45152172446250916), ('integer generalized', 0.4512033462524414), ('generalized frobenius', 0.45045140385627747)]"
1067,1067,28,1067_strong coupling limit_strong coupling_large coupling_weak coupling,"['strong coupling limit', 'strong coupling', 'large coupling', 'weak coupling', 'coupling limit', 'coupling constants', 'coupling constant', 'coupling strength', 'polaron', 'strongly coupled']","['Effective mass of the Fr\\""ohlich Polaron and the Landau-Pekar-Spohn\n  conjecture   We prove that there is a constant $\\overline C\\in (0,\\infty)$ such that the\neffective mass $m(\\alpha)$ of the Fr\\""ohlich Polaron satisfies $m(\\alpha) \\geq\n\\overline C \\alpha^4$, which is sharp according to a long-standing prediction\nof Landau-Pekar [19] from 1948 and of Spohn [35] from 1987. The method of\nproof, which demonstrates how the $\\alpha^4$ divergence rate of $m(\\alpha)$\nappears in a natural way, is based on analyzing the Gaussian representation of\nthe Polaron measure and that of the associated tilted Poisson point process\ndeveloped in [25], together with an explicit identification of local interval\nprocess in the strong coupling limit $\\alpha\\to\\infty$ in terms of functionals\nof the {\\it Pekar variational formula}.}\n', 'Effective mass of the Polaron: a lower bound   We show that the effective mass of the Fr\\""ohlich Polaron is bounded below by\n$c\\alpha^{2/5}$ for some constant $c>0$ and for all coupling constants\n$\\alpha$. The proof uses the point process representation of the path measure\nof the Fr\\""ohlich Polaron.\n', 'Divergence of the effective mass of a polaron in the strong coupling\n  limit   We consider the Fr\\""ohlich model of a polaron, and show that its effective\nmass diverges in the strong coupling limit.\n']","[('strong coupling limit', 0.5934885144233704), ('strong coupling', 0.5653469562530518), ('large coupling', 0.5507393479347229), ('weak coupling', 0.5187280774116516), ('coupling limit', 0.462556928396225), ('coupling constants', 0.46226760745048523), ('coupling constant', 0.4514969289302826), ('coupling strength', 0.44318580627441406), ('polaron', 0.4064455032348633), ('strongly coupled', 0.3983021676540375)]"
1068,1068,28,1068_piezoelectric_electromechanical_stability system_exponentially stabilizable,"['piezoelectric', 'electromechanical', 'stability system', 'exponentially stabilizable', 'stabilizability', 'exponential stability', 'beams plates', 'electrostatic', 'stabilization results', 'vibrations']","[""Dynamic and electrostatic modeling for a piezoelectric smart composite\n  and related stabilization results   A cantilevered piezoelectric smart composite beam, consisting of perfectly\nbonded elastic, viscoelastic and piezoelectric layers, is considered. The\npiezoelectric layer is actuated by a voltage source. Both fully dynamic and\nelectrostatic approaches, based on Maxwell's equations, are used to model the\npiezoelectric layer. We obtain (i) fully-dynamic and electrostatic Rao-Nakra\ntype models by assuming that the viscoelastic layer has a negligible weight and\nstiffness, (ii) fully-dynamic and electrostatic Mead-Marcus type models by\nneglecting the in-plane and rotational inertia terms. Each model is a\nperturbation of the corresponding classical smart composite beam model. These\nmodels are written in the state-space form, the existence and uniqueness of\nsolutions are obtained in appropriate Hilbert spaces. Next, the stabilization\nproblem for each closed-loop system, with a thorough analysis, is investigated\nfor the natural $B^*-$type state feedback controllers. The fully dynamic\nRao-Nakra model with four state feedback controllers is shown to be not\nasymptotically stable for certain choices of material parameters whereas the\nelectrostatic model is exponentially stable with only three state feedback\ncontrollers (by the spectral multipliers method). Similarly, the fully dynamic\nMead-Marcus model lacks of asymptotic stability for certain solutions whereas\nthe electrostatic model is exponentially stable by only one state feedback\ncontroller.stable by one feedback controller applied to the bending moment\nonly.\n"", 'On modelling and stabilizability of current-controlled piezoelectric\n  material   This paper presents a new modelling approach to fully dynamic electromagnetic\ncurrent-controlled piezoelectric composite models that require a combined\nLagrangian. To model the mechanical domains, we consider two different beam\ntheories, i.e. the Euler-Bernoulli and Timoshenko beam theories. We show that\nboth derived piezoelectric composite models are well-posed. Furthermore, we\nshow through analysis and simulations that both current-controlled\npiezoelectric composites are asymptotically stabilizable through simple\nelectric feedback, which renders the system passive in a classical way for\ncertain system parameters. In this work, we also review several related\npiezoelectric beams, actuators, and composite models.\n', 'On modelling and stabilizability of voltage-controlled piezoelectric\n  material   In this paper, we present a new piezoelectric actuator and piezoelectric\ncomposite model and show the well-posedness of these systems. Furthermore, we\nshow that the piezoelectric composite is stabilizable for certain system\nparameters. In this work, we also review several piezoelectric beams,\nactuators, and composite models and provide improved definitions of the\ndifferent electromagnetic considerations, i.e. fully dynamic electromagnetic\nfield, quasi-static electric field, and the static lectric field assumption.\n']","[('piezoelectric', 0.6070893406867981), ('electromechanical', 0.37355199456214905), ('stability system', 0.37339913845062256), ('exponentially stabilizable', 0.3428370952606201), ('stabilizability', 0.3367137014865875), ('exponential stability', 0.32023677229881287), ('beams plates', 0.30735349655151367), ('electrostatic', 0.290111243724823), ('stabilization results', 0.28533706068992615), ('vibrations', 0.2782711982727051)]"
1069,1069,28,1069_cantor sets_cantor_cantor dust_sets,"['cantor sets', 'cantor', 'cantor dust', 'sets', 'hausdorff dimension greater', 'closed intervals', 'hausdorff dimension', 'sets containing', 'large sets', 'lebesgue measure']","[""Sums of powers, and products of elements of the middle third Cantor set   The questions of the measure and finding open intervals in certain sets of\nsums and products of elements of the middle third Cantor set (or a variant of\nit), have generated considerable interest recently. A broad general framework\nthat makes it possible to deal with these questions was outlined by Astels. The\nquestion of finding the measure of the product of the middle third Cantor set\nwas considered recently in an article by Athreya, Reznick and Tyson. Astels'\nmethods apply to product sets upon considering a generalized logarithmic Cantor\nset, while Athreya, Reznick and Tyson's methods become difficult in dealing\nwith sums or products of $m$'th powers as $m$ becomes large. With a new\nelementary dynamical technique, we can deal with both the questions of sums and\nproducts in a satisfactory way, and the proofs are of the same level of\ncomplexity as that of an elementary proof of the fact that the sum of two\ncopies of the middle third Cantor set is $[0,2]$. Further, some observations\nare made on the question of intersections of one central Cantor set with an\naffine image of another central Cantor set both with arbitrary parameters.\n"", 'Open intervals in sums and products of Cantor sets   We give new arguments for sums and products of sufficient numbers of\narbitrary central Cantor sets to produce large open intervals. We further\ndiscuss the same question for $C^1$ images of such central Cantor sets. This\ngives another perspective on the results obtained by Astels through a different\nformulation on the thickness of these Cantor sets. There has been recent\ninterest in the question of products and sums of powers of Cantor sets, and\nthese are addressed by our methods.\n', 'Characterization of the algebraic difference of special affine Cantor\n  sets   We investigate some self-similar Cantor sets $C(l,r,p)$, which we call\nS-Cantor sets, generated by numbers $l,r,p \\in \\mathbb{N}$, $l+r<p$. We give a\nfull characterization of the set $C(l_1,r_1,p)-C(l_2,r_2,p)$ which can take one\nof the form: the interval $[-1,1]$, a Cantor set, an L-Cantorval, an\nR-Cantorval or an M-Cantorval. As corollaries we give examples of Cantor sets\nand Cantorvals, which can be easily described using some positional numeral\nsystems.\n']","[('cantor sets', 0.7501868009567261), ('cantor', 0.6240493655204773), ('cantor dust', 0.5024892091751099), ('sets', 0.44687744975090027), ('hausdorff dimension greater', 0.41864901781082153), ('closed intervals', 0.41475608944892883), ('hausdorff dimension', 0.4147084653377533), ('sets containing', 0.4135841727256775), ('large sets', 0.4126349091529846), ('lebesgue measure', 0.4100206792354584)]"
1070,1070,28,1070_integral group rings_rings finite groups_group rings_torsion free groups,"['integral group rings', 'rings finite groups', 'group rings', 'torsion free groups', 'group ring mathbb', 'group ring', 'torsion free group', 'ring finite group', 'twisted group rings', 'group algebras']","['Structure of group rings and the group of units of integral group rings:\n  an invitation   During the past three decades fundamental progress has been made on\nconstructing large torsion-free subgroups (i.e. subgroups of finite index) of\nthe unit group $\\U (\\Z G)$ of the integral group ring $\\Z G$ of a finite group\n$G$. These constructions rely on explicit constructions of units in $\\Z G$ and\nproofs of main results make use of the description of the Wedderburn components\nof the rational group algebra $\\Q G$. The latter relies on explicit\nconstructions of primitive central idempotents and the rational representations\nof $G$. It turns out that the existence of reduced two degree representations\nplay a crucial role. Although the unit group is far from being understood, some\nstructure results on this group have been obtained. In this paper we give a\nsurvey of some of the fundamental results and the essential needed techniques.\n', 'Units of twisted group rings and their correlations to classical group\n  rings   This paper is centered around the classical problem of extracting properties\nof a finite group $G$ from the ring isomorphism class of its integral group\nring $\\mathbb{Z} G$. This problem is considered via describing the unit group\n$\\mathcal{U}( \\mathbb{Z} G)$ generically for a finite group. Since the $`90s$\nseveral well known generic constructions of units are known to generate a\nsubgroup of finite index in $\\mathcal{U}(\\mathbb{Z } G)$ if $\\mathbb{Q} G$ does\nnot have so-called exceptional simple epimorphic images, e.g. $M_2\n(\\mathbb{Q})$. However it remained a major open problem to find a {\\it generic}\nconstruction under the presence of the latter type of simple images. In this\narticle we obtain such generic construction of units. Moreover, this new\nconstruction also exhibits new properties, such as providing generically free\nsubgroups of large rank. As an application we answer positively for several\nclasses of groups recent conjectures on the rank and the periodic elements of\nthe abelianisation $\\mathcal{U}(\\mathbb{Z} G)^{ab}$. To obtain all this, we\ninvestigate the group ring $R \\Gamma$ of an extension $\\Gamma$ of some normal\nsubgroup $N$ by a group $G$, over a domain $R$. More precisely, we obtain a\ndirect sum decomposition of the (twisted) group algebra of $\\Gamma$ over the\nfraction field $F$ of $R$ in terms of various twisted group rings of $G$ over\nfinite extensions of $F$. Furthermore, concrete information on the kernel and\ncokernel of the associated projections is obtained. Along the way we also\nlaunch the investigations of the unit group of twisted group rings and of\n$\\mathcal{U}( R\\Gamma)$ via twisted group rings.\n', 'Algorithmic aspects of units in group rings   We describe the main questions connected to torsion subgroups in the unit\ngroup of integral group rings of finite groups and algorithmic methods to\nattack these questions. We then prove the Zassenhaus Conjecture for Amitsur\ngroups and prove that any normalized torsion subgroup in the unit group of an\nintegral group of a Frobenius complement is isomorphic to a subgroup of the\ngroup base. Moreover we study the orders of torsion units in integral group\nrings of finite almost quasisimple groups and the existence of torsion-free\nnormal subgroups of finite index in the unit group.\n']","[('integral group rings', 0.6936533451080322), ('rings finite groups', 0.657214879989624), ('group rings', 0.6496871709823608), ('torsion free groups', 0.6182206869125366), ('group ring mathbb', 0.6104841232299805), ('group ring', 0.605115532875061), ('torsion free group', 0.6036231517791748), ('ring finite group', 0.5989376902580261), ('twisted group rings', 0.5764681100845337), ('group algebras', 0.5368233919143677)]"
1071,1071,28,1071_matrices spectrum_jacobi matrices_jacobi operators_spectral theory,"['matrices spectrum', 'jacobi matrices', 'jacobi operators', 'spectral theory', 'matrices spectral', 'jacobi matrix', 'periodic jacobi', 'jacobi operator', 'inverse spectral theory', 'spectral properties']","['Thin Spectra and Singular Continuous Spectral Measures for\n  Limit-Periodic Jacobi Matrices   This paper investigates the spectral properties of Jacobi matrices with\nlimit-periodic coefficients. We show that for a residual set of such matrices,\nthe spectrum is a Cantor set of zero Lebesgue measure, and the spectral\nmeasures are purely singular continuous. For a dense set of limit-periodic\nJacobi matrices we can strengthen the result and show that the spectrum is a\nCantor set of zero lower box counting dimension, and hence in particular of\nzero Hausdorff dimension, while still retaining the singular continuity of the\nspectral type. We also show how results of this nature can be established by\nfixing the off-diagonal coefficients and varying only the diagonal\ncoefficients, and, in a more restricted version, by fixing the diagonal\ncoefficients to be zero and varying only the off-diagonal coefficients. We\napply these results to produce examples of weighted Laplacians on the\nmultidimensional integer lattice having purely singular continuous spectral\ntype and zero-dimensional spectrum.\n', 'Formula for The IDS of Periodic Jacobi Matrices   We prove that on the spectrum the integrated density of states (IDS for\nshort) of periodic Jacobi matrices is related to the discriminant. The method\nis to count the number of generalized zeros of Bloch wave solutions.\n', 'Barrier nonsubordinacy and absolutely continuous spectrum of block\n  Jacobi matrices   We explore to what extent the relation between the absolute continuous\nspectrum and non-existence of subordinate generalized eigenvectors, known for\nscalar Jacobi operators, can be formulated also for block Jacobi operators with\n$d$-dimensional blocks. The main object here allowing to make some progress in\nthat direction is the new notion of the barrier nonsubordinacy. We prove that\nthe barrier nonsubordinacy implies the absolute continuity for block Jacobi\noperators. Finally, we extend some well-known $d=1$ conditions guaranteeing the\nabsolute continuity to $d \\geq 1$ and we give applications of our results to\nsome concrete classes of block Jacobi matrices.\n']","[('matrices spectrum', 0.6168661117553711), ('jacobi matrices', 0.6150011420249939), ('jacobi operators', 0.5985884070396423), ('spectral theory', 0.5806227326393127), ('matrices spectral', 0.5761284232139587), ('jacobi matrix', 0.561445951461792), ('periodic jacobi', 0.5594997406005859), ('jacobi operator', 0.5482273101806641), ('inverse spectral theory', 0.5455806851387024), ('spectral properties', 0.5445075631141663)]"
1072,1072,28,1072_polynomial chaos expansion_polynomial chaos expansions_generalized polynomial chaos_polynomial chaos,"['polynomial chaos expansion', 'polynomial chaos expansions', 'generalized polynomial chaos', 'polynomial chaos', 'sparse approximation', 'adaptive sparse', 'chaos expansion', 'chaos expansions', 'sparse polynomial', 'computation sparse']","['Automatic selection of basis-adaptive sparse polynomial chaos expansions\n  for engineering applications   Sparse polynomial chaos expansions (PCE) are an efficient and widely used\nsurrogate modeling method in uncertainty quantification for engineering\nproblems with computationally expensive models. To make use of the available\ninformation in the most efficient way, several approaches for so-called\nbasis-adaptive sparse PCE have been proposed to determine the set of polynomial\nregressors (""basis"") for PCE adaptively.\n  The goal of this paper is to help practitioners identify the most suitable\nmethods for constructing a surrogate PCE for their model. We describe three\nstate-of-the-art basis-adaptive approaches from the recent sparse PCE\nliterature and conduct an extensive benchmark in terms of global approximation\naccuracy on a large set of computational models. Investigating the synergies\nbetween sparse regression solvers and basis adaptivity schemes, we find that\nthe choice of the proper solver and basis-adaptive scheme is very important, as\nit can result in more than one order of magnitude difference in performance. No\nsingle method significantly outperforms the others, but dividing the analysis\ninto classes (regarding input dimension and experimental design size), we are\nable to identify specific sparse solver and basis adaptivity combinations for\neach class that show comparatively good performance.\n  To further improve on these findings, we introduce a novel solver and basis\nadaptivity selection scheme guided by cross-validation error. We demonstrate\nthat this automatic selection procedure provides close-to-optimal results in\nterms of accuracy, and significantly more robust solutions, while being more\ngeneral than the case-by-case recommendations obtained by the benchmark.\n', 'Polynomial chaos expansions for dependent random variables   Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty\nin models parameterized by independent random variables. The assumption of\nindependence leads to simple strategies for evaluating PCE coefficients. In\ncontrast, the application of PCE to models of dependent variables is much more\nchallenging. Three approaches can be used. The first approach uses mapping\nmethods where measure transformations, such as the Nataf and Rosenblatt\ntransformation, can be used to map dependent random variables to independent\nones; however we show that this can significantly degrade performance since the\nJacobian of the map must be approximated. A second strategy is the class of\ndominating support methods which build PCE using independent random variables\nwhose distributional support dominates the support of the true dependent joint\ndensity; we provide evidence that this approach appears to produce\napproximations with suboptimal accuracy. A third approach, the novel method\nproposed here, uses Gram-Schmidt orthogonalization (GSO) to numerically compute\northonormal polynomials for the dependent random variables. This approach has\nbeen used successfully when solving differential equations using the intrusive\nstochastic Galerkin method, and in this paper we use GSO to build PCE using a\nnon-intrusive stochastic collocation method. The stochastic collocation method\ntreats the model as a black box and builds approximations of model output from\na set of samples. Building PCE from samples can introduce ill-conditioning\nwhich does not plague stochastic Galerkin methods. To mitigate this\nill-conditioning we generate weighted Leja sequences, which are nested sample\nsets, to build accurate polynomial interpolants. We show that our proposed\napproach produces PCE which are orders of magnitude more accurate than PCE\nconstructed using mapping or dominating support methods.\n', 'Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark   Sparse polynomial chaos expansions (PCE) are a popular surrogate modelling\nmethod that takes advantage of the properties of PCE, the sparsity-of-effects\nprinciple, and powerful sparse regression solvers to approximate computer\nmodels with many input parameters, relying on only few model evaluations.\nWithin the last decade, a large number of algorithms for the computation of\nsparse PCE have been published in the applied math and engineering literature.\nWe present an extensive review of the existing methods and develop a framework\nfor classifying the algorithms. Furthermore, we conduct a unique benchmark on a\nselection of methods to identify which approaches work best in practical\napplications. Comparing their accuracy on several benchmark models of varying\ndimensionality and complexity, we find that the choice of sparse regression\nsolver and sampling scheme for the computation of a sparse PCE surrogate can\nmake a significant difference, of up to several orders of magnitude in the\nresulting mean-squared error. Different methods seem to be superior in\ndifferent regimes of model dimensionality and experimental design size.\n']","[('polynomial chaos expansion', 0.5810603499412537), ('polynomial chaos expansions', 0.5733433961868286), ('generalized polynomial chaos', 0.5401932001113892), ('polynomial chaos', 0.49802571535110474), ('sparse approximation', 0.4847261309623718), ('adaptive sparse', 0.4805680811405182), ('chaos expansion', 0.4550328850746155), ('chaos expansions', 0.44859275221824646), ('sparse polynomial', 0.4458925724029541), ('computation sparse', 0.4295075833797455)]"
1073,1073,28,1073_stochastic integrals_stratonovich stochastic_ito stratonovich_ito stochastic,"['stochastic integrals', 'stratonovich stochastic', 'ito stratonovich', 'ito stochastic', 'fourier legendre series', 'wiener process', 'stratonovich', 'fourier legendre', 'stochastic differential equations', 'stochastic differential']","['Development and Application of the Fourier Method to the Mean-Square\n  Approximation of Iterated Ito and Stratonovich Stochastic Integrals   The article is devoted to the mean-square approximation of iterated Ito and\nStratonovich stochastic integrals in the context of the numerical integration\nof Ito stochastic differential equations. The expansion of iterated Ito\nstochastic integrals of arbitrary multiplicity $k$ $(k\\in\\mathbb{N})$ and\nexpansions of iterated Stratonovich stochastic integrals of multiplicities 1 to\n6 have been obtained. Considerable attention is paid to expansions based on\nmultiple Fourier-Legendre series. The exact and approximate expressions for the\nmean-square error of approximation of iterated Ito stochastic integrals are\nderived. The results of the article will be useful for numerical integration of\nIto stochastic differential equations with non-commutative noise.\n', 'Expansion of Iterated Stratonovich Stochastic Integrals of Fifth, Sixth\n  and Seventh Multiplicity Based on Generalized Multiple Fourier Series   The article is devoted to the construction of expansions of iterated\nStratonovich stochastic integrals of fifth, sixth and seventh multiplicities\nbased on the method of generalized multiple Fourier series converging in the\nsense of norm in the Hilbert space $L_2([t, T]^k),$ $k\\in\\mathbb{N}.$\nSpecifically, we mainly use multiple Fourier-Legendre series and multiple\ntrigonometric Fourier series $(k=1,\\ldots,7)$. Recently, expansions of iterated\nStratonovich stochastic integrals of multiplicity $k,$ $k\\in\\mathbb{N}$ (the\ncase of continuous weight functions and an arbitrary complete orthonormal\nsystem of functions in $L_2([t, T])$) have been obtained (Theorems 42, 44) but\nunder one additional condition. The considered expansions converge in the\nmean-square sense and contain only one operation of the limit transition in\ncontrast to its existing analogues. Expansions of iterated Stratonovich\nstochastic integrals turned out much simpler than appropriate expansions of\niterated Ito stochastic integrals. We use expansions of the latter as a tool of\nthe proof of expansions for iterated Stratonovich stochastic integrals.\nIterated Stratonovich stochastic integrals are part of the Taylor-Stratonovich\nexpansion for solutions of Ito stochastic differential equations. That is why\nthe results of the article can be applied to the numerical integrations of Ito\nstochastic differential equations.\n', 'Mean-Square Approximation of Iterated Ito and Stratonovich Stochastic\n  Integrals of Multiplicities 1 to 6 from the Taylor-Ito and\n  Taylor-Stratonovich Expansions Using Legendre Polynomials   The article is devoted to the practical material on expansions and\nmean-square approximations of specific iterated Ito and Stratonovich stochastic\nintegrals of multiplicities 1 to 6 with respect to components of the\nmultidimensional Wiener process on the base of the method of generalized\nmultiple Fourier series. More precisely, we used the multiple Fourier--Legendre\nseries converging in the sense of norm in the space $L_2([t, T]^k)$\n$(k=1,\\ldots,6)$ for approximation of iterated Ito and Stratonovich stochastic\nintegrals. The considered iterated Ito and Stratonovich stochastic integrals\nare part of the stochastic Taylor expansions (Taylor-Ito and\nTaylor-Stratonovich expansions). Therefore, the results of the article can be\nuseful for construction of the high-order strong numerical methods for Ito\nstochastic differential equations. Expansions of iterated Ito and Stratonovich\nstochastic integrals of multiplicities 1 to 6 using Legendre polynomials are\nderived. The convergence with probability 1 of the mentioned method of\ngeneralized multiple Fourier series is proved for iterated Ito stochastic\nintegrals of multiplicities $k$ $(k\\in\\mathbb{N})$ for the cases of multiple\nFourier-Legendre series and multiple trigonometric Fourier series.\n']","[('stochastic integrals', 0.5893577337265015), ('stratonovich stochastic', 0.5566818714141846), ('ito stratonovich', 0.5560752153396606), ('ito stochastic', 0.4460030794143677), ('fourier legendre series', 0.4174611568450928), ('wiener process', 0.3785288631916046), ('stratonovich', 0.3637249767780304), ('fourier legendre', 0.352609246969223), ('stochastic differential equations', 0.3455428183078766), ('stochastic differential', 0.34086543321609497)]"
1074,1074,28,1074_nijenhuis operators_operators nijenhuis_nijenhuis operator_invariant differential operators,"['nijenhuis operators', 'operators nijenhuis', 'nijenhuis operator', 'invariant differential operators', 'linear differential operators', 'differential operators', 'partial differential operators', 'differential invariants', 'nijenhuis geometry', 'differential operators acting']","['Singularities of two-dimensional Nijenhuis operators   A Nijenhuis operator $L$ is a $(1,1)$-tensor field on a smooth manifold $M$\nwith vanishing Nijenhuis torsion ${ {\\mathcal N_L}}$. At each point $x\\in M$,\nthe algebraic type of $L(x)$ is characterized by its Jordan normal form. In\nthis paper, we study singularities of a two-dimensional Nijenhuis operator in\nthe case when its trace has a non-zero differential at the singular point. A\ndescription of such singularities reduces to studying the smoothness of some\nfunction, which is a fraction depending on partial derivatives of the\ndeterminant of $L$. We completely describe singularities for some special\nclasses of functions. We also obtained interesting examples of Nijenhuis\noperators and their singularities.\n', 'Nijenhuis operators with a unity and F-manifolds   The core object of this paper is a pair $(L, e)$, where $L$ is a Nijenhuis\noperator and $e$ is a vector field satisfying a specific Lie derivative\ncondition, i.e., $Lie_{e}L=\\operatorname{Id}$. Our research unfolds in two\nparts. In the first part, we establish a Splitting Theorem for Nijenhuis\noperators with a unity, offering an effective reduction of their study to cases\nwhere $L$ has either one real or two complex conjugate eigenvalues at a given\npoint. We further provide the normal forms for $\\mathrm{gl}$-regular Nijenhuis\noperators with a unity around algebraically generic points, along with\nsemi-normal forms for dimensions two and three. In the second part, we\nestablish the relationship between Nijenhuis operators with a unity and\n$F$-manifolds. Specifically, we prove that the class of regular $F$-manifolds\ncoincides with the class of Nijenhuis manifolds with a cyclic unity. By\nextending our results from dimension three, we reveal semi-normal forms for\ncorresponding $F$-manifolds around singularities.\n', 'Elementary Differential Singularities of Three-Dimensional Nijenhuis\n  Operators   In the paper, three-dimensional Nijenhuis operators are studied that have\ndifferential singularities, i.e., such points at which the coefficients of the\ncharacteristic polynomials are dependent. The case is studied in which the\ndifferentials of all invariants of the Nijenhuis operator are proportional, as\nwell as the case when two invariants are functionally independent and the third\ndefines a fold-type singularity. In particular, new examples of\nthree-dimensional Nijenhuis operators with singularities of the specified type\nare constructed.\n']","[('nijenhuis operators', 0.671868085861206), ('operators nijenhuis', 0.6354397535324097), ('nijenhuis operator', 0.6220506429672241), ('invariant differential operators', 0.5547492504119873), ('linear differential operators', 0.5040440559387207), ('differential operators', 0.5032667517662048), ('partial differential operators', 0.46649491786956787), ('differential invariants', 0.45898520946502686), ('nijenhuis geometry', 0.4563899636268616), ('differential operators acting', 0.44548770785331726)]"
1075,1075,28,1075_electroencephalogram_brain activity_electroencephalography_brain dynamics,"['electroencephalogram', 'brain activity', 'electroencephalography', 'brain dynamics', 'eeg', 'bci', 'brain regions', 'fmri', 'temporal patterns', 'spatial temporal patterns']","['Mining the Mind: Linear Discriminant Analysis of MEG source\n  reconstruction time series supports dynamic changes in deep brain regions\n  during meditation sessions   Meditation practices have been claimed to have a positive effect on the\nregulation of mood and emotion for quite some time by practitioners, and in\nrecent times there has been a sustained effort to provide a more precise\ndescription of the changes induced by meditation on human brain. Longitudinal\nstudies have reported morphological changes in cortical thickness and volume in\nselected brain regions due to meditation practice, which is interpreted as\nevidence for effectiveness of it beyond the subjective self reporting. Evidence\nbased on real time monitoring of meditating brain by functional imaging\nmodalities such as MEG or EEG remains a challenge. In this article we consider\nMEG data collected during meditation sessions of experienced Buddhist monks\npracticing focused attention (Samatha) and open monitoring (Vipassana)\nmeditation, contrasted by resting state with eyes closed. The MEG data is first\nmapped to time series of brain activity averaged over brain regions\ncorresponding to a standard Destrieux brain atlas, and further by bootstrapping\nand spectral analysis to data matrices representing a random sample of power\nspectral densities over bandwidths corresponding to $\\alpha$, $\\beta$,\n$\\gamma$, and $\\theta$ bands in the spectral range. We demonstrate using linear\ndiscriminant analysis (LDA) that the samples corresponding to different\nmeditative or resting states contain enough fingerprints of the brain state to\nallow a separation between different states, and we identify the brain regions\nthat appear to contribute to the separation. Our findings suggest that\ncingulate cortex, insular cortex and some of the internal structures, most\nnotably accumbens, caudate and putamen nuclei, thalamus and amygdalae stand out\nas separating regions, which seems to correlate well with earlier findings\nbased on longitudinal studies.\n', 'Explainable MST-ECoGNet Decode Visual Information from ECoG Signal   In the application of brain-computer interface (BCI), we not only need to\naccurately decode brain signals,but also need to consider the explainability of\nthe decoding process, which is related to the reliability of the model. In the\nprocess of designing a decoder or processing brain signals, we need to explain\nthe discovered phenomena in physical or physiological way. An explainable model\nnot only makes the signal processing process clearer and improves reliability,\nbut also allows us to better understand brain activities and facilitate further\nexploration of the brain. In this paper, we systematically analyze the\nmulti-classification dataset of visual brain signals ECoG, using a simple and\nhighly explainable method to explore the ways in which ECoG carry visual\ninformation, then based on these findings, we propose a model called\nMST-ECoGNet that combines traditional mathematics and deep learning. The main\ncontributions of this paper are: 1) found that ECoG time-frequency domain\ninformation carries visual information, provides important features for visual\nclassification tasks. The mathematical method of MST (Modified S Transform) can\neffectively extract temporal-frequency domain information; 2) The spatial\ndomain of ECoG signals also carries visual information, the unique spatial\nfeatures are also important features for classification tasks; 3) The real and\nimaginary information in the time-frequency domain are complementary. The\neffective combination of the two is more helpful for classification tasks than\nusing amplitude information alone; 4) Finally, compared with previous work, our\nmodel is smaller and has higher performance: for the object MonJ, the model\nsize is reduced to 10.82% of base model, the accuracy is improved by 6.63%; for\nthe object MonC, the model size is reduced to 8.78%, the accuracy is improved\nby 16.63%.\n', ""Characterising Alzheimer's Disease with EEG-based Energy Landscape\n  Analysis   Alzheimer's disease (AD) is one of the most common neurodegenerative\ndiseases, with around 50 million patients worldwide. Accessible and\nnon-invasive methods of diagnosing and characterising AD are therefore urgently\nrequired. Electroencephalography (EEG) fulfils these criteria and is often used\nwhen studying AD. Several features derived from EEG were shown to predict AD\nwith high accuracy, e.g. signal complexity and synchronisation. However, the\ndynamics of how the brain transitions between stable states have not been\nproperly studied in the case of AD and EEG data. Energy landscape analysis is a\nmethod that can be used to quantify these dynamics. This work presents the\nfirst application of this method to both AD and EEG. Energy landscape assigns\nenergy value to each possible state, i.e. pattern of activations across brain\nregions. The energy is inversely proportional to the probability of occurrence.\nBy studying the features of energy landscapes of 20 AD patients and 20 healthy\nage-matched counterparts, significant differences were found. The dynamics of\nAD patients' brain networks were shown to be more constrained - with more local\nminima, less variation in basin size, and smaller basins. We show that energy\nlandscapes can predict AD with high accuracy, performing significantly better\nthan baseline models.\n""]","[('electroencephalogram', 0.5710420608520508), ('brain activity', 0.5335397720336914), ('electroencephalography', 0.5312693119049072), ('brain dynamics', 0.5279470086097717), ('eeg', 0.4623395502567291), ('bci', 0.458059698343277), ('brain regions', 0.3916902542114258), ('fmri', 0.3743445873260498), ('temporal patterns', 0.3726823925971985), ('spatial temporal patterns', 0.3600026071071625)]"
1076,1076,28,1076_generalized quantum_mode quantum_asymmetric quantum_generalization quantum,"['generalized quantum', 'mode quantum', 'asymmetric quantum', 'generalization quantum', 'quantum', 'rabi', 'harmonic oscillators', 'hamiltonian h_', 'ground state quantum', 'state quantum']","['Analytical approximations for generalized quantum Rabi models   The quantum Rabi model is essential for understanding interacting quantum\nsystems. It serves as the simplest non-integrable yet solvable model describing\nthe interaction between a two-level system and a single mode of a bosonic\nfield. In this study, we delve into the exploration of the generalized quantum\nRabi model, wherein the bosonic mode of the field undergoes squeezing.\nUtilizing the Segal-Bargmann representation of the infinite-dimensional Hilbert\nspace, we demonstrate that the energy spectrum of the generalized quantum Rabi\nmodel, when both the Rabi coupling strength and the squeezing strength are not\nsignificantly large compared to the field mode frequency, can be analytically\ndetermined by a bi-confluent Fuchsian equation with two regular singularities\nat 0 and 1 and an irregular singularity of rank two at infinity.\n', 'Determinant expressions of constraint polynomials and the spectrum of\n  the asymmetric quantum Rabi model   The purpose of this paper is to study the exceptional eigenvalues of the\nasymmetric quantum Rabi models (AQRM), specifically, to determine the\ndegeneracy of their eigenstates. Here, the Hamiltonian\n$H^{\\epsilon}_{\\text{Rabi}}$ of the AQRM is defined by adding the fluctuation\nterm $\\epsilon \\sigma_x$, with $\\sigma_x$ being the Pauli matrix, to the\nHamiltonian of the quantum Rabi model, breaking its $\\mathbb{Z}_{2}$-symmetry.\nThe spectrum of $H^{\\epsilon}_{\\text{Rabi}}$ contains a set of exceptional\neigenvalues, considered to be remains of the eigenvalues of the uncoupled\nbosonic mode, which are further classified in two types: Juddian, associated\nwith polynomial eigensolutions, and non-Juddian exceptional. We explicitly\ndescribe the constraint relations for allowing the model to have exceptional\neigenvalues. By studying these relations we obtain the proof of the conjecture\non constraint polynomials previously proposed by the third author. In fact, we\nprove that the spectrum of the AQRM possesses degeneracies if and only if the\nparameter $\\epsilon$ is a half-integer. Moreover, we show that non-Juddian\nexceptional eigenvalues do not contribute any degeneracy and we characterize\nexceptional eigenvalues by representations of $\\mathfrak{sl}_2$. Upon these\nresults, we draw the whole picture of the spectrum of the AQRM. Furthermore,\ngenerating functions of constraint polynomials from the viewpoint of confluent\nHeun equations are also discussed.\n', 'A generalization of the quantum Rabi model: exact solution and spectral\n  structure   We consider a generalization of the quantum Rabi model where the two-level\nsystem and the single-mode cavity oscillator are coupled by an additional\nStark-like term. By adapting a method recently introduced by Braak [Phys. Rev.\nLett. {\\bf 107}, 100401 (2011)], we solve the model exactly. The low-lying\nspectrum in the experimentally relevant ultrastrong and deep strong regimes of\nthe Rabi coupling is found to exhibit two striking features absent from the\noriginal quantum Rabi model: avoided level crossings for states of the same\nparity and an anomalously rapid onset of two-fold near-degenerate levels as the\nRabi coupling increases.\n']","[('generalized quantum', 0.5208207368850708), ('mode quantum', 0.48563000559806824), ('asymmetric quantum', 0.4852248430252075), ('generalization quantum', 0.4627649784088135), ('quantum', 0.440103679895401), ('rabi', 0.42487606406211853), ('harmonic oscillators', 0.4185260832309723), ('hamiltonian h_', 0.4043932855129242), ('ground state quantum', 0.4033532440662384), ('state quantum', 0.3956473469734192)]"
1077,1077,28,1077_graph packing_subcubic graphs_coloring graph_chromatic number,"['graph packing', 'subcubic graphs', 'coloring graph', 'chromatic number', 'chromatic numbers', 'subcubic graph', 'graph partition vertex', 'graph partition', 'chromatic number chi_', 'chromatic number denoted']","[""Every subcubic graph is packing $(1,1,2,2,3)$-colorable   For a sequence $S=(s_1, \\ldots, s_k)$ of non-decreasing integers, a packing\n$S$-coloring of a graph $G$ is a partition of its vertex set $V(G)$ into $V_1,\n\\ldots, V_k$ such that for every pair of distinct vertices $u,v \\in V_i$, where\n$1 \\le i \\le k$, the distance between $u$ and $v$ is at least $s_i+1$. The\npacking chromatic number, $\\chi_p(G)$, of a graph $G$ is the smallest integer\n$k$ such that $G$ has a packing $(1,2, \\ldots, k)$-coloring. Gastineau and\nTogni asked an open question ``Is it true that the $1$-subdivision ($D(G)$) of\nany subcubic graph $G$ has packing chromatic number at most $5$?'' and later\nBre\\v{s}ar, Klav\\v{z}ar, Rall, and Wash conjectured that it is true.\n  In this paper, we prove that every subcubic graph has a packing\n$(1,1,2,2,3)$-coloring and it is sharp due to the existence of subcubic graphs\nthat are not packing $(1,1,2,2)$-colorable. As a corollary of our result,\n$\\chi_p(D(G)) \\le 6$ for every subcubic graph $G$, improving a previous bound\n($8$) due to Balogh, Kostochka, and Liu in 2019, and we are now just one step\naway from fully solving the conjecture.\n"", 'Packing $(1,1,2,4)$-coloring of subcubic outerplanar graphs   For $1\\leq s_1 \\le s_2 \\le \\ldots \\le s_k$ and a graph $G$, a packing $(s_1,\ns_2, \\ldots, s_k)$-coloring of $G$ is a partition of $V(G)$ into sets $V_1,\nV_2, \\ldots, V_k$ such that, for each $1\\leq i \\leq k$, the distance between\nany two distinct $x,y\\in V_i$ is at least $s_i + 1$. The packing chromatic\nnumber, $\\chi_p(G)$, of a graph $G$ is the smallest $k$ such that $G$ has a\npacking $(1,2, \\ldots, k)$-coloring. It is known that there are trees of\nmaximum degree 4 and subcubic graphs $G$ with arbitrarily large $\\chi_p(G)$.\nRecently, there was a series of papers on packing $(s_1, s_2, \\ldots,\ns_k)$-colorings of subcubic graphs in various classes. We show that every\n$2$-connected subcubic outerplanar graph has a packing $(1,1,2)$-coloring and\nevery subcubic outerplanar graph is packing $(1,1,2,4)$-colorable. Our results\nare sharp in the sense that there are $2$-connected subcubic outerplanar graphs\nthat are not packing $(1,1,3)$-colorable and there are subcubic outerplanar\ngraphs that are not packing $(1,1,2,5)$-colorable. We also show subcubic\nouterplanar graphs that are not packing $(1,2,2,4)$-colorable and not packing\n$(1,1,3,4)$-colorable.\n', 'Packing colorings of subcubic outerplanar graphs   Given a graph $G$ and a nondecreasing sequence $S=(s_1,\\ldots,s_k)$ of\npositive integers, the mapping $c:V(G)\\longrightarrow \\{1,\\ldots,k\\}$ is called\nan $S$-packing coloring of $G$ if for any two distinct vertices $x$ and $y$ in\n$c^{-1}(i)$, the distance between $x$ and $y$ is greater than $s_i$. The\nsmallest integer $k$ such that there exists a $(1,2,\\ldots,k)$-packing coloring\nof a graph $G$ is called the packing chromatic number of $G$, denoted\n$\\chi_{\\rho}(G)$. The question of boundedness of the packing chromatic number\nin the class of subcubic (planar) graphs was investigated in several earlier\npapers; recently it was established that the invariant is unbounded in the\nclass of all subcubic graphs.\n  In this paper, we prove that the packing chromatic number of any 2-connected\nbipartite subcubic outerplanar graph is bounded by $7$. Furthermore, we prove\nthat every subcubic triangle-free outerplanar graph has a $(1,2,2,2)$-packing\ncoloring, and that there exists a subcubic outerplanar graph with a triangle\nthat does not admit a $(1,2,2,2)$-packing coloring. In addition, there exists a\nsubcubic triangle-free outerplanar graph that does not admit a\n$(1,2,2,3)$-packing coloring. A similar dichotomy is shown for bipartite\nouterplanar graphs: every such graph admits an $S$-packing coloring for\n$S=(1,3,\\ldots,3)$, where $3$ appears $\\Delta$ times ($\\Delta$ being the\nmaximum degree of vertices), and this property does not hold if one of the\nintegers $3$ is replaced by $4$ in the sequence $S$.\n']","[('graph packing', 0.6008839011192322), ('subcubic graphs', 0.522237241268158), ('coloring graph', 0.4959760904312134), ('chromatic number', 0.4879862368106842), ('chromatic numbers', 0.48781540989875793), ('subcubic graph', 0.47037389874458313), ('graph partition vertex', 0.4702174961566925), ('graph partition', 0.45443665981292725), ('chromatic number chi_', 0.43907755613327026), ('chromatic number denoted', 0.43220123648643494)]"
1078,1078,28,1078_generalized riemann hypothesis_zeta functions_riemann hypothesis_riemann hypothesis rh,"['generalized riemann hypothesis', 'zeta functions', 'riemann hypothesis', 'riemann hypothesis rh', 'zeros dirichlet functions', 'zeros riemann zeta', 'riemann zeta', 'dirichlet functions', 'dirichlet polynomials', 'derivatives riemann zeta']","['The method of Pintz for the Ingham question about the connection of\n  distribution of $\\zeta$-zeros and order of the error in the PNT in the\n  Beurling context   We prove two results, generalizing long existing knowledge regarding the\nclassical case of the Riemann zeta function and some of its generalizations.\nThese are concerned with the question of Ingham who asked for optimal and\nexplicit order estimates for the error term $\\Delta(x):=\\psi(x)-x$, given any\nzero-free region $D(\\eta):=\\{s=\\sigma+it\\in\\mathbb{C}~:~ \\sigma:=\\Re s \\ge\n1-\\eta(t)\\}$. In the classical case essentially sharp results are due to some\n40 years old work of Pintz. Here we consider a given a system of Beurling\nprimes $\\mathcal{P}$, the generated arithmetical semigroup $\\mathcal{G}$ and\nthe corresponding integer counting function $N(x)$, and the corresponding error\nterm $\\Delta_{\\mathcal{G}}(x):=\\psi_{\\mathcal{G}}(x)-x$ in the PNT of Beurling,\nwhere $\\psi_{\\mathcal{G}}(x)$ is the Beurling analog of $\\psi(x)$. First we\nprove that if the Beurling zeta function $\\zeta_{\\mathcal{G}}$ does not vanish\nin $D(\\eta)$, then the extension of Pintz\' result holds:\n$|\\Delta_{\\mathcal{G}}(x)| \\le\nx\\exp(-(1-\\varepsilon)\\omega_\\eta(x))~(x>x_0(\\varepsilon))$, where\n$\\omega_\\eta(y)$ is the naturally occurring conjugate function to $\\eta(t)$,\nintroduced into the field by Ingham. In the second part we prove a converse: if\n$\\zeta_{\\mathcal{G}}$ has an infinitude of zeroes in the given domain, then\nanalogously to the classical case, $|\\Delta_{\\mathcal{G}}(x)| \\ge\nx\\exp(-(1+\\varepsilon)\\omega_\\eta(x))$ holds ""infinitely often"". This also\nshows that both main results are sharp apart from the arbitrarily small\n$\\varepsilon>0$.\n', ""A Riemann-von Mangoldt-type formula for the distribution of Beurling\n  primes   In this paper we work out a Riemann-von Mangoldt type formula for the\nsummatory function $\\psi(x):=\\sum_{g\\in G, |g|\\le x} \\Lambda_{G}(g)$, where $G$\nis an arithmetical semigroup (a Beurling generalized system of integers) and\n$\\Lambda_{G}$ is the corresponding von Mangoldt function attaining $\\log|p|$\nfor $g=p^k$ with a prime element $p\\in G$ and zero otherwise. On the way\ntowards this formula, we prove explicit estimates on the Beurling zeta function\n$\\zeta_{G}$, belonging to $G$, to the number of zeroes of $\\zeta_G$ in various\nregions, in particular within the critical strip where the analytic\ncontinuation exists, and to the magnitude of the logarithmic derivative of\n$\\zeta_G$, under the sole additional assumption that Knopfmacher's Axiom A is\nsatisfied. We also construct a technically useful broken line contour to which\nthe technic of integral transformation can be well applied. The whole work\nserves as a first step towards a further study of the distribution of zeros of\nthe Beurling zeta function, providing appropriate zero density and zero\nclustering estimates, to be presented in the continuation of this paper.\n"", 'The Riemann Hypothesis via the generalized von Mangoldt Function   Gonek, Graham, and Lee have shown recently that the Riemann Hypothesis (RH)\ncan be reformulated in terms of certain asymptotic estimates for twisted sums\nwith von Mangoldt function $\\Lambda$. Building on their ideas, for each\n$k\\in\\mathbb{N}$, we study twisted sums with the \\emph{generalized von Mangoldt\nfunction} $$ \\Lambda_k(n):=\\sum_{d\\,\\mid\\,n}\\mu(d)\\Big(\\log\\frac{n}{d}\\,\\Big)^k\n$$ and establish similar connections with RH. For example, for $k=2$ we show\nthat RH is equivalent to the assertion that, for any fixed $\\epsilon>0$, the\nestimate $$ \\sum_{n\\leq x}\\Lambda_2(n)n^{-iy} =\\frac{2x^{1-iy}(\\log\nx-C_0)}{(1-iy)} -\\frac{2x^{1-iy}}{(1-iy)^2} +O\\big(x^{1/2}(x+|y|)^\\epsilon\\big)\n$$ holds uniformly for all $x,y\\in\\mathbb{R}$, $x\\geq 2$; hence, the validity\nof RH is governed by the distribution of almost-primes in the integers. We\nobtain similar results for the function $$\n\\Lambda^k:=\\mathop{\\underbrace{\\,\\Lambda\\star\\cdots\\star\\Lambda\\,}}\\limits_{k\\text{~copies}}\\,,\n$$ the $k$-fold convolution of the von Mangoldt function.\n']","[('generalized riemann hypothesis', 0.5773391127586365), ('zeta functions', 0.5048821568489075), ('riemann hypothesis', 0.4926718473434448), ('riemann hypothesis rh', 0.4923691749572754), ('zeros dirichlet functions', 0.4863889813423157), ('zeros riemann zeta', 0.4740925133228302), ('riemann zeta', 0.47387051582336426), ('dirichlet functions', 0.4664391279220581), ('dirichlet polynomials', 0.45450207591056824), ('derivatives riemann zeta', 0.43855488300323486)]"
1079,1079,28,1079_gauge theories_gauge field theory_gauge theory_theories manifolds,"['gauge theories', 'gauge field theory', 'gauge theory', 'theories manifolds', 'lagrangian field theories', 'gauge fields', 'presymplectic', 'yang mills theory', 'gauge field', 'local gauge']","['Background fields in the presymplectic BV-AKSZ approach The Batalin-Vilkovisky formulation of a general local gauge theory can be encoded in the structure of a so-called presymplectic gauge PDE -- an almost-$Q$ bundle over the spacetime exterior algebra, equipped with a compatible presymplectic structure. In the case of a trivial bundle and an invertible presymplectic structure, this reduces to the well-known AKSZ sigma model construction. We develop an extension of the presympletic BV-AKSZ approach to describe local gauge theories with background fields. It turns out that such theories correspond to presymplectic gauge PDEs whose base spaces are again gauge PDEs describing background fields. As such, the geometric structure is that of a bundle over a bundle over a given spacetime. Gauge PDEs over backgrounds arise naturally when studying linearisation, coupling (gauge) fields to background geometry, gauging global symmetries, etc. Less obvious examples involve parameterised systems, Fedosov equations, and the so-called homogeneous (presymplectic) gauge PDEs. The latter are the gauge-invariant generalisations of the familiar homogeneous PDEs and they provide a very concise description of gauge fields on homogeneous spaces such as higher spin gauge fields on Minkowski, (A)dS, and conformal spaces. Finally, we briefly discuss how the higher-form symmetries and their gauging fit into the framework using the simplest example of the Maxwell field.', 'Presymplectic minimal models of local gauge theories   We elaborate on the recently proposed notion of a weak presymplectic gauge\nPDE. It is a $\\mathbb{Z}$-graded bundle over the space-time manifold, equipped\nwith a degree $1$ vector field and a compatible graded presymplectic structure.\nThis geometrical data naturally defines a Lagrangian gauge field theory.\nMoreover, it encodes not only the Lagrangian of the theory but also its\nfull-scale Batalin-Vilkovisky (BV) formulation. In particular, the respective\nfield-antifield space arises as a symplectic quotient of the super-jet bundle\nof the initial fiber bundle. A remarkable property of this approach is that\namong the variety of presymplectic gauge PDEs encoding a given gauge theory we\ncan pick a minimal one that usually turns out to be finite-dimensional, and\nunique in a certain sense. The approach can be considered as an extension of\nthe familiar AKSZ construction to not necessarily topological and\ndiffeomorphism-invariant theories. We present a variety of examples including\n$p$-forms, chiral Yang-Mills theory, Holst gravity, and conformal gravity. We\nalso explain the explicit relation to the non-BV-BRST version of the formalism,\nwhich happens to be closely related to the covariant phase space and the\nmultisymplectic approaches.\n', 'Presymplectic gauge PDEs and Lagrangian BV formalism beyond jet-bundles   A gauge PDE is a geometrical object underlying what physicists call a local\ngauge field theory defined at the level of equations of motion (i.e. without\nspecifying Lagrangian) in terms of Batalin-Vilkovisky (BV) formalism. This\nnotion extends the BV formulation in terms of jet-bundles on the one hand and\nthe geometrical approach to PDEs on the other hand. In this work we concentrate\non gauge PDEs equipped with a compatible presymplectic structure and show that\nunder some regularity conditions this data defines a jet-bundle BV formulation.\nMore precisely, the BV jet-bundle arises as the symplectic quotient of the\nsuper jet-bundle of the initial gauge PDE. In this sense, presymplectic gauge\nPDEs give an invariant geometrical approach to Lagrangian gauge systems, which\nis not limited to jet-bundles. Furthermore, the presymplectic gauge PDE\nstructure naturally descends to space-time submanifolds (in particular,\nboundaries, if any) and, in this respect, is quite similar to AKSZ sigma models\nwhich are long known to have this feature. We also introduce a notion of a weak\npresymplectic gauge PDE, where the nilpotency of the differential is replaced\nby a presymplectic analog of the BV master equation, and show that it still\ndefines a local BV system. This allows one to encode BV systems in terms of\nfinite-dimensional graded geometry, much like the AKSZ construction does in the\ncase of topological models.\n']","[('gauge theories', 0.6324546337127686), ('gauge field theory', 0.5858487486839294), ('gauge theory', 0.5816661715507507), ('theories manifolds', 0.5647037029266357), ('lagrangian field theories', 0.5243100523948669), ('gauge fields', 0.5150623321533203), ('presymplectic', 0.4459238052368164), ('yang mills theory', 0.44547268748283386), ('gauge field', 0.44002610445022583), ('local gauge', 0.43869689106941223)]"
1080,1080,28,1080_hubbard models_hubbard_fermion number_lattice,"['hubbard models', 'hubbard', 'fermion number', 'lattice', 'bosons fermions', 'ferromagnetism', 'fermions', 'spontaneous magnetization', 'bosonic fermionic', 'fock theory']","['Ferromagnetism in $d$-dimensional SU($n$) Hubbard models with nearly\n  flat bands   We present rigorous results for the SU($n$) Fermi-Hubbard models with\nfinite-range hopping in $d$ ($\\ge 2$) dimensions. The models are defined on a\nclass of decorated lattices. We first study the models with flat bands at the\nbottom of the single-particle spectrum and prove that the ground states exhibit\nSU($n$) ferromagnetism when the number of particles is equal to the number of\nunit cells. We then perturb the models by adding particular hopping terms and\nmake the bottom bands dispersive. Under the same filling condition, it is\nproved that the ground states remain SU($n$) ferromagnetic when the bottom\nbands are sufficiently flat and the Coulomb repulsion is sufficiently large.\n', 'Ferromagnetism in the SU($n$) Hubbard model with a nearly flat band   We present rigorous results for the SU($n$) Fermi-Hubbard model on the\nrailroad-trestle lattice. We first study the model with a flat band at the\nbottom of the single-particle spectrum and prove that the ground states exhibit\nSU($n$) ferromagnetism when the total fermion number is the same as the number\nof unit cells. We then perturb the model by adding extra hopping terms and make\nthe flat band dispersive. Under the same filling condition, it is proved that\nthe ground states of the perturbed model remain SU($n$) ferromagnetic when the\nbottom band is nearly flat. This is the first rigorous example of the\nferromagnetism in nonsingular SU($n$) Hubbard models in which both the\nsingle-particle density of states and the on-site repulsive interaction are\nfinite.\n', 'Flat-band ferromagnetism in the SU($N$) Hubbard and Kondo lattice models   We develop a general theory of flat-band ferromagnetism in the SU($N$)\nFermi-Hubbard model, which describes the behavior of $N$-component fermions\nwith SU($N$) symmetric interactions. We focus on the case where the\nsingle-particle spectrum has a flat band and establish a necessary and\nsufficient condition for the SU($N$) Hubbard model to exhibit ferromagnetism\nwhen the number of particles is the same as the degeneracy. We show that the\noccurrence of ferromagnetism is equivalent to the irreducibility of the\nprojection matrix onto the space of single-particle ground states. We also\ndemonstrate that this result can be exploited to establish a rigorous result\nfor the ferromagnetic SU($N$) Kondo lattice model with a flat band.\nSpecifically, we prove that when the SU($N$) Hubbard model is ferromagnetic,\nthe ferromagnetic SU($N$) Kondo lattice model with the same hopping matrix also\nexhibits SU($N$) ferromagnetism.\n']","[('hubbard models', 0.6718767285346985), ('hubbard', 0.466357558965683), ('fermion number', 0.44492045044898987), ('lattice', 0.4399169683456421), ('bosons fermions', 0.43493935465812683), ('ferromagnetism', 0.4162197411060333), ('fermions', 0.41558998823165894), ('spontaneous magnetization', 0.4118914008140564), ('bosonic fermionic', 0.40990114212036133), ('fock theory', 0.3880780339241028)]"
1081,1081,28,1081_queens_queen_combinatorial types_chessboard,"['queens', 'queen', 'combinatorial types', 'chessboard', 'chess', 'number combinatorial', 'boards', 'general counting', 'combinatorial nullstellensatz', 'hardness finding']","['Solving the n-Queens Problem in Higher Dimensions   How many mutually non-attacking queens can be placed on a d-dimensional\nchessboard of size n? The n-queens problem in higher dimensions is a\ngeneralization of the well-known n-queens problem. We present an integer\nprogramming formulation of the n-queens problem in higher dimensions and\nseveral strengthenings through additional valid inequalities. Compared to\nrecent benchmarks, we achieve a speedup in computational time between 15-70x\nover all instances of the integer programs. Our computational results prove\noptimality of certificates for several large instances. Breaking additional,\npreviously unsolved instances with the proposed methods is likely possible. On\nthe primal side, we further discuss heuristic approaches to constructing\nsolutions that turn out to be optimal when compared to the IP.\n', 'A lower bound for the $n$-queens problem   The $n$-queens puzzle is to place $n$ mutually non-attacking queens on an $n\n\\times n$ chessboard. We present a simple two stage randomized algorithm to\nconstruct such configurations. In the first stage, a random greedy algorithm\nconstructs an approximate \\textit{toroidal} $n$-queens configuration. In this\nwell-known variant the diagonals wrap around the board from left to right and\nfrom top to bottom. We show that with high probability this algorithm succeeds\nin placing $(1-o(1))n$ queens on the board. In the second stage, the method of\nabsorbers is used to obtain a complete solution to the non-toroidal problem. By\ncounting the number of choices available at each step of the random greedy\nalgorithm we conclude that there are more than $\\left( \\left( 1 - o(1) \\right)\nn e^{-3} \\right)^n$ solutions to the $n$-queens problem. This proves a\nconjecture of Rivin, Vardi, and Zimmerman in a strong form.\n', 'The $n$-queens completion problem   An $n$-queens configuration is a placement of $n$ mutually non-attacking\nqueens on an $n\\times n$ chessboard. The $n$-queens completion problem,\nintroduced by Nauck in 1850, is to decide whether a given partial configuration\ncan be completed to an $n$-queens configuration. In this paper, we study an\nextremal aspect of this question, namely: how small must a partial\nconfiguration be so that a completion is always possible? We show that any\nplacement of at most $n/60$ mutually non-attacking queens can be completed. We\nalso provide partial configurations of roughly $n/4$ queens that cannot be\ncompleted, and formulate a number of interesting problems. Our proofs connect\nthe queens problem to rainbow matchings in bipartite graphs and use\nprobabilistic arguments together with linear programming duality.\n']","[('queens', 0.4643841087818146), ('queen', 0.4433445930480957), ('combinatorial types', 0.435955286026001), ('chessboard', 0.4141976237297058), ('chess', 0.40392354130744934), ('number combinatorial', 0.384837806224823), ('boards', 0.3765065371990204), ('general counting', 0.34570425748825073), ('combinatorial nullstellensatz', 0.34221357107162476), ('hardness finding', 0.33450061082839966)]"
1082,1082,27,1082_du bois singularities_bois singularities_hypersurface singularities_singular varieties,"['du bois singularities', 'bois singularities', 'hypersurface singularities', 'singular varieties', 'canonical singularities', 'isolated singularities', 'class singularities', 'log canonical singularities', 'surface singularities', 'rational singularities']","['Higher Du Bois singularities of hypersurfaces   For a complex algebraic variety $X$, we introduce higher $p$-Du Bois\nsingularity by imposing canonical isomorphisms between the sheaves of K\\""ahler\ndifferential forms $\\Omega_X^q$ and the shifted graded pieces of the Du Bois\ncomplex $\\underline{\\Omega}_X^q$ for $q\\le p$. If $X$ is a reduced\nhypersurface, we show that higher $p$-Du~Bois singularity coincides with higher\n$p$-log canonical singularity, generalizing a well-known theorem for $p=0$. The\nassertion that $p$-log canonicity implies $p$-Du Bois has been proved by\nMustata, Olano, Popa, and Witaszek quite recently as a corollary of two\ntheorems asserting that the sheaves of reflexive differential forms\n$\\Omega_X^{[q]}$ ($q\\le p$) coincide with $\\Omega_X^q$ and\n$\\underline{\\Omega}_X^q$ respectively, and these are shown by calculating the\ndepth of the latter two sheaves. We construct explicit isomorphisms between\n$\\Omega_X^q$ and $\\underline{\\Omega}_X^q$ applying the acyclicity of a Koszul\ncomplex in a certain range. We also improve some non-vanishing assertion shown\nby them using mixed Hodge modules and the Tjurina subspectrum in the isolated\nsingularity case. This is useful for instance to estimate the lower bound of\nthe maximal root of the reduced Bernstein-Sato polynomial in the case where a\nquotient singularity is a hypersurface and its singular locus has codimension\nat most 4.\n', ""The Holomorphic Extension Property for Higher Du Bois Singularities   Let $X$ be a normal complex variety and $\\pi:\\tilde X \\to X$ a resolution of\nsingularities. We show that the inclusion morphism $\\pi_*\\Omega_{\\tilde\nX}^p\\hookrightarrow \\Omega_X^{[p]}$ is an isomorphism for $p <\n\\mathrm{codim}_X(X_{\\mathrm{sing}})$ when $X$ has du Bois singularities, giving\nan improvement on Flenner's criterion for arbitrary singularities. We also\nstudy the $k$-du Bois definition from the perspective of holomorphic extension\nand compare how different restrictions on $\\mathscr H^0(\\underline \\Omega_X^p)$\naffect the singularities of $X$, where $\\underline\\Omega_X^p$ is the\n$p^{th}$-graded piece of the du Bois complex.\n"", ""Du Bois complex and extension of forms beyond rational singularities   We establish a characterization of the Du Bois complex of a reduced pair\n$(X,Z)$ when $X\\smallsetminus Z$ has rational singularities. As an application,\nwhen $X$ has normal Du Bois singularities and $Z$ is the locus of non-rational\nsingularities of $X$, holomorphic $p$-forms on the smooth locus of $X$ extend\nregularly to forms on a resolution of singularities for $p\\le\\mathrm{codim}_X\nZ-1$, and to forms with log poles over $Z$ for $p\\ge\\mathrm{codim}_X Z$. If $X$\nis not necessarily Du Bois, then $p$-forms extend regularly for\n$p\\le\\mathrm{codim}_X Z-2$. This is a generalization of the theorems of\nFlenner, Greb-Kebekus-Kov\\'acs-Peternell, and Kebekus-Schnell on extending\nholomorphic (log) forms.\n  A by-product of our methods is a new proof of the theorem of\nKoll\\'ar-Kov\\'acs that log canonical singularities are Du Bois. We also show\nthat the Proj of the log canonical ring of a log canonical pair is Du Bois if\nthis ring is finitely generated. The proofs are based on Saito's theory of\nmixed Hodge modules.\n""]","[('du bois singularities', 0.6371415257453918), ('bois singularities', 0.6171149015426636), ('hypersurface singularities', 0.5838177800178528), ('singular varieties', 0.5593077540397644), ('canonical singularities', 0.5438647866249084), ('isolated singularities', 0.5298095345497131), ('class singularities', 0.5258080959320068), ('log canonical singularities', 0.5243040323257446), ('surface singularities', 0.5201960802078247), ('rational singularities', 0.49309805035591125)]"
1083,1083,27,1083_boundary feedback stabilization_boundary stabilization_boundary feedback control_input state stability,"['boundary feedback stabilization', 'boundary stabilization', 'boundary feedback control', 'input state stability', 'linear hyperbolic systems', 'boundary feedback', 'lyapunov functions', 'hyperbolic systems balance', 'boundary control', 'stabilization systems']","[""A De Giorgi Iteration-based Approach for the Establishment of ISS\n  Properties of a Class of Semi-linear Parabolic PDEs with Boundary and\n  In-domain Disturbances   This paper addresses input-to-state stability (ISS) properties with respect\nto boundary and in-domain disturbances for a class of semi-linear partial\ndifferential equations (PDEs) subject to Dirichlet boundary conditions. The\ndeveloped approach is a combination of the method of De Giorgi iteration and\nthe technique of Lyapunov functionals by adequately splitting the original\nproblem into two subsystems. The ISS in $L^\\infty$-norm for a 1-$D$ transport\nequation and the ISS in $L^2$-norm for Burgers' equation have been established\nusing this method. As an application of the main result for the 1-D transport\nequation, a study on ISS properties in $L^\\infty$-norm of a 1-D transport\nequation with anti-stable term under boundary feedback control is carried out.\nThis is the first time that the method of De Giorgi iteration is introduced in\nthe ISS theory for infinite dimensional systems, and the developed method can\nbe generalized for tackling some problems on multidimensional spatial domains\nand be applied to a wider class of nonlinear parabolic PDEs.\n"", 'An analysis of the input-to-state-stabilisation of linear hyperbolic\n  systems of balance laws with boundary disturbances   In this paper, a linear hyperbolic system of balance laws with boundary\ndisturbances in one dimension is considered. An explicit candidate\nInput-to-State Stability (ISS)-Lyapunov function in $ L^2- $norm is considered\nand discretised to investigate conditions for ISS of the discrete system as\nwell. Finally, experimental results on test examples including the Saint-Venant\nequations with boundary disturbances are presented. The numerical results\ndemonstrate the expected theoretical decay of the Lyapunov function.\n', 'A boundary feedback analysis for input-to-state-stabilisation of\n  non-uniform linear hyperbolic systems of balance laws with additive\n  disturbances   A boundary feedback stabilisation problem of non-uniform linear hyperbolic\nsystems of balance laws with additive disturbance is discussed. A continuous\nand a corresponding discrete Lyapunov function is defined. Using an\ninput-to-state-stability (ISS) $ L^2- $Lyapunov function, the decay of\nsolutions of linear systems of balance laws is proved. In the discrete\nframework, a first-order finite volume scheme is employed. In such cases, the\ndecay rates can be explicitly derived. The main objective is to prove the\nLyapunov stability for the $L^2$-norm for linear hyperbolic systems of balance\nlaws with additive disturbance both analytically and numerically. Theoretical\nresults are demonstrated by using numerical computations.\n']","[('boundary feedback stabilization', 0.5877106189727783), ('boundary stabilization', 0.5583452582359314), ('boundary feedback control', 0.5393832325935364), ('input state stability', 0.5359476208686829), ('linear hyperbolic systems', 0.532017707824707), ('boundary feedback', 0.4995350241661072), ('lyapunov functions', 0.49753111600875854), ('hyperbolic systems balance', 0.48931819200515747), ('boundary control', 0.4889184236526489), ('stabilization systems', 0.48836183547973633)]"
1084,1084,27,1084_hypoelliptic operators_invariant operators_pseudo differential operators_differential operators,"['hypoelliptic operators', 'invariant operators', 'pseudo differential operators', 'differential operators', 'hypoellipticity', 'invariant operator', 'evolution operators', 'global analytic', 'operators defined', 'operators mathbb times']","['Global hypoellipticity for a class of overdetermined systems of\n  pseudo-differential operators on the torus   This article studies the global hypoellipticity of a class of overdetermined\nsystems of pseudo-differential operators defined on the torus. The main goal\nconsists in establishing connections between the global hypoellipticity of the\nsystem and the global hypoellipticity of its normal form. It is proved that an\nobstruction of number-theoretical nature appears as a necessary condition to\nthe global hypoellipticity. Conversely, the sufficiency is approached\nana\\-lyzing three types of hypotheses: a H\\""{o}rmander condition, logarithmic\ngrowth and super-logarithmic growth.\n', ""Global hypoellipticity and global solvability for vector fields on\n  compact Lie groups   We present necessary and sufficient conditions to have global hypoellipticity\nand global solvability for a class of vector fields defined on a product of\ncompact Lie groups. In view of Greenfield's and Wallach's conjecture, about the\nnon-existence of globally hypoelliptic vector fields on compact manifolds\ndifferent from tori, we also investigate different notions of regularity weaker\nthan global hypoellipticity and describe completely the global hypoellipticity\nand global solvability of zero-order perturbations of our vector fields. We\nalso present a class of vector fields with variable coefficients whose\noperators can be reduced to a normal form, and we prove that the study of the\nglobal properties of such operators is equivalent to the study of the\nrespective properties for their normal forms.\n"", '(Semi-)Global Analytic Hypoellipticity for a class of ""sums of squares""\n  which fail to be locally analytic hypoelliptic   The global and semi-global analytic hypoellipticity on the torus is proved\nfor two classes of sums of squares operators, introduced in ""Analytic\nHypoellipticity for Sums of Squares and the Treves Conjecture"" by P. Albano and\nA. Bove and M. Mughetti, and in ""Analytic Hypoellipticity for Sums of Squares\nand the Treves Conjecture. II"" by A. Bove and M. Mughetti, satisfying the\nH\\""ormander condition and which fail to be neither locally nor microlocally\nanalytic hypoelliptic.\n']","[('hypoelliptic operators', 0.6941855549812317), ('invariant operators', 0.49738436937332153), ('pseudo differential operators', 0.49277451634407043), ('differential operators', 0.4903195798397064), ('hypoellipticity', 0.4687420427799225), ('invariant operator', 0.4625641703605652), ('evolution operators', 0.45898494124412537), ('global analytic', 0.4306614398956299), ('operators defined', 0.4276668131351471), ('operators mathbb times', 0.41874584555625916)]"
1085,1085,27,1085_efficiency models_measure efficiency_envelopment_efficiency,"['efficiency models', 'measure efficiency', 'envelopment', 'efficiency', 'efficiencies', 'super efficiency', 'measure performance', 'intuitionistic fuzzy', 'performance evaluation', 'inefficiency']","[""Data envelopment analysis models or the virtual gap analysis model:\n  Which should be used for identifying the best benchmark for each unit in a\n  group?   Decision-making units (DMUs) in a group convert the same resources (i.e.,\ninput indices) into the same products (i.e., output indices) at different\nscales. Performance indices have different measurement units, and their market\nprices per unit are unobtainable. Data envelopment analysis (DEA) programs\nemploy linear programming to estimate the virtual weight and best slack of\nevery input and output index for each DMU, named DMU-o, to obtain the minimum\nrelative inefficiency against the DMUs. DMU-o reduces each input's slack, the\nsurplus, and expands each output's slack, the shortage, to the benchmark. Each\nDEA program specifies an artificial goal weight for each performance index. The\nrelative inefficiencies in the primal and dual models are the sum of the\nweighted slacks and the virtual gap of the total virtual weighted inputs to the\noutputs, respectively. DEA programs have failed the uncountable attempts to\nconceive the artificial goal weight equal to the estimated virtual weight for\neach performance index; therefore, they have incomplete solutions that some of\nthe slacks could not be aggregated into the efficiency score. Our new virtual\ngap analysis program assesses DMU-o comprehensively. The four-phase procedure\nensures DMU-o has the achievable best benchmarks for implementation and its\ncompatible best peers to learn. Each DMU is a point in the 2D geometric\nintuition of the virtual technology set in assessing DMU-o. The best peers and\nthe improved DMU-o are on the best efficiency boundary. Inefficient DMUs are\nsituated underneath the boundary.\n"", 'Enhancing Top Efficiency by Minimizing Second-Best Scores: A Novel\n  Perspective on Super Efficiency Models in DEA   In this paper, we reveal a new characterization of the super-efficiency model\nfor Data Envelopment Analysis (DEA). In DEA, the efficiency of each decision\nmaking unit (DMU) is measured by the ratio the weighted sum of outputs divided\nby the weighted sum of inputs. In order to measure efficiency of a DMU, ${\\rm\nDMU}_j$, say, in CCR model, the weights of inputs and outputs are determined so\nthat the effiency of ${\\rm DMU}_j$ is maximized under the constraint that the\nefficiency of each DMU is less than or equal to one. ${\\rm DMU}_j$ is called\nCCR-efficient if its efficiency score is equal to one. It often happens that\nweights making ${\\rm DMU}_j$ CCR-efficient are not unique but form continuous\nset. This can be problematic because the weights representing CCR-efficiencty\nof ${\\rm DMU}_j$ play an important role in making decisions on its management\nstrategy. In order to resolve this problem, we propose to choose weights which\nminimize the efficency of the second best DMU enhancing the strength of ${\\rm\nDMU}_j$, and demonstrate that this problem is reduced to a linear programming\nproblem identical to the renowned super-efficiency model. We conduct numerical\nexperiments using data of Japanese commercial banks to demonstrate the\nadvantage of the supper-efficiency model.\n', 'Continuous models combining slacks-based measures of efficiency and\n  super-efficiency   In the framework of data envelopment analysis (DEA), Tone (2001) introduced\nthe slacks-based measure (SBM) of efficiency, which is a nonradial model that\nincorporates all the slacks of the evaluated decision-making units (DMUs) into\ntheir efficiency scores, unlike classical radial efficiency models. Next, Tone\n(2002) developed the SBM super-efficiency model in order to differentiate and\nrank efficient DMUs, whose SBM efficiency scores are always $1$. However, as\npointed out by Chen (2013), some interpretation problems arise when the\nso-called super-efficiency projections are weakly efficient, leading to an\noverestimation of the SBM super-efficiency score. Moreover, this overestimation\nis closely related to discontinuity issues when implementing SBM\nsuper-efficiency in conjunction with SBM efficiency. Chen (2013) and Chen et\nal. (2019) treated these problems, but they did not arrive to a fully\nsatisfactory solution. In this paper, we review these papers and propose a new\ncomplementary score, called composite SBM, that actually fixes the\ndiscontinuity problems by counteracting the overestimation of the SBM\nsuper-efficiency score. Moreover, we extend the composite SBM model to\ndifferent orientations and variable returns to scale, and propose additive\nversions. Finally, we give examples and state some open problems.\n']","[('efficiency models', 0.6480388641357422), ('measure efficiency', 0.6013374924659729), ('envelopment', 0.5491856336593628), ('efficiency', 0.5487837791442871), ('efficiencies', 0.5216966271400452), ('super efficiency', 0.4731133282184601), ('measure performance', 0.40937671065330505), ('intuitionistic fuzzy', 0.408346027135849), ('performance evaluation', 0.3951581120491028), ('inefficiency', 0.37781763076782227)]"
1086,1086,27,1086_learning multi agent_agent reinforcement learning_reinforcement learning multi_multi agent reinforcement,"['learning multi agent', 'agent reinforcement learning', 'reinforcement learning multi', 'multi agent reinforcement', 'reinforcement learning marl', 'globally optimal policy', 'agent reinforcement', 'reinforcement learning', 'cooperative multi agent', 'optimal policy']","[""Global Convergence of Localized Policy Iteration in Networked\n  Multi-Agent Reinforcement Learning   We study a multi-agent reinforcement learning (MARL) problem where the agents\ninteract over a given network. The goal of the agents is to cooperatively\nmaximize the average of their entropy-regularized long-term rewards. To\novercome the curse of dimensionality and to reduce communication, we propose a\nLocalized Policy Iteration (LPI) algorithm that provably learns a\nnear-globally-optimal policy using only local information. In particular, we\nshow that, despite restricting each agent's attention to only its $\\kappa$-hop\nneighborhood, the agents are able to learn a policy with an optimality gap that\ndecays polynomially in $\\kappa$. In addition, we show the finite-sample\nconvergence of LPI to the global optimal policy, which explicitly captures the\ntrade-off between optimality and computational complexity in choosing $\\kappa$.\nNumerical simulations demonstrate the effectiveness of LPI.\n"", ""Multi-agent Natural Actor-critic Reinforcement Learning Algorithms   Multi-agent actor-critic algorithms are an important part of the\nReinforcement Learning paradigm. We propose three fully decentralized\nmulti-agent natural actor-critic (MAN) algorithms in this work. The objective\nis to collectively find a joint policy that maximizes the average long-term\nreturn of these agents. In the absence of a central controller and to preserve\nprivacy, agents communicate some information to their neighbors via a\ntime-varying communication network. We prove convergence of all the 3 MAN\nalgorithms to a globally asymptotically stable set of the ODE corresponding to\nactor update; these use linear function approximations. We show that the\nKullback-Leibler divergence between policies of successive iterates is\nproportional to the objective function's gradient. We observe that the minimum\nsingular value of the Fisher information matrix is well within the reciprocal\nof the policy parameter dimension. Using this, we theoretically show that the\noptimal value of the deterministic variant of the MAN algorithm at each iterate\ndominates that of the standard gradient-based multi-agent actor-critic (MAAC)\nalgorithm. To our knowledge, it is a first such result in multi-agent\nreinforcement learning (MARL). To illustrate the usefulness of our proposed\nalgorithms, we implement them on a bi-lane traffic network to reduce the\naverage network congestion. We observe an almost 25\\% reduction in the average\ncongestion in 2 MAN algorithms; the average congestion in another MAN algorithm\nis on par with the MAAC algorithm. We also consider a generic $15$ agent MARL;\nthe performance of the MAN algorithms is again as good as the MAAC algorithm.\n"", 'Scalable Multi-Agent Reinforcement Learning for Networked Systems with\n  Average Reward   It has long been recognized that multi-agent reinforcement learning (MARL)\nfaces significant scalability issues due to the fact that the size of the state\nand action spaces are exponentially large in the number of agents. In this\npaper, we identify a rich class of networked MARL problems where the model\nexhibits a local dependence structure that allows it to be solved in a scalable\nmanner. Specifically, we propose a Scalable Actor-Critic (SAC) method that can\nlearn a near optimal localized policy for optimizing the average reward with\ncomplexity scaling with the state-action space size of local neighborhoods, as\nopposed to the entire network. Our result centers around identifying and\nexploiting an exponential decay property that ensures the effect of agents on\neach other decays exponentially fast in their graph distance.\n']","[('learning multi agent', 0.6000070571899414), ('agent reinforcement learning', 0.5988112688064575), ('reinforcement learning multi', 0.5915617942810059), ('multi agent reinforcement', 0.589180588722229), ('reinforcement learning marl', 0.5316115021705627), ('globally optimal policy', 0.5165696740150452), ('agent reinforcement', 0.513847827911377), ('reinforcement learning', 0.5040913224220276), ('cooperative multi agent', 0.5001658201217651), ('optimal policy', 0.48023518919944763)]"
1087,1087,27,1087_wasserstein distributionally robust_distributionally robust optimization_robust optimal control_driven distributionally robust,"['wasserstein distributionally robust', 'distributionally robust optimization', 'robust optimal control', 'driven distributionally robust', 'distributional robustness', 'robust control', 'optimal control policy', 'distributionally robust', 'wasserstein distributionally', 'novel distributionally robust']","['Wasserstein Distributionally Robust Control of Partially Observable\n  Linear Stochastic Systems   Distributionally robust control (DRC) aims to effectively manage\ndistributional ambiguity in stochastic systems. While most existing works\naddress inaccurate distributional information in fully observable settings, we\nconsider a partially observable DRC problem for discrete-time linear systems\nusing the Wasserstein metric. For a tractable solution, we propose a novel\napproximation method exploiting the Gelbrich bound of Wasserstein distance.\nUsing techniques from modern distributionally robust optimization, we derive a\nclosed-form expression for the optimal control policy and a tractable\nsemidefinite programming problem for the worst-case distribution policy in both\nfinite-horizon and infinite-horizon average-cost settings. The proposed method\nfeatures several salient theoretical properties, such as a guaranteed cost\nproperty and a probabilistic out-of-sample performance guarantee, demonstrating\nthe distributional robustness of our controller. Furthermore, the resulting\ncontroller is shown to ensure the closed-loop stability of the mean-state\nsystem. The empirical performance of our method is tested through numerical\nexperiments on a power system frequency control problem.\n', 'Infinite-Horizon Distributionally Robust Regret-Optimal Control   We study the infinite-horizon distributionally robust (DR) control of linear\nsystems with quadratic costs, where disturbances have unknown, possibly\ntime-correlated distribution within a Wasserstein-2 ambiguity set. We aim to\nminimize the worst-case expected regret-the excess cost of a causal policy\ncompared to a non-causal one with access to future disturbance. Though the\noptimal policy lacks a finite-order state-space realization (i.e., it is\nnon-rational), it can be characterized by a finite-dimensional parameter.\nLeveraging this, we develop an efficient frequency-domain algorithm to compute\nthis optimal control policy and present a convex optimization method to\nconstruct a near-optimal state-space controller that approximates the optimal\nnon-rational controller in the $\\mathit{H}_\\infty$-norm. This approach avoids\nsolving a computationally expensive semi-definite program (SDP) that scales\nwith the time horizon in the finite-horizon setting.\n', 'Wasserstein Distributionally Robust Regret-Optimal Control in the\n  Infinite-Horizon   We investigate the Distributionally Robust Regret-Optimal (DR-RO) control of\ndiscrete-time linear dynamical systems with quadratic cost over an infinite\nhorizon. Regret is the difference in cost obtained by a causal controller and a\nclairvoyant controller with access to future disturbances. We focus on the\ninfinite-horizon framework, which results in stability guarantees. In this DR\nsetting, the probability distribution of the disturbances resides within a\nWasserstein-2 ambiguity set centered at a specified nominal distribution. Our\nobjective is to identify a control policy that minimizes the worst-case\nexpected regret over an infinite horizon, considering all potential disturbance\ndistributions within the ambiguity set. In contrast to prior works, which\nassume time-independent disturbances, we relax this constraint to allow for\ntime-correlated disturbances, thus actual distributional robustness. While we\nshow that the resulting optimal controller is non-rational and lacks a\nfinite-dimensional state-space realization, we demonstrate that it can still be\nuniquely characterized by a finite dimensional parameter. Exploiting this fact,\nwe introduce an efficient numerical method to compute the controller in the\nfrequency domain using fixed-point iterations. This method circumvents the\ncomputational bottleneck associated with the finite-horizon problem, where the\nsemi-definite programming (SDP) solution dimension scales with the time\nhorizon. Numerical experiments demonstrate the effectiveness and performance of\nour framework.\n']","[('wasserstein distributionally robust', 0.6099913716316223), ('distributionally robust optimization', 0.6022929549217224), ('robust optimal control', 0.6018915176391602), ('driven distributionally robust', 0.5618734359741211), ('distributional robustness', 0.5019400119781494), ('robust control', 0.49038320779800415), ('optimal control policy', 0.488059937953949), ('distributionally robust', 0.4873521327972412), ('wasserstein distributionally', 0.48412272334098816), ('novel distributionally robust', 0.4827113449573517)]"
1088,1088,27,1088_mappings bounded_mappings satisfy_mappings continuous_mappings satisfying,"['mappings bounded', 'mappings satisfy', 'mappings continuous', 'mappings satisfying', 'mappings mappings', 'boundaries domains', 'boundary extension', 'mappings', 'extension boundary', 'mappings inverse']","['On boundary H\\""{o}lder logarithmic continuity of mappings in some\n  domains   We study mappings satisfying some estimate of distortion of modulus of\nfamilies of paths. Under some conditions on definition and mapped domains, we\nhave proved that these mappings are logarithmic H\\""{o}lder continuous at\nboundary points.\n', ""On the prime ends extension of unclosed inverse mappings   We consider mappings that distort the modulus of families of paths in the\nopposite direction in the manner of Poletsky's inequality. Here we study the\ncase when the mappings are not closed, in particular, they do not preserve the\nboundary of the domain under the mapping. Under certain conditions, we obtain\nresults on the continuous boundary extension of such mappings in the sense of\nprime ends. In addition, we obtain corresponding results on the equicontinuity\nof families of such mappings in terms of prime ends.\n"", 'Equicontinuity by the prime ends of mappings with the normalization\n  condition   We study branching mappings that satisfy some condition of distortion of the\nmodulus of families of paths. In a situation where the definition domain of\nmappings is locally connected on its boundary, the mapped domain is regular,\nand the majorant responsible for distortion of the modulus of families of paths\nis integrable, it is proved that the families of all specified mappings with\none normalization condition are equicontinuous in the closure of the given\ndomain.\n']","[('mappings bounded', 0.6015714406967163), ('mappings satisfy', 0.5292287468910217), ('mappings continuous', 0.5252553820610046), ('mappings satisfying', 0.5081366896629333), ('mappings mappings', 0.4910949170589447), ('boundaries domains', 0.4755599796772003), ('boundary extension', 0.46768081188201904), ('mappings', 0.4503568112850189), ('extension boundary', 0.44059720635414124), ('mappings inverse', 0.43488138914108276)]"
1089,1089,27,1089_deligne lusztig varieties_affine deligne lusztig_lusztig varieties_deligne lusztig,"['deligne lusztig varieties', 'affine deligne lusztig', 'lusztig varieties', 'deligne lusztig', 'lusztig', 'varieties affine', 'affine deligne', 'affine weyl group', 'dimension affine', 'varieties associated']","['Affine Deligne-Lusztig Varieties and Quantum Bruhat Graph   In this paper, we consider affine Deligne-Lusztig varieties $X_w(b)$ and\ntheir certain union $X(\\mu,b)$ inside the affine flag variety of a reductive\ngroup. Several important results in the study of affine Deligne-Lusztig\nvarieties have been established under the so-called superregularity hypothesis.\nSuch results include a description of generic Newton points in Iwahori double\ncosets of loop groups, covering relation in associated Iwahori-Weyl group and\ndimension formula for $X(\\mu,b)$. We show that one can considerably weaken the\nsuperregularity hypothesis and sometimes completely eliminate it, thus\nstrengthening these existing results.\n', 'Geometric Structure of Affine Deligne-Lusztig Varieties for $GL_3$   In this paper we study the geometric structure of affine Deligne-Lusztig\nvarieties for $GL_3$ and $b$ basic. We completely determine the irreducible\ncomponents of the affine Deligne-Lusztig variety. In particular, we classify\nthe cases where all of the irreducible components are classical Deligne-Lusztig\nvarieties times finite-dimensional affine spaces. If this is the case, then the\nirreducible components are pairwise disjoint.\n', 'On some simple geometric structure of affine Deligne-Lusztig varieties\n  for $GL_n$   In this paper we study the geometric structure of affine Deligne-Lusztig\nvarieties for $GL_n$ and $b$ basic. We introduce a new condition on $\\lambda$.\nIf this is satisfied, then the corresponding affine Deligne-Lusztig variety is\nthe disjoint union of classical Deligne-Lusztig varieties times\nfinite-dimensional affine spaces.\n']","[('deligne lusztig varieties', 0.8400465846061707), ('affine deligne lusztig', 0.7877297401428223), ('lusztig varieties', 0.7778270840644836), ('deligne lusztig', 0.700019359588623), ('lusztig', 0.616625189781189), ('varieties affine', 0.5884915590286255), ('affine deligne', 0.5306898951530457), ('affine weyl group', 0.5271930694580078), ('dimension affine', 0.5259003043174744), ('varieties associated', 0.5209840536117554)]"
1090,1090,27,1090_gravitational instantons_instantons_instanton_black hole uniqueness,"['gravitational instantons', 'instantons', 'instanton', 'black hole uniqueness', 'einstein manifolds', 'ricci flat metrics', 'dimensional ricci', 'ahler metrics', 'curvature decay', 'quadratic curvature']","[""Gravitational instantons with faster than quadratic curvature decay\n  (III)   This is our third paper in a series on the gravitational instantons. In this\npaper, we classify ALG and ALH gravitational instantons. In ALG case, we extend\nHein's construction slightly and show that it's the only ALG gravitational\ninstanton. In ALH case, we prove a Torelli-type theorem.\n"", 'Gravitational instantons with quadratic volume growth   There are two known classes of gravitational instantons with quadratic volume\ngrowth at infinity, known as type ALG and ALG$^*$. Gravitational instantons of\ntype ALG were previously classified by Chen-Chen. In this paper, we prove a\nclassification theorem for ALG$^*$ gravitational instantons. We determine the\ntopology and prove existence of ""uniform"" coordinates at infinity for both ALG\nand ALG$^*$ gravitational instantons. We also prove a result regarding the\nrelationship between ALG gravitational instantons of order $\\mathfrak{n}$ and\nthose of order $2$.\n', 'Torelli-type theorems for gravitational instantons with quadratic volume\n  growth   We prove Torelli-type uniqueness theorems for both ALG$^*$ gravitational\ninstantons and ALG gravitational instantons which are of order $2$. That is,\nthe periods uniquely characterize these types of gravitational instantons up to\ndiffeomorphism. We define a period mapping $\\mathscr{P}$, which we show is\nsurjective in the ALG cases, and open in the ALG$^*$ cases. We also construct\nsome new degenerations of hyperk\\""ahler metrics on the K3 surface which exhibit\nbubbling of ALG$^*$ gravitational instantons.\n']","[('gravitational instantons', 0.7305028438568115), ('instantons', 0.5376607775688171), ('instanton', 0.49012941122055054), ('black hole uniqueness', 0.46942436695098877), ('einstein manifolds', 0.4064123034477234), ('ricci flat metrics', 0.39617207646369934), ('dimensional ricci', 0.38758131861686707), ('ahler metrics', 0.3650491237640381), ('curvature decay', 0.36192405223846436), ('quadratic curvature', 0.35447922348976135)]"
1091,1091,27,1091_relativistic euler equations_relativistic euler_solutions relativistic_classical relativistic,"['relativistic euler equations', 'relativistic euler', 'solutions relativistic', 'classical relativistic', 'equations relativistic', 'non relativistic', 'relativistic', 'hydrodynamics', 'non relativistic limit', 'relativistic limit']","['A Lorentz invariant formulation of artificial viscosity for the\n  relativistic Euler equations   The vanishing (artificial) viscosity method has played a fundamental role in\nthe theory of classical shock waves, both by providing a mollified limit that\nidentifies the correct physical (Lax admissible) shock waves, and as a guiding\nprinciple in the design of numerical difference schemes for simulating shock\nwaves. However, for relativistic fluid flow, the underlying dissipation\nmechanism based on the Euclidean Laplace operator violates Lorentz invariance\n(and hence the speed of light bound) -- the fundamental principle of Special\nRelativity. In this paper we introduce a simple dissipation mechanism for the\nrelativistic Euler equations which is Lorentz invariant and consistent with the\nlaws of Special Relativity. To establish basic consistency of the model for the\nstudy of shock waves, we prove existence and decay of Fourier Laplace mode\nsolutions (implying dissipation), and we prove that 1-D shock profiles (viscous\ntravelling wave approximations) exist if and only if the approximated shock\nwaves are Lax admissible. Our analysis of shock profiles reveals an interesting\nsimplification over classical artificial viscosity, leading to a one\ndimensional fixed point problem, due to the speed of light bound of Relativity.\n', ""Recent developments in mathematical aspects of relativistic fluids   We review some recent developments in mathematical aspects of relativistic\nfluids. The goal is to provide a quick entry point to some research topics of\ncurrent interest that is accessible to graduate students and researchers from\nadjacent fields, as well as to researches working on broader aspects of\nrelativistic fluid dynamics interested in its mathematical formalism. Instead\nof complete proofs, which can be found in the published literature, here we\nfocus on the proofs' main ideas and key concepts. After an introduction to the\nrelativistic Euler equations, we cover the following topics: a new\nwave-transport formulation of the relativistic Euler equations tailored to\napplications; the problem of shock formation for relativistic Euler; rough\n(i.e., low-regularity) solutions to the relativistic Euler equations; the\nrelativistic Euler equations with a physical vacuum boundary; relativistic\nfluids with viscosity. We finish with a discussion of open problems and future\ndirections of research.\n"", 'The relativistic Euler equations: ESI notes on their geo-analytic\n  structures and implications for shocks in $1D$ and multi-dimensions   In this article, we provide notes that complement the lectures on the\nrelativistic Euler equations and shocks that were given by the second author at\nthe program Mathematical Perspectives of Gravitation Beyond the Vacuum Regime,\nwhich was hosted by the Erwin Schrodinger International Institute for\nMathematics and Physics in Vienna in February, 2022. We set the stage by\nintroducing a standard first-order formulation of the relativistic Euler\nequations and providing a brief overview of local well-posedness in Sobolev\nspaces. Then, using Riemann invariants, we provide the first detailed\nconstruction of a localized subset of the maximal globally hyperbolic\ndevelopments of an open set of initially smooth, shock-forming isentropic\nsolutions in 1D, with a focus on describing the singular boundary and the\nCauchy horizon that emerges from the singularity. Next, we provide an overview\nof the new second-order formulation of the 3D relativistic Euler equations\nderived in [41], its rich geometric and analytic structures, their implications\nfor the mathematical theory of shock waves, and their connection to the setup\nwe use in our 1D analysis of shocks. We then highlight some key prior results\non the study of shock formation and related problems. Furthermore, we provide\nan overview of how the formulation of the flow derived in [41] can be used to\nstudy shock formation in multiple spatial dimensions. Finally, we discuss\nvarious open problems tied to shocks.\n']","[('relativistic euler equations', 0.678602397441864), ('relativistic euler', 0.5821294784545898), ('solutions relativistic', 0.5686190128326416), ('classical relativistic', 0.5592877268791199), ('equations relativistic', 0.5559930801391602), ('non relativistic', 0.49061572551727295), ('relativistic', 0.47996845841407776), ('hydrodynamics', 0.4569753408432007), ('non relativistic limit', 0.4467912018299103), ('relativistic limit', 0.4397749602794647)]"
1092,1092,27,1092_transfer learning_learning transfer_transfer learning can_knowledge transfer,"['transfer learning', 'learning transfer', 'transfer learning can', 'knowledge transfer', 'learning estimating', 'source target distributions', 'learning high dimensional', 'high dimensional regression', 'target distributions', 'transfer']","[""TransFusion: Covariate-Shift Robust Transfer Learning for\n  High-Dimensional Regression   The main challenge that sets transfer learning apart from traditional\nsupervised learning is the distribution shift, reflected as the shift between\nthe source and target models and that between the marginal covariate\ndistributions. In this work, we tackle model shifts in the presence of\ncovariate shifts in the high-dimensional regression setting. Specifically, we\npropose a two-step method with a novel fused-regularizer that effectively\nleverages samples from source tasks to improve the learning performance on a\ntarget task with limited samples. Nonasymptotic bound is provided for the\nestimation error of the target model, showing the robustness of the proposed\nmethod to covariate shifts. We further establish conditions under which the\nestimator is minimax-optimal. Additionally, we extend the method to a\ndistributed setting, allowing for a pretraining-finetuning strategy, requiring\njust one round of communication while retaining the estimation rate of the\ncentralized version. Numerical tests validate our theory, highlighting the\nmethod's robustness to covariate shifts.\n"", 'Estimation and inference for transfer learning with high-dimensional\n  quantile regression   Transfer learning has become an essential technique to exploit information\nfrom the source domain to boost performance of the target task. Despite the\nprevalence in high-dimensional data, heterogeneity and heavy tails are\ninsufficiently accounted for by current transfer learning approaches and thus\nmay undermine the resulting performance. We propose a transfer learning\nprocedure in the framework of high-dimensional quantile regression models to\naccommodate heterogeneity and heavy tails in the source and target domains. We\nestablish error bounds of transfer learning estimator based on delicately\nselected transferable source domains, showing that lower error bounds can be\nachieved for critical selection criterion and larger sample size of source\ntasks. We further propose valid confidence interval and hypothesis test\nprocedures for individual component of high-dimensional quantile regression\ncoefficients by advocating a double transfer learning estimator, which is\none-step debiased estimator for the transfer learning estimator wherein the\ntechnique of transfer learning is designed again. By adopting data-splitting\ntechnique, we advocate a transferability detection approach that guarantees to\ncircumvent negative transfer and identify transferable sources with high\nprobability. Simulation results demonstrate that the proposed method exhibits\nsome favorable and compelling performances and the practical utility is further\nillustrated by analyzing a real example.\n', 'Conformal Prediction Under Generalized Covariate Shift with Posterior\n  Drift   In many real applications of statistical learning, collecting sufficiently\nmany training data is often expensive, time-consuming, or even unrealistic. In\nthis case, a transfer learning approach, which aims to leverage knowledge from\na related source domain to improve the learning performance in the target\ndomain, is more beneficial. There have been many transfer learning methods\ndeveloped under various distributional assumptions. In this article, we study a\nparticular type of classification problem, called conformal prediction, under a\nnew distributional assumption for transfer learning. Classifiers under the\nconformal prediction framework predict a set of plausible labels instead of one\nsingle label for each data instance, affording a more cautious and safer\ndecision. We consider a generalization of the \\textit{covariate shift with\nposterior drift} setting for transfer learning. Under this setting, we propose\na weighted conformal classifier that leverages both the source and target\nsamples, with a coverage guarantee in the target domain. Theoretical studies\ndemonstrate favorable asymptotic properties. Numerical studies further\nillustrate the usefulness of the proposed method.\n']","[('transfer learning', 0.6667847633361816), ('learning transfer', 0.6350863575935364), ('transfer learning can', 0.5932322144508362), ('knowledge transfer', 0.47463494539260864), ('learning estimating', 0.45166173577308655), ('source target distributions', 0.4292803108692169), ('learning high dimensional', 0.42302894592285156), ('high dimensional regression', 0.3844226896762848), ('target distributions', 0.38324370980262756), ('transfer', 0.3691776394844055)]"
1093,1093,27,1093_allocations_allocation_envy_fair division,"['allocations', 'allocation', 'envy', 'fair division', 'allocated among', 'freeness', 'indivisible', 'among agents', 'goods', 'fairness']","['Lower bounds on the number of envy-free divisions   We analyze lower bounds for the number of envy-free divisions, in the\nclassical Woodall-Stormquist setting and in a non-classical case, when\nenvy-freeness is combined with the equipartition of a measure.\n  1. In the first scenario, there are $r$ hungry players, and the cake (that\nis, the segment $[0,1]$) is cut into $r$ pieces. Then there exist at least two\ndifferent envy-free divisions. This bound is sharp: for each $r$, we present an\nexample of preferences such that there are exactly two envy-free divisions.\n  2. In the second (hybrid) scenario, there are $p$ not necessarily hungry\nplayers ($p$ is a prime) and a continuous measure $\\mu$ on $[0,1]$. The cake is\ncut into $2p-1$ pieces, the pieces are allocated to $p$ boxes (with some\nrestrictions) and the players choose the boxes. Then there exists at least\n$\\binom{2p-1}{p-1} \\cdot 2^{2-p}$ envy-free divisions such that the measure\n$\\mu$ is equidistributed among the players.\n', 'When Do Envy-Free Allocations Exist?   We consider a fair division setting in which $m$ indivisible items are to be\nallocated among $n$ agents, where the agents have additive utilities and the\nagents\' utilities for individual items are independently sampled from a\ndistribution. Previous work has shown that an envy-free allocation is likely to\nexist when $m=\\Omega(n\\log n)$ but not when $m=n+o(n)$, and left open the\nquestion of determining where the phase transition from non-existence to\nexistence occurs. We show that, surprisingly, there is in fact no universal\npoint of transition---instead, the transition is governed by the divisibility\nrelation between $m$ and $n$. On the one hand, if $m$ is divisible by $n$, an\nenvy-free allocation exists with high probability as long as $m\\geq 2n$. On the\nother hand, if $m$ is not ""almost"" divisible by $n$, an envy-free allocation is\nunlikely to exist even when $m=\\Theta(n\\log n/\\log\\log n)$.\n', ""Closing Gaps in Asymptotic Fair Division   We study a resource allocation setting where $m$ discrete items are to be\ndivided among $n$ agents with additive utilities, and the agents' utilities for\nindividual items are drawn at random from a probability distribution. Since\ncommon fairness notions like envy-freeness and proportionality cannot always be\nsatisfied in this setting, an important question is when allocations satisfying\nthese notions exist. In this paper, we close several gaps in the line of work\non asymptotic fair division. First, we prove that the classical round-robin\nalgorithm is likely to produce an envy-free allocation provided that\n$m=\\Omega(n\\log n/\\log\\log n)$, matching the lower bound from prior work. We\nthen show that a proportional allocation exists with high probability as long\nas $m\\geq n$, while an allocation satisfying envy-freeness up to any item (EFX)\nis likely to be present for any relation between $m$ and $n$. Finally, we\nconsider a related setting where each agent is assigned exactly one item and\nthe remaining items are left unassigned, and show that the transition from\nnon-existence to existence with respect to envy-free assignments occurs at\n$m=en$.\n""]","[('allocations', 0.553102970123291), ('allocation', 0.5188454985618591), ('envy', 0.44057798385620117), ('fair division', 0.4098873436450958), ('allocated among', 0.38688844442367554), ('freeness', 0.3503679037094116), ('indivisible', 0.33957645297050476), ('among agents', 0.3161724805831909), ('goods', 0.300130158662796), ('fairness', 0.29317107796669006)]"
1094,1094,27,1094_hidden markov models_hidden markov hmm_hidden markov_markov models hmms,"['hidden markov models', 'hidden markov hmm', 'hidden markov', 'markov models hmms', 'models hmms', 'markov hmm', 'markov models', 'markov switching', 'markov', 'markov chain']","['A New Algorithm for Hidden Markov Models Learning Problem   This research focuses on the algorithms and approaches for learning Hidden\nMarkov Models (HMMs) and compares HMM learning methods and algorithms. HMM is a\nstatistical Markov model in which the system being modeled is assumed to be a\nMarkov process. One of the essential characteristics of HMMs is their learning\ncapabilities. Learning algorithms are introduced to overcome this\ninconvenience. One of the main problems of the newly proposed algorithms is\ntheir validation. This research aims by using the theoretical and experimental\nanalysis to 1) compare HMMs learning algorithms proposed in the literature, 2)\nprovide a validation tool for new HMM learning algorithms, and 3) present a new\nalgorithm called Asexual Reproduction Optimization (ARO) with one of its\nextensions - Modified ARO (MARO) - as a novel HMM learning algorithm to use the\nvalidation tool proposed. According to the literature findings, it seems that\npopulationbased algorithms perform better among HMMs learning approaches than\nother algorithms. Also, the testing was done in nine benchmark datasets. The\nresults show that MARO outperforms different algorithms in objective functions\nin terms of accuracy and robustness.\n', 'Nonasymptotic control of the MLE for misspecified nonparametric hidden\n  Markov models   Finite state space hidden Markov models are flexible tools to model phenomena\nwith complex time dependencies: any process distribution can be approximated by\na hidden Markov model with enough hidden states.We consider the problem of\nestimating an unknown process distribution using nonparametric hidden Markov\nmodels in the misspecified setting, that is when the data-generating process\nmay not be a hidden Markov model.We show that when the true distribution is\nexponentially mixing and satisfies a forgetting assumption, the maximum\nlikelihood estimator recovers the best approximation of the true distribution.\nWe prove a finite sample bound on the resulting error and show that it is\noptimal in the minimax sense--up to logarithmic factors--when the model is well\nspecified.\n', 'Probability Bracket Notation: Markov Sequence Projector of Visible and\n  Hidden Markov Models in Dynamic Bayesian Networks   With the symbolic framework of Probability Bracket Notation (PBN), the Markov\nSequence Projector (MSP) is introduced to expand the evolution formula of\nHomogeneous Markov Chains (HMCs). The well-known weather example, a Visible\nMarkov Model (VMM), illustrates that the full joint probability of a VMM\ncorresponds to a specifically projected Markov state sequence in the expanded\nevolution formula. In a Hidden Markov Model (HMM), the probability basis\n(P-basis) of the hidden Markov state sequence and the P-basis of the\nobservation sequence exist in the sequential event space. The full joint\nprobability of an HMM is the product of the (unknown) projected hidden sequence\nof Markov states and their transformations into the observation P-bases. The\nViterbi algorithm is applied to the famous Weather-Stone HMM example to\ndetermine the most likely weather-state sequence given the observed stone-state\nsequence. Our results are verified using the Elvira software package. Using the\nPBN, we unify the evolution formulas for Markov models like VMMs, HMMs, and\nfactorial HMMs (with discrete time). We briefly investigated the extended HMM,\naddressing the feedback issue, and the continuous-time VMM and HMM (with\ndiscrete or continuous states). All these models are subclasses of Dynamic\nBayesian Networks (DBNs) essential for Machine Learning (ML) and Artificial\nIntelligence (AI).\n']","[('hidden markov models', 0.8015260696411133), ('hidden markov hmm', 0.7852964401245117), ('hidden markov', 0.767010509967804), ('markov models hmms', 0.6926591992378235), ('models hmms', 0.6565971970558167), ('markov hmm', 0.6557847857475281), ('markov models', 0.6250636577606201), ('markov switching', 0.5596117377281189), ('markov', 0.5492252707481384), ('markov chain', 0.5034039616584778)]"
1095,1095,27,1095_galerkin reduced order_reduced order methods_galerkin reduced_reduced order models,"['galerkin reduced order', 'reduced order methods', 'galerkin reduced', 'reduced order models', 'navier stokes equations', 'reduced order solutions', 'based reduced order', 'reduced basis methods', 'incompressible navier stokes', 'turbulent flows']","['A POD-Galerkin reduced order model for a LES filtering approach   We propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced\nOrder Model (ROM) for a Leray model. For the implementation of the model, we\ncombine a two-step algorithm called Evolve-Filter (EF) with a computationally\nefficient finite volume method. The main novelty of the proposed approach\nrelies in applying spatial filtering both for the collection of the snapshots\nand in the reduced order model, as well as in considering the pressure field at\nreduced level. In both steps of the EF algorithm, velocity and pressure fields\nare approximated by using different POD basis and coefficients. For the\nreconstruction of the pressures fields, we use a pressure Poisson equation\napproach. We test our ROM on two benchmark problems: 2D and 3D unsteady flow\npast a cylinder at Reynolds number 0 <= Re <= 100. The accuracy of the reduced\norder model is assessed against results obtained with the full order model. For\nthe 2D case, a parametric study with respect to the filtering radius is also\npresented.\n', 'A reduced order variational multiscale approach for turbulent flows   The purpose of this work is to present a reduced order modeling framework for\nparametrized turbulent flows with moderately high Reynolds numbers within the\nvariational multiscale (VMS) method. The Reduced Order Models (ROMs) presented\nin this manuscript are based on a POD-Galerkin approach with a VMS\nstabilization technique. Two different reduced order models are presented,\nwhich differ on the stabilization used during the Galerkin projection. In the\nfirst case the VMS stabilization method is used at both the full order and the\nreduced order level. In the second case, the VMS stabilization is used only at\nthe full order level, while the projection of the standard Navier-Stokes\nequations is performed instead at the reduced order level. The former method is\ndenoted as consistent ROM, while the latter is named non-consistent ROM, in\norder to underline the different choices made at the two levels. Particular\nattention is also devoted to the role of inf-sup stabilization by means of\nsupremizers in ROMs based on a VMS formulation. Finally, the developed methods\nare tested on a numerical benchmark.\n', 'Stabilized POD Reduced Order Models for convection-dominated\n  incompressible flows   We present a comparative computational study of two stabilized Reduced Order\nModels (ROMs) for the simulation of convection-dominated incompressible flow\n(Reynolds number of the order of a few thousands). Representative solutions in\nthe parameter space, which includes either time only or time and Reynolds\nnumber, are computed with a Finite Volume method and used to generate a reduced\nbasis via Proper Orthogonal Decomposition (POD). Galerkin projection of the\nNavier-Stokes equations onto the reduced space is used to compute the ROM\nsolution. To ensure computational efficiency, the number of POD modes is\ntruncated and ROM solution accuracy is recovered through two stabilization\nmethods: i) adding a global constant artificial viscosity to the reduced\ndimensional model, and ii) adding a different value of artificial viscosity for\nthe different POD modes. We test the stabilized ROMs for fluid flow in an\nidealized medical device consisting of a conical convergent, a narrow throat,\nand a sudden expansion. Both stabilization methods significantly improve the\nROM solution accuracy over a standard (non-stabilized) POD-Galerkin model.\n']","[('galerkin reduced order', 0.6145004034042358), ('reduced order methods', 0.5576854944229126), ('galerkin reduced', 0.5112019777297974), ('reduced order models', 0.4720350503921509), ('navier stokes equations', 0.46526649594306946), ('reduced order solutions', 0.4529579281806946), ('based reduced order', 0.44347167015075684), ('reduced basis methods', 0.4287903308868408), ('incompressible navier stokes', 0.42096444964408875), ('turbulent flows', 0.4166998267173767)]"
1096,1096,27,1096_alperin weight conjecture_simple groups lie_finite simple groups_finite groups lie,"['alperin weight conjecture', 'simple groups lie', 'finite simple groups', 'finite groups lie', 'groups lie type', 'finite reductive groups', 'blocks finite groups', 'exceptional groups lie', 'reductive groups', 'weight conjecture']","['Equivariant correspondences and the inductive Alperin weight condition\n  for type $\\mathsf A$   In this paper, we establish the inductive Alperin weight condition for the\nfinite simple groups of Lie type $\\mathsf A$, contributing to the program to\nprove the Alperin weight conjecture by checking the inductive condition for all\nfinite simple groups.\n', 'Morita equivalences and the inductive blockwise Alperin weight condition\n  for type $\\mathsf A$   As a step to establish the blockwise Alperin weight conjecture for all finite\ngroups, we verify the inductive blockwise Alperin weight condition introduced\nby Navarro--Tiep and Sp\\""ath for simple groups of Lie type $\\mathsf A$, split\nor twisted. Key to the proofs is to reduce the verification of the inductive\ncondition to the isolated (that means unipotent) blocks, using the Jordan\ndecomposition for blocks of finite reductive groups given by Bonnaf\\\'e, Dat and\nRouquier.\n', 'Inductive blockwise Alperin weight condition for type B and odd primes   By the reduction theorems of Navarro--Tiep and Sp\\""ath, a way to prove the\nAlperin weight conjecture and its blockwise version is to verify the co-called\ninductive Alperin weight condition and inductive blockwise Alperin weight\ncondition for all finie simple groups respectively. In this paper, we establish\nthe inductive blockwise Alperin weight condition for simple groups of type\n$\\mathsf B$ and odd primes, using a criterion given by Brough and Sp\\""ath\nrecently.\n']","[('alperin weight conjecture', 0.6261799931526184), ('simple groups lie', 0.575501024723053), ('finite simple groups', 0.5378764867782593), ('finite groups lie', 0.5217341780662537), ('groups lie type', 0.5109439492225647), ('finite reductive groups', 0.4924118220806122), ('blocks finite groups', 0.4833361804485321), ('exceptional groups lie', 0.4802824854850769), ('reductive groups', 0.4749578833580017), ('weight conjecture', 0.4534590542316437)]"
1097,1097,27,1097_robust planning_collision avoidance_motion planning_safety constraints,"['robust planning', 'collision avoidance', 'motion planning', 'safety constraints', 'multi robot', 'planning', 'robot', 'safe optimal', 'control multi robot', 'safety guarantees']","[""Active Uncertainty Reduction for Human-Robot Interaction: An Implicit\n  Dual Control Approach   The ability to accurately predict human behavior is central to the safety and\nefficiency of robot autonomy in interactive settings. Unfortunately, robots\noften lack access to key information on which these predictions may hinge, such\nas people's goals, attention, and willingness to cooperate. Dual control theory\naddresses this challenge by treating unknown parameters of a predictive model\nas stochastic hidden states and inferring their values at runtime using\ninformation gathered during system operation. While able to optimally and\nautomatically trade off exploration and exploitation, dual control is\ncomputationally intractable for general interactive motion planning, mainly due\nto the fundamental coupling between robot trajectory optimization and human\nintent inference. In this paper, we present a novel algorithmic approach to\nenable active uncertainty reduction for interactive motion planning based on\nthe implicit dual control paradigm. Our approach relies on sampling-based\napproximation of stochastic dynamic programming, leading to a model predictive\ncontrol problem that can be readily solved by real-time gradient-based\noptimization methods. The resulting policy is shown to preserve the dual\ncontrol effect for a broad class of predictive human models with both\ncontinuous and categorical uncertainty. The efficacy of our approach is\ndemonstrated with simulated driving examples.\n"", 'Active Uncertainty Reduction for Safe and Efficient Interaction\n  Planning: A Shielding-Aware Dual Control Approach   The ability to accurately predict others\' behavior is central to the safety\nand efficiency of interactive robotics. Unfortunately, robots often lack access\nto key information on which these predictions may hinge, such as other agents\'\ngoals, attention, and willingness to cooperate. Dual control theory addresses\nthis challenge by treating unknown parameters of a predictive model as\nstochastic hidden states and inferring their values at runtime using\ninformation gathered during system operation. While able to optimally and\nautomatically trade off exploration and exploitation, dual control is\ncomputationally intractable for general interactive motion planning. In this\npaper, we present a novel algorithmic approach to enable active uncertainty\nreduction for interactive motion planning based on the implicit dual control\nparadigm. Our approach relies on sampling-based approximation of stochastic\ndynamic programming, leading to a model predictive control problem that can be\nreadily solved by real-time gradient-based optimization methods. The resulting\npolicy is shown to preserve the dual control effect for a broad class of\npredictive models with both continuous and categorical uncertainty. To ensure\nthe safe operation of the interacting agents, we use a runtime safety filter\n(also referred to as a ""shielding"" scheme), which overrides the robot\'s dual\ncontrol policy with a safety fallback strategy when a safety-critical event is\nimminent. We then augment the dual control framework with an improved variant\nof the recently proposed shielding-aware robust planning scheme, which\nproactively balances the nominal planning performance with the risk of\nhigh-cost emergency maneuvers triggered by low-probability agent behaviors. We\ndemonstrate the efficacy of our approach with both simulated driving studies\nand hardware experiments using 1/10 scale autonomous vehicles.\n', 'SHARP: Shielding-Aware Robust Planning for Safe and Efficient\n  Human-Robot Interaction   Jointly achieving safety and efficiency in human-robot interaction (HRI)\nsettings is a challenging problem, as the robot\'s planning objectives may be at\nodds with the human\'s own intent and expectations. Recent approaches ensure\nsafe robot operation in uncertain environments through a supervisory control\nscheme, sometimes called ""shielding"", which overrides the robot\'s nominal plan\nwith a safety fallback strategy when a safety-critical event is imminent. These\nreactive ""last-resort"" strategies (typically in the form of aggressive\nemergency maneuvers) focus on preserving safety without efficiency\nconsiderations; when the nominal planner is unaware of possible safety\noverrides, shielding can be activated more frequently than necessary, leading\nto degraded performance. In this work, we propose a new shielding-based\nplanning approach that allows the robot to plan efficiently by explicitly\naccounting for possible future shielding events. Leveraging recent work on\nBayesian human motion prediction, the resulting robot policy proactively\nbalances nominal performance with the risk of high-cost emergency maneuvers\ntriggered by low-probability human behaviors. We formalize Shielding-Aware\nRobust Planning (SHARP) as a stochastic optimal control problem and propose a\ncomputationally efficient framework for finding tractable approximate solutions\nat runtime. Our method outperforms the shielding-agnostic motion planning\nbaseline (equipped with the same human intent inference scheme) on simulated\ndriving examples with human trajectories taken from the recently released Waymo\nOpen Motion Dataset.\n']","[('robust planning', 0.5532293319702148), ('collision avoidance', 0.4659905731678009), ('motion planning', 0.45100560784339905), ('safety constraints', 0.420758992433548), ('multi robot', 0.3919987380504608), ('planning', 0.3915866017341614), ('robot', 0.38821467757225037), ('safe optimal', 0.3873662054538727), ('control multi robot', 0.38491979241371155), ('safety guarantees', 0.384914755821228)]"
1098,1098,27,1098_distributed detection_testing independence_error constraints_binary hypothesis,"['distributed detection', 'testing independence', 'error constraints', 'binary hypothesis', 'binary hypothesis testing', 'privacy constraint', 'testing conditional independence', 'type error probability', 'ii error probabilities', 'error probabilities']","[""Privacy-aware Distributed Hypothesis Testing   A distributed binary hypothesis testing (HT) problem involving two parties, a\nremote observer and a detector, is studied. The remote observer has access to a\ndiscrete memoryless source, and communicates its observations to the detector\nvia a rate-limited noiseless channel. The detector observes another discrete\nmemoryless source, and performs a binary hypothesis test on the joint\ndistribution of its own observations with those of the observer. While the goal\nof the observer is to maximize the type II error exponent of the test for a\ngiven type I error probability constraint, it also wants to keep a private part\nof its observations as oblivious to the detector as possible. Considering both\nequivocation and average distortion under a causal disclosure assumption as\npossible measures of privacy, the trade-off between the communication rate from\nthe observer to the detector, the type II error exponent, and privacy is\nstudied. For the general HT problem, we establish single-letter inner bounds on\nboth the rate-error exponent-equivocation and rate-error exponent-distortion\ntrade-offs. Subsequently, single-letter characterizations for both trade-offs\nare obtained (i) for testing against conditional independence of the observer's\nobservations from those of the detector, given some additional side-information\nat the detector; and (ii) when the communication rate constraint over the\nchannel is zero. Finally, we show by providing a counterexample that, the\nstrong converse which holds for distributed HT without a privacy constraint,\ndoes not hold when a privacy constraint is imposed. This implies that, in\ngeneral, the rate-error exponent-equivocation and rate-error\nexponent-distortion trade-offs are not independent of the type I error\nprobability constraint.\n"", 'Multi-Hop Network with Multiple Decision Centers under Expected-Rate\n  Constraints   We consider a multi-hop distributed hypothesis testing problem with multiple\ndecision centers (DCs) for testing against independence and where the\nobservations obey some Markov chain. For this system, we characterize the\nfundamental type-II error exponents region, i.e., the type-II error exponents\nthat the various DCs can achieve simultaneously, under expected\nrate-constraints. Our results show that this fundamental exponents region is\nboosted compared to the region under maximum-rate constraints, and that it\ndepends on the permissible type-I error probabilities. When all DCs have equal\npermissible type-I error probabilities, the exponents region is rectangular and\nall DCs can simultaneously achieve their optimal type-II error exponents. When\nthe DCs have different permissible type-I error probabilities, a tradeoff\nbetween the type-II error exponents at the different DCs arises. New\nachievability and converse proofs are presented. For the achievability, a new\nmultiplexing and rate-sharing strategy is proposed. The converse proof is based\non applying different change of measure arguments in parallel and on proving\nasymptotic Markov chains. For the special cases $K = 2$ and $K = 3$, we provide\nsimplified expressions for the exponents region; a similar simplification is\nconjectured for arbitrary $K\\geq 2$.\n', 'Optimal Exponents In Cascaded Hypothesis Testing under Expected Rate\n  Constraints   Cascaded binary hypothesis testing is studied in this paper with two decision\ncenters at the relay and the receiver. All terminals have their own\nobservations, where we assume that the observations at the transmitter, the\nrelay, and the receiver form a Markov chain in this order. The communication\noccurs over two hops, from the transmitter to the relay and from the relay to\nthe receiver. Expected rate constraints are imposed on both communication\nlinks. In this work, we characterize the optimal type-II error exponents at the\ntwo decision centers under constraints on the allowed type-I error\nprobabilities. Our recent work characterized the optimal type-II error\nexponents in the special case when the two decision centers have same type-I\nerror constraints and provided an achievability scheme for the general setup.\nTo obtain the exact characterization for the general case, in this paper we\nprovide a new converse proof as well as a new matching achievability scheme.\nOur results indicate that under unequal type-I error constraints at the relay\nand the receiver, a tradeoff arises between the maximum type-II error\nprobabilities at these two terminals. Previous results showed that such a\ntradeoff does not exist under equal type-I error constraints or under general\ntype-I error constraints when a maximum rate constraint is imposed on the\ncommunication links.\n']","[('distributed detection', 0.44207075238227844), ('testing independence', 0.4085114002227783), ('error constraints', 0.396101713180542), ('binary hypothesis', 0.3829261064529419), ('binary hypothesis testing', 0.38258615136146545), ('privacy constraint', 0.37447747588157654), ('testing conditional independence', 0.3728945553302765), ('type error probability', 0.3666415214538574), ('ii error probabilities', 0.3580382764339447), ('error probabilities', 0.3487006723880768)]"
1099,1099,27,1099_soliton resolution conjecture_wave maps dimensional_equivariant wave_soliton resolution,"['soliton resolution conjecture', 'wave maps dimensional', 'equivariant wave', 'soliton resolution', 'critical wave', 'wave maps', 'multi solitons', 'maps wave', 'wave equations', 'wave map']","['On classification of non-radiative solutions for various energy-critical\n  wave equations   Non-radiative solutions of energy critical wave equations are such that their\nenergy in an exterior region $|x|>R+|t|$ vanishes asymptotically in both time\ndirections. This notion, introduced by Duyckaerts, Kenig and Merle (J. Eur.\nMath. Soc., 2011), has been key in solving the soliton resolution conjecture\nfor these equations in the radial case. In the present paper, we first classify\ntheir asymptotic behaviour at infinity, showing that they correspond to a\n$k$-parameters family of solutions where $k$ depends on the dimension. This\ngeneralises the previous results (Duyckaerts, Kenig and Merle, Camb. J. Math.,\n2013 and Duyckaerts, Kenig, Martel and Merle, Comm. Math. Phys., 2022) in three\nand four dimensions. We then establish a unique maximal extension of these\nsolutions.\n', 'Uniqueness of two-bubble wave maps   This is the second part of a two-paper series that establishes the uniqueness\nand regularity of a threshold energy wave map that does not scatter in both\ntime directions.\n  Consider the two-sphere valued equivariant energy critical wave maps equation\non 1+2 dimensional Minkowski space, with equivariance class k > 3. It is known\nthat every topologically trivial wave map with energy less than twice that of\nthe unique k-equivariant harmonic map Q scatters in both time directions. We\nstudy maps with precisely the threshold energy, i.e., twice the energy of Q.\n  In the first part of the series we gave a refined construction of a threshold\nwave map that asymptotically decouples into a superposition of two harmonic\nmaps (bubbles), one of which is concentrating in scale. In this paper, we show\nthat this solution is the unique (up to the natural invariances of the\nequation) two-bubble wave map. Combined with our earlier work we can now give\nan exact description of every threshold wave map.\n', 'Continuous time soliton resolution for two-bubble equivariant wave maps   We consider the energy-critical wave maps equation from 1+2 dimensional\nMinkowski space into the 2-sphere, in the equivariant case. We prove that if a\nwave map decomposes, along a sequence of times, into a superposition of at most\ntwo rescaled harmonic maps (bubbles) and radiation, then such a decomposition\nholds for continuous time. If the equivariance degree equals one or two, we\ndeduce, as a consequence of sequential soliton resolution results of C\\^ote,\nand Jia and Kenig, that any topologically trivial equivariant wave map with\nenergy less than four times the energy of the bubble asymptotically decomposes\ninto (at most two) bubbles and radiation.\n']","[('soliton resolution conjecture', 0.5613308548927307), ('wave maps dimensional', 0.5357919931411743), ('equivariant wave', 0.5144816040992737), ('soliton resolution', 0.5109255909919739), ('critical wave', 0.5083659887313843), ('wave maps', 0.4951154887676239), ('multi solitons', 0.4889969229698181), ('maps wave', 0.48296523094177246), ('wave equations', 0.4748329520225525), ('wave map', 0.4624502658843994)]"
1100,1100,27,1100_viscosity solutions hamilton_jacobi bellman equations_hamilton jacobi equations_solutions hamilton jacobi,"['viscosity solutions hamilton', 'jacobi bellman equations', 'hamilton jacobi equations', 'solutions hamilton jacobi', 'convex hamiltonians', 'existence viscosity', 'dependent hamilton jacobi', 'optimal control theory', 'value hamilton jacobi', 'hamilton jacobi bellman']","['Representation of Weak Solutions of Convex Hamilton-Jacobi-Bellman\n  Equations on Infinite Horizon   In the present paper, it is provided a representation result for the weak\nsolutions of a class of evolutionary Hamilton-Jacobi-Bellman equations on\ninfinite horizon, with Hamiltonians measurable in time and fiber convex. Such\nHamiltonians are associated with a - faithful - representation, namely\ninvolving two functions measurable in time and locally Lipschitz in the state\nand control. Our results concern the recovering of a representation of convex\nHamiltonians under a relaxed assumption on the Fenchel transform of the\nHamiltonian with respect to the fiber. We apply them to investigate the\nuniqueness of weak solutions, vanishing at infinity, of a class of\ntime-dependent Hamilton-Jacobi-Bellman equations. Assuming a viability\ncondition on the domain of the aforementioned Fenchel transform, these weak\nsolutions are regarded as an appropriate value function of an infinite horizon\ncontrol problem under state constraints.\n', 'Equivalence of minimax and viscosity solutions of path-dependent\n  Hamilton-Jacobi equations   In the paper, we consider a path-dependent Hamilton-Jacobi equation with\ncoinvariant derivatives over the space of continuous functions. Such equations\narise from optimal control problems and differential games for time-delay\nsystems. We study generalized solutions of the considered Hamilton-Jacobi\nequation both in the minimax and in the viscosity sense. A minimax solution is\ndefined as a functional which epigraph and subgraph satisfy certain conditions\nof weak invariance, while a viscosity solution is defined in terms of a pair of\ninequalities for coinvariant sub- and super-gradients. We prove that these two\nnotions are equivalent, which is the main result of the paper. As a corollary,\nwe obtain comparison and uniqueness results for viscosity solutions of a Cauchy\nproblem for the considered Hamilton-Jacobi equation and a right-end boundary\ncondition. The proof is based on a certain property of the coinvariant\nsubdifferential. To establish this property, we develop a technique going back\nto the proofs of multidirectional mean-value inequalities. In particular, the\nabsence of the local compactness property of the underlying continuous function\nspace is overcome by using Borwein-Preiss variational principle with an\nappropriate guage-type functional.\n', 'Minimax and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations for\n  Time-Delay Systems   The paper deals with a Bolza optimal control problem for a dynamical system\nwhich motion is described by a delay differential equation under an initial\ncondition defined by a piecewise continuous function. For the value functional\nin this problem, the Cauchy problem for the Hamilton-Jacobi-Bellman equation\nwith coinvariant derivatives is considered. Minimax and viscosity solutions of\nthis problem are studied. It is proved that both of these solutions exist, are\nunique and coincide with the value functional.\n']","[('viscosity solutions hamilton', 0.616407036781311), ('jacobi bellman equations', 0.5856608748435974), ('hamilton jacobi equations', 0.5679923892021179), ('solutions hamilton jacobi', 0.5593245029449463), ('convex hamiltonians', 0.5553469061851501), ('existence viscosity', 0.5162438154220581), ('dependent hamilton jacobi', 0.5126165151596069), ('optimal control theory', 0.5041811466217041), ('value hamilton jacobi', 0.4745096266269684), ('hamilton jacobi bellman', 0.46746203303337097)]"
1101,1101,27,1101_optimal boundary control_existence optimal controls_optimal control problems_optimal control,"['optimal boundary control', 'existence optimal controls', 'optimal control problems', 'optimal control', 'systems optimal control', 'optimal controls', 'class optimal control', 'optimality conditions', 'optimality conditions optimal', 'conditions optimality']","['Optimality conditions for sparse optimal control of viscous\n  Cahn-Hilliard systems with logarithmic potential   In this paper we study the optimal control of a parabolic initial-boundary\nvalue problem of viscous Cahn-Hilliard type with zero Neumann boundary\nconditions. Phase field systems of this type govern the evolution of diffusive\nphase transition processes with conserved order parameter. It is assumed that\nthe nonlinear functions driving the physical processes within the spatial\ndomain are double-well potentials of logarithmic type whose derivatives become\nsingular at the boundary of their respective domains of definition. For such\nsystems, optimal control problems have been studied in the past. We focus here\non the situation when the cost functional of the optimal control problem\ncontains a nondifferentiable term like the L1-norm, which leads to sparsity of\noptimal controls. For such cases, we establish first-order necessary and\nsecond-order sufficient optimality conditions for locally optimal controls. In\nthe approach to second-order sufficient conditions, the main novelty of this\npaper, we adapt a technique introduced by E. Casas, C. Ryll and F. Tr\\""oltzsch\nin the paper [SIAM J. Control Optim. 53 (2015), 2168-2202]. In this paper, we\nshow that this method can also be successfully applied to systems of viscous\nCahn-Hilliard type with logarithmic nonlinearity. Since the Cahn-Hilliard\nsystem corresponds to a fourth-order partial differential equation in contrast\nto the second-order systems investigated before, additional technical\ndifficulties have to be overcome.\n', 'Second-order optimality conditions for the sparse optimal control of\n  nonviscous Cahn-Hilliard systems   In this paper we study the optimal control of an initial-boundary value\nproblem for the classical nonviscous Cahn-Hilliard system with zero Neumann\nboundary conditions. Phase field systems of this type govern the evolution of\ndiffusive phase transition processes with conserved order parameter. For such\nsystems, optimal control problems have been studied in the past. We focus here\non the situation when the cost functional of the optimal control problem\ncontains a sparsity-enhancing nondifferentiable term like the L1-norm. For such\ncases, we establish first-order necessary and second-order sufficient\noptimality conditions for locally optimal controls, where in the approach to\nsecond-order sufficient conditions we employ a technique introduced by E.\nCasas, C. Ryll and F. Tr\\""oltzsch in the paper [SIAM J. Control Optim. 53\n(2015), 2168-2202]. The main novelty of this paper is that this method, which\nhas recently been successfully applied to systems of viscous Cahn-Hilliard\ntype, can be adapted also to the classical nonviscous case. Since in the case\nwithout viscosity the solutions to the state and adjoint systems turn out to be\nconsiderably less regular than in the viscous case, numerous additional\ntechnical difficulties have to be overcome, and additional conditions have to\nbe imposed. In particular, we have to restrict ourselves to the case when the\nnonlinearity driving the phase separation is regular, while in the presence of\na viscosity term also nonlinearities of logarithmic type turn could be\nadmitted. In addition, the implicit function theorem, which was employed to\nestablish the needed differentiability properties of the control-to-state\noperator in the viscous case, does not apply in our situation and has to be\nsubstituted by other arguments.\n', 'Optimal Control Problems Governed by 1-D Kobayashi-Warren-Carter Type\n  Systems   This paper is devoted to the study of a class of optimal control problems\ngoverned by 1-D Kobayashi-Warren-Carter type systems, which are based on a\nphase-field model of grain boundary motion, proposed by [Kobayashi et al,\nPhysica D, 140, 141-150, 2000]. The class consists of an optimal control\nproblem for a physically realistic state-system of Kobayashi-Warren-Carter\ntype, and its regularized approximating problems. The results of this paper are\nstated in three Main Theorems 1-3. The first Main Theorem 1 is concerned with\nthe solvability and continuous dependence for the state-systems. Meanwhile, the\nsecond Main Theorem 2 is concerned with the solvability of optimal control\nproblems, and some semi-continuous association in the class of our optimal\ncontrol problems. Finally, in the third Main Theorem 3, we derive the first\norder necessary optimality conditions for optimal controls of the regularized\napproximating problems. By taking the approximating limit, we also derive the\noptimality conditions for the optimal controls for the physically realistic\nproblem.\n']","[('optimal boundary control', 0.699048638343811), ('existence optimal controls', 0.6488648653030396), ('optimal control problems', 0.6422927975654602), ('optimal control', 0.6055967211723328), ('systems optimal control', 0.5937106013298035), ('optimal controls', 0.5655777454376221), ('class optimal control', 0.561728835105896), ('optimality conditions', 0.558392345905304), ('optimality conditions optimal', 0.5520341396331787), ('conditions optimality', 0.5393512845039368)]"
1102,1102,27,1102_quantum measurements_quantum memory_quantum state tomography_quantum communication,"['quantum measurements', 'quantum memory', 'quantum state tomography', 'quantum communication', 'quantum computers', 'quantum systems', 'quantum states', 'utilize quantum', 'quantum state', 'qubit state']","['Classical Shadows With Noise   The classical shadows protocol, recently introduced by Huang, Kueng, and\nPreskill [Nat. Phys. 16, 1050 (2020)], is a quantum-classical protocol to\nestimate properties of an unknown quantum state. Unlike full quantum state\ntomography, the protocol can be implemented on near-term quantum hardware and\nrequires few quantum measurements to make many predictions with a high success\nprobability. In this paper, we study the effects of noise on the classical\nshadows protocol. In particular, we consider the scenario in which the quantum\ncircuits involved in the protocol are subject to various known noise channels\nand derive an analytical upper bound for the sample complexity in terms of a\nshadow seminorm for both local and global noise. Additionally, by modifying the\nclassical post-processing step of the noiseless protocol, we define a new\nestimator that remains unbiased in the presence of noise. As applications, we\nshow that our results can be used to prove rigorous sample complexity upper\nbounds in the cases of depolarizing noise and amplitude damping.\n', 'Principal eigenstate classical shadows   Given many copies of an unknown quantum state $\\rho$, we consider the task of\nlearning a classical description of its principal eigenstate. Namely, assuming\nthat $\\rho$ has an eigenstate $|\\phi\\rangle$ with (unknown) eigenvalue $\\lambda\n> 1/2$, the goal is to learn a (classical shadows style) classical description\nof $|\\phi\\rangle$ which can later be used to estimate expectation values\n$\\langle \\phi |O| \\phi \\rangle$ for any $O$ in some class of observables. We\nconsider the sample-complexity setting in which generating a copy of $\\rho$ is\nexpensive, but joint measurements on many copies of the state are possible. We\npresent a protocol for this task scaling with the principal eigenvalue\n$\\lambda$ and show that it is optimal within a space of natural approaches,\ne.g., applying quantum state purification followed by a single-copy classical\nshadows scheme. Furthermore, when $\\lambda$ is sufficiently close to $1$, the\nperformance of our algorithm is optimal--matching the sample complexity for\npure state classical shadows.\n', 'On the sample complexity of purity and inner product estimation   We study the sample complexity of the prototypical tasks quantum purity\nestimation and quantum inner product estimation. In purity estimation, we are\nto estimate $tr(\\rho^2)$ of an unknown quantum state $\\rho$ to additive error\n$\\epsilon$. Meanwhile, for quantum inner product estimation, Alice and Bob are\nto estimate $tr(\\rho\\sigma)$ to additive error $\\epsilon$ given copies of\nunknown quantum state $\\rho$ and $\\sigma$ using classical communication and\nrestricted quantum communication.\n  In this paper, we show a strong connection between the sample complexity of\npurity estimation with bounded quantum memory and inner product estimation with\nbounded quantum communication and unentangled measurements. We propose a\nprotocol that solves quantum inner product estimation with $k$-qubit one-way\nquantum communication and unentangled local measurements using\n$O(median\\{1/\\epsilon^2,2^{n/2}/\\epsilon,2^{n-k}/\\epsilon^2\\})$ copies of\n$\\rho$ and $\\sigma$. Our protocol can be modified to estimate the purity of an\nunknown quantum state $\\rho$ using $k$-qubit quantum memory with the same\ncomplexity. We prove that arbitrary protocols with $k$-qubit quantum memory\nthat estimate purity to error $\\epsilon$ require\n$\\Omega(median\\{1/\\epsilon^2,2^{n/2}/\\sqrt{\\epsilon},2^{n-k}/\\epsilon^2\\})$\ncopies of $\\rho$. This indicates the same lower bound for quantum inner product\nestimation with one-way $k$-qubit quantum communication and classical\ncommunication, and unentangled local measurements. For purity estimation, we\nfurther improve the lower bound to\n$\\Omega(\\max\\{1/\\epsilon^2,2^{n/2}/\\epsilon\\})$ for any protocols using an\nidentical single-copy projection-valued measurement.\n  Additionally, we investigate a decisional variant of quantum distributed\ninner product estimation without quantum communication for mixed state and\nprovide a lower bound on the sample complexity.\n']","[('quantum measurements', 0.5314772129058838), ('quantum memory', 0.5050979256629944), ('quantum state tomography', 0.48837345838546753), ('quantum communication', 0.47189781069755554), ('quantum computers', 0.4624362289905548), ('quantum systems', 0.43714576959609985), ('quantum states', 0.42227742075920105), ('utilize quantum', 0.42003461718559265), ('quantum state', 0.4190925061702728), ('qubit state', 0.4120534062385559)]"
1103,1103,27,1103_black hole thermodynamics_black holes_black hole_hawking temperature,"['black hole thermodynamics', 'black holes', 'black hole', 'hawking temperature', 'schwarzschild black', 'quantum gravity', 'black hole mass', 'hawking', 'event horizon', 'quantum field theory']","['How an exact discrete symmetry can preserve black hole information or\n  Turning a black hole inside out   To apply the laws of General Relativity to quantum black holes, one first\nneeds to remove the horizon singularity by means of Kruskal-Szekeres\ncoordinates. This however doubles spacetime, which thereby is equipped with an\nexact binary symmetry. All particles near a black hole share the same symmetry,\nand conservation of this symmetry may completely remove the information\nparadox: the quantum black hole has no interior, or equivalently, the black\nhole interior is a quantum clone of the exterior region. These observations,\ntotally overlooked in most of the literature on quantum black holes, resolve\nsome issues concerning conservation of information. Some other problems do\nremain.\n', 'On the nature of the black hole information problem The aim of this work is to present the black hole information problem and discuss the assumptions and hypotheses necessary for its formulation. As the problem arises in the framework of semiclassical gravity, we first review the necessary notions to describe Lorentzian manifolds equipped with physical properties, as well as the physical concepts of the theory that describes the gravitational interaction as the curvature of spacetime, general relativity. From its classical perspective, we develop the formalism to study the dynamical aspects of black holes in spacetimes obeying suitable causality conditions. Equipped with conjectures that nature censors naked singularities and that black holes reach a stationary configuration after they form, the black hole uniqueness theorems allow us to review several relations for the geometrical quantities associated with them. Following considerations of the other fundamental interactions, which are described by quantum field theory, we review the arguments in the formalism of quantum field theory in curved spacetime that give rise to the effective particle creation effect, its approximately thermal character, and the concept of black hole evaporation. With a precise quantification of information in quantum mechanics and assuming that the condition for physically acceptable states is given by the Hadamard condition, we review the result that entanglement between causally complementary regions is an intrinsic feature of quantum field theory. As a consequence, we discuss how the formation and complete evaporation of black holes leads to information loss. Conscious that such a prediction follows if no deviations from the semiclassical picture occur at the Planck scale, we discuss alternatives to this nonunitary dynamical evolution and formulate the black hole information problem. Lastly, we analyze the assumptions and hypotheses that lead to the problem.', 'A pedagogical approach to the black hole information problem The semiclassical depiction of gravity has provided many important results, such as particle creation effects in expanding universes and in spacetimes containing black holes. However, many questions remain open, most notably concerning the final product of the black hole evaporation process and the conservation of information. From a pedagogical perspective, we review the concepts that lead to this state of affairs, also known as the black hole information problem, and discuss the assumptions and hypotheses necessary for its formulation. Stating the necessary conjectures and results that lead to the geometrical properties of black holes, we present the notion of black hole evaporation and the result that entanglement between causally complementary regions is an intrinsic feature of quantum field theory under the Hadamard condition. We then show that the formation and complete evaporation of a black hole leads to information loss. Comparing such a result to the main alternatives to this non-unitary dynamical evolution, we formulate the black hole information problem and show that information loss is a genuine prediction if no deviations from the semiclassical picture occur at the Planck scale.']","[('black hole thermodynamics', 0.6805717945098877), ('black holes', 0.6052748560905457), ('black hole', 0.5549786686897278), ('hawking temperature', 0.50829017162323), ('schwarzschild black', 0.501792848110199), ('quantum gravity', 0.4954400956630707), ('black hole mass', 0.49248042702674866), ('hawking', 0.42261189222335815), ('event horizon', 0.41604626178741455), ('quantum field theory', 0.4116596281528473)]"
1104,1104,27,1104_functional time series_high dimensional functional_functional principal component_multivariate functional,"['functional time series', 'high dimensional functional', 'functional principal component', 'multivariate functional', 'dimensional functional', 'functional linear regression', 'principal component analysis', 'functional principal', 'estimate high dimensional', 'autoregressive']","['On the modelling and prediction of high-dimensional functional time\n  series   We propose a two-step procedure to model and predict high-dimensional\nfunctional time series, where the number of function-valued time series $p$ is\nlarge in relation to the length of time series $n$. Our first step performs an\neigenanalysis of a positive definite matrix, which leads to a one-to-one linear\ntransformation for the original high-dimensional functional time series, and\nthe transformed curve series can be segmented into several groups such that any\ntwo subseries from any two different groups are uncorrelated both\ncontemporaneously and serially. Consequently in our second step those groups\nare handled separately without the information loss on the overall linear\ndynamic structure. The second step is devoted to establishing a\nfinite-dimensional dynamical structure for all the transformed functional time\nseries within each group. Furthermore the finite-dimensional structure is\nrepresented by that of a vector time series. Modelling and forecasting for the\noriginal high-dimensional functional time series are realized via those for the\nvector time series in all the groups. We investigate the theoretical properties\nof our proposed methods, and illustrate the finite-sample performance through\nboth extensive simulation and two real datasets.\n', 'An autocovariance-based learning framework for high-dimensional\n  functional time series   Many scientific and economic applications involve the statistical learning of\nhigh-dimensional functional time series, where the number of functional\nvariables is comparable to, or even greater than, the number of serially\ndependent functional observations. In this paper, we model observed functional\ntime series, which are subject to errors in the sense that each functional\ndatum arises as the sum of two uncorrelated components, one dynamic and one\nwhite noise. Motivated from the fact that the autocovariance function of\nobserved functional time series automatically filters out the noise term, we\npropose a three-step procedure by first performing autocovariance-based\ndimension reduction, then formulating a novel autocovariance-based block\nregularized minimum distance estimation framework to produce block sparse\nestimates, and based on which obtaining the final functional sparse estimates.\nWe investigate theoretical properties of the proposed estimators, and\nillustrate the proposed estimation procedure via three sparse high-dimensional\nfunctional time series models. We demonstrate via both simulated and real\ndatasets that our proposed estimators significantly outperform the competitors.\n', 'On Consistency and Sparsity for High-Dimensional Functional Time Series\n  with Application to Autoregressions   Modelling a large collection of functional time series arises in a broad\nspectral of real applications. Under such a scenario, not only the number of\nfunctional variables can be diverging with, or even larger than the number of\ntemporally dependent functional observations, but each function itself is an\ninfinite-dimensional object, posing a challenging task. In this paper, we\npropose a three-step procedure to estimate high-dimensional functional time\nseries models. To provide theoretical guarantees for the three-step procedure,\nwe focus on multivariate stationary processes and propose a novel functional\nstability measure based on their spectral properties. Such stability measure\nfacilitates the development of some useful concentration bounds on sample\n(auto)covariance functions, which serve as a fundamental tool for further\nconvergence analysis in high-dimensional settings. As functional principal\ncomponent analysis (FPCA) is one of the key dimension reduction techniques in\nthe first step, we also investigate the non-asymptotic properties of the\nrelevant estimated terms under a FPCA framework. To illustrate with an\nimportant application, we consider vector functional autoregressive models and\ndevelop a regularization approach to estimate autoregressive coefficient\nfunctions under the sparsity constraint. Using our derived non-asymptotic\nresults, we investigate convergence properties of the regularized estimate\nunder high-dimensional scaling. Finally, the finite-sample performance of the\nproposed method is examined through both simulations and a public financial\ndataset.\n']","[('functional time series', 0.5923609733581543), ('high dimensional functional', 0.4907125234603882), ('functional principal component', 0.4625976085662842), ('multivariate functional', 0.4610980451107025), ('dimensional functional', 0.46040573716163635), ('functional linear regression', 0.43252772092819214), ('principal component analysis', 0.41887661814689636), ('functional principal', 0.41016557812690735), ('estimate high dimensional', 0.4016049802303314), ('autoregressive', 0.3922470808029175)]"
1105,1105,27,1105_labeling graphs_magic labelings_labeling graph_magic labeling,"['labeling graphs', 'magic labelings', 'labeling graph', 'magic labeling', 'labeling vertices', 'grid graphs', 'graphs', 'graph order', 'direct graph', 'graph exists']","['Distance magic labelings of Cartesian products of cycles   A graph of order $n$ is distance magic if it admits a bijective labeling of\nits vertices with integers from $1$ to $n$ such that each vertex has the same\nsum of the labels of its neighbors. In this paper we classify all distance\nmagic Cartesian products of two cycles, thereby correcting an error in a widely\ncited paper from 2004. Additionally, we show that each distance magic labeling\nof a Cartesian product of cycles is determined by a pair or quadruple of\nsuitable sequences, thus obtaining a complete characterization of all distance\nmagic labelings of these graphs. We also determine a lower bound on the number\nof all distance magic labelings of $C_{m} \\square C_{2m}$ with $m \\ge 3$ odd.\n', 'On Structural and Spectral Properties of Distance Magic Graphs   A graph $G=(V,E)$ is said to be distance magic if there is a bijection $f$\nfrom a vertex set of $G$ to the first $|V(G)|$ natural numbers such that for\neach vertex $v$, its weight given by $\\sum_{u \\in N(v)}f(u)$ is constant, where\n$N(v)$ is an open neighborhood of a vertex $v$. In this paper, we introduce the\nconcept of $p$-distance magic labeling and establish the necessary and\nsufficient condition for a graph to be distance magic. Additionally, we\nintroduce necessary and sufficient conditions for a connected regular graph to\nexhibit distance magic properties in terms of the eigenvalues of its adjacency\nand Laplacian matrices. Furthermore, we study the spectra of distance magic\ngraphs, focusing on singular distance magic graphs. Also, we show that the\nnumber of distance magic labelings of a graph is, at most, the size of its\nautomorphism group.\n', 'Odd order $C_4$-face-magic $m \\times n$ projective grid graphs having\n  $C_4$-face-magic value $2mn+1$ or $2mn+3$   For a graph $G = (V, E)$ embedded in the projective plane, let\n$\\mathcal{F}(G)$ denote the set of faces of $G$. Then, $G$ is called a\n$C_n$-face-magic projective graph if there exists a bijection $f: V(G) \\to \\{1,\n2, \\dots, |V(G)|\\}$ such that for any $F \\in \\mathcal{F}(G)$ with $F \\cong\nC_n$, the sum of all the vertex labels around $C_n$ is a constant $S$. We\nconsider the $m \\times n$ grid graph, denoted by $\\mathcal{P}_{m,n}$, embedded\nin the projective plane in the natural way. Let $m \\geqslant 3$ and $n\n\\geqslant 3$ be odd integers. It is known that the $C_4$-face-magic value of a\n$C_4$-face-magic labeling on $\\mathcal{P}_{m,n}$ is either $2mn+1$, $2mn+2$, or\n$2mn+3$. The characterization of $C_4$-face-magic labelings on\n$\\mathcal{P}_{m,n}$ having $C_4$-face-magic value $2mn+2$ is known. In this\npaper, we determine a category of $C_4$-face-magic labelings on\n$\\mathcal{P}_{m,n}$ for which the $C_4$-face-magic value is either $2mn+1$ or\n$2mn+3$. It is conjectured that these are the only $C_4$-face-magic labeling on\n$\\mathcal{P}_{m,n}$ having $C_4$-face-magic value $2mn+1$ or $2mn+3$.\n']","[('labeling graphs', 0.5214683413505554), ('magic labelings', 0.48449966311454773), ('labeling graph', 0.46853187680244446), ('magic labeling', 0.45992371439933777), ('labeling vertices', 0.4539881944656372), ('grid graphs', 0.4317529499530792), ('graphs', 0.42299947142601013), ('graph order', 0.4180779457092285), ('direct graph', 0.3892482817173004), ('graph exists', 0.3777201473712921)]"
1106,1106,27,1106_quartic surfaces_cubic surfaces_quadratic surfaces_projective surface,"['quartic surfaces', 'cubic surfaces', 'quadratic surfaces', 'projective surface', 'cubic hypersurfaces', 'smooth projective surface', 'surfaces geometry', 'surfaces many', 'cubic surface', 'lines cubic']","['Cubic Surfaces of Characteristic Two   Cubic surfaces in characteristic two are investigated from the point of view\nof prime characteristic commutative algebra. In particular, we prove that, the\nnon-Frobenius split cubic surfaces form a linear subspace of codimension four\nin the 19-dimensional space of all cubics, and that up to projective\nequivalence, there are finitely many non-Frobenius split cubic surfaces. We\nexplicitly describe defining equations for each and characterize them as\nextremal in terms of configurations of lines on them. In particular, a\n(possibly singular) cubic surface in characteristic two fails to be Frobenius\nsplit if and only if no three lines on it form a ""triangle"".\n', 'Lines on K3 quartic surfaces in characteristic 3   We investigate the number of straight lines contained in a K3 quartic surface\n\\(X\\) defined over an algebraically closed field of characteristic 3. We prove\nthat if \\(X\\) contains 112 lines, then \\(X\\) is projectively equivalent to the\nFermat quartic surface; otherwise, \\(X\\) contains at most 67 lines. We improve\nthis bound to 58 if \\(X\\) contains a star (ie four distinct lines intersecting\nat a smooth point of \\(X\\)). Explicit equations of three 1-dimensional families\nof smooth quartic surfaces with 58 lines, and of a quartic surface with 8\nsingular points and 48 lines are provided.\n', 'Geometry of Smooth Extremal Surfaces   We study the geometry of the smooth projective surfaces that are defined by\nFrobenius forms, a class of homogenous polynomials in prime characteristic\nrecently shown to have minimal possible F-pure threshold among forms of the\nsame degree. We call these surfaces $\\textit{extremal surfaces}$, and show that\ntheir geometry is reminiscent of the geometry of smooth cubic surfaces,\nespecially non-Frobenius split cubic surfaces of characteristic two, which are\nexamples of extremal surfaces. For example, we show that an extremal surface\n$X$ contains $d^2(d^2-3d+3)$ lines where $d$ is the degree, which is notable\nsince the number of lines on a complex surface is bounded above by a quadratic\nfunction in $d$. Whenever two of those lines meet, they determine a $d$-tangent\nplane to $X$ which consists of a union of $d$ lines meeting in one point; we\ncount the precise number of such ""star points"" on $X$, showing that it is\nquintic in the degree, which recovers the fact that there are exactly 45\nEckardt points on an extremal cubic surface.\n  Finally, we generalize the classical notion of a double six for cubic\nsurfaces to a double $2d$ on an extremal surface of degree $d$. We show that,\nasymptotically in $d$, smooth extremal surfaces have at least\n$\\frac{1}{16}d^{14}$ double $2d$\'s. A key element of the proofs is using the\nlarge automorphism group of extremal surfaces which we show acts transitively\non many sets, such as the set of (triples of skew) lines on the extremal\nsurface. Extremal surfaces are closely related to finite Hermitian geometries,\nwhich we recover as the $\\mathbb F_{q^2}$-rational points of special extremal\nsurfaces defined by Hermitian forms over $\\mathbb F_{q^2}$.\n']","[('quartic surfaces', 0.6757830381393433), ('cubic surfaces', 0.6499011516571045), ('quadratic surfaces', 0.6289579272270203), ('projective surface', 0.5835766196250916), ('cubic hypersurfaces', 0.5718610882759094), ('smooth projective surface', 0.5614315271377563), ('surfaces geometry', 0.5611234307289124), ('surfaces many', 0.5570435523986816), ('cubic surface', 0.5554211735725403), ('lines cubic', 0.5299574732780457)]"
1107,1107,27,1107_witt vectors_witt_mathbb modules_commutative rings,"['witt vectors', 'witt', 'mathbb modules', 'commutative rings', 'dimensional modules', 'rings', 'functor particular', 'functor', 'commutative ring', 'functor well']","['Witt vectors and $\\delta$-Cartier rings   We give a universal property of the construction of the ring of $p$-typical\nWitt vectors of a commutative ring, endowed with Witt vectors Frobenius and\nVerschiebung, and generalize this construction to the derived setting. We\ndefine an $\\infty$-category of $p$-typical derived $\\delta$-Cartier rings and\nshow that the derived ring of $p$-typical Witt vectors of a derived ring is\nnaturally an object in this $\\infty$-category. Moreover, we show that for any\nprime $p$, the formation of the derived ring of $p$-typical Witt vectors gives\nan equivalence between the $\\infty$-category of all derived rings and the full\nsubcategory of all derived $p$-typical $\\delta$-Cartier rings consisting of\n$V$-complete objects.\n', ""Witt vectors with coefficients and TR   We give a new construction of $p$-typical Witt vectors with coefficients in\nterms of ghost maps and show that this construction is isomorphic to the one\ndefined in terms of formal power series from the authors' previous paper. We\nshow that our construction recovers Kaledin's polynomial Witt vectors in the\ncase of vector spaces over a perfect field of characteristic $p$. We then\nidentify the components of the $p$-typical TR with coefficients, originally\ndefined by Lindenstrauss and McCarthy and later reworked by the second and\nthird authors in joint work with McCandless, with the $p$-typical Witt vectors\nwith coefficients. This extends a celebrated result of Hesselholt and\nHesselholt-Madsen relating the components of TR with the Witt vectors. As an\napplication, we given an algebraic description of the components of the\nHill-Hopkins-Ravenel norm for cyclic $p$-groups in terms of $p$-typical Witt\nvectors with coefficients.\n"", '$G$-typical Witt vectors with coefficients and the norm   For a profinite group $G$ we describe an abelian group $W_G(R; M)$ of\n$G$-typical Witt vectors with coefficients in an $R$-module $M$ (where $R$ is a\ncommutative ring). This simultaneously generalises the ring $W_G(R)$ of Dress\nand Siebeneicher and the Witt vectors with coefficients $W(R; M)$ of Dotto,\nKrause, Nikolaus and Patchkoria, both of which extend the usual Witt vectors of\na ring. We use this new variant of Witt vectors to give a purely algebraic\ndescription of the zeroth equivariant stable homotopy groups of the\nHill-Hopkins-Ravenel norm $N_{\\{e\\}}^G(X)$ of a connective spectrum $X$, for\nany finite group $G$. Our construction is reasonably analogous to the\nconstructions of previous variants of Witt vectors, and as such is amenable to\nfairly explicit concrete computations.\n']","[('witt vectors', 0.6815169453620911), ('witt', 0.5135284066200256), ('mathbb modules', 0.4094384014606476), ('commutative rings', 0.40099936723709106), ('dimensional modules', 0.3767167627811432), ('rings', 0.37404412031173706), ('functor particular', 0.3724139928817749), ('functor', 0.36523982882499695), ('commutative ring', 0.3564997911453247), ('functor well', 0.3522179126739502)]"
1108,1108,27,1108_translation surfaces_translation surface_orientable surface genus_veech surfaces,"['translation surfaces', 'translation surface', 'orientable surface genus', 'veech surfaces', 'surfaces infinite', 'orientable surface', 'surfaces', 'closed orientable surface', 'surface infinite', 'surfaces namely']","['Veech groups of covers of the Chamanara surface   We consider finite normal covers of an infinite translation surface with a\nlarge Veech group - the Chamanara surface. We give a characterization for these\ncovers to have Veech groups which are large themselves, that is, which are of\nfinite index in the Veech group of the Chamanara surface. For covers of degree\n2, we study these large Veech groups in detail. As an application, we show that\nevery free group in finitely many generators can be realized as the projective\nVeech group of a translation surface of finite area.\n', 'Canonical translation surfaces for computing Veech groups   For each stratum of the space of translation surfaces, we introduce an\ninfinite translation surface containing in an appropriate manner a copy of\nevery translation surface of the stratum. Given a translation surface $(X,\n\\omega)$ in the stratum, a matrix is in its Veech group $\\mathrm{SL}(X,\\omega)$\nif and only if an associated affine automorphism of the infinite surface sends\neach of a finite set, the ``marked"" {\\em Voronoi staples}, arising from\norientation-paired segments appropriately perpendicular to Voronoi 1-cells, to\nanother pair of orientation-paired ``marked"" segments.\n  We prove a result of independent interest. For each real $a\\ge \\sqrt{2}$\nthere is an explicit hyperbolic ball such that for any Fuchsian group trivially\nstabilizing $i$, the Dirichlet domain centered at $i$ of the group already\nagrees within the ball with the intersection of the hyperbolic half-planes\ndetermined by the group elements whose Frobenius norm is at most $a$. %When\n$\\mathrm{SL}(X,\\omega)$ is a lattice we use this to give a condition\nguaranteeing that the full group $\\mathrm{SL}(X,\\omega)$ has been computed.\n  Together, these results give rise to a new algorithm for computing Veech\ngroups.\n', 'Constructing lattice surfaces with prescribed Veech groups: an algorithm   The Veech group of a translation surface is the group of Jacobians of\norientation-preserving affine automorphisms of the surface. We present an\nalgorithm which constructs all translation surfaces with a given lattice Veech\ngroup in any given stratum. In developing this algorithm, we give a new proof\nof a finiteness result of Smillie and Weiss, namely that there are only\nfinitely many unit-area translation surfaces in any stratum with the same\nlattice Veech group.\n  Our methods can be applied to obtain obstructions of lattices being realized\nas Veech groups in certain strata; in particular, we show that the square torus\nis the only translation surface in any minimal stratum whose Veech group is all\nof $\\mathrm{SL}_2\\mathbb{Z}$.\n']","[('translation surfaces', 0.6693687438964844), ('translation surface', 0.6154914498329163), ('orientable surface genus', 0.5811771154403687), ('veech surfaces', 0.5608392357826233), ('surfaces infinite', 0.5470118522644043), ('orientable surface', 0.5233641862869263), ('surfaces', 0.5003622174263), ('closed orientable surface', 0.4937153458595276), ('surface infinite', 0.4935537278652191), ('surfaces namely', 0.46519169211387634)]"
1109,1109,27,1109_solutions chern simons_blow solutions_chern simons higgs_local well posedness,"['solutions chern simons', 'blow solutions', 'chern simons higgs', 'local well posedness', 'solutions blow', 'solutions chern', 'simons higgs', 'blow dynamics', 'finite time blow', 'critical regularity']","['Soliton resolution for equivariant self-dual Chern-Simons-Schr\\""odinger\n  equation in weighted Sobolev class   We consider the self-dual Chern-Simons-Schr\\""odinger equation (CSS) under\nequivariant symmetry, which is a $L^{2}$-critical equation. It is known that\n(CSS) admits solitons and finite-time blow-up solutions. In this paper, we show\nsoliton resolution for any solutions with equivariant data in the weighted\nSobolev space $H^{1,1}$: every maximal solution decomposes into at most one\nmodulated soliton and a radiation. A striking fact is that the nonscattering\npart must be a single modulated soliton. To our knowledge, this is the first\nresult on soliton resolution in a class of nonlinear Schr\\""odinger equations\nwhich are not known to be completely integrable. The key ingredient is the\ndefocusing nature of the equation in the exterior of a soliton profile. This is\na consequence of two distinctive features of (CSS): self-duality and non-local\nnonlinearity.\n', ""Local well-posedness for the Maxwell-Chern-Simons-Higgs system in\n  Fourier-Lebesgue spaces   We consider local well-posedness for the Maxwell-Chern-Simons-Higgs system in\nLorenz gauge for data with minimal regularity assumptions in Fourier-Lebesgue\nspaces $\\widehat{H}^{s,r}$ , where $\\|u\\|_{\\widehat{H}^{s,r}} := \\| \\langle \\xi\n\\rangle^s \\widehat{u}(\\xi)\\|_{L^{r'}}$ , and $r$ and $r'$ are dual exponents.\nWe show that the gap between this regularity and the regularity with respect to\nscaling shrinks in the case $r>1$ , $r \\to 1$ compared to the classical case\n$r=2$ .\n"", 'Rigidity of smooth finite-time blow-up for equivariant self-dual\n  Chern-Simons-Schr\\""odinger equation   We consider the long time dynamics for the self-dual\nChern-Simons-Schr\\""odinger equation (CSS) within equivariant symmetry. (CSS) is\na self-dual $L^{2}$-critical equation having pseudoconformal invariance and\nsolitons. In this paper, we show that any $m$-equivariant, $m\\geq1$, $H^{3}$\nfinite-time blow-up solution to (CSS) is a pseudoconformal blow-up solution.\nMore precisely, such a solution decomposes into the sum of one modulated\nsoliton that contracts at the pseudoconformal rate $\\lambda(t)\\sim T-t$, and a\nradiation. Applying the pseudoconformal transform in reverse, we also obtain a\nrefined soliton resolution theorem for $m$-equivariant, $m\\geq1$, $H^{3,3}$\nsolutions: any such solutions blow up in the pseudoconformal regime, scatter\n(to $0$), or scatter to a modulated soliton with some fixed scale and phase. To\nour knowledge, this is the first result on the full classification of the\ndynamics of arbitrary smooth and spatially decaying solutions, including the\ndynamics of scale and phase, in the class of nonlinear Schr\\""odinger equations\nwhich are not known to be completely integrable.\n  Our analysis not only builds upon the previous works, especially the soliton\nresolution theorem by the author, Kwon, and Oh, but also refines all steps of\nthe arguments typically employed in the forward construction of blow-up\ndynamics. The key feature of the proof is that we can identify the singular and\nregular parts of any $H^{3}$ finite-time blow-up solutions, such that the\nevolution of the singular part is governed by a universal modulation dynamics\nwhile the regular part is kept $H^{3}$-bounded even up to the blow-up time. As\na byproduct, we also observe that the asymptotic profile has a universal\nsingular structure.\n']","[('solutions chern simons', 0.5371689796447754), ('blow solutions', 0.4885018467903137), ('chern simons higgs', 0.45752760767936707), ('local well posedness', 0.41963163018226624), ('solutions blow', 0.41760382056236267), ('solutions chern', 0.4043596684932709), ('simons higgs', 0.396683007478714), ('blow dynamics', 0.3890182673931122), ('finite time blow', 0.38425391912460327), ('critical regularity', 0.37161046266555786)]"
1110,1110,27,1110_collaborative filtering_recommendation system_recommendation systems_recommender system,"['collaborative filtering', 'recommendation system', 'recommendation systems', 'recommender system', 'recommender systems', 'recommender', 'recommendations', 'recommendation', 'graph attention', 'graph attention network']","[""Collaborative Filtering Based on Diffusion Models: Unveiling the\n  Potential of High-Order Connectivity   A recent study has shown that diffusion models are well-suited for modeling\nthe generative process of user-item interactions in recommender systems due to\ntheir denoising nature. However, existing diffusion model-based recommender\nsystems do not explicitly leverage high-order connectivities that contain\ncrucial collaborative signals for accurate recommendations. Addressing this\ngap, we propose CF-Diff, a new diffusion model-based collaborative filtering\n(CF) method, which is capable of making full use of collaborative signals along\nwith multi-hop neighbors. Specifically, the forward-diffusion process adds\nrandom noise to user-item interactions, while the reverse-denoising process\naccommodates our own learning model, named cross-attention-guided multi-hop\nautoencoder (CAM-AE), to gradually recover the original user-item interactions.\nCAM-AE consists of two core modules: 1) the attention-aided AE module,\nresponsible for precisely learning latent representations of user-item\ninteractions while preserving the model's complexity at manageable levels, and\n2) the multi-hop cross-attention module, which judiciously harnesses high-order\nconnectivity information to capture enhanced collaborative signals. Through\ncomprehensive experiments on three real-world datasets, we demonstrate that\nCF-Diff is (a) Superior: outperforming benchmark recommendation methods,\nachieving remarkable gains up to 7.29% compared to the best competitor, (b)\nTheoretically-validated: reducing computations while ensuring that the\nembeddings generated by our model closely approximate those from the original\ncross-attention, and (c) Scalable: proving the computational efficiency that\nscales linearly with the number of users or items.\n"", ""Criteria Tell You More than Ratings: Criteria Preference-Aware Light\n  Graph Convolution for Effective Multi-Criteria Recommendation   The multi-criteria (MC) recommender system, which leverages MC rating\ninformation in a wide range of e-commerce areas, is ubiquitous nowadays.\nSurprisingly, although graph neural networks (GNNs) have been widely applied to\ndevelop various recommender systems due to GNN's high expressive capability in\nlearning graph representations, it has been still unexplored how to design MC\nrecommender systems with GNNs. In light of this, we make the first attempt\ntowards designing a GNN-aided MC recommender system. Specifically, rather than\nstraightforwardly adopting existing GNN-based recommendation methods, we devise\na novel criteria preference-aware light graph convolution CPA-LGC method, which\nis capable of precisely capturing the criteria preference of users as well as\nthe collaborative signal in complex high-order connectivities. To this end, we\nfirst construct an MC expansion graph that transforms user--item MC ratings\ninto an expanded bipartite graph to potentially learn from the collaborative\nsignal in MC ratings. Next, to strengthen the capability of criteria preference\nawareness, CPA-LGC incorporates newly characterized embeddings, including\nuser-specific criteria-preference embeddings and item-specific criterion\nembeddings, into our graph convolution model. Through comprehensive evaluations\nusing four real-world datasets, we demonstrate (a) the superiority over\nbenchmark MC recommendation methods and benchmark recommendation methods using\nGNNs with tremendous gains, (b) the effectiveness of core components in\nCPA-LGC, and (c) the computational efficiency.\n"", 'Criteria-Aware Graph Filtering: Extremely Fast Yet Accurate\n  Multi-Criteria Recommendation   Multi-criteria (MC) recommender systems, which utilize MC rating information\nfor recommendation, are increasingly widespread in various e-commerce domains.\nHowever, the MC recommendation using training-based collaborative filtering,\nrequiring consideration of multiple ratings compared to single-criterion\ncounterparts, often poses practical challenges in achieving state-of-the-art\nperformance along with scalable model training. To solve this problem, we\npropose CA-GF, a training-free MC recommendation method, which is built upon\ncriteria-aware graph filtering for efficient yet accurate MC recommendations.\nSpecifically, first, we construct an item-item similarity graph using an MC\nuser-expansion graph. Next, we design CA-GF composed of the following key\ncomponents, including 1) criterion-specific graph filtering where the optimal\nfilter for each criterion is found using various types of polynomial low-pass\nfilters and 2) criteria preference-infused aggregation where the smoothed\nsignals from each criterion are aggregated. We demonstrate that CA-GF is (a)\nefficient: providing the computational efficiency, offering the extremely fast\nruntime of less than 0.2 seconds even on the largest benchmark dataset, (b)\naccurate: outperforming benchmark MC recommendation methods, achieving\nsubstantial accuracy gains up to 24% compared to the best competitor, and (c)\ninterpretable: providing interpretations for the contribution of each criterion\nto the model prediction based on visualizations.\n']","[('collaborative filtering', 0.5987051725387573), ('recommendation system', 0.5498754978179932), ('recommendation systems', 0.5440729856491089), ('recommender system', 0.5404468774795532), ('recommender systems', 0.5063523650169373), ('recommender', 0.4907912611961365), ('recommendations', 0.3890778422355652), ('recommendation', 0.3889077603816986), ('graph attention', 0.3861526548862457), ('graph attention network', 0.3803715705871582)]"
1111,1111,27,1111_learnability_learning theory_learnable_pac learning,"['learnability', 'learning theory', 'learnable', 'pac learning', 'information complexity', 'dimension classes', 'online learning', 'hypothesis classes', 'chervonenkis dimension', 'classes']","['Distribution Learnability and Robustness   We examine the relationship between learnability and robust (or agnostic)\nlearnability for the problem of distribution learning. We show that, contrary\nto other learning settings (e.g., PAC learning of function classes), realizable\nlearnability of a class of probability distributions does not imply its\nagnostic learnability. We go on to examine what type of data corruption can\ndisrupt the learnability of a distribution class and what is such learnability\nrobust against. We show that realizable learnability of a class of\ndistributions implies its robust learnability with respect to only additive\ncorruption, but not against subtractive corruption.\n  We also explore related implications in the context of compression schemes\nand differentially private learnability.\n', ""Ramsey Theorems for Trees and a General 'Private Learning Implies Online\n  Learning' Theorem   This work continues to investigate the link between differentially private\n(DP) and online learning. Alon, Livni, Malliaris, and Moran (2019) showed that\nfor binary concept classes, DP learnability of a given class implies that it\nhas a finite Littlestone dimension (equivalently, that it is online learnable).\nTheir proof relies on a model-theoretic result by Hodges (1997), which\ndemonstrates that any binary concept class with a large Littlestone dimension\ncontains a large subclass of thresholds. In a follow-up work, Jung, Kim, and\nTewari (2020) extended this proof to multiclass PAC learning with a bounded\nnumber of labels. Unfortunately, Hodges's result does not apply in other\nnatural settings such as multiclass PAC learning with an unbounded label space,\nand PAC learning of partial concept classes.\n  This naturally raises the question of whether DP learnability continues to\nimply online learnability in more general scenarios: indeed, Alon, Hanneke,\nHolzman, and Moran (2021) explicitly leave it as an open question in the\ncontext of partial concept classes, and the same question is open in the\ngeneral multiclass setting. In this work, we give a positive answer to these\nquestions showing that for general classification tasks, DP learnability\nimplies online learnability. Our proof reasons directly about Littlestone\ntrees, without relying on thresholds. We achieve this by establishing several\nRamsey-type theorems for trees, which might be of independent interest.\n"", 'A Characterization of Multiclass Learnability   A seminal result in learning theory characterizes the PAC learnability of\nbinary classes through the Vapnik-Chervonenkis dimension. Extending this\ncharacterization to the general multiclass setting has been open since the\npioneering works on multiclass PAC learning in the late 1980s. This work\nresolves this problem: we characterize multiclass PAC learnability through the\nDS dimension, a combinatorial dimension defined by Daniely and Shalev-Shwartz\n(2014).\n  The classical characterization of the binary case boils down to empirical\nrisk minimization. In contrast, our characterization of the multiclass case\ninvolves a variety of algorithmic ideas; these include a natural setting we\ncall list PAC learning. In the list learning setting, instead of predicting a\nsingle outcome for a given unseen input, the goal is to provide a short menu of\npredictions.\n  Our second main result concerns the Natarajan dimension, which has been a\ncentral candidate for characterizing multiclass learnability. This dimension\nwas introduced by Natarajan (1988) as a barrier for PAC learning. Whether the\nNatarajan dimension characterizes PAC learnability in general has been posed as\nan open question in several papers since. This work provides a negative answer:\nwe construct a non-learnable class with Natarajan dimension one.\n  For the construction, we identify a fundamental connection between concept\nclasses and topology (i.e., colorful simplicial complexes). We crucially rely\non a deep and involved construction of hyperbolic pseudo-manifolds by\nJanuszkiewicz and Swiatkowski. It is interesting that hyperbolicity is directly\nrelated to learning problems that are difficult to solve although no obvious\nbarriers exist. This is another demonstration of the fruitful links machine\nlearning has with different areas in mathematics.\n']","[('learnability', 0.5651937127113342), ('learning theory', 0.5051071643829346), ('learnable', 0.5010722279548645), ('pac learning', 0.49850994348526), ('information complexity', 0.475869357585907), ('dimension classes', 0.47539642453193665), ('online learning', 0.4152149260044098), ('hypothesis classes', 0.4010651111602783), ('chervonenkis dimension', 0.3950602114200592), ('classes', 0.3922328054904938)]"
1112,1112,27,1112_compressed sensing_decoding_decoder outperforms_sparse signal,"['compressed sensing', 'decoding', 'decoder outperforms', 'sparse signal', 'sparse regression', 'coding scheme', 'orthogonal sparse', 'decoder', 'ldpc codes', 'sparse']","['On Approximate Message Passing for Unsourced Access with Coded\n  Compressed Sensing   Sparse regression codes with approximate message passing (AMP) decoding have\ngained much attention in recent times. The concepts underlying this coding\nscheme extend to unsourced access with coded compressed sensing (CCS), as first\npointed out by Fengler, Jung, and Caire. More specifically, their approach uses\na concatenated coding framework with an inner AMP decoder followed by an outer\ntree decoder. In the original implementation, these two components work\nindependently of each other, with the tree decoder acting on the static output\nof the AMP decoder. This article introduces a novel framework where the inner\nAMP decoder and the outer tree decoder operate in tandem, dynamically passing\ninformation back and forth to take full advantage of the underlying CCS\nstructure. The enhanced architecture exhibits significant performance benefit\nover a range of system parameters. Simulation results are provided to\ndemonstrate the performance benefit offered by the proposed access scheme over\nexisting schemes in the literature.\n', 'Unsourced Random Access with Coded Compressed Sensing: Integrating AMP\n  and Belief Propagation   Sparse regression codes with approximate message passing (AMP) decoding have\ngained much attention in recent times. The concepts underlying this coding\nscheme extend to unsourced random access with coded compressed sensing (CCS),\nas first demonstrated by Fengler, Jung, and Caire. Specifically, their approach\nemploys a concatenated coding framework with an inner AMP decoder followed by\nan outer tree decoder. In their original implementation, these two components\nwork independently of each other, with the tree decoder acting on the static\noutput of the AMP decoder. This article introduces a novel framework where the\ninner AMP decoder and the outer tree decoder operate in tandem, dynamically\npassing information back and forth to take full advantage of the underlying CCS\nstructure. This scheme necessitates the redesign of the tree code as to enable\nbelief propagation in a computationally tractable manner. The enhanced\narchitecture exhibits significant performance benefits over a range of system\nparameters. The error performance of the proposed scheme can be accurately\npredicted through a set of equations, known as state evolution of AMP. These\nfindings are supported both analytically and through numerical methods.\n', 'Capacity-achieving Spatially Coupled Sparse Superposition Codes with AMP\n  Decoding   Sparse superposition codes, also called sparse regression codes (SPARCs), are\na class of codes for efficient communication over the AWGN channel at rates\napproaching the channel capacity. In a standard SPARC, codewords are sparse\nlinear combinations of columns of an i.i.d. Gaussian design matrix, while in a\nspatially coupled SPARC the design matrix has a block-wise structure, where the\nvariance of the Gaussian entries can be varied across blocks. A well-designed\nspatial coupling structure can significantly enhance the error performance of\niterative decoding algorithms such as Approximate Message Passing (AMP).\n  In this paper, we obtain a non-asymptotic bound on the probability of error\nof spatially coupled SPARCs with AMP decoding. Applying this bound to a simple\nband-diagonal design matrix, we prove that spatially coupled SPARCs with AMP\ndecoding achieve the capacity of the AWGN channel. The bound also highlights\nhow the decay of error probability depends on each design parameter of the\nspatially coupled SPARC. An attractive feature of AMP decoding is that its\nasymptotic mean squared error (MSE) can be predicted via a deterministic\nrecursion called state evolution. Our result provides the first proof that the\nMSE concentrates on the state evolution prediction for spatially coupled\ndesigns. Combined with the state evolution prediction, this result implies that\nspatially coupled SPARCs with the proposed band-diagonal design are\ncapacity-achieving. Using the proof technique used to establish the main\nresult, we also obtain a concentration inequality for the MSE of AMP applied to\ncompressed sensing with spatially coupled design matrices. Finally we provide\nnumerical simulation results that demonstrate the finite length error\nperformance of spatially coupled SPARCs. The performance is compared with coded\nmodulation schemes that use LDPC codes from the DVB-S2 standard.\n']","[('compressed sensing', 0.5474821329116821), ('decoding', 0.5286745429039001), ('decoder outperforms', 0.5256049036979675), ('sparse signal', 0.4979332983493805), ('sparse regression', 0.4927862584590912), ('coding scheme', 0.48578375577926636), ('orthogonal sparse', 0.4603078067302704), ('decoder', 0.45983415842056274), ('ldpc codes', 0.42154771089553833), ('sparse', 0.41920003294944763)]"
1113,1113,27,1113_flatness based control_triangular form_systems flat_system flat,"['flatness based control', 'triangular form', 'systems flat', 'system flat', 'control affine systems', 'flat outputs', 'affine systems', 'feedback linearization', 'systems generalized', 'normal forms']","['A Structurally Flat Triangular Form Based on the Extended Chained Form   In this paper, we present a structurally flat triangular form which is based\non the extended chained form. We provide a complete geometric characterization\nof the proposed triangular form in terms of necessary and sufficient conditions\nfor an affine input system with two inputs to be static feedback equivalent to\nthis triangular form. This yields a sufficient condition for an affine input\nsystem to be flat.\n', 'Differential-Geometric Decomposition of Flat Nonlinear Discrete-Time\n  Systems   We prove that every flat nonlinear discrete-time system can be decomposed by\ncoordinate transformations into a smaller-dimensional subsystem and an\nendogenous dynamic feedback. For flat continuous-time systems, no comparable\nresult is available. The advantage of such a decomposition is that the complete\nsystem is flat if and only if the subsystem is flat. Thus, by repeating the\ndecomposition at most $n-1$ times, where $n$ is the dimension of the state\nspace, the flatness of a discrete-time system can be checked in an algorithmic\nway. If the system is flat, then the algorithm yields a flat output which only\ndepends on the state variables. Hence, every flat discrete-time system has a\nflat output which does not depend on the inputs and their forward-shifts.\nAgain, no comparable result for flat continuous-time systems is available. The\nalgorithm requires in each decomposition step the construction of state- and\ninput transformations, which are obtained by straightening out certain vector\nfields or distributions with the flow-box theorem or the Frobenius theorem.\nThus, from a computational point of view, only the calculation of flows and the\nsolution of algebraic equations is needed. We illustrate our results by two\nexamples.\n', 'On a Flat Triangular Form Based on the Extended Chained Form   In this paper, we present a structurally flat triangular form which is based\non the extended chained form. We provide necessary and sufficient conditions\nfor an affine input system with two inputs to be static feedback equivalent to\nthe proposed triangular form, and thus a sufficient condition for an affine\ninput system to be flat.\n']","[('flatness based control', 0.5642570853233337), ('triangular form', 0.5414245128631592), ('systems flat', 0.5295072197914124), ('system flat', 0.52210932970047), ('control affine systems', 0.5219174027442932), ('flat outputs', 0.5073337554931641), ('affine systems', 0.48649123311042786), ('feedback linearization', 0.4391581416130066), ('systems generalized', 0.428539901971817), ('normal forms', 0.42331603169441223)]"
1114,1114,27,1114_regular graphs girth_regular graph girth_graphs girth_graph girth,"['regular graphs girth', 'regular graph girth', 'graphs girth', 'graph girth', 'regular graphs', 'regular graph order', 'regular graph', 'graph regular graph', 'order graphs', 'biregular graphs']","['A note on girth-diameter cages   In this paper, we introduce a problem closely related to the Cage Problem and\nthe Degree Diameter Problem. For integers $k\\geq 2$, $g\\geq 3$ and $d\\geq 1$,\nwe define a $(k;\\, g,d)$-graph to be a $k$-regular graph with girth $g$ and\ndiameter $d$. We denote by $n_0(k;\\,g,d)$ the smallest possible order of such a\ngraph, and, if such a graph exists, we call it a $(k;g,d)$-cage. In particular,\nwe focus on $(k;\\,5,4)$-graphs. We show that $n_0(k;\\,5,4) \\geq k^2+k+2$ for\nall $k$, and report on the determination of all $(k;\\,5,4)$-cages for $k=3, 4$\nand $5$ and examples with $k = 6$, and describe some examples of\n$(k;\\,5,4)$-graphs which prove that $n_0(k;\\,5,4) \\leq 2k^2$ for infinitely\nmany values of $k$.\n', 'Exhaustive generation of edge-girth-regular graphs   Edge-girth-regular graphs (abbreviated as $egr$ graphs) are a class of highly\nregular graphs. More specifically, for integers $v$, $k$, $g$ and $\\lambda$ an\n$egr(v,k,g,\\lambda)$ graph is a $k$-regular graph with girth $g$ on $v$\nvertices such that every edge is contained in exactly $\\lambda$ cycles of\nlength $g$. The central problem in this paper is determining $n(k,g,\\lambda)$,\nwhich is defined as the smallest integer $v$ such that an $egr(v,k,g,\\lambda)$\ngraph exists (or $\\infty$ if no such graph exists) as well as determining the\ncorresponding extremal graphs. We propose a linear time algorithm for computing\nhow often an edge is contained in a cycle of length $g$, given a graph with\ngirth $g$. We use this as one of the building blocks to propose another\nalgorithm that can exhaustively generate all $egr(v,k,g,\\lambda)$ graphs for\nfixed parameters $v, k, g$ and $\\lambda$. We implement this algorithm and use\nit in a large-scale computation to obtain several new extremal graphs and\nimprovements for lower and upper bounds from the literature for\n$n(k,g,\\lambda)$. Among others, we show that $n(3,6,2)=24, n(3,8,8)=40,\nn(3,9,6)=60, n(3,9,8)=60, n(4,5,1)=30, n(4,6,9)=35, n(6,5,20)=42$ and we\ndisprove a conjecture made by Araujo-Pardo and Leemans [Discrete Math.\n345(10):112991 (2022)] for the cubic girth 8 and girth 12 cases. Based on our\ncomputations, we conjecture that\n$n(3,7,6)=n(3,8,10)=n(3,8,12)=n(3,8,14)=\\infty.$\n', 'On vertex-girth-regular graphs: (Non-)existence, bounds and enumeration   A vertex-girth-regular $vgr(v,k,g,\\lambda)$-graph is a $k$-regular graph of\ngirth $g$ and order $v$ in which every vertex belongs to exactly $\\lambda$\ncycles of length $g$. While all vertex-transitive graphs are necessarily\nvertex-girth-regular, the majority of vertex-girth-regular graphs are not\nvertex-transitive. Similarly, while many of the smallest $k$-regular graphs of\ngirth $g$, the so-called $(k,g)$-cages, are vertex-girth-regular, infinitely\nmany vertex-girth-regular graphs of degree $k$ and girth $g$ exist for many\npairs $k,g$. Due to these connections, the study of vertex-girth-regular graphs\npromises insights into the relations between the classes of extremal, highly\nsymmetric, and locally regular graphs of given degree and girth. This paper\nlays the foundation to such study by investigating the fundamental properties\nof $vgr(v,k,g,\\lambda)$-graphs, specifically the relations necessarily\nsatisfied by the parameters $v,k,g$ and $\\lambda$ to admit the existence of a\ncorresponding vertex-girth-regular graph, by presenting constructions of\ninfinite families of $vgr(v,k,g,\\lambda)$-graphs, and by establishing lower\nbounds on the number $v$ of vertices in a $vgr(v,k,g,\\lambda)$-graph. It also\nincludes computational results determining the orders of smallest cubic and\nquartic graphs of small girths.\n']","[('regular graphs girth', 0.7177716493606567), ('regular graph girth', 0.7095779180526733), ('graphs girth', 0.6517302989959717), ('graph girth', 0.6376495957374573), ('regular graphs', 0.6229751110076904), ('regular graph order', 0.6172069311141968), ('regular graph', 0.5923910737037659), ('graph regular graph', 0.5874102711677551), ('order graphs', 0.5558324456214905), ('biregular graphs', 0.5525971055030823)]"
1115,1115,27,1115_partition graph_vertex partition_coalitions_coalition,"['partition graph', 'vertex partition', 'coalitions', 'coalition', 'graph consists', 'every vertex adjacent', 'graph maximum', 'vertex setminus', 'graphs let graph', 'graph maximum number']","['On the coalition number of trees   Let $G$ be a graph with vertex set $V$ and of order $n = |V|$, and let\n$\\delta(G)$ and $\\Delta(G)$ be the minimum and maximum degree of $G$,\nrespectively. Two disjoint sets $V_1, V_2 \\subseteq V$ form a coalition in $G$\nif none of them is a dominating set of $G$ but their union $V_1\\cup V_2$ is. A\nvertex partition $\\Psi=\\{V_1,\\ldots, V_k\\}$ of $V$ is a coalition partition of\n$G$ if every set $V_i\\in \\Psi$ is either a dominating set of $G$ with the\ncardinality $|V_i|=1$, or is not a dominating set but for some $V_j\\in \\Psi$,\n$V_i$ and $V_j$ form a coalition. The maximum cardinality of a coalition\npartition of $G$ is the coalition number $\\mathcal{C}(G)$ of $G$. Given a\ncoalition partition $\\Psi = \\{V_1, \\ldots, V_k\\}$ of $G$, a coalition graph\n$\\CG(G, \\Psi)$ is associated on $\\Psi$ such that there is a one-to-one\ncorrespondence between its vertices and the members of $\\Psi$, where two\nvertices of $\\CG(G, \\Psi)$ are adjacent if and only if the corresponding sets\nform a coalition in $G$. In this paper, we partially solve one of the open\nproblems posed in Haynes et al. \\cite{coal0} and we solve two open problems\nposed by Haynes et al. \\cite{coal1}. We characterize all graphs $G$ with\n$\\delta(G) \\le 1$ and $\\mathcal{C}(G)=n$, and we characterize all trees $T$\nwith $\\mathcal{C}(T)=n-1$. We determine the number of coalition graphs that can\nbe defined by all coalition partitions of a given path. Furthermore, we show\nthat there is no universal coalition path, a path whose coalition partitions\ndefines all possible coalition graphs.\n', 'Coalition of cubic graphs of order at most $10$   The coalition in a graph $G$ consists of two disjoint sets of vertices\n$V_{1}$ and $V_{2}$, neither of which is a dominating set but whose union\n$V_{1}\\cup V_{2}$, is a dominating set. A coalition partition in a graph $G$ is\na vertex partition $\\pi$ = $\\{V_1, V_2,..., V_k \\}$ such that every set $V_i\n\\in \\pi$ is not a dominating set but forms a coalition with another set $V_j\\in\n\\pi$ which is not a dominating set. The coalition number $C(G)$ equals the\nmaximum $k$ of a coalition partition of $G$. In this paper, we compute the\ncoalition number of all cubic graphs of order at most $10$.\n', 'Introduction to total coalitions in graphs   Let $G$ be a graph with vertex set $V$. Two disjoint sets $V_1, V_2\\subseteq\nV$ are called a total coalition in $G$, if neither $V_1$ and $V_2$ is a total\ndominating set of $G$ but $V_1\\cup V_2$ is a total dominating set. A total\ncoalition partition of $G$ is a vertex partition $\\pi=\\{V_1,V_2,\\ldots, V_k\\}$\nsuch that no set of $\\pi$ is a total dominating set but each set $V_i\\in \\pi$\nforms a total coalition with another set $V_j\\in \\pi$. The maximum cardinality\nof a total coalition partition of $G$ is called the total coalition number of\n$G$, denoted by $TC(G)$. In this paper, we initiate the study of the total\ncoalition in graphs and its properties.\n']","[('partition graph', 0.5273048877716064), ('vertex partition', 0.5122318863868713), ('coalitions', 0.4758926033973694), ('coalition', 0.4517030119895935), ('graph consists', 0.4273185431957245), ('every vertex adjacent', 0.4191276431083679), ('graph maximum', 0.4151613712310791), ('vertex setminus', 0.4128219783306122), ('graphs let graph', 0.41125598549842834), ('graph maximum number', 0.4083304703235626)]"
1116,1116,27,1116_line arrangements_arrangements complex projective_line arrangement_conic line arrangements,"['line arrangements', 'arrangements complex projective', 'line arrangement', 'conic line arrangements', 'free arrangements', 'arrangements particular', 'arrangements complex', 'plane arrangements', 'arrangements', 'arrangements mathbb']","[""On the numerical Terao's conjecture and Ziegler pairs for line\n  arrangements   In this paper we present a smallest possible counterexample to the Numerical\nTerao's Conjecture in the class of line arrangements in the complex projective\nplane. Our example consists of a pair of two arrangements with $13$ lines.\nMoreover, we use the newly discovered singular matroid realization spaces to\nconstruct new examples of pairs of line arrangements having the same underlying\nmatroid but different free resolutions of the Milnor algebras. Such rare\narrangements are called Ziegler pairs in the literature.\n"", 'On free line arrangements with double, triple and quadruple points   We show that there are only finitely many combinatorial types of free real\nline arrangements with only double, triple and quadruple intersection points,\nand we enlist all admissible weak-combinatorics of them. Then we classify all\nreal $M$-line arrangements. In particular, we show that real $M$-line\narrangements are simplicial.\n', 'On combinatorics of plus-one generated line arrangements   In this note we focus on combinatorial aspects of plus-one generated line\narrangements. We provide combinatorial constraints on such arrangements and we\nconstruct a polynomial that decodes the plus-one generated property. We present\nnew examples of plus-one generated arrangements constructed by using classical\nKlein and Wiman reflection arrangements, and we detect, among all known\nsporadic simplicial arrangements up to $27$ lines, exactly $9$ arrangements\nthat are minimal plus-one generated.\n']","[('line arrangements', 0.6480913758277893), ('arrangements complex projective', 0.6398875713348389), ('line arrangement', 0.5964239239692688), ('conic line arrangements', 0.5661579370498657), ('free arrangements', 0.5542963743209839), ('arrangements particular', 0.5431399941444397), ('arrangements complex', 0.5428758859634399), ('plane arrangements', 0.5313359498977661), ('arrangements', 0.5111998915672302), ('arrangements mathbb', 0.4984704256057739)]"
1117,1117,27,1117_codes achieve capacity_binary memoryless_coding schemes_constrained coding,"['codes achieve capacity', 'binary memoryless', 'coding schemes', 'constrained coding', 'binary memoryless symmetric', 'memoryless symmetric bms', 'capacity binary', 'reed muller codes', 'muller rm codes', 'codes achieve']","['Managing Device Lifecycle: Reconfigurable Constrained Codes for\n  M/T/Q/P-LC Flash Memories   Flash memory devices are winning the competition for storage density against\nmagnetic recording devices. This outcome results from advances in physics that\nallow storage of more than one bit per cell, coupled with advances in signal\nprocessing that reduce the effect of physical instabilities. Constrained codes\nare used in storage to avoid problematic patterns. Recently, we introduced\nbinary symmetric lexicographically-ordered constrained codes (LOCO codes) for\ndata storage and data transmission. This paper introduces simple constrained\ncodes that support non-binary physical substrates; multi, triple, quad, and the\ncurrently-in-development penta-level cell (M/T/Q/P-LC) Flash memories. The new\ncodes can be easily modified if problematic patterns change with time. These\ncodes are designed to mitigate inter-cell interference, which is a critical\nsource of error in Flash devices. The occurrence of errors is a consequence of\nparasitic capacitances in and across floating gate transistors, resulting in\ncharge propagation from cells being programmed to the highest charge level to\nneighboring cells being programmed to lower levels. The new codes are called\n$q$-ary asymmetric LOCO codes (QA-LOCO codes), and the construction subsumes\ncodes previously designed for single-level cell (SLC) Flash devices (A-LOCO\ncodes). QA-LOCO codes work for a Flash device with any number, $q$, of levels\nper cell. For $q \\geq 4$, we show that QA-LOCO codes can achieve rates greater\nthan $0.95 \\log_2 q$ information bits per coded symbol. The complexity of\nencoding and decoding is modest, and reconfiguring a code is as easy as\nreprogramming an adder. Capacity-achieving rates, affordable encoding-decoding\ncomplexity, and ease of reconfigurability support the growing development of\nM/T/Q/P-LC Flash memory devices, as well as lifecycle management as the\ncharacteristics of these devices change with time.\n', 'Reed-Muller Codes on BMS Channels Achieve Vanishing Bit-Error\n  Probability for All Rates Below Capacity   This paper considers the performance of Reed-Muller (RM) codes transmitted\nover binary memoryless symmetric (BMS) channels under bitwise\nmaximum-a-posteriori (bit-MAP) decoding. Its main result is that, for a fixed\nBMS channel, the family of binary RM codes can achieve a vanishing bit-error\nprobability at rates approaching the channel capacity. This partially resolves\na long-standing open problem that connects information theory and\nerror-correcting codes. In contrast with the earlier result for the binary\nerasure channel, the new proof does not rely on hypercontractivity. Instead, it\ncombines a nesting property of RM codes with new information inequalities\nrelating the generalized extrinsic information transfer function and the\nextrinsic minimum mean-squared error.\n', 'Read-and-Run Constrained Coding for Modern Flash Devices   The pivotal storage density win achieved by solid-state devices over magnetic\ndevices in 2015 is a result of multiple innovations in physics, architecture,\nand signal processing. One of the most important innovations in that regard is\nenabling the storage of more than one bit per cell in the Flash device, i.e.,\nhaving more than two charge levels per cell. Constrained coding is used in\nFlash devices to increase reliability via mitigating inter-cell interference\nthat stems from charge propagation among cells. Recently, capacity-achieving\nconstrained codes were introduced to serve that purpose in modern Flash\ndevices, which have more than two levels per cell. While these codes result in\nminimal redundancy via exploiting the underlying physics, they result in\nnon-negligible complexity increase and access speed limitation since pages\ncannot be read separately. In this paper, we suggest new constrained coding\nschemes that have low-complexity and preserve the desirable high access speed\nin modern Flash devices. The idea is to eliminate error-prone patterns by\ncoding data only on the left-most page while leaving data on all the remaining\npages uncoded. Our coding schemes work for any number of levels per cell, offer\nsystematic encoding and decoding, and are capacity-approaching. Since the\nproposed schemes enable the separation of pages, we refer to them as\nread-and-run (RR) constrained coding schemes as opposed to schemes adopting\nread-and-wait for other pages. We analyze the new RR coding schemes and discuss\ntheir impact on the probability of occurrence of different charge levels. We\nalso demonstrate the performance improvement achieved via RR coding on a\npractical triple-level cell Flash device.\n']","[('codes achieve capacity', 0.6028295159339905), ('binary memoryless', 0.5275400280952454), ('coding schemes', 0.5132842659950256), ('constrained coding', 0.4934699237346649), ('binary memoryless symmetric', 0.4749228358268738), ('memoryless symmetric bms', 0.47413626313209534), ('capacity binary', 0.4653168320655823), ('reed muller codes', 0.4540655314922333), ('muller rm codes', 0.4442606270313263), ('codes achieve', 0.43955159187316895)]"
1118,1118,27,1118_homology equivariant_equivariant coarse_topological equivariant_homology theories,"['homology equivariant', 'equivariant coarse', 'topological equivariant', 'homology theories', 'homology theory', 'co homology theories', 'category equivariant', 'ordinary homology', 'homology', 'co homology']","['Topological equivariant coarse K-homology   For a $C^{*}$-category with a strict $G$-action we construct examples of\nequivariant coarse homology theories. To this end we first introduce versions\nof Roe categories of objects in $C^{*}$-categories which are controlled over\nbornological coarse spaces, and then apply a homological functor. These\nequivariant coarse homology theories are then employed to verify that certain\nfunctors on the orbit category are CP-functors. This fact has consequences for\nthe injectivity of assembly maps.\n', 'Equivariant coarse homotopy theory and coarse algebraic\n  $\\boldsymbol{K}$-homology   We study equivariant coarse homology theories through an axiomatic framework.\nTo this end we introduce the category of equivariant bornological coarse spaces\nand construct the universal equivariant coarse homology theory with values in\nthe category of equivariant coarse motivic spectra. As examples of equivariant\ncoarse homology theories we discuss equivariant coarse ordinary homology and\nequivariant coarse algebraic $K$-homology. Moreover, we discuss the cone\nfunctor, its relation with equivariant homology theories in equivariant\ntopology, and assembly and forget-control maps. This is a preparation for\napplications in subsequent papers aiming at split-injectivity results for the\nFarrell-Jones assembly map.\n', 'Transfers in coarse homology   We enlarge the category of bornological coarse spaces by adding transfer\nmorphisms and introduce the notion of an equivariant coarse homology theory\nwith transfers. We then show that equivariant coarse algebraic $K$-homology and\nequivariant coarse ordinary homology can be extended to equivariant coarse\nhomology theories with transfers. In the case of a finite group we observe that\nequivariant coarse homology theories with transfers provide Mackey functors. We\nexpress standard constructions with Mackey functors in terms of coarse\ngeometry, and we demonstrate the usage of transfers in order to prove\ninjectivity results about assembly maps.\n']","[('homology equivariant', 0.7364957332611084), ('equivariant coarse', 0.6524533033370972), ('topological equivariant', 0.6295997500419617), ('homology theories', 0.6281646490097046), ('homology theory', 0.6145645380020142), ('co homology theories', 0.5884537100791931), ('category equivariant', 0.5687803030014038), ('ordinary homology', 0.5662475228309631), ('homology', 0.5546442866325378), ('co homology', 0.507285475730896)]"
1119,1119,27,1119_periodic traveling waves_wave solutions_periodic traveling_solitary waves,"['periodic traveling waves', 'wave solutions', 'periodic traveling', 'solitary waves', 'hamilton equations', 'solitary wave', 'wave interactions', 'traveling waves', 'perturbation periodic', 'traveling wave']","[""Micropteron traveling waves in diatomic Fermi-Pasta-Ulam-Tsingou\n  lattices under the equal mass limit   The diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice is an infinite chain of\nalternating particles connected by identical nonlinear springs. We prove the\nexistence of micropteron traveling waves in the diatomic FPUT lattice in the\nlimit as the ratio of the two alternating masses approaches 1, at which point\nthe diatomic lattice reduces to the well-understood monatomic FPUT lattice.\nThese are traveling waves whose profiles asymptote to a small periodic\noscillation at infinity, instead of vanishing like the classical solitary wave.\nWe produce these micropteron waves using a functional analytic method,\noriginally due to Beale, that was successfully deployed in the related long\nwave and small mass diatomic problems. Unlike the long wave and small mass\nproblems, this equal mass problem is not singularly perturbed, and so the\namplitude of the micropteron's oscillation is not necessarily small beyond all\norders (i.e., the traveling wave that we find is not necessarily a nanopteron).\nThe central challenge of this equal mass problem hinges on a hidden solvability\ncondition in the traveling wave equations, which manifests itself in the\nexistence and fine properties of asymptotically sinusoidal solutions (Jost\nsolutions) to an auxiliary advance-delay differential equation.\n"", 'Micropterons, Nanopterons and Solitary Wave Solutions to the Diatomic\n  Fermi-Pasta-Ulam-Tsingou Problem   We use a specialized boundary-value problem solver for mixed-type functional\ndifferential equations to numerically examine the landscape of traveling wave\nsolutions to the diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) problem. By using a\ncontinuation approach, we are able to uncover the relationship between the\nbranches of micropterons and nanopterons that have been rigorously constructed\nrecently in various limiting regimes. We show that the associated surfaces are\nconnected together in a nontrivial fashion and illustrate the key role that\nsolitary waves play in the branch points. Finally, we numerically show that the\ndiatomic solitary waves are stable under the full dynamics of the FPUT system.\n', ""Energy-recurrence Breakdown and Chaos in Disordered\n  Fermi-Pasta-Ulam-Tsingou Lattices   In this paper, we consider the classic Fermi-Pasta-Ulam-Tsingou system as a\nmodel of interacting particles connected by harmonic springs with a quadratic\nnonlinear term (first system) and a set of second-order ordinary differential\nequations with variability (second system) that resembles Hamilton's equations\nof motion of the Fermi-Pasta-Ulam-Tsingou system. In the absence of\nvariability, the second system becomes Hamilton's equations of motion of the\nFermi-Pasta-Ulam-Tsingou system (first system). Variability is introduced to\nHamilton's equations of motion of the Fermi-Pasta-Ulam-Tsingou system to take\ninto account inherent variations (for example, due to manufacturing processes),\ngiving rise to heterogeneity in its parameters. We demonstrate that a\npercentage of variability smaller than a threshold can break the well-known\nenergy recurrence phenomenon and induce localization in the energy normal-mode\nspace. However, percentage of variability larger than the threshold may make\nthe trajectories of the second system blow up in finite time. Using a\nmultiple-scale expansion, we derive analytically a two normal-mode\napproximation that explains the mechanism for energy localization and blow up\nin the second system. We also investigate the chaotic behavior of the two\nsystems as the percentage of variability is increased, utilising the maximum\nLyapunov exponent and Smaller Alignment Index. Our analysis shows that when\nthere is almost energy localization in the second system, it is more probable\nto observe chaos, as the number of particles increases.\n""]","[('periodic traveling waves', 0.5225685238838196), ('wave solutions', 0.45936644077301025), ('periodic traveling', 0.4547584354877472), ('solitary waves', 0.44157323241233826), ('hamilton equations', 0.4303860068321228), ('solitary wave', 0.42637762427330017), ('wave interactions', 0.41986286640167236), ('traveling waves', 0.4171299934387207), ('perturbation periodic', 0.39273393154144287), ('traveling wave', 0.38214966654777527)]"
1120,1120,27,1120_irreducible unitary representations_dirac cohomology_irreducible unitary representation_unitary representations,"['irreducible unitary representations', 'dirac cohomology', 'irreducible unitary representation', 'unitary representations', 'exceptional lie groups', 'unitary representation', 'irreducible unitary', 'type dirac', 'representations gl', 'representations non']","[""A non-vanishing criterion for Dirac cohomology   This paper gives a criterion for the non-vanishing of the Dirac cohomology of\n$\\mathcal{L}_S(Z)$, where $\\mathcal{L}_S(\\cdot)$ is the cohomological induction\nfunctor, while the inducing module $Z$ is irreducible, unitarizable, and in the\ngood range. As an application, we give a formula counting the number of strings\nin the Dirac series. Using this formula, we classify all the irreducible\nunitary representations of $E_{6(2)}$ with non-zero Dirac cohomology. Our\ncalculation continues to support Conjecture 5.7' of Salamanca-Riba and Vogan\n[SV]. Moreover, we find more unitary representations for which cancellation\nhappens between the even part and the odd part of their Dirac cohomology.\n"", ""Dirac series of $E_{7(7)}$   This paper classifies all the Dirac series (that is, irreducible unitary\nrepresentations having non-zero Dirac cohomology) of $E_{7(7)}$. Enhancing the\nHelgason-Johnson bound in 1969 for the group $E_{7(7)}$ is one key ingredient.\nOur calculation partially supports Vogan's fundamental parallelepiped (FPP)\nconjecture. As applications, when passing to Dirac index, we continue to find\ncancellation between the even part and the odd part of Dirac cohomology.\nMoreover, for the first time, we find Dirac series whose spin lowest $K$-types\nhave multiplicities.\n"", 'Dirac series of $E_{7(-5)}$   Using the sharpened Helgason-Johnson bound, this paper classifies all the\nirreducible unitary representations with non-zero Dirac cohomology of\n$E_{7(-5)}$. As an application, we find that the cancellation between the even\npart and the odd part of the Dirac cohomology continues to happen for certain\nunitary representations of $E_{7(-5)}$. Assuming the infinitesimal character\nbeing integral, we further improve the Helgason-Johnson bound for $E_{7(-5)}$.\nThis should help people to understand (part of) the unitary dual of this group.\n']","[('irreducible unitary representations', 0.563679039478302), ('dirac cohomology', 0.5600199699401855), ('irreducible unitary representation', 0.5528765320777893), ('unitary representations', 0.5204543471336365), ('exceptional lie groups', 0.48879092931747437), ('unitary representation', 0.48669007420539856), ('irreducible unitary', 0.48595911264419556), ('type dirac', 0.44805416464805603), ('representations gl', 0.4343598186969757), ('representations non', 0.42928650975227356)]"
1121,1121,27,1121_combinatorial hopf algebra_combinatorial hopf algebras_combinatorial hopf_invariants combinatorial,"['combinatorial hopf algebra', 'combinatorial hopf algebras', 'combinatorial hopf', 'invariants combinatorial', 'hopf algebras', 'hopf algebraic', 'hopf algebra', 'generalized permutohedra', 'monoid structure', 'monoids']","['The Hopf monoid of hypergraphs and its sub-monoids: basic invariant and\n  reciprocity theorem   In arXiv:1709.07504 Ardila and Aguiar give a Hopf monoid structure on\nhypergraphs as well as a general construction of polynomial invariants on Hopf\nmonoids. Using these results, we define in this paper a new polynomial\ninvariant on hypergraphs. We give a combinatorial interpretation of this\ninvariant on negative integers which leads to a reciprocity theorem on\nhypergraphs. Finally, we use this invariant to recover well-known invariants on\nother combinatorial objects (graphs, simplicial complexes, building sets etc)\nas well as the associated reciprocity theorems.\n', 'Hopf monoids of ordered simplicial complexes   We study ordered matroids and generalized permutohedra from a Hopf theoretic\npoint of view. Our main object is a Hopf monoid in the vector species of\nextended generalized permutahedra equipped with an order of the coordinates;\nthis monoid extends the Hopf monoid of generalized permutahedra studied by\nAguiar and Ardila. Our formula for the antipode is cancellation-free and\nmultiplicity-free, and is supported only on terms that are compatible with the\nlocal geometry of the polyhedron. Our result is part of a larger program to\nunderstand orderings on ground sets of simplicial complexes (for instance, on\nshifted and matroid independence complexes). In this vein, we show that shifted\nsimplicial complexes and broken circuit complexes generate Hopf monoids that\nare expected to exhibit similar behavior.\n', 'Combinatorial expressions of Hopf polynomial invariants   In 2017 Aguiar and Ardila provided a generic way to construct polynomial\ninvariants of combinatorial objects using the notions of Hopf monoids and\ncharacters of Hopf monoids. They show that it is possible to find a\ncombinatorial interpretation of these polynomials over negative integers using\nthe antipode and give a cancellation-free grouping-free formula for the\nantipode on generalized permutahedra. In this work, we give a combinatorial\ninterpretation of these polynomials over both positive integers and negative\nintegers for the Hopf monoids of generalized permutahedra and hypergraphs and\nfor every character on these two Hopf monoids. In the case of hypergraphs, we\npresent two different proofs for the interpretation on negative integers. We\nthen deduce similar results on other combinatorial objects including graphs,\nsimplicial complexes and building sets.\n']","[('combinatorial hopf algebra', 0.6088751554489136), ('combinatorial hopf algebras', 0.6042057871818542), ('combinatorial hopf', 0.5706731081008911), ('invariants combinatorial', 0.569217324256897), ('hopf algebras', 0.529546320438385), ('hopf algebraic', 0.5043015480041504), ('hopf algebra', 0.5038955807685852), ('generalized permutohedra', 0.4956580400466919), ('monoid structure', 0.4777553975582123), ('monoids', 0.4737245440483093)]"
1122,1122,27,1122_ranking pairwise_comparison models_pairwise comparisons_ranking,"['ranking pairwise', 'comparison models', 'pairwise comparisons', 'ranking', 'rankings', 'score estimation', 'rank aggregation', 'pairwise comparison', 'comparisons', 'bradley terry']","['The incomplete Analytic Hierarchy Process and Bradley-Terry model:\n  (in)consistency and information retrieval   Several methods of preference modeling, ranking, voting and multi-criteria\ndecision making include pairwise comparisons. It is usually simpler to compare\ntwo objects at a time, furthermore, some relations (e.g., the outcome of sports\nmatches) are naturally known for pairs. This paper investigates and compares\npairwise comparison models and the stochastic Bradley-Terry model. It is proved\nthat they provide the same priority vectors for consistent (complete or\nincomplete) comparisons. For incomplete comparisons, all filling in levels are\nconsidered. Recent results identified the optimal subsets and sequences of\nmultiplicative/additive/reciprocal pairwise comparisons for small sizes of\nitems (up to n = 6). Simulations of this paper show that the same subsets and\nsequences are optimal in case of the Bradley-Terry and the Thurstone models as\nwell. This, somehow surprising, coincidence suggests the existence of a more\ngeneral result. Further models of information and preference theory are subject\nto future investigation in order to identify optimal subsets of input data.\n', 'Generalized Results for the Existence and Consistency of the MLE in the\n  Bradley-Terry-Luce Model   Ranking problems based on pairwise comparisons, such as those arising in\nonline gaming, often involve a large pool of items to order. In these\nsituations, the gap in performance between any two items can be significant,\nand the smallest and largest winning probabilities can be very close to zero or\none. Furthermore, each item may be compared only to a subset of all the items,\nso that not all pairwise comparisons are observed. In this paper, we study the\nperformance of the Bradley-Terry-Luce model for ranking from pairwise\ncomparison data under more realistic settings than those considered in the\nliterature so far. In particular, we allow for near-degenerate winning\nprobabilities and arbitrary comparison designs. We obtain novel results about\nthe existence of the maximum likelihood estimator (MLE) and the corresponding\n$\\ell_2$ estimation error without the bounded winning probability assumption\ncommonly used in the literature and for arbitrary comparison graph topologies.\nCentral to our approach is the reliance on the Fisher information matrix to\nexpress the dependence on the graph topologies and the impact of the values of\nthe winning probabilities on the estimation risk and on the conditions for the\nexistence of the MLE. Our bounds recover existing results as special cases but\nare more broadly applicable.\n', 'Asymptotic comparison of identifying constraints for Bradley-Terry\n  models   The Bradley-Terry model is widely used for pairwise comparison data analysis.\nIn this paper, we analyze the asymptotic behavior of the maximum likelihood\nestimator of the Bradley-Terry model in its logistic parameterization, under a\ngeneral class of linear identifiability constraints. We show that the\nconstraint requiring the Bradley-Terry scores for all compared objects to sum\nto zero minimizes the sum of the variances of the estimated scores, and\nrecommend using this constraint in practice.\n']","[('ranking pairwise', 0.5615002512931824), ('comparison models', 0.5169150233268738), ('pairwise comparisons', 0.48270824551582336), ('ranking', 0.4812648296356201), ('rankings', 0.4726239740848541), ('score estimation', 0.4546499252319336), ('rank aggregation', 0.4540490210056305), ('pairwise comparison', 0.41767942905426025), ('comparisons', 0.39406418800354004), ('bradley terry', 0.3868101239204407)]"
1123,1123,27,1123_non orientable surfaces_orientable surfaces_curves surfaces_orientable surface,"['non orientable surfaces', 'orientable surfaces', 'curves surfaces', 'orientable surface', 'closed surfaces', 'simple closed curves', 'surfaces', 'nurbs surfaces', 'closed curves', 'triangulations']","['Universal families of arcs and curves on surfaces   The main goal of this paper is to investigate the minimal size of families of\ncurves on surfaces with the following property: a family of simple closed\ncurves $\\Gamma$ on a surface realizes all types of pants decompositions if for\nany pants decomposition of the surface, there exists a homeomorphism sending it\nto a subset of the curves in $\\Gamma$. The study of such universal families of\ncurves is motivated by questions on graph embeddings, joint crossing numbers\nand finding an elusive center of moduli space. In the case of surfaces without\npunctures, we provide an exponential upper bound and a superlinear lower bound\non the minimal size of a family of curves that realizes all types of pants\ndecompositions. We also provide upper and lower bounds in the case of surfaces\nwith punctures which we can consider labelled or unlabelled, and investigate a\nsimilar concept of universality for triangulations of polygons, where we\nprovide bounds which are tight up to logarithmic factors.\n', 'Large 1-systems of Curves in Non-orientable Surfaces   A longstanding avenue of research in orientable surface topology is to create\nand enumerate collections of curves in surfaces with certain intersection\nproperties. We look for similar collections of curves in non-orientable\nsurfaces. A surface is non-orientable if and only if it contains a M\\""obius\nband. We generalize a construction of Malestein-Rivin-Theran to non-orientable\nsurfaces to exhibit a lower bound for the maximum number of curves that\npairwise intersect 0 or 1 times in a generic non-orientable surface.\n', 'Computing shortest closed curves on non-orientable surfaces   We initiate the study of computing shortest non-separating simple closed\ncurves with some given topological properties on non-orientable surfaces.\nWhile, for orientable surfaces, any two non-separating simple closed curves are\nrelated by a self-homeomorphism of the surface, and computing shortest such\ncurves has been vastly studied, for non-orientable ones the classification of\nnon-separating simple closed curves up to ambient homeomorphism is subtler,\ndepending on whether the curve is one-sided or two-sided, and whether it is\norienting or not (whether it cuts the surface into an orientable one).\n  We prove that computing a shortest orienting (weakly) simple closed curve on\na non-orientable combinatorial surface is NP-hard but fixed-parameter tractable\nin the genus of the surface. In contrast, we can compute a shortest\nnon-separating non-orienting (weakly) simple closed curve with given sidedness\nin $g^{O(1)}.n\\log n$ time, where $g$ is the genus and $n$ the size of the\nsurface.\n  For these algorithms, we develop tools that can be of independent interest,\nto compute a variation on canonical systems of loops for non-orientable\nsurfaces based on the computation of an orienting curve, and some covering\nspaces that are essentially quotients of homology covers.\n']","[('non orientable surfaces', 0.614657461643219), ('orientable surfaces', 0.6114236116409302), ('curves surfaces', 0.5718732476234436), ('orientable surface', 0.5435120463371277), ('closed surfaces', 0.5404235124588013), ('simple closed curves', 0.5173555612564087), ('surfaces', 0.5043267011642456), ('nurbs surfaces', 0.49108582735061646), ('closed curves', 0.4908521771430969), ('triangulations', 0.45558151602745056)]"
1124,1124,26,1124_functional equations_stability generalized_quadratic functional_stability quadratic,"['functional equations', 'stability generalized', 'quadratic functional', 'stability quadratic', 'stability linear', 'spaces stability', 'following functional', 'stability following', 'additive functional', 'stability']","['Further stability results of the functional equation\n  $f(2x+y)+f\\left(\\frac{x+y}{2}\\right)\n  =\\frac{2f(x)f(y)}{f(x)+f(y)}+\\frac{2f(x+y)f(y-x)}{3f(y-x)-f(x+y)}$   In this paper, we investigate the generalized Hyers-Ulam stability of the\nfollowing reciprocal functional equation\n\\begin{equation*}f(2x+y)+f\\left(\\frac{x+y}{2}\\right)\n=\\frac{2f(x)f(y)}{f(x)+f(y)}+\\frac{2f(x+y)f(y-x)}{3f(y-x)-f(x+y)}\\end{equation*}\nin non-Archimedean space using a direct method.\n', 'Stability of additive-quadratic functional equation in modular space   Using the direct method, we prove the generalised Hyers-Ulam stability of the\nfollowing functional equation \\begin{equation} \\phi(x+y, z+w)+\\phi(x-y, z-w)-2\n\\phi(x, z)-2 \\phi(x, w)=0 \\end{equation} in modular space satisfying the Fatou\nproperty or $\\Delta_2$-condition.\n', 'On the Orthogonal Stability of the Pexiderized Quadratic Equation   The Hyers--Ulam stability of the conditional quadratic functional equation of\nPexider type f(x+y)+f(x-y)=2g(x)+2h(y), x\\perp y is established where \\perp is\na symmetric orthogonality in the sense of Ratz and f is odd.\n']","[('functional equations', 0.5737311840057373), ('stability generalized', 0.550838053226471), ('quadratic functional', 0.531152069568634), ('stability quadratic', 0.4792058765888214), ('stability linear', 0.4784328043460846), ('spaces stability', 0.4532543420791626), ('following functional', 0.445476770401001), ('stability following', 0.4434749484062195), ('additive functional', 0.42408791184425354), ('stability', 0.40784549713134766)]"
1125,1125,26,1125_quantum walks_quantum random walks_quantum walk_walk quantum,"['quantum walks', 'quantum random walks', 'quantum walk', 'walk quantum', 'grover walk', 'classical random walks', 'classical random walk', 'zeta graph', 'graph zeta', 'functions quantum']","['On the relation between quantum walks and absolute zeta functions   The quantum walk is a quantum counterpart of the classical random walk. On\nthe other hand, the absolute zeta function can be considered as a zeta function\nover F_1. This paper presents a connection between the quantum walk and the\nabsolute zeta function. First we deal with a zeta function determined by a time\nevolution matrix of the Grover walk on a graph. The Grover walk is a typical\nmodel of the quantum walk. Then we prove that the zeta function given by the\nquantum walk is an absolute automorphic form of weight depending on the number\nof edges of the graph. Furthermore we consider an absolute zeta function for\nthe zeta function based on a quantum walk. As an example, we compute an\nabsolute zeta function for the cycle graph and show that it is expressed as the\nmultiple gamma function of order 2.\n', 'Absolute zeta functions and periodicity of quantum walks on cycles   The quantum walk is a quantum counterpart of the classical random walk. On\nthe other hand, absolute zeta functions can be considered as zeta functions\nover $\\mathbb{F}_1$. This study presents a connection between quantum walks and\nabsolute zeta functions. In this paper, we focus on Hadamard walks and\n$3$-state Grover walks on cycle graphs. The Hadamard walks and the Grover walks\nare typical models of the quantum walks. We consider the periods and zeta\nfunctions of such quantum walks. Moreover, we derive the explicit forms of the\nabsolute zeta functions of corresponding zeta functions. Also, it is shown that\nour zeta functions of quantum walks are absolute automorphic forms.\n', 'Absolute zeta functions for zeta functions of quantum walks   This paper presents a connection between the quantum walk and the absolute\nmathematics. The quantum walk is a quantum counterpart of the classical random\nwalk. We especially deal with the Grover walk on a graph. The Grover walk is a\ntypical model of quantum walks. The time evolution of the Grover walk is\nobtained by a unitary matrix that is called the Grover matrix. We define the\nzeta function determined by the Grover matrix. First we prove that the zeta\nfunction of the Grover walk is the absolute automorphic form that constructs\nthe absolute zeta function. Next we calculate the absolute zeta function\ndefined by Grover walks on some graphs. The absolute zeta functions of the\nGrover walks are expressed by the multiple gamma function. Other types of\nabsolute zeta functions are obtained as an analogue of the multiple gamma\nfunction.\n']","[('quantum walks', 0.6165464520454407), ('quantum random walks', 0.6054409146308899), ('quantum walk', 0.5914878249168396), ('walk quantum', 0.5747444033622742), ('grover walk', 0.5680099129676819), ('classical random walks', 0.5487323999404907), ('classical random walk', 0.5127384662628174), ('zeta graph', 0.492228239774704), ('graph zeta', 0.47985607385635376), ('functions quantum', 0.45442062616348267)]"
1126,1126,26,1126_control quantum_quantum control_quantum optimal_optimal quantum,"['control quantum', 'quantum control', 'quantum optimal', 'optimal quantum', 'quantum algorithms quantum', 'quantum algorithms', 'quantum computing', 'robust quantum', 'implementation quantum', 'quantum gates']","[""Quandary: An open-source C++ package for high-performance optimal\n  control of open quantum systems   Quantum optimal control can be used to shape the control pulses for realizing\nunitary and non-unitary transformations of quantum states. These control pulses\nprovide the fundamental interface between the quantum compiler and the quantum\nhardware. Most current software for quantum optimal control (e.g. Qutip or\nKrotov) is restricted to run on shared memory platforms, limiting their\napplicability to smaller quantum systems, in particular if interactions with\nthe environment are taken into account. This paper gives an overview of the\nopen-source code Quandary, which is designed to solve quantum control problems\nin larger open quantum systems modelled by Lindblad's master equation.\nImplemented in C++, Quandary uses the message passing paradigm for distributed\nmemory computers that enables scalability to large numbers of compute cores.\nAccompanied by numerical examples, this paper presents an overview on existing\ntheoretical developments for open optimal quantum control realizing\nstate-to-state transfer, unitary gate optimization as well as\nstate-preparation, and presents the numerical tools and implementation aspect\nas realized in Quandary, for deployment on modern high-performance computing\nplatforms.\n"", 'Higher order traps for some strongly degenerate quantum control systems   Quantum control is necessary for a variety of modern quantum technologies as\nit allows to optimally manipulate quantum systems. An important problem in\nquantum control is to establish whether the control objective functional has\ntrapping behaviour or no, namely if it has or no traps -- controls from which\nit is difficult to escape by local search optimization methods. Higher order\ntraps were previously introduced in [A. N. Pechen, D. J. Tannor, ""Are there\ntraps in quantum control landscapes?"", Phys. Rev. Lett., 106 (2011), 120402],\nwhere 3-rd order traps were found. In this note we show that traps of\narbitrarily high order exist for controllable quantum systems with special\nsymmetry in the Hamiltonian.\n', 'Quantum control landscape for ultrafast generation of single-qubit phase\n  shift quantum gates   In this work, we consider the problem of ultrafast controlled generation of\nsingle-qubit phase shift quantum gates. Globally optimal control is a control\nwhich realizes the gate with maximal possible fidelity. Trap is a control which\nis optimal only locally but not globally. It was shown before that traps do not\nexist for controlled generation of arbitrary single-qubit quantum gates for\nsufficiently long times, as well as for fast control of quantum gates other\nthan phase shift gates. Ultrafast generation of phase-shift gates was missed in\nthe previous analysis. In this work we show, combining analytical and numerical\noptimization methods such as Gradient Ascent Pulse Engineering (GRAPE),\ndifferential evolution, and dual annealing, that control landscape for\nultrafast generation of phase shift gates is also free of traps. Mathematical\nanalysis of quantum control landscapes, which aims to prove either absence or\nexistence of traps for quantum control objective functionals, is an important\ntopic in quantum control. In this work, we provide a rigorous analysis of\nquantum control landscapes for ultrafast generation of single-qubit quantum\ngates and show, combining analytical methods based on a sophisticated analysis\nof spectrum of the Hessian, and numerical optimization methods such as Gradient\nAscent Pulse Engineering (GRAPE), differential evolution, and dual annealing,\nthat control landscape for ultrafast generation of phase shift gates is free of\ntraps.\n']","[('control quantum', 0.7716190218925476), ('quantum control', 0.764613151550293), ('quantum optimal', 0.7042518258094788), ('optimal quantum', 0.6939675807952881), ('quantum algorithms quantum', 0.6599328517913818), ('quantum algorithms', 0.659227192401886), ('quantum computing', 0.6094343066215515), ('robust quantum', 0.6053726673126221), ('implementation quantum', 0.5985099673271179), ('quantum gates', 0.589454710483551)]"
1127,1127,26,1127_statistical convergence_convergence rough_convergence statistical_convergence lattice,"['statistical convergence', 'convergence rough', 'convergence statistical', 'convergence lattice', 'convergence metric', 'sequences metric', 'spaces statistical', 'statistical limits', 'convergence strong', 'convergence sequences']","['Rough statistical convergence of sequences in a partial metric space   In this paper, using the concept of natural density, we have introduced the\nnotion of rough statistical convergence which is an extension of the notion of\nrough convergence in a partial metric space. We have defined the set of rough\nstatistical limit points of a sequence in a partial metric space and proved\nthat this set is closed and bounded. Finally, we have found out the\nrelationship between the set of statistical cluster points and the set of rough\nstatistical limit points of sequences in a partial metric space.\n', 'Statistical convergence of nets in Riesz spaces   The statistical convergence is defined for sequences with the asymptotic\ndensity on the natural numbers, in general. In this paper, we introduce the\nstatistical convergence for nets in Riesz spaces by using the finite additive\nmeasures on directed sets. Moreover, we give some relations among the\nstatistical convergence and the lattice properties such as the order\nconvergence and lattice operators.\n', 'Rough Statistical Convergence of Double Sequences in Probabilistic\n  Normed Spaces   In this paper, we have defined rough convergence and rough statistical\nconvergence of double sequences in probabilistic normed spaces which is more\ngeneralized version than the rough statistical convergence of double sequences\nin normed linear spaces. Also, we have defined rough statistical cluster points\nof double sequences and then, investigated some important results associated\nwith the set of rough statistical limits of double sequences in these spaces.\nMoreover, in the same spaces, we have proved an important relation between the\nset of all rough statistical cluster points and rough statistical limits under\ncertain condition.\n']","[('statistical convergence', 0.5738180875778198), ('convergence rough', 0.562416672706604), ('convergence statistical', 0.5554347038269043), ('convergence lattice', 0.5525538325309753), ('convergence metric', 0.49362704157829285), ('sequences metric', 0.4885692000389099), ('spaces statistical', 0.48228535056114197), ('statistical limits', 0.45986852049827576), ('convergence strong', 0.4543374180793762), ('convergence sequences', 0.4459949731826782)]"
1128,1128,26,1128_quadrotor_unmanned aerial vehicles_aerial vehicles_unmanned aerial,"['quadrotor', 'unmanned aerial vehicles', 'aerial vehicles', 'unmanned aerial', 'quadcopter', 'optimal controller', 'uav', 'controller control', 'uavs', 'unmanned']","['Control and Trajectory Optimization for Soft Aerial Manipulation   Manipulation and grasping with unmanned aerial vehicles (UAVs) currently\nrequire accurate positioning and are often executed at reduced speed to ensure\nsuccessful grasps. This is due to the fact that typical UAVs can only\naccommodate rigid manipulators with few degrees of freedom, which limits their\ncapability to compensate for disturbances caused by the vehicle positioning\nerrors. Moreover, UAVs have to minimize external contact forces in order to\nmaintain stability. Biological systems, on the other hand, exploit softness to\novercome similar limitations, and leverage compliance to enable aggressive\ngrasping. This paper investigates control and trajectory optimization for a\nsoft aerial manipulator, consisting of a quadrotor and a tendon-actuated soft\ngripper, in which the advantages of softness can be fully exploited. To the\nbest of our knowledge, this is the first work at the intersection between soft\nmanipulation and UAV control. We present a decoupled approach for the quadrotor\nand the soft gripper, combining (i) a geometric controller and a minimum-snap\ntrajectory optimization for the quadrotor (rigid) base, with (ii) a\nquasi-static finite element model and control-space interpolation for the soft\ngripper. We prove that the geometric controller asymptotically stabilizes the\nquadrotor velocity and attitude despite the addition of the soft load. Finally,\nwe evaluate the proposed system in a realistic soft dynamics simulator, and\nshow that: (i) the geometric controller is fairly insensitive to the soft\npayload, (ii) the platform can reliably grasp unknown objects despite\ninaccurate positioning and initial conditions, and (iii) the decoupled\ncontroller is amenable for real-time execution.\n', 'Geometric Control for Load Transportation with Quadrotor UAVs by Elastic\n  Cables   Groups of unmanned aerial vehicles (UAVs) are increasingly utilized in\ntransportation task as the combined strength allows to increase the maximum\npayload. However, the resulting mechanical coupling of the UAVs impose new\nchallenges in terms of the tracking control. Thus, we design a geometric\ntrajectory tracking controller for the cooperative task of four quadrotor UAVs\ncarrying and transporting a rigid body, which is attached to the quadrotors via\ninflexible elastic cables. The elasticity of the cables together with\ntechniques of singular perturbation allows a reduction in the model to that of\na similar model with inelastic cables. In this reduced model, we design a\ncontroller such that the position and attitude of the load exponentially\nconverges to a given desired trajectory. We then show that this result leads to\nan uniformly converging tracking error for the original elastic model under\nsome assumptions. Furthermore, under the presence of unstructured disturbances\non the system, we show that the error is ultimately bounded with an arbitrarily\nsmall bound. Finally, a simulation illustrates the theoretical results.\n', 'An Aerodynamic Feedforward-Feedback Architecture for Tailsitter Control\n  in Hybrid Flight Regimes   This article presents a guidance-control design methodology for the\nautonomous maneuvering of tailsitter unmanned aerial systems (UAS) in hybrid\nflight regimes (i.e. the dynamics between VTOL and fixed wing regime). The\ntailsitter guidance-control architecture consists of a trajectory planner, an\nouter loop position controller, an inner loop attitude controller, and a\ncontrol allocator. The trajectory planner uses a simplified tailsitter model,\nwith aerodynamic and wake effect considerations, to generate a set of\ntransition trajectories with associated aerodynamic force estimates based on an\noptimization metric specified by a human operator (minimum time transition).\nThe outer loop controller then uses the aerodynamic force estimate computed by\nthe trajectory planner as a feedforward signal alongside feedback linearization\nof the outer loop dynamics for 6DOF position control. The inner loop attitude\ncontroller is a standard nonlinear dynamic inversion control law that generates\nthe desired pitch, roll and yaw moments, which are then converted to the\nappropriate rotor speeds by the control allocator. Analytical conditions for\nrobust stability are derived for the outer loop position controller to\nguarantee performance in the presence of uncertainty in the feedforward\naerodynamic force compensation. Finally, both tracking performance and\nstability of the control architecture is evaluated on a high fidelity flight\ndynamics simulation of a quadrotor biplane tailsitter for flight missions that\ndemand high maneuverability in transition between flight modes.\n']","[('quadrotor', 0.5996022820472717), ('unmanned aerial vehicles', 0.5409611463546753), ('aerial vehicles', 0.5362266898155212), ('unmanned aerial', 0.5361366868019104), ('quadcopter', 0.5242797136306763), ('optimal controller', 0.5014917254447937), ('uav', 0.4756218194961548), ('controller control', 0.4267195761203766), ('uavs', 0.4202605187892914), ('unmanned', 0.41452932357788086)]"
1129,1129,26,1129_sampling reconstruction_nyquist sampling_analog signals_analog digital conversion,"['sampling reconstruction', 'nyquist sampling', 'analog signals', 'analog digital conversion', 'analog digital', 'analog digital converters', 'digital converters adcs', 'nonuniform sampling', 'spectrum sensing', 'sampling']","['Back in the US-SR: Unlimited Sampling and Sparse Super-Resolution with\n  its Hardware Validation   The Unlimited Sensing Framework (USF) is a digital acquisition protocol that\nallows for sampling and reconstruction of high dynamic range signals. By\nacquiring modulo samples, the USF circumvents the clipping or saturation\nproblem that is a fundamental bottleneck in conventional analog-to-digital\nconverters (ADCs). In the context of the USF, several works have focused on\nbandlimited function classes and recently, a hardware validation of the modulo\nsampling approach has been presented. In a different direction, in this paper\nwe focus on non-bandlimited function classes and consider the well-known\nsuper-resolution problem; we study the recovery of sparse signals (Dirac\nimpulses) from low-pass filtered, modulo samples. Taking an end-to-end approach\nto USF based super-resolution, we present a novel recovery algorithm (US-SR)\nthat leverages a doubly sparse structure of the modulo samples. We derive a\nsampling criterion for the US-SR method. A hardware experiment with the modulo\nADC demonstrates the empirical robustness of our method in a realistic, noisy\nsetting, thus validating its practical utility.\n', 'Unlimited Sampling of Bandpass Signals: Computational Demodulation via\n  Undersampling   Bandpass signals are an important sub-class of bandlimited signals that\nnaturally arise in a number of application areas but their high-frequency\ncontent poses an acquisition challenge. Consequently, ""Bandpass Sampling\nTheory"" has been investigated and applied in the literature. In this paper, we\nconsider the problem of modulo sampling of bandpass signals with the main goal\nof sampling and recovery of high dynamic range inputs. Our work is inspired by\nthe Unlimited Sensing Framework (USF). In the USF, the modulo operation folds\nhigh dynamic range inputs into low dynamic range, modulo samples. This\nfundamentally avoids signal clipping. Given that the output of the modulo\nnonlinearity is non-bandlimited, bandpass sampling conditions never hold true.\nYet, we show that bandpass signals can be recovered from a modulo\nrepresentation despite the inevitable aliasing. Our main contribution includes\nproof of sampling theorems for recovery of bandpass signals from an\nundersampled representation, reaching sub-Nyquist sampling rates. On the\nrecovery front, by considering both time-and frequency-domain perspectives, we\nprovide a holistic view of the modulo bandpass sampling problem. On the\nhardware front, we include ideal, non-ideal and generalized modulo folding\narchitectures that arise in the hardware implementation of modulo\nanalog-to-digital converters. Numerical simulations corroborate our theoretical\nresults. Bridging the theory-practice gap, we validate our results using\nhardware experiments, thus demonstrating the practical effectiveness of our\nmethods.\n', 'eSampling: Energy Harvesting ADCs   Analog-to-digital converters (ADCs) allow physical signals to be processed\nusing digital hardware. The power consumed in conversion grows with the\nsampling rate and quantization resolution, imposing a major challenge in\npower-limited systems. A common ADC architecture is based on sample-and-hold\n(S/H) circuits, where the analog signal is being tracked only for a fraction of\nthe sampling period. In this paper, we propose the concept of eSampling ADCs,\nwhich harvest energy from the analog signal during the time periods where the\nsignal is not being tracked. This harvested energy can be used to supplement\nthe ADC itself, paving the way to the possibility of zero-power consumption and\npower-saving ADCs. We analyze the tradeoff between the ability to recover the\nsampled signal and the energy harvested, and provide guidelines for setting the\nsampling rate in the light of accuracy and energy constraints. Our analysis\nindicates that eSampling ADCs operating with up to 12 bits per sample can\nacquire bandlimited analog signals such that they can be perfectly recovered\nwithout requiring power from the external source. Furthermore, our theoretical\nresults reveal that eSampling ADCs can in fact save power by harvesting more\nenergy than they consume. To verify the feasibility of eSampling ADCs, we\npresent a circuit-level design using standard complementary metal oxide\nsemiconductor (CMOS) 65 nm technology. An eSampling 8-bit ADC which samples at\n40 MHZ is designed on a Cadence Virtuoso platform. Our experimental study\ninvolving Nyquist rate sampling of bandlimited signals demonstrates that such\nADCs are indeed capable of harvesting more energy than that spent during\nanalog-to-digital conversion, without affecting the accuracy.\n']","[('sampling reconstruction', 0.5613280534744263), ('nyquist sampling', 0.543987512588501), ('analog signals', 0.4759748876094818), ('analog digital conversion', 0.45412126183509827), ('analog digital', 0.4522581696510315), ('analog digital converters', 0.43833333253860474), ('digital converters adcs', 0.4257056713104248), ('nonuniform sampling', 0.42354097962379456), ('spectrum sensing', 0.4226423501968384), ('sampling', 0.4187677204608917)]"
1130,1130,26,1130_scoring functions_scoring rules_scoring rule_forecasting,"['scoring functions', 'scoring rules', 'scoring rule', 'forecasting', 'forecasting methods', 'forecasts', 'forecaster', 'prediction intervals', 'forecast', 'scoring']","['Necessary and Sufficient Conditions for Domination Results for Proper\n  Scoring Rules   Scoring rules measure the deviation between a probabilistic forecast and\nreality. Strictly proper scoring rules have the property that for any forecast,\nthe mathematical expectation of the score of a forecast p by the lights of p is\nstrictly better than the mathematical expectation of any other forecast q by\nthe lights of p. Probabilistic forecasts need not satisfy the axioms of the\nprobability calculus, but Predd, et al. (2009) have shown that given a finite\nsample space and any strictly proper additive and continuous scoring rule, the\nscore for any forecast that does not satisfy the axioms of probability is\nstrictly dominated by the score for some probabilistically consistent forecast.\nRecently, this result has been extended to non-additive continuous scoring\nrules. In this paper, a condition weaker than continuity is given that suffices\nfor the result, and the condition is proved to be optimal.\n', 'Local scale invariance and robustness of proper scoring rules   Averages of proper scoring rules are often used to rank probabilistic\nforecasts. In many cases, the individual terms in these averages are based on\nobservations and forecasts from different distributions. We show that some of\nthe most popular proper scoring rules, such as the continuous ranked\nprobability score (CRPS), give more importance to observations with large\nuncertainty which can lead to unintuitive rankings. To describe this issue, we\ndefine the concept of local scale invariance for scoring rules. A new class of\ngeneralized proper kernel scoring rules is derived and as a member of this\nclass we propose the scaled CRPS (SCRPS). This new proper scoring rule is\nlocally scale invariant and therefore works in the case of varying uncertainty.\nLike CRPS it is computationally available for output from ensemble forecasts,\nand does not require the ability to evaluate densities of forecasts. We further\ndefine robustness of scoring rules, show why this also is an important concept\nfor average scores, and derive new proper scoring rules that are robust against\noutliers. The theoretical findings are illustrated in three different\napplications from spatial statistics, stochastic volatility models, and\nregression for count data.\n', 'Proper Scoring Rules for Multivariate Probabilistic Forecasts based on\n  Aggregation and Transformation   Proper scoring rules are an essential tool to assess the predictive\nperformance of probabilistic forecasts. However, propriety alone does not\nensure an informative characterization of predictive performance and it is\nrecommended to compare forecasts using multiple scoring rules. With that in\nmind, interpretable scoring rules providing complementary information are\nnecessary. We formalize a framework based on aggregation and transformation to\nbuild interpretable multivariate proper scoring rules.\nAggregation-and-transformation-based scoring rules are able to target specific\nfeatures of the probabilistic forecasts; which improves the characterization of\nthe predictive performance. This framework is illustrated through examples\ntaken from the literature and studied using numerical experiments showcasing\nits benefits. In particular, it is shown that it can help bridge the gap\nbetween proper scoring rules and spatial verification tools.\n']","[('scoring functions', 0.6155092120170593), ('scoring rules', 0.5529481172561646), ('scoring rule', 0.5243024230003357), ('forecasting', 0.4851688742637634), ('forecasting methods', 0.480977326631546), ('forecasts', 0.4803008437156677), ('forecaster', 0.46407580375671387), ('prediction intervals', 0.463904470205307), ('forecast', 0.4531702399253845), ('scoring', 0.43453118205070496)]"
1131,1131,26,1131_manifold anosov_anosov flows_length spectrum rigidity_geodesic flows,"['manifold anosov', 'anosov flows', 'length spectrum rigidity', 'geodesic flows', 'boundary rigidity', 'geodesic flow', 'spectrum rigidity', 'riemannian geodesic', 'sectional curvatures', 'riemannian manifold']","['Smooth rigidity for higher dimensional contact Anosov flows   We apply the matching functions technique in the setting of contact Anosov\nflows which satisfy a bunching assumption. This allows us to generalize the\n3-dimensional rigidity result of Feldman-Ornstein~\\cite{FO}. Namely, we show\nthat if two such Anosov flows are $C^0$ conjugate then they are $C^{r}$,\nconjugate for some $r\\in[1,2)$ or even $C^\\infty$ conjugate under some\nadditional assumptions. This, for example, applies to $1/4$-pinched geodesic\nflows on compact Riemannian manifolds of negative sectional curvature. We can\nalso use our result to recover Hamendst\\""adt\'s marked length spectrum rigidity\nresult for real hyperbolic manifolds.\n', 'Smooth rigidity for 3-dimensional volume preserving Anosov flows and\n  weighted marked length spectrum rigidity   Let $X_1^t$ and $X_2^t$ be volume preserving Anosov flows on a 3-dimensional\nmanifold $M$. We prove that if $X_1^t$ and $X_2^t$ are $C^0$ conjugate then the\nconjugacy is, in fact, smooth, unless $M$ is a mapping torus of an Anosov\nautomorphism of $\\mathbb T^2$ and both flows are constant roof suspension\nflows. We deduce several applications. Among them is a new result on rigidity\nof Anosov diffeorphisms on $\\mathbb T^2$ and a new ""weighted"" marked length\nspectrum rigidity result for surfaces of negative curvature.\n', 'Marked boundary rigidity for surfaces of Anosov type   Let $\\Sigma$ be a smooth compact connected oriented surface with boundary. A\nmetric on $\\Sigma$ is said to be of Anosov type if it has strictly convex\nboundary, no conjugate points, and a hyperbolic trapped set. We prove that two\nmetrics of Anosov type with the same marked boundary distance are isometric\n(via a boundary-preserving isometry isotopic to the identity). As a corollary,\nwe retrieve the boundary distance rigidity result for simple disks of Pestov\nand Uhlmann [arXiv:math/0305280]. The proof rests on a new transfer principle\nshowing that, in any dimension, the marked length spectrum rigidity conjecture\nimplies the marked boundary distance rigidity conjecture under the existence of\na suitable isometric embedding into a closed Anosov manifold. Such an isometric\nembedding result for open surfaces of Anosov type was proved by the first\nauthor with Chen and Gogolev in [arXiv:2009.13665] while the marked length\nspectrum rigidity for closed Anosov surfaces was established by the second\nauthor with Guillarmou and Paternain in [arXiv:2303.12007].\n']","[('manifold anosov', 0.6416473388671875), ('anosov flows', 0.5857757329940796), ('length spectrum rigidity', 0.5735134482383728), ('geodesic flows', 0.5617479681968689), ('boundary rigidity', 0.5240062475204468), ('geodesic flow', 0.5093421339988708), ('spectrum rigidity', 0.49013736844062805), ('riemannian geodesic', 0.4656040072441101), ('sectional curvatures', 0.451724648475647), ('riemannian manifold', 0.4403444826602936)]"
1132,1132,26,1132_theory regularity structures_singular spdes_renormalization schemes_regularity structures,"['theory regularity structures', 'singular spdes', 'renormalization schemes', 'regularity structures', 'algebraic renormalization', 'regularity structure', 'renormalization group theory', 'renormalisation group', 'renormalization', 'models regularity']","[""Bogoliubov type recursions for renormalisation in regularity structures   Hairer's regularity structures transformed the solution theory of singular\nstochastic partial differential equations. The notions of positive and negative\nrenormalisation are central and the intricate interplay between these two\nrenormalisation procedures is captured through the combination of cointeracting\nbialgebras and an algebraic Birkhoff-type decomposition of bialgebra morphisms.\nThis work revisits the latter by defining Bogoliubov-type recursions similar to\nConnes and Kreimer's formulation of BPHZ renormalisation. We then apply our\napproach to the renormalisation problem for SPDEs.\n"", 'Recursive formulae in regularity structures   We construct renormalised models of regularity structures by using a\nrecursive formulation for the structure group and for the renormalisation\ngroup. This construction covers all the examples of singular SPDEs which have\nbeen treated so far with the theory of regularity structures and improves the\nrenormalisation procedure based on Hopf algebras given in [BHZ16].\n', 'Renormalisation in the flow approach for singular SPDEs   In this work, we study the renormalisation of singular SPDEs in the flow\napproach recently developed by Duch using a bottom-up setting. We introduce a\ngeneral ansatz based on decorated trees for the solution of the flow equation.\nThe ansatz is renormalised in a recursive way, in the sense of the trees, via\nlocal extractions introduced for regularity structures. We derive the\nrenormalised equation from this ansatz and show that the renormalisation scheme\nis identical to that appearing in the context of regularity structures, thus\nmatching the BPHZ renormalisation.\n']","[('theory regularity structures', 0.6060283780097961), ('singular spdes', 0.5911208987236023), ('renormalization schemes', 0.5822295546531677), ('regularity structures', 0.5630775094032288), ('algebraic renormalization', 0.5600669980049133), ('regularity structure', 0.5469256639480591), ('renormalization group theory', 0.524739682674408), ('renormalisation group', 0.5038586854934692), ('renormalization', 0.5004381537437439), ('models regularity', 0.4931924343109131)]"
1133,1133,26,1133_random graphs constant_guessing game_optimal strategies_assignment colors,"['random graphs constant', 'guessing game', 'optimal strategies', 'assignment colors', 'one colors', 'winning strategies', 'colors', 'whose color', 'tries guess', 'hats']","['The Hats game. On maximum degree and diameter   We analyze the following version of the deterministic \\hats game. We have a\ngraph $G$, and a sage resides at each vertex of $G$. When the game starts, an\nadversary puts on the head of each sage a hat of a color arbitrarily chosen\nfrom a set of $k$ possible colors. Each sage can see the hat colors of his\nneighbors but not his own hat color. All of sages are asked to guess their own\nhat colors simultaneously, according to a predetermined guessing strategy and\nthe hat colors they see, where no communication between them is allowed. The\nstrategy is winning if it guarantees at least one correct individual guess for\nevery assignment of colors. Given a graph $G$, its hat guessing number\n${\\text{HG}}(G)$ is the maximal number $k$ such that there exists a winning\nstrategy.\n  We disprove the hypothesis that ${\\text{HG}}(G) \\le \\Delta + 1$ and\ndemonstrate that diameter of graph and ${\\text{HG}}(G$) are independent.\n', 'On the Hat Guessing Number of Graphs   The hat guessing number $HG(G)$ of a graph $G$ on $n$ vertices is defined in\nterms of the following game: $n$ players are placed on the $n$ vertices of $G$,\neach wearing a hat whose color is arbitrarily chosen from a set of $q$ possible\ncolors. Each player can see the hat colors of his neighbors, but not his own\nhat color. All of the players are asked to guess their own hat colors\nsimultaneously, according to a predetermined guessing strategy and the hat\ncolors they see, where no communication between them is allowed. The hat\nguessing number $HG(G)$ is the largest integer $q$ such that there exists a\nguessing strategy guaranteeing at least one correct guess for any hat\nassignment of $q$ possible colors.\n  In this note we construct a planar graph $G$ satisfying $HG(G)=12$, settling\na problem raised in \\cite{BDFGM}. We also improve the known lower bound of\n$(2-o(1))\\log_2 n$ for the typical hat guessing number of the random graph\n$G=G(n,1/2)$, showing that it is at least $n^{1-o(1)}$ with probability tending\nto $1$ as $n$ tends to infinity. Finally, we consider the linear hat guessing\nnumber of complete multipartite graphs.\n', 'The hat guessing number of graphs   Consider the following hat guessing game: $n$ players are placed on $n$\nvertices of a graph, each wearing a hat whose color is arbitrarily chosen from\na set of $q$ possible colors. Each player can see the hat colors of his\nneighbors, but not his own hat color. All of the players are asked to guess\ntheir own hat colors simultaneously, according to a predetermined guessing\nstrategy and the hat colors they see, where no communication between them is\nallowed. Given a graph $G$, its hat guessing number ${\\rm{HG}}(G)$ is the\nlargest integer $q$ such that there exists a guessing strategy guaranteeing at\nleast one correct guess for any hat assignment of $q$ possible colors.\n  In 2008, Butler et al. asked whether the hat guessing number of the complete\nbipartite graph $K_{n,n}$ is at least some fixed positive (fractional) power of\n$n$. We answer this question affirmatively, showing that for sufficiently large\n$n$, the complete $r$-partite graph $K_{n,\\ldots,n}$ satisfies\n${\\rm{HG}}(K_{n,\\ldots,n})=\\Omega(n^{\\frac{r-1}{r}-o(1)})$. Our guessing\nstrategy is based on a probabilistic construction and other combinatorial\nideas, and can be extended to show that\n${\\rm{HG}}(\\vec{C}_{n,\\ldots,n})=\\Omega(n^{\\frac{1}{r}-o(1)})$, where\n$\\vec{C}_{n,\\ldots,n}$ is the blow-up of a directed $r$-cycle, and where for\ndirected graphs each player sees only the hat colors of his outneighbors.\n']","[('random graphs constant', 0.44527870416641235), ('guessing game', 0.43226927518844604), ('optimal strategies', 0.38013288378715515), ('assignment colors', 0.3692990243434906), ('one colors', 0.3656388521194458), ('winning strategies', 0.35425689816474915), ('colors', 0.3537665009498596), ('whose color', 0.3437889814376831), ('tries guess', 0.34141218662261963), ('hats', 0.3328922390937805)]"
1134,1134,26,1134_catalan numbers_rational catalan_generalized catalan_catalan objects,"['catalan numbers', 'rational catalan', 'generalized catalan', 'catalan objects', 'cyclic sieving', 'catalan number', 'cyclic group actions', 'nu tamari lattices', 'cyclic sieving phenomenon', 'families combinatorial']","['Cyclic Sieving of Matchings   The cyclic sieving phenomenon (CSP) was introduced by Reiner, Stanton, and\nWhite to study combinatorial structures with actions of cyclic groups. The\ncrucial step is to find a polynomial, for example a q-analog, that satisfies\nthe CSP conditions for an action. This polynomial will give us a lot of\ninformation about the symmetry and structure of the set under the action. In\nthis paper, we study the cyclic sieving phenomenon of the cyclic group $C_{2n}$\nacting on $P_{n,k}$, which is the set of matchings of $2n$ points on a circle\nwith $k$ crossings. The noncrossing matchings ($k=0$) was recently studied as a\nCatalan object. In this paper, we study more general cases, the matchings with\nmore number of crossings. We prove that there exists $q$-analog polynomials\n$f_{n,k}(q)$ such that $(P_{n,k},f_{n,k},C_{2n})$ exhibits the cyclic sieving\nphenomenon for $k=1,2,3$. In the proof, we also introduce an efficient\nrepresentation of the elements in $P_{n,k}$, which helps us to understand the\nsymmetrical structure of the set.\n', 'Dihedral Sieving on Cluster Complexes   The cyclic sieving phenomenon of Reiner, Stanton, and White characterizes the\nstabilizers of cyclic group actions on finite sets using q-analogue\npolynomials. Eu and Fu demonstrated a cyclic sieving phenomenon on generalized\ncluster complexes of every type using the q-Catalan numbers. In this paper, we\nexhibit the dihedral sieving phenomenon, introduced for odd n by Rao and Suk,\non clusters of every type. In the type A case, we show that the Raney numbers\ncount both reflection-symmetric k-angulations of an n-gon and a particular\nevaluation of the (q,t)-Fuss--Catalan numbers. We also introduce a sieving\nphenomenon for the symmetric group, and discuss possibilities for dihedral\nsieving for even n.\n', ""Cyclic sieving on noncrossing (1,2)-configurations   Verifying a suspicion of Propp and Reiner concerning the cyclic sieving\nphenomenon (CSP), M. Thiel introduced a Catalan object called noncrossing\n$(1,2)$-configurations (denoted by $X_n$), which is a class of set partitions\nof $[n-1]$. More precisely, Thiel proved that, with a natural action of the\ncyclic group $C_{n-1}$ on $X_n$, the triple\n$\\left(X_n,C_{n-1},\\text{Cat}_n(q)\\right)$ exhibits the CSP, where\n$\\text{Cat}_n(q):=\\frac{1}{[n+1]_q}\\begin{bmatrix}\n  2n\\\\ n \\end{bmatrix}_q$ is MacMahon's $q$-Catalan number. Recently, in a\nstudy of the fermionic diagonal coinvariant ring $FDR_n$, J. Kim found a\ncombinatorial basis for $FDR_n$ indexed by $X_n$. In this paper, we continue to\nstudy $X_n$ and obtain the following results:\n  (1) We define a statistic $cwt$ on $X_n$ whose generating function is\n$\\text{Cat}_n(q)$, which answers a problem of Thiel.\n  (2) We show that $\\text{Cat}_n(q)$ is equivalent to\n$$\\sum_{\\substack{k,x,y\\\\2k+x+y=n-1}}\\begin{bmatrix}\n  n-1\n  2k,x,y\n  \\end{bmatrix}_q\\text{Cat}_k\n  (q)q^{k+\\binom{x}{2}+\\binom{y}{2}+\\binom{n}{2}}$$\n  modulo $q^{n-1}-1$, which answers a problem of Kim. As mentioned by Kim, this\nresult leads to a representation theoretic proof of the above cyclic sieving\nresult of Thiel.\n  (3) We consider the dihedral sieving, a generalization of the CSP, which was\nrecently introduced by Rao and Suk. Under a natural action of the dihedral\ngroup $I_2(n-1)$ (for even $n$), we prove a dihedral sieving result on $X_n$.\n""]","[('catalan numbers', 0.5222353339195251), ('rational catalan', 0.5125359296798706), ('generalized catalan', 0.5081505179405212), ('catalan objects', 0.49704137444496155), ('cyclic sieving', 0.47984591126441956), ('catalan number', 0.4701194167137146), ('cyclic group actions', 0.4351734519004822), ('nu tamari lattices', 0.41891834139823914), ('cyclic sieving phenomenon', 0.41666802763938904), ('families combinatorial', 0.41463395953178406)]"
1135,1135,26,1135_binary symmetric channel_adversarial channel_information theoretically secure_cryptographic,"['binary symmetric channel', 'adversarial channel', 'information theoretically secure', 'cryptographic', 'wiretap channel', 'adversary access', 'capacity channel', 'secret key agreement', 'unique decoding', 'theoretically secure']","[""Wiretapped Commitment over Binary Channels   We propose the problem of wiretapped commitment, where two parties, say\ncommitter Alice and receiver Bob, engage in a commitment protocol using a noisy\nchannel as a resource, in the presence of an eavesdropper, say Eve. Noisy\nversions of Alice's transmission over the wiretap channel are received at both\nBob and Eve. We seek to determine the maximum commitment throughput in the\npresence of an eavesdropper, i.e., wiretapped commitment capacity, where in\naddition to the standard security requirements for two-party commitment, one\nseeks to ensure that Eve doesn't learn about the commit string.\n  A key interest in this work is to explore the effect of collusion (or lack of\nit) between the eavesdropper Eve and either Alice or Bob. Toward the same, we\npresent results on the wiretapped commitment capacity under the so-called\n1-private regime (when Alice or Bob cannot collude with Eve) and the 2-private\nregime (when Alice or Bob may possibly collude with Eve).\n"", 'Commitment over Gaussian Unfair Noisy Channels   Commitment is a key primitive which resides at the heart of several\ncryptographic protocols. Noisy channels can help realize\ninformation-theoretically secure commitment schemes, however, their imprecise\nstatistical characterization can severely impair such schemes, especially their\nsecurity guarantees. Keeping our focus on channel unreliability in this work,\nwe study commitment over unreliable continuous alphabet channels called the\nGaussian unfair noisy channels or Gaussian UNCs.\n  We present the first results on the optimal throughput or commitment capacity\nof Gaussian UNCs. It is known that classical Gaussian channels have infinite\ncommitment capacity, even under finite transmit power constraints. For\nunreliable Gaussian UNCs, we prove the surprising result that their commitment\ncapacity may be finite, and in some cases, zero. When commitment is possible,\nwe present achievable rate lower bounds by constructing positive - throughput\nprotocols under given input power constraint, and (two-sided) channel\nelasticity at committer Alice and receiver Bob. Our achievability results\nestablish an interesting fact - Gaussian UNCs with zero elasticity have\ninfinite commitment capacity - which brings a completely new perspective to why\nclassic Gaussian channels, i.e., Gaussian UNCs with zero elasticity, have\ninfinite capacity. Finally, we precisely characterize the positive commitment\ncapacity threshold for a Gaussian UNC in terms of the channel elasticity, when\nthe transmit power tends to infinity.\n', 'Wiretap Secret Key Agreement Via Secure Omniscience   In this paper, we explore the connection between secret key agreement and\nsecure omniscience within the setting of the multiterminal source model with a\nwiretapper who has side information. While the secret key agreement problem\nconsiders the generation of a maximum-rate secret key through public\ndiscussion, the secure omniscience problem is concerned with communication\nprotocols for omniscience that minimize the rate of information leakage to the\nwiretapper. The starting point of our work is a lower bound on the minimum\nleakage rate for omniscience, $R_{\\mathop{\\mathrm{L}}}$, in terms of the\nwiretap secret key capacity, $C_{\\mathop{\\mathrm{W}}}$. Our interest is in\nidentifying broad classes of sources for which this lower bound is met with\nequality, in which case we say that there is a duality between secure\nomniscience and secret key agreement. We show that this duality holds in the\ncase of certain finite linear source (FLS) models, such as two-terminal FLS\nmodels and pairwise independent network models on trees with a linear\nwiretapper. Duality also holds for any FLS model in which\n$C_{\\mathop{\\mathrm{W}}}$ is achieved by a perfect linear secret key agreement\nscheme. We conjecture that the duality in fact holds unconditionally for any\nFLS model. On the negative side, we give an example of a (non-FLS) source model\nfor which duality does not hold if we limit ourselves to\ncommunication-for-omniscience protocols with at most two (interactive)\ncommunications. We also address the secure function computation problem and\nexplore the connection between the minimum leakage rate for computing a\nfunction and the wiretap secret key capacity.\n']","[('binary symmetric channel', 0.5257478356361389), ('adversarial channel', 0.5150600671768188), ('information theoretically secure', 0.501105010509491), ('cryptographic', 0.47351327538490295), ('wiretap channel', 0.4575048089027405), ('adversary access', 0.4475444257259369), ('capacity channel', 0.4323585629463196), ('secret key agreement', 0.4269713759422302), ('unique decoding', 0.4171360433101654), ('theoretically secure', 0.41682958602905273)]"
1136,1136,26,1136_extreme order statistics_stochastic order_stochastic ordering_order statistics,"['extreme order statistics', 'stochastic order', 'stochastic ordering', 'order statistics', 'stochastic ordering results', 'second order statistics', 'distributions order', 'stochastic dominance', 'stochastic comparisons', 'stochastic comparison']","[""Some new ordering results on stochastic comparisons of second largest\n  order statistics from independent and interdependent heterogeneous\n  distributions   The second-largest order statistic is of special importance in reliability\ntheory since it represents the time to failure of a $2$-out-of-$n$ system.\nConsider two $2$-out-of-$n$ systems with heterogeneous random lifetimes. The\nlifetimes are assumed to follow heterogeneous general exponentiated\nlocation-scale models. In this communication, the usual stochastic and reversed\nhazard rate orders between the systems' lifetimes are established under two\ncases. For the case of independent random lifetimes, the usual stochastic order\nand the reversed hazard rate order between the second-largest order statistics\nare obtained by using the concept of vector majorization and related orders.\nFor the dependent case, the conditions under which the usual stochastic order\nbetween the second-largest order statistics holds are investigated. To\nillustrate the theoretical findings, some special cases of the exponentiated\nlocation-scale model are considered.\n"", 'Stochastic Comparisons of Second-Order Statistics from Dependent and\n  Heterogenous Modified Proportional Hazard Rate Observations   In this manuscript, we study stochastic comparisons of the second-order\nstatistics from dependent or independent observations with modified\nproportional hazard rates models. First, we establish the usual stochastic\norder of the second-order statistics from dependent and heterogeneous\nobservations. Second, sufficient conditions are provided in the hazard rate\norder of the second-order statistics from independent observations. Then, we\ninvestigate the hazard rate order of the second-order statistics arising from\ntwo sets of independent multiple-outlier modified proportional hazard rates\nobservations. Finally, some numerical examples are given to illustrate the\ntheoretical findings.\n', 'Ordering results of extreme order statistics from multiple-outlier scale\n  models with dependence   In this paper, we focus on stochastic comparisons of extreme order statistics\nstemming from multiple-outlier scale models with dependence. Archimedean copula\nis used to model dependence structure among nonnegative random variables.\nSufficient conditions are obtained for comparison of the largest order\nstatistics in the sense of the usual stochastic, reversed hazard rate, star and\nLorenz orders. The smallest order statistics are also compared with respect to\nthe usual stochastic, hazard rate, star and Lorenz orders. To illustrate the\ntheoretical establishments, some examples are provided.\n']","[('extreme order statistics', 0.6590502262115479), ('stochastic order', 0.6283831596374512), ('stochastic ordering', 0.597769021987915), ('order statistics', 0.5975467562675476), ('stochastic ordering results', 0.596535861492157), ('second order statistics', 0.5927347540855408), ('distributions order', 0.5586917996406555), ('stochastic dominance', 0.46641597151756287), ('stochastic comparisons', 0.46459364891052246), ('stochastic comparison', 0.4619215130805969)]"
1137,1137,26,1137_frobenius manifolds_frobenius manifold_generalized frobenius_manifolds associated,"['frobenius manifolds', 'frobenius manifold', 'generalized frobenius', 'manifolds associated', 'manifolds related', 'dimensional frobenius', 'manifold structures', 'manifold underlying', 'integrable hierarchies', 'manifolds']","['Integrable hierarchies associated to infinite families of Frobenius\n  manifolds   We propose a new construction of an integrable hierarchy associated to any\ninfinite series of Frobenius manifolds satisfying a certain stabilization\ncondition. We study these hierarchies for Frobenius manifolds associated to\n$A_N$, $D_N$ and $B_N$ singularities. In the case of $A_N$ Frobenius manifolds\nour hierarchy turns out to coincide with the KP hierarchy; for $B_N$ Frobenius\nmanifolds it coincides with the BKP hierarchy; and for $D_N$ hierarchy it is a\ncertain reduction of the 2-component BKP hierarchy. As a side product to these\nresults we illustrate the enumerative meaning of certain coefficients of $A_N$,\n$D_N$ and $B_N$ Frobenius potentials.\n', 'Generalized Frobenius Manifolds with Non-flat Unity and Integrable\n  Hierarchies   For any generalized Frobenius manifold with non-flat unity, we construct a\nbihamiltonian integrable hierarchy of hydrodynamic type which is an analogue of\nthe Principal Hierarchy of a Frobenius manifold. We show that such an\nintegrable hierarchy, which we also call the Principal Hierarchy, possesses\nVirasoro symmetries and a tau structure, and the Virasoro symmetries can be\nlifted to symmetries of the tau-cover of the integrable hierarchy. We derive\nthe loop equation from the condition of linearization of actions of the\nVirasoro symmetries on the tau function, and construct the topological\ndeformation of the Principal Hierarchy of a semisimple generalized Frobenius\nmanifold with non-flat unity. We also give two examples of generalized\nFrobenius manifolds with non-flat unity and show that they are closely related\nto the well-known integrable hierarchies: the Volterra hierarchy, the\nq-deformed KdV hierarchy and the Ablowitz-Ladik hierarchy.\n', 'Generalized Legendre transformations and symmetries of the WDVV\n  equations   The Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations, as one would\nexpect from an integrable system, has many symmetries, both continuous and\ndiscrete. One class - the so-called Legendre transformations - were introduced\nby Dubrovin. They are a discrete set of symmetries between the stronger concept\nof a Frobenius manifold, and are generated by certain flat vector fields. In\nthis paper this construction is generalized to the case where the vector field\n(called here the Legendre field) is non-flat but satisfies a certain set of\ndefining equations. One application of this more general theory is to generate\nthe induced symmetry between almost-dual Frobenius manifolds whose underlying\nFrobenius manifolds are related by a Legendre transformation. This also\nprovides a map between rational and trigonometric solutions of the WDVV\nequations.\n']","[('frobenius manifolds', 0.7082231640815735), ('frobenius manifold', 0.678500235080719), ('generalized frobenius', 0.568204402923584), ('manifolds associated', 0.5572530627250671), ('manifolds related', 0.5334733128547668), ('dimensional frobenius', 0.5302738547325134), ('manifold structures', 0.528344988822937), ('manifold underlying', 0.5175291895866394), ('integrable hierarchies', 0.515609622001648), ('manifolds', 0.4975418746471405)]"
1138,1138,26,1138_space countably_measurable cardinal_cantor space_borel sets,"['space countably', 'measurable cardinal', 'cantor space', 'borel sets', 'baire category', 'mathbb countably', 'countably', 'polish topology', 'metrizable space', 'generalized continuum']","[""Countably perfectly meager sets   We study a strengthening of the notion of a perfectly meager set.\n  We say that that a subset $A$ of a perfect Polish space $X$ is countably\nperfectly meager in $X$, if for every sequence of perfect subsets $\\{P_n: n \\in\n{\\mathbb N}\\}$ of $X$, there exists an $F_\\sigma$-set $F$ in $X$ such that $A\n\\subseteq F$ and $F\\cap P_n$ is meager in $P_n$ for each $n$.\n  We give various characterizations and examples of countably perfectly meager\nsets. We prove that not every universally meager set is countably perfectly\nmeager correcting an earlier result of Bartoszy\\'nski.\n"", 'Countably perfectly meager and countably perfectly null sets   We study a strengthening of the notion of a universally meager set and its\ndual counterpart that strengthens the notion of a universally null set.\n  We say that a subset $A$ of a perfect Polish space $X$ is countably perfectly\nmeager (respectively, countably perfectly null) in $X$, if for every perfect\nPolish topology $\\tau$ on $X$, giving the original Borel structure of $X$, $A$\nis covered by an $F_\\sigma$-set $F$ in $X$ with the original Polish topology\nsuch that $F$ is meager with respect to $\\tau$ (respectively, for every finite,\nnon-atomic, Borel measure $\\mu$ on $X$, $A$ is covered by an $F_\\sigma$-set $F$\nin $X$ with $\\mu(F)=0$).\n  We prove that if $2^{\\aleph_0}\\leq \\aleph_2$, then there exists a universally\nmeager set in $2^{\\mathbb N}$ which is not countably perfectly meager in\n$2^{\\mathbb N}$ (respectively, a universally null set in $2^{\\mathbb N}$ which\nis not countably perfectly null in $2^{\\mathbb N}$).\n', 'Topology, Metric Spaces and the Generalized Continuum Hypothesis   This is a paper that aims to interpret the cardinality of a set in terms of\nBaire Category, i.e. how many closed nowhere dense sets can be deleted from a\nset before the set itself becomes negligible. . To do this natural\ntree-theoretic structures such as the Baire topology are introduced, and the\nBaire Category Theorem is extended to a statement that a $\\aleph$-sequentially\ncomplete binary tree representation of a Hausdorff topological space that has a\nclopen base of cardinality $\\aleph$ and no isolated or discrete points is not\nthe union of $<\\aleph+1$-many nowhere dense subsets for cardinal\n$\\aleph\\ge\\aleph_{0}$, where a $\\aleph$-sequentially complete topological space\nis a space where every function $f:\\aleph\\rightarrow\\{0.1\\}$ is such that\n$(\\forall x)(x\\in f\\rightarrow x\\in\\in X)\\rightarrow(f\\in X)$. It is shown that\nif $\\aleph<\\left|X\\right|\\le2^{\\aleph}$ for $\\left|X\\right|$ the cardinality of\na set $X$, then it is possible to force\n$\\left|X\\right|-\\aleph\\times\\left|X\\right|\\ne\\emptyset$ by deleting a dense\nsequence of $\\aleph$ specially selected clopen sets, while if any dense\nsequence of $\\aleph+1$ clopen sets are deleted then\n$\\left|X\\right|-(\\aleph+1)\\times\\left|X\\right|=\\emptyset$. This gives rise to\nan alternative definition of cardinality as the number of basic clopen sets\n(intervals in fact) needed to be deleted from a set to force an empty\nremainder. This alternative definition of cardinality is consistent with and\nfollows from the Generalized Continuum Hypothesis, which is shown by exhibiting\ntwo models of set theory, one an outer (modal) model, the other an inner,\ngeneralized metric model with an information minimization principle.\n']","[('space countably', 0.5221977233886719), ('measurable cardinal', 0.5091517567634583), ('cantor space', 0.5090914964675903), ('borel sets', 0.4740174412727356), ('baire category', 0.4715917706489563), ('mathbb countably', 0.4690036177635193), ('countably', 0.4568862318992615), ('polish topology', 0.4504614472389221), ('metrizable space', 0.42540597915649414), ('generalized continuum', 0.40336930751800537)]"
1139,1139,26,1139_epidemic models_fractional differential equations_fractional differential_covid 19 pandemic,"['epidemic models', 'fractional differential equations', 'fractional differential', 'covid 19 pandemic', 'effects fractional', 'fractional reaction diffusion', 'epidemic', 'fractional order', 'various fractional', 'fractional derivatives']","['Fractional Modelling and Optimal Control of COVID-19 Transmission in\n  Portugal   A fractional-order compartmental model was recently used to describe real\ndata of the first wave of the COVID-19 pandemic in Portugal [Chaos Solitons\nFractals 144 (2021), Art. 110652]. Here, we modify that model in order to\ncorrect time dimensions and use it to investigate the third wave of COVID-19\nthat occurred in Portugal from December 2020 to February 2021, and that has\nsurpassed all previous waves, both in number and consequences. A new fractional\noptimal control problem is then formulated and solved, with vaccination and\npreventive measures as controls. A cost-effectiveness analysis is carried out,\nand the obtained results are discussed.\n', ""Global stability and optimal control in a single-strain dengue model\n  with fractional-order transmission and recovery process   The current manuscript introduce a single-strain dengue model developed from\nstochastic processes incorporating fractional order transmission and recovery.\nThe fractional derivative has been introduced within the context of\ntransmission and recovery process, displaying characteristics similar to\ntempered fractional ($TF$) derivatives. It has been established that under\ncertain condition, a function's $TF$ derivatives are proportional to the\nfunction itself. Applying the following observation, we examined stability of\nseveral steady-state solutions, such as disease-free and endemic states, in\nlight of this newly formulated model, using the reproduction number (R_0). In\naddition, the precise range of epidemiological parameters for the fractional\norder model was determined by calibrating weekly registered dengue incidence in\nthe San Juan municipality of Puerto Rico, from April 9, 2010, to April 2, 2011.\nWe performed a global sensitivity analysis method to measure the influence of\nkey model parameters (along with the fractional-order coefficient) on total\ndengue cases and the basic reproduction number (R_0) using a Monte Carlo-based\npartial rank correlation coefficient (PRCC). Moreover, we formulated a\nfractional-order model with fractional control to asses the effectiveness of\ndifferent interventions, such as reduction the recruitment rate of mosquito\nbreeding, controlling adult vector, and providing individual protection. Also,\nwe established the existence of a solution for the fractional-order optimal\ncontrol problem. Finally, the numerical experiment illustrates that,\npolicymakers should place importance on the fractional order transmission and\nrecovery parameters that capture the underline mechanisms of disease along with\nreducing the spread of dengue cases, carried out through the implementation of\ntwo vector controls.\n"", 'Forecast analysis of the epidemics trend of COVID-19 in the United\n  States by a generalized fractional-order SEIR model   In this paper, a generalized fractional-order SEIR model is proposed, denoted\nby SEIQRP model, which has a basic guiding significance for the prediction of\nthe possible outbreak of infectious diseases like COVID-19 and other insect\ndiseases in the future. Firstly, some qualitative properties of the model are\nanalyzed. The basic reproduction number $R_{0}$ is derived. When $R_{0}<1$, the\ndisease-free equilibrium point is unique and locally asymptotically stable.\nWhen $R_{0}>1$, the endemic equilibrium point is also unique. Furthermore, some\nconditions are established to ensure the local asymptotic stability of\ndisease-free and endemic equilibrium points. The trend of COVID-19 spread in\nthe United States is predicted. Considering the influence of the individual\nbehavior and government mitigation measurement, a modified SEIQRP model is\nproposed, defined as SEIQRPD model. According to the real data of the United\nStates, it is found that our improved model has a better prediction ability for\nthe epidemic trend in the next two weeks. Hence, the epidemic trend of the\nUnited States in the next two weeks is investigated, and the peak of isolated\ncases are predicted. The modified SEIQRP model successfully capture the\ndevelopment process of COVID-19, which provides an important reference for\nunderstanding the trend of the outbreak.\n']","[('epidemic models', 0.5963456630706787), ('fractional differential equations', 0.4936699867248535), ('fractional differential', 0.4451577365398407), ('covid 19 pandemic', 0.4406449496746063), ('effects fractional', 0.4376985430717468), ('fractional reaction diffusion', 0.4229089319705963), ('epidemic', 0.4145365357398987), ('fractional order', 0.41126707196235657), ('various fractional', 0.40414199233055115), ('fractional derivatives', 0.3985908627510071)]"
1140,1140,26,1140_network structures_dynamic networks_dynamical network_networks partial,"['network structures', 'dynamic networks', 'dynamical network', 'networks partial', 'network structure', 'dynamical networks', 'forward networks', 'identifiability', 'directed acyclic graphs', 'networks']","['Local Network Identifiability with Partial Excitation and Measurement   This work focuses on the identifiability of dynamical networks with partial\nexcitation and measurement: a set of nodes are interconnected by unknown\ntransfer functions according to a known topology, some nodes are subject to\nexternal excitation, and some nodes are measured. The goal is to determine\nwhich transfer functions in the network can be recovered based on the\ninput-output data collected from the excited and measured nodes.\n  We propose a local version of network identifiability, representing the\nability to recover transfer functions which are approximately known, or to\nrecover them up to a discrete ambiguity. We show that local identifiability is\na generic property, establish a necessary and sufficient condition in terms of\nmatrix generic ranks, and exploit this condition to develop an algorithm\ndetermining, with probability 1, which transfer functions are locally\nidentifiable. Our implementation presents the results graphically, and is\npublicly available.\n', 'Combinatorial Characterization for Global Identifiability of Separable\n  Networks with Partial Excitation and Measurement   This work focuses on the generic identifiability of dynamical networks with\npartial excitation and measurement: a set of nodes are interconnected by\ntransfer functions according to a known topology, some nodes are excited, some\nare measured, and only a part of the transfer functions are known. Our goal is\nto determine whether the unknown transfer functions can be generically\nrecovered based on the input-output data collected from the excited and\nmeasured nodes. We introduce the notion of separable networks, for which global\nand so-called local identifiability are equivalent. A novel approach yields a\nnecessary and sufficient combinatorial characterization for local\nidentifiability for such graphs, in terms of existence of paths and conditions\non their parity. Furthermore, this yields a necessary condition not only for\nseparable networks, but for networks of any topology.\n', 'Path-Based Conditions for Local Network Identifiability -- Full Version   This work focuses on the generic identifiability of dynamical networks with\npartial excitation and measurement: a set of nodes are interconnected by\ntransfer functions according to a known topology, some nodes are excited, some\nare measured, and only a part of the transfer functions are known. Our goal is\nto determine whether the unknown transfer functions can be generically\nrecovered based on the input-output data collected from the excited and\nmeasured nodes. We propose a decoupled version of generic identifiability that\nis necessary for generic local identifiability and might be equivalent as no\ncounter-example to sufficiency has been found yet in systematic trials. This\nnew notion can be interpreted as the generic identifiability of a larger\nnetwork, obtained by duplicating the graph, exciting one copy and measuring the\nother copy. We establish a necessary condition for decoupled identifiability in\nterms of vertex-disjoint paths in the larger graph, and a sufficient one.\n']","[('network structures', 0.5383200645446777), ('dynamic networks', 0.5234977006912231), ('dynamical network', 0.5229799747467041), ('networks partial', 0.5198755264282227), ('network structure', 0.49773335456848145), ('dynamical networks', 0.48328736424446106), ('forward networks', 0.4481349289417267), ('identifiability', 0.4446600675582886), ('directed acyclic graphs', 0.4339722990989685), ('networks', 0.4222288727760315)]"
1141,1141,26,1141_pairwise comparisons_comparison matrix_pairwise comparison_comparisons among,"['pairwise comparisons', 'comparison matrix', 'pairwise comparison', 'comparisons among', 'comparisons', 'matrix efficient', 'ranking methods', 'pairwise', 'consistent matrix', 'ranking']","['Pairwise Comparisons Matrix Decomposition into Approximation and\n  Orthogonal Component Using Lie Theory   This paper examines the use of Lie group and Lie Algebra theory to construct\nthe geometry of pairwise comparisons matrices. The Hadamard product (also known\nas coordinatewise, coordinate-wise, elementwise, or element-wise product) is\nanalyzed in the context of inconsistency and inaccuracy by the decomposition\nmethod.\n  The two designed components are the approximation and orthogonal components.\nThe decomposition constitutes the theoretical foundation for the multiplicative\npairwise comparisons.\n  Keywords: approximate reasoning, subjectivity, inconsistency,\nconsistency-driven, pairwise comparison, matrix Lie group, Lie algebra,\napproximation, orthogonality, decomposition.\n', ""On the coincidence of optimal completions for small pairwise comparison\n  matrices with missing entries   Incomplete pairwise comparison matrices contain some missing judgements. A\nnatural approach to estimate these values is provided by minimising a\nreasonable measure of inconsistency after unknown entries are replaced by\nvariables. Two widely used inconsistency indices for this purpose are Saaty's\ninconsistency index and the geometric inconsistency index, which are closely\nrelated to the eigenvector and the logarithmic least squares priority deriving\nmethods, respectively. The two measures are proven to imply the same optimal\nfilling for incomplete pairwise comparison matrices up to order four but not\nnecessarily for order at least five.\n"", 'On random pairwise comparisons matrices and their geometry   We describe a framework for random pairwise comparisons matrices, inspired by\nselected constructions releted to the so called inconsistency reduction of\npairwise comparisons (PC) matrices. In to build up structures on random\npairwise comparisons matrices, the set up for (deterministic) PC matrices for\nnon-reciprocal PC matrices is completed. The extension of basic concepts such\nas inconsistency indexes and geometric mean method are extended to random\npairwise comparisons matrices and completed by new notions which seem useful to\nus. Two procedures for (random) inconsistency reduction are sketched, based on\nwell-known existing objects, and a fiber bundle-like decomposition of random\npairwise comparisons is proposed.\n']","[('pairwise comparisons', 0.6660144925117493), ('comparison matrix', 0.628416895866394), ('pairwise comparison', 0.6082063913345337), ('comparisons among', 0.4936537742614746), ('comparisons', 0.4625777006149292), ('matrix efficient', 0.45575380325317383), ('ranking methods', 0.44747814536094666), ('pairwise', 0.4319939911365509), ('consistent matrix', 0.4074065387248993), ('ranking', 0.39043447375297546)]"
1142,1142,26,1142_graphs automorphism_graph surface_group surface_surface graph,"['graphs automorphism', 'graph surface', 'group surface', 'surface graph', 'type surfaces', 'curves surface', 'surfaces mapping class', 'infinite type surfaces', 'surface genus', 'automorphisms']","['Automorphisms of the k-curve graph   Given a natural number k and an orientable surface S of finite type, define\nthe k-curve graph to be the graph with vertices corresponding to isotopy\nclasses of essential simple closed curves on S and with edges corresponding to\npairs of such curves admitting representatives that intersect at most k times.\nWe prove that the automorphism group of the k-curve graph of a surface S is\nisomorphic to the extended mapping class group for all k sufficiently small\nwith respect to the Euler characteristic of S. We prove the same result for the\nso-called systolic complex, a variant of the curve graph whose complete\nsubgraphs encode the intersection patterns for any collection of systoles with\nrespect to a hyperbolic metric. This resolves a conjecture of Schmutz Schaller.\n', 'Automorphisms of fine curve graphs for nonorientable surfaces   The fine curve graph of a surface was introduced by Bowden, Hensel, and Webb\nas a graph consisting of essential simple closed curves on the surface. Long,\nMargalit, Pham, Verberne, and Yao proved that the automorphism group of the\nfine curve graph of a closed orientable surface is isomorphic to the\nhomeomorphism group of the surface. In this paper, based on their argument, we\nprove that the automorphism group of the fine curve graph of a closed\nnonorientable surface $N$ of genus $g \\geq 4$ is isomorphic to the\nhomeomorphism group of $N$.\n', 'The model theory of the curve graph   In this paper we develop a bridge between model theory, geometric topology,\nand geometric group theory. In particular, we investigate the Ivanov\nMetaconjecture from the point of view of model theory, and more broadly we seek\nto answer the general question: why does the curve graph of a surface play such\na central role in the study of surfaces and mapping class groups?\n  More specifically, we consider a surface $\\Sigma$ of finite type and its\ncurve graph $\\mathcal C(\\Sigma)$, and we investigate its first-order theory in\nthe language of graph theory. Crucially, $\\mathcal C(\\Sigma)$ is\nbi-interpretable with a certain object called the augmented Cayley graph of the\nmapping class group of the surface. We use this bi-interpretation to prove that\nthe theory of the curve graph is $\\omega$--stable, to compute its Morley rank,\nand to show that it has quantifier elimination with respect to the class of\n$\\forall\\exists$--formulae. We also show that many of the complexes which are\nnaturally associated to a surface are interpretable in $\\mathcal C(\\Sigma)$.\nThis shows that these complexes are all $\\omega$--stable and admit certain a\npriori bounds on their Morley ranks. We are able to use Morley ranks to prove\nthat various complexes are not bi--interpretable with the curve graph. As a\nconsequence of quantifier elimination, we show that algebraic intersection\nnumber is not definable in the first order theory of the curve graph. Finally,\nwe prove that the curve graph of a surface enjoys a novel phenomenon that we\ncall interpretation rigidity. That is, if surfaces $\\Sigma_1$ and $\\Sigma_2$\nadmits curve graphs that are mutually interpretable, then $\\Sigma_1$ and\n$\\Sigma_2$ are homeomorphic to each other. Along the way, numerous technical\nresults are obtained.\n']","[('graphs automorphism', 0.6781925559043884), ('graph surface', 0.5724775791168213), ('group surface', 0.5356616377830505), ('surface graph', 0.524045467376709), ('type surfaces', 0.5193705558776855), ('curves surface', 0.5141112804412842), ('surfaces mapping class', 0.5075969099998474), ('infinite type surfaces', 0.5028195977210999), ('surface genus', 0.499921053647995), ('automorphisms', 0.4984119236469269)]"
1143,1143,26,1143_heisenberg spin_kondo_spin chains_phase transitions,"['heisenberg spin', 'kondo', 'spin chains', 'phase transitions', 'spin chain', 'anisotropic heisenberg', 'phase structure', 'majorana fermions', 'antiferromagnetic', 'ferromagnetic phase']","['The Kondo effect in the quantum $XX$ spin chain   We investigate the boundary phenomena that arise in a finite-size $XX$ spin\nchain interacting through an $XX$ interaction with a spin$-\\frac{1}{2}$\nimpurity located at its edge. Upon Jordan-Wigner transformation, the model is\ndescribed by a quadratic Fermionic Hamiltonian. Our work displays, within this\nostensibly simple model, the emergence of the Kondo effect, a quintessential\nhallmark of strongly correlated physics. We also show how the Kondo cloud\nshrinks and turns into a single particle bound state as the impurity coupling\nincreases beyond a critical value. Using both \\textit{Bethe Ansatz} and\n\\textit{exact diagonalization} techniques, we show that the local moment of the\nimpurity is screened by different mechanisms depending on the ratio of the\nboundary and bulk coupling. When the ratio falls below the critical value\n$\\sqrt{2}$, the impurity is screened via the multiparticle Kondo effect.\nHowever, when the ratio between the coupling exceeds the critical value , a\nbound mode is formed at the impurity site which screens the spin of the\nimpurity. We show that the boundary phase transition is reflected in local\nground state properties by calculating the spinon density of states, the\nmagnetization at the impurity site in the presence of a global magnetic field,\nand the finite temperature susceptibility. We find that the spinon density of\nstates in the Kondo phase has the characteristic Lorentzian peak that moves\nfrom the Fermi level to the maximum energy of the spinon as the impurity\ncoupling is increased and becomes a localized bound mode in the bound mode\nphase. Moreover, the impurity magnetization and the finite temperature impurity\nsusceptibility behave differently in the two phases. When the boundary coupling\n$J_{\\mathrm{imp}}$ exceeds the critical value $\\sqrt{2}J$, the model is no\nlonger boundary conformal invariant as a massive bound mode appears at the\nimpurity site.\n', 'Overscreened spin-$\\frac{1}{2}$ Kondo impurity and Shiba state at the\n  edge of a one-dimensional spin-1 superconducting wire   We consider a model describing a system where the superconductivity competes\nwith the overscreened Kondo effect. The model consists of a single\nspin$-\\frac{1}{2}$ quantum impurity at the edge of a quantum wire where\nspin$-1$ bulk fermions interact attractively, generating a (superconducting)\nmass gap. The competition between the Kondo screening and the superconductivity\nleads to a rich phase structure. We find that for strong Kondo coupling, there\nis a regime of phase space where the Kondo phase is stable with the impurity\n\\textit{overscreened} by a multiparticle Kondo effect, and a Kondo scale is\ndynamically generated. When the bulk and boundary interaction strength are\ncomparable, we find that a midgap state appears in the spectrum and screens the\nimpurity, while in the ground state, the impurity is unscreened. This midgap\nstate is akin to the Yu-Shiba-Rushinov (YSR) states that exist in the entire\nphase space in the BCS superconductor. Moreover, when the bulk superconducting\ninteraction strength is stronger than the boundary Kondo interaction strength,\nthe impurity can no longer be screened. Further, between the Kondo and YSR\nphases, we find a novel phase where, while the Kondo cloud overscreens the\nimpurity, a boundary excitation exists that has vanishing energy in the\nthermodynamic limit. Similar phase diagrams that result from competition\nbetween different mechanisms were found for other models, too: the dissipative\nKondo system, where dissipation competes with screening; the Kondo impurity\ncoupled to spin-1/2 attractively interacting fermions where condensation\ncompetes with screening; and the XXX-Kondo model, where the lattice cutoff and\nthe bulk spin interaction compete with screening.\n', 'Kondo effect in the isotropic Heisenberg spin chain   We investigate the boundary effects that arise when spin-$\\frac{1}{2}$\nimpurities interact with the edges of the antiferromagnetic spin-$\\frac{1}{2}$\nHeisenberg chain through spin exchange interactions. We consider both cases\nwhen the couplings are ferromagnetic or anti-ferromagnetic. We find that in the\ncase of antiferromagnetic interaction, when the impurity coupling strength is\nmuch weaker than that in the bulk, the impurity is screened in the ground state\nvia the Kondo effect. The Kondo phase is characterized by the Lorentzian\ndensity of states and dynamically generated Kondo temperature $T_K$. As the\nimpurity coupling strength increases, $T_K$ increases until it reaches its\nmaximum value $T_0=2\\pi J$ which is the maximum energy carried by a single\nspinon. When the impurity coupling strength is increased further, we enter\nanother phase, the bound mode phase, where the impurity is screened in the\nground state by a single particle bound mode exponentially localized at the\nedge to which the impurity is coupled. We find that the impurity can be\nunscreened by removing the bound mode. There exists a boundary eigenstate phase\ntransition between the Kondo and the bound-mode phases, a transition which is\ncharacterized by the change in the number of towers of the Hilbert space. The\ntransition also manifests itself in ground state quantities like local impurity\ndensity of states and the local impurity magnetization. When the impurity\ncoupling is ferromagnetic, the impurity is unscreened in the ground state;\nhowever, when the absolute value of the ratio of the impurity and bulk coupling\nstrengths is greater than $\\frac{4}{5}$, the impurity can be screened by adding\na bound mode that costs energy greater than $T_0$. When two impurities are\nconsidered, the phases exhibited by each impurity remain unchanged in the\nthermodynamic limit, but nevertheless the system exhibits a rich phase diagram.\n']","[('heisenberg spin', 0.45463863015174866), ('kondo', 0.43033918738365173), ('spin chains', 0.41941678524017334), ('phase transitions', 0.3828153908252716), ('spin chain', 0.37259817123413086), ('anisotropic heisenberg', 0.37208887934684753), ('phase structure', 0.3603487014770508), ('majorana fermions', 0.3598653972148895), ('antiferromagnetic', 0.3574228584766388), ('ferromagnetic phase', 0.3565680980682373)]"
1144,1144,26,1144_unicritical polynomials_points polynomials_unicritical polynomial_polynomials dynamical,"['unicritical polynomials', 'points polynomials', 'unicritical polynomial', 'polynomials dynamical', 'points conjecture', 'polynomial dynamical', 'families polynomials', 'integer polynomials', 'rational maps', 'polynomial dynamical systems']","['Simultaneously preperiodic points for a family of polynomials in\n  positive characteristic   In the goundbreaking paper [BD11] (which opened a wide avenue of research\nregarding unlikely intersections in arithmetic dynamics), Baker and DeMarco\nprove that for the family of polynomials $f_\\lambda(x):=x^d+\\lambda$\n(parameterized by $\\lambda\\in\\mathbb{C}$), given two starting points $a$ and\n$b$ in $\\mathbb{C}$, if there exist infinitely many $\\lambda\\in\\mathbb{C}$ such\nthat both $a$ and $b$ are preperiodic under the action of $f_\\lambda$, then\n$a^d=b^d$. In this paper we study the same question, this time working in a\nfield of characteristic $p>0$. The answer in positive characteristic is more\nnuanced, as there are three distinct cases: (i) both starting points $a$ and\n$b$ live in $\\Fpbar$; (ii) $d$ is a power of $p$; and (iii) not both $a$ and\n$b$ live in $\\Fpbar$, while $d$ is not a power of $p$. Only in case~(iii), one\nderives the same conclusion as in characteristic $0$, i.e., that $a^d=b^d$. In\ncase~(i), one has that for each $\\lambda\\in\\Fpbar$, both $a$ and $b$ are\npreperiodic under the action of $f_\\lambda$, while in case~(ii), one obtains\nthat \\emph{also} whenever $a-b\\in\\Fpbar$, then for each parameter $\\lambda$, we\nhave that $a$ is preperiodic under the action of $f_\\lambda$ if and only if $b$\nis preperiodic under the action of $f_\\lambda$.\n', 'Distribution of preperiodic points in one-parameter families of rational\n  maps   Let $f_t$ be a one-parameter family of rational maps defined over a number\nfield $K$. We show that for all $t$ outside of a set of natural density zero,\nevery $K$-rational preperiodic point of $f_t$ is the specialization of some\n$K(T)$-rational preperiodic point of $f$. Assuming a weak form of the Uniform\nBoundedness Conjecture, we also calculate the average number of $K$-rational\npreperiodic points of $f$, giving some examples where this holds\nunconditionally. To illustrate the theory, we give new estimates on the average\nnumber of preperiodic points for the quadratic family $f_t(z) = z^2 + t$ over\nthe field of rational numbers.\n', 'Gonality of dynatomic curves and strong uniform boundedness of\n  preperiodic points   Fix $d \\ge 2$ and a field $k$ such that $\\mathrm{char}~k \\nmid d$. Assume\nthat $k$ contains the $d$th roots of $1$. Then the irreducible components of\nthe curves over $k$ parameterizing preperiodic points of polynomials of the\nform $z^d+c$ are geometrically irreducible and have gonality tending to\n$\\infty$. This implies the function field analogue of the strong uniform\nboundedness conjecture for preperiodic points of $z^d+c$. It also has\nconsequences over number fields: it implies strong uniform boundedness for\npreperiodic points of bounded eventual period, which in turn reduces the full\nconjecture for preperiodic points to the conjecture for periodic points.\n']","[('unicritical polynomials', 0.4527426064014435), ('points polynomials', 0.4312018156051636), ('unicritical polynomial', 0.41556793451309204), ('polynomials dynamical', 0.4069240987300873), ('points conjecture', 0.40257927775382996), ('polynomial dynamical', 0.3901556730270386), ('families polynomials', 0.3618832230567932), ('integer polynomials', 0.35783180594444275), ('rational maps', 0.3461057245731354), ('polynomial dynamical systems', 0.33997902274131775)]"
1145,1145,26,1145_donaldson thomas invariants_modular forms_calabi yau threefolds_iia string theory,"['donaldson thomas invariants', 'modular forms', 'calabi yau threefolds', 'iia string theory', 'vafa invariants', 'thomas invariants', 'gopakumar vafa invariants', 'calabi yau threefold', 'string theory', 'invariants']","['Quantum geometry and mock modularity   In previous work, we used new mathematical relations between Gopakumar-Vafa\n(GV) invariants and rank 0 Donaldson-Thomas (DT) invariants to determine the\nfirst few terms in the generating series of Abelian D4-D2-D0 indices for a\nclass of compact one-parameter Calabi-Yau threefolds. This allowed us to obtain\nstriking checks of S-duality, namely the prediction that these series should be\nvector-valued weakly holomorphic modular forms under $SL(2,\\mathbb{Z})$. In\nthis work, we extend this analysis to the case of D4-D2-D0 indices with two\nunits of D4-brane charge, where S-duality instead predicts that the\ncorresponding generating series should be mock modular with a specific shadow.\nFor the degree 10 hypersurface in weighted projective space\n$\\mathbb{P}_{5,2,1,1,1}$, and the degree 8 hypersurface in\n$\\\\mathbb{P}_{4,1,1,1,1}$, where GV invariants can be computed to sufficiently\nhigh genus, we find that the first few terms indeed match a unique mock modular\nform with the required properties, which we determine explicitly. Turning the\nargument around, we obtain new boundary conditions on the holomorphic ambiguity\nof the topological string amplitude, which in principle allow to determine it\ncompletely up to genus 95 and 112, respectively, i.e. almost twice the maximal\ngenus obtainable using gap and ordinary Castelnuovo vanishing conditions.\n', 'Quantum geometry, stability and modularity   By exploiting new mathematical relations between Pandharipande-Thomas (PT)\ninvariants, closely related to Gopakumar-Vafa (GV) invariants, and rank 0\nDonaldson-Thomas (DT) invariants counting D4-D2-D0 BPS bound states, we\nrigorously compute the first few terms in the generating series of Abelian\nD4-D2-D0 indices for compact one-parameter Calabi-Yau threefolds of\nhypergeometric type. In all cases where GV invariants can be computed to\nsufficiently high genus, we find striking confirmation that the generating\nseries is modular, and predict infinite series of Abelian D4-D2-D0 indices.\nConversely, we use these results to provide new constraints for the direct\nintegration method, which allows to compute GV invariants (and therefore the\ntopological string partition function) to higher genus than hitherto possible.\nThe triangle of relations between GV/PT/DT invariants is powered by a new\nexplicit formula relating PT and rank 0 DT invariants, which is proven in an\nAppendix by the second named author. As a corollary, we obtain rigorous\nCastelnuovo-type bounds for PT and GV invariants for CY threefolds with Picard\nrank one.\n', 'Modular bootstrap for D4-D2-D0 indices on compact Calabi-Yau threefolds   We investigate the modularity constraints on the generating series\n$h_r(\\tau)$ of BPS indices counting D4-D2-D0 bound states with fixed D4-brane\ncharge $r$ in type IIA string theory compactified on complete intersection\nCalabi-Yau threefolds with $b_2 = 1$. For unit D4-brane, $h_1$ transforms as a\n(vector-valued) modular form under the action of $SL(2,Z)$ and thus is\ncompletely determined by its polar terms. We propose an Ansatz for these terms\nin terms of rank 1 Donaldson-Thomas invariants, which incorporates\ncontributions from a single D6-anti-D6 pair. Using an explicit overcomplete\nbasis of the relevant space of weakly holomorphic modular forms (valid for any\n$r$), we find that for 10 of the 13 allowed threefolds, the Ansatz leads to a\nsolution for $h_1$ with integer Fourier coefficients, thereby predicting an\ninfinite series of DT invariants.For $r > 1$, $h_r$ is mock modular and\ndetermined by its polar part together with its shadow. Restricting to $r = 2$,\nwe use the generating series of Hurwitz class numbers to construct a series\n$h^{an}_2$ with exactly the same modular anomaly as $h_2$, so that the\ndifference $h_{2}-h^{an}_2$ is an ordinary modular form fixed by its polar\nterms. For lack of a satisfactory Ansatz, we leave the determination of these\npolar terms as an open problem.\n']","[('donaldson thomas invariants', 0.6045555472373962), ('modular forms', 0.504206120967865), ('calabi yau threefolds', 0.46036261320114136), ('iia string theory', 0.4529677629470825), ('vafa invariants', 0.44268351793289185), ('thomas invariants', 0.44138532876968384), ('gopakumar vafa invariants', 0.415873259305954), ('calabi yau threefold', 0.41086965799331665), ('string theory', 0.4078749120235443), ('invariants', 0.40304288268089294)]"
1146,1146,26,1146_lefschetz fibrations_lefschetz fibration_torus fibrations_lefschetz,"['lefschetz fibrations', 'lefschetz fibration', 'torus fibrations', 'lefschetz', 'orientable surface genus', 'fibrations', 'surface genus', 'fibrations mathbb', 'symplectic manifolds', 'fibration']","['Low-slope Lefschetz fibrations   For $g\\geq 3$, we construct genus-$g$ Lefschetz fibrations over the\ntwo-sphere whose slopes are arbitrarily close to $2$. The total spaces of the\nLefschetz fibrations can be chosen to be minimal and simply connected. It is\nalso shown that the infimum and the supremum of slopes all Lefschetz fibrations\nare not realized as slopes.\n', ""Compatible Relative Lefschetz Fibrations On Admissible Relative Stein\n  Pairs   For more than two decades it has been known that any compact Stein surface\n(of real dimension four) admits a compatible Lefschetz fibration over a\ntwo-disk. More recently, Giroux and Pardon have generalized this result by\ngiving a complex geometric proof for the existence of compatible Lefschetz\nfibrations on Stein domains of any even dimension. As a preparatory step in\nproving the former, Akbulut and Ozbagci have shown that there exist infinitely\nmany pairwise non-equivalent Lefschetz fibrations on the four-ball by using a\nresult of Lyon constructing fibrations on the complements of (p,q)-torus links\nin the three-sphere. In this paper, we first extend this result to obtain\ncompatible Lefschetz fibrations on the six-ball whose pages are (p, q,\n2)-Brieskorn varieties, and then construct a compatible 'relative' Lefschetz\nfibrations on any Stein domain (of dimension six) which admit a certain\n('admissible') 'relative Stein pair' structure. In particular, we provide a\npurely topological proof for the existence of Lefschetz fibrations on specific\n6-dimensional Stein domains.\n"", 'Geography of symplectic Lefschetz fibrations and rational blowdowns   We produce simply connected, minimal, symplectic Lefschetz fibrations\nrealizing all the lattice points in the symplectic geography plane below the\nNoether line. This provides a symplectic extension of the classical works\npopulating the complex geography plane with holomorphic Lefschetz fibrations.\nOur examples are obtained by rationally blowing down Lefschetz fibrations with\nclustered nodal fibers, the total spaces of which are potentially new homotopy\nelliptic surfaces. Similarly, clustering nodal fibers on higher genera\nLefschetz fibrations on standard rational surfaces, we get rational blowdown\nconfigurations that yield new constructions of small symplectic exotic\n$4$-manifolds. We present an example of a construction of a minimal symplectic\nexotic $\\mathbb{CP} \\# 5\\,\\overline{\\mathbb{CP}}$ through this procedure\napplied to a genus-$3$ fibration.\n']","[('lefschetz fibrations', 0.7875679731369019), ('lefschetz fibration', 0.7584019899368286), ('torus fibrations', 0.5687659978866577), ('lefschetz', 0.5187983512878418), ('orientable surface genus', 0.49427345395088196), ('fibrations', 0.48639777302742004), ('surface genus', 0.45292720198631287), ('fibrations mathbb', 0.4300011694431305), ('symplectic manifolds', 0.42909449338912964), ('fibration', 0.4112130403518677)]"
1147,1147,26,1147_superconductivity_superconductors_superconducting_superconductor,"['superconductivity', 'superconductors', 'superconducting', 'superconductor', 'critical temperature', 'critical magnetic', 'temperature magnetic', 'second order phase', 'landau theory', 'transition temperature']","['The BCS Critical Temperature at High Density   We investigate the BCS critical temperature $T_c$ in the high-density limit\nand derive an asymptotic formula, which strongly depends on the behavior of the\ninteraction potential $V$ on the Fermi-surface. Our results include a rigorous\nconfirmation for the behavior of $T_c$ at high densities proposed by Langmann,\nTriola, and Balatsky (Phys. Rev. Lett. 122, 2019) and identify precise\nconditions under which superconducting domes arise in BCS theory.\n', 'Another operator-theoretical proof for the second-order phase transition\n  in the BCS-Bogoliubov model of superconductivity   In the preceding papers, imposing certain complicated and strong conditions,\nthe present author showed that the solution to the BCS-Bogoliubov gap equation\nin superconductivity is twice differentiable only on the neighborhoods of\nabsolute zero temperature and the transition temperature so as to show that the\nphase transition is of the second order from the viewpoint of operator theory.\nInstead, we impose a certain simple and weak condition in this paper, and show\nthat there is a unique nonnegative solution and that the solution is indeed\ntwice differentiable on a closed interval from a certain positive temperature\nto the transition temperature as well as pointing out several properties of the\nsolution. We then give another operator-theoretical proof for the second-order\nphase transition in the BCS-Bogoliubov model. Since the thermodynamic potential\nhas the squared solution in its form, we deal with the squared BCS-Bogoliubov\ngap equation. Here, the potential in the BCS-Bogoliubov gap equation is a\nfunction and need not be a constant.\n', 'An operator-theoretical proof for the second-order phase transition in\n  the BCS-Bogoliubov model of superconductivity (final version)   We show that the transition from a normal conducting state to a\nsuperconducting state is a second-order phase transition in the BCS-Bogoliubov\nmodel of superconductivity from the viewpoint of operator theory. Here we have\nno magnetic field. Moreover we obtain the exact and explicit expression for the\ngap in the specific heat at constant volume at the transition temperature. To\nthis end, we have to differentiate the thermodynamic potential with respect to\nthe temperature two times. Since there is the solution to the BCS-Bogoliubov\ngap equation in the form of the thermodynamic potential, we have to\ndifferentiate the solution with respect to the temperature two times.\nTherefore, we need to show that the solution to the BCS-Bogoliubov gap equation\nis differentiable with respect to the temperature two times as well as its\nexistence and uniqueness. We carry out its proof on the basis of fixed point\ntheorems.\n']","[('superconductivity', 0.6234946846961975), ('superconductors', 0.5009216666221619), ('superconducting', 0.462942898273468), ('superconductor', 0.4608577489852905), ('critical temperature', 0.42736127972602844), ('critical magnetic', 0.41627076268196106), ('temperature magnetic', 0.3423801362514496), ('second order phase', 0.3403249979019165), ('landau theory', 0.3400411605834961), ('transition temperature', 0.33721432089805603)]"
1148,1148,26,1148_jensen shannon divergence_kullback leibler divergence_divergence measures_statistical divergences,"['jensen shannon divergence', 'kullback leibler divergence', 'divergence measures', 'statistical divergences', 'shannon divergence', 'leibler divergence', 'based divergences', 'bregman divergences', 'divergences', 'divergence particular']","['On a generalization of the Jensen-Shannon divergence   The Jensen-Shannon divergence is a renown bounded symmetrization of the\nKullback-Leibler divergence which does not require probability densities to\nhave matching supports. In this paper, we introduce a vector-skew\ngeneralization of the scalar $\\alpha$-Jensen-Bregman divergences and derive\nthereof the vector-skew $\\alpha$-Jensen-Shannon divergences. We study the\nproperties of these novel divergences and show how to build parametric families\nof symmetric Jensen-Shannon-type divergences. Finally, we report an iterative\nalgorithm to numerically compute the Jensen-Shannon-type centroids for a set of\nprobability densities belonging to a mixture family: This includes the case of\nthe Jensen-Shannon centroid of a set of categorical distributions or normalized\nhistograms.\n', 'On $f$-divergences between Cauchy distributions   We prove that the $f$-divergences between univariate Cauchy distributions are\nall symmetric, and can be expressed as strictly increasing scalar functions of\nthe symmetric chi-squared divergence. We report the corresponding scalar\nfunctions for the total variation distance, the Kullback-Leibler divergence,\nthe squared Hellinger divergence, and the Jensen-Shannon divergence among\nothers. Next, we give conditions to expand the $f$-divergences as converging\ninfinite series of higher-order power chi divergences, and illustrate the\ncriterion for converging Taylor series expressing the $f$-divergences between\nCauchy distributions. We then show that the symmetric property of\n$f$-divergences holds for multivariate location-scale families with prescribed\nmatrix scales provided that the standard density is even which includes the\ncases of the multivariate normal and Cauchy families. However, the\n$f$-divergences between multivariate Cauchy densities with different scale\nmatrices are shown asymmetric. Finally, we present several metrizations of\n$f$-divergences between univariate Cauchy distributions and further report\ngeometric embedding properties of the Kullback-Leibler divergence.\n', 'On a generalization of the Jensen-Shannon divergence and the\n  JS-symmetrization of distances relying on abstract means   The Jensen-Shannon divergence is a renown bounded symmetrization of the\nunbounded Kullback-Leibler divergence which measures the total Kullback-Leibler\ndivergence to the average mixture distribution. However the Jensen-Shannon\ndivergence between Gaussian distributions is not available in closed-form. To\nbypass this problem, we present a generalization of the Jensen-Shannon (JS)\ndivergence using abstract means which yields closed-form expressions when the\nmean is chosen according to the parametric family of distributions. More\ngenerally, we define the JS-symmetrizations of any distance using generalized\nstatistical mixtures derived from abstract means. In particular, we first show\nthat the geometric mean is well-suited for exponential families, and report two\nclosed-form formula for (i) the geometric Jensen-Shannon divergence between\nprobability densities of the same exponential family, and (ii) the geometric\nJS-symmetrization of the reverse Kullback-Leibler divergence. As a second\nillustrating example, we show that the harmonic mean is well-suited for the\nscale Cauchy distributions, and report a closed-form formula for the harmonic\nJensen-Shannon divergence between scale Cauchy distributions. We also define\ngeneralized Jensen-Shannon divergences between matrices (e.g., quantum\nJensen-Shannon divergences) and consider clustering with respect to these novel\nJensen-Shannon divergences.\n']","[('jensen shannon divergence', 0.6769646406173706), ('kullback leibler divergence', 0.6759063005447388), ('divergence measures', 0.6646428108215332), ('statistical divergences', 0.6508214473724365), ('shannon divergence', 0.6373534202575684), ('leibler divergence', 0.6125684976577759), ('based divergences', 0.6021129488945007), ('bregman divergences', 0.5411145687103271), ('divergences', 0.5388978719711304), ('divergence particular', 0.5352733731269836)]"
1149,1149,26,1149_stochastic hamilton jacobi_optimal stochastic control_stochastic optimal control_path dependent stochastic,"['stochastic hamilton jacobi', 'optimal stochastic control', 'stochastic optimal control', 'path dependent stochastic', 'stochastic path', 'stochastic hamilton', 'viscosity solutions hamilton', 'stochastic control problems', 'stochastic differential equations', 'stochastic control']","['Viscosity Solutions to Path-Dependent HJB Equation and Applications   In this article, the notion of viscosity solution is introduced for the\npath-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with the\noptimal control problems for path-dependent stochastic differential equations.\nWe identify the value functional of the optimal control problems as unique\nviscosity solution to the associated PHJB equations. Applications to backward\nstochastic Hamilton-Jacobi-Bellman equations are also given.\n', 'Viscosity Solutions to Second Order Path-Dependent\n  Hamilton-Jacobi-Bellman Equations and Applications   In this article, a notion of viscosity solutions is introduced for second\norder path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with\noptimal control problems for path-dependent stochastic differential equations.\nWe identify the value functional of optimal control problems as unique\nviscosity solution to the associated PHJB equations. We also show that our\nnotion of viscosity solutions is consistent with the corresponding notion of\nclassical solutions, and satisfies a stability property. Applications to\nbackward stochastic Hamilton-Jacobi-Bellman equations are also given.\n', 'Viscosity Solutions to Second Order Path-Dependent\n  Hamilton-Jacobi-Bellman Equations in Hilbert Spaces   In this article, a notion of viscosity solutions is introduced for second\norder path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with\noptimal control problems for path-dependent stochastic evolution equations in\nHilbert spaces. We identify the value functional of optimal control problems as\nunique viscosity solution to the associated PHJB equations. We also show that\nour notion of viscosity solutions is consistent with the corresponding notion\nof classical solutions, and satisfies a stability property.\n']","[('stochastic hamilton jacobi', 0.6592319011688232), ('optimal stochastic control', 0.5892377495765686), ('stochastic optimal control', 0.5873731970787048), ('path dependent stochastic', 0.5826730728149414), ('stochastic path', 0.5590148568153381), ('stochastic hamilton', 0.5588857531547546), ('viscosity solutions hamilton', 0.5554624795913696), ('stochastic control problems', 0.553261399269104), ('stochastic differential equations', 0.5507156252861023), ('stochastic control', 0.5365016460418701)]"
1150,1150,26,1150_feedback stability_analysis nonlinear systems_nonlinear feedback_output feedback stabilization,"['feedback stability', 'analysis nonlinear systems', 'nonlinear feedback', 'output feedback stabilization', 'stability analysis', 'nonlinear systems', 'feedback systems', 'feedback stabilization', 'stability regions', 'boundedness stability']","['A rolled-off passivity theorem   Given two nonlinear systems which only violate incremental passivity when\ntheir incremental gains are sufficiently small, we give a condition for their\nnegative feedback interconnection to have finite incremental gain, which\ngeneralizes the incremental small gain and incremental passivity theorems. The\nproperty may be determined graphically by plotting the Scaled Relative Graphs\n(SRGs) of the systems, which provides engineering significance to the\nmathematical result.\n', ""Mixed Small Gain and Phase Theorem: A new view using Scale Relative\n  Graphs   We introduce a novel approach to feedback stability analysis for linear\ntime-invariant (LTI) systems, overcoming the limitations of the sectoriality\nassumption in the small phase theorem. While phase analysis for single-input\nsingle-output (SISO) systems is well-established, multi-input multi-output\n(MIMO) systems lack a comprehensive phase analysis until recent advances\nintroduced with the small-phase theorem.\n  A limitation of the small-phase theorem is the sectorial condition, which\nstates that an operator's eigenvalues must lie within a specified angle sector\nof the complex plane. We propose a framework based on Scaled Relative Graphs\n(SRGs) to remove this assumption. We derive two main results: a graphical\nset-based stability condition using SRGs and a small-phase theorem with no\nsectorial assumption. These results broaden the scope of phase analysis and\nfeedback stability for MIMO systems.\n"", 'Soft and Hard Scaled Relative Graphs for Nonlinear Feedback Stability   This paper presents input-output stability analysis of nonlinear feedback\nsystems based on the notion of soft and hard scaled relative graphs (SRGs). The\nsoft and hard SRGs acknowledge the distinction between incremental positivity\nand incremental passivity and reconcile them from a graphical perspective. The\nessence of our proposed analysis is that the separation of soft/hard SRGs of\ntwo open-loop systems on the complex plane guarantees closed-loop stability.\nThe main results generalize an existing soft SRG separation theorem for bounded\nopen-loop systems which was proved based on interconnection properties of soft\nSRGs under a chordal assumption. By comparison, our analysis does not require\nthis chordal assumption and applies to possibly unbounded open-loop systems.\n']","[('feedback stability', 0.501076877117157), ('analysis nonlinear systems', 0.4950142800807953), ('nonlinear feedback', 0.47354069352149963), ('output feedback stabilization', 0.4679234027862549), ('stability analysis', 0.45917144417762756), ('nonlinear systems', 0.45730045437812805), ('feedback systems', 0.4482918679714203), ('feedback stabilization', 0.4419824182987213), ('stability regions', 0.4002453088760376), ('boundedness stability', 0.39071765542030334)]"
1151,1151,26,1151_distributed gradient descent_distributed machine learning_distributed computation_learning distributed,"['distributed gradient descent', 'distributed machine learning', 'distributed computation', 'learning distributed', 'distributed computing', 'distributed learning', 'straggler mitigation', 'straggler', 'stragglers', 'distributed coded']","['Straggler-aware Distributed Learning: Communication Computation Latency\n  Trade-off   When gradient descent (GD) is scaled to many parallel workers for large scale\nmachine learning problems, its per-iteration computation time is limited by the\nstraggling workers. Straggling workers can be tolerated by assigning redundant\ncomputations and coding across data and computations, but in most existing\nschemes, each non-straggling worker transmits one message per iteration to the\nparameter server (PS) after completing all its computations. Imposing such a\nlimitation results in two main drawbacks; over-computation due to inaccurate\nprediction of the straggling behaviour, and under-utilization due to treating\nworkers as straggler/non-straggler and discarding partial computations carried\nout by stragglers. In this paper, to overcome these drawbacks, we consider\nmulti-message communication (MMC) by allowing multiple computations to be\nconveyed from each worker per iteration, and design straggler avoidance\ntechniques accordingly. Then, we analyze how the proposed designs can be\nemployed efficiently to seek a balance between the computation and\ncommunication latency to minimize the overall latency. Furthermore, through\nextensive simulations, both model-based and real implementation on Amazon EC2\nservers, we identify the advantages and disadvantages of these designs in\ndifferent settings, and demonstrate that MMC can help improve upon existing\nstraggler avoidance schemes.\n', 'Nested Gradient Codes for Straggler Mitigation in Distributed Machine\n  Learning   We consider distributed learning in the presence of slow and unresponsive\nworker nodes, referred to as stragglers. In order to mitigate the effect of\nstragglers, gradient coding redundantly assigns partial computations to the\nworker such that the overall result can be recovered from only the\nnon-straggling workers. Gradient codes are designed to tolerate a fixed number\nof stragglers. Since the number of stragglers in practice is random and unknown\na priori, tolerating a fixed number of stragglers can yield a sub-optimal\ncomputation load and can result in higher latency. We propose a gradient coding\nscheme that can tolerate a flexible number of stragglers by carefully\nconcatenating gradient codes for different straggler tolerance. By proper task\nscheduling and small additional signaling, our scheme adapts the computation\nload of the workers to the actual number of stragglers. We analyze the latency\nof our proposed scheme and show that it has a significantly lower latency than\ngradient codes.\n', 'Gradient Coding with Dynamic Clustering for Straggler-Tolerant\n  Distributed Learning   Distributed implementations are crucial in speeding up large scale machine\nlearning applications. Distributed gradient descent (GD) is widely employed to\nparallelize the learning task by distributing the dataset across multiple\nworkers. A significant performance bottleneck for the per-iteration completion\ntime in distributed synchronous GD is $straggling$ workers. Coded distributed\ncomputation techniques have been introduced recently to mitigate stragglers and\nto speed up GD iterations by assigning redundant computations to workers. In\nthis paper, we consider gradient coding (GC), and propose a novel dynamic GC\nscheme, which assigns redundant data to workers to acquire the flexibility to\ndynamically choose from among a set of possible codes depending on the past\nstraggling behavior. In particular, we consider GC with clustering, and\nregulate the number of stragglers in each cluster by dynamically forming the\nclusters at each iteration; hence, the proposed scheme is called $GC$ $with$\n$dynamic$ $clustering$ (GC-DC). Under a time-correlated straggling behavior,\nGC-DC gains from adapting to the straggling behavior over time such that, at\neach iteration, GC-DC aims at distributing the stragglers across clusters as\nuniformly as possible based on the past straggler behavior. For both\nhomogeneous and heterogeneous worker models, we numerically show that GC-DC\nprovides significant improvements in the average per-iteration completion time\nwithout an increase in the communication load compared to the original GC\nscheme.\n']","[('distributed gradient descent', 0.6239281296730042), ('distributed machine learning', 0.5713602304458618), ('distributed computation', 0.560996949672699), ('learning distributed', 0.5410386919975281), ('distributed computing', 0.5341495275497437), ('distributed learning', 0.5252576470375061), ('straggler mitigation', 0.4964335262775421), ('straggler', 0.49334535002708435), ('stragglers', 0.4854632019996643), ('distributed coded', 0.482997328042984)]"
1152,1152,26,1152_signal separation_wavelet transform_mode decomposition_signal components,"['signal separation', 'wavelet transform', 'mode decomposition', 'signal components', 'wavelets', 'frequency component', 'time frequency representation', 'frequency representation', 'signal analysis', 'wavelet frames']","['A Chirplet Transform-based Mode Retrieval Method for Multicomponent\n  Signals with Crossover Instantaneous Frequencies   In nature and engineering world, the acquired signals are usually affected by\nmultiple complicated factors and appear as multicomponent nonstationary modes.\nIn such and many other situations, it is necessary to separate these signals\ninto a finite number of monocomponents to represent the intrinsic modes and\nunderlying dynamics implicated in the source signals. In this paper, we\nconsider the mode retrieval of a multicomponent signal which has crossing\ninstantaneous frequencies (IFs), meaning that some of the components of the\nsignal overlap in the time-frequency domain. We use the chirplet transform (CT)\nto represent a multicomponent signal in the three-dimensional space of time,\nfrequency and chirp rate and introduce a CT-based signal separation scheme\n(CT3S) to retrieve modes. In addition, we analyze the error bounds for IF\nestimation and component recovery with this scheme. We also propose a\nmatched-filter along certain specific time-frequency lines with respect to the\nchirp rate to make nonstationary signals be further separated and more\nconcentrated in the three-dimensional space of CT. Furthermore, based on the\napproximation of source signals with linear chirps at any local time, we\npropose an innovative signal reconstruction algorithm, called the group\n  filter-matched CT3S (GFCT3S), which also takes a group of components into\nconsideration simultaneously. GFCT3S is suitable for signals with crossing IFs.\nIt also decreases component recovery errors when the IFs curves of different\ncomponents are not crossover, but fast-varying and close to one and other.\nNumerical experiments on synthetic and real signals show our method is more\naccurate and consistent in signal separation than the empirical mode\ndecomposition, synchrosqueezing transform, and other approaches\n', 'Signal Separation Based on Adaptive Continuous Wavelet Transform and\n  Analysis   Recently the synchrosqueezed transform (SST) was developed as an empirical\nmode decomposition (EMD)-like tool to enhance the time-frequency resolution and\nenergy concentration of a multi-component non-stationary signal and provides\nmore accurate component recovery. To recover individual components, the SST\nmethod consists of two steps. First the instantaneous frequency (IF) of a\ncomponent is estimated from the SST plane. Secondly, after IF is recovered, the\nassociated component is computed by a definite integral along the estimated IF\ncurve on the SST plane. The reconstruction accuracy for a component depends\nheavily on the accuracy of the IFs estimation carried out in the first step.\nMore recently, a direct method of the time-frequency approach, called signal\nseparation operation (SSO), was introduced for multi-component signal\nseparation. While both SST and SSO are mathematically rigorous on IF\nestimation, SSO avoids the second step of the two-step SST method in component\nrecovery (mode retrieval). The SSO method is based on some variant of the\nshort-time Fourier transform. In the present paper, we propose a direct method\nof signal separation based on the adaptive continuous wavelet-like transform\n(CWLT) by introducing two models of the adaptive CWLT-based approach for signal\nseparation: the sinusoidal signal-based model and the linear chirp-based model,\nwhich are derived respectively from sinusoidal signal approximation and the\nlinear chirp approximation at any time instant. A more accurate component\nrecovery formula is derived from linear chirp local approximation. We present\nthe theoretical analysis of our approach. For each model, we establish the\nerror bounds for IF estimation and component recovery.\n', 'Analysis of an Adaptive Short-Time Fourier Transform-Based\n  Multicomponent Signal Separation Method Derived from Linear Chirp Local\n  Approximation   The synchrosqueezing transform (SST) has been developed as a powerful\nEMD-like tool for instantaneous frequency (IF) estimation and component\nseparation of non-stationary multicomponent signals. Recently, a direct method\nof the time-frequency approach, called signal separation operation (SSO), was\nintroduced to solving the problem of multicomponent signal separation. While\nboth SST and SSO are mathematically rigorous on IF estimation, SSO avoids the\nsecond step of the two-step SST method in component recovery (mode retrieval).\nIn addition, SSO is simple: the IF of a component is estimated by a\ntime-frequency ridge of the SSO plane; and this component is recovered by\nsimply plugging the time-frequency ridge to the SSO operation. In recent paper\n""Direct signal separation via extraction of local frequencies with adaptive\ntime-varying parameters"", after showing that the SSO operation is related to\nthe adaptive short-time Fourier transform (STFT), the authors obtained a more\naccurate component recovery formula derived from the linear chirp (also called\nlinear frequency modulation signal) approximation at any local time and they\nalso proposed a recovery scheme to extract the signal components one by one\nwith the time-varying window updated for each component. However the\ntheoretical analysis of the recovery formula derived from linear chirp local\napproximation has not been studied there. In this paper, we carry out such\nanalysis and obtain error bounds for IF estimation and component recovery.\nThese results provide a mathematical guarantee to the proposed adaptive\nSTFT-based non-stationary multicomponent signal separation method.\n']","[('signal separation', 0.519076943397522), ('wavelet transform', 0.4437302350997925), ('mode decomposition', 0.4432297348976135), ('signal components', 0.44280993938446045), ('wavelets', 0.43889302015304565), ('frequency component', 0.43666061758995056), ('time frequency representation', 0.4284462630748749), ('frequency representation', 0.41196197271347046), ('signal analysis', 0.4109112024307251), ('wavelet frames', 0.4044577479362488)]"
1153,1153,26,1153_tableaux_diagrammatic_webs_symmetry,"['tableaux', 'diagrammatic', 'webs', 'symmetry', 'plabic graphs', 'give diagrammatic', 'mathfrak sl _3', 'mathfrak sl _2', 'mathfrak sl _4', 'diagrams']","['Web bases in degree two from hourglass plabic graphs   Webs give a diagrammatic calculus for spaces of $U_q(\\mathfrak{sl}_r)$-tensor\ninvariants, but intrinsic characterizations of web bases are only known in\ncertain cases. Recently, we introduced hourglass plabic graphs to give the\nfirst such $U_q(\\mathfrak{sl}_4)$-web bases. Separately, Fraser introduced a\nweb basis for Pl\\""{u}cker degree two representations of arbitrary\n$U_q(\\mathfrak{sl}_r)$. Here, we show that Fraser\'s basis agrees with that\npredicted by the hourglass plabic graph framework and give an intrinsic\ncharacterization of the resulting webs. A further compelling feature with many\napplications is that our bases exhibit rotation-invariance. Together with the\nresults of our earlier paper, this implies that hourglass plabic graphs give a\nuniform description of all known rotation-invariant $U_q(\\mathfrak{sl}_r)$-web\nbases. Moreover, this provides a single combinatorial model simultaneously\ngeneralizing the Tamari lattice, the alternating sign matrix lattice, and the\nlattice of plane partitions. As a part of our argument, we develop properties\nof square faces in arbitrary hourglass plabic graphs, a key step in our program\ntowards general $U_q(\\mathfrak{sl}_r)$-web bases.\n', 'The transition matrix between the Specht and $\\mathfrak{sl}_3$ web bases\n  is unitriangular with respect to shadow containment   Webs are planar graphs with boundary that describe morphisms in a\ndiagrammatic representation category for $\\mathfrak{sl}_k$. They are studied\nextensively by knot theorists because braiding maps provide a categorical way\nto express link diagrams in terms of webs, producing quantum invariants like\nthe well-known Jones polynomial. One important question in representation\ntheory is to identify the relationships between different bases; coefficients\nin the change-of-basis matrix often describe combinatorial, algebraic, or\ngeometric quantities (like, e.g., Kazhdan-Lusztig polynomials). By ""flattening""\nthe braiding maps, webs can also be viewed as the basis elements of a\nsymmetric-group representation.\n  In this paper, we define two new combinatorial structures for webs: band\ndiagrams and their one-dimensional projections, shadows, that measure depths of\nregions inside the web. As an application, we resolve an open conjecture that\nthe change-of-basis between the so-called Specht basis and web basis of this\nsymmetric-group representation is unitriangular for $\\mathfrak{sl}_3$-webs. We\ndo this using band diagrams and shadows to construct a new partial order on\nwebs that is a refinement of the usual partial order. In fact, we prove that\nfor $\\mathfrak{sl}_2$-webs, our new partial order coincides with the tableau\npartial order on webs studied by the authors and others. We also prove that\nthough the new partial order for $\\mathfrak{sl}_3$-webs is a refinement of the\npreviously-studied tableau order, the two partial orders do not agree for\n$\\mathfrak{sl}_3$.\n', 'Rotation-invariant web bases from hourglass plabic graphs   Webs give a diagrammatic calculus for spaces of tensor invariants. We\nintroduce hourglass plabic graphs as a new avatar of webs, and use these to\ngive the first rotation-invariant $U_q(\\mathfrak{sl}_4)$-web basis, a\nlong-sought object. The characterization of our basis webs relies on the\ncombinatorics of these new plabic graphs and associated configurations of a\nsymmetrized six-vertex model. We give growth rules, based on a novel\ncrystal-theoretic technique, for generating our basis webs from tableaux and we\nuse skein relations to give an algorithm for expressing arbitrary webs in the\nbasis. We also discuss how previously known rotation-invariant web bases can be\nunified in our framework of hourglass plabic graphs.\n']","[('tableaux', 0.5090700387954712), ('diagrammatic', 0.43359678983688354), ('webs', 0.3915174603462219), ('symmetry', 0.38697487115859985), ('plabic graphs', 0.3773285746574402), ('give diagrammatic', 0.37367793917655945), ('mathfrak sl _3', 0.3642263412475586), ('mathfrak sl _2', 0.3639690577983856), ('mathfrak sl _4', 0.3614017069339752), ('diagrams', 0.35004478693008423)]"
1154,1154,26,1154_monic integer polynomials_galois groups_polynomials conjecture_groups polynomials,"['monic integer polynomials', 'galois groups', 'polynomials conjecture', 'groups polynomials', 'galois group', 'monic polynomials degree', 'monic polynomials', 'associated galois', 'galois', 'integer polynomials degree']","[""Towards a generalization of the van der Waerden's conjecture for\n  Sn-polynomials with integral coefficients over a fixed number field extension   The van der Waerden's Conjecture states that the set\n$\\mathscr{P}_{n,N}^0(\\mathbb{Q})$ of monic integer polynomials $f(X)$ of degree\n$n$, with height $\\le N$ such that the Galois group $G_{K_f/\\mathbb{Q}}$ of the\nsplitting field $K_f/\\mathbb{Q}$ is the full symmetric group, has order\n$|\\mathscr{P}_{n,N}^0(\\mathbb{Q})|=(2N)^n+O_n(N^{n-1})$ as\n$N\\rightarrow+\\infty$. The conjecture has been shown previously for cubic and\nquartics polynomials by van der Waerden, Chow and Dietmann. Subsequently,\nBhargava proved it for $n\\ge6$. In this paper, we generalize the result for\npolynomials with coefficients in the ring of algebraic integers $\\mathcal{O}_K$\nof a fixed finite extension $K/\\mathbb{Q}$ of degree $d$, for some values of\n$n$ and $d$.\n"", ""Galois groups of random integer polynomials and van der Waerden's\n  Conjecture   Of the $(2H+1)^n$ monic integer polynomials $f(x)=x^n+a_1 x^{n-1}+\\cdots+a_n$\nwith $\\max\\{|a_1|,\\ldots,|a_n|\\}\\leq H$, how many have associated Galois group\nthat is not the full symmetric group $S_n$? There are clearly $\\gg H^{n-1}$\nsuch polynomials, as may be obtained by setting $a_n=0$. In 1936, van der\nWaerden conjectured that $O(H^{n-1})$ should in fact also be the correct upper\nbound for the count of such polynomials. The conjecture has been known\npreviously for degrees $n\\leq 4$, due to work of van der Waerden and Chow and\nDietmann. The purpose of this paper is to prove van der Waerden's Conjecture\nfor all degrees $n$.\n"", ""A proof of van der Waerden's Conjecture on random Galois groups of\n  polynomials   Of the $(2H+1)^n$ monic integer polynomials $f(x)=x^n+a_1 x^{n-1}+\\cdots+a_n$\nwith $\\max\\{|a_1|,\\ldots,|a_n|\\}\\leq H$, how many have associated Galois group\nthat is not the full symmetric group $S_n$? There are clearly $\\gg H^{n-1}$\nsuch polynomials, as may be obtained by setting $a_n=0$. In 1936, van der\nWaerden conjectured that $O(H^{n-1})$ should in fact also be the correct upper\nbound for the count of such polynomials. The conjecture has been known\npreviously for degrees $n\\leq 4$, due to work of van der Waerden and Chow and\nDietmann.\n  In this expository article, we outline a proof of van der Waerden's\nConjecture for all degrees $n$.\n""]","[('monic integer polynomials', 0.48168936371803284), ('galois groups', 0.48073771595954895), ('polynomials conjecture', 0.47735610604286194), ('groups polynomials', 0.45074012875556946), ('galois group', 0.4478837549686432), ('monic polynomials degree', 0.4330953359603882), ('monic polynomials', 0.42787012457847595), ('associated galois', 0.4213772714138031), ('galois', 0.399248868227005), ('integer polynomials degree', 0.36998429894447327)]"
1155,1155,26,1155_monte carlo methods_multilevel monte carlo_monte carlo mlmc_carlo methods,"['monte carlo methods', 'multilevel monte carlo', 'monte carlo mlmc', 'carlo methods', 'quasi monte carlo', 'carlo mlmc', 'monte carlo qmc', 'multilevel monte', 'level monte carlo', 'qmc methods']","['Quasi-Monte Carlo and discontinuous Galerkin   In this study, we consider the development of tailored quasi-Monte Carlo\n(QMC) cubatures for non-conforming discontinuous Galerkin (DG) approximations\nof elliptic partial differential equations (PDEs) with random coefficients. We\nconsider both the affine and uniform and the lognormal models for the input\nrandom field, and investigate the use of QMC cubatures to approximate the\nexpected value of the PDE response subject to input uncertainty. In particular,\nwe prove that the resulting QMC convergence rate for DG approximations behaves\nin the same way as if continuous finite elements were chosen. Notably, the\nparametric regularity bounds for DG, which are developed in this work, are also\nuseful for other methods such as sparse grids. Numerical results underline our\nanalytical findings.\n', ""Covariance estimation using h-statistics in Monte Carlo and multilevel\n  Monte Carlo methods   We present novel Monte Carlo (MC) and multilevel Monte Carlo (MLMC) methods\nto determine the unbiased covariance of random variables using h-statistics.\nThe advantage of this procedure lies in the unbiased construction of the\nestimator's mean square error in a closed form. This is in contrast to\nconventional MC and MLMC covariance estimators, which are based on biased mean\nsquare errors defined solely by upper bounds, particularly within the MLMC. The\nnumerical results of the algorithms are demonstrated by estimating the\ncovariance of the stochastic response of a simple 1D stochastic elliptic PDE\nsuch as Poisson's model.\n"", 'Multilevel Monte Carlo methods for stochastic convection-diffusion\n  eigenvalue problems   We develop new multilevel Monte Carlo (MLMC) methods to estimate the\nexpectation of the smallest eigenvalue of a stochastic convection-diffusion\noperator with random coefficients. The MLMC method is based on a sequence of\nfinite element (FE) discretizations of the eigenvalue problem on a hierarchy of\nincreasingly finer meshes. For the discretized, algebraic eigenproblems we use\nboth the Rayleigh quotient (RQ) iteration and implicitly restarted Arnoldi\n(IRA), providing an analysis of the cost in each case. By studying the variance\non each level and adapting classical FE error bounds to the stochastic setting,\nwe are able to bound the total error of our MLMC estimator and provide a\ncomplexity analysis. As expected, the complexity bound for our MLMC estimator\nis superior to plain Monte Carlo. To improve the efficiency of the MLMC\nfurther, we exploit the hierarchy of meshes and use coarser approximations as\nstarting values for the eigensolvers on finer ones. To improve the stability of\nthe MLMC method for convection-dominated problems, we employ two additional\nstrategies. First, we consider the streamline upwind Petrov--Galerkin\nformulation of the discrete eigenvalue problem, which allows us to start the\nMLMC method on coarser meshes than is possible with standard FEs. Second, we\napply a homotopy method to add stability to the eigensolver for each sample.\nFinally, we present a multilevel quasi-Monte Carlo method that replaces Monte\nCarlo with a quasi-Monte Carlo (QMC) rule on each level. Due to the faster\nconvergence of QMC, this improves the overall complexity. We provide detailed\nnumerical results comparing our different strategies to demonstrate the\npractical feasibility of the MLMC method in different use cases. The results\nsupport our complexity analysis and further demonstrate the superiority over\nplain Monte Carlo in all cases.\n']","[('monte carlo methods', 0.6033533215522766), ('multilevel monte carlo', 0.5762081146240234), ('monte carlo mlmc', 0.5615097284317017), ('carlo methods', 0.5364764332771301), ('quasi monte carlo', 0.5172909498214722), ('carlo mlmc', 0.4495626389980316), ('monte carlo qmc', 0.4374580681324005), ('multilevel monte', 0.4329337179660797), ('level monte carlo', 0.4233415722846985), ('qmc methods', 0.415538489818573)]"
1156,1156,26,1156_conformal mappings_conformal maps_connected surfaces_simply connected surfaces,"['conformal mappings', 'conformal maps', 'connected surfaces', 'simply connected surfaces', 'compute conformal', 'connected surface', 'surfaces surface', 'open surfaces', 'surfaces', 'closed surfaces']","['Ellipsoidal Density-Equalizing Map for Genus-0 Closed Surfaces   Surface parameterization is a fundamental task in geometry processing and\nplays an important role in many science and engineering applications. In recent\nyears, the density-equalizing map, a shape deformation technique based on the\nphysical principle of density diffusion, has been utilized for the\nparameterization of simply connected and multiply connected open surfaces. More\nrecently, a spherical density-equalizing mapping method has been developed for\nthe parameterization of genus-0 closed surfaces. However, for genus-0 closed\nsurfaces with extreme geometry, using a spherical domain for the\nparameterization may induce large geometric distortion. In this work, we\ndevelop a novel method for computing density-equalizing maps of genus-0 closed\nsurfaces onto an ellipsoidal domain. This allows us to achieve ellipsoidal\narea-preserving parameterizations and ellipsoidal parameterizations with\ncontrolled area change. We further propose an energy minimization approach that\ncombines density-equalizing maps and quasi-conformal maps, which allows us to\nproduce ellipsoidal density-equalizing quasi-conformal maps for achieving a\nbalance between density-equalization and quasi-conformality. Using our proposed\nmethods, we can significantly improve the performance of surface remeshing for\ngenus-0 closed surfaces. Experimental results on a large variety of genus-0\nclosed surfaces are presented to demonstrate the effectiveness of our proposed\nmethods.\n', 'Parallelizable global conformal parameterization of simply-connected\n  surfaces via partial welding   Conformal surface parameterization is useful in graphics, imaging and\nvisualization, with applications to texture mapping, atlas construction,\nregistration, remeshing and so on. With the increasing capability in scanning\nand storing data, dense 3D surface meshes are common nowadays. While meshes\nwith higher resolution better resemble smooth surfaces, they pose computational\ndifficulties for the existing parameterization algorithms. In this work, we\npropose a novel parallelizable algorithm for computing the global conformal\nparameterization of simply-connected surfaces via partial welding maps. A given\nsimply-connected surface is first partitioned into smaller subdomains. The\nlocal conformal parameterizations of all subdomains are then computed in\nparallel. The boundaries of the parameterized subdomains are subsequently\nintegrated consistently using a novel technique called partial welding, which\nis developed based on conformal welding theory. Finally, by solving the Laplace\nequation for each subdomain using the updated boundary conditions, we obtain a\nglobal conformal parameterization of the given surface, with bijectivity\nguaranteed by quasi-conformal theory. By including additional shape\nconstraints, our method can be easily extended to achieve disk conformal\nparameterization for simply-connected open surfaces and spherical conformal\nparameterization for genus-0 closed surfaces. Experimental results are\npresented to demonstrate the effectiveness of our proposed algorithm. When\ncompared to the state-of-the-art conformal parameterization methods, our method\nachieves a significant improvement in both computational time and accuracy.\n', 'A Linear Formulation for Disk Conformal Parameterization of\n  Simply-Connected Open Surfaces   Surface parameterization is widely used in computer graphics and geometry\nprocessing. It simplifies challenging tasks such as surface registrations,\nmorphing, remeshing and texture mapping. In this paper, we present an efficient\nalgorithm for computing the disk conformal parameterization of simply-connected\nopen surfaces. A double covering technique is used to turn a simply-connected\nopen surface into a genus-0 closed surface, and then a fast algorithm for\nparameterization of genus-0 closed surfaces can be applied. The symmetry of the\ndouble covered surface preserves the efficiency of the computation. A planar\nparameterization can then be obtained with the aid of a M\\""obius transformation\nand the stereographic projection. After that, a normalization step is applied\nto guarantee the circular boundary. Finally, we achieve a bijective disk\nconformal parameterization by a composition of quasi-conformal mappings.\nExperimental results demonstrate a significant improvement in the computational\ntime by over 60%. At the same time, our proposed method retains comparable\naccuracy, bijectivity and robustness when compared with the state-of-the-art\napproaches. Applications to texture mapping are presented for illustrating the\neffectiveness of our proposed algorithm.\n']","[('conformal mappings', 0.5709342956542969), ('conformal maps', 0.5605505704879761), ('connected surfaces', 0.5139795541763306), ('simply connected surfaces', 0.5073083639144897), ('compute conformal', 0.4904464781284332), ('connected surface', 0.4898128807544708), ('surfaces surface', 0.48360076546669006), ('open surfaces', 0.4821959435939789), ('surfaces', 0.48008403182029724), ('closed surfaces', 0.47883841395378113)]"
1157,1157,26,1157_groupoid algebras_groupoid algebra_semigroup algebras_group algebras,"['groupoid algebras', 'groupoid algebra', 'semigroup algebras', 'group algebras', 'subalgebras algebras', 'path algebras', 'algebras characterize', 'algebra graded', 'irreducible module', 'cartan subalgebras']","['A classification of ideals in Steinberg and Leavitt path algebras over\n  arbitrary rings   We give a one-to-one correspondence between ideals in the Steinberg algebra\nof a Hausdorff ample groupoid $G$, and certain families of ideals in the group\nalgebras of isotropy groups in $G$. This generalises a known ideal\ncorrespondence theorem for Steinberg algebras of strongly effective groupoids.\nWe use this to give a complete graph-theoretic description of the ideal lattice\nof Leavitt path algebras over arbitrary commutative rings, generalising the\nclassification of ideals in Leavitt path algebras over fields.\n', 'On Steinberg algebras of Hausdorff ample groupoids over commutative\n  semirings   We investigate the algebra of a Hausdorff ample groupoid, introduced by\nSteinberg, over a commutative semiring S. In particular, we obtain a complete\ncharacterization of congruence-simpleness for such Steinberg algebras,\nextending the well-known characterizations when S is a field or a commutative\nring. We also provide a criterion for the Steinberg algebra of the graph\ngroupoid associated to an arbitrary graph to be congruence-simple. Motivated by\na result of Clark and Sims, we show that, over the Boolean semifield, the\nnatural homomorphism from the Leavitt path algebra to the Steinberg algebra is\nan isomorphism if and only if the associated graph is row-finite. Moreover, we\nestablish the Reduction Theorem and Uniqueness Theorems for Leavitt path\nalgebras of row-finite graphs over the Boolean semifield.\n', 'Chain Conditions for Etale Groupoid Algebras   Let $R$ be a unital commutative ring with unit and $\\mathscr{G}$ an ample\ngroupoid. Using the topology of the groupoid $\\mathscr{G}$, Steinberg defined\nan etale groupoid algebra $R\\mathscr{G}$. These etale groupoid algebras\ngeneralize various algebras including group algebras, commutative algebras over\na field generated by idempotents, traditional groupoid algebras, Leavitt path\nalgebras, higher-rank graph algebras, and inverse semigroup algebras. Steinberg\nlater characterized the classical chain conditions for etale groupoid algebras.\nWe characterize categorically noetherian and artinian, locally noetherian and\nartinian, and semisimple etale groupoid algebras, generalizing existing results\nfor Leavitt path algebras.\n']","[('groupoid algebras', 0.6291153430938721), ('groupoid algebra', 0.565112292766571), ('semigroup algebras', 0.5357769131660461), ('group algebras', 0.5100854635238647), ('subalgebras algebras', 0.46084728837013245), ('path algebras', 0.4384658932685852), ('algebras characterize', 0.4055633842945099), ('algebra graded', 0.38895556330680847), ('irreducible module', 0.3759751319885254), ('cartan subalgebras', 0.3744781017303467)]"
1158,1158,26,1158_knot theory_knot invariants_knots_knot types,"['knot theory', 'knot invariants', 'knots', 'knot types', 'knotted', 'virtual knots', 'knot', 'knotting', 'knot type', 'fixed knot']","['Characterising knotting properties of polymers in nanochannels   Using a lattice model of polymers in a tube, we define one way to\ncharacterise different configurations of a given knot as either ""local"" or\n""non-local"" and, for several ring polymer models, we provide both theoretical\nand numerical evidence that, at equilibrium, the non-local configurations are\nmore likely than the local ones. These characterisations are based on a\nstandard approach for measuring the ""size"" of a knot within a knotted polymer\nchain. The method involves associating knot-types to subarcs of the chain, and\nthen identifying a knotted subarc with minimal arclength; this arclength is\nthen the knot-size. If the resulting knot-size is small relative to the whole\nlength of the chain, then the knot is considered to be localised or ""local"". If\non the other hand the knot-size is comparable to the length of the chain, then\nthe knot is considered to be ""non-local"".\n  Using this definition, we establish that all but exponentially few\nsufficiently long self-avoiding polygons (closed chains) in a tubular\nsublattice of the simple cubic lattice are ""non-locally"" knotted. This is shown\nto also hold for the case when the same polygons are subject to an external\ntensile force, as well as in the extreme case when they are as compact as\npossible (no empty lattice sites). We also provide numerical evidence for small\ntube sizes that at equilibrium non-local knotting is more likely than local\nknotting, regardless of the strength of the stretching or compressing force. We\nnote however that because of the tube confinement, the occurrence of non-local\nknotting in walks (open chains) is significantly different than for polygons.\nThe relevance of these results to recent experiments involving DNA knots in\nsolid-state nanopores is also discussed.\n', 'Knot Theory for Proteins: Gauss Codes, Quandles and Bondles   Proteins are linear molecular chains that often fold to function. The\ntopology of folding is widely believed to define its properties and function,\nand knot theory has been applied to study protein structure and its\nimplications. More that 97% of proteins are, however, classified as unknots\nwhen intra-chain interactions are ignored. This raises the question as to\nwhether knot theory can be extended to include intra-chain interactions and\nthus be able to categorize topology of the proteins that are otherwise\nclassified as unknotted. Here, we develop knot theory for folded linear\nmolecular chains and apply it to proteins. For this purpose, proteins will be\nthought of as an embedding of a linear segment into three dimensions, with\nadditional structure coming from self-bonding. We then project to a\ntwo-dimensional diagram and consider the basic rules of equivalence between two\ndiagrams. We further consider the representation of projections of proteins\nusing Gauss codes, or strings of numbers and letters, and how we can equate\nthese codes with changes allowed in the diagrams. Finally, we explore the\npossibility of applying the algebraic structure of quandles to distinguish the\ntopologies of proteins. Because of the presence of bonds, we extend the theory\nto define bondles, a type of quandle particularly adapted to distinguishing the\ntopological types of proteins.\n', 'Knotting and weak knotting in confined, open random walks using virtual\n  knots   We probe the character of knotting in open, confined polymers, assigning knot\ntypes to open curves by identifying their projections as virtual knots. In this\nsense, virtual knots are transitional, lying in between classical knot types,\nwhich are useful to classify the ambiguous nature of knotting in open curves.\nModelling confined polymers using both lattice walks and ideal chains, we find\nan ensemble of random, tangled open curves whose knotting is not dominated by\nany single knot type, a behaviour we call weakly knotted. We compare cubically\nconfined lattice walks and spherically confined ideal chains, finding the weak\nknotting probability in both families is quite similar and growing with length,\ndespite the overall knotting probability being quite different. In contrast,\nthe probability of weak knotting in unconfined walks is small at all lengths\ninvestigated. For spherically confined ideal chains, weak knotting is strongly\ncorrelated with the degree of confinement but is almost entirely independent of\nlength. For ideal chains confined to tubes and slits, weak knotting is\ncorrelated with an adjusted degree of confinement, again with length having\nnegligible effect.\n']","[('knot theory', 0.7223449349403381), ('knot invariants', 0.6426017880439758), ('knots', 0.603226363658905), ('knot types', 0.6019339561462402), ('knotted', 0.5966895222663879), ('virtual knots', 0.5784186124801636), ('knot', 0.5739913582801819), ('knotting', 0.5642814040184021), ('knot type', 0.5523266792297363), ('fixed knot', 0.5029926896095276)]"
1159,1159,26,1159_coupled networks_lattice invariant_cluster synchronization_network dynamics,"['coupled networks', 'lattice invariant', 'cluster synchronization', 'network dynamics', 'network adjacency', 'synchronization heterogeneous', 'synchronization', 'coupled dynamical systems', 'subspaces invariant', 'networks higher order']","['Synchrony and Anti-synchrony in Weighted Networks   We consider weighted coupled cell networks, that is networks where the\ninteractions between any two cells have an associated weight that is a real\nvalued number. Weighted networks are ubiquitous in real-world applications. We\nconsider a dynamical systems perspective by associating to each network a set\nof continuous dynamical systems, the ones that respect the graph structure of\nthe network. For weighted networks it is natural for the admissible coupled\ncell systems to have an additive input structure. We present a characterization\nof the synchrony subspaces and the anti-synchrony subspaces for a weighted\nnetwork depending on the restrictions that are imposed to their admissible\ninput-additive coupled cell systems. These subspaces are flow-invariant by\nthose systems and are generalized polydiagonal subspaces, that is, are\ncharacterized by conditions on the cell coordinates of the types $x_i = x_j$\nand/or $x_k = -x_l$ and/or $x_m=0$. The existence and identification of the\nsynchrony and anti-synchony subspaces for a weighted network are deeply\nrelevant from the applications and dynamics point of view. Our characterization\nof the synchrony and anti-synchrony subspaces of a weighted network follows\nfrom our results where we give necessary and sufficient conditions for a\ngeneralized polydiagonal to be left invariant by the adjacency matrix and/or\nthe Laplacian matrix of the network.\n', 'Invariant Synchrony and Anti-Synchrony Subspaces of Weighted Networks   The internal state of a cell in a coupled cell network is often described by\nan element of a vector space. Synchrony or anti-synchrony occurs when some of\nthe cells are in the same or the opposite state. Subspaces of the state space\ncontaining cells in synchrony or anti-synchrony are called polydiagonal\nsubspaces. We study the properties of several types of polydiagonal subspaces\nof weighted coupled cell networks. In particular, we count the number of such\nsubspaces and study when they are dynamically invariant. Of special interest\nare the evenly tagged anti-synchrony subspaces in which the number of cells in\na certain state is equal to the number of cells in the opposite state. Our main\ntheorem shows that the dynamically invariant polydiagonal subspaces determined\nby certain types of couplings are either synchrony subspaces or evenly tagged\nanti-synchrony subspaces. A special case of this result confirms a conjecture\nabout difference-coupled graph network systems.\n', 'Reduced Lattices of Synchrony Subspaces and their Indices   For a regular coupled cell network, synchrony subspaces are the polydiagonal\nsubspaces that are invariant under the network adjacency matrix. The complete\nlattice of synchrony subspaces of an $n$-cell regular network can be seen as an\nintersection of the partition lattice of $n$ elements and a lattice of\ninvariant subspaces of the associated adjacency matrix. We assign integer\ntuples with synchrony subspaces, and use them for identifying equivalent\nsynchrony subspaces to be merged. Based on this equivalence, the initial\nlattice of synchrony subspaces can be reduced to a lattice of synchrony\nsubspaces which corresponds to a simple eigenvalue case discussed in our\nprevious work. The result is a reduced lattice of synchrony subspaces, which\naffords a well-defined non-negative integer index that leads to bifurcation\nanalysis in regular coupled cell networks.\n']","[('coupled networks', 0.5063363909721375), ('lattice invariant', 0.4906923472881317), ('cluster synchronization', 0.4644423723220825), ('network dynamics', 0.4497450590133667), ('network adjacency', 0.4434834420681), ('synchronization heterogeneous', 0.4391544461250305), ('synchronization', 0.4385264813899994), ('coupled dynamical systems', 0.4256449043750763), ('subspaces invariant', 0.4216831922531128), ('networks higher order', 0.42075952887535095)]"
1160,1160,26,1160_sum markov games_markov games_multi agent reinforcement_agent reinforcement learning,"['sum markov games', 'markov games', 'multi agent reinforcement', 'agent reinforcement learning', 'multi agent games', 'policy optimization', 'approximate nash equilibrium', 'stochastic games', 'agent reinforcement', 'policy gradient methods']","['Faster Last-iterate Convergence of Policy Optimization in Zero-Sum\n  Markov Games   Multi-Agent Reinforcement Learning (MARL) -- where multiple agents learn to\ninteract in a shared dynamic environment -- permeates across a wide range of\ncritical applications. While there has been substantial progress on\nunderstanding the global convergence of policy optimization methods in\nsingle-agent RL, designing and analysis of efficient policy optimization\nalgorithms in the MARL setting present significant challenges, which\nunfortunately, remain highly inadequately addressed by existing theory. In this\npaper, we focus on the most basic setting of competitive multi-agent RL, namely\ntwo-player zero-sum Markov games, and study equilibrium finding algorithms in\nboth the infinite-horizon discounted setting and the finite-horizon episodic\nsetting. We propose a single-loop policy optimization method with symmetric\nupdates from both agents, where the policy is updated via the\nentropy-regularized optimistic multiplicative weights update (OMWU) method and\nthe value is updated on a slower timescale. We show that, in the\nfull-information tabular setting, the proposed method achieves a finite-time\nlast-iterate linear convergence to the quantal response equilibrium of the\nregularized problem, which translates to a sublinear last-iterate convergence\nto the Nash equilibrium by controlling the amount of regularization. Our\nconvergence results improve upon the best known iteration complexities, and\nlead to a better understanding of policy optimization in competitive Markov\ngames.\n', ""Incentivize without Bonus: Provably Efficient Model-based Online\n  Multi-agent RL for Markov Games   Multi-agent reinforcement learning (MARL) lies at the heart of a plethora of\napplications involving the interaction of a group of agents in a shared unknown\nenvironment. A prominent framework for studying MARL is Markov games, with the\ngoal of finding various notions of equilibria in a sample-efficient manner,\nsuch as the Nash equilibrium (NE) and the coarse correlated equilibrium (CCE).\nHowever, existing sample-efficient approaches either require tailored\nuncertainty estimation under function approximation, or careful coordination of\nthe players. In this paper, we propose a novel model-based algorithm, called\nVMG, that incentivizes exploration via biasing the empirical estimate of the\nmodel parameters towards those with a higher collective best-response values of\nall the players when fixing the other players' policies, thus encouraging the\npolicy to deviate from its current equilibrium for more exploration. VMG is\noblivious to different forms of function approximation, and permits\nsimultaneous and uncoupled policy updates of all players. Theoretically, we\nalso establish that VMG achieves a near-optimal regret for finding both the NEs\nof two-player zero-sum Markov games and CCEs of multi-player general-sum Markov\ngames under linear function approximation in an online environment, which\nnearly match their counterparts with sophisticated uncertainty quantification.\n"", 'Robustness and sample complexity of model-based MARL for general-sum\n  Markov games   Multi-agent reinforcement learning (MARL) is often modeled using the\nframework of Markov games (also called stochastic games or dynamic games). Most\nof the existing literature on MARL concentrates on zero-sum Markov games but is\nnot applicable to general-sum Markov games. It is known that the best-response\ndynamics in general-sum Markov games are not a contraction. Therefore,\ndifferent equilibria in general-sum Markov games can have different values.\nMoreover, the Q-function is not sufficient to completely characterize the\nequilibrium. Given these challenges, model based learning is an attractive\napproach for MARL in general-sum Markov games.\n  In this paper, we investigate the fundamental question of \\emph{sample\ncomplexity} for model-based MARL algorithms in general-sum Markov games. We\nshow two results. We first use Hoeffding inequality based bounds to show that\n$\\tilde{\\mathcal{O}}( (1-\\gamma)^{-4} \\alpha^{-2})$ samples per state-action\npair are sufficient to obtain a $\\alpha$-approximate Markov perfect equilibrium\nwith high probability, where $\\gamma$ is the discount factor, and the\n$\\tilde{\\mathcal{O}}(\\cdot)$ notation hides logarithmic terms. We then use\nBernstein inequality based bounds to show that $\\tilde{\\mathcal{O}}(\n(1-\\gamma)^{-1} \\alpha^{-2} )$ samples are sufficient. To obtain these results,\nwe study the robustness of Markov perfect equilibrium to model approximations.\nWe show that the Markov perfect equilibrium of an approximate (or perturbed)\ngame is always an approximate Markov perfect equilibrium of the original game\nand provide explicit bounds on the approximation error. We illustrate the\nresults via a numerical example.\n']","[('sum markov games', 0.5910826325416565), ('markov games', 0.5757348537445068), ('multi agent reinforcement', 0.5660169124603271), ('agent reinforcement learning', 0.5502590537071228), ('multi agent games', 0.5353113412857056), ('policy optimization', 0.5331130027770996), ('approximate nash equilibrium', 0.5245009064674377), ('stochastic games', 0.5113445520401001), ('agent reinforcement', 0.5061032176017761), ('policy gradient methods', 0.503795862197876)]"
1161,1161,26,1161_optimal designs_designs optimal_optimal design_robust designs,"['optimal designs', 'designs optimal', 'optimal design', 'robust designs', 'optimum design', 'designs robust', 'optimal experimental', 'constructing optimal', 'experimental designs', 'designs finite']","[""The adaptive Wynn-algorithm in generalized linear models with univariate\n  response   For a nonlinear regression model the information matrices of designs depend\non the parameter of the model. The adaptive Wynn-algorithm for D-optimal design\nestimates the parameter at each step on the basis of the employed design points\nand observed responses so far, and selects the next design point as in the\nclassical Wynn-algorithm for D-optimal design. The name `Wynn-algorithm' is in\nhonor of Henry P. Wynn who established the latter `classical' algorithm in his\n1970 paper. The asymptotics of the sequences of designs and maximum likelihood\nestimates generated by the adaptive algorithm is studied for an important class\nof nonlinear regression models: generalized linear models whose (univariate)\nresponse variables follow a distribution from a one-parameter exponential\nfamily. Under the assumptions of compactness of the experimental region and of\nthe parameter space together with some natural continuity assumptions it is\nshown that the adaptive ML-estimators are strongly consistent and the design\nsequence is asymptotically locally D-optimal at the true parameter point. If\nthe true parameter point is an interior point of the parameter space then under\nsome smoothness assumptions the asymptotic normality of the adaptive\nML-estimators is obtained.\n"", 'EW D-optimal Designs for Experiments with Mixed Factors We characterize EW D-optimal designs as robust designs against unknown parameter values for experiments under a general parametric model with discrete and continuous factors. When a pilot study is available, we recommend sample-based EW D-optimal designs for subsequent experiments. Otherwise, we recommend EW D-optimal designs under a prior distribution for model parameters. We propose an EW ForLion algorithm for finding EW D-optimal designs with mixed factors, and justify that the designs found by our algorithm are EW D-optimal. To facilitate potential users in practice, we also develop a rounding algorithm that converts an approximate design with mixed factors to exact designs with prespecified grid points and the number of experimental units. By applying our algorithms for real experiments under multinomial logistic models or generalized linear models, we show that our designs are highly efficient with respect to locally D-optimal designs and more robust against parameter value misspecifications.', ""Optimal Designs for Regression on Lie Groups   We consider a linear regression model with complex-valued response and\npredictors from a compact and connected Lie group. The regression model is\nformulated in terms of eigenfunctions of the Laplace-Beltrami operator on the\nLie group. We show that the normalized Haar measure is an approximate optimal\ndesign with respect to all Kiefer's $\\Phi_p$-criteria. Inspired by the concept\nof $t$-designs in the field of algebraic combinatorics, we then consider\nso-called $\\lambda$-designs in order to construct exact $\\Phi_p$-optimal\ndesigns for fixed sample sizes in the considered regression problem. In\nparticular, we explicitly construct $\\Phi_p$-optimal designs for regression\nmodels with predictors in the Lie groups $\\mathrm{SU}(2)$ and $\\mathrm{SO}(3)$,\nthe groups of $2\\times 2$ unitary matrices and $3\\times 3$ orthogonal matrices\nwith determinant equal to $1$, respectively. We also discuss the advantages of\nthe derived theoretical results in a concrete biological application.\n""]","[('optimal designs', 0.7477228045463562), ('designs optimal', 0.7186670303344727), ('optimal design', 0.6292698979377747), ('robust designs', 0.5714523792266846), ('optimum design', 0.5649546384811401), ('designs robust', 0.5517234802246094), ('optimal experimental', 0.5122395157814026), ('constructing optimal', 0.5072775483131409), ('experimental designs', 0.4867185652256012), ('designs finite', 0.4837251901626587)]"
1162,1162,26,1162_oscillatory integral estimates_oscillatory integrals_oscillatory integral_singular integrals,"['oscillatory integral estimates', 'oscillatory integrals', 'oscillatory integral', 'singular integrals', 'integral estimates', 'asymptotic expansions', 'integrals smooth', 'amplitude functions', 'integrals terms', 'phase functions']","['On oscillatory integrals associated to phase functions with degenerate\n  singular points   In this note, by using the result in one variable, we obtain asymptotic\nexpansions of oscillatory integrals for certain multivariable phase functions\nwith {\\bf degenerate} singular points. Moreover by using this result, we have\nasymptotic expansions of oscillatory integrals with phase function of type\n$A_{k}$, $E_6$, $E_8$-function germs.\n', ""Estimates for oscillatory integrals with phase having $D$ type\n  singularities   In this paper, we consider estimates for the two-dimensional oscillatory\nintegrals. The phase function of the oscillatory integrals is the linear\nperturbation of a function having $D$ type singularities. We consider estimates\nfor the oscillatory integrals in terms of the Randol's type maximal functions.\nWe obtain a sharp $L^p_{loc}$ estimates for the Randol's maximal functions.\nMoreover, we investigate the sharp exponent $p$ depending on whether, the phase\nfunction has linearly adapted coordinates system or not.\n"", 'Oscillatory integrals with phase functions of positive real powers and\n  asymptotic expansions   As to methods for expanding an oscillatory integral into an asymptotic series\nwith respect to the parameter, the method of stationary phase for the\nnon-degenerate phases and the method of using resolution of singularities for\ndegenerate phases are known. The aim of this paper is to extend the former for\ndegenerate phases with positive real powers without using resolution of\nsingularities. For this aim, we first generalize Fresnel integrals as\noscillatory integrals with phase functions of positive real powers. Next, by\nusing this result, we have asymptotic expansions of oscillatory integrals for\ndegenerate phases with positive real powers including moderate oscillations and\nfor a wider amplitude class in one variable. Moreover, we obtain asymptotic\nexpansions of oscillatory integrals for degenerate phases consisting of sums of\nmonomials in each variable including the types $A_{k}$, $E_6$, $E_8$ in\nmultivariable.\n']","[('oscillatory integral estimates', 0.7268361449241638), ('oscillatory integrals', 0.7200972437858582), ('oscillatory integral', 0.6344273686408997), ('singular integrals', 0.5988026857376099), ('integral estimates', 0.5292039513587952), ('asymptotic expansions', 0.48806482553482056), ('integrals smooth', 0.48302704095840454), ('amplitude functions', 0.4745834171772003), ('integrals terms', 0.4683429002761841), ('phase functions', 0.4599594473838806)]"
1163,1163,26,1163_thermal states_quantum systems_thermalization_closed quantum systems,"['thermal states', 'quantum systems', 'thermalization', 'closed quantum systems', 'macroscopic quantum', 'quantum many body', 'state quantum', 'quantum many', 'states one dimensional', 'invariant quantum']","['Typical thermalization of low-entanglement states   Proving thermalization from the unitary evolution of a closed quantum system\nis one of the oldest questions that is still nowadays only partially resolved.\nSeveral efforts have led to various formulations of what is called the\neigenstate thermalization hypothesis, which leads to thermalization under\ncertain conditions on the initial states. These conditions, however, are\nsensitive to the precise formulation of the hypothesis. In this work, we focus\non the important case of low entanglement initial states, which are\noperationally accessible in many natural physical settings, including\nexperimental schemes for testing thermalization and for quantum simulation. We\nprove thermalization of these states under precise conditions that have\noperational significance. More specifically, motivated by arguments of\nunavoidable finite resolution, we define a random energy smoothing on local\nHamiltonians that leads to local thermalization when the initial state has low\nentanglement. Finally we show that such a transformation affects neither the\nGibbs state locally nor, under generic smoothness conditions on the spectrum,\nthe short-time dynamics.\n', 'Rapid thermalization of dissipative many-body dynamics of commuting\n  Hamiltonians   Quantum systems typically reach thermal equilibrium rather quickly when\ncoupled to a thermal environment. The usual way of bounding the speed of this\nprocess is by estimating the spectral gap of the dissipative generator. However\nthe gap, by itself, does not always yield a reasonable estimate for the\nthermalization time in many-body systems: without further structure, a uniform\nlower bound on it only constrains the thermalization time to grow polynomially\nwith system size.\n  Here, instead, we show that for a large class of geometrically-2-local models\nof Davies generators with commuting Hamiltonians, the thermalization time is\nmuch shorter than one would na\\""ively estimate from the gap: at most\nlogarithmic in the system size. This yields the so-called rapid mixing of\ndissipative dynamics. The result is particularly relevant for 1D systems, for\nwhich we prove rapid thermalization with a system size independent decay rate\nonly from a positive gap in the generator. We also prove that systems in\nhypercubic lattices of any dimension, and exponential graphs, such as trees,\nhave rapid mixing at high enough temperatures. We do this by introducing a\nnovel notion of clustering which we call ""strong local indistinguishability""\nbased on a max-relative entropy, and then proving that it implies a lower bound\non the modified logarithmic Sobolev inequality (MLSI) for nearest neighbour\ncommuting models.\n  This has consequences for the rate of thermalization towards Gibbs states,\nand also for their relevant Wasserstein distances and transportation cost\ninequalities. Along the way, we show that several measures of decay of\ncorrelations on Gibbs states of commuting Hamiltonians are equivalent, a result\nof independent interest. At the technical level, we also show a direct relation\nbetween properties of Davies and Schmidt dynamics, that allows to transfer\nresults of thermalization between both.\n', 'Thermalization without eigenstate thermalization   In an isolated quantum many-body system undergoing unitary evolution, we\nstudy the thermalization of a subsystem, treating the rest of the system as a\nbath. In this setting, the eigenstate thermalization hypothesis (ETH) was\nproposed to explain thermalization. Consider a nearly integrable\nSachdev-Ye-Kitaev model obtained by adding random all-to-all 4-body\ninteractions as a perturbation to a random free-fermion model. When the\nsubsystem size is larger than the square root of but is still a vanishing\nfraction of the system size, we prove thermalization if the system is\ninitialized in a random product state, while almost all eigenstates violate the\nETH. In this sense, the ETH is not a necessary condition for thermalization.\n']","[('thermal states', 0.60206139087677), ('quantum systems', 0.491231232881546), ('thermalization', 0.48944398760795593), ('closed quantum systems', 0.4891895353794098), ('macroscopic quantum', 0.4816984236240387), ('quantum many body', 0.47016894817352295), ('state quantum', 0.45901060104370117), ('quantum many', 0.44542211294174194), ('states one dimensional', 0.4376046061515808), ('invariant quantum', 0.43758007884025574)]"
1164,1164,26,1164_green functions_boundary value conditions_boundary conditions explicit_dynamical boundary condition,"['green functions', 'boundary value conditions', 'boundary conditions explicit', 'dynamical boundary condition', 'linear boundary conditions', 'dynamical boundary conditions', 'boundary conditions', 'boundary value problems', 'derivatives green', 'inhomogeneous boundary conditions']","[""Relationship of the Green's functions related to the Hill's equation\n  coupled to different boundary value conditions   In this paper we will deduce several properties of the Green's functions\nrelated to the Hill's equation coupled to various boundary value conditions. In\nparticular, the idea is to study the Green's functions of the second order\ndifferential operator coupled to Neumann, Dirichlet, Periodic and Mixed\nboundary conditions, by expressing the Green's function of a given problem as a\nlinear combination of the Green's function of the other ones. This will allow\nus to compare different Green's functions when they have constant sign.\nFinally, such properties of the Green's function of the linear problem will be\nfundamental to deduce the existence of solutions to the nonlinear problem. The\nresults are derived from the fixed point theory applied to related operators\ndefined on suitable cones in Banach spaces.\n"", ""An explicit formula of the parameter dependence of de partial\n  derivatives of the Green's functions related to arbitrary two-point boundary\n  conditions   In this paper we obtain an explicit formula of the parameter dependence of\nthe partial derivatives of the Green's functions related to two-point boundary\nconditions. Such expression follows as an integral of both kernels times the\ndifference of the corresponding parameters of each Green's function. As a\ndirect consequence, we deduce a simpler proof of the monotony of the constant\nsign of the partial derivative of a Green's function with respect to a real\nparameter. As a consequence, we improve the results obtained in \\cite{C1},\nwhere the monotone dependence was proved for the constant sign Green's function\n(not for any ot its partial derivatives) and under weaker assumptions on the\nGreen's function. The arguments are valid for any other types of Ordinary\nDifferential Equations coupled to Nonlocal Conditions. Moreover, analogous\nideas could be developed for Partial and Fractional Differential Equations.\n"", ""Spectral characterization of the constant sign derivatives of Green's\n  function related to two point boundary value conditions   In this paper we will study the set of parameters in which certain partial\nderivatives of the Green's function, related to a $n$-order linear operator\n$T_{n}[M]$, depending on a real parameter $M$, coupled to different two-point\nboundary conditions, are of constant sign. We will do it without using the\nexplicit expression of the Green's function. The constant sign interval will be\ncharacterized by the first eigenvalue related to suitable boundary conditions\nof the studied operator. As a consequence of the main result, we will be able\nto give sufficient conditions to ensure that the derivatives of Green's\nfunction cannot be nonpositive (nonnegative). These characterizations and the\nobtained results can be used to deduce the existence of solutions of nonlinear\nproblems under additional conditions on the nonlinear part. To illustrate the\nobtained results, some examples are given.\n""]","[('green functions', 0.5671893358230591), ('boundary value conditions', 0.5587310791015625), ('boundary conditions explicit', 0.555906355381012), ('dynamical boundary condition', 0.5319914817810059), ('linear boundary conditions', 0.5306990742683411), ('dynamical boundary conditions', 0.5262268781661987), ('boundary conditions', 0.5140117406845093), ('boundary value problems', 0.496132493019104), ('derivatives green', 0.4820587933063507), ('inhomogeneous boundary conditions', 0.46916767954826355)]"
1165,1165,26,1165_graphs trees_graphs_general graphs_graph order,"['graphs trees', 'graphs', 'general graphs', 'graph order', 'graph classes', 'graph smallest', 'graphs minimum', 'graphs graph', 'hypergraphs', 'graph class']","[""Extending Graph Burning to Hypergraphs   Graph burning is a round-based game or process that discretely models the\nspread of influence throughout a network. We introduce a generalization of\ngraph burning which applies to hypergraphs, as well as a variant called\n''lazy'' hypergraph burning. Interestingly, lazily burning a graph is trivial,\nwhile lazily burning a hypergraph can be quite complicated. Moreover, the lazy\nburning model is a useful tool for analyzing the round-based model. One of our\nkey results is that arbitrary hypergraphs do not satisfy a bound analogous to\nthe one in the Burning Number Conjecture for graphs. We also obtain bounds on\nthe burning number and lazy burning number of a hypergraph in terms of its\nparameters, and present several open problems in the field of (lazy) hypergraph\nburning.\n"", 'A survey of graph burning   Graph burning is a deterministic, discrete-time process that models how\ninfluence or contagion spreads in a graph. Associated to each graph is its\nburning number, which is a parameter that quantifies how quickly the influence\nspreads. We survey results on graph burning, focusing on bounds, conjectures,\nand algorithms related to the burning number. We will discuss state-of-the-art\nresults on the burning number conjecture, burning numbers of graph classes, and\nalgorithmic complexity. We include a list of conjectures, variants, and open\nproblems on graph burning.\n', 'Graph Burning: Bounds and Hardness   For an undirected graph $G$, graph burning is defined as follows: at step\n$t=0$ all vertices in $G$ are unburned. At each step $t\\ge 1$, one new unburned\nvertex is selected to burn until we exhaust all the vertices. If a vertex is\nburned at step $t$, then all its unburned neighbors are burned in step $t+1$,\nand the process continues until there are no unburned vertices in $G$. The\nburning number of a graph $G$, denoted by $b(G)$, is the minimum number of\nsteps required to burn all the vertices of $G$. The Burning Number problem asks\nwhether the burning number of an input graph $G$ is at most $k$ or not. In this\npaper, we study the Burning Number problem both from an algorithmic and a\nstructural point of view. The Burning Number problem is known to be NP-complete\nfor trees with maximum degree at most three and interval graphs. Here, we prove\nthat this problem is NP-complete even when restricted to connected cubic graphs\nand connected proper interval graphs. The well-known burning number conjecture\nasserts that all the vertices of a graph of order $n$ can be burned in $\\lceil\n\\sqrt{n}~\\rceil$ steps. In line with this conjecture, upper and lower bounds of\n$b(G)$ are well-studied for various graph classes. Here, we provide an improved\nupper bound for the burning number of connected $P_k$-free graphs and show that\nthe bound is tight up to an additive constant $1$. Finally, we study two\nvariants of the problem, namely edge burning (only edges are burned) and total\nburning (both vertices and edges are burned). In particular, we establish their\nrelationship with the burning number problem and evaluate the algorithmic\ncomplexity of these variants.\n']","[('graphs trees', 0.5996564030647278), ('graphs', 0.5690789222717285), ('general graphs', 0.5310863852500916), ('graph order', 0.5277209877967834), ('graph classes', 0.5190269947052002), ('graph smallest', 0.5130035877227783), ('graphs minimum', 0.5114196538925171), ('graphs graph', 0.5100564360618591), ('hypergraphs', 0.5004026293754578), ('graph class', 0.4937562942504883)]"
1166,1166,25,1166_witten spin_witten conjecture_spin theories_theory genus,"['witten spin', 'witten conjecture', 'spin theories', 'theory genus', 'spin theory', 'moduli spaces', 'classes moduli space', 'boundary moduli space', 'frobenius manifold', 'moduli space']","[""Open $r$-spin theory II: The analogue of Witten's conjecture for\n  $r$-spin disks   We conclude the construction of $r$-spin theory in genus zero for Riemann\nsurfaces with boundary. In particular, we define open $r$-spin intersection\nnumbers, and we prove that their generating function is closely related to the\nwave function of the $r$th Gelfand-Dickey integrable hierarchy. This provides\nan analogue of Witten's $r$-spin conjecture in the open setting and a first\nstep toward the construction of an open version of Fan-Jarvis-Ruan-Witten\ntheory. As an unexpected consequence, we establish a mysterious relationship\nbetween open $r$-spin theory and an extension of Witten's closed theory.\n"", ""Open r-spin theory I: Foundations   We lay the foundation for a version of $r$-spin theory in genus zero for\nRiemann surfaces with boundary. In particular, we define the notion of $r$-spin\ndisks, their moduli space, and the Witten bundle, we show that the moduli space\nis a compact smooth orientable orbifold with corners, and we prove that the\nWitten bundle is canonically relatively oriented relative to the moduli space.\nIn the sequel to this paper, we use these constructions to define open $r$-spin\nintersection theory and relate it to the Gelfand-Dickey hierarchy, thus\nproviding an analogue of Witten's $r$-spin conjecture in the open setting.\n"", ""Tautological relations via r-spin structures   Relations among tautological classes on the moduli space of stable curves are\nobtained via the study of Witten's r-spin theory for higher r. In order to\ncalculate the quantum product, a new formula relating the r-spin correlators in\ngenus 0 to the representation theory of sl2 is proven. The Givental-Teleman\nclassification of CohFTs is used at two special semisimple points of the\nassociated Frobenius manifold. At the first semisimple point, the R-matrix is\nexactly solved in terms of hypergeometric series. As a result, an explicit\nformula for Witten's r-spin class is obtained (along with tautological\nrelations in higher degrees). As an application, the r=4 relations are used to\nbound the Betti numbers of the tautological ring of the moduli of nonsingular\ncurves. At the second semisimple point, the form of the R-matrix implies a\npolynomiality property in r of Witten's r-spin class.\n  In the Appendix (with F. Janda), a conjecture relating the r=0 limit of\nWitten's r-spin class to the class of the moduli space of holomorphic\ndifferentials is presented.\n""]","[('witten spin', 0.5421255826950073), ('witten conjecture', 0.5353272557258606), ('spin theories', 0.5002526640892029), ('theory genus', 0.47465062141418457), ('spin theory', 0.46012017130851746), ('moduli spaces', 0.45594048500061035), ('classes moduli space', 0.4497949182987213), ('boundary moduli space', 0.444504976272583), ('frobenius manifold', 0.43926510214805603), ('moduli space', 0.43659740686416626)]"
1167,1167,25,1167_hilliard navier stokes_cahn hilliard equations_hilliard equations_energy stable numerical,"['hilliard navier stokes', 'cahn hilliard equations', 'hilliard equations', 'energy stable numerical', 'navier stokes equations', 'solving cahn hilliard', 'navier stokes system', 'stokes equations', 'energy stable scheme', 'navier stokes']","['On fully decoupled MSAV schemes for the Cahn-Hilliard-Navier-Stokes\n  model of Two-Phase Incompressible Flows   We construct first- and second-order time discretization schemes for the\nCahn-Hilliard-Navier-Stokes system based on the multiple scalar auxiliary\nvariables approach (MSAV) approach for gradient systems and (rotational)\npressure-correction for Navier-Stokes equations. These schemes are linear,\nfully decoupled, unconditionally energy stable, and only require solving a\nsequence of elliptic equations with constant coefficients at each time step. We\ncarry out a rigorous error analysis for the first-order scheme, establishing\noptimal convergence rate for all relevant functions in different norms. We also\nprovide numerical experiments to verify our theoretical results.\n', 'Convergence analysis of decoupled mixed FEM for the\n  Cahn-Hilliard-Navier-Stokes equations   We develop a decoupled, first-order, fully discrete, energy-stable scheme for\nthe Cahn-Hilliard-Navier-Stokes equations. This scheme calculates the\nCahn-Hilliard and Navier-Stokes equations separately, thus effectively\ndecoupling the entire system. To further separate the velocity and pressure\ncomponents in the Navier-Stokes equations, we use the pressure-correction\nprojection method. We demonstrate that the scheme is primitively energy stable\nand prove the optimal $L^2$ error estimate of the fully discrete scheme in the\n$P_r\\times P_r\\times P_r\\times P_{r-1}$ finite element spaces, where the phase\nfield, chemical potential, velocity and pressure satisfy the first-order\naccuracy in time and the $\\left(r+1,r+1,r+1,r\\right)th$-order accuracy in\nspace, respectively. Furthermore, numerical experiments are conducted to\nsupport these theoretical findings. Notably, compared to other numerical\nschemes, our algorithm is more time-efficient and numerically shown to be\nunconditionally stable.\n', 'A new decoupled unconditionally stable scheme and its optimal error\n  analysis for the Cahn-Hilliard-Navier-Stokes equations   We construct a decoupled, first-order, fully discrete, and unconditionally\nenergy stable scheme for the Cahn-Hilliard-Navier-Stokes equations. The scheme\nis divided into two main parts. The first part involves the calculation of the\nCahn-Hilliard equations, and the other part is calculating the Navier-Stokes\nequations subsequently by utilizing the phase field and chemical potential\nvalues obtained from the above step. Specifically, the velocity in the\nCahn-Hilliard equation is discretized explicitly at the discrete time level,\nwhich enables the computation of the Cahn-Hilliard equations is fully decoupled\nfrom that of Navier-Stokes equations. Furthermore, the pressure-correction\nprojection method, in conjunction with the scalar auxiliary variable approach\nnot only enables the discrete scheme to satisfy unconditional energy stability,\nbut also allows the convective term in the Navier-Stokes equations to be\ntreated explicitly. We subsequently prove that the time semi-discrete scheme is\nunconditionally stable and analyze the optimal error estimates for the fully\ndiscrete scheme. Finally, several numerical experiments validate the\ntheoretical results.\n']","[('hilliard navier stokes', 0.5473130941390991), ('cahn hilliard equations', 0.5418907403945923), ('hilliard equations', 0.5112096667289734), ('energy stable numerical', 0.5002685189247131), ('navier stokes equations', 0.4987078905105591), ('solving cahn hilliard', 0.4745212197303772), ('navier stokes system', 0.46274498105049133), ('stokes equations', 0.4331133961677551), ('energy stable scheme', 0.42967286705970764), ('navier stokes', 0.4211450517177582)]"
1168,1168,25,1168_zariski dense_projective varieties_projective variety_smooth projective variety,"['zariski dense', 'projective varieties', 'projective variety', 'smooth projective variety', 'quasi projective varieties', 'projective variety defined', 'abelian varieties', 'endomorphisms projective', 'polynomial maps', 'smooth projective']","['Propagation of Zariski Dense Orbits   Let $X/K$ be a smooth projective variety defined over a number field, and let\n$f:X\\to{X}$ be a morphism defined over $K$. We formulate a number of statements\nof varying strengths asserting, roughly, that if there is at least one point\n$P_0\\in{X(K)}$ whose $f$-orbit\n$\\mathcal{O}_f(P_0):=\\bigl\\{f^n(P):n\\in\\mathbb{N}\\bigr\\}$ is Zariski dense,\nthen there are many such points. For example, a weak conclusion would be that\n$X(K)$ is not the union of finitely many (grand) $f$-orbits, while a strong\nconclusion would be that any set of representatives for the Zariski dense grand\n$f$-orbits is Zariski dense. We prove statements of this sort for various\nclasses of varieties and maps, including projective spaces, abelian varieties,\nand surfaces.\n', 'The existence of Zariski dense orbits for endomorphisms of projective\n  surfaces (with an appendix in collaboration with Thomas Tucker)   In this paper we prove the following theorem. Let $f$ be a dominant\nendomorphism of a smooth projective surface over an algebraically closed field\nof characteristic $0$. If there is no nonconstant invariant rational function\nunder $f$, then there exists a closed point whose orbit under $f$ is Zariski\ndense. This result gives us a positive answer to the Zariski dense orbit\nconjecture proposed by Medvedev and Scanlon, by Amerik, Bogomolov and Rovinsky,\nand by Zhang, for endomorphisms of smooth projective surfaces.\n  Moreover, we define a new canonical topology on varieties over an\nalgebraically closed field which has finite transcendence degree over\n$\\mathbb{Q}$. We call it the adelic topology. The adelic topology is stronger\nthan the Zariski topology and an irreducible variety is still irreducible in\nthis topology. Using the adelic topology, we propose an adelic verison of the\nZariski dense orbit conjecture. This version is stronger then the original one\nand it quantifies how many such orbits there are. We also proved this adelic\nversion for endomorphisms of smooth projective surfaces. Moreover, we proved\nthe adelic verison of the Zariski dense orbit conjecture for endomorphisms of\nabelian varieties and split polynomial maps. This yields new proofs for the\noriginal version in this two cases.\n  In Appendix A, we study the endomorphisms on the $k$-affinoid spaces. We show\nthat for certain endomorphism $f$ on a $k$-affinoid space $X$, the attractor\n$Y$ of $f$ is a Zariski closed subset and the dynamics of $f$ semi-conjugates\nto its restriction on $Y.$ A special case of this result is used in the proof\nof the main theorem.\n  In Appendix B, written in collaboration with Thomas Tucker, we prove the\nZariski dense orbit conjecture for endomorphisms of $(\\mathbb{P}^1)^N.$\n', 'Potential density of projective varieties having an int-amplified\n  endomorphism   We consider the potential density of rational points on an algebraic variety\ndefined over a number field $K$, i.e., the property that the set of rational\npoints of $X$ becomes Zariski dense after a finite field extension of $K$. For\na non-uniruled projective variety with an int-amplified endomorphism, we show\nthat it always satisfies potential density. When a rationally connected variety\nadmits an int-amplified endomorphism, we prove that there exists some rational\ncurve with a Zariski dense forward orbit, assuming the Zariski dense orbit\nconjecture in lower dimensions. As an application, we prove the potential\ndensity for projective varieties with int-amplified endomorphisms in dimension\n$\\leq 3$. We also study the existence of densely many rational points with the\nmaximal arithmetic degree over a sufficiently large number field.\n']","[('zariski dense', 0.5648056864738464), ('projective varieties', 0.5591779351234436), ('projective variety', 0.5411352515220642), ('smooth projective variety', 0.5277479290962219), ('quasi projective varieties', 0.5231121182441711), ('projective variety defined', 0.5084871649742126), ('abelian varieties', 0.4813328683376312), ('endomorphisms projective', 0.4769984185695648), ('polynomial maps', 0.4433252513408661), ('smooth projective', 0.4396262764930725)]"
1169,1169,25,1169_stirling numbers_involving stirling numbers_sums powers_polynomials stirling,"['stirling numbers', 'involving stirling numbers', 'sums powers', 'polynomials stirling', 'stirling numbers first', 'sum powers', 'stirling numbers second', 'power sums', 'involving stirling', 'sum th powers']","[""A remark on an explicit formula for the sums of powers of integers   Recently, E. Samsonadze (arXiv:2411.11859v1) has given an explicit formula\nfor the sums of powers of integers $S_k(n) = 1^k +2^k +\\cdots + n^k$. In this\nshort note, we show that Samsonadze's formula corresponds to a well-known\nformula for $S_k(n)$ involving the Stirling numbers of the second kind.\n"", 'A note on the hyper-sums of powers of integers, hyperharmonic\n  polynomials and r-Stirling numbers of the first kind   Recently, Kargin et al. (arXiv:2008.00284 [math.NT]) obtained (among many\nother things) the following formula for the hyper-sums of powers of integers\n$S_k^{(m)}(n)$ \\begin{equation*} S_k^{(m)}(n) = \\frac{1}{m!} \\sum_{i=0}^{m}\n(-1)^i \\genfrac{[}{]}{0pt}{}{m+n+1}{i+n+1}_{n+1} S_{k+i}(n), \\end{equation*}\nwhere $S_k^{(0)}(n) \\equiv S_k(n)$ is the ordinary power sum $1^k + 2^k +\n\\cdots + n^k$. In this note we point out that a formula equivalent to the\npreceding one was already established in a different form, namely, a form in\nwhich $\\genfrac{[}{]}{0pt}{}{m+n+1}{i+n+1}_{n+1}$ is given explicitly as a\npolynomial in $n$ of degree $m-i$. We find out the connection between this\npolynomial and the so-called $r$-Stirling polynomials of the first kind.\nFurthermore, we determine the hyperharmonic polynomials and their successive\nderivatives in terms of the $r$-Stirling polynomials of the first kind, and\nshow the relationship between the (exponential) complete Bell polynomials and\nthe $r$-Stirling numbers of the first kind. Finally, we derive some identities\ninvolving the Bernoulli numbers and polynomials, the $r$-Stirling numbers of\nthe first kind, the Stirling numbers of both kinds, and the harmonic numbers.\n', 'Sums of powers of integers and hyperharmonic numbers   In this paper, we derive a formula for the sums of powers of the first $n$\npositive integers, $S_k(n)$, that involves the hyperharmonic numbers and the\nStirling numbers of the second kind. Then, using an explicit representation for\nthe hyperharmonic numbers, we generalize this formula to the sums of powers of\nan arbitrary arithmetic progression. Moreover, we express the Bernoulli\npolynomials in terms of hyperharmonic polynomials and Stirling numbers of the\nsecond kind. Finally, we extend the obtained formula for $S_k(n)$ to negative\nvalues of $n$.\n']","[('stirling numbers', 0.6272366642951965), ('involving stirling numbers', 0.5988105535507202), ('sums powers', 0.5974752306938171), ('polynomials stirling', 0.5962681174278259), ('stirling numbers first', 0.5812974572181702), ('sum powers', 0.5731457471847534), ('stirling numbers second', 0.5693320631980896), ('power sums', 0.5566180944442749), ('involving stirling', 0.5501186847686768), ('sum th powers', 0.5379927754402161)]"
1170,1170,25,1170_mmwave massive mimo_estimation mmwave_mmwave mimo_mmwave channels,"['mmwave massive mimo', 'estimation mmwave', 'mmwave mimo', 'mmwave channels', 'mmwave channel', 'millimeter wave mmwave', 'mmwave massive multiple', 'aided mmwave', 'channel estimation', 'massive mimo systems']","['Gradient Pursuit-Based Channel Estimation for MmWave Massive MIMO\n  Systems with One-Bit ADCs   In this paper, channel estimation for millimeter wave (mmWave) massive\nmultiple-input multiple-output (MIMO) systems with one-bit analog-to-digital\nconverters (ADCs) is considered. In the mmWave band, the number of propagation\npaths is small, which results in sparse virtual channels. To estimate sparse\nvirtual channels based on the maximum a posteriori (MAP) criterion,\nsparsity-constrained optimization comes into play. In general, optimizing\nobjective functions with sparsity constraints is NP-hard because of their\ncombinatorial complexity. Furthermore, the coarse quantization of one-bit ADCs\nmakes channel estimation a challenging task. In the field of compressed sensing\n(CS), the gradient support pursuit (GraSP) and gradient hard thresholding\npursuit (GraHTP) algorithms were proposed to approximately solve\nsparsity-constrained optimization problems iteratively by pursuing the gradient\nof the objective function via hard thresholding. The accuracy guarantee of\nthese algorithms, however, breaks down when the objective function is\nill-conditioned, which frequently occurs in the mmWave band. To prevent the\nbreakdown of gradient pursuit-based algorithms, the band maximum selecting\n(BMS) technique, which is a hard thresholder selecting only the ""band maxima,""\nis applied to GraSP and GraHTP to propose the BMSGraSP and BMSGraHTP algorithms\nin this paper.\n', 'FCFGS-CV-Based Channel Estimation for Wideband MmWave Massive MIMO\n  Systems with Low-Resolution ADCs   In this paper, the fully corrective forward greedy selection-cross\nvalidation-based (FCFGS-CV-based) channel estimator is proposed for wideband\nmillimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems\nwith low-resolution analog-to-digital converters (ADCs). The sparse nature of\nthe mmWave virtual channel in the angular and delay domains is exploited to\nconvert the maximum a posteriori (MAP) channel estimation problem to an\noptimization problem with a concave objective function and sparsity constraint.\nThe FCFGS algorithm, which is the generalized orthogonal matching pursuit (OMP)\nalgorithm, is used to solve the sparsity-constrained optimization problem.\nFurthermore, the CV technique is adopted to determine the proper termination\ncondition by detecting overfitting when the sparsity level is unknown.\n', 'Spatial Wideband Channel Estimation for MmWave Massive MIMO Systems with\n  Hybrid Architectures and Low-Resolution ADCs   In this paper, a channel estimator for wideband millimeter wave (mmWave)\nmassive multiple-input multiple-output (MIMO) systems with hybrid architectures\nand low-resolution analog-to-digital converters (ADCs) is proposed. To account\nfor the propagation delay across the antenna array, which cannot be neglected\nin wideband mmWave massive MIMO systems, the discrete time channel that models\nthe spatial wideband effect is developed. Also, the training signal design that\naddresses inter-frame, inter-user, and inter-symbol interferences is\ninvestigated when the spatial wideband effect is not negligible. To estimate\nthe channel parameters over the continuum based on the maximum a posteriori\n(MAP) criterion, the Newtonized fully corrective forward greedy selection-cross\nvalidation-based (NFCFGS-CV-based) channel estimator is proposed. NFCFGS-CV is\na gridless compressed sensing (CS) algorithm, whose termination condition is\ndetermined by the CV technique. The CV-based termination condition is proved to\nachieve the minimum squared error (SE). The simulation results show that\nNFCFGS-CV outperforms state-of-the-art on-grid CS-based channel estimators.\n']","[('mmwave massive mimo', 0.6383867263793945), ('estimation mmwave', 0.5725246071815491), ('mmwave mimo', 0.5522268414497375), ('mmwave channels', 0.5472090244293213), ('mmwave channel', 0.5305740237236023), ('millimeter wave mmwave', 0.5262585878372192), ('mmwave massive multiple', 0.5118444561958313), ('aided mmwave', 0.5097280740737915), ('channel estimation', 0.5062559247016907), ('massive mimo systems', 0.5056185722351074)]"
1171,1171,25,1171_electrical impedance tomography_impedance tomography eit_impedance tomography_tomography eit,"['electrical impedance tomography', 'impedance tomography eit', 'impedance tomography', 'tomography eit', 'tomography', 'medical imaging', 'complete electrode', 'convolution neural', 'electrical impedance', 'electrode']","['Optimizing electrode positions in 2D Electrical Impedance Tomography\n  using deep learning   Electrical Impedance Tomography (EIT) is a powerful tool for non-destructive\nevaluation, state estimation, and process tomography - among numerous other use\ncases. For these applications, and in order to reliably reconstruct images of a\ngiven process using EIT, we must obtain high-quality voltage measurements from\nthe target of interest. As such, it is obvious that the locations of electrodes\nused for measuring plays a key role in this task. Yet, to date, methods for\noptimally placing electrodes either require knowledge on the EIT target (which\nis, in practice, never fully known) or are computationally difficult to\nimplement numerically. In this paper, we circumvent these challenges and\npresent a straightforward deep learning based approach for optimizing\nelectrodes positions. It is found that the optimized electrode positions\noutperformed ""standard"" uniformly-distributed electrode layouts in all test\ncases. Further, it is found that the use of optimized electrode positions\ncomputed using the approach derived herein can reduce errors in EIT\nreconstructions as well as improve the distinguishability of EIT measurements.\n', 'Stroke classification using Virtual Hybrid Edge Detection from in silico\n  electrical impedance tomography data   Electrical impedance tomography (EIT) is a non-invasive imaging method for\nrecovering the internal conductivity of a physical body from electric boundary\nmeasurements. EIT combined with machine learning has shown promise for the\nclassification of strokes. However, most previous works have used raw EIT\nvoltage data as network inputs. We build upon a recent development which\nsuggested the use of special noise-robust Virtual Hybrid Edge Detection (VHED)\nfunctions as network inputs, although that work used only highly simplified and\nmathematically ideal models. In this work we strengthen the case for the use of\nEIT, and VHED functions especially, for stroke classification. We design models\nwith high detail and mathematical realism to test the use of VHED functions as\ninputs. Virtual patients are created using a physically detailed 2D head model\nwhich includes features known to create challenges in real-world imaging\nscenarios. Conductivity values are drawn from statistically realistic\ndistributions, and phantoms are afflicted with either hemorrhagic or ischemic\nstrokes of various shapes and sizes. Simulated noisy EIT electrode data,\ngenerated using the realistic Complete Electrode Model (CEM) as opposed to the\nmathematically ideal continuum model, is processed to obtain VHED functions. We\ncompare the use of VHED functions as inputs against the alternative paradigm of\nusing raw EIT voltages. Our results show that (i) stroke classification can be\nperformed with high accuracy using 2D EIT data from physically detailed and\nmathematically realistic models, and (ii) in the presence of noise, VHED\nfunctions outperform raw data as network inputs.\n', 'Classification of stroke using Neural Networks in Electrical Impedance\n  Tomography   Electrical Impedance Tomography (EIT) is an emerging non-invasive medical\nimaging modality. It is based on feeding electrical currents into the patient,\nmeasuring the resulting voltages at the skin, and recovering the internal\nconductivity distribution. The mathematical task of EIT image reconstruction is\na nonlinear and ill-posed inverse problem. Therefore any EIT image\nreconstruction method needs to be regularized, typically resulting in blurred\nimages. One promising application is stroke-EIT, or classification of stroke\ninto either ischemic or hemorrhagic. Ischemic stroke involves a blood clot,\npreventing blood flow to a part of the brain causing a low-conductivity region.\nHemorrhagic stroke means bleeding in the brain causing a high-conductivity\nregion. In both cases the symptoms are identical, so a cost-effective and\nportable classification device is needed. Typical EIT are not optimal for\nstroke-EIT because of blurriness. This paper explores the possibilities of\nmachine learning in improving the classification results. Two paradigms are\ncompared: (a) learning from the EIT data, that is Dirichlet-to-Neumann (DN)\nmaps and (b) extracting robust features from data and learning from them. The\nfeatures of choice are Virtual Hybrid Edge Detection (VHED) functions\n[Greenleaf {\\it et al.}, Analysis \\& PDE 11, 2018] that have a geometric\ninterpretation and whose computation from EIT data does not involve calculating\na full image of the conductivity. We report the measures of accuracy,\nsensitivity and specificity of the networks trained with EIT data and VHED\nfunctions separately. Computational evidence based on simulated noisy EIT data\nsuggests that the regularized grey-box paradigm (b) leads to significantly\nbetter classification results than the black-box paradigm (a).\n']","[('electrical impedance tomography', 0.6339439153671265), ('impedance tomography eit', 0.5810343027114868), ('impedance tomography', 0.572511613368988), ('tomography eit', 0.4937906861305237), ('tomography', 0.44215038418769836), ('medical imaging', 0.3776067793369293), ('complete electrode', 0.3637855350971222), ('convolution neural', 0.3637077510356903), ('electrical impedance', 0.3542637825012207), ('electrode', 0.3491860032081604)]"
1172,1172,25,1172_polytopes_matching polytopes_linear programs_polyhedron,"['polytopes', 'matching polytopes', 'linear programs', 'polyhedron', 'linear programming', 'polytope', 'case computational complexity', 'worst case computational', 'polyhedra', 'integer programs']","['The Polyhedral Geometry of Pivot Rules and Monotone Paths   Motivated by the analysis of the performance of the simplex method we study\nthe behavior of families of pivot rules of linear programs. We introduce\nnormalized-weight pivot rules which are fundamental for the following reasons:\nFirst, they are memory-less, in the sense that the pivots are governed by local\ninformation encoded by an arborescence. Second, many of the most used pivot\nrules belong to that class, and we show this subclass is critical for\nunderstanding the complexity of all pivot rules. Finally, normalized-weight\npivot rules can be parametrized in a natural continuous manner.\n  We show the existence of two polytopes, the pivot rule polytopes and the\nneighbotopes, that capture the behavior of normalized-weight pivot rules on\npolytopes and linear programs. We explain their face structure in terms of\nmulti-arborescences. We compute upper bounds on the number of coherent\narborescences, that is, vertices of our polytopes.\n  Beyond optimization, our constructions provide new perspectives on classical\ngeometric combinatorics. We introduce a normalized-weight pivot rule, we call\nthe max-slope pivot rule which generalizes the shadow-vertex pivot rule. The\ncorresponding pivot rule polytopes and neighbotopes refine monotone path\npolytopes of Billera--Sturmfels. Moreover special cases of our polytopes yield\npermutahedra, associahedra, and multiplihedra. For the greatest improvement\npivot rules we draw connections to sweep polytopes and polymatroids.\n', ""On the facet pivot simplex method for linear programming II: a linear\n  iteration bound   The Hirsch Conjecture stated that any $d$-dimensional polytope with n facets\nhas a diameter at most equal to $n - d$. This conjecture was disproved by\nSantos (A counterexample to the Hirsch Conjecture, Annals of Mathematics,\n172(1) 383-412, 2012). The implication of Santos' work is that all {\\it vertex}\npivot algorithms cannot solve the linear programming problem in the worst case\nin $n - d$ vertex pivot iterations.\n  In the first part of this series of papers, we proposed a {\\it facet} pivot\nmethod. In this paper, we show that the proposed facet pivot method can solve\nthe canonical linear programming problem in the worst case in at most $n-d$\nfacet pivot iterations. This work was inspired by Smale's Problem 9\n(Mathematical problems for the next century, In Arnold, V. I.; Atiyah, M.; Lax,\nP.; Mazur, B. Mathematics: frontiers and perspectives, American Mathematical\nSociety, 271-294, 1999).\n"", ""On the facet pivot simplex method for linear programming I: algorithms\n  and numerical test   The Hirsch Conjecture stated that any d-dimensional polytope with n facets\nhas a diameter at most equal to n - d. This conjecture was disproven by Santos\n(A counterexample to the Hirsch Conjecture, Annals of Mathematics, 172(1)\n383-412, 2012). The implication of Santos' work is that all vertex pivot\nalgorithms cannot solve the linear programming problem in the worst case in n -\nd vertex pivot iterations.\n  In this paper, the first part in this series of papers, we propose a facet\npivot method and perform some numerical tests to demonstrate its superiority to\nthe existing vertex pivot method. In the second part of this series, we show\nthat the proposed facet pivot method can solve the canonical linear programming\nproblem in the worst case in at most n - d facet pivot iterations. This series\nof the papers was inspired by Smale's Problem 9 (Mathematical problems for the\nnext century, In Arnold, V. I.; Atiyah, M.; Lax, P.; Mazur, B. Mathematics:\nfrontiers and perspectives, American Mathematical Society, 271-294, 1999).\n""]","[('polytopes', 0.4804422855377197), ('matching polytopes', 0.4736080467700958), ('linear programs', 0.4707808196544647), ('polyhedron', 0.4674766957759857), ('linear programming', 0.43904218077659607), ('polytope', 0.4366738498210907), ('case computational complexity', 0.4346342980861664), ('worst case computational', 0.4336102306842804), ('polyhedra', 0.4072795808315277), ('integer programs', 0.39463627338409424)]"
1173,1173,25,1173_minor free graphs_vertex deletion_free graphs_parameterized complexity,"['minor free graphs', 'vertex deletion', 'free graphs', 'parameterized complexity', 'graph search', 'contain graphs', 'graphs', 'complexity np', 'graph operation', 'graph minor']","['Reducing Graph Parameters by Contractions and Deletions   We consider the following problem: for a given graph $G$ and two integers $k$\nand $d$, can we apply a fixed graph operation at most $k$ times in order to\nreduce a given graph parameter $\\pi$ by at least $d$? We show that this problem\nis NP-hard when the parameter is the independence number and the graph\noperation is vertex deletion or edge contraction, even for fixed $d=1$ and when\nrestricted to chordal graphs. We give a polynomial time algorithm for bipartite\ngraphs when the operation is edge contraction, the parameter is the\nindependence number and $d$ is fixed. Further, we complete the complexity\ndichotomy on $H$-free graphs when the parameter is the clique number and the\noperation is edge contraction by showing that this problem is NP-hard in\n$(C_3+P_1)$-free graphs even for fixed $d=1$. When the operation is edge\ndeletion and the parameter is the chromatic number, we determine the\ncomputational complexity of the associated problem on cographs and complete\nmultipartite graphs. Our results answer several open questions stated in [Diner\net al., Theoretical Computer Science, 746, p. 49-72 (2012)].\n', 'Hitting minors on bounded treewidth graphs. III. Lower bounds   For a finite collection of graphs ${\\cal F}$, the ${\\cal F}$-M-DELETION\nproblem consists in, given a graph $G$ and an integer $k$, decide whether there\nexists $S \\subseteq V(G)$ with $|S| \\leq k$ such that $G \\setminus S$ does not\ncontain any of the graphs in ${\\cal F}$ as a minor. We are interested in the\nparameterized complexity of ${\\cal F}$-M-DELETION when the parameter is the\ntreewidth of $G$, denoted by $tw$. Our objective is to determine, for a fixed\n${\\cal F}$, the smallest function $f_{{\\cal F}}$ such that ${\\cal\nF}$-M-DELETION can be solved in time $f_{{\\cal F}}(tw) \\cdot n^{O(1)}$ on\n$n$-vertex graphs. We provide lower bounds under the ETH on $f_{{\\cal F}}$ for\nseveral collections ${\\cal F}$. We first prove that for any ${\\cal F}$\ncontaining connected graphs of size at least two, $f_{{\\cal F}}(tw)=\n2^{\\Omega(tw)}$, even if the input graph $G$ is planar. Our main contribution\nconsists of superexponential lower bounds for a number of collections ${\\cal\nF}$, inspired by a reduction of Bonnet et al.~[IPEC, 2017]. In particular, we\nprove that when ${\\cal F}$ contains a single connected graph $H$ that is either\n$P_5$ or is not a minor of the banner (that is, the graph consisting of a $C_4$\nplus a pendent edge), then $f_{{\\cal F}}(tw)= 2^{\\Omega(tw \\cdot \\log tw)}$.\nThis is the third of a series of articles on this topic, and the results given\nhere together with other ones allow us, in particular, to provide a tight\ndichotomy on the complexity of $\\{H\\}$-M-DELETION, in terms of $H$, when $H$ is\nconnected.\n', 'Hitting minors on bounded treewidth graphs. II. Single-exponential\n  algorithms   For a finite collection of graphs ${\\cal F}$, the ${\\cal F}$-M-DELETION\n(resp. ${\\cal F}$-TM-DELETION) problem consists in, given a graph $G$ and an\ninteger $k$, decide whether there exists $S \\subseteq V(G)$ with $|S| \\leq k$\nsuch that $G \\setminus S$ does not contain any of the graphs in ${\\cal F}$ as a\nminor (resp. topological minor). We are interested in the parameterized\ncomplexity of both problems when the parameter is the treewidth of $G$, denoted\nby $tw$, and specifically in the cases where ${\\cal F}$ contains a single\nconnected planar graph $H$. We present algorithms running in time $2^{O(tw)}\n\\cdot n^{O(1)}$, called single-exponential, when $H$ is either $P_3$, $P_4$,\n$C_4$, the paw, the chair, and the banner for both $\\{H\\}$-M-DELETION and\n$\\{H\\}$-TM-DELETION, and when $H=K_{1,i}$, with $i \\geq 1$, for\n$\\{H\\}$-TM-DELETION. Some of these algorithms use the rank-based approach\nintroduced by Bodlaender et al. [Inform Comput, 2015]. This is the second of a\nseries of articles on this topic, and the results given here together with\nother ones allow us, in particular, to provide a tight dichotomy on the\ncomplexity of $\\{H\\}$-M-DELETION in terms of $H$.\n']","[('minor free graphs', 0.6056129336357117), ('vertex deletion', 0.5684696435928345), ('free graphs', 0.5271521806716919), ('parameterized complexity', 0.5038933157920837), ('graph search', 0.4484637379646301), ('contain graphs', 0.4382495582103729), ('graphs', 0.4344399869441986), ('complexity np', 0.4336176812648773), ('graph operation', 0.43347200751304626), ('graph minor', 0.43057456612586975)]"
1174,1174,25,1174_variational bayesian inference_variational inference_variational bayes_variational approximation,"['variational bayesian inference', 'variational inference', 'variational bayes', 'variational approximation', 'sampling variational', 'methods variational', 'approximate inference', 'mean field variational', 'large scale bayesian', 'variational distribution']","['A Particle Algorithm for Mean-Field Variational Inference   Variational inference is a fast and scalable alternative to Markov chain\nMonte Carlo and has been widely applied to posterior inference tasks in\nstatistics and machine learning. A traditional approach for implementing\nmean-field variational inference (MFVI) is coordinate ascent variational\ninference (CAVI), which relies crucially on parametric assumptions on complete\nconditionals. In this paper, we introduce a novel particle-based algorithm for\nmean-field variational inference, which we term PArticle VI (PAVI). Notably,\nour algorithm does not rely on parametric assumptions on complete conditionals,\nand it applies to the nonparametric setting. We provide non-asymptotic\nfinite-particle convergence guarantee for our algorithm. To our knowledge, this\nis the first end-to-end guarantee for particle-based MFVI.\n', 'Extending Mean-Field Variational Inference via Entropic Regularization:\n  Theory and Computation   Variational inference (VI) has emerged as a popular method for approximate\ninference for high-dimensional Bayesian models. In this paper, we propose a\nnovel VI method that extends the naive mean field via entropic regularization,\nreferred to as $\\Xi$-variational inference ($\\Xi$-VI). $\\Xi$-VI has a close\nconnection to the entropic optimal transport problem and benefits from the\ncomputationally efficient Sinkhorn algorithm. We show that $\\Xi$-variational\nposteriors effectively recover the true posterior dependency, where the\ndependence is downweighted by the regularization parameter. We analyze the role\nof dimensionality of the parameter space on the accuracy of $\\Xi$-variational\napproximation and how it affects computational considerations, providing a\nrough characterization of the statistical-computational trade-off in $\\Xi$-VI.\nWe also investigate the frequentist properties of $\\Xi$-VI and establish\nresults on consistency, asymptotic normality, high-dimensional asymptotics, and\nalgorithmic stability. We provide sufficient criteria for achieving\npolynomial-time approximate inference using the method. Finally, we demonstrate\nthe practical advantage of $\\Xi$-VI over mean-field variational inference on\nsimulated and real data.\n', ""f-Divergence Variational Inference   This paper introduces the $f$-divergence variational inference ($f$-VI) that\ngeneralizes variational inference to all $f$-divergences. Initiated from\nminimizing a crafty surrogate $f$-divergence that shares the statistical\nconsistency with the $f$-divergence, the $f$-VI framework not only unifies a\nnumber of existing VI methods, e.g. Kullback-Leibler VI, R\\'{e}nyi's\n$\\alpha$-VI, and $\\chi$-VI, but offers a standardized toolkit for VI subject to\narbitrary divergences from $f$-divergence family. A general $f$-variational\nbound is derived and provides a sandwich estimate of marginal likelihood (or\nevidence). The development of the $f$-VI unfolds with a stochastic optimization\nscheme that utilizes the reparameterization trick, importance weighting and\nMonte Carlo approximation; a mean-field approximation scheme that generalizes\nthe well-known coordinate ascent variational inference (CAVI) is also proposed\nfor $f$-VI. Empirical examples, including variational autoencoders and Bayesian\nneural networks, are provided to demonstrate the effectiveness and the wide\napplicability of $f$-VI.\n""]","[('variational bayesian inference', 0.7172468900680542), ('variational inference', 0.7039240002632141), ('variational bayes', 0.6206696629524231), ('variational approximation', 0.5928102731704712), ('sampling variational', 0.585232138633728), ('methods variational', 0.580461859703064), ('approximate inference', 0.5735408663749695), ('mean field variational', 0.5293008089065552), ('large scale bayesian', 0.5278231501579285), ('variational distribution', 0.5066294074058533)]"
1175,1175,25,1175_lenses_morphisms_diagrammatic_optics,"['lenses', 'morphisms', 'diagrammatic', 'optics', 'category theory', 'lens', 'functor', 'functors', 'string diagrams', 'category functors']","['Delta lenses as coalgebras for a comonad   Delta lenses are a kind of morphism between categories which are used to\nmodel bidirectional transformations between systems. Classical state-based\nlenses, also known as very well-behaved lenses, are both algebras for a monad\nand coalgebras for a comonad. Delta lenses generalise state-based lenses, and\nwhile delta lenses have been characterised as certain algebras for a\nsemi-monad, it is natural to ask if they also arise as coalgebras.\n  This short paper establishes that delta lenses are coalgebras for a comonad,\nthrough showing that the forgetful functor from the category of delta lenses\nover a base, to the category of cofunctors over a base, is comonadic. The proof\nutilises a diagrammatic approach to delta lenses, and clarifies several results\nin the literature concerning the relationship between delta lenses and\ncofunctors. Interestingly, while this work does not generalise the\ncorresponding result for state-based lenses, it does provide new avenues for\nexploring lenses as coalgebras.\n', 'Fibre optics   Lenses, optics and dependent lenses (or equivalently morphisms of containers,\nor equivalently natural transformations of polynomial functors) are all widely\nused in applied category theory as models of bidirectional processes. From the\ndefinition of lenses over a finite product category, optics weaken the required\nstructure to actions of monoidal categories, and dependent lenses make use of\nthe additional property of finite completeness (or, in case of polynomials,\neven local cartesian closure). This has caused a split in the applied category\ntheory literature between those using optics and those using dependent lenses.\nThe goal of this paper is to unify optics with dependent lenses, by finding a\ndefinition of fibre optics admitting both as special cases.\n', 'String Diagrams for Optics   Optics are a data representation for compositional data access, with lenses\nas a popular special case. Hedges has presented a diagrammatic calculus for\nlenses, but in a way that does not generalize to other classes of optic. We\npresent a calculus that works for all optics, not just lenses; this is done by\nembedding optics into their presheaf category, which naturally features string\ndiagrams. We apply our calculus to the common case of lenses, extend it to\neffectful lenses, and explore how the laws of optics manifest in this setting.\n']","[('lenses', 0.5583082437515259), ('morphisms', 0.5366895794868469), ('diagrammatic', 0.5126662254333496), ('optics', 0.5041918754577637), ('category theory', 0.4884326159954071), ('lens', 0.4725334346294403), ('functor', 0.4497879147529602), ('functors', 0.4475196599960327), ('string diagrams', 0.43644657731056213), ('category functors', 0.43156328797340393)]"
1176,1176,25,1176_type markov chain_markov chains also_analysis markov chains_markov chains,"['type markov chain', 'markov chains also', 'analysis markov chains', 'markov chains', 'type markov', 'reversible markov', 'markov jump processes', 'markov chain', 'time markov chains', 'markov jump']","['On Convergence of General Truncation-Augmentation Schemes for\n  Approximating Stationary Distributions of Markov Chains   In the analysis of Markov chains and processes, it is sometimes convenient to\nreplace an unbounded state space with a ""truncated"" bounded state space. When\nsuch a replacement is made, one often wants to know whether the equilibrium\nbehavior of the truncated chain or process is close to that of the untruncated\nsystem. For example, such questions arise naturally when considering numerical\nmethods for computing stationary distributions on unbounded state space. In\nthis paper, we study general truncation-augmentation schemes, in which the\nsubstochastic truncated ""northwest corner"" of the transition matrix or kernel\nis stochasticized (or augmented) arbitrarily. In the presence of a Lyapunov\ncondition involving a coercive function, we show that such schemes are\ngenerally convergent in countable state space, provided that the truncation is\nchosen as a sublevel set of the Lyapunov function. For stochastically monotone\nMarkov chains on $\\mathbb Z_+$, we prove that we can always choose the\ntruncation sets to be of the form $\\{0,1,...,n\\}$. We then provide sufficient\nconditions for weakly continuous Markov chains under which general\ntruncation-augmentation schemes converge weakly in continuous state space.\nFinally, we briefly discuss the extension of the theory to continuous time\nMarkov jump processes.\n', 'Level-wise Subgeometric Convergence of the Level-increment Truncation\n  Approximation of M/G/1-type Markov Chains   This paper considers the level-increment (LI) truncation approximation of\nM/G/1-type Markov chains. The LI truncation approximation is useful for\nimplementing the M/G/1 paradigm, which is the framework for computing the\nstationary distribution of M/G/1-type Markov chains. The main result of this\npaper is a subgeometric convergence formula for the total variation distance\nbetween the original stationary distribution and its LI truncation\napproximation. Suppose that the equilibrium level-increment distribution is\nsubexponential, and that the downward transition matrix is rank one. We then\nshow that the convergence rate of the total variation error of the LI\ntruncation approximation is equal to that of the tail of the equilibrium\nlevel-increment distribution and that of the tail of the original stationary\ndistribution.\n', ""A Subgeometric Convergence Formula for Total-variation Error of the\n  Level-increment Truncation Approximation of M/G/1-type Markov Chains   This paper considers the level-increment (LI) truncation approximation of\nM/G/1-type Markov chains. The LI truncation approximation is usually used to\nimplement Ramaswami's recursion for the stationary distribution in M/G/1-type\nMarkov chains. The main result of this paper is a subgeometric convergence\nformula for the total-variation distance between the stationary distribution\nand its LI truncation approximation.\n""]","[('type markov chain', 0.5627132654190063), ('markov chains also', 0.5489034056663513), ('analysis markov chains', 0.5315333604812622), ('markov chains', 0.5205993056297302), ('type markov', 0.5121603608131409), ('reversible markov', 0.5079251527786255), ('markov jump processes', 0.5055469274520874), ('markov chain', 0.4873339831829071), ('time markov chains', 0.4835178852081299), ('markov jump', 0.47774776816368103)]"
1177,1177,25,1177_played graphs_pebbles_graph smallest_game played graphs,"['played graphs', 'pebbles', 'graph smallest', 'game played graphs', 'pebble', 'vertex one', 'intermediate vertex', 'neighbouring vertex', 'vertex', 'adjacent vertex']","['Herscovici Conjecture on Pebbling   Consider a configuration of pebbles on the vertices of a connected graph. A\npebbling move is to remove two pebbles from a vertex and to place one pebble at\nthe neighbouring vertex of the vertex from which the pebbles are removed.\n  For a positive integer $t$, with every configuration of $\\pi_t(G)$(least\npositive integer) pebbles, if we can transfer $t$ pebbles to any target through\na number of pebbling moves then $\\pi_t(G)$ is called the $t$-pebbling number of\n$G$.\n  We discuss the computation of the $t$-pebbling number, the $2t-$ pebbling\nproperty and Herscovici conjecture considering total graphs.\n  \\bigskip \\noindent Keywords: pebbling moves, $t$- pebbling number,\n$2t$-pebbling property, Herscovici conjecture, total graphs.\n', 'Restricted optimal pebbling is NP-hard   Consider a distribution of pebbles on a graph. A pebbling move removes two\npebbles from a vertex and place one at an adjacent vertex. A vertex is\nreachable under a pebble distribution if it has a pebble after the application\nof a sequence of pebbling moves. A pebble distribution is solvable if each\nvertex is reachable under it. The size of a pebble distribution is the total\nnumber of pebbles. The optimal pebbling number $\\pi^*(G)$ is the size of the\nsmallest solvable distribution. A $t$-restricted pebble distribution places at\nmost $t$ pebbles at each vertex. The $t$-restricted optimal pebbling number\n$\\pi_t^*(G)$ is the size of the smallest solvable $t$-restricted pebble\ndistribution. We show that deciding whether $\\pi^*_2(G)\\leq k$ is NP-complete.\nWe prove that $\\pi_t^*(G)=\\pi^*(G)$ if $\\delta(G)\\geq \\frac{2|V(G)|}{3}-1$ and\nwe show infinitely many graphs which satisfies $\\delta(H)\\approx\n\\frac{1}{2}|V(H)|$ but $\\pi_t^*(H)\\neq\\pi^*(H)$, where $\\delta$ denotes the\nminimum degree.\n', ""Target Pebbling in Trees   Graph pebbling is a game played on graphs with pebbles on their vertices. A\npebbling move removes two pebbles from one vertex and places one pebble on an\nadjacent vertex. A configuration $C$ is a supply of pebbles at various vertices\nof a graph $G$, and a distribution $D$ is a demand of pebbles at various\nvertices of $G$. The $D$-pebbling number, $\\pi(G, D)$, of a graph $G$ is\ndefined to be the minimum number $m$ such that every configuration of $m$\npebbles can satisfy the demand $D$ via pebbling moves. The special case in\nwhich $t$ pebbles are demanded on vertex $v$ is denoted $D=v^t$, and the\n$t$-fold pebbling number, $\\pi_{t}(G)$, equals $\\max_{v\\in G}\\pi(G,v^t)$. It\nwas conjectured by Alc\\'on, Gutierrez, and Hurlbert that the pebbling numbers\nof chordal graphs forbidding the pyramid graph can be calculated in polynomial\ntime. Trees, of course, are the most prominent of such graphs. In 1989, Chung\ndetermined $\\pi_t(T)$ for all trees $T$. In this paper, we provide a\npolynomial-time algorithm to compute the pebbling numbers $\\pi(T,D)$ for all\ndistributions $D$ on any tree $T$, and characterize maximum-size configurations\nthat do not satisfy $D$.\n""]","[('played graphs', 0.4726882576942444), ('pebbles', 0.4531526267528534), ('graph smallest', 0.43987542390823364), ('game played graphs', 0.4359709322452545), ('pebble', 0.43539613485336304), ('vertex one', 0.4316673278808594), ('intermediate vertex', 0.41784846782684326), ('neighbouring vertex', 0.4169800877571106), ('vertex', 0.4128458499908447), ('adjacent vertex', 0.38874441385269165)]"
1178,1178,25,1178_polar coding_polar codes_binary erasure channels_polar code,"['polar coding', 'polar codes', 'binary erasure channels', 'polar code', 'decoding complexity', 'binary erasure channel', 'memoryless channel', 'memoryless channels', 'capacity achieving codes', 'polarization']","[""The Penalty in Scaling Exponent for Polar Codes is Analytically\n  Approximated by the Golden Ratio   The polarization process of conventional polar codes in binary erasure\nchannel (BEC) is recast to the Domany-Kinzel cellular automaton model of\ndirected percolation in a tilted square lattice. Consequently, the former's\nscaling exponent, $\\mu$, can be analogously expressed as the inverse of the\npercolation critical exponent, $\\beta$. Relying on the vast percolation theory\nliterature and the best known numerical estimate for $\\beta$, the scaling\nexponent can be easily estimated as\n$\\mu_{\\text{num}}^{\\text{perc}}\\simeq1/0.276486(8)\\simeq3.617$, which is only\nabout $0.25\\%$ away from the known exponent computation from coding theory\nliterature based on numerical approximation, $\\mu_{\\text{num}}\\simeq3.627$.\nRemarkably, this numerical result for the critical exponent, $\\beta$, can be\nanalytically approximated (within only $0.028\\%$) leading to the closed-form\nexpression for the scaling exponent\n$\\mu\\simeq2+\\varphi=2+1.618\\ldots\\simeq3.618$, where\n$\\varphi\\triangleq(1+\\sqrt{5})/2$ is the ubiquitous golden ratio. As the\nultimate achievable scaling exponent is quadratic, this implies that the\npenalty for polar codes in BEC, in terms of the scaling exponent, can be very\nwell estimated by the golden ratio, $\\varphi$, itself.\n"", 'Modular Arithmetic Erasure Channels and Their Multilevel Channel\n  Polarization   This study proposes \\emph{modular arithmetic erasure channels} (MAECs), a\nnovel class of erasure-like channels with an input alphabet that need not be\nbinary. This class contains the binary erasure channel (BEC) and some other\nknown erasure-like channels as special cases. For MAECs, we provide recursive\nformulas of Ar{\\i}kan-like polar transform to simulate channel polarization. In\nother words, we show that the synthetic channels of MAECs are equivalent to\nother MAECs. This is a generalization of well-known recursive formulas of the\npolar transform for BECs. Using our recursive formulas, we also show that a\nrecursive application of the polar transform for MAECs results in\n\\emph{multilevel channel polarization,} which is an asymptotic phenomenon that\nis characteristic of non-binary polar codes. Specifically, we establish a\nmethod to calculate the limiting proportions of the partially noiseless and\nnoisy channels that are generated as a result of multilevel channel\npolarization for MAECs. In the particular case of MAECs, this calculation\nmethod solves an open problem posed by Nasser (2017) in the study of non-binary\npolar codes.\n', ""Accelerating Polarization via Alphabet Extension   Polarization is an unprecedented coding technique in that it not only\nachieves channel capacity, but also does so at a faster speed of convergence\nthan any other coding technique. This speed is measured by the ``scaling\nexponent'' and its importance is three-fold. Firstly, estimating the scaling\nexponent is challenging and demands a deeper understanding of the dynamics of\ncommunication channels. Secondly, scaling exponents serve as a benchmark for\ndifferent variants of polar codes that helps us select the proper variant for\nreal-life applications. Thirdly, the need to optimize for the scaling exponent\nsheds light on how to reinforce the design of polar codes.\n  In this paper, we generalize the binary erasure channel (BEC), the simplest\ncommunication channel and the protagonist of many coding theory studies, to the\n``tetrahedral erasure channel'' (TEC). We then invoke Mori--Tanaka's $2 \\times\n2$ matrix over GF$(4)$ to construct polar codes over TEC. Our main contribution\nis showing that the dynamic of TECs converges to an almost--one-parameter\nfamily of channels, which then leads to an upper bound of $3.328$ on the\nscaling exponent. This is the first non-binary matrix whose scaling exponent is\nupper-bounded. It also polarizes BEC faster than all known binary matrices up\nto $23 \\times 23$ in size. Our result indicates that expanding the alphabet is\na more effective and practical alternative to enlarging the matrix in order to\nachieve faster polarization.\n""]","[('polar coding', 0.6291641592979431), ('polar codes', 0.5951606035232544), ('binary erasure channels', 0.5804253816604614), ('polar code', 0.574874758720398), ('decoding complexity', 0.5519580245018005), ('binary erasure channel', 0.541947066783905), ('memoryless channel', 0.4948895275592804), ('memoryless channels', 0.48180294036865234), ('capacity achieving codes', 0.45794379711151123), ('polarization', 0.45753809809684753)]"
1179,1179,25,1179_cooperative relaying_cooperative communications_wireless information power_relay networks,"['cooperative relaying', 'cooperative communications', 'wireless information power', 'relay networks', 'relay selection', 'relaying', 'simultaneous wireless information', 'af relaying', 'relay assisted', 'relay network']","['Outage Analysis in SWIPT Enabled Cooperative AF/DF Relay Assisted\n  Two-Way Spectrum Sharing Communication   This paper reports relative performance of decode-and-forward (DF) and\namplify-and-forward (AF) relaying in a multi-antenna cooperative cognitive\nradio network (CCRN) that supports device-to-device (D2D) communications using\nspectrum sharing technique in cellular network. In this work, cellular system\nis considered as primary and internet of things devices (IoDs), engaged in D2D\ncommunications, are considered to be secondary system. The devices access the\nlicensed spectrum by means of the cooperation in two-way primary\ncommunications. Furthermore, IoDs are energized by harvesting the energy from\nradio frequency (RF) signals, using simultaneous wireless information and power\ntransfer (SWIPT) protocol. Closed form expressions of outage probability for\nboth cellular and D2D communications are derived and the impact of various\ndesign parameters for both AF and DF relaying techniques are studied. Based on\nthe simulation results, it is found that the proposed spectrum sharing\nprotocol, for both DF relaying and AF relaying schemes, outperform another\nsimilar network architecture in terms of spectrum efficiency. It is also\nobserved that the performance of the proposed system using DF relaying is\nbetter than AF relaying scheme in terms of energy efficiency at same transmit\npower.\n', 'System Outage Probability of PS-SWIPT Enabled Two-Way AF Relaying with\n  Hardware Impairments   In this paper, we investigate the system outage probability of a simultaneous\nwireless information and power transfer (SWIPT) based two-way\namplify-and-forward (AF) relay network considering transceiver hardware\nimpairments (HIs), where the energy-constrained relay node processes the\nreceived signals based on a power splitting protocol and the two terminals\nemploy a selection combining (SC) scheme to exploit the signals from the direct\nand relaying links. Assuming independent but non-identically distributed\nNakagami-m fading channels, we derive the system outage probability in a\nclosed-form, which enables us to identify two crucial ceiling effects on the\nsystem outage probability caused by HIs in the high data rate regions, i.e.,\nrelay cooperation ceiling (RCC) and overall system ceiling (OSC). Specifically,\nthe RCC prevents the relaying link from participating in cooperative\ncommunications, while the OSC leaves the overall system in outage. Furthermore,\nwe derive the achievable diversity gain of the considered network, which shows\nthat the diversity gain equals either the shape parameter of the direct link or\nzero. Computer simulations are provided to validate the correctness of our\nanalytical results, and study the effects of various system parameters on the\nsystem outage performance and the optimal power splitting ratio, as well as the\nenergy efficiency.\n', 'System Outage Probability and Diversity Analysis of SWIPT Enabled\n  Two-Way DF Relaying under Hardware Impairments   This paper investigates the system outage performance of a simultaneous\nwireless information and power transfer (SWIPT) based two-way\ndecode-and-forward (DF) relay network, where potential hardware impairments\n(HIs) in all transceivers are considered. After harvesting energy and decoding\nmessages simultaneously via a power splitting scheme, the energy-limited relay\nnode forwards the decoded information to both terminals. Each terminal combines\nthe signals from the direct and relaying links via selection combining. We\nderive the system outage probability under independent but non-identically\ndistributed Nakagami-m fading channels. It reveals an overall system ceiling\n(OSC) effect, i.e., the system falls in outage if the target rate exceeds an\nOSC threshold that is determined by the levels of HIs. Furthermore, we derive\nthe diversity gain of the considered network. The result reveals that when the\ntransmission rate is below the OSC threshold, the achieved diversity gain\nequals the sum of the shape parameter of the direct link and the smaller shape\nparameter of the terminal-to-relay links; otherwise, the diversity gain is\nzero. This is different from the amplify-and-forward (AF) strategy, under which\nthe relaying links have no contribution to the diversity gain. Simulation\nresults validate the analytical results and reveal that compared with the AF\nstrategy, the SWIPT based two-way relaying links under the DF strategy are more\nrobust to HIs and achieve a lower system outage probability.\n']","[('cooperative relaying', 0.5672768950462341), ('cooperative communications', 0.5230110883712769), ('wireless information power', 0.5213585495948792), ('relay networks', 0.4951269030570984), ('relay selection', 0.46906566619873047), ('relaying', 0.4675799310207367), ('simultaneous wireless information', 0.4604499936103821), ('af relaying', 0.458534836769104), ('relay assisted', 0.444261759519577), ('relay network', 0.4396221339702606)]"
1180,1180,25,1180_stiefel whitney classes_stiefel whitney class_representations gl_representations mathrm gl,"['stiefel whitney classes', 'stiefel whitney class', 'representations gl', 'representations mathrm gl', 'whitney classes', 'representations pi', 'special linear groups', 'irreducible unitary representations', 'orthogonal groups', 'orthogonal representations']","['Stiefel-Whitney Classes for Finite Special Linear Groups of Even Rank   We compute the total Stiefel-Whitney Classes (SWCs) for orthogonal\nrepresentations of special linear groups $\\text{SL}(n,q)$ when $n$ and $q$ are\nodd. These classes are expressed in terms of character values at diagonal\nelements of order $2$. We give several consequences, and work out the $4$th SWC\nexplicitly, and the $8$th SWC when the $4$th vanishes.\n', 'Total Stiefel Whitney classes for real representations of\n  $\\mathrm{GL}_n$ over $\\mathbb{F}_q, \\mathbb{R}$ and $\\mathbb{C}$   We compute the total Stiefel Whitney class for a real representation $\\pi$ of\n$\\mathrm{GL}_n(\\mathbb{F}_q)$, where $q$ is odd in terms of character values of\n$\\pi$ on order $2$ diagonal elements. We also compute the total Stiefel Whitney\nclass of real representations of $\\mathrm{GL}_n(\\mathbb{R})$ and\n$\\mathrm{GL}_n(\\mathbb{C})$.\n', 'Stiefel-Whitney Classes of Representations of $\\text{SL}(2,q)$   We describe the Stiefel-Whitney classes (SWCs) of orthogonal representations\n$\\pi$ of the finite special linear groups $G=\\text{SL}(2,\\mathbb F_q)$, in\nterms of character values of $\\pi$. From this calculation, we can answer\ninteresting questions about SWCs of $\\pi$. For instance, we determine the\nsubalgebra of $H^*(G,\\mathbb Z/2\\mathbb Z)$ generated by the SWCs of orthogonal\n$\\pi$, and we also determine which $\\pi$ have nontrivial mod $2$ Euler class.\n']","[('stiefel whitney classes', 0.614023745059967), ('stiefel whitney class', 0.5907491445541382), ('representations gl', 0.5353614091873169), ('representations mathrm gl', 0.5128423571586609), ('whitney classes', 0.5000954866409302), ('representations pi', 0.4950798749923706), ('special linear groups', 0.48213034868240356), ('irreducible unitary representations', 0.4817877411842346), ('orthogonal groups', 0.47994592785835266), ('orthogonal representations', 0.47233375906944275)]"
1181,1181,25,1181_information geometry_statistical manifolds_information geometric_statistical manifold,"['information geometry', 'statistical manifolds', 'information geometric', 'statistical manifold', 'geometry statistical', 'geometry information', 'statistical theory', 'statistical structure', 'fisher information', 'fisher metric']","['Beyond scalar quasi-arithmetic means: Quasi-arithmetic averages and\n  quasi-arithmetic mixtures in information geometry   We generalize quasi-arithmetic means beyond scalars by considering the\ngradient map of a Legendre type real-valued function. The gradient map of a\nLegendre type function is proven strictly comonotone with a global inverse. It\nthus yields a generalization of strictly mononotone and differentiable\nfunctions generating scalar quasi-arithmetic means. Furthermore, the Legendre\ntransformation gives rise to pairs of dual quasi-arithmetic averages via the\nconvex duality. We study the invariance and equivariance properties under\naffine transformations of quasi-arithmetic averages via the lens of dually flat\nspaces of information geometry. We show how these quasi-arithmetic averages are\nused to express points on dual geodesics and sided barycenters in the dual\naffine coordinate systems. We then consider quasi-arithmetic mixtures and\ndescribe several parametric and non-parametric statistical models which are\nclosed under the quasi-arithmetic mixture operation.\n', 'Information Geometry for the Working Information Theorist   Information geometry is a study of statistical manifolds, that is, spaces of\nprobability distributions from a geometric perspective. Its classical\ninformation-theoretic applications relate to statistical concepts such as\nFisher information, sufficient statistics, and efficient estimators. Today,\ninformation geometry has emerged as an interdisciplinary field that finds\napplications in diverse areas such as radar sensing, array signal processing,\nquantum physics, deep learning, and optimal transport. This article presents an\noverview of essential information geometry to initiate an information theorist,\nwho may be unfamiliar with this exciting area of research. We explain the\nconcepts of divergences on statistical manifolds, generalized notions of\ndistances, orthogonality, and geodesics, thereby paving the way for concrete\napplications and novel theoretical investigations. We also highlight some\nrecent information-geometric developments, which are of interest to the broader\ninformation theory community.\n', 'Information geometry of warped product spaces   Information geometry is an important tool to study statistical models. There\nare some important examples in statistical models which are regarded as warped\nproducts. In this paper, we study information geometry of warped products. We\nconsider the case where the warped product and its fiber space are equipped\nwith dually flat connections and, in the particular case of a cone,\ncharacterize the connections on the base space $\\mathbb{R}_{>0}$. The resulting\nconnections turn out to be the $\\alpha$-connections with $\\alpha = \\pm{1}$.\n']","[('information geometry', 0.6375797986984253), ('statistical manifolds', 0.6282685399055481), ('information geometric', 0.6118653416633606), ('statistical manifold', 0.608636200428009), ('geometry statistical', 0.534522533416748), ('geometry information', 0.5136211514472961), ('statistical theory', 0.4866889715194702), ('statistical structure', 0.47983893752098083), ('fisher information', 0.4264366924762726), ('fisher metric', 0.4180065393447876)]"
1182,1182,25,1182_vehicular networks_cellular networks_hop relaying_stochastic geometry,"['vehicular networks', 'cellular networks', 'hop relaying', 'stochastic geometry', 'wireless networks', 'vehicular', 'poisson point process', 'cellular', 'poisson line process', 'relaying']","['ADDENDUM Details of the Derivation of the Probability of Coverage for\n  the Relaying Scheme (Section IV in the paper: ""A Poisson Line Process based\n  Framework for Determining the Needed RSU Density and Relaying Hops in\n  Vehicular Networks\'\')   This paper develops a framework to study multi-hop relaying in a vehicular\nnetwork consisting of vehicles and Road Side Units (RSUs), and the effect of\nthis relaying on the network coverage and the communication delay. We use a\nstochastic geometry model that consists of a combination of Poisson Line\nProcess (PLP) and 1D Poisson Point Process (PPP) to reliably characterize the\nvehicular network layout and the locations of the vehicles and the RSUs. Using\nthis model, we analyze the effect of the different network parameters on the\ncoverage provided by the RSUs to the vehicles. Then, we investigate how the\nuncovered vehicles can receive their intended packets by relaying them through\nmultiple hops that form connected paths to the RSUs. We also analyze the delay\nintroduced to packet delivery due to multi-hop relaying. Namely, we present\nresults that illustrate the coverage gains achieved through multi-hop relaying\nand the delays induced. Such results could be used by network planners and\noperators to decide on the different configurations and operational parameters\nof the vehicular network to suit particular scenarios and objectives.\n', 'Periodic handover skipping in cellular networks: Spatially stochastic\n  modeling and analysis   Handover (HO) management is one of the most crucial tasks in dense cellular\nnetworks with mobile users. A problem in the HO management is to deal with\nincreasing HOs due to network densification in the 5G evolution and various HO\nskipping techniques have so far been studied in the literature to suppress\nexcessive HOs. In this paper, we propose yet another HO skipping scheme, called\nperiodic HO skipping. The proposed scheme prohibits the HOs of a mobile user\nequipment (UE) for a certain period of time, referred to as skipping period,\nthereby enabling flexible operation of the HO skipping by adjusting the length\nof the skipping period. We investigate the performance of the proposed scheme\non the basis of stochastic geometry. Specifically, we derive analytical\nexpressions of two performance metrics -- the HO rate and the expected downlink\ndata rate -- when a UE adopts the periodic HO skipping. Numerical results based\non the analysis demonstrate that the periodic HO skipping scenario can\noutperform the scenario without any HO skipping in terms of a certain utility\nmetric representing the trade-off between the HO rate and the expected downlink\ndata rate, in particular when the UE moves fast. Furthermore, we numerically\nshow that there can exist an optimal length of the skipping period, which\nlocally maximizes the utility metric, and approximately provide the optimal\nskipping period in a simple form. Numerical comparison with some other HO\nskipping techniques is also conducted.\n', 'Time-based Handover Skipping in Cellular Networks: Spatially Stochastic\n  Modeling and Analysis   Handover (HO) management has attracted attention of research in the context\nof wireless cellular communication networks. One crucial problem of HO\nmanagement is to deal with increasing HOs experienced by a mobile user. To\naddress this problem, HO skipping techniques have been studied in recent years.\nIn this paper, we propose a novel HO skipping scheme, namely, time-based HO\nskipping. In the proposed scheme, HOs of a user are controlled by a certain\nfixed period of time, which we call skipping time. The skipping time can be\nmanaged as a system parameter, thereby enabling flexible operation of HO\nskipping. We analyze the transmission performance of the proposed scheme on the\nbasis of a stochastic geometry approach. In the scenario where a user performs\nthe time-based HO skipping, we derive the analytical expressions for two\nperformance metrics: the HO rate and the expected data rate. The analysis\nresults demonstrate that the scenario with the time-based HO skipping\noutperforms the scenario without HO skipping particularly when the user moves\nfast. Furthermore, we reveal that there is a unique optimal skipping time\nmaximizing the transmission performance, which we obtain approximately.\n']","[('vehicular networks', 0.5247946381568909), ('cellular networks', 0.49099981784820557), ('hop relaying', 0.38067129254341125), ('stochastic geometry', 0.37475821375846863), ('wireless networks', 0.36795586347579956), ('vehicular', 0.35703760385513306), ('poisson point process', 0.34423068165779114), ('cellular', 0.3252856135368347), ('poisson line process', 0.3251349627971649), ('relaying', 0.31887397170066833)]"
1183,1183,25,1183_nonlinear parabolic_parabolic inverse_inverse numerical_nonlinear parabolic equations,"['nonlinear parabolic', 'parabolic inverse', 'inverse numerical', 'nonlinear parabolic equations', 'numerical reconstruction', 'nonlinear inverse', 'parabolic equations', 'convergent numerical', 'inverse recovering', 'carleman estimate']","['The Carleman-Newton method to globally reconstruct a source term for\n  nonlinear parabolic equation   We propose to combine the Carleman estimate and the Newton method to solve an\ninverse source problem for nonlinear parabolic equations from lateral boundary\ndata. The stability of this inverse source problem is conditionally\nlogarithmic. Hence, numerical results due to the conventional least squares\noptimization might not be reliable. In order to enhance the stability, we\napproximate this problem by truncating the high frequency terms of the Fourier\nseries that represents the solution to the governing equation. By this, we\nderive a system of nonlinear elliptic PDEs whose solution consists of Fourier\ncoefficients of the solution to the parabolic governing equation. We solve this\nsystem by the Carleman-Newton method. The Carleman-Newton method is a newly\ndeveloped algorithm to solve nonlinear PDEs. The strength of the\nCarleman-Newton method includes (1) no good initial guess is required and (2)\nthe computational cost is not expensive. These features are rigorously proved.\nHaving the solutions to this system in hand, we can directly compute the\nsolution to the proposed inverse problem. Some numerical examples are\ndisplayed.\n', 'Convergent numerical methods for parabolic equations with reversed time\n  via a new Carleman estimate   The key tool of this paper is a new Carleman estimate for an arbitrary\nparabolic operator of the second order for the case of reversed time data. This\nestimate works on an arbitrary time interval. On the other hand, the previously\nknown Carleman estimate for the reversed time case works only on a sufficiently\nsmall time interval. First, a stability estimate is proven. Next, the\nquasi-reversibility numerical method is proposed for an arbitrary time interval\nfor the linear case. This is unlike a sufficiently small time interval in the\nprevious work. The convergence rate for the quasi-reversibility method is\nestablished. Finally, the quasilinear parabolic equation with reversed time is\nconsidered. A weighted globally strictly convex Tikhonov-like functional is\nconstructed. The weight is the Carleman Weight Function which is involved in\nthat Carleman estimate. The global convergence of the gradient projection\nmethod to the exact solution is proved for this functional.\n', 'The Carleman Contraction Mapping Method for a Coefficient Inverse\n  Problem of the Epidemiology   It is proposed to monitor spatial and temporal spreads of epidemics via\nsolution of a Coefficient Inverse Problem for a system of three coupled\nnonlinear parabolic equations. To solve this problem numerically, a version of\nthe so-called Carleman contraction mapping method is developed for this\nproblem. On each iteration, a linear problem with the incomplete lateral Cauchy\ndata is solved by the weighted Quasi-Reversibility Method, where the weight is\nthe Carleman Weight Function. This is the function, which is involved as the\nweight in the Carleman estimate for the corresponding parabolic operator.\nConvergence analysis ensures the global convergence of this procedure.\nNumerical results demonstrate an accurate performance of this technique for\nnoisy data.\n']","[('nonlinear parabolic', 0.549666166305542), ('parabolic inverse', 0.5378196239471436), ('inverse numerical', 0.5069501996040344), ('nonlinear parabolic equations', 0.49483877420425415), ('numerical reconstruction', 0.47600656747817993), ('nonlinear inverse', 0.45385512709617615), ('parabolic equations', 0.42485716938972473), ('convergent numerical', 0.4136633276939392), ('inverse recovering', 0.4108937680721283), ('carleman estimate', 0.41059407591819763)]"
1184,1184,25,1184_wireless communications_spatial modulation_modulation scheme_mimo scheme,"['wireless communications', 'spatial modulation', 'modulation scheme', 'mimo scheme', 'modulation schemes', 'index modulation im', 'receive antennas', 'modulation im', 'transmit', 'index modulation']","['RIS-Assisted Receive Quadrature Spatial Modulation with Low-Complexity\n  Greedy Detection   In this paper, we propose a novel reconfigurable intelligent surface\n(RIS)-assisted wireless communication scheme which uses the concept of spatial\nmodulation, namely RIS-assisted receive quadrature spatial modulation\n(RIS-RQSM). In the proposed RIS-RQSM system, the information bits are conveyed\nvia both the indices of the two selected receive antennas and the conventional\nin-phase/quadrature (IQ) modulation. We propose a novel methodology to adjust\nthe phase shifts of the RIS elements in order to maximize the signal-to-noise\nratio (SNR) and at the same time to construct two separate PAM symbols at the\nselected receive antennas, as the in-phase and quadrature components of the\ndesired IQ symbol. An energy-based greedy detector (GD) is implemented at the\nreceiver to efficiently detect the received signal with minimal channel state\ninformation (CSI) via the use of an appropriately designed one-tap\npre-equalizer. We also derive a closed-form upper bound on the average bit\nerror probability (ABEP) of the proposed RIS-RQSM system. Then, we formulate an\noptimization problem to minimize the ABEP in order to improve the performance\nof the system, which allows the GD to act as a near-optimal receiver. Extensive\nnumerical results are provided to demonstrate the error rate performance of the\nsystem and to compare with that of a prominent benchmark scheme. The results\nverify the remarkable superiority of the proposed RIS-RQSM system over the\nbenchmark scheme.\n', ""Space-Time Block Coded Reconfigurable Intelligent Surface-Based Received\n  Spatial Modulation   Reconfigurable intelligent surface (RIS) structures reflect the incident\nsignals by adjusting phase adaptively according to the channel condition where\ndoing transmission in order to increase signal quality at the receiver.\nBesides, the spatial modulation (SM) technique is a possible candidate for\nfuture energy-efficient wireless communications due to providing better\nthroughput, low-cost implementation and good error performance. Also,\nAlamouti's space-time block coding (ASBC) is an important space and time coding\ntechnique in terms of diversity gain and simplified ML detection. In this\npaper, we proposed the RIS assisted received spatial modulation (RSM) scheme\nwith ASBC, namely RIS-RSM-ASBC. The termed RIS is portioned by two parts in the\nproposed system model. Each one is utilized as an access point (AP) to transmit\nits Alamouti coded information while reflecting passive signals to the selected\nreceived antenna. The optimal maximum likelihood (ML) detector is designed for\nthe proposed RIS-RSM-ASBC scheme. Extensive computer simulations are conducted\nto corroborate theoretical derivations. Results show that RIS-RSM-ASBC system\nis highly reliable and provides data rate enhancement in contrast to\nconventional RIS assisted transmit SM (RIS-TSM), RIS assisted transmit\nquadrature SM (RIS-TQSM), RIS assisted received SM (RIS-RSM), RIS assisted\ntransmit space shift keying with ASBC (RIS-TSSK-ASBC) and RIS-TSSK-VBLAST\nschemes.\n"", 'RIS-Assisted Receive Quadrature Space-Shift Keying: A New Paradigm and\n  Performance Analysis   Reconfigurable intelligent surfaces (RISs) represent a promising candidate\nfor sixth-generation (6G) wireless networks, as the RIS technology provides a\nnew solution to control the propagation channel in order to improve the\nefficiency of a wireless link through enhancing the received signal power. In\nthis paper, we propose RIS-assisted receive quadrature space-shift keying\n(RIS-RQSSK), which enhances the spectral efficiency of an RIS-based index\nmodulation (IM) system by using the real and imaginary dimensions independently\nfor the purpose of IM. Therefore, the error rate performance of the system is\nimproved as all RIS elements reflect the incident transmit signal toward both\nselected receive antennas. At the receiver, a low-complexity but effective\ngreedy detector (GD) can be employed which determines the maximum energy per\ndimension at the receive antennas. A max-min optimization problem is defined to\nmaximize the received signal-to-noise ratio (SNR) components at both selected\nreceive antennas; an analytical solution is provided based on Lagrange duality.\nIn particular, the multi-variable optimization problem is shown to reduce to\nthe solution of a single-variable equation, which results in a very simple\ndesign procedure. In addition, we investigate the average bit error probability\n(ABEP) of the proposed RIS-RQSSK system and derive a closed-form approximate\nupper bound on the ABEP. We also provide extensive numerical simulations to\nvalidate our derivations. Numerical results show that the proposed RIS-RQSSK\nscheme substantially outperforms recent prominent benchmark schemes. This\nenhancement considerably increases with an increasing number of receive\nantennas.\n']","[('wireless communications', 0.4760034382343292), ('spatial modulation', 0.4584364891052246), ('modulation scheme', 0.4323809742927551), ('mimo scheme', 0.4278770089149475), ('modulation schemes', 0.4128373861312866), ('index modulation im', 0.3951960802078247), ('receive antennas', 0.39387863874435425), ('modulation im', 0.39325132966041565), ('transmit', 0.3871985673904419), ('index modulation', 0.3706313371658325)]"
1185,1185,25,1185_blow dynamics_blow solutions_supercritical dimensions_stability blow,"['blow dynamics', 'blow solutions', 'supercritical dimensions', 'stability blow', 'finite time blow', 'finite time blowup', 'wave equations dimensions', 'blowup solutions', 'wave maps dimensional', 'self similar blowup']","['Stable blowup for supercritical wave maps into perturbed spheres   We consider wave maps from $(1+d)$-dimensional Minkowski space, $d\\geq3$,\ninto rotationally symmetric manifolds which arise from small perturbations of\nthe sphere $\\mathbb S^d$. We prove the existence of co-rotational self-similar\nfinite time blowup solutions with smooth blowup profiles. Furthermore, we show\nthe nonlinear asymptotic stability of these solutions under suitably small\nco-rotational perturbations on the full space.\n', ""Globally stable blowup profile for supercritical wave maps in all\n  dimensions   We consider wave maps from the $(1+d)$-dimensional Minkowski space into the\n$d$-sphere. It is known from the work of Bizo\\'n and Biernat \\cite{BizBie15}\nthat in the energy-supercritical case, i.e., for $d \\geq 3$, this model admits\na closed-form corotational self-similar blowup solution. We show that this\nblowup profile is globally nonlinearly stable for all $d \\geq 3$, thereby\nverifying a perturbative version of the conjecture posed in \\cite{BizBie15}\nabout the generic large data blowup behavior for this model. To accomplish\nthis, we develop a novel stability analysis approach based on similarity\nvariables posed on the whole space $\\mathbb{R}^d$. As a result, we draw a\ngeneral road map for studying spatially global stability of self-similar blowup\nprofiles for nonlinear wave equations in the radial case for arbitrary\ndimension $d \\geq 3$.\n"", 'On stable self-similar blowup for corotational wave maps and equivariant\n  Yang-Mills connections   We consider corotational wave maps from Minkowski spacetime into the sphere\nand the equivariant Yang-Mills equation for all energy-supercritical\ndimensions. Both models have explicit self-similar finite time blowup\nsolutions, which continue to exist even past the singularity. We prove the\nnonlinear asymptotic stability of these solutions in spacetime regions that\napproach the future light cone of the singularity. For this, we develop a\ngeneral functional analytic framework in adapted similarity coordinates that\nallows to evolve the stable wave flow near a self-similar blowup solution in\nsuch spacetime regions.\n']","[('blow dynamics', 0.5342671275138855), ('blow solutions', 0.5277097821235657), ('supercritical dimensions', 0.5126606822013855), ('stability blow', 0.48866474628448486), ('finite time blow', 0.4827558398246765), ('finite time blowup', 0.4723831117153168), ('wave equations dimensions', 0.4457867443561554), ('blowup solutions', 0.43921327590942383), ('wave maps dimensional', 0.43636515736579895), ('self similar blowup', 0.42884036898612976)]"
1186,1186,25,1186_graph finite group_cayley graphs_regular cayley graph_graphs perfect,"['graph finite group', 'cayley graphs', 'regular cayley graph', 'graphs perfect', 'cayley graph', 'cayley graphs let', 'group perfect', 'code graph', 'vertex transitive graphs', 'subgroup containing']","['On subgroup perfect codes in Cayley graphs   A perfect code in a graph $\\Gamma = (V, E)$ is a subset $C$ of $V$ such that\nno two vertices in $C$ are adjacent and every vertex in $V \\setminus C$ is\nadjacent to exactly one vertex in $C$. A subgroup $H$ of a group $G$ is called\na subgroup perfect code of $G$ if there exists a Cayley graph of $G$ which\nadmits $H$ as a perfect code. Equivalently, $H$ is a subgroup perfect code of\n$G$ if there exists an inverse-closed subset $A$ of $G$ containing the identity\nelement such that $(A, H)$ is a tiling of $G$ in the sense that every element\nof $G$ can be uniquely expressed as the product of an element of $A$ and an\nelement of $H$. In this paper we obtain multiple results on subgroup perfect\ncodes of finite groups, including a few necessary and sufficient conditions for\na subgroup of a finite group to be a subgroup perfect code, a few results\ninvolving $2$-subgroups in the study of subgroup perfect codes, and several\nresults on subgroup perfect codes of metabelian groups, generalized dihedral\ngroups, nilpotent groups and $2$-groups.\n', 'Subgroup perfect codes in Cayley graphs   Let $\\Gamma$ be a graph with vertex set $V(\\Gamma)$. A subset $C$ of\n$V(\\Gamma)$ is called a perfect code in $\\Gamma$ if $C$ is an independent set\nof $\\Gamma$ and every vertex in $V(\\Gamma)\\setminus C$ is adjacent to exactly\none vertex in $C$. A subset $C$ of a group $G$ is called a perfect code of $G$\nif there exists a Cayley graph of $G$ which admits $C$ as a perfect code. A\ngroup $G$ is said to be code-perfect if every proper subgroup of $G$ is a\nperfect code of $G$. In this paper we prove that a group is code-perfect if and\nonly if it has no elements of order $4$. We also prove that a proper subgroup\n$H$ of an abelian group $G$ is a perfect code of $G$ if and only if the Sylow\n$2$-subgroup of $H$ is a perfect code of the Sylow $2$-subgroup of $G$. This\nreduces the problem of determining when a given subgroup of an abelian group is\na perfect code to the case of abelian $2$-groups. Finally, we determine all\nsubgroup perfect codes in any generalized quaternion group.\n', 'On subgroup perfect codes in vertex-transitive graphs   A subset $C$ of the vertex set $V$ of a graph $\\Gamma$ is called a perfect\ncode in $\\Gamma$ if every vertex in $V\\setminus C$ is adjacent to exactly one\nvertex in $C$. Given a group $G$ and a subgroup $H$ of $G$, a subgroup $A$ of\n$G$ containing $H$ is called a perfect code of the pair $(G,H)$ if there exists\na coset graph $\\mathrm{Cos}(G,H,U)$ such that the set of left cosets of $H$ in\n$A$ is a perfect code in $\\mathrm{Cos}(G,H,U)$. In particular, $A$ is called a\nperfect code of $G$ if $A$ is a perfect code of the pair $(G,1)$. In this\npaper, we give a characterization of $A$ to be a perfect code of the pair\n$(G,H)$ under the assumption that $H$ is a perfect code of $G$. As a corollary,\nwe derive an additional sufficient and necessary condition for $A$ to be a\nperfect code of $G$. Moreover, we establish conditions under which $A$ is not a\nperfect code of $(G,H)$, which is applied to construct infinitely many\ncounterexamples to a question posed by Wang and Zhang\n[\\emph{J.~Combin.~Theory~Ser.~A}, 196 (2023) 105737]. Furthermore, we initiate\nthe study of determining which maximal subgroups of $S_n$ are perfect codes.\n']","[('graph finite group', 0.5585294961929321), ('cayley graphs', 0.5032740831375122), ('regular cayley graph', 0.5020596385002136), ('graphs perfect', 0.4857390522956848), ('cayley graph', 0.4801630973815918), ('cayley graphs let', 0.47746506333351135), ('group perfect', 0.4481917917728424), ('code graph', 0.4290967583656311), ('vertex transitive graphs', 0.42840903997421265), ('subgroup containing', 0.4263119399547577)]"
1187,1187,25,1187_polynomials matroids_chow rings_polynomial matroid_theory matroids,"['polynomials matroids', 'chow rings', 'polynomial matroid', 'theory matroids', 'chow ring', 'standard monomials', 'monomial basis', 'matroid', 'matroids', 'polynomials hilbert']","[""Chow rings and augmented Chow rings of uniform matroids and their\n  $q$-analogs   We study the natural representations of $\\mathfrak{S}_n$ and\n$GL_n(\\mathbb{F}_q)$ on the (augmented) Chow rings of uniform matroids and\n$q$-uniform matroids. The Frobenius series for uniform matroids and their\n$q$-analogs are computed. As a byproduct, we recover Hameister, Rao, and\nSimpson's formula of Hilbert series of Chow rings of $q$-uniform matroids in\nterms of permutations and further obtain their augmented counterpart in terms\nof decorated permutations.\n  We also show that equivariant Charney-Davis quantities of (augmented) Chow\nrings of general matroids are nonnegative (i.e. genuine representations of the\nautomorphism group of the matroid). When the matroid is a uniform matroid, the\nrepresentations either vanish or are Specht modules of some skew hook shapes.\nWhen descending to the usual Charney-Davis quantities, we obtain an elegant\ncombinatorial interpretation of Hameister, Rao, and Simpson's formula for Chow\nrings of $q$-uniform matroids and its augmented counterpart.\n"", ""Chow rings of matroids are Koszul   Chow rings of matroids were instrumental in the resolution of the\nHeron-Rota-Welsh Conjecture by Adiprasito, Huh, and Katz and in the resolution\nof the Top-Heavy Conjecture by Braden, Huh, Matherne, Proudfoot, and Wang. The\nChow ring of a matroid is a commutative, graded, Artinian, Gorenstein algebra\nwith linear and quadratic relations defined by the matroid. Dotsenko\nconjectured that the Chow ring of any matroid is Koszul. The purpose of this\npaper is to prove Dotsenko's conjecture. We also show that the augmented Chow\nring of a matroid is Koszul. As a corollary, we show that the Chow rings and\naugmented Chow rings of matroids have rational Poincar\\'{e} series.\n"", ""Hilbert-Poincar\\'e series of matroid Chow rings and intersection\n  cohomology   We study the Hilbert series of four objects arising in the Chow-theoretic and\nKazhdan-Lusztig framework of matroids. These are, respectively, the Hilbert\nseries of the Chow ring, the augmented Chow ring, the intersection cohomology\nmodule, and its stalk at the empty flat. We develop a parallelism between the\nKazhdan-Lusztig polynomial of a matroid and the Hilbert series of its Chow\nring. This extends to a parallelism between the $Z$-polynomial of a matroid and\nthe Hilbert series of its augmented Chow ring. This suggests to bring ideas\nfrom one framework to the other. Our two main motivations are the\nreal-rootedness conjecture for all of these polynomials, and the problem of\ncomputing them. We provide several intrinsic definitions of these invariants;\nalso, by leveraging that they are valuations under matroid polytope\nsubdivisions, we deduce a fast way for computing them for a large class of\nmatroids. Uniform matroids are a case of combinatorial interest; we link the\nresulting polynomials with certain real-rooted families such as the (binomial)\nEulerian polynomials, and we settle a conjecture of Hameister, Rao, and\nSimpson. Furthermore, we prove the real-rootedness of the Hilbert series of the\naugmented Chow rings of uniform matroids via a result of Haglund and Zhang; and\nin addition, we prove a version of a conjecture of Gedeon in the Chow setting:\nuniform matroids maximize coefficient-wisely these polynomials for matroids\nwith fixed rank and size. By relying on the nonnegativity of the\nKazhdan-Lusztig polynomials and the semi-small decompositions of Braden, Huh,\nMatherne, Proudfoot, and Wang, we strengthen the unimodality of the Hilbert\nseries of Chow rings, augmented Chow rings, and intersection cohomologies to\n$\\gamma$-positivity, a property for palindromic polynomials that lies between\nunimodality and real-rootedness; this settles a conjecture of Ferroni, Nasr,\nand Vecchi.\n""]","[('polynomials matroids', 0.5713724493980408), ('chow rings', 0.5628268122673035), ('polynomial matroid', 0.5397107601165771), ('theory matroids', 0.5305703282356262), ('chow ring', 0.5200235843658447), ('standard monomials', 0.4085056781768799), ('monomial basis', 0.4027024805545807), ('matroid', 0.4023634195327759), ('matroids', 0.40011921525001526), ('polynomials hilbert', 0.39724311232566833)]"
1188,1188,25,1188_semi algebraic sets_semi algebraic_algebraic complexity_algebraic map,"['semi algebraic sets', 'semi algebraic', 'algebraic complexity', 'algebraic map', 'computing homology', 'polynomial maps', 'algebraic sets', 'planar algebraic', 'algebraic geometry', 'algebraic subset']","['Efficient computation of a semi-algebraic basis of the first homology\n  group of a semi-algebraic set   Let $\\mathrm{R}$ be a real closed field and $\\mathrm{C}$ the algebraic\nclosure of $\\mathrm{R}$. We give an algorithm for computing a semi-algebraic\nbasis for the first homology group, $\\mathrm{H}_1(S,\\mathbb{F})$, with\ncoefficients in a field $\\mathbb{F}$, of any given semi-algebraic set $S\n\\subset \\mathrm{R}^k$ defined by a closed formula. The complexity of the\nalgorithm is bounded singly exponentially. It is not known how to compute such\na basis for the higher homology groups with singly exponential complexity.\n  As an intermediate step in our algorithm we construct a semi-algebraic subset\n$\\Gamma$ of the given semi-algebraic set $S$, such that $\\mathrm{H}_q(S,\\Gamma)\n= 0$ for $q=0,1$. We relate this construction to a basic theorem in complex\nalgebraic geometry stating that for any affine variety $X$ of dimension $n$,\nthere exists Zariski closed subsets \\[ Z^{(n-1)} \\supset \\cdots \\supset Z^{(1)}\n\\supset Z^{(0)} \\] with $\\dim_{\\mathrm{C}} Z^{(i)} \\leq i$, and\n$\\mathrm{H}_q(X,Z^{(i)}) = 0$ for $0 \\leq q \\leq i$. We conjecture a\nquantitative version of this result in the semi-algebraic category, with $X$\nand $Z^{(i)}$ replaced by closed semi-algebraic sets. We make initial progress\non this conjecture by proving the existence of $Z^{(0)}$ and $Z^{(1)}$ with\ncomplexity bounded singly exponentially (previously, such an algorithm was\nknown only for constructing $Z_0$).\n', 'Persistent homology of semi-algebraic sets   We give an algorithm with singly exponential complexity for computing the\nbarcodes up to dimension $\\ell$ (for any fixed $\\ell \\geq 0$) of the filtration\nof a given semi-algebraic set by the sub-level sets of a given polynomial. Our\nalgorithm is the first algorithm for this problem with singly exponential\ncomplexity, and generalizes the corresponding results for computing the Betti\nnumbers up to dimension $\\ell$ of semi-algebraic sets with no filtration\npresent.\n', 'Computing the homology functor on semi-algebraic maps and diagrams   Developing an algorithm for computing the Betti numbers of semi-algebraic\nsets with singly exponential complexity has been a holy grail in algorithmic\nsemi-algebraic geometry and only partial results are known. In this paper we\nconsider the more general problem of computing the image under the homology\nfunctor of a semi-algebraic map $f:X \\rightarrow Y$ between closed and bounded\nsemi-algebraic sets. For every fixed $\\ell \\geq 0$ we give an algorithm with\nsingly exponential complexity that computes bases of the homology groups\n$\\mathrm{H}_i(X), \\mathrm{H}_i(Y)$ (with rational coefficients) and a matrix\nwith respect to these bases of the induced linear maps\n$\\mathrm{H}_i(f):\\mathrm{H}_i(X) \\rightarrow \\mathrm{H}_i(Y), 0 \\leq i \\leq\n\\ell$. We generalize this algorithm to more general (zigzag) diagrams of maps\nbetween closed and bounded semi-algebraic sets and give a singly exponential\nalgorithm for computing the homology functors on such diagrams. This allows us\nto give an algorithm with singly exponential complexity for computing barcodes\nof semi-algebraic zigzag persistent homology in small dimensions.\n']","[('semi algebraic sets', 0.6133248805999756), ('semi algebraic', 0.5983973741531372), ('algebraic complexity', 0.5252667665481567), ('algebraic map', 0.5157362222671509), ('computing homology', 0.4859406352043152), ('polynomial maps', 0.47752800583839417), ('algebraic sets', 0.45135876536369324), ('planar algebraic', 0.4438127875328064), ('algebraic geometry', 0.44102242588996887), ('algebraic subset', 0.4264895021915436)]"
1189,1189,25,1189_rayleigh enard convection_rayleigh benard convection_navier slip boundary_bounds heat,"['rayleigh enard convection', 'rayleigh benard convection', 'navier slip boundary', 'bounds heat', 'slip boundary conditions', 'enard convection', 'slip boundary', 'nard convection', 'benard convection', 'convection']","[""Scaling laws for Rayleigh-B\\'enard convection between Navier-slip\n  boundaries   We consider the two-dimensional Rayeigh-B\\'enard convection problem between\nNavier-slip fixed-temperature boundary conditions and present a new upper bound\nfor the Nusselt number. The result, based on a localization principle for the\nNusselt number and an interpolation bound, exploits the regularity of the flow.\nOn one hand our method yields a shorter proof of the celebrated result in\nWhitehead & Doering (2011) in the case of free-slip boundary conditions. On the\nother hand, its combination with a new, refined estimate for the pressure gives\na substantial improvement of the interpolation bounds in Drivas et al. (2022)\nfor slippery boundaries. A rich description of the scaling behaviour arises\nfrom our result: depending on the magnitude of the Prandtl number and\nslip-length, our upper bounds indicate five possible scaling laws: $\\textit{Nu}\n\\sim (L_s^{-1}\\textit{Ra})^{\\frac{1}{3}}$, $\\textit{Nu} \\sim\n(L_s^{-\\frac{2}{5}}\\textit{Ra})^{\\frac{5}{13}}$, $\\textit{Nu} \\sim\n\\textit{Ra}^{\\frac{5}{12}}$, $\\textit{Nu} \\sim \\textit{Pr}^{-\\frac{1}{6}}\n(L_s^{-\\frac{4}{3}}\\textit{Ra})^{\\frac{1}{2}}$ and $\\textit{Nu} \\sim\n\\textit{Pr}^{-\\frac{1}{6}} (L_s^{-\\frac{1}{3}}\\textit{Ra})^{\\frac{1}{2}}$\n"", ""Rigorous scaling laws for internally heated convection at infinite\n  Prandtl number   New bounds are proven on the mean vertical convective heat transport,\n$\\overline{\\langle wT \\rangle}$, for uniform internally heated (IH) convection\nin the limit of infinite Prandtl number. For fluid in a horizontally-periodic\nlayer between isothermal boundaries, we show that $\\overline{\\langle wT\n\\rangle} \\leq \\frac12 - c R^{-2}$, where $R$ is a nondimensional `flux'\nRayleigh number quantifying the strength of internal heating and $c = 216$.\nThen, $\\overline{\\langle wT \\rangle} = 0$ corresponds to vertical heat\ntransport by conduction alone, while $\\overline{\\langle wT \\rangle} > 0$\nrepresents the enhancement of vertical heat transport upwards due to convective\nmotion. If, instead, the lower boundary is a thermal insulator, then we obtain\n$\\overline{\\langle wT \\rangle} \\leq \\frac12 - c R^{-4}$, with $c\\approx\n0.0107$. This result implies that the Nusselt number $Nu$, defined as the ratio\nof the total-to-conductive heat transport, satisfies $Nu \\lesssim R^{4}$. Both\nbounds are obtained by combining the background method with a minimum principle\nfor the fluid's temperature and with Hardy--Rellich inequalities to exploit the\nlink between the vertical velocity and temperature. In both cases, power-law\ndependence on $R$ improves the previously best-known bounds, which, although\nvalid at both infinite and finite Prandtl numbers, approach the uniform bound\nexponentially with $R$.\n"", ""Infinite Prandtl number convection with Navier-slip boundary conditions   We are concerned with infinite Prandtl number Rayleigh--B\\'enard convection\nwith Navier-slip boundary conditions. The goal of this work is to estimate the\naverage upward heat flux measured by the nondimensional Nusselt number $Nu$ in\nterms of the Rayleigh number $Ra$, which is a nondimensional quantity measuring\nthe imposed temperature gradient. We derive bounds on the Nusselt number that\ncoincide for relatively small slip lengths with the optimal Nusselt number\nscaling for no-slip boundaries, $Nu\\lesssim Ra^{1/3}$; for relatively large\nslip lengths, we recover scaling estimates for free-slip boundaries,\n$Nu\\lesssim Ra^{5/12}$.\n""]","[('rayleigh enard convection', 0.6226419806480408), ('rayleigh benard convection', 0.6055358052253723), ('navier slip boundary', 0.5857051014900208), ('bounds heat', 0.5804333686828613), ('slip boundary conditions', 0.545833945274353), ('enard convection', 0.4982371926307678), ('slip boundary', 0.49374350905418396), ('nard convection', 0.4859023988246918), ('benard convection', 0.48267027735710144), ('convection', 0.444366455078125)]"
1190,1190,25,1190_secret key generation_secret key rate_secret key_secret keys,"['secret key generation', 'secret key rate', 'secret key', 'secret keys', 'key generation', 'physical layer security', 'covert communications', 'secure key', 'wireless channels', 'wireless channel']","['Physical Layer Secret Key Generation in Static Environments   Two legitimate parties, referred to as Alice and Bob, wish to generate secret\nkeys from the wireless channel in the presence of an eavesdropper, referred to\nas Eve, in order to use such keys for encryption and decryption. In general,\nthe secret key rate highly depends on the coherence time of the channel. In\nparticular, a straightforward method of generating secret keys in static\nenvironments results in ultra-low rates. In order to resolve this problem, we\nintroduce a low-complexity method called induced randomness. In this method,\nAlice and Bob independently generate local randomness to be used together with\nthe uniqueness of the wireless channel coefficients in order to enable\nhigh-rate secret key generation. In this work, two scenarios are considered:\nfirst, when Alice and Bob share a direct communication channel, and second,\nwhen Alice and Bob do not have a direct link and communicate through an\nuntrusted relay. After exchanging the induced randomness, post-processing is\ndone by Alice and Bob to generate highly-correlated samples that are used for\nthe key generation. Such samples are then converted into bits, disparities\nbetween the sequences generated by Alice and Bob are mitigated, and the\nresulting sequences are then hashed to compensate for the information leakage\nto the eavesdropper and to allow consistency checking of the generated key bit\nsequences. We utilize semantic security measures and information-theoretic\ninequalities to upper bound the probability of successful eavesdropping attack\nin terms of the mutual information measures that can be numerically computed.\nGiven certain reasonable system parameters this bound is numerically evaluated\nto be $2^{-31}$ and $2^{-10.57}$ in the first and the second scenario,\nrespectively.\n', ""Random Matrix based Physical Layer Secret Key Generation in Static\n  Channels   Physical layer secret key generation exploits the reciprocal channel\nrandomness for key generation and has proven to be an effective addition\nsecurity layer in wireless communications. However, static or scarcely random\nchannels require artificially induced dynamics to improve the secrecy\nperformance, e.g., using intelligent reflecting surface (IRS). One key\nchallenge is that the induced random phase from IRS is also reflected in the\ndirection to eavesdroppers (Eve). This leakage enables Eve nodes to estimate\nthe legitimate channels and secret key via a globally known pilot sequence. To\nmitigate the secret key leakage issue, we propose to exploit random matrix\ntheory to inform the design of a new physical layer secret key generation\n(PL-SKG) algorithm. We prove that, when sending appropriate random Gaussian\nmatrices, the singular values of Alice's and Bob's received signals follow a\nsimilar probability distribution. Leveraging these common singular values, we\npropose a random Gaussian matrix based PL-SKG (RGM PL-SKG), which avoids the\nusages of the globally known pilot and thereby prevents the aforementioned\nleakage issue. Our results show the following: (i) high noise resistance which\nleads to superior secret key rate (SKR) improvement (up to 300%) in low SNR\nregime, and (ii) general improved SKR performance against multiple colluded\nEves. We believe our combination of random matrix theory and PL-SKG shows a new\nparadigm to secure the wireless communication channels.\n"", 'Scalable Group Secret Key Generation over Wireless Channels   In this paper, we consider the problem of secret key generation for multiple\nparties. Multi-user networks usually require a trusted party to efficiently\ndistribute keys to the legitimate users and this process is a weakness against\neavesdroppers. With the help of the physical layer security techniques, users\ncan securely decide on a secret key without a trusted party by exploiting the\nunique properties of the channel. In this context, we develop a physical layer\ngroup key generation scheme that is also based on the ideas of the analog\nfunction computation studies. We firstly consider the key generation as a\nfunction to be computed over the wireless channel and propose two novel methods\ndepending on the users transmission capability (i.e. half-duplex and\nfull-duplex transmissions). Secondly, we exploit the uniqueness of the prime\nintegers in order to enable the simultaneous transmission of the users for key\ngeneration. As a result, our approach contributes to the scalability of the\nexisting physical layer key generation algorithms since all users transmit\nsimultaneously rather than using pairwise communications. We prove that our\nhalf-duplex network model reduces the required number of communications for\ngroup key generation down to a linear scale. Furthermore, the full-duplex\nnetwork model reduces to a constant scale.\n']","[('secret key generation', 0.6301334500312805), ('secret key rate', 0.5135388374328613), ('secret key', 0.505200207233429), ('secret keys', 0.5025037527084351), ('key generation', 0.4903273582458496), ('physical layer security', 0.44091856479644775), ('covert communications', 0.44021910429000854), ('secure key', 0.4288337528705597), ('wireless channels', 0.4231836497783661), ('wireless channel', 0.4198376536369324)]"
1191,1191,25,1191_entanglement entropy_entropy entanglement_capacity entanglement_entanglement properties,"['entanglement entropy', 'entropy entanglement', 'capacity entanglement', 'entanglement properties', 'entanglement quantum', 'maximal entanglement', 'quantum entanglement', 'entanglement', 'entanglement two', 'von neumann entropy']","['Skewness of von Neumann entanglement entropy   We study quantum bipartite systems in a random pure state, where von Neumann\nentropy is considered as a measure of the entanglement. Expressions of the\nfirst and second exact cumulants of von Neumann entropy, relevant respectively\nto the average and fluctuation behavior, are known in the literature. The focus\nof this paper is on its skewness that specifies the degree of asymmetry of the\ndistribution. Computing the skewness requires additionally the third cumulant,\nan exact formula of which is the main result of this work. In proving the main\nresult, we obtain as a byproduct various summation identities involving\npolygamma and related functions. The derived third cumulant also leads to an\nimproved approximation to the distribution of von Neumann entropy.\n', 'Kurtosis of von Neumann entanglement entropy   In this work, we study the statistical behavior of entanglement in quantum\nbipartite systems under the Hilbert-Schmidt ensemble as assessed by the\nstandard measure - the von Neumann entropy. Expressions of the first three\nexact cumulants of von Neumann entropy are known in the literature. The main\ncontribution of the present work is the exact formula of the corresponding\nfourth cumulant that controls the tail behavior of the distribution. As a key\ningredient in deriving the result, we make use of newly observed unsimplifiable\nsummation bases that lead to a complete cancellation. In addition to providing\nfurther evidence of the conjectured Gaussian limit of the von Neumann entropy,\nthe obtained formula also provides an improved finite-size approximation to the\ndistribution.\n', 'Second-order statistics of fermionic Gaussian states   We study the statistical behavior of entanglement in quantum bipartite\nsystems over fermionic Gaussian states as measured by von Neumann entropy and\nentanglement capacity. The focus is on the variance of von Neumann entropy and\nthe mean entanglement capacity that belong to the so-defined second-order\nstatistics. The main results are the exact yet explicit formulas of the two\nconsidered second-order statistics for fixed subsystem dimension differences.\nWe also conjecture the exact variance of von Neumann entropy valid for\narbitrary subsystem dimensions. Based on the obtained results, we analytically\nstudy the numerically observed phenomena of Gaussianity of von Neumann entropy\nand linear growth of average capacity.\n']","[('entanglement entropy', 0.7492600083351135), ('entropy entanglement', 0.7291901707649231), ('capacity entanglement', 0.6508378982543945), ('entanglement properties', 0.6073920130729675), ('entanglement quantum', 0.5836849212646484), ('maximal entanglement', 0.5834921002388), ('quantum entanglement', 0.5730248093605042), ('entanglement', 0.5639398097991943), ('entanglement two', 0.5507211685180664), ('von neumann entropy', 0.5479474067687988)]"
1192,1192,25,1192_trees uniquely_labelled trees_binary trees_cayley trees,"['trees uniquely', 'labelled trees', 'binary trees', 'cayley trees', 'trees vertices', 'number trees', 'labeled trees', 'trees fixed', 'increasing trees', 'trees']","['Refined enumeration of $k$-plane trees and $k$-noncrossing trees   A $k$-plane tree is a plane tree whose vertices are assigned labels between\n$1$ and $k$ in such a way that the sum of the labels along any edge is no\ngreater than $k+1$. These trees are known to be related to $(k+1)$-ary trees,\nand they are counted by a generalised version of the Catalan numbers. We prove\na surprisingly simple refined counting formula, where we count trees with a\nprescribed number of labels of each kind. Several corollaries are derived from\nthis formula, and an analogous theorem is proven for $k$-noncrossing trees, a\nsimilarly defined family of labelled noncrossing trees that are related to\n$(2k+1)$-ary trees.\n', ""Cayley trees and increasing 1,2-trees: let's twist!   An increasing 1,2-tree is a labeled graph formed by starting with a vertex\nand then repeatedly attaching a leaf to a vertex or a triangle to an edge, the\nlabeling of the vertices corresponding to the order in which the vertices are\nadded. Equivalently, increasing 1,2-trees are connected chordal graphs of\ntreewidth at most 2 labeled with a reversed perfect elimination ordering. We\nprove that this family is equinumerous with Cayley trees, which are\nunconstrained labeled trees. In particular, the number of triangles in an\nincreasing 1,2-tree corresponds to the number of twists. A twist (also called\nimproper edge) is an edge whose endpoint closer to vertex 1 has a greater label\nthan some vertex in the subtree rooted at the other endpoint of the edge. We\nprovide three proofs of this result, the rst being based on similar recursive\ndecompositions, the second on the resolution of generating functions, and the\nthird describing a bijection. Finally, we propose ecient random generators for\nthese two combinatorial families.\n"", ""A combinatorial bijection on di-sk trees   A di-sk tree is a rooted binary tree whose nodes are labeled by $\\oplus$ or\n$\\ominus$, and no node has the same label as its right child. The di-sk trees\nare in natural bijection with separable permutations. We construct a\ncombinatorial bijection on di-sk trees proving the two quintuples\n$(\\LMAX,\\LMIN,\\DESB,\\iar,\\comp)$ and $(\\LMAX,\\LMIN,\\DESB,\\comp,\\iar)$ have the\nsame distribution over separable permutations. Here for a permutation $\\pi$,\n$\\LMAX(\\pi)/\\LMIN(\\pi)$ is the set of values of the left-to-right maxima/minima\nof $\\pi$ and $\\DESB(\\pi)$ is the set of descent bottoms of $\\pi$, while\n$\\comp(\\pi)$ and $\\iar(\\pi)$ are respectively the number of components of $\\pi$\nand the length of initial ascending run of $\\pi$.\n  Interestingly, our bijection specializes to a bijection on $312$-avoiding\npermutations, which provides (up to the classical {\\em Knuth--Richards\nbijection}) an alternative approach to a result of Rubey (2016) that asserts\nthe two triples $(\\LMAX,\\iar,\\comp)$ and $(\\LMAX,\\comp,\\iar)$ are\nequidistributed on $321$-avoiding permutations. Rubey's result is a symmetric\nextension of an equidistribution due to Adin--Bagno--Roichman, which implies\nthe class of $321$-avoiding permutations with a prescribed number of components\nis Schur positive.\n  Some equidistribution results for various statistics concerning tree\ntraversal are presented in the end.\n""]","[('trees uniquely', 0.6862834095954895), ('labelled trees', 0.6564798355102539), ('binary trees', 0.644740104675293), ('cayley trees', 0.6225230097770691), ('trees vertices', 0.6154911518096924), ('number trees', 0.6153728365898132), ('labeled trees', 0.6138272881507874), ('trees fixed', 0.5835107564926147), ('increasing trees', 0.5819772481918335), ('trees', 0.573959231376648)]"
1193,1193,25,1193_graded modules_graded modules graded_modules graded_graded module,"['graded modules', 'graded modules graded', 'modules graded', 'graded module', 'graded commutative ring', 'graded rings', 'graded ring', 'graded ideals', 'rings graded', 'graded ideal']","['On Graded classical 2-absorbing second submodules of graded modules over\n  graded commutative rings   Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative\nring and $M$ a graded $R$-module. In this paper, we introduce the concept of\ngraded classical and graded strongly classical 2-absorbing second submodules of\ngraded modules over a graded commutative rings. A number of results concerning\nthese classes of graded submodules and their homogeneous components are given.\n', 'On graded $A$-2-absorbing submodules of graded modules over graded\n  commutative rings   Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative\nring, $M$ a graded $R$-module and $A\\subseteq h(R)$ a multiplicatively closed\nsubset of $R$. In this paper, we introduce the concept of graded\n$A$-2-absorbing submodules of $M$ as a generalization of graded 2-absorbing\nsubmodules and graded $A$-prime submodules of $M.$ We investigate some\nproperties of this class of graded submodules.\n', 'On graded primary-like submodules of graded modules over graded\n  commutative rings   Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative\nring and $M$ a graded $R$-module. In this paper, we introduce the concept of\ngraded primary-like submodules as a new generalization of graded primary ideals\nand give some basic results about graded primary-like submodules of graded\nmodules. Special attention has been paid, when graded submodules satisfies the\ngr-primeful property, to find extra properties of these graded submodules.\n']","[('graded modules', 0.7496311068534851), ('graded modules graded', 0.7330913543701172), ('modules graded', 0.7298671007156372), ('graded module', 0.7078093886375427), ('graded commutative ring', 0.6329352259635925), ('graded rings', 0.630723774433136), ('graded ring', 0.6169824600219727), ('graded ideals', 0.6095677018165588), ('rings graded', 0.5940168499946594), ('graded ideal', 0.5826405882835388)]"
1194,1194,25,1194_lithium ion battery_lithium ion batteries_lithium ion_lithium,"['lithium ion battery', 'lithium ion batteries', 'lithium ion', 'lithium', 'ion battery', 'ion batteries', 'electrochemical', 'modeling simulation', 'energy storage', 'elastic strain']","['MULTIBAT: Unified workflow for fast electrochemical 3D simulations of\n  lithium-ion cells combining virtual stochastic microstructures,\n  electrochemical degradation models and model order reduction   We present a simulation workflow for efficient investigations of the\ninterplay between 3D lithium-ion electrode microstructures and electrochemical\nperformance, with emphasis on lithium plating. Our approach addresses several\nchallenges. First, the 3D microstructures of porous electrodes are generated by\na parametric stochastic model, in order to significantly reduce the necessity\nof tomographic imaging. Secondly, we integrate a consistent microscopic, 3D\nspatially-resolved physical model for the electrochemical behavior of the\nlithium-ion cells taking lithium plating and stripping into account. This\nhighly non-linear mathematical model is solved numerically on the complex 3D\nmicrostructures to compute the transient cell behavior. Due to the complexity\nof the model and the considerable size of realistic microstructures even a\nsingle charging cycle of the battery requires several hours computing time.\nThis renders large scale parameter studies extremely time consuming. Hence, we\ndevelop a mathematical model order reduction scheme. We demonstrate how these\naspects are integrated into one unified workflow, which is a step towards\ncomputer aided engineering for the development of more efficient lithium-ion\ncells.\n', 'High-order transient multidimensional simulation of a\n  thermo-electro-chemo-mechanical model for Lithium-ion batteries   We build a transient multidimensional multiphysical model based on continuum\ntheories, involving the coupled mechanical, thermal and electrochemical\nphenomena occurring simultaneously in the discharge or charge of lithium-ion\nbatteries. The process delivers a system of coupled nonlinear partial\ndifferential equations. Besides initial and boundary conditions, we highlight\nthe treatment of the electrode-electrolyte interface condition, which\ncorresponds to a Butler-Volmer reaction kinetics equation. We present the\nderivation of the strong and weak forms of the model, as well as the\ndiscretization procedure in space and in time. The discretized model is\ncomputationally solved in two dimensions by means of a finite element method\nthat employs $hp$ layered meshes, along with staggered second order\nsemi-implicit time integration. The expected error estimate is of higher order\nthan any other similar work, both in space and in time. A representative\nbattery cell geometry, under distinct operating scenarios, is simulated. The\nnumerical results show that the full model allows for important additional\ninsights to be drawn than when caring only for the electrochemical coupling.\nConsidering the multiphysics becomes more important as the applied current is\nincreased, whether for discharge or for charge. Our full model provides battery\ndesign professionals with a valuable tool to optimize designs and advance the\nenergy storage industry.\n', ""Modeling and Simulation of Chemo-Elasto-Plastically Coupled Battery\n  Active Particles   As an anode material for lithium-ion batteries, amorphous silicon offers a\nsignificantly higher energy density than the graphite anodes currently used.\nAlloying reactions of lithium and silicon, however, induce large deformation\nand lead to volume changes up to 300%. We formulate a thermodynamically\nconsistent continuum model for the chemo-elasto-plastic diffusion-deformation\nbehavior of amorphous silicon and it's alloy with lithium based on finite\ndeformations. In this paper, two plasticity theories, i.e. a rate-independent\ntheory with linear isotropic hardening and a rate-dependent one, are formulated\nto allow the evolution of plastic deformations and reduce occurring stresses.\nUsing modern numerical techniques, such as higher order finite element methods\nas well as efficient space and time adaptive solution algorithms, the\ndiffusion-deformation behavior resulting from both theories is compared. In\norder to further increase the computational efficiency, an automatic\ndifferentiation scheme is used, allowing for a significant speed up in\nassembling time as compared to an algorithmic linearization for the global\nfinite element Newton scheme. Both plastic approaches lead to a more\nheterogeneous concentration distribution and to a change to tensile tangential\nCauchy stresses at the particle surface at the end of one charging cycle.\nDifferent parameter studies show how an amplification of the plastic\ndeformation is affected. Interestingly, an elliptical particle shows only\nplastic deformation at the smaller half axis. With the demonstrated efficiency\nof the applied methods, results after five charging cycles are also discussed\nand can provide indications for the performance of lithium-ion batteries in\nlong term use.\n""]","[('lithium ion battery', 0.46754565834999084), ('lithium ion batteries', 0.4579206109046936), ('lithium ion', 0.3958849608898163), ('lithium', 0.36252444982528687), ('ion battery', 0.3437546491622925), ('ion batteries', 0.33750519156455994), ('electrochemical', 0.2722914516925812), ('modeling simulation', 0.27029934525489807), ('energy storage', 0.26849234104156494), ('elastic strain', 0.25237953662872314)]"
1195,1195,25,1195_safety constraints_probabilistic safety_control stochastic_safety critical control,"['safety constraints', 'probabilistic safety', 'control stochastic', 'safety critical control', 'safety guarantees', 'guarantees stochastic', 'control barrier functions', 'stochastic uncertainties', 'stochastic uncertainty', 'ensuring safety']","['Real-Time Risk-Bounded Tube-Based Trajectory Safety Verification   In this paper, we address the real-time risk-bounded safety verification\nproblem of continuous-time state trajectories of autonomous systems in the\npresence of uncertain time-varying nonlinear safety constraints. Risk is\ndefined as the probability of not satisfying the uncertain safety constraints.\nExisting approaches to address the safety verification problems under\nuncertainties either are limited to particular classes of uncertainties and\nsafety constraints, e.g., Gaussian uncertainties and linear constraints, or\nrely on sampling based methods. In this paper, we provide a fast convex\nalgorithm to efficiently evaluate the probabilistic nonlinear safety\nconstraints in the presence of arbitrary probability distributions and long\nplanning horizons in real-time, without the need for uncertainty samples and\ntime discretization. The provided approach verifies the safety of the given\nstate trajectory and its neighborhood (tube) to account for the execution\nuncertainties and risk. In the provided approach, we first use the moments of\nthe probability distributions of the uncertainties to transform the\nprobabilistic safety constraints into a set of deterministic safety\nconstraints. We then use convex methods based on sum-of-squares polynomials to\nverify the obtained deterministic safety constraints over the entire planning\ntime horizon without time discretization. To illustrate the performance of the\nproposed method, we apply the provided method to the safety verification\nproblem of self-driving vehicles and autonomous aerial vehicles.\n', 'Risk-Aware Adaptive Control Barrier Functions for Safe Control of\n  Nonlinear Systems under Stochastic Uncertainty   This paper addresses the challenge of ensuring safety in stochastic control\nsystems with high-relative-degree constraints, while maintaining feasibility\nand mitigating conservatism in risk evaluation. Control Barrier Functions\n(CBFs) provide an effective framework for enforcing safety constraints in\nnonlinear systems. However, existing methods struggle with feasibility issues\nand multi-step uncertainties. To address these challenges, we introduce\nRisk-aware Adaptive CBFs (RACBFs), which integrate Discrete-time\nAuxiliary-Variable adaptive CBFs (DAVCBFs) with coherent risk measures. DAVCBFs\nintroduce auxiliary variables to improve the feasibility of the optimal control\nproblem, while RACBFs incorporate risk-aware formulations to balance safety and\nrisk evaluation performance. By extending discrete-time high-order CBF\nconstraints over multiple steps, RACBFs effectively handle multi-step\nuncertainties that propagate through the system dynamics. We demonstrate the\neffectiveness of our approach on a stochastic unicycle system, showing that\nRACBFs maintain safety and feasibility while reducing unnecessary conservatism\ncompared to standard robust formulations of discrete-time CBF methods.\n', 'Control Barrier Functions for Stochastic Systems and Safety-critical\n  Control Designs   In recent years, the analysis of a control barrier function has received\nconsiderable attention because it is helpful for the safety-critical control\nrequired in many control application problems. While the extension of the\nanalysis to a stochastic system studied by many researchers, it remains a\nchallenging issue. In this paper, we consider sufficient conditions for\nreciprocal and zeroing control barrier functions ensuring safety with\nprobability one and design a control law using the functions. Then, we propose\nanother version of a stochastic zeroing control barrier function to evaluate a\nprobability of a sample path staying in a safe set and confirm the convergence\nof a specific expectation related to the attractiveness of a safe set. We also\nshow a way of deisgning a safety-critical control law based on our stochastic\nzeroing control barrier function. Finally, we confirm the validity of the\nproposed control design and the analysis using the control barrier functions\nvia simple examples with their numerical simulation.\n']","[('safety constraints', 0.5700163841247559), ('probabilistic safety', 0.5637690424919128), ('control stochastic', 0.5350512266159058), ('safety critical control', 0.5341415405273438), ('safety guarantees', 0.5330621600151062), ('guarantees stochastic', 0.52634596824646), ('control barrier functions', 0.49255645275115967), ('stochastic uncertainties', 0.49206236004829407), ('stochastic uncertainty', 0.4731179177761078), ('ensuring safety', 0.4589865207672119)]"
1196,1196,25,1196_lie algebra structure_algebra lie group_lie group_post lie algebra,"['lie algebra structure', 'algebra lie group', 'lie group', 'post lie algebra', 'lie groupoid', 'connections principal bundles', 'principal bundle', 'principal bundles', 'lie algebra lie', 'covariant']","['Second-order infinitesimal groups and affine connections   This paper presents new research in infinitesimal algebra by introducing the\nconcept of an infinitesimal group and exploring its properties and\nramifications. The author investigates first- and second-order subgroups of Lie\ngroups and demonstrates the use of the second-order infinitesimal group\nstructure to define a Lie bracket of points intrinsic to the Lie group. This\nconstruction allows for the derivation of a second-order\nBaker-Campbell-Hausdorff formula for the infinitesimal group operation and\nprovides a means to reconstruct the Lie bracket of the Lie algebra of a Lie\ngroup. The author also characterises all second-order infinitesimal group\nstructures on KL vector spaces as deformations of vector addition by bilinear\nmaps. The main contribution of the paper is the generalisation of the\npreviously established correspondence between symmetric affine connections and\nsecond-order infinitesimally affine structures to manifolds with non-symmetric\naffine connections via second-order infinitesimal groups.\n', 'Lorentzian Cayley Form   Cayley 4-form Phi on an 8-dimensional manifold M is a real differential form\nof a special algebraic type, which determines a Riemannian metric on M as well\nas a unit real Weyl spinor. It defines a Spin(7) structure on M, and this\nSpin(7) structure is integrable if and only if Phi is closed. We introduce the\nnotion of a complex Cayley form. This is a one-parameter family of complex\n4-forms Phi_tau on M of a special algebraic type. Each Phi_tau determines a\nreal Riemannian metric on M, as well as a complex unit Weyl spinor psi_tau. The\nsubgroup of GL(8,R) that stabilises Phi_tau, tau not=0 is SU(4), and Phi_tau\ndefines on $M$ an SU(4) structure. We show that this SU(4) structure is\nintegrable if and only if Phi_tau is closed.\n  We carry out a similar construction for the split signature case. There are\nnow two one-parameter families of complex Cayley forms. A complex Cayley form\nof one type defines an SU(2,2) structure, a form of the other type defines an\nSL(4,R) structure on M. As in the Riemannian case, these structures are\nintegrable if and only of the corresponding complex Cayley forms are closed.\nOur central observation is that there exists a special member of the second\none-parameter family of complex Cayley forms, which we call the Lorentzian\nCayley form. This 4-form has the property that it is calibrated by Lorentzian\n4-dimensional subspaces H,H^perp. In particular, in a basis adapted to such a\ncalibration, the Lorentzian Cayley form is built from the complex self-dual\n2-forms for H,H^perp. We explain how these observations solve a certain puzzle\nthat existed in the context of 4-dimensional Lorentzian geometry.\n', 'Geometry of Spin(10) Symmetry Breaking   We provide a new characterisation of the Standard Model gauge group GSM as a\nsubgroup of Spin(10). The new description of GSM relies on the geometry of pure\nspinors. We show that GSM is the subgroup that stabilises a pure spinor Psi_1\nand projectively stabilises another pure spinor Psi_2, with Psi_1, Psi_2\northogonal and such that their arbitrary linear combination is still a pure\nspinor. Our characterisation of GSM relies on the facts that projective pure\nspinors describe complex structures on R^{10}, and the product of two commuting\ncomplex structures is a what is known as a product structure. For the pure\nspinors Psi_1, Psi_2 satisfying the stated conditions the complex structures\ndetermined by Psi_1, Psi_2 commute and the arising product structure is R^{10}\n= R^6 + R^4, giving rise to a copy of Pati-Salam gauge group inside Spin(10).\nOur main statement then follows from the fact that GSM is the intersection of\nthe Georgi-Glashow SU(5) that stabilises Psi_1, and the Pati-Salam Spin(6) x\nSpin(4) arising from the product structure determined by Psi_1, Psi_2. We have\ntried to make the paper self-contained and provided a detailed description of\nthe creation/annihilation operator construction of the Clifford algebras Cl(2n)\nand the geometry of pure spinors in dimensions up to and including ten.\n']","[('lie algebra structure', 0.6015552282333374), ('algebra lie group', 0.585335910320282), ('lie group', 0.5293002724647522), ('post lie algebra', 0.5156274437904358), ('lie groupoid', 0.4939144551753998), ('connections principal bundles', 0.48907706141471863), ('principal bundle', 0.4887298345565796), ('principal bundles', 0.47491195797920227), ('lie algebra lie', 0.45266035199165344), ('covariant', 0.44569510221481323)]"
1197,1197,25,1197_digital nets_randomized quasi monte_nets sequences_quasi monte carlo,"['digital nets', 'randomized quasi monte', 'nets sequences', 'quasi monte carlo', 'randomized quasi', 'monte carlo methods', 'monte carlo estimators', 'carlo methods', 'carlo estimators', 'nets']","[""On the quasi-uniformity properties of quasi-Monte Carlo digital nets and\n  sequences   We study the quasi-uniformity properties of digital nets, a class of\nquasi-Monte Carlo point sets. Quasi-uniformity is a space-filling property used\nfor instance in experimental designs and radial basis function approximation.\nHowever, it has not been investigated so far whether common low-discrepancy\ndigital nets are quasi-uniform, with the exception of the two-dimensional\nSobol' sequence, which has recently been shown not to be quasi-uniform. In this\npaper, with the goal of constructing quasi-uniform low-discrepancy digital\nnets, we introduce the notion of \\emph{well-separated} point sets and provide\nan algebraic criterion to determine whether a given digital net is\nwell-separated. Using this criterion, we present an example of a\ntwo-dimensional digital net which has low-discrepancy and is quasi-uniform.\nAdditionally, we provide several counterexamples of low-discrepancy digital\nnets that are not quasi-uniform. The quasi-uniformity properties of quasi-Monte\nCarlo lattice point sets and sequences will be studied in a forthcoming paper.\n"", ""Improved bounds on the gain coefficients for digital nets in prime power\n  base   We study randomized quasi-Monte Carlo integration by scrambled nets. The\nscrambled net quadrature has long gained its popularity because it is an\nunbiased estimator of the true integral, allows for a practical error\nestimation, achieves a high order decay of the variance for smooth functions,\nand works even for $L^p$-functions with any $p\\geq 1$. The variance of the\nscrambled net quadrature for $L^2$-functions can be evaluated through the set\nof the so-called gain coefficients.\n  In this paper, based on the system of Walsh functions and the concept of dual\nnets, we provide improved upper bounds on the gain coefficients for digital\nnets in general prime power base. Our results explain the known bound by Owen\n(1997) for Faure sequences, the recently improved bound by Pan and Owen (2021)\nfor digital nets in base 2 (including Sobol' sequences as a special case), and\ntheir finding that all the nonzero gain coefficients for digital nets in base 2\nmust be powers of two, all in a unified way.\n"", 'Digital Nets and Sequences for Quasi-Monte Carlo Methods   Quasi-Monte Carlo methods are a way of improving the efficiency of Monte\nCarlo methods. Digital nets and sequences are one of the low discrepancy point\nsets used in quasi-Monte Carlo methods. This thesis presents the three new\nresults pertaining to digital nets and sequences: implementing randomized\ndigital nets, finding the distribution of the discrepancy of scrambled digital\nnets, and obtaining better quality of digital nets through evolutionary\ncomputation. Finally, applications of scrambled and non-scrambled digital nets\nare provided.\n']","[('digital nets', 0.5083698630332947), ('randomized quasi monte', 0.5055239796638489), ('nets sequences', 0.49338141083717346), ('quasi monte carlo', 0.4827750325202942), ('randomized quasi', 0.46343910694122314), ('monte carlo methods', 0.43778741359710693), ('monte carlo estimators', 0.4326461851596832), ('carlo methods', 0.41597068309783936), ('carlo estimators', 0.4104618430137634), ('nets', 0.36635822057724)]"
1198,1198,25,1198_wasserstein distance measures_wasserstein distance empirical_wasserstein distance probability_sliced wasserstein distance,"['wasserstein distance measures', 'wasserstein distance empirical', 'wasserstein distance probability', 'sliced wasserstein distance', 'wasserstein distances', 'wasserstein distance', 'wasserstein metrics', 'wasserstein metric', 'measures wasserstein', 'distance probability measures']","['Max-sliced 2-Wasserstein distance   This note is a continuation of the author\'s previous work on ""Sharp bounds\nfor the max-sliced Wasserstein distance."" We use the same technique to obtain\nan upper bound for the expected max-sliced 2-Wasserstein distance between a\ncompactly supported symmetric probability measure on a Euclidean space and its\nsymmetrized empirical distribution.\n', 'Sharp bounds for max-sliced Wasserstein distances   We obtain essentially matching upper and lower bounds for the expected\nmax-sliced 1-Wasserstein distance between a probability measure on a separable\nHilbert space and its empirical distribution from $n$ samples. By proving a\nBanach space version of this result, we also obtain an upper bound, that is\nsharp up to a log factor, for the expected max-sliced 2-Wasserstein distance\nbetween a symmetric probability measure $\\mu$ on a Euclidean space and its\nsymmetrized empirical distribution in terms of the operator norm of the\ncovariance matrix of $\\mu$ and the diameter of the support of $\\mu$.\n', 'Sliced Wasserstein Distance between Probability Measures on Hilbert\n  Spaces   The sliced Wasserstein distance as well as its variants have been widely\nconsidered in comparing probability measures defined on $\\mathbb R^d$. Here we\nderive the notion of sliced Wasserstein distance for measures on an infinite\ndimensional separable Hilbert spaces, depict the relation between sliced\nWasserstein distance and narrow convergence of measures and quantize the\napproximation via empirical measures.\n']","[('wasserstein distance measures', 0.7665095925331116), ('wasserstein distance empirical', 0.7553982138633728), ('wasserstein distance probability', 0.7461155652999878), ('sliced wasserstein distance', 0.704784631729126), ('wasserstein distances', 0.7041171193122864), ('wasserstein distance', 0.7021475434303284), ('wasserstein metrics', 0.687059760093689), ('wasserstein metric', 0.655724287033081), ('measures wasserstein', 0.6342564821243286), ('distance probability measures', 0.5841778516769409)]"
1199,1199,25,1199_almost complex manifolds_almost complex manifold_manifolds fixed_complex manifolds,"['almost complex manifolds', 'almost complex manifold', 'manifolds fixed', 'complex manifolds', 'manifold fixed', 'manifold dimension 2n', 'compact symplectic manifold', 'complex manifold', 'oriented manifolds', 'symplectic manifold dimension']","['Lower bound on the number of fixed points for circle actions on\n  10-dimensional almost complex manifolds   For a circle action on a compact almost complex manifold with a fixed point,\nthe lower bound on the number of fixed points is known in dimension up to 12\nexcept 10. In this paper, we show that if the circle group acts on a\n10-dimensional compact almost complex manifold with a fixed point, then there\nare at least 6 fixed points. This minimum is attained by $\\mathbb{CP}^5$ and\n$S^6 \\times \\mathbb{CP}^2$. We establish this lower bound by showing that there\ndoes not exist a circle action on a 10-dimensional compact almost complex\nmanifold with 4 fixed points.\n', ""Almost complex torus manifolds -- graphs, Hirzebruch genera, and problem\n  of Petrie type   Let a $k$-dimensional torus $T^k$ act on a $2n$-dimensional compact connected\nalmost complex manifold $M$ with isolated fixed points. As for circle actions,\nwe show that there exists a (directed labeled) multigraph that encodes weights\nat the fixed points of $M$. This includes the notion of a GKM graph as a\nspecial case that weights at each fixed point are pairwise linearly\nindependent. If in addition $k=n$, i.e., $M$ is an almost complex torus\nmanifold, the multigraph is a graph; it has no multiple edges. We show that the\nHirzebruch $\\chi_y$-genus $\\chi_y(M)=\\sum_{i=0}^n a_i(M) \\cdot (-y)^i$ of an\nalmost complex torus manifold $M$ satisfies $a_i(M) > 0$ for $0 \\leq i \\leq n$.\nIn particular, the Todd genus of $M$ is positive and there are at least $n+1$\nfixed points. Petrie's conjecture asserts that if a homotopy $\\mathbb{CP}^n$\nadmits a non-trivial circle action, its Pontryagin class agrees with that of\n$\\mathbb{CP}^n$. Petrie proved this conjecture if instead it admits a\n$T^n$-action. We prove that if a $2n$-dimensional almost complex torus manifold\n$M$ only shares the Euler number with the complex projective space\n$\\mathbb{CP}^n$, an associated graph agrees with that of a linear $T^n$-action\non $\\mathbb{CP}^n$; consequently $M$ has the same weights at the fixed points,\nChern numbers, equivariant cobordism class, Hirzebruch $\\chi_y$-genus, Todd\ngenus, and signature as $\\mathbb{CP}^n$. If furthermore $M$ is equivariantly\nformal, the equivariant cohomology and the Chern classes of $M$ and\n$\\mathbb{CP}^n$ also agree.\n"", 'Circle actions on almost complex manifolds with isolated fixed points   The author proved that if the circle acts symplectically on a compact,\nconnected symplectic manifold $M$ with three fixed points, then $M$ is\nequivariantly symplectomorphic to some standard action on $\\mathbb{CP}^2$. In\nthis paper, we extend the result to a circle action on an almost complex\nmanifold; if the circle acts on a compact, connected almost complex manifold\n$M$ with exactly three fixed points, then $\\dim M=4$. Moreover, we deal with\nthe cases of one fixed point and two fixed points.\n']","[('almost complex manifolds', 0.626366913318634), ('almost complex manifold', 0.6057959794998169), ('manifolds fixed', 0.5841559767723083), ('complex manifolds', 0.5714497566223145), ('manifold fixed', 0.5485996603965759), ('manifold dimension 2n', 0.5482284426689148), ('compact symplectic manifold', 0.5399568676948547), ('complex manifold', 0.5388449430465698), ('oriented manifolds', 0.5292532444000244), ('symplectic manifold dimension', 0.5277518033981323)]"
1200,1200,25,1200_stochastic parabolic equations_stochastic parabolic_null controllability_controllability linear,"['stochastic parabolic equations', 'stochastic parabolic', 'null controllability', 'controllability linear', 'approximate controllability', 'controllability established', 'null controllability class', 'controllability', 'controllability results', 'linear backward stochastic']","['Null Controllability for Cascade systems of Coupled Backward Stochastic\n  Parabolic Equations with One Distributed Control   We prove the null controllability of a cascade system of \\(n\\) coupled\nbackward stochastic parabolic equations involving both reaction and convection\nterms, as well as general second-order parabolic operators, with \\(n \\geq 2\\).\nTo achieve this, we apply a single distributed control to the first equation,\nwhile the other equations are controlled through the coupling. To obtain our\nresults, we develop a new global Carleman estimate for the forward stochastic\nparabolic adjoint system with some terms in the \\(H^{-1}\\)-space. Subsequently,\nwe derive the appropriate observability inequality, and by employing the\nclassical duality argument, we establish our null controllability result.\nAdditionally, we provide an estimate for the null control cost with respect to\nthe final time \\(T\\) and the potentials.\n', 'Null controllability for stochastic fourth order parabolic equations   We establish the null controllability for linear stochastic fourth order\nparabolic equations. Utilizing the duality argument, the null controllability\nis reduced to the observability for backward fourth order stochastic parabolic\nequations, and the desired observability estimate is obtained by a new global\nCarleman estimate. Our Carleman estimate is based on a new fundamental identity\nfor a stochastic fourth order parabolic operator.\n', 'Null Controllability for Backward Stochastic Parabolic\n  Convection-Diffusion Equations with Dynamic Boundary Conditions   This paper is concerned with the null controllability for linear backward\nstochastic parabolic equations with dynamic boundary conditions and convection\nterms. Using the classical duality argument, the null controllability is\nobtained via an appropriate observability inequality of the corresponding\nadjoint forward stochastic parabolic equation. To prove this observability\ninequality, we develop a new global Carleman estimate for forward stochastic\nparabolic equations that contains some first-order terms in the weak divergence\nform. Our Carleman estimate is established by applying the duality technique.\nMoreover, an estimate of the null-control cost is provided.\n']","[('stochastic parabolic equations', 0.6023446917533875), ('stochastic parabolic', 0.5691125392913818), ('null controllability', 0.5548848509788513), ('controllability linear', 0.5233494639396667), ('approximate controllability', 0.5225496888160706), ('controllability established', 0.5130632519721985), ('null controllability class', 0.5123032927513123), ('controllability', 0.4993082582950592), ('controllability results', 0.48473235964775085), ('linear backward stochastic', 0.4795137345790863)]"
1201,1201,24,1201_infinitely divisible distributions_infinitely divisible distribution_divisible distributions_valued distributions,"['infinitely divisible distributions', 'infinitely divisible distribution', 'divisible distributions', 'valued distributions', 'distribution functions', 'class distributions', 'distributions mathbb', 'divisible distribution', 'characteristic functions', 'distribution mu mathbb']","['On a denseness result for quasi-infinitely divisible distributions   A probability distribution $\\mu$ on $\\mathbb{R}^d$ is quasi-infinitely\ndivisible if its characteristic function has the representation $\\widehat{\\mu}\n= \\widehat{\\mu_1}/\\widehat{\\mu_2}$ with infinitely divisible distributions\n$\\mu_1$ and $\\mu_2$. In \\cite[Thm. 4.1]{lindner2018} it was shown that the\nclass of quasi-infinitely divisible distributions on $\\mathbb{R}$ is dense in\nthe class of distributions on $\\mathbb{R}$ with respect to weak convergence. In\nthis paper, we show that the class of quasi-infinitely divisible distributions\non $\\mathbb{R}^d$ is not dense in the class of distributions on $\\mathbb{R}^d$\nwith respect to weak convergence if $d \\geq 2$.\n', ""Subexponentialiy of densities of infinitely divisible distributions   We show the equivalence of three properties for an infinitely divisible\ndistribution: the subexponentiality of the density, the subexponentiality of\nthe density of its L\\'evy measure and the tail equivalence between the density\nand its L\\'evy measure density, under monotonic-type assumptions on the L\\'evy\nmeasure density. The key assumption is that tail of the L\\'evy measure density\nis asymptotic to a non-increasing function or is eventually non-increasing. Our\nconditions are novel and cover a rather wide class of infinitely divisible\ndistributions. Several significant properties for analyzing the\nsubexponentiality of densities have been derived such as closure properties of\n[ convolution, convolution roots and asymptotic equivalence ] and the\nfactorization property. Moreover, we illustrate that the results are applicable\nfor developing the statistical inference of subexponential infinitely divisible\ndistributions which are absolutely continuous.\n"", 'On multivariate quasi-infinitely divisible distributions   A quasi-infinitely divisible distribution on $\\mathbb{R}^d$ is a probability\ndistribution $\\mu$ on $\\mathbb{R}^d$ whose characteristic function can be\nwritten as the quotient of the characteristic functions of two infinitely\ndivisible distributions on $\\mathbb{R}^d$. Equivalently, it can be\ncharacterised as a probability distribution whose characteristic function has a\nL\\\'evy--Khintchine type representation with a ""signed L\\\'evy measure"", a so\ncalled quasi--L\\\'evy measure, rather than a L\\\'evy measure. A systematic study\nof such distributions in the univariate case has been carried out in Lindner,\nPan and Sato \\cite{lindner}. The goal of the present paper is to collect some\nknown results on multivariate quasi-infinitely divisible distributions and to\nextend some of the univariate results to the multivariate setting. In\nparticular, conditions for weak convergence, moment and support properties are\nconsidered. A special emphasis is put on examples of such distributions and in\nparticular on $\\mathbb{Z}^d$-valued quasi-infinitely divisible distributions.\n']","[('infinitely divisible distributions', 0.6966946125030518), ('infinitely divisible distribution', 0.601926863193512), ('divisible distributions', 0.5606454014778137), ('valued distributions', 0.4850490093231201), ('distribution functions', 0.4648193120956421), ('class distributions', 0.45858892798423767), ('distributions mathbb', 0.4317709505558014), ('divisible distribution', 0.43176305294036865), ('characteristic functions', 0.42805835604667664), ('distribution mu mathbb', 0.42688074707984924)]"
1202,1202,24,1202_cayley graph symmetric_normal cayley graphs_cayley graphs_cayley graph,"['cayley graph symmetric', 'normal cayley graphs', 'cayley graphs', 'cayley graph', 'eigenvalues adjacency', 'eigenvalues adjacency matrix', 'graph symmetric group', 'normal cayley', 'adjacency matrix', 'graphs symmetric']","['The second largest eigenvalue of normal Cayley graphs on symmetric\n  groups generated by cycles   We study the normal Cayley graphs $\\mathrm{Cay}(S_n, C(n,I))$ on the\nsymmetric group $S_n$, where $I\\subseteq \\{2,3,\\ldots,n\\}$ and $C(n,I)$ is the\nset of all cycles in $S_n$ with length in $I$. We prove that the strictly\nsecond largest eigenvalue of $\\mathrm{Cay}(S_n,C(n,I))$ can only be achieved by\nat most four irreducible representations of $S_n$, and we determine further the\nmultiplicity of this eigenvalue in several special cases. As a corollary, in\nthe case when $I$ contains neither $n-1$ nor $n$ we know exactly when\n$\\mathrm{Cay}(S_n, C(n,I))$ has the Aldous property, namely the strictly second\nlargest eigenvalue is attained by the standard representation of $S_n$, and we\nobtain that $\\mathrm{Cay}(S_n, C(n,I))$ does not have the Aldous property\nwhenever $n \\in I$. As another corollary of our main results, we prove a recent\nconjecture on the second largest eigenvalue of $\\mathrm{Cay}(S_n, C(n,\\{k\\}))$\nwhere $2 \\le k \\le n-2$.\n', 'HS-integral and Eisenstein integral normal mixed Cayley graphs   A mixed graph is said to be HS-\\emph{integral} if the eigenvalues of its\nHermitian-adjacency matrix of the second kind are integers. A mixed graph is\ncalled \\emph{Eisenstein integral} if the eigenvalues of its (0, 1)-adjacency\nmatrix are Eisenstein integers. We characterize the set $S$ for which the\nnormal mixed Cayley graph $\\text{Cay}(\\Gamma, S)$ is HS-integral for any finite\ngroup $\\Gamma$. We further show that a normal mixed Cayley graph is HS-integral\nif and only if it is Eisenstein integral. This paper generalizes the results of\n[M. Kadyan, B. Bhattacharjya. HS-integral and Eisenstein integral mixed Cayley\ngraphs over abelian groups. Linear Algebra Appl. 645:68-90, 2022].\n', 'HS-integral and Eisenstein integral mixed Cayley graphs over abelian\n  groups   A mixed graph is called \\emph{second kind hermitian integral}(or\n\\emph{HS-integral}) if the eigenvalues of its Hermitian-adjacency matrix of\nsecond kind are integers. A mixed graph is called \\emph{Eisenstein integral} if\nthe eigenvalues of its (0, 1)-adjacency matrix are Eisenstein integers. Let\n$\\Gamma$ be an abelian group. We characterize the set $S$ for which a mixed\nCayley graph $\\text{Cay}(\\Gamma, S)$ is HS-integral. We also show that a mixed\nCayley graph is Eisenstein integral if and only if it is HS-integral.\n']","[('cayley graph symmetric', 0.608360230922699), ('normal cayley graphs', 0.5983837842941284), ('cayley graphs', 0.594769299030304), ('cayley graph', 0.5688143372535706), ('eigenvalues adjacency', 0.5058601498603821), ('eigenvalues adjacency matrix', 0.4815785586833954), ('graph symmetric group', 0.46249106526374817), ('normal cayley', 0.3995600640773773), ('adjacency matrix', 0.39341285824775696), ('graphs symmetric', 0.3883613049983978)]"
1203,1203,24,1203_wiener hopf technique_diffraction_wave scattering_wiener hopf,"['wiener hopf technique', 'diffraction', 'wave scattering', 'wiener hopf', 'scattered wave', 'complex wave', 'plane wave', 'interfacial waves', 'scattering', 'scattering process']","[""Recycling solutions of boundary value problems: the Wiener--Hopf\n  perspective on embedding formula   Embedding formula allows to recycle solution of a family boundary value\nproblems by expressing all the solutions in terms of a small number of\nsolutions. Such formulas have been previously derived in the context of\ndiffraction by applying a cleverly chosen operator to the solution and the\nconstruction of edge Green's functions which are introduced in an elaborate\nmanner specific for each problem. We demonstrate that embedding formula\nnaturally appears from a matrix Wiener--Hopf equation, and the embedding\nformula is derived from the canonical solution to this matrix Wiener--Hopf\nproblem. This allows to drive the embedding formula in any context where the\nproblem can be formulated as a Wiener--Hopf equation. We illustrate the\neffectiveness of this approach by revisiting known problems, such as the\nproblem of diffraction by half-line, a strip and the problem of diffraction by\na wedge. Additionally, a new matrix Wiener--Hopf formulation is derived for\nwedge problems.\n"", ""Diffraction by a Right-Angled No-Contrast Penetrable Wedge Revisited: A\n  Double Wiener-Hopf Approach   In this paper, we revisit Radlow's innovative approach to diffraction by a\npenetra ble wedge by means of a double Wiener-Hopf technique. We provide a\nconstructive way of obtaining his ansatz and give yet another reason for why\nhis ansatz cannot be the true solution to the diffraction problem at hand. The\ntwo-complex-variable Wiener-Hopf equation is reduced to a system of two\nequations, one of which contains Radlow's ansatz plus some correction term\nconsisting of an explicitly known integral operator applied to a yet unknown\nfunction, whereas the other equation, the compatibility equation, governs the\nbehaviour of this unknown function.\n"", 'Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical\n  Continuation of Spectral Functions   We study the problem of diffraction by a right-angled no-contrast penetrable\nwedge by means of a two-complex-variable Wiener-Hopf approach. Specifically,\nthe analyticity properties of the unknown (spectral) functions of the\ntwo-complex-variable Wiener-Hopf equation are studied. We show that these\nspectral functions can be analytically continued onto a two-complex dimensional\nmanifold, and unveil their singularities in $\\mathbb{C}^2$. To do so, integral\nrepresentation formulae for the spectral functions are given and thoroughly\nused. It is shown that the novel concept of additive crossing holds for the\npenetrable wedge diffraction problem and that we can reformulate the physical\ndiffraction problem as a functional problem using this concept.\n']","[('wiener hopf technique', 0.5645835995674133), ('diffraction', 0.5236287713050842), ('wave scattering', 0.4894125461578369), ('wiener hopf', 0.45767614245414734), ('scattered wave', 0.44603610038757324), ('complex wave', 0.4191513955593109), ('plane wave', 0.40731361508369446), ('interfacial waves', 0.40512871742248535), ('scattering', 0.40173712372779846), ('scattering process', 0.37988173961639404)]"
1204,1204,24,1204_finite difference methods_meshfree methods_meshless methods_radial basis functions,"['finite difference methods', 'meshfree methods', 'meshless methods', 'radial basis functions', 'based radial basis', 'fd methods', 'radial basis', 'basis functions rbfs', 'pdes surfaces', 'polyharmonic splines']","['An Efficient High-Order Meshless Method for Advection-Diffusion\n  Equations on Time-Varying Irregular Domains   We present a high-order radial basis function finite difference (RBF-FD)\nframework for the solution of advection-diffusion equations on time-varying\ndomains. Our framework is based on a generalization of the recently developed\nOverlapped RBF-FD method that utilizes a novel automatic procedure for\ncomputing RBF-FD weights on stencils in variable-sized regions around stencil\ncenters. This procedure eliminates the overlap parameter $\\delta$, thereby\nenabling tuning-free assembly of RBF-FD differentiation matrices on moving\ndomains. In addition, our framework utilizes a simple and efficient procedure\nfor updating differentiation matrices on moving domains tiled by node sets of\ntime-varying cardinality. Finally, advection-diffusion in time-varying domains\nis handled through a combination of rapid node set modification, a new\nhigh-order semi-Lagrangian method that utilizes the new tuning-free overlapped\nRBF-FD method, and a high-order time-integration method. The resulting\nframework has no tuning parameters and has $O(N \\log N)$ time complexity. We\ndemonstrate high-orders of convergence for advection-diffusion equations on\ntime-varying 2D and 3D domains for both small and large Peclet numbers. We also\npresent timings that verify our complexity estimates. Finally, we utilize our\nmethod to solve a coupled 3D problem motivated by models of platelet\naggregation and coagulation, once again demonstrating high-order convergence\nrates on a moving domain.\n', 'Generalized moving least squares vs. radial basis function finite\n  difference methods for approximating surface derivatives   Approximating differential operators defined on two-dimensional surfaces is\nan important problem that arises in many areas of science and engineering. Over\nthe past ten years, localized meshfree methods based on generalized moving\nleast squares (GMLS) and radial basis function finite differences (RBF-FD) have\nbeen shown to be effective for this task as they can give high orders of\naccuracy at low computational cost, and they can be applied to surfaces defined\nonly by point clouds. However, there have yet to be any studies that perform a\ndirect comparison of these methods for approximating surface differential\noperators (SDOs). The first purpose of this work is to fill that gap. For this\ncomparison, we focus on an RBF-FD method based on polyharmonic spline kernels\nand polynomials (PHS+Poly) since they are most closely related to the GMLS\nmethod. Additionally, we use a relatively new technique for approximating SDOs\nwith RBF-FD called the tangent plane method since it is simpler than previous\ntechniques and natural to use with PHS+Poly RBF-FD. The second purpose of this\nwork is to relate the tangent plane formulation of SDOs to the local coordinate\nformulation used in GMLS and to show that they are equivalent when the tangent\nspace to the surface is known exactly. The final purpose is to use ideas from\nthe GMLS SDO formulation to derive a new RBF-FD method for approximating the\ntangent space for a point cloud surface when it is unknown. For the numerical\ncomparisons of the methods, we examine their convergence rates for\napproximating the surface gradient, divergence, and Laplacian as the point\nclouds are refined for various parameter choices. We also compare their\nefficiency in terms of accuracy per computational cost, both when including and\nexcluding setup costs.\n', 'Stability analysis of RBF-FD and WLS based local strong form meshless\n  methods on scattered nodes   The popularity of local meshless methods in the field of numerical\nsimulations has increased greatly in recent years. This is mainly due to the\nfact that they can operate on scattered nodes and that they allow a direct\ncontrol over the approximation order and basis functions. In this paper we\nanalyse two popular variants of local strong form meshless methods, namely the\nradial basis function-generated finite differences (RBF-FD) using polyharmonic\nsplines (PHS) augmented with monomials, and the weighted least squares (WLS)\napproach using only monomials. Our analysis focuses on the accuracy and\nstability of the numerical solution computed on scattered nodes in a two- and\nthree-dimensional domain. We show that while the WLS variant is a better choice\nwhen lower order approximations are sufficient, the RBF-FD variant exhibits a\nmore stable behavior and a higher accuracy of the numerical solution for higher\norder approximations, but at the cost of higher computational complexity.\n']","[('finite difference methods', 0.5462919473648071), ('meshfree methods', 0.5386596918106079), ('meshless methods', 0.5366719365119934), ('radial basis functions', 0.5060381889343262), ('based radial basis', 0.49863722920417786), ('fd methods', 0.4365769028663635), ('radial basis', 0.42869022488594055), ('basis functions rbfs', 0.4087121784687042), ('pdes surfaces', 0.3834547698497772), ('polyharmonic splines', 0.3801237642765045)]"
1205,1205,24,1205_tensor methods_high order tensor_methods convex optimization_convex nonconvex optimization,"['tensor methods', 'high order tensor', 'methods convex optimization', 'convex nonconvex optimization', 'nonconvex optimization', 'third order tensor', 'minimizing nonconvex', 'methods smooth convex', 'adaptive regularization', 'accelerated scheme']","['Tensor Methods for Minimizing Convex Functions with H\\""{o}lder\n  Continuous Higher-Order Derivatives   In this paper we study $p$-order methods for unconstrained minimization of\nconvex functions that are $p$-times differentiable ($p\\geq 2$) with\n$\\nu$-H\\""{o}lder continuous $p$th derivatives. We propose tensor schemes with\nand without acceleration. For the schemes without acceleration, we establish\niteration complexity bounds of\n$\\mathcal{O}\\left(\\epsilon^{-1/(p+\\nu-1)}\\right)$ for reducing the functional\nresidual below a given $\\epsilon\\in (0,1)$. Assuming that $\\nu$ is known, we\nobtain an improved complexity bound of\n$\\mathcal{O}\\left(\\epsilon^{-1/(p+\\nu)}\\right)$ for the corresponding\naccelerated scheme. For the case in which $\\nu$ is unknown, we present a\nuniversal accelerated tensor scheme with iteration complexity of\n$\\mathcal{O}\\left(\\epsilon^{-p/[(p+1)(p+\\nu-1)]}\\right)$. A lower complexity\nbound of $\\mathcal{O}\\left(\\epsilon^{-2/[3(p+\\nu)-2]}\\right)$ is also obtained\nfor this problem class.\n', 'Second-order methods for quartically-regularised cubic polynomials, with\n  applications to high-order tensor methods   There has been growing interest in high-order tensor methods for nonconvex\noptimization, with adaptive regularization, as they possess better/optimal\nworst-case evaluation complexity globally and faster convergence\nasymptotically. These algorithms crucially rely on repeatedly minimizing\nnonconvex multivariate Taylor-based polynomial sub-problems, at least locally.\nFinding efficient techniques for the solution of these sub-problems, beyond the\nsecond-order case, has been an open question. This paper proposes a\nsecond-order method, Quadratic Quartic Regularisation (QQR), for efficiently\nminimizing nonconvex quartically-regularized cubic polynomials, such as the\nAR$p$ sub-problem [3] with $p=3$. Inspired by [35], QQR approximates the\nthird-order tensor term by a linear combination of quadratic and quartic terms,\nyielding (possibly nonconvex) local models that are solvable to global\noptimality. In order to achieve accuracy $\\epsilon$ in the first-order\ncriticality of the sub-problem in finitely many iterations, we show that the\nerror in the QQR method decreases either linearly or by at least\n$\\mathcal{O}(\\epsilon^{4/3})$ for locally convex iterations, while in the\nnonconvex case, by at least $\\mathcal{O}(\\epsilon)$; thus improving, on these\ntypes of iterations, the general cubic-regularization bound. Preliminary\nnumerical experiments indicate that two QQR variants perform competitively with\nstate-of-the-art approaches such as ARC (also known as AR$p$ with $p=2$),\nachieving either a lower objective value or iteration counts.\n', 'Tensor Methods for Finding Approximate Stationary Points of Convex\n  Functions   In this paper we consider the problem of finding $\\epsilon$-approximate\nstationary points of convex functions that are $p$-times differentiable with\n$\\nu$-H\\""{o}lder continuous $p$th derivatives. We present tensor methods with\nand without acceleration. Specifically, we show that the non-accelerated\nschemes take at most $\\mathcal{O}\\left(\\epsilon^{-1/(p+\\nu-1)}\\right)$\niterations to reduce the norm of the gradient of the objective below a given\n$\\epsilon\\in (0,1)$. For accelerated tensor schemes we establish improved\ncomplexity bounds of\n$\\mathcal{O}\\left(\\epsilon^{-(p+\\nu)/[(p+\\nu-1)(p+\\nu+1)]}\\right)$ and\n$\\mathcal{O}\\left(|\\log(\\epsilon)|\\epsilon^{-1/(p+\\nu)}\\right)$, when the\nH\\""{o}lder parameter $\\nu\\in [0,1]$ is known. For the case in which $\\nu$ is\nunknown, we obtain a bound of\n$\\mathcal{O}\\left(\\epsilon^{-(p+1)/[(p+\\nu-1)(p+2)]}\\right)$ for a universal\naccelerated scheme. Finally, we also obtain a lower complexity bound of\n$\\mathcal{O}\\left(\\epsilon^{-2/[3(p+\\nu)-2]}\\right)$ for finding\n$\\epsilon$-approximate stationary points using $p$-order tensor methods.\n']","[('tensor methods', 0.6029929518699646), ('high order tensor', 0.5628884434700012), ('methods convex optimization', 0.5448728799819946), ('convex nonconvex optimization', 0.541766881942749), ('nonconvex optimization', 0.5156236886978149), ('third order tensor', 0.5153288245201111), ('minimizing nonconvex', 0.4926143288612366), ('methods smooth convex', 0.4912171959877014), ('adaptive regularization', 0.47869783639907837), ('accelerated scheme', 0.4682965874671936)]"
1206,1206,24,1206_variational autoencoder vae_variational autoencoder_variational autoencoders_autoencoder vae,"['variational autoencoder vae', 'variational autoencoder', 'variational autoencoders', 'autoencoder vae', 'autoencoders', 'autoencoder', 'latent representations', 'encoders', 'deep generative models', 'deep generative']","['Quantitative Understanding of VAE as a Non-linearly Scaled Isometric\n  Embedding   Variational autoencoder (VAE) estimates the posterior parameters (mean and\nvariance) of latent variables corresponding to each input data. While it is\nused for many tasks, the transparency of the model is still an underlying\nissue. This paper provides a quantitative understanding of VAE property through\nthe differential geometric and information-theoretic interpretations of VAE.\nAccording to the Rate-distortion theory, the optimal transform coding is\nachieved by using an orthonormal transform with PCA basis where the transform\nspace is isometric to the input. Considering the analogy of transform coding to\nVAE, we clarify theoretically and experimentally that VAE can be mapped to an\nimplicit isometric embedding with a scale factor derived from the posterior\nparameter. As a result, we can estimate the data probabilities in the input\nspace from the prior, loss metrics, and corresponding posterior parameters, and\nfurther, the quantitative importance of each latent variable can be evaluated\nlike the eigenvalue of PCA.\n', 'VMI-VAE: Variational Mutual Information Maximization Framework for VAE\n  With Discrete and Continuous Priors   Variational Autoencoder is a scalable method for learning latent variable\nmodels of complex data. It employs a clear objective that can be easily\noptimized. However, it does not explicitly measure the quality of learned\nrepresentations. We propose a Variational Mutual Information Maximization\nFramework for VAE to address this issue. It provides an objective that\nmaximizes the mutual information between latent codes and observations. The\nobjective acts as a regularizer that forces VAE to not ignore the latent code\nand allows one to select particular components of it to be most informative\nwith respect to the observations. On top of that, the proposed framework\nprovides a way to evaluate mutual information between latent codes and\nobservations for a fixed VAE model.\n', 'Variational Mutual Information Maximization Framework for VAE Latent\n  Codes with Continuous and Discrete Priors   Learning interpretable and disentangled representations of data is a key\ntopic in machine learning research. Variational Autoencoder (VAE) is a scalable\nmethod for learning directed latent variable models of complex data. It employs\na clear and interpretable objective that can be easily optimized. However, this\nobjective does not provide an explicit measure for the quality of latent\nvariable representations which may result in their poor quality. We propose\nVariational Mutual Information Maximization Framework for VAE to address this\nissue. In comparison to other methods, it provides an explicit objective that\nmaximizes lower bound on mutual information between latent codes and\nobservations. The objective acts as a regularizer that forces VAE to not ignore\nthe latent variable and allows one to select particular components of it to be\nmost informative with respect to the observations. On top of that, the proposed\nframework provides a way to evaluate mutual information between latent codes\nand observations for a fixed VAE model. We have conducted our experiments on\nVAE models with Gaussian and joint Gaussian and discrete latent variables. Our\nresults illustrate that the proposed approach strengthens relationships between\nlatent codes and observations and improves learned representations.\n']","[('variational autoencoder vae', 0.7257801294326782), ('variational autoencoder', 0.7073183655738831), ('variational autoencoders', 0.7040479779243469), ('autoencoder vae', 0.6272192597389221), ('autoencoders', 0.6042917966842651), ('autoencoder', 0.559194028377533), ('latent representations', 0.5279702544212341), ('encoders', 0.5053083300590515), ('deep generative models', 0.49970895051956177), ('deep generative', 0.48505932092666626)]"
1207,1207,24,1207_railway_scheduling_train network_routing scheduling,"['railway', 'scheduling', 'train network', 'routing scheduling', 'optimal schedules', 'trains', 'public transportation', 'timetables', 'traffic management', 'integer programming']","['Digitalizing Railway Operations: An Optimization-Based Train\n  Rescheduling Model for Urban and Interurban Disrupted Networks   This study introduces a novel methodology for managing train network\ndisruptions across the entire rail network, leveraging digital tools and\nmethodologies. The approach involves two stages, taking into account possible\nand practical features such as allowing trains to occupy opposite tracks and\nconsidering infrastructure capacity for train stops. In the first stage,\nimportant nodes within the train network are identified, considering both a\ntopological feature and passenger demand. Subsequently, the network is\naggregated based on these important nodes, employing a digital approach to\nreduce problem complexity. In the second stage, we develop an Integer\nProgramming model for train rescheduling. We then solve this model using the\nCPLEX solver to evaluate its efficiency. The first case study applies this\nmethodology to the Iranian railway, which is known as a sparse rail network.\nThe results show minimal deviation from the initial train timetable due to the\nlow frequency of trips in each block. Although the approach successfully\naddresses the train rescheduling problem for various disruption scenarios on\nthe Iranian railway, the excessive computational time required by the\noptimization model prompts us to make adjustments. Finally, the second case\nstudy demonstrates the implementation of the adjusted model in a busy test\nnetwork. This adaptation significantly reduces computational time by up to 88%.\nIt can be effectively utilized for disruption management in busy networks,\nwhere trains need to receive a secondary timetable promptly when facing\ndisruptions.\n', 'A model for pricing freight rail transport access costs: economic and\n  environmental perspectives   In deregulated railway markets, efficient management of infrastructure\ncharges is essential for sustaining railway systems. This study sets out a\nmethod for infrastructure managers to price access to railway infrastructure,\nfocusing on freight transport in deregulated market contexts. The proposed\nmethodology integrates negative externalities directly into the pricing\nstructure in a novel way, balancing economic and environmental objectives. it\ndevelops a dynamic freight flow model to represent the railway system, using a\nlogit model to capture the modal split between rail and road modes based on\ncost, thereby reflecting demand elasticity. The model is temporally\ndiscretized, resulting in a mesoscopic, discrete-event simulation framework,\nintegrated into an optimization model that determines train path charges based\non real-time capacity and demand. This approach aims both to maximize revenue\nfor the infrastructure manager and to reduce the negative externalities of road\ntransport. The methodology is demonstrated through a case study on the\nMediterranean Rail Freight Corridor, showcasing the scale of access charges\nderived from the model. Results indicate that reducing track-access charges can\nyield substantial societal benefits by shifting freight demand to rail. This\nresearch provides a valuable framework for transport policy, suggesting that\nexternality-sensitive infrastructure charges can promote more efficient and\nsustainable use of railway infrastructure.\n', ""Robust Railway Network Design based on Strategic Timetables   Using strategic timetables as input for railway network design has become\nincreasingly popular among western European railway infrastructure operators.\nAlthough both railway timetabling and railway network design on their own are\nwell covered by academic research, there is still a gap in the literature\nconcerning timetable-based network design. Therefore, we propose a\nmixed-integer linear program to design railway infrastructure so that the\ndemand derived from a strategic timetable can be satisfied with minimal\ninfrastructure costs. The demand is given by a list of trains, each featuring\nstart and destination nodes as well as time bounds and a set of frequency and\ntransfer constraints that capture the strategic timetable's main\ncharacteristics. During the optimization, the solver decides which railway\nlines need to be built or expanded and whether travel or headway times must be\nshortened to meet the demand. Since strategic timetables are subject to\nuncertainty, we expand the optimization model to a robust version. Uncertain\ntimetables are modelled as discrete scenarios, while uncertain freight train\ndemand is modelled using optional trains, which can be inserted into the\nresulting timetable if they do not require additional infrastructure. We\npresent computational results for both the deterministic and the robust case\nand give an outlook on further research.\n""]","[('railway', 0.5057966709136963), ('scheduling', 0.4999886155128479), ('train network', 0.4976103901863098), ('routing scheduling', 0.49741679430007935), ('optimal schedules', 0.47405388951301575), ('trains', 0.47222211956977844), ('public transportation', 0.42418742179870605), ('timetables', 0.41988033056259155), ('traffic management', 0.4198037087917328), ('integer programming', 0.41856664419174194)]"
1208,1208,24,1208_group algebras finite_group algebra finite_algebra finite group_group algebras,"['group algebras finite', 'group algebra finite', 'algebra finite group', 'group algebras', 'group finite field', 'group algebras let', 'group algebra', 'group algebra mathbb', 'groups field', 'unit groups']","['Isomorphism problem of Unitary Subgroups of Group Algebras   Let V_* be the normalized unitary subgroup of the modular group algebra FG of\na finite p-group G over a finite field F with the classical involution *. We\ninvestigate the isomorphism problem for the group V_*, that asks when the group\nV_* is determined by its group algebra FG. We confirm it for classes of finite\nabelian p-groups, 2-groups of maximal class and non-abelian 2-groups of order\nat most 16.\n', 'A reduction theorem for the isomorphism problem of group algebras over\n  fields   We prove that the isomorphism problem for group algebras reduces to group\nalgebras over finite extensions of the prime field. In particular, the modular\nisomorphism problem reduces to finite modular group algebras.\n', 'On the Unitary Subgroups of group algebras   Let $FG$ be the group algebra of a finite $p$-group $G$ over a finite field\n$F$ of characteristic $p$ and $*$ the classical involution of $FG$. The\n$*$-unitary subgroup of $FG$, denoted by $V_*(FG)$, is defined to be the set of\nall normalized units $u$ satisfying the property $u^*=u^{-1}$. In this paper we\ngive a recursive method how to compute the order of the $*$-unitary subgroup\nfor many non-commutative group algebras. We also prove a variant of the modular\nisomorphism question of group algebras, where $F$ is a finite field of\ncharacteristic two, that is $V_*(FG)$ determines the basic group $G$ for all\nnon-abelian $2$-groups $G$ of order at most $2^4$.\n']","[('group algebras finite', 0.681410551071167), ('group algebra finite', 0.6652736067771912), ('algebra finite group', 0.6524688601493835), ('group algebras', 0.6394898891448975), ('group finite field', 0.6315770745277405), ('group algebras let', 0.600886344909668), ('group algebra', 0.5865949392318726), ('group algebra mathbb', 0.5257977247238159), ('groups field', 0.5257335305213928), ('unit groups', 0.5139300227165222)]"
1209,1209,24,1209_epidemic models_dynamics epidemic_nonlocal diffusions_nonlocal diffusion,"['epidemic models', 'dynamics epidemic', 'nonlocal diffusions', 'nonlocal diffusion', 'vanishing spreading', 'asymptotic spreading', 'diffusions', 'dynamics diffusive', 'diffusion', 'epidemic']","['Dynamics of an epidemic model with nonlocal di?usion and a free boundary   An epidemic model, where the dispersal is approximated by nonlocal diffusion\noperator and spatial domain has one ?xed boundary and one free boundary, is\nconsidered in this paper. Firstly, using some elementary analysis instead of\nvariational characterization, we show the existence and asymptotic behaviors of\nthe principal eigenvalue of a cooperative system which can be used to\ncharacterize more epidemic models, not just ours. Then we study the existence,\nuniqueness and stability of a related steady state problem. Finally, we obtain\na rather complete understanding for long time behaviors, spreading-vanishing\ndichotomy, criteria for spreading and vanishing, and spreading speed.\nParticularly, we prove that the asymptotic spreading speed of solution\ncomponent (u; v) is equal to the spreading speed of free boundary which is\n?nite if and only if a threshold condition holds for kernel functions.\n', 'Longtime behaviors of an epidemic model with nonlocal diffusions and a\n  free boundary: spreading-vanishing dichotomy   We propose a nonlocal epidemic model whose spatial domain evolves over time\nand is represented by $[0,h(t)]$ with $h(t)$ standing for the spreading front\nof epidemic. It is assumed that the agents can cross the fixed boundary $x=0$,\nbut they will die immediately if they do it, which implies that the area\n$(-\\infty,0)$ is a hostile environment for the agents. We first show that this\nmodel is well posed, then prove that the longtime behaviors are governed by a\nspreading-vanishing dichotomy and finally give some criteria determining\nspreading and vanishing. Particularly, we obtain the asymptotical behaviors of\nthe principal eigenvalue of a cooperative system with nonlocal diffusions\nwithout assuming the related nonlocal operator is self-adjoint, and the steady\nstate problem of such cooperative system on half space $[0,\\infty)$ is studied\nin detail.\n', 'The free boundary problem of an epidemic model with nonlocal diffusions\n  and nonlocal reactions: spreading-vanishing dichotomy   This paper concerns the free boundary problem of an epidemic model. The\nspatial movements of the infectious agents and the infective humans are\napproximated by nonlocal diffusion operators. Especially, both the growth rate\nof the agents and the infective rate of humans are represented by nonlocal\nreaction terms. Thus our model has four integral terms which bring some\ndiffculties for the study of the corresponding principal eigenvalue problem.\nFirstly, using some elementray analysis instead of Krein-Rutman theorem and the\nvariational characteristic, we obtain the existence and asymptotic behaviors of\nprincipal eigenvalue. Then a spreading-vanishing dichotomy is proved to hold,\nand the criteria for spreading and vanishing are derived. Lastly, comparing our\nresults with those in the existing works, we discuss the effect of nonlocal\nreaction term on spreading and vanishing, finding that the more nonlocal\nreaction terms a model has, the harder spreading happens.\n']","[('epidemic models', 0.6737530827522278), ('dynamics epidemic', 0.6350005865097046), ('nonlocal diffusions', 0.5724407434463501), ('nonlocal diffusion', 0.5597088932991028), ('vanishing spreading', 0.5400327444076538), ('asymptotic spreading', 0.5378826260566711), ('diffusions', 0.5242534279823303), ('dynamics diffusive', 0.5225520730018616), ('diffusion', 0.516276478767395), ('epidemic', 0.5160430669784546)]"
1210,1210,24,1210_quantum spin systems_quantum systems_many body quantum_spin systems,"['quantum spin systems', 'quantum systems', 'many body quantum', 'spin systems', 'discrete symmetry', 'quantum many body', 'state quantum spin', 'topological entanglement', 'body quantum', 'topological entanglement entropy']","['General Lieb-Schultz-Mattis type theorems for quantum spin chains   We develop a general operator algebraic method which focuses on projective\nrepresentations of symmetry group for proving Lieb-Schultz-Mattis type\ntheorems, i.e., no-go theorems that rule out the existence of a unique gapped\nground state (or, more generally, a pure split state), for quantum spin chains\nwith on-site symmetry. We first prove a theorem for translation invariant spin\nchains that unifies and extends two theorems proved by two of the authors in\n[OT1]. We then prove a Lieb-Schultz-Mattis type theorem for spin chains that\nare invariant under the reflection about the origin and not necessarily\ntranslation invariant.\n', 'Geometric approach to Lieb-Schultz-Mattis theorem without translation\n  symmetry under inversion or rotation symmetry   We propose a geometric {approach to Lieb-Schultz-Mattis theorem for} quantum\nmany-body systems with discrete spin-rotation symmetries and lattice inversion\nor rotation symmetry, but without translation symmetry assumed. Under\nsymmetry-twisting on a $(d-1)$-dimensional plane, we find that any\n$d$-dimensional inversion-symmetric spin system possesses a doubly degenerate\nspectrum when it hosts a half-integer spin at the inversion-symmetric point. We\nalso show that any rotation-symmetric generalized spin model with a projective\nrepresentation at the rotation center has a similar degeneracy under\nsymmetry-twisting. We argue that these degeneracies imply that {a unique\nsymmetric gapped ground state that is smoothly connected to product states} is\nforbidden in the original untwisted systems -- generalized\ninversional/rotational Lieb-Schultz-Mattis theorems without lattice translation\nsymmetry imposed. The traditional Lieb-Schultz-Mattis theorems with\ntranslations also fit in the proposed framework.\n', ""The Lieb-Schultz-Mattis Theorem: A Topological Point of View   We review the Lieb-Schultz-Mattis theorem and its variants, which are no-go\ntheorems that state that a quantum many-body system with certain conditions\ncannot have a locally-unique gapped ground state. We restrict ourselves to\none-dimensional quantum spin systems and discuss both the generalized\nLieb-Schultz-Mattis theorem for models with U(1) symmetry and the extended\nLieb-Schultz-Mattis theorem for models with discrete symmetry. We also discuss\nthe implication of the same arguments to systems on the infinite cylinder, both\nwith the periodic boundary conditions and with the spiral boundary conditions.\n  For models with U(1) symmetry, we here present a rearranged version of the\noriginal proof of Lieb, Schultz, and Mattis based on the twist operator. As the\ntitle suggests we take a modern topological point of view and prove the\ngeneralized Lieb-Schultz-Mattis theorem by making use of a topological index\n(which coincides with the filling factor). By a topological index, we mean an\nindex that characterizes a locally-unique gapped ground state and is invariant\nunder continuous (or smooth) modification of the ground state.\n  For models with discrete symmetry, we describe the basic idea of the most\ngeneral proof based on the topological index introduced in the context of\nsymmetry-protected topological phases. We start from background materials such\nas the classification of projective representations of the symmetry group.\n  We also review the notion that we call a locally-unique gapped ground state\nof a quantum spin system on an infinite lattice and present basic theorems.\nThis notion turns out to be natural and useful from the physicists' point of\nview.\n  We have tried to make the present article readable and almost self-contained.\nWe only assume basic knowledge about quantum spin systems.\n""]","[('quantum spin systems', 0.5590405464172363), ('quantum systems', 0.5052306056022644), ('many body quantum', 0.490576833486557), ('spin systems', 0.4858682453632355), ('discrete symmetry', 0.47729548811912537), ('quantum many body', 0.47550126910209656), ('state quantum spin', 0.4752454459667206), ('topological entanglement', 0.46614840626716614), ('body quantum', 0.4617062211036682), ('topological entanglement entropy', 0.4600498378276825)]"
1211,1211,24,1211_nonlinear predictive control_predictive controllers_based koopman operator_predictive control,"['nonlinear predictive control', 'predictive controllers', 'based koopman operator', 'predictive control', 'predictive control mpc', 'driven koopman', 'control nonlinear', 'koopman operator', 'nonlinear control', 'controllers nonlinear']","['Kernel EDMD for data-driven nonlinear Koopman MPC with stability\n  guarantees   Extended dynamic mode decomposition (EDMD) is a popular data-driven method to\npredict the action of the Koopman operator, i.e., the evolution of an\nobservable function along the flow of a dynamical system. In this paper, we\nleverage a recently-introduced kernel EDMD method for control systems for\ndata-driven model predictive control. Building upon pointwise error bounds\nproportional in the state, we rigorously show practical asymptotic stability of\nthe origin w.r.t. the MPC closed loop without stabilizing terminal conditions.\nThe key novelty is that we avoid restrictive invariance conditions. Last, we\nverify our findings by numerical simulations.\n', ""Data-Enabled Predictive Control for Nonlinear Systems Based on a Koopman\n  Bilinear Realization   This paper extends the Willems' Fundamental Lemma to nonlinear control-affine\nsystems using the Koopman bilinear realization. This enables us to bypass the\nExtended Dynamic Mode Decomposition (EDMD)-based system identification step in\nconventional Koopman-based methods and design controllers for nonlinear systems\ndirectly from data. Leveraging this result, we develop a Data-Enabled\nPredictive Control (DeePC) framework for nonlinear systems with unknown\ndynamics. A case study demonstrates that our direct data-driven control method\nachieves improved optimality compared to conventional Koopman-based methods.\nFurthermore, in examples where an exact Koopman realization with a\nfinite-dimensional lifting function set of the controlled nonlinear system does\nnot exist, our method exhibits advanced robustness to finite Koopman\napproximation errors compared to existing methods.\n"", 'Data-driven Model Predictive Control: Asymptotic Stability despite Approximation Errors exemplified in the Koopman framework In this paper, we analyze nonlinear model predictive control (MPC) using data-driven surrogates in the prediction and optimization step. First, we establish asymptotic stability of the origin, a controlled steady state, w.r.t. the MPC closed loop without stabilizing terminal conditions. To this end, we prove that cost controllability of the original system is preserved if proportional bounds on the approximation error hold. Here, proportional refers to state and control, while the respective constants depend on the approximation accuracy. The proportionality of the error bounds is a key element to derive asymptotic stability in presence of modeling errors and not only practical asymptotic stability. Second, we exemplarily verify the imposed assumptions for data-driven surrogates generated with kernel extended dynamic mode decomposition based on the Koopman operator. Hereby, we do not impose invariance assumptions on finite dictionaries, but rather derive all conditions under non-restrictive data requirements. Finally, we verify our findings with numerical simulations.']","[('nonlinear predictive control', 0.5605123043060303), ('predictive controllers', 0.4883287250995636), ('based koopman operator', 0.47451674938201904), ('predictive control', 0.4690278172492981), ('predictive control mpc', 0.4483206570148468), ('driven koopman', 0.4437634348869324), ('control nonlinear', 0.4358412027359009), ('koopman operator', 0.43027207255363464), ('nonlinear control', 0.4294668734073639), ('controllers nonlinear', 0.4265148937702179)]"
1212,1212,24,1212_semi supervised learning_semi supervised_graph laplacian regularization_learning graphs,"['semi supervised learning', 'semi supervised', 'graph laplacian regularization', 'learning graphs', 'based semi supervised', 'learning graph', 'supervised learning', 'graphs laplacian', 'laplacian regularization', 'supervised learning problems']","['Analysis and algorithms for $\\ell_p$-based semi-supervised learning on\n  graphs   This paper addresses theory and applications of $\\ell_p$-based Laplacian\nregularization in semi-supervised learning. The graph $p$-Laplacian for $p>2$\nhas been proposed recently as a replacement for the standard ($p=2$) graph\nLaplacian in semi-supervised learning problems with very few labels, where\nLaplacian learning is degenerate.\n  In the first part of the paper we prove new discrete to continuum convergence\nresults for $p$-Laplace problems on $k$-nearest neighbor ($k$-NN) graphs, which\nare more commonly used in practice than random geometric graphs. Our analysis\nshows that, on $k$-NN graphs, the $p$-Laplacian retains information about the\ndata distribution as $p\\to \\infty$ and Lipschitz learning ($p=\\infty$) is\nsensitive to the data distribution. This situation can be contrasted with\nrandom geometric graphs, where the $p$-Laplacian forgets the data distribution\nas $p\\to \\infty$. We also present a general framework for proving discrete to\ncontinuum convergence results in graph-based learning that only requires\npointwise consistency and monotonicity.\n  In the second part of the paper, we develop fast algorithms for solving the\nvariational and game-theoretic $p$-Laplace equations on weighted graphs for\n$p>2$. We present several efficient and scalable algorithms for both\nformulations, and present numerical results on synthetic data indicating their\nconvergence properties. Finally, we conduct extensive numerical experiments on\nthe MNIST, FashionMNIST and EMNIST datasets that illustrate the effectiveness\nof the $p$-Laplacian formulation for semi-supervised learning with few labels.\nIn particular, we find that Lipschitz learning ($p=\\infty$) performs well with\nvery few labels on $k$-NN graphs, which experimentally validates our\ntheoretical findings that Lipschitz learning retains information about the data\ndistribution (the unlabeled data) on $k$-NN graphs.\n', 'Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label\n  Rates   We propose a new framework, called Poisson learning, for graph based\nsemi-supervised learning at very low label rates. Poisson learning is motivated\nby the need to address the degeneracy of Laplacian semi-supervised learning in\nthis regime. The method replaces the assignment of label values at training\npoints with the placement of sources and sinks, and solves the resulting\nPoisson equation on the graph. The outcomes are provably more stable and\ninformative than those of Laplacian learning. Poisson learning is efficient and\nsimple to implement, and we present numerical experiments showing the method is\nsuperior to other recent approaches to semi-supervised learning at low label\nrates on MNIST, FashionMNIST, and Cifar-10. We also propose a graph-cut\nenhancement of Poisson learning, called Poisson MBO, that gives higher accuracy\nand can incorporate prior knowledge of relative class sizes.\n', 'Consistency of semi-supervised learning, stochastic tug-of-war games,\n  and the p-Laplacian   In this paper we give a broad overview of the intersection of partial\ndifferential equations (PDEs) and graph-based semi-supervised learning. The\noverview is focused on a large body of recent work on PDE continuum limits of\ngraph-based learning, which have been used to prove well-posedness of\nsemi-supervised learning algorithms in the large data limit. We highlight some\ninteresting research directions revolving around consistency of graph-based\nsemi-supervised learning, and present some new results on the consistency of\n$p$-Laplacian semi-supervised learning using the stochastic tug-of-war game\ninterpretation of the $p$-Laplacian. We also present the results of some\nnumerical experiments that illustrate our results and suggest directions for\nfuture work.\n']","[('semi supervised learning', 0.698935866355896), ('semi supervised', 0.6569991707801819), ('graph laplacian regularization', 0.6512765288352966), ('learning graphs', 0.6342195868492126), ('based semi supervised', 0.6088035702705383), ('learning graph', 0.6030508875846863), ('supervised learning', 0.5649471282958984), ('graphs laplacian', 0.5573488473892212), ('laplacian regularization', 0.5464722514152527), ('supervised learning problems', 0.5443295836448669)]"
1213,1213,24,1213_matrix estimation_matrix denoising_spectral estimators_rank matrix estimation,"['matrix estimation', 'matrix denoising', 'spectral estimators', 'rank matrix estimation', 'random matrix theory', 'gaussian noise', 'invariant estimator', 'random matrix models', 'invariant noise', 'signal matrix']","['Rectangular Rotational Invariant Estimator for High-Rank Matrix\n  Estimation   We consider estimating a matrix from noisy observations coming from an\narbitrary additive bi-rotational invariant perturbation. We propose an\nestimator which is optimal among the class of rectangular rotational invariant\nestimators and can be applied irrespective of the prior on the signal. For the\nparticular case of Gaussian noise, we prove the optimality of the proposed\nestimator, and we find an explicit expression for the MMSE in terms of the\nlimiting singular value distribution of the observation matrix. Moreover, we\nprove a formula linking the asymptotic mutual information and the limit of a\nlog-spherical integral of rectangular matrices. We also provide numerical\nchecks for our results for general bi-rotational invariant noise, as well as\nGaussian noise, which match our theoretical predictions.\n', 'On the phase diagram of extensive-rank symmetric matrix denoising beyond\n  rotational invariance   Matrix denoising is central to signal processing and machine learning. Its\nstatistical analysis when the matrix to infer has a factorised structure with a\nrank growing proportionally to its dimension remains a challenge, except when\nit is rotationally invariant. In this case the information theoretic limits and\nan efficient Bayes-optimal denoising algorithm, called rotational invariant\nestimator [1,2], are known. Beyond this setting few results can be found. The\nreason is that the model is not a usual spin system because of the growing rank\ndimension, nor a matrix model (as appearing in high-energy physics) due to the\nlack of rotation symmetry, but rather a hybrid between the two. Here we make\nprogress towards the understanding of Bayesian matrix denoising when the signal\nis a factored matrix $XX^\\intercal$ that is not rotationally invariant. Monte\nCarlo simulations suggest the existence of a \\emph{denoising-factorisation\ntransition} separating a phase where denoising using the rotational invariant\nestimator remains Bayes-optimal due to universality properties of the same\nnature as in random matrix theory, from one where universality breaks down and\nbetter denoising is possible, though algorithmically hard. We argue that it is\nonly beyond the transition that factorisation, i.e., estimating $X$ itself,\nbecomes possible up to irresolvable ambiguities. On the theory side, we combine\nmean-field techniques in an interpretable multiscale fashion in order to access\nthe minimum mean-square error and mutual information. Interestingly, our\nalternative method yields equations reproducible by the replica approach of\n[3]. Using numerical insights, we delimit the portion of phase diagram where we\nconjecture the mean-field theory to be exact, and correct it using universality\nwhen it is not. Our complete ansatz matches well the numerics in the whole\nphase diagram when considering finite size effects.\n', 'The price of ignorance: how much does it cost to forget noise structure\n  in low-rank matrix estimation?   We consider the problem of estimating a rank-1 signal corrupted by structured\nrotationally invariant noise, and address the following question: how well do\ninference algorithms perform when the noise statistics is unknown and hence\nGaussian noise is assumed? While the matched Bayes-optimal setting with\nunstructured noise is well understood, the analysis of this mismatched problem\nis only at its premises. In this paper, we make a step towards understanding\nthe effect of the strong source of mismatch which is the noise statistics. Our\nmain technical contribution is the rigorous analysis of a Bayes estimator and\nof an approximate message passing (AMP) algorithm, both of which incorrectly\nassume a Gaussian setup. The first result exploits the theory of spherical\nintegrals and of low-rank matrix perturbations; the idea behind the second one\nis to design and analyze an artificial AMP which, by taking advantage of the\nflexibility in the denoisers, is able to ""correct"" the mismatch. Armed with\nthese sharp asymptotic characterizations, we unveil a rich and often unexpected\nphenomenology. For example, despite AMP is in principle designed to efficiently\ncompute the Bayes estimator, the former is outperformed by the latter in terms\nof mean-square error. We show that this performance gap is due to an incorrect\nestimation of the signal norm. In fact, when the SNR is large enough, the\noverlaps of the AMP and the Bayes estimator coincide, and they even match those\nof optimal estimators taking into account the structure of the noise.\n']","[('matrix estimation', 0.5868078470230103), ('matrix denoising', 0.5410816669464111), ('spectral estimators', 0.5221665501594543), ('rank matrix estimation', 0.5218387842178345), ('random matrix theory', 0.510869562625885), ('gaussian noise', 0.5099318027496338), ('invariant estimator', 0.49614912271499634), ('random matrix models', 0.48350223898887634), ('invariant noise', 0.45841479301452637), ('signal matrix', 0.4470161199569702)]"
1214,1214,24,1214_viscoelasticity_viscoelastic_finite strain_thermomechanics,"['viscoelasticity', 'viscoelastic', 'finite strain', 'thermomechanics', 'visco elastic', 'elastic inelastic', 'viscous stress', 'elastodynamics', 'order viscosity', 'deformation gradient']","['Thermodynamics of viscoelastic solids, its Eulerian formulation, and\n  existence of weak solutions   The thermodynamical model of visco-elastic deformable solids at finite\nstrains is formulated in a fully Eulerian way in rates. Also effects of thermal\nexpansion or buoyancy due to evolving mass density in a gravity field are\ncovered. The Kelvin-Voigt rheology with a higher-order viscosity (exploiting\nthe concept of multipolar materials) is used, allowing for physically relevant\nframe-indifferent stored energies and for local invertibility of deformation.\nThe model complies with energy conservation and Clausius-Duhem entropy\ninequality. Existence and a certain regularity of weak solutions is proved by a\nFaedo-Galerkin semi-discretization and a suitable regularization. Subtle\nphysical limitations of the model are illustrated on thermally expanding\nneo-Hookean materials or materials with phase transitions.\n', ""Time discretization in convected linearized thermo-visco-elastodynamics\n  at large displacements   The fully-implicit time discretization (i.e. the backward Euler formula) is\napplied to compressible nonlinear dynamical models of thermo-viscoelastic\nsolids in the Eulerian description, i.e. in the actual deforming configuration,\nformulated in terms of rates. The Kelvin-Voigt rheology or also, in the\ndeviatoric part, the Jeffreys rheology (covering creep or plasticity) are\nconsidered, using the additive Green-Naghdi's decomposition of total strain\ninto the elastic and the inelastic strains formulated in terms of (objective)\nrates exploiting the Zaremba-Jaumann time derivative. A linearized convective\nmodel at large displacements is considered, focusing on the case where the\ninternal energy additively splits the (convex) mechanical and the thermal\nparts. The time-discrete suitably regularized scheme is devised. The numerical\nstability and, considering the multipolar 2nd-grade viscosity, also convergence\ntowards weak solutions are proved, exploiting the convexity of the kinetic\nenergy when written in terms of linear momentum instead of velocity and\nestimating the temperature gradient from the entropy-like inequality.\n"", 'Time discretization in visco-elastodynamics at large displacements and\n  strains in the Eulerian frame   The fully-implicit time discretization (i.e. the backward Euler formula) is\napplied to compressible nonlinear dynamical models of viscoelastic solids in\nthe Eulerian description, i.e. in the actual deforming configuration. The\nKelvin-Voigt rheology or also, in the deviatoric part, the Jeffreys rheology\nare considered. Both a linearized convective model at large displacements with\na convex stored energy and the fully nonlinear large strain variant with a\n(possibly generalized) polyconvex stored energy are considered. The\ntime-discrete suitably regularized schemes are devised for both cases. The\nnumerical stability and, considering the multipolar 2nd-grade viscosity, also\nconvergence towards weak solutions are proved, exploiting the convexity of the\nkinetic energy when written in terms of linear momentum instead of velocity. In\nthe fully nonlinear case, the examples of neo-Hookean and Mooney-Rivlin\nmaterials are presented. A comparison with models of viscoelastic barotropic\nfluids is also made.\n']","[('viscoelasticity', 0.6348318457603455), ('viscoelastic', 0.5943810939788818), ('finite strain', 0.5443146824836731), ('thermomechanics', 0.4738604426383972), ('visco elastic', 0.46004176139831543), ('elastic inelastic', 0.4529677629470825), ('viscous stress', 0.442582905292511), ('elastodynamics', 0.4345169961452484), ('order viscosity', 0.4283181428909302), ('deformation gradient', 0.4199669361114502)]"
1215,1215,24,1215_covariant phase space_spacetime manifold_gauge covariant_covariant,"['covariant phase space', 'spacetime manifold', 'gauge covariant', 'covariant', 'covariant phase', 'hamiltonian formulations', 'general relativity', 'invariant hamiltonian', 'symplectic structures', 'hamiltonian formulation']","['On the on-shell equivalence of general relativity and Holst theories\n  with nonmetricity, torsion, and boundaries   We study a generalization of the Holst action where we admit nonmetricity and\ntorsion in manifolds with timelike boundaries (both in the metric and tetrad\nformalism). We prove that its space of solutions is equal to the one of the\nPalatini action. Therefore, we conclude that the metric sector is in fact\nidentical to GR, which is defined by the Einstein-Hilbert action. We further\nprove that, despite defining the same space of solutions, the Palatini and (the\ngeneralized) Holst Lagrangians are not cohomologically equal. Thus, the\npresymplectic structure and charges provided by the Covariant Phase Space\nmethod might differ. However, using the relative bicomplex framework, we show\nthe covariant phase spaces of both theories are equivalent (and in fact\nequivalent to GR), as well as their charges, clarifying some open problems\nregarding dual charges and their equivalence in different formulations.\n', 'Canonical analysis of $n$-dimensional Palatini action without\n  second-class constraints   We carry out the canonical analysis of the $n$-dimensional Palatini action\nwith or without a cosmological constant $(n\\geq3)$ introducing neither\nsecond-class constraints nor resorting to any gauge fixing. This is\naccomplished by providing an expression for the spatial components of the\nconnection that allows us to isolate the nondynamical variables present among\nthem, which can later be eliminated from the action by using their own equation\nof motion. As a result, we obtain the description of the phase space of general\nrelativity in terms of manifestly $SO(n-1,1)$ [or $SO(n)$] covariant variables\nsubject to first-class constraints only, with no second-class constraints\narising during the process. Afterwards, we perform, at the covariant level, a\ncanonical transformation to a set of variables in terms of which the above\nconstraints take a simpler form. Finally, we impose the time gauge and make\ncontact with the $SO(n-1)$ ADM formalism.\n', 'Canonical analysis of Holst action without second-class constraints   We perform the canonical analysis of the Holst action for general relativity\nwith a cosmological constant without introducing second-class constraints. Our\napproach consists in identifying the dynamical and nondynamical parts of the\ninvolved variables from the very outset. After integrating out the nondynamical\nvariables associated with the connection, we obtain the description of phase\nspace in terms of manifestly $SO(3,1)$ [or $SO(4)$, depending on the signature]\ncovariant canonical variables and first-class constraints only. We impose the\ntime gauge on them and show that the Ashtekar-Barbero formulation of general\nrelativity emerges. Later, we discuss a family of canonical transformations\nthat allows us to construct new $SO(3,1)$ [or $SO(4)$] covariant canonical\nvariables for the phase space of the theory and compare them with the ones\nalready reported in the literature, pointing out the presence of a set of\ncanonical variables not considered before. Finally, we resort to the time gauge\nagain and find that the theory, when written in terms of the new canonical\nvariables, either collapses to the $SO(3)$ ADM formalism or to the\nAshtekar-Barbero formalism with a rescaled Immirzi parameter.\n']","[('covariant phase space', 0.5381215214729309), ('spacetime manifold', 0.5048324465751648), ('gauge covariant', 0.4778590798377991), ('covariant', 0.4763309061527252), ('covariant phase', 0.4742591679096222), ('hamiltonian formulations', 0.4692046046257019), ('general relativity', 0.45342960953712463), ('invariant hamiltonian', 0.3982754349708557), ('symplectic structures', 0.3892677128314972), ('hamiltonian formulation', 0.38912901282310486)]"
1216,1216,24,1216_dominating graph_dominating sets_graph np complete_fault tolerant,"['dominating graph', 'dominating sets', 'graph np complete', 'fault tolerant', 'graph families', 'graphs np', 'np completeness', 'arbitrary graph', 'graph np', 'vertex contains']","['Fault-Tolerant Locating-Dominating sets with Error-correction   A locating-dominating set is a subset of vertices representing ""detectors"" in\na graph G; each detector monitors its closed neighborhood and can distinguish\nits own location from its neighbors, and given all sensor input, the system can\nlocate an ""intruder"" anywhere in the graph. We explore a fault-tolerant variant\nof locating-dominating sets, error-correcting locating-dominating (ERR:LD)\nsets, which can tolerate an incorrect signal from a single detector. In\nparticular, we characterize error-correcting locating-dominating sets, and\nderive its existence criteria. We also prove that the problem of determining\nthe minimum cardinality of ERR:LD set in arbitrary graphs is NP-complete.\nAdditionally, we establish lower and upper bounds for the minimum density of\nERR:LD sets in infinite grids and cubic graphs, and prove the lower bound for\ncubic graphs is sharp.\n', 'On Redundant Locating-Dominating Sets   A locating-dominating set in a graph G is a subset of vertices representing\n""detectors"" which can locate an ""intruder"" given that each detector covers its\nclosed neighborhood and can distinguish its own location from its neighbors. We\nexplore a fault-tolerant variant of locating-dominating sets called redundant\nlocating-dominating sets, which can tolerate one detector malfunctioning (going\noffline or being removed). In particular, we characterize redundant\nlocating-dominating sets and prove that the problem of determining the minimum\ncardinality of a redundant locating-dominating set is NP-complete. We also\ndetermine tight bounds for the minimum density of redundant locating-dominating\nsets in several classes of graphs including paths, cycles, ladders, k-ary\ntrees, and the infinite hexagonal and triangular grids. We find tight lower and\nupper bounds on the size of minimum redundant locating-dominating sets for all\ntrees of order $n$, and characterize the family of trees which achieve these\ntwo extremal values, along with polynomial time algorithms to classify a tree\nas minimum extremal or not.\n', 'Open-locating-dominating sets with error correction   An open-locating-dominating set of a graph models a detection system for a\nfacility with a possible ""intruder"" or a multiprocessor network with a possible\nmalfunctioning processor. A ""sensor"" or ""detector"" is assumed to be installed\nat a subset of vertices where it can detect an intruder or a malfunctioning\nprocessor in their neighborhood, but not at itself. We consider a\nfault-tolerant variant of an open-locating-dominating set called an\nerror-correcting open-locating-dominating set, which can correct a\nfalse-positive or a false-negative signal from a detector. In particular, we\nprove the problem of finding a minimum error-correcting\nopen-locating-dominating set in an arbitrary graph is NP-complete.\nAdditionally, we characterize the existence criteria for an error-correcting\nopen-locating-dominating sets for an arbitrary graph. We also consider extremal\ngraphs that require every vertex to be a detector and minimum error-correcting\nopen-locating-dominating sets in infinite grids.\n']","[('dominating graph', 0.6226393580436707), ('dominating sets', 0.5243601202964783), ('graph np complete', 0.4922983646392822), ('fault tolerant', 0.44258973002433777), ('graph families', 0.439713716506958), ('graphs np', 0.43312034010887146), ('np completeness', 0.4299476146697998), ('arbitrary graph', 0.42047780752182007), ('graph np', 0.4063396155834198), ('vertex contains', 0.4051782786846161)]"
1217,1217,24,1217_multi bubble_bubble_bubbles_conjectures,"['multi bubble', 'bubble', 'bubbles', 'conjectures', 'euclidean spherical', 'voronoi cells', 'surface tensions', 'weighted perimeter', 'conjecture mathbb', 'spherical spaces']","['Stable soap bubble clusters with multiple torus bubbles   In the last two centuries and more particularly in the last decades, the\ngeometry of foams has become an important research domain, in mathematics,\nphysics, material sciences and biology. Most of the simplest geometrical\nobservations of bubble clusters have long resisted rigorous mathematical\nproofs. Geometries can even get more complicated if immiscible fluids are\nconsidered. Although they have to fulfill Plateau\'s laws like soap bubble\nclusters if the surface tensions are close to unity, this is not the case in\ngeneral. In 1996, Frederick J. Almgren asked whether there is ""any stable\ncluster of bubbles in $\\mathbb{R}^3$ with some bubble being topologically a\ntorus"". We propose to answer the latter numerically with simple numerical\nexamples. We build stable soap bubble clusters with a triple torus bubble, a\nfivefold torus bubble or an elevenfold torus bubble. The construction uses the\ngeometry of a simple immiscible fluids cluster with a torus bubble.\n', 'The Structure of Isoperimetric Bubbles on $\\mathbb{R}^n$ and\n  $\\mathbb{S}^n$   The multi-bubble isoperimetric conjecture in $n$-dimensional Euclidean and\nspherical spaces from the 1990\'s asserts that standard bubbles uniquely\nminimize total perimeter among all $q-1$ bubbles enclosing prescribed volume,\nfor any $q \\leq n+2$. The double-bubble conjecture on $\\mathbb{R}^3$ was\nconfirmed in 2000 by Hutchings-Morgan-Ritor\\\'e-Ros, and is nowadays fully\nresolved for all $n \\geq 2$. The double-bubble conjecture on $\\mathbb{S}^2$ and\ntriple-bubble conjecture on $\\mathbb{R}^2$ have also been resolved, but all\nother cases are in general open. We confirm the conjecture on $\\mathbb{R}^n$\nand on $\\mathbb{S}^n$ for all $q \\leq \\min(5,n+1)$, namely: the double-bubble\nconjectures for $n \\geq 2$, the triple-bubble conjectures for $n \\geq 3$ and\nthe quadruple-bubble conjectures for $n \\geq 4$. In fact, we show that for all\n$q \\leq n+1$, a minimizing cluster necessarily has spherical interfaces, and\nafter stereographic projection to $\\mathbb{S}^n$, its cells are obtained as the\nVoronoi cells of $q$ affine-functions, or equivalently, as the intersection\nwith $\\mathbb{S}^n$ of convex polyhedra in $\\mathbb{R}^{n+1}$. Moreover, the\ncells (including the unbounded one) are necessarily connected and intersect a\ncommon hyperplane of symmetry, resolving a conjecture of Heppes. We also show\nfor all $q \\leq n+1$ that a minimizer with non-empty interfaces between all\npairs of cells is necessarily a standard bubble. The proof makes crucial use of\nconsidering $\\mathbb{R}^n$ and $\\mathbb{S}^n$ in tandem and of M\\""obius\ngeometry and conformal Killing fields; it does not rely on establishing a PDI\nfor the isoperimetric profile as in the Gaussian setting, which seems out of\nreach in the present one.\n', 'Plateau Bubbles and the Quintuple Bubble Theorem on $\\mathbb{S}^n$   Sullivan\'s multi-bubble isoperimetric conjectures in $n$-dimensional\nEuclidean and spherical spaces assert that standard bubbles uniquely minimize\ntotal perimeter among all $q-1$ bubbles enclosing prescribed volume, for any $q\n\\leq n+2$. The double-bubble conjecture on $\\mathbb{R}^3$ was confirmed by\nHutchings-Morgan-Ritor\\\'e-Ros (and later extended to $\\mathbb{R}^n$). The\ndouble-bubble conjecture on $\\mathbb{S}^n$ ($n \\geq 2$) and the triple- and\nquadruple- bubble conjectures on $\\mathbb{R}^n$ and $\\mathbb{S}^n$ (for $n \\geq\n3$ and $n \\geq 4$, respectively) were recently confirmed in our previous work,\nbut the approach employed there does not seem to allow extending these results\nfurther.\n  In this work, we confirm the quintuple-bubble conjecture on $\\mathbb{S}^n$\n($n \\geq 5$), and as a consequence, by approximation, also the quintuple-bubble\nconjecture on $\\mathbb{R}^n$ ($n \\geq 5$) but without the uniqueness assertion.\nMoreover, we resolve the conjectures on $\\mathbb{S}^n$ and on $\\mathbb{R}^n$\n(without uniqueness) for all $q \\leq n+1$, conditioned on the assumption that\nthe singularities which appear at the meeting locus of several bubbles obey a\nhigher-dimensional analogue of Plateau\'s laws. Another scenario we can deal\nwith is when the bubbles are full-dimensional (""in general position""), or\narrange in some good lower-dimensional configurations.\n  To this end, we develop the spectral theory of the corresponding Jacobi\noperator (finding analogies with the quantum-graph formalism), and a new method\nfor deforming the bubbles into a favorable configuration. As a by-product, we\nshow that the Jacobi operator on a minimizing configuration always has index\nprecisely $q-1$ and hence the corresponding isoperimetric profile is concave,\nanswering a question of Heppes. Several compelling conjectures are proposed,\nwhich would allow extending our results to all $q \\leq n+1$ unconditionally.\n']","[('multi bubble', 0.5422706604003906), ('bubble', 0.4925667345523834), ('bubbles', 0.49003270268440247), ('conjectures', 0.36918461322784424), ('euclidean spherical', 0.3571856915950775), ('voronoi cells', 0.32275548577308655), ('surface tensions', 0.30892282724380493), ('weighted perimeter', 0.30716660618782043), ('conjecture mathbb', 0.295482337474823), ('spherical spaces', 0.2922765612602234)]"
1218,1218,24,1218_surface contact_droplet spreading_droplets_surface tension,"['surface contact', 'droplet spreading', 'droplets', 'surface tension', 'motion surface', 'droplet', 'rough surface', 'coarsening dynamics', 'surface', 'contact angles']","['Contact angle hysteresis and static friction for two-dimensional\n  droplets   Contact angle hysteresis of droplets will be examined in light of static\nfriction between liquid drop and solid surface. Unlike frictions in solid-solid\ninterfaces, pinning forces at contact points or contact lines would be the\ncause of friction. We will define coefficients of static friction and relate\nthem with advancing and receding contact angles for the case of two-dimensional\ndroplets. In our work sessile drops in an inclined plane, and pendent drops in\na slanted ceiling will all be analyzed within a single framework with the\ninclination angle as a free parameter. We can then visualize the gradual change\nof shapes of a droplet put on a plane as the inclination angle changes\nadiabatically to make a complete turn. We point out that there could be two\ndistinct stable configurations of pendent droplets for the same physical\nconditions, hence dubbed the bifurcation. And in the case of pendent droplets\nwe investigate at what ranges of parameters pinch-offs occur, and find an\ninteresting relation between the fallen-out volume and the Bond number.\n', 'Gradient flow formulation and second order numerical method for motion\n  by mean curvature and contact line dynamics on rough surface   We study the dynamics of a droplet moving on an inclined rough surface in the\nabsence of inertial and viscous stress effects. In this case, the dynamics of\nthe droplet is a purely geometric motion in terms of the wetting domain and the\ncapillary surface. Using a single graph representation, we interpret this\ngeometric motion as a gradient flow on a Hilbert manifold. We propose\nunconditionally stable first/second order numerical schemes to simulate this\ngeometric motion of the droplet, which is described using motion by mean\ncurvature coupled with moving contact lines. The schemes are based on (i)\nexplicit moving boundaries, which decouple the dynamic updates of the contact\nlines and the capillary surface, (ii) a semi-Lagrangian method on moving grids\nand (iii) a predictor-corrector method with a nonlinear elliptic solver upto\nsecond order accuracy. For the case of quasi-static dynamics with continuous\nspatial variable in the numerical schemes, we prove the stability and\nconvergence of the first/second order numerical schemes. To demonstrate the\naccuracy and long-time validation of the proposed schemes, several challenging\ncomputational examples - including breathing droplets, droplets on\ninhomogeneous rough surfaces and quasi-static Kelvin pendant droplets - are\nconstructed and compared with exact solutions to quasi-static dynamics obtained\nby desingularized differential-algebraic system of equations (DAEs).\n', ""Surfactant-dependent contact line dynamics and droplet spreading on\n  textured substrates: derivations and computations   We study spreading of a droplet, with insoluble surfactant covering its\ncapillary surface, on a textured substrate. In this process, the\nsurfactant-dependent surface tension dominates the behaviors of the whole\ndynamics, particularly the moving contact lines. This allows us to derive the\nfull dynamics of the droplets laid by the insoluble surfactant: (i) the moving\ncontact lines, (ii) the evolution of the capillary surface, (iii) the\nsurfactant dynamics on this moving surface with a boundary condition at the\ncontact lines and (iv) the incompressible viscous fluids inside the droplet.\nOur derivations base on Onsager's principle with Rayleigh dissipation\nfunctionals for either the viscous flow inside droplets or the motion by mean\ncurvature of the capillary surface. We also prove the Rayleigh dissipation\nfunctional for viscous flow case is stronger than the one for the motion by\nmean curvature. After incorporating the textured substrate profile, we design a\nnumerical scheme based on unconditionally stable explicit boundary updates and\nmoving grids, which enable efficient computations for many challenging examples\nshowing significant impacts of the surfactant to the deformation of droplets.\n""]","[('surface contact', 0.5386847853660583), ('droplet spreading', 0.49801361560821533), ('droplets', 0.4945325553417206), ('surface tension', 0.48373594880104065), ('motion surface', 0.44640159606933594), ('droplet', 0.41626161336898804), ('rough surface', 0.4104578495025635), ('coarsening dynamics', 0.39793312549591064), ('surface', 0.38284289836883545), ('contact angles', 0.366489052772522)]"
1219,1219,24,1219_pinching antenna_transmit power minimization_antenna assisted_antenna systems,"['pinching antenna', 'transmit power minimization', 'antenna assisted', 'antenna systems', 'flexible antenna', 'antennas', 'antennas can', 'antenna', 'antenna system', 'antenna technology']","[""Energy-Efficient Resource Allocation for NOMA-Assisted Uplink Pinching-Antenna Systems The pinching-antenna architecture has emerged as a promising solution for reconfiguring wireless propagation environments and enhancing system performance. While prior research has primarily focused on sum-rate maximization or transmit power minimization of pinching-antenna systems, the critical aspect of energy efficiency (EE) has received limited attention. Given the increasing importance of EE in future wireless communication networks, this work investigates EE optimization in a non-orthogonal multiple access (NOMA)-assisted multi-user pinching-antenna uplink system. The problem entails the joint optimization of the users' transmit power and the pinching-antenna position. The resulting optimization problem is non-convex due to tightly coupled variables. To tackle this, we employ an alternating optimization framework to decompose the original problem into two subproblems: one focusing on power allocation and the other on antenna positioning. A low-complexity optimal solution is derived for the power allocation subproblem, while the pinching-antenna positioning subproblem is addressed using a particle swarm optimization algorithm to obtain a high-quality near-optimal solution. Simulation results demonstrate that the proposed scheme significantly outperforms both conventional-antenna configurations and orthogonal multiple access-based pinching-antenna systems in terms of EE."", 'Flexible-Antenna Systems: A Pinching-Antenna Perspective   Flexible-antenna systems have recently received significant research interest\ndue to their capability to reconfigure wireless channels intelligently. This\npaper focuses on a new type of flexible-antenna technology, termed pinching\nantennas, which can be realized by applying small dielectric particles on a\nwaveguide. Analytical results are first developed for the simple case with a\nsingle pinching antenna and a single waveguide, where the unique feature of the\npinching-antenna system to create strong line-of-sight links and mitigate\nlarge-scale path loss is demonstrated. An advantageous feature of\npinching-antenna systems is that multiple pinching antennas can be activated on\na single waveguide at no extra cost; however, they must be fed with the same\nsignal. This feature motivates the application of non-orthogonal multiple\naccess (NOMA), and analytical results are provided to demonstrate the superior\nperformance of NOMA-assisted pinching-antenna systems. Finally, the case with\nmultiple pinching antennas and multiple waveguides is studied, which resembles\na classical multiple-input single-input (MISO) interference channel. By\nexploiting the capability of pinching antennas to reconfigure the wireless\nchannel, it is revealed that a performance upper bound on the interference\nchannel becomes achievable, where the achievability conditions are also\nidentified. Computer simulation results are presented to verify the developed\nanalytical results and demonstrate the superior performance of pinching-antenna\nsystems.\n', ""Sum Rate Maximization for NOMA-Assisted Uplink Pinching-Antenna Systems   In this paper, we investigate an uplink communication scenario in which\nmultiple users communicate with an access point (AP) employing non-orthogonal\nmultiple access (NOMA). A pinching antenna, which can be activated at an\narbitrary point along a dielectric waveguide, is deployed at the AP to\ndynamically reconfigure user channels. The objective is to maximize the system\nsum rate by jointly optimizing the pinching-antenna's position and the users'\ntransmit powers. The formulated optimization problem is non-convex, and\naddressed using the particle swarm optimization (PSO) algorithm. For\nperformance benchmarking, two time division multiple access (TDMA) schemes are\nconsidered: one based on the pinching antenna individually activated for each\nuser, and the other based on the single-pinching-antenna configuration serving\nall users. Numerical results demonstrate that the use of the pinching antenna\nsignificantly enhances the system sum rate compared to conventional antenna\narchitectures. Moreover, the NOMA-based scheme outperforms the TDMA-based\nscheme with a single pinching antenna but is outperformed by the TDMA-based\napproach when the pinching antenna is adaptively configured for each user.\nFinally, the proposed PSO-based method is shown to achieve near-optimal\nperformance for both NOMA and TDMA with a common pinching-antenna\nconfiguration.\n""]","[('pinching antenna', 0.579371452331543), ('transmit power minimization', 0.45772573351860046), ('antenna assisted', 0.4486059248447418), ('antenna systems', 0.4183017909526825), ('flexible antenna', 0.4175207316875458), ('antennas', 0.41345182061195374), ('antennas can', 0.40285229682922363), ('antenna', 0.40083956718444824), ('antenna system', 0.3952282965183258), ('antenna technology', 0.393746554851532)]"
1220,1220,24,1220_reflected brownian motion_reflected brownian_reflecting brownian_brownian motions,"['reflected brownian motion', 'reflected brownian', 'reflecting brownian', 'brownian motions', 'reflected diffusions', 'brownian excursion', 'brownian motion two', 'skew brownian motion', 'brownian motion', 'brownian motion non']","['A dual skew symmetry for transient reflected Brownian motion in an\n  orthant   We introduce a transient reflected Brownian motion in a multidimensional\northant, which is either absorbed at the apex of the cone or escapes to\ninfinity. We address the question of computing the absorption probability, as a\nfunction of the starting point of the process. We provide a necessary and\nsufficient condition for the absorption probability to admit an exponential\nproduct form, namely, that the determinant of the reflection matrix is zero. We\ncall this condition a dual skew symmetry. It recalls the famous skew symmetry\nintroduced by Harrison, which characterizes the exponential stationary\ndistributions in the recurrent case. The duality comes from that the partial\ndifferential equation satisfied by the absorption probability is dual to the\none associated with the stationary distribution in the recurrent case.\n', 'Diffusion limits in the quarter plane and non-semimartingale reflected\n  Brownian motion   We consider a continuous-time random walk in the quarter plane for which the\ntransition intensities are constant on each of the four faces $(0,\\infty)^2$,\n$F_1=\\{0\\}\\times(0,\\infty)$, $F_2=(0,\\infty)\\times\\{0\\}$ and $\\{(0,0)\\}$. We\nshow that when rescaled diffusively it converges in law to a Brownian motion\nwith oblique reflection direction $d^{(i)}$ on face $F_i$, $i=1,2$, defined via\nthe Varadhan-Williams submartingale problem. A parameter denoted by $\\alpha$\nwas introduced in \\cite{vw}, measuring the extent to which $d^{(i)}$ are\ninclined toward the origin. In the case of the quarter plane, $\\alpha$ takes\nvalues in $(-2,2)$, and it is known that the reflected Brownian motion is a\nsemimartingale if and only if $\\alpha\\in(-2,1)$. Convergence results via both\nthe Skorohod map and the invariance principle for semimartingale reflected\nBrownian motion are known to hold in various settings in arbitrary dimension.\nIn the case of the quarter plane, the invariance principle was proved for\n$\\alpha \\in (-2,1)$ whereas for tools based on the Skorohod map to be\napplicable it is necessary (but not sufficient) that $\\alpha \\in [-1,1)$.\nAnother tool that has been used to prove convergence in general dimension is\nthe extended Skorohod map, which in the case of the quarter plane provides\nconvergence for $\\alpha=1$. This paper focuses on the range $\\alpha \\in (1,2)$,\nwhere the Skorohod problem and the extended Skorohod problem do not possess a\nunique solution, the limit process is not a semimartingale, and convergence to\nreflected Brownian motion has not been shown before. The result has\nimplications on the asymptotic analysis of two Markovian queueing models: The\n{\\it generalized processor sharing model with parallelization slowdown}, and\nthe {\\it coupled processor model}.\n', 'On the stationary distribution of reflected Brownian motion in a\n  non-convex wedge   We study the stationary reflected Brownian motion in a non-convex wedge,\nwhich, compared to its convex analogue model, has been much rarely analyzed in\nthe probabilistic literature. We prove that its stationary distribution can be\nfound by solving a two dimensional vector boundary value problem (BVP) on a\nsingle curve for the associated Laplace transforms. The reduction to this kind\nof vector BVP seems to be new in the literature. As a matter of comparison, one\nsingle boundary condition is sufficient in the convex case. When the parameters\nof the model (drift, reflection angles and covariance matrix) are symmetric\nwith respect to the bisector line of the cone, the model is reducible to a\nstandard reflected Brownian motion in a convex cone. Finally, we construct a\none-parameter family of distributions, which surprisingly provides, for any\nwedge (convex or not), one particular example of stationary distribution of a\nreflected Brownian motion.\n']","[('reflected brownian motion', 0.6687513589859009), ('reflected brownian', 0.6599191427230835), ('reflecting brownian', 0.6330140829086304), ('brownian motions', 0.5653331875801086), ('reflected diffusions', 0.5562193393707275), ('brownian excursion', 0.5380252599716187), ('brownian motion two', 0.5369512438774109), ('skew brownian motion', 0.5071521997451782), ('brownian motion', 0.5064462423324585), ('brownian motion non', 0.5010724067687988)]"
1221,1221,24,1221_fractional diffusion equations_time fractional diffusion_fractional diffusion_order time fractional,"['fractional diffusion equations', 'time fractional diffusion', 'fractional diffusion', 'order time fractional', 'fractional time', 'fractional differential equations', 'caputo fractional derivative', 'fractional derivatives', 'fractional differential', 'fractional derivative']","['Efficient numerical method for multi-term time-fractional diffusion\n  equations with Caputo-Fabrizio derivatives   In this paper, we consider a numerical method for the multi-term\nCaputo-Fabrizio time-fractional diffusion equations (with orders\n$\\alpha_i\\in(0,1)$, $i=1,2,\\cdots,n$). The proposed method employs a fast\nfinite difference scheme to approximate multi-term fractional derivatives in\ntime, requiring only $O(1)$ storage and $O(N_T)$ computational complexity,\nwhere $N_T$ denotes the total number of time steps. Then we use a Legendre\nspectral collocation method for spatial discretization. The stability and\nconvergence of the scheme have been thoroughly discussed and rigorously\nestablished. We demonstrate that the proposed scheme is unconditionally stable\nand convergent with an order of $O(\\left(\\Delta t\\right)^{2}+N^{-m})$, where\n$\\Delta t$, $N$, and $m$ represent the timestep size, polynomial degree, and\nregularity in the spatial variable of the exact solution, respectively.\nNumerical results are presented to validate the theoretical predictions.\n', 'Robust fast method for variable-order time-fractional diffusion\n  equations without regularity assumptions   In this paper, we develop a robust fast method for mobile-immobile\nvariable-order (VO) time-fractional diffusion equations (tFDEs), superiorly\nhandling the cases of small or vanishing lower bound of the VO function. The\nvalid fast approximation of the VO Caputo fractional derivative is obtained\nusing integration by parts and the exponential-sum-approximation method.\nCompared with the general direct method, the proposed algorithm ($RF$-$L1$\nformula) reduces the acting memory from $\\mathcal{O}(n)$ to $\\mathcal{O}(\\log^2\nn)$ and computational cost from $\\mathcal{O}(n^2)$ to $\\mathcal{O}(n \\log^2\nn)$, respectively, where $n$ is the number of time levels. Then $RF$-$L1$\nformula is applied to construct the fast finite difference scheme for the VO\ntFDEs, which sharp decreases the memory requirement and computational\ncomplexity. The error estimate for the proposed scheme is studied only under\nsome assumptions of the VO function, coefficients, and the source term, but\nwithout any regularity assumption of the true solutions. Numerical experiments\nare presented to verify the effectiveness of the proposed method.\n', 'Exponential-sum-approximation technique for variable-order\n  time-fractional diffusion equations   In this paper, we study the variable-order (VO) time-fractional diffusion\nequations. For a VO function $\\alpha(t)\\in(0,1)$, we develop an\nexponential-sum-approximation (ESA) technique to approach the VO Caputo\nfractional derivative. The ESA technique keeps both the quadrature exponents\nand the number of exponentials in the summation unchanged at the different time\nlevels. Approximating parameters are properly selected to achieve efficient\naccuracy. Compared with the general direct method, the proposed method reduces\nthe storage requirement from $\\mathcal{O}(n)$ to $\\mathcal{O}(\\log^2 n)$ and\nthe computational cost from $\\mathcal{O}(n^2)$ to $\\mathcal{O}(n\\log^2 n)$,\nrespectively, with $n$ being the number of the time levels. When this fast\nalgorithm is exploited to construct a fast ESA scheme for the VO\ntime-fractional diffusion equations, the computational complexity of the\nproposed scheme is only of $\\mathcal{O}(mn\\log^2 n)$ with\n$\\mathcal{O}(m\\log^2n)$ storage requirement, where $m$ denotes the number of\nspatial grids. Theoretically, the unconditional stability and error analysis of\nthe fast ESA scheme are given. The effectiveness of the proposed algorithm is\nverified by numerical examples.\n']","[('fractional diffusion equations', 0.6529850959777832), ('time fractional diffusion', 0.6499508619308472), ('fractional diffusion', 0.627357542514801), ('order time fractional', 0.5435555577278137), ('fractional time', 0.5182042717933655), ('fractional differential equations', 0.5065163969993591), ('caputo fractional derivative', 0.502352237701416), ('fractional derivatives', 0.4955143630504608), ('fractional differential', 0.479607492685318), ('fractional derivative', 0.47725939750671387)]"
1222,1222,24,1222_invariant gibbs measures_invariance gibbs measure_gibbs measures associated_gibbs measures,"['invariant gibbs measures', 'invariance gibbs measure', 'gibbs measures associated', 'gibbs measures', 'gibbs measure', 'construction gibbs measures', 'invariance gibbs', 'invariant gibbs', 'construction gibbs', 'construct gibbs']","['Gibbs measure for the focusing fractional NLS on the torus   We study the construction of the Gibbs measures for the {\\it focusing}\nmass-critical fractional nonlinear Schr\\""odinger equation on the\nmulti-dimensional torus. We identify the sharp mass threshold for\nnormalizability and non-normalizability of the focusing Gibbs measures, which\ngeneralizes the influential works of Lebowitz-Rose-Speer (1988), Bourgain\n(1994), and Oh-Sosoe-Tolomeo (2021) on the one-dimensional nonlinear\nSchr\\""odinger equations. To this purpose, we establish an almost sharp\nfractional Gagliardo-Nirenberg-Sobolev inequality on the torus, which is of\nindependent interest.\n', 'Invariant Gibbs measures for the three-dimensional wave equation with a\n  Hartree nonlinearity I: Measures   In this two-paper series, we prove the invariance of the Gibbs measure for a\nthree-dimensional wave equation with a Hartree nonlinearity. The main novelty\nis the singularity of the Gibbs measure with respect to the Gaussian free\nfield. The singularity has several consequences in both measure-theoretic and\ndynamical aspects of our argument.\n  In this paper, we construct and study the Gibbs measure. Our approach is\nbased on earlier work of Barashkov and Gubinelli for the $\\Phi^4_3$-model. Most\nimportantly, our truncated Gibbs measures are tailored towards the dynamical\naspects in the second part of the series. In addition, we develop new tools\ndealing with the non-locality of the Hartree interaction. We also determine the\nexact threshold between singularity and absolute continuity of the Gibbs\nmeasure depending on the regularity of the interaction potential.\n', ""A remark on Gibbs measures with log-correlated Gaussian fields   We study Gibbs measures with log-correlated base Gaussian fields on the\n$d$-dimensional torus. In the defocusing case, the construction of such Gibbs\nmeasures follows from Nelson's argument. In this paper, we consider the\nfocusing case with a quartic interaction. Using the variational formulation, we\nprove non-normalizability of the Gibbs measure. When $d = 2$, our argument\nprovides an alternative proof of the non-normalizability result for the\nfocusing $\\Phi^4_2$-measure by Brydges and Slade (1996). Furthermore, we\nprovide a precise rate of divergence, where the constant is characterized by\nthe optimal constant for a certain Bernstein's inequality on $\\mathbb{R}^d$. We\nalso go over the construction of the focusing Gibbs measure with a cubic\ninteraction. In the appendices, we present (a) non-normalizability of the Gibbs\nmeasure for the two-dimensional Zakharov system and (b) the construction of\nfocusing quartic Gibbs measures with smoother base Gaussian measures, showing a\ncritical nature of the log-correlated Gibbs measure with a focusing quartic\ninteraction.\n""]","[('invariant gibbs measures', 0.6704010963439941), ('invariance gibbs measure', 0.6553173661231995), ('gibbs measures associated', 0.6514292359352112), ('gibbs measures', 0.6473389267921448), ('gibbs measure', 0.6231208443641663), ('construction gibbs measures', 0.6085342168807983), ('invariance gibbs', 0.5966457724571228), ('invariant gibbs', 0.5732885599136353), ('construction gibbs', 0.4378754794597626), ('construct gibbs', 0.41507747769355774)]"
1223,1223,24,1223_rankin selberg integrals_rankin selberg integral_selberg integrals_rankin selberg,"['rankin selberg integrals', 'rankin selberg integral', 'selberg integrals', 'rankin selberg', 'selberg integral', 'automorphic representations', 'mathrm gl _2', 'automorphic functions', 'cuspidal automorphic', 'forms mathrm gl']","[""The unramified computation of a Shimura integral for\n  $\\mathrm{SL}(2)\\times \\mathrm{GL}(2)$   In this note, we revisit the Rankin-Selberg integral of Shimura type for\ngeneric representations of $\\mathrm{SL}_2\\times \\mathrm{GL}_2$, constructed by\nGinzburg, Rallis, and Soudry. We give a different and more ``intrinsic'' proof\nof the unramified computation. In contrast to their proof we avoid local\nfunctional equation for the general linear groups but use the Casselman-Shalika\nformulas for unramified Whittaker functions for $\\mathrm{SL}_2$ and\n$\\mathrm{GL}_2$.\n"", ""On Rankin-Selberg integral structures and Euler systems for\n  $\\mathrm{GL}_2\\times \\mathrm{GL}_2$   We study how Rankin-Selberg periods interact with integral structures in\nspherical Whittaker type representations. Using this representation-theoretic\nframework, we show that the local Euler factors appearing in the construction\nof the motivic Rankin-Selberg Euler system for a product of modular forms are\nintegrally optimal; i.e. any construction of this type with any choice of\nintegral input data would give local factors appearing in tame norm relations\nat $p$ which are integrally divisible by the Euler factor\n$\\mathcal{P}_p^{'}(\\mathrm{Frob}_p^{-1})$ modulo $p-1$.\n"", 'Integrality of $\\mathrm{GL}_2\\times\\mathrm{GL}_2$ Rankin-Selberg\n  integrals for ramified representations   Let $\\pi_1,\\pi_2$ be irreducible admissible generic tempered representations\nof $\\mathrm{GL}_2(F)$ for some $p$-adic field $F$ of odd residue\ncharacteristic. We introduce a natural notion of general\n$(\\pi_1\\times\\pi_2)$-integral data $(\\phi,g_1,g_2)\\in\n\\mathcal{S}(F^2)\\times\\mathrm{GL}_2(F)^2$ at which the Rankin-Selberg integral\ncan be evaluated. This is inspired by work of Loeffler, and previous work of\nthe author, on unramified zeta integrals. We then establish an integral variant\nof a result of Jacquet-Langlands for the local Rankin-Selberg zeta integral\nassociated to $\\pi_1\\times\\pi_2$; i.e. we show that for any such integral datum\n$(\\phi,g_1,g_2)$, we have\n$$\\frac{Z(\\phi,g_1W_{\\pi_1}^\\mathrm{new},g_2W_{\\pi_2}^\\mathrm{new};s)}{L(\\pi_1\\times\\pi_2,s)}=\\Phi(\\phi,g_1W_{\\pi_1}^\\mathrm{new},g_2W_{\\pi_2}^\\mathrm{new};q^s)\\in\n\\mathbf{Z}[q^{-1},\\Sigma^1][q^s,q^{-s}]$$for a finite set\n$\\Sigma^1\\subseteq\\mathbf{C}^\\times$ of roots of unity and unitary character\nvalues, depending only on $\\pi_1,\\pi_2$. This is compatible with the notion of\nintegrality coming from newforms $f_1,f_2$ of even integral weights, satisfying\na mild local dihedral condition at $2$. We show that if $\\pi_1,\\pi_2$ are local\npieces of $f_1,f_2$ at any prime $p$, the coefficient algebra is\n$\\mathcal{O}_{K}[p^{-1}]$ with $K$ a number field only depending on $f_1,f_2$.\nOur approach relies on a reinterpretation of the local Rankin-Selberg integral,\nand works of Assing and Saha on values of $p$-adic Whittaker new-vectors.\n']","[('rankin selberg integrals', 0.7267246842384338), ('rankin selberg integral', 0.6730587482452393), ('selberg integrals', 0.6006088852882385), ('rankin selberg', 0.5791500210762024), ('selberg integral', 0.5233606696128845), ('automorphic representations', 0.5064470767974854), ('mathrm gl _2', 0.48910224437713623), ('automorphic functions', 0.4674992561340332), ('cuspidal automorphic', 0.45896559953689575), ('forms mathrm gl', 0.43831896781921387)]"
1224,1224,24,1224_uniform roe algebra_roe algebras_roe algebra_continuous field algebras,"['uniform roe algebra', 'roe algebras', 'roe algebra', 'continuous field algebras', 'algebras operators', 'local algebras', 'algebras metric', 'uniform roe', 'cartan subalgebras', 'algebras isomorphic']","['Bounded Derivations on Uniform Roe Algebras   We show that if $C_u^*(X)$ is a uniform Roe algebra associated to a bounded\ngeometry metric space X, then all bounded derivations on $C^*_u(X)$ are inner.\n', ""Cartan subalgebras in uniform Roe algebras   In this paper we study structural and uniqueness questions for Cartan\nsubalgebras of uniform Roe algebras. We characterise when an inclusion\n$B\\subseteq A$ of $\\mathrm{C}^*$-algebras is isomorphic to the canonical\ninclusion of $\\ell^\\infty(X)$ inside a uniform Roe algebra $C^*_u(X)$\nassociated to a metric space of bounded geometry. We obtain uniqueness results\nfor `Roe Cartans' inside uniform Roe algebras up to automorphism when $X$\ncoarsely embeds into Hilbert space, and up to inner automorphism when $X$ has\nproperty A.\n"", 'On the uniform Roe algebra as a Banach algebra and embeddings of\n  $\\ell_p$ uniform Roe algebras   We work on $\\ell_p$ uniform Roe algebras associated to metric spaces, and on\ntheir mutual embedding. We generalize results of I. Farah and the authors to\nmutual embeddings of uniform Roe algebras of operators on $\\ell_p$ spaces.\nSimultaneously, we obtain rigidity results for the classic uniform Roe\n$\\mathrm{C}^*$-algebras which depend only on their Banach algebra structure.\n']","[('uniform roe algebra', 0.6936852335929871), ('roe algebras', 0.6150801181793213), ('roe algebra', 0.5343520045280457), ('continuous field algebras', 0.5123984813690186), ('algebras operators', 0.4755978584289551), ('local algebras', 0.44836926460266113), ('algebras metric', 0.44465968012809753), ('uniform roe', 0.43330636620521545), ('cartan subalgebras', 0.43304041028022766), ('algebras isomorphic', 0.4210745394229889)]"
1225,1225,24,1225_hodge conjecture_conjecture hodge_abelian surfaces_abelian fourfolds,"['hodge conjecture', 'conjecture hodge', 'abelian surfaces', 'abelian fourfolds', 'hodge structures', 'integral hodge', 'abelian varieties', 'abelian surface', 'adic hodge theory', 'abelian variety']","['Failure of the integral Hodge conjecture for threefolds of Kodaira\n  dimension zero   We prove that the product of an Enriques surface and a very general curve of\ngenus at least 1 does not satisfy the integral Hodge conjecture for 1-cycles.\nThis provides the first examples of smooth projective complex threefolds of\nKodaira dimension zero for which the integral Hodge conjecture fails, and the\nfirst examples of non-algebraic torsion cohomology classes of degree 4 on\nsmooth projective complex threefolds.\n', 'On the integral Hodge conjecture for real abelian threefolds   We prove the real integral Hodge conjecture for several classes of real\nabelian threefolds. For instance, we prove the property for real abelian\nthreefolds $A$ whose real locus $A(\\mathbb R)$ is connected, and for real\nabelian threefolds $A$ which are a product $A = B \\times E$ of an abelian\nsurface $B$ and an elliptic curve $E$ with connected real locus $E(\\mathbb R)$.\nMoreover, we show that every real abelian threefold satisfies the real integral\nHodge conjecture modulo torsion, and reduce the general case to the Jacobian\ncase.\n', 'On the integral Hodge conjecture for real varieties, II   We establish the real integral Hodge conjecture for 1-cycles on various\nclasses of uniruled threefolds (conic bundles, Fano threefolds with no real\npoint, some del Pezzo fibrations) and on conic bundles over higher-dimensional\nbases which themselves satisfy the real integral Hodge conjecture for 1-cycles.\nIn addition, we show that rationally connected threefolds over non-archimedean\nreal closed fields do not satisfy the real integral Hodge conjecture in general\nand that over such fields, Br\\""ocker\'s EPT theorem remains true for simply\nconnected surfaces of geometric genus zero but fails for some K3 surfaces.\n']","[('hodge conjecture', 0.6788614988327026), ('conjecture hodge', 0.6679123640060425), ('abelian surfaces', 0.593530535697937), ('abelian fourfolds', 0.5636463165283203), ('hodge structures', 0.5567355751991272), ('integral hodge', 0.5521510243415833), ('abelian varieties', 0.5477814674377441), ('abelian surface', 0.5374525189399719), ('adic hodge theory', 0.5344182848930359), ('abelian variety', 0.5216183066368103)]"
1226,1226,24,1226_lattice gauge theory_gibbs measures_phase transition random_lattice gauge,"['lattice gauge theory', 'gibbs measures', 'phase transition random', 'lattice gauge', 'gibbs measure', 'percolation mathbb', 'gibbs states', 'potts models', 'transition random', 'renormalization']","['Structure of Gibbs measures for planar FK-percolation and Potts models   We prove that all Gibbs measures of the $q$-state Potts model on\n$\\mathbb{Z}^2$ are linear combinations of the extremal measures obtained as\nthermodynamic limits under free or monochromatic boundary conditions. In\nparticular all Gibbs measures are invariant under translations. This statement\nis new at points of first-order phase transition, that is at $T=T_{c}(q)$ when\n$q>4$. In this case the structure of Gibbs measures is the most complex in the\nsense that there exist $q+1$ distinct extremal measures.\n  Most of the work is devoted to the FK-percolation model on $\\mathbb{Z}^{2}$\nwith $q\\geq 1$, where we prove that every Gibbs measure is a linear combination\nof the free and wired ones. The arguments are non-quantitative and follow the\nspirit of the seminal works of Aizenman and Higuchi, which established the\nGibbs structure for the two-dimensional Ising model. Infinite-range\ndependencies in FK-percolation (i.e., a weaker spatial Markov property) pose\nserious additional difficulties compared to the case of the Ising model. For\nexample, it is not automatic, albeit true, that thermodynamic limits are Gibbs.\nThe result for the Potts model is then derived using the Edwards-Sokal coupling\nand auto-duality. The latter ingredient is necessary since applying the\nEdwards-Sokal procedure to a Gibbs measure for the Potts model does not\nautomatically produce a Gibbs measure for FK-percolation.\n  Finally, the proof is generic enough to adapt to the FK-percolation and Potts\nmodels on the triangular and hexagonal lattices and to the loop $O(n)$ model in\nthe range of parameters for which its spin representation is positively\nassociated.\n', 'Topological Phases in the Plaquette Random-Cluster Model and Potts\n  Lattice Gauge Theory   The $i$-dimensional plaquette random-cluster model on a finite cubical\ncomplex is the random complex of $i$-plaquettes with each configuration having\nprobability proportional to $$p^{\\text{# of plaquettes}}(1-p)^{\\text{# of\ncomplementary plaquettes}}q^{\\mathbf{ b}_{i-1}},$$ where $q\\geq 1$ is a real\nparameter and $\\mathbf{b}_{i-1}$ denotes the rank of the $(i-1)$-homology group\nwith coefficients in a specified coefficient field. When $q$ is prime and the\ncoefficient field is $\\mathbb{F}_q$, this model is coupled with the\n$(i-1)$-dimensional $q$-state Potts lattice gauge theory. We prove that the\nprobability that an $(i-1)$-cycle in $\\mathbb{Z}^d$ is null-homologous in the\nplaquette random-cluster model equals the expectation of the corresponding\ngeneralized Wilson loop variable. This provides the first rigorous\njustification for a claim of Aizenman, Chayes, Chayes, Fr\\""olich, and Russo\nthat there is an exact relationship between Wilson loop variables and the event\nthat a loop is bounded by a surface in an interacting system of plaquettes. We\nalso prove that the $i$-dimensional plaquette random-cluster model on the\n$2i$-dimensional torus exhibits a sharp phase transition at the self-dual point\n$p_{\\mathrm{sd}} \\mathrel{\\vcenter{:}}= \\frac{\\sqrt{q}}{1+\\sqrt{q}}$ in the\nsense of homological percolation. This implies a qualitative change in the\ngeneralized Swendsen--Wang dynamics from local to non-local behavior.\n', 'A Sharp Deconfinement Transition for Potts Lattice Gauge Theory in\n  Codimension Two   In 1983, Aizenman, Chayes, Chayes, Fr\\""ohlich, and Russo proved that\n$2$-dimensional Bernoulli plaquette percolation in $\\mathbb{Z}^3$ exhibits a\nsharp phase transition for the event that a large rectangular loop is ""bounded\nby a surface of plaquettes.\'\' We extend this result both to $(d-1)$-dimensional\nplaquette percolation in $\\mathbb{Z}^d,$ and to a dependent model of plaquette\npercolation called the plaquette random-cluster model. As a consequence, we\nobtain a sharp phase transition for Wilson loop expectations in\n$(d-2)$-dimensional $q$-state Potts hyperlattice gauge theory on $\\mathbb{Z}^d$\ndual to that of the Potts model. Our proof is unconditional for Ising lattice\ngauge theory, but relies on a regularity conjecture for the random-cluster\nmodel in slabs when $q>2.$ We also further develop the general theory of the\n$i$-plaquette random cluster model and its relationship with\n$(i-1)$-dimensional Potts lattice gauge\n']","[('lattice gauge theory', 0.5197277665138245), ('gibbs measures', 0.4527706205844879), ('phase transition random', 0.45052531361579895), ('lattice gauge', 0.4335213303565979), ('gibbs measure', 0.43222659826278687), ('percolation mathbb', 0.4279134273529053), ('gibbs states', 0.4069472849369049), ('potts models', 0.36479416489601135), ('transition random', 0.3479364514350891), ('renormalization', 0.343686580657959)]"
1227,1227,24,1227_optical wireless communication_optical communication_optical wireless_bit error rate,"['optical wireless communication', 'optical communication', 'optical wireless', 'bit error rate', 'space optical fso', 'ratio snr', 'noise ratio snr', 'wireless', 'average bit error', 'optical fso']","['Multiple RIS-Assisted Mixed FSO-RF Transmission Over Generalized Fading\n  Channels   In this paper, we analyze the performance of a reconfigurable intelligent\nsurface (RIS)-assisted multi-hop transmission by employing multiple RIS units\nto enable favorable communication for a mixed free-space optical (FSO) and\nradio-frequency (RF) system. We consider a single-element RIS since it is hard\nto realize phase compensation for multiple-element RIS in the multi-hop\nscenario. We develop statistical results for the product of the signal-to-noise\nratio (SNR) of the cascaded multiple RIS-equipped wireless communication. We\nuse decode-and-forward (DF) and fixed-gain (FG) relaying protocols to mix\nmulti-RIS transmissions over RF and FSO technologies and derive probability\ndensity and distribution functions for both the relaying schemes by considering\nindependent and nonidentical double generalized gamma (dGG) distribution models\nfor RF transmissions with line-of-sight (LOS) and inverse-Gamma shadowing\neffect and atmospheric turbulence for FSO system combined with pointing errors.\nWe analyze the outage probability, and average bit-error rate (BER) performance\nof the considered system. We also present an asymptotic analysis of the outage\nprobability using gamma functions to provide insight into the considered system\nin the high SNR regime. We use computer simulations to validate the derived\nanalytical expressions and demonstrate the performance for different system\nparameters on the RIS-assisted multi-hop transmissions for a vehicular\ncommunication system.\n', 'Unified Performance Assessment of Optical Wireless Communication over\n  Multi-Layer Underwater Channels   In this paper, we model the multi-layer vertical underwater link as a\ncascaded channel and unify the performance analysis for the underwater optical\ncommunication (UWOC) system using generalized Gamma (GG), exponential GG (EGG),\nexponentiated Weibull (EW), and Gamma-Gamma ({\\Gamma}{\\Gamma}) oceanic\nturbulence models. We derive unified analytical expressions for probability\ndensity function (PDF) and cumulative distribution function (CDF) for the\nsignal-to-noise ratios (SNR) considering independent and non-identical\n(i.ni.d.) turbulent models and zero bore-sight model for pointing errors. We\ndevelop performance metrics of the considered UWOC system using outage\nprobability, average bit error rate (BER), and ergodic capacity with asymptotic\nexpressions for outage probability and average BER. We develop the diversity\norder of the proposed system to provide a better insight into the system\nperformance at a high SNR. We also integrate a terrestrial OWC (TOWC) subjected\nto the combined effect of generalized Malaga atmospheric turbulence,\nfog-induced random path gain, and pointing errors to communicate with the UWOC\nlink using the fixed-gain amplify-and-forward (AF) relaying. We analyze the\nperformance of the mixed TWOC and multi-layer UWOC system by deriving PDF, CDF,\noutage probability, and average BER using the bivariate Fox H-function. We use\nMonte-Carlo simulation results to validate our exact and asymptotic expressions\nand demonstrate the performance of the considered underwater UWOC system using\nmeasurement-based parametric data available for turbulent oceanic channels.\n', 'Multihop RIS-Assisted FSO-RF System Over Double Generalized Gamma Fading   Reconfigurable intelligent surface (RIS) is a promising technology to avoid\nsignal blockage by creating virtual line-of-sight (LOS) connectivity for\nfree-space optical (FSO) and radio frequency (RF) wireless systems. This paper\nconsiders a mixed FSO-RF system by employing multiple RISs in both the links\nfor multihop transmissions to extend the communication range. We develop\nprobability density function (PDF) and cumulative density function (CDF) of the\nsignal-to-noise ratio (SNR) for the cascaded channels by considering double\ngeneralized gamma (dGG) turbulence with pointing errors for the FSO link and\nthe dGG distribution to model the signal fading for the RF. We derive exact\nclosed-form expressions of the outage probability, average bit-error-rate\n(BER), and ergodic capacity using the decode-and-forward (DF) relaying for the\nmixed system. We also present asymptotic analysis on the performance in the\nhigh SNR regime depicting the impact of channel parameters on the diversity\norder of the system. We use computer simulations to demonstrate the effect of\nsystem and channel parameters on the RIS-aided multihop transmissions.\n']","[('optical wireless communication', 0.45905283093452454), ('optical communication', 0.4243645668029785), ('optical wireless', 0.3651110827922821), ('bit error rate', 0.335473895072937), ('space optical fso', 0.32261961698532104), ('ratio snr', 0.29826265573501587), ('noise ratio snr', 0.2960875928401947), ('wireless', 0.2919078767299652), ('average bit error', 0.29150447249412537), ('optical fso', 0.28369271755218506)]"
1228,1228,24,1228_curve shortening flow_flow closed curves_elastic flow_flow curves,"['curve shortening flow', 'flow closed curves', 'elastic flow', 'flow curves', 'flow elastic', 'shortening flow', 'curve shortening', 'planar curves', 'gradient flow', 'motion curvature']","[""Length-constrained, length-penalised and free elastic flows of planar\n  curves inside cones   We study families of smooth, embedded, regular planar curves $ \\alpha : \\left\n[-1,1 \\right ]\\times \\left [0,T \\right )\\to \\mathbb{R}^{2}$ with generalised\nNeumann boundary conditions inside cones, satisfying three variants of the\nfourth-order nonlinear $L^2$- gradient flow for the elastic energy: (1) elastic\nflow with a length penalisation, (2) elastic flow with fixed length and (3) the\nunconstrained or `free' elastic flow. Assuming neither end of the evolving\ncurve reaches the cone tip, existence of smooth solutions for all time given\nquite general initial data is well known, but classification of limiting shapes\nis generally not known. For cone angles not too large and with suitable\nsmallness conditions on the $L^2$-norm of the first arc length derivative of\ncurvature of the initial curve, we prove in cases (1) and (2) smooth\nexponential convergence of solutions in the $C^\\infty$-topology to particular\ncircular arcs, while in case (3), we show smooth convergence to an expanding\nself-similar arc.\n"", ""The free elastic flow for closed planar curves The free elastic flow is the $L^2$-gradient flow for Euler's elastic energy, or equivalently the Willmore flow with translation invariant initial data. In contrast to elastic flows under length penalisation or preservation, it is more challenging to study the free elastic flow's asymptotic behavior, and convergence for closed curves is lost. In this paper, we nevertheless determine the asymptotic shape of the flow for initial curves that are geometrically close to circles, possibly multiply-covered, proving that an appropriate rescaling smoothly converges to a unique round circle."", ""A new energy method for shortening and straightening complete curves We introduce a novel energy method that reinterprets ``curve shortening'' as ``tangent aligning''. This conceptual shift enables the variational study of infinite-length curves evolving by the curve shortening flow, as well as higher order flows such as the elastic flow, which involves not only the curve shortening but also the curve straightening effect. For the curve shortening flow, we prove convergence to a straight line under mild assumptions on the ends of the initial curve. For the elastic flow, we establish a global well-posedness theory, and investigate the precise long-time behavior of solutions. In fact, our method applies to a more general class of geometric evolution equations including the surface diffusion flow, Chen's flow, and the free elastic flow.""]","[('curve shortening flow', 0.6691074371337891), ('flow closed curves', 0.6342884302139282), ('elastic flow', 0.6075778603553772), ('flow curves', 0.586857795715332), ('flow elastic', 0.5654019713401794), ('shortening flow', 0.5084022879600525), ('curve shortening', 0.4996558427810669), ('planar curves', 0.48640596866607666), ('gradient flow', 0.4820237457752228), ('motion curvature', 0.47930094599723816)]"
1229,1229,24,1229_robin boundary conditions_dirichlet boundary conditions_dirichlet boundary condition_boundary conditions one,"['robin boundary conditions', 'dirichlet boundary conditions', 'dirichlet boundary condition', 'boundary conditions one', 'boundary conditions', 'boundary problems', 'dirichlet boundary', 'problems dirichlet boundary', 'robin boundary', 'generalized laplacian']","['Extremizing Temperature Functions of Rods with Robin Boundary Conditions   We compare the solutions of two one-dimensional Poisson problems on an\ninterval with Robin boundary conditions, one with given data, and one where the\ndata has been symmetrized. When the Robin parameter is positive and the\nsymmetrization is symmetric decreasing rearrangement, we prove that the\nsolution to the symmetrized problem has larger increasing convex means. When\nthe Robin parameter equals zero (so that we have Neumann boundary conditions)\nand the symmetrization is decreasing rearrangement, we similarly show that the\nsolution to the symmetrized problem has larger convex means.\n', 'Comparison results for solutions to p-Laplace equations with Robin\n  boundary conditions   In the last decades comparison results of Talenti type for Elliptic Problems\nwith Dirichlet boundary conditions have been widely investigated. In this\npaper, we generalize the results obtained in arXiv:1909.11950 to the case of\np-Laplace operator with Robin boundary conditions. The point-wise comparison,\nobtained in arXiv:1909.11950 only in the planar case, holds true in any\ndimension if p is sufficiently small.\n', 'A Talenti comparison result for solutions to elliptic problems with\n  Robin boundary conditions   Comparison results of Talenti type for Elliptic Problems with Dirichlet\nboundary conditions have been widely investigated in the last decades. In this\npaper, we deal with Robin boundary conditions. Surprisingly, contrary to the\nDirichlet case, Robin boundary conditions make the comparison sensitive to the\ndimension, and while the planar case seems to be completely settled, in higher\ndimensions some open problems are yet unsolved.\n']","[('robin boundary conditions', 0.6961143612861633), ('dirichlet boundary conditions', 0.6282641887664795), ('dirichlet boundary condition', 0.6069715619087219), ('boundary conditions one', 0.6006466746330261), ('boundary conditions', 0.5961693525314331), ('boundary problems', 0.5542756915092468), ('dirichlet boundary', 0.5400497317314148), ('problems dirichlet boundary', 0.5391082763671875), ('robin boundary', 0.5235931873321533), ('generalized laplacian', 0.5155669450759888)]"
1230,1230,24,1230_fractional brownian motion_fractional stochastic_stochastic fractional_fractional brownian,"['fractional brownian motion', 'fractional stochastic', 'stochastic fractional', 'fractional brownian', 'discretization stochastic', 'brownian motion hurst', 'fractional diffusion', 'fractional gaussian noise', 'approximation stochastic', 'nonlinear fractional diffusion']","['Strong convergence of an fractional exponential integrator scheme for\n  the finite element discretization of time-fractional SPDE driven by standard\n  and fractional Brownian motions   The aim of this work is to provide the first strong convergence result of\nnumerical approximation of a general time-fractional second order stochastic\npartial differential equation involving a Caputo derivative in time of order\n$\\alpha\\in(\\frac 12; 1)$ and driven simultaneously by a multiplicative standard\nBrownian motion and additive fBm with Hurst parameter $H\\in(\\frac 12, 1)$, more\nrealistic to model the random effects on transport of particles in medium with\nthermal memory. We prove the existence and uniqueness results and perform the\nspatial discretization using the finite element and the temporal discretization\nusing a fractional exponential integrator scheme. We provide the temporal and\nspatial convergence proofs for our fully discrete scheme and the result shows\nthat the convergence orders depend on the regularity of the initial data, the\npower of the fractional derivative, and the Hurst parameter $H$.\n', 'Strong convergence of some Magnus-type schemes for the finite element\n  discretization of non-autonomous parabolic SPDEs driven by additive\n  fractional Brownian motion and Poisson random measure   The aim of this work is to provide the strong convergence results of\nnumerical approximations of a general second order non-autonomous semilinear\nstochastic partial differential equation (SPDE) driven simultaneously by an\nadditive fractional Brownian motion (fBm) with Hurst parameter H \\in (1/2,1)\nand a Poisson random measure, more realistic in modelling real world phenomena.\n  Approximations in space are performed by the standard finite element method\nand in time by the stochastic Magnus-type integrator or the linear\nsemi-implicit Euler method. We investigate the mean-square errors estimates of\nour fully discrete schemes and the results show how the convergence orders\ndepend on the regularity of the initial data and the driven processes. To the\nbest of our knowledge, these two schemes are the first numerical methods to\napproximate the non-autonomous semilinear stochastic partial differential\nequation (SPDE) driven simultaneously by an additive fractional Brownian motion\nwith Hurst parameter H and a Poisson random measure.\n', 'Optimal strong convergence rates of some Euler-type timestepping schemes\n  for the finite element discretization SPDEs driven by additive fractional\n  Brownian motion and Poisson random measure   In this paper, we study the numerical approximation of a general second order\nsemilinear stochastic partial differential equation (SPDE) driven by a additive\nfractional Brownian motion (fBm) with Hurst parameter $H>\\frac 12$ and Poisson\nrandom measure, more realistic in modelling real world phenomena. To the best\nof our knowledge, numerical schemes for such SPDE have been lacked in\nscientific literature. The approximation is done with the standard finite\nelement method in space and three Euler-type timestepping methods in time, more\nprecisely\n  linear implicit method, exponential integrator and exponential Rosenbrock\nscheme are used for time discretisation.\n  In contract to the current literature in the field for SPDE driven only by\nfBm, our linear operator is not necessary self-adjoint and optimal strong\nconvergence rates have been achieved for SPDE driven only by fBm and SPDE\ndriven by fBm and Poisson measure.\n  The results examine how the convergence orders depend on the regularity of\nthe noise and the initial data and reveal that the full discretization attains\nan optimal convergence rate of order $\\mathcal{O}(h^2+\\Delta t)$ for the\nexponential integrator and implicit schemes (linear operator $A$ self-adjoint\nfor implicit).\n  Numerical experiments are provided to illustrate our theoretical results for\nthe case of SPDE driven with fBm noise.\n']","[('fractional brownian motion', 0.6711873412132263), ('fractional stochastic', 0.6673045754432678), ('stochastic fractional', 0.6588130593299866), ('fractional brownian', 0.6457518339157104), ('discretization stochastic', 0.590298593044281), ('brownian motion hurst', 0.580093264579773), ('fractional diffusion', 0.545806884765625), ('fractional gaussian noise', 0.5354493260383606), ('approximation stochastic', 0.5229731798171997), ('nonlinear fractional diffusion', 0.5213529467582703)]"
1231,1231,24,1231_delay differential equations_linear delay differential_delay differential_linear delay,"['delay differential equations', 'linear delay differential', 'delay differential', 'linear delay', 'delay systems', 'delay linear', 'linear time delay', 'delay value', 'time delay systems', 'delayed differential']","['Effects of Roots of Maximal Multiplicity on the Stability of Some\n  Classes of Delay Differential-Algebraic Systems: The Lossless Propagation\n  Case   It has been observed in several recent works that, for some classes of linear\ntime-delay systems, spectral values of maximal multiplicity are dominant, a\nproperty known as multiplicity-induced-dominancy (MID). This paper starts the\ninvestigation of whether MID holds for delay differential-algebraic systems by\nconsidering a single-delay system composed of two scalar equations. After\nmotivating this problem and recalling some recent results for retarded delay\ndifferential equations, we prove that the MID property holds for the delay\ndifferential-algebraic system of interest and present some applications.\n', 'Insights into the multiplicity-induced-dominancy for scalar\n  delay-differential equations with two delays   It has been observed in recent works that, for several classes of linear\ntime-invariant time-delay systems of retarded or neutral type with a single\ndelay, if a root of its characteristic equation attains its maximal\nmultiplicity, then this root is the rightmost spectral value, and hence it\ndetermines the exponential behavior of the system, a property usually referred\nto as multiplicity-induced-dominancy (MID). In this paper, we investigate the\nMID property for one of the simplest cases of systems with two delays, a scalar\ndelay-differential equation of first order with two delayed terms of order\nzero. We discuss the standard approach based on the argument principle for\nestablishing the MID property for single-delay systems and some of its\nlimitations in the case of our simple system with two delays, before proposing\na technique based on crossing imaginary roots that allows to conclude that the\nMID property holds in our setting.\n', ""Multiplicity-induced-dominancy for delay-differential equations of\n  retarded type   An important question of ongoing interest for linear time-delay systems is to\nprovide conditions on its parameters guaranteeing exponential stability of\nsolutions. Recent works have explored spectral techniques to show that, for\nsome low-order delay-differential equations of retarded type, spectral values\nof maximal multiplicity are dominant, and hence determine the asymptotic\nbehavior of the system, a property known as multiplicity-induced-dominancy.\nThis work further explores such a property and shows its validity for general\nlinear delay-differential equations of retarded type of arbitrary order\nincluding a single delay in the system's representation. More precisely, an\ninteresting link between characteristic functions with a real root of maximal\nmultiplicity and Kummer's confluent hypergeometric functions is exploited. We\nalso provide examples illustrating our main result.\n""]","[('delay differential equations', 0.7098900079727173), ('linear delay differential', 0.6428097486495972), ('delay differential', 0.6311054825782776), ('linear delay', 0.5917903780937195), ('delay systems', 0.583336591720581), ('delay linear', 0.5763369798660278), ('linear time delay', 0.5673285722732544), ('delay value', 0.5608676075935364), ('time delay systems', 0.5582042336463928), ('delayed differential', 0.5566481947898865)]"
1232,1232,24,1232_prime graphs_prime graph_graph prime_prime vertex,"['prime graphs', 'prime graph', 'graph prime', 'prime vertex', 'graphs constructed', 'divisor graph', 'circulant graphs', 'conjecture prime', 'graphs can generated', 'transitive graphs']","['Odd Prime Graph Labelings   An odd prime labeling is a variation of a prime labeling in which the\nvertices of a graph of order~$n$ are labeled with the distinct odd integers $1$\nto $2n-1$ so that the labels of adjacent vertices are relatively prime. This\npaper investigates many different classes of graphs including disjoint unions\nof cycles, stacked prisms, and particular types of caterpillars, by using\nvarious methods to construct odd prime labelings. We also demonstrate progress\ntoward proving a conjecture that all prime graphs have an odd prime labeling.\n', 'Combinatorial refinement on circulant graphs   The combinatorial refinement techniques have proven to be an efficient\napproach to isomorphism testing for particular classes of graphs. If the number\nof refinement rounds is small, this puts the corresponding isomorphism problem\nin a low-complexity class. We investigate the round complexity of the\n2-dimensional Weisfeiler-Leman algorithm on circulant graphs, i.e. on Cayley\ngraphs of the cyclic group $\\mathbb{Z}_n$, and prove that the number of rounds\nuntil stabilization is bounded by $\\mathcal{O}(d(n)\\log n)$, where $d(n)$ is\nthe number of divisors of $n$. As a particular consequence, isomorphism can be\ntested in NC for connected circulant graphs of order $p^\\ell$ with $p$ an odd\nprime, $\\ell>3$ and vertex degree $\\Delta$ smaller than $p$.\n  We also show that the color refinement method (also known as the\n1-dimensional Weisfeiler-Leman algorithm) computes a canonical labeling for\nevery non-trivial circulant graph with a prime number of vertices after\nindividualization of two appropriately chosen vertices. Thus, the canonical\nlabeling problem for this class of graphs has at most the same complexity as\ncolor refinement, which results in a time bound of $\\mathcal{O}(\\Delta n\\log\nn)$. Moreover, this provides a first example where a sophisticated approach to\nisomorphism testing put forward by Tinhofer has a real practical meaning.\n', 'Prime Multiple Missing Graphs   The famous Goldbach conjecture remains open for nearly three centuries.\nRecently Goldbach graphs are introduced to relate the problem with the\nliterature of Graph Theory. It is shown that the connectedness of the graphs is\nequivalent to the affirmative answer of the conjecture. Some modified version\nof the graphs, say, near Goldbach graphs are shown to be Hamiltonian for small\nnumber of vertices. In this context, we introduce a class of graphs, namely,\nprime multiple missing graphs such that near Goldbach graphs are finite\nintersections of these graphs. We study these graphs for primes 3,5 and in\ngeneral for any odd prime p. We prove that these graphs are connected with\ndiameter at most 3 and Hamiltonian for even (>2) vertices. Next the\nintersection of prime multiple missing graphs for primes 3 and 5 are studied.\nWe prove that these graphs are connected with diameter at most 4 and they are\nalso Hamiltonian for even (>2) vertices. We observe that the diameters of\nfinite Goldbach graphs and near Goldbach graphs are bounded by 5 (up to 10000\nvertices). We believe further study on these graphs with big data analysis will\nhelp to understand structures of near Goldbach graphs.\n']","[('prime graphs', 0.7716832160949707), ('prime graph', 0.7213773131370544), ('graph prime', 0.7093286514282227), ('prime vertex', 0.6366109848022461), ('graphs constructed', 0.549936056137085), ('divisor graph', 0.5374558568000793), ('circulant graphs', 0.5285726189613342), ('conjecture prime', 0.510299801826477), ('graphs can generated', 0.5098426342010498), ('transitive graphs', 0.5010102391242981)]"
1233,1233,24,1233_dimensional simplicial complexes_dimensional simplicial complex_simplicial complexes_dimensional complexes,"['dimensional simplicial complexes', 'dimensional simplicial complex', 'simplicial complexes', 'dimensional complexes', 'abstract simplicial complexes', 'dimensional simplicial', 'simplicial complexes mathbb', 'simplicial complex', 'abstract simplicial complex', 'geometric embedding']","['Hardness of almost embedding simplicial complexes in $\\mathbb R^d$   A map $f\\colon K\\to \\mathbb R^d$ of a simplicial complex is an almost\nembedding if $f(\\sigma)\\cap f(\\tau)=\\emptyset$ whenever $\\sigma,\\tau$ are\ndisjoint simplices of $K$.\n  Theorem. Fix integers $d,k\\ge2$ such that $d=\\frac{3k}2+1$.\n  (a) Assume that $P\\ne NP$. Then there exists a finite $k$-dimensional complex\n$K$ that does not admit an almost embedding in $\\mathbb R^d$ but for which\nthere exists an equivariant map $\\tilde K\\to S^{d-1}$.\n  (b) The algorithmic problem of recognition almost embeddability of finite\n$k$-dimensional complexes in $\\mathbb R^d$ is NP hard.\n  The proof is based on the technique from the Matou\\v{s}ek-Tancer-Wagner paper\n(proving an analogous result for embeddings), and on singular versions of the\nhigher-dimensional Borromean rings lemma and a generalized van Kampen--Flores\ntheorem.\n', ""Embeddings of $k$-complexes in $2k$-manifolds and minimum rank of\n  partial symmetric matrices   Let $K$ be a $k$-dimensional simplicial complex having $n$ faces of dimension\n$k$, and $M$ a closed $(k-1)$-connected PL $2k$-dimensional manifold. We prove\nthat for $k\\ge3$ odd $K$ embeds into $M$ if and only if there are\n  $\\bullet$ a skew-symmetric $n\\times n$-matrix $A$ with $\\mathbb Z$-entries\nwhose rank over $\\mathbb Q$ does not exceed $rk H_k(M;\\mathbb Z)$,\n  $\\bullet$ a general position PL map $f:K\\to\\mathbb R^{2k}$, and\n  $\\bullet$ orientations on $k$-faces of $K$ such that for any nonadjacent\n$k$-faces $\\sigma,\\tau$ of $K$ the element $A_{\\sigma,\\tau}$ equals to the\nalgebraic intersection of $f\\sigma$ and $f\\tau$.\n  We prove some analogues of this result including those for $\\mathbb Z_2$- and\n$\\mathbb Z$-embeddability. Our results generalize the Bikeev-Fulek-Kyn\\v cl\ncriteria for the $\\mathbb Z_2$- and $\\mathbb Z$-embeddability of graphs to\nsurfaces, and are related to the Harris-Krushkal-Johnson-Pat\\'ak-Tancer\ncriteria for the embeddability of $k$-complexes into $2k$-manifolds.\n"", 'Instability of the Smith Index Under Joins and Applications to\n  Embeddability   We say a $d$-dimensional simplicial complex embeds into double dimension if\nit embeds into the Euclidean space of dimension $2d$. For instance, a graph is\nplanar iff it embeds into double dimension. We study the conditions under which\nthe join of two simplicial complexes embeds into double dimension. Quite\nunexpectedly, we show that there exist complexes which do not embed into double\ndimension, however their join embeds into the respective double dimension. We\nfurther derive conditions, in terms of the van Kampen obstructions of the two\ncomplexes, under which the join will not be embeddable into the double\ndimension. Our main tool in this study is the definition of the van Kampen\nobstruction as a Smith class. We determine the Smith classes of the join of two\n$\\mathbb{Z}_p$-complexes in terms of the Smith classes of the factors. We show\nthat in general the Smith index is not stable under joins. This allows us to\nprove our embeddability results.\n']","[('dimensional simplicial complexes', 0.6222870945930481), ('dimensional simplicial complex', 0.5969699621200562), ('simplicial complexes', 0.5482841730117798), ('dimensional complexes', 0.5412256121635437), ('abstract simplicial complexes', 0.5411346554756165), ('dimensional simplicial', 0.5389258861541748), ('simplicial complexes mathbb', 0.538813054561615), ('simplicial complex', 0.5144122242927551), ('abstract simplicial complex', 0.5121188759803772), ('geometric embedding', 0.47538310289382935)]"
1234,1234,24,1234_symplectic varieties_irreducible symplectic_symplectic variety_symplectic surfaces,"['symplectic varieties', 'irreducible symplectic', 'symplectic variety', 'symplectic surfaces', 'symplectic manifolds', 'projective symplectic', 'symplectic manifolds including', 'symplectic manifold particular', 'ahler orbifolds', 'theory symplectic']","['Fujiki relations and fibrations of irreducible symplectic varieties   This paper concerns different types of singular complex projective varieties\ngeneralizing irreducible symplectic manifolds. We deduce from known results\nthat the generalized Beauville-Bogomolov form satisfies the Fujiki relations\nand has the same rank as in the smooth case. This enables us to study\nfibrations of these varieties; imposing the newer definition from [GKP16,\nDefinition 8.16.2] we show that they behave much like irreducible symplectic\nmanifolds.\n', 'Wall divisors on irreducible symplectic orbifolds of Nikulin-type   We determine the wall divisors on irreducible symplectic orbifolds which are\ndeformation equivalent to a special type of examples, called Nikulin orbifolds.\nThe Nikulin orbifolds are obtained as partial resolutions in codimension 2 of a\nquotient by a symplectic involution of a Hilbert scheme of 2 points on a K3\nsurface. This builds on the previous article arXiv:2009.04873 in which the\ntheory of wall divisors was generalized to orbifold singularities.\n', 'Irreducible symplectic varieties with a large second Betti number   We prove a general result on the existence of irreducible symplectic\ncompactifications of non-compact Lagrangian fibrations. As an application, we\nshow that the relative Jacobian fibration of cubic fivefolds containing a fixed\ncubic fourfold can be compactified by a $\\mathbb{Q}$-factorial terminal\nirreducible symplectic variety with the second Betti number at least 24, and\nadmits a Lagrangian fibration whose base is a weighted projective space. In\nparticular, it belongs to a new deformation type of irreducible symplectic\nvarieties.\n']","[('symplectic varieties', 0.6999156475067139), ('irreducible symplectic', 0.6682020425796509), ('symplectic variety', 0.6603744626045227), ('symplectic surfaces', 0.6458303332328796), ('symplectic manifolds', 0.6451720595359802), ('projective symplectic', 0.6252661347389221), ('symplectic manifolds including', 0.6228212714195251), ('symplectic manifold particular', 0.6133216023445129), ('ahler orbifolds', 0.6019914746284485), ('theory symplectic', 0.5626605153083801)]"
1235,1235,24,1235_trisections_trisection_four manifolds_triangulations,"['trisections', 'trisection', 'four manifolds', 'triangulations', 'many manifolds', 'manifolds introduced', 'manifolds', 'pl manifolds', 'manifolds admitting', 'manifold']","['Trisections with Kirby-Thompson length 2   Kirby and Thompson introduced a length of a trisection. They also defined the\nlength of a 4-manifold as the minimum of length among all lengths of trisection\nof a 4-manifold. In this paper, we consider trisections whose Kirby-Thompson\nlength is 2. Kirby and Thompson conjectured that length 2 trisection is a\ntrisection of 4-manifold with length 0. We shall prove this conjecture in this\npaper.\n', 'Diagrams of *-Trisections   In this note, we provide a generalization for the definition of a trisection\nof a 4-manifold with boundary. We demonstrate the utility of this more general\ndefinition by finding a trisection diagram for the Cacime Surface, and also by\nfinding a trisection-theoretic way to perform logarithmic surgery. In addition,\nwe describe how to perform 1-surgery on closed trisections. The insight gained\nfrom this description leads us to the classification of an infinite family of\ngenus three trisections. We include an appendix where we extend two classic\nresults for relative trisections for the case when the trisection surface is\nclosed.\n', ""Right-left equivalent maps of simplified $(2, 0)$-trisections with\n  different configurations of vanishing cycles   Trisection maps are certain stable maps from closed $4$--manifolds to\n$\\mathbf{R}^2$. A simpler but reasonable class of trisection maps was\nintroduced by Baykur and Saeki, called a simplified $(g, k)$-trisection. We\nfocus on the right-left equivalence classes of simplified $(2, 0)$-trisections.\nSimplified trisections are determined by their simplified trisection diagrams,\nwhich are diagrams on a genus-$2$ surface consisting of simple closed curves of\nvanishig cycles with labels. The aim of this paper is to study how the\nreplacement of reference paths changes simplified trisection diagrams up to\nupper-triangular handle-slides. We show that for a simplified trisection $f$\nsatisfying a certain condition, there exists at least two simplified $(2,\n0)$-trisections $f'$ and $f''$ such that $f, f'$ and $f''$ are right-left\nequivalent to each other but their simplified trisection diagrams are not\nrelated by automorphisms of a genus-$2$ surface and upper-triangular\nhandle-slides.\n""]","[('trisections', 0.6622794270515442), ('trisection', 0.6333256959915161), ('four manifolds', 0.6274398565292358), ('triangulations', 0.5635336637496948), ('many manifolds', 0.538366973400116), ('manifolds introduced', 0.5362754464149475), ('manifolds', 0.5041840076446533), ('pl manifolds', 0.4753914773464203), ('manifolds admitting', 0.4741802215576172), ('manifold', 0.45495176315307617)]"
1236,1236,24,1236_oscillatory systems_stochastic lyapunov_stochastic stability_lyapunov functions,"['oscillatory systems', 'stochastic lyapunov', 'stochastic stability', 'lyapunov functions', 'stochastic perturbations', 'stochastically stable', 'asymptotically autonomous', 'perturbed system', 'lyapunov', 'lyapunov exponent']","['Resonances in asymptotically autonomous systems with a decaying\n  chirped-frequency excitation   The influence of oscillatory perturbations on autonomous strongly nonlinear\nsystems in the plane is investigated. It is assumed that the intensity of\nperturbations decays with time, and their frequency increases according to a\npower law. The long-term behaviour of perturbed trajectories is discussed. It\nis shown that, depending on the structure and the parameters of perturbations,\nthere are at least two different asymptotic regimes: a phase locking and a\nphase drifting. In the case of phase locking, resonant solutions with an\nunlimitedly growing energy occur. The stability and asymptotics at infinity of\nsuch solutions are investigated. The proposed analysis is based on a\ncombination of the averaging technique and the method of Lyapunov functions.\n', 'Resonance in isochronous systems with decaying oscillatory and\n  stochastic perturbations   The combined influence of oscillatory excitations and multiplicative\nstochastic perturbations of white noise type on isochronous systems in the\nplane is investigated. It is assumed that the intensity of perturbations decays\nwith time and the excitation frequency satisfies a resonance condition. The\noccurrence and stochastic stability of solutions with an asymptotically\nconstant amplitude are discussed. By constructing an averaging transformation,\nwe derive a model truncated deterministic system that describes possible\nasymptotic regimes for perturbed solutions. The persistence of resonant\nsolutions in the phase locking and the phase drifting modes is justified by\nconstructing suitable Lyapunov functions for the complete stochastic system. In\nparticular, we show that decaying stochastic perturbations can shift the\nboundary of stability domain for resonant solutions.\n', 'Stability of asymptotically Hamiltonian systems with damped oscillatory\n  and stochastic perturbations   A class of asymptotically autonomous systems on the plane with oscillatory\ncoefficients is considered. It is assumed that the limiting system is\nHamiltonian with a stable equilibrium. The effect of damped multiplicative\nstochastic perturbations of white noise type on the stability of the system is\ndiscussed. It is shown that different long-term asymptotic regimes for\nsolutions are admissible in the system and the stochastic stability of the\nequilibrium depends on the realized regime. In particular, we show that stable\nphase locking is possible in the system due to decaying stochastic\nperturbations. The proposed analysis is based on a combination of the averaging\ntechnique and the construction of stochastic Lyapunov functions.\n']","[('oscillatory systems', 0.5746697783470154), ('stochastic lyapunov', 0.5527154803276062), ('stochastic stability', 0.5503763556480408), ('lyapunov functions', 0.5274456739425659), ('stochastic perturbations', 0.5114820003509521), ('stochastically stable', 0.5025002956390381), ('asymptotically autonomous', 0.5022308230400085), ('perturbed system', 0.4857040345668793), ('lyapunov', 0.48190852999687195), ('lyapunov exponent', 0.47735756635665894)]"
1237,1237,24,1237_heat kernel asymptotics_heat kernels_heat kernel_kernel asymptotics,"['heat kernel asymptotics', 'heat kernels', 'heat kernel', 'kernel asymptotics', 'kernel laplace', 'generalized laplacian', 'spectral estimates', 'compact riemannian', 'bounds spectral', 'operator smooth']","['Semi-classical Heat Kernel Asymptotics and Morse Inequalities   In this paper, we study the asymptotic behavior of the heat kernel with\nrespect to the Witten Laplacian. We introduce the localization and the scaling\ntechnique in semi-classical analysis, and study the semi-classical asymptotic\nbehavior of the family of the heat kernel, indexed by $k$, near the critical\npoint $p$ of a given Morse function, as $k\\to \\infty$. It is shown that this\nfamily is approximately close to the heat kernel with respect to a system of\nthe harmonic oscillators attached to $p$. We also furnish some asymptotic\nresults regarding heat kernels away from the critical points. These heat kernel\nasymptotic results lead to a novel proof of the Morse inequalities.\n', ""Global Automorphic Sobolev Theory and The Automorphic Heat Kernel   Heat kernels arise in a variety of contexts including probability, geometry,\nand functional analysis; the automorphic heat kernel is particularly important\nin number theory and string theory. The typical construction of an automorphic\nheat kernel as a Poincar\\'{e} series presents analytic difficulties, which can\nbe dealt with in special cases (e.g. hyperbolic spaces) but are often\nsidestepped in higher rank by restricting to the compact quotient case. In this\npaper, we present a new approach, using global automorphic Sobolev theory, a\nrobust framework for solving automorphic PDEs that does not require any\nsimplifying assumptions about the rank of the symmetric space or the\ncompactness of the arithmetic quotient. We construct an automorphic heat kernel\nvia its automorphic spectral expansion in terms of cusp forms, Eisenstein\nseries, and residues of Eisenstein series. We then prove uniqueness of the\nautomorphic heat kernel as an application of operator semigroup theory.\nFinally, we prove the smoothness of the automorphic heat kernel by proving that\nits automorphic spectral expansion converges in the $C^\\infty$-topology.\n"", 'Strong Short Time Asymptotics and Convolution Approximation of the Heat\n  Kernel   We give a short proof of a strong version of the short time asymptotic\nexpansion of heat kernels associated to Laplace type operators acting on\nsections of vector bundles over compact Riemannian manifolds, including\nexponential decay of the difference of the approximate heat kernel and the true\nheat kernel. We use this to show that repeated convolution of the approximate\nheat kernels can be used to approximate the heat kernel on all of $M$, which is\nrelated to expressing the heat kernel as a path integral. This scheme is then\napplied to obtain a short-time asymptotic expansion of the heat kernel at the\ncut locus.\n']","[('heat kernel asymptotics', 0.7577808499336243), ('heat kernels', 0.6820711493492126), ('heat kernel', 0.6483816504478455), ('kernel asymptotics', 0.5663267374038696), ('kernel laplace', 0.5570510029792786), ('generalized laplacian', 0.5205181837081909), ('spectral estimates', 0.4776197075843811), ('compact riemannian', 0.4744209349155426), ('bounds spectral', 0.43953388929367065), ('operator smooth', 0.42847463488578796)]"
1238,1238,24,1238_monoids finite_monoids whose_monoids_variety algebras,"['monoids finite', 'monoids whose', 'monoids', 'variety algebras', 'commutative monoids', 'monoids results', 'variety finitely', 'ordered monoids', 'monoid', 'lattice subvarieties']","['Classification of limit varieties of J-trivial monoids   A variety of algebras is called limit if it is non-finitely based but all its\nproper subvarieties are finitely based. We present a new pair of limit\nvarieties of monoids and show that together with the five limit varieties of\nmonoids previously discovered by Jackson, Zhang and Luo and the first-named\nauthor, there are exactly seven limit varieties of J-trivial monoids.\n', 'Minimal monoids generating varieties with complex subvariety lattices   A variety is finitely universal if its lattice of subvarieties contains an\nisomorphic copy of every finite lattice. We show that the 6-element Brandt\nmonoid generates a finitely universal variety of monoids and, by the previous\nresults, it is the smallest generator for a monoid variety with this property.\nIt is also deduced that the join of two Cross varieties of monoids can be\nfinitely universal. In particular, we exhibit a finitely universal variety of\nmonoids with uncountably many subvarieties which is the join of two Cross\nvarieties of monoids whose lattices of subvarieties are the 6-element and the\n7-element chains, respectively.\n', 'Limit varieties of aperiodic monoids with commuting idempotents   A variety of algebras is called limit if it is non-finitely based but all its\nproper subvarieties are finitely based. A monoid is aperiodic if all its\nsubgroups are trivial. We classify all limit varieties of aperiodic monoids\nwith commuting idempotents.\n']","[('monoids finite', 0.6714964509010315), ('monoids whose', 0.6175556778907776), ('monoids', 0.5990213751792908), ('variety algebras', 0.5973495841026306), ('commutative monoids', 0.5971344709396362), ('monoids results', 0.5690252184867859), ('variety finitely', 0.5603743195533752), ('ordered monoids', 0.5474246144294739), ('monoid', 0.5199612975120544), ('lattice subvarieties', 0.5146434903144836)]"
1239,1239,24,1239_computational electromagnetics_electromagnetic scattering problems_electromagnetic scattering_field integral equations,"['computational electromagnetics', 'electromagnetic scattering problems', 'electromagnetic scattering', 'field integral equations', 'maxwell equations', 'equations electromagnetic', 'integral formulations', 'scattering problems', 'integral solver', 'surface integral']","[""Software frameworks for integral equations in electromagnetic scattering\n  based on Calder\\'on identities   In recent years there have been tremendous advances in the theoretical\nunderstanding of boundary integral equations for Maxwell problems. In\nparticular, stable dual pairing of discretisation spaces have been developed\nthat allow robust formulations of the preconditioned electric field, magnetic\nfield and combined field integral equations. Within the BEM++ boundary element\nlibrary we have developed implementations of these frameworks that allow an\nintuitive formulation of the typical Maxwell boundary integral formulations\nwithin a few lines of code. The basis of these developments is an efficient and\nrobust implementations of Calder\\'on identities together with a product algebra\nthat hides and automates most technicalities involved in assembling Galerkin\nboundary integral equations. In this paper we demonstrate this framework and\nuse it to derive very simple and robust software formulations of the standard\npreconditioned electric field, magnetic field and regularised combined field\nintegral equations for Maxwell.\n"", ""Code-Verification Techniques for the Method-of-Moments Implementation of\n  the Magnetic-Field Integral Equation   For computational physics simulations, code verification plays a major role\nin establishing the credibility of the results by assessing the correctness of\nthe implementation of the underlying numerical methods. In computational\nelectromagnetics, surface integral equations, such as the method-of-moments\nimplementation of the magnetic-field integral equation, are frequently used to\nsolve Maxwell's equations on the surfaces of electromagnetic scatterers. These\nelectromagnetic surface integral equations yield many code-verification\nchallenges due to the various sources of numerical error and their possible\ninteractions. In this paper, we provide approaches to separately measure the\nnumerical errors arising from these different error sources. We demonstrate the\neffectiveness of these approaches for cases with and without coding errors.\n"", 'A stabilized time-domain combined field integral equation using the\n  quasi-Helmholtz projectors   This paper introduces a time-domain combined field integral equation for\nelectromagnetic scattering by a perfect electric conductor. The new equation is\nobtained by leveraging the quasi-Helmholtz projectors, which separate both the\nunknown and the source fields into solenoidal and irrotational components.\nThese two components are then appropriately rescaled to cure the solution from\na loss of accuracy occurring when the time step is large. Yukawa-type integral\noperators of a purely imaginary wave number are also used as a Calderon\npreconditioner to eliminate the ill-conditioning of matrix systems. The\nstabilized time-domain electric and magnetic field integral equations are\nlinearly combined in a Calderon-like fashion, then temporally discretized using\nan appropriate pair of trial functions, resulting in a marching-on-in-time\nlinear system. The novel formulation is immune to spurious resonances, dense\ndiscretization breakdown, large-time step breakdown and dc instabilities\nstemming from non-trivial kernels. Numerical results for both simply-connected\nand multiply-connected scatterers corroborate the theoretical analysis.\n']","[('computational electromagnetics', 0.5849815607070923), ('electromagnetic scattering problems', 0.5813469290733337), ('electromagnetic scattering', 0.5500319600105286), ('field integral equations', 0.5282666683197021), ('maxwell equations', 0.5277751088142395), ('equations electromagnetic', 0.4845529794692993), ('integral formulations', 0.4709450304508209), ('scattering problems', 0.4571188688278198), ('integral solver', 0.45353543758392334), ('surface integral', 0.4333787262439728)]"
1240,1240,24,1240_sample points_sampling point_discrepancy bound_random points,"['sample points', 'sampling point', 'discrepancy bound', 'random points', 'quasi monte carlo', 'carlo algorithms', 'stratified sampling', 'curse dimensionality', 'error threshold', 'sampling']","['On a partition with a lower expected $\\mathcal{L}_2$-discrepancy than\n  classical jittered sampling   We prove that classical jittered sampling of the $d$-dimensional unit cube\ndoes not yield the smallest expected $\\mathcal{L}_2$-discrepancy among all\nstratified samples with $N=m^d$ points. Our counterexample can be given\nexplicitly and consists of convex partitioning sets of equal volume.\n', 'The $L_p$-discrepancy for finite $p>1$ suffers from the curse of\n  dimensionality   The $L_p$-discrepancy is a classical quantitative measure for the\nirregularity of distribution of an $N$-element point set in the $d$-dimensional\nunit cube. Its inverse for dimension $d$ and error threshold $\\varepsilon \\in\n(0,1)$ is the number of points in $[0,1)^d$ that is required such that the\nminimal normalized $L_p$-discrepancy is less or equal $\\varepsilon$. It is well\nknown, that the inverse of $L_2$-discrepancy grows exponentially fast with the\ndimension $d$, i.e., we have the curse of dimensionality, whereas the inverse\nof $L_{\\infty}$-discrepancy depends exactly linearly on $d$. The behavior of\ninverse of $L_p$-discrepancy for general $p \\not\\in \\{2,\\infty\\}$ was an open\nproblem since many years. Recently, the curse of dimensionality for the\n$L_p$-discrepancy was shown for an infinite sequence of values $p$ in $(1,2]$,\nbut the general result seemed to be out of reach. In the present paper we show\nthat the $L_p$-discrepancy suffers from the curse of dimensionality for all $p$\nin $(1,\\infty)$ and only the case $p=1$ is still open. This result follows from\na more general result that we show for the worst-case error of positive\nquadrature formulas for an anchored Sobolev space of once differentiable\nfunctions in each variable whose first mixed derivative has finite $L_q$-norm,\nwhere $q$ is the H\\""older conjugate of $p$.\n', 'Star discrepancy for new stratified random sampling I: optimal expected\n  star discrepancy   We introduce a class of convex equivolume partitions. Expected star\ndiscrepancy results are compared for stratified samples under these partitions,\nincluding simple random samples. There are four main parts of our results.\nFirst, among these newly designed partitions, there is one that minimizes the\nexpected star discrepancy, thus we partly answer an open question in [F.\nPausinger, S. Steinerberger, J. Complex. 2016]. Second, there are an infinite\nnumber of such class of partitions, which generate point sets with smaller\nexpected discrepancy than classical jittered sampling for large sampling\nnumber, leading to an open question in [M. Kiderlen, F. Pausinger, Monatsh.\nMath. 2021] being solved. Third, we prove a strong partition principle and\ngeneralize the expected star discrepancy under these partition models from\n$L_2-$discrepancy to star discrepancy, hence an open question in [M. Kiderlen,\nF. Pausinger, J. Complex. 2021] is answered. In the end, optimal expected star\ndiscrepancy upper bound under this class of partitions is given, which is\nbetter than using jittered sampling.\n']","[('sample points', 0.3911098837852478), ('sampling point', 0.3839256465435028), ('discrepancy bound', 0.37536758184432983), ('random points', 0.37007462978363037), ('quasi monte carlo', 0.3574238121509552), ('carlo algorithms', 0.3378591537475586), ('stratified sampling', 0.3342422544956207), ('curse dimensionality', 0.33381491899490356), ('error threshold', 0.3284375071525574), ('sampling', 0.3218287527561188)]"
1241,1241,24,1241_modular curve x_0_points modular curves_modular curves_modular curve,"['modular curve x_0', 'points modular curves', 'modular curves', 'modular curve', 'points modular', 'elliptic curves', 'rational points curves', 'mathbb curves', 'mathbb rational points', 'mordell weil group']","['Cubic and quartic points on modular curves using generalised symmetric\n  Chabauty   Answering a question of Zureick-Brown, we determine the cubic points on the\nmodular curves $X_0(N)$ for $N \\in \\{53,57,61,65,67,73\\}$ as well as the\nquartic points on $X_0(65)$. To do so, we develop a ""partially relative""\nsymmetric Chabauty method. Our results generalise current symmetric Chabauty\ntheorems, and improve upon them by lowering the involved prime bound. For our\ncurves a number of novelties occur. We prove a ""higher order"" Chabauty theorem\nto deal with these cases. Finally, to study the isolated quartic points on\n$X_0(65)$, we rigorously compute the full rational Mordell--Weil group of its\nJacobian.\n', ""Quadratic points on bielliptic modular curves   Bruin and Najman, Ozman and Siksek, and Box described all the quadratic\npoints on the modular curves of genus $2\\leq g(X_0(n)) \\leq 5$. Since all the\nhyperelliptic curves $X_0(n)$ are of genus $\\leq 5$ and as a curve can have\ninfinitely many quadratic points only if it is either of genus $\\leq 1$,\nhyperelliptic or bielliptic, the question of describing the quadratic points on\nthe bielliptic modular curves $X_0(n)$ naturally arises; this question has\nrecently also been posed by Mazur.\n  We answer Mazur's question completely and describe the quadratic points on\nall the bielliptic modular curves $X_0(n)$ for which this has not been done\nalready. The values of $n$ that we deal with are\n$n=60,62,69,79,83,89,92,94,95,101,119$ and $131$; the curves $X_0(n)$ are of\ngenus up to $11$. We find all the exceptional points on these curves and show\nthat they all correspond to CM elliptic curves. The two main methods we use are\nBox's relative symmetric Chabauty method and an application of a moduli\ndescription of $\\Q$-curves of degree $d$ with an independent isogeny of degree\n$m$, which reduces the problem to finding the rational points on several\nquotients of modular curves.\n"", 'Quadratic points on modular curves with infinite Mordell--Weil group   Bruin--Najman and Ozman--Siksek have recently determined the quadratic points\non all modular curves $X_0(N)$ of genus 2, 3, 4, and 5 whose Mordell--Weil\ngroup has rank 0. In this paper we do the same for the $X_0(N)$ of genus 2, 3,\n4, and 5 and positive Mordell--Weil rank. The values of $N$ are 37, 43, 53, 61,\n57, 65, 67 and 73. The main tool used is a relative symmetric Chabauty method,\nin combination with the Mordell--Weil sieve. Often the quadratic points are not\nfinite, as the degree 2 map $X_0(N)\\to X_0(N)^+$ can be a source of infinitely\nmany such points. In such cases, we describe this map and the rational points\non $X_0(N)^+$, and we specify the exceptional quadratic points on $X_0(N)$ not\ncoming from $X_0(N)^+$. In particular we determine the $j$-invariants of the\ncorresponding elliptic curves and whether they are $\\mathbb{Q}$-curves or have\ncomplex multiplication.\n']","[('modular curve x_0', 0.658854067325592), ('points modular curves', 0.642912745475769), ('modular curves', 0.6165698170661926), ('modular curve', 0.5398440361022949), ('points modular', 0.5308353304862976), ('elliptic curves', 0.5278647541999817), ('rational points curves', 0.4741579592227936), ('mathbb curves', 0.448127418756485), ('mathbb rational points', 0.4475630819797516), ('mordell weil group', 0.44064921140670776)]"
1242,1242,24,1242_event triggered control_triggered control_event triggering mechanism_event triggering,"['event triggered control', 'triggered control', 'event triggering mechanism', 'event triggering', 'based event triggered', 'delay systems', 'event triggered', 'time delay systems', 'control systems', 'triggering mechanism']","['Output Feedback Periodic-Event and Self-Triggered Control of Coupled\n  $2\\times 2$ Linear Hyperbolic PDEs   In this paper, we expand recently introduced observer-based periodic\nevent-triggered control (PETC) and self-triggered control (STC) schemes for\nreaction-diffusion PDEs to boundary control of $2\\times2$ coupled hyperbolic\nPDEs in canonical form and with anti-collocated measurement and actuation\nprocesses. The class of problem under study governs transport phenomena arising\nin water management systems, oil drilling, and traffic flow, to name a few.\nRelative to the state of the art in observer-based event-triggered control of\nhyperbolic PDEs, our contribution goes two steps further by proposing\nobserver-based PETC and STC for the considered class of systems. These designs\narise from a non-trivial redesign of an existing continuous-time\nevent-triggered control (CETC) scheme. PETC and STC eliminate the need for\nconstant monitoring of an event-triggering function as in CETC; PETC requires\nonly periodic evaluations of the triggering function for event detection,\nwhereas STC is a predictor-feedback that anticipates the next event time at the\ncurrent event exploiting continuously accessible output measurements. The\nintroduced resource-aware designs act as input holding mechanisms allowing for\nthe update of the input signal only at events. Subject to the designed boundary\noutput feedback PETC and STC control laws characterized by a set of\nevent-trigger design parameters, the resulting closed-loop systems, which are\ninherently Zeno-free by design, achieve exponential convergence to zero in the\nspatial $L^2$ norm. We illustrate the feasibility of the approach by applying\nthe control laws to the linearized Saint-Venant model, which describes the\ndynamics of shallow water waves in a canal and is used to design flow\nstabilizer feedback laws via gate actuation. The provided simulation results\nillustrate the proposed theory.\n', ""Observer-based Periodic Event-triggered and Self-triggered Boundary\n  Control of a Class of Parabolic PDEs   This paper introduces the first observer-based periodic event-triggered\ncontrol (PETC) and self-triggered control (STC) for boundary control of a class\nof parabolic PDEs using PDE backstepping control. We introduce techniques to\nconvert a certain class of continuous-time event-triggered control into PETC\nand STC, eliminating the need for continuous monitoring of the event-triggering\nfunction. For the PETC, the event-triggering function requires only periodic\nevaluations to detect events, while the STC proactively computes the time of\nthe next event right at the current event time using the system model and the\ncontinuously available measurements. For both strategies, the control input is\nupdated exclusively at events and is maintained using a zero-order hold between\nevents. We demonstrate that the closed-loop system is Zeno-free. We offer\ncriteria for selecting an appropriate sampling period for the PETC and for\ndetermining the time until the next event under the STC. We prove the system's\nglobal exponential convergence to zero in the spatial $L^2$ norm for both\nanti-collocated and collocated sensing and actuation under the PETC. For the\nSTC, local exponential convergence to zero in the spatial $L^2$ norm for\ncollocated sensing and actuation is proven. Simulations are provided to\nillustrate the theoretical claims.\n"", 'A Note on Stability of Event-Triggered Control Systems with Time Delays   This note studies stability of event-triggered control systems with the\nevent-triggered control algorithm proposed in [1]. We construct a novel\nHalanay-type inequality, which is used to show that sufficient conditions of\nthe main results in [1] ensure stability of the event-triggered control systems\nthat was missing in [1]. It is also shown that a positive parameter in the\nproposed event-triggering condition in [1] can be freely selected to exclude\nZeno behavior from the event-triggered control system. An illustrative example\nis investigated to demonstrate the theoretical results of this study with\nnumerical simulations.\n  [1] K. Zhang, B. Gharesifard, and E. Braverman, Event-triggered control for\nnonlinear time-delay systems, IEEE Transactions on Automatic Control, vol. 67,\nno. 2, pp. 1031-1037, 2022.\n']","[('event triggered control', 0.6369245052337646), ('triggered control', 0.5359365344047546), ('event triggering mechanism', 0.532633900642395), ('event triggering', 0.5167520046234131), ('based event triggered', 0.49985188245773315), ('delay systems', 0.49034878611564636), ('event triggered', 0.4740299582481384), ('time delay systems', 0.47246435284614563), ('control systems', 0.4697786569595337), ('triggering mechanism', 0.4595355987548828)]"
1243,1243,24,1243_periodic homogenization_periodic parabolic_boundary estimates_oscillating boundary,"['periodic homogenization', 'periodic parabolic', 'boundary estimates', 'oscillating boundary', 'homogenization problems', 'second order parabolic', 'convergence periodic', 'parabolic equations', 'periodic coefficients', 'asymptotic expansion solutions']","['Approximate Two-Sphere One-Cylinder Inequality in Parabolic Periodic\n  Homogenization   In this paper, for a family of second-order parabolic equation with rapidly\noscillating and time-dependent periodic coefficients, we are interested in an\napproximate two-sphere one-cylinder inequality for these solutions in parabolic\nperiodic homogenization, which implies an approximate quantitative propagation\nof smallness. The proof relies on the asymptotic behavior of fundamental\nsolutions and the Lagrange interpolation technique.\n', 'Parabolic Homogenization with an Interface   This paper considers a family of second-order parabolic equations in\ndivergence form with rapidly oscillating and time-dependent periodic\ncoefficients and an interface between two periodic structures. Following a\nframework initiated by Blanc, Le Bris and Lions and a generalized two-scale\nexpansion in divergence form of elliptic homogenization with an interface by\nJosien, we can determine the effective (or homogenized) equation with the\ncoefficient matrix being piecewise constant and discontinuous across the\ninterface. Moreover, we obtain the $O(\\varepsilon)$ convergence rates in\n$L^{2(d+2)/{d}}_{x,t}$ with $\\varepsilon$-smoothing method and the uniform\ninterior Lipschitz estimates via compactness argument.\n', 'Large-scale boundary estimates of parabolic homogenization over rough\n  boundaries   In this paper, for a family of second-order parabolic system or equation with\nrapidly oscillating and time-dependent periodic coefficients over rough\nboundaries, we obtain the large-scale boundary estimates, by a quantitative\napproach. The quantitative approach relies on approximating twice: we first\napproximate the original parabolic problem over rough boundary by the same\nequation over a non-oscillating boundary and then approximate the oscillating\nequation over a non-oscillating boundary by its homogenized equation over the\nsame non-oscillating boundary.\n']","[('periodic homogenization', 0.5792549252510071), ('periodic parabolic', 0.5428861379623413), ('boundary estimates', 0.5021201968193054), ('oscillating boundary', 0.4774286448955536), ('homogenization problems', 0.46594753861427307), ('second order parabolic', 0.44390133023262024), ('convergence periodic', 0.4270058274269104), ('parabolic equations', 0.41075965762138367), ('periodic coefficients', 0.4001197814941406), ('asymptotic expansion solutions', 0.40002334117889404)]"
1244,1244,24,1244_algebraic curves_plane algebraic curves_numerical algebraic geometry_curves,"['algebraic curves', 'plane algebraic curves', 'numerical algebraic geometry', 'curves', 'plane curves', 'curve whose', 'plane algebraic', 'obius transformations', 'parametric curves', 'curve']","['Spirals, Tic-Tac-Toe Partition, and Deep Diagonal Maps The deep diagonal map $T_k$ acts on planar polygons by connecting the $k$-th diagonals and intersecting them successively. The map $T_2$ is the pentagram map, and $T_k$ is a generalization. We study the action of $T_k$ on two subsets of the so-called twisted polygons, which we term type-$\\alpha$ and type-$\\beta$ $k$-spirals. For $k \\geq 2$, $T_{k}$ preserves both types of $k$-spirals. In particular, we show that for $k = 2$ and $k = 3$, both types of $k$-spirals have precompact forward and backward $T_k$-orbits modulo projective transformations. We derive a rational formula for $T_3$, which generalizes the $y$-variables transformation formula by M. Glick and P. Pylyavskyy. We also present four algebraic invariants of $T_3$. These special orbits in the moduli space are partitioned into cells of a $3 \\times 3$ tic-tac-toe grid. This establishes the action of $T_k$ on $k$-spirals as a geometric generalization of $T_2$ on convex polygons.', 'Exploration of offsets of Cayley ovals and their singularities We explore offsets of Cayley ovals, by networking with different kinds of software. Using their specific abilities, algebraic, geometric, dynamic, we conjecture interesting properties of the offsets. For a given progenitor (the given plane curve whose offsets are studied), changes in the offset distance induce great changes in the shape and the topology of the offset. Such a study has been performed in the past for classical curves, and recently for non classical ones.Here we relate to Cayley ovals; despite them being non singular, their offsets have intriguing properties, cusps, and self-intersections. We begin with a short study of envelopes of families of circles with constant radius centered on the oval (these constructs are often studied together with offsets, but they are different objects). Then we study the offsets, which are defined as geometric loci. Both approaches are supported by the automated methods provided by the software.', 'Envelopes of Circles Centered on a Kiss Curve   Envelopes of parameterized families of plane curves is an important topic,\nboth for the mathematics involved and for its applications. Nowadays, it is\ngenerally studied in a technology-rich environment, and automated methods are\ndeveloped and implemented in software. The exploration involves a dialog\nbetween a Dynamic Geometry System (used mostly for interactive exploration and\nconjectures) and a Computer Algebra System (for algebraic manipulations). We\nstudy envelopes of families of circles centered on the so-called kiss curve and\noffsets of this curve, observing the differences between constructs. Both\nparametric presentations and implicit equations are used, switching from\nparametric to polynomial representation being based on packages for Gr\\""obner\nbases and Elimination. Singular points, both cusps and points of\nself-intersection (crunodes), are analyzed.\n']","[('algebraic curves', 0.6454241275787354), ('plane algebraic curves', 0.639085054397583), ('numerical algebraic geometry', 0.5863555073738098), ('curves', 0.5573244094848633), ('plane curves', 0.5322123169898987), ('curve whose', 0.5249703526496887), ('plane algebraic', 0.49951520562171936), ('obius transformations', 0.4633129835128784), ('parametric curves', 0.4604463279247284), ('curve', 0.4531899392604828)]"
1245,1245,24,1245_random projections_large deviation principles_dimensional random vectors_large deviation principle,"['random projections', 'large deviation principles', 'dimensional random vectors', 'large deviation principle', 'norms random', 'large deviations', 'large deviations random', 'sequence empirical measures', 'projections high dimensional', 'dimensional random vector']","['Quenched large deviation principles for random projections of $\\ell_p^n$\n  balls   Let $(k_n)_{n \\in \\mathbb{N}}$ be a sequence of positive integers growing to\ninfinity at a sublinear rate, $k_n \\rightarrow \\infty$ and $k_n/n \\rightarrow\n0$ as $n \\rightarrow \\infty$. Given a sequence of $n$-dimensional random\nvectors $\\{Y^{(n)}\\}_{n \\in \\mathbb{N}}$ belonging to a certain class, which\nincludes uniform distributions on suitably scaled $\\ell_p^n$-balls or\n$\\ell_p^n$-spheres, $p \\geq 2$, and product distributions with sub-Gaussian\nmarginals, we study the large deviations behavior of the corresponding sequence\nof $k_n$-dimensional orthogonal projections $n^{-1/2} \\boldsymbol{a}_{n,k_n}\nY^{(n)}$, where $\\boldsymbol{a}_{n,k_n}$ is an $(n \\times k_n)$-dimensional\nprojection matrix lying in the Stiefel manifold of orthonormal $k_n$-frames in\n$\\mathbb{R}^n$. For almost every sequence of projection matrices, we establish\na large deviation principle (LDP) for the corresponding sequence of\nprojections, with a fairly explicit rate function that does not depend on the\nsequence of projection matrices. As corollaries, we also obtain quenched LDPs\nfor sequences of $\\ell_2$-norms and $\\ell_\\infty$-norms of the coordinates of\nthe projections. Past work on LDPs for projections with growing dimension has\nmainly focused on the annealed setting, where one also averages over the random\nprojection matrix, chosen from the Haar measure, in which case the coordinates\nof the projection are exchangeable. The quenched setting lacks such symmetry\nproperties, and gives rise to significant new challenges in the setting of\ngrowing projection dimension. Along the way, we establish new Gaussian\napproximation results on the Stiefel manifold that may be of independent\ninterest. Such LDPs are of relevance in asymptotic convex geometry, statistical\nphysics and high-dimensional statistics.\n', 'Large deviation principles induced by the Stiefel manifold, and random\n  multi-dimensional projections   Given an $n$-dimensional random vector $X^{(n)}$ , for $k < n$, consider its\n$k$-dimensional projection $\\mathbf{a}_{n,k}X^{(n)}$, where $\\mathbf{a}_{n,k}$\nis an $n \\times k$-dimensional matrix belonging to the Stiefel manifold\n$\\mathbb{V}_{n,k}$ of orthonormal $k$-frames in $\\mathbb{R}^n$. For a class of\nsequences $\\{X^{(n)}\\}$ that includes the uniform distributions on scaled\n$\\ell_p^n$ balls, $p \\in (1,\\infty]$, and product measures with sufficiently\nlight tails, it is shown that the sequence of projected vectors\n$\\{\\mathbf{a}_{n,k}^\\intercal X^{(n)}\\}$ satisfies a large deviation principle\nwhenever the empirical measures of the rows of $\\sqrt{n} \\mathbf{a}_{n,k}$\nconverge, as $n \\rightarrow \\infty$, to a probability measure on\n$\\mathbb{R}^k$. In particular, when $\\mathbf{A}_{n,k}$ is a random matrix drawn\nfrom the Haar measure on $\\mathbb{V}_{n,k}$, this is shown to imply a large\ndeviation principle for the sequence of random projections\n$\\{\\mathbf{A}_{n,k}^\\intercal X^{(n)}\\}$ in the quenched sense (that is,\nconditioned on almost sure realizations of $\\{\\mathbf{A}_{n,k}\\}$). Moreover, a\nvariational formula is obtained for the rate function of the large deviation\nprinciple for the annealed projections $\\{\\mathbf{A}_{n,k}^\\intercal\nX^{(n)}\\}$, which is expressed in terms of a family of quenched rate functions\nand a modified entropy term. A key step in this analysis is a large deviation\nprinciple for the sequence of empirical measures of rows of $\\sqrt{n}\n\\mathbf{A}_{n,k}$, which may be of independent interest. The study of\nmulti-dimensional random projections of high-dimensional measures is of\ninterest in asymptotic functional analysis, convex geometry and statistics.\nPrior results on quenched large deviations for random projections of $\\ell_p^n$\nballs have been essentially restricted to the one-dimensional setting.\n', 'An asymptotic thin shell condition and large deviations for random\n  multidimensional projections   Consider the projection of an $n$-dimensional random vector onto a random\n$k_n$-dimensional basis, $k_n \\leq n$, drawn uniformly from the Haar measure on\nthe Stiefel manifold of orthonormal $k_n$-frames in $\\mathbb{R}^n$, in three\ndifferent asymptotic regimes as $n \\rightarrow \\infty$: ""constant"" ($k_n=k$),\n""sublinear"" ($k_n \\rightarrow \\infty$ but $k_n/n \\rightarrow 0$) and ""linear""\n$k_n/n \\rightarrow \\lambda$ with $0 < \\lambda \\le 1$). When the sequence of\nrandom vectors satisfies a certain ""asymptotic thin shell condition"", we\nestablish annealed large deviation principles (LDPs) for the corresponding\nsequence of random projections in the constant regime, and for the sequence of\nempirical measures of the coordinates of the random projections in the\nsublinear and linear regimes. We also establish LDPs for certain scaled\n$\\ell_q$ norms of the random projections in these different regimes. Moreover,\nwe verify our assumptions for various sequences of random vectors of interest,\nincluding those distributed according to Gibbs measures with superquadratic\ninteraction potential, or the uniform measure on suitably scaled $\\ell_p^n$\nballs, for $p \\in [1,\\infty)$, and generalized Orlicz balls defined via a\nsuperquadratic function. Our results complement the central limit theorem for\nconvex sets and related results which are known to hold under a ""thin shell""\ncondition. These results also substantially extend existing large deviation\nresults for random projections, which are first, restricted to the setting of\nmeasures on $\\ell_p^n$ balls, and secondly, limited to univariate LDPs (i.e.,\nin $\\mathbb{R}$) involving either the norm of a $k_n$-dimensional projection or\nthe projection of $X^{(n)}$ onto a random one-dimensional subspace. Random\nprojections of high-dimensional random vectors are of interest in a range of\nfields including asymptotic convex geometry and high-dimensional statistics.\n']","[('random projections', 0.548366367816925), ('large deviation principles', 0.44998571276664734), ('dimensional random vectors', 0.441961407661438), ('large deviation principle', 0.42863109707832336), ('norms random', 0.4110153615474701), ('large deviations', 0.4049875736236572), ('large deviations random', 0.39829516410827637), ('sequence empirical measures', 0.39486828446388245), ('projections high dimensional', 0.3916148543357849), ('dimensional random vector', 0.3903680741786957)]"
1246,1246,24,1246_cremona group_algebraic subgroups_algebraic subgroup_group algebraically closed,"['cremona group', 'algebraic subgroups', 'algebraic subgroup', 'group algebraically closed', 'group algebraically', 'finite subgroups', 'cremona', 'subgroups rank', 'maximal subgroups', 'subgroups']","['On linearization problems in the plane Cremona group   We study finite non-linearizable subgroups of the plane Cremona group which\npotentially could be stably linearizable.\n', 'A note on 3-subgroups in the space Cremona group   We prove that a finite $3$-group in the Cremona group\n$\\mathrm{Cr}_3(\\mathbb{C})$ can be generated by at most $4$ elements. This\nprovides the last missing piece in bounding the ranks of finite $p$-subgroups\nin the space Cremona group.\n', 'The Cremona group and its subgroups   This survey deals with the Cremona group via its subgroups.\n']","[('cremona group', 0.7179492115974426), ('algebraic subgroups', 0.6276322603225708), ('algebraic subgroup', 0.6077483892440796), ('group algebraically closed', 0.5650244951248169), ('group algebraically', 0.5236760377883911), ('finite subgroups', 0.5163087248802185), ('cremona', 0.5134099125862122), ('subgroups rank', 0.5069814920425415), ('maximal subgroups', 0.49070391058921814), ('subgroups', 0.48917335271835327)]"
1247,1247,24,1247_poroelasticity_deformable porous media_deformable porous_poroelastic,"['poroelasticity', 'deformable porous media', 'deformable porous', 'poroelastic', 'viscoelastic', 'poro elastic', 'elastic matrix', 'energy elastic', 'elastic plate', 'porous media']","[""Uniqueness of Weak Solutions for Biot-Stokes Interactions   We resolve the issue of uniqueness of weak solutions for linear, inertial\nfluid-poroelastic-structure coupled dynamics. The model comprises a 3D Biot\nporoelastic system coupled to a 3D incompressible Stokes flow via a 2D\ninterface, where kinematic, stress-matching, and tangential-slip conditions are\nprescribed. Our previous work provided a construction of weak solutions, these\nsatisfying an associated finite energy inequality. However, several\nwell-established issues related to the dynamic coupling, hinder a direct\napproach to obtaining uniqueness and continuous dependence. In particular, low\nregularity of the hyperbolic (Lam\\'e) component of the model precludes the use\nof the solution as a test function, which would yield the necessary a priori\nestimate. In considering degenerate and non-degenerate cases separately, we\nutilize two different approaches. In the former, energy estimates are obtained\nfor arbitrary weak solutions through a systematic decoupling of the constituent\ndynamics, and well-posedness of weak solutions is inferred. In the latter case,\nan abstract semigroup approach is utilized to obtain uniqueness via a precise\ncharacterization of the adjoint of the dynamics operator. The results here can\nbe adapted to other systems of poroelasticity, as well as to the general theory\nof weak solutions for hyperbolic-parabolic coupled systems.\n"", ""Actively deforming porous media in an incompressible fluid: a\n  variational approach   Many parts of biological organisms are comprised of deformable porous media.\nThe biological media is both pliable enough to deform in response to an outside\nforce and can deform by itself using the work of an embedded muscle. For\nexample, the recent work (Ludeman et al., 2014) has demonstrated interesting\n'sneezing' dynamics of a freshwater sponge, when the sponge contracts and\nexpands to clear itself from surrounding polluted water. We derive the\nequations of motion for the dynamics of such an active porous media (i.e., a\ndeformable porous media that is capable of applying a force to itself with\ninternal muscles), filled with an incompressible fluid. These equations of\nmotion extend the earlier derived equation for a passive porous media filled\nwith an incompressible fluid. We use a variational approach with a Lagrangian\nwritten as the sum of terms representing the kinetic and potential energy of\nthe elastic matrix, and the kinetic energy of the fluid, coupled through the\nconstraint of incompressibility. We then proceed to extend this theory by\ncomputing the case when both the active porous media and the fluid are\nincompressible, with the porous media still being deformable, which is often\nthe case for biological applications. For the particular case of a uniform\ninitial state, we rewrite the equations of motion in terms of two coupled\ntelegraph-like equations for the material (Lagrangian) particles expressed in\nthe Eulerian frame of reference, particularly suitable for numerical\nsimulations, formulated for both the compressible media/incompressible fluid\ncase and the doubly incompressible case. We derive interesting conservation\nlaws for the motion, perform numerical simulations in both cases and show the\npossibility of self-propulsion of a biological organism due to particular\nrunning wave-like application of the muscle stress.\n"", ""Geometric variational approach to the dynamics of porous media filled\n  with incompressible fluid   We derive the equations of motion for the dynamics of a porous media filled\nwith an incompressible fluid. We use a variational approach with a Lagrangian\nwritten as the sum of terms representing the kinetic and potential energy of\nthe elastic matrix, and the kinetic energy of the fluid, coupled through the\nconstraint of incompressibility. As an illustration of the method, the\nequations of motion for both the elastic matrix and the fluid are derived in\nthe spatial (Eulerian) frame. Such an approach is of relevance e.g. for\nbiological problems, such as sponges in water, where the elastic porous media\nis highly flexible and the motion of the fluid has a 'primary' role in the\nmotion of the whole system. We then analyze the linearized equations of motion\ndescribing the propagation of waves through the media. In particular, we derive\nthe propagation of S-waves and P-waves in an isotropic media. We also analyze\nthe stability criteria for the wave equations and show that they are equivalent\nto the physicality conditions of the elastic matrix. Finally, we show that the\ncelebrated Biot's equations for waves in porous media are obtained for certain\nvalues of parameters in our models.\n""]","[('poroelasticity', 0.5799857974052429), ('deformable porous media', 0.5556028485298157), ('deformable porous', 0.5381386876106262), ('poroelastic', 0.5297805070877075), ('viscoelastic', 0.48367246985435486), ('poro elastic', 0.45886170864105225), ('elastic matrix', 0.44737371802330017), ('energy elastic', 0.43857479095458984), ('elastic plate', 0.4256683886051178), ('porous media', 0.4115315079689026)]"
1248,1248,23,1248_virtual element methods_linear elasticity problems_nonconforming virtual element_problems linear elasticity,"['virtual element methods', 'linear elasticity problems', 'nonconforming virtual element', 'problems linear elasticity', 'linear elasticity', 'free virtual element', 'elasticity problems', 'virtual element vem', 'incompressible elasticity', 'virtual element space']","['Stress-hybrid virtual element method on six-noded triangular meshes for\n  compressible and nearly-incompressible linear elasticity   In this paper, we present a first-order Stress-Hybrid Virtual Element Method\n(SH-VEM) on six-noded triangular meshes for linear plane elasticity. We adopt\nthe Hellinger--Reissner variational principle to construct a weak equilibrium\ncondition and a stress based projection operator. On applying the divergence\ntheorem to the weak strain-displacement relations, the stress projection\noperator is expressed in terms of the nodal displacements, which leads to a\ndisplacement-based formulation. This stress-hybrid approach assumes a globally\ncontinuous displacement field while the stress field is discontinuous across\neach element. The stress field is initially represented by divergence-free\ntensor polynomials based on Airy stress functions. However, for flexibility in\nchoosing basis functions, we also present a formulation that uses a penalty\nterm to enforce the element equilibrium conditions. This method is referred to\nas the Penalty Stress-Hybrid Virtual Element Method (PSH-VEM). Numerical\nresults are presented for PSH-VEM and SH-VEM, and we compare their convergence\nto the composite triangle FEM and B-bar VEM on benchmark problems in linear\nelasticity. The SH-VEM converges optimally in the $L^2$ norm of the\ndisplacement, energy seminorm, and the $L^2$ norm of hydrostatic stress.\nFurthermore, the results reveal that PSH-VEM converges in most cases at a\nfaster rate than the expected optimal rate, but it requires the selection of a\nsuitably chosen penalty parameter.\n', 'Stress-hybrid virtual element method on quadrilateral meshes for\n  compressible and nearly-incompressible linear elasticity   In this paper, we propose a robust low-order stabilization-free virtual\nelement method on quadrilateral meshes for linear elasticity that is based on\nthe stress-hybrid principle. We refer to this approach as the Stress-Hybrid\nVirtual Element Method (SH-VEM). In this method, the Hellinger$-$Reissner\nvariational principle is adopted, wherein both the equilibrium equations and\nthe strain-displacement relations are variationally enforced. We consider\nsmall-strain deformations of linear elastic solids in the compressible and\nnear-incompressible regimes over quadrilateral (convex and nonconvex) meshes.\nWithin an element, the displacement field is approximated as a linear\ncombination of canonical shape functions that are $\\textit{virtual}$. The\nstress field, similar to the stress-hybrid finite element method of Pian and\nSumihara, is represented using a linear combination of symmetric tensor\npolynomials. A 5-parameter expansion of the stress field is used in each\nelement, with stress transformation equations applied on distorted\nquadrilaterals. In the variational statement of the strain-displacement\nrelations, the divergence theorem is invoked to express the stress coefficients\nin terms of the nodal displacements. This results in a formulation with solely\nthe nodal displacements as unknowns. Numerical results are presented for\nseveral benchmark problems from linear elasticity. We show that SH-VEM is free\nof volumetric and shear locking, and it converges optimally in the $L^2$ norm\nand energy seminorm of the displacement field, and in the $L^2$ norm of the\nhydrostatic stress.\n', ""Lowest-order virtual element methods for linear elasticity problems   We present two kinds of lowest-order virtual element methods for planar\nlinear elasticity problems. For the first one we use the nonconforming virtual\nelement method with a stabilizing term. It can be interpreted as a modification\nof the nonconforming Crouzeix-Raviart finite element method as suggested in\n[22] to the virtual element method. For the second one we use the conforming\nvirtual element for one component of the displacement vector and the\nnonconforming virtual element for the other. This approach can be seen as an\nextension of the idea of Kouhia and Stenberg suggested in [23] to the virtual\nelement method. We show that our proposed methods satisfy the discrete Korn's\ninequality. We also prove that the methods are convergent uniformly for the\nnearly incompressible case and the convergence rates are optimal.\n""]","[('virtual element methods', 0.5952438116073608), ('linear elasticity problems', 0.5534642338752747), ('nonconforming virtual element', 0.5024659633636475), ('problems linear elasticity', 0.5019177794456482), ('linear elasticity', 0.49789825081825256), ('free virtual element', 0.47289907932281494), ('elasticity problems', 0.47188353538513184), ('virtual element vem', 0.4703180193901062), ('incompressible elasticity', 0.4523630738258362), ('virtual element space', 0.4493594467639923)]"
1249,1249,23,1249_spherical codes_spherical code_sphere packing_programming bounds,"['spherical codes', 'spherical code', 'sphere packing', 'programming bounds', 'codes attain', 'spherical designs', 'codes designs', 'linear programming bounds', 'universal bounds', 'bound spherical']","[""Stiefel manifolds and upper bounds for spherical codes and packings   We improve upper bounds on sphere packing densities and sizes of spherical\ncodes in high dimensions. In particular, we prove that the maximal sphere\npacking densities $\\delta_n$ in $\\mathbb{R}^n$ satisfy \\[\\delta_n\\leq\n\\frac{1+o(1)}{e}\\cdot \\delta^{\\text{KL}}_{n}\\] for large $n$, where\n$\\delta^{\\text{KL}}_{n}$ is the best bound on $\\delta_n$ obtained essentially\nby Kabatyanskii and Levenshtein from the 1970s with improvements over the\nyears. We also obtain the same improvement factor for the maximal size\n$M(n,\\theta)$ of $\\theta$-spherical codes in $S^{n-1}$: for angles\n$0<\\theta<\\theta'\\leq\\frac{\\pi}{2}$, \\[M(n,\\theta)\\leq \\frac{1+o(1)}{e}\\cdot\n\\frac{M_{\\text{Lev}}(n-1,\\theta')}{\\mu_n(\\theta,\\theta')}\\] for large $n$,\nwhere $\\mu_n(\\theta,\\theta')$ is the mass of the spherical cap in the unit\nsphere $S^{n-1}$ of radius $\\frac{\\sin(\\theta/2)}{\\sin(\\theta'/2)}$, and\n$M_{\\text{Lev}}(n-1,\\theta')$ is Levenshtein's upper bound on $M(n-1,\\theta')$\nwhen applying the Delsarte linear programming method to Levenshtein's optimal\npolynomials. In fact, we prove that there are no analytic losses in our\narguments and that the constant $\\frac{1}{e}=0.367...$ is optimal for the class\nof functions considered. Our results also show that the improvement factor does\nnot depend on the special angle $\\theta^*=62.997...^{\\circ}$, explaining the\nnumerics in arXiv:2001.00185. In the spherical codes case, the above inequality\nimproves the Kabatyanskii--Levenshtein bound by a factor of $0.2304...$ on\ngeometric average. Along the way, we construct a general class of functions\nusing Stiefel manifolds for which we prove general results and study the\nimprovement factors obtained from them in various settings.and study the\nimprovement factors obtained from them in various settings.\n"", 'Universal optimality of $T$-avoiding spherical codes and designs   Given an open set (a union of open intervals), $T\\subset [-1,1]$ we introduce\nthe concepts of $T$-avoiding spherical codes and designs, that is, spherical\ncodes that have no inner products in the set $T$. We show that certain codes\nfound in the minimal vectors of the Leech lattices, as well as the minimal\nvectors of the Barnes--Wall lattice and codes derived from strongly regular\ngraphs, are universally optimal in the restricted class of $T$-avoiding codes.\nWe also extend a result of Delsarte--Goethals--Seidel about codes with three\ninner products $\\alpha, \\beta, \\gamma$ (in our terminology\n$(\\alpha,\\beta)$-avoiding $\\gamma$-codes). Parallel to the notion of tight\nspherical designs, we also derive that these codes are minimal (tight)\n$T$-avoiding spherical designs of fixed dimension and strength. In some cases,\nwe also find that codes under consideration have maximal cardinality in their\n$T$-avoiding class for given dimension and minimum distance.\n', 'Universal bounds for spherical codes: the Levenshtein framework lifted   Based on the Delsarte-Yudin linear programming approach, we extend\nLevenshtein\'s framework to obtain lower bounds for the minimum $h$-energy of\nspherical codes of prescribed dimension and cardinality, and upper bounds on\nthe maximal cardinality of spherical codes of prescribed dimension and minimum\nseparation. These bounds are universal in the sense that they hold for a large\nclass of potentials $h$ and in the sense of Levenshtein. Moreover, codes\nattaining the bounds are universally optimal in the sense of Cohn-Kumar.\nReferring to Levenshtein bounds and the energy bounds of the authors as ``first\nlevel"", our results can be considered as ``next level"" universal bounds as they\nhave the same general nature and imply necessary and sufficient conditions for\ntheir local and global optimality. For this purpose, we introduce the notion of\nUniversal Lower Bound space (ULB-space), a space that satisfies certain\nquadrature and interpolation properties. While there are numerous cases for\nwhich our method applies, we will emphasize the model examples of $24$ points\n($24$-cell) and $120$ points ($600$-cell) on $\\mathbb{S}^3$. In particular, we\nprovide a new proof that the $600$-cell is universally optimal, and in so\ndoing, we derive optimality of the $600$-cell on a class larger than the\nabsolutely monotone potentials considered by Cohn-Kumar.\n']","[('spherical codes', 0.6447276473045349), ('spherical code', 0.570056140422821), ('sphere packing', 0.5210044980049133), ('programming bounds', 0.49576535820961), ('codes attain', 0.4880436658859253), ('spherical designs', 0.4758163392543793), ('codes designs', 0.4679645299911499), ('linear programming bounds', 0.44645586609840393), ('universal bounds', 0.4435039758682251), ('bound spherical', 0.44282564520835876)]"
1250,1250,23,1250_reduced order modeling_orthogonal decomposition pod_orthogonal decomposition reduced_reduced order models,"['reduced order modeling', 'orthogonal decomposition pod', 'orthogonal decomposition reduced', 'reduced order models', 'decomposition reduced order', 'orthogonal decomposition', 'proper orthogonal decomposition', 'time reduced order', 'based reduced order', 'decomposition least']","['Uniform Bounds with Difference Quotients for Proper Orthogonal\n  Decomposition Reduced Order Models of the Burgers Equation   In this paper, we prove uniform error bounds for proper orthogonal\ndecomposition (POD) reduced order modeling (ROM) of Burgers equation,\nconsidering difference quotients (DQs), introduced in [26]. In particular, we\nstudy the behavior of the DQ ROM error bounds by considering $L^2(\\Omega)$ and\n$H^1_0(\\Omega)$ POD spaces and $l^{\\infty}(L^2)$ and natural-norm errors. We\npresent some meaningful numerical tests checking the behavior of error bounds.\nBased on our numerical results, DQ ROM errors are several orders of magnitude\nsmaller than noDQ ones (in which the POD is constructed in a standard way,\ni.e., without the DQ approach) in terms of the energy kept by the ROM basis.\nFurther, noDQ ROM errors have an optimal behavior, while DQ ROM errors, where\nthe DQ is added to the POD process, demonstrate an optimality/super-optimality\nbehavior. It is conjectured that this possibly occurs because the DQ inner\nproducts allow the time dependency in the ROM spaces to make an impact.\n', 'A new approach to proper orthogonal decomposition with difference\n  quotients   In a recent work [B. Koc et al., arXiv:2010.03750, SIAM J. Numer. Anal., to\nappear], the authors showed that including difference quotients (DQs) is\nnecessary in order to prove optimal pointwise in time error bounds for proper\northogonal decomposition (POD) reduced order models of the heat equation. In\nthis work, we introduce a new approach to including DQs in the POD procedure.\nInstead of computing the POD modes using all of the snapshot data and DQs, we\nonly use the first snapshot along with all of the DQs and special POD weights.\nWe show that this approach retains all of the numerical analysis benefits of\nthe standard POD DQ approach, while using a POD data set that has half the\nnumber of snapshots as the standard POD DQ approach, i.e., the new approach is\nmore computationally efficient. We illustrate our theoretical results with\nnumerical experiments.\n', 'A New Proper Orthogonal Decomposition Method with Second Difference\n  Quotients for the Wave Equation   Recently, researchers have investigated the relationship between proper\northogonal decomposition (POD), difference quotients (DQs), and pointwise in\ntime error bounds for POD reduced order models of partial differential\nequations. In a recent work (Eskew and Singler, Adv. Comput. Math., 49, 2023,\nno. 2, Paper No. 13), a new approach to POD with DQs was developed that is more\ncomputationally efficient than the standard DQ POD approach and it also retains\nthe guaranteed pointwise in time error bounds of the standard method. In this\nwork, we extend this new DQ POD approach to the case of second difference\nquotients (DDQs). Specifically, a new POD method utilizing DDQs and only one\nsnapshot and one DQ is developed and used to prove ROM error bounds for the\ndamped wave equation. This new approach eliminates data redundancy in the\nstandard DDQ POD approach that uses all of the snapshots, DQs, and DDQs. We\nshow that this new DDQ approach also has pointwise in time data error bounds\nsimilar to DQ POD and use it to prove pointwise and energy ROM error bounds. We\nprovide numerical results for the POD errors and ROM errors to demonstrate the\ntheoretical results. We also explore an application of POD to simulating ROMs\npast the training interval for collecting the snapshot data for the standard\nPOD approach and the DDQ POD method.\n']","[('reduced order modeling', 0.5682281255722046), ('orthogonal decomposition pod', 0.5184025764465332), ('orthogonal decomposition reduced', 0.5017828345298767), ('reduced order models', 0.49538159370422363), ('decomposition reduced order', 0.4862692058086395), ('orthogonal decomposition', 0.47992080450057983), ('proper orthogonal decomposition', 0.45533299446105957), ('time reduced order', 0.44951868057250977), ('based reduced order', 0.3998005986213684), ('decomposition least', 0.39635056257247925)]"
1251,1251,23,1251_massive mimo systems_massive mimo system_free massive mimo_massive mimo,"['massive mimo systems', 'massive mimo system', 'free massive mimo', 'massive mimo', 'mimo systems', 'mimo reconfigurable intelligent', 'mimo system', 'output mimo', 'multiple output mimo', 'mimo reconfigurable']","['Statistical CSI-based Design for Reconfigurable Intelligent\n  Surface-aided Massive MIMO Systems with Direct Links   This paper investigates the performance of reconfigurable intelligent surface\n(RIS)-aided massive multiple-input multiple-output (MIMO) systems with direct\nlinks, and the phase shifts of the RIS are designed based on the statistical\nchannel state information (CSI). We first derive the closed-form expression of\nthe uplink ergodic data rate. Then, based on the derived expression, we use the\ngenetic algorithm (GA) to solve the sum data rate maximization problem. With\nlow-complexity maximal-ratio combination (MRC) and low-overhead statistical\nCSI-based scheme, we validate that the RIS can still bring significant\nperformance gains to traditional massive MIMO systems.\n', 'Two-Timescale Design for Reconfigurable Intelligent Surface-Aided\n  Massive MIMO Systems with Imperfect CSI   This paper investigates the two-timescale transmission design for\nreconfigurable intelligent surface (RIS)-aided massive multiple-input\nmultiple-output (MIMO) systems, where the beamforming at the base station (BS)\nis adapted to the rapidly-changing instantaneous channel state information\n(CSI), while the passive beamforming at the RIS is adapted to the\nslowly-changing statistical CSI.\n  Specifically, we first propose a linear minimum mean square error (LMMSE)\nestimator to obtain the aggregated channel from the users to the BS in each\nchannel coherence interval. Based on the estimated channel, we apply the\nlow-complexity maximal ratio combining (MRC) beamforming at the BS, and then\nderive the ergodic achievable rate in a closed form expression.\n  To draw design insights, we perform a detailed theoretical analysis departing\nfrom the derived ergodic achievable rate. If the BS-RIS channel is Rician\ndistributed, we prove that the transmit power can be scaled proportionally to\n$1/M$, as the number of BS antennas, $M$, grows to infinity while maintaining a\nnon-zero rate.\n  If the BS-RIS channel is Rayleigh distributed, the transmit power can be\nscaled either proportionally to $1/\\sqrt{M}$ as $M$ grows large, or\nproportionally to $1/N$ as the number of reflecting elements, $N$, grows large,\nwhile still maintaining a non-zero rate.\n  By capitalizing on the derived expression of the data rate under the\nstatistical knowledge of the CSI, we maximize the minimum user rate by\ndesigning the passive beamforming at the RIS.\n  Numerical results confirm that, even in the presence of imperfect CSI, the\nintegration of an RIS in massive MIMO systems results in promising performance\ngains. In addition, the obtained results reveal that it is favorable to place\nthe RIS close to the users rather than close to the BS.\n', 'Ergodic Rate Analysis of Reconfigurable Intelligent Surface-Aided\n  Massive MIMO Systems with ZF Detectors   This letter investigates the reconfigurable intelligent surface (RIS)-aided\nmassive multiple-input multiple-output (MIMO) systems with a two-timescale\ndesign. First, the zero-forcing (ZF) detector is applied at the base station\n(BS) based on instantaneous aggregated CSI, which is the superposition of the\ndirect channel and the cascaded user-RIS-BS channel. Then, by leveraging the\nchannel statistical property, we derive the closed-form ergodic achievable rate\nexpression. Using a gradient ascent method, we design the RIS passive\nbeamforming only relying on the long-term statistical CSI. We prove that the\nergodic rate can reap the gains on the order of\n$\\mathcal{O}\\left(\\log_{2}\\left(MN\\right)\\right)$, where $M$ and $N$ denote the\nnumber of BS antennas and RIS elements, respectively. We also prove the\nstriking superiority of the considered RIS-aided system with ZF detectors over\nthe RIS-free systems and RIS-aided systems with maximum-ratio combining (MRC).\n']","[('massive mimo systems', 0.6846807599067688), ('massive mimo system', 0.6530582308769226), ('free massive mimo', 0.638324499130249), ('massive mimo', 0.6376447677612305), ('mimo systems', 0.5855592489242554), ('mimo reconfigurable intelligent', 0.535973072052002), ('mimo system', 0.529849112033844), ('output mimo', 0.5105649828910828), ('multiple output mimo', 0.49833452701568604), ('mimo reconfigurable', 0.49169713258743286)]"
1252,1252,23,1252_banach frames_banach spaces also_schauder basis_banach spaces,"['banach frames', 'banach spaces also', 'schauder basis', 'banach spaces', 'banach space', 'subsets banach spaces', 'separable banach spaces', 'separable banach space', 'hilbert spaces', 'bessel sequences']","['On characterizations of a some classes of Schauder frames in Banach\n  spaces   In this paper, we prove the following results. There exists a Banach space\nwithout basis which has a Schauder frame. There exists an universal Banach\nspace $B$ (resp. $\\tilde{B}$) with a basis (resp. an unconditional basis) such\nthat, a Banach $X$ has a Schauder frame (resp. an unconditional Schauder frame\n) if and only if $X$ is isomorphic to a complemented subspace of $B$ (resp.\n$\\tilde{B}$). For a weakly sequentially complete Banach space, a Schauder frame\nis unconditional if and only if it is besselian. A separable Banach space $X$\nhas a Schauder frame if and only if it has the bounded approximation property.\nConsequenty, The Banach space $\\mathcal{L}(\\mathcal{H},\\mathcal{H})$ of all\nbounded linear operators on a Hilbert space $\\mathcal{H}$ has no Schauder\nframe. Also, if $X$ and $Y$ are Banach spaces with Schauder frames then, the\nBanach space $ X\\widehat{\\otimes}_{\\pi}Y$ (the projective tensor product of $X$\nand $Y$) has a Schauder frame. From the Faber$-$Schauder system we construct a\nSchauder frame for the Banach space $C[0,1]$ (the Banach space of continuous\nfunctions on the closed interval $ [0,1]$) which is not a Schauder basis of\n$C[0,1]$. Finally, we give a positive answer to some open problems related to\nthe Schauder bases (In the Schauder frames setting).\n', 'Perturbation of Schauder frames and besselian Schauder frames in Banach\n  spaces   We consider the stability of Schauder frames and besselian Schauder frames\nunder perturbations. Our results are inspirit close to the results of Heil\n[18].\n', 'About Schauder frames and besselian Schauder frames of Banach spaces   In this paper, we introduce, for a separable Banach spacea new notion of\nbesselian paires and of besselian Schauder frames for which we prove for some\nfundamental results.\n']","[('banach frames', 0.5894823670387268), ('banach spaces also', 0.5657916069030762), ('schauder basis', 0.5606204271316528), ('banach spaces', 0.5397748947143555), ('banach space', 0.5133463740348816), ('subsets banach spaces', 0.5040565729141235), ('separable banach spaces', 0.49649834632873535), ('separable banach space', 0.4630996286869049), ('hilbert spaces', 0.4399084150791168), ('bessel sequences', 0.4196273386478424)]"
1253,1253,23,1253_distributional approximation_type estimators_estimators_estimators including,"['distributional approximation', 'type estimators', 'estimators', 'estimators including', 'distribution generalization', 'asymptotic approximations', 'distribution alpha', 'gamma distribution', 'gaussian distributions', 'new asymptotic']","['Strong uniform laws of large numbers for bootstrap means and other\n  randomly weighted sums   This article establishes novel strong uniform laws of large numbers for\nrandomly weighted sums such as bootstrap means. By leveraging recent advances,\nthese results extend previous work in their general applicability to a wide\nrange of weighting procedures and in their flexibility with respect to the\neffective bootstrap sample size. In addition to the standard multinomial\nbootstrap and the m-out-of-n bootstrap, our results apply to a large class of\nrandomly weighted sums involving negatively orthant dependent (NOD) weights,\nincluding the Bayesian bootstrap, jackknife, resampling without replacement,\nsimple random sampling with over-replacement, independent weights, and\nmultivariate Gaussian weighting schemes. Weights are permitted to be\nnon-identically distributed and possibly even negative. Our proof technique is\nbased on extending a proof of the i.i.d. strong uniform law of large numbers to\nemploy strong laws for randomly weighted sums; in particular, we exploit a\nrecent Marcinkiewicz--Zygmund strong law for NOD weighted sums.\n', ""Bounds for distributional approximation in the multivariate delta method\n  by Stein's method   We obtain bounds to quantify the distributional approximation in the delta\nmethod for vector statistics (the sample mean of $n$ independent random\nvectors) for normal and non-normal limits, measured using smooth test\nfunctions. For normal limits, we obtain bounds of the optimal order $n^{-1/2}$\nrate of convergence, but for a wide class of non-normal limits, which includes\nquadratic forms amongst others, we achieve bounds with a faster order $n^{-1}$\nconvergence rate. We apply our general bounds to derive explicit bounds to\nquantify distributional approximations of an estimator for Bernoulli variance,\nseveral statistics of sample moments, order $n^{-1}$ bounds for the chi-square\napproximation of a family of rank-based statistics, and we also provide an\nefficient independent derivation of an order $n^{-1}$ bound for the chi-square\napproximation of Pearson's statistic. In establishing our general results, we\ngeneralise recent results on Stein's method for functions of multivariate\nnormal random vectors to vector-valued functions and sums of independent random\nvectors whose components may be dependent. These bounds are widely applicable\nand are of independent interest.\n"", 'Multivariate $\\alpha$-normal distributions   The Weibull distribution can be obtained using a power transformation from\nthe standard exponential distribution. In this article, we will consider a\nsymmetrized power transformation of a random variable with the standard normal\ndistribution. We will call its distribution the $\\alpha$-{\\it normal (Gaussian)\ndistribution}. We examine properties of this distribution in detail. We\ncalculate moments and consider the moment problem of $\\alpha$-normal\ndistribution. We derive the formula of its differential entropy and\n(exponential) Orlicz norm. % of $\\alpha$-normal random variables. Moreover, we\ndefine the joint distribution function of the multivariate $\\alpha$-normal\ndistribution as a meta-Gaussian distribution with $\\alpha$-normal marginals. We\nconsider also the limiting distribution as $\\alpha$ tends to infinity.\n']","[('distributional approximation', 0.5007631182670593), ('type estimators', 0.48422208428382874), ('estimators', 0.4746391177177429), ('estimators including', 0.442501425743103), ('distribution generalization', 0.44153380393981934), ('asymptotic approximations', 0.4372744560241699), ('distribution alpha', 0.4114111363887787), ('gamma distribution', 0.39695581793785095), ('gaussian distributions', 0.3886868357658386), ('new asymptotic', 0.381115585565567)]"
1254,1254,23,1254_relu networks_relu neural networks_networks relu_neural networks finite,"['relu networks', 'relu neural networks', 'networks relu', 'neural networks finite', 'shallow relu neural', 'relu neural network', 'shallow neural networks', 'relu network', 'relu neural', 'shallow neural']","['ReLU Deep Neural Networks and Linear Finite Elements   In this paper, we investigate the relationship between deep neural networks\n(DNN) with rectified linear unit (ReLU) function as the activation function and\ncontinuous piecewise linear (CPWL) functions, especially CPWL functions from\nthe simplicial linear finite element method (FEM). We first consider the\nspecial case of FEM. By exploring the DNN representation of its nodal basis\nfunctions, we present a ReLU DNN representation of CPWL in FEM. We\ntheoretically establish that at least $2$ hidden layers are needed in a ReLU\nDNN to represent any linear finite element functions in $\\Omega \\subseteq\n\\mathbb{R}^d$ when $d\\ge2$. Consequently, for $d=2,3$ which are often\nencountered in scientific and engineering computing, the minimal number of two\nhidden layers are necessary and sufficient for any CPWL function to be\nrepresented by a ReLU DNN. Then we include a detailed account on how a general\nCPWL in $\\mathbb R^d$ can be represented by a ReLU DNN with at most\n$\\lceil\\log_2(d+1)\\rceil$ hidden layers and we also give an estimation of the\nnumber of neurons in DNN that are needed in such a representation. Furthermore,\nusing the relationship between DNN and FEM, we theoretically argue that a\nspecial class of DNN models with low bit-width are still expected to have an\nadequate representation power in applications. Finally, as a proof of concept,\nwe present some numerical results for using ReLU DNNs to solve a two point\nboundary problem to demonstrate the potential of applying DNN for numerical\nsolution of partial differential equations.\n', ""Better Neural Network Expressivity: Subdividing the Simplex This work studies the expressivity of ReLU neural networks with a focus on their depth. A sequence of previous works showed that $\\lceil \\log_2(n+1) \\rceil$ hidden layers are sufficient to compute all continuous piecewise linear (CPWL) functions on $\\mathbb{R}^n$. Hertrich, Basu, Di Summa, and Skutella (NeurIPS'21) conjectured that this result is optimal in the sense that there are CPWL functions on $\\mathbb{R}^n$, like the maximum function, that require this depth. We disprove the conjecture and show that $\\lceil\\log_3(n-1)\\rceil+1$ hidden layers are sufficient to compute all CPWL functions on $\\mathbb{R}^n$.\n  A key step in the proof is that ReLU neural networks with two hidden layers can exactly represent the maximum function of five inputs. More generally, we show that $\\lceil\\log_3(n-2)\\rceil+1$ hidden layers are sufficient to compute the maximum of $n\\geq 4$ numbers. Our constructions almost match the $\\lceil\\log_3(n)\\rceil$ lower bound of Averkov, Hojny, and Merkert (ICLR'25) in the special case of ReLU networks with weights that are decimal fractions. The constructions have a geometric interpretation via polyhedral subdivisions of the simplex into ``easier'' polytopes."", 'Shallow ReLU neural networks and finite elements   We point out that (continuous or discontinuous) piecewise linear functions on\na convex polytope mesh can be represented by two-hidden-layer ReLU neural\nnetworks in a weak sense. In addition, the numbers of neurons of the two hidden\nlayers required to weakly represent are accurately given based on the numbers\nof polytopes and hyperplanes involved in this mesh. The results naturally hold\nfor constant and linear finite element functions. Such weak representation\nestablishes a bridge between shallow ReLU neural networks and finite element\nfunctions, and leads to a perspective for analyzing approximation capability of\nReLU neural networks in $L^p$ norm via finite element functions. Moreover, we\ndiscuss the strict representation for tensor finite element functions via the\nrecent tensor neural networks.\n']","[('relu networks', 0.6239239573478699), ('relu neural networks', 0.578095018863678), ('networks relu', 0.568760335445404), ('neural networks finite', 0.5655317902565002), ('shallow relu neural', 0.5614851713180542), ('relu neural network', 0.5534970164299011), ('shallow neural networks', 0.5491368770599365), ('relu network', 0.4893045127391815), ('relu neural', 0.4842694103717804), ('shallow neural', 0.47126221656799316)]"
1255,1255,23,1255_growth fragmentation_fragmentation processes_fragmentation process_fragmentation models,"['growth fragmentation', 'fragmentation processes', 'fragmentation process', 'fragmentation models', 'fragmentation', 'dimensional brownian motion', 'markov processes', 'coalescence', 'similar markov processes', 'solutions growth']","[""A growth-fragmentation model related to Ornstein-Uhlenbeck type\n  processes   Growth-fragmentation processes describe systems of particles in which each\nparticle may grow larger or smaller, and divide into smaller ones as time\nproceeds. Unlike previous studies, which have focused mainly on the\nself-similar case, we introduce a new type of growth-fragmentation which is\nclosely related to L\\'evy driven Ornstein-Uhlenbeck type processes. Our model\ncan be viewed as a generalization of compensated fragmentation processes\nintroduced by Bertoin, or the stochastic counterpart of a family of\ngrowth-fragmentation equations. We establish a convergence criterion for a\nsequence of such growth-fragmentations. We also prove that, under certain\nconditions, this system fulfills a law of large numbers.\n"", 'Growth-fragmentation process embedded in a planar Brownian excursion   The aim of this paper is to present a self-similar growth-fragmentation\nprocess linked to a Brownian excursion in the upper half-plane $\\mathbb{H}$,\nobtained by cutting the excursion at horizontal levels. We prove that the\nassociated growth-fragmentation is related to one of the growth-fragmentation\nprocesses introduced by Bertoin, Budd, Curien and Kortchemski.\n', 'Growth-fragmentation processes and bifurcators   Markovian growth-fragmentation processes introduced by Bertoin model a system\nof growing and splitting cells in which the size of a typical cell evolves as a\nMarkov process $X$ without positive jumps. We find that two\ngrowth-fragmentation processes associated respectively with two processes $X$\nand $Y$ (with different laws) may have the same distribution, if $(X,Y)$ is a\nbifurcator, roughly speaking, which means that they coincide up to a\nbifurcation time and then evolve independently. Using this criterion, we deduce\nthat the law of a self-similar growth-fragmentation is determined by a cumulant\nfunction $\\kappa$ and its index of self-similarity.\n']","[('growth fragmentation', 0.7018988132476807), ('fragmentation processes', 0.6959892511367798), ('fragmentation process', 0.6792997717857361), ('fragmentation models', 0.6408039331436157), ('fragmentation', 0.6395830512046814), ('dimensional brownian motion', 0.42195624113082886), ('markov processes', 0.406673789024353), ('coalescence', 0.4057094156742096), ('similar markov processes', 0.4033116400241852), ('solutions growth', 0.40292051434516907)]"
1256,1256,23,1256_irradiation_scattering_stability theory_forward scattering,"['irradiation', 'scattering', 'stability theory', 'forward scattering', 'stabilizing effect', 'scattering coefficient', 'stability findings', 'stability', 'suspension', 'stability analysis']","['Effect of Rotation in an Isotropic Scattering Algal Suspension with\n  Oblique Collimated Irradiation   The linear stability of a suspension of isotropic scattering phototactic\nalgae is investigated numerically with particular emphasis on the effects of\nTaylor number in the rotating medium. The suspension is illuminated by the\noblique collimated irradiation. The solutions show a transition of the most\nunstable mode from stationary to an overstable state or vice versa for certain\nparameters at the variation in the Taylor number. Oscillatory instabilities are\nalso observed at the three-quarter height of the suspension for some\nparameters.\n', 'Effect of oblique irradiation on the onset of thermal phototactic\n  bioconvection in non-scattering medium   The linear stability of a suspension of phototactic algae is investigated\nnumerically with particular emphasis on the effects of the angle of incidence\nof the illuminating oblique collimated irradiation with thermal effects. The\nsuspension is illuminated by the oblique collimated irradiation from the top\nand heated/cooled from the bottom. The linear stability analysis shows that the\nsuspension becomes more unstable as the angle of incidence increases.\n', 'Effect of oblique irradiation on the onset of\n  thermal-phototactic-bioconvection in an isotropic scattering algal suspension   In this study, our focus is mainly to check the effect of light scattering on\nthe onset of thermal-phototactic-bioconvection in an algal suspension where the\nsuspension is illuminated by the collimated oblique irradiation from above\nwhile simultaneously applying heating or cooling from below. We conduct a\nnumerical investigation into the linear stability of a suspension containing\nphototactic algae, focusing particularly on how the angle of incidence of\noblique collimated irradiation influences the system. Our solutions reveal a\ntransition of the most unstable mode from a stationary to an overstable state,\nor vice versa, under certain parameter configurations as the angle of incidence\nvaries. Additionally, we frequently observe oscillatory instabilities in cases\nwhere the upper surface is rigid, particularly as the angle of incidence\nincreases within the suspension.\n']","[('irradiation', 0.3293617367744446), ('scattering', 0.3234904110431671), ('stability theory', 0.3046411871910095), ('forward scattering', 0.29493558406829834), ('stabilizing effect', 0.28971442580223083), ('scattering coefficient', 0.2881464660167694), ('stability findings', 0.2780909240245819), ('stability', 0.2680094540119171), ('suspension', 0.2573114037513733), ('stability analysis', 0.253020316362381)]"
1257,1257,23,1257_computability theoretic_computability theory_algorithmic randomness_reducibility,"['computability theoretic', 'computability theory', 'algorithmic randomness', 'reducibility', 'computably enumerable', 'computability', 'weakly random', 'randomness', 'computable', 'turing degrees']","['KL-randomness and effective dimension under strong reducibility   We show that the (truth-table) Medvedev degree KLR of Kolmogorov--Loveland\nrandomness coincides with that of Martin L\\""of randomness, MLR, answering a\nquestion of Miyabe. Next, an analogue of complex packing dimension is studied\nwhich gives rise to a set of weak truth-table Medvedev degrees isomorphic to\nthe Turing degrees.\n', 'A total Solovay reducibility and totalizing of the notion of\n  speedability   While the set of Martin-L\\""of random left-c.e. reals is equal to the maximum\ndegree of Solovay reducibility, Miyabe, Nies and\nStephan(DOI:10.4115/jla.2018.10.3) have shown that the left-c.e. Schnorr random\nreals are not closed upwards under Solovay reducibility. Recall that for two\nleft-c.e. reals~$\\alpha$ and~$\\beta$, the former is Solovay reducible to the\nlatter in case there is a partially computable function $\\varphi$ and\nconstant~$c$ such that for all rational numbers $q < \\beta$ we have \\[\\alpha -\n\\varphi(q) < c(\\beta - q).\\] By requiring the translation function $\\varphi$ to\nbe total, we introduce a total version of Solovay reducibility that implies\nSchnorr reducibility. Accordingly, by Downey and Griffiths\n(DOI:10.2178/jsl/1082418542), the set of Schnorr random left-c.e. reals is\nclosed upwards relative to total Solovay reducibility.\n  Furthermore, we observe that the notion of speedability introduced by Merkle\nand Titov (DOI:10.1007/978-3-030-50026-9_22) can be equivalently characterized\nvia partial computable translation functions in a way that resembles Solovay\nreducibility. By requiring the translation function to be total, we obtain the\nconcept of total speedability. Like for speedability, this notion does not\ndepend on the choice of the speeding constant.\n', 'Degrees of Randomized Computability   In this survey we discuss work of Levin and V\'yugin on collections of\nsequences that are non-negligible in the sense that they can be computed by a\nprobabilistic algorithm with positive probability. More precisely, Levin and\nV\'yugin introduced an ordering on collections of sequences that are closed\nunder Turing equivalence. Roughly speaking, given two such collections\n$\\mathcal{A}$ and $\\mathcal{B}$, $\\mathcal{A}$ is below $\\mathcal{B}$ in this\nordering if $\\mathcal{A}\\setminus\\mathcal{B}$ is negligible. The degree\nstructure associated with this ordering, the Levin-V\'yugin degrees (or\nLV-degrees), can be shown to be a Boolean algebra, and in fact a measure\nalgebra.\n  We demonstrate the interactions of this work with recent results in\ncomputability theory and algorithmic randomness: First, we recall the\ndefinition of the Levin-V\'yugin algebra and identify connections between its\nproperties and classical properties from computability theory. In particular,\nwe apply results on the interactions between notions of randomness and Turing\nreducibility to establish new facts about specific LV-degrees, such as the\nLV-degree of the collection of 1-generic sequences, that of the collection of\nsequences of hyperimmune degree, and those collections corresponding to various\nnotions of effective randomness. Next, we provide a detailed explanation of a\ncomplex technique developed by V\'yugin that allows the construction of\nsemi-measures into which computability-theoretic properties can be encoded. We\nprovide two examples of the use of this technique by explicating a result of\nV\'yugin\'s about the LV-degree of the collection of Martin-L\\""of random\nsequences and extending the result to the LV-degree of the collection of\nsequences of DNC degree.\n']","[('computability theoretic', 0.5873975157737732), ('computability theory', 0.5733027458190918), ('algorithmic randomness', 0.5209351778030396), ('reducibility', 0.5159754753112793), ('computably enumerable', 0.48782557249069214), ('computability', 0.4859570264816284), ('weakly random', 0.4575660824775696), ('randomness', 0.4563398063182831), ('computable', 0.44810059666633606), ('turing degrees', 0.4471488893032074)]"
1258,1258,23,1258_stochastic hamilton jacobi_stochastic homogenization_viscous hamilton jacobi_viscous hamilton,"['stochastic hamilton jacobi', 'stochastic homogenization', 'viscous hamilton jacobi', 'viscous hamilton', 'variational solutions', 'stochastic hamilton', 'degenerate viscous', 'regularity stochastic', 'hamilton jacobi equations', 'stationary ergodic']","['Homogenization of nonconvex viscous Hamilton-Jacobi equations in\n  stationary ergodic media in one dimension   We establish homogenization for nondegenerate viscous Hamilton-Jacobi\nequations in one space dimension when the diffusion coefficient $a(x,\\omega) >\n0$ and the Hamiltonian $H(p,x,\\omega)$ are general stationary ergodic processes\nin $x$. Our result is valid under mild regularity assumptions on $a$ and $H$\nplus standard coercivity and growth assumptions (in $p$) on the latter. In\nparticular, we impose neither any additional condition on the law of the media\nnor any shape restriction on the graph of $p\\mapsto H(p,x,\\omega)$. Our\napproach consists of two main steps: (i) constructing a suitable candidate\n$\\overline{H}$ for the effective Hamiltonian; (ii) proving homogenization. In\nthe first step, we work with the set $E$ of all points at which $\\overline{H}$\nis naturally determined by correctors with stationary derivatives. We prove\nthat $E$ is a closed subset of $\\mathbb{R}$ that is unbounded from above and\nbelow, and, if $E\\neq\\mathbb{R}$, then $\\overline{H}$ can be extended\ncontinuously to $\\mathbb{R}$ by setting it to be constant on each connected\ncomponent of $E^c$. In the second step, we use a key bridging lemma, comparison\narguments and several general results to verify that homogenization holds with\nthis $\\overline{H}$ as the effective Hamiltonian.\n', 'Stochastic homogenization of a class of quasiconvex viscous\n  Hamilton-Jacobi equations in one space dimension   We prove homogenization for a class of viscous Hamilton-Jacobi equations in\nthe stationary and ergodic setting in one space dimension. Our assumptions\ninclude most notably the following: the Hamiltonian is of the form $G(p) +\n\\beta V(x,\\omega)$, the function $G$ is coercive and strictly quasiconvex,\n$\\min G = 0$, $\\beta>0$, the random potential $V$ takes values in $[0,1]$ with\nfull support and it satisfies a hill condition that involves the diffusion\ncoefficient. Our approach is based on showing that, for every direction outside\nof a bounded interval $(\\theta_1(\\beta),\\theta_2(\\beta))$, there is a unique\nsublinear corrector with certain properties. We obtain a formula for the\neffective Hamiltonian and deduce that it is coercive, identically equal to\n$\\beta$ on $(\\theta_1(\\beta),\\theta_2(\\beta))$, and strictly monotone\nelsewhere.\n', ""Stochastic homogenization of nonconvex viscous Hamilton-Jacobi equations\n  in one space dimension   We prove homogenization for viscous Hamilton-Jacobi equations with a\nHamiltonian of the form $G(p)+V(x,\\omega)$ for a wide class of stationary\nergodic random media in one space dimension. The momentum part $G(p)$ of the\nHamiltonian is a general (nonconvex) continuous function with superlinear\ngrowth at infinity, and the potential $V(x,\\omega)$ is bounded and Lipschitz\ncontinuous. The class of random media we consider is defined by an explicit\nhill and valley condition on the diffusivity-potential pair which is fulfilled\nas long as the environment is not ``rigid''.\n""]","[('stochastic hamilton jacobi', 0.6495854258537292), ('stochastic homogenization', 0.6127980351448059), ('viscous hamilton jacobi', 0.6056408882141113), ('viscous hamilton', 0.5693391561508179), ('variational solutions', 0.5586128234863281), ('stochastic hamilton', 0.5486692190170288), ('degenerate viscous', 0.5317937731742859), ('regularity stochastic', 0.5005919933319092), ('hamilton jacobi equations', 0.4764757454395294), ('stationary ergodic', 0.4611060917377472)]"
1259,1259,23,1259_markov semigroups_markov semigroup_semigroup markov_transition semigroup,"['markov semigroups', 'markov semigroup', 'semigroup markov', 'transition semigroup', 'continuous markov', 'ergodic measure', 'semigroups', 'semigroup space', 'markov feller', 'limit semigroup']","[""Ergodicity for eventually continuous Markov--Feller semigroups on Polish\n  spaces   This paper investigates the ergodicity of Markov--Feller semigroups on Polish\nspaces, focusing on very weak regularity conditions, particularly the Ces\\`aro\neventual continuity. First, it is showed that the Ces\\`aro average of such\nsemigroups weakly converges to an ergodic measure when starting from its\nsupport. This leads to a characterization of the relationship between Ces\\`aro\neventual continuity, Ces\\`aro e-property, and weak-* mean ergodicity. Next,\nserval criteria are provided for the existence and uniqueness of invariant\nmeasures via Ces\\`aro eventual continuity and lower bound conditions,\nestablishing an equivalence relation between weak-* mean ergodicity and a lower\nbound condition. Additionally, some refined properties of ergodic decomposition\nare derived. Finally, the results are applied to several non-trivial examples,\nincluding iterated function systems, Hopf's turbulence model with random\nforces, and Lorenz system with noisy perturbations, either with or without\nCes\\`aro eventual continuity.\n"", 'The e-property of asymptotically stable Markov semigroups   The relations between asymptotic stability, the eventual e-property and the\ne-property of Markov semigroups, acting on measures defined on general (Polish)\nmetric spaces, are studied. While usually much attention is paid to asymptotic\nstability (and the e-property has been for years verified only to establish\nit), it should be noted that the e-property itself is also important as it,\ne.g., ensures that numerical errors in simulations are negligible.\n  Here, it is shown that any asymptotically stable Markov-Feller semigroup with\nan invariant measure such that the interior of its support is non-empty\nsatisfies the eventual e-property. Moreover, we prove that any Markov-Feller\nsemigroup, which is strongly stochastically continuous, and which possesses the\neventual e-property, also has the e-property. We also present an example\nhighlighting that strong stochastic continuity cannot be replaced by its weak\ncounterpart, unless a state space of a process corresponding to a Markov\nsemigroup is a compact metric space.\n', 'Relation between the eventual continuity and the e-property for\n  Markov-Feller semigroups   We investigate the relation between the e-property and the eventual\ncontinuity, or called the asymptotic equicontinuity, which is a generalization\nof the e-property. We prove that, for any discrete-time or strongly continuous\ncontinuous-time eventually continuous Markov-Feller semigroup with an ergodic\nmeasure, if the interior of the support of the ergodic measure is nonempty,\nthen the e-property is satisfied on the interior of the support. In particular,\nit implies that, restricted on the support of each ergodic measure, the\ne-property and the eventual continuity are equivalent for the discrete-time and\nthe strongly continuous continuous-time Markov-Feller semigroups.\n']","[('markov semigroups', 0.7194849252700806), ('markov semigroup', 0.6917837262153625), ('semigroup markov', 0.6680599451065063), ('transition semigroup', 0.5658559799194336), ('continuous markov', 0.5582672953605652), ('ergodic measure', 0.5429261326789856), ('semigroups', 0.5303409695625305), ('semigroup space', 0.5289983153343201), ('markov feller', 0.5207040309906006), ('limit semigroup', 0.49877530336380005)]"
1260,1260,23,1260_vacuum spacetimes_spacetimes compact cauchy_vacuum spacetime_spacetimes compact,"['vacuum spacetimes', 'spacetimes compact cauchy', 'vacuum spacetime', 'spacetimes compact', 'cauchy horizon', 'einstein vacuum equations', 'spacetimes establish', 'zero cosmological', 'cauchy surfaces', 'black holes']","[""On the existence of Killing fields in smooth spacetimes with a compact\n  Cauchy horizon   We prove that the surface gravity of a compact non-degenerate Cauchy horizon\nin a smooth vacuum spacetime, can be normalized to a non-zero constant. This\nresult, combined with a recent result by Oliver Petersen and Istv\\'an R\\'acz,\nend up proving the Isenberg-Moncrief conjecture on the existence of Killing\nfields, in the smooth differentiability class. The well known corollary of\nthis, in accordance with the strong cosmic censorship conjecture, is that the\npresence of compact Cauchy horizons is a non-generic phenomenon. Though we work\nin 3+1, the result is valid line by line in any n+1-dimensions.\n"", ""Extension of Killing vector fields beyond compact Cauchy horizons   We prove that any compact Cauchy horizon with constant non-zero surface\ngravity in a smooth vacuum spacetime is a smooth Killing horizon. The novelty\nhere is that the Killing vector field is shown to exist on both sides of the\nhorizon. This generalises classical results by Moncrief and Isenberg, by\ndropping the assumption that the metric is analytic. In previous work by R\\'acz\nand the author, the Killing vector field was constructed on the globally\nhyperbolic side of the horizon. In this paper, we prove a new unique\ncontinuation theorem for wave equations through smooth compact lightlike\n(characteristic) hypersurfaces which allows us to extend the Killing vector\nfield beyond the horizon. The main ingredient in the proof of this theorem is a\nnovel Carleman type estimate. Using a well-known construction, our result\napplies in particular to smooth stationary asymptotically flat vacuum black\nhole spacetimes with event horizons with constant non-zero surface gravity. As\na special case, we therefore recover Hawking's local rigidity theorem for such\nblack holes, which was recently proven by Alexakis-Ionescu-Klainerman using a\ndifferent Carleman type estimate.\n"", ""Symmetries of vacuum spacetimes with a compact Cauchy horizon of\n  constant non-zero surface gravity   We prove that any smooth vacuum spacetime containing a compact Cauchy horizon\nwith surface gravity that can be normalised to a non-zero constant admits a\nKilling vector field. This proves a conjecture by Moncrief and Isenberg from\n1983 under the assumption on the surface gravity and generalises previous\nresults due to Moncrief-Isenberg and Friedrich-R\\'acz-Wald, where the\ngenerators of the Cauchy horizon were closed or densely filled a 2-torus.\nConsequently, the maximal globally hyperbolic vacuum development of generic\ninitial data cannot be extended across a compact Cauchy horizon with surface\ngravity that can be normalised to a non-zero constant. Our result supports,\nthereby, the validity of the strong cosmic censorship conjecture in the\nconsidered special case. The proof consists of two main steps. First, we show\nthat the Killing equation can be solved up to infinite order at the Cauchy\nhorizon. Second, by applying a recent result of the first author on wave\nequations with initial data on a compact Cauchy horizon, we show that this\nKilling vector field extends to the globally hyperbolic region.\n""]","[('vacuum spacetimes', 0.5592913031578064), ('spacetimes compact cauchy', 0.5532580614089966), ('vacuum spacetime', 0.5367348790168762), ('spacetimes compact', 0.5228875875473022), ('cauchy horizon', 0.5120164155960083), ('einstein vacuum equations', 0.502903938293457), ('spacetimes establish', 0.47866594791412354), ('zero cosmological', 0.4772455394268036), ('cauchy surfaces', 0.45471131801605225), ('black holes', 0.4500286877155304)]"
1261,1261,23,1261_driven sdes_stochastic differential_alpha stable processes_sdes driven,"['driven sdes', 'stochastic differential', 'alpha stable processes', 'sdes driven', 'distributional drift', 'sde driven', 'stable process alpha', 'driven alpha stable', 'alpha stable process', 'stable processes']","['SDE driven by cylindrical $\\alpha$-stable process with distributional\n  drift and application   For $\\alpha \\in (1,2)$, we study the following stochastic differential\nequation driven by a non-degenerate symmetric $\\alpha$-stable process in\n${\\mathbb R}^d$:\n  \\begin{align*} {\\mathord{{\\rm d}}} X_t=b(t,X_t){\\mathord{{\\rm d}}}\nt+\\sigma(t,X_{t-}){\\mathord{{\\rm d}}} L_t^{(\\alpha)},\\ \\ X_0 =x \\in {\\mathbb\nR}^d, \\end{align*} where $b$ belongs to $ L^\\infty({\\mathbb R}_+;{\\mathbf\nB}_{\\infty,\\infty}^{-\\beta}({\\mathbb R}^d))$ with some\n$\\beta\\in(0,\\frac{\\alpha-1}{2})$, and $\\sigma:{\\mathbb R}_+\\times {\\mathbb R}^d\n\\to {\\mathbb R}^d \\otimes {\\mathbb R}^d$ is a $d \\times d $ matrix-valued\nmeasurable function. We point out that the noise could be a cylindrical\n$\\alpha$-stable process. We first show the generalized martingale problems and\nthen establish the stability estimates of solutions. As an application, we give\nthe weak convergence rate of the Euler scheme for additive noises with drift\ncoefficient $b=b(x)$.\n', ""Optimal Wasserstein-$1$ distance between SDEs driven by Brownian motion\n  and stable processes   We are interested in the following two $\\mathbb{R}^d$-valued stochastic\ndifferential equations (SDEs):\n  \\begin{gather*}\n  d X_t=b(X_t)\\,d t + \\sigma\\,d L_t, \\quad X_0=x,\n  %\\label{BM-SDE}\n  d Y_t=b(Y_t)\\,d t + \\sigma\\,d B_t, \\quad Y_0=y,\n  \\end{gather*}\n  where $\\sigma$ is an invertible $d\\times d$ matrix, $L_t$ is a rotationally\nsymmetric $\\alpha$-stable L\\'evy process, and $B_t$ is a $d$-dimensional\nstandard Brownian motion (note that $B_t$ is a rotationally symmetric\n$\\alpha$-stable L\\'evy process with $\\alpha=2$). We show that for any $\\alpha_0\n\\in (1,2)$ the Wasserstein-$1$ distance $W_1$ satisfies for $\\alpha \\in\n[\\alpha_0,2)$\n  \\begin{gather*}\n  W_{1}\\left(X_{t}^x, Y_{t}^y\\right)\n  \\leq C_1 e^{-C_2t}|x-y|\n  +\\frac{C}{\\alpha_0-1}(2-\\alpha)d\\log(1+d),\n  \\end{gather*}\n  which implies, in particular,\n  \\begin{equation} \\label{e:W1Rate}\n  W_1(\\mu_\\alpha, \\mu_2)\n  \\leq \\frac{C}{\\alpha_0-1}(2-\\alpha)d\\log(1+d),\n  \\end{equation}\n  where $\\mu_\\alpha$ and $\\mu_2$ are the ergodic measures of $X_t$ and $Y_t$\nrespectively.\n  For the special case of a $d$-dimensional Ornstein--Uhlenbeck system, we show\nthat $W_1(\\mu_\\alpha, \\mu_2) \\geq C_{d} (2-\\alpha)$ for all $\\alpha\\in(1,2)$;\nthis indicates that the convergence rate with respect to $\\alpha$ in the second\nbound is optimal. The term $d\\log(1+d)$ appearing in this bound seems to be\noptimal for the dimension $d$ as well.\n"", 'Ergodicity of supercritical SDEs driven by $\\alpha$-stable processes and\n  heavy-tailed sampling   Let $\\alpha\\in(0,2)$ and $d\\in\\mathbb{N}$. Consider the following stochastic\ndifferential equation (SDE) driven by $\\alpha$-stable process in\n$\\mathbb{R}^d$: $$ dX_t=b(X_t)dt+\\sigma(X_{t-})d L^{\\alpha}_t, \\quad\nX_0=x\\in\\mathbb{R}^d, $$ where $b:\\mathbb{R}^d\\to\\mathbb{R}^d$ and\n$\\sigma:\\mathbb{R}^d\\to\\mathbb{R}^d\\otimes\\mathbb{R}^d$ are locally\n$\\gamma$-H\\""older continuous with $\\gamma\\in(0\\vee(1-\\alpha)^+,1]$,\n$L^\\alpha_t$ is a $d$-dimensional rotationally invariant $\\alpha$-stable\nprocess. Under some dissipative and non-degenerate assumptions on $b,\\sigma$,\nwe show the $V$-uniformly exponential ergodicity for the semigroup $P_t$\nassociated with $(X_t(x),t\\geq 0)$. Our proofs are mainly based on the heat\nkernel estimates recently established in \\cite{MZ20} through showing the strong\nFeller property and the irreducibility of $P_t$. It is interesting that when\n$\\alpha$ goes to zero, the diffusion coefficient $\\sigma$ can grow faster than\ndrift $b$. As applications, we put forward a new heavy-tailed sampling scheme.\n']","[('driven sdes', 0.49425071477890015), ('stochastic differential', 0.4637106955051422), ('alpha stable processes', 0.46124714612960815), ('sdes driven', 0.4437759816646576), ('distributional drift', 0.4437101483345032), ('sde driven', 0.43142303824424744), ('stable process alpha', 0.4283701181411743), ('driven alpha stable', 0.4257858097553253), ('alpha stable process', 0.4173940122127533), ('stable processes', 0.41330552101135254)]"
1262,1262,23,1262_interaction kernels_interaction kernel_interacting particle systems_interacting particles,"['interaction kernels', 'interaction kernel', 'interacting particle systems', 'interacting particles', 'systems interacting particles', 'interacting systems', 'interacting particle', 'nonparametric inference', 'equations interacting', 'systems interacting']","['Learning interaction kernels in stochastic systems of interacting\n  particles from multiple trajectories   We consider stochastic systems of interacting particles or agents, with\ndynamics determined by an interaction kernel which only depends on pairwise\ndistances. We study the problem of inferring this interaction kernel from\nobservations of the positions of the particles, in either continuous or\ndiscrete time, along multiple independent trajectories. We introduce a\nnonparametric inference approach to this inverse problem, based on a\nregularized maximum likelihood estimator constrained to suitable hypothesis\nspaces adaptive to data. We show that a coercivity condition enables us to\ncontrol the condition number of this problem and prove the consistency of our\nestimator, and that in fact it converges at a near-optimal learning rate, equal\nto the min-max rate of $1$-dimensional non-parametric regression. In\nparticular, this rate is independent of the dimension of the state space, which\nis typically very high. We also analyze the discretization errors in the case\nof discrete-time observations, showing that it is of order $1/2$ in terms of\nthe time gaps between observations. This term, when large, dominates the\nsampling error and the approximation error, preventing convergence of the\nestimator. Finally, we exhibit an efficient parallel algorithm to construct the\nestimator from data, and we demonstrate the effectiveness of our algorithm with\nnumerical tests on prototype systems including stochastic opinion dynamics and\na Lennard-Jones model.\n', 'On the Identifiablility of Nonlocal Interaction Kernels in First-Order\n  Systems of Interacting Particles on Riemannian Manifolds   In this paper, we tackle a critical issue in nonparametric inference for\nsystems of interacting particles on Riemannian manifolds: the identifiability\nof the interaction functions. Specifically, we define the function spaces on\nwhich the interaction kernels can be identified given infinite i.i.d\nobservational derivative data sampled from a distribution. Our methodology\ninvolves casting the learning problem as a linear statistical inverse problem\nusing a operator theoretical framework. We prove the well-posedness of inverse\nproblem by establishing the strict positivity of a related integral operator\nand our analysis allows us to refine the results on specific manifolds such as\nthe sphere and Hyperbolic space. Our findings indicate that a numerically\nstable procedure exists to recover the interaction kernel from finite (noisy)\ndata, and the estimator will be convergent to the ground truth. This also\nanswers an open question in [MMQZ21] and demonstrate that least square\nestimators can be statistically optimal in certain scenarios. Finally, our\ntheoretical analysis could be extended to the mean-field case, revealing that\nthe corresponding nonparametric inverse problem is ill-posed in general and\nnecessitates effective regularization techniques.\n', 'Learning interaction kernels in heterogeneous systems of agents from\n  multiple trajectories   Systems of interacting particles or agents have wide applications in many\ndisciplines such as Physics, Chemistry, Biology and Economics. These systems\nare governed by interaction laws, which are often unknown: estimating them from\nobservation data is a fundamental task that can provide meaningful insights and\naccurate predictions of the behaviour of the agents. In this paper, we consider\nthe inverse problem of learning interaction laws given data from multiple\ntrajectories, in a nonparametric fashion, when the interaction kernels depend\non pairwise distances. We establish a condition for learnability of interaction\nkernels, and construct estimators that are guaranteed to converge in a suitable\n$L^2$ space, at the optimal min-max rate for 1-dimensional nonparametric\nregression. We propose an efficient learning algorithm based on least squares,\nwhich can be implemented in parallel for multiple trajectories and is therefore\nwell-suited for the high dimensional, big data regime. Numerical simulations on\na variety examples, including opinion dynamics, predator-swarm dynamics and\nheterogeneous particle dynamics, suggest that the learnability condition is\nsatisfied in models used in practice, and the rate of convergence of our\nestimator is consistent with the theory. These simulations also suggest that\nour estimators are robust to noise in the observations, and produce accurate\npredictions of dynamics in relative large time intervals, even when they are\nlearned from data collected in short time intervals.\n']","[('interaction kernels', 0.6381872892379761), ('interaction kernel', 0.5873146057128906), ('interacting particle systems', 0.49830710887908936), ('interacting particles', 0.4478837251663208), ('systems interacting particles', 0.44492775201797485), ('interacting systems', 0.43967875838279724), ('interacting particle', 0.41611263155937195), ('nonparametric inference', 0.39043766260147095), ('equations interacting', 0.38927212357521057), ('systems interacting', 0.3794105052947998)]"
1263,1263,23,1263_modular curves_elliptic curves_hyperelliptic curves_mordell weil rank,"['modular curves', 'elliptic curves', 'hyperelliptic curves', 'mordell weil rank', 'rational points curves', 'elliptic curve', 'genus curves', 'curves arbitrary genus', 'genus two curves', 'mordell weil']","['Chabauty-Coleman computations on rank 1 Picard curves   We provably compute the full set of rational points on 1403 Picard curves\ndefined over $\\mathbb{Q}$ with Jacobians of Mordell-Weil rank $1$ using the\nChabauty-Coleman method. To carry out this computation, we extend Magma code of\nBalakrishnan and Tuitman for Coleman integration. The new code computes\n$p$-adic (Coleman) integrals on curves to points defined over number fields\nwhere the prime $p$ splits completely and implements effective Chabauty for\ncurves whose Jacobians have infinite order points that are not the image of a\nrational point under the Abel-Jacobi map. We discuss several interesting\nexamples of curves where the Chabauty-Coleman set contains points defined over\nnumber fields.\n', ""Quadratic Chabauty for (bi)elliptic curves and Kim's conjecture   We explore a number of problems related to the quadratic Chabauty method for\ndetermining integral points on hyperbolic curves. We remove the assumption of\nsemistability in the description of the quadratic Chabauty sets\n$\\mathcal{X}(\\mathbb{Z}_p)_2$ containing the integral points\n$\\mathcal{X}(\\mathbb{Z})$ of an elliptic curve of rank at most $1$. Motivated\nby a conjecture of Kim, we then investigate theoretically and computationally\nthe set-theoretic difference $\\mathcal{X}(\\mathbb{Z}_p)_2\\setminus\n\\mathcal{X}(\\mathbb{Z})$. We also consider some algorithmic questions arising\nfrom Balakrishnan--Dogra's explicit quadratic Chabauty for the rational points\nof a genus-two bielliptic curve. As an example, we provide a new solution to a\nproblem of Diophantus which was first solved by Wetherell. Computationally, the\nmain difference from the previous approach to quadratic Chabauty is the use of\nthe $p$-adic sigma function in place of a double Coleman integral.\n"", 'A geometric linear Chabauty comparison theorem   The Chabauty-Coleman method is a $p$-adic method for finding all rational\npoints on curves of genus $g$ whose Jacobians have Mordell-Weil rank $r < g$.\nRecently, Edixhoven and Lido developed a geometric quadratic Chabauty method\nthat was adapted by Spelier to cover the case of geometric linear Chabauty. We\ncompare the geometric linear Chabauty method and the Chabauty-Coleman method\nand show that geometric linear Chabauty can outperform Chabauty-Coleman in\ncertain cases. However, as Chabauty-Coleman remains more practical for general\ncomputations, we discuss how to strengthen Chabauty-Coleman to make it\ntheoretically equivalent to geometric linear Chabauty. We apply these methods\nto genus 2 and genus 3 curves.\n']","[('modular curves', 0.549796998500824), ('elliptic curves', 0.5435431003570557), ('hyperelliptic curves', 0.5347351431846619), ('mordell weil rank', 0.5250982642173767), ('rational points curves', 0.5154765248298645), ('elliptic curve', 0.47661522030830383), ('genus curves', 0.45119285583496094), ('curves arbitrary genus', 0.4509202241897583), ('genus two curves', 0.45039501786231995), ('mordell weil', 0.4347270131111145)]"
1264,1264,23,1264_noise decoding grand_decoding performance_additive noise decoding_high rate codes,"['noise decoding grand', 'decoding performance', 'additive noise decoding', 'high rate codes', 'noise decoding', 'decoding technique', 'decoding grand', 'decoding', 'ml decoding', 'decoders']","[""Ordered Reliability Bits Guessing Random Additive Noise Decoding   Error correction techniques traditionally focus on the co-design of\nrestricted code-structures in tandem with code-specific decoders that are\ncomputationally efficient when decoding long codes in hardware. Modern\napplications are, however, driving demand for ultra-reliable low-latency\ncommunications (URLLC), rekindling interest in the performance of shorter,\nhigher-rate error correcting codes, and raising the possibility of revisiting\nuniversal, code-agnostic decoders.\n  To that end, here we introduce a soft-detection variant of Guessing Random\nAdditive Noise Decoding (GRAND) called Ordered Reliability Bits GRAND that can\naccurately decode any moderate redundancy block-code. It is designed with\nefficient circuit implementation in mind, and determines accurate decodings\nwhile retaining the original hard detection GRAND algorithm's suitability for a\nhighly parallelized implementation in hardware.\n  ORBGRAND is shown to provide excellent soft decision block error performance\nfor codes of distinct classes (BCH, CA-Polar and RLC) with modest complexity,\nwhile providing better block error rate performance than CA-SCL, a state of the\nart soft detection CA-Polar decoder. ORBGRAND offers the possibility of an\naccurate, energy efficient soft detection decoder suitable for delivering URLLC\nin a single hardware realization.\n"", ""Ordered Reliability Bits Guessing Random Additive Noise Decoding   Modern applications are driving demand for ultra-reliable low-latency\ncommunications, rekindling interest in the performance of short, high-rate\nerror correcting codes. To that end, here we introduce a soft-detection variant\nof Guessing Random Additive Noise Decoding (GRAND) called Ordered Reliability\nBits GRAND that can decode any short, high-rate block-code. For a code of $n$\nbits, it avails of no more than $\\lceil\\log_2(n)\\rceil$ bits of\ncode-book-independent quantized soft detection information per received bit to\ndetermine an accurate decoding while retaining the original algorithm's\nsuitability for a highly parallelized implementation in hardware. ORBGRAND is\nshown to provide similar block error performance for codes of distinct classes\n(BCH, CA-Polar and RLC) with low complexity, while providing better block error\nrate performance than CA-SCL, a state of the art soft detection CA-Polar\ndecoder.\n"", 'High-Throughput and Energy-Efficient VLSI Architecture for Ordered\n  Reliability Bits GRAND   Ultra-reliable low-latency communication (URLLC), a major 5G New-Radio use\ncase, is the key enabler for applications with strict reliability and latency\nrequirements. These applications necessitate the use of short-length and\nhigh-rate codes. Guessing Random Additive Noise Decoding (GRAND) is a recently\nproposed Maximum Likelihood (ML) decoding technique for these short-length and\nhigh-rate codes. Rather than decoding the received vector, GRAND tries to infer\nthe noise that corrupted the transmitted codeword during transmission through\nthe communication channel. As a result, GRAND can decode any code, structured\nor unstructured. GRAND has hard-input as well as soft-input variants. Among\nthese variants, Ordered Reliability Bits GRAND (ORBGRAND) is a soft-input\nvariant that outperforms hard-input GRAND and is suitable for parallel hardware\nimplementation. This work reports the first hardware architecture for ORBGRAND,\nwhich achieves an average throughput of up to $42.5$ Gbps for a code length of\n$128$ at a target FER of $10^{-7}$. Furthermore, the proposed hardware can be\nused to decode any code as long as the length and rate constraints are met. In\ncomparison to the GRANDAB, a hard-input variant of GRAND, the proposed\narchitecture enhances decoding performance by at least $2$ dB. When compared to\nthe state-of-the-art fast dynamic successive cancellation flip decoder\n(Fast-DSCF) using a 5G polar $(128,105)$ code, the proposed ORBGRAND VLSI\nimplementation has $49\\times$ higher average throughput, $32\\times$ times more\nenergy efficiency, and $5\\times$ more area efficiency while maintaining similar\ndecoding performance.\n']","[('noise decoding grand', 0.5941805839538574), ('decoding performance', 0.5808907151222229), ('additive noise decoding', 0.5477860569953918), ('high rate codes', 0.4967118203639984), ('noise decoding', 0.4895663857460022), ('decoding technique', 0.47765791416168213), ('decoding grand', 0.4663541615009308), ('decoding', 0.46354472637176514), ('ml decoding', 0.44875189661979675), ('decoders', 0.4290922284126282)]"
1265,1265,23,1265_grassmann manifolds_grassmann manifold_grassmannians_grassmannian,"['grassmann manifolds', 'grassmann manifold', 'grassmannians', 'grassmannian', 'lagrangian grassmannians', 'lagrangian grassmannian', 'isotropic grassmannian', 'grassmann', 'cohomology algebra', 'mod cohomology algebra']","['4-torsion classes in the integral cohomology of oriented Grassmannians   We investigate the existence of 4-torsion in the integral cohomology of\noriented Grassmannians. We prove a general criterion for the appearance of\n4-torsion classes based on (twisted) Steenrod squares and show that there are\nmany cases where this criterion is satisfied for minimal-degree anomalous\nclasses, assuming a conjecture on the characteristic rank. We also establish\nthe upper bound in the characteristic rank conjecture for oriented\nGrassmannians $\\tilde{Gr}_k(n)$, and prove the equality in the cases $k=5,\nn=2^t-1,2^t$ and $k=6, n=2^t$. This provides infinitely many examples of\noriented Grassmannians having 4-torsion in their integral cohomology. On the\nway, we clarify the relation between minimal-degree anomalous classes and\nresults of Stong on the height of the first Stiefel-Whitney class $w_1$ in the\nmod 2 cohomology of real Grassmannians, for which we give an independent proof.\nWe also establish some bounds on torsion exponents for the integral cohomology\nof oriented flag manifolds. Based on these findings and further computational\nevidence, we formulate a conjectural relationship between the torsion exponent\nin the integral cohomology of homogeneous spaces and their deficiency.\n', 'Gr\\""obner bases in the mod $2$ cohomology of oriented Grassmann\n  manifolds $\\widetilde G_{2^t,3}$   For $n$ a power of two, we give a complete description of the cohomology\nalgebra $H^*(\\widetilde G_{n,3};\\mathbb Z_2)$ of the Grassmann manifold\n$\\widetilde G_{n,3}$ of oriented $3$-planes in $\\mathbb R^n$. We do this by\nfinding a reduced Gr\\""obner basis for an ideal closely related to this\ncohomology algebra. Using this Gr\\""obner basis we also present an additive\nbasis for $H^*(\\widetilde G_{n,3};\\mathbb Z_2)$.\n', 'The mod 2 cohomology rings of oriented Grassmannians via Koszul\n  complexes   We study the structure of mod 2 cohomology rings of oriented Grassmannians\n$\\tilde{\\operatorname{Gr}}_k(n)$ of oriented $k$-planes in $\\mathbb{R}^n$. Our\nmain focus is on the structure of the cohomology ring ${\\rm\nH}^*(\\tilde{\\operatorname{Gr}}_k(n);\\mathbb{F}_2)$ as a module over the\ncharacteristic subring $C$, which is the subring generated by the\nStiefel-Whitney classes $w_2,\\ldots, w_k$. We identify this module structure\nusing Koszul complexes, which involves the syzygies between the relations\ndefining $C$. We give an infinite family of such syzygies, which results in a\nnew upper bound on the characteristic rank of\n$\\tilde{\\operatorname{Gr}}_k(2^t)$, and formulate a conjecture on the exact\nvalue of the characteristic rank of $\\tilde{\\operatorname{Gr}}_k(n)$. For the\ncase $k=3$, we use the Koszul complex to compute a presentation of the\ncohomology ring $H={\\rm H}^*(\\tilde{\\operatorname{Gr}}_3(n);\\mathbb{F}_2)$ for\n$2^{t-1}<n\\leq 2^t-4$, complementing existing descriptions in the\n$n=2^t-3,...,2^t$ cases. More precisely, as a $C$-module, $H$ splits as a\ndirect sum of the characteristic subring $C$ and the anomalous module $H/C$,\nand we compute a complete presentation of $H/C$ as a $C$-module from the Koszul\ncomplex. We also discuss various issues that arise for the cases $k>3$,\nsupported by computer calculation.\n']","[('grassmann manifolds', 0.6886557936668396), ('grassmann manifold', 0.672417163848877), ('grassmannians', 0.6642788648605347), ('grassmannian', 0.6507903933525085), ('lagrangian grassmannians', 0.6383414268493652), ('lagrangian grassmannian', 0.5968645811080933), ('isotropic grassmannian', 0.5547352433204651), ('grassmann', 0.5481650829315186), ('cohomology algebra', 0.5419299006462097), ('mod cohomology algebra', 0.510094940662384)]"
1266,1266,23,1266_hyperbolic knots_alternating knots_knots sphere_classical knots,"['hyperbolic knots', 'alternating knots', 'knots sphere', 'classical knots', 'knot sphere', 'knot theory', 'volume hyperbolic manifolds', 'hyperbolic manifolds', 'knots knots', 'knots']","['Fully Augmented Links in the Thickened Torus   In this paper we study the geometry of fully augmented link complements in\nthe thickened torus and describe their geometric properties, generalizing the\nstudy of fully augmented links in $S^3$. We classify which fully augmented\nlinks in the thickened torus are hyperbolic, show that their complements in the\nthickened torus decompose into ideal right-angled torihedra, and that the edges\nof this decomposition are canonical. We also study volume density of fully\naugmented links in $S^3$, defined to be the ratio of its volume and the number\nof augmentations. We prove the Volume Density Conjecture for fully augmented\nlinks which states that the volume density of a sequence of fully augmented\nlinks in $S^3$ which diagrammatically converge to a biperiodic link, converges\nto the volume density of that biperiodic link.\n', 'Alternating links on surfaces and volume bounds   Weakly generalised alternating knots are knots with an alternating projection\nonto a closed surface in a compact irreducible 3-manifold, and they share many\nhyperbolic geometric properties with usual alternating knots. For example,\nusual alternating knots have volume bounded above and below by the twist number\nof the alternating diagram due to Lackenby. Howie and Purcell showed that a\nsimilar lower bound holds for weakly generalised alternating knots. In this\npaper, we show that a generalisation of the upper volume bound does not hold,\nby producing a family of weakly generalised alternating knots in the 3-sphere\nwith fixed twist number but unbounded volumes. As a corollary, generalised\nalternating knots can have arbitrarily small cusp density, in contrast with\nusual alternating knots whose cusp densities are bounded away from zero due to\nLackenby and Purcell. On the other hand, we show that the twist number of a\nweakly generalised alternating projection does gives two sided linear bounds on\nvolume inside a thickened surface; we state some related open questions.\n', 'Generalized Augmented Cellular Alternating Links in Thickened Surfaces\n  are Hyperbolic   Menasco proved that nontrivial links in the 3-sphere with connected prime\nalternating non-2-braid projections are hyperbolic. This was further extended\nto augmented alternating links wherein non-isotopic trivial components bounding\ndisks punctured twice by the alternating link were added. Lackenby proved that\nthe first and second collections of links together form a closed subset of the\nset of all finite volume hyperbolic 3-manifolds in the geometric topology.\nAdams showed hyperbolicity for generalized augmented alternating links, which\ninclude additional trivial components that bound n-punctured disks for $n \\geq\n2$. Here we prove that generalized augmented cellular alternating links in\nI-bundles over closed surfaces are also hyperbolic and that in $S \\times I$,\nthe cellular alternating links and the augmented cellular alternating together\nform a closed subset of finite volume hyperbolic 3-manifolds in the geometric\ntopology. Explicit examples of additional links in $S \\times I$ to which these\nresults apply are included.\n']","[('hyperbolic knots', 0.655449628829956), ('alternating knots', 0.610431969165802), ('knots sphere', 0.5884522795677185), ('classical knots', 0.5704908967018127), ('knot sphere', 0.5565615296363831), ('knot theory', 0.5543735027313232), ('volume hyperbolic manifolds', 0.5474919676780701), ('hyperbolic manifolds', 0.5304086208343506), ('knots knots', 0.5296738147735596), ('knots', 0.5118021965026855)]"
1267,1267,23,1267_traffic assignment_traffic congestion_traffic dynamics_dynamic traffic,"['traffic assignment', 'traffic congestion', 'traffic dynamics', 'dynamic traffic', 'traffic flows', 'macroscopic traffic', 'traffic networks', 'traffic', 'optimal routing', 'congestion']","['The Role of Differentiation in Tolling of Traffic Networks with Mixed\n  Autonomy   With autonomous vehicles now sharing roads with human drivers, the era of\nmixed autonomy brings new challenges in dealing with congestion. One cause of\ncongestion is when vehicle users choose their routes selfishly to minimize\ntheir personal travel delay rather than a global travel delay, and prior works\naddress this phenomenon using tolling to influence routing choices, but do not\naddress the setting of mixed autonomy. Tolls may be differentiated, meaning\ndifferent users of a road experience different tolls, or they may be anonymous;\nthe latter is desirable to allay concerns of fairness and privacy, as well as\nlogistical challenges. In this work we examine the role of differentiation in\ntraffic networks with mixed autonomy. Specifically, we first establish\ndifferentiated tolls which completely eliminate inefficiency due to selfish\nrouting. We then show the fundamental limitations of anonymous tolls in our\nsetting, and we provide anonymous tolls with mild performance guarantees. We\nshow that in parallel networks, an infinitesimal differentiation in tolls is\nenough to guarantee optimality, and finally we establish a lower bound on the\ninefficiency of variable marginal cost tolling in the mixed autonomy setting.\n', 'Joint routing and pricing control in congested mixed autonomy networks   Routing controllability of connected and autonomous vehicles (CAVs) has been\nshown to reduce the adverse effects of selfish routing on the network\nefficiency. However, the assumption that CAV owners would readily allow\nthemselves to be controlled externally by a central agency for the good of the\nsystem is unrealistic. In this paper, we propose a joint routing and pricing\ncontrol scheme that aims to incentivize CAVs to seek centrally controlled\nsystem-optimal (SO) routing by saving on tolls while user equilibrium (UE)\nseeking human-driven vehicles (HVs) are subject to a congestion charge. The\nproblem is formulated as a bi-level optimization program where the upper level\noptimizes the dynamic toll rates using the network fundamental diagram (NFD)\nand the lower level is a mixed equilibrium simulation-based dynamic traffic\nassignment model (SBDTA) considering different combinations of SO-seeking CAVs.\nWe apply a feedback-based controller to solve for the optimal spatially\ndifferentiated distance-based congestion charge from which SO-seeking CAVs are\nexempt; but UE-seeking HVs are subject to the charge for entering the city\ncenter. To capture the distinct microscopic behavior of CAVs in the mixed\nautonomy traffic, we also implement an adaptive link fundamental diagram (FD)\nwithin the SBDTA model. The proposed joint control scheme encourages CAV owners\nto seek SO routing resulting in less total system travel time. It also\ndiscourages UE-seeking HVs from congesting the city center. We demonstrate the\nperformance of the proposed scheme in both a small network and a large-scale\nnetwork of Melbourne, Australia.\n', ""Bridging the user equilibrium and the system optimum in static traffic\n  assignment: how the cooperation among drivers can solve the congestion\n  problem in city networks   Solving the road congestion problem is one of the most pressing issues in\nmoderncities since it causes time wasting, pollution, higher industrial costs\nand huge roadmaintenance costs. Advances in ITS technologies and the advent of\nautonomousvehicles are changing mobility dramatically. They enable the\nimplementation of acoordination mechanism, called coordinated traffic\nassignment, among the sat-navdevices aiming at assigning paths to drivers to\neliminate congestion and to re-duce the total travel time in traffic networks.\nAmong possible congestion avoidance methods, coordinated traffic assignment is\na valuable choice since it does not involvehuge investments to expand the road\nnetwork. Traffic assignments are traditionally devoted to two main perspectives\non which the well-known Wardropian principlesare inspired: the user equilibrium\nand the system optimum. User equilibrium is a user-driven traffic assignment in\nwhich each user chooses the most convenientpath selfishly. It guarantees that\nfairness among users is respected since, whenthe equilibrium is reached, all\nusers sharing the same origin and destination willexperience the same travel\ntime. The main drawback in a user equilibrium is thatthe system total travel\ntime is not minimized and, hence, the so-called Price ofAnarchy is paid. On the\nother hand, the system optimum is an efficient system-wide traffic assignment\nin which drivers are routed on the network in such a waythe total travel time\nis minimized but users might experience travel times that arehigher than the\nother users travelling from the same origin to the same destina-tion affecting\nthe compliance. Thus, drawbacks in implementing one of the two assignments can\nbe overcome by hybridizing the two approaches aiming at bridging users'\nfairness to system-wide efficiency. The survey reviews the state-of-the-art of\nthese trade-off approaches\n""]","[('traffic assignment', 0.6060509085655212), ('traffic congestion', 0.6032719016075134), ('traffic dynamics', 0.5926716923713684), ('dynamic traffic', 0.5658595561981201), ('traffic flows', 0.5175126791000366), ('macroscopic traffic', 0.5083200335502625), ('traffic networks', 0.4895550310611725), ('traffic', 0.48551028966903687), ('optimal routing', 0.47788748145103455), ('congestion', 0.4561317265033722)]"
1268,1268,23,1268_computable structure theory_computability theoretic_computable structure_computability theory,"['computable structure theory', 'computability theoretic', 'computable structure', 'computability theory', 'algebraic structures', 'partial computable', 'computability', 'theoretic characterization', 'computable functions', 'countability']","['Countability constraints in order-theoretic approaches to computability   Computability on uncountable sets has no standard formalization, unlike that\non countable sets, which is given by Turing machines. Some of the approaches to\ndefine computability in these sets rely on order-theoretic structures to\ntranslate such notions from Turing machines to uncountable spaces. Since these\nmachines are used as a baseline for computability in these approaches,\ncountability restrictions on the ordered structures are fundamental. Here, we\nshow several relations between the usual countability restrictions in\norder-theoretic theories of computability and some more common order-theoretic\ncountability constraints, like order density properties and functional\ncharacterizations of the order structure in terms of multi-utilities. As a\nresult, we show how computability can be introduced in some order structures\nvia countability order density and multi-utility constraints.\n', 'Learning families of algebraic structures from informant   We combine computable structure theory and algorithmic learning theory to\nstudy learning of families of algebraic structures. Our main result is a\nmodel-theoretic characterization of the class $\\mathbf{InfEx}_{\\cong}$,\nconsisting of the structures whose isomorphism types can be learned in the\nlimit. We show that a family of structures $\\mathfrak{K}$ is\n$\\mathbf{InfEx}_{\\cong}$-learnable if and only if the structures from\n$\\mathfrak{K}$ can be distinguished in terms of their\n$\\Sigma^{\\mathrm{inf}}_2$-theories. We apply this characterization to familiar\ncases and we show the following: there is an infinite learnable family of\ndistributive lattices; no pair of Boolean algebras is learnable; no infinite\nfamily of linear orders is learnable.\n', 'On the Turing complexity of learning finite families of algebraic\n  structures   In previous work, we have combined computable structure theory and\nalgorithmic learning theory to study which families of algebraic structures are\nlearnable in the limit (up to isomorphism). In this paper, we measure the\ncomputational power that is needed to learn finite families of structures. In\nparticular, we prove that, if a family of structures is both finite and\nlearnable, then any oracle which computes the Halting set is able to achieve\nsuch a learning. On the other hand, we construct a pair of structures which is\nlearnable but no computable learner can learn it.\n']","[('computable structure theory', 0.7154157757759094), ('computability theoretic', 0.6602616310119629), ('computable structure', 0.6565786004066467), ('computability theory', 0.6308433413505554), ('algebraic structures', 0.5470556616783142), ('partial computable', 0.5438486933708191), ('computability', 0.5395060777664185), ('theoretic characterization', 0.5302878022193909), ('computable functions', 0.525225818157196), ('countability', 0.5216707587242126)]"
1269,1269,23,1269_boundedness wave operators_schr odinger operators_schr odinger operator_odinger operators delta,"['boundedness wave operators', 'schr odinger operators', 'schr odinger operator', 'odinger operators delta', 'boundedness wave', 'odinger operator delta', 'odinger operators', 'schr odinger equations', 'wave operators w_', 'odinger operator']","['$L^p$-boundedness of wave operators for fourth order Schr\\""odinger operators with zero resonances on $\\mathbb{R}^3$ Let $H = \\Delta^2 + V$ be the fourth-order Schr\\""odinger operator on $\\mathbb{R}^3$ with a real-valued fast-decaying potential $V$. If zero is neither a resonance nor an eigenvalue of $H$, then it was recently shown that the wave operators $W_\\pm(H, \\Delta^2)$ are bounded on $L^p(\\mathbb{R}^3)$ for all $1 < p < \\infty$ and unbounded at the endpoints $p=1$ and $p=\\infty$.\n  This paper is to further establish the $L^p$-boundedness of $W_\\pm(H, \\Delta^2)$ that exhibit all types of singularities at the zero energy threshold. We first prove that $W_\\pm(H, \\Delta^2)$ are bounded on $L^p(\\mathbb{R}^3)$ for all $1 < p < \\infty$ in the first kind resonance case, and then proceed to establish for the second kind resonance case that they are bounded on $L^p(\\mathbb{R}^3)$ for all $1 < p < 3$, but not if $3 \\le p \\le \\infty$. In the third kind resonance case, we also show that $W_\\pm(H, \\Delta^2)$ are bounded on $L^p(\\mathbb{R}^3)$ for all $1<p<3$ and generically unbounded on $L^p(\\R^3)$ for any $3\\le p\\le\\infty$. Moreover, it is also shown that $W_\\pm(H, \\Delta^2)$ are bounded on $L^p(\\R^3)$ for all $3\\le p<\\infty$ if in addition $H$ has the zero eigenvalue, but no $p$-wave zero resonances and all zero eigenfunctions are orthogonal to $x_ix_jx_kV$ in $L^2(\\R^3)$ for all $i,j,k=1,2,3$ with $x=(x_1,x_2,x_3)\\in \\R^3$.\n  These results describe precisely the validity of the $L^p$-boundedness of $W_\\pm(H, \\Delta^2)$ in $\\mathbb{R}^3$ for all types of singularities at the zero energy threshold with some exceptions for the endpoint cases $p=1,\\infty$. As an application, $L^p$-$L^q$ decay estimates are also derived for the fourth-order Schr\\""odinger equations and Beam equations with zero resonance singularities.', 'Counterexamples and weak (1,1) estimates of wave operators for\n  fourth-order Schr\\""odinger operators in dimension three   This paper is dedicated to investigating the $L^p$-bounds of wave operators\n$W_\\pm(H,\\Delta^2)$ associated with fourth-order Schr\\""odinger operators\n$H=\\Delta^2+V$ on $\\mathbb{R}^3$. We consider that real potentials satisfy\n$|V(x)|\\lesssim \\langle x\\rangle^{-\\mu}$ for some $\\mu>0$. A recent work by\nGoldberg and Green \\cite{GoGr21} has demonstrated that wave operators\n$W_\\pm(H,\\Delta^2)$ are bounded on $L^p(\\mathbb{R}^3)$ for all $1<p<\\infty$\nunder the condition that $\\mu>9$, and zero is a regular point of $H$. In this\npaper, we aim to further establish endpoint estimates for $W_\\pm(H,\\Delta^2)$\nin two significant ways. First, we provide counterexamples that illustrate the\nunboundedness of $W_\\pm(H,\\Delta^2)$ on the endpoint spaces $L^1(\\mathbb{R}^3)$\nand $L^\\infty(\\mathbb{R}^3)$, even for non-zero compactly supported potentials\n$V$. Second, we establish weak (1,1) estimates for the wave operators\n$W_\\pm(H,\\Delta^2)$ and their dual operators $W_\\pm(H,\\Delta^2)^*$ in the case\nwhere zero is a regular point and $\\mu>11$. These estimates depend critically\non the singular integral theory of Calder\\\'on-Zygmund on a homogeneous space\n$(X,d\\omega)$ with a doubling measure $d\\omega$.\n', 'The $L^p$-boundedness of wave operators for higher order Schr\\""odinger operator with zero singularities in low odd dimensions This paper investigates the $L^p$-bounds of wave operators for higher-order Schr\\""odinger operators $H = (-\\Delta)^m + V$ on $\\mathbb{R}^n$, with $m \\ge 2$ and real-valued decaying potentials $V$. Our main objective is to establish the sharp $L^p$-boundedness of the wave operators $W_\\pm(H; (-\\Delta)^m)$ in the presence of all types of zero-resonance singularities, for all odd dimensions $1 \\le n \\le 4m - 1$.\n  Specifically, for odd $n$ with $1 \\le n \\le 4m - 1$, there exist $m_n$ types of zero resonances for $H$, along with a critical type $k_c$ (both depending on $n$ and $m$). If zero is a regular point of $H$ or a $\\mathbf{k}$-th kind resonance with $1 \\le \\mathbf{k} \\le k_c$, the wave operators $W_\\pm(H; (-\\Delta)^m)$ are bounded on $L^p(\\mathbb{R}^n)$ for all $1 < p < \\infty$. If zero is a $\\mathbf{k}$-th kind resonance with $k_c < \\mathbf{k} \\le m_n$, we show that the range of $p$-boundedness for $W_\\pm(H; (-\\Delta)^m)$ narrows to $1 < p < p_{\\mathbf{k}}$, where $$p_{\\mathbf{k}} = \\frac{n}{n - 2m + \\mathbf{k} + k_c - 1}.$$ Additionally, if zero is an eigenvalue of $H$ (i.e., $\\mathbf{k} = m_n + 1$), then $W_\\pm(H; (-\\Delta)^m)$ are bounded on $L^p(\\mathbb{R}^n)$ for all $1 < p < \\frac{2n}{n - 1}$.\n  Furthermore, it is shown that the wave operators $W_\\pm(H; (-\\Delta)^m)$ are unbounded on $L^p(\\mathbb{R}^n)$ for all $p_{\\mathbf{k}} < p \\le \\infty$ if $k_c < \\mathbf{k} \\le m_n$, and for all $\\frac{2n}{n - 1} < p \\le \\infty$ if zero is an eigenvalue of $H$ with a non-zero solution $\\phi$ to $H\\phi = 0$ in $\\bigcap_{s < -\\frac{1}{2}} L^{2}_{s}(\\mathbb{R}^n) \\setminus L^2(\\mathbb{R}^n)$(referred to as a $p$-wave resonance). The key idea of the proof is to reduce the $L^p$-unboundedness to establishing the optimality of time-decay estimates for $e^{itH}P_{ac}(H)$ in weighted $L^2$ spaces.']","[('boundedness wave operators', 0.5783010125160217), ('schr odinger operators', 0.5630887746810913), ('schr odinger operator', 0.5394262671470642), ('odinger operators delta', 0.5304447412490845), ('boundedness wave', 0.5285916924476624), ('odinger operator delta', 0.5170352458953857), ('odinger operators', 0.48386266827583313), ('schr odinger equations', 0.47063013911247253), ('wave operators w_', 0.464337021112442), ('odinger operator', 0.45737549662590027)]"
1270,1270,23,1270_constrained optimal control_solutions optimal control_solving optimal control_optimal control problems,"['constrained optimal control', 'solutions optimal control', 'solving optimal control', 'optimal control problems', 'optimal control', 'trajectory optimization', 'time optimal control', 'dynamic optimization problems', 'dynamic optimization', 'discretization mesh']","['Adaptive Mesh Refinement and Error Estimation Method for Optimal Control\n  Using Direct Collocation   An adaptive mesh refinement and error estimation method for numerically\nsolving optimal control problems is developed using Legendre-Gauss-Radau direct\ncollocation. In regions of the solution where the desired accuracy tolerance\nhas not been met, the mesh is refined by either increasing the degree of the\napproximating polynomial in a mesh interval or dividing a mesh interval into\nsubintervals. In regions of the solution where the desired accuracy tolerance\nhas been met, the mesh size may be reduced by either merging adjacent mesh\nintervals or decreasing the degree of the approximating polynomial in a mesh\ninterval. Coupled with the mesh refinement method described in this paper is a\nnewly developed relative error estimate that is based on the differences\nbetween solutions obtained from the collocation method and those obtained by\nsolving initial-value and terminal-value problems in each mesh interval using\nan interpolated control obtained from the collocation method. Because the error\nestimate is based on explicit simulation, the solution obtained via collocation\nis in close agreement with the solution obtained via explicit simulation using\nthe control on the final mesh, which ensures that the control is an accurate\napproximation of the true optimal control. The method is demonstrated on three\nexamples from the open literature, and the results obtained show an improvement\nin final mesh size when compared against previously developed mesh refinement\nmethods.\n', 'Modified Legendre-Gauss Collocation Method for Solving Optimal Control\n  Problems with Nonsmooth Solutions   A modified form of Legendre-Gauss orthogonal direct collocation is developed\nfor solving optimal control problems whose solutions are nonsmooth due to\ncontrol discontinuities. This new method adds switch-time variables, control\nvariables, and collocation conditions at both endpoints of a mesh interval,\nwhereas these new variables and collocation conditions are not included in\nstandard Legendre-Gauss orthogonal collocation. The modified Legendre-Gauss\ncollocation method alters the search space of the resulting nonlinear\nprogramming problem and enables determining accurately the location of the\nnonsmoothness in the optimal control. The transformed adjoint system of the\nmodified Legendre-Gauss collocation method is then derived and shown to satisfy\na discrete form of the continuous variational necessary conditions for\noptimality. The method is motivated via a control-constrained triple-integrator\nminimum-time optimal control problem where the solution possesses a two-switch\nbang-bang optimal control structure. In addition, the method developed in this\npaper is compared with existing Gaussian quadrature collocation methods. The\nmethod developed in this paper is shown to be capable of accurately solving\noptimal control problems with a discontinuous optimal control.\n', 'Modified Legendre-Gauss-Radau Collocation Method for Solving Optimal\n  Control Problems with Nonsmooth Solutions   A new method is developed for solving optimal control problems whose\nsolutions are nonsmooth. The method developed in this paper employs a modified\nform of the Legendre-Gauss-Radau orthogonal direct collocation method. This\nmodified Legendre-Gauss-Radau method adds two variables and two constraints at\nthe end of a mesh interval when compared with a previously developed standard\nLegendre-Gauss-Radau collocation method. The two additional variables are the\ntime at the interface between two mesh intervals and the control at the end of\neach mesh interval. The two additional constraints are a collocation condition\nfor those differential equations that depend upon the control and an inequality\nconstraint on the control at the endpoint of each mesh interval. The additional\nconstraints modify the search space of the nonlinear programming problem such\nthat an accurate approximation to the location of the nonsmoothness is\nobtained. The transformed adjoint system of the modified Legendre-Gauss-Radau\nmethod is then developed. Using this transformed adjoint system, a method is\ndeveloped to transform the Lagrange multipliers of the nonlinear programming\nproblem to the costate of the optimal control problem. Furthermore, it is shown\nthat the costate estimate satisfies one of the Weierstrass-Erdmann optimality\nconditions. Finally, the method developed in this paper is demonstrated on an\nexample whose solution is nonsmooth.\n']","[('constrained optimal control', 0.5056104063987732), ('solutions optimal control', 0.4934254288673401), ('solving optimal control', 0.48850974440574646), ('optimal control problems', 0.48603230714797974), ('optimal control', 0.4416590631008148), ('trajectory optimization', 0.43441227078437805), ('time optimal control', 0.4157288372516632), ('dynamic optimization problems', 0.4080389440059662), ('dynamic optimization', 0.38699233531951904), ('discretization mesh', 0.3848496377468109)]"
1271,1271,23,1271_stochastic control_backward stochastic_forward backward stochastic_backward stochastic differential,"['stochastic control', 'backward stochastic', 'forward backward stochastic', 'backward stochastic differential', 'stochastic control problems', 'filter stability', 'stochastic optimal control', 'nonlinear stochastic', 'ergodicity markov', 'stochastic optimal']","[""Duality for nonlinear filtering   This thesis is concerned with the stochastic filtering problem for a hidden\nMarkov model (HMM) with the white noise observation model. For this filtering\nproblem, we make three types of original contributions: (1) dual\ncontrollability characterization of stochastic observability, (2) dual minimum\nvariance optimal control formulation of the stochastic filtering problem, and\n(3) filter stability analysis using the dual optimal control formulation.\n  For the first contribution of this thesis, a backward stochastic differential\nequation (BSDE) is proposed as the dual control system. The observability\n(detectability) of the HMM is shown to be equivalent to the controllability\n(stabilizability) of the dual control system. For the linear-Gaussian model,\nthe dual relationship reduces to classical duality in linear systems theory.\n  The second contribution is to transform the minimum variance estimation\nproblem into an optimal control problem. The constraint is given by the dual\ncontrol system. The optimal solution is obtained via two approaches: (1) by an\napplication of maximum principle and (2) by the martingale characterization of\nthe optimal value. The optimal solution is used to derive the nonlinear filter.\n  The third contribution is to carry out filter stability analysis by studying\nthe dual optimal control problem. Two approaches are presented through Chapters\n7 and 8. In Chapter 7, conditional Poincar\\'e inequality (PI) is introduced.\nBased on conditional PI, various convergence rates are obtained and related to\nliterature. In Chapter 8, the stabilizability of the dual control system is\nshown to be a necessary and sufficient condition for filter stability on\ncertain finite state space model.\n"", ""The Conditional Poincar\\'e Inequality for Filter Stability   This paper is concerned with the problem of nonlinear filter stability of\nergodic Markov processes. The main contribution is the conditional Poincar\\'e\ninequality (PI), which is shown to yield filter stability. The proof is based\nupon a recently discovered duality which is used to transform the nonlinear\nfiltering problem into a stochastic optimal control problem for a backward\nstochastic differential equation (BSDE). Based on these dual formalisms, a\ncomparison is drawn between the stochastic stability of a Markov process and\nthe filter stability. The latter relies on the conditional PI described in this\npaper, whereas the former relies on the standard form of PI.\n"", ""Variance Decay Property for Filter Stability   This paper is concerned with the problem of nonlinear (stochastic) filter\nstability of a hidden Markov model (HMM) with white noise observations. A\ncontribution is the variance decay property which is used to conclude filter\nstability. For this purpose, a new notion of the Poincar\\'e inequality (PI) is\nintroduced for the nonlinear filter. PI is related to both the ergodicity of\nthe Markov process as well as the observability of the HMM. The proofs are\nbased upon a recently discovered minimum variance duality which is used to\ntransform the nonlinear filtering problem into a stochastic optimal control\nproblem for a backward stochastic differential equation (BSDE).\n""]","[('stochastic control', 0.5610983967781067), ('backward stochastic', 0.5581724643707275), ('forward backward stochastic', 0.554291307926178), ('backward stochastic differential', 0.538124144077301), ('stochastic control problems', 0.5242555141448975), ('filter stability', 0.5134260654449463), ('stochastic optimal control', 0.5129941701889038), ('nonlinear stochastic', 0.4685266315937042), ('ergodicity markov', 0.4598626494407654), ('stochastic optimal', 0.45293712615966797)]"
1272,1272,23,1272_gromov hausdorff distance_gromov hausdorff metric_metric spaces equipped_hausdorff metric,"['gromov hausdorff distance', 'gromov hausdorff metric', 'metric spaces equipped', 'hausdorff metric', 'hausdorff distance', 'metric spaces', 'invariant metric spaces', 'gromov hausdorff', 'class metric spaces', 'distances metric']","['Metric Space Recognition by Gromov-Hausdorff Distances to Simplexes   In the present paper a distinguishability of bounded metric spaces by the set\nof the Gromov--Hausdorff distances to so-called simplexes (metric spaces with\nunique non-zero distance) is investigated. It is easy to construct an example\nof non-isometric metric spaces such that the Gromov--Hausdorff distance between\nthem vanishes. Such spaces are non-distinguishable, of course. But we give\nexamples of non-distinguishable metric spaces, the Gromov--Hausdorff distance\nbetween which is non-zero. More over, we prove several sufficient and necessary\nconditions for metric spaces to be non-distinguishable.\n', 'On the Gromov-Hausdorff distance between the cloud of bounded metric spaces and a cloud with nontrivial stabilizer The paper studies the class of all metric spaces considered up to zero Gromov-Hausdorff distance between them. In this class, we examine clouds - classes of spaces situated at finite Gromov-Hausdorff distances from a reference space. We prove that all clouds are proper classes. The Gromov-Hausdorff distance is defined for clouds similarly with the case of that for metric spaces. A multiplicative group of transformations of clouds is defined which is called stabilizer. We show that under certain restrictions the distance between the cloud of bounded metric spaces and a cloud with a nontrivial stabilizer is finite. In particular, the distance between the cloud of bounded metric spaces and the cloud containing the real line is calculated.', 'Lectures on Hausdorff and Gromov-Hausdorff Distance Geometry   The course was given at Peking University, Fall 2019.\n  We discuss the following subjects:\n  (1) Introduction to general topology, hyperspaces, metric and pseudometric\nspaces, graph theory.\n  (2) Graphs in metric spaces, minimum spanning tree, Steiner minimal tree,\nGromov minimal filling.\n  (3) Hausdorff distance, Vietoris topology, Limits theory, inheritance of\ncompleteness, total boundedness, compactness by hyperspaces.\n  (4) Gromov-Hausdorff distance, triangle inequality, positive definiteness for\nisometry classes of compact spaces, counterexample for boundedly compact\nspaces.\n  (5) Gromov-Hausdorff distance for separable spaces in terms of their\nisometric images in \\ell_\\infty, correspondences, Gromov-Hausdorff distance in\nterms of correspondences.\n  (6) Epsilon-isometries and Gromov-Hausdorff distance.\n  (7) Irreducible correspondences and Gromov-Hausdorff distance.\n  (8) Gromov-Hausdorff convergence, inheritance of metric and topological\nproperties while Gromov-Hausdorff convergence.\n  (9) Gromov-Hausdorff space (GH-space), optimal correspondences, existence of\nclosed optimal correspondences for compact metric spaces, GH-space is geodesic.\n  (10) Cover number, packing number, total boundedness, completeness, and\nseparability of GH-space.\n  (11) mst-spectrum in terms of GH-distances to simplexes, Steiner problem in\nGH-space.\n  (12) GH-distance to simplexes with more points, GH-distance to simplexes with\nat most the same number of points.\n  (13) Generalized Borsuk problem, solution of Generalized Borsuk problem in\nterms of GH-distances, clique covering number and chromatic number of simple\ngraphs, their dualities, calculating these numbers in terms of GH-distances.\n']","[('gromov hausdorff distance', 0.7369483709335327), ('gromov hausdorff metric', 0.7318442463874817), ('metric spaces equipped', 0.6878847479820251), ('hausdorff metric', 0.6626338362693787), ('hausdorff distance', 0.6487045884132385), ('metric spaces', 0.6415873765945435), ('invariant metric spaces', 0.6166616678237915), ('gromov hausdorff', 0.6114750504493713), ('class metric spaces', 0.6111354231834412), ('distances metric', 0.6026753187179565)]"
1273,1273,23,1273_agent reinforcement learning_reinforcement learning rl_deep reinforcement learning_reinforcement learning drl,"['agent reinforcement learning', 'reinforcement learning rl', 'deep reinforcement learning', 'reinforcement learning drl', 'reinforcement learning', 'ev charging', 'agent reinforcement', 'reinforcement learning marl', 'electricity market', 'multi agent reinforcement']","['Temporal-Aware Deep Reinforcement Learning for Energy Storage Bidding in\n  Energy and Contingency Reserve Markets   The battery energy storage system (BESS) has immense potential for enhancing\ngrid reliability and security through its participation in the electricity\nmarket. BESS often seeks various revenue streams by taking part in multiple\nmarkets to unlock its full potential, but effective algorithms for joint-market\nparticipation under price uncertainties are insufficiently explored in the\nexisting research. To bridge this gap, we develop a novel BESS joint bidding\nstrategy that utilizes deep reinforcement learning (DRL) to bid in the spot and\ncontingency frequency control ancillary services (FCAS) markets. Our approach\nleverages a transformer-based temporal feature extractor to effectively respond\nto price fluctuations in seven markets simultaneously and helps DRL learn the\nbest BESS bidding strategy in joint-market participation. Additionally, unlike\nconventional ""black-box"" DRL model, our approach is more interpretable and\nprovides valuable insights into the temporal bidding behavior of BESS in the\ndynamic electricity market. We validate our method using realistic market\nprices from the Australian National Electricity Market. The results show that\nour strategy outperforms benchmarks, including both optimization-based and\nother DRL-based strategies, by substantial margins. Our findings further\nsuggest that effective temporal-aware bidding can significantly increase\nprofits in the spot and contingency FCAS markets compared to individual market\nparticipation.\n', 'Agent-Based Decentralized Energy Management of EV Charging Station with Solar Photovoltaics via Multi-Agent Reinforcement Learning In the pursuit of energy net zero within smart cities, transportation electrification plays a pivotal role. The adoption of Electric Vehicles (EVs) keeps increasing, making energy management of EV charging stations critically important. While previous studies have managed to reduce energy cost of EV charging while maintaining grid stability, they often overlook the robustness of EV charging management against uncertainties of various forms, such as varying charging behaviors and possible faults in faults in some chargers. To address the gap, a novel Multi-Agent Reinforcement Learning (MARL) approach is proposed treating each charger to be an agent and coordinate all the agents in the EV charging station with solar photovoltaics in a more realistic scenario, where system faults may occur. A Long Short-Term Memory (LSTM) network is incorporated in the MARL algorithm to extract temporal features from time-series. Additionally, a dense reward mechanism is designed for training the agents in the MARL algorithm to improve EV charging experience. Through validation on a real-world dataset, we show that our approach is robust against system uncertainties and faults and also effective in minimizing EV charging costs and maximizing charging service satisfaction.', 'An Efficient Distributed Multi-Agent Reinforcement Learning for EV\n  Charging Network Control   The increasing trend in adopting electric vehicles (EVs) will significantly\nimpact the residential electricity demand, which results in an increased risk\nof transformer overload in the distribution grid. To mitigate such risks, there\nare urgent needs to develop effective EV charging controllers. Currently, the\nmajority of the EV charge controllers are based on a centralized approach for\nmanaging individual EVs or a group of EVs. In this paper, we introduce a\ndecentralized Multi-agent Reinforcement Learning (MARL) charging framework that\nprioritizes the preservation of privacy for EV owners. We employ the\nCentralized Training Decentralized Execution-Deep Deterministic Policy Gradient\n(CTDE-DDPG) scheme, which provides valuable information to users during\ntraining while maintaining privacy during execution. Our results demonstrate\nthat the CTDE framework improves the performance of the charging network by\nreducing the network costs. Moreover, we show that the Peak-to-Average Ratio\n(PAR) of the total demand is reduced, which, in turn, reduces the risk of\ntransformer overload during the peak hours.\n']","[('agent reinforcement learning', 0.5219769477844238), ('reinforcement learning rl', 0.4897387623786926), ('deep reinforcement learning', 0.4698379635810852), ('reinforcement learning drl', 0.464398592710495), ('reinforcement learning', 0.4586440622806549), ('ev charging', 0.43764442205429077), ('agent reinforcement', 0.4221745729446411), ('reinforcement learning marl', 0.40980276465415955), ('electricity market', 0.4094601273536682), ('multi agent reinforcement', 0.40932050347328186)]"
1274,1274,23,1274_approximate controllability_controllability properties_navier stokes systems_navier stokes system,"['approximate controllability', 'controllability properties', 'navier stokes systems', 'navier stokes system', 'compressible navier stokes', 'controllability results', 'null controllability', 'incompressible navier stokes', 'controllability', 'controllability coupled']","[""Controllability and Stabilizability of the Linearized Compressible\n  Navier-Stokes System with Maxwell's Law   In this paper, we study the control properties of the linearized compressible\nNavier-Stokes system with Maxwell's law around a constant steady state\n$(\\rho_s, u_s, 0), \\rho_s>0, u_s>0$ in the interval $(0, 2\\pi)$ with periodic\nboundary data. We explore the exact controllability of the coupled system by\nmeans of a localized interior control acting in any of the equations when time\nis large enough. We also study the boundary exact controllability of the\nlinearized system using a single control force when the time is sufficiently\nlarge. In both cases, we prove the exact controllability of the system in the\nspace $L^2(0,2\\pi)\\times L^2(0, 2\\pi)\\times L^2(0, 2\\pi)$. We establish the\nexact controllability results by proving an observability inequality with the\nhelp of an Ingham-type inequality. Moreover, we prove that the system is\nexactly controllable at any time if the control acts everywhere in the domain\nin any of the equations. Next, we prove the small time lack of controllability\nof the concerned system.\n  Further, using a Gramian-based approach demonstrated by Urquiza, we prove the\nexponential stabilizability of the corresponding closed-loop system with an\narbitrary prescribed decay rate using boundary feedback control law.\n"", 'Boundary null-controllability of 1d linearized compressible\n  Navier-Stokes system by one control force   In this article, we study the boundary null-controllability properties of the\none-dimensional linearized (around $(Q_0,V_0)$ with constants $Q_0>0, V_0>0$)\ncompressible Navier-Stokes equations in the interval $(0,1)$ when a control\nfunction is acting either on the density or velocity component at one end of\nthe interval. We first prove that the linearized system, with a Dirichlet\nboundary control on the density component and homogeneous Dirichlet boundary\nconditions on the velocity component, is null-controllable in $H^s_{per}(0,1)\n\\times L^2(0,1)$ for any $s > 1/2$ provided the time $T > 1$, where\n$H^s_{per}(0,1)$ denotes the Sobolev space of periodic functions. The proof is\nbased on solving a mixed parabolic-hyperbolic moments problem and to do so, we\nperform a spectral analysis for the associated adjoint operator which is the\nmain involved part of this work. As a corollary, we also prove that the system\nis approximately controllable in $L^2(0,1) \\times L^2(0,1)$ when $T>1$.\n  On the other hand, assuming that the density is equal on the two boundary\npoints w.r.t. time, when a control is applied on the velocity part through a\nDirichlet condition, we can only able to prove that the system is\nnull-controllable in a strict subspace of finite codimension\n$\\mathcal{H}\\subset H^s_{per}(0,1) \\times L^2(0,1)$ for $s>1/2$ when $T>1$.\nMore precisely, in this case we are able to show that all the eigenfunctions of\nthe associated adjoint operator are observable for higher frequencies whereas\nfor the lower frequencies it is hard to conclude anything. A\nparabolic-hyperbolic joint Ingham-type inequality which we prove in this\narticle, leads to an observability inequality in the space $\\mathcal{H}^*$ and\nthe controllability result follows. The significant point is that the moments\nmethod does not yield a better space for the null-controllability when a\ncontrol acts on the velocity part.\n', 'Null controllability of one-dimensional barotropic and non-barotropic\n  linearized compressible Navier-Stokes system using one boundary control   In this article, we study boundary null controllability properties of the\nlinearized compressible Navier-Stokes equations in the interval $(0,2\\pi)$ for\nboth barotropic and non-barotropic fluids using only one boundary control. We\nconsider all the possible cases of the act of control for both systems\n(density, velocity and temperature). These controls are acting on the boundary\nand are given as the difference of the values at $x=0$ and $x=2\\pi$. In this\nsetup, using a boundary control acting in density, we first prove null\ncontrollability of both the barotropic and non-barotropic systems at large time\nin the spaces $(\\dot{L}^2(0,2\\pi))^2$ and $(\\dot{L}^2(0,2\\pi))^3$ respectively\n(where the dot represents functions with mean value zero). When the control is\nacting in the velocity component, we prove null controllability at large time\nin the spaces $\\dot{H}^1_{\\text{per}}(0,2\\pi)\\times\\dot{L}^2(0,2\\pi)$ and\n$\\dot{H}^1_{\\text{per}}(0,2\\pi)\\times(\\dot{L}^2(0,2\\pi))^2$ respectively.\nFurther, in both cases, we prove that these null controllability results are\nsharp with respect to the regularity of the initial states in velocity/\ntemperature case, and time in the density case. Finally, for both barotropic\nand non-barotropic fluids, we prove that, under some assumptions, the system\ncannot be approximately controllable at any time, whether there is a control\nacting in density, velocity or temperature.\n']","[('approximate controllability', 0.5785229206085205), ('controllability properties', 0.5605390667915344), ('navier stokes systems', 0.5588721632957458), ('navier stokes system', 0.5499770641326904), ('compressible navier stokes', 0.549827516078949), ('controllability results', 0.5380548238754272), ('null controllability', 0.5278175473213196), ('incompressible navier stokes', 0.5246133804321289), ('controllability', 0.5217817425727844), ('controllability coupled', 0.5206124782562256)]"
1275,1275,23,1275_paley wiener spaces_wiener spaces_wiener space_wiener type,"['paley wiener spaces', 'wiener spaces', 'wiener space', 'wiener type', 'paley wiener', 'schwartz space', 'spaces schwartz', 'schwartz functions', 'wiener', 'schwartz class']","['Paley-Wiener Theorems For Slice Regular Functions   We prove two theorems of Paley and Wiener in the slice regular setting. As an\napplication, we can compute the reproducing kernel for the slice regular\nPaley-Wiener space, and obtain a related sampling theorem.\n', 'Paley-Wiener theorems for slice monogenic functions   In this paper, we prove some Paley-Wiener theorems for function spaces\nconsisting of slice monogenic functions such as Paley-Wiener, Hardy and Bergman\nspaces. As applications, we can compute the reproducing kernel functions for\nthe related function spaces.\n', 'Real Paley-Wiener theorems and local spectral radius formulas   We systematically develop real Paley-Wiener theory for the Fourier transform\non R^d for Schwartz functions, L^p-functions and distributions, in an\nelementary treatment based on the inversion theorem. As an application, we show\nhow versions of classical Paley-Wiener theorems can be derived from the real\nones via an approach which does not involve domain shifting and which may be\nput to good use for other transforms of Fourier type as well. An explanation is\nalso given why the easily applied classical Paley-Wiener theorems are unlikely\nto be able to yield information about the support of a function or distribution\nwhich is more precise than giving its convex hull, whereas real Paley-Wiener\ntheorems can be used to reconstruct the support precisely, albeit at the cost\nof combinatorial complexity. We indicate a possible application of real\nPaley-Wiener theory to partial differential equations in this vein and\nfurthermore we give evidence that a number of real Paley-Wiener results can be\nexpected to have an interpretation as local spectral radius formulas. A\ncomprehensive overview of the literature on real Paley-Wiener theory is\nincluded.\n']","[('paley wiener spaces', 0.8106140494346619), ('wiener spaces', 0.7051283121109009), ('wiener space', 0.6812833547592163), ('wiener type', 0.557399570941925), ('paley wiener', 0.5088002681732178), ('schwartz space', 0.49438008666038513), ('spaces schwartz', 0.46364516019821167), ('schwartz functions', 0.4544934630393982), ('wiener', 0.42329803109169006), ('schwartz class', 0.39784008264541626)]"
1276,1276,23,1276_games generalized_various topological_games involving_compact subsets,"['games generalized', 'various topological', 'games involving', 'compact subsets', 'topology pointwise', 'space game', 'uniform spaces', 'open games', 'topologies', 'countably compact']","['Some observations on the mildly Menger property and topological games   In this paper, we defined two new games - the mildly Menger game and the\ncompact-clopen game. In a zero-dimensional space, the Menger game is equivalent\nto the mildly Menger game and the compact-open game is equivalent to the\ncompact-clopen game. An example is given for a space on which the mildly Menger\ngame is undetermined. Also we introduced a new game namely\nK-quasi-component-clopen game and proved that this game is equivalent to the\ncompact-clopen game. Then we proved that if a topological space is a union of\ncountably many quasi-components of compact sets, then TWO has a winning\nstrategy in the mildly Menger game.\n', ""Translation Results for some Selection Games with Minimal Cusco Maps   We establish relationships between various topological selection games\ninvolving the space of minimal cusco maps into the real line and the underlying\ndomain. These connections occur across different topologies, including the\ntopology of pointwise convergence and the topology of uniform convergence on\ncompacta. Full and limited-information strategies are investigated. The primary\ngames we consider are Rothberger-like games, generalized point-open games,\nstrong fan-tightness games, Tkachuk's closed discrete selection game, and\nGruenhage's W-games. We also comment on the difficulty of generalizing the\ngiven results to other classes of functions.\n"", 'Translation Results for Some Star-Selection Games   We continue to explore the ways in which high-level topological connections\narise from connections between fundamental features of the spaces, in this case\nfocusing on star-selection principles in Pixley-Roy hyperspaces and uniform\nspaces. First, we find a way to write star-selection principles as ordinary\nselection principles, allowing us to apply our translation theorems to\nstar-selection games. For Pixley-Roy hyperspaces, we are able to extend work of\nM. Sakai and connect the star-Menger/Rothberger games on the hyperspace to the\n$\\omega$-Menger/Rothberger games on the ground space. Along the way, we uncover\nconnections between cardinal invariants. For uniform spaces, we show that the\nstar-Menger/Rothberger game played with uniform covers is equivalent to the\nMenger/Rothberger game played with uniform covers, reinforcing an observation\nof Lj. Ko\\v{c}inac.\n']","[('games generalized', 0.6164014339447021), ('various topological', 0.5109732151031494), ('games involving', 0.4909668564796448), ('compact subsets', 0.4376385509967804), ('topology pointwise', 0.4342421889305115), ('space game', 0.42631179094314575), ('uniform spaces', 0.41572919487953186), ('open games', 0.4136565327644348), ('topologies', 0.4089575707912445), ('countably compact', 0.40883103013038635)]"
1277,1277,23,1277_magic squares_magic square_squares_squares every,"['magic squares', 'magic square', 'squares', 'squares every', 'magic labelings', 'squares order', 'magic labeling', 'squares also', 'two squares', 'diagonals']","['Some Thoughts on the Search for $5 \\times 5$ and $6 \\times 6$\n  Additive-Multiplicative Magic Squares   An additive-multiplicative magic square is a square grid of numbers whose\nrows, columns, and long diagonals all have the same sum (called the magic sum)\nand the same product (called the magic product). There are numerous open\nproblems about magic squares by Christian Boyer on multimagie.com. One such\nproblem is to construct or prove the impossibility of a $5 \\times 5$ or $6\n\\times 6$ additive-multiplicative magic square of distinct positive integers.\nHere, we present a possible approach to this problem and some partial results.\nWe observe that such a square can be described by a form determined by the\nprime factorizations of its entries and that identifying these forms might be\nhelpful in finding such a square or ruling out specific magic products.\n', 'Binary Color-Coded Magic Squares: A Study of Uniqueness Under\n  Rotation/Reflection, PCA, and LDA Analysis   In this paper, we study the concept of ""binary color-coded magic squares"" by\nassigning two distinct colors to the even and odd numbers within a magic\nsquare. We investigate the uniqueness of patterns within these squares using\nthree different analytical methods, including rotation/reflection, PCA, and\nLDA. Our investigation covers all 880 magic squares of order 4, all 48,544\nassociative magic squares of order 5, and all 368,640 Franklin magic squares of\norder 8. Our investigation reveals striking patterns that were previously\nunknown in traditional magic squares, shedding light on the potential for\nbinary color-coded magic squares to contribute to the field of mathematics.\n', ""Spectrum of MATLABs magic squares   This article looks at the eigenvalues of magic squares generated by the\nMATLAB's magic($n$) function. The magic($n$) function constructs doubly even\n($n = 4k$) magic squares, singly even ($n = 4k+2$) magic squares and odd ($n =\n2k+1$) magic squares using different algorithms. The doubly even magic squares\nare constructed by a criss-cross method that involves reflecting the entries of\na simple square about the center. The odd magic squares are constructed using\nthe Siamese method. The singly even magic squares are constructed using a\nlower-order odd magic square (Strachey method). We obtain approximations of\neigenvalues of odd and singly even magic squares and prove error bounds on the\napproximation. For the sake of completeness, we also obtain the eigenpairs of\ndoubly even magic squares generated by MATLAB. The approximation of the spectra\ninvolves some interesting connections with the spectrum of g-circulant matrices\nand the use of Bauer-Fike theorem.\n""]","[('magic squares', 0.7337368130683899), ('magic square', 0.6653373837471008), ('squares', 0.4822846055030823), ('squares every', 0.465847909450531), ('magic labelings', 0.4437269866466522), ('squares order', 0.43095242977142334), ('magic labeling', 0.4278987646102905), ('squares also', 0.4276006817817688), ('two squares', 0.42530402541160583), ('diagonals', 0.3977273404598236)]"
1278,1278,23,1278_odinger operators periodic_periodic schr odinger_schr odinger operators_graphs spectrum,"['odinger operators periodic', 'periodic schr odinger', 'schr odinger operators', 'graphs spectrum', 'periodic operators', 'operators periodic', 'schr odinger operator', 'periodic graphs', 'discrete schr odinger', 'spectral band']","['Trace formulas for magnetic Schr\\""odinger operators on periodic graphs\n  and their applications   We consider Schr\\""odinger operators with periodic magnetic and electric\npotentials on periodic discrete graphs. The spectrum of such operators consists\nof a finite number of bands. We determine trace formulas for the magnetic\nSchr\\""odinger operators. The traces of the fiber operators are expressed as\nfinite Fourier series of the quasimomentum. The coefficients of the Fourier\nseries are given in terms of the magnetic fluxes, electric potentials and\ncycles in the quotient graph from some specific cycle sets. Using the trace\nformulas we obtain new lower estimates of the total bandwidth for the magnetic\nSchr\\""odinger operator in terms of geometric parameters of the graph, magnetic\nfluxes and electric potentials. We show that these estimates are sharp.\n', 'Spectrum of Schr\\""odinger operators on subcovering graphs   We consider discrete Schr\\""odinger operators with real periodic potentials on\nperiodic graphs. The spectra of the operators consist of a finite number of\nbands. By ""rolling up"" a periodic graph along some appropriate directions we\nobtain periodic graphs of smaller dimensions called subcovering graphs. For\nexample, rolling up a planar hexagonal lattice along different directions will\nlead to nanotubes with various chiralities. We describe connections between\nspectra of the Schr\\""odinger operators on a periodic graph and its\nsubcoverings. In particular, we provide a simple criterion for the subcovering\ngraph to be isospectral to the original periodic graph. By isospectrality of\nperiodic graphs we mean that the spectra of the Schr\\""odinger operators on the\ngraphs consist of the same number of bands and the corresponding bands coincide\nas sets. We also obtain asymptotics of the band edges of the Schr\\""odinger\noperator on the subcovering graph as the ""chiral"" (roll up) vectors are long\nenough.\n', 'Trace formulas for Schr\\""odinger operators on periodic graphs   We consider Schr\\""odinger operators with periodic potentials on periodic\ndiscrete graphs. Their spectrum consists of a finite number of bands. We\ndetermine trace formulas for the Schr\\""odinger operators. The proof is based on\nthe decomposition of the Schr\\""odinger operators into a direct integral and a\nspecific representation of fiber operators. The traces of the fiber operators\nare expressed as finite Fourier series of the quasimomentum. The coefficients\nof the Fourier series are given in terms of the potentials and cycles in the\nquotient graph from some specific cycle sets. We also present the trace\nformulas for the heat kernel and the resolvent of the Schr\\""odinger operators\nand the determinant formulas.\n']","[('odinger operators periodic', 0.6542163491249084), ('periodic schr odinger', 0.6023669838905334), ('schr odinger operators', 0.592595636844635), ('graphs spectrum', 0.5863796472549438), ('periodic operators', 0.5736907720565796), ('operators periodic', 0.5574145317077637), ('schr odinger operator', 0.5553229451179504), ('periodic graphs', 0.5551046133041382), ('discrete schr odinger', 0.5469390749931335), ('spectral band', 0.5269905924797058)]"
1279,1279,23,1279_shell models_isometric deformations_elasticity theory_thin shell,"['shell models', 'isometric deformations', 'elasticity theory', 'thin shell', 'curvature terms', 'thin shells', 'isotropic elastic', 'curvature', 'curvature energy', 'nonlinear elasticity']","['A linear isotropic Cosserat shell model including terms up to $O(h^5)$.\n  Existence and uniqueness   In this paper we derive the linear elastic Cosserat shell model incorporating\neffects up to order $O(h^5)$ in the shell thickness $h$ as a particular case of\nthe recently introduced geometrically nonlinear elastic Cosserat shell model.\nThe existence and uniqueness of the solution is proven in suitable admissible\nsets. To this end, inequalities of Korn-type for shells are established which\nallow to show coercivity in the Lax-Milgram theorem. We are also showing an\nexistence and uniqueness result for a truncated $O(h^3)$ model. Main issue is\nthe suitable treatment of the curved reference configuration of the shell. Some\nconnections to the classical Koiter membrane-bending model are highlighted.\n', 'A geometrically nonlinear Cosserat (micropolar) curvy shell model via\n  Gamma convergence   Using $\\Gamma$-convergence arguments, we construct a nonlinear membrane-like\nCosserat shell model on a curvy reference configuration starting from a\ngeometrically nonlinear, physically linear three-dimensional isotropic Cosserat\nmodel. Even if the theory is of order $O(h)$ in the shell thickness $h$, by\ncomparison to the membrane shell models proposed in classical nonlinear\nelasticity, beside the change of metric, the membrane-like Cosserat shell model\nis still capable to capture the transverse shear deformation and the\n{Cosserat}-curvature due to remaining Cosserat effects.\n  We formulate the limit problem by scaling both unknowns, the deformation and\nthe microrotation tensor, and by expressing the parental three-dimensional\nCosserat energy with respect to a fictitious flat configuration. The model\nobtained via $\\Gamma$-convergence is similar to the membrane {(no $O(h^3)$\nflexural terms, but still depending on the Cosserat-curvature)} Cosserat shell\nmodel derived via a derivation approach but these two models do not coincide.\nComparisons to other shell models are also included.\n', 'A constrained Cosserat shell model up to order $O(h^5)$: Modelling,\n  existence of minimizers, relations to classical shell models and scaling\n  invariance of the bending tensor   We consider a recently introduced geometrically nonlinear elastic Cosserat\nshell model incorporating effects up to order $O(h^5)$ in the shell thickness\n$h$. We develop the corresponding geometrically nonlinear constrained Cosserat\nshell model, we show the existence of minimizers for the $O(h^5)$ and $O(h^3)$\ncase and we draw some connections to existing models and classical shell strain\nmeasures. Notably, the role of the appearing new bending tensor is highlighted\nand investigated with respect to an invariance condition of Acharya [Int. J.\nSolids and Struct., 2000] which will be further strengthened.\n']","[('shell models', 0.4983333945274353), ('isometric deformations', 0.49547767639160156), ('elasticity theory', 0.4902395009994507), ('thin shell', 0.46161195635795593), ('curvature terms', 0.46153268218040466), ('thin shells', 0.4534899890422821), ('isotropic elastic', 0.4503958821296692), ('curvature', 0.4467886686325073), ('curvature energy', 0.43952077627182007), ('nonlinear elasticity', 0.43788981437683105)]"
1280,1280,23,1280_subconvex bound_rankin selberg_hilbert modular forms_hecke functions,"['subconvex bound', 'rankin selberg', 'hilbert modular forms', 'hecke functions', 'formula moments', 'spectral parameter', 'asymptotic formula', 'primitive dirichlet character', 'infinity bound', 'selberg']","['Hybrid subconvexity for Maass form symmetric-square $L$-functions   Recently R. Khan and M. Young proved a mean Lindel\\""{o}f estimate for the\nsecond moment of Maass form symmetric-square $L$-functions $L(\\text{sym}^2\nu_{j},1/2+it)$ on the short interval of length $G\\gg\n|t_j|^{1+\\epsilon}/t^{2/3}$, where $t_j$ is a spectral parameter of the\ncorresponding Maass form. Their estimate yields a subconvexity estimate for\n$L(\\text{sym}^2 u_{j},1/2+it)$ as long as $|t_j|^{6/7+\\delta} \\ll\nt<(2-\\delta)|t_j|$. We obtain a mean Lindel\\""{o}f estimate for the same moment\nin shorter intervals, namely for $G\\gg |t_j|^{1+\\epsilon}/t$. As a corollary,\nwe prove a subconvexity estimate for $L(\\text{sym}^2 u_{j},1/2+it)$ on the\ninterval $|t_j|^{2/3+\\delta}\\ll t\\ll |t_j|^{6/7-\\delta}$.\n', 'The cubic moment of Hecke--Maass cusp forms and moments of $L$-functions   In this paper, we prove the smooth cubic moments vanish for the Hecke--Maass\ncusp forms, which gives a new case of the random wave conjecture. In fact, we\ncan prove a polynomial decay for the smooth cubic moments, while for the smooth\nsecond moment (i.e. QUE) no rate of decay is known unconditionally for general\nHecke--Maass cusp forms. The proof bases on various estimates of moments of\ncentral $L$-values. We prove the Lindel\\""of on average bound for the first\nmoment of $\\rm GL(3)\\times GL(2)$ $L$-functions in short intervals of the\nsubconvexity strength length, and the convexity strength upper bound for the\nmixed moment of $\\rm GL(2)$ and the triple product $L$-functions. In\nparticular, we prove new subconvexity bounds of certain $\\rm GL(3)\\times GL(2)$\n$L$-functions.\n', 'Moments and hybrid subconvexity for symmetric-square L-functions   We establish sharp bounds for the second moment of symmetric-square\n$L$-functions attached to Hecke Maass cusp forms $u_j$ with spectral parameter\n$t_j$, where the second moment is a sum over $t_j$ in a short interval. At the\ncentral point $s=1/2$ of the $L$-function, our interval is smaller than\nprevious known results. More specifically, for $|t_j|$ of size $T$, our\ninterval is of size $T^{1/5}$, while the previous best was $T^{1/3}$ from work\nof Lam. A little higher up on the critical line, our second moment yields a\nsubconvexity bound for the symmetric-square $L$-function. More specifically, we\nget subconvexity at $s=1/2+it$ provided $|t_j|^{6/7+\\delta}\\le |t| \\le\n(2-\\delta)|t_j|$ for any fixed $\\delta>0$. Since $|t|$ can be taken\nsignificantly smaller than $|t_j|$, this may be viewed as an approximation to\nthe notorious subconvexity problem for the symmetric-square $L$-function in the\nspectral aspect at $s=1/2$.\n']","[('subconvex bound', 0.3935977816581726), ('rankin selberg', 0.3644329905509949), ('hilbert modular forms', 0.324529767036438), ('hecke functions', 0.31502899527549744), ('formula moments', 0.3104414641857147), ('spectral parameter', 0.3053267300128937), ('asymptotic formula', 0.2879708409309387), ('primitive dirichlet character', 0.28166481852531433), ('infinity bound', 0.28079840540885925), ('selberg', 0.2794349193572998)]"
1281,1281,23,1281_equidistribution theorems_asymptotic equidistribution_effective equidistribution_equidistribution,"['equidistribution theorems', 'asymptotic equidistribution', 'effective equidistribution', 'equidistribution', 'equidistributes', 'uniform lattices', 'sl _2 mathbb', 'modular surface', 'uniform lattice', 'mathrm sl _2']","['Translates of rational points along expanding closed horocycles on the\n  modular surface   We study the limiting distribution of the rational points under a horizontal\ntranslation along a sequence of expanding closed horocycles on the modular\nsurface. Using spectral methods we confirm equidistribution of these sample\npoints for any translate when the sequence of horocycles expands within a\ncertain polynomial range. We show that the equidistribution fails for generic\ntranslates and a slightly faster expanding rate. We also prove both\nequidistribution and non-equidistribution results by obtaining explicit\nlimiting measures while allowing the sequence of horocycles to expand\narbitrarily fast. Similar results are also obtained for translates of primitive\nrational points.\n', 'Polynomial effective equidistribution   We prove effective equidistribution theorems, with polynomial error rate, for\norbits of the unipotent subgroups of $\\operatorname{SL}_2(\\mathbb R)$ in\narithmetic quotients of $\\operatorname{SL}_2(\\mathbb C)$ and\n$\\operatorname{SL}_2(\\mathbb R)\\times\\operatorname{SL}_2(\\mathbb R)$. The proof\nis based on the use of a Margulis function, tools from incidence geometry, and\nthe spectral gap of the ambient space.\n', 'Effective equidistribution for some one parameter unipotent flows   We prove effective equidistribution theorems, with polynomial error rate, for\norbits of the unipotent subgroups of $\\operatorname{SL}_2(\\mathbb R)$ in\narithmetic quotients of $\\operatorname{SL}_2(\\mathbb C)$ and\n$\\operatorname{SL}_2(\\mathbb R)\\times\\operatorname{SL}_2(\\mathbb R)$.\n  The proof is based on the use of a Margulis function, tools from incidence\ngeometry, and the spectral gap of the ambient space.\n']","[('equidistribution theorems', 0.5757728219032288), ('asymptotic equidistribution', 0.4901790916919708), ('effective equidistribution', 0.46218112111091614), ('equidistribution', 0.43480855226516724), ('equidistributes', 0.3900270164012909), ('uniform lattices', 0.3648643493652344), ('sl _2 mathbb', 0.3523104786872864), ('modular surface', 0.3418251574039459), ('uniform lattice', 0.3274652361869812), ('mathrm sl _2', 0.3218200206756592)]"
1282,1282,23,1282_elliptic operators_operators unbounded_analytic semigroups_unbounded linear operators,"['elliptic operators', 'operators unbounded', 'analytic semigroups', 'unbounded linear operators', 'operator unbounded', 'fractional sobolev spaces', 'unbounded coefficients', 'odinger operators', 'schr odinger operators', 'sobolev spaces']","['Fourth-order operators with unbounded coefficients   We prove that operators of the form $A=-a(x)^2\\Delta^{2}$, with $|D a(x)|\\leq\nc a(x)^\\frac{1}{2}$, generate analytic semigroups in $L^p(\\mathbb{R}^N)$ for\n$1<p\\leq\\infty$ and in $C_b(\\mathbb{R}^N)$. In particular, we deduce generation\nresults for the operator $A :=- (1+|x|^2)^{\\alpha} \\Delta^{2}$,\n$0\\leq\\alpha\\leq2$. Moreover, we characterize the maximal domain of such\noperators in $L^p(\\mathbb{R}^N)$ for $1<p<\\infty$.\n', 'Generation results for vector-valued elliptic operators with unbounded\n  coefficients in L^p spaces   We consider a class of vector-valued elliptic operators with unbounded\ncoefficients, coupled up to the first-order, in the Lebesgue space L^p(R^d;R^m)\nwith p in (1,\\infty). Sufficient conditions to prove generation results of an\nanalytic C_0-semigroup T(t), together with a characterization of the domain of\nits generator, are given. Some results related to the hypercontractivity and\nthe ultraboundedness of the semigroup are also established.\n', 'Equivalence of Sobolev norms in Lebesgue spaces for Hardy operators in a\n  half-space   We consider Hardy operators, i.e., homogeneous Schr\\""odinger operators\nconsisting of the ordinary or fractional Laplacian in a half-space plus a\npotential, which only depends on the appropriate power of the distance to the\nboundary of the half-space. We compare the scales of homogeneous $L^p$-Sobolev\nspaces generated by these Hardy operators with and without potential with each\nother. To that end, we prove and use new square function estimates for\noperators with slowly decaying heat kernels. Our results hold for all\nadmissible coupling constants in the local case and for repulsive potentials in\nthe fractional case, and extend those obtained recently in $L^2$. They also\ncover attractive potentials in the fractional case, once expected heat kernel\nestimates are available.\n']","[('elliptic operators', 0.6003841757774353), ('operators unbounded', 0.6000165939331055), ('analytic semigroups', 0.5993240475654602), ('unbounded linear operators', 0.5684788227081299), ('operator unbounded', 0.5602008104324341), ('fractional sobolev spaces', 0.5363995432853699), ('unbounded coefficients', 0.5116096138954163), ('odinger operators', 0.49379247426986694), ('schr odinger operators', 0.48979493975639343), ('sobolev spaces', 0.4765481948852539)]"
1283,1283,23,1283_riemannian symmetric spaces_riemannian symmetric space_riemannian homogeneous spaces_action symmetric,"['riemannian symmetric spaces', 'riemannian symmetric space', 'riemannian homogeneous spaces', 'action symmetric', 'isometric actions', 'isometric lie group', 'actions symmetric', 'isometric action', 'principal orbits', 'riemannian symmetric']","[""Curvatures and austere property of orbits of path group actions induced\n  by Hermann actions   It is known that an isometric action of a Lie group on a compact symmetric\nspace gives rise to a proper Fredholm action of a path group on a path space\nvia the gauge transformations. In this paper, supposing that the isometric\naction is a Hermann action (i.e. an isometric action of a symmetric subgroup of\nthe isometry group) we give an explicit formula for the principal curvatures of\norbits of the path group action and study the condition for those orbits to be\naustere, that is, the set of principal curvatures in the direction of each\nnormal vector is invariant under the multiplication by minus one. To prove the\nresults we essentially use the facts that Hermann actions are hyperpolar and\nall orbits of Hermann actions are curvature-adapted submanifolds. The results\ngreatly extend the author's previous result in the case of the standard sphere\nand show that there exist a larger number of infinite dimensional austere\nsubmanifolds in Hilbert spaces.\n"", 'Cohomogeneity one actions on symmetric spaces of noncompact type and\n  higher rank   We develop a new structural result for cohomogeneity one actions on (not\nnecessarily irreducible) symmetric spaces of noncompact type and arbitrary\nrank. We apply this result to classify cohomogeneity one actions on\nSL(n,R)/SO(n), n>1, up to orbit equivalence. We also reduce the classification\nproblem on a reducible space to the classification on each one of its\nirreducible factors, which in particular allows to classify cohomogeneity one\nactions on any finite product of hyperbolic spaces.\n', 'On cohomogeneity one hyperpolar actions related to $G_{2}$   Cohomogeneity one actions on irreducible Riemannian symmetric spaces of\ncompact type are classified into three cases: Hermann actions, actions induced\nby the linear isotropy representation of a Riemannian symmetric space of rank\n2, and exceptional actions. In this paper, we consider exceptional actions\nrelated to the exceptional compact Lie group $G_{2}$ and investigate some\nproperties of their orbits as Riemannian submanifolds. In particular, we\nexamine the principal curvatures of principal orbits and classify principal\norbits that are minimal, austere, weakly reflective, and proper biharmonic.\n']","[('riemannian symmetric spaces', 0.6075157523155212), ('riemannian symmetric space', 0.5913048982620239), ('riemannian homogeneous spaces', 0.5795378088951111), ('action symmetric', 0.5789474248886108), ('isometric actions', 0.5708072185516357), ('isometric lie group', 0.5604398250579834), ('actions symmetric', 0.55804044008255), ('isometric action', 0.5501893758773804), ('principal orbits', 0.5079874992370605), ('riemannian symmetric', 0.5031026601791382)]"
1284,1284,23,1284_coded distributed computing_coded distributed_distributed computing_distributed computing systems,"['coded distributed computing', 'coded distributed', 'distributed computing', 'distributed computing systems', 'distributed computing framework', 'coded computing', 'mapreduce', 'distributed nodes', 'computing servers', 'distributed']","['A Combinatorial Design for Cascaded Coded Distributed Computing on\n  General Networks   Coding theoretic approached have been developed to significantly reduce the\ncommunication load in modern distributed computing system. In particular, coded\ndistributed computing (CDC) introduced by Li et al. can efficiently trade\ncomputation resources to reduce the communication load in MapReduce like\ncomputing systems. For the more general cascaded CDC, Map computations are\nrepeated at r nodes to significantly reduce the communication load among nodes\ntasked with computing Q Reduce functions s times. In this paper, we propose a\nnovel low-complexity combinatorial design for cascaded CDC which 1) determines\nboth input file and output function assignments, 2) requires significantly less\nnumber of input files and output functions, and 3) operates on heterogeneous\nnetworks where nodes have varying storage and computing capabilities. We\nprovide an analytical characterization of the computation-communication\ntradeoff, from which we show the proposed scheme can outperform the\nstate-of-the-art scheme proposed by Li et al. for the homogeneous networks.\nFurther, when the network is heterogeneous, we show that the performance of the\nproposed scheme can be better than its homogeneous counterpart. In addition,\nthe proposed scheme is optimal within a constant factor of the information\ntheoretic converse bound while fixing the input file and the output function\nassignments.\n', 'A New Combinatorial Coded Design for Heterogeneous Distributed Computing   Coded Distributed Computing (CDC) introduced by Li et al. in 2015 offers an\nefficient approach to trade computing power to reduce the communication load in\ngeneral distributed computing frameworks such as MapReduce and Spark. In\nparticular, increasing the computation load in the Map phase by a factor of r\ncan create coded multicasting opportunities to reduce the communication load in\nthe Shuffle phase by the same factor. However, the CDC scheme is designed for\nthe homogeneous settings, where the storage, computation load and communication\nload on the computing nodes are the same. In addition, it requires an\nexponentially large number of input files (data batches), reduce functions and\nmulticasting groups relative to the number of nodes to achieve the promised\ngain. We address the CDC limitations by proposing a novel CDC approach based on\na combinatorial design, which accommodates heterogeneous networks where nodes\nhave varying storage and computing capabilities. In addition, the proposed\napproach requires an exponentially less number of input files compared to the\noriginal CDC scheme proposed by Li et al. Meanwhile, the resulting\ncomputation-communication trade-off maintains the multiplicative gain compared\nto conventional uncoded unicast and asymptotically achieves the optimal\nperformance proposed by Li et al.\n', 'Cascaded Coded Distributed Computing Schemes Based on Placement Delivery\n  Arrays   Li {\\it et al}. introduced coded distributed computing (CDC) scheme to reduce\nthe communication load in general distributed computing frameworks such as\nMapReduce. They also proposed cascaded CDC schemes where each output function\nis computed multiple times, and proved that such schemes achieved the\nfundamental trade-off between computation load and communication load. However,\nthese schemes require exponentially large numbers of input files and output\nfunctions when the number of computing nodes gets large. In this paper, by\nusing the structure of placement delivery arrays (PDAs), we construct several\ninfinite classes of cascaded CDC schemes. We also show that the numbers of\noutput functions in all the new schemes are only a factor of the number of\ncomputing nodes, and the number of input files in our new schemes is much\nsmaller than that of input files in CDC schemes derived by Li {\\it et al}.\n']","[('coded distributed computing', 0.720499575138092), ('coded distributed', 0.64991694688797), ('distributed computing', 0.6395618319511414), ('distributed computing systems', 0.5730630159378052), ('distributed computing framework', 0.5632010698318481), ('coded computing', 0.5261719822883606), ('mapreduce', 0.49463456869125366), ('distributed nodes', 0.4843141734600067), ('computing servers', 0.48345085978507996), ('distributed', 0.46978166699409485)]"
1285,1285,23,1285_auction_bidding strategy_real time bidding_bidding,"['auction', 'bidding strategy', 'real time bidding', 'bidding', 'auctions', 'time bidding', 'bids', 'bid', 'bidders', 'near optimal regret']","[""Learning to Bid in Non-Stationary Repeated First-Price Auctions   First-price auctions have recently gained significant traction in digital\nadvertising markets, exemplified by Google's transition from second-price to\nfirst-price auctions. Unlike in second-price auctions, where bidding one's\nprivate valuation is a dominant strategy, determining an optimal bidding\nstrategy in first-price auctions is more complex. From a learning perspective,\nthe learner (a specific bidder) can interact with the environment (other\nbidders) sequentially to infer their behaviors. Existing research often assumes\nspecific environmental conditions and benchmarks performance against the best\nfixed policy (static benchmark). While this approach ensures strong learning\nguarantees, the static benchmark can deviate significantly from the optimal\nstrategy in environments with even mild non-stationarity. To address such\nscenarios, a dynamic benchmark, which represents the sum of the best possible\nrewards at each time step, offers a more suitable objective. However, achieving\nno-regret learning with respect to the dynamic benchmark requires additional\nconstraints. By inspecting reward functions in online first-price auctions, we\nintroduce two metrics to quantify the regularity of the bidding sequence, which\nserve as measures of non-stationarity. We provide a minimax-optimal\ncharacterization of the dynamic regret when either of these metrics is\nsub-linear in the time horizon.\n"", ""Learning to Bid Optimally and Efficiently in Adversarial First-price\n  Auctions   First-price auctions have very recently swept the online advertising\nindustry, replacing second-price auctions as the predominant auction mechanism\non many platforms. This shift has brought forth important challenges for a\nbidder: how should one bid in a first-price auction, where unlike in\nsecond-price auctions, it is no longer optimal to bid one's private value\ntruthfully and hard to know the others' bidding behaviors? In this paper, we\ntake an online learning angle and address the fundamental problem of learning\nto bid in repeated first-price auctions, where both the bidder's private\nvaluations and other bidders' bids can be arbitrary. We develop the first\nminimax optimal online bidding algorithm that achieves an\n$\\widetilde{O}(\\sqrt{T})$ regret when competing with the set of all Lipschitz\nbidding policies, a strong oracle that contains a rich set of bidding\nstrategies. This novel algorithm is built on the insight that the presence of a\ngood expert can be leveraged to improve performance, as well as an original\nhierarchical expert-chaining structure, both of which could be of independent\ninterest in online learning. Further, by exploiting the product structure that\nexists in the problem, we modify this algorithm--in its vanilla form\nstatistically optimal but computationally infeasible--to a computationally\nefficient and space efficient algorithm that also retains the same\n$\\widetilde{O}(\\sqrt{T})$ minimax optimal regret guarantee. Additionally,\nthrough an impossibility result, we highlight that one is unlikely to compete\nthis favorably with a stronger oracle (than the considered Lipschitz bidding\npolicies). Finally, we test our algorithm on three real-world first-price\nauction datasets obtained from Verizon Media and demonstrate our algorithm's\nsuperior performance compared to several existing bidding algorithms.\n"", ""Multi-Platform Budget Management in Ad Markets with Non-IC Auctions   In online advertising markets, budget-constrained advertisers acquire ad\nplacements through repeated bidding in auctions on various platforms. We\npresent a strategy for bidding optimally in a set of auctions that may or may\nnot be incentive-compatible under the presence of budget constraints. Our\nstrategy maximizes the expected total utility across auctions while satisfying\nthe advertiser's budget constraints in expectation. Additionally, we\ninvestigate the online setting where the advertiser must submit bids across\nplatforms while learning about other bidders' bids over time. Our algorithm has\n$O(T^{3/4})$ regret under the full-information setting. Finally, we demonstrate\nthat our algorithms have superior cumulative regret on both synthetic and\nreal-world datasets of ad placement auctions, compared to existing adaptive\npacing algorithms.\n""]","[('auction', 0.639582633972168), ('bidding strategy', 0.6136447191238403), ('real time bidding', 0.6088691353797913), ('bidding', 0.6082608699798584), ('auctions', 0.5866284966468811), ('time bidding', 0.5568462014198303), ('bids', 0.5510575771331787), ('bid', 0.503943145275116), ('bidders', 0.4876585900783539), ('near optimal regret', 0.4559755027294159)]"
1286,1286,23,1286_quantum control systems_quantum systems_quantum system_open quantum systems,"['quantum control systems', 'quantum systems', 'quantum system', 'open quantum systems', 'linear quantum', 'quantum stochastic', 'dimensional quantum systems', 'quantum linear', 'quantum computers', 'learning quantum']","['Robust feedback stabilization of N-level quantum spin systems   In this paper, we consider N-level quantum angular momentum systems\ninteracting with electromagnetic fields undergoing continuous-time\nmeasurements. We suppose unawareness of the initial state and physical\nparameters, entailing the introduction of an additional state representing the\nestimated quantum state. The evolution of the quantum state and its estimation\nis described by a coupled stochastic master equation. Here, we study the\nasymptotic behavior of such a system in presence of a feedback controller. We\nprovide sufficient conditions on the feedback controller and on the estimated\nparameters that guarantee exponential stabilization of the coupled stochastic\nsystem towards an eigenstate of the measurement operator. Furthermore, we\nestimate the corresponding rate of convergence. We also provide parametrized\nfeedback laws satisfying such conditions. Our results show the robustness of\nthe feedback stabilization strategy considered in [21] in case of imprecise\ninitialization of the estimated state and with respect to the unknown physical\nparameters.\n', ""Dissipative Quantum Gibbs Sampling   Systems in thermal equilibrium at non-zero temperature are described by their\nGibbs state. For classical many-body systems, the Metropolis-Hastings algorithm\ngives a Markov process with a local update rule that samples from the Gibbs\ndistribution. For quantum systems, sampling from the Gibbs state is\nsignificantly more challenging. Many algorithms have been proposed, but these\nare more complex than the simple local update rule of classical Metropolis\nsampling, requiring non-trivial quantum algorithms such as phase estimation as\na subroutine.\n  Here, we show that a dissipative quantum algorithm with a simple, local\nupdate rule is able to sample from the quantum Gibbs state. In contrast to the\nclassical case, the quantum Gibbs state is not generated by converging to the\nfixed point of a Markov process, but by the states generated at the stopping\ntime of a conditionally stopped process. This gives a new answer to the\nlong-sought-after quantum analogue of Metropolis sampling. Compared to previous\nquantum Gibbs sampling algorithms, the local update rule of the process has a\nsimple implementation, which may make it more amenable to near-term\nimplementation on suitable quantum hardware. This dissipative Gibbs sampler\nworks for arbitrary quantum Hamiltonians, without any assumptions on or\nknowledge of its properties, and comes with certifiable precision and run-time\nbounds. We also show that the algorithm benefits from some measure of built-in\nresilience to faults and errors (``fault resilience'').\n  Finally, we also demonstrate how the stopping statistics of an ensemble of\nruns of the dissipative Gibbs sampler can be used to estimate the partition\nfunction.\n"", 'Model robustness for feedback stabilization of open quantum systems   This paper generalizes the results in [30] concerning feedback stabilization\nof target states for N-level quantum angular momentum systems undergoing\nquantum non-demolition measurements (QND) in absence of the knowledge about\ninitial states and parameters. Here we consider multiple measurement operators\nand study the stabilization toward a chosen target subspace which is a common\neigenspace of measurement operators. Under the QND conditions, we show that\nthis analysis provides necessary tools to ensure feedback stabilization based\non a simplified filter whose state is a N-dimensional vector. A numerical\nanalysis has been proposed in [18]. This paper provides a complete proof for\nthe use of a simplified filter in feedback stabilization. This has important\npractical use as the dimension of quantum systems is usually high. This paper\nopens the way toward a complete proof concerning the robustness of a\nstabilizing feedback with respect to approximate filters, which is lacking.\n']","[('quantum control systems', 0.6963037252426147), ('quantum systems', 0.6416323781013489), ('quantum system', 0.620733380317688), ('open quantum systems', 0.5872835516929626), ('linear quantum', 0.5793044567108154), ('quantum stochastic', 0.569190263748169), ('dimensional quantum systems', 0.555236279964447), ('quantum linear', 0.5535487532615662), ('quantum computers', 0.5455487370491028), ('learning quantum', 0.5377100110054016)]"
1287,1287,23,1287_toroidal graphs_maps semi_maps surfaces_surface euler genus,"['toroidal graphs', 'maps semi', 'maps surfaces', 'surface euler genus', 'cycles vertices', 'maps surface', 'homogeneous map', 'map surface', 'homogeneous semi', 'minimal cover']","['Vertex-transitive covers of semi-equivelar toroidal maps   A map $X$ on a surface is called vertex-transitive if the automorphism group\nof $X$ acts transitively on the set of vertices of $X$. If the face-cycles at\nall the vertices in a map are of same type then the map is called\nsemi-equivelar. In general, semi-equivelar maps on a surface form a bigger\nclass than vertex-transitive maps. There are semi-equivelar toroidal maps which\nare not vertex-transitive. In this article, we show that semi-equivelar\ntoroidal maps are quotients of vertex-transitive toroidal maps. More\nexplicitly, we prove that each semi-equivelar toroidal map has a finite\nvertex-transitive cover. In 2019, Drach {\\em et al.} have shown that each\nvertex-transitive toroidal map has a minimal almost regular cover. Therefore,\nsemi-equivelar toroidal maps are quotients of almost regular toroidal maps.\n', ""Semi-equivelar toroidal maps and their k-edge covers   If the face\\mbox{-}cycles at all the vertices in a map are of same type then\nthe map is called semi\\mbox{-}equivelar. A tiling is edge-homogeneous if any\ntwo edges with vertices of congruent face-cycles. In general, edge-homogeneous\nmaps on a surface form a bigger class than edge-transitive maps. There are\nedge-homogeneous toroidal maps which are not edge\\mbox{-}transitive. An\nedge-homogeneous map is called $k$-edge-homogeneous if it contains $k$ number\nof edge orbits. In particular, if $k=1$ then it is called edge-transitive map.\nIn general, a map is called $k$-edge orbital or $k$-orbital if it contains $k$\nnumber of edge orbits. A map is called minimal if the number of edges is\nminimal. A surjective mapping $\\eta \\colon M \\to K$ from a map $M$ to a map $K$\nis called a covering if it preserves adjacency and sends vertices, edges, faces\nof $M$ to vertices, edges, faces of $K$ respectively. Orbani{\\' c} et al. and\n{\\v S}ir{\\'a}{\\v n} et al. have shown that every edge-homogeneous toroidal map\nhas edge-transitive cover. In this article, we show the bounds of edge orbits\nof edge-homogeneous toroidal maps. Using these bounds, we show the bounds of\nedge orbits of non-edge-homogeneous semi-equivelar toroidal maps. We also prove\nthat if a edge-homogeneous map is $k$ edge orbital then it has a finite index\n$m$-edge orbital minimal cover for $m \\le k$. We also show the existence and\nclassification of $n$ sheeted covers of edge-homogeneous toroidal maps for each\n$n \\in \\mathbb{N}$. We extend this to non-edge-homogeneous semi-equivelar\ntoroidal maps and prove the same results, i.e., if a non-edge-homogeneous map\nis $k$ edge orbital then it has a finite index $m$-edge orbital minimal cover\n(non-edge-homogeneous) for $m \\le k$ and then classify them for each sheet.\n"", 'Semi-equivelar toroidal maps and their vertex covers   If the face\\mbox{-}cycles at all the vertices in a map are of same type then\nthe map is called semi\\mbox{-}equivelar. A map is called minimal if the number\nof vertices is minimal. We know the bounds of number of vertex orbits of\nsemi-equivelar toroidal maps. These bounds are sharp. Datta \\cite{BD2020} has\nproved that every semi-equivelar toroidal map has a vertex-transitive cover. In\nthis article, we prove that if a semi-equivelar map is $k$ orbital then it has\na finite index $m$-orbital minimal cover for $m \\le k$. We also show the\nexistence and classification of $n$-sheeted covers of semi-equivelar toroidal\nmaps for each $n \\in \\mathbb{N}$.\n']","[('toroidal graphs', 0.504265308380127), ('maps semi', 0.4936651587486267), ('maps surfaces', 0.42335522174835205), ('surface euler genus', 0.4098401665687561), ('cycles vertices', 0.38005968928337097), ('maps surface', 0.378653347492218), ('homogeneous map', 0.35756805539131165), ('map surface', 0.3570580780506134), ('homogeneous semi', 0.3550911247730255), ('minimal cover', 0.34874263405799866)]"
1288,1288,23,1288_graphs homomorphism_graphs isomorphic_isomorphism graphs_graph isomorphism,"['graphs homomorphism', 'graphs isomorphic', 'isomorphism graphs', 'graph isomorphism', 'graph isomorphism test', 'graph homomorphism', 'two graphs isomorphic', 'graphs equivalent', 'class graphs', 'graph classification']","['The Weisfeiler-Leman Algorithm and Recognition of Graph Properties   The $k$-dimensional Weisfeiler-Leman algorithm ($k$-WL) is a very useful\ncombinatorial tool in graph isomorphism testing. We address the applicability\nof $k$-WL to recognition of graph properties. Let $G$ be an input graph with\n$n$ vertices. We show that, if $n$ is prime, then vertex-transitivity of $G$\ncan be seen in a straightforward way from the output of 2-WL on $G$ and on the\nvertex-individualized copies of $G$. However, if $n$ is divisible by 16, then\n$k$-WL is unable to distinguish between vertex-transitive and\nnon-vertex-transitive graphs with $n$ vertices as long as $k=o(\\sqrt n)$.\nSimilar results are obtained for recognition of arc-transitivity.\n', ""Homomorphism-Distinguishing Closedness for Graphs of Bounded Tree-Width   Two graphs are homomorphism indistinguishable over a graph class\n$\\mathcal{F}$, denoted by $G \\equiv_{\\mathcal{F}} H$, if\n$\\operatorname{hom}(F,G) = \\operatorname{hom}(F,H)$ for all $F \\in \\mathcal{F}$\nwhere $\\operatorname{hom}(F,G)$ denotes the number of homomorphisms from $F$ to\n$G$. A classical result of Lov\\'{a}sz shows that isomorphism between graphs is\nequivalent to homomorphism indistinguishability over the class of all graphs.\nMore recently, there has been a series of works giving natural algebraic and/or\nlogical characterizations for homomorphism indistinguishability over certain\nrestricted graph classes.\n  A class of graphs $\\mathcal{F}$ is homomorphism-distinguishing closed if, for\nevery $F \\notin \\mathcal{F}$, there are graphs $G$ and $H$ such that $G\n\\equiv_{\\mathcal{F}} H$ and $\\operatorname{hom}(F,G) \\neq\n\\operatorname{hom}(F,H)$. Roberson conjectured that every class closed under\ntaking minors and disjoint unions is homomorphism-distinguishing closed which\nimplies that every such class defines a distinct equivalence relation between\ngraphs. In this note, we confirm this conjecture for the classes\n$\\mathcal{T}_k$, $k \\geq 1$, containing all graphs of tree-width at most $k$.\n  As an application of this result, we also characterize which subgraph counts\nare detected by the $k$-dimensional Weisfeiler-Leman algorithm. This answers an\nopen question from [Arvind et al., J. Comput. Syst. Sci., 2020].\n"", ""Oddomorphisms and homomorphism indistinguishability over graphs of\n  bounded degree   We introduce (weak) oddomorphisms of graphs which are homomorphisms with\nadditional constraints based on parity. These maps turn out to have interesting\nproperties (e.g., they preserve planarity), particularly in relation to\nhomomorphism indistinguishability.\n  Graphs $G$ and $H$ are *homomorphism indistinguishable* over a family\n$\\mathcal{F}$ if $\\hom(F,G) = \\hom(F,H)$ for all $F \\in \\mathcal{F}$, where\n$\\hom(F,G)$ is the number of homomorphisms from $F$ to $G$. A classical result\nof Lov\\'{a}sz says that isomorphism is equivalent to homomorphism\nindistinguishability over the class of all graphs. In recent years it has been\nshown that many homomorphism indistinguishability relations have natural\nalgebraic and/or logical formulations. Currently, much research in this area is\nfocused on finding such reformulations. We aim to broaden the scope of current\nresearch on homomorphism indistinguishability by introducing new\nconcepts/constructions and proposing several conjectures/questions. In\nparticular, we conjecture that every family closed under disjoint unions and\nminors gives rise to a distinct homomorphism indistinguishability relation.\n  We also show that if $\\mathcal{F}$ is a family of graphs closed under\ndisjoint unions, restrictions to connected components, and weak oddomorphisms,\nthen $\\mathcal{F}$ satisfies a certain maximality or closure property:\nhomomorphism indistinguishability over $\\mathcal{F}$ of $G$ and $H$ does not\nimply $\\hom(F,G) = \\hom(F,H)$ for any $F \\notin \\mathcal{F}$. This allows us to\nanswer a question raised over ten years ago, showing that homomorphism\nindistinguishability over graphs of bounded degree is not equivalent to\nisomorphism.\n""]","[('graphs homomorphism', 0.6860154271125793), ('graphs isomorphic', 0.6846305727958679), ('isomorphism graphs', 0.6745526790618896), ('graph isomorphism', 0.6615615487098694), ('graph isomorphism test', 0.6582332849502563), ('graph homomorphism', 0.6472269892692566), ('two graphs isomorphic', 0.6199243664741516), ('graphs equivalent', 0.5962240099906921), ('class graphs', 0.5211449265480042), ('graph classification', 0.4929194152355194)]"
1289,1289,23,1289_wasserstein spaces_wasserstein space_space wasserstein_isometric embeddings,"['wasserstein spaces', 'wasserstein space', 'space wasserstein', 'isometric embeddings', 'space isometrically', 'isometry group', 'spaces isometrically', 'isometry', 'isometric embedding', 'embeds isometrically']","[""The isometry group of Wasserstein spaces: the Hilbertian case   Motivated by Kloeckner's result on the isometry group of the quadratic\nWasserstein space $\\mathcal{W}_2\\left(\\mathbb{R}^n\\right)$, we describe the\nisometry group $\\mathrm{Isom}\\left(\\mathcal{W}_p (E)\\right)$ for all parameters\n$0 < p < \\infty$ and for all separable real Hilbert spaces $E.$ In particular,\nwe show that $\\mathcal{W}_p(X)$ is isometrically rigid for all Polish space $X$\nwhenever $0<p<1$. This is a consequence of our more general result: we prove\nthat $\\mathcal{W}_1(X)$ is isometrically rigid if $X$ is a complete separable\nmetric space that satisfies the strict triangle inequality. Furthermore, we\nshow that this latter rigidity result does not generalise to parameters $p>1$,\nby solving Kloeckner's problem affirmatively on the existence of mass-splitting\nisometries.\n"", 'Isometries and isometric embeddings of Wasserstein spaces over the\n  Heisenberg group   Our purpose in this paper is to study isometries and isometric embeddings of\nthe $p$-Wasserstein space $\\mathcal{W}_p(\\mathbb{H}^n)$ over the Heisenberg\ngroup $\\mathbb{H}^n$ for all $p>1$ and for all $n\\geq 1$. First, we create a\nlink between optimal transport maps in the Euclidean space $\\mathbb{R}^{2n}$\nand the Heisenberg group $\\mathbb{H}^n$. Then we use this link to understand\nisometric embeddings of $\\mathbb{R}$ and $\\mathbb{R}_+$ into\n$\\mathcal{W}_p(\\mathbb{H}^n)$ for $p>1$. That is, we characterize complete\ngeodesics and geodesic rays in the Wasserstein space. Using these results we\ndetermine the metric rank of $\\mathcal{W}_p(\\mathbb{H}^n)$. Namely, we show\nthat $\\mathbb{R}^k$ can be embedded isometrically into\n$\\mathcal{W}_p(\\mathbb{H}^n)$ for $p>1$ if and only if $k\\leq n$. As a\nconsequence, we conclude that $\\mathcal{W}_p(\\mathbb{R}^k)$ and\n$\\mathcal{W}_p(\\mathbb{H}^k)$ can be embedded isometrically into\n$\\mathcal{W}_p(\\mathbb{H}^n)$ if and only if $k\\leq n$. In the second part of\nthe paper, we study the isometry group of $\\mathcal{W}_p(\\mathbb{H}^n)$ for\n$p>1$. We find that these spaces are all isometrically rigid meaning that for\nevery isometry $\\Phi:\\mathcal{W}_p(\\mathbb{H}^n)\\to\\mathcal{W}_p(\\mathbb{H}^n)$\nthere exists a $\\psi:\\mathbb{H}^n\\to\\mathbb{H}^n$ such that $\\Phi=\\psi_{\\#}$.\n', 'Isometric study of Wasserstein spaces --- the real line   Recently Kloeckner described the structure of the isometry group of the\nquadratic Wasserstein space $\\mathcal{W}_2\\left(\\mathbb{R}^n\\right)$. It turned\nout that the case of the real line is exceptional in the sense that there\nexists an exotic isometry flow. Following this line of investigation, we\ncompute $\\mathrm{Isom}\\left(\\mathcal{W}_p(\\mathbb{R})\\right)$, the isometry\ngroup of the Wasserstein space $\\mathcal{W}_p(\\mathbb{R})$ for all $p \\in [1,\n\\infty)\\setminus\\{2\\}$. We show that $\\mathcal{W}_2(\\mathbb{R})$ is also\nexceptional regarding the parameter $p$: $\\mathcal{W}_p(\\mathbb{R})$ is\nisometrically rigid if and only if $p\\neq 2$. Regarding the underlying space,\nwe prove that the exceptionality of $p=2$ disappears if we replace $\\mathbb{R}$\nby the compact interval $[0,1]$. Surprisingly, in that case,\n$\\mathcal{W}_p\\left([0,1]\\right)$ is isometrically rigid if and only if\n$p\\neq1$. Moreover, $\\mathcal{W}_1\\left([0,1]\\right)$ admits isometries that\nsplit mass, and $\\mathrm{Isom}\\left(\\mathcal{W}_1\\left([0,1]\\right)\\right)$\ncannot be embedded into $\\mathrm{Isom}\\left(\\mathcal{W}_1(\\mathbb{R})\\right).$\n']","[('wasserstein spaces', 0.659311830997467), ('wasserstein space', 0.6550420522689819), ('space wasserstein', 0.5616999864578247), ('isometric embeddings', 0.5584275722503662), ('space isometrically', 0.5521035194396973), ('isometry group', 0.5513842105865479), ('spaces isometrically', 0.5492342114448547), ('isometry', 0.5437901020050049), ('isometric embedding', 0.5435104370117188), ('embeds isometrically', 0.5324927568435669)]"
1290,1290,23,1290_varieties action_affine algebraic group_algebraic action_affine varieties,"['varieties action', 'affine algebraic group', 'algebraic action', 'affine varieties', 'algebraic groups', 'actions affine', 'finite group scheme', 'subgroups affine', 'reductive algebraic group', 'algebraic group']","['On the existence of $B$-root subgroups on affine spherical varieties   Let $X$ be an irreducible affine algebraic variety that is spherical with\nrespect to an action of a connected reductive group $G$. In this paper we\nprovide sufficient conditions, formulated in terms of weight combinatorics, for\nthe existence of one-parameter additive actions on $X$ normalized by a Borel\nsubgroup $B \\subset G$. As an application, we prove that every $G$-stable prime\ndivisor in $X$ can be connected with the open $G$-orbit by means of a suitable\n$B$-normalized one-parameter additive action.\n', 'Root subgroups on horospherical varieties   Given a connected reductive algebraic group $G$ and a spherical $G$-variety\n$X$, a $B$-root subgroup on $X$ is a one-parameter additive group of\nautomorphisms of $X$ normalized by a Borel subgroup $B \\subset G$. We obtain a\ncomplete description of all $B$-root subgroups on a certain open subset of $X$.\nWhen $X$ is horospherical, we extend the construction of standard $B$-root\nsubgroups introduced earlier by Arzhantsev and Avdeev for affine $X$ and obtain\na complete description of all standard $B$-root subgroups, which naturally\ngeneralizes the well-known description of root subgroups on toric varieties. As\nan application, for horospherical $X$ that is either complete or contains a\nunique closed $G$-orbit, we determine all $G$-stable prime divisors in $X$ that\ncan be connected with the open $G$-orbit via the action of a suitable $B$-root\nsubgroup. For horospherical $X$, we also find sufficient conditions for the\nexistence of $B$-root subgroups on $X$ that preserve the open $B$-orbit in $X$.\nFinally, when $G$ is of semisimple rank $1$ and $X$ is horospherical and\ncomplete, we determine all $B$-root subgroups on $X$, which enables us to\ndescribe the Lie algebra of the connected automorphism group of $X$.\n', 'Root subgroups on affine spherical varieties   Given a connected reductive algebraic group $G$ and a Borel subgroup $B\n\\subseteq G$, we study $B$-normalized one-parameter additive group actions on\naffine spherical $G$-varieties. We establish basic properties of such actions\nand their weights and discuss many examples exhibiting various features. We\npropose a construction of such actions that generalizes the well-known\nconstruction of normalized one-parameter additive group actions on affine toric\nvarieties. Using this construction, for every affine horospherical $G$-variety\n$X$ we obtain a complete description of all $G$-normalized one-parameter\nadditive group actions on $X$ and show that the open $G$-orbit in $X$ can be\nconnected with every $G$-stable prime divisor via a suitable choice of a\n$B$-normalized one-parameter additive group action. Finally, when $G$ is of\nsemisimple rank $1$, we obtain a complete description of all $B$-normalized\none-parameter additive group actions on affine spherical $G$-varieties having\nan open orbit of a maximal torus $T \\subseteq B$.\n']","[('varieties action', 0.6020125150680542), ('affine algebraic group', 0.5845370888710022), ('algebraic action', 0.5322688221931458), ('affine varieties', 0.5288374423980713), ('algebraic groups', 0.5221750736236572), ('actions affine', 0.5082688927650452), ('finite group scheme', 0.5034364461898804), ('subgroups affine', 0.5008165240287781), ('reductive algebraic group', 0.49203920364379883), ('algebraic group', 0.4832448661327362)]"
1291,1291,23,1291_optimization markov decision_optimization markov_markov decision processes_markov decision process,"['optimization markov decision', 'optimization markov', 'markov decision processes', 'markov decision process', 'horizon markov decision', 'markov decision', 'optimal robust', 'decision processes mdps', 'robust policy', 'finite horizon markov']","['Robust Phi-Divergence MDPs   In recent years, robust Markov decision processes (MDPs) have emerged as a\nprominent modeling framework for dynamic decision problems affected by\nuncertainty. In contrast to classical MDPs, which only account for\nstochasticity by modeling the dynamics through a stochastic process with a\nknown transition kernel, robust MDPs additionally account for ambiguity by\noptimizing in view of the most adverse transition kernel from a prescribed\nambiguity set. In this paper, we develop a novel solution framework for robust\nMDPs with s-rectangular ambiguity sets that decomposes the problem into a\nsequence of robust Bellman updates and simplex projections. Exploiting the rich\nstructure present in the simplex projections corresponding to phi-divergence\nambiguity sets, we show that the associated s-rectangular robust MDPs can be\nsolved substantially faster than with state-of-the-art commercial solvers as\nwell as a recent first-order solution scheme, thus rendering them attractive\nalternatives to classical MDPs in practical applications.\n', 'An Efficient Solution to s-Rectangular Robust Markov Decision Processes   We present an efficient robust value iteration for \\texttt{s}-rectangular\nrobust Markov Decision Processes (MDPs) with a time complexity comparable to\nstandard (non-robust) MDPs which is significantly faster than any existing\nmethod. We do so by deriving the optimal robust Bellman operator in concrete\nforms using our $L_p$ water filling lemma. We unveil the exact form of the\noptimal policies, which turn out to be novel threshold policies with the\nprobability of playing an action proportional to its advantage.\n', 'Partial Policy Iteration for L1-Robust Markov Decision Processes   Robust Markov decision processes (MDPs) allow to compute reliable solutions\nfor dynamic decision problems whose evolution is modeled by rewards and\npartially-known transition probabilities. Unfortunately, accounting for\nuncertainty in the transition probabilities significantly increases the\ncomputational complexity of solving robust MDPs, which severely limits their\nscalability. This paper describes new efficient algorithms for solving the\ncommon class of robust MDPs with s- and sa-rectangular ambiguity sets defined\nby weighted $L_1$ norms. We propose partial policy iteration, a new, efficient,\nflexible, and general policy iteration scheme for robust MDPs. We also propose\nfast methods for computing the robust Bellman operator in quasi-linear time,\nnearly matching the linear complexity the non-robust Bellman operator. Our\nexperimental results indicate that the proposed methods are many orders of\nmagnitude faster than the state-of-the-art approach which uses linear\nprogramming solvers combined with a robust value iteration.\n']","[('optimization markov decision', 0.6544825434684753), ('optimization markov', 0.6091468334197998), ('markov decision processes', 0.5873247385025024), ('markov decision process', 0.583391547203064), ('horizon markov decision', 0.5717226266860962), ('markov decision', 0.5474734306335449), ('optimal robust', 0.5461394786834717), ('decision processes mdps', 0.5414351224899292), ('robust policy', 0.5362341403961182), ('finite horizon markov', 0.5068419575691223)]"
1292,1292,23,1292_brownian sphere_random planar maps_construction brownian_brownian,"['brownian sphere', 'random planar maps', 'construction brownian', 'brownian', 'process brownian', 'spatial markov', 'random maps', 'random metric', 'planar maps', 'uniform infinite planar']","['Isoperimetric inequalities in the Brownian plane   We consider the model of the Brownian plane, which is a pointed non-compact\nrandom metric space with the topology of the complex plane. The Brownian plane\ncan be obtained as the scaling limit in distribution of the uniform infinite\nplanar triangulation or the uniform infinite planar quadrangulation and is\nconjectured to be the universal scaling limit of many others random planar\nlattices. We establish sharp bounds on the probability of having a short cycle\nseparating the ball of radius $r$ centered at the distinguished point from\ninfinity. Then we prove a strong version of the spatial Markov property of the\nBrownian plane. Combining our study of short cycles with this strong spatial\nMarkov property we obtain sharp isoperimetric bounds for the Brownian plane.\n', 'Compact Brownian surfaces II. Orientable surfaces   Fix an arbitrary compact orientable surface with a boundary and consider a\nuniform bipartite random quadrangulation of this surface with $n$ faces and\nboundary component lengths of order $\\sqrt n$ or of lower order. Endow this\nquadrangulation with the usual graph metric renormalized by $n^{-1/4}$, mark it\non each boundary component, and endow it with the counting measure on its\nvertex set renormalized by $n^{-1}$, as well as the counting measure on each\nboundary component renormalized by $n^{-1/2}$. We show that, as $n\\to\\infty$,\nthis random marked measured metric space converges in distribution for the\nGromov--Hausdorff--Prokhorov topology, toward a random limiting marked measured\nmetric space called a Brownian surface.\n  This extends known convergence results of uniform random planar\nquadrangulations with at most one boundary component toward the Brownian sphere\nand toward the Brownian disk, by considering the case of quadrangulations on\ngeneral compact orientable surfaces. Our approach consists in cutting a\nBrownian surface into elementary pieces that are naturally related to the\nBrownian sphere and the Brownian disk and their noncompact analogs, the\nBrownian plane and the Brownian half-plane, and to prove convergence results\nfor these elementary pieces, which are of independent interest.\n', ""The snake in the Brownian sphere   The Brownian sphere is a random metric space, homeomorphic to the\ntwo-dimensional sphere, which arises as the universal scaling limit of many\ntypes of random planar maps. The direct construction of the Brownian sphere is\nvia a continuous analogue of the Cori--Vauquelin--Schaeffer (CVS) bijection.\nThe CVS bijection maps labeled trees to planar maps, and the continuous version\nmaps Aldous' continuum random tree with Brownian labels (the Brownian snake) to\nthe Brownian sphere. In this work, we describe the inverse of the continuous\nCVS bijection, by constructing the Brownian snake as a measurable function of\nthe Brownian sphere. Special care is needed to work with the orientation of the\nBrownian sphere.\n""]","[('brownian sphere', 0.645308792591095), ('random planar maps', 0.5756679773330688), ('construction brownian', 0.5549221634864807), ('brownian', 0.4932163655757904), ('process brownian', 0.46712973713874817), ('spatial markov', 0.459886372089386), ('random maps', 0.453108549118042), ('random metric', 0.44350653886795044), ('planar maps', 0.442685604095459), ('uniform infinite planar', 0.4358363151550293)]"
1293,1293,23,1293_neural networks recurrent_networks recurrent neural_networks rnns_recurrent neural networks,"['neural networks recurrent', 'networks recurrent neural', 'networks rnns', 'recurrent neural networks', 'recurrent neural', 'neural networks rnns', 'networks recurrent', 'short term memory', 'rnns', 'long term memory']","['Recurrent neural networks: vanishing and exploding gradients are not the\n  end of the story   Recurrent neural networks (RNNs) notoriously struggle to learn long-term\nmemories, primarily due to vanishing and exploding gradients. The recent\nsuccess of state-space models (SSMs), a subclass of RNNs, to overcome such\ndifficulties challenges our theoretical understanding. In this paper, we delve\ninto the optimization challenges of RNNs and discover that, as the memory of a\nnetwork increases, changes in its parameters result in increasingly large\noutput variations, making gradient-based learning highly sensitive, even\nwithout exploding gradients. Our analysis further reveals the importance of the\nelement-wise recurrence design pattern combined with careful parametrizations\nin mitigating this effect. This feature is present in SSMs, as well as in other\narchitectures, such as LSTMs. Overall, our insights provide a new explanation\nfor some of the difficulties in gradient-based learning of RNNs and why some\narchitectures perform better than others.\n', 'RNNs of RNNs: Recursive Construction of Stable Assemblies of Recurrent\n  Neural Networks   Recurrent neural networks (RNNs) are widely used throughout neuroscience as\nmodels of local neural activity. Many properties of single RNNs are well\ncharacterized theoretically, but experimental neuroscience has moved in the\ndirection of studying multiple interacting areas, and RNN theory needs to be\nlikewise extended. We take a constructive approach towards this problem,\nleveraging tools from nonlinear control theory and machine learning to\ncharacterize when combinations of stable RNNs will themselves be stable.\nImportantly, we derive conditions which allow for massive feedback connections\nbetween interacting RNNs. We parameterize these conditions for easy\noptimization using gradient-based techniques, and show that\nstability-constrained ""networks of networks"" can perform well on challenging\nsequential-processing benchmark tasks. Altogether, our results provide a\nprincipled approach towards understanding distributed, modular function in the\nbrain.\n', 'Inverse Approximation Theory for Nonlinear Recurrent Neural Networks   We prove an inverse approximation theorem for the approximation of nonlinear\nsequence-to-sequence relationships using recurrent neural networks (RNNs). This\nis a so-called Bernstein-type result in approximation theory, which deduces\nproperties of a target function under the assumption that it can be effectively\napproximated by a hypothesis space. In particular, we show that nonlinear\nsequence relationships that can be stably approximated by nonlinear RNNs must\nhave an exponential decaying memory structure - a notion that can be made\nprecise. This extends the previously identified curse of memory in linear RNNs\ninto the general nonlinear setting, and quantifies the essential limitations of\nthe RNN architecture for learning sequential relationships with long-term\nmemory. Based on the analysis, we propose a principled reparameterization\nmethod to overcome the limitations. Our theoretical results are confirmed by\nnumerical experiments. The code has been released in\nhttps://github.com/radarFudan/Curse-of-memory\n']","[('neural networks recurrent', 0.6808953881263733), ('networks recurrent neural', 0.6693846583366394), ('networks rnns', 0.6690953373908997), ('recurrent neural networks', 0.6683963537216187), ('recurrent neural', 0.6675269603729248), ('neural networks rnns', 0.6665173172950745), ('networks recurrent', 0.6659227609634399), ('short term memory', 0.6189802885055542), ('rnns', 0.6104205250740051), ('long term memory', 0.6085341572761536)]"
1294,1294,23,1294_graded betti numbers_homogeneous ideals_ideal codimension_determine graded betti,"['graded betti numbers', 'homogeneous ideals', 'ideal codimension', 'determine graded betti', 'graded betti', 'rees algebras', 'minimal graded free', 'homogeneous ideal', 'ideals codimension', 'betti numbers']","['Structure theorems for Gorenstein ideals of codimension four with small\n  number of generators   In this article we study minimal free resolutions of Gorenstein ideals of\ncodimension four, using methods coming from representation theory. We introduce\nfamilies of higher structure maps associated with such resolution, defined\nsimilarly to the codimension three case. As our main application, we prove that\nevery Gorenstein ideal of codimension four minimally generated by six elements\nis a hyperplane section of a Gorenstein ideal of codimension three,\nstrengthening a result by Herzog-Miller and Vasconcelos-Villarreal. We state\nanalogous conjectural results for ideals minimally generated by seven and eight\nelements.\n', 'Equigenerated Gorenstein ideals of codimension three   We focus on the structure of a homogeneous Gorenstein ideal $I$ of\ncodimension three in a standard polynomial ring $R=\\kk[x_1,\\ldots,x_n]$ over a\nfield $\\kk$, assuming that $I$ is generated in a fixed degree $d$. For such an\nideal $I$ this degree comes along with the minimal number of generators of $I$\nand the degree of the entries of the associated skew-symmetric matrix in a\nsimple formula. We give an elementary characteristic-free argument to the\neffect that, for any such data linked by this formula, there exists a\nGorenstein ideal $I$ of codimension three filling them. We conjecture that, for\narbitrary $n\\geq 2$, an ideal $I\\subset \\kk[x_1,\\ldots,x_n]$ generated by a\ngeneral set of $r\\geq n+2$ forms of degree $d\\geq 2$ is Gorenstein if and only\nif $d=2$ and $r= {{n+1}\\choose 2}-1$. We prove the `only if\' implication of\nthis conjecture when $n=3$. For arbitrary $n\\geq 2$, we prove that if $d=2$ and\n$r\\geq (n+2)(n+1)/6$ then the ideal is Gorenstein if and only if\n$r={{n+1}\\choose 2}-1$, which settles the `if\' assertion of the conjecture for\n$n\\leq 5$. Finally, we elaborate around one of the questions of\nFr\\""oberg--Lundqvist. In a different direction, we reveal a connection between\nthe Macaulay inverse and the so-called Newton dual, a matter so far not brought\nout to our knowledge. Finally, we consider the question as to when the link\n$(\\ell_1^m,\\ldots,\\ell_n^m):\\mathfrak{f}$ is equigenerated, where\n$\\ell_1,\\ldots,\\ell_n$ are independent linear forms and $\\mathfrak{f}$ is a\nform, is given a solution in some important cases.\n', 'Some new Betti numbers of ideals generated by n+1 generic forms in n\n  variables   Very little is known on the Hilbert series of graded algebras $\\mathbb\nC[x_1,\\ldots,x_n]/(g_1,\\ldots,g_r)$, $r>n$, $g_i$ generic form of degree $e_i$,\nin general. One instance when the series is known, is for $n+1$ forms in $n$\nvariables, \\cite{St}. Of course even less is known about Betti numbers. There\nare some general results on the Betti table by Pardue and Richert in\n\\cite{Pa-Ri,Pa-Ri1}, and by Diem in \\cite{Di}. Then there are results on Betti\nnumbers in the case $n+1$ relations in $n$ variables, described below, by\nMigliore and Mir\\`o-Roig in \\cite{Mi-Mi}, and more partial results in the\ngeneral case by the same authors in \\cite{Mi-Mi1}. In this paper we consider\nthe same case as in \\cite{Mi-Mi}, $n+1$ forms in $n$ variables. Our results can\nbe described as follows. We can determine all graded Betti numbers of $\\mathbb\nC[x_1,\\ldots,x_n]/(g_1,\\ldots,g_{n+1})$, $g_i$ generic, at least if\n$\\sum_{i=1}^{n+1}\\deg(g_i)-n$ is even, often in more cases. Thus, given {\\em\nany} set $\\{ e_1,\\ldots,e_n\\}$, $e_i\\ge2$ for all $i$, such that\n$\\deg(g_i)=e_i$, $i=1,\\ldots,n$, we get many numbers $D_j$, so that we can\ndetermine all graded Betti numbers of $\\mathbb\nC[x_1,\\ldots,x_n]/(g_1,\\ldots,g_{n+1})$, $\\deg(g_i)=e_i$, $1\\le i\\le n$,\n$\\deg(g_{n+1})=D_j$. The main ingredients of the proof is a theorem by Pardue\nand Richert, \\cite{Pa-Ri,Pa-Ri1}, and later by Diem,\\cite{Di}, and a new short\nproof of a theorem on Hilbert series of artinian complete intersections by\nReid, Roberts, and Roitman, \\cite{R-R-R}. We also give examples of algebras\nwith many so called ""ghost terms"" in the minimal resolution.\n']","[('graded betti numbers', 0.6654900312423706), ('homogeneous ideals', 0.5648701190948486), ('ideal codimension', 0.5422958135604858), ('determine graded betti', 0.5405009388923645), ('graded betti', 0.5232034921646118), ('rees algebras', 0.511506974697113), ('minimal graded free', 0.5077416300773621), ('homogeneous ideal', 0.5063663721084595), ('ideals codimension', 0.5053352117538452), ('betti numbers', 0.48411253094673157)]"
1295,1295,23,1295_digraphs bounded_acyclic digraphs_digraph smallest_number digraphs,"['digraphs bounded', 'acyclic digraphs', 'digraph smallest', 'number digraphs', 'acyclic digraph', 'digraphs directed', 'characterize digraphs', 'every digraph', 'digraphs', 'dichromatic number']","['Various bounds on the minimum number of arcs in a $k$-dicritical digraph   The dichromatic number $\\vec{\\chi}(G)$ of a digraph $G$ is the least integer\n$k$ such that $G$ can be partitioned into $k$ acyclic digraphs. A digraph is\n$k$-dicritical if $\\vec{\\chi}(G) = k$ and each proper subgraph $H$ of $G$\nsatisfies $\\vec{\\chi}(H) \\leq k-1$. %An oriented graph is a digraph with no\ncycle of length $2$. We prove various bounds on the minimum number of arcs in a\n$k$-dicritical digraph, a structural result on $k$-dicritical digraphs and a\nresult on list-dicolouring.\n  We characterise $3$-dicritical digraphs $G$ with $(k-1)|V(G)| + 1$ arcs. For\n$k \\geq 4$, we characterise $k$-dicritical digraphs $G$ on at least $k+1$\nvertices and with $(k-1)|V(G)| + k-3$ arcs, generalising a result of Dirac. We\nprove that, for $k \\geq 5$, every $k$-dicritical digraph $G$ has at least\n$(k-1/2 - 1/(k-1)) |V(G)| - k(1/2 - 1/(k-1))$ arcs, which is the best known\nlower bound. We prove that the number of connected components induced by the\nvertices of degree $2(k-1)$ of a $k$-dicritical digraph is at most the number\nof connected components in the rest of the digraph, generalising a result of\nStiebitz. Finally, we generalise a Theorem of Thomassen on list-chromatic\nnumber of undirected graphs to list-dichromatic number of digraphs.\n', 'Dichromatic number of chordal graphs   The dichromatic number of a digraph is the minimum integer $k$ such that it\nadmits a $k$-dicolouring, i.e. a partition of its vertices into $k$ acyclic\nsubdigraphs. We say that a digraph $D$ is a super-orientation of an undirected\ngraph $G$ if $G$ is the underlying graph of $D$. If $D$ does not contain any\npair of symmetric arcs, we just say that $D$ is an orientation of $G$. In this\nwork, we give both lower and upper bounds on the dichromatic number of\nsuper-orientations of chordal graphs. We also show a family of orientations of\ncographs for which the dichromatic number is equal to the clique number of the\nunderlying graph.\n', 'Subdivisions in dicritical digraphs with large order or digirth   Aboulker et al. proved that a digraph with large enough dichromatic number\ncontains any fixed digraph as a subdivision. The dichromatic number of a\ndigraph is the smallest order of a partition of its vertex set into acyclic\ninduced subdigraphs. A digraph is dicritical if the removal of any arc or\nvertex decreases its dichromatic number. In this paper we give sufficient\nconditions on a dicritical digraph of large order or large directed girth to\ncontain a given digraph as a subdivision. In particular, we prove that (i) for\nevery integers $k,\\ell$, large enough dicritical digraphs with dichromatic\nnumber $k$ contain an orientation of a cycle with at least $\\ell$ vertices;\n(ii) there are functions $f,g$ such that for every subdivision $F^*$ of a\ndigraph $F$, digraphs with directed girth at least $f(F^*)$ and dichromatic\nnumber at least $g(F)$ contain a subdivision of $F^*$, and if $F$ is a tree,\nthen $g(F)=|V(F)|$; (iii) there is a function $f$ such that for every\nsubdivision $F^*$ of $TT_3$ (the transitive tournament on three vertices),\ndigraphs with directed girth at least $f(F^*)$ and minimum out-degree at least\n$2$ contain $F^*$ as a subdivision.\n']","[('digraphs bounded', 0.6397754549980164), ('acyclic digraphs', 0.6170493364334106), ('digraph smallest', 0.6087692975997925), ('number digraphs', 0.5951387286186218), ('acyclic digraph', 0.5699498057365417), ('digraphs directed', 0.5616928339004517), ('characterize digraphs', 0.5558737516403198), ('every digraph', 0.5555648803710938), ('digraphs', 0.555097222328186), ('dichromatic number', 0.5502133369445801)]"
1296,1296,23,1296_dirichlet character modulo_dirichlet character chi_dirichlet characters_quadratic dirichlet character,"['dirichlet character modulo', 'dirichlet character chi', 'dirichlet characters', 'quadratic dirichlet character', 'dirichlet character', 'character sums', 'character modulo', 'sum_ chi', 'modulo large prime', 'characters chi']","[""The frequency and the structure of large character sums   Let $M(\\chi)$ denote the maximum of $|\\sum_{n\\le N}\\chi(n)|$ for a given\nnon-principal Dirichlet character $\\chi \\pmod q$, and let $N_\\chi$ denote a\npoint at which the maximum is attained. In this article we study the\ndistribution of $M(\\chi)/\\sqrt{q}$ as one varies over characters $\\pmod q$,\nwhere $q$ is prime, and investigate the location of $N_\\chi$. We show that the\ndistribution of $M(\\chi)/\\sqrt{q}$ converges weakly to a universal distribution\n$\\Phi$, uniformly throughout most of the possible range, and get (doubly\nexponential decay) estimates for $\\Phi$'s tail. Almost all $\\chi$ for which\n$M(\\chi)$ is large are odd characters that are $1$-pretentious. Now,\n$M(\\chi)\\ge |\\sum_{n\\le q/2}\\chi(n)| = \\frac{|2-\\chi(2)|}\\pi \\sqrt{q}\n|L(1,\\chi)|$, and one knows how often the latter expression is large, which has\nbeen how earlier lower bounds on $\\Phi$ were mostly proved. We show, though,\nthat for most $\\chi$ with $M(\\chi)$ large, $N_\\chi$ is bounded away from $q/2$,\nand the value of $M(\\chi)$ is little bit larger than $\\frac{\\sqrt{q}}{\\pi}\n|L(1,\\chi)|$.\n"", ""Large Sums of High Order Characters   Let $\\chi$ be a primitive character modulo a prime $q$, and let $\\delta > 0$.\nIt has previously been observed that if $\\chi$ has large order $d \\geq\nd_0(\\delta)$ then $\\chi(n) \\neq 1$ for some $n \\leq q^{\\delta}$, in analogy\nwith Vinogradov's conjecture on quadratic non-residues. We give a new and\nsimple proof of this fact. We show, furthermore, that if $d$ is squarefree then\nfor any $d$th root of unity $\\alpha$ the number of $n \\leq x$ such that\n$\\chi(n) = \\alpha$ is $o_{d \\to \\infty}(x)$ whenever $x > q^\\delta$.\nConsequently, when $\\chi$ has sufficiently large order the sequence\n$(\\chi(n))_{n \\leq q^\\delta}$ cannot cluster near $1$ for any $\\delta > 0$.\n  Our proof relies on a second moment estimate for short sums of the characters\n$\\chi^\\ell$, averaged over $1 \\leq \\ell \\leq d-1$, that is non-trivial whenever\n$d$ has no small prime factors. In particular, given any $\\delta > 0$ we show\nthat for all but $o(d)$ powers $1 \\leq \\ell \\leq d-1$, the partial sums of\n$\\chi^\\ell$ exhibit cancellation in intervals $n \\leq q^\\delta$ as long as $d\n\\geq d_0(\\delta)$ is prime, going beyond Burgess' theorem. Our argument blends\ntogether results from pretentious number theory and additive combinatorics.\n  Finally, we show that, uniformly over prime $3 \\leq d \\leq q-1$, the\nP\\'{o}lya-Vinogradov inequality may be improved for $\\chi^\\ell$ on average over\n$1 \\leq \\ell \\leq d-1$, extending work of Granville and Soundararajan.\n"", 'The distribution of the maximum of cubic character sums   For a primitive Dirichlet character $\\chi\\pmod q$ we let \\[M(\\chi):=\n\\frac{1}{\\sqrt{q}}\\max_{1\\leq t \\leq q} \\Big|\\sum_{n \\leq t} \\chi(n) \\Big|.\\]\nIn this paper, we investigate the distribution of $M(\\chi)$, as $\\chi$ ranges\nover primitive cubic characters $\\chi\\pmod q$ with $(q,3)=1$ and $q\\leq Q$. Our\nfirst result gives an estimate for the proportion of such characters for which\n$M(\\chi)>V$, in a uniform range of $V$, which is best possible under the\nassumption of the Generalized Riemann Hypothesis. In particular, we show that\nthe distribution of large cubic character sums behaves very differently from\nthose in the family of non-principal characters modulo a large prime, and the\nfamily of quadratic characters. We also investigate the location of the number\n$N_{\\chi}$ where the maximum of $|\\sum_{n\\leq N} \\chi(n)|$ is attained, and\nshow the surprising result that for almost all primitive cubic characters\n$\\chi\\pmod q$ with $M(\\chi)>V$, $N_{\\chi}/q$ is very close to a reduced\nfraction with a large denominator of size $(\\log V)^{1/2+o(1)}$. This\ncontradicts the common belief that for an even character $\\chi$, $N_{\\chi}/q$\nis located near a rational of small denominator and gives a striking difference\nwith the case of even characters in the other two families mentioned above, for\nwhich $N_{\\chi}/q\\approx 1/3$ or $2/3$ for almost all even $\\chi$. Furthermore,\nin the case of cubic characters, the works of Granville-Soundararajan,\nGoldmakher, and Lamzouri-Mangerel show that if $M(\\chi)$ is large, then $\\chi$\npretends to be $\\xi(n)n^{it}$ for some small $t$, where $\\xi$ is an odd\ncharacter of small conductor $m$. We show that for almost all such characters,\nwe have $M(\\chi)=m^{-1/2+o(1)}\\big|L(1+it, \\chi\\overline{\\xi})\\big|.$\n']","[('dirichlet character modulo', 0.6050165295600891), ('dirichlet character chi', 0.5755825042724609), ('dirichlet characters', 0.5699713826179504), ('quadratic dirichlet character', 0.5525295734405518), ('dirichlet character', 0.5215361714363098), ('character sums', 0.517372727394104), ('character modulo', 0.45836469531059265), ('sum_ chi', 0.4450644552707672), ('modulo large prime', 0.42659011483192444), ('characters chi', 0.42139580845832825)]"
1297,1297,23,1297_quantum walks_time quantum walks_quantum walk_time quantum walk,"['quantum walks', 'time quantum walks', 'quantum walk', 'time quantum walk', 'eigenfunctions quantum', 'one dimensional quantum', 'localization quantum', 'discrete time quantum', 'dimensional quantum', 'eigenfunctions']","['Localization of space-inhomogeneous three-state quantum walks   Mathematical analysis on the existence of eigenvalues is essential because it\nis equivalent to the occurrence of localization, which is an exceptionally\ncrucial property of quantum walks. We construct the method for the eigenvalue\nproblem via the transfer matrix for space-inhomogeneous $n$-state quantum walks\nin one dimension with $n-2$ self-loops, which is an extension of the technique\nin a previous study (Quantum Inf. Process 20(5), 2021). This method reveals the\nnecessary and sufficient condition for the eigenvalue problem of a two-phase\nthree-state quantum walk with one defect whose time evolution varies in the\nnegative part, positive part, and at the origin.\n', 'Generalized eigenfunctions for quantum walks via path counting approach   We consider the time-independent scattering theory for time evolution\noperators of one-dimensional two-state quantum walks. The scattering matrix\nassociated with the position-dependent quantum walk naturally appears in the\nasymptotic behavior at spatial infinity of generalized eigenfunctions. The\nasymptotic behavior of generalized eigenfunctions is a consequence of an\nexplicit expression of the Green function associated with the free quantum\nwalk. When the position-dependent quantum walk is a finite rank perturbation of\nthe free quantum walk, we derive a kind of combinatorial constructions of the\nscattering matrix by counting paths of quantum walkers. We also mention some\nremarks on the tunneling effect.\n', 'Strongly trapped space-inhomogeneous quantum walks in one dimension   Localization is a characteristic phenomenon of space-inhomogeneous quantum\nwalks in one dimension, where particles remain localized around their initial\nposition. The existence of eigenvalues of time evolution operators is a\nnecessary and sufficient condition for the occurrence of localization, and\ntheir associated eigenvectors are deeply related to the amount of localization,\ni.e., the probability that the walker stays around the starting position in the\nlong-time limit. In a previous study by authors, the eigenvalues of two-phase\nquantum walks with one defect were studied using a transfer matrix, which\nfocused on the occurrence of localization (Quantum Inf. Process 20(5), 2021).\nIn this paper, we introduce the analytical method to calculate eigenvectors\nusing the transfer matrix and also extend our results to characterize\neigenvalues not only for two-phase quantum walks with one defect but also for a\nmore general space-inhomogeneous model.\n  With these results, we quantitatively evaluate localization and study the\nstrong trapping property by deriving the time-averaged limit distributions of\nfive models studied previously.\n']","[('quantum walks', 0.7315495610237122), ('time quantum walks', 0.7179060578346252), ('quantum walk', 0.7159432172775269), ('time quantum walk', 0.7052038908004761), ('eigenfunctions quantum', 0.558733344078064), ('one dimensional quantum', 0.5193913578987122), ('localization quantum', 0.5028608441352844), ('discrete time quantum', 0.4973112642765045), ('dimensional quantum', 0.4753599166870117), ('eigenfunctions', 0.47396448254585266)]"
1298,1298,23,1298_mean ergodic_ergodicity_ergodic_composition operators spaces,"['mean ergodic', 'ergodicity', 'ergodic', 'composition operators spaces', 'composition operators', 'operators spaces', 'operators infty', 'weighted composition operators', 'composition operator', 'operators']","['Mean ergodic composition operators on spaces of smooth functions and\n  distributions   We investigate (uniform) mean ergodicity of weighted composition operators on\nthe space of smooth functions and the space of distributions, both over an open\nsubset of the real line. Among other things, we prove that a composition\noperator with a real analytic diffeomorphic symbol is mean ergodic on the space\nof distributions if and only if it is periodic with period 2. Our results are\nbased on a characterization of mean ergodicity in terms of Ces\\`aro boundedness\nand a growth property of the orbits for operators on Montel spaces which is of\nindependent interest.\n', 'Ergodic behaviors of composition operators acting on space of bounded\n  holomorphic functions   We completely characterize the mean ergodic composition operators on\n$H^\\infty(\\mathbb{B}_n)$. In particular, we show that a composition operator\nacting on this space is mean ergodic if and only if it is uniformly mean\nergodic.\n', 'Mean ergodic composition operators on $H^\\infty(\\mathbb{B}_n)$   In this paper, we study (uniformly) mean ergodic composition operators on\n$H^\\infty(\\mathbb{B}_n)$. Under some additional assumptions, it is shown that\nmean ergodic operators have norm convergent iterates in\n$H^\\infty(\\mathbb{B}_n)$, and that they are always uniformly mean ergodic.\n']","[('mean ergodic', 0.6162198781967163), ('ergodicity', 0.5566309690475464), ('ergodic', 0.5442432761192322), ('composition operators spaces', 0.5330720543861389), ('composition operators', 0.4761190116405487), ('operators spaces', 0.46132218837738037), ('operators infty', 0.45931577682495117), ('weighted composition operators', 0.45883235335350037), ('composition operator', 0.4490823447704315), ('operators', 0.38423851132392883)]"
1299,1299,23,1299_liquid drop_droplets_drops_liquid crystal,"['liquid drop', 'droplets', 'drops', 'liquid crystal', 'liquid', 'drop', 'droplet', 'existence minimizers', 'potential decays', 'anisotropic surface energy']","[""Local and Nonlocal Liquid Drop Models   We consider some extensions of Gamow's liquid drop model for an atomic\nnucleus. We present a review of the classical model and then we illustrate some\nrecent developments on a nonlocal variant, where the perimeter term is replaced\nby the fractional perimeter.\n"", ""Anisotropic liquid drop models   We introduce and study certain variants of Gamow's liquid drop model in which\nan anisotropic surface energy replaces the perimeter. After existence and\nnonexistence results are established, the shape of minimizers is analyzed.\nUnder suitable regularity and ellipticity assumptions on the surface tension,\nWulff shapes are minimizers in this problem if and only if the surface energy\nis isotropic. In sharp contrast, Wulff shapes are the unique minimizers for\ncertain crystalline surface tensions. We also introduce and study several\nrelated liquid drop models with anisotropic repulsion for which the Wulff shape\nis the minimizer in the small mass regime.\n"", ""On minimizers in the liquid drop model   We prove that round balls of volume $\\leq 1$ uniquely minimize in Gamow's\nliquid drop model.\n""]","[('liquid drop', 0.6210099458694458), ('droplets', 0.4960402250289917), ('drops', 0.4426080882549286), ('liquid crystal', 0.4425204396247864), ('liquid', 0.42477166652679443), ('drop', 0.4072926938533783), ('droplet', 0.37053847312927246), ('existence minimizers', 0.3241526484489441), ('potential decays', 0.3168899416923523), ('anisotropic surface energy', 0.315748006105423)]"
1300,1300,23,1300_class groups surfaces_class group surface_mapping class groups_infinite type surfaces,"['class groups surfaces', 'class group surface', 'mapping class groups', 'infinite type surfaces', 'groups closed surfaces', 'groups surfaces', 'mapping class group', 'infinite type surface', 'groups mapping class', 'surface infinite type']","['Coarse Geometry of Pure Mapping Class Groups of Infinite Graphs   We discuss the large-scale geometry of pure mapping class groups of locally\nfinite, infinite graphs, motivated by recent work of Algom-Kfir--Bestvina and\nthe work of Mann--Rafi on the large-scale geometry of mapping class groups of\ninfinite-type surfaces. Using the framework of Rosendal for coarse geometry of\nnon-locally compact groups, we classify when the pure mapping class group of a\nlocally finite, infinite graph is globally coarsely bounded (an analog of\ncompact) and when it is locally coarsely bounded (an analog of locally\ncompact). Our techniques give lower bounds on the first integral cohomology of\nthe pure mapping class group for some graphs and allow us to compute the\nasymptotic dimension of all locally coarsely bounded pure mapping class groups\nof infinite rank graphs. This dimension is always either zero or infinite.\n', 'Mapping class groups of surfaces with noncompact boundary components   We show that the pure mapping class group is uniformly perfect for a certain\nclass of infinite type surfaces with noncompact boundary components. We then\ncombine this result with recent work in the remaining cases to give a complete\nclassification of the perfect and uniformly perfect pure mapping class groups\nfor infinite type surfaces. We also develop a method to cut a general surface\ninto simpler surfaces and extend some mapping class group results to the\ngeneral case.\n', ""Coarsely bounded generating sets for mapping class groups of infinite-type surfaces Mann and Rafi's seminal work initiated the study of the coarse geometry of big mapping class groups. Specifically, they construct coarsely bounded (CB) generating sets for mapping class groups of a large class of infinite-type surfaces. In this expository note, we illustrate examples of surfaces whose mapping class groups admit such generating sets, as well as those that do not, with the goal of exploring the context of Mann--Rafi's hypotheses.""]","[('class groups surfaces', 0.6971442103385925), ('class group surface', 0.6617456078529358), ('mapping class groups', 0.6329153776168823), ('infinite type surfaces', 0.6208952069282532), ('groups closed surfaces', 0.6164015531539917), ('groups surfaces', 0.6137720942497253), ('mapping class group', 0.6035860180854797), ('infinite type surface', 0.5952228307723999), ('groups mapping class', 0.5891945362091064), ('surface infinite type', 0.5714347958564758)]"
1301,1301,23,1301_numerical framework_reparametrizations_numerical approaches_riemannian metrics,"['numerical framework', 'reparametrizations', 'numerical approaches', 'riemannian metrics', 'jacobian matrix', 'differential algebraic', 'system differential algebraic', 'shape analysis', 'system jacobian', 'riemannian']","['Structural Preprocessing Method for Nonlinear Differential-Algebraic\n  Equations Using Linear Symbolic Matrices   Differential-algebraic equations (DAEs) have been used in modeling various\ndynamical systems in science and engineering. Several preprocessing methods for\nDAEs, such as consistent initialization and index reduction, use structural\ninformation on DAEs. Unfortunately, these methods may fail when the system\nJacobian, which is a functional matrix, derived from the DAE is singular.\n  To transform a DAE with a singular system Jacobian into a nonsingular system,\nseveral regularization methods have been proposed. Most of all existing\nregularization methods rely on symbolic computation to eliminate the system\nJacobian for finding a certificate of singularity, resulting in much\ncomputational time. Iwata--Oki--Takamatsu (2019) proposed a method (IOT-method)\nto find a certificate without symbolic computations. The IOT method\napproximates the system Jacobian by a simpler symbolic matrix, called a layered\nmixed matrix, which admits a fast combinatorial algorithm for singularity\ntesting. However, it often overlooks the singularity of the system Jacobian\nsince the approximation largely discards algebraic relationships among entries\nin the original system Jacobian.\n  In this study, we propose a new regularization method extending the idea of\nthe IOT method. Instead of layered mixed matrices, our method approximates the\nsystem Jacobian by more expressive symbolic matrices, called rank-1 coefficient\nmixed (1CM) matrices. This makes our method more widely applicable. We give a\nfast combinatorial algorithm for finding a singularity certificate of\n1CM-matrices, which is free from symbolic elimination. Our method is also\nadvantageous in that it globally preserves the solution set to the DAE. Through\nnumerical experiments, we confirmed that our method runs fast for large-scale\nDAEs from real instances.\n', 'Index Reduction for Degenerated Differential-Algebraic Equations by\n  Embedding   To find consistent initial data points for a system of differential-algebraic\nequations, requires the identification of its missing constraints. An efficient\nclass of structural methods exploiting a dependency graph for this task was\ninitiated by Pantiledes. More complete methods rely on differential-algebraic\ngeometry but suffer from other issues (e.g. high complexity). In this paper we\ngive a new class of efficient structural methods combined with new tools from\nnumerical real algebraic geometry that has much improved completeness\nproperties. Existing structural methods may fail for a system of\ndifferential-algebraic equations if its Jacobian matrix after differentiation\nis still singular due to symbolic cancellation or numerical degeneration.\nExisting structural methods can only handle degenerated cases caused by\nsymbolic cancellation. However, if a system has parameters, then its parametric\nJacobian matrix may be still singular after application of the structural\nmethod for certain values of the parameters. This case is called numerical\ndegeneration.\n  For polynomially nonlinear systems of differential-algebraic equations,\nnumerical methods are given to solve both degenerated cases using numerical\nreal algebraic geometry. First, we introduce a witness point method, which\nproduces at least one witness point on every constraint component. This can\nhelp to ensure constant rank and detection of degeneration on all components of\nsuch systems. Secondly, we present a Constant Rank Embedding Lemma, and based\non it propose an Index Reduction by Embedding (IRE) method which can construct\nan equivalent system with a full rank Jacobian matrix. Thirdly, IRE leads to a\nglobal structural differentiation method, to solve degenerated\ndifferential-algebraic equations on all components numerically. Application\nexamples from circuits, mechanics, are used to demonstrate our method.\n', ""Elastic Metrics on Spaces of Euclidean Curves: Theory and Algorithms   A main goal in the field of statistical shape analysis is to define\ncomputable and informative metrics on spaces of immersed manifolds, such as the\nspace of curves in a Euclidean space. The approach taken in the elastic shape\nanalysis framework is to define such a metric by starting with a\nreparameterization-invariant Riemannian metric on the space of parameterized\nshapes and inducing a metric on the quotient by the group of diffeomorphisms.\nThis quotient metric is computed, in practice, by finding a registration of two\nshapes over the diffeomorphism group. For spaces of Euclidean curves, the\ninitial Riemannian metric is frequently chosen from a two-parameter family of\nSobolev metrics, called elastic metrics. Elastic metrics are especially\nconvenient because, for several parameter choices, they are known to be locally\nisometric to Riemannian metrics for which one is able to solve the geodesic\nboundary problem explictly -- well-known examples of these local isometries\ninclude the complex square root transform of Younes, Michor, Mumford and Shah\nand square root velocity (SRV) transform of Srivastava, Klassen, Joshi and\nJermyn. In this paper, we show that the SRV transform extends to elastic\nmetrics for all choices of parameters, for curves in any dimension, thereby\nfully generalizing the work of many authors over the past two decades. We give\na unified treatment of the elastic metrics: we extend results of Trouv\\'{e} and\nYounes, Bruveris as well as Lahiri, Robinson and Klassen on the existence of\nsolutions to the registration problem, we develop algorithms for computing\ndistances and geodesics, and we apply these algorithms to metric learning\nproblems, where we learn optimal elastic metric parameters for statistical\nshape analysis tasks.\n""]","[('numerical framework', 0.4291597306728363), ('reparametrizations', 0.4192352294921875), ('numerical approaches', 0.40796995162963867), ('riemannian metrics', 0.4075786769390106), ('jacobian matrix', 0.40291857719421387), ('differential algebraic', 0.3955453932285309), ('system differential algebraic', 0.3879258334636688), ('shape analysis', 0.3758431673049927), ('system jacobian', 0.3729292154312134), ('riemannian', 0.3707410395145416)]"
1302,1302,23,1302_one dimensional heat_heat conduction_thermal conductivity_heat transfer coefficient,"['one dimensional heat', 'heat conduction', 'thermal conductivity', 'heat transfer coefficient', 'analysis heat', 'dimensional heat', 'stationary heat', 'heat transfer', 'time dependent heat', 'solutions heat']","[""Numerical solution of the heat conduction problem with memory   It is necessary to use more general models than the classical Fourier heat\nconduction law to describe small-scale thermal conductivity processes. The\neffects of heat flow memory and heat capacity memory (internal energy) in\nsolids are considered in first-order integrodifferential evolutionary equations\nwith difference-type kernels. The main difficulties in applying such nonlocal\nin-time mathematical models are associated with the need to work with a\nsolution throughout the entire history of the process. The paper develops an\napproach to transforming a nonlocal problem into a computationally simpler\nlocal problem for a system of first-order evolution equations. Such a\ntransition is applicable for heat conduction problems with memory if the\nrelaxation functions of the heat flux and heat capacity are represented as a\nsum of exponentials. The correctness of the auxiliary linear problem is ensured\nby the obtained estimates of the stability of the solution concerning the\ninitial data and the right-hand side in the corresponding Hilbert spaces. The\nstudy's main result is to prove the unconditional stability of the proposed\ntwo-level scheme with weights for the evolutionary system of equations for\nmodeling heat conduction in solid media with memory. In this case, finding an\napproximate solution on a new level in time is not more complicated than the\nclassical heat equation. The numerical solution of a model one-dimensional in\nspace heat conduction problem with memory effects is presented.\n"", ""Error Estimators for the Small-Biot Lumped Approximation for the\n  Conduction Dunking Problem   We consider the dunking problem: a solid body at uniform temperature\n$T_{\\text i}$ is placed in a environment characterized by farfield temperature\n$T_\\infty$ and spatially uniform time-independent heat transfer coefficient. We\npermit heterogeneous material composition: spatially dependent density,\nspecific heat, and thermal conductivity. Mathematically, the problem is\ndescribed by a heat equation with Robin boundary conditions. The crucial\nparameter is the Biot number -- a nondimensional heat transfer (Robin)\ncoefficient; we consider the limit of small Biot number.\n  We introduce first-order and second-order asymptotic approximations (in Biot\nnumber) for several quantities of interest, notably the spatial domain average\ntemperature as a function of time; the first-order approximation is simply the\nstandard engineering `lumped' model. We then provide asymptotic error estimates\nfor the first-order and second-order approximations for small Biot number, and\nalso, for the first-order approximation, alternative strict bounds valid for\nall Biot number. Companion numerical solutions of the heat equation confirm the\neffectiveness of the error estimates for small Biot number.\n  The second-order approximation and the first-order and second-order error\nestimates depend on several functional outputs associated to an elliptic\npartial differential equation; the latter is derived from Biot-sensitivity\nanalysis of the heat equation eigenproblem in the limit of small Biot number.\nMost important is $\\phi$, the only functional output required for the\nfirst-order error estimates; $\\phi$ admits a simple physical interpretation in\nterms of conduction length scale. We investigate the domain and property\ndependence of $\\phi$: most notably, we characterize spatial domains for which\nthe standard lumped-model error criterion -- Biot number (based on\nvolume-to-area length scale) small -- is deficient.\n"", ""Certified Lumped Approximations for the Conduction Dunking Problem   We consider the dunking problem: a solid body at uniform temperature\n$T_\\text{i}$ is placed in a environment characterized by farfield temperature\n$T_\\infty$ and time-independent spatially uniform heat transfer coefficient; we\npermit heterogeneous material composition. The problem is described by a heat\nequation with Robin boundary conditions. The crucial parameter is the Biot\nnumber, a nondimensional heat transfer coefficient; we consider the limit of\nsmall Biot number.\n  We introduce first-order and second-order asymptotic approximations (in Biot\nnumber) for the spatial domain average temperature as a function of time; the\nfirst-order approximation is the standard `lumped model'. We provide asymptotic\nerror estimates for the first-order and second-order approximations for small\nBiot number, and also, for the first-order approximation, non-asymptotic bounds\nvalid for all Biot number. We also develop a second-order approximation and\nassociated asymptotic error estimate for the normalized difference in the\ndomain average and boundary average temperatures. Companion numerical solutions\nof the heat equation confirm the effectiveness of the error estimates for small\nBiot number.\n  The second-order approximation and the first-order and second-order error\nestimates depend on several functional outputs associated with an elliptic\npartial differential equation; the latter can be derived from Biot-sensitivity\nanalysis of the heat equation eigenproblem in the limit of small Biot number.\nMost important is the functional output $\\phi$, the only functional output\nrequired for the first-order error estimate and also the second-order\napproximation; $\\phi$ admits a simple physical interpretation in terms of\nconduction length scale. We characterize a class of spatial domains for which\nthe standard lumped-model criterion -- Biot number (based on volume-to-area\nlength scale) small -- is deficient.\n""]","[('one dimensional heat', 0.6101701855659485), ('heat conduction', 0.6042090654373169), ('thermal conductivity', 0.5984313488006592), ('heat transfer coefficient', 0.5970190167427063), ('analysis heat', 0.5909212231636047), ('dimensional heat', 0.5658580660820007), ('stationary heat', 0.5388901829719543), ('heat transfer', 0.5354493856430054), ('time dependent heat', 0.5136774778366089), ('solutions heat', 0.4978668987751007)]"
1303,1303,23,1303_integrable theories_integrable models_conformal field theories_conformal field theory,"['integrable theories', 'integrable models', 'conformal field theories', 'conformal field theory', 'conformal theory', 'integrable deformations', 'associative yang baxter', 'integrable structures', 'dimensional sigma models', 'sigma models']","['Probabilistic construction of the $\\mathbb{H}^3$-Wess-Zumino-Witten\n  conformal field theory and correspondence with Liouville theory   Wess-Zumino-Witten (WZW) models are among the most basic and most studied\nConformal Field Theories (CFT). They have had a huge influence not only in\nphysics but also in mathematics, in representation theory and geometry. However\ntheir rigorous probabilistic construction and analysis starting from the path\nintegral is still missing and all their properties have been obtained\nalgebraically from their postulated affine Lie algebra symmetry. Initially\nconsidered as taking values in a compact semisimple Lie Group G, the WZW model\nalso has a ""dual"" formulation where the group $G$ is replaced by the homogenous\nspace $G^{\\mathbb{C}}/G$, where $G^{\\mathbb{C}}$ is the complexification of\n$G$, and it has been argued that the former can be (re-)constructed from the\nlatter. For $G={\\rm SU}(2)$, the space ${\\rm SL}(2,\\mathbb{C})/{\\rm SU}(2)$ can\nbe identified with the three dimensional hyperbolic space $\\mathbb{H}^3$ and,\nin physics, the corresponding CFT has been studied as the simplest example of\nthe AdS/CFT correspondence. A surprising correspondence between the\n$\\mathbb{H}^3$-WZW CFT and the Liouville CFT was found by Ribault and Teschner\nand later generalised by Hikida and Shomerus. This correspondence has been\ndubbed by Gaiotto-Teschner as the ""quantum analytic Langlands correspondence""\nsince the analytic Langlands correspondence of Etingof, Frenkel and Kazhdan\nseems to emerge in its formal semi classical limit. In this paper we give a\nrigorous construction of the path integral for the $\\mathbb{H}^3$-WZW model on\na closed Riemann surface $\\Sigma$, twisted by an arbitrary smooth gauge field\non $\\Sigma$. Using the probabilistic path integral we prove a correspondence\nbetween the correlation functions of the primary fields of the $\\mathbb{H}^3$\nmodel and those of Liouville CFT extending the expressions proposed by\nRibault-Teschner and by Hikida-Schomerus to this general setup.\n', 'Lax pairs for new $\\mathbb{Z}_N$-symmetric coset $\\sigma$-models and\n  their Yang-Baxter deformations   Two-dimensional $\\sigma$-models with $\\mathbb{Z}_N$-symmetric homogeneous\ntarget spaces have been shown to be classically integrable when introducing\nWZ-terms in a particular way. This article continues the search for new models\nof this type now allowing some kinetic terms to be absent, analogously to the\nGreen-Schwarz superstring $\\sigma$-model on $\\mathbb{Z}_4$-symmetric\nhomogeneous spaces. A list of such integrable $\\mathbb{Z}_N$-symmetric\n(super)coset $\\sigma$-models for $N \\leq 6$ and their Lax pairs is presented.\nFor arbitrary $N$, a big class of integrable models is constructed that\nincludes both the known pure spinor and Green-Schwarz superstring on\n$\\mathbb{Z}_4$-symmetric cosets.\n  Integrable Yang-Baxter deformations of this class of $\\mathbb{Z}_N$-symmetric\n(super)coset $\\sigma$-models can be constructed in same way as in the known\n$\\mathbb{Z}_2$- or $\\mathbb{Z}_4$-cases. Deformations based on solutions of the\nmodified classical Yang-Baxter equation, the so-called $\\eta$-deformation,\nrequire deformation of the constants defining the Lagrangian and the\ncorresponding Lax pair. Homogeneous Yang-Baxter deformations (i.e. those based\non solutions to the classical Yang-Baxter equation) leave the equations of\nmotion and consequently the Lax pair invariant and are expected to be\nclassically equivalent to the undeformed model.\n  As an example, the relationship between $\\mathbb{Z}_3$-symmetric homogeneous\nspaces and nearly (para-)K\\""ahler geometries is revisited. Confirming existing\nliterature it is shown that the integrable choice of WZ-term in the\n$\\mathbb{Z}_3$-symmetric coset $\\sigma$-model associated to a nearly K\\""ahler\nbackground gives an imaginary contribution to the action.\n', ""Integrable sigma models at RG fixed points: quantisation as affine\n  Gaudin models   The goal of this paper is to make first steps towards the quantisation of\nintegrable non-linear sigma models using the formalism of affine Gaudin models,\nby approaching these theories through their conformal limits. We focus mostly\non the example of the Klim\\v{c}\\'{i}k model, which is a two-parameter\ndeformation of the Principal Chiral Model on a Lie group $G$. We show that the\nUV fixed point of this theory is described classically by two decoupled chiral\naffine Gaudin models, encoding its left- and right-moving degrees of freedom,\nand give a detailed analysis of the chiral and integrable structures of these\nmodels. Their quantisation is then explored within the framework of Feigin and\nFrenkel. We study the quantum local integrals of motion using the formalism of\nquantised affine Gaudin models and show agreement of the first two integrals\nwith known results in the literature for $G={\\rm SU}(2)$. Evidence is given for\nthe existence of a monodromy matrix satisfying the Yang-Baxter algebra for this\nmodel, thus paving the way for the quantisation of the non-local integrals of\nmotion. We conclude with various perspectives, including on generalisations of\nthis program to a larger class of integrable sigma models and applications of\nthe ODE/IQFT correspondence to the description of their quantum spectrum.\n""]","[('integrable theories', 0.595141589641571), ('integrable models', 0.5771892666816711), ('conformal field theories', 0.5768349170684814), ('conformal field theory', 0.5410512089729309), ('conformal theory', 0.5344884991645813), ('integrable deformations', 0.4971921741962433), ('associative yang baxter', 0.4648144543170929), ('integrable structures', 0.4607788324356079), ('dimensional sigma models', 0.4536954462528229), ('sigma models', 0.43683263659477234)]"
1304,1304,23,1304_fractional laplacian_inverse conductivity_inverse problems fractional_inverse fractional,"['fractional laplacian', 'inverse conductivity', 'inverse problems fractional', 'inverse fractional', 'fractional dirichlet', 'unique continuation fractional', 'formulation fractional', 'dirichlet neumann map', 'properties fractional', 'continuation fractional']","[""Fractional Calder\\'on problems and Poincar\\'e inequalities on unbounded\n  domains   We generalize many recent uniqueness results on the fractional Calder\\'on\nproblem to cover the cases of all domains with nonempty exterior. The highlight\nof our work is the characterization of uniqueness and nonuniqueness of partial\ndata inverse problems for the fractional conductivity equation on domains that\nare bounded in one direction for conductivities supported in the whole\nEuclidean space and decaying to a constant background conductivity at infinity.\nWe generalize the uniqueness proof for the fractional Calder\\'on problem by\nGhosh, Salo and Uhlmann to a general abstract setting in order to use the full\nstrength of their argument. This allows us to observe that there are also\nuniqueness results for many inverse problems for higher order local\nperturbations of a lower order fractional Laplacian. We give concrete example\nmodels to illustrate these curious situations and prove Poincar\\'e inequalities\nfor the fractional Laplacians of any order on domains that are bounded in one\ndirection. We establish Runge approximation results in these general settings,\nimprove regularity assumptions also in the cases of bounded sets and prove\ngeneral exterior determination results. Counterexamples to uniqueness in the\ninverse fractional conductivity problem with partial data are constructed in\nanother companion work.\n"", ""On an inverse problem for a fractional semilinear elliptic equation\n  involving a magnetic potential   We study a class of fractional semilinear elliptic equations and formulate\nthe corresponding Calder\\'on problem. We determine the nonlinearity from the\nexterior partial measurements of the Dirichlet-to-Neumann map by using first\norder linearization and the Runge approximation property.\n"", 'The global inverse fractional conductivity problem   We prove \\emph{global} uniqueness for an inverse problem for the fractional\nconductivity equation on domains that are bounded in one direction. The\nconductivities are assumed to be isotropic and nontrivial in the exterior of\nthe domain, while the data is given in the form of partial Dirichlet-to-Neumann\n(DN) maps measured in nondisjoint open subsets of the exterior. This can be\nseen as the fractional counterpart of the classical inverse conductivity\nproblem. The proof is based on a unique continuation property (UCP) for the DN\nmaps and an exterior determination method from the partial exterior DN maps.\nThis is analogous to the classical boundary determination method by Kohn and\nVogelius. The most important technical novelty is the construction of sequences\nof special solutions to the fractional conductivity equation whose Dirichlet\nenergies in the limit can be concentrated at any given point in the exterior.\nThis is achieved independently of the UCP and despite the nonlocality of the\nequation. Due to the recent counterexamples by the last two authors, our\nresults almost completely characterize uniqueness for the inverse fractional\nconductivity problem with partial data for isotropic global conductivities.\n']","[('fractional laplacian', 0.5723949074745178), ('inverse conductivity', 0.5577805638313293), ('inverse problems fractional', 0.5342654585838318), ('inverse fractional', 0.49442172050476074), ('fractional dirichlet', 0.476477712392807), ('unique continuation fractional', 0.47638729214668274), ('formulation fractional', 0.4602055847644806), ('dirichlet neumann map', 0.450242817401886), ('properties fractional', 0.43736904859542847), ('continuation fractional', 0.4369131326675415)]"
1305,1305,23,1305_structured tensors_positive tensor_bound tensor_tensors,"['structured tensors', 'positive tensor', 'bound tensor', 'tensors', 'tensor establish', 'linear complementarity problems', 'tensor furthermore', 'tensor', 'sparse tensor', 'defined tensor']","['Column competent tensors and tensor complementarity problem   In multilinear algebra, some special classes of matrices are extended to\nhigher order structured tensors. The local $w$-uniqueness solution to the\nlinear complementarity problem can be identified by the column competent\nmatrix. Motivated by this $w$-uniqueness property, we introduce column\ncompetent tensor in the context of tensor complementarity problem. We consider\nsome important properties. In the theory of linear complementarity problem,\ncolumn competent matrices are introduced to study local $w$-uniqueness property\nof LCP solution. We present the inheritance property and invariance property of\ncolumn competent tensors. We study the tensor complementarity problem using\ncolumn competent tensors and several results are established. Some examples are\nillustrated to support the results. Keywords: Tensor complementarity problem,\ncolumn competent tensor, nondegenerate tensor, $\\omega$-solution. AMS subject\nclassifications: 90C33, 90C30, 15A69, 46G25.\n', 'Some properties of the solution of the vertical tensor complementarity\n  problem   In this paper, we mainly focus on the existence and uniqueness of the\nvertical tensor complementarity problem. Firstly, combining the\ngeneralized-order linear complementarity problem with the tensor\ncomplementarity problem, the vertical tensor complementarity problem is\nintroduced. Secondly, we define some sets of special tensors, and illustrate\nthe inclusion relationships. Finally, we show that the solution set of the\nvertical tensor complementarity problem is bounded under certain conditions,\nand some sufficient conditions for the existence and uniqueness of the solution\nof the vertical tensor complementarity problem are obtained from the view of\nthe degree theory and the equal form of the minimum function.\n', 'Properties of Solution set of Tensor Complementarity Problem   The tensor complementarity problem is a specially structured nonlinear\ncomplementarity problem, then it has its particular and nice properties other\nthan ones of the classical nonlinear complementarity problem. In this paper, it\nis proved that a tensor is an S-tensor if and only if the tensor\ncomplementarity problem is feasible, and each Q-tensor is an S-tensor.\nFurthermore, the boundedness of solution set of the tensor complementarity\nproblem is equivalent to the uniqueness of solution for such a problem with\nzero vector. For the tensor complementarity problem with a strictly\nsemi-positive tensor, we proved the global upper bounds for solution of such a\nproblem. In particular, the upper bounds keep in close contact with the\nsmallest Pareto $H-$($Z-$)eigenvalue.\n']","[('structured tensors', 0.6325927376747131), ('positive tensor', 0.5980812907218933), ('bound tensor', 0.595893919467926), ('tensors', 0.5937157869338989), ('tensor establish', 0.5891728401184082), ('linear complementarity problems', 0.5864095687866211), ('tensor furthermore', 0.5858519673347473), ('tensor', 0.5555014610290527), ('sparse tensor', 0.5546154379844666), ('defined tensor', 0.5544754266738892)]"
1306,1306,23,1306_finite coloring_monochromatic_finite colouring_coloring mathbb,"['finite coloring', 'monochromatic', 'finite colouring', 'coloring mathbb', 'coloring', 'conjectured finite', 'finite products', 'sums products', 'every finite', 'finite partition']","['Matrix Formulation of Moreira Theorem   In a celebrated article, Moreira proved for every finite coloring of the set\nof naturals, there exists a monochromatic copy of the form $\\{x,x+y,xy\\},$\nwhich gives a partial answer to one of the central open problems of Ramsey\ntheory asking whether $\\{x,y,x+y,xy\\}$ is partition regular. In this article,\nwe prove the matrix version of the Moreira theorem. We prove that if $A$ and\n$B$ are two finite image partition regular matrices of the same order, then for\nevery finite coloring of the set of naturals, there exist two vectors\n$\\overrightarrow{X}, \\overrightarrow{Y}$ such that $\\{A\\overrightarrow{X},\nA\\overrightarrow{X}+B\\overrightarrow{Y}, A \\overrightarrow{X}\\cdot\nB\\overrightarrow{Y}\\}$ is monochromatic, where addition and multiplication are\ndefined coordinate-wise.\n', ""Additive and multiplicative Gower's Ramsey theorem   W. T. Gower generalized Hindman's Finite sum theorem over $X_{k}=\\left\\{\n\\left(n_{1},n_{2},\\ldots,n_{k}\\right):n_{1}\\neq0\\right\\} $ by showing that for\nany finite coloring of $X_{k}$ there exists a sequence such that the Gower\nsubspace generated by that sequence is monochromatic. For $k=1,$ this\nimmediately gives the finite sum theorem. In this article we will show that for\nany finite coloring of $X_{k}$ there exist two sequences $\\left\\{\n\\mathbf{n_{i}}:i\\in I\\right\\} $ and $\\left\\{ \\mathbf{m_{i}}:i\\in I\\right\\} $\nsuch that the Gower subspace generated by $\\left\\{ \\mathbf{n_{i}}:i\\in\nI\\right\\} $ and set of all finite products of $\\left\\{ \\mathbf{m_{i}}:i\\in\nI\\right\\} $ are in a single color. This immediately generalize a result of V.\nBergelson and N. Hindman which says that for any finite coloring of\n$\\mathbb{N}$, there exist two sequences $\\left(x_{n}\\right)_{n}$ and\n$\\left(y_{n}\\right)_{n}$ such that the finite sum and product generated by\n$\\left(x_{n}\\right)_{n}$ and $\\left(y_{n}\\right)_{n}$ are in a same color.\n"", ""Monochromatic Sums and Products over $\\mathbb{Q}$   Hindman's finite sums theorem states that in any finite coloring of the\nnaturals, there is an infinite sequence all of whose finite subset sums are the\nsame color. In 1979, Hindman showed that there is a finite coloring of the\nnaturals so that no infinite sequence has all of its pairwise sums and pairwise\nproducts the same color. Hindman conjectured that for any $n$, a finite\ncoloring of the naturals contains $n$ numbers all of whose subset sums and\nsubset products are the same color. In this paper we prove the version of this\nstatement where we color the rationals instead of the integers. In other words,\nwe show that the pattern $\\{ \\sum_{i \\in S}x_i, \\prod_{i \\in S}x_i \\}$, where\n$S$ ranges over all nonempty subsets of $[n]$, is partition regular over the\nrationals.\n""]","[('finite coloring', 0.647855818271637), ('monochromatic', 0.5693825483322144), ('finite colouring', 0.549965500831604), ('coloring mathbb', 0.4615592360496521), ('coloring', 0.4442301094532013), ('conjectured finite', 0.4359685778617859), ('finite products', 0.431971937417984), ('sums products', 0.39058831334114075), ('every finite', 0.38443106412887573), ('finite partition', 0.3655378818511963)]"
1307,1307,23,1307_rational homology spheres_homology spheres_manifolds rational_hyperbolic manifolds,"['rational homology spheres', 'homology spheres', 'manifolds rational', 'hyperbolic manifolds', 'cusped hyperbolic manifolds', 'manifolds', 'orientable manifolds', 'manifolds every', 'manifolds surface', 'hyperbolic manifold']","['Strongly chiral rational homology spheres with hyperbolic fundamental\n  groups   For each $m\\geq0$ and any prime $p\\equiv3\\ \\mathrm{(mod \\ 4)}$, we construct\nstrongly chiral rational homology $(4m+3)$-spheres, which have real hyperbolic\nfundamental groups and only non-zero integral intermediate homology groups\nisomorphic to $\\mathbb{Z}_{2p}$ in degrees $1,2m+1$ and $4m+1$. This gives\ngroup theoretic analogues in high dimensions of the existence of strongly\nchiral hyperbolic rational homology $3$-spheres, as well as of the existence of\nstrongly chiral hyperbolic manifolds of any dimension that are not rational\nhomology spheres, which was shown by Weinberger. One of our tools will be\n$r$-spins. We thus investigate the relationship between the sets of degrees of\nself-maps of a given manifold and its $r$-spins, and give classes of manifolds\nfor which the sets are equal.\n', 'Infinitely many arithmetic hyperbolic rational homology 3-spheres that\n  bound geometrically   In this paper we provide the first examples of arithmetic hyperbolic\n3-manifolds that are rational homology spheres and bound geometrically either\ncompact or cusped hyperbolic 4-manifolds.\n', ""Achirality of Sol 3-Manifolds, Stevenhagen Conjecture and Shimizu's\n  L-series   A closed orientable manifold is {\\em achiral} if it admits an orientation\nreversing homeomorphism. A commensurable class of closed manifolds is achiral\nif it contains an achiral element, or equivalently, each manifold in $\\CM$ has\nan achiral finite cover.\n  Each commensurable class containing non-orientable elements must be achiral.\n  It is natural to wonder how many\n  commensurable classes are achiral and how many achiral classes have\nnon-orientable elements.\n  We study this problem for Sol 3-manifolds. Each commensurable class $\\CM$ of\nSol 3-manifold has a complete topological invariant $D_{\\CM}$, the discriminant\nof $\\CM$. Our main result is:\n  (1) Among all commensurable classes of Sol 3-manifolds, there are infinitely\nmany achiral classes; however ordered by discriminants, the density of achiral\ncommensurable classes is 0.\n  (2) Among all achiral commensurable classes of Sol 3-manifolds, ordered by\ndiscriminants, the density of classes containing non-orientable elements is\n$1-\\rho$,\n  where $$\\rho:=\\prod_{j=1}^\\infty \\left(1+2^{-j}\\right)^{-1} =\n0.41942\\cdots.$$\n""]","[('rational homology spheres', 0.6742436289787292), ('homology spheres', 0.6566523909568787), ('manifolds rational', 0.5779030919075012), ('hyperbolic manifolds', 0.5738879442214966), ('cusped hyperbolic manifolds', 0.5534509420394897), ('manifolds', 0.5534128546714783), ('orientable manifolds', 0.5511422157287598), ('manifolds every', 0.5264418721199036), ('manifolds surface', 0.5085509419441223), ('hyperbolic manifold', 0.5083994269371033)]"
1308,1308,22,1308_magnetic laplacian_laplacian magnetic_spectral asymptotics_dirichlet laplacian,"['magnetic laplacian', 'laplacian magnetic', 'spectral asymptotics', 'dirichlet laplacian', 'neumann laplacian', 'laplacian higher', 'eigenvalue asymptotics', 'laplacian', 'laplacian smooth', 'dirichlet neumann operator']","['The magnetic Laplacian on the Disc for strong magnetic fields   The magnetic Laplacian on a planar domain under a strong constant magnetic\nfield has eigenvalues close to the Landau levels. We study the case when the\ndomain is a disc and the spectrum consists of branches of eigenvalues of one\ndimensional operators. Under Neumann boundary condition and strong magnetic\nfield, we derive asymptotics of the eigenvalues with accurate estimates of\nexponentially small remainders. Our approach is purely variational and applies\nto the Dirichlet boundary condition as well, which allows us to recover recent\nresults by Baur and Weidl.\n', 'The Magnetic Laplacian with a Higher-order Vanishing Magnetic Field in a\n  Bounded Domain   This paper is concerned with spectrum properties of the magnetic Laplacian\nwith a higher-order vanishing magnetic field in a bounded domain. We study the\nasymptotic behaviors of ground state energies for the Dirichlet Laplacian, the\nNeumann Laplacian, and the Dirichlet-to-Neumann operator, as the field strength\nparameter $\\beta$ goes to infinite. Assume that the magnetic field does not\nvanish to infinite order, we establish the leading orders of $\\beta$. We also\nobtain the first terms in the asymptotic expansions with remainder estimates\nunder additional assumptions on an invariant subspace for a Taylor polynomial\nof the magnetic field. Our aim is to provide a unified approach to all three\ncases.\n', 'Magnetic perturbations of the Robin Laplacian in the strong coupling\n  limit   This paper is devoted to the asymptotic analysis of the eigenvalues of the\nLaplace operator with a strong magnetic field and Robin boundary condition on a\nsmooth planar domain and with a negative boundary parameter. We study the\nsingular limit when the Robin parameter tends to infinity which is equivalent\nto a semi-classical limit involving a small positive semi-classical parameter.\nThe main result is a comparison between the spectrum of the Robin Laplacian\nwith an effective operator defined on the boundary of the domain via the\nBorn-Oppenheimer approximation. More precisely, the low-lying eigenvalue of the\nRobin Laplacian is approximated by the those of the effective operator. When\nthe curvature has a unique non-degenerate maximum, we estimate the spectral gap\nand find that the magnetic field does not contribute to the three-term\nexpansion of the eigenvalues. In the case of the disc domains, the eigenvalue\nasymptotics displays the contribution of the magnetic field explicitly.\n']","[('magnetic laplacian', 0.6791024804115295), ('laplacian magnetic', 0.6665278077125549), ('spectral asymptotics', 0.5782045125961304), ('dirichlet laplacian', 0.5778074264526367), ('neumann laplacian', 0.5771230459213257), ('laplacian higher', 0.5466281175613403), ('eigenvalue asymptotics', 0.546271800994873), ('laplacian', 0.5419143438339233), ('laplacian smooth', 0.5324625372886658), ('dirichlet neumann operator', 0.514187216758728)]"
1309,1309,22,1309_heisenberg uncertainty principle_heisenberg uncertainty_type uncertainty principle_uncertainty principle,"['heisenberg uncertainty principle', 'heisenberg uncertainty', 'type uncertainty principle', 'uncertainty principle', 'uncertainty principles', 'properties fourier', 'heisenberg type', 'fourier transform', 'weyl uncertainty', 'new uncertainty']","[""Uncertainty principles for the windowed Hankel transform   The aim of this paper is to prove some new uncertainty principles for the\nwindowed Hankel transform. They include uncertainty principle for orthonormal\nsequence, local uncertainty principle, logarithmic uncertainty principle and\nHeisenberg-type uncertainty principle. As a side result, we obtain the\nShapiro's dispersion theorem for the windowed Hankel transform.\n"", ""Uncertainty principles for the windowed Opdam--Cherednik transform   In this paper, we study a few versions of the uncertainty principle for the\nwindowed Opdam--Cherednik transform. In particular, we establish the\nuncertainty principle for orthonormal sequences, Donoho--Stark's uncertainty\nprinciple, Benedicks-type uncertainty principle, Heisenberg-type uncertainty\nprinciple and local uncertainty inequality for this transform. We also obtain\nthe Heisenberg-type uncertainty inequality using the $k$-entropy of the\nwindowed Opdam--Cherednik transform.\n"", ""Uncertainty principles for the short-time Fourier transform on the\n  lattice   In this paper, we study a few versions of the uncertainty principle for the\nshort-time Fourier transform on the lattice $\\mathbb Z^n \\times \\mathbb T^n$.\nIn particular, we establish the uncertainty principle for orthonormal\nsequences, Donoho--Stark's uncertainty principle, Benedicks-type uncertainty\nprinciple, Heisenberg-type uncertainty principle and local uncertainty\ninequality for this transform on $\\mathbb Z^n \\times \\mathbb T^n$. Also, we\nobtain the Heisenberg-type uncertainty inequality using the $k$-entropy of the\nshort-time Fourier transform on $\\mathbb Z^n \\times \\mathbb T^n$.\n""]","[('heisenberg uncertainty principle', 0.6907418966293335), ('heisenberg uncertainty', 0.6304262280464172), ('type uncertainty principle', 0.5725129842758179), ('uncertainty principle', 0.5687003135681152), ('uncertainty principles', 0.5411249995231628), ('properties fourier', 0.47643905878067017), ('heisenberg type', 0.44868433475494385), ('fourier transform', 0.4410032033920288), ('weyl uncertainty', 0.43724626302719116), ('new uncertainty', 0.4354200065135956)]"
1310,1310,22,1310_network revenue management_optimal regret_dynamic resource allocation_offline optimal,"['network revenue management', 'optimal regret', 'dynamic resource allocation', 'offline optimal', 'regret lower bound', 'near optimal', 'regret upper bound', 'resource allocation', 'allocation problems', 'revenue management']","['Degeneracy is OK: Logarithmic Regret for Network Revenue Management with\n  Indiscrete Distributions   We study the classical Network Revenue Management (NRM) problem with\naccept/reject decisions and $T$ IID arrivals. We consider a distributional form\nwhere each arrival must fall under a finite number of possible categories, each\nwith a deterministic resource consumption vector, but a random value\ndistributed continuously over an interval. We develop an online algorithm that\nachieves $O(\\log^2 T)$ regret under this model, with the only (necessary)\nassumption being that the probability densities are bounded away from 0. We\nderive a second result that achieves $O(\\log T)$ regret under an additional\nassumption of second-order growth. To our knowledge, these are the first\nresults achieving logarithmic-level regret in an NRM model with continuous\nvalues that do not require any kind of ""non-degeneracy"" assumptions. Our\nresults are achieved via new techniques including a new method of bounding\nmyopic regret, a ""semi-fluid"" relaxation of the offline allocation, and an\nimproved bound on the ""dual convergence"".\n', 'An Improved Analysis of LP-based Control for Revenue Management   In this paper, we study a class of revenue management problems where the\ndecision maker aims to maximize the total revenue subject to budget constraints\non multiple type of resources over a finite horizon. At each time, a new\norder/customer/bid is revealed with a request of some resource(s) and a reward,\nand the decision maker needs to either accept or reject the order. Upon the\nacceptance of the order, the resource request must be satisfied and the\nassociated revenue (reward) can be collected. We consider a stochastic setting\nwhere all the orders are i.i.d. sampled, i.e., the reward-request pair at each\ntime is drawn from an unknown distribution with finite support. The formulation\ncontains many classic applications such as the quantity-based network revenue\nmanagement problem and the Adwords problem. We focus on the classic LP-based\nadaptive algorithm and consider regret as the performance measure defined by\nthe gap between the optimal objective value of the certainty-equivalent linear\nprogram (LP) and the expected revenue obtained by the online algorithm. Our\ncontribution is two-fold: (i) when the underlying LP is nondegenerate, the\nalgorithm achieves a problem-dependent regret upper bound that is independent\nof the horizon/number of time periods $T$; (ii) when the underlying LP is\ndegenerate, the algorithm achieves a regret upper bound that scales on the\norder of $\\sqrt{T}\\log T$. To our knowledge, both results are new and improve\nthe best existing bounds for the LP-based adaptive algorithm in the\ncorresponding setting. We conclude with numerical experiments to further\ndemonstrate our findings.\n', 'Fairer LP-based Online Allocation via Analytic Center   In this paper, we consider an online resource allocation problem where a\ndecision maker accepts or rejects incoming customer requests irrevocably in\norder to maximize expected reward given limited resources. At each time, a new\norder/customer/bid is revealed with a request of some resource(s) and a reward.\nWe consider a stochastic setting where all the orders are i.i.d. sampled from\nan unknown distribution. Such formulation arises from many classic applications\nsuch as the canonical (quantity-based) network revenue management problem and\nthe Adwords problem. While the literature on the topic mainly focuses on regret\nminimization, our paper considers the \\textit{fairness} aspect of the problem.\nOn a high level, we define the fairness in a way that a fair online algorithm\nshould treat similar agents/customers similarly, and the decision made for\nsimilar agents/customers should be consistent over time. To achieve this goal,\nwe define the fair offline solution as the analytic center of the offline\noptimal solution set, and introduce \\textit{cumulative unfairness} as the\ncumulative deviation from the online solutions to the fair offline solution\nover time. We propose a fair algorithm based on an interior-point LP solver and\na mechanism that dynamically detects unfair resource spending. Our algorithm\nachieves cumulative unfairness on the scale of order $O(\\log(T))$, while\nmaintains the regret to be bounded without dependency on $T$. In addition,\ncompared to the literature, our result is produced under less restrictive\nassumptions on the degeneracy of the underlying linear program.\n']","[('network revenue management', 0.5265973806381226), ('optimal regret', 0.5258228182792664), ('dynamic resource allocation', 0.4891582727432251), ('offline optimal', 0.46494001150131226), ('regret lower bound', 0.45095282793045044), ('near optimal', 0.4506389796733856), ('regret upper bound', 0.44795697927474976), ('resource allocation', 0.43923085927963257), ('allocation problems', 0.4371337592601776), ('revenue management', 0.4352712333202362)]"
1311,1311,22,1311_well posedness stochastic_posedness stochastic_stochastic wave_stochastic nonlinear,"['well posedness stochastic', 'posedness stochastic', 'stochastic wave', 'stochastic nonlinear', 'additive stochastic forcing', 'stochastic damped', 'stochastic forcing', 'global well posedness', 'dynamics stochastic', 'local well posedness']","[""Stochastic nonlinear wave dynamics on compact surfaces   We study the Cauchy problem for the nonlinear wave equations (NLW) with\nrandom data and/or stochastic forcing on a two-dimensional compact Riemannian\nmanifold without boundary. (i) We first study the defocusing stochastic damped\nNLW driven by additive space-time white-noise, and with initial data\ndistributed according to the Gibbs measure. By introducing a suitable\nspace-dependent renormalization, we prove local well-posedness of the\nrenormalized equation. Bourgain's invariant measure argument then allows us to\nestablish almost sure global well-posedness and invariance of the Gibbs measure\nfor the renormalized stochastic damped NLW. (ii) Similarly, we study the random\ndata defocusing NLW (without stochastic forcing), and establish the same\nresults as in the previous setting. (iii) Lastly, we study the stochastic NLW\nwithout damping. By introducing a space-time dependent renormalization, we\nprove its local well-posedness with deterministic initial data in all\nsubcritical spaces.\n  These results extend the corresponding recent results on the two-dimensional\ntorus obtained by (i) Gubinelli-Koch-Oh-Tolomeo (2018), (ii) Oh-Thomann (2017),\nand (iii) Gubinelli-Koch-Oh (2018), to a general class of compact manifolds.\nThe main ingredient is the Green's function estimate for the Laplace-Beltrami\noperator in this setting to study regularity properties of stochastic terms\nappearing in each of the problems.\n"", 'Global well-posedness of the two-dimensional stochastic viscous\n  nonlinear wave equations   We study well-posedness of viscous nonlinear wave equations (vNLW) on the\ntwo-dimensional torus with a stochastic forcing. In particular, we prove\npathwise global well-posedness of the stochastic defocusing vNLW with an\nadditive stochastic forcing $D^\\alpha \\xi$, where $\\alpha < \\frac 12$ and $\\xi$\ndenotes the space-time white noise.\n', ""Global dynamics for the two-dimensional stochastic nonlinear wave\n  equations   We study global-in-time dynamics of the stochastic nonlinear wave equations\n(SNLW) with an additive space-time white noise forcing, posed on the\ntwo-dimensional torus. Our goal in this paper is two-fold. (i) By introducing a\nhybrid argument, combining the $I$-method in the stochastic setting with a\nGronwall-type argument, we first prove global well-posedness of the\n(renormalized) cubic SNLW in the defocusing case. Our argument yields a double\nexponential growth bound on the Sobolev norm of a solution. (ii) We then study\nthe stochastic damped nonlinear wave equations (SdNLW) in the defocusing case.\nIn particular, by applying Bourgain's invariant measure argument, we prove\nalmost sure global well-posedness of the (renormalized) defocusing SdNLW with\nrespect to the Gibbs measure and invariance of the Gibbs measure.\n""]","[('well posedness stochastic', 0.6560412049293518), ('posedness stochastic', 0.6184170246124268), ('stochastic wave', 0.5814148187637329), ('stochastic nonlinear', 0.5724238753318787), ('additive stochastic forcing', 0.5512230396270752), ('stochastic damped', 0.5441605448722839), ('stochastic forcing', 0.5390094518661499), ('global well posedness', 0.490269273519516), ('dynamics stochastic', 0.48386117815971375), ('local well posedness', 0.45297539234161377)]"
1312,1312,22,1312_wreath products_wreath_symmetric groups_hyperoctahedral groups,"['wreath products', 'wreath', 'symmetric groups', 'hyperoctahedral groups', 'symmetric group s_', 'hyperoctahedral group', 'symmetric group', 'character theory', 'irreducible character', 'classical matrix groups']","['Revisiting Foulkes characters of wreath products   The article is concerned with the Foulkes characters of wreath products,\nwhich are block characters of wreath products, i.e., the positive-definite\nclass functions depending only on the length of its elements. Inspired by the\nworks of Gnedin--Gorin--Kerov and Miller, we introduce two specializations of\nthe Schur--Weyl--Sergeev duality for wreath products and obtain two families of\nblock characters, which provide a decomposition and an alternative construction\nof the Foulkes characters of wreath products. In particular, we give\nalternative proofs on some remarkable properties of the Foulkes characters.\nAlong the way, we show that the Foulkes characters are the extreme rays of the\ncone of the block characters of wreath products and construct the\nrepresentations with traces being the Foulkes characters via the coinvariant\nalgebra of wreath products.\n', 'A Relationship Between Character Values Of Wreath Products And The\n  Symmetric Group   A relation between certain irreducible character values of the\nhyperoctahedral group $B_n$ ($\\mathbb{Z}/2\\mathbb{Z} \\wr S_n$) and the\nsymmetric group $S_{2n}$ was proved by F. L\\""ubeck and D. Prasad in 2021. Their\nproof is algebraic in nature and uses Lie theory. Using combinatorial methods,\nR. Adin and Y. Roichman proved a similar relation between certain character\nvalues of $G\\wr S_n$ and $S_{rn}$, where $G$ is an abelian group of order $r$\n(generalizing the result of L\\""ubeck-Prasad). Using their result, we prove yet\nanother relation between certain irreducible character values of $G\\wr S_n$ and\n$S_{rn}$, where $G$ is an abelian group of order $r$.\n', 'Generalized characters of the generalized symmetric group   We prove that $(\\mathbb{Z}_k \\wr \\mathcal{S}_n \\times \\mathbb{Z}_k \\wr\n\\mathcal{S}_{n-1}, \\text{diag} (\\mathbb{Z}_k \\wr \\mathcal{S}_{n-1}) )$ is a\nsymmetric Gelfand pair, where $\\mathbb{Z}_k \\wr \\mathcal{S}_n$ is the wreath\nproduct of the cyclic group $\\mathbb{Z}_k$ with the symmetric group\n$\\mathcal{S}_n.$ The proof is based on the study of the $\\mathbb{Z}_k \\wr\n\\mathcal{S}_{n-1}$-conjugacy classes of $\\mathbb{Z}_k \\wr \\mathcal{S}_n.$ We\ndefine the generalized characters of $\\mathbb{Z}_k \\wr \\mathcal{S}_n$ using the\nzonal spherical functions of $(\\mathbb{Z}_k \\wr \\mathcal{S}_n \\times\n\\mathbb{Z}_k \\wr \\mathcal{S}_{n-1}, \\text{diag} (\\mathbb{Z}_k \\wr\n\\mathcal{S}_{n-1}) ).$ We show that these generalized characters have\nproperties similar to usual characters. A Murnaghan-Nakayama rule for the\ngeneralized characters of the hyperoctahedral group is presented. The\ngeneralized characters of the symmetric group were first studied by Strahov in\n[7].\n']","[('wreath products', 0.607817530632019), ('wreath', 0.519955575466156), ('symmetric groups', 0.5147580504417419), ('hyperoctahedral groups', 0.5068164467811584), ('symmetric group s_', 0.49100926518440247), ('hyperoctahedral group', 0.47709885239601135), ('symmetric group', 0.46504083275794983), ('character theory', 0.44740086793899536), ('irreducible character', 0.4274132549762726), ('classical matrix groups', 0.4040490984916687)]"
1313,1313,22,1313_mean curvature flows_mean curvature flow_curvature flow existence_curvature flow,"['mean curvature flows', 'mean curvature flow', 'curvature flow existence', 'curvature flow', 'preserving mean curvature', 'solutions mean curvature', 'anisotropic mean curvature', 'mean curvature', 'weighted mean curvature', 'flow convergence']","[""A new varifold solution concept for mean curvature flow: Convergence of\n  the Allen-Cahn equation and weak-strong uniqueness   We propose a new weak solution concept for (two-phase) mean curvature flow\nwhich enjoys both (unconditional) existence and (weak-strong) uniqueness\nproperties. These solutions are evolving varifolds, just as in Brakke's\nformulation, but are coupled to the phase volumes by a simple transport\nequation. First, we show that, in the exact same setup as in Ilmanen's proof\n[J. Differential Geom. 38, 417-461, (1993)], any limit point of solutions to\nthe Allen-Cahn equation is a varifold solution in our sense. Second, we prove\nthat any calibrated flow in the sense of Fischer et al. [arXiv:2003.05478] -\nand hence any classical solution to mean curvature flow - is unique in the\nclass of our new varifold solutions. This is in sharp contrast to the case of\nBrakke flows, which a priori may disappear at any given time and are therefore\nfatally non-unique. Finally, we propose an extension of the solution concept to\nthe multi-phase case which is at least guaranteed to satisfy a weak-strong\nuniqueness principle.\n"", ""On obstacle problem for Brakke's mean curvature flow   We consider the obstacle problem of the weak solution for the mean curvature\nflow, in the sense of Brakke's mean curvature flow. We prove the global\nexistence of the weak solution with obstacles which have $C^{1,1}$ boundaries,\nin two and three space dimensions. To obtain the weak solution, we use the\nAllen-Cahn equation with forcing term.\n"", 'Quantitative convergence of the vectorial Allen-Cahn equation towards\n  multiphase mean curvature flow   Phase-field models such as the Allen-Cahn equation may give rise to the\nformation and evolution of geometric shapes, a phenomenon that may be analyzed\nrigorously in suitable scaling regimes. In its sharp-interface limit, the\nvectorial Allen-Cahn equation with a potential with $N\\geq 3$ distinct minima\nhas been conjectured to describe the evolution of branched interfaces by\nmultiphase mean curvature flow.\n  In the present work, we give a rigorous proof for this statement in two and\nthree ambient dimensions and for a suitable class of potentials: As long as a\nstrong solution to multiphase mean curvature flow exists, solutions to the\nvectorial Allen-Cahn equation with well-prepared initial data converge towards\nmultiphase mean curvature flow in the limit of vanishing interface width\nparameter $\\varepsilon\\searrow 0$. We even establish the rate of convergence\n$O(\\varepsilon^{1/2})$.\n  Our approach is based on the gradient flow structure of the Allen-Cahn\nequation and its limiting motion: Building on the recent concept of ""gradient\nflow calibrations"" for multiphase mean curvature flow, we introduce a notion of\nrelative entropy for the vectorial Allen-Cahn equation with multi-well\npotential. This enables us to overcome the limitations of other approaches,\ne.g. avoiding the need for a stability analysis of the Allen-Cahn operator or\nadditional convergence hypotheses for the energy at positive times.\n']","[('mean curvature flows', 0.7555477619171143), ('mean curvature flow', 0.731328547000885), ('curvature flow existence', 0.7134032249450684), ('curvature flow', 0.6601387858390808), ('preserving mean curvature', 0.6318844556808472), ('solutions mean curvature', 0.5960298776626587), ('anisotropic mean curvature', 0.5795005559921265), ('mean curvature', 0.5695610642433167), ('weighted mean curvature', 0.5480087995529175), ('flow convergence', 0.5061797499656677)]"
1314,1314,22,1314_dynamical degree_dynamical degrees_maps projective_dynamical mordell lang,"['dynamical degree', 'dynamical degrees', 'maps projective', 'dynamical mordell lang', 'dynamical mordell', 'birational self map', 'birational maps', 'algebraic dynamics', 'map projective', 'polynomial automorphisms']","[""Spectral interpretations of dynamical degrees and applications   We prove that dynamical degrees of rational self-maps on projective varieties\ncan be interpreted as spectral radii of naturally defined operators on suitable\nBanach spaces. Generalizing Shokurov's notion of b-divisors, we consider the\nspace of b-classes of higher codimension cycles, and endow this space with\nvarious Banach norms. Building on these constructions, we design a natural\nextension to higher dimensions of the Picard-Manin space introduced by Cantat\nand Boucksom-Favre-Jonsson in the case of surfaces. We prove a version of the\nHodge index theorem, and a surprising compactness result in this Banach space.\nWe use these two theorems to infer a precise control of the sequence of degrees\nof iterates of a map under the assumption that the square of the first\ndynamical degree is strictly larger than the second dynamical degree. As a\nconsequence, we obtain that the dynamical degrees of an automorphism of the\naffine 3-space are all algebraic numbers.\n"", 'Periodic points and arithmetic degrees of certain rational self-maps   Consider a cohomologically hyperbolic birational self-map defined over the\nalgebraic numbers, for example, a birational self-map in dimension two with the\nfirst dynamical degree greater than one, or in dimension three with the first\nand the second dynamical degrees distinct. We give a boundedness result about\nheights of its periodic points. This is motivated by a conjecture of Silverman\nfor polynomial automorphisms of affine spaces. We also study the\nKawaguchi--Silverman conjecture concerning dynamical and arithmetic degrees for\ncertain rational self-maps in dimension two. In particular, we reduce the\nproblem to the dynamical Mordell--Lang conjecture and verify the\nKawaguchi--Silverman conjecture for some new cases. As a byproduct of the\nargument, we show the existence of Zariski dense orbits in these cases.\n', 'Arithmetic degrees and Zariski dense orbits of cohomologically\n  hyperbolic maps   A dominant rational self-map on a projective variety is called\n$p$-cohomologically hyperbolic if the $p$-th dynamical degree is strictly\nlarger than other dynamical degrees. For such a map defined over\n$\\overline{\\mathbb{Q}}$, we study lower bounds of the arithmetic degrees,\nexistence of points with Zariski dense orbit, and finiteness of preperiodic\npoints. In particular, we prove that, if $f$ is an $1$-cohomologically\nhyperbolic map on a smooth projective variety, then (1) the arithmetic degree\nof a $\\overline{\\mathbb{Q}}$-point with generic $f$-orbit is equal to the first\ndynamical degree of $f$; and (2) there are $\\overline{\\mathbb{Q}}$-points with\ngeneric $f$-orbit. Applying our theorem to the recently constructed rational\nmap with transcendental dynamical degree, we confirm that the arithmetic degree\ncan be transcendental.\n']","[('dynamical degree', 0.5078376531600952), ('dynamical degrees', 0.4951143264770508), ('maps projective', 0.49446678161621094), ('dynamical mordell lang', 0.49428337812423706), ('dynamical mordell', 0.4833420217037201), ('birational self map', 0.4790824055671692), ('birational maps', 0.4737319350242615), ('algebraic dynamics', 0.472750186920166), ('map projective', 0.47064968943595886), ('polynomial automorphisms', 0.4651336073875427)]"
1315,1315,22,1315_spatially homogeneous boltzmann_homogeneous boltzmann_boltzmann hard_solutions boltzmann,"['spatially homogeneous boltzmann', 'homogeneous boltzmann', 'boltzmann hard', 'solutions boltzmann', 'boltzmann', 'system boltzmann', 'generalized kac', 'stochastic particle system', 'stochastic particle', 'interacting particles']","['Rate of convergence of the Kac particle system for the Boltzmann\n  equation with hard potentials   In this paper, we prove that the Kac stochastic particle system converges to\nthe weak solution of the spatially homogeneous Boltzmann equation for hard\npotentials and hard spheres. We give, under the initial data with finite\nexponential moment assumption, an explicit rate of propagation of chaos in\nsquared Wasserstein distance with quadratic cost by using a double coupling\ntechnique.\n', 'Grand Canonical Evolution for the Kac Model   We study a model of random colliding particles interacting with an infinite\nreservoir at fixed temperature and chemical potential. Interaction between the\nparticles is modeled via a Kac master equation \\cite{kac}. Moreover, particles\ncan leave the system toward the reservoir or enter the system from the\nreservoir. The system admits a unique steady state given by the Grand Canonical\nEnsemble at temperature $T=\\beta^{-1}$ and chemical potential $\\chi$. We show\nthat any initial state converges exponentially fast to equilibrium by computing\nthe spectral gap of the generator in a suitable $L^2$ space and by showing\nexponential decrease of the relative entropy with respect to the steady state.\nWe also show propagation of chaos and thus the validity of a Boltzmann-Kac type\nequation for the particle density in the infinite system limit.\n', 'Rate of convergence of the Kac-like particle system   In this paper, we consider the Kac stochastic particle system associated to\nthe spatially homogeneous Boltzmann equation for true hard potentials. We\nestablish a rate of propagation of chaos of the particle system to the unique\nsolution of the Boltzmann equation. We use a probabilistic coupling method and\ngive, under suitable assumptions on the initial condition, a rate of\nconvergence of the empirical measure of the particle system to the solution of\nthe Boltzmann equation for this singular interaction.\n']","[('spatially homogeneous boltzmann', 0.6213347911834717), ('homogeneous boltzmann', 0.5885315537452698), ('boltzmann hard', 0.5736212730407715), ('solutions boltzmann', 0.5644494891166687), ('boltzmann', 0.5427930355072021), ('system boltzmann', 0.537993311882019), ('generalized kac', 0.5170602798461914), ('stochastic particle system', 0.512045681476593), ('stochastic particle', 0.4818401634693146), ('interacting particles', 0.4508228302001953)]"
1316,1316,22,1316_boltzmann collision operator_boltzmann collision_spatially homogeneous boltzmann_homogeneous boltzmann,"['boltzmann collision operator', 'boltzmann collision', 'spatially homogeneous boltzmann', 'homogeneous boltzmann', 'boltzmann', 'collisional kinetic equations', 'collisional kinetic', 'galerkin spectral', 'spectral methods', 'fast fourier transform']","['Spectral computation of low probability tails for the homogeneous\n  Boltzmann equation   We apply the spectral-Lagrangian method of Gamba and Tharkabhushanam for\nsolving the homogeneous Boltzmann equation to compute the low probability tails\nof the velocity distribution function, $f$, of a particle species. This method\nis based on a truncation, $Q^{\\operatorname{tr}}(f,f)$, of the Boltzmann\ncollision operator, $Q(f,f)$, whose Fourier transform is given by a weighted\nconvolution. The truncated collision operator models the situation in which two\ncolliding particles ignore each other if their relative speed exceeds a\nthreshold, $g_{\\text{tr}}$. We demonstrate that the choice of truncation\nparameter plays a critical role in the accuracy of the numerical computation of\n$Q$. Significantly, if $g_{\\text{tr}}$ is too large, then accurate numerical\ncomputation of the weighted convolution integral is not feasible, since the\ndecay rate and degree of oscillation of the convolution weighting function both\nincrease as $g_{\\text{tr}}$ increases. We derive an upper bound on the\npointwise error between $Q$ and $Q^{\\text{tr}}$, assuming that both operators\nare computed exactly. This bound provides some additional theoretical\njustification for the spectral-Lagrangian method, and can be used to guide the\nchoice of $g_{\\text{tr}}$ in numerical computations. We then demonstrate how to\nchoose $g_{\\text{tr}}$ and the numerical discretization parameters so that the\ncomputation of the truncated collision operator is a good approximation to $Q$\nin the low probability tails. Finally, for several different initial\nconditions, we demonstrate the feasibility of accurately computing the time\nevolution of the velocity pdf down to probability density levels ranging from\n$10^{-5}$ to $10^{-9}$.\n', 'A fast Fourier spectral method for the linearized Boltzmann collision\n  operator   We introduce a fast Fourier spectral method to compute linearized collision\noperators of the Boltzmann equation for variable hard-sphere gases. While the\nstate-of-the-art method provides a computational cost O(MN^4 log N), with N\nbeing the number of modes in each direction and M being the number of\nquadrature points on a hemisphere, our method reduces the cost to O(N^4 log N),\nremoving the factor M, which could be large in our numerical tests. The method\nis applied in a numerical solver for the steady-state Boltzmann equation with\nquadratic collision operators. Numerical experiments for both spatially\nhomogeneous and inhomogeneous Boltzmann equations have been carried out to test\nthe accuracy and efficiency of our method.\n', 'A fast Petrov-Galerkin spectral method for the multi-dimensional\n  Boltzmann equation using mapped Chebyshev functions   Numerical approximation of the Boltzmann equation presents a challenging\nproblem due to its high-dimensional, nonlinear, and nonlocal collision\noperator. Among the deterministic methods, the Fourier-Galerkin spectral method\nstands out for its relative high accuracy and possibility of being accelerated\nby the fast Fourier transform. However, this method requires a domain\ntruncation which is unphysical since the collision operator is defined in\n$\\mathbb{R}^d$. In this paper, we introduce a Petrov-Galerkin spectral method\nfor the Boltzmann equation in the unbounded domain. The basis functions (both\ntest and trial functions) are carefully chosen mapped Chebyshev functions to\nobtain desired convergence and conservation properties. Furthermore, thanks to\nthe close relationship of the Chebyshev functions and the Fourier cosine\nseries, we are able to construct a fast algorithm with the help of the\nnon-uniform fast Fourier transform (NUFFT). We demonstrate the superior\naccuracy of the proposed method in comparison to the Fourier spectral method\nthrough a series of 2D and 3D examples.\n']","[('boltzmann collision operator', 0.7029457688331604), ('boltzmann collision', 0.6501479148864746), ('spatially homogeneous boltzmann', 0.5576382279396057), ('homogeneous boltzmann', 0.5324821472167969), ('boltzmann', 0.4976397156715393), ('collisional kinetic equations', 0.4807383716106415), ('collisional kinetic', 0.43532535433769226), ('galerkin spectral', 0.43368035554885864), ('spectral methods', 0.4332256615161896), ('fast fourier transform', 0.3790551424026489)]"
1317,1317,22,1317_scaffolds_scaffold_tissue growth_stem cells,"['scaffolds', 'scaffold', 'tissue growth', 'stem cells', 'cell migration', 'tissue', 'tissues', 'cell boundary', 'regeneration', 'microstructure']","['Cell seeding dynamics in a porous scaffold material designed for\n  meniscus tissue regeneration   We study the dynamics of a seeding experiment where a fibrous scaffold\nmaterial is colonized by two types of cell populations. The specific\napplication that we have in mind is related to the idea of meniscus tissue\nregeneration. In order to support the development of a promising replacement\nmaterial, we discuss certain rate equations for the densities of human\nmesenchymal stem cells and chondrocytes and for the production of\ncollagen-containing extracellular matrix. For qualitative studies, we start\nwith a system of ordinary differential equations and refine then the model to\ninclude spatial effects of the underlying nonwoven scaffold structure.\nNumerical experiments as well as a complete set of parameters for future\nbenchmarking are provided.\n', 'Three Dimensional Optimization of Scaffold Porosities for Bone Tissue\n  Engineering   We consider the scaffold design optimization problem associated to the three\ndimensional, time dependent model for scaffold mediated bone regeneration\nconsidered in Dondl et al. (2021). We prove existence of optimal scaffold\ndesigns and present numerical evidence that optimized scaffolds mitigate stress\nshielding effects from exterior fixation of the scaffold at the defect site.\n', 'An in-silico approach to meniscus tissue regeneration: Modeling,\n  numerical simulation, and experimental analysis   We develop a model the dynamics of human mesenchymal stem cells (hMSCs) and\nchondrocytes evolving in a nonwoven polyethylene terephtalate (PET) scaffold\nimpregnated with hyaluron and supplied with a differentiation medium. The\nscaffold and the cells are assumed to be contained in a bioreactor with fluid\nperfusion. The differentiation of hMSCs into chondrocytes favors the production\nof extracellular matrix (ECM) and is influenced by fluid stress. The model\ntakes deformations of ECM and PET scaffold into account. The scaffold structure\nis explicitly included by statistical assessment of the fibre distribution from\nCT images. The effective macroscopic equations are obtained by appropriate\nupscaling from dynamics on lower (microscopic and mesoscopic) scales and\nfeature in the motility terms an explicit cell diffusion tensor encoding the\nassessed anisotropic scaffold structure. Numerical simulations show its\ninfluence on the overall cell and tissue dynamics.\n']","[('scaffolds', 0.4608904719352722), ('scaffold', 0.444563627243042), ('tissue growth', 0.4180130958557129), ('stem cells', 0.37466543912887573), ('cell migration', 0.3577270805835724), ('tissue', 0.3479575216770172), ('tissues', 0.3370587229728699), ('cell boundary', 0.3285180330276489), ('regeneration', 0.31954753398895264), ('microstructure', 0.3027830123901367)]"
1318,1318,22,1318_semidefinite programming relaxations_semidefinite programming_semidefinite programs_semidefinite programs sdps,"['semidefinite programming relaxations', 'semidefinite programming', 'semidefinite programs', 'semidefinite programs sdps', 'semidefinite program sdp', 'sparse semidefinite', 'polynomial optimization', 'polynomial optimization problems', 'programming relaxations', 'sdp relaxations']","['On Positive Duality Gaps in Semidefinite Programming   We present a novel analysis of semidefinite programs (SDPs) with positive\nduality gaps, i.e. different optimal values in the primal and dual problems.\nThese SDPs are extremely pathological, often unsolvable, and also serve as\nmodels of more general pathological convex programs. However, despite their\nallure, they are not well understood even when they have just two variables.\n  We first completely characterize two variable SDPs with positive gaps; in\nparticular, we transform them into a standard form that makes the positive gap\ntrivial to recognize. The transformation is very simple, as it mostly uses\nelementary row operations coming from Gaussian elimination. We next show that\nthe two variable case sheds light on larger SDPs with positive gaps: we present\nSDPs in any dimension in which the positive gap is caused by the same structure\nas in the two variable case. We analyze a fundamental parameter, the {\\em\nsingularity degree} of the duals of our SDPs, and show that it is the largest\nthat can result in a positive gap.\n  We finally generate a library of difficult SDPs with positive gaps (some of\nthese SDPs have only two variables) and present a computational study.\n', 'Sparse convex relaxations in polynomial optimization   We present a novel, general, and unifying point of view on sparse approaches\nto polynomial optimization. Solving polynomial optimization problems to global\noptimality is a ubiquitous challenge in many areas of science and engineering.\nHistorically, different approaches on how to solve nonconvex polynomial\noptimization problems based on convex relaxations have been developed in\ndifferent scientific communities. Here, we introduce the concept of monomial\npatterns. A pattern determines what monomials are to be linked by convex\nconstraints in a convex relaxation of a polynomial optimization problem. This\nconcept helps to understand existing approaches from different schools of\nthought, to develop novel relaxation schemes, and to derive a flexible duality\ntheory, which can be specialized to many concrete situations that have been\nconsidered in the literature. We unify different approaches to polynomial\noptimization including polyhedral approximations, dense semidefinite\nrelaxations, SONC, SAGE, and TSSOS in a self-contained exposition. We also\ncarry out computational experiments to demonstrate the practical advantages of\na flexible usage of pattern-based sparse relaxations of polynomial optimization\nproblems.\n', 'A more efficient reformulation of complex SDP as real SDP   This note proposes a new reformulation of complex semidefinite programs\n(SDPs) as real SDPs. As an application, we present an economical reformulation\nof complex SDP relaxations of complex polynomial optimization problems as real\nSDPs and derive some further reductions by exploiting inner structure of the\ncomplex SDP relaxations. Various numerical examples demonstrate that our new\nreformulation runs significantly faster than the usual popular reformulation.\n']","[('semidefinite programming relaxations', 0.8125048875808716), ('semidefinite programming', 0.7242259979248047), ('semidefinite programs', 0.7135260105133057), ('semidefinite programs sdps', 0.6980262994766235), ('semidefinite program sdp', 0.6794952750205994), ('sparse semidefinite', 0.5860778093338013), ('polynomial optimization', 0.5773838758468628), ('polynomial optimization problems', 0.5656806230545044), ('programming relaxations', 0.5643635988235474), ('sdp relaxations', 0.549170970916748)]"
1319,1319,22,1319_feynman graphs_tensor models_random tensors_tensorial,"['feynman graphs', 'tensor models', 'random tensors', 'tensorial', 'lattice models', 'double scaling limit', 'tensor', 'lattice fermions', 'conformal field theory', 'multi matrix models']","['Combinatorial decompositions for deformed or decorated classes of maps   The perturbative expansion of tensorial field theories in Feynman graphs can\nbe interpreted as weighted generating series of some piecewise linear\nvarieties. This simple fact establishes a link between two a priori distinct\nfields: the combinatorics of discrete manifolds on one hand and tensorial field\ntheories on the other hand. In this thesis, we study different aspects\nrevolving around this connection between combinatorics and field theory. First,\nwe consider constellations model, which generalize maps and their algebraic\nproperties. This makes them suited to probe the b-deformation, a deformation of\nthe algebra of symmetric functions. We will study the constraints satisfied by\nthe generating series of cubical b-deformed constellations. Second, we analyze\nthe double scaling limit of particular tensor models of order 3. For tensor of\norder greater than two, the nature of the 1/N-expansion is qualitatively\ndifferent from the matrix case of order 2. In particular, only the leading\norder graphs are fully characterized. Despite this fact, it is possible to\nidentify graphs of subleading orders contributing to the double scaling limit\nby implementing the scheme decomposition for Feynman graphs of these theories.\nAn analysis of the singularity of the schemes then allows us to give a complete\ncharacterization of the graphs contributing to the double scaling limit.\nFinally, we investigate a particular link between a tensor and a vector field\ntheory which both admit a melonic limit. Namely, we will show that we can\nobtain the vectorial Amit-Roginski model by considering perturbations around a\nclassical solution of the Boulatov model, a tensorial theory. We give\nsufficient conditions on the classical solution so that the effective action\nfor the perturbation around this solution takes the form of the Amit-Roginski\naction.\n', 'Double scaling limit of multi-matrix models at large $D$   In this paper, we study a double scaling limit of two multi-matrix models:\nthe $U(N)^2 \\times O(D)$-invariant model with all quartic interactions and the\nbipartite $U(N) \\times O(D)$-invariant model with tetrahedral interaction ($D$\nbeing here the number of matrices and $N$ being the size of each matrix). Those\nmodels admit a double, large $N$ and large $D$ expansion. While $N$ tracks the\ngenus of the Feynman graphs, $D$ tracks another quantity called the grade. In\nboth models, we rewrite the sum over Feynman graphs at fixed genus and grade as\na finite sum over combinatorial objects called schemes. This is a result of\ncombinatorial nature which remains true in the quantum mechanical setting and\nin quantum field theory. Then we proceed to the double scaling limit at large\n$D$, i.e. for vanishing grade. In particular, we find that the most singular\nschemes, in both models, are the same as those found in Benedetti et al. for\nthe $U(N)^2 \\times O(D)$-invariant model restricted to its tetrahedral\ninteraction. This is a different universality class than in the 1-matrix model\nwhose double scaling is not summable.\n', 'Double scaling limit for the $O(N)^3$-invariant tensor model   We study the double scaling limit of the $O(N)^3$-invariant tensor model,\ninitially introduced in Carrozza and Tanasa, Lett. Math. Phys. (2016). This\nmodel has an interacting part containing two types of quartic invariants, the\ntetrahedric and the pillow one. For the 2-point function, we rewrite the sum\nover Feynman graphs at each order in the $1/N$ expansion as a \\emph{finite}\nsum, where the summand is a function of the generating series of melons and\nchains (a.k.a. ladders). The graphs which are the most singular in the\ncontinuum limit are characterized at each order in the $1/N$ expansion. This\nleads to a double scaling limit which picks up contributions from all orders in\nthe $1/N$ expansion. In contrast with matrix models, but similarly to previous\ndouble scaling limits in tensor models, this double scaling limit is summable.\nThe tools used in order to prove our results are combinatorial, namely a\nthorough diagrammatic analysis of Feynman graphs, as well as an analysis of the\nsingularities of the relevant generating series.\n']","[('feynman graphs', 0.5426022410392761), ('tensor models', 0.493723601102829), ('random tensors', 0.45756766200065613), ('tensorial', 0.45486828684806824), ('lattice models', 0.40431922674179077), ('double scaling limit', 0.3827776312828064), ('tensor', 0.3592602014541626), ('lattice fermions', 0.3465981185436249), ('conformal field theory', 0.3351331651210785), ('multi matrix models', 0.32949477434158325)]"
1320,1320,22,1320_geodesic flows surfaces_geodesic flows_geodesic flow_definite riemannian,"['geodesic flows surfaces', 'geodesic flows', 'geodesic flow', 'definite riemannian', 'riemannian metrics', 'magnetic geodesic', 'riemannian', 'flow riemannian', 'geodesics', 'geodesic']","['Integrable magnetic geodesic flows on 2-surfaces   We study the magnetic geodesic flows on 2-surfaces having an additional first\nintegral which is independent of the Hamiltonian at a fixed energy level. The\nfollowing two cases are considered: when there exists a quadratic in momenta\nintegral, and also the case of a rational in momenta integral with a linear\nnumerator and denominator. In both cases certain semi-Hamiltonian systems of\nPDEs appear. In this paper we construct exact solutions (generally speaking,\nlocal ones) to these systems: in the first case via the generalized hodograph\nmethod, in the second case via the Legendre transformation and the method of\nseparation of variables.\n', 'Complete separation of variables in the geodesic Hamilton--Jacobi\n  equation in four dimensions   We list all metrics of arbitrary signature in four dimensions which admit\ncomplete separation of variables in the Hamilton--Jacobi equation for geodesic\nHamiltonians. There are only ten classes of separable metrics admitting\ncommuting Killing vector fields, indecomposable quadratic conservation laws,\nand coisotropic coordinates. Canonical separable metrics parameterized by\nseveral (up to twelve) arbitrary functions of single coordinates are written\nexplicitly. The full set of independent conservation laws in involution for\neach canonical metrics is also found.\n', 'Complete separation of variables in the geodesic Hamilton-Jacobi\n  equation   We consider a (pseudo)Riemannian manifold of arbitrary dimension. The\nHamilton-Jacobi equation for geodesic Hamiltonian admits complete separation of\nvariables for some (separable) metrics in some (separable) coordinate systems.\nSeparable metrics are very important in mathematics and physics. The St\\""ackel\nproblem is: ``Which metrics admit complete separation of variables in the\ngeodesic Hamilton-Jacobi equation?\'\' This problem was solved for inverse\nmetrics with nonzero diagonal elements, in particular, for positive definite\nRiemannian metrics long ago. However the question is open for indefinite\nmetrics having zeroes on diagonals. We propose the solution. Separable metrics\nare divided into equivalence classes characterised by the number of commuting\nKilling vector fields, quadratic indecomposable conservation laws for\ngeodesics, and the number of coisotropic coordinates. The paper contains\ndetailed proofs, sometimes new, of previous results as well as new cases. As an\nexample, we list all canonical separable metrics in each equivalence class in\ntwo, three, and four dimensions. Thus the St\\""ackel problem is completely\nsolved for metrics of any signature in any number of dimensions.\n']","[('geodesic flows surfaces', 0.6656953692436218), ('geodesic flows', 0.6608524322509766), ('geodesic flow', 0.608967661857605), ('definite riemannian', 0.5753250122070312), ('riemannian metrics', 0.5741053819656372), ('magnetic geodesic', 0.5611377954483032), ('riemannian', 0.5609843730926514), ('flow riemannian', 0.555106520652771), ('geodesics', 0.5490119457244873), ('geodesic', 0.545005202293396)]"
1321,1321,22,1321_legendre symbols_legendre symbol_quadratic residues_determinants,"['legendre symbols', 'legendre symbol', 'quadratic residues', 'determinants', 'quadratic residues modulo', 'determinant', 'jacobi symbol', 'legendre', 'modulo primes', 'equiv pmod4']","['On a determinant involving linear combinations of Legendre symbols   In this paper, we prove a conjecture of the second author by evaluating the\ndeterminant\n  $$\\det\\left[x+\\left(\\frac{i-j}p\\right)+\\left(\\frac ip\\right)y+\\left(\\frac\njp\\right)z+\\left(\\frac{ij}p\\right)w\\right]_{0\\le i,j\\le(p-3)/2}$$\n  for any odd prime $p$, where $(\\frac{\\cdot}p)$ denotes the Legendre symbol.\nIn particular, the determinant is equal to $x$ when $p\\equiv 3\\pmod4$.\n', 'On determinants involving $(\\frac{j+k}p)\\pm(\\frac{j-k}p)$   Let $p=2n+1$ be an odd prime. In this paper, we mainly evaluate determinants\ninvolving $(\\frac {j+k}p)\\pm(\\frac{j-k}p)$, where $(\\frac{\\cdot}p)$ denotes the\nLegendre symbol. When $p\\equiv1\\pmod4$, we determine the characteristic\npolynomials of the matrices\n$$\\left[\\left(\\frac{j+k}p\\right)+\\left(\\frac{j-k}p\\right)\\right]_{1\\le j,k\\le\nn}\\ \\ \\text{and}\\ \\\n\\left[\\left(\\frac{j+k}p\\right)-\\left(\\frac{j-k}p\\right)\\right]_{1\\le j,k\\le\nn},$$ and also establish the general identity \\begin{align*} &\\\n\\left|x+\\left(\\frac{j+k}p\\right)+\\left(\\frac{j-k}p\\right)+\\left(\\frac\njp\\right)y+\\left(\\frac kp\\right)z+\\left(\\frac{jk}p\\right)w\\right|_{1\\le j,k\\le\nn} \\\\=&\\\n(-p)^{(p-5)/4}\\left(\\left(\\frac{p-1}2\\right)^2wx-\\left(\\frac{p-1}2y-1\\right)\\left(\\frac{p-1}2z-1\\right)\\right).\n\\end{align*}\n', 'Problems and results on determinants involving Legendre symbols   In this paper we investigate determinants whose entries are linear\ncombinations of Legendre symbols. We deduce some new results in this direction;\nfor example, we prove that for any prime $p\\equiv3\\pmod4$ we have\n$$\\det\\left[x+\\left(\\frac{j-k}p\\right)+\\left(\\frac jp\\right)-\\left(\\frac\nkp\\right)\\right]_{0\\le j,k\\le(p-1)/2}=4,$$ where $(\\frac{\\cdot}p)$ is the\nLegendre symbol. We also pose many conjectures for further research. For\nexample, for any prime $p>3$ we conjecture that \\begin{align*}&\\\n\\det\\left[\\left(\\frac{j+k}p\\right)+\\left(\\frac{j-k}p\\right)+\\left(\\frac{jk}p\\right)\\right]_{1\\le\nj,k\\le(p-1)/2} \\\\=&\\ \\begin{cases}(\\frac 2p)p^{(p-5)/4}&\\text{if}\\\np\\equiv1\\pmod4, \\\\(-1)^{(h(-p)-1)/2}(1-(2-(\\frac\n2p))h(-p))p^{(p-3)/4}&\\text{if}\\ p\\equiv3\\pmod4, \\end{cases}\\end{align*} where\n$h(-p)$ is the class number of the imaginary quadratic field $\\mathbb\nQ(\\sqrt{-p})$.\n']","[('legendre symbols', 0.47369661927223206), ('legendre symbol', 0.44186174869537354), ('quadratic residues', 0.41702231764793396), ('determinants', 0.3830013573169708), ('quadratic residues modulo', 0.37732720375061035), ('determinant', 0.35088488459587097), ('jacobi symbol', 0.3227823078632355), ('legendre', 0.320977121591568), ('modulo primes', 0.3114337921142578), ('equiv pmod4', 0.30652400851249695)]"
1322,1322,22,1322_apn functions_functions finite field_perfect nonlinear functions_functions generalize,"['apn functions', 'functions finite field', 'perfect nonlinear functions', 'functions generalize', 'power functions', 'functions mathbb', 'functions dimension', 'functions', 'functions two', 'apn']","['Equivalences of biprojective almost perfect nonlinear functions   Two important problems on almost perfect nonlinear (APN) functions are the\nenumeration and equivalence problems. In this paper, we solve these two\nproblems for any biprojective APN function family by introducing a strong group\ntheoretic method for those functions. Roughly half of the known APN families of\nfunctions on even dimensions are biprojective. By our method, we settle the\nequivalence problem for all known biprojective APN functions. Furthermore, we\ngive a new family of biprojective APN functions. Using our method, we count the\nnumber of inequivalent APN functions in all known biprojective APN families and\nshow that the new family found in this paper gives exponentially many new\ninequivalent APN functions. Quite recently, the Taniguchi family of APN\nfunctions was shown to contain an exponential number of inequivalent APN\nfunctions by Kaspers and Zhou (J. Cryptol. 34 (1), 2021) which improved their\nprevious count (J. Comb. Th. A 186, 2022) for the Zhou-Pott family. Our group\ntheoretic method substantially simplifies the work required for proving those\nresults and provides a generic natural method for every family in the large\nsuper-class of biprojective APN functions that contains these two family along\nwith many others.\n', 'Two new infinite classes of APN functions   In this paper, we present two new infinite classes of APN functions over\n$\\gf_{{2^{2m}}}$ and $\\gf_{{2^{3m}}}$, respectively. The first one is with\nbivariate form and obtained by adding special terms,\n$\\sum(a_ix^{2^i}y^{2^i},b_ix^{2^i}y^{2^i})$, to a known class of APN functions\nby {G{\\""{o}}lo{\\v{g}}lu} over $\\gf_{{2^m}}^2$. The second one is of the form\n$L(z)^{2^m+1}+vz^{2^m+1}$ over $\\gf_{{2^{3m}}}$, which is a generalization of\none family of APN functions by Bracken et al. [Cryptogr. Commun. 3 (1): 43-53,\n2011].\n  The calculation of the CCZ-invariants $\\Gamma$-ranks of our APN classes over\n$\\gf_{{2^8}}$ or $\\gf_{{2^9}}$ indicates that they are CCZ-inequivalent to all\nknown infinite families of APN functions. Moreover, by using the code\nisomorphism, we see that our first APN family covers an APN function over\n$\\gf_{{2^8}}$ obtained through the switching method by Edel and Pott in [Adv.\nMath. Commun. 3 (1): 59-81, 2009].\n', 'More infinite classes of APN-like Power Functions   In the literature, there are many APN-like functions that generalize the APN\nproperties or are similar to APN functions, e.g. locally-APN functions, 0-APN\nfunctions or those with boomerang uniformity 2.\n  In this paper, we study the problem of constructing infinite classes of\nAPN-like but not APN power functions.\n  For one thing, we find two infinite classes of locally-APN but not APN power\nfunctions over $\\gf_{2^{2m}}$ with $m$ even, i.e.,\n$\\mathcal{F}_1(x)=x^{j(2^m-1)}$ with $\\gcd(j,2^m+1)=1$ and\n$\\mathcal{F}_2(x)=x^{j(2^m-1)+1}$ with $j = \\frac{2^m+2}{3}$. As far as the\nauthors know, our infinite classes of locally-APN but not APN functions are the\nonly two discovered in the last eleven years. Moreover, we also prove that this\ninfinite class $\\mathcal{F}_1$ is not only with the optimal boomerang\nuniformity $2$, but also has an interesting property that its differential\nuniformity is strictly greater than its boomerang uniformity. For another\nthing, using the multivariate method, including the above infinite class\n$\\mathcal{F}_1$, we construct seven new infinite classes of 0-APN but not APN\npower functions.\n']","[('apn functions', 0.5426712036132812), ('functions finite field', 0.39944860339164734), ('perfect nonlinear functions', 0.3858422338962555), ('functions generalize', 0.3736523687839508), ('power functions', 0.3726445436477661), ('functions mathbb', 0.363490492105484), ('functions dimension', 0.35743293166160583), ('functions', 0.3547179698944092), ('functions two', 0.32355576753616333), ('apn', 0.3051314353942871)]"
1323,1323,22,1323_magnetic skyrmions_skyrmions_skyrmion_dimensional magnetic,"['magnetic skyrmions', 'skyrmions', 'skyrmion', 'dimensional magnetic', 'theory magnetic', 'dimensional chiral', 'two dimensional magnetic', 'models magnetic', 'magnetic systems', 'magnetic']","['Higher-dimensional magnetic Skyrmions   We propose a generalization of the theory of magnetic Skyrmions in chiral\nmagnets in two dimensions to a higher-dimensional theory with magnetic\nSkyrmions in three dimensions and an $S^3$ target space, requiring a\n4-dimensional magnetization vector. A physical realization of our theory could\nbe made using a synthetic dimension, recently promoted and realized in\ncondensed matter physics. In the simplest incarnation of the theory, we find a\nSkyrmion and a sphaleron - the latter being an unstable soliton. Including also\nthe Skyrme term in the theory enriches the spectrum to a small metastable\nSkyrmion, an unstable sphaleron and a large stable Skyrmion.\n', 'Unraveling the role of dipolar versus Dzyaloshinskii-Moriya interaction\n  in stabilizing compact magnetic skyrmions   Magnetic skyrmions have been the subject of extensive experimental studies in\nferromagnetic thin films and multilayers, revealing a diversity in their size,\nstability and internal structure. While the orthodox skyrmion theory focuses on\nthe Dzyaloshinskii-Moryia interaction (DMI) and neglects higher-order energy\nterms, it is becoming clear that the full stray field energy needs to be taken\ninto account to understand these recent observations. Here we present a\nmicromagnetic study based on rigorous mathematical analysis which allows to\naccount for the full stray field energy in the thin film and low DMI regime. In\nthis regime, the skyrmion profile is close to a Belavin-Polyakov profile, which\nyields analytical expressions for the equilibrium skyrmion radius and energy.\nThe obtained formulas provide a clear identification of Dzyaloshinskii-Moryia\nand long-range dipolar interactions as two physical mechanisms determining\nskyrmion size and stability, a consideration of importance for the optimization\nof skyrmion characteristics for spintronic applications.\n', 'Chiral skyrmions of large radius   We study the structure of an axially symmetric magnetic skyrmion in a\nferromagnet with the Dzyaloshinskii-Moriya interaction. We examine the regime\nof large skyrmions and we identify rigorously the critical value of the\ndimensionless parameter at which the skyrmion radius diverges to infinity,\nwhile the skyrmion energy converges to zero. This critical value coincides with\nthe expected transition point from the uniform phase, which accommodates the\nskyrmion as an excited state, to the helical phase, which has negative energy.\nWe give the profile field at the skyrmion core, its outer field, and the\nintermediate field at the skyrmion domain wall. Moreover, we derive an explicit\nformula for the leading asymptotic behavior of the energy as well as the\nleading term and first asymptotic correction for the value of the critical\nparameter. The key leading to the results is a parity theorem that utilizes\nexact formulae for the asymptotic behavior of the solutions of the static\nLandau-Lifshitz equation centered at the skyrmion domain wall. The skyrmion\nenergy is shown to be an odd function of the radius and the dimensionless\nparameter to be an even function.\n']","[('magnetic skyrmions', 0.8185010552406311), ('skyrmions', 0.5983206033706665), ('skyrmion', 0.561012864112854), ('dimensional magnetic', 0.4633198082447052), ('theory magnetic', 0.455990731716156), ('dimensional chiral', 0.4305287301540375), ('two dimensional magnetic', 0.42910581827163696), ('models magnetic', 0.41547268629074097), ('magnetic systems', 0.40437179803848267), ('magnetic', 0.36758503317832947)]"
1324,1324,22,1324_conjugacy classes finite_maximal cyclic subgroups_finite group prime_classes finite group,"['conjugacy classes finite', 'maximal cyclic subgroups', 'finite group prime', 'classes finite group', 'number conjugacy classes', 'finite groups whose', 'finite group whose', 'conjugacy classes', 'finite groups', 'metacyclic groups']","['Conjugacy classes of maximal cyclic subgroups of metacyclic $p$-groups   In this paper, we set $\\eta (G)$ to be the number of conjugacy classes of\nmaximal cyclic subgroups of a finite group $G$. We compute $\\eta (G)$ for all\nmetacyclic $p$-groups. We show that if $G$ is a metacyclic $p$-group of order\n$p^n$ that is not dihedral, generalized quaternion, or semi-dihedral, then\n$\\eta (G) \\ge n-2$, and we determine when equality holds.\n', 'Conjugacy classes of maximal cyclic subgroups   In this paper, we set $\\eta (G)$ to be the number of conjugacy classes of\nmaximal cyclic subgroups of $G$. We consider $\\eta$ and direct and semi-direct\nproducts. We characterize the normal subgroups $N$ so that $\\eta (G/N) = \\eta\n(G)$. We set $G^- = \\{ g \\in G \\mid \\langle g \\rangle {\\rm ~is~not\n~maximal~cyclic} \\}$. We show if $\\langle G^- \\rangle < G$, then $G/\\langle G^-\n\\rangle$ is either (1) an elementary abelian $p$-group for some prime $p$, (2)\na Frobenius group whose Frobenius kernel is a $p$-group of exponent $p$ and a\nFrobenius complement has order $q$ for distinct primes $p$ and $q$, or (3)\nisomorphic to $A_5$.\n', 'Conjugacy classes of maximal cyclic subgroups and nilpotence class of\n  $p$-groups   In this paper, we set $\\eta (G)$ to be the number of conjugacy classes of\nmaximal cyclic subgroups of $G$. We prove that if $G$ is a $p$-group of order\n$p^n$ and nilpotence class $l$, then $\\eta (G)$ is bounded below by a linear\nfunction in $n/l$.\n']","[('conjugacy classes finite', 0.5897799134254456), ('maximal cyclic subgroups', 0.5842790007591248), ('finite group prime', 0.54985111951828), ('classes finite group', 0.5440731048583984), ('number conjugacy classes', 0.5287788510322571), ('finite groups whose', 0.5264379382133484), ('finite group whose', 0.5249985456466675), ('conjugacy classes', 0.4997871220111847), ('finite groups', 0.49832552671432495), ('metacyclic groups', 0.47990652918815613)]"
1325,1325,22,1325_tridiagonal matrices_range matrix_numerical ranges_numerical range,"['tridiagonal matrices', 'range matrix', 'numerical ranges', 'numerical range', 'matrix pencils', 'properties numerical', 'tridiagonal', 'boundary numerical range', 'matrices constant', 'joint numerical range']","['The numerical range of some periodic tridiagonal operators is the convex\n  hull of the numerical ranges of two finite matrices   In this paper we prove a conjecture stated by the first two authors\nestablishing the closure of the numerical range of a certain class of\n$n+1$-periodic tridiagonal operators as the convex hull of the numerical ranges\nof two tridiagonal $(n+1) \\times (n+1)$ matrices. Furthermore, when $n+1$ is\nodd, we show that the size of such matrices simplifies to $\\frac{n}{2}+1$.\n', ""The convex algebraic geometry of higher-rank numerical ranges   The higher-rank numerical range is a convex compact set generalizing the\nclassical numerical range of a square complex matrix, first appearing in the\nstudy of quantum error correction. We will discuss some of the real algebraic\nand convex geometry of these sets, including a generalization of Kippenhahn's\ntheorem, and describe an algorithm to explicitly calculate the higher-rank\nnumerical range of a given matrix.\n"", 'Low-dimensional reciprocal matrices with elliptical components of their\n  Kippenhahn curves   By definition, reciprocal matrices are tridiagonal $n$-by-$n$ matrices $A$\nwith constant main diagonal and such that $a_{i,i+1}a_{i+1,i}=1$ for\n$i=1,\\ldots,n-1$. For $n\\leq 6$, we establish criteria under which the\nnumerical range generating curves (also called Kippenhahn curves) of such\nmatrices consist of elliptical components only. As a corollary, we also provide\na complete description of higher-rank numerical ranges when the criteria are\nmet.\n']","[('tridiagonal matrices', 0.5874282121658325), ('range matrix', 0.5096392035484314), ('numerical ranges', 0.4991524815559387), ('numerical range', 0.46854856610298157), ('matrix pencils', 0.43810704350471497), ('properties numerical', 0.4329955279827118), ('tridiagonal', 0.4211953282356262), ('boundary numerical range', 0.4199807643890381), ('matrices constant', 0.4135749638080597), ('joint numerical range', 0.4004402756690979)]"
1326,1326,22,1326_hodge theory_hodge modules_singularities hypersurfaces_mixed hodge modules,"['hodge theory', 'hodge modules', 'singularities hypersurfaces', 'mixed hodge modules', 'hodge filtration', 'hodge module', 'singular varieties', 'local cohomology', 'cohomology smooth projective', 'complex algebraic variety']","['Differential Forms and Hodge Structures on Singular Varieties   We compare a couple of notions of differential form on singular complex\nalgebraic varieties, and relate them to the outermost associated graded spaces\nof the Hodge filtration of ordinary and intersection cohomology. In particular,\nwe introduce and study singularities, that we call quasi-rational, which are\nnormal and such that for all p, the zeroth cohomology sheaf of the complex of\nDu Bois p-forms is isomorphic to the direct image of p-forms from a\ndesingularization. We show that an isolated singularity is rational if and only\nif it is quasi-rational, Du Bois, and certain Hodge numbers of the local mixed\nHodge structures vanish.\n', 'Higher Du Bois and higher rational singularities of hypersurfaces   In this note, we give several equivalent characterizations of higher Du Bois\nand higher rational singularities in the context of globally defined\nhypersurfaces. As a key input, we characterize these singularities using the\nHodge filtration on the vanishing cycle mixed Hodge module. As an application,\nwe indicate a homological criterion for detecting higher Du Bois and higher\nrational hypersurface singularities, formulated in terms of the spectral\nHirzebruch-Milnor characteristic classes.\n', 'Hodge filtration on local cohomology, Du Bois complex, and local\n  cohomological dimension   We study the Hodge filtration on the local cohomology sheaves of a smooth\ncomplex algebraic variety along a closed subscheme Z in terms of log\nresolutions, and derive applications regarding the local cohomological\ndimension, the Du Bois complex, local vanishing, and reflexive differentials\nassociated to Z.\n']","[('hodge theory', 0.6459312438964844), ('hodge modules', 0.6121277213096619), ('singularities hypersurfaces', 0.6098394393920898), ('mixed hodge modules', 0.5856873393058777), ('hodge filtration', 0.5837414264678955), ('hodge module', 0.5786190629005432), ('singular varieties', 0.5734727382659912), ('local cohomology', 0.5671151280403137), ('cohomology smooth projective', 0.5367129445075989), ('complex algebraic variety', 0.5283597111701965)]"
1327,1327,22,1327_bifurcation_ginzburg landau equations_modulation equations_traveling wave solutions,"['bifurcation', 'ginzburg landau equations', 'modulation equations', 'traveling wave solutions', 'modulation theory', 'stable modes', 'stability periodic', 'periodic traveling', 'nonlinear stability', 'landau system']","['Modulating traveling fronts for the Swift-Hohenberg equation in the case\n  of an additional conservation law   We consider the one-dimensional Swift-Hohenberg equation coupled to a\nconservation law. As a parameter increases the system undergoes a Turing\nbifurcation. We study the dynamics near this bifurcation. First, we show that\nstationary, periodic solutions bifurcate from a homogeneous ground state.\nSecond, we construct modulating traveling fronts which model an invasion of the\nunstable ground state by the periodic solutions. This provides a mechanism of\npattern formation for the studied system. The existence proof uses center\nmanifold theory for a reduction to a finite-dimensional problem. This is\npossible despite the presence of infinitely many imaginary eigenvalues for\nvanishing bifurcation parameter since the eigenvalues leave the imaginary axis\nwith different velocities if the parameter increases. Furthermore, compared to\nnon-conservative systems, we address new difficulties arising from an\nadditional neutral mode at Fourier wave number $k=0$ by exploiting that the\namplitude of the conserved variable is small compared to the other variables.\n', 'Modulating traveling fronts in a dispersive Swift-Hohenberg equation\n  coupled to an additional conservation law   We consider a one-dimensional Swift-Hohenberg equation coupled to a\nconservation law, where both equations contain additional dispersive terms\nbreaking the reflection symmetry $x \\mapsto -x$. This system exhibits a Turing\ninstability and we study the dynamics close to the onset of this instability.\nFirst, we show that periodic traveling waves bifurcate from a homogeneous\nground state. Second, fixing the bifurcation parameter close to the onset of\ninstability, we construct modulating traveling fronts, which capture the\nprocess of pattern-formation by modeling the transition from the homogeneous\nground state to the periodic traveling wave through an invading front. The\nexistence proof is based on center manifold reduction to a finite-dimensional\nsystem. Here, the dimension of the center manifold depends on the relation\nbetween the spreading speed of the invading modulating front and the linear\ngroup velocities of the system. Due to the broken reflection symmetry, the\ncoefficients in the reduced equation are genuinely complex. Therefore, the main\nchallenge is the construction of persistent heteroclinic connections on the\ncenter manifold, which correspond to modulating traveling fronts in the full\nsystem.\n', 'Geometric blow-up of a dynamic Turing instability in the Swift-Hohenberg\n  equation   We present a rigorous analysis of the slow passage through a Turing\nbifurcation in the Swift-Hohenberg equation using a novel approach based on\ngeometric blow-up. We show that the formally derived multiple scales ansatz\nwhich is known from classical modulation theory can be adapted for use in the\nfast-slow setting, by reformulating it as a blow-up transformation. This leads\nto dynamically simpler modulation equations posed in the blown-up space, via a\nformal procedure which directly extends the established approach to the\ntime-dependent setting. The modulation equations take the form of\nnon-autonomous Ginzburg-Landau equations, which can be analysed within the\nblow-up. The asymptotics of solutions in weighted Sobelev spaces are given in\ntwo different cases: (i) A symmetric case featuring a delayed loss of\nstability, and (ii) A second case in which the symmetry is broken by a source\nterm. In order to characterise the dynamics of the Swift-Hohenberg equation\nitself we derive rigorous estimates on the error of the dynamic modulation\napproximation. These estimates are obtained by bounding weak solutions to an\nevolution equation for the error which is also posed in the blown-up space.\nUsing the error estimates obtained, we are able to infer the asymptotics of a\nlarge class of solutions to the dynamic Swift-Hohenberg equation. We provide\nrigorous asymptotics for solutions in both cases (i) and (ii). We also prove\nthe existence of the delayed loss of stability in the symmetric case (i), and\nprovide a lower bound for the delay time.\n']","[('bifurcation', 0.4923364818096161), ('ginzburg landau equations', 0.47131332755088806), ('modulation equations', 0.4503796398639679), ('traveling wave solutions', 0.443011999130249), ('modulation theory', 0.4304755926132202), ('stable modes', 0.3844392001628876), ('stability periodic', 0.3828141987323761), ('periodic traveling', 0.3825601041316986), ('nonlinear stability', 0.3816104829311371), ('landau system', 0.38121646642684937)]"
1328,1328,22,1328_shrinkage estimators_covariance matrix estimation_shrinkage estimator_covariance matrix estimator,"['shrinkage estimators', 'covariance matrix estimation', 'shrinkage estimator', 'covariance matrix estimator', 'covariance estimation', 'matrix estimator', 'covariance estimators', 'high dimensional covariance', 'optimal covariance', 'covariance estimator']","['Analysis of a multi-target linear shrinkage covariance estimator   Multi-target linear shrinkage is an extension of the standard single-target\nlinear shrinkage for covariance estimation. We combine several constant\nmatrices - the targets - with the sample covariance matrix. We derive the\noracle and a \\textit{bona fide} multi-target linear shrinkage estimator with\nexact and empirical mean. In both settings, we proved its convergence towards\nthe oracle under Kolmogorov asymptotics. Finally, we show empirically that it\noutperforms other standard estimators in various situations.\n', 'Ledoit-Wolf linear shrinkage with unknown mean   This work addresses large dimensional covariance matrix estimation with\nunknown mean. The empirical covariance estimator fails when dimension and\nnumber of samples are proportional and tend to infinity, settings known as\nKolmogorov asymptotics. When the mean is known, Ledoit and Wolf (2004) proposed\na linear shrinkage estimator and proved its convergence under those\nasymptotics. To the best of our knowledge, no formal proof has been proposed\nwhen the mean is unknown. To address this issue, we propose to extend the\nlinear shrinkage and its convergence properties to translation-invariant\nestimators. We expose four estimators respecting those conditions, proving\ntheir properties. Finally, we show empirically that a new estimator we propose\noutperforms other standard estimators.\n', 'A Geometric Unification of Distributionally Robust Covariance\n  Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set   The state-of-the-art methods for estimating high-dimensional covariance\nmatrices all shrink the eigenvalues of the sample covariance matrix towards a\ndata-insensitive shrinkage target. The underlying shrinkage transformation is\neither chosen heuristically - without compelling theoretical justification - or\noptimally in view of restrictive distributional assumptions. In this paper, we\npropose a principled approach to construct covariance estimators without\nimposing restrictive assumptions. That is, we study distributionally robust\ncovariance estimation problems that minimize the worst-case Frobenius error\nwith respect to all data distributions close to a nominal distribution, where\nthe proximity of distributions is measured via a divergence on the space of\ncovariance matrices. We identify mild conditions on this divergence under which\nthe resulting minimizers represent shrinkage estimators. We show that the\ncorresponding shrinkage transformations are intimately related to the\ngeometrical properties of the underlying divergence. We also prove that our\nrobust estimators are efficiently computable and asymptotically consistent and\nthat they enjoy finite-sample performance guarantees. We exemplify our general\nmethodology by synthesizing explicit estimators induced by the\nKullback-Leibler, Fisher-Rao, and Wasserstein divergences. Numerical\nexperiments based on synthetic and real data show that our robust estimators\nare competitive with state-of-the-art estimators.\n']","[('shrinkage estimators', 0.6906833648681641), ('covariance matrix estimation', 0.6484031677246094), ('shrinkage estimator', 0.6456658244132996), ('covariance matrix estimator', 0.6010959148406982), ('covariance estimation', 0.581056535243988), ('matrix estimator', 0.5783295035362244), ('covariance estimators', 0.577317476272583), ('high dimensional covariance', 0.5336562991142273), ('optimal covariance', 0.5319583415985107), ('covariance estimator', 0.5246384143829346)]"
1329,1329,22,1329_quasiconformal mappings_quasiconformal maps_quasiconformal mapping_quasiconformal map,"['quasiconformal mappings', 'quasiconformal maps', 'quasiconformal mapping', 'quasiconformal map', 'quasiconformality', 'conformal mappings', 'quasiconformal', 'mappings uniformly', 'mappings unit disk', 'quasiregular']","['Sharp Pointwise Contraction of Mappings with Integrable Distortion Which\n  Are Quasiconformal in a Disk   We consider quasiconformal mappings of the unit disk that have a planar\nextension which have $p$-integrable distortion. In this paper, we establish a\nbound for the modulus of continuity for the inverse mapping and show sharpness\nof this bound. Furthermore, we also obtain bounds for the compression\nmultifractal spectra of such mappings.\n', 'Stretching and Rotation of Planar Quasiconformal Mappings on a Line   In this article, we examine stretching and rotation of planar quasiconformal\nmappings on a line. We show that for almost every point on the line, the set of\ncomplex stretching exponents (describing stretching and rotation jointly) is\ncontained in the disk $ \\overline{B}(1/(1-k^4),k^2/(1-k^4))$. This yields a\nquadratic improvement over the known optimal estimate for general sets of\nHausdorff dimension $1$. Our proof is based on holomorphic motions and\nestimates for dimensions of quasicircles. We also give a lower bound for the\ndimension of the image of a $1$-dimensional subset of a line under a\nquasiconformal mapping.\n', 'On mappings of finite distortion that are quasiconformal in the unit\n  disk   We study quasiconformal mappings of the unit disk that have planar extension\nwith controlled distortion. For these mappings we prove a bound for the modulus\nof continuity of the inverse map, which somewhat surprisingly is almost as good\nas for global quasiconformal maps. Furthermore, we give examples which improve\nthe known bounds for the three point property of generalized quasidisks.\nFinally, we establish optimal regularity of such maps when the image of the\nunit disk has cusp type singularities.\n']","[('quasiconformal mappings', 0.7325902581214905), ('quasiconformal maps', 0.7211609482765198), ('quasiconformal mapping', 0.7198257446289062), ('quasiconformal map', 0.7038951516151428), ('quasiconformality', 0.607265055179596), ('conformal mappings', 0.5998618602752686), ('quasiconformal', 0.5863876342773438), ('mappings uniformly', 0.4589303731918335), ('mappings unit disk', 0.4485873281955719), ('quasiregular', 0.4476410448551178)]"
1330,1330,22,1330_maximal lyapunov_lyapunov functions_maximal lyapunov exponent_lyapunov,"['maximal lyapunov', 'lyapunov functions', 'maximal lyapunov exponent', 'lyapunov', 'compute lyapunov', 'dynamical systems', 'semidefinite programming', 'polynomial systems', 'positively invariant sets', 'local asymptotic stability']","['Finding positively invariant sets and proving exponential stability of\n  limit cycles using Sum-of-Squares decompositions   The dynamics of many systems from physics, economics, chemistry, and biology\ncan be modelled through polynomial functions. In this paper, we provide a\ncomputational means to find positively invariant sets of polynomial dynamical\nsystems by using semidefinite programming to solve sum-of-squares (SOS)\nprogrammes. With the emergence of SOS programmes, it is possible to efficiently\nsearch for Lyapunov functions that guarantee stability of polynomial systems.\nYet, SOS computations often fail to find functions, such that the conditions\nhold in the entire state space. We show here that restricting the SOS\noptimisation to specific domains enables us to obtain positively invariant\nsets, thus facilitating the analysis of the dynamics by considering separately\neach positively invariant set. In addition, we go beyond classical Lyapunov\nstability analysis and use SOS decompositions to computationally implement\nsufficient positivity conditions that guarantee existence, uniqueness, and\nexponential stability of a limit cycle. Importantly, this approach is\napplicable to systems of any dimension and, thus, goes beyond classical methods\nthat are restricted to two-dimensional phase space. We illustrate our different\nresults with applications to classical systems, such as the van der Pol\noscillator, the Fitzhugh-Nagumo neuronal equation, and the Lorenz system.\n', 'A Converse Sum of Squares Lyapunov Function for Outer Approximation of\n  Minimal Attractor Sets of Nonlinear Systems   Many dynamical systems described by nonlinear ODEs are unstable. Their\nassociated solutions do not converge towards an equilibrium point, but rather\nconverge towards some invariant subset of the state space called an attractor\nset. For a given ODE, in general, the existence, shape and structure of the\nattractor sets of the ODE are unknown. Fortunately, the sublevel sets of\nLyapunov functions can provide bounds on the attractor sets of ODEs. In this\npaper we propose a new Lyapunov characterization of attractor sets that is well\nsuited to the problem of finding the minimal attractor set. We show our\nLyapunov characterization is non-conservative even when restricted to\nSum-of-Squares (SOS) Lyapunov functions. Given these results, we propose a SOS\nprogramming problem based on determinant maximization that yields an SOS\nLyapunov function whose 1-sublevel set has minimal volume, is an attractor set\nitself, and provides an optimal outer approximation of the minimal attractor\nset of the ODE. Several numerical examples are presented including the Lorenz\nattractor and Van-der-Pol oscillator.\n', 'Converse Lyapunov Functions and Converging Inner Approximations to\n  Maximal Regions of Attraction of Nonlinear Systems   This paper considers the problem of approximating the ""maximal"" region of\nattraction (the set that contains all asymptotically stable sets) of any given\nset of locally exponentially stable nonlinear Ordinary Differential Equations\n(ODEs) with a sufficiently smooth vector field. Given a locally exponential\nstable ODE with a differentiable vector field, we show that there exists a\nglobally Lipschitz continuous converse Lyapunov function whose 1-sublevel set\nis equal to the maximal region of attraction of the ODE. We then propose a\nsequence of d-degree Sum-of-Squares (SOS) programming problems that yields a\nsequence of polynomials that converges to our proposed converse Lyapunov\nfunction uniformly from above in the L1 norm. We show that each member of the\nsequence of 1-sublevel sets of the polynomial solutions to our proposed\nsequence of SOS programming problems are certifiably contained inside the\nmaximal region of attraction of the ODE, and moreover, we show that this\nsequence of sublevel sets converges to the maximal region of attraction of the\nODE with respect to the volume metric. We provide numerical examples of\nestimations of the maximal region of attraction for the Van der Pol oscillator\nand a three dimensional servomechanism.\n']","[('maximal lyapunov', 0.5822150707244873), ('lyapunov functions', 0.5737036466598511), ('maximal lyapunov exponent', 0.5380414128303528), ('lyapunov', 0.5288004875183105), ('compute lyapunov', 0.48694056272506714), ('dynamical systems', 0.4610110819339752), ('semidefinite programming', 0.45540711283683777), ('polynomial systems', 0.41603654623031616), ('positively invariant sets', 0.41398128867149353), ('local asymptotic stability', 0.41300317645072937)]"
1331,1331,22,1331_wasserstein spaces_jacobi bellman equations_stochastic hamilton jacobi_wasserstein space,"['wasserstein spaces', 'jacobi bellman equations', 'stochastic hamilton jacobi', 'wasserstein space', 'continuous viscosity solutions', 'notion viscosity', 'wasserstein space probability', 'comparison principle viscosity', 'unique viscosity', 'viscosity theory']","['Optimal control problem for reflected McKean-Vlasov SDEs   This work investigates the optimal control problem for reflected\nMcKean-Vlasov SDEs and the viscosity solutions to Hamilton-Jacobi-Bellman(HJB)\nequations on the Wasserstein space in terms of intrinsic derivative. It follows\nfrom the flow property of reflected McKean-Vlasov SDEs that the dynamic\nprogramming principle holds. Applying the decoupling method and the heat kernel\nestimates for parabolic equations, we show that the value function is a\nviscosity solution to an appropriate HJB equation on the Wasserstein space,\nwhere the characterization of absolutely continuous curves on the Wasserstein\nspace by the continuity equations plays an important role. To establish the\nuniqueness of viscosity solution, we generalize the construction of a distance\nlike function initiated in Burzoni et al.(SICON, 2020) to the Wasserstein space\nover multidimensional space and show its effectiveness to cope with HJB\nequations in terms of intrinsic derivative on the Wasserstein space.\n', 'Hamilton-Jacobi-Bellman Equations in the Wasserstein Space for the\n  Optimal Control of the Kushner-Stratonovich Equation   This paper develops a comparison theorem for viscosity solutions of a new\nclass of Hamilton-Jacobi-Bellman (HJB) equations, which is used to solve the\nseparated problem governed by the K-S equation in the Wasserstein space. A\ndistinctive feature of these HJB equations is the simultaneous presence of\nvariational and Lions derivatives, an inevitable consequence of a nonzero\nobservation function. Moreover, the presence of state-dependent correlated\nnoise adds further complexity to the analysis, making the proof of the\ncomparison theorem more challenging. The core proof strategy for the comparison\ntheorem is to introduce a novel adaptation of the doubling variables argument,\nspecifically tailored to tackle the challenges posed by the Wasserstein space.\nTo this end, we construct an entirely new bivariate functional that combines\nviscosity sub/supsolutions, a smooth gauge-type function, and two Gaussian\nregularized entropy penalizations. The gauge-type function compensates for the\nnon-differentiability (in the Lions sense) of the 2-Wasserstein distance, while\nthe entropy penalizations ensure that the maximal point of the functional is\nwell-behaved. Another major contribution of this paper is the derivation of the\nsecond-order variational and Lions derivatives of the gauge-type function and\nentropy functional, which are crucial for dealing with the second-order HJB\nequation. Meanwhile, the simple structure and pleasing regularity of these\nderivatives make the methodologies developed in this paper applicable within a\nwider range of theoretical settings. This paper gives the first result\nconcerning the uniqueness of viscosity solutions for second-order HJB equations\nwith variational derivatives in the Wasserstein space.\n', ""Viscosity solutions to HJB equations associated with optimal control\n  problem for McKean-Vlasov SDEs   This work concerns the optimal control problem for McKean-Vlasov SDEs. In\norder to characterize the value function, we develop the viscosity solution\ntheory for Hamilton-Jacobi-Bellman (HJB) equations on the Wasserstein space\nusing Mortensen's derivative. In particular, a comparison principle for\nviscosity solution is established. Our approach is based on Borwein-Preiss\nvariational principle to overcome the loss of compactness for bounded sets in\nthe Wasserstein space.\n""]","[('wasserstein spaces', 0.5425454378128052), ('jacobi bellman equations', 0.5308088064193726), ('stochastic hamilton jacobi', 0.5284684896469116), ('wasserstein space', 0.5151724219322205), ('continuous viscosity solutions', 0.5015142560005188), ('notion viscosity', 0.48510831594467163), ('wasserstein space probability', 0.47943681478500366), ('comparison principle viscosity', 0.4725894033908844), ('unique viscosity', 0.46973085403442383), ('viscosity theory', 0.4690140187740326)]"
1332,1332,22,1332_interacting bosons_many body quantum_quantum dynamics_lieb robinson bound,"['interacting bosons', 'many body quantum', 'quantum dynamics', 'lieb robinson bound', 'lieb robinson bounds', 'quantum many body', 'interactions quantum', 'quantum information', 'body quantum', 'interacting boson']","[""On Lieb-Robinson bounds for a class of continuum fermions   We consider the quantum dynamics of a many-fermion system in $\\mathbb R^d$\nwith an ultraviolet regularized pair interaction as previously studied in [M.\nGebert, B. Nachtergaele, J. Reschke, and R. Sims, Ann. Henri Poincar\\'e 21.11\n(2020)]. We provide a Lieb-Robinson bound under substantially relaxed\nassumptions on the potentials. We also improve the associated one-body\nLieb-Robinson bound on $L^2$-overlaps to an almost ballistic one (i.e., an\nalmost linear light cone) under the same relaxed assumptions. Applications\ninclude the existence of the infinite-volume dynamics and clustering of ground\nstates in the presence of a spectral gap. We also develop a fermionic continuum\nnotion of conditional expectation and use it to approximate time-evolved\nfermionic observables by local ones, which opens the door to other applications\nof the Lieb-Robinson bounds.\n"", 'Lieb-Robinson bounds imply locality of interactions   Discrete lattice models are a cornerstone of quantum many-body physics. They\narise as effective descriptions of condensed matter systems and\nlattice-regularized quantum field theories. Lieb-Robinson bounds imply that if\nthe degrees of freedom at each lattice site only interact locally with each\nother, correlations can only propagate with a finite group velocity through the\nlattice, similarly to a light cone in relativistic systems. Here we show that\nLieb-Robinson bounds are equivalent to the locality of the interactions: a\nsystem with k-body interactions fulfills Lieb-Robinson bounds in exponential\nform if and only if the underlying interactions decay exponentially in space.\nIn particular, our result already follows from the behavior of two-point\ncorrelation functions for single-site observables and generalizes to different\ndecay behaviours as well as fermionic lattice models. As a side-result, we thus\nfind that Lieb-Robinson bounds for single-site observables imply Lieb-Robinson\nbounds for bounded observables with arbitrary support.\n', 'Hierarchy of linear light cones with long-range interactions   In quantum many-body systems with local interactions, quantum information and\nentanglement cannot spread outside of a linear light cone, which expands at an\nemergent velocity analogous to the speed of light. Local operations at\nsufficiently separated spacetime points approximately commute -- given a\nmany-body state, $\\mathcal{O}_x(t) \\mathcal{O}_y |\\psi\\rangle \\approx\n\\mathcal{O}_y\\mathcal{O}_x(t) |\\psi\\rangle$ with arbitrarily small errors -- so\nlong as $|x-y|\\gtrsim vt$, where $v$ is finite. Yet most non-relativistic\nphysical systems realized in nature have long-range interactions: two degrees\nof freedom separated by a distance $r$ interact with potential energy $V(r)\n\\propto 1/r^{\\alpha}$. In systems with long-range interactions, we rigorously\nestablish a hierarchy of linear light cones: at the same $\\alpha$, some quantum\ninformation processing tasks are constrained by a linear light cone while\nothers are not. In one spatial dimension, this linear light cone exists for\nevery many-body state when $\\alpha>3$ (Lieb-Robinson light cone); for a typical\nstate chosen uniformly at random from the Hilbert space when\n$\\alpha>\\frac{5}{2}$ (Frobenius light cone); for every state of a\nnon-interacting system when $\\alpha>2$ (free light cone). These bounds apply to\ntime-dependent systems and are optimal up to subalgebraic improvements. Our\ntheorems regarding the Lieb-Robinson and free light cones -- and their\ntightness -- also generalize to arbitrary dimensions. We discuss the\nimplications of our bounds on the growth of connected correlators and of\ntopological order, the clustering of correlations in gapped systems, and the\ndigital simulation of systems with long-range interactions. In addition, we\nshow that universal quantum state transfer, as well as many-body quantum chaos,\nare bounded by the Frobenius light cone, and therefore are poorly constrained\nby all Lieb-Robinson bounds.\n']","[('interacting bosons', 0.515842080116272), ('many body quantum', 0.5096616148948669), ('quantum dynamics', 0.5060975551605225), ('lieb robinson bound', 0.49920395016670227), ('lieb robinson bounds', 0.49586841464042664), ('quantum many body', 0.48431944847106934), ('interactions quantum', 0.4515560269355774), ('quantum information', 0.4494304955005646), ('body quantum', 0.4483448565006256), ('interacting boson', 0.44305646419525146)]"
1333,1333,22,1333_stiefel manifolds_stiefel manifold_riemannian geodesics_riemannian metrics,"['stiefel manifolds', 'stiefel manifold', 'riemannian geodesics', 'riemannian metrics', 'geodesic distances', 'curvature bounds', 'geodesic distance', 'bounds geodesic', 'family riemannian metrics', 'geodesics respect']","['On the Injectivity Radius of the Stiefel Manifold: Numerical\n  investigations and an explicit construction of a cut point at short distance   Arguably, geodesics are the most important geometric objects on a\ndifferentiable manifold. They describe candidates for shortest paths and are\nguaranteed to be unique shortest paths when the starting velocity stays within\nthe so-called injectivity radius of the manifold. In this work, we investigate\nthe injectivity radius of the Stiefel manifold under the canonical metric. The\nStiefel manifold $St(n,p)$ is the set of rectangular matrices of dimension\n$n$-by-$p$ with orthogonal columns, sometimes also called the space of\northogonal $p$-frames in $\\mathbb{R}^n$. Using a standard curvature argument,\nRentmeesters has shown in 2013 that the injectivity radius of the Stiefel\nmanifold is bounded by $\\sqrt{\\frac{4}{5}}\\pi$. It is an open question, whether\nthis bound is sharp. With the definition of the injectivity radius via cut\npoints of geodesics, we gain access to the information of the injectivity\nradius by investigating geodesics. More precisely, we consider the behavior of\nspecial variations of geodesics, called Jacobi fields. By doing so, we are able\nto present an explicit example of a cut point. In addition, since the\ntheoretical analysis of geodesics for cut points and especially conjugate\npoints as a type of cut points is difficult, we investigate the question of the\nsharpness of the bound by means of numerical experiments.\n', 'The ultimate upper bound on the injectivity radius of the Stiefel\n  manifold   We exhibit conjugate points on the Stiefel manifold endowed with any member\nof the family of Riemannian metrics introduced by H\\""uper et al. (2021). This\nfamily contains the well-known canonical and Euclidean metrics. An upper bound\non the injectivity radius of the Stiefel manifold in the considered metric is\nthen obtained as the minimum between the length of the geodesic along which the\npoints are conjugate and the length of certain geodesic loops. Numerical\nexperiments support the conjecture that the obtained upper bound is in fact\nequal to the injectivity radius.\n', 'Computing the Riemannian logarithm on the Stiefel manifold: metrics,\n  methods and performance   We address the problem of computing Riemannian normal coordinates on the\nreal, compact Stiefel manifold of orthogonal frames. The Riemannian normal\ncoordinates are based on the so-called Riemannian exponential and the\nRiemannian logarithm maps and enable to transfer almost any computational\nprocedure to the realm of the Stiefel manifold. To compute the Riemannian\nlogarithm is to solve the (local) geodesic endpoint problem. Instead of\nrestricting the consideration to geodesics with respect to a single selected\nmetric, we consider a family of Riemannian metrics introduced by H\\""uper,\nMarkina and Silva-Leite that includes the Euclidean and the canonical metric as\nprominent examples.\n  As main contributions, we provide (1) a unified, structured, reduced formula\nfor the Stiefel geodesics for the complete family of metrics, (2) a unified\nmethod to tackle the geodesic endpoint problem, (3) an improvement of the\nexisting Riemannian log map under the canonical metric. The findings are\nillustrated by means of numerical examples, where the novel algorithms prove to\nbe the most efficient methods known to this date.\n']","[('stiefel manifolds', 0.6447060704231262), ('stiefel manifold', 0.6381477117538452), ('riemannian geodesics', 0.6271457076072693), ('riemannian metrics', 0.6248188018798828), ('geodesic distances', 0.6116846203804016), ('curvature bounds', 0.5753660798072815), ('geodesic distance', 0.5706130862236023), ('bounds geodesic', 0.5672222971916199), ('family riemannian metrics', 0.5334445238113403), ('geodesics respect', 0.5246877670288086)]"
1334,1334,22,1334_sample complexity widetilde_efficient learning_polynomial time learning_complexity widetilde,"['sample complexity widetilde', 'efficient learning', 'polynomial time learning', 'complexity widetilde', 'super polynomial time', 'halfspaces', 'agnostic learning', 'sample computational complexity', 'halfspace', 'efficient algorithms']","[""Improved Hardness Results for Learning Intersections of Halfspaces   We show strong (and surprisingly simple) lower bounds for weakly learning\nintersections of halfspaces in the improper setting. Strikingly little is known\nabout this problem. For instance, it is not even known if there is a\npolynomial-time algorithm for learning the intersection of only two halfspaces.\nOn the other hand, lower bounds based on well-established assumptions (such as\napproximating worst-case lattice problems or variants of Feige's 3SAT\nhypothesis) are only known (or are implied by existing results) for the\nintersection of super-logarithmically many halfspaces [KS09,KS06,DSS16]. With\nintersections of fewer halfspaces being only ruled out under less standard\nassumptions [DV21] (such as the existence of local pseudo-random generators\nwith large stretch). We significantly narrow this gap by showing that even\nlearning $\\omega(\\log \\log N)$ halfspaces in dimension $N$ takes\nsuper-polynomial time under standard assumptions on worst-case lattice problems\n(namely that SVP and SIVP are hard to approximate within polynomial factors).\nFurther, we give unconditional hardness results in the statistical query\nframework. Specifically, we show that for any $k$ (even constant), learning $k$\nhalfspaces in dimension $N$ requires accuracy $N^{-\\Omega(k)}$, or\nexponentially many queries -- in particular ruling out SQ algorithms with\npolynomial accuracy for $\\omega(1)$ halfspaces. To the best of our knowledge\nthis is the first unconditional hardness result for learning a super-constant\nnumber of halfspaces.\n  Our lower bounds are obtained in a unified way via a novel connection we make\nbetween intersections of halfspaces and the so-called parallel pancakes\ndistribution [DKS17,BLPR19,BRST21] that has been at the heart of many lower\nbound constructions in (robust) high-dimensional statistics in the past few\nyears.\n"", 'Near-Optimal Statistical Query Hardness of Learning Halfspaces with\n  Massart Noise   We study the problem of PAC learning halfspaces with Massart noise. Given\nlabeled samples $(x, y)$ from a distribution $D$ on $\\mathbb{R}^{d} \\times \\{\n\\pm 1\\}$ such that the marginal $D_x$ on the examples is arbitrary and the\nlabel $y$ of example $x$ is generated from the target halfspace corrupted by a\nMassart adversary with flipping probability $\\eta(x) \\leq \\eta \\leq 1/2$, the\ngoal is to compute a hypothesis with small misclassification error. The best\nknown $\\mathrm{poly}(d, 1/\\epsilon)$-time algorithms for this problem achieve\nerror of $\\eta+\\epsilon$, which can be far from the optimal bound of\n$\\mathrm{OPT}+\\epsilon$, where $\\mathrm{OPT} = \\mathbf{E}_{x \\sim D_x}\n[\\eta(x)]$. While it is known that achieving $\\mathrm{OPT}+o(1)$ error requires\nsuper-polynomial time in the Statistical Query model, a large gap remains\nbetween known upper and lower bounds.\n  In this work, we essentially characterize the efficient learnability of\nMassart halfspaces in the Statistical Query (SQ) model. Specifically, we show\nthat no efficient SQ algorithm for learning Massart halfspaces on\n$\\mathbb{R}^d$ can achieve error better than $\\Omega(\\eta)$, even if\n$\\mathrm{OPT} = 2^{-\\log^{c} (d)}$, for any universal constant $c \\in (0, 1)$.\nFurthermore, when the noise upper bound $\\eta$ is close to $1/2$, our error\nlower bound becomes $\\eta - o_{\\eta}(1)$, where the $o_{\\eta}(1)$ term goes to\n$0$ when $\\eta$ approaches $1/2$. Our results provide strong evidence that\nknown learning algorithms for Massart halfspaces are nearly best possible,\nthereby resolving a longstanding open problem in learning theory.\n', 'Learning General Halfspaces with General Massart Noise under the\n  Gaussian Distribution   We study the problem of PAC learning halfspaces on $\\mathbb{R}^d$ with\nMassart noise under the Gaussian distribution. In the Massart model, an\nadversary is allowed to flip the label of each point $\\mathbf{x}$ with unknown\nprobability $\\eta(\\mathbf{x}) \\leq \\eta$, for some parameter $\\eta \\in\n[0,1/2]$. The goal is to find a hypothesis with misclassification error of\n$\\mathrm{OPT} + \\epsilon$, where $\\mathrm{OPT}$ is the error of the target\nhalfspace. This problem had been previously studied under two assumptions: (i)\nthe target halfspace is homogeneous (i.e., the separating hyperplane goes\nthrough the origin), and (ii) the parameter $\\eta$ is strictly smaller than\n$1/2$. Prior to this work, no nontrivial bounds were known when either of these\nassumptions is removed. We study the general problem and establish the\nfollowing:\n  For $\\eta <1/2$, we give a learning algorithm for general halfspaces with\nsample and computational complexity\n$d^{O_{\\eta}(\\log(1/\\gamma))}\\mathrm{poly}(1/\\epsilon)$, where $\\gamma\n=\\max\\{\\epsilon, \\min\\{\\mathbf{Pr}[f(\\mathbf{x}) = 1],\n\\mathbf{Pr}[f(\\mathbf{x}) = -1]\\} \\}$ is the bias of the target halfspace $f$.\nPrior efficient algorithms could only handle the special case of $\\gamma =\n1/2$. Interestingly, we establish a qualitatively matching lower bound of\n$d^{\\Omega(\\log(1/\\gamma))}$ on the complexity of any Statistical Query (SQ)\nalgorithm.\n  For $\\eta = 1/2$, we give a learning algorithm for general halfspaces with\nsample and computational complexity $O_\\epsilon(1) d^{O(\\log(1/\\epsilon))}$.\nThis result is new even for the subclass of homogeneous halfspaces; prior\nalgorithms for homogeneous Massart halfspaces provide vacuous guarantees for\n$\\eta=1/2$. We complement our upper bound with a nearly-matching SQ lower bound\nof $d^{\\Omega(\\log(1/\\epsilon))}$, which holds even for the special case of\nhomogeneous halfspaces.\n']","[('sample complexity widetilde', 0.47056785225868225), ('efficient learning', 0.4581303596496582), ('polynomial time learning', 0.4304278790950775), ('complexity widetilde', 0.4287586212158203), ('super polynomial time', 0.3994310200214386), ('halfspaces', 0.3982412815093994), ('agnostic learning', 0.396646112203598), ('sample computational complexity', 0.3938601613044739), ('halfspace', 0.39191538095474243), ('efficient algorithms', 0.3537011444568634)]"
1335,1335,22,1335_distributed estimation_distributed sensor_robust distributed_distributed target,"['distributed estimation', 'distributed sensor', 'robust distributed', 'distributed target', 'tolerant distributed', 'distributed single', 'sensor networks', 'distributed linear', 'proposed distributed', 'wireless sensor networks']","['On the Design of Resilient Distributed Single Time-Scale Estimators: A\n  Graph-Theoretic Approach   Distributed estimation in interconnected systems has gained increasing\nattention due to its relevance in diverse applications such as sensor networks,\nautonomous vehicles, and cloud computing. In real practice, the sensor network\nmay suffer from communication and/or sensor failures. This might be due to\ncyber-attacks, faults, or environmental conditions. Distributed estimation\nresilient to such conditions is the topic of this paper. By representing the\nsensor network as a graph and exploiting its inherent structural properties, we\nintroduce novel techniques that enhance the robustness of distributed\nestimators. As compared to the literature, the proposed estimator (i) relaxes\nthe network connectivity of most existing single time-scale estimators and (ii)\nreduces the communication load of the existing double time-scale estimators by\navoiding the inner consensus loop.\n  On the other hand, the sensors might be subject to faults or attacks,\nresulting in biased measurements. Removing these sensor data may result in\nobservability loss. Therefore, we propose resilient design on the definitions\nof $q$-node-connectivity and $q$-link-connectivity, which capture robust\nstrong-connectivity under link or sensor node failure. By proper design of the\nsensor network, we prove Schur stability of the proposed distributed estimation\nprotocol under failure of up to $q$ sensors or $q$ communication links.\n', ""Distributed Target Tracking based on Localization with Linear\n  Time-Difference-of-Arrival Measurements: A Delay-Tolerant Networked\n  Estimation Approach   This paper considers target tracking based on a beacon signal's\ntime-difference-of-arrival (TDOA) to a group of cooperating sensors. The\nsensors receive a reflected signal from the target where the time-of-arrival\n(TOA) renders the distance information. The existing approaches include: (i)\nclassic centralized solutions which gather and process the target data at a\ncentral unit, (ii) distributed solutions which assume that the target data is\nobservable in the dense neighborhood of each sensor (to be filtered locally),\nand (iii) double time-scale distributed methods with high rates of\ncommunication/consensus over the network. This work, in order to reduce the\nnetwork connectivity in (i)-(ii) and communication rate in (iii), proposes a\ndistributed single time-scale technique, which can also handle heterogeneous\nconstant data-exchange delays over the static sensor network. This work assumes\nonly distributed observability (in contrast to local observability in some\nexisting works categorized in (ii)), i.e., the target is observable globally\nover a (strongly) connected network. The (strong) connectivity further allows\nfor survivable network and $q$-redundant observer design. Each sensor locally\nshares information and processes the received data in its immediate\nneighborhood via local linear-matrix-inequalities (LMI) feedback gains to\nensure tracking error stability. The same gain matrix works in the presence of\nheterogeneous delays with no need of redesigning algorithms. Since most\nexisting distributed estimation scenarios are linear (based on consensus), many\nworks use linearization of the existing nonlinear TDOA measurement models where\nthe output matrix is a function of the target position.\n"", ""Linear TDOA-based Measurements for Distributed Estimation and Localized\n  Tracking   We propose a linear time-difference-of-arrival (TDOA) measurement model to\nimprove \\textit{distributed} estimation performance for localized target\ntracking. We design distributed filters over sparse (possibly large-scale)\ncommunication networks using consensus-based data-fusion techniques. The\nproposed distributed and localized tracking protocols considerably reduce the\nsensor network's required connectivity and communication rate. We, further,\nconsider $\\kappa$-redundant observability and fault-tolerant design in case of\nlosing communication links or sensor nodes. We present the minimal conditions\non the remaining sensor network (after link/node removal) such that the\ndistributed observability is still preserved and, thus, the sensor network can\ntrack the (single) maneuvering target. The motivation is to reduce the\ncommunication load versus the processing load, as the computational units are,\nin general, less costly than the communication devices. We evaluate the\ntracking performance via simulations in MATLAB.\n""]","[('distributed estimation', 0.6190983653068542), ('distributed sensor', 0.5789650082588196), ('robust distributed', 0.5251644253730774), ('distributed target', 0.47093501687049866), ('tolerant distributed', 0.42654579877853394), ('distributed single', 0.422395259141922), ('sensor networks', 0.41518285870552063), ('distributed linear', 0.3828139901161194), ('proposed distributed', 0.3750705122947693), ('wireless sensor networks', 0.3711223900318146)]"
1336,1336,22,1336_category coherent sheaves_coherent sheaves_quasi coherent sheaves_derived stacks,"['category coherent sheaves', 'coherent sheaves', 'quasi coherent sheaves', 'derived stacks', 'coherent sheaf', 'sheaves modules', 'algebraic stacks', 'derived category coherent', 'deligne mumford stacks', 'mumford stacks']","['Brauer Spaces of Spectral Algebraic Stacks   We study the question of whether the Brauer group is isomorphic to the\ncohomological one in spectral algebraic geometry. For this, we prove the\ncompact generation of the derived category of twisted sheaves for quasi-compact\nspectral algebraic stacks with quasi-affine diagonal, which admit a\nquasi-finite presentation; in particular, we obtain the compact generation of\nthe unbounded derived category of quasi-coherent sheaves and the existence of\ncompact perfect complexes with prescribed support for such stacks. We also\nstudy the relationship between derived and spectral algebraic stacks, so that\nour results can be extended to the setting of derived algebraic geometry.\n', ""Equivalences of derived categories of sheaves on tame stacks   Building on Olander's work on algebraic spaces, we prove Orlov's\nrepresentability theorem relating fully faithful functors and Fourier--Mukai\ntransforms between the bounded derived category of coherent sheaves to the case\nof smooth, proper, and tame algebraic stacks. This extends previous results of\nKawamata for Deligne--Mumford stacks with generically trivial stabilizers and\nprojective coarse moduli spaces.\n"", 'A generalized Bondal-Orlov full faithfulness criterion for\n  Deligne-Mumford stacks   Let $X$, $Y$ be smooth projective varieties over $\\mathbf{C}$. Let $K$ be a\nbounded complex of coherent sheaves on $X\\times Y$ and let $\\Phi_K \\colon\n\\mathsf{D}^b_{\\mathsf{Coh}}(X) \\to \\mathsf{D}^b_{\\mathsf{Coh}}(Y)$ be the\nresulting Fourier-Mukai functor. There is a well-known criterion due to\nBondal-Orlov for $\\Phi_K$ to be fully faithful. This criterion was recently\nextended to smooth Deligne-Mumford stacks with projective coarse moduli schemes\nby Lim-Polischuk. We extend this to all smooth, proper Deligne-Mumford stacks\nover arbitrary fields of characteristic $0$. Along the way, we establish a\nnumber of foundational results for bounded derived categories of proper and\ntame morphisms of noetherian algebraic stacks (e.g., coherent duality).\n']","[('category coherent sheaves', 0.623276948928833), ('coherent sheaves', 0.6012413501739502), ('quasi coherent sheaves', 0.6009378433227539), ('derived stacks', 0.5871747732162476), ('coherent sheaf', 0.5800610780715942), ('sheaves modules', 0.567659854888916), ('algebraic stacks', 0.5628852844238281), ('derived category coherent', 0.5421924591064453), ('deligne mumford stacks', 0.5360465049743652), ('mumford stacks', 0.5231937170028687)]"
1337,1337,22,1337_chern cohomology_bott chern cohomology_sheaves complex_chern weil theory,"['chern cohomology', 'bott chern cohomology', 'sheaves complex', 'chern weil theory', 'coherent sheaves', 'holomorphic vector bundles', 'chern forms', 'theory chern', 'chern classes', 'bundles terms']","['The Hodge Chern character of holomorphic connections as a map of\n  simplicial presheaves   We define a map of simplicial presheaves, the Chern character, that assigns\nto every sequence of composable non connection preserving isomorphisms of\nvector bundles with holomorphic connections an appropriate sequence of\nholomorphic forms. We apply this Chern character map to the Cech nerve of a\ngood cover of a complex manifold and assemble the data by passing to the\ntotalization to obtain a map of simplicial sets. In simplicial degree 0, this\nmap gives a formula for the Chern character of a bundle in terms of the\nclutching functions. In simplicial degree 1, this map gives a formula for the\nChern character of bundle maps. In each simplicial degree beyond 1, these\ninvariants, defined in terms of the transition functions, govern the\ncompatibilities between the invariants assigned in previous simplicial degrees.\nIn addition to this, we also apply this Chern character to complex Lie\ngroupoids to obtain invariants of bundles on them in terms of the simplicial\ndata. For group actions, these invariants land in suitable complexes\ncalculating various Hodge equivariant cohomologies. In contrast, the de Rham\nChern character formula involves additional terms and will appear in a sequel\npaper. In a sense, these constructions build on a point of view of\n""characteristic classes in terms of transition functions"" advocated by Raoul\nBott, which has been addressed over the years in various forms and degrees,\nconcerning the existence of formulae for the Hodge and de Rham characteristic\nclasses of bundles solely in terms of their clutching functions.\n', 'Cech - de Rham Chern character on the stack of holomorphic vector\n  bundles   We provide a formula for the Chern character of a holomorphic vector bundle\nin the hyper-cohomology of the de Rham complex of holomorphic sheaves on a\ncomplex manifold. This Chern character can be thought of as a completion of the\nChern character in Hodge cohomology obtained as the trace of the exponential of\nthe Atiyah class, which is \\v{C}ech closed, to one that is \\v{C}ech-Del closed.\nSuch a completion is a key step toward lifting O\'Brian-Toledo-Tong invariants\nof coherent sheaves from Hodge cohomology to de Rham cohomology. An alternate\napproach toward the same end goal, instead using simplicial differential forms\nand Green complexes, can be found in Hosgood\'s works [Ho1, Ho2]. In the\nalgebraic setting, and more generally for K\\""{a}hler manifolds, where Hodge and\nde Rham cohomologies agree, such extensions are not necessary, whereas in the\nnon-K\\""{a}hler, or equivariant settings the two theories differ. We provide our\nformulae as a map of simplicial presheaves, which readily extend the results to\nthe equivariant setting and beyond. This paper can be viewed as a sequel to\n[GMTZ1] which covered such a discussion in Hodge cohomology. As an aside, we\ngive a conceptual understanding of how formulas obtained by Bott and Tu for\nChern classes using transition functions and those from Chern-Weil theory using\nconnections, are part of a natural unifying story.\n', ""Chern character for infinity vector bundles   Coherent sheaves on general complex manifolds do not necessarily have\nresolutions by finite complexes of vector bundles. However D. Toledo and Y.L.L.\nTong showed that one can resolve coherent sheaves by objects analogous to chain\ncomplexes of holomorphic vector bundles, whose cocycle relations are governed\nby a coherent infinite system of homotopies. In the modern language such\nobjects are obtained by the infinity-sheafification of the simplicial presheaf\nof chain complexes of holomorphic vector bundles. We define a Chern character\nas a map of simplicial presheaves, whereby the connected components of its\nsheafification recovers the Chern character of Toledo and Tong. As a\nconsequence our construction extends Toledo Tong and O'Brian Toledo Tong's\ndefinition of the Chern character to the settings of stacks and in particular\nthe equivariant setting. Even in the classical setting of complex manifolds,\nthe induced maps on higher homotopy groups provide new Chern-Simons, and higher\nChern-Simons, invariants for coherent sheaves.\n""]","[('chern cohomology', 0.6940022110939026), ('bott chern cohomology', 0.6342923045158386), ('sheaves complex', 0.629148006439209), ('chern weil theory', 0.5976986885070801), ('coherent sheaves', 0.5831664800643921), ('holomorphic vector bundles', 0.5789926052093506), ('chern forms', 0.5764456391334534), ('theory chern', 0.5598992109298706), ('chern classes', 0.555092453956604), ('bundles terms', 0.5324931144714355)]"
1338,1338,22,1338_iwasawa theory_iwasawa invariants_number spanning trees_towers finite,"['iwasawa theory', 'iwasawa invariants', 'number spanning trees', 'towers finite', 'trees finite', 'spanning trees', 'iwasawa module', 'cayley graphs', 'multigraphs', 'iwasawa lambda']","[""An analogue of Kida's formula in graph theory   Let $\\ell$ be a rational prime and let $p:Y\\rightarrow X$ be a Galois cover\nof finite graphs whose Galois group is a finite $\\ell$-group. Consider a\n$\\mathbb{Z}_{\\ell}$-tower above $X$ and its pullback along $p$. Assuming that\nall the graphs in the pullback are connected, one obtains a\n$\\mathbb{Z}_{\\ell}$-tower above $Y$. Under the assumption that the Iwasawa\n$\\mu$-invariant of the tower above $X$ vanishes, we prove a formula relating\nthe Iwasawa $\\lambda$-invariant of the $\\mathbb{Z}_{\\ell}$-tower above $X$ to\nthe Iwasawa $\\lambda$-invariant of the pullback. This formula is analogous to\nKida's formula in classical Iwasawa theory. We present an application to the\nstudy of structural properties of certain noncommutative pro-$\\ell$ towers of\ngraphs, based on an analogy with classical results of Cuoco on the growth of\nIwasawa invariants in $\\mathbb{Z}_\\ell^2$-extensions of number fields. Our\ninvestigations are illustrated by explicit examples.\n"", 'On abelian $\\ell$-towers of multigraphs II   Let $\\ell$ be a rational prime. Previously, abelian $\\ell$-towers of\nmultigraphs were introduced which are analogous to\n$\\mathbb{Z}_{\\ell}$-extensions of number fields. It was shown that for a\ncertain class of towers of bouquets, the growth of the $\\ell$-part of the\nnumber of spanning trees behaves in a predictable manner (analogous to a\nwell-known theorem of Iwasawa for $\\mathbb{Z}_{\\ell}$-extensions of number\nfields). In this paper, we give a generalization to a broader class of regular\nabelian $\\ell$-towers of bouquets than was originally considered. To carry this\nout, we observe that certain shifted Chebyshev polynomials are members of a\ncontinuously parametrized family of power series with coefficients in\n$\\mathbb{Z}_{\\ell}$ and then study the special value at $s=1$ of the\nArtin-Ihara $L$-function $\\ell$-adically.\n', ""Iwasawa theory for branched $\\mathbb{Z}_{p}$-towers of finite graphs   We initiate the study of Iwasawa theory for branched $\\mathbb{Z}_{p}$-towers\nof finite connected graphs. These towers are more general than what have been\nstudied so far, since the morphisms of graphs involved are branched covers, a\nparticular kind of harmonic morphisms of graphs. We prove an analogue of\nIwasawa's asymptotic class number formula for the $p$-part of the number of\nspanning trees in this setting. Moreover, we find an explicit generator for the\ncharacteristic ideal of the torsion Iwasawa module governing the growth of the\n$p$-part of the number of spanning trees in such towers.\n""]","[('iwasawa theory', 0.5489915609359741), ('iwasawa invariants', 0.5354607701301575), ('number spanning trees', 0.49809640645980835), ('towers finite', 0.47379961609840393), ('trees finite', 0.4379121661186218), ('spanning trees', 0.42207640409469604), ('iwasawa module', 0.4109755754470825), ('cayley graphs', 0.4051332175731659), ('multigraphs', 0.39377227425575256), ('iwasawa lambda', 0.3849349021911621)]"
1339,1339,22,1339_subspace optimization_subspace methods_subspace algorithms_free optimization,"['subspace optimization', 'subspace methods', 'subspace algorithms', 'free optimization', 'random subspace', 'stochastic optimization random', 'iterative minimization', 'free optimization dfo', 'derivative free optimization', 'large scale optimization']","['$Q$-fully Quadratic Modeling and its Application in a Random Subspace\n  Derivative-free Method   Model-based derivative-free optimization (DFO) methods are an important class\nof DFO methods that are known to struggle with solving high-dimensional\noptimization problems. Recent research has shown that incorporating random\nsubspaces into model-based DFO methods has the potential to improve their\nperformance on high-dimensional problems. However, most of the current\ntheoretical and practical results are based on linear approximation models due\nto the complexity of quadratic approximation models. This paper proposes a\nrandom subspace trust-region algorithm based on quadratic approximations.\nUnlike most of its precursors, this algorithm does not require any special form\nof objective function. We study the geometry of sample sets, the error bounds\nfor approximations, and the quality of subspaces. In particular, we provide a\ntechnique to construct $Q$-fully quadratic models, which is easy to analyze and\nimplement. We present an almost-sure global convergence result of our algorithm\nand give an upper bound on the expected number of iterations to find a\nsufficiently small gradient. We also develop numerical experiments to compare\nthe performance of our algorithm using both linear and quadratic approximation\nmodels. The numerical results demonstrate the strengths and weaknesses of using\nquadratic approximations.\n', 'Stochastic trust-region algorithm in random subspaces with convergence\n  and expected complexity analyses   This work proposes a framework for large-scale stochastic derivative-free\noptimization (DFO) by introducing STARS, a trust-region method based on\niterative minimization in random subspaces. This framework is both an\nalgorithmic and theoretical extension of an algorithm for stochastic\noptimization with random models (STORM). Moreover, STARS achieves scalability\nby minimizing interpolation models that approximate the objective in\nlow-dimensional affine subspaces, thus significantly reducing per-iteration\ncosts in terms of function evaluations and yielding strong performance on\nlarge-scale stochastic DFO problems. The user-determined dimension of these\nsubspaces, when the latter are defined, for example, by the columns of\nso-called Johnson--Lindenstrauss transforms, turns out to be independent of the\ndimension of the problem. For convergence purposes, both a particular quality\nof the subspace and the accuracies of random function estimates and models are\nrequired to hold with sufficiently high, but fixed, probabilities. Using\nmartingale theory under the latter assumptions, an almost sure global\nconvergence of STARS to a first-order stationary point is shown, and the\nexpected number of iterations required to reach a desired first-order accuracy\nis proved to be similar to that of STORM and other stochastic DFO algorithms,\nup to constants.\n', ""Krylov Cubic Regularized Newton: A Subspace Second-Order Method with\n  Dimension-Free Convergence Rate   Second-order optimization methods, such as cubic regularized Newton methods,\nare known for their rapid convergence rates; nevertheless, they become\nimpractical in high-dimensional problems due to their substantial memory\nrequirements and computational costs. One promising approach is to execute\nsecond-order updates within a lower-dimensional subspace, giving rise to\nsubspace second-order methods. However, the majority of existing subspace\nsecond-order methods randomly select subspaces, consequently resulting in\nslower convergence rates depending on the problem's dimension $d$. In this\npaper, we introduce a novel subspace cubic regularized Newton method that\nachieves a dimension-independent global convergence rate of\n${O}\\left(\\frac{1}{mk}+\\frac{1}{k^2}\\right)$ for solving convex optimization\nproblems. Here, $m$ represents the subspace dimension, which can be\nsignificantly smaller than $d$. Instead of adopting a random subspace, our\nprimary innovation involves performing the cubic regularized Newton update\nwithin the Krylov subspace associated with the Hessian and the gradient of the\nobjective function. This result marks the first instance of a\ndimension-independent convergence rate for a subspace second-order method.\nFurthermore, when specific spectral conditions of the Hessian are met, our\nmethod recovers the convergence rate of a full-dimensional cubic regularized\nNewton method. Numerical experiments show our method converges faster than\nexisting random subspace methods, especially for high-dimensional problems.\n""]","[('subspace optimization', 0.5727471113204956), ('subspace methods', 0.5355672836303711), ('subspace algorithms', 0.5222095251083374), ('free optimization', 0.5129922032356262), ('random subspace', 0.5098304748535156), ('stochastic optimization random', 0.507946789264679), ('iterative minimization', 0.4924807846546173), ('free optimization dfo', 0.47865912318229675), ('derivative free optimization', 0.4706292152404785), ('large scale optimization', 0.45597386360168457)]"
1340,1340,22,1340_quantum graphs_quantum graph_spectral behavior_spectral gaps,"['quantum graphs', 'quantum graph', 'spectral behavior', 'spectral gaps', 'periodic quantum', 'lattice graph', 'spectrum periodic', 'chain graphs', 'negative spectrum', 'symmetric quantum']","['Vertex coupling interpolation in quantum chain graphs   We analyze band spectrum of the periodic quantum graph in the form of a chain\nof rings connected by line segments with the vertex coupling which violates the\ntime reversal invariance, interpolating between the $\\delta$ coupling and the\none determined by a simple circulant matrix. We find that flat bands are\ngenerically absent and that the negative spectrum is nonempty even for\ninterpolation with a non-attractive $\\delta$ coupling; we also determine the\nhigh-energy asymptotic behavior of the bands.\n', 'Cairo lattice with time-reversal non-invariant vertex couplings   We analyze the spectrum of a periodic quantum graph of the Cairo lattice\nform. The used vertex coupling violates the time reversal invariance and its\nhigh-energy behavior depends on the vertex degree parity; in the considered\nexample both odd and even parities are involved. The presence of the former\nimplies that the spectrum is dominated by gaps. In addition, we discuss two\nmodifications of the model in which this is not the case, the zero limit of the\nlength parameter in the coupling, and the sign switch of the coupling matrix at\nthe vertices of degree three; while different they both yield the same\nprobability that a randomly chosen positive energy lies in the spectrum.\n', 'Magnetic ring chains with vertex coupling of a preferred orientation   We discuss spectral properties of an periodic quantum graph consisting of an\narray of rings coupled either tightly or loosely through connecting links,\nassuming that the vertex coupling is manifestly non-invariant with respect to\nthe time reversal and a homogeneous magnetic field perpendicular to the graph\nplane is present. It is shown that the vertex parity determines the spectral\nbehavior at high energies and the Band-Berkolaiko universality holds whenever\nthe edges are incommensurate. The magnetic field influences the probability\nthat an energy belongs to the spectrum in the tight-chain case, and also it can\nturn some spectral bands into infinitely degenerate eigenvalues.\n']","[('quantum graphs', 0.719921886920929), ('quantum graph', 0.6952961087226868), ('spectral behavior', 0.5146017670631409), ('spectral gaps', 0.5024096965789795), ('periodic quantum', 0.49649178981781006), ('lattice graph', 0.48544201254844666), ('spectrum periodic', 0.4753812849521637), ('chain graphs', 0.46888330578804016), ('negative spectrum', 0.4676862061023712), ('symmetric quantum', 0.46351271867752075)]"
1341,1341,22,1341_optimal stopping times_optimal stopping_stochastic game_dynkin games,"['optimal stopping times', 'optimal stopping', 'stochastic game', 'dynkin games', 'games markov', 'games optimal', 'strategy markov', 'markov perfect equilibrium', 'existence markov', 'general markovian']","[""On the value of non-Markovian Dynkin games with partial and asymmetric\n  information   We prove that zero-sum Dynkin games in continuous time with partial and\nasymmetric information admit a value in randomised stopping times when the\nstopping payoffs of the players are general \\cadlag measurable processes. As a\nby-product of our method of proof we also obtain existence of optimal\nstrategies for both players. The main novelties are that we do not assume a\nMarkovian nature of the game nor a particular structure of the information\navailable to the players. This allows us to go beyond the variational methods\n(based on PDEs) developed in the literature on Dynkin games in continuous time\nwith partial/asymmetric information. Instead, we focus on a probabilistic and\nfunctional analytic approach based on the general theory of stochastic\nprocesses and Sion's min-max theorem (M. Sion, Pacific J. Math., 8, 1958, pp.\n171-176). Our framework encompasses examples found in the literature on\ncontinuous time Dynkin games with asymmetric information and we provide\ncounterexamples to show that our assumptions cannot be further relaxed.\n"", 'On the existence of Markovian randomized equilibria in Dynkin games of\n  war-of-attrition-type   In optimal stopping problems, a Markov structure guarantees Markovian optimal\nstopping times (first exit times). Surprisingly, there is no analogous result\nfor Markovian stopping games once randomization is required. This paper\naddresses this gap by proving the existence of Markov-perfect equilibria in a\nspecific type of stopping game - a general nonzero-sum Dynkin games of the\nwar-of-attrition type with underlying linear diffusions. Our main mathematical\ncontribution lies in the development of appropriate topologies for Markovian\nrandomized stopping times. This allows us to establish the existence of\nequilibria within a tractable and interpretable class of stopping times, paving\nthe way for further analysis of Markovian stopping games.\n', 'On Dynkin Games with Unordered Payoff Processes   A Dynkin game is a zero-sum, stochastic stopping game between two players\nwhere either player can stop the game at any time for an observable payoff.\nTypically the payoff process of the max-player is assumed to be smaller than\nthe payoff process of the min-player, while the payoff process for simultaneous\nstopping is in between the two. In this paper, we study general Dynkin games\nwhose payoff processes are in arbitrary positions. In both discrete and\ncontinuous time settings, we provide necessary and sufficient conditions for\nthe existence of pure strategy Nash equilibria and epsilon-optimal stopping\ntimes in all possible subgames.\n']","[('optimal stopping times', 0.6204535365104675), ('optimal stopping', 0.6023907661437988), ('stochastic game', 0.5958425402641296), ('dynkin games', 0.5499758124351501), ('games markov', 0.5082688331604004), ('games optimal', 0.49920833110809326), ('strategy markov', 0.4910154640674591), ('markov perfect equilibrium', 0.48145627975463867), ('existence markov', 0.471914142370224), ('general markovian', 0.468450129032135)]"
1342,1342,22,1342_covariance steering_optimal covariance_stochastic optimal control_constrained stochastic,"['covariance steering', 'optimal covariance', 'stochastic optimal control', 'constrained stochastic', 'optimal control linear', 'chance constrained stochastic', 'optimal control', 'linear stochastic systems', 'stochastic optimal', 'convex program']","['Chance-Constrained Covariance Steering for Discrete-Time Markov Jump Linear Systems In this paper, we propose a novel convex optimization framework to solve the optimal covariance steering problem for discrete-time Markov Jump Linear Systems (MJLS) with chance constraints. We derive the analytical expressions for the mean and covariance trajectories of time-varying discrete-time MJLS and show that they cannot be separated even without chance constraints, unlike the single-mode dynamics case. To solve the covariance steering problem, we propose a two-step convex optimization framework, which optimizes the mean and covariance subproblems sequentially. Further, we use Gaussian approximations to incorporate chance constraints and propose an iterative optimization framework to solve the chance-constrained covariance steering problem. Both problems are originally nonconvex, and we derive convex relaxations which are proved to be lossless at optimality using the Karush-Kuhn-Tucker (KKT) conditions. Numerical simulations demonstrate the proposed method by achieving target covariances while respecting chance constraints under Gaussian noise and Markovian jump dynamics.', 'Computationally Efficient Covariance Steering for Systems Subject to\n  Parametric Disturbances and Chance Constraints   This work investigates the finite-horizon optimal covariance steering problem\nfor discrete-time linear systems subject to both additive and multiplicative\nuncertainties as well as state and input chance constraints. In particular, a\ntractable convex approximation of the optimal covariance steering problem is\ndeveloped by tightening the chance constraints and by introducing a suitable\nchange of variables. The solution of the convex approximation is shown to be a\nvalid (albeit potentially suboptimal) solution to the original\nchance-constrained covariance steering problem.\n', 'Covariance Control of Discrete-Time Gaussian Linear Systems Using Affine\n  Disturbance Feedback Control Policies   In this paper, we present a new control policy parametrization for the\nfinite-horizon covariance steering problem for discrete-time Gaussian linear\nsystems (DTGLS) which can reduce the latter stochastic optimal control problem\nto a tractable optimization problem. The covariance steering problem seeks for\na feedback control policy that will steer the state covariance of a DTGLS to a\ndesired positive definite matrix in finite time. We consider two different\nformulations of the covariance steering problem, one with hard terminal LMI\nconstraints (hard-constrained covariance steering) and another one with soft\nterminal constraints in the form of a terminal cost which corresponds to the\nsquared Wasserstein distance between the actual terminal state (Gaussian)\ndistribution and the desired one (soft-constrained covariance steering). We\npropose a solution approach that relies on the affine disturbance feedback\nparametrization for both problem formulations. We show that this particular\nparametrization allows us to reduce the hard-constrained covariance steering\nproblem into a semi-definite program (SDP) and the soft-constrained covariance\nsteering problem into a difference of convex functions program(DCP). Finally,\nwe show the advantages of our approach over other covariance steering\nalgorithms in terms of computational complexity and computation time by means\nof theoretical analysis and numerical simulations.\n']","[('covariance steering', 0.6380545496940613), ('optimal covariance', 0.5511491298675537), ('stochastic optimal control', 0.5452754497528076), ('constrained stochastic', 0.5176360011100769), ('optimal control linear', 0.45899027585983276), ('chance constrained stochastic', 0.44031578302383423), ('optimal control', 0.43149709701538086), ('linear stochastic systems', 0.4249776601791382), ('stochastic optimal', 0.4189208149909973), ('convex program', 0.4184064567089081)]"
1343,1343,22,1343_stochastic gradient descent_backward stochastic differential_stochastic differential bsde_stochastic differential equations,"['stochastic gradient descent', 'backward stochastic differential', 'stochastic differential bsde', 'stochastic differential equations', 'forward backward stochastic', 'deep learning', 'stochastic differential', 'backward stochastic', 'deep neural', 'deep neural networks']","['Deep learning algorithms for solving high dimensional nonlinear backward\n  stochastic differential equations   In this work, we propose a new deep learning-based scheme for solving high\ndimensional nonlinear backward stochastic differential equations (BSDEs). The\nidea is to reformulate the problem as a global optimization, where the local\nloss functions are included. Essentially, we approximate the unknown solution\nof a BSDE using a deep neural network and its gradient with automatic\ndifferentiation. The approximations are performed by globally minimizing the\nquadratic local loss function defined at each time step, which always includes\nthe terminal condition. This kind of loss functions are obtained by iterating\nthe Euler discretization of the time integrals with the terminal condition. Our\nformulation can prompt the stochastic gradient descent algorithm not only to\ntake the accuracy at each time layer into account, but also converge to a good\nlocal minima. In order to demonstrate performances of our algorithm, several\nhigh-dimensional nonlinear BSDEs including pricing problems in finance are\nprovided.\n', 'A forward differential deep learning-based algorithm for solving\n  high-dimensional nonlinear backward stochastic differential equations   In this work, we present a novel forward differential deep learning-based\nalgorithm for solving high-dimensional nonlinear backward stochastic\ndifferential equations (BSDEs). Motivated by the fact that differential deep\nlearning can efficiently approximate the labels and their derivatives with\nrespect to inputs, we transform the BSDE problem into a differential deep\nlearning problem. This is done by leveraging Malliavin calculus, resulting in a\nsystem of BSDEs. The unknown solution of the BSDE system is a triple of\nprocesses $(Y, Z, \\Gamma)$, representing the solution, its gradient, and the\nHessian matrix. The main idea of our algorithm is to discretize the integrals\nusing the Euler-Maruyama method and approximate the unknown discrete solution\ntriple using three deep neural networks. The parameters of these networks are\nthen optimized by globally minimizing a differential learning loss function,\nwhich is novelty defined as a weighted sum of the dynamics of the discretized\nsystem of BSDEs. Through various high-dimensional examples, we demonstrate that\nour proposed scheme is more efficient in terms of accuracy and computation time\ncompared to other contemporary forward deep learning-based methodologies.\n', 'A backward differential deep learning-based algorithm for solving\n  high-dimensional nonlinear backward stochastic differential equations   In this work, we propose a novel backward differential deep learning-based\nalgorithm for solving high-dimensional nonlinear backward stochastic\ndifferential equations (BSDEs), where the deep neural network (DNN) models are\ntrained not only on the inputs and labels but also the differentials of the\ncorresponding labels. This is motivated by the fact that differential deep\nlearning can provide an efficient approximation of the labels and their\nderivatives with respect to inputs. The BSDEs are reformulated as differential\ndeep learning problems by using Malliavin calculus. The Malliavin derivatives\nof solution to a BSDE satisfy themselves another BSDE, resulting thus in a\nsystem of BSDEs. Such formulation requires the estimation of the solution, its\ngradient, and the Hessian matrix, represented by the triple of processes\n$\\left(Y, Z, \\Gamma\\right).$ All the integrals within this system are\ndiscretized by using the Euler-Maruyama method. Subsequently, DNNs are employed\nto approximate the triple of these unknown processes. The DNN parameters are\nbackwardly optimized at each time step by minimizing a differential learning\ntype loss function, which is defined as a weighted sum of the dynamics of the\ndiscretized BSDE system, with the first term providing the dynamics of the\nprocess $Y$ and the other the process $Z$. An error analysis is carried out to\nshow the convergence of the proposed algorithm. Various numerical experiments\nup to $50$ dimensions are provided to demonstrate the high efficiency. Both\ntheoretically and numerically, it is demonstrated that our proposed scheme is\nmore efficient compared to other contemporary deep learning-based\nmethodologies, especially in the computation of the process $\\Gamma$.\n']","[('stochastic gradient descent', 0.6159260272979736), ('backward stochastic differential', 0.5542647242546082), ('stochastic differential bsde', 0.5201841592788696), ('stochastic differential equations', 0.4870031476020813), ('forward backward stochastic', 0.4865981936454773), ('deep learning', 0.47336360812187195), ('stochastic differential', 0.46413299441337585), ('backward stochastic', 0.45968979597091675), ('deep neural', 0.44441819190979004), ('deep neural networks', 0.44420772790908813)]"
1344,1344,22,1344_complexity sampling_efficient sampling_bounds sampling_log concave distributions,"['complexity sampling', 'efficient sampling', 'bounds sampling', 'log concave distributions', 'gibbs sampling', 'sampling algorithms', 'algorithms sampling', 'log concave distribution', 'strongly log concave', 'sampling achieves']","[""Improved dimension dependence of a proximal algorithm for sampling   We propose a sampling algorithm that achieves superior complexity bounds in\nall the classical settings (strongly log-concave, log-concave,\nLogarithmic-Sobolev inequality (LSI), Poincar\\'e inequality) as well as more\ngeneral settings with semi-smooth or composite potentials. Our algorithm is\nbased on the proximal sampler introduced in~\\citet{lee2021structured}. The\nperformance of this proximal sampler is determined by that of the restricted\nGaussian oracle (RGO), a key step in the proximal sampler. The main\ncontribution of this work is an inexact realization of RGO based on approximate\nrejection sampling. To bound the inexactness of RGO, we establish a new\nconcentration inequality for semi-smooth functions over Gaussian distributions,\nextending the well-known concentration inequality for Lipschitz functions.\nApplying our RGO implementation to the proximal sampler, we achieve\nstate-of-the-art complexity bounds in almost all settings. For instance, for\nstrongly log-concave distributions, our method has complexity bound\n$\\tilde\\mathcal{O}(\\kappa d^{1/2})$ without warm start, better than the minimax\nbound for MALA. For distributions satisfying the LSI, our bound is $\\tilde\n\\mathcal{O}(\\hat \\kappa d^{1/2})$ where $\\hat \\kappa$ is the ratio between\nsmoothness and the LSI constant, better than all existing bounds.\n"", ""Faster high-accuracy log-concave sampling via algorithmic warm starts   Understanding the complexity of sampling from a strongly log-concave and\nlog-smooth distribution $\\pi$ on $\\mathbb{R}^d$ to high accuracy is a\nfundamental problem, both from a practical and theoretical standpoint. In\npractice, high-accuracy samplers such as the classical Metropolis-adjusted\nLangevin algorithm (MALA) remain the de facto gold standard; and in theory, via\nthe proximal sampler reduction, it is understood that such samplers are key for\nsampling even beyond log-concavity (in particular, for distributions satisfying\nisoperimetric assumptions).\n  In this work, we improve the dimension dependence of this sampling problem to\n$\\tilde{O}(d^{1/2})$, whereas the previous best result for MALA was\n$\\tilde{O}(d)$. This closes the long line of work on the complexity of MALA,\nand moreover leads to state-of-the-art guarantees for high-accuracy sampling\nunder strong log-concavity and beyond (thanks to the aforementioned reduction).\n  Our starting point is that the complexity of MALA improves to\n$\\tilde{O}(d^{1/2})$, but only under a warm start (an initialization with\nconstant R\\'enyi divergence w.r.t. $\\pi$). Previous algorithms took much longer\nto find a warm start than to use it, and closing this gap has remained an\nimportant open problem in the field. Our main technical contribution settles\nthis problem by establishing the first $\\tilde{O}(d^{1/2})$ R\\'enyi mixing\nrates for the discretized underdamped Langevin diffusion. For this, we develop\nnew differential-privacy-inspired techniques based on R\\'enyi divergences with\nOrlicz--Wasserstein shifts, which allow us to sidestep longstanding challenges\nfor proving fast convergence of hypocoercive differential equations.\n"", 'Structured Logconcave Sampling with a Restricted Gaussian Oracle   We give algorithms for sampling several structured logconcave families to\nhigh accuracy. We further develop a reduction framework, inspired by proximal\npoint methods in convex optimization, which bootstraps samplers for regularized\ndensities to improve dependences on problem conditioning. A key ingredient in\nour framework is the notion of a ""restricted Gaussian oracle"" (RGO) for $g:\n\\mathbb{R}^d \\rightarrow \\mathbb{R}$, which is a sampler for distributions\nwhose negative log-likelihood sums a quadratic and $g$. By combining our\nreduction framework with our new samplers, we obtain the following bounds for\nsampling structured distributions to total variation distance $\\epsilon$. For\ncomposite densities $\\exp(-f(x) - g(x))$, where $f$ has condition number\n$\\kappa$ and convex (but possibly non-smooth) $g$ admits an RGO, we obtain a\nmixing time of $O(\\kappa d \\log^3\\frac{\\kappa d}{\\epsilon})$, matching the\nstate-of-the-art non-composite bound; no composite samplers with better mixing\nthan general-purpose logconcave samplers were previously known. For logconcave\nfinite sums $\\exp(-F(x))$, where $F(x) = \\frac{1}{n}\\sum_{i \\in [n]} f_i(x)$\nhas condition number $\\kappa$, we give a sampler querying $\\widetilde{O}(n +\n\\kappa\\max(d, \\sqrt{nd}))$ gradient oracles to $\\{f_i\\}_{i \\in [n]}$; no\nhigh-accuracy samplers with nontrivial gradient query complexity were\npreviously known. For densities with condition number $\\kappa$, we give an\nalgorithm obtaining mixing time $O(\\kappa d \\log^2\\frac{\\kappa d}{\\epsilon})$,\nimproving the prior state-of-the-art by a logarithmic factor with a\nsignificantly simpler analysis; we also show a zeroth-order algorithm attains\nthe same query complexity.\n']","[('complexity sampling', 0.5996370315551758), ('efficient sampling', 0.5816066265106201), ('bounds sampling', 0.5780014991760254), ('log concave distributions', 0.5518627166748047), ('gibbs sampling', 0.5279470086097717), ('sampling algorithms', 0.5160357356071472), ('algorithms sampling', 0.514300525188446), ('log concave distribution', 0.5112341046333313), ('strongly log concave', 0.507148027420044), ('sampling achieves', 0.4981771409511566)]"
1345,1345,22,1345_distribution lattice_lattice point counting_lattice random_lattice points,"['distribution lattice', 'lattice point counting', 'lattice random', 'lattice points', 'lattice point', 'number lattice points', 'integer lattice points', 'points lattice', 'unimodular lattices', 'lattices']","[""On the Distribution of the Number of Lattice Points in Norm Balls on the\n  Heisenberg Groups   We investigate the fluctuations in the number of integral lattice points on\nthe Heisenberg groups which lie inside a Cygan-Kor{\\'a}nyi norm ball of large\nradius. Let\n$\\mathcal{E}_{q}(x)=\\big|\\mathbb{Z}^{2q+1}\\cap\\delta_{x}\\mathcal{B}\\big|-\\textit{vol}\\big(\\mathcal{B}\\big)x^{2q+2}$\ndenote the error term which occurs for this lattice point counting problem on\nthe Heisenberg group $\\mathbb{H}_{q}$, where $\\mathcal{B}$ is the unit ball in\nthe Cygan-Kor{\\'a}nyi norm and $\\delta_{x}$ is the Heisenberg-dilation by\n$x>0$. For $q\\geq3$ we consider the suitably normalized error term\n$\\mathcal{E}_{q}(x)/x^{2q-1}$, and prove it has a limiting value distribution\nwhich is absolutely continuous with respect to the Lebesgue measure. We show\nthat the defining density for this distribution, denoted by\n$\\mathcal{P}_{q}(\\alpha)$, can be extended to the whole complex plane\n$\\mathbb{C}$ as an entire function of $\\alpha$ and satisfies for any\nnon-negative integer $j\\geq0$ and any $\\alpha\\in\\mathbb{R}$,\n$|\\alpha|>\\alpha_{q,j}$, the bound: \\begin{equation*} \\begin{split}\n\\big|\\mathcal{P}^{(j)}_{q}(\\alpha)\\big|\\leq\\exp{\\Big(-|\\alpha|^{4-\\beta/\\log\\log{|\\alpha|}}\\Big)}\n{split} {equation*} where $\\beta>0$ is an absolute constant. In addition, we\ngive an explicit formula for the $j$-th integral moment of the density\n$\\mathcal{P}_{q}(\\alpha)$ for any integer $j\\geq1$.\n"", ""Distribution and Moments of the Error Term in the Lattice Point Counting\n  Problem for 3-Dimensional Cygan-Kor\\'anyi Balls   We study fluctuations of the error term for the number of integer lattice\npoints lying inside a 3-dimensional Cygan-Kor\\'anyi ball of large radius. We\nprove that the error term, suitably normalized, has a limiting value\ndistribution which is absolutely continuous, and we provide estimates for the\ndecay rate of the corresponding density on the real line. In addition, we\nestablish the existence of all moments for the normalized error term, and we\nprove that these are given by the moments of the corresponding density.\n"", 'Limit laws in the lattice problem. II. The case of ovals   We study the error of the number of unimodular lattice points that fall into\na dilated and centred ellipse around $0$. We first show that the study of the\nerror, when the error is normalized by $\\sqrt{t}$ with $t$ the parameter of\ndilatation of the ellipse, when $t$ tends to infinity and when the lattice is\nrandom, is reduced to the study of a Siegel transform $\\mathcal{S}(f_{t})(L)$\nthat depends on $t$. Then, by making $t \\rightarrow \\infty$, we see that\n$\\mathcal{S}(f_{t})$ converges in law towards a modified Siegel transform with\nrandom weights $\\mathcal{S}(F)(\\theta,L)$ where $\\theta$ is a second random\nparameter. Finally, we show that this last quantity converges almost surely and\nwe study the existence of the moments of its law.\n']","[('distribution lattice', 0.5666613578796387), ('lattice point counting', 0.5641690492630005), ('lattice random', 0.5613853931427002), ('lattice points', 0.5439920425415039), ('lattice point', 0.5185633301734924), ('number lattice points', 0.5173168778419495), ('integer lattice points', 0.5162451863288879), ('points lattice', 0.5072418451309204), ('unimodular lattices', 0.4730801284313202), ('lattices', 0.46544453501701355)]"
1346,1346,22,1346_gradient estimates solutions_conductivity_gradient solutions_gradient estimates,"['gradient estimates solutions', 'conductivity', 'gradient solutions', 'gradient estimates', 'bound gradient', 'conductivities', 'gradient estimate', 'bounds gradient', 'optimal gradient', 'perfect conductor']","['Optimal gradient estimates of solutions to the insulated conductivity\n  problem in dimension greater than two   We study the insulated conductivity problem with inclusions embedded in a\nbounded domain in $\\mathbb{R}^n$. The gradient of solutions may blow up as\n$\\varepsilon$, the distance between inclusions, approaches to $0$. It was known\nthat the optimal blow up rate in dimension $n = 2$ is of order\n$\\varepsilon^{-1/2}$. It has recently been proved that in dimensions $n \\ge 3$,\nan upper bound of the gradient is of order $\\varepsilon^{-1/2 + \\beta}$ for\nsome $\\beta > 0$. On the other hand, optimal values of $\\beta$ have not been\nidentified. In this paper, we prove that when the inclusions are balls, the\noptimal value of $\\beta$ is $[-(n-1)+\\sqrt{(n-1)^2+4(n-2)}~]/4 \\in (0,1/2)$ in\ndimensions $n \\ge 3$.\n', 'Gradient estimates for the insulated conductivity problem: the\n  non-umbilical case   We study the insulated conductivity problem with inclusions embedded in a\nbounded domain in $\\mathbb R^n$, for $n \\ge 3$. The gradient of solutions may\nblow up as $\\varepsilon$, the distance between inclusions, approaches to $0$.\nWe established in a recent paper optimal gradient estimates for a class of\ninclusions including balls. In this paper, we prove such gradient estimates for\ngeneral strictly convex inclusions. Unlike the perfect conductivity problem,\nthe estimates depend on the principal curvatures of the inclusions, and we show\nthat these estimates are characterized by the first non-zero eigenvalue of a\ndivergence form elliptic operator on $\\mathbb S^{n-2}$.\n', 'Gradient estimates for the insulated conductivity problem: the case of\n  $m$-convex inclusions   We consider an insulated conductivity model with two neighboring inclusions\nof $m$-convex shapes in $\\mathbb{R}^{d}$ when $m\\geq2$ and $d\\geq3$. We\nestablish the pointwise gradient estimates for the insulated conductivity\nproblem and capture the gradient blow-up rate of order\n$\\varepsilon^{-1/m+\\beta}$ with\n$\\beta=[-(d+m-3)+\\sqrt{(d+m-3)^{2}+4(d-2)}]/(2m)\\in(0,1/m)$, as the distance\n$\\varepsilon$ between these two insulators tends to zero. In particular, the\noptimality of the blow-up rate is also demonstrated for a class of axisymmetric\n$m$-convex inclusions.\n']","[('gradient estimates solutions', 0.5371963977813721), ('conductivity', 0.47407278418540955), ('gradient solutions', 0.4723435044288635), ('gradient estimates', 0.44104307889938354), ('bound gradient', 0.42924126982688904), ('conductivities', 0.4276357889175415), ('gradient estimate', 0.4138013422489166), ('bounds gradient', 0.4109842777252197), ('optimal gradient', 0.38824859261512756), ('perfect conductor', 0.36900874972343445)]"
1347,1347,22,1347_global optimization algorithms_efficient global optimization_global optimization_based global optimization,"['global optimization algorithms', 'efficient global optimization', 'global optimization', 'based global optimization', 'global optimization problems', 'free optimization', 'derivative free optimization', 'optimization algorithms', 'blackbox optimization', 'optimization']","['An extensive numerical benchmark study of deterministic vs. stochastic\n  derivative-free global optimization algorithms   Research in derivative-free global optimization is under active development,\nand many solution techniques are available today. Therefore, the experimental\ncomparison of previous and emerging algorithms must be kept up to date. This\npaper considers the solution to the bound-constrained, possibly black-box\nglobal optimization problem. It compares 64 derivative-free deterministic\nalgorithms against classic and state-of-the-art stochastic solvers. Among\ndeterministic ones, a particular emphasis is on DIRECT-type, where, in recent\nyears, significant progress has been made. A set of 800 test problems generated\nby the well-known GKLS generator and 397 traditional test problems from\nDIRECTGOLib v1.2 collection are utilized in a computational study. More than\n239400 solver runs were carried out, requiring more than 531 days of single CPU\ntime to complete them. It has been found that deterministic algorithms perform\nexcellently on GKLS-type and low-dimensional problems, while stochastic\nalgorithms have shown to be more efficient in higher dimensions.\n', 'DIRECTGO: A new DIRECT-type MATLAB toolbox for derivative-free global\n  optimization   In this work, we introduce DIRECTGO, a new MATLAB toolbox for derivative-free\nglobal optimization. DIRECTGO collects various deterministic derivative-free\nDIRECT-type algorithms for box-constrained, generally-constrained, and problems\nwith hidden constraints. Each sequential algorithm is implemented in two ways:\nusing static and dynamic data structures for more efficient information storage\nand organization. Furthermore, parallel schemes are applied to some promising\nalgorithms within DIRECTGO. The toolbox is equipped with a graphical user\ninterface (GUI), ensuring the user-friendly use of all functionalities\navailable in DIRECTGO. Available features are demonstrated in detailed\ncomputational studies using a comprehensive DIRECTGOLib v1.0 library of global\noptimization test problems. Additionally, eleven classical engineering design\nproblems illustrate the potential of DIRECTGO to solve challenging real-world\nproblems. Finally, the appendix gives examples of accompanying MATLAB programs\nand provides a synopsis of its use on the test problems with box and general\nconstraints.\n', ""A New Challenging Curve Fitting Benchmark Test Set for Global\n  Optimization   Benchmark sets are extremely important for evaluating and developing global\noptimization algorithms and related solvers. A new test set named PCC benchmark\nis proposed especially for optimization problems of nonlinear curve fitting for\nthe first time, with the aspiration of helping developers to investigate and\ncompare the performance of different global optimization solvers, as well as\nmore effective optimization algorithms could be developed. Compared with the\nwell-known classical nonlinear curve fitting benchmark set given by the\nNational Institute of Standards and Technology (NIST) of USA, the most\ndistinguishable features of the PCC benchmark are small problem dimensions,\nunconstrained with free search domain and high level of difficulty for\nobtaining global optimization solutions, which make the PCC benchmark be not\nonly suitable for validating the effectiveness of different global optimization\nalgorithms, but also more ideal for verifying and comparing various related\nsolvers. Seven of the world's leading global optimization solvers, including\nBaron, Antigone, Couenne, Lingo, Scip, Matlab-GA and 1stOpt, are employed to\ntest NIST and PCC benchmark thoroughly in terms of both effectiveness and\nefficiency. The results showed that the NIST benchmark is relatively simple and\nnot suitable for global optimization testing, meanwhile the PCC benchmark is a\nunique, challenging and effective test dataset for global optimization.\n""]","[('global optimization algorithms', 0.7325371503829956), ('efficient global optimization', 0.7240925431251526), ('global optimization', 0.706455409526825), ('based global optimization', 0.6803658604621887), ('global optimization problems', 0.6765525341033936), ('free optimization', 0.6648300886154175), ('derivative free optimization', 0.644443154335022), ('optimization algorithms', 0.6094655394554138), ('blackbox optimization', 0.5754358768463135), ('optimization', 0.5695982575416565)]"
1348,1348,22,1348_dice_winning probabilities_asymptotic probability_three random,"['dice', 'winning probabilities', 'asymptotic probability', 'three random', 'gambling', 'winning probability', 'rock scissors', 'rolls', 'intransitivity', 'exact probabilities']","['The Paradox of Anti-Inductive Dice   We identify a new type of paradoxical behavior in dice, where the sum of\nindependent rolls produces a deceptive sequence of dominance relations. We call\nthese ``anti-inductive dice"". Consider a game with two players and two\nnon-identical dice. Each rolls their die $k$ times, adding the results, and the\nplayer with the highest sum wins. For each $k$, this induces a dominance\nrelation between dice, with $A[k]\\succ B[k]$ if $A$ is more likely than $B$ to\nwin after $k$ rolls, and vice versa. For certain classes of dice, the limiting\nbehavior of these relations is well-established in the literature, but the\ntransient behavior, the subject of this paper, is less well-understood. This\ntransient behavior, even for dice with only 4 faces, contains an immensely rich\nparameter space with fractal-like behavior.\n', 'A Central Limit Theorem for intransitive dice   Intransitive dice $D^{(1)}, \\ldots, D^{(\\ell)}$ are dice such that $D^{(1)}$\nhas advantage when played against $D^{(2)}$, dice $D^{(2)}$ has advantage when\nplayed against $D^{(3)}$ and so on, up to $D^{(\\ell)}$, which has advantage\nover $D^{(1)}$. In this twofold work, we first present (deterministic) results\non the existence of general intransitive dice. Second and mainly, a central\nlimit theorem for the vector of normalized victories of a die against the next\none in the list when the faces of a die are i.i.d.\\ random variables and all\ndice are independent, but different dice may have distinct distributions\nassociated with them, as well as they may have distinct numbers of faces.\nExploiting this central limit theorem, we derive two major consequences. First,\nwe are able to obtain first order exponential asymptotics for the number of\n$\\ell$-tuples of intransitive dice, when the number of faces of the dice grows.\nSecond, we obtain a criterion to ensure that the asymptotic probability of\nobserving intransitive dice is null, which applies to many cases, including all\ncontinuous distributions and many discrete ones.\n', 'Intransitive dice tournament is not quasirandom   We settle a version of the conjecture about intransitive dice posed by\nConrey, Gabbard, Grant, Liu and Morrison in 2016 and Polymath in 2017. We\nconsider generalized dice with $n$ faces and we say that a die $A$ beats $B$ if\na random face of $A$ is more likely to show a higher number than a random face\nof $B$. We study random dice with faces drawn iid from the uniform distribution\non $[0,1]$ and conditioned on the sum of the faces equal to $n/2$. Considering\nthe ""beats"" relation for three such random dice, Polymath showed that each of\neight possible tournaments between them is asymptotically equally likely. In\nparticular, three dice form an intransitive cycle with probability converging\nto $1/4$. In this paper we prove that for four random dice not all tournaments\nare equally likely and the probability of a transitive tournament is strictly\nhigher than $3/8$.\n']","[('dice', 0.5167696475982666), ('winning probabilities', 0.3919577896595001), ('asymptotic probability', 0.33772513270378113), ('three random', 0.3335712254047394), ('gambling', 0.3254265785217285), ('winning probability', 0.315395325422287), ('rock scissors', 0.3083670437335968), ('rolls', 0.2964228391647339), ('intransitivity', 0.2825673520565033), ('exact probabilities', 0.2772766649723053)]"
1349,1349,22,1349_feynman integral_feynman path_path integrals_path integration,"['feynman integral', 'feynman path', 'path integrals', 'path integration', 'path integral', 'feynman', 'propagators', 'quantum field theory', 'propagator', 'integration theory']","['On the mathematical formulation of the restricted Feynman path integrals\n  through broken line paths   The restricted Feynman path integrals (RFPIs) have been proposed to study\ncontinuous quantum measurements in physics. The RFPIs are heuristically\ndetermined in terms of the usual probability amplitude multiplied by weight for\neach path, which contains information about the results and the resolution of\nthe measuring device. In the present paper we will consider the RFPIs\nparticularly for the position measurements and will prove rigorously that these\nRFPIs are well defined in the $L^{2}$ space and are the solutions to the\nnon-self-adjoint Schroedinger equations. Our results in the present paper give\na generalization of the results on the usual Feynman path integrals for the\nSchroedinger equations.Furthermore, our results are extended to quantum spin\nsystems.\n', 'The Feynman integral path a Henstock integral: a survey and open\n  problems   The Feynman path integral is defined over the space $\\mathbb{R}^T$ of all\npossible paths; it has been a powerful tool to develop Quantum Mechanics. The\nabsolute value of Feynman\'s integrand is not integrable, then Lebesgue\nintegration theory could not be used by Feynman. However, it exists formally as\na Henstock integral (which does not require the measure concept) and is a\nsuitable alternative to the ordinary integrals that normally appear in path\nintegrals. Feynman proved the equivalence of his theory with the traditional\nformulation of Quantum Mechanics, since his path integral satisfies\nSchr\\""odinger\'s equation. On the other hand, Feynman\'s path integral is related\nto the diagrams of Feynman. For the application of this integral in Feynman\'s\ndiagrams it is necessary to exchange the integral $\\int_{\\mathbb{R}^T}$ and the\nseries. We discuss the impossibility to exchange the integral and the sum,\nconsidering integral of Henstock and the version of Dominated Convergence\nTheorem. Even it has not been proved through the several mathematical\nformalisms that have been used.\n', 'On approximations of Feynman path integrals   We study approximations of Feynman path integrals in finite dimensional\nspaces and how the approximations determine the propagator.\n']","[('feynman integral', 0.6667000651359558), ('feynman path', 0.6424776911735535), ('path integrals', 0.6297368407249451), ('path integration', 0.5575906038284302), ('path integral', 0.5329022407531738), ('feynman', 0.5075061321258545), ('propagators', 0.4782510995864868), ('quantum field theory', 0.46923011541366577), ('propagator', 0.44560179114341736), ('integration theory', 0.4420718550682068)]"
1350,1350,22,1350_generalized geometry_generalized duality_lie duality_hermitian geometry,"['generalized geometry', 'generalized duality', 'lie duality', 'hermitian geometry', 'total space bundle', 'duality', 'string theory', 'hermitian manifold', 'gauge symmetry', 'field theories']","['Doubled Aspects of Vaisman Algebroid and Gauge Symmetry in Double Field\n  Theory   The metric algebroid proposed by Vaisman (the Vaisman algebroid) governs the\ngauge symmetry algebra generated by the C-bracket in double field theory (DFT).\nWe show that the Vaisman algebroid is obtained by an analogue of the Drinfel\'d\ndouble of Lie algebroids. Based on a geometric realization of doubled\nspace-time as a para-Hermitian manifold, we examine exterior algebras and a\npara-Dolbeault cohomology on DFT and discuss the structure of the Drinfel\'d\ndouble behind the DFT gauge symmetry. Similar to the Courant algebroid in the\ngeneralized geometry, Lagrangian subbundles $(L,\\tilde{L})$ in a para-Hermitian\nmanifold play Dirac-like structures in the Vaisman algebroid. We find that an\nalgebraic origin of the strong constraint in DFT is traced back to the\ncompatibility condition needed for $(L,\\tilde{L})$ be a Lie bialgebroid. The\nanalysis provides a foundation toward the ""coquecigrue problem"" for the gauge\nsymmetry in DFT.\n', 'Global Double Field Theory is Higher Kaluza-Klein Theory   Kaluza-Klein Theory states that a metric on the total space of a principal\nbundle $P\\rightarrow M$, if it is invariant under the principal action of $P$,\nnaturally reduces to a metric together with a gauge field on the base manifold\n$M$. We propose a generalization of this Kaluza-Klein principle to higher\nprincipal bundles and higher gauge fields. For the particular case of the\nabelian gerbe of Kalb-Ramond field, this Higher Kaluza-Klein geometry provides\na natural global formulation for Double Field Theory (DFT). In this framework\nthe doubled space is the total space of a higher principal bundle and the\ninvariance under its higher principal action is exactly a global formulation of\nthe familiar strong constraint. The patching problem of DFT is naturally solved\nby gluing the doubled space with a higher group of symmetries in a higher\ncategory. Locally we recover the familiar picture of an ordinary para-Hermitian\nmanifold equipped with Born geometry. Infinitesimally we recover the familiar\npicture of a higher Courant algebroid twisted by a gerbe (also known as\nExtended Riemannian Geometry). As first application we show that on a\ntorus-compactified spacetime the Higher Kaluza-Klein reduction gives\nautomatically rise to abelian T-duality, while on a general principal bundle it\ngives rise to non-abelian T-duality. As final application we define a natural\nnotion of Higher Kaluza-Klein monopole by directly generalizing the ordinary\nGross-Perry one. Then we show that under Higher Kaluza-Klein reduction, this\nmonopole is exactly the NS5-brane on a $10d$ spacetime. If, instead, we smear\nit along a compactified direction we recover the usual DFT monopole on a $9d$\nspacetime.\n', ""More on Doubled Aspects of Algebroids in Double Field Theory   We continue to study doubled aspects of algebroid structures equipped with\nthe C-bracket in double field theory (DFT). We find that a family of\nalgebroids, the Vaisman (metric or pre-DFT), the pre- and the ante-Courant\nalgebroids are constructed by the analogue of the Drinfel'd double of Lie\nalgebroid pairs. We examine geometric implementations of these algebroids in\nthe para-Hermitian manifold, which is a realization of the doubled space-time\nin DFT. We show that the strong constraint in DFT is necessary to realize the\ndoubled and non-trivial Poisson structures but can be relaxed for some\nalgebroids. The doubled structures of twisted brackets and those associated\nwith group manifolds are briefly discussed.\n""]","[('generalized geometry', 0.5223024487495422), ('generalized duality', 0.4853644073009491), ('lie duality', 0.47693246603012085), ('hermitian geometry', 0.46892133355140686), ('total space bundle', 0.4597366452217102), ('duality', 0.4291429817676544), ('string theory', 0.425753116607666), ('hermitian manifold', 0.4196477234363556), ('gauge symmetry', 0.4194025993347168), ('field theories', 0.4038724899291992)]"
1351,1351,22,1351_homotopy theory_homotopy types_homotopy equivalent_homotopy equivalences,"['homotopy theory', 'homotopy types', 'homotopy equivalent', 'homotopy equivalences', 'homology theories', 'homotopy', 'structure homotopy', 'structure flows', 'homotopy type', 'category homotopy']","[""Directed degeneracy maps for precubical sets   Symmetric transverse sets were introduced to make the construction of the\nparallel product with synchronization for process algebras functorial. It is\nproved that one can do directed homotopy on symmetric transverse sets in the\nfollowing sense. A q-realization functor from symmetric transverse sets to\nflows is introduced using a q-cofibrant replacement functor of flows. By\ntopologizing the cotransverse maps, the cotransverse topological cube is\nconstructed. It can be regarded both as a cotransverse topological space and as\na cotransverse Lawvere metric space. A natural realization functor from\nsymmetric transverse sets to flows is introduced using Raussen's notion of\nnatural $d$-path extended to symmetric transverse sets thanks to their\nstructure of Lawvere metric space. It is proved that these two realization\nfunctors are homotopy equivalent on cofibrant symmetric transverse sets by\nusing the fact that the small category defining symmetric transverse sets is\nc-Reedy in Shulman's sense. This generalizes to symmetric transverse sets\nresults previously obtained for precubical sets.\n"", ""Homotopy theory of Moore flows (III)   The previous paper of this series shows that the q-model categories of\n$\\mathcal{G}$-multipointed $d$-spaces and of $\\mathcal{G}$-flows are Quillen\nequivalent. In this paper, the same result is established by replacing the\nreparametrization category $\\mathcal{G}$ by the reparametrization category\n$\\mathcal{M}$. Unlike the case of $\\mathcal{G}$, the execution paths of a\ncellular $\\mathcal{M}$-multipointed $d$-space can have stop intervals. The\ntechnical tool to overcome this obstacle is the notion of globular\nnaturalization. It is the globular analogue of Raussen's naturalization of a\ndirected path in the geometric realization of a precubical set. The notion of\nglobular naturalization working both for $\\mathcal{G}$ and $\\mathcal{M}$, the\nproof of the Quillen equivalence we obtain is valid for the two\nreparametrization categories. Together with the results of the first paper of\nthis series, we then deduce that $\\mathcal{G}$-multipointed $d$-spaces and\n$\\mathcal{M}$-multipointed $d$-spaces have Quillen equivalent q-model\nstructures. Finally, we prove that the saturation hypothesis can be added\nwithout any modification in the main theorems of the paper.\n"", 'Comparing cubical and globular directed paths   A flow is a directed space structure on a homotopy type. It is already known\nthat the underlying homotopy type of the realization of a precubical set as a\nflow is homotopy equivalent to the realization of the precubical set as a\ntopological space. This realization depends on the non-canonical choice of a\nq-cofibrant replacement. We construct a new realization functor from precubical\nsets to flows which is homotopy equivalent to the previous one and which does\nnot depend on the choice of any cofibrant replacement functor. The main tool is\nthe notion of natural $d$-path introduced by Raussen. The flow we obtain for a\ngiven precubical set is not anymore q-cofibrant but is still m-cofibrant. As an\napplication, we prove that the space of execution paths of the realization of a\nprecubical set as a flow is homotopy equivalent to the space of nonconstant\n$d$-paths between vertices in the geometric realization of the precubical set.\n']","[('homotopy theory', 0.5128732919692993), ('homotopy types', 0.5118622779846191), ('homotopy equivalent', 0.5025520920753479), ('homotopy equivalences', 0.48568183183670044), ('homology theories', 0.46889805793762207), ('homotopy', 0.46671411395072937), ('structure homotopy', 0.4651429057121277), ('structure flows', 0.4570337235927582), ('homotopy type', 0.45673736929893494), ('category homotopy', 0.4527271091938019)]"
1352,1352,22,1352_pseudodifferential operators_class pseudodifferential operators_pseudodifferential operator_elliptic differential operators,"['pseudodifferential operators', 'class pseudodifferential operators', 'pseudodifferential operator', 'elliptic differential operators', 'elliptic operators', 'potential operators', 'operators smooth', 'class pseudodifferential', 'differential operators', 'elliptic operator']","[""Layer potentials and essentially translation invariant\n  pseudodifferential operators on manifolds with cylindrical ends   Motivated by the study of layer potentials on manifolds with straight conical\nor cylindrical ends, we introduce and study two classes (or calculi) of\npseudodifferential operators defined on manifolds with cylindrical ends: the\nclass of pseudodifferential operators that are ``translation invariant at\ninfinity'' and the class of ``essentially translation invariant operators.''\nThese are ``minimal'' classes of pseudodifferential operators containing the\nlayer potential operators of interest. Both classes are close to the\n$b$-calculus considered by Melrose and Schulze and to the $c$-calculus\nconsidered by Melrose and Mazzeo-Melrose. Our calculi, however, are different\nand, while some of their properties follow from those of the $b$- or\n$c$-calculi, many of their properties do not. In particular, we prove that the\n``essentially translation invariant calculus'' is spectrally invariant, a\nproperty not enjoyed by the ``translation invariant at infinity'' calculus or\nthe $b$-calculus. For our calculi, we provide easy, intuitive proofs of the\nusual properties: stability for products and adjoints, mapping and boundedness\nproperties for operators acting between Sobolev spaces, regularity properties,\nexistence of a quantization map, topological properties of our algebras, and\nthe Fredholm property. Since our applications will be to the Stokes operator,\nwe systematically work in the setting of \\ADN-elliptic operators. We also show\nthat our calculi behave well with respect to restrictions to (suitable)\nsubmanifolds, which is crucial for our applications to layer potential\noperators.\n"", ""$L^2$ boundedness of pseudodifferential operators on manifolds with ends   We investigate properties of pseudodifferential operators on $L^2$ space on\nmanifold with ends including asymptotically conical or hyperbolic ends. Our\npseudodifferential operators are a generalization of the canonical quantization\nwhich naturally appears in the quantum mechanics on curved spaces. We prove a\nCalder\\'on-Vaillancourt type theorem for our pseudodifferential operators and\ndiscuss a construction of parametrix of elliptic differential operators on\nmanifolds with ends.\n"", 'Invariant subspaces of elliptic systems I: pseudodifferential\n  projections   Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on\n$m$-columns of half-densities on a closed manifold $M$, whose principal symbol\nis assumed to have simple eigenvalues. We show existence and uniqueness of $m$\northonormal pseudodifferential projections commuting with the operator $A$ and\nprovide an algorithm for the computation of their full symbols, as well as\nexplicit closed formulae for their subprincipal symbols. Pseudodifferential\nprojections yield a decomposition of $L^2(M)$ into invariant subspaces under\nthe action of $A$ modulo $C^\\infty(M)$. Furthermore, they allow us to decompose\n$A$ into $m$ distinct sign definite pseudodifferential operators. Finally, we\nrepresent the modulus and the Heaviside function of the operator $A$ in terms\nof pseudodifferential projections and discuss physically meaningful examples.\n']","[('pseudodifferential operators', 0.7437433004379272), ('class pseudodifferential operators', 0.7327897548675537), ('pseudodifferential operator', 0.7103449106216431), ('elliptic differential operators', 0.6413654088973999), ('elliptic operators', 0.5893856287002563), ('potential operators', 0.5704696774482727), ('operators smooth', 0.5677622556686401), ('class pseudodifferential', 0.5563108325004578), ('differential operators', 0.5541933178901672), ('elliptic operator', 0.5458453893661499)]"
1353,1353,22,1353_stochastic volterra equations_stochastic volterra_backward stochastic volterra_stochastic volterra integral,"['stochastic volterra equations', 'stochastic volterra', 'backward stochastic volterra', 'stochastic volterra integral', 'solutions stochastic', 'continuous diffusion coefficients', 'one dimensional stochastic', 'volterra integral equations', 'volterra equations', 'equations driven brownian']","['Path independence for the additive functionals of stochastic Volterra\n  equations with singular kernels and H\\""older continuous coefficients   In this paper, we are concerned with stochastic Volterra equations with\nsingular kernels and H\\""older continuous coefficients. We first establish the\nwell-posedness of these equations by utilising the Yamada-Watanabe approach.\nThen, we aim to characterise the path-independence for additive functionals of\nthese equations. The main challenge here is that the solutions of stochastic\nVolterra equations are not semimartingales nor Markov processes, thus the\nexisting techniques for obtaining the path-independence of usual,\nsemimartingale type stochastic differential equations are no longer applicable.\nTo overcome this difficulty, we link the concerned stochastic Volterra\nequations to mild formulation of certain parabolic type stochastic partial\ndifferential equations, and further apply our previous results on the\npath-independence for stochastic evolution equations to get the desired result.\nFinally, as an important application, we consider a class of stochastic\nVolterra equations whose kernels are related with fractional Brownian motions\nand derive the path-independence of additive functionals for them.\n', 'Pathwise uniqueness for singular stochastic Volterra equations with\n  H\\""older coefficients   Pathwise uniqueness is established for a class of one-dimensional stochastic\nVolterra equations driven by Brownian motion with singular kernels and H\\""older\ncontinuous diffusion coefficients. Consequently, the existence of unique strong\nsolutions is obtained for this class of stochastic Volterra equations.\n', 'On the existence of weak solutions to stochastic Volterra equations   The existence of weak solutions is established for stochastic Volterra\nequations with time-inhomogeneous coefficients allowing for general kernels in\nthe drift and convolutional or bounded kernels in the diffusion term. The\npresented approach is based on a newly formulated local martingale problem\nassociated to stochastic Volterra equations.\n']","[('stochastic volterra equations', 0.7940975427627563), ('stochastic volterra', 0.6762880086898804), ('backward stochastic volterra', 0.672504186630249), ('stochastic volterra integral', 0.6600407361984253), ('solutions stochastic', 0.5623674392700195), ('continuous diffusion coefficients', 0.5423720479011536), ('one dimensional stochastic', 0.5101050138473511), ('volterra integral equations', 0.5057032108306885), ('volterra equations', 0.49317657947540283), ('equations driven brownian', 0.47702696919441223)]"
1354,1354,22,1354_asymptotic fluctuations_exclusion processes_exclusion process tasep_exclusion process asep,"['asymptotic fluctuations', 'exclusion processes', 'exclusion process tasep', 'exclusion process asep', 'asymmetric simple exclusion', 'exclusion process', 'simple exclusion process', 'tail large deviation', 'large deviation principle', 'stationary measures']","['Upper-tail large deviation principle for the ASEP   We consider the asymmetric simple exclusion process (ASEP) on $\\mathbb{Z}$\nstarted from step initial data and obtain the exact Lyapunov exponents for\n$H_0(t)$, the integrated current of ASEP. As a corollary, we derive an explicit\nformula for the upper-tail large deviation rate function for $-H_0(t)$. Our\nresult matches with the rate function for the integrated current of the totally\nasymmetric simple exclusion process (TASEP) obtained in [Johansson\n00](arXiv:math/9903134).\n', 'Large deviation principle for the stationary measures of open asymmetric\n  simple exclusion processes   We consider the stationary measure of the asymmetric simple exclusion process\n(ASEP) on a finite interval in $\\mathbb{Z}$ with open boundaries. Fixing all\nthe jump rates and letting the system size approach infinity, the height\nprofile of such a sequence of stationary measures satisfies a large deviation\nprinciple (LDP), whose rate function was predicted in the physics work\narXiv:cond-mat/0205353. In this paper, we provide the first rigorous proof of\nthe large deviation principle in the ""fan region"" part of the phase diagram.\nOur proof relies on two key ingredients: a two-layer expression of the\nstationary measure of open ASEP, arising from the Enaud-Derrida representation\narXiv:cond-mat/0307023 of the matrix product ansatz, and the large deviation\nprinciple of the open totally asymmetric simple exclusion process (TASEP)\nrecently established in arXiv:2403.03275.\n', 'Shock fluctuations in TASEP under a variety of time scalings   We consider the totally asymmetric simple exclusion process (TASEP) with two\ndifferent initial conditions with shock discontinuities formed by blocks of\nfully packed particles. Initially a second class particle is at the left of a\nshock discontinuity. Using multicolored TASEP we derive exact formulas for the\ndistribution of the second class particle and colored height functions. These\nare given in terms of the height function at different positions of a single\nTASEP configuration. We study the limiting distributions of second class\nparticles (and colored height functions). The result depends on how the width\nblocks of particles scale with the observation time; we study a variety of such\nscalings.\n']","[('asymptotic fluctuations', 0.5239961743354797), ('exclusion processes', 0.522087812423706), ('exclusion process tasep', 0.4979892671108246), ('exclusion process asep', 0.49492737650871277), ('asymmetric simple exclusion', 0.47608882188796997), ('exclusion process', 0.444933146238327), ('simple exclusion process', 0.4368828237056732), ('tail large deviation', 0.36423179507255554), ('large deviation principle', 0.361782044172287), ('stationary measures', 0.3563701808452606)]"
1355,1355,22,1355_weyl groups type_weyl group corresponding_conjugacy classes weyl_representations weyl,"['weyl groups type', 'weyl group corresponding', 'conjugacy classes weyl', 'representations weyl', 'weyl groups', 'weyl group', 'group weyl', 'weyl group give', 'let weyl group', 'classes weyl']","['Positive conjugacy classes in Weyl groups   Let W be a Weyl group. We introduce the notion of positive conjugacy class in\nW. This generalizes the notion of regular elliptic conjugacy class in the sense\nof Springer.\n', ""Springer's work on unipotent classes and Weyl group representations   In this paper we discuss some of Springer's work on unipotent elements in a\nreductive groups and on representations of Weyl groups. Among the topics\nconsidered are Springer's bijection from the unipotent variety to the nilpotent\nvariety, Springer's example of nonrationality of certain representations of the\nHecke algebras associated to a Weyl group and the Springer representation of\nthe Weyl group associated to a unipotent element.\n"", 'From classes in the Weyl group to strata   In a 2015 paper we have defined a map from the set of conjugacy classes in a\nWeyl group W to the set of irreducible representations of W (its image\nparametrizes the strata of a reductive group with Weyl group W). In this paper\nwe provide evidence that this map makes sense even when W is replaced by a\nnoncrystallographic Coxeter group.\n']","[('weyl groups type', 0.7644317150115967), ('weyl group corresponding', 0.7486025094985962), ('conjugacy classes weyl', 0.7456051707267761), ('representations weyl', 0.7388944625854492), ('weyl groups', 0.7295247912406921), ('weyl group', 0.6878136396408081), ('group weyl', 0.6590973734855652), ('weyl group give', 0.6392344236373901), ('let weyl group', 0.6388198733329773), ('classes weyl', 0.5806408524513245)]"
1356,1356,22,1356_predator prey models_extinction persistence_stochastic evolutionary_persistence extinction,"['predator prey models', 'extinction persistence', 'stochastic evolutionary', 'persistence extinction', 'mean extinction', 'extinction population', 'extinction', 'predator prey', 'system stochastic', 'prey']","['Persistence and extinction dynamics in a stochastic predator-prey model\n  with emergent Allee effects   The Allee effect describes a decline in population fitness at low densities,\npotentially leading to extinction. In predator-prey systems, an emergent Allee\neffect can arise due to interactions such as density-dependent maturation rates\nand predation constraints. This work studies a stochastic predator-prey model\nwhere the prey population is structured into juvenile and adult stages, with\nmaturation following a nonlinear function. We introduce Ito-type stochastic\nperturbations in mortality rates to account for environmental variability. We\nfirst establish the positivity of solutions and derive sufficient conditions\nfor the stability of the trivial equilibrium, prey extinction, and conditional\npredator extinction. We then analyze prey persistence under specific maturation\nrate functions. Finally, numerical simulations illustrate the theoretical\nresults and their ecological implications.\n', 'Predator-prey density-dependent branching processes   Two density-dependent branching processes are considered to model\npredator-prey populations. For both models, preys are considered to be the main\nfood supply of predators. Moreover, in each generation the number of\nindividuals of each species is distributed according to a binomial distribution\nwith size given by the species population size and probability of success\ndepending on the density of preys per predator at the current generation. The\ndifference between the two proposed processes lies in the food supply of preys.\nIn the first one, we consider that preys have all the food they need at their\ndisposal while in the second one, we assume that the natural resources of the\nenvironment are limited and therefore there exists a competition among preys\nfor food supplies. Results on the fixation and extinction of both species as\nwell as conditions for the coexistence are provided for the first model. On the\nevent of coexistence of both populations and on the prey fixation event, the\nlimiting growth rates are obtained. For the second model, we prove that the\nextinction of the entire system occurs almost surely. Finally, the evolution of\nboth models over the generations is illustrated by simulated examples. Those\nexamples validate our analytical findings.\n', 'Long-time dynamics of a stochastic density dependent predator-prey model\n  with Holling II functional response and jumps   The existence and uniqueness of a global positive solution is proven for the\nsystem of stochastic differential equations describing a nonautonomous\nstochastic density dependent predator-prey model with Holling-type II\nfunctional response disturbed by white noise, centered and non-centered Poisson\nnoises. Sufficient conditions are obtained for stochastic ultimate boundedness,\nstochastic permanence, non-persistence in the mean, weak persistence in the\nmean and extinction of a population densities in the considered stochastic\npredator-prey model.\n']","[('predator prey models', 0.6217182278633118), ('extinction persistence', 0.5991255044937134), ('stochastic evolutionary', 0.5659799575805664), ('persistence extinction', 0.5647072792053223), ('mean extinction', 0.5308682322502136), ('extinction population', 0.5278751254081726), ('extinction', 0.5051882266998291), ('predator prey', 0.4864645004272461), ('system stochastic', 0.4655711352825165), ('prey', 0.4627152383327484)]"
1357,1357,22,1357_theory independence_theories particular_order theories_theory new notion,"['theory independence', 'theories particular', 'order theories', 'theory new notion', 'theories relative', 'theories symmetric', '_2 theories', 'first order theories', 'stable theory', 'theories give']","['Transitivity, lowness, and ranks in NSOP$_1$ theories   We develop the theory of Kim-independence in the context of NSOP$_{1}$\ntheories satsifying the existence axiom. We show that, in such theories,\nKim-independence is transitive and that $\\ind^{K}$-Morley sequences witness\nKim-dividing. As applications, we show that, under the assumption of existence,\nin a low NSOP$_{1}$ theory, Shelah strong types and Lascar strong types\ncoincide and, additionally, we introduce a notion of rank for NSOP$_{1}$\ntheories.\n', 'Kim-independence in positive logic   An important dividing line in the class of unstable theories is being\nNSOP$_1$, which is more general than being simple. In NSOP$_1$ theories forking\nindependence may not be as well-behaved as in stable or simple theories, so it\nis replaced by another independence notion, called Kim-independence. We\ngeneralise Kim-independence over models in NSOP$_1$ theories to positive logic\n-- a proper generalisation of first-order logic where negation is not built in,\nbut can be added as desired. For example, an important application is that we\ncan add hyperimaginary sorts to a positive theory to get another positive\ntheory, preserving NSOP$_1$ and various other properties. We prove that, in a\nthick positive NSOP$_1$ theory, Kim-independence over existentially closed\nmodels has all the nice properties that it is known to have in a first-order\nNSOP$_1$ theory. We also provide a Kim-Pillay style theorem, characterising\nwhich thick positive theories are NSOP$_1$ by the existence of a certain\nindependence relation. Furthermore, this independence relation must then be the\nsame as Kim-independence. Thickness is the mild assumption that being an\nindiscernible sequence is type-definable.\n  In first-order logic Kim-independence is defined in terms of Morley sequences\nin global invariant types. These may not exist in thick positive theories. We\nsolve this by working with Morley sequences in global Lascar-invariant types,\nwhich do exist in thick positive theories. We also simplify certain tree\nconstructions that were used in the study of Kim-independence in first-order\ntheories. In particular, we only work with trees of finite height.\n', 'Existence in NSOP$_1$ theories   We show that Kim-forking satisfies existence in all NSOP$_1$ theories.\n']","[('theory independence', 0.5107612609863281), ('theories particular', 0.5106398463249207), ('order theories', 0.5104109048843384), ('theory new notion', 0.504999577999115), ('theories relative', 0.48995378613471985), ('theories symmetric', 0.4699130058288574), ('_2 theories', 0.46878913044929504), ('first order theories', 0.4594323933124542), ('stable theory', 0.45065975189208984), ('theories give', 0.4333104193210602)]"
1358,1358,22,1358_coulomb friction_frictional contact_frictionless contact_friction coefficient,"['coulomb friction', 'frictional contact', 'frictionless contact', 'friction coefficient', 'friction law', 'viscoelastic', 'dry friction', 'boundary variational', 'variational inequalities', 'variational inequality']","['Well-posedness of evolutionary differential variational-hemivariational\n  inequalities and applications to frictional contact mechanics   In this paper, we study the well-posedness of a class of evolutionary\nvariational-hemivariational inequalities coupled with a nonlinear ordinary\ndifferential equation in Banach spaces. The proof is based on an iterative\napproximation scheme showing that the problem has a unique mild solution. In\naddition, we established the continuity of the flow map with respect to the\ninitial data. Under the general framework, we consider two new applications for\nmodelling of frictional contact for viscoelastic materials. In the first\napplication, we consider Coulomb friction with normal compliance, and in the\nsecond, normal damped response. The structure of the friction coefficient $\\mu$\nis new with motivation from geophysical applications in earth sciences with\ndependence on an external state variable $\\alpha$ and the slip rate\n$|\\dot{u}_\\tau|$.\n', 'Well-posedness of Constrained Evolutionary Differential\n  Variational-Hemivariational Inequalities   A system of a first order history-dependent evolutionary\nvariational-hemivariational inequality with unilateral constraints coupled with\na nonlinear ordinary differential equation in a Banach space is studied. Based\non a fixed point theorem for history dependent operators, results on the\nwell-posedness of the system are proved. Existence, uniqueness, continuous\ndependence of the solution on the data, and the solution regularity are\nestablished. Two applications of dynamic problems from contact mechanics\nillustrate the abstract results. First application is a unilateral viscoplastic\nfrictionless contact problem which leads to a hemivariational inequality for\nthe velocity field, and the second one deals with a viscoelastic frictional\ncontact problem which is described by a variational inequality.\n', 'A new class of history-dependent quasi variational-hemivariational\n  inequalities with constraints   In this paper we consider an abstract class of time-dependent quasi\nvariational-hemivariational inequalities which involves history-dependent\noperators and a set of unilateral constraints. First, we establish the\nexistence and uniqueness of solution by using a recent result for elliptic\nvariational-hemivariational inequalities in reflexive Banach spaces combined\nwith a fixed-point principle for history-dependent operators. Then, we apply\nthe abstract result to show the unique weak solvability to a quasistatic\nviscoelastic frictional contact problem. The contact law involves a unilateral\nSignorini-type condition for the normal velocity and the nonmonotone normal\ndamped response condition while the friction condition is a version of the\nCoulomb law of dry friction in which the friction bound depends on the\naccumulated slip.\n']","[('coulomb friction', 0.5019946694374084), ('frictional contact', 0.4925195574760437), ('frictionless contact', 0.4784381687641144), ('friction coefficient', 0.47793251276016235), ('friction law', 0.4665462374687195), ('viscoelastic', 0.43516141176223755), ('dry friction', 0.43354862928390503), ('boundary variational', 0.4247238039970398), ('variational inequalities', 0.4204599857330322), ('variational inequality', 0.4120662212371826)]"
1359,1359,22,1359_two dimensional lattice_bound states_schr odinger operators_operators lattices,"['two dimensional lattice', 'bound states', 'schr odinger operators', 'operators lattices', 'number bound states', 'dimensional lattice', 'many eigenvalues', 'discrete spectrum', 'particle schr odinger', 'isolated eigenvalues']","['The number and location of two particle Schr\\""odinger operators on a\n  lattice   We study the Schr\\""odinger operators ${H}_{\\lambda\\mu}(K)$ with\n$K\\in\\mathbb{T}^2$ being the fixed quasimomentum of a pair of particles,\nassociated with a system of two arbitrary particles on a two-dimensional\nlattice $\\mathbb{Z}^2$ with on-site and nearest-neighbor interactions of\nstrengths $\\lambda\\in\\mathbb{R}$ and $\\mu\\in\\mathbb{R}$, respectively. We\ndivide the $(\\lambda,\\mu)$-plane of parameters $\\lambda$ and $\\mu$ into\nconnected components, such that in each component, the Schr\\""{o}dinger operator\n$H_{\\lambda\\mu}(0)$ has a fixed number of eigenvalues. These eigenvalues are\nlocated both below the bottom of the essential spectrum and above its top.\nAdditionally, we establish a sharp lower bound for the number of isolated\neigenvalues of $H_{\\lambda\\mu}(K)$ within each connected component.\n', 'The number and location of eigenvalues for the two-particle\n  Schr\\""odinger operators on lattices   We study the Schr\\""odinger operators $H_{\\gamma \\lambda \\mu}(K)$, $K\\in\\T$\nbeing a fixed (quasi)momentum of the particles pair, associated with a system\nof two identical bosons on the one-dimensional lattice $\\mathbb{Z}$, where the\nreal quantities $\\gamma$, $\\lambda$ and $\\mu$ describe the interactions between\npairs of particles on one site, two nearest neighboring sites and next two\nneighboring sites, respectively. We found a partition of the three-dimensional\nspace $(\\gamma, \\lambda,\\mu)$ of interaction parameters into connected\ncomponents and the exact number of eigenvalues of this operator that lie below\nand above the essential spectrum, in each component. Moreover, we show that for\nany $K\\in\\T^d$ the number of eigenvalues of $H_{\\gamma\\lambda\\mu}(K)$ is not\nless than the corresponding number of eigenvalues of $H_{\\gamma\\lambda\\mu}(0)$.\n', 'Number of bound states of the Hamiltonian of a lattice two-boson system\n  with interactions up to the next neighbouring sites   We study the family $H_{\\gamma \\lambda \\mu}(K)$, $K\\in \\mathbb{T}^2,$ of\ndiscrete Schr\\""odinger operators, associated to the Hamiltonian of a system of\ntwo identical bosons on the two-dimen\\-sional lattice $\\mathbb{Z}^2,$\ninteracting through on one site, nearest-neighbour sites and\nnext-nearest-neighbour sites with interaction magnitudes $\\gamma,\\lambda$ and\n$\\mu,$ respectively. We prove there existence an important invariant subspace\nof operator $H_{\\gamma \\lambda \\mu}(0)$ such that the restriction of the\noperator $H_{\\gamma \\lambda \\mu}(0)$ on this subspace has at most two\neigenvalues lying both as below the essential spectrum as well as above it,\ndepending on the interaction magnitude $\\lambda,\\mu\\in \\mathbb{R}$ (only). We\nalso give a sharp lower bound for the number of eigenvalues of\n$H_{\\gamma\\lambda\\mu}(K)$.\n']","[('two dimensional lattice', 0.464608758687973), ('bound states', 0.43181365728378296), ('schr odinger operators', 0.42571279406547546), ('operators lattices', 0.4243329167366028), ('number bound states', 0.4226199984550476), ('dimensional lattice', 0.4219374656677246), ('many eigenvalues', 0.3970651924610138), ('discrete spectrum', 0.3867434561252594), ('particle schr odinger', 0.3830823600292206), ('isolated eigenvalues', 0.36335405707359314)]"
1360,1360,22,1360_jordan curves_jordan curve_smooth jordan_classical jordan,"['jordan curves', 'jordan curve', 'smooth jordan', 'classical jordan', 'curve admits', 'convex curves', 'curves every', 'quadrilaterals', 'closed curve', 'simple closed curve']","['Square-like quadrilaterals inscribed in embedded space curves   The square-peg problem asks if every Jordan curve in the plane has four\npoints which are the vertices of a square. The problem is open for continuous\nJordan curves, but it has been resolved for various regularity classes of\ncurves between continuous and $C^1$-smooth Jordan curves. Here, in a\ngeneralization of the square-peg problem, we consider embedded curves in space,\nand ask if they have inscribed quadrilaterals with equal sides and equal\ndiagonals. We call these quadrilaterals ""square-like"". We give a regularity\nclass (finite total curvature without cusps) in which we can prove that every\nembedded curve has an inscribed square-like quadrilateral. The key idea is to\nuse local data to show that short enough arcs have small curvature, thus ruling\nout small squares. This allows us to successfully use a limiting argument on\napproximating curves.\n', ""A Jordan Curve Theorem for 2-dimensional Tilings   The classical Jordan curve theorem for digital curves asserts that the Jordan\ncurve theorem remains valid in the Khalimsky plane. Since the Khalimsky plane\nis a quotient space of $\\mathbb R^2$ induced by a tiling of squares, it is\nnatural to ask for which other tilings of the plane it is possible to obtain a\nsimilar result. In this paper we prove a Jordan curve theorem which is valid\nfor every locally finite tiling of $\\mathbb R^2$. As a corollary of our result,\nwe generalize some classical Jordan curve theorems for grids of points,\nincluding Rosenfeld's theorem.\n"", ""On the Constructive Theory of Jordan Curves   Using a definition of Jordan curve similar to that of Dieudonn\\'e, we prove\nthat our notion is equivalent to that used by Berg et al. in their constructive\nproof of the Jordan Curve Theorem. We then establish a number of properties of\nJordan curves and their corresponding index functions, including the important\nProposition 32 and its corollaries about lines crossing a Jordan curve at a\nsmooth point. The final section is dedicated to proving that the index of a\npoint with respect to a piecewise smooth Jordan curve in the complex plane is\nidentical to the familiar winding number of the curve around that point. The\npaper is written within the framework of Bishop's constructive analysis.\nAlthough the work in Sections 3--5 is almost entirely new, the paper contains a\nsubstantial amount of expository material for the benefit of the reader.\n""]","[('jordan curves', 0.7113167643547058), ('jordan curve', 0.6658174395561218), ('smooth jordan', 0.5079368948936462), ('classical jordan', 0.5013576149940491), ('curve admits', 0.46708032488822937), ('convex curves', 0.4383649230003357), ('curves every', 0.42916685342788696), ('quadrilaterals', 0.39808371663093567), ('closed curve', 0.3863905072212219), ('simple closed curve', 0.38267987966537476)]"
1361,1361,22,1361_combinatorial curvature_circle packings_circle packing_sphere packings,"['combinatorial curvature', 'circle packings', 'circle packing', 'sphere packings', 'geodesic curvatures', 'curvature flows', 'hyperbolic metrics', 'curvatures', 'geodesic curvature', 'geodesic boundaries']","[""Hyperbolic Circle Packings and Total Geodesic Curvatures on Surfaces\n  with Boundary   This paper investigates a generalized hyperbolic circle packing (including\ncircles, horocycles or hypercycles) with respect to the total geodesic\ncurvatures on the surface with boundary. We mainly focus on the existence and\nrigidity of circle packing whose contact graph is the $1$-skeleton of a finite\npolygonal cellular decomposition, which is analogous to the construction of\nBobenko and Springborn [4]. Motivated by Colin de Verdi\\`ere's method [6], we\nintroduce the variational principle for generalized hyperbolic circle packings\non polygons. By analyzing limit behaviours of generalized circle packings on\npolygons, we give an existence and rigidity for the generalized hyperbolic\ncircle packing with conical singularities regarding the total geodesic\ncurvature on each vertex of the contact graph. As a consequence, we introduce\nthe combinatoral Ricci flow to find a desired circle packing with a prescribed\ntotal geodesic curvature on each vertex of the contact graph.\n"", 'Circle packings and total geodesic curvatures in hyperbolic background\n  geometry   In this paper, we study a new type of circle packings in hyperbolic\nbackground geometry. Horocycles and hypercycles are also considered in this\npacking. We give the existence and rigidity of this type of circle packing with\nconical singularities in terms of the total geodesic curvature. Moreover, we\nintroduce the combinatorial curvature flow on surfaces to find the desired\ncircle packing with the prescribed total geodesic curvature.\n', 'Combinatorial p-th Calabi Flows for Total Geodesic Curvatures in\n  hyperbolic background geometry   In hyperbolic background geometry, we investigate a generalized circle\npacking (including circles, horocycles and hypercycles) with conical\nsingularities on a surface with boundary, which has a total geodesic curvature\non each generalized circle of this circle packing and a discrete Gaussian\ncurvature on the center of each dual circle. The purpose of this paper is to\nfind this type of circle packings with prescribed total geodesic curvatures on\ngeneralized circles and discrete Gaussian curvatures on centers of dual\ncircles. To achieve this goal, we firstly establish existence and rigidity on\nthis type of circle packings by the variational principle. Secondly, for $p>1$,\nwe introduce combinatorial $p$-th Calabi flows to find the circle packing with\nprescribed total geodesic curvatures on generalized circles and discrete\nGaussian curvatures on centers of dual circles for the first time.\n']","[('combinatorial curvature', 0.6173940300941467), ('circle packings', 0.6063219904899597), ('circle packing', 0.593816339969635), ('sphere packings', 0.544108510017395), ('geodesic curvatures', 0.5288918614387512), ('curvature flows', 0.5099586844444275), ('hyperbolic metrics', 0.5063775777816772), ('curvatures', 0.5028194785118103), ('geodesic curvature', 0.49741724133491516), ('geodesic boundaries', 0.4884406626224518)]"
1362,1362,22,1362_symplectic structures_holomorphic symplectic manifolds_symplectic manifolds_symplectic structure,"['symplectic structures', 'holomorphic symplectic manifolds', 'symplectic manifolds', 'symplectic structure', 'structures symplectic', 'symplectic manifold', 'symplectic spaces', 'symplectic singularities', 'symplectic forms', 'holomorphic symplectic']","['Type one generalized Calabi--Yaus   We study type one generalized complex and generalized Calabi--Yau manifolds.\nWe introduce a cohomology class that obstructs the existence of a globally\ndefined, closed 2-form which agrees with the symplectic form on the leaves of\nthe generalized complex structure, the twisting class. We prove that in a\ncompact, type one, 4n-dimensional generalized complex manifold the Euler\ncharacteristic must be even and equal to the signature modulo four. The\ngeneralized Calabi--Yau condition places much stronger constrains: a compact\ntype one generalized Calabi--Yau fibers over the 2-torus and if the structure\nhas one compact leaf, then this fibration can be chosen to be the fibration by\nthe symplectic leaves of the generalized complex structure. If the twisting\nclass vanishes, one can always deform the structure so that it has a compact\nleaf. Finally we prove that every symplectic fibration over the 2-torus admits\na type one generalized Calabi--Yau structure.\n', 'Space of circle patterns on tori and its symplectic form   We consider circle patterns on closed tori equipped with complex projective\nstructures. There is an embedding of the space of circle patterns to the\nTeichm\\""{u}ller space of a punctured surface. Via the embedding, the\nWeil-Petersson symplectic form is pulled back to the space of circle patterns.\nWe investigate its non-degeneracy. On the other hand, we also complete a\nconjecture that the space of circle patterns is homeomorphic to the\nTeichm\\""{u}ller space of the closed torus.\n', 'Pullback of symplectic forms to the space of circle patterns   We consider circle patterns on surfaces with complex projective structures.\nWe investigate two symplectic forms pulled back to the deformation space of\ncircle patterns. The first one is Goldman\'s symplectic form on the space of\ncomplex projective structures on closed surfaces. The other is the\nWeil-Petersson symplectic form on the Teichm\\""uller space of punctured\nsurfaces. We show that their pullbacks to the space of circle patterns\ncoincide. It is applied to prove the smoothness of the deformation space, which\nis an essential step to the conjecture that the space of circle patterns is\nhomeomorphic to the Teichm\\""uller space of the closed surface. We further\nconjecture that the pullback of the symplectic forms is non-degenerate and\ndefines a symplectic structure on the space of circle patterns.\n']","[('symplectic structures', 0.7094211578369141), ('holomorphic symplectic manifolds', 0.7063241600990295), ('symplectic manifolds', 0.6993478536605835), ('symplectic structure', 0.6780487895011902), ('structures symplectic', 0.6760333776473999), ('symplectic manifold', 0.6664906144142151), ('symplectic spaces', 0.6604540348052979), ('symplectic singularities', 0.6513897180557251), ('symplectic forms', 0.6252570152282715), ('holomorphic symplectic', 0.6206395626068115)]"
1363,1363,22,1363_bundle compact ahler_compact ahler manifolds_ahler manifolds_holomorphic vector bundles,"['bundle compact ahler', 'compact ahler manifolds', 'ahler manifolds', 'holomorphic vector bundles', 'holomorphic vector bundle', 'vector bundles holomorphic', 'bundles holomorphic', 'hermitian yang mills', 'compact ahler surface', 'hermitian metrics']","['$Z$-critical equations for holomorphic vector bundles on K\\""ahler\n  surfaces   We prove that the existence of a $Z$-positive and $Z$-critical Hermitian\nmetric on a rank 2 holomorphic vector bundle over a compact K\\""ahler surface\nimplies that the bundle is $Z$-stable. As particular cases, we obtain stability\nresults for the deformed Hermitian Yang-Mills equation and the almost\nHermite-Einstein equation for rank 2 bundles over surfaces. We show examples of\n$Z$-unstable bundles and $Z$-critical metrics away from the large volume limit.\n', '$Z$-critical connections and Bridgeland stability conditions   We associate geometric partial differential equations on holomorphic vector\nbundles to Bridgeland stability conditions. We call solutions to these\nequations $Z$-critical connections, with $Z$ a central charge. Deformed\nHermitian Yang--Mills connections are a special case. We explain how our\nequations arise naturally through infinite dimensional moment maps.\n  Our main result shows that in the large volume limit, a sufficiently smooth\nholomorphic vector bundle admits a $Z$-critical connection if and only if it is\nasymptotically $Z$-stable. Even for the deformed Hermitian Yang--Mills\nequation, this provides the first examples of solutions in higher rank.\n', 'Hermitian-Yang-Mills connections on some complete non-compact K\\""ahler\n  manifolds   We give an algebraic criterion for the existence of projectively\nHermitian-Yang-Mills metrics on a holomorphic vector bundle $E$ over some\ncomplete non-compact K\\""ahler manifolds $(X,\\omega)$, where $X$ is the\ncomplement of a divisor in a compact K\\""ahler manifold and we impose some\nconditions on the cohomology class and the asymptotic behaviour of the K\\""ahler\nform $\\omega$. We introduce the notion of stability with respect to a pair of\n$(1,1)$-classes which generalizes the standard slope stability. We prove that\nthis new stability condition is both sufficient and necessary for the existence\nof projectively Hermitian-Yang-Mills metrics in our setting.\n']","[('bundle compact ahler', 0.6574971675872803), ('compact ahler manifolds', 0.6500148773193359), ('ahler manifolds', 0.6414226293563843), ('holomorphic vector bundles', 0.6263095736503601), ('holomorphic vector bundle', 0.6130351424217224), ('vector bundles holomorphic', 0.6099909543991089), ('bundles holomorphic', 0.6072176098823547), ('hermitian yang mills', 0.5803601145744324), ('compact ahler surface', 0.5775608420372009), ('hermitian metrics', 0.5363404750823975)]"
1364,1364,22,1364_tutte polynomials_polynomials matroids_tutte polynomial_polynomial matroid,"['tutte polynomials', 'polynomials matroids', 'tutte polynomial', 'polynomial matroid', 'graphs matroids', 'polynomials lattice', 'oriented matroids', 'invariant graphs', 'oriented matroid', 'valuated matroids']","[""Universal Tutte polynomial   The Tutte polynomial is a well-studied invariant of graphs and matroids. We\nfirst extend the Tutte polynomial from graphs to hypergraphs, and more\ngenerally from matroids to polymatroids, as a two-variable polynomial. Our\ndefinition is related to previous works of Cameron and Fink and of K\\'alm\\'an\nand Postnikov. We then define the universal Tutte polynomial $\\T_n$, which is a\npolynomial of degree $n$ in $2+(2^n-1)$ variables that specializes to the Tutte\npolynomials of all polymatroids (hence all matroids) on a ground set with $n$\nelements. The universal polynomial $\\T_n$ admits three kinds of symmetries:\ntranslation invariance, $S_n$-invariance, and duality.\n"", ""Invariants of Tutte Partitions and a $q$-Analogue   We describe a construction of the Tutte polynomial for both matroids and\n$q$-matroids based on an appropriate partition of the underlying support\nlattice into intervals that correspond to prime-free minors, which we call a\nTutte partition. We show that such partitions in the matroid case include the\nclass of partitions arising in Crapo's definition of the Tutte polynomial,\nwhile not representing a direct $q$-analogue of such partitions. We propose\naxioms of $q$-Tutte-Grothendiek invariance and show that this yields a\n$q$-analogue of Tutte-Grothendiek invariance. We establish the connection\nbetween the rank polynomial and the Tutte polynomial, showing that one can be\nobtained from the other by convolution.\n"", 'Extreme coefficients of multiplicity Tutte polynomials   The multiplicity Tutte polynomial, which includes the arithmetic Tutte\npolynomial, is a generalization of the classical Tutte polynomial of matroids.\nIn this paper, we obtain an expression of the general coefficient and the\nexpressions of six extreme coefficients of multiplicity Tutte polynomials. In\nparticular, an expression of the general coefficient and the expressions of\ncorresponding extreme coefficients of classical Tutte polynomial of matroids\nare deduced.\n']","[('tutte polynomials', 0.7164775133132935), ('polynomials matroids', 0.6884650588035583), ('tutte polynomial', 0.6855432391166687), ('polynomial matroid', 0.6436945199966431), ('graphs matroids', 0.5226323008537292), ('polynomials lattice', 0.5058237910270691), ('oriented matroids', 0.4899689555168152), ('invariant graphs', 0.4854951798915863), ('oriented matroid', 0.4643609821796417), ('valuated matroids', 0.4632572829723358)]"
1365,1365,22,1365_hyperbolic polynomials_negative roots_positive roots_roots positive,"['hyperbolic polynomials', 'negative roots', 'positive roots', 'roots positive', 'polynomial roots', 'descartes rule signs', 'coefficients roots', 'real polynomials', 'signs coefficients', 'roots real']","[""Hyperbolic polynomials and canonical sign patterns   A real univariate polynomial is hyperbolic if all its roots are real. By\nDescartes' rule of signs a hyperbolic polynomial (HP) with all coefficients\nnonvanishing has exactly $c$ positive and exactly $p$ negative roots counted\nwith multiplicity, where $c$ and $p$ are the numbers of sign changes and sign\npreservations in the sequence of its coefficients. We discuss the question: If\nthe moduli of all $c+p$ roots are distinct and ordered on the positive\nhalf-axis, then at which positions can the $p$ moduli of negative roots be\ndepending on the positions of the positive and negative signs of the\ncoefficients of the polynomial? We are especially interested in the choices of\nthese signs for which exactly one order of the moduli of the roots is possible.\n"", ""Descartes' rule of signs and moduli of roots   A hyperbolic polynomial (HP) is a real univariate polynomial with all roots\nreal. By Descartes' rule of signs a HP with all coefficients nonvanishing has\nexactly $c$ positive and exactly $p$ negative roots counted with multiplicity,\nwhere $c$ and $p$ are the numbers of sign changes and sign preservations in the\nsequence of its coefficients. For $c=1$ and $2$, we discuss the question: When\nthe moduli of all the roots of a HP are arranged in the increasing order on the\nreal half-line, at which positions can be the moduli of its positive roots\ndepending on the positions of the sign changes in the sequence of coefficients?\n"", ""Degree 5 polynomials and Descartes' rule of signs   For a univariate real polynomial without zero coefficients, Descartes' rule\nof signs (completed by an observation of Fourier) says that its numbers $pos$\nof positive and $neg$ of negative roots (counted with multiplicity) are\nmajorized respectively by the numbers $c$ and $p$ of sign changes and sign\npreservartions in the sequence of its coefficients, and that the differences\n$c-pos$ and $p-neg$ are even numbers. For degree 5 polynomials, it has been\nproved by A.~Albouy and Y.~Fu that there exist no such polynomials having three\ndistinct positive and no negative roots and whose signs of the coefficients are\n$(+,+,-,+,-,-)$ (or having three distinct negative and no positive roots and\nwhose signs of the coefficients are $(+,-,-,-,-,+)$). For degree 5 and when the\nleading coefficient is positive, these are all cases of numbers of positive and\nnegative roots (all distinct) and signs of the coefficients which are\ncompatible with Descartes' rule of signs, but for which there exist no such\npolynomials. We explain this non-existence and the existence in all other cases\nwith $d=5$ by means of pictures showing the discriminant set of the family of\npolynomials $x^5+x^4+ax^3+bx^2+cx+d$ together with the coordinate axes.\n""]","[('hyperbolic polynomials', 0.5713803172111511), ('negative roots', 0.47668397426605225), ('positive roots', 0.47222256660461426), ('roots positive', 0.4703420400619507), ('polynomial roots', 0.47018516063690186), ('descartes rule signs', 0.46377307176589966), ('coefficients roots', 0.4542670249938965), ('real polynomials', 0.43613332509994507), ('signs coefficients', 0.4343627095222473), ('roots real', 0.43020087480545044)]"
1366,1366,21,1366_harmonic measures_boundary partial omega_harmonic measure_quasiconformal harmonic,"['harmonic measures', 'boundary partial omega', 'harmonic measure', 'quasiconformal harmonic', 'harmonic functions', 'partial omega', 'subset partial omega', 'positive harmonic', 'setminus overline omega', 'boundary unique']","['A counterexample regarding a two-phase problem for harmonic measure in\n  VMO   Let $\\Omega^+\\subset\\mathbb R^{n+1}$ be a vanishing Reifenberg flat domain\nsuch that $\\Omega^+$ and $\\Omega^-=\\mathbb R^{n+1}\\setminus\\overline\n{\\Omega^+}$ have joint big pieces of chord-arc subdomains and the outer unit\nnormal to $\\Omega^+$ belongs to $VMO(\\omega^+)$, where $\\omega^\\pm$ is the\nharmonic measure of $\\Omega^\\pm$. Up to now it was an open question if these\nconditions imply that $\\log\\dfrac{d\\omega^-}{d\\omega^+} \\in VMO(\\omega^+)$. In\nthis paper we answer this question in the negative by constructing an\nappropriate counterexample in $\\mathbb R^2$, with the additional property that\nthe outer unit normal to $\\Omega^+$ is constant $\\omega^+$-a.e. in\n$\\partial\\Omega^+$.\n', 'The two-phase problem for harmonic measure in VMO and the chord-arc\n  condition   Let $\\Omega^+\\subset\\mathbb R^{n+1}$ be a bounded $\\delta$-Reifenberg flat\ndomain, with $\\delta>0$ small enough, possibly with locally infinite surface\nmeasure. Assume also that $\\Omega^-= \\mathbb R^{n+1}\\setminus\n\\overline{\\Omega^+}$ is an NTA domain as well and denote by $\\omega^+$ and\n$\\omega^-$ the respective harmonic measures of $\\Omega^+$ and $\\Omega^-$ with\npoles $p^\\pm\\in\\Omega^\\pm$. In this paper we show that the condition that\n$\\log\\dfrac{d\\omega^-}{d\\omega^+} \\in VMO(\\omega^+)$ is equivalent to\n$\\Omega^+$ being a chord-arc domain with inner normal belonging to\n$VMO(H^n|_{\\partial\\Omega^+})$.\n', 'The two-phase problem for harmonic measure in VMO   Let $\\Omega^+\\subset\\mathbb R^{n+1}$ be an NTA domain and let $\\Omega^-=\n\\mathbb R^{n+1}\\setminus \\overline{\\Omega^+}$ be an NTA domain as well. Denote\nby $\\omega^+$ and $\\omega^-$ their respective harmonic measures. Assume that\n$\\Omega^+$ is a $\\delta$-Reifenberg flat domain for some $\\delta>0$ small\nenough. In this paper we show that $\\log\\frac{d\\omega^-}{d\\omega^+}\\in\nVMO(\\omega^+)$ if and only if $\\Omega^+$ is vanishing Reifenberg flat,\n$\\Omega^+$ and $\\Omega^-$ have joint big pieces of chord-arc subdomains, and\nthe inner unit normal of $\\Omega^+$ has vanishing oscillation with respect to\nthe approximate normal. This result can be considered as a two-phase\ncounterpart of a more well known related one-phase problem for harmonic measure\nsolved by Kenig and Toro.\n']","[('harmonic measures', 0.559009850025177), ('boundary partial omega', 0.5563587546348572), ('harmonic measure', 0.5307415723800659), ('quasiconformal harmonic', 0.5045135617256165), ('harmonic functions', 0.42905890941619873), ('partial omega', 0.42547380924224854), ('subset partial omega', 0.42056962847709656), ('positive harmonic', 0.40790626406669617), ('setminus overline omega', 0.4036756455898285), ('boundary unique', 0.37561658024787903)]"
1367,1367,21,1367_edge computing_network edge_edge ai_edge intelligence,"['edge computing', 'network edge', 'edge ai', 'edge intelligence', 'wireless edge', 'edge networks', 'edge device', 'edge server', 'edge devices', 'edge']","['Integrated Sensing-Communication-Computation for Edge Artificial\n  Intelligence   Edge artificial intelligence (AI) has been a promising solution towards 6G to\nempower a series of advanced techniques such as digital twins, holographic\nprojection, semantic communications, and auto-driving, for achieving\nintelligence of everything. The performance of edge AI tasks, including edge\nlearning and edge AI inference, depends on the quality of three highly coupled\nprocesses, i.e., sensing for data acquisition, computation for information\nextraction, and communication for information transmission. However, these\nthree modules need to compete for network resources for enhancing their own\nquality-of-services. To this end, integrated sensing-communication-computation\n(ISCC) is of paramount significance for improving resource utilization as well\nas achieving the customized goals of edge AI tasks. By investigating the\ninterplay among the three modules, this article presents various kinds of ISCC\nschemes for federated edge learning tasks and edge AI inference tasks in both\napplication and physical layers.\n', 'Green Edge AI: A Contemporary Survey   Artificial intelligence (AI) technologies have emerged as pivotal enablers\nacross a multitude of industries largely due to their significant resurgence\nover the past decade. The transformative power of AI is primarily derived from\nthe utilization of deep neural networks (DNNs), which require extensive data\nfor training and substantial computational resources for processing.\nConsequently, DNN models are typically trained and deployed on resource-rich\ncloud servers. However, due to potential latency issues associated with cloud\ncommunications, deep learning (DL) workflows are increasingly being\ntransitioned to wireless edge networks in proximity to end-user devices (EUDs).\nThis shift is designed to support latency-sensitive applications and has given\nrise to a new paradigm of edge AI, which will play a critical role in upcoming\nsixth-generation (6G) networks to support ubiquitous AI applications. Despite\nits considerable potential, edge AI faces substantial challenges, mostly due to\nthe dichotomy between the resource limitations of wireless edge networks and\nthe resource-intensive nature of DL. Specifically, the acquisition of\nlarge-scale data, as well as the training and inference processes of DNNs, can\nrapidly deplete the battery energy of EUDs. This necessitates an\nenergy-conscious approach to edge AI to ensure both optimal and sustainable\nperformance. In this paper, we present a contemporary survey on green edge AI.\nWe commence by analyzing the principal energy consumption components of edge AI\nsystems to identify the fundamental design principles of green edge AI. Guided\nby these principles, we then explore energy-efficient design methodologies for\nthe three critical tasks in edge AI systems, including training data\nacquisition, edge training, and edge inference. Finally, we underscore\npotential future research directions to further enhance the energy efficiency\nof edge AI.\n', 'Integrated Sensing and Edge AI: Realizing Intelligent Perception in 6G   Sensing and edge artificial intelligence (AI) are envisioned as two essential\nand interconnected functions in sixth-generation (6G) mobile networks. On the\none hand, sensing-empowered applications rely on powerful AI models to extract\nfeatures and understand semantics from ubiquitous wireless sensors. On the\nother hand, the massive amount of sensory data serves as the fuel to\ncontinuously refine edge AI models. This deep integration of sensing and edge\nAI has given rise to a new task-oriented paradigm known as integrated sensing\nand edge AI (ISEA), which features a holistic design approach to communication,\nAI computation, and sensing for optimal sensing-task performance. In this\narticle, we present a comprehensive survey for ISEA. We first provide technical\npreliminaries for sensing, edge AI, and new communication paradigms in ISEA.\nThen, we study several use cases of ISEA to demonstrate its practical relevance\nand introduce current standardization and industrial progress. Next, the design\nprinciples, metrics, tradeoffs, and architectures of ISEA are established,\nfollowed by a thorough overview of ISEA techniques, including digital air\ninterface, over-the-air computation, and advanced signal processing. Its\ninterplay with various 6G advancements, e.g., new physical-layer and networking\ntechniques, are presented. Finally, we present future research opportunities in\nISEA, including the integration of foundation models, convergence of ISEA and\nintegrated sensing and communications (ISAC), and ultra-low-latency ISEA.\n']","[('edge computing', 0.7210689187049866), ('network edge', 0.6334623098373413), ('edge ai', 0.6312509775161743), ('edge intelligence', 0.6287999153137207), ('wireless edge', 0.6092740893363953), ('edge networks', 0.6050879955291748), ('edge device', 0.6038856506347656), ('edge server', 0.5894603729248047), ('edge devices', 0.5869961977005005), ('edge', 0.536927342414856)]"
1368,1368,21,1368_fluid structure interaction_thin films_thin film_film thickness,"['fluid structure interaction', 'thin films', 'thin film', 'film thickness', 'thin liquid', 'surface tension', 'fluid structure', 'solutions thin', 'flow incompressible', 'thin layer']","['Applications and Novel Regularization of the Thin-Film Equation   The classical no-slip boundary condition of the Navier-Stokes equations fails\nto describe the spreading motion of a droplet on a substrate due to the missing\nsmall-scale physics near the contact line. In this thesis, we introduce a novel\nregularization of the thin-film equation to model droplet spreading. The\nsolution of the regularized thin-film equation -- the Geometric Thin-Film\nEquation is studied and characterized. Two robust numerical solvers are\ndiscussed, notably, a fast and mesh-free numerical scheme for simulating\nthin-film flows in two and three spatial dimensions. Moreover, we prove the\nregularity and convergence of the numerical solutions. The existence and\nuniqueness of the solution of the Geometric Thin-Film Equation with respect to\na wide range of measure-valued initial conditions are also discussed.\n', 'Origin of filaments in finite-time in Newtonian and non-Newtonian\n  thin-films   The sticky fluids found in pitcher plant leaf vessels can leave fractal-like\nfilaments behind when dewetting from a substrate. To understand the origin of\nthese filaments, we investigate the dynamics of a retreating thin-film of\naqueous polyethylene oxide (PEO) solutions which partially wet polydimethyl\nsiloxane (PDMS) substrates. Under certain conditions the retreating film\ngenerates regularly-spaced liquid filaments. The early-stage thin-film dynamics\nof dewetting are investigated to identify a theoretical criterion for liquid\nfilament formation. Starting with a linear stability analysis of a Newtonian or\nsimple non-Newtonian (power-law) thin-film, a critical film thickness is\nidentified which depends on the Hamaker constant for the fluid-substrate pair\nand the surface tension of the fluid. When the measured film thickness is\nsmaller than this value, the film is unstable and forms filaments as a result\nof van der Waals forces dominating its behaviour. This critical film-height is\ncompared with experimental measurements of film thickness obtained for receding\nfilms of Newtonian (glycerol-water mixtures) and non-Newtonian (PEO) solutions\ngenerated on substrates inclined at angles 0 $^{\\circ}$, 30 $^{\\circ}$, and 60\n$^{\\circ}$ to the vertical. The observations of filament and its absence show\ngood agreement with the theory. The evolution of the thin-film shape is\nmodelled numerically to show that the formation of filaments arises because the\nthin-film equation features a singular solution after a finite-time, hence\ntermed a ""finite-time singularity"".\n', 'Justification of a nonlinear sixth-order thin-film equation as the\n  reduced model for a fluid -- structure interaction problem   Starting from a nonlinear 2D/1D fluid-structure interaction problem between a\nthin layer of a viscous fluid and a thin elastic structure, on the vanishing\nlimit of the relative fluid thickness, we rigorously derive a sixth-order\nthin-film equation describing the dynamics of vertical displacements of the\nstructure. The procedure is essentially based on quantitative energy estimates,\nquantified in terms of the relative fluid thickness, and a uniform no-contact\nresult between the structure and the solid substrate. The sixth-order thin-film\nequation is justified in the sense of strong convergence of rescaled structure\ndisplacements to the unique positive classical solution of the thin-film\nequation. Moreover, the limit fluid velocity and the pressure can be expressed\nsolely in terms of the solution to the thin-film equation.\n']","[('fluid structure interaction', 0.530007541179657), ('thin films', 0.5270666480064392), ('thin film', 0.4910011291503906), ('film thickness', 0.48194992542266846), ('thin liquid', 0.4453456699848175), ('surface tension', 0.44015029072761536), ('fluid structure', 0.42385008931159973), ('solutions thin', 0.37680482864379883), ('flow incompressible', 0.36257439851760864), ('thin layer', 0.35235458612442017)]"
1369,1369,21,1369_image reconstruction_reconstructed images_image reconstructions_deconvolution,"['image reconstruction', 'reconstructed images', 'image reconstructions', 'deconvolution', 'deep image prior', 'image prior', 'magnetization dynamics', 'reconstruction scheme', 'magnetization', 'reconstruction process']","['An $\\ell^1$-Plug-and-Play Approach for MPI Using a Zero Shot Denoiser\n  with Evaluation on the 3D Open MPI Dataset   Objective: Magnetic particle imaging (MPI) is an emerging medical imaging\nmodality which has gained increasing interest in recent years. Among the\nbenefits of MPI are its high temporal resolution, and that the technique does\nnot expose the specimen to any kind of ionizing radiation. It is based on the\nnon-linear response of magnetic nanoparticles to an applied magnetic field.\nFrom the electric signal measured in receive coils, the particle concentration\nhas to be reconstructed. Due to the ill-posedness of the reconstruction\nproblem, various regularization methods have been proposed for reconstruction\nranging from early stopping methods, via classical Tikhonov regularization and\niterative methods to modern machine learning approaches. In this work, we\ncontribute to the latter class: we propose a plug-and-play approach based on a\ngeneric zero-shot denoiser with an $\\ell^1$-prior.\n  Approach: We validate the reconstruction parameters of the method on a hybrid\ndataset and compare it with the baseline Tikhonov, DIP and the previous PP-MPI,\nwhich is a plug-and-play method with denoiser trained on MPI-friendly data.\n  Main results: We offer a quantitative and qualitative evaluation of the\nzero-shot plug-and-play approach on the 3D Open MPI dataset. Moreover, we show\nthe quality of the approach with different levels of preprocessing of the data.\n  Significance: The proposed method employs a zero-shot denoiser which has not\nbeen trained for the MPI task and therefore saves the cost for training.\nMoreover, it offers a method that can be potentially applied in future MPI\ncontexts.\n', 'Fast Trajectory-Independent Model-Based Reconstruction Algorithm for Multi-Dimensional Magnetic Particle Imaging Magnetic Particle Imaging (MPI) is a promising tomographic technique for visualizing the spatio-temporal distribution of superparamagnetic nanoparticles, with applications ranging from cancer detection to real-time cardiovascular monitoring. Traditional MPI reconstruction relies on either time-consuming calibration (measured system matrix) or model-based simulation of the forward operator. Recent developments have shown the applicability of Chebyshev polynomials to multi-dimensional Lissajous Field-Free Point (FFP) scans. This method is bound to the particular choice of sinusoidal scanning trajectories. In this paper, we present the first reconstruction on real 2D MPI data with a trajectory-independent model-based MPI reconstruction algorithm. We further develop the zero-shot Plug-and-Play (PnP) algorithm of the authors -- with automatic noise level estimation -- to address the present deconvolution problem, leveraging a state-of-the-art denoiser trained on natural images without retraining on MPI-specific data. We evaluate our method on the publicly available 2D FFP MPI dataset ``MPIdata: Equilibrium Model with Anisotropy"", featuring scans of six phantoms acquired using a Bruker preclinical scanner. Moreover, we show reconstruction performed on custom data on a 2D scanner with additional high-frequency excitation field and partial data. Our results demonstrate strong reconstruction capabilities across different scanning scenarios -- setting a precedent for general-purpose, flexible model-based MPI reconstruction.', 'Learned Discrepancy Reconstruction and Benchmark Dataset for Magnetic\n  Particle Imaging   Magnetic Particle Imaging (MPI) is an emerging imaging modality based on the\nmagnetic response of superparamagnetic iron oxide nanoparticles to achieve\nhigh-resolution and real-time imaging without harmful radiation. One key\nchallenge in the MPI image reconstruction task arises from its underlying noise\nmodel, which does not fulfill the implicit Gaussian assumptions that are made\nwhen applying traditional reconstruction approaches. To address this challenge,\nwe introduce the Learned Discrepancy Approach, a novel learning-based\nreconstruction method for inverse problems that includes a learned discrepancy\nfunction. It enhances traditional techniques by incorporating an invertible\nneural network to explicitly model problem-specific noise distributions. This\napproach does not rely on implicit Gaussian noise assumptions, making it\nespecially suited to handle the sophisticated noise model in MPI and also\napplicable to other inverse problems. To further advance MPI reconstruction\ntechniques, we introduce the MPI-MNIST dataset - a large collection of\nsimulated MPI measurements derived from the MNIST dataset of handwritten\ndigits. The dataset includes noise-perturbed measurements generated from\nstate-of-the-art model-based system matrices and measurements of a preclinical\nMPI scanner device. This provides a realistic and flexible environment for\nalgorithm testing. Validated against the MPI-MNIST dataset, our method\ndemonstrates significant improvements in reconstruction quality in terms of\nstructural similarity when compared to classical reconstruction techniques.\n']","[('image reconstruction', 0.45217540860176086), ('reconstructed images', 0.42995327711105347), ('image reconstructions', 0.42390477657318115), ('deconvolution', 0.40745335817337036), ('deep image prior', 0.38977134227752686), ('image prior', 0.37830591201782227), ('magnetization dynamics', 0.3777821362018585), ('reconstruction scheme', 0.37724587321281433), ('magnetization', 0.37543705105781555), ('reconstruction process', 0.3729044497013092)]"
1370,1370,21,1370_shape optimization_dimensional design_reducing dimensionality_shape design,"['shape optimization', 'dimensional design', 'reducing dimensionality', 'shape design', 'dimensionality reduction', 'design optimization', 'reduced dimensionality', 'design optimization problems', 'design parameter', 'design variables']","['A Survey on Design-space Dimensionality Reduction Methods for Shape\n  Optimization   The rapidly evolving field of engineering design of functional surfaces\nnecessitates sophisticated tools to manage the inherent complexity of\nhigh-dimensional design spaces. This survey paper offers a scoping review,\ni.e., a literature mapping synthesis borrowed from clinical medicine, delving\ninto the field of design-space dimensionality reduction techniques tailored for\nshape optimization, bridging traditional methods and cutting-edge technologies.\nDissecting the spectrum of these techniques, from classical linear approaches\nlike principal component analysis to more nuanced nonlinear methods such as\nautoencoders, the discussion extends to innovative physics-informed methods\nthat integrate physical data into the dimensionality reduction process,\nenhancing the physical relevance and effectiveness of reduced design spaces. By\nintegrating these methods into optimization frameworks, it is shown how they\nsignificantly mitigate the curse of dimensionality, streamline computational\nprocesses, and refine the design exploration and optimization of complex\nfunctional surfaces. The survey provides a classification of methods and\nhighlights the transformative impact of these techniques in simplifying design\nchallenges, thereby fostering more efficient and effective engineering\nsolutions.\n', 'Generative Models for Anomaly Detection and Design-Space Dimensionality\n  Reduction in Shape Optimization   Our work presents a novel approach to shape optimization, with the twofold\nobjective to improve the efficiency of global optimization algorithms while\npromoting the generation of high-quality designs during the optimization\nprocess free of geometrical anomalies. This is accomplished by reducing the\nnumber of the original design variables defining a new reduced subspace where\nthe geometrical variance is maximized and modeling the underlying generative\nprocess of the data via probabilistic linear latent variable models such as\nfactor analysis and probabilistic principal component analysis. We show that\nthe data follows approximately a Gaussian distribution when the shape\nmodification method is linear and the design variables are sampled uniformly at\nrandom, due to the direct application of the central limit theorem. The degree\nof anomalousness is measured in terms of Mahalanobis distance, and the paper\ndemonstrates that abnormal designs tend to exhibit a high value of this metric.\nThis enables the definition of a new optimization model where anomalous\ngeometries are penalized and consequently avoided during the optimization loop.\nThe procedure is demonstrated for hull shape optimization of the DTMB 5415\nmodel, extensively used as an international benchmark for shape optimization\nproblems. The global optimization routine is carried out using Bayesian\noptimization and the DIRECT algorithm. From the numerical results, the new\nframework improves the convergence of global optimization algorithms, while\nonly designs with high-quality geometrical features are generated through the\noptimization routine thereby avoiding the wastage of precious computationally\nexpensive simulations.\n', 'Extending Parametric Model Embedding with Physical Information for\n  Design-space Dimensionality Reduction in Shape Optimization   In this work, an extension of the parametric model embedding (PME) approach\nis presented, aiming to achieve more effective design-space dimensionality\nreduction for shape optimization in vehicle design. PME, rooted in principal\ncomponent analysis (PCA), not only identifies a reduced set of critical modes\nbut also re-parameterizes the original design space, enabling direct and\ninterpretable manipulations of shape modifications within the reduced space.\nAlongside the ""physics-informed"" version (PI-PME), which enriches geometry with\nlow-fidelity distributed and lumped physical quantities, a ""physics-driven""\nvariant (PD-PME) is introduced that focuses exclusively on physical parameters.\nBoth formulations employ PCA to capture the principal modes of variability yet\ndiffer in their balance between geometric and physical information, through the\nad-hoc definition of a weighted inner product. Through test cases involving the\nRAE-2822 airfoil, a bio-inspired underwater glider, a naval propeller, and the\nDTMB-5415 destroyer-type vessel, it is shown how the resulting frameworks\nprovide a first-level assessment of design variability, offer interpretability\nregarding which original variables most strongly affect performance, and\nefficiently bridge geometric and physical parameters. Furthermore, lumped\nphysical parameters can serve as a low-fidelity foundation for multi-fidelity\noptimization, directly leveraging the linear re-parameterization to drive the\nreduced design variables. Meanwhile, distributed physical parameters enable the\nconstruction of machine-learning-based reduced-order models to infer integral\nquantities of interest. By allowing the user to embed these insights early in\nthe design process, PI-PME and PD-PME facilitate more robust, cost-effective\nexploration, paving the way for subsequent high-fidelity optimization.\n']","[('shape optimization', 0.6099062561988831), ('dimensional design', 0.594551682472229), ('reducing dimensionality', 0.5441738367080688), ('shape design', 0.5339481830596924), ('dimensionality reduction', 0.5054928660392761), ('design optimization', 0.4658038020133972), ('reduced dimensionality', 0.4442622661590576), ('design optimization problems', 0.4333658218383789), ('design parameter', 0.42884504795074463), ('design variables', 0.4024972915649414)]"
1371,1371,21,1371_clusterings_semidefinite programming relaxations_semidefinite programming relaxation_cluster,"['clusterings', 'semidefinite programming relaxations', 'semidefinite programming relaxation', 'cluster', 'clustering', 'clusters', 'semidefinite programming', 'means clustering', 'clustering clustering', 'semidefinite relaxation']","['An Exact Algorithm for Semi-supervised Minimum Sum-of-Squares Clustering   The minimum sum-of-squares clustering (MSSC), or k-means type clustering, is\ntraditionally considered an unsupervised learning task. In recent years, the\nuse of background knowledge to improve the cluster quality and promote\ninterpretability of the clustering process has become a hot research topic at\nthe intersection of mathematical optimization and machine learning research.\nThe problem of taking advantage of background information in data clustering is\ncalled semi-supervised or constrained clustering. In this paper, we present a\nbranch-and-cut algorithm for semi-supervised MSSC, where background knowledge\nis incorporated as pairwise must-link and cannot-link constraints. For the\nlower bound procedure, we solve the semidefinite programming relaxation of the\nMSSC discrete optimization model, and we use a cutting-plane procedure for\nstrengthening the bound. For the upper bound, instead, by using integer\nprogramming tools, we use an adaptation of the k-means algorithm to the\nconstrained case. For the first time, the proposed global optimization\nalgorithm efficiently manages to solve real-world instances up to 800 data\npoints with different combinations of must-link and cannot-link constraints and\nwith a generic number of features. This problem size is about four times larger\nthan the one of the instances solved by state-of-the-art exact algorithms.\n', 'On the power of linear programming for K-means clustering   In [SIAM J. Optim., 2022], the authors introduced a new linear programming\n(LP) relaxation for K-means clustering. In this paper, we further investigate\nboth theoretical and computational properties of this relaxation. As evident\nfrom our numerical experiments with both synthetic real-world data sets, the\nproposed LP relaxation is almost always tight; i.e. its optimal solution is\nfeasible for the original nonconvex problem. To better understand this\nunexpected behaviour, on the theoretical side, we focus on K-means clustering\nwith two clusters, and we obtain sufficient conditions under which the LP\nrelaxation is tight. We further analyze the sufficient conditions when the\ninput is generated according to a popular stochastic model and obtain recovery\nguarantees for the LP relaxation. We conclude our theoretical study by\nconstructing a family of inputs for which the LP relaxation is never tight.\nDenoting by $n$ the number of data points to be clustered, the LP relaxation\ncontains $\\Omega(n^3)$ inequalities making it impractical for large data sets.\nTo address the scalability issue, by building upon a cutting-plane algorithm\ntogether with the GPU implementation of PDLP, a first-order method LP solver,\nwe develop an efficient algorithm that solves the proposed LP and hence the\nK-means clustering problem, for up to $n \\leq 4000$ data points.\n', 'The ratio-cut polytope and K-means clustering   We introduce the ratio-cut polytope defined as the convex hull of ratio-cut\nvectors corresponding to all partitions of $n$ points in $\\mathbb R^m$ into at\nmost $K$ clusters. This polytope is closely related to the convex hull of the\nfeasible region of a number of clustering problems such as K-means clustering\nand spectral clustering. We study the facial structure of the ratio-cut\npolytope and derive several types of facet-defining inequalities. We then\nconsider the problem of K-means clustering and introduce a novel linear\nprogramming (LP) relaxation for it. Subsequently, we focus on the case of two\nclusters and derive sufficient conditions under which the proposed LP\nrelaxation recovers the underlying clusters exactly. Namely, we consider the\nstochastic ball model, a popular generative model for K-means clustering, and\nwe show that if the separation distance between cluster centers satisfies\n$\\Delta > 1+\\sqrt 3$, then the LP relaxation recovers the planted clusters with\nhigh probability. This is a major improvement over the only existing recovery\nguarantee for an LP relaxation of K-means clustering stating that recovery is\npossible with high probability if and only if $\\Delta > 4$. Our numerical\nexperiments indicate that the proposed LP relaxation significantly outperforms\na popular semidefinite programming relaxation in recovering the planted\nclusters.\n']","[('clusterings', 0.585199773311615), ('semidefinite programming relaxations', 0.5843568444252014), ('semidefinite programming relaxation', 0.5761993527412415), ('cluster', 0.5283669829368591), ('clustering', 0.5271127223968506), ('clusters', 0.5101697444915771), ('semidefinite programming', 0.49791109561920166), ('means clustering', 0.4922597110271454), ('clustering clustering', 0.49086788296699524), ('semidefinite relaxation', 0.486300528049469)]"
1372,1372,21,1372_nevanlinna functions_herglotz nevanlinna functions_herglotz nevanlinna_holomorphic functions,"['nevanlinna functions', 'herglotz nevanlinna functions', 'herglotz nevanlinna', 'holomorphic functions', 'nevanlinna pick', 'finite blaschke products', 'nevanlinna', 'analytic functions', 'functions material', 'functions disc']","['Characterizations of Herglotz-Nevanlinna functions using positive\n  semi-definite functions and the Nevanlinna kernel in several variables   In this paper, we give several characterizations of Herglotz-Nevanlinna\nfunctions in terms of a specific type of positive semi-definite functions\ncalled Poisson-type functions. This allows us to propose a multidimensional\nanalogue of the classical Nevanlinna kernel and a definition of generalized\nNevanlinna functions in several variables. Furthermore, a characterization of\nthe symmetric extension of a Herglotz-Nevanlinna function is also given. The\nsubclass of Loewner functions is also discussed, as well as an interpretation\nof the main result in terms of holomorphic functions on the unit polydisk with\nnon-negative real part.\n', 'On applications of Herglotz-Nevanlinna functions in material sciences,\n  I: classical theory and applications of sum rules   This is the first part of the review article which focuses on theory and\napplications of Herglotz-Nevanlinna functions in material sciences. It starts\nwith the definition of scalar valued Herglotz-Nevanlinna functions and explains\nin detail the theorems that are pertinent to applications, followed by a short\noverview of the matrix-valued and operator-valued versions of these functions\nand the properties that carry over from scalar cases. The theory is\ncomplemented by some applications from electromagnetics that are related to the\nsum rules. More applications of Herglotz Nevanlinnna functions in material\nsciences can be found in Part II.\n', 'On applications of Herglotz-Nevanlinna functions in material sciences,\n  II: extended applications and generalized theory   Part II of the review article focuses on the applications of\nHerglotz-Nevanlinna functions in material sciences. It presents a diverse set\nof applications with details and the role of Herglotz-Nevanlinna functions\nclearly pointed out. This paper is concluded by a collection of existent\ngeneralizations of the class of Herglotz-Nevanlinna functions that are\nmotivated by potential applications.\n']","[('nevanlinna functions', 0.6360498070716858), ('herglotz nevanlinna functions', 0.5653047561645508), ('herglotz nevanlinna', 0.4517764747142792), ('holomorphic functions', 0.42614275217056274), ('nevanlinna pick', 0.4195386469364166), ('finite blaschke products', 0.40108612179756165), ('nevanlinna', 0.39493340253829956), ('analytic functions', 0.392879843711853), ('functions material', 0.3921319246292114), ('functions disc', 0.38308149576187134)]"
1373,1373,21,1373_control lyapunov functions_control lyapunov clf_control barrier functions_control lyapunov,"['control lyapunov functions', 'control lyapunov clf', 'control barrier functions', 'control lyapunov', 'lyapunov clf', 'lyapunov functions', 'stabilizing control law', 'control barrier', 'safety stability', 'stability safety']","['Safe and Stable Filter Design Using a Relaxed Compatibitlity Control\n  Barrier -- Lyapunov Condition   In this paper, we propose a quadratic programming-based filter for safe and\nstable controller design, via a Control Barrier Function (CBF) and a Control\nLyapunov Function (CLF). Our method guarantees safety and local asymptotic\nstability without the need for an asymptotically stabilizing control law.\nFeasibility of the proposed program is ensured under a mild regularity\ncondition, termed relaxed compatibility between the CLF and CBF. The resulting\noptimal control law is guaranteed to be locally Lipschitz continuous. We also\nanalyze the closed-loop behaviour by characterizing the equilibrium points, and\nverifying that there are no equilibrium points in the interior of the control\ninvariant set except at the origin. For a polynomial system and a\nsemi-algebraic safe set, we provide a sum-of-squares program to design a\nrelaxed compatible pair of CLF and CBF. The proposed approach is compared with\nother methods in the literature using numerical examples, exhibits superior\nfilter performance and guarantees safety and local stability.\n', 'Control Synthesis for Stability and Safety by Differential\n  Complementarity Problem   This paper develops a novel control synthesis method for safe stabilization\nof control-affine systems as a Differential Complementarity Problem (DCP). Our\ndesign uses a control Lyapunov function (CLF) and a control barrier function\n(CBF) to define complementarity constraints in the DCP formulation to certify\nstability and safety, respectively. The CLF-CBF-DCP controller imposes\nstability as a soft constraint, which is automatically relaxed when the safety\nconstraint is active, without the need for parameter tuning or optimization. We\nstudy the closed-loop system behavior with the CLF-CBF-DCP controller and\nidentify conditions on the existence of local equilibria. Although in certain\ncases the controller yields undesirable local equilibria, those can be confined\nto a small subset of the safe set boundary by proper choice of the control\nparameters. Then, our method can avoid undesirable equilibria that CLF-CBF\nquadratic programming techniques encounter.\n', 'Converse Theorems for Certificates of Safety and Stability   Motivated by the key role of control barrier functions (CBFs) in assessing\nsafety and enabling the synthesis of safe controllers in nonlinear control\nsystems, this paper presents a suite of converse results on CBFs. Given any\nsafe set, we first identify a set of general sufficient conditions which\nguarantee the existence of a CBF. Our technical analysis also enables us to\ndefine an extended notion of CBF which is always guaranteed to exist if the set\nis safe. We next turn our attention to the problem of joint safety and\nstability, and give conditions under which the notions of control\nLyapunov-barrier function (CLBF) and compatible control Lyapunov function (CLF)\nand CBF pair are guaranteed to exist. Finally, we identify conditions under\nwhich a CLBF and a compatible CLF-CBF pair can be constructed from a\nnon-compatible CLF-CBF pair. Throughout the paper, we intersperse different\nexamples and counterexamples to motivate our results and position them within\nthe state of the art.\n']","[('control lyapunov functions', 0.6411155462265015), ('control lyapunov clf', 0.6387235522270203), ('control barrier functions', 0.5988990068435669), ('control lyapunov', 0.5898647308349609), ('lyapunov clf', 0.5648557543754578), ('lyapunov functions', 0.5569519996643066), ('stabilizing control law', 0.5420554876327515), ('control barrier', 0.5310603380203247), ('safety stability', 0.5175075531005859), ('stability safety', 0.5091074109077454)]"
1374,1374,21,1374_yang mills theory_mathcal super yang_supersymmetric yang mills_positive grassmannian,"['yang mills theory', 'mathcal super yang', 'supersymmetric yang mills', 'positive grassmannian', 'scattering amplitudes', 'grassmannian gr', 'super yang mills', 'grassmannian', 'supersymmetric yang', 'orthogonal grassmannian']","['The Amplituhedron BCFW Triangulation   The amplituhedron Ank4 is a geometric object, introduced by Arkani-Hamed and\nTrnka (2013) in the study of scattering amplitudes in quantum field theories.\nThey conjecture that Ank4 admits a decomposition into images of BCFW positroid\ncells, arising from the Britto--Cachazo--Feng--Witten recurrence (2005). We\nprove that this conjecture is true.\n', 'The positive tropical Grassmannian, the hypersimplex, and the m=2\n  amplituhedron   The study of the moment map from the Grassmannian to the hypersimplex, and\nthe relation between torus orbits and matroid polytopes, dates back to the\nfoundational 1987 work of Gelfand-Goresky-MacPherson-Serganova. On the other\nhand, the amplituhedron is a very new object, defined by Arkani-Hamed-Trnka in\nconnection with scattering amplitudes in $\\mathcal{N}=4$ super Yang-Mills\ntheory. In this paper we discover a striking duality between the moment map\n$\\mu:Gr^{\\geq0}_{k+1,n}\\to\\Delta_{k+1,n}$ from the positive Grassmannian\n$Gr^{\\geq0}_{k+1,n}$ to the hypersimplex, and the amplituhedron map\n$\\tilde{Z}:Gr^{\\geq0}_{k,n}\\to\\mathcal{A}_{n,k,2}(Z)$ from $Gr^{\\geq0}_{k,n}$\nto the $m=2$ amplituhedron. We consider the positroid dissections of both\nobjects, which informally, are subdivisions of $\\Delta_{k+1,n}$ (respectively,\n$\\mathcal{A}_{n,k,2}(Z)$) into a disjoint union of images of positroid cells of\nthe positive Grassmannian. At first glance, $\\Delta_{k+1,n}$ and\n$\\mathcal{A}_{n,k,2}(Z)$ seem very different - the former is an\n$(n-1)$-dimensional polytope, while the latter is a $2k$-dimensional\nnon-polytopal subset of $Gr_{k,k+2}$. Nevertheless, we conjecture that\npositroid dissections of $\\Delta_{k+1,n}$ are in bijection with positroid\ndissections of $\\mathcal{A}_{n,k,2}(Z)$ via a map we call T-duality. We prove\nthis conjecture for the (infinite) class of BCFW dissections and give\nadditional experimental evidence. Moreover, we prove that the positive tropical\nGrassmannian is the secondary fan for the regular positroid subdivisions of the\nhypersimplex, and propose that it also controls the T-dual positroid\nsubdivisions of the amplituhedron. Along the way, we prove that a matroid\npolytope is a positroid polytope if and only if all two-dimensional faces are\npositroid polytopes. Towards the goal of generalizing T-duality for higher $m$,\nwe also define the momentum amplituhedron for any even $m$.\n', 'BCFW tilings and cluster adjacency for the amplituhedron   In 2005, Britto, Cachazo, Feng and Witten gave a recurrence (now known as the\nBCFW recurrence) for computing scattering amplitudes in N=4 super Yang Mills\ntheory. Arkani-Hamed and Trnka subsequently introduced the amplituhedron to\ngive a geometric interpretation of the BCFW recurrence. Arkani-Hamed and Trnka\nconjectured that each way of iterating the BCFW recurrence gives a\n""triangulation"" or ""tiling"" of the m=4 amplituhedron. In this article we prove\nthe BCFW tiling conjecture of Arkani-Hamed and Trnka. We also prove the cluster\nadjacency conjecture for BCFW tiles of the amplituhedron, which says that\nfacets of tiles are cut out by collections of compatible cluster variables for\nthe Grassmannian Gr(4,n). Moreover we show that each BCFW tile is the subset of\nthe Grassmannian where certain cluster variables have particular signs.\n']","[('yang mills theory', 0.5132643580436707), ('mathcal super yang', 0.4892003536224365), ('supersymmetric yang mills', 0.48614680767059326), ('positive grassmannian', 0.46855026483535767), ('scattering amplitudes', 0.46105432510375977), ('grassmannian gr', 0.452642023563385), ('super yang mills', 0.43622881174087524), ('grassmannian', 0.4269271790981293), ('supersymmetric yang', 0.4223412573337555), ('orthogonal grassmannian', 0.40598490834236145)]"
1375,1375,21,1375_existence global attractor_global attractor_global attractors_classical navier stokes,"['existence global attractor', 'global attractor', 'global attractors', 'classical navier stokes', 'navier stokes equations', 'navier stokes', 'attractor mathcal', 'dimensional navier stokes', 'stokes equations existence', 'bounds attractor']","[""Asymptotic behavior of a generalized Navier-Stokes-alpha model and\n  applications to related models   We consider a generalized alpha-type model in the whole three-dimensional\nspace and driven by a stationary (time-independent) external force. This model\ncontains as particular cases some relevant equations of the fluid dynamics,\namong them the Navier-Stokes-Bardina's model, the critical alpha-model, the\nfractional and the classical Navier-Stokes equations with an additional\ndrag/friction term. First, we study the existence and in some cases the\nuniqueness of finite energy solutions. Then, we use a general framework to\nstudy their long time behavior with respect to the weak and the strong topology\nof the phase space. When the uniqueness of solutions is known, we prove the\nexistence of a strong global attractor. Moreover, we proof the existence of a\nweak global attractor in the case when the uniqueness of solutions is unknown.\n  The weak/global attractor contains a particular kind of solutions to our\nmodel, so-called the stationary solutions. In all generality we construct these\nsolutions, and we study their uniqueness, orbital and asymptotic stability in\nthe case when some physical constants in our model are large enough. As a\nbi-product, we show that in some cases the weak/global attractor reduces down\nto the unique stationary solution.\n"", 'On the long-time behavior for a damped Navier-Stokes-Bardina model   In this paper, we consider a damped Navier-Stokes-Bardina model posed on the\nwhole three-dimensional. These equations have an important physical motivation\nand they arise from some oceanic model. From the mathematical point of view,\nthey write down as the well-know Navier-Stokes equations with an additional\nnonlocal operator in their nonlinear transport term, and moreover, with an\nadditional damping term depending of a parameter $\\beta>0$. We study first the\nexistence and uniqueness of global in time weak solutions in the energy space.\nThereafter, our main objective is to describe the long time behavior of these\nsolutions. For this, we use some tools in the theory of dynamical systems to\nprove the existence of a global attractor, which is a compact subset in the\nenergy space attracting all the weak solutions when the time goes to infinity.\nMoreover, we derive an upper bound for the fractal dimension of the global\nattractor associated to these equations.\n  Finally, we find a range of values for the damping parameter $\\beta>0$, where\nwe are able to give an acutely description of the internal structure of the\nglobal attractor. More precisely, we prove that the global attractor only\ncontains the stationary (time-independing) solution of the damped\nNavier-Stokes-Bardina equations.\n', 'Weak global attractor for the $3D$-Navier-Stokes equations via the\n  globally modified Navier-Stokes equations   In this paper we obtain the existence of a weak global attractor for the\nthree-dimensional Navier-Stokes equations, that is, a weakly compact set with\nan invariance property, that uniformly attracts solutions, with respect to the\nweak topology, for initial data in bounded sets. To that end, we define this\nweak global attractor in terms of limits of solutions of the globally modified\nNavier-Stokes equations in the weak topology. We use the theory of semilinear\nparabolic equations and $\\epsilon$-regularity to obtain the local well\nposedness for the globally modified Navier-Stokes equations and the existence\nof a global attractor and its regularity.\n']","[('existence global attractor', 0.6988993287086487), ('global attractor', 0.6175581216812134), ('global attractors', 0.6087902188301086), ('classical navier stokes', 0.5795769691467285), ('navier stokes equations', 0.5729464888572693), ('navier stokes', 0.559617817401886), ('attractor mathcal', 0.5525898933410645), ('dimensional navier stokes', 0.549566924571991), ('stokes equations existence', 0.5479966402053833), ('bounds attractor', 0.5227794647216797)]"
1376,1376,21,1376_chow rings_curves genus three_chow ring_stable curves genus,"['chow rings', 'curves genus three', 'chow ring', 'stable curves genus', 'ring moduli space', 'equivariant chow', 'rings moduli', 'curves genus', 'hyperelliptic curves genus', 'moduli stacks']","['The (almost) integral Chow ring of $\\widetilde{\\mathcal{M}}_3^7$   This paper is the third in a series of four papers aiming to describe the\n(almost integral) Chow ring of $\\overline{\\mathcal{M}}_3$, the moduli stack of\nstable curves of genus $3$. In this paper, we compute the Chow ring of\n$\\widetilde{\\mathcal{M}}_3^7$ with $\\mathbb{Z}[1/6]$-coefficients.\n', 'The (almost) integral Chow ring of $\\overline{\\mathcal{M}}_3$   This paper is the fourth in a series of four papers aiming to describe the\n(almost integral) Chow ring of $\\overline{\\mathcal{M}}_3$, the moduli stack of\nstable curves of genus $3$. In this paper, we finally compute the Chow ring of\n$\\overline{\\mathcal{M}}_3$ with $\\mathbb{Z}[1/6]$-coefficients.\n', '$A_r$-stable curves and the Chow ring of $\\overline{\\mathcal{M}}_3$   In this work, we introduce the moduli stack $\\widetilde{\\mathcal{M}}_{g,n}^r$\nof $n$-pointed, $A_r$-stable curves of genus $g$ and use it to compute the Chow\nring of $\\overline{\\mathcal{M}}_3$. As a byproduct, we also compute the Chow\nring of $\\widetilde{\\mathcal{M}}_3^7$. All the Chow rings are assumed to be\nwith coefficients in $\\mathbb{Z}[1/6]$.\n']","[('chow rings', 0.5850546360015869), ('curves genus three', 0.5721181035041809), ('chow ring', 0.5714902281761169), ('stable curves genus', 0.5321334004402161), ('ring moduli space', 0.5116882920265198), ('equivariant chow', 0.5033814311027527), ('rings moduli', 0.5010390281677246), ('curves genus', 0.4980088770389557), ('hyperelliptic curves genus', 0.4898262619972229), ('moduli stacks', 0.4897995889186859)]"
1377,1377,21,1377_metric projections_metric projection_directional differentiability_hilbert spaces generalized,"['metric projections', 'metric projection', 'directional differentiability', 'hilbert spaces generalized', 'smooth banach spaces', 'operator hilbert spaces', 'projection operator', 'smooth banach space', 'uniformly smooth banach', 'hilbert spaces']","['Strict Frechet and generalized differentiability of the metric\n  projection operator onto balls in Hilbert spaces   In this paper, we prove strict Frechet differentiability of the metric\nprojection operator onto closed balls in Hilbert spaces, and we find exact\nexpressions for Frechet derivatives. Since Frechet differentiability implies\nGateaux directional differentiability, the results obtained in this paper\nstrengthens the results in [8] and [10] about the directional differentiability\nof the metric projection operator onto closed balls in Hilbert spaces. We apply\nthe Frechet differentiability of the metric projection onto closed balls in\nHilbert spaces to study the generalized differentiability of the metric\nprojection operator.\n', 'Mordukhovich derivatives of the metric projection operator in uniformly\n  convex and uniformly smooth Banach spaces   In this paper, we investigate the properties of the Mordukhovich derivatives\nof the metric projection operator onto closed balls, closed and convex\ncylinders and positive cones in uniformly convex and uniformly smooth Banach\nspaces. We find the exact expressions for Mordukhovich derivatives of the\nmetric projection operator.\n', 'Frechet differentiability of the metric projection operator in Banach\n  spaces   In this paper, we prove Frechet differentiability of the metric projection\noperator onto closed balls, closed and convex cylinders and positives cones in\nuniformly convex and uniformly smooth Banach spaces. With respect to these\nclosed and convex subsets, we find the exact expressions for Frechet\nderivatives and Gateaux directional derivatives of the metric projection\noperator.\n']","[('metric projections', 0.5644853711128235), ('metric projection', 0.5611218810081482), ('directional differentiability', 0.508832573890686), ('hilbert spaces generalized', 0.5037838816642761), ('smooth banach spaces', 0.49253150820732117), ('operator hilbert spaces', 0.4864048659801483), ('projection operator', 0.48464435338974), ('smooth banach space', 0.48451197147369385), ('uniformly smooth banach', 0.4711064100265503), ('hilbert spaces', 0.4695378541946411)]"
1378,1378,21,1378_self propelled particles_propelled particles_particle dynamics_self propelled,"['self propelled particles', 'propelled particles', 'particle dynamics', 'self propelled', 'collective motion', 'particle systems', 'flocking', 'swarming', 'propelled', 'swarms']","[""Stability of Translating States for Self-propelled Swarms with Quadratic\n  Potential   The main result of this paper is proving the stability of translating states\n(flocking states) for the system of $n$-coupled self-propelled agents governed\nby $\\ddot r_k = (1-|\\dot r_k|^2)\\dot r_k - \\frac{1}{n}\\sum_{j=1}^n(r_k-r_j)$,\n$r_k\\in \\mathbb R^2$. A flocking state is a solution where all agents move with\nidentical velocity, of magnitude one. Numerical explorations have shown that\nfor a large set of initial conditions, after some drift, the particles'\nvelocities align, and the distance between agents tends to zero. We prove that\nevery solution starting near a translating state asymptotically approaches a\ntranslating state nearby, an asymptotic behavior exclusive to swarms in the\nplane. We quantify the rate of convergence for the directional drift, the mean\nfield speed, and the oscillations in the direction normal to the motion. The\nlatter decay at a rate of $1/ \\sqrt t$, mimicking the oscillations of some\nsystems with almost periodic coefficients and cubic nonlinearities. We give\nsufficient conditions for that class of systems to have an asymptotically\nstable origin.\n"", 'Large-scale dynamics of self-propelled particles moving through\n  obstacles: model derivation and pattern formation   We model and study the patterns created through the interaction of\ncollectively moving self-propelled particles (SPPs) and elastically tethered\nobstacles. Simulations of an individual-based model reveal at least three\ndistinct large-scale patterns: travelling bands, trails and moving clusters.\nThis motivates the derivation of a macroscopic partial differential equations\nmodel for the interactions between the self-propelled particles and the\nobstacles, for which we assume large tether stiffness. The result is a coupled\nsystem of non-linear, non-local partial differential equations. Linear\nstability analysis shows that patterning is expected if the interactions are\nstrong enough and allows for the predictions of pattern size from model\nparameters. The macroscopic equations reveal that the obstacle interactions\ninduce short-ranged SPP aggregation, irrespective of whether obstacles and SPPs\nare attractive or repulsive.\n', ""On Spatial Cohesiveness of Second-Order Self-Propelled Swarming Systems   The study of emergent behavior of swarms is of great interest for applied\nsciences. One of the most fundamental questions for self-organizing swarms is\nwhether the swarms disperse or remain in a spatially cohesive configuration. In\nthe paper we study dissipativity properties and spatial cohesiveness of the\nswarm of self-propelled particles governed by the model $\\ddot r_k = -p_k(|\\dot\nr_k|)\\dot r_k - \\sum_m a_{k,m}r_m$, where $r_k\\in \\mathbb R^d$, $k=1,\\ldots,n$,\nand $A = \\{a_{k,m}\\}$ is a symmetric positive-semidefinie matrix. The\nself-propulsion term is assumed to be continuously differentiable and to grow\nfaster than $1/z$, that is, $p_k(z)z\\to\\infty $ as $z\\to\\infty$. We establish\nthat the velocity and acceleration of the particles are ultimately bounded. We\nshow that when $\\ker (A)$ is trivial, the positions of the particles are also\nultimately bounded. For systems with $\\ker (A)\\neq \\{0\\}$, we show that, while\nthe system might infinitely drift away from its initial location, the particles\nremain within a bounded distance from the generalized center of mass of the\nsystem, which geometrically coincides with the weighted average of agent\npositions. The weights are determined by the coefficients of the projection\nmatrix onto $\\ker (A)$. We also include the proof of the ultimate boundedness\nof velocities and accelerations for systems with bounded coupling, including\nsystems coupled via the Morse potential.\n  In our proof we switch to the velocity-acceleration coordinates and focus on\nthe study of dissipativity properties for a more general class of Li\\'enard\nsystems $\\ddot x_k = -\\mathbb F_k(x_k)\\cdot \\dot x_k -\\sum_{m} a_{k,m}x_m$,\n$k=1,\\ldots,n$, $\\mathbb F_k(x) = \\nabla F_k(x)$ with $F_k: \\mathbb\nR^d\\rightarrow \\mathbb R^d$ given by $F_k(x) = p_k(|x|)x$.\n""]","[('self propelled particles', 0.6668226718902588), ('propelled particles', 0.5943695306777954), ('particle dynamics', 0.5407085418701172), ('self propelled', 0.5225757360458374), ('collective motion', 0.5201654434204102), ('particle systems', 0.4618660807609558), ('flocking', 0.44693416357040405), ('swarming', 0.4331108629703522), ('propelled', 0.4153320789337158), ('swarms', 0.40316012501716614)]"
1379,1379,21,1379_squeezing_bounded domains_polydisk_kobayashi metric,"['squeezing', 'bounded domains', 'polydisk', 'kobayashi metric', 'boundary behavior', 'strongly convex domains', 'higher dimensional hyperbolic', 'planar domains', 'convex domains', 'mathbb convex domains']","['$d$-balanced squeezing function   We introduce the notion of squeezing function corresponding to $d$-balanced\ndomains motivated by the concept of generalized squeezing function given by\nRong and Yang. In this work we study some of its properties and its relation\nwith Fridman invariant.\n', 'The squeezing function on doubly-connected domains via the Loewner\n  differential equation   For any bounded domains $\\Omega$ in $\\mathbb{C}^{n}$, Deng, Guan and Zhang\nintroduced the squeezing function $S_\\Omega (z)$ which is a biholomorphic\ninvariant of bounded domains. We show that for $n=1$, the squeezing function on\nan annulus $A_r = \\lbrace z \\in \\mathbb{C} : r <|z| <1 \\rbrace$ is given by\n$S_{A_r}(z)= \\max \\left\\lbrace |z| ,\\frac{r}{|z|} \\right\\rbrace$ for all\n$0<r<1$. This disproves the conjectured formula for the squeezing function\nproposed by Deng, Guan and Zhang and establishes (up to biholomorphisms) the\nsqueezing function for all doubly-connected domains in $\\mathbb{C}$ other than\nthe punctured plane. It provides the first non-trivial formula for the\nsqueezing function for a wide class of plane domains and answers a question of\nWold. Our main tools used to prove this result are the Schottky-Klein prime\nfunction (following the work of Crowdy) and a version of the Loewner\ndifferential equation on annuli due to Komatu. We also show that these results\ncan be used to obtain lower bounds on the squeezing function for certain\nproduct domains in $\\mathbb{C}^{n}$.\n', 'Squeezing function corresponding to polydisk   In the present article, we define squeezing function corresponding to\npolydisk and study its properties. We investigate relationship between\nsqueezing fuction and squeezing function corresponding to polydisk.\n']","[('squeezing', 0.5275031924247742), ('bounded domains', 0.37408140301704407), ('polydisk', 0.3517809212207794), ('kobayashi metric', 0.2904953360557556), ('boundary behavior', 0.2879430949687958), ('strongly convex domains', 0.28105050325393677), ('higher dimensional hyperbolic', 0.27044877409935), ('planar domains', 0.26588746905326843), ('convex domains', 0.2657817304134369), ('mathbb convex domains', 0.2635830342769623)]"
1380,1380,21,1380_2d stochastic_directed polymers random_stochastic heat_polymers random,"['2d stochastic', 'directed polymers random', 'stochastic heat', 'polymers random', 'polymer models', 'extension stochastic', 'polymer measures', 'directed polymers', 'stochastic', 'brownian motions']","['Continuum polymer measures corresponding to the critical 2d stochastic\n  heat flow   We construct continuum directed polymer measures corresponding to the\ncritical 2d stochastic heat flow (2d SHF) introduced by Caravenna, Sun, and\nZygouras in their recent article [Inventiones mathematicae 233, 325--460\n(2023)]. For this purpose, we prove a Chapman-Kolmogorov relation for the 2d\nSHF along with a related elementary conditional expectation formula. We explore\nsome basic properties of the continuum polymer measures, with our main focus\nbeing on their second moments. In particular, we show that the form of their\nsecond moments is consistent with the family of continuum polymer measures,\nindexed by a disorder strength parameter, having a conditional Gaussian\nmultiplicative chaos distributional interrelationship similar to that\npreviously found in an analogous hierarchical toy model.\n', 'The Critical 2d Stochastic Heat Flow   We consider directed polymers in random environment in the critical dimension\n$d = 2$, focusing on the intermediate disorder regime when the model undergoes\na phase transition. We prove that, at criticality, the diffusively rescaled\nrandom field of partition functions has a unique scaling limit: a universal\nprocess of random measures on $\\mathbb{R}^2$ with logarithmic correlations,\nwhich we call the *Critical 2d Stochastic Heat Flow*. It is the natural\ncandidate for the long sought solution of the critical 2d Stochastic Heat\nEquation with multiplicative space-time white noise.\n', 'The Critical 2d Stochastic Heat Flow and Related Models   In these lecture notes, we review recent progress in the study of the\nstochastic heat equation and its discrete analogue, the directed polymer model,\nin spatial dimension 2. It was discovered that a phase transition emerges on an\nintermediate disorder scale, with Edwards-Wilkinson (Gaussian) fluctuations in\nthe sub-critical regime. In the critical window, a unique scaling limit has\nbeen identified and named the critical 2d stochastic heat flow. This gives a\nmeaning to the solution of the stochastic heat equation in the critical\ndimension 2, which lies beyond existing solution theories for singular SPDEs.\nWe outline the proof ideas, introduce the key ingredients, and discuss related\nliterature on disordered systems and singular SPDEs. A list of open questions\nis also provided.\n']","[('2d stochastic', 0.5549613833427429), ('directed polymers random', 0.5453653335571289), ('stochastic heat', 0.542993426322937), ('polymers random', 0.4879503548145294), ('polymer models', 0.44692665338516235), ('extension stochastic', 0.44423529505729675), ('polymer measures', 0.4412706196308136), ('directed polymers', 0.41808733344078064), ('stochastic', 0.4135471284389496), ('brownian motions', 0.41332289576530457)]"
1381,1381,21,1381_dynamical boundary conditions_damping coefficient_euler bernoulli beam_euler bernoulli beams,"['dynamical boundary conditions', 'damping coefficient', 'euler bernoulli beam', 'euler bernoulli beams', 'clamped boundary conditions', 'elastic beam', 'damped euler', 'bernoulli beam', 'boundary conditions', 'bernoulli beams']","['Vibration modes of the Euler-Bernoulli beam equation with singularities   We consider the time dependent Euler--Bernoulli beam equation with\ndiscontinuous and singular coefficients. Using an extension of the H\\""ormander\nproduct of distributions with non-intersecting singular supports [L.\nH\\""ormander, The Analysis of Linear Partial Diffe\\-rential Operators I,\nSpringer-Verlag, 1983], we obtain an explicit formulation of the differential\nproblem which is strictly defined within the space of Schwartz distributions.\nWe determine the general structure of its separable solutions and prove\nexistence, uniqueness and regularity results under quite general conditions.\nThis formalism is used to study the dynamics of an Euler--Bernoulli beam model\nwith discontinuous flexural stiffness and structural cracks. We consider the\ncases of simply supported and clamped--clamped boundary conditions and study\nthe relation between the characteristic frequencies of the beam and the\nposition, magnitude and structure of the singularities in the flexural\nstiffness. Our results are compared with some recent formulations of the same\nproblem.\n', ""Exponential stability of Euler-Bernoulli beam under boundary controls in\n  rotation and angular velocity   This paper addresses the analysis of a boundary feedback system involving a\nnon-homogeneous Euler-Bernoulli beam governed by the equation\n$m(x)u_{tt}+\\mu(x)u_{t}$$+\\left(r(x)u_{xx}\\right)_{xx}=0$, subject to the\ninitial $u(x,0)=u_0(x)$, $u_t(x,0)=v_0(x)$ and boundary conditions $u(0,t)=0$,\n$\\left (-r(x)u_{xx}(x,t)\\right )_{x=0}=-k^{-}_r u_{x}(0,t)-k^{-}_a\nu_{xt}(0,t)$, $u(\\ell,t)=0$, $\\left (-r(x)u_{xx}(x,t)\\right )_{x=\\ell}=-k^{+}_r\nu_{x}(\\ell,t)-k^{+}_a u_{xt}(\\ell,t)$, with boundary control at both ends\nresulting from the rotation and angular velocity. The approach proposed in this\nstudy relies on the utilization of regular weak solutions, energy identity, and\na physically motivated Lyapunov function. By imposing natural assumptions\nconcerning physical parameters and other inputs, which ensure the existence of\na regular weak solution, we successfully derive a uniform exponential decay\nestimate for the system's energy. The decay rate constant featured in this\nestimate is solely dependent on the physical and geometric properties of the\nbeam. These properties encompass crucial parameters such as the viscous\nexternal damping coefficient $\\mu(x)$, as well as the boundary springs\n$k^{-}_r,k^+_r $ and dampers $k^{-}_a,k^+_a$. To illustrate the practical\neffectiveness of our theoretical findings, numerical examples are provided.\nThese examples serve to demonstrate the applicability and relevance of our\nderived results in real-world scenarios.\n"", 'Exponential stability of damped Euler-Bernoulli beam controlled by\n  boundary springs and dampers   In this paper, the vibration model of an elastic beam, governed by the damped\nEuler-Bernoulli equation\n$\\rho(x)u_{tt}+\\mu(x)u_{t}$$+\\left(r(x)u_{xx}\\right)_{xx}=0$, subject to the\nclamped boundary conditions $u(0,t)=u_x(0,t)=0$ at $x=0$, and the boundary\nconditions $\\left(-r(x)u_{xx}\\right)_{x=\\ell}=k_r u_x(\\ell,t)+k_a\nu_{xt}(\\ell,t)$, $\\left(-\\left(r(x)u_{xx}\\right)_{x}\\right )_{x=\\ell}$$=- k_d\nu(\\ell,t)-k_v u_{t}(\\ell,t)$ at $x=\\ell$, is analyzed. The boundary conditions\nat $x=\\ell$ correspond to linear combinations of damping moments caused by\nrotation and angular velocity and also, of forces caused by displacement and\nvelocity, respectively. The system stability analysis based on well-known\nLyapunov approach is developed. Under the natural assumptions guaranteeing the\nexistence of a regular weak solution, uniform exponential decay estimate for\nthe energy of the system is derived. The decay rate constant in this estimate\ndepends only on the physical and geometric parameters of the beam, including\nthe viscous external damping coefficient $\\mu(x) \\ge 0$, and the boundary\nsprings $k_r,k_d \\ge 0$ and dampers $k_a,k_v \\ge 0$. Some numerical examples\nare given to illustrate the role of the damping coefficient and the boundary\ndampers.\n']","[('dynamical boundary conditions', 0.5301075577735901), ('damping coefficient', 0.5114448666572571), ('euler bernoulli beam', 0.5077530145645142), ('euler bernoulli beams', 0.4964347779750824), ('clamped boundary conditions', 0.4761276841163635), ('elastic beam', 0.4732550382614136), ('damped euler', 0.4540451467037201), ('bernoulli beam', 0.43933239579200745), ('boundary conditions', 0.4363798201084137), ('bernoulli beams', 0.41586774587631226)]"
1382,1382,21,1382_brinkman forchheimer equations_convective brinkman forchheimer_navier stokes equations_stokes equations,"['brinkman forchheimer equations', 'convective brinkman forchheimer', 'navier stokes equations', 'stokes equations', 'forchheimer equations', 'convective brinkman', 'navier stokes', 'stochastic convective', 'brinkman forchheimer', 'equations damping']","[""Martingale solutions of two and three dimensional stochastic convective\n  Brinkman-Forchheimer equations forced by L\\'evy noise   The convective Brinkman-Forchheimer equations given by\n  $$ \\frac{\\partial \\boldsymbol{u}}{\\partial t}-\\mu\n\\Delta\\boldsymbol{u}+(\\boldsymbol{u}\\cdot\\nabla)\\boldsymbol{u}+\\alpha\\boldsymbol{u}+\\beta|\\boldsymbol{u}|^{r-1}\\boldsymbol{u}+\\nabla\np=\\boldsymbol{f}, \\ \\nabla\\cdot\\boldsymbol{u}=0, $$ where $\\mu,\\alpha,\\beta>0$\nand $r\\in[1,\\infty)$ describe the motion of incompressible fluid flows in a\nsaturated porous medium. In bounded domains (for $d=2,3$ and $r\\in[1,\\infty)$),\nthe existence of a weak martingale solution for stochastic convective\nBrinkman-Forchheimer equations forced by L\\'evy noise consisting of a\n$\\mathrm{Q}$-Wiener process and a compensated time homogeneous Poisson random\nmeasure is established in this work. Using the classical Faedo-Galerkin\napproximation, a compactness method and a version of the Skorokhod embedding\ntheorem for nonmetric spaces, we prove the existence of a weak martingale\nsolution. For $d=2$, $r\\in[1,\\infty)$ and $d=3$, $r\\in[3,\\infty)$, we prove\nthat the martingale solution has stronger regularity properties such as it\nsatisfies the energy equality (It\\^o's formula) and hence the trajectories are\nequal almost everywhere to an $\\mathbb{H}$-valued c\\`adl\\`ag function defined\non $[0, T ]$, ${\\mathbb{P}}$-a.s. Furthermore, for $d=2$, $r\\in[1,\\infty)$ and\n$d=3$, $r\\in[3,\\infty)$ ($2\\beta\\mu\\geq 1$ for $r=3$), we show the pathwise\nuniqueness of solutions and use the classical Yamada-Watanabe argument to\nderive the existence of a strong solution and uniqueness in law.\n"", 'Approximations of 2D and 3D Stochastic Convective Brinkman-Forchheimer\n  Extended Darcy Equations   In this article, we consider two- and three- dimensional stochastic\nconvective Brinkman-Forchheimer extended Darcy (CBFeD) equations\n\\begin{equation*} \\frac{\\partial \\boldsymbol{u}}{\\partial t}-\\mu\n\\Delta\\boldsymbol{u}+(\\boldsymbol{u}\\cdot\\nabla)\\boldsymbol{u}+\\alpha|\\boldsymbol{u}|^{q-1}\\boldsymbol{u}+\\beta|\\boldsymbol{u}|^{r-1}\\boldsymbol{u}+\\nabla\np=\\boldsymbol{f},\\ \\nabla\\cdot\\boldsymbol{u}=0, \\end{equation*} on a torus,\nwhere $\\mu,\\beta>0$, $\\alpha\\in\\mathbb{R}$, $r\\in[1,\\infty)$ and $q\\in[1,r)$.\nThe goal is to show that the solutions of 2D and 3D stochastic CBFeD equations\ndriven by Brownian motion can be approximated by 2D and 3D stochastic CBFeD\nequations forced by pure jump noise/random kicks on on the state space\n$\\mathrm{D}([0,T];\\mathbb{H})$. The results are established for\n$d=2,r\\in[1,\\infty)$ and $d=3,r\\in[3,\\infty)$ with $2\\beta\\mu\\geq 1$ for\n$d=r=3,$ and by using less regular assumptions on the noise coefficient.\n', '2D and 3D convective Brinkman-Forchheimer equations perturbed by a\n  subdifferential and applications to control problems   The following convective Brinkman-Forchheimer (CBF) equations (or damped\nNavier-Stokes equations) with potential\n  \\begin{equation*}\n  \\frac{\\partial \\boldsymbol{y}}{\\partial t}-\\mu\n\\Delta\\boldsymbol{y}+(\\boldsymbol{y}\\cdot\\nabla)\\boldsymbol{y}+\\alpha\\boldsymbol{y}+\\beta|\\boldsymbol{y}|^{r-1}\\boldsymbol{y}+\\nabla\np+\\Psi(\\boldsymbol{y})\\ni\\boldsymbol{g},\\ \\nabla\\cdot\\boldsymbol{y}=0,\n  \\end{equation*}\n  in a $d$-dimensional torus is considered in this work, where $d\\in\\{2,3\\}$,\n$\\mu,\\alpha,\\beta>0$ and $r\\in[1,\\infty)$. For $d=2$ with $r\\in[1,\\infty)$ and\n$d=3$ with $r\\in[3,\\infty)$ ($2\\beta\\mu\\geq 1$ for $d=r=3$), we establish the\nexistence of \\textsf{\\emph{a unique global strong solution}} for the above\nmulti-valued problem with the help of the \\textsf{\\emph{abstract theory of\n$m$-accretive operators}}. %for nonlinear differential equations of accretive\ntype in Banach spaces.\n  Moreover, we demonstrate that the same results hold \\textsf{\\emph{local in\ntime}} for the case $d=3$ with $r\\in[1,3)$ and $d=r=3$ with $2\\beta\\mu<1$. We\nexplored the $m$-accretivity of the nonlinear as well as multi-valued\noperators, Yosida approximations and their properties, and several higher order\nenergy estimates in the proofs. For $r\\in[1,3]$, we {quantize (modify)} the\nNavier-Stokes nonlinearity $(\\boldsymbol{y}\\cdot\\nabla)\\boldsymbol{y}$ to\nestablish the existence and uniqueness results, while for $r\\in[3,\\infty)$\n($2\\beta\\mu\\geq1$ for $r=3$), we handle the Navier-Stokes nonlinearity by the\nnonlinear damping term $\\beta|\\boldsymbol{y}|^{r-1}\\boldsymbol{y}$. Finally, we\ndiscuss the applications of the above developed theory in feedback control\nproblems like flow invariance, time optimal control and stabilization.\n']","[('brinkman forchheimer equations', 0.5376536250114441), ('convective brinkman forchheimer', 0.4627751111984253), ('navier stokes equations', 0.442851722240448), ('stokes equations', 0.41581836342811584), ('forchheimer equations', 0.40206244587898254), ('convective brinkman', 0.3987405002117157), ('navier stokes', 0.3785869777202606), ('stochastic convective', 0.3650214970111847), ('brinkman forchheimer', 0.32884883880615234), ('equations damping', 0.31114211678504944)]"
1383,1383,21,1383_iwasawa theory_conjecture iwasawa_iwasawa theoretic_iwasawa modules,"['iwasawa theory', 'conjecture iwasawa', 'iwasawa theoretic', 'iwasawa modules', 'iwasawa module', 'equivariant tamagawa number', 'beilinson conjecture', 'adic lie extension', 'equivariant tamagawa', 'classical iwasawa']","[""On non-commutative Iwasawa theory and derivatives of Euler systems   We describe the relative $K_0$-groups of orders in finite dimensional\nseparable algebras over the fraction fields of Dedekind domains of\ncharacteristic zero in terms of the theory of reduced determinant functors\nintroduced in [20]. We then use this approach to formulate, for each odd prime\n$p$, a main conjecture of non-commutative $p$-adic Iwasawa theory for\n$\\mathbb{G}_m$ over arbitrary number fields. This conjecture predicts a precise\nrelation between a canonical Rubin-Stark non-commutative Euler system that we\ndefine and the compactly supported $p$-adic cohomology of $\\mathbb{Z}_p$ and\nsimultaneously extends both the higher rank (commutative) main conjecture for\n$\\mathbb{G}_m$ studied by Kurihara and the present authors and the formalism of\nmain conjectures in non-commutative Iwasawa theory due to Ritter and Weiss and\nto Coates, Fukaya, Kato, Sujatha and Venjakob. Our approach also suggests a\nprecise conjectural `higher derivative formula' for the Rubin-Stark\nnon-commutative Euler system that extends the classical Gross-Stark Conjecture\nto the setting of Galois extensions of arbitrary number fields. We present\nstrong evidence in support of both of these conjectures in the setting of\narbitrary Galois CM extensions of totally real fields. In addition, in the\ngeneral case, we show that the conjectures can be combined to establish a new\nstrategy for obtaining evidence in support of the equivariant Tamagawa Number\nConjecture for $\\mathbb{G}_m$ over arbitrary Galois extensions.\n"", 'An Integral Equivariant Refinement of the Iwasawa Main Conjecture for\n  Totally Real Fields   For an abelian, CM extension $H/F$ of a totally real number field $F$, we\nimprove upon the reformulation of the Equivariant Tamagawa Number Conjecture\nfor the Artin motive $h_{H/F}$ by Atsuta-Kataoka in \\cite{Atsuta-Kataoka-ETNC}\nand extend the results proved in \\cite{Bullach-Burns-Daoud-Seo},\n\\cite{Dasgupta-Kakde-Silliman-ETNC}, \\cite{gambheera-popescu} and\n\\cite{Dasgupta-Kakde} on conjectures by Burns-Kurihara-Sano\n\\cite{Burns-Kurihara-Sano} and Kurihara \\cite{Kurihara}. Then, we consider the\n$\\mathbb{Z}_p[[Gal(H_\\infty/F)]]-$module $X_S^{T}$ where $p>2$ is a prime and\n$H_{\\infty}$ is the cyclotomic $\\mathbb{Z}_p-$ extension of $H$. This is a\ngeneralization of the classical unramified Iwasawa module $X$. By taking the\nprojective limits of the results proved at finite layers of the Iwasawa tower,\nas our main result, extending the earlier results of Gambheera-Popescu in\n\\cite{gampheera-popescu-RW}, we calculate the Fitting ideal of $X_S^{T,-}$ for\nnon-empty $T$, which is an integral equivariant refinement of the Iwasawa main\nconjecture for totally real fields proved by Wiles. We also give a conjectural\nanswer to the Fitting ideal of the module $X^-$.\n', 'Equivariant Iwasawa Theory for Ritter-Weiss Modules and Applications   We consider a finite, abelian, CM extension $H/F$ of a totally real number\nfield $F$, and construct a $\\mathbb{Z}_p[[G(H_\\infty/F)]]-$module\n$\\nabla_S^T(H_\\infty)_p$, where $p>2$ is a prime and $H_\\infty$ is the\ncyclotomic $\\Bbb Z_p$-extension of $H$. This is the Iwasawa theoretic analogue\nof a module introduced by Ritter and Weiss in \\cite{Ritter-Weiss} and studied\nfurther by Dasgupta and Kakde in \\cite{Dasgupta-Kakde}. Our main result states\nthat the $\\Bbb Z_p[[G(H_\\infty/F]]^-$-module $\\nabla_S^T(H_\\infty)_p$ is of\nprojective dimension $1$, is quadratically presented, and that its Fitting\nideal is principal, generated by an equivariant $p$-adic $L$-function\n$\\Theta_S^T(H_\\infty/F)$. As a first application, we compute the Fitting ideal\nof an arithmetically interesting $\\Bbb Z_p[[G(H_\\infty/F)]]^-$-module\n$X_S^{T,-}$, which is a variant of the classical unramified Iwasawa module $X$\n(the Galois group of the maximal abelian, unramified, pro-$p$ extension of\n$H_\\infty$), extending earlier results of Greither-Kataoka-Kurihara\n\\cite{Greither-Kataoka-Kurihara}. These are all instances of what is now called\nan Equivariant Main Conjecture in the Iwasawa theory of totally real number\nfields, and refine the classical main conjecture, proved by Wiles in\n\\cite{wiles}. As a final application, we give a short, Iwasawa theoretic proof\nof the minus $p$-part of the far-reaching Equivariant Tamagawa Number\nConjecture for the Artin motive $h_{H/F}$, for all primes $p>2$, a result also\nobtained, independently and with different (Euler system) methods, by\nBullack-Burns-Daoud-Seo \\cite{Bullach-Burns-Daoud-Seo} and\nDasgupta-Kakde-Silliman \\cite{Dasgupta-Kakde-Silliman-ETNC}.\n']","[('iwasawa theory', 0.6383838057518005), ('conjecture iwasawa', 0.6249499320983887), ('iwasawa theoretic', 0.5890116095542908), ('iwasawa modules', 0.5796269774436951), ('iwasawa module', 0.5192140340805054), ('equivariant tamagawa number', 0.49492642283439636), ('beilinson conjecture', 0.4805057942867279), ('adic lie extension', 0.4623771011829376), ('equivariant tamagawa', 0.4408559501171112), ('classical iwasawa', 0.4300585389137268)]"
1384,1384,21,1384_flow harmonic maps_harmonic map heat_harmonic map flow_harmonic maps,"['flow harmonic maps', 'harmonic map heat', 'harmonic map flow', 'harmonic maps', 'heat flow harmonic', 'harmonic map', 'map heat flow', 'riemannian manifold compact', 'riemannian manifold', 'riemannian manifolds']","['Smoothness of conformal heat flow of harmonic maps   The conformal heat flow of harmonic maps is a system of evolution equations\ncombined with harmonic map flow with metric evolution in conformal direction.\nIt is known that global weak solution of the flow exists and smooth except at\nmostly finitely many singular points. In this paper, we show that no finite\ntime singularity occurs, unlike the usual harmonic map flow. And if the initial\nenergy is small, we can obtain the uniform convergence of the map to a point\nand the conformal factor of the metric under some time sequence $t_n \\to\n\\infty$. Also, under the assumption that energy concentration is uniform in\ntime, we show that there exists a sequence of time $t_n \\to \\infty$ such that\n$f(\\cdot,t_n)$ converges to a harmonic map in $W^{1,2}$ on any compact set away\nfrom at most finitely many points.\n', 'Short time existence for harmonic map heat flow with time-dependent\n  metrics   In this work, we obtain a short time existence result for harmonic map heat\nflow coupled with a smooth family of complete metrics in the domain manifold.\nOur results generalize short time existence results for harmonic map heat flow\nby Li-Tam [The heat equation and harmonic maps of complete manifolds, Invent.\nMath., 1991] and Chen-Zhu [Uniqueness of the Ricci flow on complete noncompact\nmanifolds, J. Differential Geometry, 2006]. In particular, we prove the short\ntime existence of harmonic map heat flow along a complete Ricci flow $g(t)$ on\n$M$ into a complete manifold with curvature bounded from above with a smooth\ninitial map of uniformly bounded energy density, under the assumptions that\n$|\\text{Rm}(g(t))|\\leq a/t$ and $g(t)$ is uniformly equivalent to $g(0)$.\n', 'Regularized $n$-Conformal heat flow and global smoothness   In this paper, we introduce the regularized conformal heat flow of\n$n$-harmonic maps, or simply regularized $n$-conformal heat flow from\n$n$-dimensional Riemannian manifold. This is a system of evolution equations\ncombined with regularized $n$-harmonic map flow and a metric evolution equation\nin conformal direction. For $n=2$, the conformal heat flow does not develop\nfinite time singularity unlike usual harmonic map flow \\cite{P23} (Park, 2024).\nIn this paper, we show the analogous result, that regularized $n$-conformal\nheat flow does not develop finite time singularity unlike the (regularized)\n$n$-harmonic map flow.\n']","[('flow harmonic maps', 0.6309067606925964), ('harmonic map heat', 0.6240158081054688), ('harmonic map flow', 0.6173079013824463), ('harmonic maps', 0.5691821575164795), ('heat flow harmonic', 0.5284990072250366), ('harmonic map', 0.5202169418334961), ('map heat flow', 0.5047311186790466), ('riemannian manifold compact', 0.5028336048126221), ('riemannian manifold', 0.49982669949531555), ('riemannian manifolds', 0.4959563910961151)]"
1385,1385,21,1385_primality_prime numbers_primes_large prime,"['primality', 'prime numbers', 'primes', 'large prime', 'classified prime', 'prime', 'odd prime divisor', 'testing algorithms', 'composite number', 'fermat']","['Primality tests, linear recurrent sequences and the Pell equation   We study new primality tests based on linear recurrent sequences of degree\ntwo exploiting a matricial approach. The classical Lucas test arises as a\nparticular case and we see how it can be easily improved. Moreover, this\napproach shows clearly how the Lucas pseudoprimes are connected to the Pell\nequation and the Brahamagupta product. We also introduce a new specific\nprimality test, which we will call generalized Pell test. We perform some\nnumerical computations on the new primality tests and, for the generalized Pell\ntest, we do not any pseudoprime up to $10^{10}$.\n', 'Gauss-Euler Primality Test   This paper presents two efficient primality tests that quickly and accurately\ntest all integers up to $2^{64}$.\n', 'Strengthening the Baillie-PSW primality test   The Baillie-PSW primality test combines Fermat and Lucas probable prime\ntests. It reports that a number is either composite or probably prime. No odd\ncomposite integer has been reported to pass this combination of primality tests\nif the parameters are chosen in an appropriate way. Here, we describe a\nsignificant strengthening of this test that comes at almost no additional\ncomputational cost. This is achieved by including in the test what we call\nLucas-V pseudoprimes, of which there are only five less than $10^{15}$.\n']","[('primality', 0.65570068359375), ('prime numbers', 0.5710082650184631), ('primes', 0.5548180341720581), ('large prime', 0.5478300452232361), ('classified prime', 0.537083089351654), ('prime', 0.5267093777656555), ('odd prime divisor', 0.4665925204753876), ('testing algorithms', 0.4665832221508026), ('composite number', 0.4370739459991455), ('fermat', 0.4133313298225403)]"
1386,1386,21,1386_navier stokes equations_large eddy simulation_incompressible viscous flows_eddy simulation,"['navier stokes equations', 'large eddy simulation', 'incompressible viscous flows', 'eddy simulation', 'incompressible fluid flows', 'monte carlo numerical', 'turbulent flows', 'compressible navier stokes', 'vortex dynamics', 'viscous flows']","['Tracking Brownian fluid particles in large eddy simulations In this paper, we establish a numerical method for simulation of wall-bounded incompressible turbulent flows by integrating the technology of random vortex method with the core idea of Large Eddy Simulation (LES). Specifically, we utilize the filtering function in LES, interpreted as spatial averaging, along with the integral representation theorem for parabolic equations,to achieve a closure numerical scheme which may be used for calculating solutions of Navier-Stokes equations. This approach circumvents the challenge associated with handling the non-locally integrable 3-dimensional integral kernel in the random vortex method and facilitates the computation of numerical solutions for flow systems via Monte-Carlo method. Comprehensive numerical simulations are carried out for turbulent and laminar flows in full space and wall-bounded space, considering both two-dimensional and three-dimensional cases, thereby demonstrating the validity and effectiveness of the method.', 'Random vortex dynamics and Monte-Carlo simulations for wall-bounded\n  viscous flows   Functional integral representations for solutions of the motion equations for\nwall-bounded incompressible viscous flows, expressed (implicitly) in terms of\ndistributions of solutions to stochastic differential equations of\nMcKean-Vlasov type, are established by using a perturbation technique. These\nrepresentations are used to obtain exact random vortex dynamics for\nwall-bounded viscous flows. Numerical schemes therefore are proposed and the\nconvergence of the numerical schemes for random vortex dynamics with an\nadditional force term is established. Several numerical experiments are carried\nout for demonstrating the motion of a viscous flow within a thin layer next to\nthe fluid boundary.\n', 'Random large eddy simulation for 3-dimensional incompressible viscous\n  flows   We develop a numerical method for simulation of incompressible viscous flows\nby integrating the technology of random vortex method with the core idea of\nLarge Eddy Simulation (LES). Specifically, we utilize the filtering method in\nLES, interpreted as spatial averaging, along with the integral representation\ntheorem for parabolic equations, to achieve a closure scheme which may be used\nfor calculating solutions of Navier-Stokes equations. This approach circumvents\nthe challenge associated with handling the non-locally integrable 3-dimensional\nintegral kernel in the random vortex method and facilitates the computation of\nnumerical solutions for flow systems via Monte-Carlo method. Numerical\nsimulations are carried out for both laminar and turbulent flows, demonstrating\nthe validity and effectiveness of the method.\n']","[('navier stokes equations', 0.5276005864143372), ('large eddy simulation', 0.5141452550888062), ('incompressible viscous flows', 0.5074994564056396), ('eddy simulation', 0.507005512714386), ('incompressible fluid flows', 0.48161402344703674), ('monte carlo numerical', 0.47868800163269043), ('turbulent flows', 0.4733152389526367), ('compressible navier stokes', 0.47025802731513977), ('vortex dynamics', 0.4696560502052307), ('viscous flows', 0.4686848521232605)]"
1387,1387,21,1387_sensor fusion_multi sensor_target tracking_object tracking,"['sensor fusion', 'multi sensor', 'target tracking', 'object tracking', 'fusion based', 'single sensor', 'gaussian mixtures', 'gaussian mixture', 'kalman filters', 'multi target']","['Arithmetic Average Density Fusion -- Part I: Some Statistic and\n  Information-theoretic Results   Finite mixture such as the Gaussian mixture is a flexible and powerful\nprobabilistic modeling tool for representing the multimodal distribution widely\ninvolved in many estimation and learning problems. The core of it is\nrepresenting the target distribution by the arithmetic average (AA) of a finite\nnumber of sub-distributions which constitute a mixture. While the mixture has\nbeen widely used for single sensor filter design, it is only recent that the AA\nfusion demonstrates compelling performance for multi-sensor filter design. In\nthis paper, some statistic and information-theoretic results are given on the\ncovariance consistency, mean square error, mode-preservation capacity, and the\ninformation divergence of the AA fusion approach. In particular, based on the\nconcept of conservative fusion, the relationship of the AA fusion with the\nexisting conservative fusion approaches such as covariance union and covariance\nintersection is exposed. A suboptimal weighting approach has been proposed,\nwhich jointly with the best mixture-fit property of the AA fusion leads to a\nmax-min optimization problem. Linear Gaussian models are considered for\nalgorithm illustration and simulation comparison, resulting in the first-ever\nAA fusion-based multi-sensor Kalman filter.\n', 'Heterogeneous Multi-sensor Fusion with Random Finite Set Multi-object\n  Densities   This paper addresses the density based multi-sensor cooperative fusion using\nrandom finite set (RFS) type multi-object densities (MODs). Existing fusion\nmethods use scalar weights to characterize the relative information confidence\namong the local MODs, and in this way the portion of contribution of each local\nMOD to the fused global MOD can be tuned via adjusting these weights. Our\nanalysis shows that the fusion mechanism of using a scalar coefficient can be\noversimplified for practical scenarios, as the information confidence of an MOD\nis complex and usually space-varying due to the imperfection of sensor ability\nand the various impacts from surveillance environment. Consequently, severe\nfusion performance degradation can be observed when these scalar weights fail\nto reflect the actual situation. We make two contributions towards addressing\nthis problem. Firstly, we propose a novel heterogeneous fusion method to\nperform the information averaging among local RFS MODs. By factorizing each\nlocal MODs into a number of smaller size sub-MODs, it can transform the\noriginal complicated fusion problem into a much easier parallelizable\nmulti-cluster fusion problem. Secondly, as the proposed fusion strategy is a\ngeneral procedure without any particular model assumptions, we further derive\nthe detailed heterogeneous fusion equations, with centralized network\narchitecture, for both the probability hypothesis density (PHD) filter and the\nmulti-Bernoulli (MB) filter. The Gaussian mixture implementations of the\nproposed fusion algorithms are also presented. Various numerical experiments\nare designed to demonstrate the efficacy of the proposed fusion methods.\n', 'Track Initialization and Re-Identification for~3D Multi-View\n  Multi-Object Tracking   We propose a 3D multi-object tracking (MOT) solution using only 2D detections\nfrom monocular cameras, which automatically initiates/terminates tracks as well\nas resolves track appearance-reappearance and occlusions. Moreover, this\napproach does not require detector retraining when cameras are reconfigured but\nonly the camera matrices of reconfigured cameras need to be updated. Our\napproach is based on a Bayesian multi-object formulation that integrates track\ninitiation/termination, re-identification, occlusion handling, and data\nassociation into a single Bayes filtering recursion. However, the exact filter\nthat utilizes all these functionalities is numerically intractable due to the\nexponentially growing number of terms in the (multi-object) filtering density,\nwhile existing approximations trade-off some of these functionalities for\nspeed. To this end, we develop a more efficient approximation suitable for\nonline MOT by incorporating object features and kinematics into the measurement\nmodel, which improves data association and subsequently reduces the number of\nterms. Specifically, we exploit the 2D detections and extracted features from\nmultiple cameras to provide a better approximation of the multi-object\nfiltering density to realize the track initiation/termination and\nre-identification functionalities. Further, incorporating a tractable geometric\nocclusion model based on 2D projections of 3D objects on the camera planes\nrealizes the occlusion handling functionality of the filter. Evaluation of the\nproposed solution on challenging datasets demonstrates significant improvements\nand robustness when camera configurations change on-the-fly, compared to\nexisting multi-view MOT solutions. The source code is publicly available at\nhttps://github.com/linh-gist/mv-glmb-ab.\n']","[('sensor fusion', 0.5715191960334778), ('multi sensor', 0.4925794303417206), ('target tracking', 0.42650213837623596), ('object tracking', 0.4153245687484741), ('fusion based', 0.4141068756580353), ('single sensor', 0.3918262720108032), ('gaussian mixtures', 0.39014142751693726), ('gaussian mixture', 0.38185837864875793), ('kalman filters', 0.3798419237136841), ('multi target', 0.3720870316028595)]"
1388,1388,21,1388_hyperbolic relaxation_boundary conditions hyperbolic_hyperbolic conservation_boundary conditions,"['hyperbolic relaxation', 'boundary conditions hyperbolic', 'hyperbolic conservation', 'boundary conditions', 'relaxation limit', 'discontinuous flux', 'conditions relaxation', 'nonlocal conservation laws', 'conditions hyperbolic', 'relaxation systems']","['Construction of Boundary Conditions for Hyperbolic Relaxation\n  Approximations II: Jin-Xin Relaxation Model   This is our second work in the series about constructing boundary conditions\nfor hyperbolic relaxation approximations. The present work is concerned with\nthe one-dimensional linearized Jin-Xin relaxation model, a convenient\napproximation of hyperbolic conservation laws, with non-characteristic\nboundaries. Assume that proper boundary conditions are given for the\nconservation laws. We construct boundary conditions for the relaxation model\nwith the expectation that the resultant initial-boundary-value problems are\napproximations to the given conservation laws with the boundary conditions. The\nconstructed boundary conditions are highly non-unique. Their satisfaction of\nthe generalized Kreiss condition is analyzed. The compatibility with initial\ndata is studied. Furthermore, by resorting to a formal asymptotic expansion, we\nprove the effectiveness of the approximations.\n', 'Convergence rates of monotone schemes for conservation laws with\n  discontinuous flux   We prove that a class of monotone finite volume schemes for scalar\nconservation laws with discontinuous flux converge at a rate of $\\sqrt{\\Delta\nx}$ in $\\mathrm{L}^1$, whenever the flux is strictly monotone in $u$ and the\nspatial dependency of the flux is piecewise constant with finitely many\ndiscontinuities. We also present numerical experiments to illustrate the main\nresult. To the best of our knowledge, this is the first proof of any type of\nconvergence rate for numerical methods for conservation laws with\ndiscontinuous, nonlinear flux. Our proof relies on convergence rates for\nconservation laws with initial and boundary value data. Since those are not\nreadily available in the literature we establish convergence rates in that case\nen passant in the Appendix.\n', 'Flux-stability for conservation laws with discontinuous flux and\n  convergence rates of the front tracking method   We prove that adapted entropy solutions of scalar conservation laws with\ndiscontinuous flux are stable with respect to changes in the flux under the\nassumption that the flux is strictly monotone in u and the spatial dependency\nis piecewise constant with finitely many discontinuities. We use this stability\nresult to prove a convergence rate for the front tracking method -- a numerical\nmethod which is widely used in the field of conservation laws with\ndiscontinuous flux. To the best of our knowledge, both of these results are the\nfirst of their kind in the literature on conservation laws with discontinuous\nflux. We also present numerical experiments verifying the convergence rate\nresults and comparing numerical solutions computed with the front tracking\nmethod to finite volume approximations.\n']","[('hyperbolic relaxation', 0.615177571773529), ('boundary conditions hyperbolic', 0.593603789806366), ('hyperbolic conservation', 0.5641261339187622), ('boundary conditions', 0.5093026161193848), ('relaxation limit', 0.4821432828903198), ('discontinuous flux', 0.4774153530597687), ('conditions relaxation', 0.4772450029850006), ('nonlocal conservation laws', 0.471620112657547), ('conditions hyperbolic', 0.46063199639320374), ('relaxation systems', 0.43895140290260315)]"
1389,1389,21,1389_symplectic invariants_symplectic_integrable hamiltonian systems_invariants families,"['symplectic invariants', 'symplectic', 'integrable hamiltonian systems', 'invariants families', 'integrable systems', 'invariants', 'dimensional integrable systems', 'completely integrable systems', 'singular orbits', 'hamiltonian systems']","['$C^\\infty$ symplectic invariants of parabolic orbits and flaps in\n  integrable Hamiltonian systems   In the present paper, we consider a smooth $C^\\infty$ symplectic\nclassification of Lagrangian fibrations near cusp singularities, parabolic\norbits and cuspidal tori. We show that for these singularities as well as for\nan arrangement of singularities known as a flap, which arises in the integrable\nsubcritical Hamiltonian Hopf bifurcation, the action variables form a complete\nset of $C^\\infty$ symplectic invariants. We also give a symplectic\nclassification for parabolic orbits in the real-analytic case. Namely, we prove\nthat a complete symplectic invariant in this case is given by a real-analytic\nfunction germ in two variables. Additionally, we construct several symplectic\nnormal forms in the $C^\\infty$ and/or real-analytic categories, including\nreal-analytic right and right-left symplectic normal forms for parabolic\norbits.\n', 'Symplectic invariants for parabolic orbits and cusp singularities of integrable systems with two degrees of freedom We discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics and can be considered as the simplest example of degenerate singularities. We also suggest some new techniques which apparently can be used for studying symplectic invariants of degenerate singularities of more general type.', ""Symplectic classification for universal unfoldings of $A_n$ singularities in integrable systems In the present paper, we obtain real-analytic symplectic normal forms for integrable Hamiltonian systems with $n$ degrees of freedom near singular points having the type ``universal unfolding of $A_n$ singularity'', $n\\ge1$ (local singularities), as well as near compact orbits containing such singular points (semi-local singularities). We also obtain a classification, up to real-analytic symplectic equivalence, of real-analytic Lagrangian foliations in saturated neighborhoods of such singular orbits (semi-global classification). These singularities (local, semi-local and semi-global ones) are structurally stable. It turns out that all integrable systems are symplectically equivalent near their singular points of this type (thus, there are no local symplectic invariants). A complete semi-local (respectively, semi-global) symplectic invariant of the singularity is given by a tuple of $n-1$ (respectively $n-1+\\ell$) real-analytic function germs in $n$ variables, where $\\ell$ is the number of connected components of the complement of the singular orbit in the fiber. The case $n=1$ corresponds to non-degenerate singularities (of elliptic and hyperbolic types) of one-degree of freedom Hamiltonians; their symplectic classifications were known. The case $n=2$ corresponds to parabolic points, parabolic orbits and cuspidal tori, and the case $n\\ge3$ -- to their higher-dimensional analogs.""]","[('symplectic invariants', 0.721071720123291), ('symplectic', 0.6257236003875732), ('integrable hamiltonian systems', 0.5917061567306519), ('invariants families', 0.552937924861908), ('integrable systems', 0.5178405046463013), ('invariants', 0.5153468251228333), ('dimensional integrable systems', 0.5136764645576477), ('completely integrable systems', 0.5089355707168579), ('singular orbits', 0.5042248368263245), ('hamiltonian systems', 0.4928167760372162)]"
1390,1390,21,1390_zeros random_complex gaussian random_density zeros_gaussian analytic,"['zeros random', 'complex gaussian random', 'density zeros', 'gaussian analytic', 'invariant gaussian', 'gaussian coefficients', 'gaussian random functions', 'complex gaussian', 'zero distribution', 'polynomials random matrices']","['Expected number of zeros of random power series with finitely dependent\n  Gaussian coefficients   We are concerned with zeros of random power series with coefficients being a\nstationary, centered, complex Gaussian process. We show that the expected\nnumber of zeros in every smooth domain in the disk of convergence is less than\nthat of the hyperbolic GAF with i.i.d. coefficients. When coefficients are\nfinitely dependent, i.e., the spectral density is a trigonometric polynomial,\nwe derive precise asymptotics of the expected number of zeros inside the disk\nof radius $r$ centered at the origin as $r$ tends to the radius of convergence,\nin the proof of which we clarify that the negative contribution to the number\nof zeros stems from the zeros of the spectral density.\n', 'Hyperuniformity and non-hyperuniformity of zeros of Gaussian\n  Weyl-Heisenberg Functions   We study zero sets of twisted stationary Gaussian random functions on the\ncomplex plane, i.e., Gaussian random functions that are stochastically\ninvariant under the action of the Weyl-Heisenberg group. This model includes\ntranslation invariant Gaussian entire functions (GEFs), and also many other\nnon-analytic examples, in which case winding numbers around zeros can be either\npositive or negative. We investigate zero statistics both when zeros are\nweighted with their winding numbers (charged zero set) and when they are not\n(uncharged zero set). We show that the variance of the charged zero statistic\nalways grows linearly with the radius of the observation disk\n(hyperuniformity). Importantly, this holds for functions with possibly non-zero\nmeans and without assuming additional symmetries such as radiality. With\nrespect to uncharged zero statistics, we provide an example for which the\nvariance grows with the area of the observation disk (non-hyperuniformity).\nThis is used to show that, while the zeros of GEFs are hyperuniform, the set of\ntheir critical points fails to be so. Our work contributes to recent\ndevelopments in statistical signal processing, where the time-frequency profile\nof a non-stationary signal embedded into noise is revealed by performing a\nstatistical test on the zeros of its spectrogram (``silent points\'\'). We show\nthat empirical spectrogram zero counts enjoy moderate deviation from their\nensemble averages over large observation windows (something that was previously\nknown only for pure noise). In contrast, we also show that spectogram maxima\n(``loud points"") fail to enjoy a similar property. This gives the first formal\nevidence for the statistical superiority of silent points over the competing\nfeature of loud points, a fact that has been noted by practitioners.\n', ""Zeros of Gaussian power series, Hardy spaces and determinantal point\n  processes   Given a sequence $(\\xi_n)$ of standard i.i.d complex Gaussian random\nvariables, Peres and Vir\\'ag (in the paper ``Zeros of the i.i.d. Gaussian power\nseries: a conformally invariant determinantal process'' {\\it Acta Math.} (2005)\n194, 1-35) discovered the striking fact that the zeros of the random power\nseries $f(z) = \\sum_{n=1}^\\infty \\xi_n z^{n-1}$ in the complex unit disc\n$\\mathbb{D}$ constitute a determinantal point process. The study of the zeros\nof the general random series\n  $f(z)$ where the restriction of independence is relaxed upon the random\nvariables $(\\xi_n)$ is an important open problem. This paper proves that if\n$(\\xi_n)$ is an infinite sequence of complex Gaussian random variables such\nthat their covariance matrix is invertible and its inverse is a Toeplitz\nmatrix, then the zero set of $f(z)$ constitutes a determinantal point process\nwith the same distribution as the case of i.i.d variables studied by Peres and\nVir\\'ag. The arguments are based on some interplays between Hardy spaces and\nreproducing kernels. Illustrative examples are constructed from classical\nToeplitz matrices and the classical fractional Gaussian noise.\n""]","[('zeros random', 0.48272496461868286), ('complex gaussian random', 0.46907129883766174), ('density zeros', 0.4603969156742096), ('gaussian analytic', 0.4464517831802368), ('invariant gaussian', 0.44116419553756714), ('gaussian coefficients', 0.43096745014190674), ('gaussian random functions', 0.4257505238056183), ('complex gaussian', 0.4029736816883087), ('zero distribution', 0.40036797523498535), ('polynomials random matrices', 0.3847540318965912)]"
1391,1391,21,1391_spectrum self adjoint_spectral properties_spectrum bounded_self adjoint operators,"['spectrum self adjoint', 'spectral properties', 'spectrum bounded', 'self adjoint operators', 'spectral gaps', 'selfadjoint operator', 'self adjoint operator', 'spectral', 'continuous spectrum', 'spectrum contained']","['Perturbation of operators and approximation of spectrum   Let A(x) be a holomorphic family of bounded self-adjoint operators on a\nseparable Hilbert space H and let A(x)_n be the orthogonal compressions of A(x)\nto the span of first n elements of an orthonormal basis of H. The problem\nconsidered here is to approximate the spectrum of A(x) using the sequence of\neigenvalues of A(x)_n. We show that the bounds of the essential spectrum and\nthe discrete spectral values outside the bounds of essential spectrum of A(x)\ncan be approximated uniformly on all compact subsets by the sequence of\neigenvalue functions of A(x)_n. The known results for a bounded selfadjoint\noperator, are translated into the case of a holomorphic family of operators.\nAlso an attempt is made to predict the existence of spectral gaps that may\noccur between the bounds of essential spectrum of A(0) = A and study the effect\nof holomorphic perturbation of operators in the prediction of spectral gaps. As\nan example, gap issues of some block Toeplitz-Laurent operators are discussed.\nThe pure linear algebraic approach is the main advantage of the results here.\n', 'The essential numerical range and a theorem of Simon on the absorption\n  of eigenvalues   Let $A(t)$ be a holomorphic family of self-adjoint operators of type (B) on a\ncomplex Hilbert space $\\mathcal{H}$. Kato-Rellich perturbation theory says that\nisolated eigenvalues of $A(t)$ will be analytic functions of $t$ as long as\nthey remain below the minimum of the essential spectrum of $A(t)$. At a\nthreshold value $t_0$ where one of these eigenvalue functions hits the\nessential spectrum, the corresponding point in the essential spectrum might or\nmight not be an eigenvalue of $A(t_0)$. Our results generalize a theorem of\nSimon to give a sufficient condition for the minimum of the essential spectrum\nto be an eigenvalue of $A(t_0)$ based on the rate at which eigenvalues approach\nthe essential spectrum. We also show that the rates at which the eigenvalues of\n$A(t)$ can approach the essential spectrum from below correspond to eigenvalues\nof a bounded self-adjoint operator. The key insight behind these results is the\nessential numerical range which was recently extended to unbounded operators by\nB\\""{o}gli, Marletta, and Tretter.\n', ""Various form closures associated with a fixed non-semibounded\n  self-adjoint operator   If $T$ is a semibounded self-adjoint operator in a Hilbert space $(H, \\,\n(\\cdot , \\cdot))$ then the closure of the sesquilinear form $(T \\cdot , \\cdot)$\nis a unique Hilbert space completion. In the non-semibounded case a closure is\na Kre\\u{\\i}n space completion and generally, it is not unique. Here, all such\nclosures are studied. A one-to-one correspondence between all closed symmetric\nforms (with ``gap point'' $0$) and all J-non-negative, J-self-adjoint and\nboundedly invertible Kre\\u{\\i}n space operators is observed. Their\neigenspectral functions are investigated, in particular near the critical point\ninfinity. An example for infinitely many closures of a fixed form $(T \\cdot ,\n\\cdot)$ is discussed in detail using a non-semibounded self-adjoint\nmultiplication operator $T$ in a model Hilbert space. These observations\nindicate that closed symmetric forms may carry more information than\nself-adjoint Hilbert space operators.\n""]","[('spectrum self adjoint', 0.6540452241897583), ('spectral properties', 0.6083328723907471), ('spectrum bounded', 0.604467511177063), ('self adjoint operators', 0.5905995965003967), ('spectral gaps', 0.5660063028335571), ('selfadjoint operator', 0.5606442093849182), ('self adjoint operator', 0.5487527251243591), ('spectral', 0.544417142868042), ('continuous spectrum', 0.5431973934173584), ('spectrum contained', 0.5422717332839966)]"
1392,1392,21,1392_perfectoid ring_local rings_perfect rings_ring characteristic,"['perfectoid ring', 'local rings', 'perfect rings', 'ring characteristic', 'local ring', 'complete noetherian local', 'valuation rings', 'rings complete', 'complete noetherian', 'almost cohen macaulay']","[""Singularities in mixed characteristic via perfectoid big Cohen-Macaulay\n  algebras   We utilize recent results of Andr\\'e and Gabber on the existence of weakly\nfunctorial integral perfectoid big Cohen-Macaulay (BCM) algebras to study\nsingularities of local rings in mixed characteristic. In particular, we\nintroduce a mixed characteristic BCM-variant of rational/$F$-rational\nsingularities, of log terminal/$F$-regular singularities and of multiplier/test\nideals of divisor pairs. We prove a number of results about these objects\nincluding a restriction theorem for perfectoid BCM multiplier/test ideals and\ndeformation statements for perfectoid BCM-regular and BCM-rational\nsingularities. As an application, we obtain results on the behavior of\n$F$-regular and $F$-rational singularities in arithmetic families.\n"", 'A mixed characteristic analogue of the perfection of rings and its\n  almost Cohen-Macaulay property   Over a complete Noetherian local domain of mixed characteristic with perfect\nresidue field, we construct a perfectoid ring which is similar to an explicit\nrepresentation of a perfect closure in positive characteristic. Then we\ndemonstrate that this perfectoid ring is almost Cohen-Macaulay in the sense of\nalmost ring theory. The proof of this result uses Andr\\\'e\'s flatness lemma\nalong with Riemann\'s extension theorem. We stress that the idea partially\noriginates from the ""perfectoidization"" in the theory of prismatic cohomology.\n', ""A variant of perfectoid Abhyankar's lemma and almost Cohen-Macaulay\n  algebras   In this paper, we prove that a complete Noetherian local domain of mixed\ncharacteristic $p>0$ with perfect residue field has an integral extension that\nis an integrally closed, almost Cohen-Macaulay domain such that the Frobenius\nmap is surjective modulo $p$. This result is seen as a mixed characteristic\nanalogue of the fact that the perfect closure of a complete local domain in\npositive characteristic is almost Cohen-Macaulay. To this aim, we carry out a\ndetailed study of decompletion of perfectoid rings and establish the\nWitt-perfect (decompleted) version of Andr\\'e's perfectoid Abhyankar's lemma\nand Riemann's extension theorem.\n""]","[('perfectoid ring', 0.5673828125), ('local rings', 0.5637117028236389), ('perfect rings', 0.547589898109436), ('ring characteristic', 0.5244831442832947), ('local ring', 0.5233464241027832), ('complete noetherian local', 0.5099642276763916), ('valuation rings', 0.5082502365112305), ('rings complete', 0.47746747732162476), ('complete noetherian', 0.45604991912841797), ('almost cohen macaulay', 0.45392000675201416)]"
1393,1393,21,1393_polynomial time algorithms_algorithms analyzed_combinatorial constructions_algorithms,"['polynomial time algorithms', 'algorithms analyzed', 'combinatorial constructions', 'algorithms', 'parallel algorithms', 'local search algorithms', 'algorithmic applications', 'probabilistic combinatorics', 'hybrid algorithms', 'probabilistic']","[""The Moser-Tardos Framework with Partial Resampling   The resampling algorithm of Moser \\& Tardos is a powerful approach to develop\nconstructive versions of the Lov\\'{a}sz Local Lemma (LLL). We generalize this\nto partial resampling: when a bad event holds, we resample an\nappropriately-random subset of the variables that define this event, rather\nthan the entire set as in Moser & Tardos. This is particularly useful when the\nbad events are determined by sums of random variables. This leads to several\nimproved algorithmic applications in scheduling, graph transversals, packet\nrouting etc. For instance, we settle a conjecture of Szab\\'{o} & Tardos (2006)\non graph transversals asymptotically, and obtain improved approximation ratios\nfor a packet routing problem of Leighton, Maggs, & Rao (1994).\n"", ""Parallel algorithms and concentration bounds for the Lovasz Local Lemma\n  via witness DAGs   The Lov\\'{a}sz Local Lemma (LLL) is a cornerstone principle in the\nprobabilistic method of combinatorics, and a seminal algorithm of Moser &\nTardos (2010) provides an efficient randomized algorithm to implement it. This\ncan be parallelized to give an algorithm that uses polynomially many processors\nand runs in $O(\\log^3 n)$ time on an EREW PRAM, stemming from $O(\\log n)$\nadaptive computations of a maximal independent set (MIS). Chung et al. (2014)\ndeveloped faster local and parallel algorithms, potentially running in time\n$O(\\log^2 n)$, but these algorithms require more stringent conditions than the\nLLL.\n  We give a new parallel algorithm that works under essentially the same\nconditions as the original algorithm of Moser & Tardos but uses only a single\nMIS computation, thus running in $O(\\log^2 n)$ time on an EREW PRAM. This can\nbe derandomized to give an NC algorithm running in time $O(\\log^2 n)$ as well,\nspeeding up a previous NC LLL algorithm of Chandrasekaran et al. (2013).\n  We also provide improved and tighter bounds on the run-times of the\nsequential and parallel resampling-based algorithms originally developed by\nMoser & Tardos. These apply to any problem instance in which the tighter\nShearer LLL criterion is satisfied.\n"", 'New bounds for the Moser-Tardos distribution   The Lovasz Local Lemma (LLL) is a probabilistic tool which has been used to\nshow the existence of a variety of combinatorial structures with good ""local""\nproperties. The ""LLL-distribution"" can be used to show that the resulting\nstructures have good global properties in expectation.\n  The simplest, variable-based setting of the LLL was covered by the seminal\nalgorithm of Moser & Tardos (2010). This has since been extended to other\nprobability spaces including random permutations. One can similarly define an\n""MT-distribution"" for these algorithms, that is, the distribution of the\nconfiguration they produce. Haeupler et al. (2011) showed bounds on the\nMT-distribution which essentially match the LLL-distribution for the\nvariable-assignment setting; Harris & Srinivasan showed similar results for the\npermutation setting.\n  In this work, we show new bounds on the MT-distribution which are\nsignificantly stronger than those known to hold for the LLL-distribution. In\nthe variable-assignment setting, we show a tighter bound on the probability of\na disjunctive event or singleton event. As a consequence, in $k$-SAT instances\nwith bounded variable occurrence, the MT-distribution satisfies an\n$\\epsilon$-approximate independence condition asymptotically stronger than the\nLLL-distribution. We use this to show a nearly tight bound on the minimum\nimplicate size of a CNF boolean formula. Another noteworthy application is\nconstructing independent transversals which avoid a given subset of vertices;\nthis provides a constructive analogue to a result of Rabern (2014).\n  In the permutation LLL setting, we show a new type of bound which is similar\nto the cluster-expansion LLL criterion of Bissacot et al. (2011), but is\nstronger and takes advantage of the extra structure in permutations. We\nillustrate with improved bounds on weighted Latin transversals and partial\nLatin transversals.\n']","[('polynomial time algorithms', 0.47292089462280273), ('algorithms analyzed', 0.4535374045372009), ('combinatorial constructions', 0.45155203342437744), ('algorithms', 0.4447496235370636), ('parallel algorithms', 0.43771666288375854), ('local search algorithms', 0.43602895736694336), ('algorithmic applications', 0.40018028020858765), ('probabilistic combinatorics', 0.3949736952781677), ('hybrid algorithms', 0.39463379979133606), ('probabilistic', 0.3744437098503113)]"
1394,1394,21,1394_lifetime distribution_failure rate_robust estimators_failure times,"['lifetime distribution', 'failure rate', 'robust estimators', 'failure times', 'robust inference', 'lifetime', 'lifetimes', 'test statistics', 'restricted estimators', 'density power divergence']","[""Robust inference for an interval-monitored step-stress experiment with\n  competing risks for failure   Accelerated life-tests (ALTs) are used for inferring lifetime characteristics\nof highly reliable products. In particular, step-stress ALTs increase the\nstress level at which units under test are subject at certain pre-fixed times,\nthus accelerating the product's wear and inducing its failure. In some cases,\ndue to cost or product nature constraints, continuous monitoring of devices is\ninfeasible, and so the units are inspected for failures at particular\ninspection time points. In a such setup, the ALT response is interval-censored.\nFurthermore, when a test unit fails, there are often more than one fatal cause\nfor the failure, known as competing risks. In this paper, we assume that all\ncompeting risks are independent and follow exponential distributions with scale\nparameters depending on the stress level. Under this setup, we present a family\nof robust estimators based on density power divergence, including the classical\nmaximum likelihood estimator (MLE) as a particular case. We derive asymptotic\nand robustness properties of the Minimum Density Power Divergence Estimator\n(MDPDE), showing its consistency for large samples. Based on these MDPDEs,\nestimates of the lifetime characteristics of the product as well as estimates\nof cause-specific lifetime characteristics are then developed. Direct\nasymptotic, transformed and, bootstrap confidence intervals for the mean\nlifetime to failure, reliability at a mission time and, distribution quantiles\nare proposed, and their performance is then compared through Monte Carlo\nsimulations. Moreover, the performance of the MDPDE family has been examined\nthrough an extensive numerical study and the methods of inference discussed\nhere are finally illustrated with a real-data example concerning electronic\ndevices.\n"", 'The restricted minimum density power divergence estimator for\n  non-destructive one-shot device testing the under step-stress model with\n  exponential lifetimes   One-shot devices data represent an extreme case of interval censoring.Some\nkind of one-shot units do not get destroyed when tested, and so, survival units\ncan continue within the test providing extra information about their lifetime.\nMoreover, one-shot devices may last for long times under normal operating\nconditions, and so accelerated life tests (ALTs) may be used for inference.\nALTs relate the lifetime distribution of an unit with the stress level at which\nit is tested via log-linear relationship.Then, mean lifetime of the devices are\nreduced during the test by increasing the stress level and inference results on\nincreased stress levels can be easily extrapolated to normal operating\nconditions. In particular, the step-stress ALT model increases the stress level\nat pre-fixed times gradually during the life-testing experiment, which may be\nspecially advantageous for non-destructive one-shot devices. However, when the\nnumber of units under test are few, outlying data may greatly influence the\nparameter estimation. In this paper, we develop robust restricted estimators\nbased on the density power divergence (DPD) under linearly restricted\nsubspaces, for non-destructive one-shot devices under the step-stress ALTs with\nexponential lifetime distributions. We theoretically study the asymptotic and\nrobustness properties of the restricted estimators and we empirically\nillustrate such properties through a simulation study.\n', 'Robust inference for non-destructive one-shot device testing under\n  step-stress model with exponential lifetimes   One-shot devices analysis involves an extreme case of interval censoring,\nwherein one can only know whether the failure time is either before or after\nthe test time. Some kind of one-shot devices do not get destroyed when tested,\nand so can continue within the experiment, providing extra information for\ninference, if they did not fail before an inspection time. In addition, their\nreliability can be rapidly estimated via accelerated life tests (ALTs) by\nrunning the tests at varying and higher stress levels than working conditions.\nIn particular, step-stress tests allow the experimenter to increase the stress\nlevels at pre-fixed times gradually during the life-testing experiment. The\ncumulative exposure model is commonly assumed for step-stress models, relating\nthe lifetime distribution of units at one stress level to the lifetime\ndistributions at preceding stress levels. In this paper,vwe develop robust\nestimators and Z-type test statistics based on the density power divergence\n(DPD) for testing linear null hypothesis for non-destructive one-shot devices\nunder the step-stress ALTs with exponential lifetime distribution. We study\nasymptotic and robustness properties of the estimators and test statistics,\nyielding point estimation and confidence intervals for different lifetime\ncharacteristic such as reliability, distribution quantiles and mean lifetime of\nthe devices. A simulation study is carried out to assess the performance of the\nmethods of inference developed here and some real-life data sets are analyzed\nfinally for illustrative purpose.\n']","[('lifetime distribution', 0.4358936548233032), ('failure rate', 0.4172683656215668), ('robust estimators', 0.3699263334274292), ('failure times', 0.336689829826355), ('robust inference', 0.32628175616264343), ('lifetime', 0.3245471119880676), ('lifetimes', 0.32118675112724304), ('test statistics', 0.30927804112434387), ('restricted estimators', 0.3047688901424408), ('density power divergence', 0.2985842823982239)]"
1395,1395,21,1395_invariant tori_hamiltonian systems_symplectic_hamiltonian system,"['invariant tori', 'hamiltonian systems', 'symplectic', 'hamiltonian system', 'periodic hamiltonian', 'dimensional tori', 'unstable manifolds', 'hamiltonian', 'hamiltonian suitable', 'conformally symplectic']","['Numerical computation of critical surfaces for the breakup of invariant\n  tori in Hamiltonian systems   We compute the critical surface for the existence of invariant tori of a\nfamily of Hamiltonian systems with two and three degrees of freedom. We use and\ncompare two methods to compute the critical surfaces: renormalization-group\ntransformations and conjugation in configuration space. We unveil the presence\nof cusps in the critical surface for the breakup of three-dimensional invariant\ntori, whereas the critical surface of two-dimensional invariant tori is\nexpected to be smooth.\n', 'Flow map parameterization methods for invariant tori in quasi-periodic\n  Hamiltonian systems   The purpose of this paper is to present a method to compute parameterizations\nof invariant tori and bundles in non-autonomous quasi-periodic Hamiltonian\nsystems. We generalize flow map parameterization methods to the quasi-periodic\nsetting. To this end, we introduce the notion of fiberwise isotropic tori and\nsketch definitions and results on fiberwise symplectic deformations and their\nmoment maps. These constructs are vital to work in a suitable setting and lead\nto the proofs of magic cancellations that guarantee the existence of solutions\nof cohomological equations. We apply our algorithms in the Elliptic Restricted\nThree Body Problem and compute non-resonant 3-dimensional invariant tori and\ntheir invariant bundles around the L1 point.\n', 'Arnold diffusion and Nekhoroshev theory   Starting with Arnold\'s pioneering work, the term ""Arnold diffusion"" has been\nused to describe the slow diffusion taking place in the space of the actions in\nHamiltonian nonlinear dynamical systems with three or more degrees of freedom.\nThe present text is an elaborated transcript of the introductory course given\nin the Milano I-CELMECH school on the topic of Arnold diffusion and its\nrelation to Nekhoroshev theory. The course introduces basic concepts related to\nour current understanding of the mechanisms leading to Arnold diffusion.\nEmphasis is placed upon the identification of those invariant objects in phase\nspace which drive chaotic diffusion, such as the stable and unstable manifolds\nemanating from (partially) hyperbolic invariant objects. Besides a qualitative\nunderstanding of the diffusion mechanisms, a precise quantification of the\nspeed of Arnold diffusion can be achieved by methods based on canonical\nperturbation theory, i.e. by the construction of a suitable normal form at\noptimal order. As an example of such methods, we discuss the\n(quasi-)stationary-phase approximation for the selection of remainder terms\nacting as driving terms for the diffusion. Finally, we discuss the efficiency\nof such methods through numerical examples in which the optimal normal form is\ndetermined by a computer-algebraic implementation of a normalization algorithm.\n']","[('invariant tori', 0.6236929893493652), ('hamiltonian systems', 0.5834363698959351), ('symplectic', 0.5516397356987), ('hamiltonian system', 0.5337209701538086), ('periodic hamiltonian', 0.5323312282562256), ('dimensional tori', 0.5145400166511536), ('unstable manifolds', 0.5058122873306274), ('hamiltonian', 0.5033885836601257), ('hamiltonian suitable', 0.49782323837280273), ('conformally symplectic', 0.4916667640209198)]"
1396,1396,21,1396_fixed point sets_fixed point properties_fixed points_fixed point approximate,"['fixed point sets', 'fixed point properties', 'fixed points', 'fixed point approximate', 'digital images', 'approximate fixed point', 'digital image', 'fixed point', 'approximate fixed', 'point sets']","['Remarks on Fixed Point Assertions in Digital Topology, 7   This paper continues a series discussing flaws in published assertions\nconcerning fixed points in digital images.\n', 'Cold and Freezing Sets in the Digital Plane   Cold sets and freezing sets belong to the theory of (approximate) fixed\npoints for continuous self-maps on digital images. We study some properties of\ncold sets for digital images in the digital plane, and we examine some\nrelationships between cold sets and freezing sets.\n', 'Convexity and AFPP in the Digital Plane   We examine the relationship between convexity and the approximate fixed point\nproperty (AFPP) for digital images in Z^2.\n']","[('fixed point sets', 0.6169188618659973), ('fixed point properties', 0.6016830801963806), ('fixed points', 0.5850759744644165), ('fixed point approximate', 0.5689285397529602), ('digital images', 0.564211905002594), ('approximate fixed point', 0.5467978119850159), ('digital image', 0.5413347482681274), ('fixed point', 0.5332849621772766), ('approximate fixed', 0.44289177656173706), ('point sets', 0.42356109619140625)]"
1397,1397,21,1397_affine hecke algebras_graded hecke algebras_affine hecke algebra_hecke algebras,"['affine hecke algebras', 'graded hecke algebras', 'affine hecke algebra', 'hecke algebras', 'iwahori hecke algebra', 'hecke algebra mathcal', 'hecke algebra', 'affine hecke', 'adic groups', 'graded hecke']","['Structure of Hecke algebras arising from types   Let $G$ denote a connected reductive group over a nonarchimedean local field\n$F$ of residue characteristic $p$, and let $\\mathcal{C}$ denote an\nalgebraically closed field of characteristic $\\ell \\neq p$. If $\\rho$ is an\nirreducible, smooth $\\mathcal{C}$-representation of a compact, open subgroup\n$K$ of $G(F)$, then the pair $(K,\\rho)$ gives rise to a Hecke algebra\n$\\mathcal{H}(G(F),(K, \\rho))$. For a large class of pairs $(K,\\rho)$, we show\nthat $\\mathcal{H}(G(F),(K, \\rho))$ is a semi-direct product of an affine Hecke\nalgebra with explicit parameters with a twisted group algebra, and that it is\nisomorphic to $\\mathcal{H}(G^0(F),(K^0, \\rho^0))$ for some reductive subgroup\n$G^0 \\subset G$ with compact, open subgroup $K^0$ and depth-zero representation\n$\\rho^0$ of $K^0$.\n  The class of pairs that we consider includes all depth-zero types. In\ndescribing their Hecke algebras, we thus recover a result of Morris as a\nspecial case. In a second paper, we will show that our class also contains all\nthe types constructed by Kim and Yu, and hence we obtain as a corollary that\narbitrary Bernstein blocks are equivalent to depth-zero Bernstein blocks under\nminor tameness assumptions.\n  The pairs to which our results apply are described in an axiomatic way so\nthat the results can be applied to other constructions of types by only\nverifying that the relevant axioms are satisfied. The Hecke algebra\nisomorphisms are given in an explicit manner and are support preserving.\n', 'Reduction to depth zero for tame p-adic groups via Hecke algebra\n  isomorphisms   Let $F$ be a nonarchimedean local field of residual characteristic $p$. Let\n$G$ denote a connected reductive group over $F$ that splits over a tamely\nramified extension of $F$. Let $(K ,\\rho)$ be a type as constructed by Kim and\nYu. We show that there exists a twisted Levi subgroup $G^0 \\subset G$ and a\ntype $(K^0, \\rho^0)$ for $G^0$ such that the corresponding Hecke algebras\n$\\mathcal{H}(G(F), (K, \\rho))$ and $\\mathcal{H}(G^0(F), (K^0, \\rho^0))$ are\nisomorphic. If $p$ does not divide the order of the absolute Weyl group of $G$,\nthen every Bernstein block is equivalent to modules over such a Hecke algebra.\nHence, under this assumption on $p$, our result implies that every Bernstein\nblock is equivalent to a depth-zero Bernstein block. This allows one to reduce\nmany problems about (the category of) smooth, complex representations of\n$p$-adic groups to analogous problems about (the category of) depth-zero\nrepresentations.\n  Our isomorphism of Hecke algebras is very explicit and also includes an\nexplicit description of the Hecke algebras as semi-direct products of an affine\nHecke with a twisted group algebra. Moreover, we work with arbitrary\nalgebraically closed fields of characteristic different from $p$ as our\ncoefficient field.\n  This paper relies on a prior axiomatic result about the structure of Hecke\nalgebras by the same authors and a key ingredient consists of extending the\nquadratic character of Fintzen--Kaletha--Spice to the support of the Hecke\nalgebra, which might be of independent interest.\n', ""On parameters of Hecke algebras for $p$-adic groups Let $F$ be a non-archimedean local field with residue characteristic $p$ and $G$ be a connected reductive group defined over $F$. In earlier joint works with Jeffrey D. Adler, Jessica Fintzen, and Manish Mishra, we proved that the Hecke algebras attached to types constructed by Kim and Yu are isomorphic to the Hecke algebras attached to depth-zero types. Note that if $G$ splits over a tamely ramified extension of $F$ and $p$ does not divide the order of the absolute Weyl group of $G$, such Hecke algebras cover the Hecke algebras attached to arbitrary Bernstein blocks. We also proved that for a depth-zero type $(K, \\rho)$, the corresponding Hecke algebra $\\mathcal{H}(G(F), (K, \\rho))$ has an explicit description as a semi-direct product of an affine Hecke algebra $\\mathcal{H}(W(\\rho_M)_{\\mathrm{aff}}, q)$ with a twisted group algebra $\\mathbb{C}[\\Omega(\\rho_{M}), \\mu]$, generalizing prior work of Morris.\n  In this paper, we show that the affine Hecke algebra $\\mathcal{H}(W(\\rho_M)_{\\mathrm{aff}}, q)$ appearing in the description of the Hecke algebra $\\mathcal{H}(G(F), (K, \\rho))$ attached to a depth-zero type $(K, \\rho)$ is isomorphic to the one attached to a unipotent type for a connected reductive group splitting over an unramified extension of $F$. This makes it possible to calculate the parameters of the affine Hecke algebras for depth-zero types and types constructed by Kim and Yu explicitly. In particular, we prove a version of Lusztig's conjecture that the parameters of the Hecke algebra attached to an arbitrary Bernstein block agree with those of a unipotent Bernstein block under the assumption that $G$ splits over a tamely ramified extension of $F$ and $p$ does not divide the order of the absolute Weyl group of $G$.""]","[('affine hecke algebras', 0.6741496324539185), ('graded hecke algebras', 0.6687096357345581), ('affine hecke algebra', 0.6338819265365601), ('hecke algebras', 0.5937747955322266), ('iwahori hecke algebra', 0.5586504936218262), ('hecke algebra mathcal', 0.515472948551178), ('hecke algebra', 0.5052655339241028), ('affine hecke', 0.4600524306297302), ('adic groups', 0.45556965470314026), ('graded hecke', 0.42889490723609924)]"
1398,1398,21,1398_solvable groups_solvable groups whose_finite solvable group_non solvable groups,"['solvable groups', 'solvable groups whose', 'finite solvable group', 'non solvable groups', 'degree graphs', 'graphs solvable', 'vertices prime', 'solvable group', 'graphs finite simple', 'graph whose vertices']","['Non-solvable groups whose character degree graph has a cut-vertex. III   Let $G$ be a finite group. Denoting by ${\\rm{cd}}(G)$ the set of the degrees\nof the irreducible complex characters of $G$, we consider the {\\it character\ndegree graph} of $G$: this is the (simple, undirected) graph whose vertices are\nthe prime divisors of the numbers in ${\\rm{cd}}(G)$, and two distinct vertices\n$p$, $q$ are adjacent if and only if $pq$ divides some number in\n${\\rm{cd}}(G)$. This paper completes the classification, started in [5] and\n[6], of the finite non-solvable groups whose character degree graph has a {\\it\ncut-vertex}, i.e. a vertex whose removal increases the number of connected\ncomponents of the graph. More specifically, it was proved in [6] that these\ngroups have a unique non-solvable composition factor $S$, and that $S$ is\nisomorphic to a group belonging to a restricted list of non-abelian simple\ngroups. In [5] and [6] all isomorphism types for $S$ were treated, except the\ncase \\(S\\cong{\\rm{PSL}}_2(2^a)\\) for some integer $a\\geq 2$; the remaining case\nis addressed in the present paper.\n', 'Non-solvable groups whose character degree graph has a cut-vertex. II   Let $G$ be a finite group, and let ${\\rm{cd}}(G)$ denote the set of degrees\nof the irreducible complex characters of $G$. Define then the character degree\ngraph $\\Delta(G)$ as the (simple undirected) graph whose vertices are the prime\ndivisors of the numbers in ${\\rm{cd}}(G)$, and two distinct vertices $p$, $q$\nare adjacent if and only if $pq$ divides some number in ${\\rm{cd}}(G)$. This\npaper continues the work, started in [7], toward the classification of the\nfinite non-solvable groups whose degree graph possesses a cut-vertex, i.e., a\nvertex whose removal increases the number of connected components of the graph.\nWhile, in [7], groups with no composition factors isomorphic to\n${\\rm{PSL}}_2(t^a)$ (for any prime power $t^a\\geq 4$) were treated, here we\nconsider the complementary situation in the case when $t$ is odd and $t^a> 5$.\nThe proof of this classification will be then completed in the third and last\npaper of this series ([8]), that deals with the case $t=2$.\n', 'Non-solvable groups whose character degree graph has a cut-vertex. I   Let G be a finite group. Denoting by cd(G) the set of degrees of the\nirreducible complex characters of G, we consider the character degree graph of\nG: this is the (simple undirected) graph whose vertices are the prime divisors\nof the numbers in cd(G), and two distinct vertices p, q are adjacent if and\nonly if pq divides some number in cd(G). In the series of three papers starting\nwith the present one, we analyze the structure of the finite non-solvable\ngroups whose character degree graph possesses a cut-vertex, i.e., a vertex\nwhose removal increases the number of connected components of the graph.\n']","[('solvable groups', 0.5279566049575806), ('solvable groups whose', 0.5081912875175476), ('finite solvable group', 0.5065327882766724), ('non solvable groups', 0.5044971108436584), ('degree graphs', 0.4797855019569397), ('graphs solvable', 0.4685319662094116), ('vertices prime', 0.46673583984375), ('solvable group', 0.46120893955230713), ('graphs finite simple', 0.4514281451702118), ('graph whose vertices', 0.44149985909461975)]"
1399,1399,21,1399_morse smale diffeomorphisms_flows manifolds_smale diffeomorphisms_manifold admits,"['morse smale diffeomorphisms', 'flows manifolds', 'smale diffeomorphisms', 'manifold admits', 'manifolds', 'orientable manifolds', 'diffeomorphisms sphere', 'diffeomorphisms', 'orientable manifold', 'manifold admitting']","[""Morse-Smale 3-diffeomorphisms with saddles of the same unstable manifold\n  dimension   In this paper, we consider a class of Morse-Smale diffeomorphisms defined on\na closed 3-manifold (non-necessarily orientable) under the assumption that all\ntheir saddle points have the same dimension of the unstable manifolds. The\nsimplest example of such diffeomorphisms is the well-known ``source-sink'' or\n``north pole - south pole'' diffeomorphism, whose non-wandering set consists of\nexactly one source and one sink. Such systems, as Reeb showed back in 1946, can\nbe realized only on the sphere. We generalize his result, namely, we show that\ndiffeomorphisms from the considered class also can be defined only on the\n3-sphere.\n"", 'Knot as a complete invariant of a Morse-Smale 3-diffeomorphism with four\n  fixed points   Lens spaces are the only 3-manifolds that admit gradient-like flows with four\nfixed points. This is an immediate corollary of Morse inequality and of the\nMorse function with four critical points existence. A similar question for\ngradient-like diffeomorphisms is open. Solution can be approached by describing\na complete topological conjugacy invariant of the class of considered\ndiffeomorphisms and constructing of representative diffeomorphism for every\nconjugacy class by the abstract invariant. Ch. Bonnati and V. Z. Grines proved\nthat the topological conjugacy class of Morse-Smale flows with unique saddle is\ndefined by the equivalence class of the Hopf knot in $\\mathbb S^2\\times\\mathbb\nS^1$ which is projection of one-dimensional saddle separatrice and used the\nmentioned approach to prove that the ambient manifold of a diffeomorphism of\nthis class is the three-dimensional sphere. In the present paper similar result\nis obtained for the gradient-like diffeomorphisms with exactly two saddle\npoints and the unique heteroclinic curve.\n', 'On the topology of 3-manifolds admitting Morse-Smale diffeomorphisms\n  with four fixed points of pairwise different Morse indices   In the present paper we consider class $G$ of orientation preserving\nMorse-Smale diffeomorphisms $f$, which defined on closed 3-manifold $M^3$, and\nwhose non-wandering set consist of four fixed points with pairwise different\nMorse indices. It follows from S. Smale and K. Meyer results that all\ngradient-like flows with similar properties has Morse energy function with four\ncritical points of pairwise different Morse indices. This implies, that\nsupporting manifold $M^3$ for these flows admits a Heegaard decomposition of\ngenus 1 and hence it is homeomorphic to a lens space $L_{p,q}$. Despite the\nsimple structure of the non-wandering set in class $G$ there exist\ndiffeomorphisms with wild embedded separatrices. According to V. Grines, F.\nLaudenbach, O. Pochinka results such diffeomorphisms do not possesses an energy\nfunction, and question about topology their supporting manifold is open.\nAccording to V. Grines, E. Zhuzhoma and V. Medvedev results $M^3$ is\nhomeomorphic to a lens space $L_{p,q}$ in case of tame embedding of closures of\none-dimensional separatrices of diffeomorphism $f\\in G$. Moreover, the\nwandering set of $f$ contains at least $p$ non-compact heteroclinic curves. In\nthe present paper similar result was received for arbitrary diffeomorphisms of\nclass $G$. Also we construct diffeomorphisms from $G$ with wild embedding\none-dimensional separatrices on every lens space $L_{p,q}$. Such examples were\nknown previously only on the 3-sphere.\n']","[('morse smale diffeomorphisms', 0.7275049686431885), ('flows manifolds', 0.6581393480300903), ('smale diffeomorphisms', 0.6438645124435425), ('manifold admits', 0.5741547346115112), ('manifolds', 0.5736207962036133), ('orientable manifolds', 0.5638522505760193), ('diffeomorphisms sphere', 0.558851957321167), ('diffeomorphisms', 0.5517592430114746), ('orientable manifold', 0.5488380193710327), ('manifold admitting', 0.5413549542427063)]"
1400,1400,21,1400_multistage stochastic programming_stochastic dynamic programming_multistage stochastic optimization_stochastic dual dynamic,"['multistage stochastic programming', 'stochastic dynamic programming', 'multistage stochastic optimization', 'stochastic dual dynamic', 'dynamic programming stochastic', 'stochastic dual', 'stochastic programming', 'dual dynamic programming', 'stochastic optimization', 'stochastic programs']","['Dual SDDP for risk-averse multistage stochastic programs   Risk-averse multistage stochastic programs appear in multiple areas and are\nchallenging to solve. Stochastic Dual Dynamic Programming (SDDP) is a\nwell-known tool to address such problems under time-independence assumptions.\nWe show how to derive a dual formulation for these problems and apply an SDDP\nalgorithm, leading to converging and deterministic upper bounds for risk-averse\nproblems.\n', 'Inexact cuts in SDDP applied to multistage stochastic nondifferentiable\n  problems   In [13], an Inexact variant of Stochastic Dual Dynamic Programming (SDDP)\ncalled ISDDP was introduced which uses approximate (instead of exact with SDDP)\nprimal dual solutions of the problems solved in the forward and backward passes\nof the method. That variant of SDDP was studied in [13] for linear and for\ndifferentiable nonlinear Multistage Stochastic Programs (MSPs). In this paper,\nwe extend ISDDP to nondifferentiable MSPs. We first provide formulas for\ninexact cuts for value functions of convex nondifferentiable optimization\nproblems. We then combine these cuts with SDDP to describe ISDDP for\nnondifferentiable MSPs and analyze the convergence of the method. More\nprecisely, for a problem with T stages, we show that for errors bounded from\nabove by epsilon, the limit superior and limit inferior of sequences of upper\nand lower bounds on the optimal value of the problem are at most at distance\n3*epsilon*T to the optimal value and that for asymptotically vanishing errors\nISDDP converges to an optimal policy.\n  [13] V. Guigues, Inexact cuts in Stochastic Dual Dynamic Programming, Siam\nJournal on Optimization, 30(1), 407-438, 2020.\n', 'Regularized Stochastic Dual Dynamic Programming for convex nonlinear\n  optimization problems   We define a regularized variant of the Dual Dynamic Programming algorithm\ncalled REDDP (REgularized Dual Dynamic Programming) to solve nonlinear dynamic\nprogramming equations. We extend the algorithm to solve nonlinear stochastic\ndynamic programming equations. The corresponding algorithm, called SDDP-REG,\ncan be seen as an extension of a regularization of the Stochastic Dual Dynamic\nProgramming (SDDP) algorithm recently introduced which was studied for linear\nproblems only and with less general prox-centers. We show the convergence of\nREDDP and SDDP-REG. We assess the performance of REDDP and SDDP-REG on\nportfolio models with direct transaction and market impact costs. In\nparticular, we propose a risk-neutral portfolio selection model which can be\ncast as a multistage stochastic second-order cone program. The formulation is\nmotivated by the impact of market impact costs on large portfolio rebalancing\noperations. Numerical simulations show that REDDP is much quicker than DDP on\nall problem instances considered (up to 184 times quicker than DDP) and that\nSDDP-REG is quicker on the instances of portfolio selection problems with\nmarket impact costs tested and much faster on the instance of risk-neutral\nmultistage stochastic linear program implemented (8.2 times faster).\n']","[('multistage stochastic programming', 0.6864701509475708), ('stochastic dynamic programming', 0.6664848923683167), ('multistage stochastic optimization', 0.6519498825073242), ('stochastic dual dynamic', 0.6442901492118835), ('dynamic programming stochastic', 0.6356896758079529), ('stochastic dual', 0.6326860785484314), ('stochastic programming', 0.6251387596130371), ('dual dynamic programming', 0.6106657385826111), ('stochastic optimization', 0.5988714694976807), ('stochastic programs', 0.5980582237243652)]"
1401,1401,21,1401_heat transport_dynamics perturbed_macroscopic limit_equilibrium fluctuations,"['heat transport', 'dynamics perturbed', 'macroscopic limit', 'equilibrium fluctuations', 'hydrodynamic limit', 'harmonic oscillators', 'energy converge', 'boundary conditions', 'boundary conditions respectively', 'chain particles']","['Heat flow in a periodically forced, unpinned thermostatted chain   We prove the hydrodynamic limit for a one-dimensional harmonic chain of\ninteracting atoms with a random flip of the momentum sign. The system is open:\nat the left boundary it is attached to a heat bath at temperature $T_-$, while\nat the right endpoint it is subject to an action of a force which reads as\n$\\bar F + \\frac 1{\\sqrt n} \\widetilde{\\mathcal F} (n^2 t)$, where $\\bar F \\ge0$\nand $\\widetilde{\\mathcal F}(t)$ is a periodic function. Here $n$ is the size of\nthe microscopic system. Under a diffusive scaling of space-time, we prove that\nthe empirical profiles of the two locally conserved quantities - the volume\nstretch and the energy - converge, as $n\\to+\\infty$, to the solution of a\nnon-linear diffusive system of conservative partial differential equations with\na Dirichlet type and Neumann boundary conditions on the left and the right\nendpoints, respectively.\n', 'Heat flow in a periodically forced, thermostatted chain II   We derive a macroscopic heat equation for the temperature of a pinned\nharmonic chain subject to a periodic force at its right side and in contact\nwith a heat bath at its left side.\n  The microscopic dynamics in the bulk is given by the Hamiltonian equation of\nmotion plus a reversal of the velocity of a particle occurring independently\nfor each particle at exponential times, with rate $\\gamma$. The latter produces\na finite heat conductivity. Starting with an initial probability distribution\nfor a chain of $n$ particles we compute the local temperature given by the\nexpected value of the local energy and current. Scaling space and time\ndiffusively yields, in the $n\\to+\\infty$ limit, the heat equation for the\nmacroscopic temperature profile $T(t,u),$ $t>0$, $u \\in [0,1]$. It is to be\nsolved for initial conditions $T(0,u)$ and specified $T(t,0)=T_-$, the\ntemperature of the left heat reservoir and a fixed heat flux $J$, entering the\nsystem at $u=1$. $J$ is the work done by the periodic force which is computed\nexplicitly for each $n$.\n', 'On the Conversion of Work into Heat: Microscopic Models and Macroscopic\n  Equations   We summarize and extend some of the results obtained recently for the\nmicroscopic and macroscopic behavior of a pinned harmonic chain, with random\nvelocity flips at Poissonian times, acted on by a periodic force {at one end}\nand in contact with a heat bath at the other end. Here we consider the case\nwhere the system is in contact with two heat baths at different temperatures\nand a periodic force is applied at any position. This leads in the hydrodynamic\nlimit to a heat equation for the temperature profile with a discontinuous slope\nat the position where the force acts. Higher dimensional systems, unpinned\ncases and anharmonic interactions are also considered.\n']","[('heat transport', 0.4518999755382538), ('dynamics perturbed', 0.39939749240875244), ('macroscopic limit', 0.3851708769798279), ('equilibrium fluctuations', 0.38354766368865967), ('hydrodynamic limit', 0.3746723234653473), ('harmonic oscillators', 0.3684096932411194), ('energy converge', 0.3660118281841278), ('boundary conditions', 0.3648592233657837), ('boundary conditions respectively', 0.3446543216705322), ('chain particles', 0.3426368534564972)]"
1402,1402,21,1402_grassmann graphs_linear codes_codes finite fields_hamming graphs,"['grassmann graphs', 'linear codes', 'codes finite fields', 'hamming graphs', 'graphs projective', 'grassmann', 'transitive codes', 'finite field f_q', 'vertices dimensional', 'dimensional subspaces']","['Tops of graphs of non-degenerate linear codes   Let $\\Gamma_k(V)$ be the Grassmann graph whose vertex set ${\\mathcal\nG}_{k}(V)$ is formed by all $k$-dimensional subspaces of an $n$-dimensional\nvector space $V$ over the finite field $F_q$ consisting of $q$ elements. We\ndiscuss its subgraph $\\Gamma(n,k)_q$ with the vertex set ${\\mathcal C}(n,k)_q$\nconsisting of all non-degenerate linear $[n, k]_q$ codes. %We assume that\n$1<k<n-1$. We study maximal cliques $\\langle U]^{c}_{k}$ of $\\Gamma(n,k)_q$,\nwhich are intersections of tops of $\\Gamma_k(V)$ with ${\\mathcal C}(n,k)_q$. We\nshow when they are contained in a line of ${\\mathcal G}_{k}(V)$ and then we\nprove that $\\langle U]^{c}_{k}$ is a maximal clique of $\\Gamma(n,k)_q$ when it\nis not contained in a line of ${\\mathcal G}_{k}(V)$. Furthermore, we show that\nthe automorphism group of the set of such maximal cliques is isomorphic with\nthe automorphism group of $\\Gamma(n,k+1)_{q}$.\n', 'On the graph of non-degenerate linear $[n,2]_2$ codes   Consider the Grassmann graph of $k$-dimensional subspaces of an\n$n$-dimensional vector space over the $q$-element field, $1<k<n-1$. Every\nautomorphism of this graph is induced by a semilinear automorphism of the\ncorresponding vector space or a semilinear isomorphism to the dual vector\nspace; the second possibility is realized only for $n=2k$. Let $\\Gamma(n,k)_q$\nbe the subgraph of the Grassman graph formed by all non-degenerate linear\n$[n,k]_q$ codes. If $q\\ge 3$ or $k\\ge 3$, then every isomorphism of\n$\\Gamma(n,k)_{q}$ to a subgraph of the Grassmann graph can be uniquely extended\nto an automorphism of the Grassmann graph. For $q=k=2$ there is an isomorphism\nof $\\Gamma(n,k)_{q}$ to a subgraph of the Grassmann graph which does not have\nthis property. In this paper, we show that such exceptional isomorphism is\nunique up to an automorphism of the Grassmann graph.\n', 'The graphs of non-degenerate linear codes   We consider the Grassmann graph of $k$-dimensional subspaces of an\n$n$-dimensional vector space over the $q$-element field and its subgraph\n$\\Gamma(n,k)_q$ formed by non-degenerate linear $[n,k]_q$ codes. We assume that\n$1<k<n-1$. It is well-known that every automorphism of the Grassmann graph is\ninduced by a semilinear automorphism of the corresponding vector space or a\nsemilinear isomorphism to the dual vector space; the second possibility is\nrealized only if $n=2k$. Our results are the following: if $q\\ge 3$ or $k\\ne\n2$, then every isomorphism of $\\Gamma(n,k)_{q}$ to a subgraph of the Grassmann\ngraph can be uniquely extended to an automorphism of the Grassmann graph; in\nthe case when $q=k=2$, there are subgraphs of the Grassmann graph isomorphic to\n$\\Gamma(n,k)_{q}$ and such that isomorphisms between these subgraphs and\n$\\Gamma(n,k)_{q}$ cannot be extended to automorphisms of the Grassmann graph.\n']","[('grassmann graphs', 0.6548527479171753), ('linear codes', 0.49778997898101807), ('codes finite fields', 0.4940751791000366), ('hamming graphs', 0.48311179876327515), ('graphs projective', 0.4348222613334656), ('grassmann', 0.4088369309902191), ('transitive codes', 0.39704522490501404), ('finite field f_q', 0.3599095046520233), ('vertices dimensional', 0.3509727418422699), ('dimensional subspaces', 0.3445061445236206)]"
1403,1403,21,1403_visual perception_cortex_neural fields_cortical,"['visual perception', 'cortex', 'neural fields', 'cortical', 'primary visual', 'neural activity', 'neural field', 'neuronal', 'neural', 'perception']","['A mathematical model of the visual MacKay effect   This paper investigates the intricate connection between visual perception\nand the mathematical modeling of neural activity in the primary visual cortex\n(V1). The focus is on modeling the visual MacKay effect [D. M. MacKay, Nature,\n180 (1957), pp. 849--850]. While bifurcation theory has been a prominent\nmathematical approach for addressing issues in neuroscience, especially in\ndescribing spontaneous pattern formations in V1 due to parameter changes, it\nfaces challenges in scenarios with localized sensory inputs. This is evident,\nfor instance, in MacKay\'s psychophysical experiments, where the redundancy of\nvisual stimuli information results in irregular shapes, making bifurcation\ntheory and multiscale analysis less effective. To address this, we follow a\nmathematical viewpoint based on the input-output controllability of an\nAmari-type neural fields model. In this framework, we consider sensory input as\na control function, a cortical representation via the retino-cortical map of\nthe visual stimulus that captures its distinct features. This includes highly\nlocalized information in the center of MacKay\'s funnel pattern ""MacKay rays"".\nFrom a control theory point of view, the Amari-type equation\'s exact\ncontrollability property is discussed for linear and nonlinear response\nfunctions. For the visual MacKay effect modeling, we adjust the parameter\nrepresenting intra-neuron connectivity to ensure that cortical activity\nexponentially stabilizes to the stationary state in the absence of sensory\ninput. Then, we perform quantitative and qualitative studies to demonstrate\nthat they capture all the essential features of the induced after-image\nreported by MacKay.\n', 'Reproducing sensory induced hallucinations via neural fields   Understanding sensory-induced cortical patterns in the primary visual cortex\nV1 is an important challenge both for physiological motivations and for\nimproving our understanding of human perception and visual organisation. In\nthis work, we focus on pattern formation in the visual cortex when the cortical\nactivity is driven by a geometric visual hallucination-like stimulus. In\nparticular, we present a theoretical framework for sensory-induced\nhallucinations which allows one to reproduce novel psychophysical results such\nas the MacKay effect (Nature, 1957) and the Billock and Tsou experiences (PNAS,\n2007).\n', 'Conformal models for hypercolumns in the primary visual cortex V1   We propose a differential geometric model of hypercolumns in the primary\nvisual cortex V1 that combines features of the symplectic model of the primary\nvisual cortex by A. Sarti, G. Citti and J. Petitot and of the spherical model\nof hypercolumns by P. Bressloff and J. Cowan. The model is based on classical\nresults in Conformal Geometry.\n']","[('visual perception', 0.5783647894859314), ('cortex', 0.5516847968101501), ('neural fields', 0.525799036026001), ('cortical', 0.5072073340415955), ('primary visual', 0.49804380536079407), ('neural activity', 0.49142879247665405), ('neural field', 0.48392847180366516), ('neuronal', 0.48250338435173035), ('neural', 0.47910523414611816), ('perception', 0.44771572947502136)]"
1404,1404,21,1404_critical graphs_graph strong_critical graph_spanning subgraph,"['critical graphs', 'graph strong', 'critical graph', 'spanning subgraph', 'mathcal connected graphs', 'graphs spanning', 'leq vertex', 'graph contains', 'subgraph graph', 'graph p_']","['Distance spectral conditions for $ID$-factor-critical and fractional\n  $[a, b]$-factor of graphs   Let $G=(V(G), E(G))$ be a graph with vertex set $V(G)$ and edge set $E(G)$. A\ngraph is $ID$-factor-critical if for every independent set $I$ of $G$ whose\nsize has the same parity as $|V(G)|$, $G-I$ has a perfect matching. For two\npositive integers $a$ and $b$ with $a\\leq b$, let $h$: $E(G)\\rightarrow [0, 1]$\nbe a function on $E(G)$ satisfying $a\\leq\\sum _{e\\in E_{G}(v_{i})}h(e)\\leq b$\nfor any vertex $v_{i}\\in V(G)$. Then the spanning subgraph with edge set\n$E_{h}$, denoted by $G[E_{h}]$, is called a fractional $[a, b]$-factor of $G$\nwith indicator function $h$, where $E_{h}=\\{e\\in E(G)\\mid h(e)>0\\}$ and\n$E_{G}(v_{i})=\\{e\\in E(G)\\mid e$ is incident with $v_{i}$ in $G$\\}. A graph is\ndefined as a fractional $[a, b]$-deleted graph if for any $e\\in E(G)$, $G-e$\ncontains a fractional $[a, b]$-factor. For any integer $k\\geq 1$, a graph has a\n$k$-factor if it contains a $k$-regular spanning subgraph. In this paper, we\nfirstly give a distance spectral radius condition of $G$ to guarantee that $G$\nis $ID$-factor-critical. Furthermore, we provide sufficient conditions in terms\nof distance spectral radius and distance signless Laplacian spectral radius for\na graph to contain a fractional $[a, b]$-factor, fractional $[a,\nb]$-deleted-factor and $k$-factor.\n', ""Sufficient conditions for the existence of path-factors with given\n  properties   A spanning subgraph $H$ of a graph $G$ is called a $P_{\\geq k}$-factor of $G$\nif every component of $H$ is isomorphic to a path of order at least $k$, where\n$k\\geq2$ is an integer. A graph $G$ is called a $(P_{\\geq k},l)$-factor\ncritical graph if $G-V'$ contains a $P_{\\geq k}$-factor for any $V'\\subseteq\nV(G)$ with $|V'|=l$. A graph $G$ is called a $(P_{\\geq k},m)$-factor deleted\ngraph if $G-E'$ has a $P_{\\geq k}$-factor for any $E'\\subseteq E(G)$ with\n$|E'|=m$. Intuitively, if a graph is dense enough, it will have a $P_{\\geq\n3}$-factor. In this paper, we give some sufficient conditions for a graph to be\na $(P_{\\geq 3},l)$-factor critical graph or a $(P_{\\geq 3},m)$-factor deleted\ngraph. In this paper, we demonstrate that (i) $G$ is a $(P_{\\geq 3},l)$-factor\ncritical graph if its sun toughness $s(G)>\\frac{l+1}{3}$ and $\\kappa(G)\\geq\nl+2$. (ii) $G$ is a $(P_{\\geq 3},l)$-factor critical graph if its degree sum\n$\\sigma_3(G)\\geq n+2l$ and $\\kappa(G)\\geq l+1$. (iii) $G$ is a $(P_{\\geq\n3},m)$-factor deleted graph if its sun toughness $s(G)\\geq \\frac{m+1}{m+2}$ and\n$\\kappa(G)\\geq 2m+1$. (iv) $G$ is a $(P_{\\geq 3},m)$-factor deleted graph if\nits degree sum $\\sigma_3(G)\\geq n+2m$ and $\\kappa(G)\\geq 2m+1$.\n"", 'Some existence theorems on path-factor critical avoidable graphs   A spanning subgraph $F$ of $G$ is called a path factor if every component of\n$F$ is a path of order at least 2. Let $k\\geq2$ be an integer. A $P_{\\geq\nk}$-factor of $G$ means a path factor in which every component has at least $k$\nvertices. A graph $G$ is called a $P_{\\geq k}$-factor avoidable graph if for\nany $e\\in E(G)$, $G$ has a $P_{\\geq k}$-factor avoiding $e$. A graph $G$ is\ncalled a $(P_{\\geq k},n)$-factor critical avoidable graph if for any\n$W\\subseteq V(G)$ with $|W|=n$, $G-W$ is a $P_{\\geq k}$-factor avoidable graph.\nIn other words, $G$ is $(P_{\\geq k},n)$-factor critical avoidable if for any\n$W\\subseteq V(G)$ with $|W|=n$ and any $e\\in E(G-W)$, $G-W-e$ admits a $P_{\\geq\nk}$-factor. In this article, we verify that (\\romannumeral1) an\n$(n+r+2)$-connected graph $G$ is $(P_{\\geq2},n)$-factor critical avoidable if\n$I(G)>\\frac{n+r+3}{2(r+2)}$; (\\romannumeral2) an $(n+r+2)$-connected graph $G$\nis $(P_{\\geq3},n)$-factor critical avoidable if $t(G)>\\frac{n+r+2}{2(r+2)}$;\n(\\romannumeral3) an $(n+r+2)$-connected graph $G$ is $(P_{\\geq3},n)$-factor\ncritical avoidable if $I(G)>\\frac{n+3(r+2)}{2(r+2)}$; where $n$ and $r$ are two\nnonnegative integers.\n']","[('critical graphs', 0.5021178722381592), ('graph strong', 0.47796204686164856), ('critical graph', 0.46221885085105896), ('spanning subgraph', 0.45465967059135437), ('mathcal connected graphs', 0.44163772463798523), ('graphs spanning', 0.4282562732696533), ('leq vertex', 0.42130064964294434), ('graph contains', 0.41176649928092957), ('subgraph graph', 0.3932842016220093), ('graph p_', 0.38883328437805176)]"
1405,1405,21,1405_random hypergraph_graph detection_random graphs_dense subgraph,"['random hypergraph', 'graph detection', 'random graphs', 'dense subgraph', 'densest subgraph', 'subgraph', 'erd enyi graphs', 'nyi random graph', 'hypergraph', 'random graph']","['Inferring Hidden Structures in Random Graphs   We study the two inference problems of detecting and recovering an isolated\ncommunity of \\emph{general} structure planted in a random graph. The detection\nproblem is formalized as a hypothesis testing problem, where under the null\nhypothesis, the graph is a realization of an Erd\\H{o}s-R\\\'{e}nyi random graph\n$\\mathcal{G}(n,q)$ with edge density $q\\in(0,1)$; under the alternative, there\nis an unknown structure $\\Gamma_k$ on $k$ nodes, planted in $\\mathcal{G}(n,q)$,\nsuch that it appears as an \\emph{induced subgraph}. In case of a successful\ndetection, we are concerned with the task of recovering the corresponding\nstructure. For these problems, we investigate the fundamental limits from both\nthe statistical and computational perspectives. Specifically, we derive lower\nbounds for detecting/recovering the structure $\\Gamma_k$ in terms of the\nparameters $(n,k,q)$, as well as certain properties of $\\Gamma_k$, and exhibit\ncomputationally unbounded optimal algorithms that achieve these lower bounds.\nWe also consider the problem of testing in polynomial-time. As is customary in\nmany similar structured high-dimensional problems, our model undergoes an\n""easy-hard-impossible"" phase transition and computational constraints can\nseverely penalize the statistical performance. To provide an evidence for this\nphenomenon, we show that the class of low-degree polynomials algorithms match\nthe statistical performance of the polynomial-time algorithms we develop.\n', 'Planted Bipartite Graph Detection   We consider the task of detecting a hidden bipartite subgraph in a given\nrandom graph. This is formulated as a hypothesis testing problem, under the\nnull hypothesis, the graph is a realization of an Erd\\H{o}s-R\\\'{e}nyi random\ngraph over $n$ vertices with edge density $q$. Under the alternative, there\nexists a planted $k_{\\mathsf{R}} \\times k_{\\mathsf{L}}$ bipartite subgraph with\nedge density $p>q$. We characterize the statistical and computational barriers\nfor this problem. Specifically, we derive information-theoretic lower bounds,\nand design and analyze optimal algorithms matching those bounds, in both the\ndense regime, where $p,q = \\Theta\\left(1\\right)$, and the sparse regime where\n$p,q = \\Theta\\left(n^{-\\alpha}\\right), \\alpha \\in \\left(0,2\\right]$. We also\nconsider the problem of testing in polynomial-time. As is customary in similar\nstructured high-dimensional problems, our model undergoes an\n""easy-hard-impossible"" phase transition and computational constraints penalize\nthe statistical performance. To provide an evidence for this statistical\ncomputational gap, we prove computational lower bounds based on the low-degree\nconjecture, and show that the class of low-degree polynomials algorithms fail\nin the conjecturally hard region.\n', ""Detection threshold for correlated Erd\\H{o}s-R\\'enyi graphs via densest\n  subgraphs   The problem of detecting edge correlation between two Erd\\H{o}s-R\\'enyi\nrandom graphs on $n$ unlabeled nodes can be formulated as a hypothesis testing\nproblem: under the null hypothesis, the two graphs are sampled independently;\nunder the alternative, the two graphs are independently sub-sampled from a\nparent graph which is Erd\\H{o}s-R\\'enyi $\\mathbf{G}(n, p)$ (so that their\nmarginal distributions are the same as the null). We establish a sharp\ninformation-theoretic threshold when $p = n^{-\\alpha+o(1)}$ for $\\alpha\\in (0,\n1]$ which sharpens a constant factor in a recent work by Wu, Xu and Yu. A key\nnovelty in our work is an interesting connection between the detection problem\nand the densest subgraph of an Erd\\H{o}s-R\\'enyi graph.\n""]","[('random hypergraph', 0.5435888767242432), ('graph detection', 0.5157333612442017), ('random graphs', 0.5133839845657349), ('dense subgraph', 0.5054489970207214), ('densest subgraph', 0.4957611858844757), ('subgraph', 0.4907253682613373), ('erd enyi graphs', 0.483741819858551), ('nyi random graph', 0.4590354561805725), ('hypergraph', 0.45281893014907837), ('random graph', 0.4422776401042938)]"
1406,1406,21,1406_conformal field theories_conformal field theory_field theories cfts_chiral algebras,"['conformal field theories', 'conformal field theory', 'field theories cfts', 'chiral algebras', 'dimensional conformal field', 'theories cfts', 'conformal field', 'chiral algebra', 'dimensional conformal', 'conformal blocks']","['Algebraic structures in two-dimensional conformal field theory   This is an invited contribution to the 2nd edition of the Encyclopedia of\nMathematical Physics. We review the following algebraic structures which appear\nin two-dimensional conformal field theory (CFT):\n  The symmetries of two-dimensional conformal field theories (CFTs) can be\nformalised as chiral algebras, vertex operator algebras or nets of observable\nalgebras. Their representation categories are abelian categories having\nadditional structures, which are induced by properties of conformal blocks,\ni.e. of vector bundles over the moduli space of curves with marked points,\nwhich can be constructed from the symmetry structure.\n  These mathematical notions pertain to the description of chiral CFTs. In a\nfull local CFT one deals in addition with correlators, which are specific\nelements in the spaces of conformal blocks. In fact, a full CFT is the same as\na consistent system of correlators for arbitrary conformal surfaces with any\nnumber and type of field insertions in the bulk as well as on boundaries and on\ntopological defect lines. We present algebraic structures that allow one to\nconstruct such systems of correlators.\n', 'Meromorphic Cosets and the Classification of Three-Character CFT   We investigate the admissible vector-valued modular forms having three\nindependent characters and vanishing Wronskian index and determine which ones\ncorrespond to genuine 2d conformal field theories. This is done by finding\nbilinear coset-type relations that pair them into meromorphic characters with\ncentral charges 8, 16, 24, 32 and 40. Such pairings allow us to identify some\ncharacters with definite CFTs and rule out others. As a key result we classify\nall unitary three-character CFT with vanishing Wronskian index, excluding\n$c=8,16$. The complete list has two infinite affine series $B_{r,1},D_{r,1}$\nand 45 additional theories. As a by-product, at higher values of the total\ncentral charge we also find constraints on the existence or otherwise of\nmeromorphic theories. We separately list several cases that potentially\ncorrespond to Intermediate Vertex Operator Algebras.\n', ""Tensor Product CFTs and One-Character Extensions   We study one-character CFTs obtained as one-character extensions of the\ntensor products of a single CFT $\\mathcal{C}$. The motivation comes from the\nfact that $28$ of the $71$ CFTs in the Schelleken's list of $c = 24$ CFTs are\nsuch CFTs. We study for $\\mathcal{C}$ : (i) any two-character WZW CFT with\nvanishing Wronskian index, (ii) the Ising CFT, (iii) the infinite class of\n$D_{r,1}$ CFTs and the $A_{4,1}$ CFT. The characters being $S$-invariant\nhomogenous polynomials of the characters of $\\mathcal{C}$, when organised in\nterms of a $S$-invariant basis, take compact forms allowing for closed form\nanswers for high central charges. We find a $S$-invariant basis for each of the\nCFTs studied. As an example, one can find an explicit expression for the\ncharacter of the monster CFT as a degree-$48$ polynomial of the characters of\nthe Ising CFT. In some CFTs, some of the $S$-invariant polynomials of\ncharacters compute, after using the $q$-series of the characters, to a constant\nvalue. Hence, the characters of one-character extensions are more properly\nelements of the quotient ring of polynomials (of characters) with the ideal\nneeded for the quotient, generated by $S$-invariant polynomials that compute to\na constant.\n""]","[('conformal field theories', 0.6846150159835815), ('conformal field theory', 0.6475697755813599), ('field theories cfts', 0.586409330368042), ('chiral algebras', 0.5607882142066956), ('dimensional conformal field', 0.5417481660842896), ('theories cfts', 0.5341604351997375), ('conformal field', 0.5148487091064453), ('chiral algebra', 0.5131811499595642), ('dimensional conformal', 0.5099089741706848), ('conformal blocks', 0.4893275201320648)]"
1407,1407,21,1407_alzheimer disease_neurodegenerative diseases_alzheimer_neurodegenerative,"['alzheimer disease', 'neurodegenerative diseases', 'alzheimer', 'neurodegenerative', 'numerical modelling', 'proteins', 'space discretization', 'beta tau', 'modelling', 'protein']","[""The role of beta-amyloid and tau proteins in Alzheimer's disease: a\n  mathematical model on graph   In this Note we study a mathematical model for the progression of Alzheimer's\nDisease in the human brain. The novelty of our approach consists in the\nrepresentation of the brain as two superposed graphs where toxic proteins\ndiffuse, the connectivity graph which represents the neural network, and the\nproximity graph which takes into account the extracellular space. Toxic\nproteins such as beta-amyloid and tau play in fact a crucial role in the\ndevelopment of Alzheimer's disease and, separately, have been targets of\nmedical treatments. Recent biomedical literature stresses the potential impact\nof the synergetic action of these proteins. We numerically test various\nmodelling hypotheses which confirm the relevance of this synergy.\n"", ""Nonlocal Models in the Analysis of Brain Neurodegenerative Protein\n  Dynamics with Application to Alzheimer's Disease   It is well known that today nearly one in six of the world's population has\nto deal with neurodegenerative disorders. While a number of medical devices\nhave been developed for the detection, prevention, and treatments of such\ndisorders, some fundamentals of the progression of associated diseases are in\nurgent need of further clarification. In this paper, we focus on Alzheimer's\ndisease, where it is believed that the concentration changes in amyloid-beta\nand tau proteins play a central role in its onset and development. A multiscale\nmodel is proposed to analyze the propagation of these concentrations in the\nbrain connectome. In particular, we consider a modified heterodimer model for\nthe protein-protein interactions. Higher toxic concentrations of amyloid-beta\nand tau proteins destroy the brain cell. We have studied these propagations for\nthe primary and secondary and their mixed tauopathy. We model the damage of a\nbrain cell by the nonlocal contributions of these toxic loads present in the\nbrain cells. With the help of rigorous analysis, we check the stability\nbehaviour of the stationary points corresponding to the homogeneous system.\nAfter integrating the brain connectome data into the developed model, we see\nthat the spreading patterns of the toxic concentrations for the whole brain are\nthe same, but their concentrations are different in different regions. Also,\nthe time to propagate the damage in each region of the brain connectome is\ndifferent.\n"", ""A network aggregation model for the dynamics and treatment of\n  neurodegenerative diseases at the brain scale   Neurodegenerative diseases are associated with the assembly of specific\nproteins into oligomers and fibrillar aggregates. At the brain scale, these\nprotein assemblies can diffuse through the brain and seed other regions,\ncreating an autocatalytic protein progression. The growth and transport of\nthese assemblies depend on various mechanisms that can be targeted\ntherapeutically. Here, we use spatially-extended\nnucleation-aggregation-fragmentation models for the dynamics of prion-like\nneurodegenerative protein-spreading in the brain to study the effect of\ndifferent drugs on whole-brain Alzheimer's disease progression.\n""]","[('alzheimer disease', 0.42331045866012573), ('neurodegenerative diseases', 0.4056972563266754), ('alzheimer', 0.3789096176624298), ('neurodegenerative', 0.36241331696510315), ('numerical modelling', 0.33590829372406006), ('proteins', 0.31003767251968384), ('space discretization', 0.2775976061820984), ('beta tau', 0.27468574047088623), ('modelling', 0.2653988003730774), ('protein', 0.25941163301467896)]"
1408,1408,21,1408_quantum information theory_quantum channels_quantum spaces_completely positive maps,"['quantum information theory', 'quantum channels', 'quantum spaces', 'completely positive maps', 'von neumann algebras', 'quantum information', 'correlations quantum', 'decomposition quantum', 'positive maps', 'positive trace preserving']","['On the Extremality of the Tensor Product of Quantum Channels   Completely positive and trace preserving (CPT) maps are important for Quantum\nInformation Theory, because they describe a broad class of of transformations\nof quantum states. There are also two other related classes of maps, the unital\ncompletely positive (UCP) maps and the unital completely positive and trace\npreserving (UCPT) maps. For these three classes, the maps from a finite\ndimensional Hilbert space $X$ to another one $Y$ is a compact convex set and,\nas such, it is the convex hull of its extreme points. The extreme points of\nthese convex sets are yet not well understood. In this article we investigate\nthe preservation of extremality under the tensor product. We prove that\nextremality is preserved for CPT or UCP maps, but for UCPT it is not always\npreserved.\n', 'Quantum correlations on quantum spaces   For given quantum (non-commutative) spaces $\\mathbb{P}$ and $\\mathbb{O}$ we\nstudy the quantum space of maps $\\mathbb{M}_{\\mathbb{P},\\mathbb{O}}$ from\n$\\mathbb{P}$ to $\\mathbb{O}$. In case of finite quantum spaces these objects\nturn out to be behind a large class of maps which generalize the classical\n$\\mathrm{qc}$-correlations known from quantum information theory to the setting\nof quantum input and output sets. We prove a number of important functorial\nproperties of the mapping\n$(\\mathbb{P},\\mathbb{O})\\mapsto\\mathbb{M}_{\\mathbb{P},\\mathbb{O}}$ and use them\nto study various operator algebraic properties of the $\\mathrm{C}^*$-algebras\n$\\operatorname{C}(\\mathbb{M}_{\\mathbb{P},\\mathbb{O}})$ such as the lifting\nproperty and residual finite dimensionality. Inside\n$\\operatorname{C}(\\mathbb{M}_{\\mathbb{P},\\mathbb{O}})$ we construct a universal\noperator system $\\mathbb{S}_{\\mathbb{P},\\mathbb{O}}$ related to $\\mathbb{P}$\nand $\\mathbb{O}$ and show, among other things, that the embedding\n$\\mathbb{S}_{\\mathbb{P},\\mathbb{O}}\\subset\\operatorname{C}(\\mathbb{M}_{\\mathbb{P},\\mathbb{O}})$\nis hyperrigid, $\\operatorname{C}(\\mathbb{M}_{\\mathbb{P},\\mathbb{O}})$ is the\n$\\mathrm{C}^*$-envelope of $\\mathbb{S}_{\\mathbb{P},\\mathbb{O}}$ and that a\nlarge class of non-signalling correlations on the quantum sets $\\mathbb{P}$ and\n$\\mathbb{O}$ arise from states on\n$\\operatorname{C}(\\mathbb{M}_{\\mathbb{P},\\mathbb{O}})\\otimes_{\\rm{max}}\\operatorname{C}(\\mathbb{M}_{\\mathbb{P},\\mathbb{O}})$\nas well as states on the commuting tensor product\n$\\mathbb{S}_{\\mathbb{P},\\mathbb{O}}\\otimes_{\\rm{c}}\\mathbb{S}_{\\mathbb{P},\\mathbb{O}}$.\nFinally we introduce and study the notion of a synchronous correlation with\nquantum input and output sets, prove several characterizations of such\ncorrelations and their relation to traces on\n$\\operatorname{C}(\\mathbb{M}_{\\mathbb{P},\\mathbb{O}})$.\n', 'Decomposable Pauli diagonal maps and Tensor Squares of Qubit Maps   It is a well-known result due to E. St{\\o}rmer that every positive qubit map\nis decomposable into a sum of a completely positive map and a completely\ncopositive map. Here, we generalize this result to tensor squares of qubit\nmaps. Specifically, we show that any positive tensor product of a qubit map\nwith itself is decomposable. This solves a recent conjecture by S. Fillipov and\nK. Magadov. We contrast this result with examples of non-decomposable positive\nmaps arising as the tensor product of two distinct qubit maps or as the tensor\nsquare of a decomposable map from a qubit to a ququart. To show our main\nresult, we reduce the problem to Pauli diagonal maps. We then characterize the\ncone of decomposable ququart Pauli diagonal maps by determining all 252\nextremal rays of ququart Pauli diagonal maps that are both completely positive\nand completely copositive. These extremal rays split into three disjoint orbits\nunder a natural symmetry group, and two of these orbits contain only\nentanglement breaking maps. Finally, we develop a general combinatorial method\nto determine the extremal rays of Pauli diagonal maps that are both completely\npositive and completely copositive between multi-qubit systems using the\nordered spectra of their Choi matrices. Classifying these extremal rays beyond\nququarts is left as an open problem.\n']","[('quantum information theory', 0.5492583513259888), ('quantum channels', 0.5403200387954712), ('quantum spaces', 0.5402210354804993), ('completely positive maps', 0.5227988958358765), ('von neumann algebras', 0.5185624361038208), ('quantum information', 0.5069820880889893), ('correlations quantum', 0.5052461624145508), ('decomposition quantum', 0.499636173248291), ('positive maps', 0.49784040451049805), ('positive trace preserving', 0.4920148253440857)]"
1409,1409,21,1409_poisson algebras_poisson cohomology_poisson algebra_poisson manifolds,"['poisson algebras', 'poisson cohomology', 'poisson algebra', 'poisson manifolds', 'poisson manifold', 'twisted poisson', 'poisson structures', 'poisson structure', 'structure poisson', 'poincar duality']","[""The Poisson linearization problem for $\\mathfrak{sl}_2(\\mathbb{C})$.\n  Part II: The Nash-Moser method   This is the second of two papers, in which we prove a version of Conn's\nlinearization theorem for the Lie algebra $\\mathfrak{sl}_2(\\mathbb{C})\\simeq\n\\mathfrak{so}(3,1)$. Namely, we show that any Poisson structure whose linear\napproximation at a zero is isomorphic to the Poisson structure associated to\n$\\mathfrak{sl}_2(\\mathbb{C})$ is linearizable. In the first part, we calculated\nthe Poisson cohomology associated to $\\mathfrak{sl}_2(\\mathbb{C})$, and we\nconstructed bounded homotopy operators for the Poisson complex of multivector\nfields that are flat at the origin. In this second part, we obtain the\nlinearization result, which works for a more general class of Lie algebras. For\nthe proof, we develop a Nash-Moser method for functions that are flat at a\npoint.\n"", 'Poincare Duality For Smooth Poisson Algebras And BV Structure On Poisson\n  Cohomology   Similar to the modular vector fields in Poisson geometry, modular derivations\nare defined for smooth Poisson algebras with trivial canonical bundle. By\ntwisting Poisson module with the modular derivation, the Poisson cochain\ncomplex with values in any Poisson module is proved to be isomorphic to the\nPoisson chain complex with values in the corresponding twisted Poisson module.\nThen a version of twisted Poincar\\\'{e} duality is proved between the Poisson\nhomologies and cohomologies. Furthermore, a notion of pseudo-unimodular Poisson\nstructure is defined. It is proved that the Poisson cohomology as a\nGerstenhaber algebra admits a Batalin-Vilkovisky operator inherited from some\none of its Poisson cochain complex if and only if the Poisson structure is\npseudo-unimodular. This generalizes the geometric version due to P. Xu. The\nmodular derivation and Batalin-Vilkovisky operator are also described by using\nthe dual basis of the K\\""{a}hler differential module.\n', ""The Poisson linearization problem for $\\mathfrak{sl}_2(\\mathbb{C})$.\n  Part I: Poisson cohomology   This is the first of two papers, in which we prove a version of Conn's\nlinearization theorem for the Lie algebra $\\mathfrak{sl}_2(\\mathbb{C})\\simeq\n\\mathfrak{so}(3,1)$. Namely, we show that any Poisson structure whose linear\napproximation at a zero is isomorphic to the Poisson structure associated to\n$\\mathfrak{sl}_2(\\mathbb{C})$ is linearizable. In this first part, we calculate\nthe Poisson cohomology associated to $\\mathfrak{sl}_2(\\mathbb{C})$, and we\nconstruct bounded homotopy operators for the Poisson complex of multivector\nfields that are flat at the origin. In the second part, we will obtain the\nlinearization result, which works for a more general class of Lie algebras. For\nthe proof, we will develop a Nash-Moser method for functions that are flat at a\npoint.\n""]","[('poisson algebras', 0.7477998733520508), ('poisson cohomology', 0.7199183106422424), ('poisson algebra', 0.703170657157898), ('poisson manifolds', 0.6597611308097839), ('poisson manifold', 0.6201513409614563), ('twisted poisson', 0.5803685784339905), ('poisson structures', 0.5760790705680847), ('poisson structure', 0.5645143985748291), ('structure poisson', 0.5416771173477173), ('poincar duality', 0.5395958423614502)]"
1410,1410,21,1410_communications channel estimation_channel estimation ris_channel estimation framework_channel estimation challenging,"['communications channel estimation', 'channel estimation ris', 'channel estimation framework', 'channel estimation challenging', 'channel estimation', 'joint channel estimation', 'channel estimation signal', 'wireless communications', 'ris assisted wireless', 'user channels']","[""Channel Estimation for RIS-Empowered Multi-User MISO Wireless\n  Communications   Reconfigurable Intelligent Surfaces (RISs) have been recently considered as\nan energy-efficient solution for future wireless networks due to their fast and\nlow-power configuration, which has increased potential in enabling massive\nconnectivity and low-latency communications. Accurate and low-overhead channel\nestimation in RIS-based systems is one of the most critical challenges due to\nthe usually large number of RIS unit elements and their distinctive hardware\nconstraints. In this paper, we focus on the uplink of a RIS-empowered\nmulti-user Multiple Input Single Output (MISO) uplink communication systems and\npropose a channel estimation framework based on the parallel factor\ndecomposition to unfold the resulting cascaded channel model. We present two\niterative estimation algorithms for the channels between the base station and\nRIS, as well as the channels between RIS and users. One is based on alternating\nleast squares (ALS), while the other uses vector approximate message passing to\niteratively reconstruct two unknown channels from the estimated vectors. To\ntheoretically assess the performance of the ALS-based algorithm, we derived its\nestimation Cram\\'er-Rao Bound (CRB). We also discuss the downlink achievable\nsum rate computation with estimated channels and different precoding schemes\nfor the base station. Our extensive simulation results show that our algorithms\noutperform benchmark schemes and that the ALS technique achieves the CRB. It is\nalso demonstrated that the sum rate using the estimated channels always reach\nthat of perfect channels under various settings, thus, verifying the\neffectiveness and robustness of the proposed estimation algorithms.\n"", 'Channel Estimation for Reconfigurable Intelligent Surface-Aided\n  Multiuser Communication Systems Exploiting Statistical CSI of Correlated\n  RIS-User Channels   Reconfigurable intelligent surface (RIS) is a promising candidate technology\nfor the upcoming Sixth Generation (6G) communication system for its ability to\nmanipulate the wireless communication environment by controlling the\ncoefficients of reflection elements (REs). However, since the RIS usually\nconsists of a large number of passive REs, the pilot overhead for channel\nestimation in the RIS-aided system is prohibitively high. In this paper, the\nchannel estimation problem for a RIS-aided multi-user\nmultiple-input-single-output (MISO) communication system with clustered users\nis investigated. First, to describe the correlated feature for RIS-user\nchannels, a beam domain channel model is developed for RIS-user channels. Then,\na pilot reuse strategy is put forward to reduce the pilot overhead and\ndecompose the channel estimation problem into several subproblems. Finally, by\nleveraging the correlated nature of RIS-user channels, an eigenspace projection\n(EP) algorithm is proposed to solve each subproblem respectively. Simulation\nresults show that the proposed EP channel estimation scheme can achieve\naccurate channel estimation with lower pilot overhead than existing schemes.\n', 'Parallel Factor Decomposition Channel Estimation in RIS-Assisted\n  Multi-User MISO Communication   Reconfigurable Intelligent Surfaces (RISs) have been recently considered as\nan energy-efficient solution for future wireless networks due to their fast and\nlow power configuration enabling massive connectivity and low latency\ncommunications. Channel estimation in RIS-based systems is one of the most\ncritical challenges due to the large number of reflecting unit elements and\ntheir distinctive hardware constraints. In this paper, we focus on the downlink\nof a RIS-assisted multi-user Multiple Input Single Output (MISO) communication\nsystem and present a method based on the PARAllel FACtor (PARAFAC)\ndecomposition to unfold the resulting cascaded channel model. The proposed\nmethod includes an alternating least squares algorithm to iteratively estimate\nthe channel between the base station and RIS, as well as the channels between\nRIS and users. Our selective simulation results show that the proposed\niterative channel estimation method outperforms a benchmark scheme using\ngenie-aided information. We also provide insights on the impact of different\nRIS settings on the proposed algorithm.\n']","[('communications channel estimation', 0.6511353850364685), ('channel estimation ris', 0.6146014928817749), ('channel estimation framework', 0.6078729033470154), ('channel estimation challenging', 0.6055293679237366), ('channel estimation', 0.5957842469215393), ('joint channel estimation', 0.5759890675544739), ('channel estimation signal', 0.5392789840698242), ('wireless communications', 0.4347642958164215), ('ris assisted wireless', 0.42878809571266174), ('user channels', 0.4215880036354065)]"
1411,1411,21,1411_probabilistic numerical_numerical solvers_probabilistic uncertainty_numerically robust,"['probabilistic numerical', 'numerical solvers', 'probabilistic uncertainty', 'numerically robust', 'numerical differential equations', 'numerical methods', 'ode solvers', 'probabilistic formulation', 'adaptive probabilistic', 'numerical differential']","['Probabilistic Numerical Method of Lines for Time-Dependent Partial\n  Differential Equations   This work develops a class of probabilistic algorithms for the numerical\nsolution of nonlinear, time-dependent partial differential equations (PDEs).\nCurrent state-of-the-art PDE solvers treat the space- and time-dimensions\nseparately, serially, and with black-box algorithms, which obscures the\ninteractions between spatial and temporal approximation errors and misguides\nthe quantification of the overall error. To fix this issue, we introduce a\nprobabilistic version of a technique called method of lines. The proposed\nalgorithm begins with a Gaussian process interpretation of finite difference\nmethods, which then interacts naturally with filtering-based probabilistic\nordinary differential equation (ODE) solvers because they share a common\nlanguage: Bayesian inference. Joint quantification of space- and\ntime-uncertainty becomes possible without losing the performance benefits of\nwell-tuned ODE solvers. Thereby, we extend the toolbox of probabilistic\nprograms for differential equation simulation to PDEs.\n', 'Propagating Model Uncertainty through Filtering-based Probabilistic\n  Numerical ODE Solvers   Filtering-based probabilistic numerical solvers for ordinary differential\nequations (ODEs), also known as ODE filters, have been established as efficient\nmethods for quantifying numerical uncertainty in the solution of ODEs. In\npractical applications, however, the underlying dynamical system often contains\nuncertain parameters, requiring the propagation of this model uncertainty to\nthe ODE solution. In this paper, we demonstrate that ODE filters, despite their\nprobabilistic nature, do not automatically solve this uncertainty propagation\nproblem. To address this limitation, we present a novel approach that combines\nODE filters with numerical quadrature to properly marginalize over uncertain\nparameters, while accounting for both parameter uncertainty and numerical\nsolver uncertainty. Experiments across multiple dynamical systems demonstrate\nthat the resulting uncertainty estimates closely match reference solutions.\nNotably, we show how the numerical uncertainty from the ODE solver can help\nprevent overconfidence in the propagated uncertainty estimates, especially when\nusing larger step sizes. Our results illustrate that probabilistic numerical\nmethods can effectively quantify both numerical and parametric uncertainty in\ndynamical systems.\n', 'Parallel-in-Time Probabilistic Numerical ODE Solvers   Probabilistic numerical solvers for ordinary differential equations (ODEs)\ntreat the numerical simulation of dynamical systems as problems of Bayesian\nstate estimation. Aside from producing posterior distributions over ODE\nsolutions and thereby quantifying the numerical approximation error of the\nmethod itself, one less-often noted advantage of this formalism is the\nalgorithmic flexibility gained by formulating numerical simulation in the\nframework of Bayesian filtering and smoothing. In this paper, we leverage this\nflexibility and build on the time-parallel formulation of iterated extended\nKalman smoothers to formulate a parallel-in-time probabilistic numerical ODE\nsolver. Instead of simulating the dynamical system sequentially in time, as\ndone by current probabilistic solvers, the proposed method processes all time\nsteps in parallel and thereby reduces the span cost from linear to logarithmic\nin the number of time steps. We demonstrate the effectiveness of our approach\non a variety of ODEs and compare it to a range of both classic and\nprobabilistic numerical ODE solvers.\n']","[('probabilistic numerical', 0.6193093657493591), ('numerical solvers', 0.5384669303894043), ('probabilistic uncertainty', 0.5270137190818787), ('numerically robust', 0.4911423325538635), ('numerical differential equations', 0.4801879823207855), ('numerical methods', 0.4641817510128021), ('ode solvers', 0.4590469002723694), ('probabilistic formulation', 0.4583524167537689), ('adaptive probabilistic', 0.4516414701938629), ('numerical differential', 0.4492487907409668)]"
1412,1412,21,1412_brascamp lieb inequalities_brascamp lieb inequality_lieb inequalities_lieb inequality,"['brascamp lieb inequalities', 'brascamp lieb inequality', 'lieb inequalities', 'lieb inequality', 'inequality convex geometry', 'inequalities generalization', 'brascamp lieb', 'inequalities various', 'inequalities estimate', 'new inequalities']","[""The case of equality in geometric instances of Barthe's reverse\n  Brascamp-Lieb inequalit   The works of Bennett, Carbery, Christ, Tao and of Valdimarsson have clarified\nwhen equality holds in the Brascamp-Lieb inequality. Here we characterize the\ncase of equality in the Geometric case of Barthe's reverse Brascamp-Lieb\ninequality.\n"", ""Regularized Brascamp--Lieb inequalities   Given any (forward) Brascamp--Lieb inequality on euclidean space, a famous\ntheorem of Lieb guarantees that gaussian near-maximizers always exist.\nRecently, Barthe and Wolff used mass transportation techniques to establish a\ncounterpart to Lieb's theorem for all non-degenerate cases of the inverse\nBrascamp--Lieb inequality. Here we build on work of Chen--Dafnis--Paouris and\nemploy heat-flow techniques to understand the inverse Brascamp--Lieb inequality\nfor certain regularized input functions, in particular extending the\nBarthe--Wolff theorem to such a setting. Inspiration arose from work of\nBennett, Carbery, Christ and Tao for the forward inequality, and we recover\ntheir generalized Lieb's theorem using a clever limiting argument of Wolff. In\nfact, we use Wolff's idea to deduce regularized inequalites in the broader\nframework of the forward-reverse Brascamp--Lieb inequality, in particular\nallowing us to recover the gaussian saturation property in this framework first\nobtained by Courtade, Cuff, Liu and Verd\\'u.\n"", 'Singular Brascamp-Lieb inequalities with cubical structure   We prove a singular Brascamp-Lieb inequality, stated in Theorem 1, with a\nlarge group of involutive symmetries.\n']","[('brascamp lieb inequalities', 0.8397207260131836), ('brascamp lieb inequality', 0.8369483351707458), ('lieb inequalities', 0.6969778537750244), ('lieb inequality', 0.6836073398590088), ('inequality convex geometry', 0.5881499648094177), ('inequalities generalization', 0.5236030220985413), ('brascamp lieb', 0.5177225470542908), ('inequalities various', 0.4616296887397766), ('inequalities estimate', 0.4540024995803833), ('new inequalities', 0.4514991044998169)]"
1413,1413,21,1413_heisenberg groups_dimensional heisenberg group_heisenberg group_lipschitz graphs,"['heisenberg groups', 'dimensional heisenberg group', 'heisenberg group', 'lipschitz graphs', 'heisenberg group mathbb', 'first heisenberg group', 'dimensional heisenberg', 'lipschitz graph', 'heisenberg', 'lipschitz functions']","['Vertical curves and vertical fibers in the Heisenberg group   Let $\\mathbb H$ denote the three-dimensional Heisenberg group. In this paper,\nwe study vertical curves in $\\mathbb H$ and fibers of maps $\\mathbb H \\to\n\\mathbb R^2$ from a metric perspective. We say that a set in $\\mathbb H$ is a\nvertical curve if it satisfies a cone condition with respect to a homogeneous\ncone with axis $\\langle Z \\rangle$, the center of $\\mathbb H$. This is\nanalogous to the cone condition used to define intrinsic Lipschitz graphs.\n  In the first part of the paper, we prove that connected vertical curves are\nlocally biH\\""older equivalent to intervals. We also show that the class of\nvertical curves coincides with the class of intersections of intrinsic\nLipschitz graphs satisfying a transversality condition. Unlike intrinsic\nLipschitz graphs, the Hausdorff dimension of a vertical curve can vary; we\nconstruct vertical curves with Hausdorff dimension either strictly larger or\nstrictly smaller than 2. Consequently, there are intersections of intrinsic\nLipschitz graphs with Hausdorff dimension either strictly larger or strictly\nsmaller than 2.\n  In the second part of the paper, we consider smooth functions $\\beta$ from\nthe unit ball $B$ in $\\mathbb H$ to $\\mathbb R^2$. We show that, in contrast to\nthe situation in Euclidean space, there are maps such that $\\beta$ is\narbitrarily close to the projection $\\pi$ from $\\mathbb H$ to the horizontal\nplane, but the average $\\mathcal{H}^2$ measure of a fiber of $\\beta$ in $B$ is\narbitrarily small.\n', ""Extensions and corona decompositions of low-dimensional intrinsic\n  Lipschitz graphs in Heisenberg groups   This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense\nof Franchi, Serapioni, and Serra Cassano, in the Heisenberg group\n$\\mathbb{H}^n$, $n\\in \\mathbb{N}$. For $1\\leq k\\leq n$, we show that every\nintrinsic $L$-Lipschitz graph over a subset of a $k$-dimensional horizontal\nsubgroup $\\mathbb{V}$ of $\\mathbb{H}^n$ can be extended to an intrinsic\n$L'$-Lipschitz graph over the entire subgroup $\\mathbb{V}$, where $L'$ depends\nonly on $L$, $k$, and $n$. We further prove that $1$-dimensional intrinsic\n$1$-Lipschitz graphs in $\\mathbb{H}^n$, $n\\in \\mathbb{N}$, admit corona\ndecompositions by intrinsic Lipschitz graphs with smaller Lipschitz constants.\nThis complements results that were known previously only in the first\nHeisenberg group $\\mathbb{H}^1$. The main difference to this case arises from\nthe fact that for $1\\leq k<n$, the complementary vertical subgroups of\n$k$-dimensional horizontal subgroups in $\\mathbb{H}^n$ are not commutative.\n"", ""Lipschitz graphs and currents in Heisenberg groups   The main result of the present paper is a Rademacher-type theorem for\nintrinsic Lipschitz graphs of codimension $k\\leq n$ in sub-Riemannian\nHeisenberg groups $\\mathbb H^n$. For the purpose of proving such a result we\nsettle several related questions pertaining both to the theory of intrinsic\nLipschitz graphs and to the one of currents. First, we prove an extension\nresult for intrinsic Lipschitz graphs as well as a uniform approximation\ntheorem by means of smooth graphs: these results stem both from a new\ndefinition (equivalent to the one introduced by F. Franchi, R. Serapioni and F.\nSerra Cassano) of intrinsic Lipschitz graphs and are valid for a more general\nclass of intrinsic Lipschitz graphs in Carnot groups. Second, our proof of\nRademacher's Theorem heavily uses the language of currents in Heisenberg\ngroups: one key result is, for us, a version of the celebrated Constancy\nTheorem. Inasmuch as Heisenberg currents are defined in terms of Rumin's\ncomplex of differential forms, we also provide a convenient basis of Rumin's\nspaces. Eventually, we provide some applications of Rademacher's Theorem\nincluding a Lusin-type result for intrinsic Lipschitz graphs, the equivalence\nbetween $\\mathbb H$-rectifiability and ``Lipschitz'' $\\mathbb\nH$-rectifiability, and an area formula for intrinsic Lipschitz graphs in\nHeisenberg groups.\n""]","[('heisenberg groups', 0.5641377568244934), ('dimensional heisenberg group', 0.5508055090904236), ('heisenberg group', 0.519690752029419), ('lipschitz graphs', 0.5154969692230225), ('heisenberg group mathbb', 0.47457006573677063), ('first heisenberg group', 0.4646279513835907), ('dimensional heisenberg', 0.45804017782211304), ('lipschitz graph', 0.4124816060066223), ('heisenberg', 0.3376781642436981), ('lipschitz functions', 0.29852932691574097)]"
1414,1414,21,1414_entropy estimation_entropy models_shannon entropy_information theoretic metrics,"['entropy estimation', 'entropy models', 'shannon entropy', 'information theoretic metrics', 'entropy various', 'entropy based', 'entropy fundamental', 'existing entropy', 'entropy', 'profile entropy']","[""Asymptotic Normality for Plug-in Estimators of Generalized Shannon's\n  Entropy   Shannon's entropy is one of the building blocks of information theory and an\nessential aspect of Machine Learning methods (e.g., Random Forests). Yet, it is\nonly finitely defined for distributions with fast decaying tails on a countable\nalphabet. The unboundedness of Shannon's entropy over the general class of all\ndistributions on an alphabet prevents its potential utility from being fully\nrealized. To fill the void in the foundation of information theory, Zhang\n(2020) proposed generalized Shannon's entropy, which is finitely defined\neverywhere. The plug-in estimator, adopted in almost all entropy-based ML\nmethod packages, is one of the most popular approaches to estimating Shannon's\nentropy. The asymptotic distribution for Shannon's entropy's plug-in estimator\nwas well studied in the existing literature. This paper studies the asymptotic\nproperties for the plug-in estimator of generalized Shannon's entropy on\ncountable alphabets. The developed asymptotic properties require no assumptions\non the original distribution. The proposed asymptotic properties allow interval\nestimation and statistical tests with generalized Shannon's entropy.\n"", ""Statistical tests based on R\\'{e}nyi entropy estimation   Entropy and its various generalizations are important in many fields,\nincluding mathematical statistics, communication theory, physics and computer\nscience, for characterizing the amount of information associated with a\nprobability distribution. In this paper we propose goodness-of-fit statistics\nfor the multivariate Student and multivariate Pearson type II distributions,\nbased on the maximum entropy principle and a class of estimators for R\\'{e}nyi\nentropy based on nearest neighbour distances. We prove the L^2-consistency of\nthese statistics using results on the subadditivity of Euclidean functionals on\nnearest neighbour graphs, and investigate their rate of convergence and\nasymptotic distribution using Monte Carlo methods. In addition we present a\nnovel iterative method for estimating the shape parameter of the multivariate\nStudent and multivariate Pearson type II distributions.\n"", 'Statistical tests based on Renyi entropy estimation   Entropy and its various generalizations are important in many fields,\nincluding mathematical statistics, communication theory, physics and computer\nscience, for characterizing the amount of information associated with a\nprobability distribution. In this paper we propose goodness-of-fit statistics\nfor the multivariate Student and multivariate Pearson type II distributions,\nbased on the maximum entropy principle and a class of estimators for Renyi\nentropy based on nearest neighbour distances. We prove the L2-consistency of\nthese statistics using results on the subadditivity of Euclidean functionals on\nnearest neighbour graphs, and investigate their rate of convergence and\nasymptotic distribution using Monte Carlo methods.\n']","[('entropy estimation', 0.6790211200714111), ('entropy models', 0.6025722622871399), ('shannon entropy', 0.5998904705047607), ('information theoretic metrics', 0.5759283900260925), ('entropy various', 0.5599191188812256), ('entropy based', 0.5331425666809082), ('entropy fundamental', 0.5284793972969055), ('existing entropy', 0.5263188481330872), ('entropy', 0.5180856585502625), ('profile entropy', 0.5123575329780579)]"
1415,1415,21,1415_loop groups_moufang loops_moufang loop_loops also,"['loop groups', 'moufang loops', 'moufang loop', 'loops also', 'loops', 'loops called', 'abelian normal subgroup', 'loop order', 'abelian', 'abelian normal']","['Supernilpotent groups and $3$-supernilpotent loops   We find a short equational basis for the variety of $3$-supernilpotent loops.\nWe also present a conceptually simple proof that $k$-nilpotence and\n$k$-supernilpotence are equivalent for groups. Connections between\n$3$-supernilpotent loops, Moufang loops, code loops, automorphic loops and AIM\nloops are explored.\n', 'On abelian-by-cyclic Moufang loops   We study abelian-by-cyclic Moufang loops. We construct all split\n$3$-divisible abelian-by-cyclic Moufang loops from so-called Moufang\npermutations on abelian groups $(X,+)$, which are permutations that deviate\nfrom an automorphism of $(X,+)$ by an alternating biadditive mapping\n(satisfying certain properties). More generally, we obtain additional\nabelian-by-cyclic Moufang loops from so-called construction pairs. As an aside,\nwe show that in the Moufang loops $Q$ obtained from a construction pair on\n$(X,+)$ the abelian normal subgroup $(X,+)$ induces an abelian congruence of\n$Q$ if and only if $Q$ is a group.\n', ""Abelian congruences and solvability in Moufang loops   In groups, an abelian normal subgroup induces an abelian congruence. We\nconstruct a class of centrally nilpotent Moufang loops containing an abelian\nnormal subloop that does not induce an abelian congruence. On the other hand,\nwe prove that in $6$-divisible Moufang loops, every abelian normal subloop\ninduces an abelian congruence.\n  In loops, congruence solvability adopted from the universal-algebraic\ncommutator theory of congruence modular varieties is strictly stronger than\nclassical solvability adopted from group theory. It is an open problem whether\nthe two notions of solvability coincide in Moufang loops. We prove that they\ncoincide in $6$-divisible Moufang loops and in Moufang loops of odd order. In\nfact, we show that every Moufang loop of odd order is congruence solvable, thus\nstrengthening Glauberman's Odd Order Theorem for Moufang loops.\n""]","[('loop groups', 0.6182451844215393), ('moufang loops', 0.5626755356788635), ('moufang loop', 0.5392429232597351), ('loops also', 0.4641683101654053), ('loops', 0.4507954716682434), ('loops called', 0.3958856165409088), ('abelian normal subgroup', 0.36871427297592163), ('loop order', 0.3658234477043152), ('abelian', 0.36575061082839966), ('abelian normal', 0.3557806611061096)]"
1416,1416,21,1416_identification nonlinear dynamics_latent space dynamics_sparse identification nonlinear_dynamics identification,"['identification nonlinear dynamics', 'latent space dynamics', 'sparse identification nonlinear', 'dynamics identification', 'identification nonlinear', 'dimensional nonlinear dynamical', 'high dimensional nonlinear', 'high fidelity models', 'sparse identification', 'latent dynamics']","[""Physics-informed active learning with simultaneous weak-form latent\n  space dynamics identification   The parametric greedy latent space dynamics identification (gLaSDI) framework\nhas demonstrated promising potential for accurate and efficient modeling of\nhigh-dimensional nonlinear physical systems. However, it remains challenging to\nhandle noisy data. To enhance robustness against noise, we incorporate the\nweak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed\nweak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained\nsimultaneously to discover intrinsic nonlinear latent-space dynamics of\nhigh-dimensional data. Compared to the standard sparse identification of\nnonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction\nand robust latent space discovery, therefore leading to more accurate and\nefficient reduced-order modeling. Furthermore, the greedy physics-informed\nactive learning in WgLaSDI enables adaptive sampling of optimal training data\non the fly for enhanced modeling accuracy. The effectiveness of the proposed\nframework is demonstrated by modeling various nonlinear dynamical problems,\nincluding viscous and inviscid Burgers' equations, time-dependent radial\nadvection, and the Vlasov equation for plasma physics. With data that contains\n5-10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude,\nachieving 1-7% relative errors. Compared with the high-fidelity models, WgLaSDI\nachieves 121 to 1,779x speed-up.\n"", 'GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics\n  Identification through Deep Autoencoder   Numerically solving partial differential equations (PDEs) can be challenging\nand computationally expensive. This has led to the development of reduced-order\nmodels (ROMs) that are accurate but faster than full order models (FOMs).\nRecently, machine learning advances have enabled the creation of non-linear\nprojection methods, such as Latent Space Dynamics Identification (LaSDI). LaSDI\nmaps full-order PDE solutions to a latent space using autoencoders and learns\nthe system of ODEs governing the latent space dynamics. By interpolating and\nsolving the ODE system in the reduced latent space, fast and accurate ROM\npredictions can be made by feeding the predicted latent space dynamics into the\ndecoder. In this paper, we introduce GPLaSDI, a novel LaSDI-based framework\nthat relies on Gaussian process (GP) for latent space ODE interpolations. Using\nGPs offers two significant advantages. First, it enables the quantification of\nuncertainty over the ROM predictions. Second, leveraging this prediction\nuncertainty allows for efficient adaptive training through a greedy selection\nof additional training data points. This approach does not require prior\nknowledge of the underlying PDEs. Consequently, GPLaSDI is inherently\nnon-intrusive and can be applied to problems without a known PDE or its\nresidual. We demonstrate the effectiveness of our approach on the Burgers\nequation, Vlasov equation for plasma physics, and a rising thermal bubble\nproblem. Our proposed method achieves between 200 and 100,000 times speed-up,\nwith up to 7% relative error.\n', 'gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics\n  Identification   A parametric adaptive physics-informed greedy Latent Space Dynamics\nIdentification (gLaSDI) method is proposed for accurate, efficient, and robust\ndata-driven reduced-order modeling of high-dimensional nonlinear dynamical\nsystems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic\nnonlinear latent representations of high-dimensional data, while dynamics\nidentification (DI) models capture local latent-space dynamics. An interactive\ntraining algorithm is adopted for the autoencoder and local DI models, which\nenables identification of simple latent-space dynamics and enhances accuracy\nand efficiency of data-driven reduced-order modeling. To maximize and\naccelerate the exploration of the parameter space for the optimal model\nperformance, an adaptive greedy sampling algorithm integrated with a\nphysics-informed residual-based error indicator and random-subset evaluation is\nintroduced to search for the optimal training samples on the fly. Further, to\nexploit local latent-space dynamics captured by the local DI models for an\nimproved modeling accuracy with a minimum number of local DI models in the\nparameter space, a k-nearest neighbor convex interpolation scheme is employed.\nThe effectiveness of the proposed framework is demonstrated by modeling various\nnonlinear dynamical problems, including Burgers equations, nonlinear heat\nconduction, and radial advection. The proposed adaptive greedy sampling\noutperforms the conventional predefined uniform sampling in terms of accuracy.\nCompared with the high-fidelity models, gLaSDI achieves 17 to 2,658x speed-up\nwith 1 to 5% relative errors.\n']","[('identification nonlinear dynamics', 0.549696683883667), ('latent space dynamics', 0.5357604026794434), ('sparse identification nonlinear', 0.5276991128921509), ('dynamics identification', 0.5081649422645569), ('identification nonlinear', 0.46589571237564087), ('dimensional nonlinear dynamical', 0.46562767028808594), ('high dimensional nonlinear', 0.45756077766418457), ('high fidelity models', 0.4383847415447235), ('sparse identification', 0.43195289373397827), ('latent dynamics', 0.4299706518650055)]"
1417,1417,21,1417_exponential fields_field real_real closed fields_ordered field,"['exponential fields', 'field real', 'real closed fields', 'ordered field', 'fields omega', 'exponential field', 'subfield mathbb', 'real closed field', 'fields', 'subfields']","[""On all numbers great and small (Topological fields of Conway's numbers\n  and their completions)   The proper Class $\\bf{No}$ of all Conway's numbers $\\cite{l3}$ is considered\nas a region of investigation. It turns out to be a total ordered Field (i.e., a\nfield whose domain is a proper Class) and this totally, or linear ordered\nClass, containing the real numbers ${\\mathbb R}$ and the ordinal numbers {\\bf\nOn}.\n  For any subfield $F$ of $\\bf{No}$, i.e., $F$ is a set nor proper class,\nconsidered with topology induced by a linear ordering on $F$ a completion\n$\\tilde F$ is constructed; in particular, for $\\zeta=\\omega^{\\omega^\\mu}$,\n$0\\leq\\mu<\\Omega$, and for a specially defined subfield $F={\\mathbb\nP}_\\zeta\\subset{\\bf No}$ a complete subfield ${\\mathbb R}_\\zeta\\subset{\\bf No}$\nis defined as $\\tilde {\\mathbb P}_\\zeta$.\n  Fundamental (Cauchy) sequences $(x_\\alpha)_{0\\leq\\alpha<\\zeta}$ are\nconsidered in a subfield $F\\subset {\\mathbb P}_\\zeta\\subset{\\bf No}$, where\n$\\zeta$ is the smallest ordinal number which does not belong to $F$, and they\nare the main instrument in the paper.\n  A fragment of Mathematical Analysis in ${\\mathbb R}_\\zeta$ is given and two\nof its non-trivial results are presented: every positive number $x\\in{\\mathbb\nR}_\\zeta$ has a unique $n$-th root in ${\\mathbb R}_\\zeta$, for each positive\ninteger $n$ and every odd-degree polynomial with coefficients in ${\\mathbb\nR}_\\zeta$ has a root in ${\\mathbb R}_\\zeta$. Hence so-called fundamental\ntheorem of algebra: the ring ${\\mathbb R}_\\zeta[i]\\stackrel{def}{=}{\\mathbb\nC}_\\zeta$ of all numbers of the form $x+iy$ ($x,y\\in{\\mathbb R}_\\zeta$),\n$i^2=-1$, is an algebraically closed field.\n"", 'Surreal fields stable under exponential, logarithmic, derivative and\n  anti-derivative functions   The class of surreal numbers, denoted by $\\textbf{No}$, initially proposed by\nConway, is a universal ordered field in the sense that any ordered field can be\nembedded in it. They include in particular the real numbers and the ordinal\nnumbers. They have strong relations with other fields such as field of\ntransseries. Following Gonshor, surreal numbers can be seen as signs sequences\nof ordinal length, with some exponential and logarithmic functions that extend\nthe usual functions over the reals. $\\textbf{No}$ can actually be seen as an\nelegant (generalized) power series field with real coefficients, namely Hahn\nseries with exponents in $\\textbf{No}$ itself.\n  Some years ago, Berarducci and Mantova considered derivation over the surreal\nnumbers, seeing them as germs of functions, in correspondence to transseries.\nIn this article, following our previous work, we exhibit a sufficient condition\non the structure of a surreal field to be stable under all operations among\nexponential, logarithm, derivation and anti-derivation. Motivated, in the long\nterm, by computability considerations, we also provide a non-trivial\napplication of this theorem: the existence of a pretty reasonable field that\nonly requires ordinals up to $\\epsilon_\\omega$, which is far smaller than\n$\\omega_1^{CK}$ (resp. $\\omega_1$), the first non-computable (resp.\nuncountable) ordinal.\n', 'Surreal fields stable under exponential and logarithmic functions   Surreal numbers, have a very rich and elegant theory. This class of numbers,\ndenoted by No, includes simultaneously the ordinal numbers and the real\nnumbers, and forms a universal huge real closed field: It is universal in the\nsense that any real closed field can be embedded in it. Following Gonshor,\nsurreal numbers can also be seen as signs sequences of ordinal length, with\nsome exponential and logarithmic functions that extend the usual functions over\nthe reals. No can actually also be seen as an elegant particular (generalized)\npower series field with real coefficients, namely Hahn series with exponents in\nNo itself. It can also be considered as a particular field of transseries,\nproviding tools to do some analysis and asymptotic analysis for functions over\nthe continuum, providing natural concepts for discussing hyperexponential or\nsublogarithm functions, and their asymptotics. In this article, we consider\nstability of subfields of No under exponential and logarithmic functions.\nNamely, we consider the set surreal numbers whose signs sequences have length\nless than some ordinal {\\lambda}. Extending the discussion from van den Dries\nand Ehrlich, we show that is stable by exponential and logarithm iff {\\lambda}\nis some {\\epsilon}-number. Motivated in a longer term by computability issues\nusing ordinal machines, we consider subfields stables by exponential and\nlogarithmic functions defined by Hahn series that does not require to go up to\ncardinal lengths and exponents. We prove that No can be expressed as a strict\nhierarchy of subfields stable by exponential and logarithmic functions. This\nprovides many explicit examples of subfields of No stable by exponential and\nlogarithmic functions, and does not require to go up to a cardinal {\\lambda} to\nprovide such examples.\n']","[('exponential fields', 0.4584954082965851), ('field real', 0.43771815299987793), ('real closed fields', 0.4219566583633423), ('ordered field', 0.39623868465423584), ('fields omega', 0.3932249844074249), ('exponential field', 0.3835514783859253), ('subfield mathbb', 0.36565372347831726), ('real closed field', 0.36261627078056335), ('fields', 0.35313037037849426), ('subfields', 0.35218217968940735)]"
1418,1418,21,1418_complex polynomials_complex polynomial_zeros polynomials_zeros polynomial,"['complex polynomials', 'complex polynomial', 'zeros polynomials', 'zeros polynomial', 'polynomial generalization', 'algebraic polynomials', 'analytic surface', 'distinct zeros', 'polynomials', 'mathcal z_0']","[""Analyticity domains of critical points of polynomials. A proof of\n  Sendov's conjecture   Let $\\P_{n}^c(\\bar{\\mu},\\bar{\\nu})$ be the set of all complex polynomials\n$p(z)=\\prod_{i=1}^{m}(z-z_i)^{\\mu_i}$, $\\sum_{i=1}^m\\mu_i=n$, with derivatives\nof the form $$\np'(z)=n\\prod_{i=1}^{m}(z-z_i)^{\\mu_i-1}\\prod_{j=1}^{k}(z-\\xi_j)^{\\nu_j},\n~\\sum_{j=1}^k\\nu_j=m-1. $$\n  In this note we prove the following:\\par\\medskip {\\it \\noindent For a fixed\nordering $\\alpha=(1,2,\\ldots,m)$, the distinct zeros $\\{z_i\\}_{i=1}^m$ and the\ndistinct critical points of the second kind $\\{\\xi_j\\}_{j=1}^k$ of polynomials\nfrom $\\P_{n}^c(\\bar{\\mu},\\bar{\\nu})$ are analytic functions\n$\\{z_i^{\\alpha\\beta}\\}_{i=1}^m$ and $\\{\\xi_j^{\\alpha\\beta}\\}_{j=1}^k$, resp.,\n$\\beta=(i_1,i_2,\\ldots,i_{k+1})$, of any of the variables\n$(z_{i_1},z_{i_2},\\ldots,z_{i_{k+1}})$ in the domain $$\n  \\{(z_{i_1},z_{i_2},\\ldots,z_{i_{k+1}})\\in \\C^{k+1}~\\vert~p\\in\n\\P_{n}^c(\\bar{\\mu},\\bar{\\nu}) \\}, $$ being also continuous on its\nboundary.}\\par\\medskip\\noindent This statement gives an immediate proof to the\nwell-known conjecture of Bl. Sendov \\cite{sen}: \\par\\medskip {\\it \\noindent If\n$n\\ge 2$ and $p(z)=\\prod_{i=1}^n (z-z_i)$ is a polynomial of degree $n$ such\nthat $z_i\\in \\C$, $\\vert z_i\\vert\\le 1$, $i=1,2,\\ldots,n$, then for every\n$i=1,2,\\ldots,n$, the disk $\\{z\\in \\C\\,|\\,\\vert z_i-z\\vert \\le 1\\}$ contains at\nleast one zero of $p'(z)$.}\n"", ""C*-algebraic Schoenberg Conjecture   Based on Schoenberg conjecture \\textit{[Amer. Math. Monthly.,\n1986]}/Malamud-Pereira theorem \\textit{[J. Math. Anal. Appl, 2003]},\n\\textit{[Trans. Amer. Math. Soc., 2005]} we formulate the following conjecture\nwhich we call C*-algebraic Schoenberg Conjecture.\\\\ \\textbf{ C*-algebraic\nSchoenberg Conjecture : Let $\\mathcal{A}$ be a C*-algebra. Let $d\\in\n\\mathbb{N}\\setminus\\{1\\}$, $P(z)= (z-a_1)(z-a_2)\\cdots (z-a_d)$ be a polynomial\nover $\\mathcal{A}$ with $a_1, a_2, \\dots, a_d \\in \\mathcal{A} $. If $P'$ can be\nwritten as $P'(z)= d(z-b_1)(z-b_2)\\cdots (z-b_{d-1})$ on $\\mathcal{A}$ with\n$b_1, b_2, \\dots, b_{d-1} \\in \\mathcal{A} $, then \\begin{align*}\n\\sum_{k=1}^{d-1}b_kb_k^*\\leq\n\\frac{1}{d^2}\\left[\\sum_{j=1}^{d}a_j\\right]\\left[\\sum_{j=1}^{d}a_j\\right]^*+\n\\frac{d-2}{d}\\sum_{j=1}^{d}a_ja_j^* \\end{align*} and \\begin{align*}\n\\sum_{k=1}^{d-1}b_k^*b_k\\leq\n\\frac{1}{d^2}\\left[\\sum_{j=1}^{d}a_j\\right]^*\\left[\\sum_{j=1}^{d}a_j\\right]+\n\\frac{d-2}{d}\\sum_{j=1}^{d}a_j^*a_j. \\end{align*}} We show that C*-algebraic\nSchoenberg conjecture holds for degree 2 C*-algebraic polynomials over\nC*-algebras.\n"", ""C*-algebraic Smale Mean Value Conjecture and Dubinin-Sugawa Dual Mean\n  Value Conjecture   Based on Smale mean value conjecture \\textit{[Bull. Amer. Math. Soc., 1981]}\nand Dubinin-Sugawa dual mean value conjecture \\textit{[Proc. Japan Acad. Ser. A\nMath. Sci., 2009]} we formulate the following conjectures.\n  \\textbf{C*-algebraic Smale Mean Value Conjecture : Let $\\mathcal{A}$ be a\ncommutative C*-algebra. Let $P(z)= (z-a_1)\\cdots (z-a_n)$ be a polynomial of\ndegree $n\\geq 2$ over $\\mathcal{A}$, $a_1, \\dots, a_n \\in \\mathcal{A}$. If\n$z\\in\\mathcal{A}$ is not a critical point of $P$, then there exists a critical\npoint $w\\in \\mathcal{A}$ of $P$ such that \\begin{align*}\n  \\frac{\\|P(z)-P(w)\\|}{\\|z-w\\|}\\leq 1 \\|P'(z)\\| \\end{align*} or \\begin{align*}\n  \\frac{\\|P(z)-P(w)\\|}{\\|z-w\\|}\\leq \\frac{n-1}{n}\n\\|P'(z)\\|=\\frac{\\operatorname{deg} (P)-1}{\\operatorname{deg} (P)} \\|P'(z)\\|.\n  \\end{align*}}\n  \\textbf{C*-algebraic Dubinin-Sugawa Dual Mean Value Conjecture : Let\n$\\mathcal{A}$ be a commutative C*-algebra. Let $P(z)= (z-a_1)\\cdots (z-a_n)$ be\na polynomial of degree $n\\geq 2$ over $\\mathcal{A}$, $a_1, \\dots, a_n \\in\n\\mathcal{A}$. If $z\\in \\mathcal{A}$ is not a critical point of $P$, then there\nexists a critical point $w\\in \\mathcal{A}$ of $P$ such that\n  \\begin{align*}\n  \\frac{\\|P'(z)\\|}{\\operatorname{deg} (P)} =\\frac{\\|P'(z)\\|}{n} \\leq\n\\frac{\\|P(z)-P(w)\\|}{\\|z-w\\|}. \\end{align*}} We show that (even a strong form\nof) C*-algebraic Smale mean value conjecture and C*-algebraic Dubinin-Sugawa\ndual mean value conjecture hold for degree 2 C*-algebraic polynomials over\ncommutative C*-algebras.\n""]","[('complex polynomials', 0.5179027915000916), ('complex polynomial', 0.462173730134964), ('zeros polynomials', 0.4448808431625366), ('zeros polynomial', 0.42841601371765137), ('polynomial generalization', 0.42021968960762024), ('algebraic polynomials', 0.4201659560203552), ('analytic surface', 0.3479418158531189), ('distinct zeros', 0.3403242230415344), ('polynomials', 0.3380356729030609), ('mathcal z_0', 0.32931843400001526)]"
1419,1419,21,1419_stochastic homogenization_stochastic solutions_periodic homogenization_stochastic,"['stochastic homogenization', 'stochastic solutions', 'periodic homogenization', 'stochastic', 'notion stochastic', 'stochastic two', 'related stochastic', 'shown stochastic', 'nonlocal diffusion', 'nonlocal diffusion equations']","['Stochastic homogenization on perforated domains I -- Extension operators   We study the existence of uniformly bounded extension and trace operators for\nW^{1,p}-functions on randomly perforated domains, where the geometry is assumed\nto be stationary ergodic. Such extension and trace operators are important for\ncompactness in stochastic homogenization. In contrast to former approaches and\nresults, we use very weak assumptions on the geometry which we call local\n(\\delta,M)-regularity, isotropic cone mixing and bounded average connectivity.\nThe first concept measures local Lipschitz regularity of the domain while the\nsecond measures the mesoscopic distribution of void space. The third is the\nmost tricky part and measures the ""mesoscopic"" connectivity of the geometry.\n  In contrast to former approaches we do not require a minimal distance between\nthe inclusions and we allow for globally unbounded Lipschitz constants and\npercolating holes. We will illustrate our method by applying it to the Boolean\nmodel based on a Poisson point process and to a Delaunay pipe process.\n  This is Part I of a series of 3 papers that will be uploaded during the next\nweeks. It is part of a major revision of the original ArXiv 2001.10373. The\noriginal work was corrected, improved and extended significantly. In\nparticular, the theory is now able to also deal with extensions that preserve\nthe norm of the symmetrized gradient.\n', 'Stochastic unfolding and homogenization   The notion of periodic two-scale convergence and the method of periodic\nunfolding are prominent and useful tools in multiscale modeling and analysis of\nPDEs with rapidly oscillating periodic coefficients. In this paper we are\ninterested in the theory of stochastic homogenization for continuum mechanical\nmodels in form of PDEs with random coefficients, describing random\nheterogeneous materials. The notion of periodic two-scale convergence has been\nextended in different ways to the stochastic case. In this work we introduce a\nstochastic unfolding method that features many similarities to periodic\nunfolding. In particular it allows to characterize the notion of stochastic\ntwo-scale convergence in the mean by mere weak convergence in an extended\nspace. We illustrate the method on the (classical) example of stochastic\nhomogenization of convex integral functionals, and prove a new result on\nstochastic homogenization for a non-convex evolution equation of Allen-Cahn\ntype. Moreover, we discuss the relation of stochastic unfolding to previously\nintroduced notions of (quenched and mean) stochastic two-scale convergence. The\nmethod described in the present paper extends to the continuum setting the\nnotion of discrete stochastic unfolding, as recently introduced by the second\nand third author in the context of discrete-to-continuum transition.\n', 'Stochastic homogenization on randomly perforated domains   We study the existence of uniformly bounded extension and trace operators for\n$W^{1,p}$-functions on randomly perforated domains, where the geometry is\nassumed to be stationary ergodic. Such extension and trace operators are\nimportant for compactness in stochastic homogenization. In contrast to former\napproaches and results, we use very weak assumptions on the geometry which we\ncall local $(\\delta,M)$-regularity, isotropic cone mixing and bounded average\nconnectivity. The first concept measures local Lipschitz regularity of the\ndomain while the second measures the mesoscopic distribution of void space. The\nthird is the most tricky part and measures the ""mesoscopic"" connectivity of the\ngeometry. In contrast to former approaches we do not require a minimal distance\nbetween the inclusions and we allow for globally unbounded Lipschitz constants\nand percolating holes. We will illustrate our method by applying it to the\nBoolean model based on a Poisson point process and to a Delaunay pipe process.\nWe finally introduce suitable Sobolev spaces on $\\mathbb{R}^d$ and $\\Omega$ in\norder to construct a stochastic two-scale convergence method and apply the\nresulting theory to the homogenization of a $p$-Laplace problem on a randomly\nperforated domain.\n']","[('stochastic homogenization', 0.7236840128898621), ('stochastic solutions', 0.5687562227249146), ('periodic homogenization', 0.5279411673545837), ('stochastic', 0.5178687572479248), ('notion stochastic', 0.5162397027015686), ('stochastic two', 0.47606927156448364), ('related stochastic', 0.4551507532596588), ('shown stochastic', 0.45129528641700745), ('nonlocal diffusion', 0.4497254192829132), ('nonlocal diffusion equations', 0.44440221786499023)]"
1420,1420,21,1420_free curves_hypersurfaces projective_generated curves_rational surfaces,"['free curves', 'hypersurfaces projective', 'generated curves', 'rational surfaces', 'planar curves', 'quartic curves', 'singular curves', 'rational curves', 'curves mathbb whose', 'plane curves']","['Counting planar curves in $\\mathbb{P}^3$ with degenerate singularities   In this paper, we consider the following question: how many degree $d$ curves\nare there in $\\mathbb{P}^3$ (passing through the right number of generic lines\nand points), whose image lies inside a $\\mathbb{P}^2$, having $\\delta$ nodes\nand one singularity of codimension $k$. We obtain an explicit formula for this\nnumber when $\\delta+k \\leq 4$ (i.e. the total codimension of the singularities\nis not more than four). We use a topological method to compute the degenerate\ncontribution to the Euler class; it is an extension of the method that\noriginates in a paper by A. Zinger and which is further pursued by S. Basu and\nthe second author. Using this method, we have obtained formulas when the\nsingularities present are more degenerate than nodes (such as cusps, tacnodes\nand triple points). When the singularities are only nodes, we have verified\nthat our answers are consistent with those obtained by by S. Kleiman and R.\nPiene and by T. Laarakker. We also verify that our answer for the\ncharacteristic number of planar cubics with a cusp and the number of planar\nquartics with two nodes and one cusp is consistent with the answer obtained by\nR. Singh and the second author, where they compute the characteristic number of\nrational planar curves in $\\mathbb{P}^3$ with a cusp. We also verify some of\nthe numbers predicted by the conjecture made by Pandharipande, regarding the\nenumerativity of BPS numbers for $\\mathbb{P}^3$.\n', ""Rational Cuspidal Curves in a moving family of $\\mathbb{P}^2$   In this paper we obtain a formula for the number of rational degree d curves\nin $\\mathbb{P}^3$ having a cusp, whose image lies in a $\\mathbb{P}^2$ and that\npasses through $r$ lines and $s$ points (where $r + 2s = 3d + 1$). This problem\ncan be viewed as a family version of the classical question of counting\nrational cuspidal curves in $\\mathbb{P}^2$, which has been studied earlier by\nZ. Ran, R. Pandharipande and A. Zinger. We obtain this number by computing the\nEuler class of a relevant bundle and then finding out the corresponding\ndegenerate contribution to the Euler class. The method we use is closely based\non the method followed by A. Zinger and I. Biswas, S. D'Mello, R. Mukherjee and\nV. Pingali. We also verify that our answer for the characteristic numbers of\nrational cuspidal planar cubics and quartics is consistent with the answer\nobtained by N. Das and the first author, where they compute the characteristic\nnumber of $\\delta$-nodal planar curves in $\\mathbb{P}^3$ with one cusp (for\n$\\delta \\leq 2$).\n"", 'Enumeration of rational curves in a moving family of $\\mathbb{P}^2$   We obtain a recursive formula for the number of rational degree $d$ curves in\n$\\mathbb{P}^3$, whose image lies in a $\\mathbb{P}^2$, passing through $r$ lines\nand $s$ points, where $r + 2s = 3d+2$. This can be viewed as a family version\nof the classical question of counting rational curves in $\\mathbb{P}^2$. We\nverify that our numbers are consistent with those obtained by T. Laarakker,\nwhere he studies the parallel question of counting $\\delta$-nodal degree $d$\ncurves in $\\mathbb{P}^3$ whose image lies inside a $\\mathbb{P}^2$. Our numbers\ngive evidence to support the conjecture, that the polynomials obtained by T.\nLaarakker are enumerative when $d \\geq 1 + [\\frac{\\delta}{2}]$, which is\nanalogous to the {G}\\""ottsche threshold for counting nodal curves in\n$\\mathbb{P}^2$.\n']","[('free curves', 0.5196290612220764), ('hypersurfaces projective', 0.5098928809165955), ('generated curves', 0.508594810962677), ('rational surfaces', 0.5014625191688538), ('planar curves', 0.4946965277194977), ('quartic curves', 0.48844119906425476), ('singular curves', 0.4860914647579193), ('rational curves', 0.4741339087486267), ('curves mathbb whose', 0.45523691177368164), ('plane curves', 0.45124202966690063)]"
1421,1421,21,1421_alternating knots_torus knots_knot invariants_classical knot,"['alternating knots', 'torus knots', 'knot invariants', 'classical knot', 'torus knot', 'knots', 'trivial knot', 'non trivial knot', 'knot floer homology', 'knot admits']","['A non-torus positive 2-bridge knot does not admit chirally cosmetic\n  surgeries   We prove that a positive two-bridge knot other than the $(2,k)$ torus knot\ndoes not admit chirally cosmetic surgeries, a pair of Dehn surgeries along\ndistinct slopes yielding orientation-reversingly homeomorphic 3-manifolds.\n', 'Alternating odd pretzel knots and chirally cosmetic surgeries   A pair of surgeries on a knot is chirally cosmetic if they result in\nhomeomorphic manifolds with opposite orientations. Using recent methods of\nIchihara, Ito, and Saito, we show that, except for the (2,5) and (2,7)-torus\nknots, the genus 2 and 3 alternating odd pretzel knots do not admit any\nchirally cosmetic surgeries. Further, we show that for a fixed genus, at most\nfinitely many alternating odd pretzel knots admit chirally cosmetic surgeries.\n', 'Heegaard Floer homology and chirally cosmetic surgeries   A pair of surgeries on a knot is chirally cosmetic if they result in\nhomeomorphic manifolds with opposite orientations. We find new obstructions to\nthe existence of such surgeries coming from Heegaard Floer homology; in\nparticular, we make use of immersed curve formulations of knot Floer homology\nand the corresponding surgery formula. As an application, we completely\nclassify chirallly cosmetic surgeries on odd alternating pretzel knots, and we\nrule out such surgeries for a large class of Whitehead doubles. Furthermore, we\nrule out cosmetic surgeries for L-space knots along slopes with opposite signs.\n']","[('alternating knots', 0.6667188405990601), ('torus knots', 0.6566815376281738), ('knot invariants', 0.6563298106193542), ('classical knot', 0.6223753690719604), ('torus knot', 0.6140294075012207), ('knots', 0.6133350729942322), ('trivial knot', 0.5883294939994812), ('non trivial knot', 0.5860500335693359), ('knot floer homology', 0.5818455815315247), ('knot admits', 0.5719180703163147)]"
1422,1422,20,1422_cycle decompositions_complete multipartite_graph decompositions_decompositions complete,"['cycle decompositions', 'complete multipartite', 'graph decompositions', 'decompositions complete', 'decompositions', 'complete multipartite graph', 'arrays', 'multipartite', 'array entries', 'empty cells']","['Non-zero sum Heffter arrays and their applications   In this paper we introduce a new class of partially filled arrays that, as\nHeffter arrays, are related to difference families, graph decompositions and\nbiembeddings. A non-zero sum Heffter array $\\mathrm{N}\\mathrm{H}(m,n; h,k)$ is\nan $m \\times n$ p. f. array with entries in $\\mathbb{Z}_{2nk+1}$ such that:\neach row contains $h$ filled cells and each column contains $k$ filled cells;\nfor every $x\\in \\mathbb{Z}_{2nk+1}\\setminus\\{0\\}$, either $x$ or $-x$ appears\nin the array; the sum of the elements in every row and column is different from\n$0$ (in $\\mathbb{Z}_{2nk+1}$). Here first we explain the connections with\nrelative difference families and with path decompositions of the complete\nmultipartite graph. Then we present a complete solution for the existence\nproblem and a constructive complete solution for the square case and for the\nrectangular case with no empty cells when the additional, very restrictive,\nproperty of ""globally simple"" is required. Finally, we show how these arrays\ncan be used to construct biembeddings of complete graphs.\n', 'Relative Heffter arrays and biembeddings   Relative Heffter arrays, denoted by $\\mathrm{H}_t(m,n; s,k)$, have been\nintroduced as a generalization of the classical concept of Heffter array. A\n$\\mathrm{H}_t(m,n; s,k)$ is an $m\\times n$ partially filled array with elements\nin $\\mathbb{Z}_v$, where $v=2nk+t$, whose rows contain $s$ filled cells and\nwhose columns contain $k$ filled cells, such that the elements in every row and\ncolumn sum to zero and, for every $x\\in \\mathbb{Z}_v$ not belonging to the\nsubgroup of order $t$, either $x$ or $-x$ appears in the array. In this paper\nwe show how relative Heffter arrays can be used to construct biembeddings of\ncyclic cycle decompositions of the complete multipartite graph\n$K_{\\frac{2nk+t}{t}\\times t}$ into an orientable surface. In particular, we\nconstruct such biembeddings providing integer globally simple square relative\nHeffter arrays for $t=k=3,5,7,9$ and $n\\equiv 3 \\pmod 4$ and for $k=3$ with\n$t=n,2n$, any odd $n$.\n', 'On the existence of integer relative Heffter arrays   Let $v=2ms+t$ be a positive integer, where $t$ divides $2ms$, and let $J$ be\nthe subgroup of order $t$ of the cyclic group $\\mathbb{Z}_v$. An integer\nHeffter array $H_t(m,n;s,k)$ over $\\mathbb{Z}_v$ relative to $J$ is an $m\\times\nn$ partially filled array with elements in $\\mathbb{Z}_v$ such that: (a) each\nrow contains $s$ filled cells and each column contains $k$ filled cells; (b)\nfor every $x\\in \\mathbb{Z}_v \\setminus J$, either $x$ or $-x$ appears in the\narray; (c) the elements in every row and column, viewed as integers in\n$\\pm\\left\\{ 1, \\ldots, \\left\\lfloor \\frac{v}{2}\\right\\rfloor \\right\\}$, sum to\n$0$ in $\\mathbb{Z}$.\n  In this paper we study the existence of an integer $H_t(m,n;s,k)$ when $s$\nand $k$ are both even, proving the following results. Suppose that $4\\leq s\\leq\nn$ and $4\\leq k \\leq m$ are such that $ms=nk$. Let $t$ be a divisor of $2ms$.\n(a) If $s,k \\equiv 0 \\pmod 4$, there exists an integer $H_t(m,n;s,k)$. (b) If\n$s\\equiv 2\\pmod 4$ and $k\\equiv 0 \\pmod 4$, there exists an integer\n$H_t(m,n;s,k)$ if and only if $m$ is even. (c) If $s\\equiv 0\\pmod 4$ and\n$k\\equiv 2 \\pmod 4$, then there exists an integer $H_t(m,n;s,k)$ if and only if\n$n$ is even. (d) Suppose that $m$ and $n$ are both even. If $s,k\\equiv 2 \\pmod\n4$, then there exists an integer $H_t(m,n;s,k)$.\n']","[('cycle decompositions', 0.37935560941696167), ('complete multipartite', 0.36225244402885437), ('graph decompositions', 0.3509632647037506), ('decompositions complete', 0.33244064450263977), ('decompositions', 0.3322594165802002), ('complete multipartite graph', 0.32459142804145813), ('arrays', 0.31661516427993774), ('multipartite', 0.3069290816783905), ('array entries', 0.28465068340301514), ('empty cells', 0.28131306171417236)]"
1423,1423,20,1423_dynamical low rank_low rank methods_low rank approximation_vlasov dynamics,"['dynamical low rank', 'low rank methods', 'low rank approximation', 'vlasov dynamics', 'low rank tensor', 'dimensional vlasov', 'nonlinear vlasov poisson', 'nonlinear vlasov', 'rank approximation dlra', 'rank approximation']","['An efficient dynamical low-rank algorithm for the Boltzmann-BGK equation\n  close to the compressible viscous flow regime   It has recently been demonstrated that dynamical low-rank algorithms can\nprovide robust and efficient approximation to a range of kinetic equations.\nThis is true especially if the solution is close to some asymptotic limit where\nit is known that the solution is low-rank. A particularly interesting case is\nthe fluid dynamic limit that is commonly obtained in the limit of small Knudsen\nnumber. However, in this case the Maxwellian which describes the corresponding\nequilibrium distribution is not necessarily low-rank; because of this, the\nmethods known in the literature are only applicable to the weakly compressible\ncase. In this paper, we propose an efficient dynamical low-rank integrator that\ncan capture the fluid limit -- the Navier-Stokes equations -- of the\nBoltzmann-BGK model even in the compressible regime. This is accomplished by\nwriting the solution as $f=Mg$, where $M$ is the Maxwellian and the low-rank\napproximation is only applied to $g$. To efficiently implement this\ndecomposition within a low-rank framework requires, in the isothermal case,\nthat certain coefficients are evaluated using convolutions, for which fast\nalgorithms are known. Using the proposed decomposition also has the advantage\nthat the rank required to obtain accurate results is significantly reduced\ncompared to the previous state of the art. We demonstrate this by performing a\nnumber of numerical experiments and also show that our method is able to\ncapture sharp gradients/shock waves.\n', 'A mass, momentum, and energy conservative dynamical low-rank scheme for\n  the Vlasov equation   The primary challenge in solving kinetic equations, such as the Vlasov\nequation, is the high-dimensional phase space. In this context, dynamical\nlow-rank approximations have emerged as a promising way to reduce the high\ncomputational cost imposed by such problems. However, a major disadvantage of\nthis approach is that the physical structure of the underlying problem is not\npreserved. In this paper, we propose a dynamical low-rank algorithm that\nconserves mass, momentum, and energy as well as the corresponding continuity\nequations. We also show how this approach can be combined with a conservative\ntime and space discretization.\n', 'Dynamical low-rank integrator for the linear Boltzmann equation: error\n  analysis in the diffusion limit   Dynamical low-rank algorithms are a class of numerical methods that compute\nlow-rank approximations of dynamical systems. This is accomplished by\nprojecting the dynamics onto a low-dimensional manifold and writing the\nsolution directly in terms of the low-rank factors. The approach has been\nsuccessfully applied to many types of differential equations. Recently,\nefficient dynamical low-rank algorithms have been applied to treat kinetic\nequations, including the Vlasov--Poisson and the Boltzmann equation, where it\nwas demonstrated that the methods are able to capture the low-rank structure of\nthe solution and significantly reduce numerical cost, while often maintaining\nhigh accuracy. However, no numerical analysis is currently available.\n  In this paper, we investigate the error analysis for a dynamical low-rank\nalgorithm applied to the multi-scale linear Boltzmann equation (a classical\nmodel in kinetic theory) to showcase the validity of the application of\ndynamical low-rank algorithms to kinetic theory. The equation, in its parabolic\nregime, is known to be rank one theoretically, and we will prove that the\nscheme can dynamically and automatically capture this low-rank structure. This\nwork thus serves as the first mathematical error analysis for a dynamical\nlow-rank approximation applied to a kinetic problem.\n']","[('dynamical low rank', 0.5299439430236816), ('low rank methods', 0.5215166807174683), ('low rank approximation', 0.5172125101089478), ('vlasov dynamics', 0.510402500629425), ('low rank tensor', 0.4764536917209625), ('dimensional vlasov', 0.4634380638599396), ('nonlinear vlasov poisson', 0.4612880051136017), ('nonlinear vlasov', 0.45434439182281494), ('rank approximation dlra', 0.43826207518577576), ('rank approximation', 0.4210352599620819)]"
1424,1424,20,1424_graphs girth least_well covered graphs_graphs bounded_graphs girth,"['graphs girth least', 'well covered graphs', 'graphs bounded', 'graphs girth', 'covered graphs', 'graph treewidth', 'exceptional graphs', 'sparse graphs', 'graph induced', 'subgraphs']","['Size of the Largest Induced Forest in Subcubic Graphs of Girth at least\n  Four and Five   In this paper, we address the maximum number of vertices of induced forests\nin subcubic graphs with girth at least four or five. We provide a unified\napproach to prove that every 2-connected subcubic graph on $n$ vertices and $m$\nedges with girth at least four or five, respectively, has an induced forest on\nat least $n-\\frac{2}{9}m$ or $n-\\frac{1}{5}m$ vertices, respectively, except\nfor finitely many exceptional graphs. Our results improve a result of Liu and\nZhao and are tight in the sense that the bounds are attained by infinitely many\n2-connected graphs. Equivalently, we prove that such graphs admit feedback\nvertex sets with size at most $\\frac{2}{9}m$ or $\\frac{1}{5}m$, respectively.\nThose exceptional graphs will be explicitly constructed, and our result can be\neasily modified to drop the 2-connectivity requirement.\n', 'On Almost Well-Covered Graphs of Girth at Least 6   We consider a relaxation of the concept of well-covered graphs, which are\ngraphs with all maximal independent sets of the same size. The extent to which\na graph fails to be well-covered can be measured by its independence gap,\ndefined as the difference between the maximum and minimum sizes of a maximal\nindependent set in $G$. While the well-covered graphs are exactly the graphs of\nindependence gap zero, we investigate in this paper graphs of independence gap\none, which we also call almost well-covered graphs. Previous works due to\nFinbow et al. (1994) and Barbosa et al. (2013) have implications for the\nstructure of almost well-covered graphs of girth at least $k$ for $k\\in\n\\{7,8\\}$. We focus on almost well-covered graphs of girth at least $6$. We show\nthat every graph in this class has at most two vertices each of which is\nadjacent to exactly $2$ leaves. We give efficiently testable characterizations\nof almost well-covered graphs of girth at least $6$ having exactly one or\nexactly two such vertices. Building on these results, we develop a\npolynomial-time recognition algorithm of almost well-covered\n$\\{C_3,C_4,C_5,C_7\\}$-free graphs.\n', ""Treewidth is Polynomial in Maximum Degree on Weakly Sparse Graphs\n  Excluding a Planar Induced Minor   A graph $G$ contains a graph $H$ as an induced minor if $H$ can be obtained\nfrom $G$ after vertex deletions and edge contractions. We show that for every\n$k$-vertex planar graph $H$, every graph $G$ excluding $H$ as an induced minor\nand $K_{t,t}$ as a subgraph has treewidth at most $\\Delta(G)^{f(k,t)}$ where\n$\\Delta(G)$ denotes the maximum degree of $G$. Without requiring the absence of\na $K_{t,t}$ subgraph, Korhonen [JCTB '23] has shown the upper bound of\n$k^{O(1)} 2^{\\Delta(G)^5}$ whose dependence in $\\Delta(G)$ is exponential. Our\nresult partially answers a question of Chudnovsky [Dagstuhl seminar '23] asking\nwhether the treewidth of graphs with $\\Delta(G)=O(\\log{|V(G)|})$ excluding both\na $k$-vertex planar graph as an induced minor and the biclique $K_{t,t}$ as a\nsubgraph is in $O_{k,t}(\\log |V(G)|)$. We confirm that the treewidth is in this\ncase polylogarithmic in $|V(G)|$.\n""]","[('graphs girth least', 0.6558051705360413), ('well covered graphs', 0.6219103336334229), ('graphs bounded', 0.6164143681526184), ('graphs girth', 0.6147398948669434), ('covered graphs', 0.602839469909668), ('graph treewidth', 0.5736550688743591), ('exceptional graphs', 0.5554542541503906), ('sparse graphs', 0.5513689517974854), ('graph induced', 0.5466412901878357), ('subgraphs', 0.5456979870796204)]"
1425,1425,20,1425_tilted algebras_cluster tilted algebra_tilted algebra_tau tilting modules,"['tilted algebras', 'cluster tilted algebra', 'tilted algebra', 'tau tilting modules', 'nakayama algebras', 'tilting modules', 'hereditary algebras', 'finite dimensional algebras', 'local algebras', 'algebra quiver']","['Extending silted algebras to cluster-tilted algebras   It is well known that the relation-extensions of tilted algebras are\ncluster-tilted algebras. In this paper, we extend the result to silted algebras\nand prove some extension of silted algebras are cluster-tilted algebras.\n', 'Rigid and Schurian modules over cluster-tilted algebras of tame type   We give an example of a cluster-tilted algebra A with quiver Q, such that the\nassociated cluster algebra has a denominator vector which is not the dimension\nvector of any indecomposable A-module. This answers a question posed by T.\nNakanishi. The relevant example is a cluster-tilted algebra associated with a\ntame hereditary algebra. We show that for such a cluster-tilted algebra A, we\ncan write any denominator vector as a sum of the dimension vectors of at most\nthree indecomposable rigid A-modules. In order to do this it is necessary, and\nof independent interest, to first classify the indecomposable rigid A-modules\nin this case.\n', 'On the radical of Cluster tilted algebras   We determine the minimal lower bound $n$, with $n \\geq 1$, where the $n$-th\npower of the radical of the module category of a representation-finite cluster\ntilted algebra vanishes. We give such a bound in terms of the number of\nvertices of the underline quiver. Consequently, we get the nilpotency index of\nthe radical of the module category for representation-finite self-injective\ncluster tilted algebras. We also study the non-zero composition of $m$, $m \\ge\n2$, irreducible morphisms between indecomposable modules in\nrepresentation-finite cluster tilted algebras lying in the $(m+1)$-th power of\nthe radical of their module category.\n']","[('tilted algebras', 0.7117304801940918), ('cluster tilted algebra', 0.6796440482139587), ('tilted algebra', 0.6195105314254761), ('tau tilting modules', 0.6192935109138489), ('nakayama algebras', 0.5993991494178772), ('tilting modules', 0.5959330797195435), ('hereditary algebras', 0.5759155750274658), ('finite dimensional algebras', 0.5627153515815735), ('local algebras', 0.546517550945282), ('algebra quiver', 0.5348473191261292)]"
1426,1426,20,1426_accelerated gradient descent_nesterov accelerated gradient_accelerated gradient methods_accelerated methods,"['accelerated gradient descent', 'nesterov accelerated gradient', 'accelerated gradient methods', 'accelerated methods', 'accelerated gradient', 'nesterov accelerated', 'accelerated first order', 'accelerated convergence', 'nesterov acceleration', 'gradient based optimization']","[""A novel interpretation of Nesterov's acceleration via variable step-size\n  linear multistep methods   Nesterov's acceleration in continuous optimization can be understood in a\nnovel way when Nesterov's accelerated gradient (NAG) method is considered as a\nlinear multistep (LM) method for gradient flow. Although the NAG method for\nstrongly convex functions (NAG-sc) has been fully discussed, the NAG method for\n$L$-smooth convex functions (NAG-c) has not. To fill this gap, we show that the\nexisting NAG-c method can be interpreted as a variable step size LM (VLM) for\nthe gradient flow. Surprisingly, the VLM allows linearly increasing step sizes,\nwhich explains the acceleration in the convex case. Here, we introduce a novel\ntechnique for analyzing the absolute stability of VLMs. Subsequently, we prove\nthat NAG-c is optimal in a certain natural class of VLMs. Finally, we construct\na new broader class of VLMs by optimizing the parameters in the VLM for\nill-conditioned problems. According to numerical experiments, the proposed\nmethod outperforms the NAG-c method in ill-conditioned cases. These results\nimply that the numerical analysis perspective of the NAG is a promising working\nenvironment, and considering a broader class of VLMs could further reveal novel\nmethods.\n"", ""Revisiting the acceleration phenomenon via high-resolution differential\n  equations   Nesterov's accelerated gradient descent (NAG) is one of the milestones in the\nhistory of first-order algorithms. It was not successfully uncovered until the\nhigh-resolution differential equation framework was proposed in [Shi et al.,\n2022] that the mechanism behind the acceleration phenomenon is due to the\ngradient correction term. To deepen our understanding of the high-resolution\ndifferential equation framework on the convergence rate, we continue to\ninvestigate NAG for the $\\mu$-strongly convex function based on the techniques\nof Lyapunov analysis and phase-space representation in this paper. First, we\nrevisit the proof from the gradient-correction scheme. Similar to [Chen et al.,\n2022], the straightforward calculation simplifies the proof extremely and\nenlarges the step size to $s=1/L$ with minor modification. Meanwhile, the way\nof constructing Lyapunov functions is principled. Furthermore, we also\ninvestigate NAG from the implicit-velocity scheme. Due to the difference in the\nvelocity iterates, we find that the Lyapunov function is constructed from the\nimplicit-velocity scheme without the additional term and the calculation of\niterative difference becomes simpler. Together with the optimal step size\nobtained, the high-resolution differential equation framework from the\nimplicit-velocity scheme of NAG is perfect and outperforms the\ngradient-correction scheme.\n"", ""Lyapunov Analysis For Monotonically Forward-Backward Accelerated\n  Algorithms   In the realm of gradient-based optimization, Nesterov's accelerated gradient\nmethod (NAG) is a landmark advancement, achieving an accelerated convergence\nrate that outperforms the vanilla gradient descent method for convex function.\nHowever, for strongly convex functions, whether NAG converges linearly remains\nan open question, as noted in the comprehensive review by Chambolle and Pock\n[2016]. This issue, aside from the critical step size, was addressed by Li et\nal. [2024a] using a high-resolution differential equation framework.\nFurthermore, Beck [2017, Section 10.7.4] introduced a monotonically convergent\nvariant of NAG, referred to as M-NAG. Despite these developments, the Lyapunov\nanalysis presented in [Li et al., 2024a] cannot be directly extended to M-NAG.\nIn this paper, we propose a modification to the iterative relation by\nintroducing a gradient term, leading to a new gradient-based iterative\nrelation. This adjustment allows for the construction of a novel Lyapunov\nfunction that excludes kinetic energy. The linear convergence derived from this\nLyapunov function is independent of both the parameters of the strongly convex\nfunctions and the step size, yielding a more general and robust result.\nNotably, we observe that the gradient iterative relation derived from M-NAG is\nequivalent to that from NAG when the position-velocity relation is applied.\nHowever, the Lyapunov analysis does not rely on the position-velocity relation,\nallowing us to extend the linear convergence to M-NAG. Finally, by utilizing\ntwo proximal inequalities, which serve as the proximal counterparts of strongly\nconvex inequalities, we extend the linear convergence to both the fast\niterative shrinkage-thresholding algorithm (FISTA) and its monotonic\ncounterpart (M-FISTA).\n""]","[('accelerated gradient descent', 0.6918196678161621), ('nesterov accelerated gradient', 0.6753039360046387), ('accelerated gradient methods', 0.6666834354400635), ('accelerated methods', 0.61872798204422), ('accelerated gradient', 0.608779788017273), ('nesterov accelerated', 0.5654972791671753), ('accelerated first order', 0.5557484030723572), ('accelerated convergence', 0.5519759654998779), ('nesterov acceleration', 0.546728789806366), ('gradient based optimization', 0.5350508689880371)]"
1427,1427,20,1427_besov spaces_spaces besov spaces_anisotropic besov spaces_spaces besov,"['besov spaces', 'spaces besov spaces', 'anisotropic besov spaces', 'spaces besov', 'spaces modulation spaces', 'coorbit theory', 'modulation spaces', 'weighted modulation spaces', 'quasi banach spaces', 'banach frames']","['Coorbit Theory for Coefficients in Weighted Lebesgue Spaces, and its\n  Application to the Wavelet Transform and the Short-Time Fourier Transform   Starting with an integrable unitary representation of a locally compact group\nand its associated voice transform, coorbit theory describes the construction\nand investigation of the so-called coorbit spaces. A coorbit space consists of\ndistributions of which the voice transform is contained in a given function\nspace. We construct coorbit spaces which elements have voice transforms in\nweighted Lebesgue spaces. By applying this construction to the wavelet\ntransform and short-time Fourier transform, we obtain special cases of the\nhomogeneous Besov spaces and the modulation spaces, respectively. We also\ndiscretize the coorbit spaces in terms of Banach frames, where the frame\nvectors are contained in the orbit of some suitable element under the group\naction. For the two examples of the wavelet transform and the short-time\nFourier transform, we derive sufficient conditions for a wavelet respectively a\nGabor window to be suitable to generate such a Banach frame in the respective\ncontext.\n', 'Coorbit spaces associated to integrably admissible dilation groups   This paper considers coorbit spaces parametrized by mixed, weighted Lebesgue\nspaces with respect to the quasi-regular representation of the semi-direct\nproduct of Euclidean space and a suitable matrix dilation group. The class of\ndilation groups that we allow, the so-called integrably admissible dilation\ngroups, contains the matrix groups yielding an irreducible, square-integrable\nquasi-regular representation as a proper subclass. The obtained scale of\ncoorbit spaces extends therefore the well-studied wavelet coorbit spaces\nassociated to discrete series representations. We show that for any integrably\nadmissible dilation group there exists a convienent space of smooth, admissible\nanalyzing vectors that can be used to define a consistent coorbit space\npossessing all the essential properties that are known to hold in the setting\nof discrete series representations. In particular, the obtained coorbit spaces\ncan be realized as Besov-type decomposition spaces by means of a\nLittlewood-Paley type characterization. The classes of anisotropic Besov spaces\nassociated to expansive matrices are shown to coincide precisely with the\ncoorbit spaces induced by the integrably admissible one-parameter groups.\n', ""A Primer on Coorbit Theory -- From Basics to Recent Developments   Coorbit theory is a powerful machinery that constructs a family of Banach\nspaces, the so-called coorbit spaces, from well-behaved unitary representations\nof locally compact groups. A core feature of coorbit spaces is that they can be\ndiscretized in a way that reflects the geometry of the underlying locally\ncompact group. Many established function spaces such as modulation spaces,\nBesov spaces, Sobolev-Shubin spaces, and shearlet spaces are examples of\ncoorbit spaces. The goal of this survey is to give an overview of coorbit\ntheory with the aim of presenting the main ideas in an accessible manner.\nCoorbit theory is generally seen as a complicated theory, filled with both\ntechnicalities and conceptual difficulties. Faced with this obstacle, we feel\nobliged to convince the reader of the theory's elegance. As such, this survey\nis a showcase of coorbit theory and should be treated as a stepping stone to\nmore complete sources.\n""]","[('besov spaces', 0.5878824591636658), ('spaces besov spaces', 0.5789910554885864), ('anisotropic besov spaces', 0.5685111880302429), ('spaces besov', 0.5642760992050171), ('spaces modulation spaces', 0.5164269804954529), ('coorbit theory', 0.5117900371551514), ('modulation spaces', 0.4984358251094818), ('weighted modulation spaces', 0.49309656023979187), ('quasi banach spaces', 0.4604637026786804), ('banach frames', 0.4577796459197998)]"
1428,1428,20,1428_quasiconformal mappings_quasiconformal map_quasiregular mappings_quasiconformality,"['quasiconformal mappings', 'quasiconformal map', 'quasiregular mappings', 'quasiconformality', 'quasiconformal', 'sobolev mappings', 'sobolev mapping', 'sobolev regularity', 'quasiregular', 'sobolev class']","[""Finely quasiconformal mappings   We introduce a relaxed version of the metric definition of quasiconformality\nthat is natural also for mappings of low regularity, including\n$W_{\\mathrm{loc}}^{1,1}(\\mathbb{R}^n;\\mathbb{R}^n)$-mappings. Then we show on\nthe plane that this relaxed definition can be used to prove Sobolev regularity,\nand that these ``finely quasiconformal'' mappings are in fact quasiconformal.\n"", ""Deformations of Bi-conformal Energy and a new Characterization of\n  Quasiconformality   The concept of hyperelastic deformations of bi-conformal energy is developed\nas an extension of quasiconformality. These are homeomorphisms $h:X \\to Y$\nbetween domains $ X, Y \\subset \\mathbb R^n$ of the Sobolev class $W^{1,n}_{loc}\n(X, Y)$ whose inverse $f =h^{-1}:Y \\to X$ also belongs to $W^{1,n}_{loc}(Y,\nX)$. Thus the paper opens new topics in Geometric Function Theory with\nconnections to mathematical models of Nonlinear Elasticity. In seeking\ndifferences and similarities with quasiconformal mappings we examine closely\nthe modulus of continuity of deformations of bi-conformal energy. This leads us\nto a new characterization of quasiconformality. Specifically, it is observed\nthat quasiconformal mappings behave locally at every point like radial\nstretchings. Without going into detail, if a quasiconformal map $h$ admits a\nfunction $\\phi$ as its optimal modulus of continuity at a point $x_0$, then $f\n= h^{-1}$ admits the inverse function $\\psi = \\phi^{-1}$ as its modulus of\ncontinuity at $y_0 = h(x_0)$. That is to say; a poor continuity of $h$ at a\ngiven point $x_0$ is always compensated by a better continuity of $f$ at $y_0$,\nand vice versa. Such a gain/loss property, seemingly overlooked by many\nauthors, is actually characteristic of quasiconformal mappings.\n  It turns out that the elastic deformations of bi-conformal energy are very\ndifferent in this respect. Unexpectedly, such a map may have the same optimal\nmodulus of continuity as its inverse deformation. In line with Hooke's Law,\nwhen trying to restore the original shape of the body (by the inverse\ntransformation) the modulus of continuity may neither be improved nor become\nworse. However, examples to confirm this phenomenon are far from being obvious.\nWe eventually hope that our examples will gain an interest in the materials\nscience, particularly in mathematical models of hyperelasticity.\n"", 'Quasiconformal curves and quasiconformal maps in metric spaces   In this paper we study quasiconformal curves which are a special case of\nquasiregular curves. Namely embeddings $\\Omega\\rightarrow\\mathbb{R}^m$ from\nsome domain $\\Omega\\subset\\mathbb{R}^n$ to $\\mathbb{R}^m$, where $n\\leq m$,\nwhich belong in a suitable Sobolev class and satisfy a certain distortion\ninequality for some smooth, closed and non-vanishing $n$-form in\n$\\mathbb{R}^m$. These mappings can be seen as quasiconformal mappings between\n$\\Omega$ and $f(\\Omega)$. We prove that a quasiconformal curve always satisfies\nthe analytic definition of quasiconformal mappings and the lower half of the\nmodulus inequality. Moreover, we give a sufficient condition for a\nquasiconformal curve to satisfy the metric definition of quasiconformal\nmappings. We also show that a quasiconformal map from $\\Omega$ to\n$f(\\Omega)\\subset \\mathbb{R}^m$ is a quasiconformal $\\omega$ curve for some\nform $\\omega$ under suitable assumptions. Finally, we show the same is true\nwhen we equip the target space $f(\\Omega)$ with its intrinsic metric instead of\nthe Euclidean one.\n']","[('quasiconformal mappings', 0.7567064762115479), ('quasiconformal map', 0.7027202248573303), ('quasiregular mappings', 0.7005081176757812), ('quasiconformality', 0.6575071811676025), ('quasiconformal', 0.6396257877349854), ('sobolev mappings', 0.6188520789146423), ('sobolev mapping', 0.5693889856338501), ('sobolev regularity', 0.5635119080543518), ('quasiregular', 0.47678041458129883), ('sobolev class', 0.4318125247955322)]"
1429,1429,20,1429_sum stochastic games_stochastic games_stochastic game_markov games,"['sum stochastic games', 'stochastic games', 'stochastic game', 'markov games', 'stationary nash', 'markov game', 'zero sum stochastic', 'stationary nash equilibrium', 'markov decision processes', 'zero sum games']","['Discrete-time Zero-Sum Games for Markov chains with risk-sensitive\n  average cost criterion   We study zero-sum stochastic games for controlled discrete time Markov chains\nwith risk-sensitive average cost criterion with countable state space and Borel\naction spaces. The payoff function is nonnegative and possibly unbounded. Under\na certain Lyapunov stability assumption on the dynamics, we establish the\nexistence of a value and saddle point equilibrium. Further we completely\ncharacterize all possible saddle point strategies in the class of stationary\nMarkov strategies. Finally, we present and analyze an illustrative example.\n', 'Nonzero-sum Discrete-time Stochastic Games with Risk-sensitive Ergodic\n  Cost Criterion   In this paper we study infinite horizon nonzero-sum stochastic games for\ncontrolled discrete-time Markov chains on a Polish state space with\nrisk-sensitive ergodic cost criterion. Under suitable assumptions we show that\nthe associated ergodic optimality equations admit unique solutions. Finally,\nthe existence of Nash-equilibrium in randomized stationary strategies is\nestablished by showing that an appropriate set-valued map has a fixed point.\n', 'Nonzero-sum risk-sensitive continuous-time stochastic games with ergodic\n  costs   We study nonzero-sum stochastic games for continuous time Markov decision\nprocesses on a denumerable state space with risk-sensitive ergodic cost\ncriterion. Transition rates and cost rates are allowed to be unbounded. Under a\nLyapunov type stability assumption, we show that the corresponding system of\ncoupled HJB equations admits a solution which leads to the existence of a Nash\nequilibrium in stationary strategies. We establish this using an approach\ninvolving principal eigenvalues associated with the HJB equations. Furthermore,\nexploiting appropriate stochastic representation of principal eigenfunctions,\nwe completely characterize Nash equilibria in the space of stationary Markov\nstrategies.\n']","[('sum stochastic games', 0.6592267751693726), ('stochastic games', 0.6220512390136719), ('stochastic game', 0.6007815599441528), ('markov games', 0.5948063135147095), ('stationary nash', 0.5458211898803711), ('markov game', 0.5451916456222534), ('zero sum stochastic', 0.5300530791282654), ('stationary nash equilibrium', 0.5150458216667175), ('markov decision processes', 0.5130605101585388), ('zero sum games', 0.5120968818664551)]"
1430,1430,20,1430_homoclinic tangencies_homoclinic tangency_heterodimensional cycles_robust complex,"['homoclinic tangencies', 'homoclinic tangency', 'heterodimensional cycles', 'robust complex', 'diffeomorphisms', 'hyperbolic periodic', 'hyperbolic sets', 'unfoldings', 'periodic orbits', 'dimensional robust']","['Blender-producing mechanisms and a dichotomy for local dynamics for\n  heterodimensional cycles   Blenders are special hyperbolic sets used to produce various robust dynamical\nphenomena which appear fragile at first glance. We prove for $C^r$\ndiffeomorphisms ($r=2,\\dots,\\infty,\\omega$) that blenders naturally exist\n(without perturbation) near non-degenerate heterodimensional cycles of\ncoindex-1, and the existence is determined by arithmetic properties of moduli\nof topological conjugacy for diffeomorphisms with heterodimensional cycles. In\nparticular, we obtain a $C^r$-generic dichotomy for dynamics in any small\nneighborhood $U$ of a non-degenerate heterodimensional cycle: either there\nexist infinitely many blenders accumulating on the cycle, forming robust\nheterodimensional dynamics in most cases, or there are no orbits other than\nthose constituting the cycle lying entirely in $U$.\n', ""Homoclinic tangencies leading to robust heterodimensional cycles   We consider $C^r$ ($r\\geqslant 1$) diffeomorphisms $f$ defined on manifolds\nof dimension $\\geqslant 3$ with homoclinic tangencies associated to saddles.\nUnder generic properties, we show that if the saddle is homoclinically related\nto a blender then the diffeomorphism $f$ can be {$C^r$} approximated by\ndiffeomorphisms with {$C^1$} robust heterodimensional cycles. As an\napplication, we show that the classic Simon-Asaoka's examples of\ndiffeomorphisms with $C^1$ robust homoclinic tangencies also display {$C^1$}\nrobust heterodimensional cycles. In a second application, we consider\nhomoclinic tangencies associated to hyperbolic sets. When the entropy of these\nsets is large enough we obtain $C^1$ robust cycles after $C^1$ perturbations.\n"", 'Robust heterodimensional cycles in two-parameter unfolding of homoclinic\n  tangencies   We consider $C^r$ $(r=3,\\dots,\\infty,\\omega)$ diffeomorphisms with a generic\nhomoclinic tangency to a hyperbolic periodic point, where this point has at\nleast one complex (non-real) central multiplier and some explicit assumptions\non central multipliers are satisfied so that the dynamics near the homoclinic\ntangency is not effectively one-dimensional. We prove that $C^1$-robust\nheterodimensional cycles of co-index one appear in any generic two-parameter\n$C^r$-unfolding of such a tangency. These heterodimensional cycles also have\n$C^1$-robust homoclinic tangencies.\n']","[('homoclinic tangencies', 0.5268936157226562), ('homoclinic tangency', 0.5221107006072998), ('heterodimensional cycles', 0.4569719135761261), ('robust complex', 0.43200403451919556), ('diffeomorphisms', 0.41572603583335876), ('hyperbolic periodic', 0.394643634557724), ('hyperbolic sets', 0.38197076320648193), ('unfoldings', 0.38051772117614746), ('periodic orbits', 0.3710876405239105), ('dimensional robust', 0.3666911721229553)]"
1431,1431,20,1431_gaussian mixture models_gaussian mixture distribution_gaussian mixture_mixture distributions,"['gaussian mixture models', 'gaussian mixture distribution', 'gaussian mixture', 'mixture distributions', 'finite mixture models', 'mixture models', 'finite mixtures', 'gaussian random vectors', 'mixture distribution', 'approximation fisher']","['Differentiability and Approximation of Probability Functions under\n  Gaussian Mixture Models: A Bayesian Approach   In this work, we study probability functions associated with Gaussian mixture\nmodels. Our primary focus is on extending the use of spherical radial\ndecomposition for multivariate Gaussian random vectors to the context of\nGaussian mixture models, which are not inherently spherical but only\nconditionally so. Specifically, the conditional probability distribution, given\na random parameter of the random vector, follows a Gaussian distribution,\nallowing us to apply Bayesian analysis tools to the probability function. This\nassumption, together with spherical radial decomposition for Gaussian random\nvectors, enables us to represent the probability function as an integral over\nthe Euclidean sphere. Using this representation, we establish sufficient\nconditions to ensure the differentiability of the probability function and\nprovide and integral representation of its gradient. Furthermore, leveraging\nthe Bayesian decomposition, we approximate the probability function using\nrandom sampling over the parameter space and the Euclidean sphere. Finally, we\npresent numerical examples that illustrate the advantages of this approach over\nclassical approximations based on random vector sampling.\n', 'Minimum $\\Phi$-distance estimators for finite mixing measures   Finite mixture models have long been used across a variety of fields in\nengineering and sciences. Recently there has been a great deal of interest in\nquantifying the convergence behavior of the mixing measure, a fundamental\nobject that encapsulates all unknown parameters in a mixture distribution. In\nthis paper we propose a general framework for estimating the mixing measure\narising in finite mixture models, which we term minimum $\\Phi$-distance\nestimators. We establish a general theory for the minimum $\\Phi$-distance\nestimator, where sharp probability bounds are obtained on the estimation error\nfor the mixing measures in terms of the suprema of the associated empirical\nprocesses for a suitably chosen function class $\\Phi$.\n  Our framework includes several existing and seemingly distinct estimation\nmethods as special cases but also motivates new estimators. For instance, it\nextends the minimum Kolmogorov-Smirnov distance estimator to the multivariate\nsetting, and it extends the method of moments to cover a broader family of\nprobability kernels beyond the Gaussian. Moreover, it also includes methods\nthat are applicable to complex (e.g., non-Euclidean) observation domains, using\ntools from reproducing kernel Hilbert spaces. It will be shown that under\ngeneral conditions the methods achieve optimal rates of estimation under\nWasserstein metrics in either minimax or pointwise sense of convergence; the\nlatter case can be achieved when no upper bound on the finite number of\ncomponents is given.\n', 'Quasi-Monte Carlo methods for mixture distributions and approximated\n  distributions via piecewise linear interpolation   We study numerical integration over bounded regions in $\\mathbb{R}^s, s\\ge1$\nwith respect to some probability measure. We replace random sampling with\nquasi-Monte Carlo methods, where the underlying point set is derived from\ndeterministic constructions that aim to fill the space more evenly than random\npoints. Such quasi-Monte Carlo point sets are ordinarily designed for the\nuniform measure, and the theory only works for product measures when a\ncoordinate-wise transformation is applied. Going beyond this setting, we first\nconsider the case where the target density is a mixture distribution where each\nterm in the mixture comes from a product distribution. Next we consider target\ndensities which can be approximated with such mixture distributions. We require\nthe approximation to be a sum of coordinate-wise products and the approximation\nto be positive everywhere (so that they can be re-scaled to probability density\nfunctions). We use tensor product hat function approximations for this purpose\nhere, since a hat function approximation of a positive function is itself\npositive.\n  We also study more complex algorithms, where we first approximate the target\ndensity with a general Gaussian mixture distribution and approximate the\nmixtures with an adaptive hat function approximation on rotated intervals. The\nGaussian mixture approximation allows us to locate the essential parts of the\ntarget density, whereas the adaptive hat function approximation allows us to\napproximate the finer structure of the target density. We prove convergence\nrates for each of the integration techniques based on quasi-Monte Carlo\nsampling for integrands with bounded partial mixed derivatives. The employed\nalgorithms are based on digital $(t,s)$-sequences over the finite field\n$\\mathbb{F}_2$ and an inversion method. Numerical examples illustrate the\nperformance of the algorithms for some target densities and integrands.\n']","[('gaussian mixture models', 0.5901840925216675), ('gaussian mixture distribution', 0.558473527431488), ('gaussian mixture', 0.5484475493431091), ('mixture distributions', 0.5476090908050537), ('finite mixture models', 0.5241630673408508), ('mixture models', 0.4805750846862793), ('finite mixtures', 0.4805372357368469), ('gaussian random vectors', 0.4584411084651947), ('mixture distribution', 0.4552757740020752), ('approximation fisher', 0.45489501953125)]"
1432,1432,20,1432_shuffles_shuffle_deck cards_guessing game,"['shuffles', 'shuffle', 'deck cards', 'guessing game', 'decks', 'shuffled', 'cards', 'deck', 'optimal strategy', 'maximum expected']","[""The Card Guessing Game: A generating function approach   Consider a card guessing game with complete feedback in which a deck of $n$\ncards ordered $1,\\dots, n$ is riffle-shuffled once. With the goal to maximize\nthe number of correct guesses, a player guesses cards from the top of the deck\none at a time under the optimal strategy until no cards remain. We provide an\nexpression for the expected number of correct guesses with arbitrary number of\nterms, an accuracy improvement over the results of Liu (2021). In addition,\nusing generating functions, we give a unified framework for systematically\ncalculating higher-order moments. Although the extension of the framework to\n$k\\geq2$ shuffles is not immediately straightforward, we are able to settle a\nlong-standing McGrath's conjectured optimal strategy described in Bayer and\nDiaconis (1992) by showing that the optimal guessing strategy for $k=1$ riffle\nshuffle does not necessarily apply to $k\\geq2$ shuffles.\n"", 'On Card guessing games: limit law for one-time riffle shuffle   We consider a card guessing game with complete feedback. A ordered deck of n\ncards labeled 1 up to n is riffle-shuffled exactly one time. Then, the goal of\nthe game is to maximize the number of correct guesses of the cards, where one\nafter another a single card is drawn from the top, and shown to the guesser\nuntil no cards remain. Improving earlier results, we provide a limit law for\nthe number of correct guesses. As a byproduct, we relate the number of correct\nguesses in this card guessing game to the number of correct guesses under a\ntwo-color card guessing game with complete feedback. Using this connection to\ntwo-color card guessing, we can also show a limiting distribution result for\nthe first occurrence of a pure luck guess.\n', 'On Card guessing games: limit law for no feedback one-time riffle\n  shuffle   We consider the following card guessing game with no feedback. An ordered\ndeck of n cards labeled 1 up to n is riffle-shuffled exactly one time. Then,\nthe goal of the game is to maximize the number of correct guesses of the cards.\nOne after another a single card is drawn from the top, the guesser makes a\nguess without seeing the card and gets no response if the guess was correct or\nnot. Building upon and improving earlier results, we provide a limit law for\nthe number of correct guesses and also show convergence of the integer moments.\n']","[('shuffles', 0.5499182343482971), ('shuffle', 0.53715980052948), ('deck cards', 0.533215343952179), ('guessing game', 0.5056367516517639), ('decks', 0.4649435579776764), ('shuffled', 0.44250598549842834), ('cards', 0.4367660582065582), ('deck', 0.41695359349250793), ('optimal strategy', 0.41423696279525757), ('maximum expected', 0.39739543199539185)]"
1433,1433,20,1433_controllability time_approximate controllability_feedback stabilization_stabilization control,"['controllability time', 'approximate controllability', 'feedback stabilization', 'stabilization control', 'stabilizing feedback', 'controllability linear', 'controllability systems', 'delay systems', 'delay equations', 'controllability finite']","['New Features of P3$\\delta$ Software. Insights and Demos   This paper presents the software entitled ""Partial Pole Placement via Delay\nAction"", or ""P3$\\delta$"" for short. P3$\\delta$ is a Python software with a\nfriendly user interface for the design of parametric stabilizing feedback laws\nwith time-delays for dynamical systems. After recalling the theoretical\nfoundation of the so-called ""Partial Pole Placement"" methodology we propose as\nwell the main features of the current version of P3$\\delta$. We illustrate its\nuse in feedback stabilization of several control systems operating under time\ndelays.\n', 'Partial Pole Placement via Delay Action: A Python Software for Delayed\n  Feedback Stabilizing Design   This paper presents a new Python software for the parametric design of\nstabilizing feedback laws with time delays, called Partial Pole Placement via\nDelay Action (P3$\\delta$). After an introduction recalling recent theoretical\nresults on the multiplicity-induced-dominancy (MID) and coexisting real\nroots-induced-dominancy (CRRID) properties and their use for the feedback\nstabilization of control systems operating under time delays, the paper\npresents the current version of P3$\\delta$, which relies on the MID property to\ncompute delayed stabilizing feedback laws for scalar differential equations\nwith a single delay. We detail in particular its graphical user interface\n(GUI), which allows the user to input the necessary information and obtain the\nresults of the analysis done by the software. These results include the\nparameters stabilizing the closed-loop system, graphical representations of the\nspectrum of the closed-loop system, simulations of solutions in the time\ndomain, and a sensitivity analysis with respect to uncertain delays.\n', ""New Features of P3$\\delta$ software: Partial Pole Placement via Delay\n  Action   This paper presents the software Partial Pole Placement via Delay Action, or\nP3$\\delta$ for short. P3$\\delta$ is a Python software with a friendly user\ninterface for the design of parametric stabilizing feedback laws with\ntime-delays, thanks to two properties of the distribution of quasipolynomials'\nzeros, called multiplicity-induced-dominancy and coexisting real\nroots-induced-dominancy. After recalling recent theoretical results on these\nproperties and their use for the feedback stabilization of control systems\noperating under time delays, the paper presents the main features of the\ncurrent version of P3$\\delta$. We detail, in particular, the assignable\nadmissible region (the set of allowable dominant roots and the corresponding\ndelay), which helps the user in the choice of input information, allowing a\nreliable stabilizing delayed feedback. We also present the newly set online\nversion of P3$\\delta$.\n""]","[('controllability time', 0.6049781441688538), ('approximate controllability', 0.5767118334770203), ('feedback stabilization', 0.5660667419433594), ('stabilization control', 0.5647134780883789), ('stabilizing feedback', 0.5618444681167603), ('controllability linear', 0.5600582361221313), ('controllability systems', 0.5490075945854187), ('delay systems', 0.5468899607658386), ('delay equations', 0.5416070222854614), ('controllability finite', 0.5270325541496277)]"
1434,1434,20,1434_massless particles_spinless_general relativity quantum_quantum space,"['massless particles', 'spinless', 'general relativity quantum', 'quantum space', 'quantum gravity', 'momentum space', 'massive particles', 'gravitons', 'photons', 'relativity quantum']","[""Photon topology   The topology of photons in vacuum is interesting because there are no photons\nwith $\\boldsymbol{k}=0$, creating a hole in momentum space. We show that while\nthe set of all photons forms a trivial vector bundle $\\gamma$ over this\nmomentum space, the $R$- and $L$-photons form topologically nontrivial\nsubbundles $\\gamma_\\pm$ with first Chern numbers $\\mp2$. In contrast, $\\gamma$\nhas no linearly polarized subbundles, and there is no Chern number associated\nwith linear polarizations. It is a known difficulty that the standard version\nof Wigner's little group method produces singular representations of the\nPoincar\\'{e} group for massless particles. By considering representations of\nthe Poincar\\'{e} group on vector bundles we obtain a version of Wigner's little\ngroup method for massless particles which avoids these singularities. We show\nthat any massless bundle representation of the Poincar\\'{e} group can be\ncanonically decomposed into irreducible bundle representations labeled by\nhelicity, which in turn can be associated to smooth irreducible Hilbert space\nrepresentations. This proves that the $R$- and $L$-photons are globally\nwell-defined as particles and that the photon wave function can be uniquely\nsplit into $R$- and $L$-components. This formalism offers a method of\nquantizing the EM field without invoking discontinuous polarization vectors as\nin the traditional scheme. We also demonstrate that the spin-Chern number of\nphotons is not a purely topological quantity. Lastly, there has been an\nextended debate on whether photon angular momentum can be split into spin and\norbital parts. Our work explains the precise issues that prevent this\nsplitting. Photons do not admit a spin operator; instead, the angular momentum\nassociated with photons' internal degree of freedom is described by a\nhelicity-induced subalgebra corresponding to the translational symmetry of\n$\\gamma$.\n"", ""Zero curvature is a necessary and sufficient condition for a\n  spin-orbital decomposition   There has been an extended debate regarding the existence of a spin-orbital\ndecomposition of the angular momentum of photons and other massless particles.\nIt was recently shown that there are both geometric and topological\nobstructions preventing any such decomposition. Here we show that any geometric\nconnection on a particle's state space induces a splitting of the angular\nmomentum into two operators. These operators are well-defined angular momentum\noperators if and only if the connection has zero curvature. Massive particles\nhave two canonical curved connections corresponding to boosts and rotations,\nrespectively. These can be uniquely combined to produce a flat connection, and\nthis gives a novel derivation of the Newton-Wigner position operator and the\ncorresponding spin and orbital angular momenta for relativistic massive\nparticles. When the mass is taken to zero, transverse boosts and rotations\ndegenerate, leaving only a single connection for massless particles. This\nconnection produces a commonly proposed splitting of the massless angular\nmomentum into two operators. However, the connection is not flat, explaining\nwhy these operators do not satisfy the angular momentum commutation relations\nand are thus not true spin and orbital angular momentum operators.\n"", 'Four no-go theorems on the existence of spin and orbital angular\n  momentum of massless bosons   The past decades have seen substantial interest in the so-called orbital\nangular momentum (OAM) of light, driven largely by its diverse range of\napplications. However, there are fundamental theoretical issues with\ndecomposing the angular momentum of massless particles, such as photons, into\nspin (SAM) and orbital angular momentum parts. While the angular momentum of\nmassive particles has a natural splitting into the Wigner SAM and OAM, there\nare numerous proposed splittings for photons and no consensus about which is\ncorrect. Moreover, it has been shown that most of the proposed SAM and OAM\noperators do not satisfy the defining commutation relations of angular momentum\noperators and are thus not legitimate splittings. Here, we prove that it is\ngenerally impossible to split the total angular momentum operator of massless\nbosons, such as photons and gravitons, into spin and orbital parts. We prove\ntwo further generalizations of this result, showing that there are no SAM-OAM\nsplittings even if (1) the SAM operator generates non-internal symmetries or\n(2) if one allows the SAM and OAM operators to generate non-SO(3) symmetries.\n']","[('massless particles', 0.5104821920394897), ('spinless', 0.432036817073822), ('general relativity quantum', 0.41955697536468506), ('quantum space', 0.41475972533226013), ('quantum gravity', 0.39719754457473755), ('momentum space', 0.39466214179992676), ('massive particles', 0.3937973082065582), ('gravitons', 0.3668304681777954), ('photons', 0.3606231212615967), ('relativity quantum', 0.3510828912258148)]"
1435,1435,20,1435_helmholtz problems_solving helmholtz_helmholtz wavenumber_frequency helmholtz,"['helmholtz problems', 'solving helmholtz', 'helmholtz wavenumber', 'frequency helmholtz', 'high frequency helmholtz', 'helmholtz exterior', 'galerkin', 'finite element fem', 'helmholtz', 'impedance boundary conditions']","['The $hp$-FEM applied to the Helmholtz equation with PML truncation does\n  not suffer from the pollution effect   We consider approximation of the variable-coefficient Helmholtz equation in\nthe exterior of a Dirichlet obstacle using perfectly-matched-layer (PML)\ntruncation; it is well known that this approximation is exponentially accurate\nin the PML width and the scaling angle, and the approximation was recently\nproved to be exponentially accurate in the wavenumber $k$ in [Galkowski,\nLafontaine, Spence, 2021].\n  We show that the $hp$-FEM applied to this problem does not suffer from the\npollution effect, in that there exist $C_1,C_2>0$ such that if $hk/p\\leq C_1$\nand $p \\geq C_2 \\log k$ then the Galerkin solutions are quasioptimal (with\nconstant independent of $k$), under the following two conditions (i) the\nsolution operator of the original Helmholtz problem is polynomially bounded in\n$k$ (which occurs for ""most"" $k$ by [Lafontaine, Spence, Wunsch, 2021]), and\n(ii) either there is no obstacle and the coefficients are smooth or the\nobstacle is analytic and the coefficients are analytic in a neighbourhood of\nthe obstacle and smooth elsewhere.\n  This $hp$-FEM result is obtained via a decomposition of the PML solution into\n""high-"" and ""low-frequency"" components, analogous to the decomposition for the\noriginal Helmholtz solution recently proved in [Galkowski, Lafontaine, Spence,\nWunsch, 2022]. The decomposition is obtained using tools from semiclassical\nanalysis (i.e., the PDE techniques specifically designed for studying Helmholtz\nproblems with large $k$).\n', 'Higher-order FEM and CIP-FEM for Helmholtz equation with high wave\n  number and perfectly matched layer truncation   The high-frequency Helmholtz equation on the entire space is truncated into a\nbounded domain using the perfectly matched layer (PML) technique and\nsubsequently, discretized by the higher-order finite element method (FEM) and\nthe continuous interior penalty finite element method (CIP-FEM). By formulating\nan elliptic problem involving a linear combination of a finite number of\neigenfunctions related to the PML differential operator, a wave-number-explicit\ndecomposition lemma is proved for the PML problem, which implies that the PML\nsolution can be decomposed into a non-oscillating elliptic part and an\noscillating but analytic part. The preasymptotic error estimates in the energy\nnorm for both the $p$-th order CIP-FEM and FEM are proved to be $C_1(kh)^p +\nC_2k(kh)^{2p} +C_3 E^{\\rm PML}$ under the mesh condition that $k^{2p+1}h^{2p}$\nis sufficiently small, where $k$ is the wave number, $h$ is the mesh size, and\n$E^{\\rm PML}$ is the PML truncation error which is exponentially small. In\nparticular, the dependences of coefficients $C_j~(j=1,2)$ on the source $f$ are\nimproved. Numerical experiments are presented to validate the theoretical\nfindings, illustrating that the higher-order CIP-FEM can greatly reduce the\npollution errors.\n', 'A simple proof that the $hp$-FEM does not suffer from the pollution\n  effect for the constant-coefficient full-space Helmholtz equation   In $d$ dimensions, approximating an arbitrary function oscillating with\nfrequency $\\lesssim k$ requires $\\sim k^d$ degrees of freedom. A numerical\nmethod for solving the Helmholtz equation (with wavenumber $k$) suffers from\nthe pollution effect if, as $k\\to \\infty$, the total number of degrees of\nfreedom needed to maintain accuracy grows faster than this natural threshold.\n  While the $h$-version of the finite element method (FEM) (where accuracy is\nincreased by decreasing the meshwidth $h$ and keeping the polynomial degree $p$\nfixed) suffers from the pollution effect, the celebrated papers [Melenk, Sauter\n2010], [Melenk, Sauter 2011], [Esterhazy, Melenk 2012], and [Melenk, Parsania,\nSauter 2013] showed that the $hp$-FEM (where accuracy is increased by\ndecreasing the meshwidth $h$ and increasing the polynomial degree $p$) applied\nto a variety of constant-coefficient Helmholtz problems does not suffer from\nthe pollution effect.\n  The heart of the proofs of these results is a PDE result splitting the\nsolution of the Helmholtz equation into ""high"" and ""low"" frequency components.\nIn this expository paper we prove this splitting for the constant-coefficient\nHelmholtz equation in full space (i.e., in $\\mathbb{R}^d$) using only\nintegration by parts and elementary properties of the Fourier transform; this\nis in contrast to the proof for this set-up in [Melenk, Sauter 2010] which uses\nsomewhat-involved bounds on Bessel and Hankel functions. The proof in this\npaper is motivated by the recent proof in [Lafontaine, Spence, Wunsch 2022] of\nthis splitting for the variable-coefficient Helmholtz equation in full space;\nindeed, the proof in [Lafontaine, Spence, Wunsch 2022] uses more-sophisticated\ntools that reduce to the elementary ones above for constant coefficients.\n']","[('helmholtz problems', 0.5328327417373657), ('solving helmholtz', 0.5195149183273315), ('helmholtz wavenumber', 0.5082151889801025), ('frequency helmholtz', 0.49783533811569214), ('high frequency helmholtz', 0.4915212094783783), ('helmholtz exterior', 0.4435208737850189), ('galerkin', 0.40632152557373047), ('finite element fem', 0.39120611548423767), ('helmholtz', 0.3786558210849762), ('impedance boundary conditions', 0.3571253716945648)]"
1436,1436,20,1436_stein variational gradient_stein variational_variational gradient descent_variational inference,"['stein variational gradient', 'stein variational', 'variational gradient descent', 'variational inference', 'variational gradient', 'wasserstein gradient flow', 'version stein', 'stein', 'gradient descent', 'stein discrepancy']","['A stochastic version of Stein Variational Gradient Descent for efficient\n  sampling   We propose in this work RBM-SVGD, a stochastic version of Stein Variational\nGradient Descent (SVGD) method for efficiently sampling from a given\nprobability measure and thus useful for Bayesian inference. The method is to\napply the Random Batch Method (RBM) for interacting particle systems proposed\nby Jin et al to the interacting particle systems in SVGD. While keeping the\nbehaviors of SVGD, it reduces the computational cost, especially when the\ninteracting kernel has long range. Numerical examples verify the efficiency of\nthis new version of SVGD.\n', 'Stein Variational Gradient Descent: many-particle and long-time\n  asymptotics   Stein variational gradient descent (SVGD) refers to a class of methods for\nBayesian inference based on interacting particle systems. In this paper, we\nconsider the originally proposed deterministic dynamics as well as a stochastic\nvariant, each of which represent one of the two main paradigms in Bayesian\ncomputational statistics: variational inference and Markov chain Monte Carlo.\nAs it turns out, these are tightly linked through a correspondence between\ngradient flow structures and large-deviation principles rooted in statistical\nphysics. To expose this relationship, we develop the cotangent space\nconstruction for the Stein geometry, prove its basic properties, and determine\nthe large-deviation functional governing the many-particle limit for the\nempirical measure. Moreover, we identify the Stein-Fisher information (or\nkernelised Stein discrepancy) as its leading order contribution in the\nlong-time and many-particle regime in the sense of $\\Gamma$-convergence,\nshedding some light on the finite-particle properties of SVGD. Finally, we\nestablish a comparison principle between the Stein-Fisher information and\nRKHS-norms that might be of independent interest.\n', 'Regularized Stein Variational Gradient Flow   The Stein Variational Gradient Descent (SVGD) algorithm is a deterministic\nparticle method for sampling. However, a mean-field analysis reveals that the\ngradient flow corresponding to the SVGD algorithm (i.e., the Stein Variational\nGradient Flow) only provides a constant-order approximation to the Wasserstein\nGradient Flow corresponding to the KL-divergence minimization. In this work, we\npropose the Regularized Stein Variational Gradient Flow, which interpolates\nbetween the Stein Variational Gradient Flow and the Wasserstein Gradient Flow.\nWe establish various theoretical properties of the Regularized Stein\nVariational Gradient Flow (and its time-discretization) including convergence\nto equilibrium, existence and uniqueness of weak solutions, and stability of\nthe solutions. We provide preliminary numerical evidence of the improved\nperformance offered by the regularization.\n']","[('stein variational gradient', 0.685127854347229), ('stein variational', 0.6465398073196411), ('variational gradient descent', 0.5768404603004456), ('variational inference', 0.5237185955047607), ('variational gradient', 0.49791768193244934), ('wasserstein gradient flow', 0.46265512704849243), ('version stein', 0.4360680878162384), ('stein', 0.43543896079063416), ('gradient descent', 0.408081978559494), ('stein discrepancy', 0.40121063590049744)]"
1437,1437,20,1437_linear programming milp_space mission_space exploration_integer linear programming,"['linear programming milp', 'space mission', 'space exploration', 'integer linear programming', 'mission design', 'modeling optimization', 'linear programming', 'optimization formulation', 'logistics', 'optimization mixed']","['Hierarchical Framework for Space Exploration Campaign Schedule\n  Optimization   Space exploration plans are becoming increasingly complex as public agencies\nand private companies target deep-space locations, such as cislunar space and\nbeyond, which require long-duration missions and many supporting systems and\npayloads. Optimizing multi-mission exploration campaigns is challenging due to\nthe large number of required launches as well as their sequencing and\ncompatibility requirements, making the conventional space logistics\nformulations not scalable. To tackle this challenge, this paper proposes an\nalternative approach that leverages a two-level hierarchical optimization\nalgorithm: a genetic algorithm is used to explore the campaign scheduling\nsolution space, and each of the solutions is then evaluated using a\ntime-expanded multi-commodity flow mixed-integer linear program. A number of\ncase studies, focusing on the Artemis lunar exploration program, demonstrate\nhow the method can be used to analyze potential campaign architectures. The\nmethod enables a potential mission planner to study the sensitivity of a\ncampaign to program-level parameters such as logistics vehicle availability and\nperformance, payload launch windows, and in-situ resource utilization\ninfrastructure efficiency.\n', 'Generalizing Space Logistics Network Optimization with Integrated\n  Machine Learning and Mathematical Programming   Recent growing complexity in space missions has led to an active research\nfield of space logistics and mission design. This research field leverages the\nkey ideas and methods used to handle complex terrestrial logistics to tackle\nspace logistics design problems. A typical goal in space logistics is to\noptimize the commodity flow to satisfy some mission objectives with the lowest\ncost. One of the successful space logistics approaches is network flow modeling\nand optimization using mixed-integer linear programming (MILP). A caveat of the\nconventional MILP-based network approach for space logistics is its\nincapability of handling nonlinearity. For example, in the MILP formulation,\nthe spacecraft structure mass and fuel/payload capacity are approximated by a\nlinear relationship. However, this oversimplified relationship cannot\ncharacterize a realistic spacecraft design. Other types of nonlinearity can\nappear when a nonlinear time-dependent trajectory model is considered in an\nevent-driven network, where the time step of each event itself is a variable.\nIn response to this challenge, this Note develops a new systematic general\nframework to handle nonlinearity in the MILP-based space logistics formulation\nusing machine learning (ML). Specifically, we replace the nonlinear constraints\nin the space logistics formulation with trained ML models that are compatible\nwith MILP. The MILP-compatible ML model includes linear regression, PWL\napproximations, neural networks (NN) with Rectified Linear Unit (ReLU)\nactivations, decision tree regression, and random forest regression, among\nothers; these models can be translated into MILP formulations with a definition\nof additional variables and constraints while maintaining the linearity. This\nNote provides the first demonstration of using such trained ML models directly\nin a MILP-based space logistics optimization formulation.\n', 'Event-Driven Network Model for Space Mission Optimization with\n  High-Thrust and Low-Thrust Spacecraft   Numerous high-thrust and low-thrust space propulsion technologies have been\ndeveloped in the recent years with the goal of expanding space exploration\ncapabilities; however, designing and optimizing a multi-mission campaign with\nboth high-thrust and low-thrust propulsion options are challenging due to the\ncoupling between logistics mission design and trajectory evaluation.\nSpecifically, this computational burden arises because the deliverable mass\nfraction (i.e., final-to-initial mass ratio) and time of flight for low-thrust\ntrajectories can can vary with the payload mass; thus, these trajectory metrics\ncannot be evaluated separately from the campaign-level mission design. To\ntackle this challenge, this paper develops a novel event-driven space logistics\nnetwork optimization approach using mixed-integer linear programming for space\ncampaign design. An example case of optimally designing a cislunar propellant\nsupply chain to support multiple lunar surface access missions is used to\ndemonstrate this new space logistics framework. The results are compared with\nan existing stochastic combinatorial formulation developed for incorporating\nlow-thrust propulsion into space logistics design; our new approach provides\nsuperior results in terms of cost as well as utilization of the vehicle fleet.\nThe event-driven space logistics network optimization method developed in this\npaper can trade off cost, time, and technology in an automated manner to\noptimally design space mission campaigns.\n']","[('linear programming milp', 0.4987577795982361), ('space mission', 0.4651973843574524), ('space exploration', 0.44431376457214355), ('integer linear programming', 0.4272804260253906), ('mission design', 0.42287811636924744), ('modeling optimization', 0.4202536344528198), ('linear programming', 0.41875532269477844), ('optimization formulation', 0.40661266446113586), ('logistics', 0.40357720851898193), ('optimization mixed', 0.39423948526382446)]"
1438,1438,20,1438_blow solutions_isolated singularities_isolated singularity_liouville equations,"['blow solutions', 'isolated singularities', 'isolated singularity', 'liouville equations', 'solutions liouville', 'liouville type equations', 'blowup solutions', 'solutions blowup', 'solutions singular', 'equations blow']","['Estimates for Liouville equation with quantized singularities   For Liouville equations with singular sources, the interpretation of the\nequation and its impact are most significant if the singular sources are\nquantized: the strength of each Dirac mass is a mutliple of $4\\pi$. However the\nstudy of bubbling solutions around a quantized singular source is particularly\nchallenging: near the singular source, the spherical Harnack inequality may not\nhold and there are multiple local maximums of bubbling solutions all swarming\nto the singular source. In this article we seek to provide a complete\nunderstanding of the blowup picture in this core difficulty and we establish\ntwo major types of results: First we prove that not only the first derivatives\nof coefficient functions tend to zero at the singular source, the second\nderivatives also have a vanishing estimate. Second we derive pointwise\nestimates for bubbling solutions to be approximated by global solutions, which\nhave crucial applications in a number of important projects. Since bubbling\nsolutions near a singular source are very commonly observed in geometry and\nphysics, it seems that the estimates in this article can also be applied to\nmany related equations and systems with various backgrounds.\n', 'Uniqueness of bubbling solutions of mean field equations with\n  non-quantized singularities   For singular mean field equations defined on a compact Riemann surface, we\nprove the uniqueness of bubbling solutions if some blowup points coincide with\nbubbling sources. If the strength of the bubbling sources at blowup points are\nnot multiple of $4\\pi$ we prove that bubbling solutions are unique under\nnon-degeneracy assumptions. This work extends a previous work of Bartolucci,\net, al \\cite{bart-4}.\n', 'Asymptotic Analysis and Uniqueness of blowup solutions of non-quantized\n  singular mean field equations   For singular mean field equations defined on a compact Riemann surface, we\nprove the uniqueness of bubbling solutions as far as blowup points are either\nregular points or non-quantized singular sources. In particular the uniqueness\nresult covers the most general case extending or improving all previous works\nof Bartolucci-Jevnikar-Lee-Yang \\cite{bart-4,bart-4-2} and Wu-Zhang\n\\cite{wu-zhang-ccm}. For example, unlike previous results, we drop the\nassumption of singular sources being critical points of a suitably defined\nKirchoff-Routh type functional. Our argument is based on refined estimates,\nrobust and flexible enough to be applied to a wide range of problems requiring\na delicate blowup analysis. In particular we come up with several new estimates\nof independent interest about the concentration phenomenon for Liouville-type\nequations.\n']","[('blow solutions', 0.5355023741722107), ('isolated singularities', 0.5147433876991272), ('isolated singularity', 0.4770868122577667), ('liouville equations', 0.4663444757461548), ('solutions liouville', 0.4647507965564728), ('liouville type equations', 0.4621805250644684), ('blowup solutions', 0.4555082619190216), ('solutions blowup', 0.44766947627067566), ('solutions singular', 0.44464805722236633), ('equations blow', 0.4368232488632202)]"
1439,1439,20,1439_clifford algebras_clifford algebra_clifford group_clifford geometric,"['clifford algebras', 'clifford algebra', 'clifford group', 'clifford geometric', 'lie algebras', 'twisted group algebras', 'geometric algebras', 'central simple algebras', 'lie algebra', 'algebras lie']","['On some Lie groups containing spin group in Clifford algebra   In this paper we consider some Lie groups in complexified Clifford algebras.\nUsing relations between operations of conjugation in Clifford algebras and\nmatrix operations we prove isomorphisms between these groups and classical\nmatrix groups (symplectic, orthogonal, linear, unitary) in the cases of\narbitrary dimension and arbitrary signature. Also we obtain isomorphisms of\ncorresponding Lie algebras which are direct sums of subspaces of quaternion\ntypes. Spin group is a subgroup of all considered groups and it coincides with\none of them in the cases $n\\leq 5$. We present classical matrix Lie groups that\ncontain spin group in the case of arbitrary dimension.\n', 'Generalized Degenerate Clifford and Lipschitz Groups This paper introduces and studies generalized degenerate Clifford and Lipschitz groups in geometric (Clifford) algebras. These Lie groups preserve the direct sums of the subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations in degenerate geometric algebras. We prove that the generalized degenerate Clifford and Lipschitz groups can be defined using centralizers and twisted centralizers of fixed grades subspaces and the norm functions that are widely used in the theory of spin groups. We study the relations between these groups and consider them in the particular cases of plane-based geometric algebras and Grassmann algebras. The corresponding Lie algebras are studied. The presented groups are interesting for the study of generalized degenerate spin groups and applications in computer science, physics, and engineering.', 'On the bundle of Clifford algebras over the space of quadratic forms   For each quadratic form Q in Quad(V) over a given vector space over a field R\nwe have the Clifford algebra Cl(V,Q) defined as the quotient T(V)/I(Q) of the\ntensor algebra T(V) over the two-sided ideal generated by expressions of the\nform $x x-Q(x),x in V. In the present paper we consider the whole family\nCl(V,Q) in a geometric way as a Z2-graded vector bundle over the base manifold\nQuad(V). Bilinear forms F from Bil(V) act on this bundle providing natural\nbijective linear mappings lambda_F between Clifford algebras for different\nCl(V,Q). Alternate (or antisymmetric) forms induce vertical automorphisms,\nwhich we propose to consider as \'gauge transformations\'. We develop here the\nformalism of N. Bourbaki, which generalizes the well known Chevalley\'s\nisomorphism Cl(V,Q)->End(Wedge(V)->Wedge(V). In particular we realize the\nClifford algebra twisting gauge trnsformations induced by antisymmetric\nbilinear forms as exponentials of contractions with elements of $Wedge(V^*\nrepresenting these forms. Throughtout all this paper we intentionally avoid\nusing the so far accepted term ""Clifford algebra of a bilinear form"" (known\notherwise as ""Quantum Clifford algebra""), which we consider as possibly\nmisleading, as it does not represent any well defined mathematical object.\nInstead we show explicitly how any given Clifford algebra Cl(Q) can be\nnaturally realized as acting via endomorphisms of any other Clifford algebra\nCl(Q\') if Q\'=Q+Q_F,and Q_F(x)=F(x,x). Possible physical meaning of such\ntransformations are also mentioned.\n']","[('clifford algebras', 0.8060027956962585), ('clifford algebra', 0.7594298720359802), ('clifford group', 0.6687139868736267), ('clifford geometric', 0.6127228736877441), ('lie algebras', 0.6039747595787048), ('twisted group algebras', 0.5886428356170654), ('geometric algebras', 0.5652695894241333), ('central simple algebras', 0.5427783727645874), ('lie algebra', 0.542222797870636), ('algebras lie', 0.5359637141227722)]"
1440,1440,20,1440_blow finite time_semilinear wave equations_solutions semilinear wave_robertson walker spacetimes,"['blow finite time', 'semilinear wave equations', 'solutions semilinear wave', 'robertson walker spacetimes', 'flrw spacetimes', 'existence solutions semilinear', 'semilinear wave', 'wave generalized', 'wave equations', 'blow solutions']","[""On Glassey's conjecture for semilinear wave equations in\n  Friedmann-Lema\\^itre-Robertson-Walker spacetime   Consider nonlinear wave equations in the spatially flat\nFriedmann-Lema\\^itre-Robertson-Walker (FLRW) spacetimes. We show blow-up in\nfinite time of solutions and upper bounds of the lifespan of blow-up solutions\nto give the FLRW spacetime version of Glassey's conjecture for the time\nderivative nonlinearity. We also show blow-up results for the space time\nderivative nonlinearity.\n"", 'Existence of solutions of semilinear wave equations with time-dependent propagation speed and time derivative nonlinearity Consider wave equations with time derivative nonlinearity and time-dependent propagation speed which are generalized versions of the wave equations in the Friedmann-Lema\\^itre-Robertson-Walker (FLRW) spacetime, the de Sitter spacetime and the anti-de Sitter space time. We show lower bounds of the lifespan of solutions as well as the global existence by providing an integrability condition on the propagation speed function, which is applicable to the nonlinear wave equation in the expanding FLRW spacetime including the de Sitter spacetime. We also prove that blow-up in a finite time occurs for the generalized form of the equation in contracting universes such as the anti-de Sitter spacetime, as well as upper bounds of the lifespan of blow-up solutions.', 'Blow up of solutions of semilinear wave equations related to nonlinear\n  waves in de Sitter spacetime   Consider a nonlinear wave equation for a massless scalar field with\nself-interaction in the spatially flat de Sitter spacetime. We show that\nblow-up in a finite time occurs for the equation with arbitrary power\nnonlinearity as well as upper bounds of the lifespan of blow-up solutions.The\nblow-up condition is the same as in the accelerated expanding\nFriedmann-Lema\\^itre-Robertson-Walker (FLRW) spacetime. We also show the same\nresults for the space derivative nonlinear term.\n']","[('blow finite time', 0.5336513519287109), ('semilinear wave equations', 0.5271322131156921), ('solutions semilinear wave', 0.5110150575637817), ('robertson walker spacetimes', 0.47143012285232544), ('flrw spacetimes', 0.46575191617012024), ('existence solutions semilinear', 0.4564042389392853), ('semilinear wave', 0.4362168610095978), ('wave generalized', 0.41655102372169495), ('wave equations', 0.41599220037460327), ('blow solutions', 0.4099084436893463)]"
1441,1441,20,1441_salem number_algebraic numbers_algebraic integers_algebraic number,"['salem number', 'algebraic numbers', 'algebraic integers', 'algebraic number', 'number beta', 'numbers alpha', 'sequences algebraic', 'beta expansions', 'salem', 'numbers quasi']","['Transcendence for Pisot Morphic Words over an Algebraic Base It is known that for a uniform morphic sequence\n  $\\boldsymbol u = \\langle u_n\\rangle_{n=0}^\\infty$ and an algebraic\n  number $\\beta$ such that $|\\beta|>1$, the number\n  $[\\![\\boldsymbol{u} ]\\!]_\\beta:=\\sum_{n=0}^\\infty\n  \\frac{u_n}{\\beta^n}$ either lies in $\\mathbb Q(\\beta)$ or is\n  transcendental. In this paper we show a similar\n  rational-transcendental dichotomy for sequences defined by\n  irreducible Pisot morphisms. Subject to the Pisot conjecture (an\n  irreducible Pisot morphism has pure discrete spectrum), we\n  generalise the latter result to arbitrary finite alphabets. In\n  certain cases we are able to show transcendence of\n  $[\\![\\boldsymbol{u}]\\!]_{\\beta}$ outright. In particular, for\n  $k\\geq 2$, if $\\boldsymbol u$ is the $k$-bonacci word then\n  $[\\![\\boldsymbol{u}]\\!]_{\\beta}$ is transcendental.', 'Salem numbers less than 49/37   A certain number of lists of small Salem numbers, some of which are certified\nas complete, are available online. Notably, the website of M. J. Mossinghoff\nfeatures a list of 47 Salem numbers smaller than 1.3, as well as complete lists\nof Salem numbers of fixed degrees that are smaller than various bounds. The\nobjective of this work is to advance the understanding of Salem numbers by\nproviding a list of Salem numbers smaller than a threshold of 49/37 (â\x89\x88\n1.324324) through the implementation of a method based on integer linear\nprogramming and uniform sampling of root separators. Beyond the intrinsic\ninterest of the newly detected Salem numbers, the rediscovery of already known\nSalem numbers through this alternative method could offer valuable insights\ninto the potential completeness of already existing lists for degrees where it\nhas not yet been proven.\n', 'The digit exchanges in the rotational beta expansions of algebraic\n  numbers   In this article, we investigate the $\\beta$-expansions of real algebraic\nnumbers. In particular, we give new lower bounds for the number of digit\nexchanges in the case where $\\beta$ is a Pisot or Salem number. Moreover, we\ndefine a new class of algebraic numbers, quasi-Pisot numbers and quasi-Salem\nnumbers, which gives a generalization of Pisot numbers and Salem numbers. Our\nmethod is applicable also to the digit expansions of complex algebraic numbers,\nwhich gives new estimation. In particular, we investigate the digits of\nrotational beta expansion by Akiyama and Caalim $[3]$ and zeta-expansion by\nSurer $[20]$, where the base is a quasi-Pisot or quasi-Salem number.\n']","[('salem number', 0.5291512608528137), ('algebraic numbers', 0.525874137878418), ('algebraic integers', 0.501812756061554), ('algebraic number', 0.49757757782936096), ('number beta', 0.4497906267642975), ('numbers alpha', 0.40392181277275085), ('sequences algebraic', 0.3842311501502991), ('beta expansions', 0.3759059011936188), ('salem', 0.37432482838630676), ('numbers quasi', 0.3681526184082031)]"
1442,1442,20,1442_membranes_membrane_biomembranes_vesicles,"['membranes', 'membrane', 'biomembranes', 'vesicles', 'vesicle', 'phase field simulations', 'lipid', 'dynamics phase field', 'phase separation', 'phase field']","['Phase-separated lipid vesicles: continuum modeling, simulation, and\n  validation   The paper presents a complete research cycle comprising continuum-based\nmodeling, computational framework development, and validation setup to predict\nphase separation and surface hydrodynamics in lipid bilayer membranes. We\nstarting with an overview of the key physical characteristics of lipid\nbilayers, including their composition, mechanical properties, and\nthermodynamics, and then discuss continuum models of multi-component bilayers.\nThe most complex model is a Navier--Stokes--Cahn--Hilliard (NSCH) type system,\ndescribing the coupling of incompressible surface fluid dynamics with\nphase-field dynamics on arbitrarily curved geometries. It is discretized using\ntrace finite element methods, which offer geometric flexibility and stability\nin representing surface PDEs. Numerical studies are conducted to examine\nphysical features such as coarsening rates and interfacial dynamics. The\ncomputational results obtained from the NSCH model are compared against\nexperimental data for membrane compositions with distinct phase behaviors,\ndemonstrating that including both phase-field models and surface hydrodynamics\nis essential to accurately reproduce domain evolution observed in\nepi-fluorescence microscopy. Lastly, we extend the model to incorporate\nexternal forces that enable the simulation of vesicles containing cationic\nlipids, used to enhance membrane fusion.\n', 'Experimental validation of a phase-field model to predict coarsening\n  dynamics of lipid domains in multicomponent membranes   Membrane phase-separation is a mechanism that biological membranes often use\nto locally concentrate specific lipid species in order to organize diverse\nmembrane processes. Phase separation has also been explored as a tool for the\ndesign of liposomes with heterogeneous and spatially organized surfaces. These\n""patchy"" liposomes are promising platforms for delivery purposes, however their\ndesign and optimization through experimentation can be expensive and\ntime-consuming. We developed a computationally efficient method based on the\nsurface Cahn-Hilliard phase-field model to complement experimental\ninvestigations in the design of patchy liposomes. The method relies on\nthermodynamic considerations to set the initial state for numerical\nsimulations. We show that our computational approach delivers not only\nqualitative pictures, but also accurate quantitative information about the\ndynamics of the membrane organization. In particular, the computational and\nexperimental results are in excellent agreement in terms of raft area fraction,\ntotal raft perimeter over time and total number of rafts over time for two\ndifferent membrane compositions (DOPC:DPPC with a 2:1 molar ratio with 20% Chol\nand DOPC:DPPC with a 3:1 molar ratio with 20% Chol). Thus, the computational\nphase-field model informed by experiments has a considerable potential to\nassist in the design of liposomes with spatially organized surfaces, thereby\ncontaining the cost and time required by the design process.\n', 'Lipid domain coarsening and fluidity in multicomponent lipid vesicles: A\n  continuum based model and its experimental validation   Liposomes that achieve a heterogeneous and spatially organized surface\nthrough phase separation have been recognized to be a promising platform for\ndelivery purposes. However, their design and optimization through\nexperimentation can be expensive and time-consuming. To assist with the design\nand reduce the associated cost, we propose a computational platform for\nmodeling membrane coarsening dynamics based on the principles of continuum\nmechanics and thermodynamics. This model couples phase separation to lateral\nflow and accounts for different membrane fluidity within the different phases,\nwhich is known to affect the coarsening dynamics on lipid membranes. The\nsimulation results are in agreement with the experimental data in terms of\nliquid ordered domains area fraction, total domains perimeter over time and\ntotal number of domains over time for two different membrane compositions\n(DOPC:DPPC with a 1:1 molar ratio with 15% Chol and DOPC:DPPC with a 1:2 molar\nratio with 25% Chol) that yield opposite and nearly inverse phase behavior.\nThis quantitative validation shows that the developed platform can be a\nvaluable tool in complementing experimental practice. Keywords: Multicomponent\nMembranes; Membrane fluidity; Membrane Phase Separation; Computational\nModeling; Fluorescence Microscopy; Liposomes\n']","[('membranes', 0.506913423538208), ('membrane', 0.4670589566230774), ('biomembranes', 0.44353944063186646), ('vesicles', 0.4243773818016052), ('vesicle', 0.4009716212749481), ('phase field simulations', 0.38087883591651917), ('lipid', 0.3747864365577698), ('dynamics phase field', 0.3747440278530121), ('phase separation', 0.357240229845047), ('phase field', 0.31618401408195496)]"
1443,1443,20,1443_modular hamiltonian_modular theory_quantum field theory_hamiltonian associated,"['modular hamiltonian', 'modular theory', 'quantum field theory', 'hamiltonian associated', 'hamiltonian provide', 'hamiltonian', 'algebraic qft', 'quantum field', 'neumann algebras', 'conformal field theory']","['Relating the modular Hamiltonian to two-point functions   We consider the modular Hamiltonian associated to standard subspaces for a\nfree scalar field in a globally hyperbolic spacetime in an arbitrary Gaussian\nstate. We show how the modular Hamiltonian is related to the two-point function\nof the theory. For the restriction of the modular Hamiltonian to the subspace,\nwe recover formulas that were obtained previously by Peschel, Casini and\nHuerta. We also show how the same results can be obtained more directly from\nthe KMS condition, and generalize our results to general CCR algebras.\n', 'The massive modular Hamiltonian for a double cone   The Tomita-Takesaki modular operator for local algebras plays an important\nrole in quantum field theory, and more recently in the study of relative\nentropy. However, the explicit expression of this operator, except for the case\nof wedges, is difficult to describe mathematically. We have obtained instead\nnumerical results for the form of the modular Hamiltonian for a double cone in\na massive scalar free field in (1+1)- and (3+1)-dimensional Minkowski space,\nwhich shows how it differs from the wedge case, in particular regarding the\ndependence of the modular Hamiltonian on the mass of the field.\n', 'The massless modular Hamiltonian   We compute the vacuum local modular Hamiltonian associated with a space ball\nregion in the free scalar massless Quantum Field Theory. We give an explicit\nexpression on the one particle Hilbert space in terms of the higher dimensional\nLegendre differential operator. The quadratic form of the massless modular\nHamiltonian is expressed in terms of an integral of the energy density with the\nparabolic distribution. We then get the formula for the local entropy of a wave\npacket. This gives the vacuum relative entropy of a coherent state on the\ndouble cone von Neumann algebras associated with the free scalar QFT. Among\nother points, we provide the passivity characterisation of the modular\nHamiltonian within the standard subspace setup.\n']","[('modular hamiltonian', 0.6636989712715149), ('modular theory', 0.525859534740448), ('quantum field theory', 0.5053309202194214), ('hamiltonian associated', 0.49352461099624634), ('hamiltonian provide', 0.47470951080322266), ('hamiltonian', 0.438199907541275), ('algebraic qft', 0.42393064498901367), ('quantum field', 0.41118791699409485), ('neumann algebras', 0.41017991304397583), ('conformal field theory', 0.4050590395927429)]"
1444,1444,20,1444_thermodynamic phase space_structure thermodynamic_thermodynamic systems_thermodynamical,"['thermodynamic phase space', 'structure thermodynamic', 'thermodynamic systems', 'thermodynamical', 'riemannian structures', 'thermodynamic phase', 'thermodynamic', 'thermodynamics', 'non equilibrium thermodynamics', 'quantum thermodynamics']","['Contact polarizations and associated metrics in geometric thermodynamics   In this work we show that a Legendre transformation is nothing but a mere\nchange of contact polarization from the point of view of contact geometry.\nThen, we construct a set of Riemannian and pseudo-Riemannian metrics on a\ncontact manifold by introducing almost contact and para-contact structures and\nwe analyze their isometries. We show that it is not possible to find a class of\nmetric tensors which fulfills two properties: on the one hand, to be\npolarization independent i.e. the Legendre transformations are the\ncorresponding isometries and, on the other, that it induces a Hessian metric\ninto the corresponding Legendre submanifolds. This second property is motivated\nby the well known Riemannian structures of the geometric description of\nthermodynamics which are based on Hessian metrics on the space of equilibrium\nstates and whose properties are related to the fluctuations of the system. We\nfind that to define a Riemannian structure with such properties it is necessary\nto abandon the idea of an associated metric to an almost contact or\npara-contact structure. We find that even extending the contact metric\nstructure of the thermodynamic phase space the thermodynamic desiderata cannot\nbe fulfilled.\n', 'Reparametrizations and metric structures in thermodynamic phase space   We investigate the consequences of reparametrizations in the geometric\ndescription of thermodynamics analyzing the effects on the thermodynamic phase\nspace. It is known that the contact and Riemannian structures of the\nthermodynamic phase space are related to thermodynamic equilibrium and\nstatistical fluctuations in the Boltzmann-Gibbs statistical mechanics. The\nphysical motivation for this analysis rests upon the possibility of having,\ninstead of a direct control of the intensive parameters determining the state\nof the corresponding physical reservoirs, the control of a set of\ndifferentiable functions of the original variables. Likewise, we consider a set\nof differentiable functions of the extensive variables accounting for the\npossibility of not having direct access to the original variables. We find that\nthe effect of reparametrizations on the thermodynamic phase space can be\ncodified, in geometrical terms, in its contact and Riemannian structures. In\nparticular, we single out a rank-two tensor that enters in the definition of\nthe metric which geometrically comprises the information about such\nreparametrizations. We notice that even if these geometric structures are\nmodified by the reparametrizations, the metric structure on the thermodynamic\nspace of equilibrium states is preserved.\n', 'Affine geometric description of thermodynamics   Thermodynamics provides a unified perspective of thermodynamic properties of\nvarious substances. To formulate thermodynamics in the language of\nsophisticated mathematics, thermodynamics is described by a variety of\ndifferential geometries, including contact and symplectic geometries. Meanwhile\naffine geometry is a branch of differential geometry and is compatible with\ninformation geometry, where information geometry is known to be compatible with\nthermodynamics. By combining above, it is expected that thermodynamics is\ncompatible with affine geometry, and is expected that several affine geometric\ntools can be introduced in the analysis of thermodynamic systems. In this paper\naffine geometric descriptions of equilibrium and nonequilibrium thermodynamics\nare proposed. For equilibrium systems, it is shown that several thermodynamic\nquantities can be identified with geometric objects in affine geometry, and\nthat several geometric objects can be introduced in thermodynamics. Examples of\nthese include: specific heat is identified with the affine fundamental form, a\nflat connection is introduced in thermodynamic phase space. For nonequilibrium\nsystems, two classes of relaxation processes are shown to be described in the\nlanguage of an extension of affine geometry. Finally this affine geometric\ndescription of thermodynamics for equilibrium and nonequilibrium systems is\ncompared with a contact geometric description.\n']","[('thermodynamic phase space', 0.6367079615592957), ('structure thermodynamic', 0.5881069302558899), ('thermodynamic systems', 0.574749767780304), ('thermodynamical', 0.5344899892807007), ('riemannian structures', 0.5338776707649231), ('thermodynamic phase', 0.515376627445221), ('thermodynamic', 0.5116796493530273), ('thermodynamics', 0.45892030000686646), ('non equilibrium thermodynamics', 0.4582415223121643), ('quantum thermodynamics', 0.4549323618412018)]"
1445,1445,20,1445_parabolic stochastic partial_parabolic spde_partial differential spde_parabolic stochastic,"['parabolic stochastic partial', 'parabolic spde', 'partial differential spde', 'parabolic stochastic', 'stochastic partial differential', 'differential spde', 'linear stochastic partial', 'parabolic spdes', 'stochastic partial', 'driven wiener process']","['Estimation for linear parabolic SPDEs in two space dimensions with\n  unknown damping parameters   We study parametric estimation for second order linear parabolic stochastic\npartial differential equations (SPDEs) in two space dimensions driven by two\ntypes of $Q$-Wiener processes based on high frequency spatio-temporal data.\nFirst, we give estimators for damping parameters of the $Q$-Wiener processes of\nthe SPDE using realized quadratic variations based on temporal and spatial\nincrements. We next propose minimum contrast estimators of four coefficient\nparameters in the SPDE and obtain estimators of the rest of unknown parameters\nin the SPDE using an approximate coordinate process. We also examine numerical\nsimulations of the proposed estimators.\n', 'Small dispersion asymptotics for an SPDE in two space dimensions using\n  triple increments   We consider parametric estimation for a second order linear parabolic\nstochastic partial differential equation (SPDE) in two space dimensions driven\nby a $Q$-Wiener process with a small noise based on high frequency\nspatio-temporal data. We first provide estimators of the diffusive and\nadvective parameters in the SPDE using temporal and spatial increments. We then\nconstruct an estimator of the reaction parameter in the SPDE based on an\napproximate coordinate process. We also give simulation results of the proposed\nestimators.\n', 'Parameter estimation for linear parabolic SPDEs in two space dimensions\n  based on high frequency data   We consider parameter estimation for a linear parabolic second-order\nstochastic partial differential equation (SPDE) in two space dimensions driven\nby two types $Q$-Wiener processes based on high frequency data in time and\nspace. We first estimate the parameters which appear in the coordinate process\nof the SPDE using the minimum contrast estimator based on the thinned data with\nrespect to space, and then construct an approximate coordinate process of the\nSPDE. Furthermore, we propose estimators of the coefficient parameters of the\nSPDE utilizing the approximate coordinate process based on the thinned data\nwith respect to time. We also give some simulation results.\n']","[('parabolic stochastic partial', 0.5936192870140076), ('parabolic spde', 0.5704110264778137), ('partial differential spde', 0.557197630405426), ('parabolic stochastic', 0.5408006310462952), ('stochastic partial differential', 0.5281012058258057), ('differential spde', 0.5266103148460388), ('linear stochastic partial', 0.5229402184486389), ('parabolic spdes', 0.5208259224891663), ('stochastic partial', 0.4910934865474701), ('driven wiener process', 0.4866882860660553)]"
1446,1446,20,1446_matchings graphs_fractional matching_matching number graph_matching graph,"['matchings graphs', 'fractional matching', 'matching number graph', 'matching graph', 'maximal matchings', 'graph fractional', 'maximum matching', 'size maximum matching', 'perfect matchings', 'matching theory']","['Fractional matching preclusion of fault Hamiltonian graphs   Matching preclusion is a measure of robustness in the event of edge failure\nin interconnection networks. As a generalization of matching preclusion, the\nfractional matching preclusion number (FMP number for short) of a graph is the\nminimum number of edges whose deletion results in a graph that has no\nfractional perfect matchings, and the fractional strong matching preclusion\nnumber (FSMP number for short) of a graph is the minimum number of edges and/or\nvertices whose deletion leaves a resulting graph with no fractional perfect\nmatchings. A graph $G$ is said to be $f$-fault Hamiltonian if there exists a\nHamiltonian cycle in $G-F$ for any set $F$ of vertices and/or edges with\n$|F|\\leq f$. In this paper, we establish the FMP number and FSMP number of\n$(\\delta-2)$-fault Hamiltonian graphs with minimum degree $\\delta\\geq 3$. As\napplications, the FMP number and FSMP number of some well-known networks are\ndetermined.\n', 'Fractional matching preclusion for generalized augmented cubes   The \\emph{matching preclusion number} of a graph is the minimum number of\nedges whose deletion results in a graph that has neither perfect matchings nor\nalmost perfect matchings. As a generalization, Liu and Liu recently introduced\nthe concept of fractional matching preclusion number. The \\emph{fractional\nmatching preclusion number} of $G$ is the minimum number of edges whose\ndeletion leaves the resulting graph without a fractional perfect matching. The\n\\emph{fractional strong matching preclusion number} of $G$ is the minimum\nnumber of vertices and edges whose deletion leaves the resulting graph without\na fractional perfect matching. In this paper, we obtain the fractional matching\npreclusion number and the fractional strong matching preclusion number for\ngeneralized augmented cubes. In addition, all the optimal fractional strong\nmatching preclusion sets of these graphs are categorized.\n', 'Fractional matching preclusion for restricted hypercube-like graphs   The restricted hypercube-like graphs, variants of the hypercube, were\nproposed as desired interconnection networks of parallel systems. The matching\npreclusion number of a graph is the minimum number of edges whose deletion\nresults in the graph with neither perfect matchings nor almost perfect\nmatchings. The fractional perfect matching preclusion and fractional strong\nperfect matching preclusion are generalizations of the concept matching\npreclusion. In this paper, we obtain fractional matching preclusion number and\nfractional strong matching preclusion numbers of restricted hypercube-like\ngraphs, which extend some known results.\n']","[('matchings graphs', 0.6555470824241638), ('fractional matching', 0.6482230424880981), ('matching number graph', 0.6371647119522095), ('matching graph', 0.6214495301246643), ('maximal matchings', 0.5905812978744507), ('graph fractional', 0.5727567076683044), ('maximum matching', 0.5503315329551697), ('size maximum matching', 0.5479289293289185), ('perfect matchings', 0.5421020984649658), ('matching theory', 0.5264790058135986)]"
1447,1447,20,1447_gauge theories_anomaly free_gauge groups_gauge theory,"['gauge theories', 'anomaly free', 'gauge groups', 'gauge theory', 'anomalous', 'anomalies', 'anomaly equations', 'field theories', 'gauge group', 'yang mills theory']","[""Anomaly and Cobordism Constraints Beyond Grand Unification: Energy\n  Hierarchy   A recent work [2006.16996] suggests that a 4d nonperturbative global anomaly\nof mod 16 class hinting a possible new hidden gapped topological sector beyond\nthe Standard Model (SM) and Georgi-Glashow $su(5)$ Grand Unified Theory (GUT)\nwith 15n chiral Weyl fermions and a discrete $\\mathbb{Z}_{4,X}$ symmetry of\n$X=5({\\bf B- L})-4Y$. This $\\mathbb{Z}_{16}$ class global anomaly is a mixed\ngauge-gravitational anomaly between the discrete $X$ and spacetime backgrounds.\nThe new topological sector has a GUT scale high energy gap, below its low\nenergy encodes either a 4d noninvertible topological quantum field theory\n(TQFT), or a 5d short-range entangled invertible TQFT, or their combinations.\nThis hidden topological sector provides the 't Hooft anomaly matching of the\nmissing sterile right-handed neutrinos (3 generations of 16th Weyl fermions),\nand possibly also accounts for the Dark Matter sector. In the SM and $su(5)$\nGUT, the discrete $X$ can be either a global symmetry or gauged. In the\n$so(10)$ GUT, the $X$ must become gauged, the 5d TQFT becomes noninvertible and\nlong-range entangled (which can couple to dynamical gravity). In this work, we\nfurther examine the anomaly and cobordism constraints at higher energy scales\nabove the $su(5)$ GUT to $so(10)$ GUT and $so(18)$ GUT (with Spin(10) and\nSpin(18) gauge groups precisely). We also find [2006.16996]'s proposal on new\nhidden gapped topological sectors can be consistent with anomaly matching under\nthe energy/mass hierarchy. Novel ingredients along tuning the energy include\nvarious energy scales of anomaly-free symmetric mass generation (i.e.,\nKitaev-Wen mechanism), the Topological Mass/Energy Gap from anomalous symmetric\ntopological order (attachable to a 5d $\\mathbb{Z}_{4,X}$-symmetric topological\nsuperconductor), possible topological quantum phase transitions, and Ultra\nUnification that includes GUT with new topological sectors.\n"", ""Beyond Standard Models and Grand Unifications: Anomalies, Topological\n  Terms, and Dynamical Constraints via Cobordisms   We classify and characterize all invertible anomalies and all allowed\ntopological terms related to various Standard Models (SM), Grand Unified\nTheories (GUT), and Beyond Standard Model (BSM) physics. By all anomalies, we\nmean the inclusion of (1) perturbative/local anomalies captured by perturbative\nFeynman diagram loop calculations, classified by $\\mathbb{Z}$ free classes, and\n(2) non-perturbative/global anomalies, classified by finite group\n$\\mathbb{Z}_N$ torsion classes. Our work built from [arXiv:1812.11967] fuses\nthe math tools of Adams spectral sequence, Thom-Madsen-Tillmann spectra, and\nFreed-Hopkins theorem. For example, we compute bordism groups $\\Omega^{G}_d$\nand their invertible topological field theory invariants, which characterize\n$d$d topological terms and $(d-1)$d anomalies, protected by the following\nsymmetry group $G$: $Spin\\times \\frac{SU(3)\\times SU(2)\\times\nU(1)}{\\mathbb{Z}_q}$ for SM with $q=1,2,3,6$; $\\frac{Spin \\times\nSpin(n)}{\\mathbb{Z}_2^F}$ or $Spin \\times Spin(n)$ for SO(10) or SO(18) GUT as\n$n=10, 18$; $Spin \\times SU(n)$ for Georgi-Glashow SU(5) GUT as $n=5$;\n$\\frac{Spin\\times \\frac{SU(4)\\times(SU(2)\\times\nSU(2))}{\\mathbb{Z}_{q'}}}{\\mathbb{Z}_2^F}$ for Pati-Salam GUT as $q'=1,2$; and\nothers. For SM with an extra discrete symmetry, we obtain new anomaly matching\nconditions of $\\mathbb{Z}_{16}$, $\\mathbb{Z}_{4}$, and $\\mathbb{Z}_{2}$ classes\nin 4d beyond the familiar Witten anomaly. Our approach offers an alternative\nview of all anomaly matching conditions built from the lower-energy (B)SM or\nGUT, in contrast to high-energy Quantum Gravity or String Theory Landscape v.s.\nSwampland program, as bottom-up/top-down complements. Symmetries and anomalies\nprovide constraints of kinematics, we further suggest constraints of quantum\ngauge dynamics, and new predictions of possible extended defects/excitations\nplus hidden BSM non-perturbative topological sectors.\n"", ""Anomaly and Cobordism Constraints Beyond the Standard Model: Topological\n  Force   Standard lore uses local anomalies to check the kinematic consistency of\ngauge theories coupled to chiral fermions, e.g. Standard Models (SM). Based on\na systematic cobordism classification, we examine constraints from invertible\nquantum anomalies (including all perturbative local and nonperturbative global\nanomalies) for gauge theories. We also clarify the different uses of these\nanomalies: including (1) anomaly cancellations of dynamical gauge fields, (2)\n't Hooft anomaly matching conditions of background fields of global symmetries,\nand others. We apply several 4d $\\mathbb{Z}_{n}$ anomaly constraints of\n$n=16,4,2$ classes, beyond the familiar Feynman-graph perturbative $\\mathbb{Z}$\nclass local anomalies. As an application, for\n(SU(3)$\\times$SU(2)$\\times$U(1))/$\\mathbb{Z}_q$ SM (with $q=1,2,3,6$) and SU(5)\nGrand Unification with 15n chiral Weyl fermions and with a discrete baryon\nminus lepton number $X=5({\\bf B}- {\\bf L})-4Y$ preserved, we discover a new\nhidden gapped sector previously unknown to the SM and Georgi-Glashow model. The\ngapped sector at low energy contains either (1) 4d non-invertible topological\nquantum field theory (TQFT, above the energy gap with heavy fractionalized\nanyon excitations from 1d particle worldline and 2d string worldsheet,\ninaccessible directly from Dirac or Majorana mass gap of the 16th Weyl fermions\n[i.e., right-handed neutrinos], but accessible via a topological quantum phase\ntransition), or (2) 5d invertible TQFT in extra dimensions. Above a higher\nenergy scale, the discrete $X$ becomes dynamically gauged, the entangled\nUniverse in 4d and 5d is mediated by Topological Force. Our model potentially\nresolves puzzles, surmounting sterile neutrinos and dark matter, in fundamental\nphysics.\n""]","[('gauge theories', 0.5562478303909302), ('anomaly free', 0.5100185871124268), ('gauge groups', 0.4985610246658325), ('gauge theory', 0.48145630955696106), ('anomalous', 0.480266273021698), ('anomalies', 0.47191545367240906), ('anomaly equations', 0.46227455139160156), ('field theories', 0.456136554479599), ('gauge group', 0.4510755240917206), ('yang mills theory', 0.44976943731307983)]"
1448,1448,20,1448_geometric topological_configurations points lines_pentagonal_symmetric configurations,"['geometric topological', 'configurations points lines', 'pentagonal', 'symmetric configurations', 'topological combinatorial', 'geometries', 'configurations combinatorial', 'plane arrangements', 'geometric', 'points lines projective']","['On topological and geometric $(19_4)$ configurations   An $(n_k)$ configuration is a set of $n$ points and $n$ lines such that each\npoint lies on $k$ lines while each line contains $k$ points. The configuration\nis geometric, topological, or combinatorial depending on whether lines are\nconsidered to be straight lines, pseudolines, or just combinatorial lines. The\nexistence and enumeration of $(n_k)$ configurations for a given $k$ has been\nsubject to active research. A current front of research concerns geometric\n$(n_4)$ configurations: it is now known that geometric $(n_4)$ configurations\nexist for all $n \\ge 18$, apart from sporadic exceptional cases. In this paper,\nwe settle by computational techniques the first open case of $(19_4)$\nconfigurations: we obtain all topological $(19_4)$ configurations among which\nnone are geometrically realizable.\n', 'Generalized pentagonal geometries -- II   A generalized pentagonal geometry PENT($k$,$r$,$w$) is a partial linear\nspace, where every line is incident with $k$ points, every point is incident\nwith $r$ lines, and for each point, $x$, the set of points not collinear with\n$x$ forms the point set of a Steiner system $S(2,k,w)$ whose blocks are lines\nof the geometry. If $w = k$, the structure is called a pentagonal geometry and\ndenoted by PENT($k$,$r$). The deficiency graph of a PENT($k$,$r$,$w$) has as\nits vertices the points of the geometry, and there is an edge between $x$ and\n$y$ precisely when $x$ and $y$ are not collinear.\n  Our primary objective is to investigate generalized pentagonal geometries\nPENT($k$,$r$,$w$) where the deficiency graph has girth 4. We describe some\nconstruction methods, including a procedure that preserves deficiency graph\nconnectedness, and we prove a number of theorems regarding the existence\nspectra for $k = 3$ and various values of $w$. In addition, we present some new\nPENT(4,$r$) (including PENT(4,25)) and PENT(5,$r$) with connected deficiency\ngraphs. Consequently, we prove that there exist pentagonal geometries\nPENT($k$,$r$) with deficiency graphs of girth at least 5 for $r \\ge 13$, $r$\ncongruent to 1 modulo 4 when $k = 4$, and for $r \\ge 200000$, $r$ congruent to\n0 or 1 modulo 5 when $k = 5$. We conclude with a discussion of appropriately\ndefined identifying codes for pentagonal geometries.\n', 'Pentagonal geometries with block sizes 3, 4 and 5   A pentagonal geometry PENT($k$, $r$) is a partial linear space, where every\nline, or block, is incident with $k$ points, every point is incident with $r$\nlines, and for each point $x$, there is a line incident with precisely those\npoints that are not collinear with $x$. An opposite line pair in a pentagonal\ngeometry consists of two parallel lines such that each point on one of the\nlines is not collinear with precisely those points on the other line.\n  We give a direct construction for an infinite sequence of pentagonal\ngeometries with block size 3 and connected deficiency graphs. Also we present\n39 new pentagonal geometries with block size 4 and five with block size 5, all\nwith connected deficiency graphs. Consequentially we determine the existence\nspectrum up to a few possible exceptions for PENT(4, $r$) that do not contain\nopposite line pairs and for PENT(4, $r$) with one opposite line pair. More\ngenerally, given $j$ we show that there exists a PENT(4, $r$) with $j$ opposite\nline pairs for all sufficiently large admissible $r$. Using some new group\ndivisible designs with block size 5 (including types $2^{35}$, $2^{71}$ and\n$10^{23}$) we significantly extend the known existence spectrum for PENT(5,\n$r$).\n']","[('geometric topological', 0.5348631143569946), ('configurations points lines', 0.5161677598953247), ('pentagonal', 0.5101994872093201), ('symmetric configurations', 0.5035581588745117), ('topological combinatorial', 0.4914538562297821), ('geometries', 0.4775448143482208), ('configurations combinatorial', 0.47516918182373047), ('plane arrangements', 0.46923911571502686), ('geometric', 0.46607017517089844), ('points lines projective', 0.4651116132736206)]"
1449,1449,20,1449_power series solutions_series solutions_generalized power series_formal power series,"['power series solutions', 'series solutions', 'generalized power series', 'formal power series', 'power series coefficients', 'difference equations', 'solutions difference equations', 'series coefficients', 'differential difference equations', 'analytic solutions']","['On the convergence of generalized power series solutions of\n  $q$-difference equations   A sufficient condition for the convergence of a generalized formal power\nseries solution to an algebraic $q$-difference equation is provided. The main\nresult leans on a geometric property related to the semi-group of (complex)\npower exponents of such a series. This property corresponds to the situation in\nwhich the small divisors phenomenon does not arise. Some examples illustrating\nthe cases where the obtained sufficient condition can be or cannot be applied\nare also depicted.\n', 'On the summability and convergence of formal solutions of linear\n  $q$-difference-differential equations with constant coefficients   We consider the Cauchy problem for homogeneous linear\n$q$-difference-differential equations with constant coefficients. We\ncharacterise convergent, $k$-summable and multisummable formal power series\nsolutions in terms of analytic continuation properties and growth estimates of\nthe Cauchy data. We also introduce and characterise sequences preserving\nsummability, which make a very useful tool, especially in the context of moment\ndifferential equations.\n', 'Small divisors in the problem of the convergence of generalized power\n  series solutions of $q$-difference equations   The question of the convergence of generalized formal power series (with\ncomplex power exponents) solutions of $q$-difference equations is studied in\nthe situation where the small divisors phenomenon arises; a sufficient\ncondition of convergence generalizing corresponding conditions for classical\npower series solutions is obtained.\n']","[('power series solutions', 0.625723659992218), ('series solutions', 0.5800097584724426), ('generalized power series', 0.5784747004508972), ('formal power series', 0.5407487750053406), ('power series coefficients', 0.5122782588005066), ('difference equations', 0.4727132320404053), ('solutions difference equations', 0.4721738398075104), ('series coefficients', 0.45905202627182007), ('differential difference equations', 0.4544549584388733), ('analytic solutions', 0.44613340497016907)]"
1450,1450,20,1450_sparse random matrices_random matrices_random sparse_symmetric random matrices,"['sparse random matrices', 'random matrices', 'random sparse', 'symmetric random matrices', 'sparse random', 'linear spectral statistics', 'stochastic matrices', 'spectral statistics', 'matrices sparse', 'sparse matrices']","[""Spectral Theory of Sparse Non-Hermitian Random Matrices   Sparse non-Hermitian random matrices arise in the study of disordered\nphysical systems with asymmetric local interactions, and have applications\nranging from neural networks to ecosystem dynamics. The spectral\ncharacteristics of these matrices provide crucial information on system\nstability and susceptibility, however, their study is greatly complicated by\nthe twin challenges of a lack of symmetry and a sparse interaction structure.\nIn this review we provide a concise and systematic introduction to the main\ntools and results in this field. We show how the spectra of sparse\nnon-Hermitian matrices can be computed via an analogy with infinite dimensional\noperators obeying certain recursion relations. With reference to three\nillustrative examples -- adjacency matrices of regular oriented graphs,\nadjacency matrices of oriented Erd\\H{o}s-R\\'{e}nyi graphs, and adjacency\nmatrices of weighted oriented Erd\\H{o}s-R\\'{e}nyi graphs -- we demonstrate the\nuse of these methods to obtain both analytic and numerical results for the\nspectrum, the spectral distribution, the location of outlier eigenvalues, and\nthe statistical properties of eigenvectors.\n"", ""Eigenvalue spectral properties of sparse random matrices obeying Dale's\n  law   This paper examines the relationship between sparse random network\narchitectures and neural network stability by examining the eigenvalue spectral\ndistribution. Specifically, we generalise classical eigenspectral results to\nsparse connectivity matrices obeying Dale's law: neurons function as either\nexcitatory (E) or inhibitory (I). By defining sparsity as the probability that\na neutron is connected to another neutron, we give explicit formulae that shows\nhow sparsity interacts with the E/I population statistics to scale key features\nof the eigenspectrum, in both the balanced and unbalanced cases. Our results\nshow that the eigenspectral outlier is linearly scaled by sparsity, but the\neigenspectral radius and density now depend on a nonlinear interaction between\nsparsity, the E/I population means and variances. Contrary to previous results,\nwe demonstrate that a non-uniform eigenspectral density results if any of the\nE/I population statistics differ, not just the E/I population variances. We\nalso find that 'local' eigenvalue-outliers are present for sparse random\nmatrices obeying Dale's law, and demonstrate that these eigenvalues can be\ncontrolled by a modified zero row-sum constraint for the balanced case,\nhowever, they persist in the unbalanced case. We examine all levels of\nconnection (sparsity), and distributed E/I population weights, to describe a\ngeneral class of sparse connectivity structures which unifies all the previous\nresults as special cases of our framework. Sparsity and Dale's law are both\nfundamental anatomical properties of biological neural networks. We generalise\ntheir combined effects on the eigenspectrum of random neural networks, thereby\ngaining insight into network stability, state transitions and the\nstructure-function relationship.\n"", 'Sparse Random Block Matrices : universality   We study ensembles of sparse random block matrices generated from the\nadjacency matrix of a Erd\\""os-Renyi random graph with $N$ vertices of average\ndegree $Z$, inserting a real symmetric $d \\times d$ random block at each\nnon-vanishing entry.\n  We consider some ensembles of random block matrices with rank $r < d$ and\nwith maximal rank, $r=d$. The spectral moments of the sparse random block\nmatrix are evaluated for $N \\to \\infty$, $d$ finite or infinite, and several\nprobability distributions for the blocks (e.g. fixed trace, bounded trace and\nGaussian).\n  Because of the concentration of the probability measure in the $d \\to \\infty$\nlimit, the spectral moments are independent of the probability measure of the\nblocks (with mild assumptions of isotropy, smoothness and sub-gaussian tails).\n  The Effective Medium Approximation is the limiting spectral density of the\nsparse random block ensembles with finite rank. Analogous classes of\nuniversality hold for the Laplacian sparse block ensemble. The same limiting\ndistributions are obtained using random regular graphs instead of Erd\\""os-Renyi\ngraphs.\n']","[('sparse random matrices', 0.7648037075996399), ('random matrices', 0.6550391912460327), ('random sparse', 0.6216965913772583), ('symmetric random matrices', 0.613435685634613), ('sparse random', 0.5978458523750305), ('linear spectral statistics', 0.5899673104286194), ('stochastic matrices', 0.5835467576980591), ('spectral statistics', 0.5821077227592468), ('matrices sparse', 0.5747021436691284), ('sparse matrices', 0.5721279978752136)]"
1451,1451,20,1451_infinite dimensional systems_input state stability_stability infinite_infinite dimensional system,"['infinite dimensional systems', 'input state stability', 'stability infinite', 'infinite dimensional system', 'lyapunov functionals', 'input output stability', 'input state stable', 'lyapunov functions', 'stability theory', 'lyapunov functional']","['Semi-uniform Input-to-state Stability of Infinite-dimensional Systems   We introduce the notions of semi-uniform input-to-state stability and its\nsubclass, polynomial input-to-state stability, for infinite-dimensional\nsystems. We establish a characterization of semi-uniform input-to-state\nstability based on attractivity properties as in the uniform case. Sufficient\nconditions for linear systems to be polynomially input-to-state stable are\nprovided, which restrict the range of the input operator depending on the rate\nof polynomial decay of the product of the semigroup and the resolvent of its\ngenerator. We also show that a class of bilinear systems are polynomially\nintegral input-to-state stable under a certain smoothness assumption on\nnonlinear operators.\n', 'Input-to-state stability of distributed parameter systems   Input-to-state stability (ISS) allows estimating the impact of inputs and\ninitial conditions on both the intermediate values and the asymptotic bound on\nthe solutions. ISS has unified the input-output and Lyapunov stability theories\nand is a crucial property in the stability theory of control systems as well as\nfor many applications whose dynamics depend on parameters, unknown\nperturbations, or other inputs. In this habilitation thesis, we provide a broad\npicture of infinite-dimensional input-to-state stability theory.\n', 'Input-to-state stability of infinite-dimensional systems: recent results\n  and open questions   In a pedagogical but exhaustive manner, this survey reviews the main results\non input-to-state stability (ISS) for infinite-dimensional systems. This\nproperty allows estimating the impact of inputs and initial conditions on both\nthe intermediate values and the asymptotic bound on the solutions. ISS has\nunified the input-output and Lyapunov stability theories and is a crucial\nproperty in the stability theory of control systems as well as for many\napplications whose dynamics depend on parameters, unknown perturbations, or\nother inputs. In this paper, starting from classic results for nonlinear\nordinary differential equations, we motivate the study of ISS property for\ndistributed parameter systems. Then fundamental properties are given, as an ISS\nsuperposition theorem and characterizations of (global and local) ISS in terms\nof Lyapunov functions. We explain in detail the functional-analytic approach to\nISS theory of linear systems with unbounded input operators, with special\nattention devoted to ISS theory of boundary control systems. The Lyapunov\nmethod is shown to be very useful for both linear and nonlinear models,\nincluding parabolic and hyperbolic partial differential equations. Next, we\nshow the efficiency of the ISS framework to study the stability of large-scale\nnetworks, coupled either via the boundary or via the interior of the spatial\ndomain. ISS methodology allows reducing the stability analysis of complex\nnetworks, by considering the stability properties of its components and the\ninterconnection structure between the subsystems. An extra section is devoted\nto ISS theory of time-delay systems with the emphasis on techniques, which are\nparticularly suited for this class of systems. Finally, numerous applications\nare considered in this survey, where ISS properties play a crucial role in\ntheir study. This survey suggests many open problems throughout the paper.\n']","[('infinite dimensional systems', 0.6117716431617737), ('input state stability', 0.5989891886711121), ('stability infinite', 0.5917052030563354), ('infinite dimensional system', 0.5684316158294678), ('lyapunov functionals', 0.5471867322921753), ('input output stability', 0.5318834781646729), ('input state stable', 0.5180031061172485), ('lyapunov functions', 0.5145158171653748), ('stability theory', 0.5025824308395386), ('lyapunov functional', 0.5009993314743042)]"
1452,1452,20,1452_sobolev embeddings_sobolev type embeddings_sobolev embedding_sobolev spaces,"['sobolev embeddings', 'sobolev type embeddings', 'sobolev embedding', 'sobolev spaces', 'besov spaces', 'sobolev type spaces', 'sobolev spaces setting', 'compactness sobolev', 'compact sobolev', 'optimal sobolev']","['Different degrees of non-compactness for optimal Sobolev embeddings   The structure of non-compactness of optimal Sobolev embeddings of $m$-th\norder into the class of Lebesgue spaces and into that of all\nrearrangement-invariant function spaces is quantitatively studied. Sharp\ntwo-sided estimates of Bernstein numbers of such embeddings are obtained. It is\nshown that, whereas the optimal Sobolev embedding within the class of Lebesgue\nspaces is finitely strictly singular, the optimal Sobolev embedding in the\nclass of all rearrangement-invariant function spaces is not even strictly\nsingular.\n', ""Non-strict singularity of optimal Sobolev embeddings We investigate the operator-theoretic property of strict singularity for optimal Sobolev embeddings within the general framework of rearrangement-invariant function spaces (r.i. spaces).\n  More specifically, we focus on studying the ``quality'' of non-compactness for optimal Sobolev embeddings $V^m_0X(\\Omega)\\to Y_X(\\Omega)$, where $X$ is a given r.i. space and $Y_X$ is the corresponding optimal target r.i. space (i.e., the smallest among all r.i. spaces).\n  For the class of sub-limiting norms (i.e., the norms whose fundamental function satisfies $\\varphi_{Y_X}(t)\\approx t^{-m/n}\\varphi_X(t)$ as $t\\to0^+$), we construct suitable spike-function sequences that establish a general framework for proving non-strict singularity of optimal (and thus non-compact) sublimiting Sobolev embeddings.\n  As an application, we show that optimal sublimiting Sobolev embeddings are not strictly singular in a rather large subclass of r.i. spaces, namely weighted Lambda spaces $X=\\Lambda^q_w$, $q\\in[1, \\infty)$. Except for the endpoint case $X=L^{n/m,1}$, our spike-function construction enables us to construct a subspace of $V^m_0X$ that is isomorphic to $\\ell_q$, which we then leverage to prove the non-strict singularity of the corresponding optimal Sobolev embedding."", 'Optimal Embeddings for Triebel-Lizorkin and Besov Spaces on Quasi-Metric\n  Measure Spaces   In this article, via certain lower bound conditions on the measures under\nconsideration, the authors fully characterize the Sobolev embeddings for the\nscales of Haj{\\l}asz-Triebel-Lizorkin and Haj{\\l}asz-Besov spaces in the\ngeneral context of quasi-metric measure spaces for an optimal range of the\nsmoothness parameter $s$. An interesting facet of this work is how the range of\n$s$ for which the above characterizations of these embeddings hold true is\nintimately linked (in a quantitative manner) to the geometric makeup of the\nunderlying space. Moreover, although stated for Haj{\\l}asz-Triebel-Lizorkin and\nHaj{\\l}asz-Besov spaces in the context of quasi-metric spaces, the main results\nin this article improve known work even for Sobolev spaces in the metric\nsetting.\n']","[('sobolev embeddings', 0.717245876789093), ('sobolev type embeddings', 0.683485746383667), ('sobolev embedding', 0.6823362112045288), ('sobolev spaces', 0.6507717967033386), ('besov spaces', 0.6467307209968567), ('sobolev type spaces', 0.6461789011955261), ('sobolev spaces setting', 0.6151050329208374), ('compactness sobolev', 0.6045374274253845), ('compact sobolev', 0.5852800011634827), ('optimal sobolev', 0.5507837533950806)]"
1453,1453,20,1453_higman thompson groups_thompson groups_thompson group_automorphism group,"['higman thompson groups', 'thompson groups', 'thompson group', 'automorphism group', 'baumslag solitar groups', 'groups finitely', 'finitely presented groups', 'finitely generated group', 'solitar groups', 'groups g_']","['Stabilizers in Higman-Thompson groups   We investigate stabilizers of finite sets of rational points in Cantor space\nfor the Higman-Thompson groups $V_{n,r}$. We prove that the pointwise\nstabilizer is an iterated ascending HNN extension of $V_{n,q}$ for any $q\\geq\n1$. We also prove that the commutator subgroup of the pointwise stabilizer is\nsimple, and we compute the abelianization. Finally, for each $n$ we classify\nsuch pointwise stabilizers up to isomorphism.\n', 'Automorphisms of shift spaces and the Higman--Thompson groups: the\n  one-sided case   Let $1 \\le r < n$ be integers. We give a proof that the group\n$\\mathop{\\mathrm{Aut}}({X_{n}^{\\mathbb{N}}, \\sigma_{n}})$ of automorphisms of\nthe one-sided shift on $n$ letters embeds naturally as a subgroup\n$\\mathcal{H}_{n}$ of the outer automorphism group\n$\\mathop{\\mathrm{Out}}({G_{n,r}})$ of the Higman-Thompson group $G_{n,r}$. From\nthis, we can represent the elements of\n$\\mathop{\\mathrm{Aut}}({X_{n}^{\\mathbb{N}}, \\sigma_{n}})$ by finite state\nnon-initial transducers admitting a very strong synchronizing condition.\n  Let $H \\in \\mathcal{H}_{n}$ and write $|H|$ for the number of states of the\nminimal transducer representing $H$. We show that $H$ can be written as a\nproduct of at most $|H|$ torsion elements. This result strengthens a similar\nresult of Boyle, Franks and Kitchens, where the decomposition involves more\ncomplex torsion elements and also does not support practical \\textit{a priori}\nestimates of the length of the resulting product.\n  We also explore the number of foldings of de Bruijn graphs and give a\ncounting result for these for word length $2$ and alphabet size $n$.\n  Finally, we offer new proofs of some known results about\n$\\mathop{\\mathrm{Aut}}({X_{n}^{\\mathbb{N}}, \\sigma_{n}})$.\n', 'Automorphisms of the two-sided shift and the Higman--Thompson groups\n  III: extensions   We aim to interpret important constructions in the theory of automorphisms of\nthe shift dynamical system in terms of subgroups $\\mathcal{L}_{n,r}$ of the\nouter-automorphism groups $\\mathcal{O}_{n,r}$ of the Higman--Thompson group\n$G_{n,r}$, and to extend results and techniques in\n$\\operatorname{Aut}(X_n^{\\mathbb{Z}}, \\sigma_{n})$ to the groups of\nautomorphisms $\\operatorname{Aut}(G_{n,r})$ and outerautomrphisms of the\nHigman--Thompson group $G_{n,r}$.\n  Our mains results are a concrete realisation of the ""inert subgroup"",\nimportant subgroup in the study of automorphism groups of shift spaces, as a\nsubgroup $\\mathcal{K}_{n}$ of $\\mathcal{L}_{n,n-1}$.\n  Using this realisation, we show that the $\\operatorname{Aut}(G_{n,r})$\ncontains an isomorphic copy of $\\operatorname{Aut}(X_{m}^{\\mathbb{Z}},\n\\sigma_{m})$ for all $m \\ge 2$.\n  A survey of the literature then yields that $\\operatorname{Aut}(G_{n,r})$\ncontains isomorphic copies of finite groups, finitely generated abelian groups,\nfree groups, free products of finite groups, fundamental groups of 2-manifolds,\ngraph groups and countable locally finite residually finite groups to name a\nfew.\n  We extend a result for $\\operatorname{Aut}(X_n^{\\mathbb{Z}}, \\sigma_{n})$ to\nthe group $\\mathcal{O}_{n,n-1}$. The homeomorphism\n$\\overleftarrow{\\phantom{a}}$ of $X_n^{\\mathbb{Z}}$ which maps a sequence\n$(x_i)_{i \\in \\mathbb{Z}}$ to the sequence $(y_{i})_{i \\in \\mathbb{Z}}$ defined\nsuch that $y_{i} = x_{-i}$ induces an automorphism\n$\\overleftarrow{\\mathfrak{r}}$ of $\\operatorname{Aut}(X_n^{\\mathbb{Z}},\n\\sigma_{n})$, and consequently, an automorphism of $\\mathcal{L}_{n}$. We extend\nthe automorphism $\\overleftarrow{{\\mathfrak{r}}}$ to the group\n$\\mathcal{O}_{n,n-1}$.\n  In a forthcoming article, we demonstrate that the group $\\mathcal{O}_{n}$ is\nisomorphic to the mapping class group of the full two-sided shift over $n$\nletters.\n']","[('higman thompson groups', 0.6197371482849121), ('thompson groups', 0.5823228359222412), ('thompson group', 0.5168271064758301), ('automorphism group', 0.4735119640827179), ('baumslag solitar groups', 0.4473103880882263), ('groups finitely', 0.44491010904312134), ('finitely presented groups', 0.4333895444869995), ('finitely generated group', 0.42457887530326843), ('solitar groups', 0.42207071185112), ('groups g_', 0.4212804436683655)]"
1454,1454,20,1454_quantum algorithms_quantum computation_efficient quantum_quantum phase estimation,"['quantum algorithms', 'quantum computation', 'efficient quantum', 'quantum phase estimation', 'quantum computing', 'signal processing quantum', 'polynomials quantum', 'processing quantum', 'quantum computers', 'quantum linear']","[""Robust iterative method for symmetric quantum signal processing in all\n  parameter regimes   This paper addresses the problem of solving nonlinear systems in the context\nof symmetric quantum signal processing (QSP), a powerful technique for\nimplementing matrix functions on quantum computers. Symmetric QSP focuses on\nrepresenting target polynomials as products of matrices in SU(2) that possess\nsymmetry properties. We present a novel Newton's method tailored for\nefficiently solving the nonlinear system involved in determining the phase\nfactors within the symmetric QSP framework. Our method demonstrates rapid and\nrobust convergence in all parameter regimes, including the challenging scenario\nwith ill-conditioned Jacobian matrices, using standard double precision\narithmetic operations. For instance, solving symmetric QSP for a highly\noscillatory target function $\\alpha \\cos(1000 x)$ (polynomial degree $\\approx\n1433$) takes $6$ iterations to converge to machine precision when $\\alpha=0.9$,\nand the number of iterations only increases to $18$ iterations when\n$\\alpha=1-10^{-9}$ with a highly ill-conditioned Jacobian matrix. Leveraging\nthe matrix product states the structure of symmetric QSP, the computation of\nthe Jacobian matrix incurs a computational cost comparable to a single function\nevaluation. Moreover, we introduce a reformulation of symmetric QSP using\nreal-number arithmetics, further enhancing the method's efficiency. Extensive\nnumerical tests validate the effectiveness and robustness of our approach,\nwhich has been implemented in the QSPPACK software package.\n"", 'Infinite quantum signal processing   Quantum signal processing (QSP) represents a real scalar polynomial of degree\n$d$ using a product of unitary matrices of size $2\\times 2$, parameterized by\n$(d+1)$ real numbers called the phase factors. This innovative representation\nof polynomials has a wide range of applications in quantum computation. When\nthe polynomial of interest is obtained by truncating an infinite polynomial\nseries, a natural question is whether the phase factors have a well defined\nlimit as the degree $d\\to \\infty$. While the phase factors are generally not\nunique, we find that there exists a consistent choice of parameterization so\nthat the limit is well defined in the $\\ell^1$ space. This generalization of\nQSP, called the infinite quantum signal processing, can be used to represent a\nlarge class of non-polynomial functions. Our analysis reveals a surprising\nconnection between the regularity of the target function and the decay\nproperties of the phase factors. Our analysis also inspires a very simple and\nefficient algorithm to approximately compute the phase factors in the $\\ell^1$\nspace. The algorithm uses only double precision arithmetic operations, and\nprovably converges when the $\\ell^1$ norm of the Chebyshev coefficients of the\ntarget function is upper bounded by a constant that is independent of $d$. This\nis also the first numerically stable algorithm for finding phase factors with\nprovable performance guarantees in the limit $d\\to \\infty$.\n', 'Efficient phase-factor evaluation in quantum signal processing   Quantum signal processing (QSP) is a powerful quantum algorithm to exactly\nimplement matrix polynomials on quantum computers. Asymptotic analysis of\nquantum algorithms based on QSP has shown that asymptotically optimal results\ncan in principle be obtained for a range of tasks, such as Hamiltonian\nsimulation and the quantum linear system problem. A further benefit of QSP is\nthat it uses a minimal number of ancilla qubits, which facilitates its\nimplementation on near-to-intermediate term quantum architectures. However,\nthere is so far no classically stable algorithm allowing computation of the\nphase factors that are needed to build QSP circuits. Existing methods require\nthe usage of variable precision arithmetic and can only be applied to\npolynomials of relatively low degree. We present here an optimization based\nmethod that can accurately compute the phase factors using standard double\nprecision arithmetic operations. We demonstrate the performance of this\napproach with applications to Hamiltonian simulation, eigenvalue filtering, and\nthe quantum linear system problems. Our numerical results show that the\noptimization algorithm can find phase factors to accurately approximate\npolynomials of degree larger than $10,000$ with error below $10^{-12}$.\n']","[('quantum algorithms', 0.6732165813446045), ('quantum computation', 0.6448862552642822), ('efficient quantum', 0.6192565560340881), ('quantum phase estimation', 0.5956704616546631), ('quantum computing', 0.5889472365379333), ('signal processing quantum', 0.5485765337944031), ('polynomials quantum', 0.5455237627029419), ('processing quantum', 0.5418628454208374), ('quantum computers', 0.5406395196914673), ('quantum linear', 0.5201172232627869)]"
1455,1455,20,1455_incidence algebras_incidence algebra_finite poset_algebras let finite,"['incidence algebras', 'incidence algebra', 'finite poset', 'algebras let finite', 'unital ring', 'arbitrary poset', 'algebra locally', 'induced poset', 'primitive idempotents', 'automorphisms']","['Invertibility preservers of finitary incidence algebras   Let $X$ be an arbitrary poset and $K$ an arbitrary field. We describe linear\nunital invertibility preservers of the finitary incidence algebra $FI(X,K)$ in\nterms of certain maps of the power set algebra $\\mathcal{P}(X)$ and linear maps\n$FI(X,K)\\to J(FI(X,K))$.\n', 'Anti-isomorphisms and involutions on the idealization of the incidence\n  space over the finitary incidence algebra   Let $K$ be a field and $X$ a partially ordered set (poset). Let $FI(X,K)$ and\n$I(X,K)$ be the finitary incidence algebra and the incidence space of $X$ over\n$K$, respectively, and let $D(X,K)=FI(X,K)(+)I(X,K)$ be the idealization of the\n$FI(X,K)$-bimodule $I(X,K)$. In the first part of this paper, we show that\n$D(X,K)$ has an anti-automorphism (involution) if and only if $X$ has an\nanti-automorphism (involution). We also present a characterization of the\nanti-automorphisms and involutions on $D(X,K)$. In the second part, we obtain\nthe classification of involutions on $D(X,K)$ to the case when characteristic\nof $K$ is different from 2 and $X$ is a connected poset such that every\nmultiplicative automorphism of $FI(X,K)$ is inner and every derivation from\n$FI(X,K)$ to $I(X,K)$ is inner (in particular, when $X$ has an element that is\ncomparable with all its elements).\n', 'Higher Derivations of Finitary Incidence Algebras   Let $P$ be a partially ordered set, $R$ a commutative unital ring and\n$FI(P,R)$ the finitary incidence algebra of $P$ over $R$. We prove that each\n$R$-linear higher derivation of $FI(P,R)$ decomposes into the product of an\ninner higher derivation of $FI(P,R)$ and the higher derivation of $FI(P,R)$\ninduced by a higher transitive map on the set of segments of $P$.\n']","[('incidence algebras', 0.699159562587738), ('incidence algebra', 0.6260624527931213), ('finite poset', 0.413186639547348), ('algebras let finite', 0.4033689796924591), ('unital ring', 0.39869341254234314), ('arbitrary poset', 0.39014187455177307), ('algebra locally', 0.3788241744041443), ('induced poset', 0.3776853382587433), ('primitive idempotents', 0.3659723997116089), ('automorphisms', 0.3646371364593506)]"
1456,1456,20,1456_approximations pi_formula pi_formulas pi_pi approx,"['approximations pi', 'formula pi', 'formulas pi', 'pi approx', 'approx pi', 'number pi', 'pi obtained', 'successive approximations', 'pi', 'representation pi']","['A new form of the Machin-like formula for pi by iteration with\n  increasing integers   We present a new form of the Machin-like formula for $\\pi$ that can be\ngenerated by using iteration. This form of the Machin-like formula may be\npromising for computation of the constant $\\pi$ due to rapidly increasing\nintegers at each step of the iteration. The computational test we performed\nshows that, with an integer $k \\ge 17$, the Lehmer measure remains small and\npractically does not increase after $18$ steps of iteration.\n', ""Unconditional applicability of Lehmer's measure to the two-term\n  Machin-like formula for $\\pi$   Lehmer defined a measure $$\n\\mu=\\sum\\limits_{j=1}^J\\frac{1}{\\log_{10}\\left(\\left|\\beta_j\\right|\\right)}, $$\nwhere the $\\beta_j$ may be either integers or rational numbers in a Machin-like\nformula for $\\pi$. When the $\\beta_j$ are integers, Lehmer's measure can be\nused to determine the computational efficiency of the given Machin-like formula\nfor $\\pi$. However, because the computations are complicated, it is unclear if\nLehmer's measure applies when one or more of the $\\beta_j$ are rational. In\nthis article, we develop a new algorithm for a two-term Machin-like formula for\n$\\pi$ as an example of the unconditional applicability of Lehmer's measure.\nThis approach does not involve any irrational numbers and may allow calculating\n$\\pi$ rapidly by the Newton$-$Raphson iteration method for the tangent\nfunction.\n"", 'A method to reduce the Lehmer measure in a multi-term Machin-like\n  formula for $\\pi$   Previously we have proposed a new method of transforming quotients into\ninteger reciprocals in the Machin-like formulas for $\\pi$. As a further\ndevelopment, here we show how to generate a multi-term Machin-like formula for\n$\\pi$ with a reduced Lehmer measure. The Mathematica codes validating these\nresults are presented.\n']","[('approximations pi', 0.6026300191879272), ('formula pi', 0.5448689460754395), ('formulas pi', 0.5416391491889954), ('pi approx', 0.5316431522369385), ('approx pi', 0.5127728581428528), ('number pi', 0.5022668838500977), ('pi obtained', 0.44465917348861694), ('successive approximations', 0.41902294754981995), ('pi', 0.4146884083747864), ('representation pi', 0.4143748879432678)]"
1457,1457,20,1457_solutions kirchhoff type_solutions kirchhoff_kirchhoff type_degenerate kirchhoff,"['solutions kirchhoff type', 'solutions kirchhoff', 'kirchhoff type', 'degenerate kirchhoff', 'existence weak solutions', 'kirchhoff problems', 'weak solutions', 'neumann boundary conditions', 'ekeland variational principle', 'variational principle']","['The Neumann problem for a class of generalized Kirchhoff-type potential\n  systems   In this paper, we are concerned with the Neumann problem for a class of\nquasilinear stationary Kirchhoff-type potential systems, which involves general\nvariable exponents elliptic operators with critical growth and real positive\nparameter. We show that the problem has at least one solution, which converges\nto zero in the norm of the space as the real positive parameter tends to\ninfinity, via combining the truncation technique, variational method, and the\nconcentration-compactness principle for variable exponent under suitable\nassumptions on the nonlinearities.\n', 'Multiple Solutions for Nonlinear Generalized-Kirchhoff type potential\n  Systems in Unbounded Domains   In this paper, we consider a class of quasilinear stationary Kirchhoff type\npotential systems in unbounded domains, which involves a general variable\nexponent elliptic operator. Under some suitable conditions on the\nnonlinearities, we establish existence of at least three weak solutions for the\nproblem. The proof of our main result uses variational methods and the critical\ntheorem of Bonanno and Marano.\n', 'Generalized critical Kirchhoff-type potential systems With Neumann\n  Boundary conditions   In this paper, we consider a class of quasilinear stationary Kirchhoff type\npotential systems with Neumann Boundary conditions, which involves a general\nvariable exponent elliptic operator with critical growth. Under some suitable\nconditions on the nonlinearities, we establish existence and multiplicity of\nsolutions for the problem by using the concentration-compactness principle of\nLions for variable exponents found in [5, 7] and the Mountain Pass Theorem\nwithout the Palais-Smale condition given in [43].\n']","[('solutions kirchhoff type', 0.6643953919410706), ('solutions kirchhoff', 0.5959482192993164), ('kirchhoff type', 0.5421432852745056), ('degenerate kirchhoff', 0.5271163582801819), ('existence weak solutions', 0.5075471997261047), ('kirchhoff problems', 0.5050048828125), ('weak solutions', 0.5019975304603577), ('neumann boundary conditions', 0.4918202757835388), ('ekeland variational principle', 0.48472124338150024), ('variational principle', 0.4612121284008026)]"
1458,1458,20,1458_gradient estimates solutions_gradient estimates positive_local gradient estimates_elliptic gradient,"['gradient estimates solutions', 'gradient estimates positive', 'local gradient estimates', 'elliptic gradient', 'estimates positive solutions', 'gradient estimates', 'solutions nonlinear elliptic', 'ricci curvature bounded', 'ricci curvature nonnegative', 'nonlinear elliptic']","['Local and Global Log-Gradient estimates of solutions to\n  $\\Delta_pv+bv^q+cv^r =0$ on manifolds and applications   In this paper, we employ the Nash-Moser iteration technique to study local\nand global properties of positive solutions to the equation\n$$\\Delta_pv+bv^q+cv^r =0$$ on complete Riemannian manifolds with Ricci\ncurvature bounded from below, where $b, c\\in\\mathbb R$, $p>1$, and $q\\leq r$\nare some real constants. Assuming certain conditions on $b,\\, c,\\, p,\\, q$ and\n$r$, we derive succinct Cheng-Yau type gradient estimates for positive\nsolutions, which is of sharp form. These gradient estimates allow us to obtain\nsome Liouville-type theorems and Harnack inequalities. Our Liouville-type\nresults are novel even in Euclidean spaces. Based on the local gradient\nestimates and a trick of Sung and Wang, we also obtain the global gradient\nestimates for such solutions. As applications we show the uniqueness of\npositive solutions to some generalized Allen-Cahn equation and Fisher-KPP\nequation.\n', ""Gradient estimates and Liouville theorems for Lichnerowicz-type equation\n  on Riemannian manifolds   In this paper we consider the gradient estimates on positive solutions to the\nfollowing elliptic (Lichnerowicz) equation defined on a complete Riemannian\nmanifold $(M,\\,g)$: $$\\Delta v + \\mu v + a v^{p+1} +b v^{-q+1} =0,$$ where\n$p\\geq-1$, $q\\geq1$, $\\mu$, $a$ and $b$ are real constants.\n  In the case $\\mu\\geq0$ and $b\\geq0$ or $\\mu<0$ , $a>0$ and $b>0$ ($\\mu$ has a\nlower bound), we employ the Nash-Moser iteration technique to obtain some\nrefined gradient estimates of the solutions to the above equation, if $(M,\\,g)$\nsatisfies $Ric \\geq -(n-1)\\kappa$ , where $n\\geq3$ is the dimension of $M$ and\n$\\kappa$ is a nonnegative constant, and $\\mu$ , $a$ , $b$ , $p$ and $q$ satisfy\nsome technique conditions. By the obtained gradient estimates we also derive\nsome Liouville type theorems for the above equation under some suitable\ngeometric and analysis conditions. As applications, we can derive some\nCheng-Yau's type gradient estimates for solutions to the $n$-dimensional\nEinstein-scalar field Lichnerowicz equation where $n\\geq3$.\n"", 'Liouville theorems and new gradient estimates for positive solutions to\n  $\\Delta_pv+a(v+b)^q=0$ on a complete manifold   In this paper, we use the Saloff-Coste Sobolev inequality and Nash-Moser\niteration method to study the local and global behaviors of positive solutions\nto the nonlinear elliptic equation $\\Delta_pv+a(v+b)^q=0$ defined on a complete\nRiemannian manifold $\\left(M,g\\right)$ with Ricci lower bound, where $p>1$ is a\nconstant and $\\Delta_pv=\\mathrm{div}\\left(\\left|\\nabla v\\right|^{p-2}\\nabla\nv\\right)$ is the usual $p$-Laplace operator. Under certain assumptions on $a$,\n$p$ and $q$, we derive some gradient estimates and Liouville type theorems for\npositive solutions to the above equation. In particular, under certain\nassumptions on $a$, $b$, $p$ and $q$ we show whether or not the exact Cheng-Yau\n$\\log$-gradient estimates for the positive solutions to $\\Delta_pv+av^q=0$ on\n$\\left(M,g\\right)$ with Ricci lower bound hold true is equivalent to whether or\nnot the positive solutions to this equation fulfill Harnack inequality, and\nhence some new Cheng-Yau $\\log$-gradient estimates are established.\n']","[('gradient estimates solutions', 0.5735880136489868), ('gradient estimates positive', 0.5181925892829895), ('local gradient estimates', 0.49099522829055786), ('elliptic gradient', 0.4713519215583801), ('estimates positive solutions', 0.47042033076286316), ('gradient estimates', 0.46890413761138916), ('solutions nonlinear elliptic', 0.46605372428894043), ('ricci curvature bounded', 0.46571311354637146), ('ricci curvature nonnegative', 0.45914435386657715), ('nonlinear elliptic', 0.44654980301856995)]"
1459,1459,20,1459_hyperk ahler fourfolds_hyperk ahler manifolds_bundles hyperk ahler_hyperk ahler manifold,"['hyperk ahler fourfolds', 'hyperk ahler manifolds', 'bundles hyperk ahler', 'hyperk ahler manifold', 'hyper ahler manifolds', 'ahler varieties', 'ahler fourfolds', 'ahler manifolds', 'ahler variety', 'ahler manifold']","['Constructions of derived equivalent hyper-K\\""ahler fourfolds   We study twisted derived equivalences of hyper-K\\""ahler fourfolds. We\ndescribe when two hyper-K\\""ahler fourfolds of $K3^{[2]}$-type of Picard rank\n$1$ with isomorphic transcendental lattices are derived equivalent. Then we\npresent new constructions of pairs of twisted derived equivalent hyper-K\\""ahler\nmanifolds of Picard rank $\\geq 2$.\n', 'On Hyperk\\""ahler manifolds of K3$^{[n]}$-type with large Picard number   Inspired by well-known examples of hyperk\\""ahler manifolds, we show that any\nhyperk\\""ahler manifold $X$ of K3$^{[n]}$-type with Picard number $\\rho(X) \\geq\n4$ is always isomorphic to a moduli space of twisted stable sheaves on a K3\nsurface. Additionally, we provide explicit descriptions of hyperk\\""ahler\nmanifolds of K3$^{[n]}$-type with Picard ranks below this crucial value (e.g.,\n$\\rho(X)=3$) that are not birational to such moduli spaces.\n', 'Computing Riemann-Roch polynomials and classifying hyper-K\\""ahler\n  fourfolds   We prove that a hyper-K\\""ahler fourfold satisfying a mild topological\nassumption is of K3$^{[2]}$ deformation type. This proves in particular a\nconjecture of O\'Grady stating that hyper-K\\""ahler fourfolds of K3$^{[2]}$\nnumerical type are of K3$^{[2]}$ deformation type. Our topological assumption\nconcerns the existence of two integral degree-2 cohomology classes satisfying\ncertain numerical intersection conditions.\n  There are two main ingredients in the proof. We first prove a topological\nversion of the statement, by showing that our topological assumption forces the\nBetti numbers, the Fujiki constant, and the Huybrechts-Riemann-Roch polynomial\nof the hyper-K\\""ahler fourfold to be the same as those of K3$^{[2]}$\nhyper-K\\""ahler fourfolds. The key part of the article is then to prove the\nhyper-K\\""ahler SYZ conjecture for hyper-K\\""ahler fourfolds for divisor classes\nsatisfying the numerical condition mentioned above.\n']","[('hyperk ahler fourfolds', 0.7273625731468201), ('hyperk ahler manifolds', 0.7107464075088501), ('bundles hyperk ahler', 0.6969887614250183), ('hyperk ahler manifold', 0.6802405118942261), ('hyper ahler manifolds', 0.679968535900116), ('ahler varieties', 0.6276450157165527), ('ahler fourfolds', 0.6246707439422607), ('ahler manifolds', 0.5977451801300049), ('ahler variety', 0.5759013295173645), ('ahler manifold', 0.5550730228424072)]"
1460,1460,20,1460_semidefinite programming relaxation_semidefinite programming bounds_semidefinite programming sdp_semidefinite programming,"['semidefinite programming relaxation', 'semidefinite programming bounds', 'semidefinite programming sdp', 'semidefinite programming', 'semidefinite program', 'semidefinite relaxation', 'programming bounds', 'sdp relaxations', 'linear programs', 'programming relaxation']","[""Application of the Lov\\'asz-Schrijver Lift-and-Project Operator to\n  Compact Stable Set Integer Programs   The Lov\\'asz theta function $\\theta(G)$ provides a very good upper bound on\nthe stability number of a graph $G$. It can be computed in polynomial time by\nsolving a semidefinite program (SDP), which also turns out to be fairly\ntractable in practice. Consequently, $\\theta(G)$ achieves a hard-to-beat\ntrade-off between computational effort and strength of the bound. Indeed,\nseveral attempts to improve the theta bound are documented, mainly based on\nplaying around the application of the $N_+(\\cdot)$ lifting operator of Lov\\'asz\nand Schrijver to the classical formulation of the maximum stable set problem.\nExperience shows that solving such SDP-s often struggles against practical\nintractability and requires highly specialized methods. We investigate the\napplication of such an operator to two different linear formulations based on\nclique and nodal inequalities, respectively. Fewer inequalities describe these\ntwo and yet guarantee that the resulting SDP bound is at least as strong as\n$\\theta(G)$. Our computational experience, including larger graphs than those\npreviously documented, shows that upper bounds stronger than $\\theta(G)$ can be\naccessed by a reasonable additional effort using the clique-based formulation\non sparse graphs and the nodal-based one on dense graphs.\n"", ""Rounding the Lov\\'asz Theta Function with a Value Function Approximation   The Lov\\'asz theta function is a semidefinite programming (SDP) relaxation\nfor the maximum weighted stable set problem, which is tight for perfect graphs.\nHowever, even for perfect graphs, there is no known rounding method guaranteed\nto extract an optimal stable set from the SDP solution. In this paper, we\ndevelop a novel rounding scheme for the theta function that constructs a value\nfunction approximation from the SDP solution and then constructs a stable set\nusing dynamic programming. Our method provably recovers an optimal stable set\nin several sub-classes of perfect graphs, including generalized split graphs,\nwhich asymptotically cover almost all perfect graphs. To the best of our\nknowledge, this is the only known rounding strategy for the theta function that\nrecovers an optimal stable set for large classes of perfect graphs. Our\nrounding scheme relies on simple linear algebra computations; we only solve one\nSDP. In contrast, existing methods for computing an optimal stable set in\nperfect graphs require solving multiple SDPs. Computational experiments show\nthat our method produces good solutions even on imperfect graphs.\n"", ""An SDP-Based Approach for Computing the Stability Number of a Graph   Finding the stability number of a graph, i.e., the maximum number of vertices\nof which no two are adjacent, is a well known NP-hard combinatorial\noptimization problem. Since this problem has several applications in real life,\nthere is need to find efficient algorithms to solve this problem. Recently,\nGaar and Rendl enhanced semidefinite programming approaches to tighten the\nupper bound given by the Lov\\'asz theta function. This is done by carefully\nselecting some so-called exact subgraph constraints (ESC) and adding them to\nthe semidefinite program of computing the Lov\\'asz theta function.\n  First, we provide two new relaxations that allow to compute the bounds faster\nwithout substantial loss of the quality of the bounds. One of these two\nrelaxations is based on including violated facets of the polytope representing\nthe ESCs, the other one adds separating hyperplanes for that polytope.\n  Furthermore, we implement a branch and bound (B&B) algorithm using these\ntightened relaxations in our bounding routine. We compare the efficiency of our\nB&B algorithm using the different upper bounds. It turns out that already the\nbounds of Gaar and Rendl drastically reduce the number of nodes to be explored\nin the B&B tree as compared to the Lov\\'asz theta bound. However, this comes\nwith a high computational cost. Our new relaxations improve the run time of the\noverall B&B algorithm, while keeping the number of nodes in the B&B tree small.\n""]","[('semidefinite programming relaxation', 0.6353513598442078), ('semidefinite programming bounds', 0.6069976687431335), ('semidefinite programming sdp', 0.5939394235610962), ('semidefinite programming', 0.5819023251533508), ('semidefinite program', 0.532202959060669), ('semidefinite relaxation', 0.4908635914325714), ('programming bounds', 0.4721266031265259), ('sdp relaxations', 0.4641341269016266), ('linear programs', 0.4530634880065918), ('programming relaxation', 0.4478309452533722)]"
1461,1461,20,1461_hypergraphs bounded_uniform hypergraphs_hypergraphs maximum_graphs hypergraphs,"['hypergraphs bounded', 'uniform hypergraphs', 'hypergraphs maximum', 'graphs hypergraphs', 'hypergraphs', 'uniform hypergraph', 'partite uniform hypergraph', 'zero free regions', 'polynomials graphs', 'hypergraph']","[""On complex roots of the independence polynomial   It is known from the work of Shearer (1985) (and also Scott and Sokal (2005))\nthat the independence polynomial $Z_G(\\lambda)$ of a graph $G$ of maximum\ndegree at most $d+1$ does not vanish provided that $\\vert{\\lambda}\\vert \\leq\n\\frac{d^d}{(d+1)^{d+1}}$. Significant extensions of this result have recently\nbeen given in the case $\\Re \\lambda \\geq 0$ by Peters and Regts (2019) and\nBencs and Csikv\\'ari (arxiv:1807.08963). In this paper, our motivation is to\nfurther extend these results and find zero free regions when $\\Re \\lambda \\leq\n0$.\n  We begin by giving new geometric criteria for establishing zero-free regions\nas well as for carrying out semi-rigorous numerical explorations. We then\nprovide two examples of the (rigorous) use of these criteria, by establishing\ntwo new zero-free regions in the left-half plane. We also improve upon the\nresults of Bencs and Csikv\\'ari (arxiv:1807.08963) for the right half-plane\nusing our framework. By a direct application of the interpolation method of\nBarvinok, combined with extensions due to Patel and Regts, these results also\nimply deterministic polynomial time approximation algorithms for the\nindependence polynomial of bounded degree graphs in the new zero-free regions.\n"", 'Optimal zero-free regions for the independence polynomial of bounded\n  degree hypergraphs   In this paper we investigate the distribution of zeros of the independence\npolynomial of hypergraphs of maximum degree $\\Delta$. For graphs the largest\nzero-free disk around zero was described by Shearer as having radius\n$\\lambda_s(\\Delta)=(\\Delta-1)^{\\Delta-1}/\\Delta^\\Delta$. Recently it was shown\nby Galvin et al. that for hypergraphs the disk of radius $\\lambda_s(\\Delta+1)$\nis zero-free; however, it was conjectured that the actual truth should be\n$\\lambda_s(\\Delta)$. We show that this is indeed the case. We also show that\nthere exists an open region around the interval\n$[0,(\\Delta-1)^{\\Delta-1}/(\\Delta-2)^\\Delta)$ that is zero-free for hypergraphs\nof maximum degree $\\Delta$, which extends the result of Peters and Regts from\ngraphs to hypergraphs. Finally, we determine the radius of the largest\nzero-free disk for the family of bounded degree $k$-uniform linear hypertrees\nin terms of $k$ and $\\Delta$.\n', ""On the zeroes of hypergraph independence polynomials   We study the locations of complex zeroes of independence polynomials of\nbounded degree hypergraphs. For graphs, this is a long-studied subject with\napplications to statistical physics, algorithms, and combinatorics. Results on\nzero-free regions for bounded-degree graphs include Shearer's result on the\noptimal zero-free disk, along with several recent results on other zero-free\nregions. Much less is known for hypergraphs. We make some steps towards an\nunderstanding of zero-free regions for bounded-degree hypergaphs by proving\nthat all hypergraphs of maximum degree $\\Delta$ have a zero-free disk almost as\nlarge as the optimal disk for graphs of maximum degree $\\Delta$ established by\nShearer (of radius $\\sim 1/(e \\Delta)$). Up to logarithmic factors in $\\Delta$\nthis is optimal, even for hypergraphs with all edge-sizes strictly greater than\n$2$. We conjecture that for $k\\ge 3$, $k$-uniform linear hypergraphs have a\nmuch larger zero-free disk of radius $\\Omega(\\Delta^{- \\frac{1}{k-1}} )$. We\nestablish this in the case of linear hypertrees.\n""]","[('hypergraphs bounded', 0.6195507645606995), ('uniform hypergraphs', 0.6177570223808289), ('hypergraphs maximum', 0.5597130656242371), ('graphs hypergraphs', 0.5570076107978821), ('hypergraphs', 0.5475705862045288), ('uniform hypergraph', 0.5443772673606873), ('partite uniform hypergraph', 0.52735835313797), ('zero free regions', 0.46347132325172424), ('polynomials graphs', 0.4545902907848358), ('hypergraph', 0.4505455791950226)]"
1462,1462,20,1462_noisy quantum_quantum error mitigation_learning quantum_quantum machine learning,"['noisy quantum', 'quantum error mitigation', 'learning quantum', 'quantum machine learning', 'quantum noise', 'quantum algorithms', 'quantum information processing', 'quantum computing', 'algorithms quantum', 'quantum algorithms quantum']","['Foundations for learning from noisy quantum experiments   Understanding what can be learned from experiments is central to scientific\nprogress. In this work, we use a learning-theoretic perspective to study the\ntask of learning physical operations in a quantum machine when all operations\n(state preparation, dynamics, and measurement) are a priori unknown. We prove\nthat, without any prior knowledge, if one can explore the full quantum state\nspace by composing the operations, then every operation can be learned. When\none cannot explore the full state space but all operations are approximately\nknown and noise in Clifford gates is gate-independent, we find an efficient\nalgorithm for learning all operations up to a single unlearnable parameter\ncharacterizing the fidelity of the initial state. For learning a noise channel\non Clifford gates to a fixed accuracy, our algorithm uses quadratically fewer\nexperiments than previously known protocols. Under more general conditions, the\ntrue description of the noise can be unlearnable; for example, we prove that no\nbenchmarking protocol can learn gate-dependent Pauli noise on Clifford+T gates\neven under perfect state preparation and measurement. Despite not being able to\nlearn the noise, we show that a noisy quantum computer that performs entangled\nmeasurements on multiple copies of an unknown state can yield a large advantage\nin learning properties of the state compared to a noiseless device that\nmeasures individual copies and then processes the measurement data using a\nclassical computer. Concretely, we prove that noisy quantum computers with\ntwo-qubit gate error rate $\\epsilon$ can achieve a learning task using $N$\ncopies of the state, while $N^{\\Omega(1/\\epsilon)}$ copies are required\nclassically.\n', ""Efficient Noise Mitigation Technique for Quantum Computing   Quantum computers have enabled solving problems beyond the current computers'\ncapabilities. However, this requires handling noise arising from unwanted\ninteractions in these systems. Several protocols have been proposed to address\nefficient and accurate quantum noise profiling and mitigation. In this work, we\npropose a novel protocol that efficiently estimates the average output of a\nnoisy quantum device to be used for quantum noise mitigation. The multi-qubit\nsystem average behavior is approximated as a special form of a Pauli Channel\nwhere Clifford gates are used to estimate the average output for circuits of\ndifferent depths. The characterized Pauli channel error rates, and state\npreparation and measurement errors are then used to construct the outputs for\ndifferent depths thereby eliminating the need for large simulations and\nenabling efficient mitigation. We demonstrate the efficiency of the proposed\nprotocol on four IBM Q 5-qubit quantum devices. Our method demonstrates\nimproved accuracy with efficient noise characterization. We report up to 88\\%\nand 69\\% improvement for the proposed approach compared to the unmitigated, and\npure measurement error mitigation approaches, respectively.\n"", 'Demonstration of Robust and Efficient Quantum Property Learning with\n  Shallow Shadows   Extracting information efficiently from quantum systems is a major component\nof quantum information processing tasks. Randomized measurements, or classical\nshadows, enable predicting many properties of arbitrary quantum states using\nfew measurements. While random single-qubit measurements are experimentally\nfriendly and suitable for learning low-weight Pauli observables, they perform\npoorly for nonlocal observables. Prepending a shallow random quantum circuit\nbefore measurements maintains this experimental friendliness, but also has\nfavorable sample complexities for observables beyond low-weight Paulis,\nincluding high-weight Paulis and global low-rank properties such as fidelity.\nHowever, in realistic scenarios, quantum noise accumulated with each additional\nlayer of the shallow circuit biases the results. To address these challenges,\nwe propose the \\emph{robust shallow shadows protocol}. Our protocol uses\nBayesian inference to learn the experimentally relevant noise model and\nmitigate it in postprocessing. This mitigation introduces a bias-variance\ntrade-off: correcting for noise-induced bias comes at the cost of a larger\nestimator variance. Despite this increased variance, as we demonstrate on a\nsuperconducting quantum processor, our protocol correctly recovers state\nproperties such as expectation values, fidelity, and entanglement entropy,\nwhile maintaining a lower sample complexity compared to the random single qubit\nmeasurement scheme. We also theoretically analyze the effects of noise on\nsample complexity and show how the optimal choice of the shallow shadow depth\nvaries with noise strength. This combined theoretical and experimental analysis\npositions the robust shallow shadow protocol as a scalable, robust, and\nsample-efficient protocol for characterizing quantum states on current quantum\ncomputing platforms.\n']","[('noisy quantum', 0.6742439866065979), ('quantum error mitigation', 0.670096755027771), ('learning quantum', 0.6599618196487427), ('quantum machine learning', 0.6596534252166748), ('quantum noise', 0.6378677487373352), ('quantum algorithms', 0.6366972923278809), ('quantum information processing', 0.628285825252533), ('quantum computing', 0.6205548048019409), ('algorithms quantum', 0.6095764636993408), ('quantum algorithms quantum', 0.6047545075416565)]"
1463,1463,20,1463_gentle algebras_auslander algebras_finite dimensional algebras_auslander algebra,"['gentle algebras', 'auslander algebras', 'finite dimensional algebras', 'auslander algebra', 'class algebras', 'algebras local', 'gentle algebra', 'algebras finite representation', 'algebras hereditary', 'auslander reiten quivers']","[""A geometric model for semilinear locally gentle algebras   We consider certain generalizations of gentle algebras that we call\nsemilinear locally gentle algebras. These rings are examples of semilinear\nclannish algebras as introduced by the second author and Crawley-Boevey. We\ngeneralise the notion of a nodal algebra from work of Burban and Drozd and\nprove that semilinear gentle algebras are nodal by adapting a theorem of\nZembyk. We also provide a geometric realization of Zembyk's proof, which\ninvolves cutting the surface into simpler pieces in order to endow our locally\ngentle algebra with a semilinear structure. We then consider this surface glued\nback together, with the seams in place, and use it to give a geometric model\nfor the finite-dimensional modules over the semilinear locally gentle algebra.\n"", ""Homological conditions on locally gentle algebras   Gentle algebras are a class of special biserial algebra whose representation\ntheory has been thoroughly described. In this paper, we consider the infinite\ndimensional generalizations of gentle algebras, referred to as locally gentle\nalgebras. We give combinatorial descriptions of the center, prime spectrum, and\nhomological dimensions of a locally gentle algebra, including an explicit\ninjective resolution. We classify when these algebras are Artin-Schelter\nGorenstein, Artin-Schelter regular, and Cohen-Macaulay, and provide an analogue\nof Stanley's theorem for locally gentle algebras.\n"", 'Folded Gentle Algebras   We use folding techniques to define a new class of gentle-like algebras that\ngeneralise the iterated tilted algebras of type $C$ and $\\widetilde{C}$, which\nwe call folded gentle algebras. We then show that folded gentle algebras\nsatisfy many of the same remarkable properties of gentle algebras, and that the\nproof of these properties follows directly from folding arguments. In\nparticular, we classify the indecomposable modules of folded gentle algebras in\nterms symmetric and asymmetric string and band modules. We classify the\nAuslander-Reiten sequences over these algebras, showing that irreducible\nmorphisms between string modules are given by adding/deleting hooks and cohooks\nto/from strings. Finally, we show that the class of folded gentle algebras are\nclosed under derived equivalence.\n']","[('gentle algebras', 0.6333747506141663), ('auslander algebras', 0.6292990446090698), ('finite dimensional algebras', 0.5690451860427856), ('auslander algebra', 0.5688818097114563), ('class algebras', 0.5278082489967346), ('algebras local', 0.5266375541687012), ('gentle algebra', 0.509283721446991), ('algebras finite representation', 0.5019985437393188), ('algebras hereditary', 0.49882692098617554), ('auslander reiten quivers', 0.4909570813179016)]"
1464,1464,20,1464_perturbation theory_similar approximation_order perturbation theory_approximation theory,"['perturbation theory', 'similar approximation', 'order perturbation theory', 'approximation theory', 'perturbative series', 'renormalization', 'perturbation', 'order perturbation', 'renormalization group', 'approximants']","['Self-similar extrapolation in quantum field theory   Calculations in field theory are usually accomplished by employing some\nvariants of perturbation theory, for instance using loop expansions. These\ncalculations result in asymptotic series in powers of small coupling\nparameters, which as a rule are divergent for finite values of the parameters.\nIn this paper, a method is described allowing for the extrapolation of such\nasymptotic series to finite values of the coupling parameters, and even to\ntheir infinite limits. The method is based on self-similar approximation\ntheory. This theory approximates well a large class of functions, rational,\nirrational, and transcendental. A method is presented, resulting in\nself-similar factor approximants allowing for the extrapolation of functions to\narbitrary values of coupling parameters from only the knowledge of expansions\nin powers of small coupling parameters. The efficiency of the method is\nillustrated by several problems of quantum field theory.\n', ""Optimized Self-Similar Borel Summation   The method of Fractional Borel Summation is suggested in conjunction with\nself-similar factor approximants. The method used for extrapolating asymptotic\nexpansions at small variables to large variables, including the variables\ntending to infinity, is described. The method is based on the combination of\noptimized perturbation theory, self-similar approximation theory, and\nBorel-type transformations. General Borel Fractional transformation of the\noriginal series is employed. The transformed series is resummed in order to\nadhere to the asymptotic power laws. The starting point is the formulation of\ndynamics in the approximations space by employing the notion of\nself-similarity. The flow in the approximation space is controlled, and\n``deep'' control is incorporated into the definitions of the self-similar\napproximants. The class of self-similar approximations, satisfying, by design,\nthe power law behavior, such as the use of self-similar factor approximants, is\nchosen for the reasons of transparency, explicitness, and convenience. A\ndetailed comparison of different methods is performed on a rather large set of\nexamples, employing self-similar factor approximants, self-similar iterated\nroot approximants, as well as the approximation technique of self-similarly\nmodified Pade - Borel approximations.\n"", 'Self-similar extrapolation of nonlinear problems from small-variable to\n  large-variable limit   Complicated physical problems usually are solved by resorting to perturbation\ntheory leading to solutions in the form of asymptotic series in powers of small\nparameters. However, finite, and even large values of the parameters often are\nof the main physical interest. A method is described for predicting the\nlarge-variable behavior of solutions to nonlinear problems from the knowledge\nof only their small-variable expansions. The method is based on self-similar\napproximation theory resulting in self-similar factor approximants. The latter\ncan well approximate a large class of functions, rational, irrational, and\ntranscendental. The method is illustrated by several examples from statistical\nand condensed matter physics, where the self-similar predictions can be\ncompared with the available large-variable behavior. It is shown that the\nmethod allows for finding the behavior of solutions at large variables when\nknowing just a few terms of small-variable expansions. Numerical convergence of\napproximants is demonstrated.\n']","[('perturbation theory', 0.5836700797080994), ('similar approximation', 0.5518989562988281), ('order perturbation theory', 0.5516301989555359), ('approximation theory', 0.5393949747085571), ('perturbative series', 0.5176049470901489), ('renormalization', 0.49711060523986816), ('perturbation', 0.4780222475528717), ('order perturbation', 0.4679814875125885), ('renormalization group', 0.4447799026966095), ('approximants', 0.4250144958496094)]"
1465,1465,20,1465_diffusion reaction equations_system diffusion_diffusion reaction_convection diffusion reaction,"['diffusion reaction equations', 'system diffusion', 'diffusion reaction', 'convection diffusion reaction', 'transport equations', 'wastewater', 'reaction equations', 'reactors', 'convection diffusion', 'sedimentation']","['A model of reactive settling of activated sludge: comparison with\n  experimental data   A non-negligible part of the biological reactions in the activated sludge\nprocess for treatment of wastewater takes place in secondary settling tanks\nthat follow biological reactors. It is therefore of interest to develop models\nof so-called reactive settling that describe the spatial variability of\nreaction rates caused by the variation of local concentration of biomass due to\nhindered settling and compression. A reactive-settling model described by a\nsystem of nonlinear partial differential equations and a numerical scheme are\nintroduced for the simulation of hindered settling of flocculated particles,\ncompression at high concentrations, dispersion of the flocculated particles in\nthe suspension, dispersion of the dissolved substrates in the fluid, and the\nmixing that occurs near the feed inlet. The model is fitted to experiments from\na pilot plant where the sedimentation tank has a varying cross-sectional area.\nFor the reactions, a modified version of the activated sludge model no. 1\n(ASM1) is used with standard coefficients. The constitutive functions for\nhindered settling and compression are adjusted to a series of conventional\nbatch settling experiments after the initial induction period of turbulence and\nreflocculation has been transformed away. Further (but not substantial)\nimprovements of prediction of experimental steady-state scenarios can be\nachieved by also fitting additional terms modelling hydrodynamic dispersion.\n', 'A moving-boundary model of reactive settling in wastewater treatment.\n  Part 2: Numerical scheme   A numerical scheme is proposed for the simulation of reactive settling in\nsequencing batch reactors (SBRs) in wastewater treatment plants. Reactive\nsettling is the process of sedimentation of flocculated particles (biomass;\nactivated sludge) consisting of several material components that react with\nsubstrates dissolved in the fluid. An SBR is operated in cycles of consecutive\nfill, react, settle, draw and idle stages, which means that the volume in the\ntank varies and the surface moves with time. The process is modelled by a\nsystem of spatially one-dimensional, nonlinear, strongly degenerate parabolic\nconvection-diffusion-reaction equations. This system is coupled via conditions\nof mass conservation to transport equations on a half line whose origin is\nlocated at a moving boundary and that models the effluent pipe. A\nfinite-difference scheme is proved to satisfy an invariant-region property (in\nparticular, it is positivity preserving) if executed in a simple splitting way.\nSimulations are presented with a modified variant of the established activated\nsludge model no.~1 (ASM1).\n', 'A moving-boundary model of reactive settling in wastewater treatment.\n  Part 1: Governing equations   Reactive settling is the process of sedimentation of small solid particles in\na fluid with simultaneous reactions between the components of the solid and\nliquid phases. This process is important in sequencing batch reactors (SBRs) in\nwastewater treatment plants. In that application the particles are biomass\n(bacteria; activated sludge) and the liquid contains substrates (nitrogen,\nphosphorus) to be removed through reactions with the biomass. The operation of\nan SBR in cycles of consecutive fill, react, settle, draw, and idle stages is\nmodelled by a system of spatially one-dimensional, nonlinear, strongly\ndegenerate parabolic convection-diffusion-reaction equations. This system is\ncoupled via conditions of mass conservation to transport equations on a half\nline, whose origin is located at a moving boundary and that model the effluent\npipe. An invariant-region-preserving finite difference scheme is used to\nsimulate operating cycles and the denitrification process within an SBR.\n']","[('diffusion reaction equations', 0.5146921873092651), ('system diffusion', 0.4388449192047119), ('diffusion reaction', 0.4386216700077057), ('convection diffusion reaction', 0.43327221274375916), ('transport equations', 0.40470370650291443), ('wastewater', 0.3900599181652069), ('reaction equations', 0.3887712061405182), ('reactors', 0.3785221576690674), ('convection diffusion', 0.3612922430038452), ('sedimentation', 0.34126022458076477)]"
1466,1466,20,1466_monomial ideals_monomial ideal_monomial ideals let_ideal x_1 ldots,"['monomial ideals', 'monomial ideal', 'monomial ideals let', 'ideal x_1 ldots', 'homogeneous ideals', 'homogeneous ideal', 'monomial generators', 'edge ideal', 'depth depth', 'depth functions']","['Comparing Hilbert depth of $I$ with Hilbert depth of $S/I$. III   Let $I$ be a squarefree monomial ideal of $S=K[x_1,\\ldots,x_n]$. We prove\nthat if $\\operatorname{hdepth}(S/I)\\leq 8$ or $n\\leq 10$ then\n$\\operatorname{hdepth}(I)\\geq \\operatorname{hdepth}(S/I)-1$.\n', 'Depth functions of symbolic powers of homogeneous ideals   This paper addresses the problem of comparing minimal free resolutions of\nsymbolic powers of an ideal. Our investigation is focused on the behavior of\nthe function depth R/I^(t) = dim R - pd I^(t) - 1, where I^(t) denotes the t-th\nsymbolic power of a homogeneous ideal I in a noetherian polynomial ring R and\npd denotes the projective dimension.\n  It has been an open question whether the function depth R/I^(t) is\nnon-increasing if I is a squarefree monomial ideal. We show that depth R/I^(t)\nis almost non-increasing in the sense that depth R/I^(s) \\ge depth R/I^(t) for\nall s \\ge 1 and t \\in E(s), where\n  E(s) = \\cup_{i \\ge 1} {t \\in N| i(s-1)+1 \\le t \\le is}\n  (which contains all integers t \\ge (s-1)^2+1). The range E(s) is the best\npossible since we can find squarefree monomial ideals I such that depth R/I^(s)\n< depth R/I^(t) for t \\not\\in E(s), which gives a negative answer to the above\nquestion.\n  Another open question asks whether the function depth R/I^(t) is always\nconstant for t \\gg 0. We are able to construct counter-examples to this\nquestion by monomial ideals. On the other hand, we show that if I is a monomial\nideal such that I^(t) is integrally closed for t \\gg 0 (e.g. if I is a\nsquarefree monomial ideal), then depth R/I^(t) is constant for t \\gg 0 with\nlim_{t \\to \\infty} depth R/I^(t) = dim R - dim \\oplus_{t \\ge 0} I^(t)/m I^(t).\n  Our last result (which is the main contribution of this paper) shows that for\nany positive numerical function \\phi(t) which is periodic for t \\gg 0, there\nexist a polynomial ring R and a homogeneous ideal I such that depth R/I^(t) =\n\\phi(t) for all t \\ge 1. As a consequence, for any non-negative numerical\nfunction \\psi(t) which is periodic for t \\gg 0, there is a homogeneous ideal I\nand a number c such that pd I^(t) = \\psi(t) + c for all t \\ge 1.\n', 'The normalized depth function of squarefree powers   The depth of squarefree powers of a squarefree monomial ideal is introduced.\nLet $I$ be a squarefree monomial ideal of the polynomial ring\n$S=K[x_1,\\ldots,x_n]$. The $k$-th squarefree power $I^{[k]}$ of $I$ is the\nideal of $S$ generated by those squarefree monomials $u_1\\cdots u_k$ with each\n$u_i\\in G(I)$, where $G(I)$ is the unique minimal system of monomial generators\nof $I$. Let $d_k$ denote the minimum degree of monomials belonging to\n$G(I^{[k]})$. One has $\\operatorname{depth}(S/I^{[k]}) \\geq d_k -1$. Setting\n$g_I(k) = \\operatorname{depth}(S/I^{[k]}) - (d_k - 1)$, one calls $g_I(k)$ the\nnormalized depth function of $I$. The computational experience strongly invites\nus to propose the conjecture that the normalized depth function is\nnonincreasing. In the present paper, especially the normalized depth function\nof the edge ideal of a finite simple graph is deeply studied.\n']","[('monomial ideals', 0.5654820799827576), ('monomial ideal', 0.5448533296585083), ('monomial ideals let', 0.5277290940284729), ('ideal x_1 ldots', 0.5068461894989014), ('homogeneous ideals', 0.4813041687011719), ('homogeneous ideal', 0.43570953607559204), ('monomial generators', 0.41363197565078735), ('edge ideal', 0.3990612328052521), ('depth depth', 0.398715078830719), ('depth functions', 0.3933703899383545)]"
1467,1467,20,1467_lossless source coding_lossless compression_random coding_encoders,"['lossless source coding', 'lossless compression', 'random coding', 'encoders', 'lossless source', 'memoryless sources', 'encoder', 'decoder proposed', 'lossy compression', 'coding scheme']","['$D$-semifaithful codes that are universal over both memoryless sources\n  and distortion measures   We prove the existence of codebooks for d-semifaithful lossy compression that\nare simultaneously universal with respect to both the class of finite-alphabet\nmemoryless sources and the class of all bounded additive distortion measures.\nBy applying independent random selection of the codewords according to a\nmixture of all memoryless sources, we achieve redundancy rates that are within\nO(log n/n) close to the empirical rate-distortion function of every given\nsource vector with respect to every bounded distortion measure. As outlined in\nthe last section, the principal ideas can also be extended significantly beyond\nthe class of memoryless sources, namely, to the setting of individual sequences\nencoded by finite-state machines.\n', 'On Universal D-Semifaithful Coding for Memoryless Sources with Infinite\n  Alphabets   The problem of variable length and fixed-distortion universal source coding\n(or D-semifaithful source coding) for stationary and memoryless sources on\ncountably infinite alphabets ($\\infty$-alphabets) is addressed in this paper.\nThe main results of this work offer a set of sufficient conditions (from weaker\nto stronger) to obtain weak minimax universality, strong minimax universality,\nand corresponding achievable rates of convergences for the worse-case\nredundancy for the family of stationary memoryless sources whose densities are\ndominated by an envelope function (or the envelope family) on\n$\\infty$-alphabets. An important implication of these results is that universal\nD-semifaithful source coding is not feasible for the complete family of\nstationary and memoryless sources on $\\infty$-alphabets. To demonstrate this\ninfeasibility, a sufficient condition for the impossibility is presented for\nthe envelope family. Interestingly, it matches the well-known impossibility\ncondition in the context of lossless (variable-length) universal source coding.\nMore generally, this work offers a simple description of what is needed to\nachieve universal D-semifaithful coding for a family of distributions\n$\\Lambda$. This reduces to finding a collection of quantizations of the product\nspace at different block-lengths -- reflecting the fixed distortion restriction\n-- that satisfy two asymptotic requirements: the first is a universal\nquantization condition with respect to $\\Lambda$, and the second is a vanishing\ninformation radius (I-radius) condition for $\\Lambda$ reminiscent of the\ncondition known for lossless universal source coding.\n', 'Universal Weak Variable-Length Source Coding on Countable Infinite\n  Alphabets   Motivated from the fact that universal source coding on countably infinite\nalphabets is not feasible, this work introduces the notion of almost lossless\nsource coding. Analog to the weak variable-length source coding problem studied\nby Han (IEEE TIT, 2000, 46, 1217-1226), almost lossless source coding aims at\nrelaxing the lossless block-wise assumption to allow an average per-letter\ndistortion that vanishes asymptotically as the block-length tends to infinity.\nIn this setup, we show on one hand that Shannon entropy characterizes the\nminimum achievable rate (similarly to the case of finite alphabet sources)\nwhile on the other that almost lossless universal source coding becomes\nfeasible for the family of finite-entropy stationary memoryless sources with\ninfinite alphabets. Furthermore, we study a stronger notion of almost lossless\nuniversality that demands uniform convergence of the average per-letter\ndistortion to zero, where we establish a necessary and sufficient condition for\nthe so-called family of envelope distributions to achieve it. Remarkably, this\ncondition is the same necessary and sufficient condition needed for the\nexistence of a strongly minimax (lossless) universal source code for the family\nof envelope distributions. Finally, we show that an almost lossless coding\nscheme offers faster rate of convergence for the (minimax) redundancy compared\nto the well-known information radius developed for the lossless case at the\nexpense of tolerating a non-zero distortion that vanishes to zero as the\nblock-length grows. This shows that even when lossless universality is\nfeasible, an almost lossless scheme can offer different regimes on the rates of\nconvergence of the (worst case) redundancy versus the (worst case) distortion.\n']","[('lossless source coding', 0.7187365293502808), ('lossless compression', 0.5944535732269287), ('random coding', 0.5690804123878479), ('encoders', 0.5185904502868652), ('lossless source', 0.4891505837440491), ('memoryless sources', 0.4850468635559082), ('encoder', 0.4843055009841919), ('decoder proposed', 0.4791596233844757), ('lossy compression', 0.4754561185836792), ('coding scheme', 0.46261683106422424)]"
1468,1468,20,1468_rearrangements_genomes_genome_dna sequences,"['rearrangements', 'genomes', 'genome', 'dna sequences', 'rearrangement', 'sequencing', 'sequence similarity', 'sequence alignment', 'genomics', 'genomic']","['A symmetry-inclusive algebraic approach to genome rearrangement   Of the many modern approaches to calculating evolutionary distance via models\nof genome rearrangement, most are tied to a particular set of genomic modelling\nassumptions and to a restricted class of allowed rearrangements. The ""position\nparadigm"", in which genomes are represented as permutations signifying the\nposition (and orientation) of each region, enables a refined model-based\napproach, where one can select biologically plausible rearrangements and assign\nto them relative probabilities/costs. Here, one must further incorporate any\nunderlying structural symmetry of the genomes into the calculations and ensure\nthat this symmetry is reflected in the model. In our recently-introduced\nframework of {\\em genome algebras}, each genome corresponds to an element that\nsimultaneously incorporates all of its inherent physical symmetries. The\nrepresentation theory of these algebras then provides a natural model of\nevolution via rearrangement as a Markov chain. Whilst the implementation of\nthis framework to calculate distances for genomes with `practical\' numbers of\nregions is currently computationally infeasible, we consider it to be a\nsignificant theoretical advance: one can incorporate different genomic\nmodelling assumptions, calculate various genomic distances, and compare the\nresults under different rearrangement models. The aim of this paper is to\ndemonstrate some of these features.\n', 'Rearrangement Events on Circular Genomes   Early literature on genome rearrangement modelling views the problem of\ncomputing evolutionary distances as an inherently combinatorial one. In\nparticular, attention was given to estimating distances using the minimum\nnumber of events required to transform one genome into another. In hindsight,\nthis approach is analogous to early methods for inferring phylogenetic trees\nfrom DNA sequences such as maximum parsimony -- both are motivated by the\nprinciple that the true distance minimises evolutionary change, and both are\neffective if this principle is a true reflection of reality. Recent literature\nconsiders genome rearrangement under statistical models, continuing this\nparallel with DNA-based methods; the goal here is to use model-based methods\n(for example maximum likelihood techniques) to compute distance estimates that\nincorporate the large number of rearrangement paths that can transform one\ngenome into another. Crucially, this approach requires one to decide upon a set\nof feasible rearrangement events and, in this paper, we focus on characterising\nwell-motivated models for signed, uni-chromosomal circular genomes, where the\nnumber of regions remains fixed. Since rearrangements are often mathematically\ndescribed using permutations, we isolate the sets of permutations representing\nrearrangements that are biologically reasonable in this context, for example\ninversions and translocations. We provide precise mathematical expressions for\nthese rearrangements, and then describe them in terms of the set of cuts made\nin the genome when they are applied. We directly compare cuts to breakpoints,\nand use this concept to count the distinct rearrangement actions which apply a\ngiven number of cuts. Finally, we provide some examples of rearrangement\nmodels, and include a discussion of some questions that arise when defining\nplausible models.\n', 'On the Complexity of the Median and Closest Permutation Problems   Genome rearrangements are events where large blocks of DNA exchange places\nduring evolution. The analysis of these events is a promising tool for\nunderstanding evolutionary genomics, providing data for phylogenetic\nreconstruction based on genome rearrangement measures. Many pairwise\nrearrangement distances have been proposed, based on finding the minimum number\nof rearrangement events to transform one genome into the other, using some\npredefined operation. When more than two genomes are considered, we have the\nmore challenging problem of rearrangement-based phylogeny reconstruction. Given\na set of genomes and a distance notion, there are at least two natural ways to\ndefine the ""target"" genome. On the one hand, finding a genome that minimizes\nthe sum of the distances from this to any other, called the median genome.\nFinding a genome that minimizes the maximum distance to any other, called the\nclosest genome. Considering genomes as permutations, some distance metrics have\nbeen extensively studied. We investigate median and closest problems on\npermutations over the metrics: breakpoint, swap, block-interchange,\nshort-block-move, and transposition. In biological matters some values are\nusually small, such as the solution value d or the number k of input\npermutations. For each of these metrics and parameters d or k, we analyze the\nclosest and the median problems from the viewpoint of parameterized complexity.\nWe obtain the following results: NP-hardness for finding the median/closest\npermutation for some metrics, even for k = 3; Polynomial kernels for the\nproblems of finding the median permutation of all studied metrics, considering\nthe target distance d as parameter; NP-hardness result for finding the closest\npermutation by short-block-moves; FPT algorithms and infeasibility of\npolynomial kernels for finding the closest permutation for some metrics\nparameterized by the target distance d.\n']","[('rearrangements', 0.5078645348548889), ('genomes', 0.4988653063774109), ('genome', 0.4842830300331116), ('dna sequences', 0.4646056294441223), ('rearrangement', 0.4631180465221405), ('sequencing', 0.43594446778297424), ('sequence similarity', 0.43056967854499817), ('sequence alignment', 0.4166617691516876), ('genomics', 0.414264053106308), ('genomic', 0.40936827659606934)]"
1469,1469,20,1469_minimax estimation_estimators adaptive_rate optimal estimation_nonparametric estimation,"['minimax estimation', 'estimators adaptive', 'rate optimal estimation', 'nonparametric estimation', 'estimator achieves minimax', 'adaptive estimation', 'conditional density estimation', 'density estimation', 'density estimator', 'adaptive minimax']","['Generalized multi-view model: Adaptive density estimation under low-rank\n  constraints   We study the problem of bivariate discrete or continuous probability density\nestimation under low-rank constraints.For discrete distributions, we assume\nthat the two-dimensional array to estimate is a low-rank probability matrix. In\nthe continuous case, we assume that the density with respect to the Lebesgue\nmeasure satisfies a generalized multi-view model, meaning that it is\n$\\beta$-H{\\""o}lder and can be decomposed as a sum of $K$ components, each of\nwhich is a product of one-dimensional functions. In both settings, we propose\nestimators that achieve, up to logarithmic factors, the minimax optimal\nconvergence rates under such low-rank constraints. In the discrete case, the\nproposed estimator is adaptive to the rank $K$. In the continuous case, our\nestimator converges with the $L_1$ rate $\\min((K/n)^{\\beta/(2\\beta+1)},\nn^{-\\beta/(2\\beta+2)})$ up to logarithmic factors, and it is adaptive to the\nunknown support as well as to the smoothness $\\beta$ and to the unknown number\nof separable components $K$. We present efficient algorithms for computing our\nestimators.\n', 'Minimax Optimal Conditional Density Estimation under Total Variation\n  Smoothness   This paper studies the minimax rate of nonparametric conditional density\nestimation under a weighted absolute value loss function in a multivariate\nsetting. We first demonstrate that conditional density estimation is impossible\nif one only requires that $p_{X|Z}$ is smooth in $x$ for all values of $z$.\nThis motivates us to consider a sub-class of absolutely continuous\ndistributions, restricting the conditional density $p_{X|Z}(x|z)$ to not only\nbe H\\""older smooth in $x$, but also be total variation smooth in $z$. We\npropose a corresponding kernel-based estimator and prove that it achieves the\nminimax rate. We give some simple examples of densities satisfying our\nassumptions which imply that our results are not vacuous. Finally, we propose\nan estimator which achieves the minimax optimal rate adaptively, i.e., without\nthe need to know the smoothness parameter values in advance. Crucially, both of\nour estimators (the adaptive and non-adaptive ones) impose no assumptions on\nthe marginal density $p_Z$, and are not obtained as a ratio between two kernel\nsmoothing estimators which may sound like a go to approach in this problem.\n', 'A Non-Classical Parameterization for Density Estimation Using Sample\n  Moments   Probability density estimation is a core problem of statistics and signal\nprocessing. Moment methods are an important means of density estimation, but\nthey are generally strongly dependent on the choice of feasible functions,\nwhich severely affects the performance. In this paper, we propose a\nnon-classical parametrization for density estimation using sample moments,\nwhich does not require the choice of such functions. The parametrization is\ninduced by the squared Hellinger distance, and the solution of it, which is\nproved to exist and be unique subject to a simple prior that does not depend on\ndata, and can be obtained by convex optimization. Statistical properties of the\ndensity estimator, together with an asymptotic error upper bound are proposed\nfor the estimator by power moments. Applications of the proposed density\nestimator in signal processing tasks are given. Simulation results validate the\nperformance of the estimator by a comparison to several prevailing methods. To\nthe best of our knowledge, the proposed estimator is the first one in the\nliterature for which the power moments up to an arbitrary even order exactly\nmatch the sample moments, while the true density is not assumed to fall within\nspecific function classes.\n']","[('minimax estimation', 0.6274914741516113), ('estimators adaptive', 0.5889090299606323), ('rate optimal estimation', 0.581322968006134), ('nonparametric estimation', 0.5781263113021851), ('estimator achieves minimax', 0.5700113773345947), ('adaptive estimation', 0.5667008757591248), ('conditional density estimation', 0.5660024285316467), ('density estimation', 0.5633175373077393), ('density estimator', 0.5468182563781738), ('adaptive minimax', 0.5166916847229004)]"
1470,1470,20,1470_shimura varieties_shimura curves_shimura variety_shimura,"['shimura varieties', 'shimura curves', 'shimura variety', 'shimura', 'subvarieties moduli', 'hyperelliptic curves genus', 'subvarieties moduli space', 'covers elliptic curves', 'curves moduli space', 'abelian covers']","['Shimura subvarieties in the Prym locus of ramified Galois coverings   We study Shimura (special) subvarieties in the moduli space $A_{p,D}$ of\ncomplex abelian varieties of dimension $p$ and polarization type $D$. These\nsubvarieties arise from families of covers compatible with a fixed group action\non the base curve such that the quotient of the base curve by the group is\nisomorphic to $\\mathbb{P}^1$. We give a criterion for the image of these\nfamilies under the Prym map to be a special subvariety and, using computer\nalgebra, obtain 210 Shimura subvarieties contained in the Prym locus.\n', 'Unlikely intersections with Hecke translates of a special subvariety   We prove some cases of the Zilber-Pink conjecture on unlikely intersections\nin Shimura varieties. Firstly, we prove that the Zilber-Pink conjecture holds\nfor intersections between a curve and the union of the Hecke translates of a\nfixed special subvariety, conditional on arithmetic conjectures. Secondly, we\nprove the conjecture unconditionally for intersections between a curve and the\nunion of Hecke correspondences on the moduli space of principally polarised\nabelian varieties, subject to some technical hypotheses. This generalises\nresults of Habegger and Pila on the Zilber-Pink conjecture for products of\nmodular curves.\n  The conditional proof uses the Pila-Zannier method, relying on a\npoint-counting theorem of Habegger and Pila and a functional transcendence\nresult of Gao. The unconditional results are deduced from this using a variety\nof arithmetic ingredients: the Masser-W\\""ustholz isogeny theorem, comparison\nbetween Faltings and Weil heights, a super-approximation theorem of Salehi\nGolsefidy, and a result on expansion and gonality due to Ellenberg, Hall and\nKowalski.\n', ""A note on unlikely intersections in Shimura varieties   We discuss the relationships between the Andr\\'e-Oort, Andr\\'e-Pink-Zannier,\nand Mordell-Lang conjectures for Shimura varieties. We then combine the latter\nwith the geometric Zilber-Pink conjecture to obtain some new results on\nunlikely intersections in Shimura varieties.\n""]","[('shimura varieties', 0.7709184885025024), ('shimura curves', 0.7543201446533203), ('shimura variety', 0.7442144155502319), ('shimura', 0.5629196166992188), ('subvarieties moduli', 0.527727484703064), ('hyperelliptic curves genus', 0.5270881652832031), ('subvarieties moduli space', 0.5233275890350342), ('covers elliptic curves', 0.5158255696296692), ('curves moduli space', 0.4983385503292084), ('abelian covers', 0.49737313389778137)]"
1471,1471,20,1471_riccati equations_algebraic riccati equations_differential riccati_quadratic optimal control,"['riccati equations', 'algebraic riccati equations', 'differential riccati', 'quadratic optimal control', 'algebraic riccati', 'unique optimal control', 'optimal boundary control', 'linear quadratic control', 'optimal control', 'lq optimal control']","['On the Approximation of Operator-Valued Riccati Equations in Hilbert\n  Spaces   In this work, we present an abstract theory for the approximation of\noperator-valued Riccati equations posed on Hilbert spaces. It is demonstrated\nhere that the error of the approximate solution to the operator-valued Riccati\nequation is bounded above by the approximation error of the governing\nsemigroup, under the assumption of boundedness on the semigroup and compactness\non the coefficient operators. One significant outcome of this result is the\ncorrect prediction of optimal convergence for finite element approximations of\nthe operator-valued Riccati equations for when the governing semigroup involves\nparabolic, as well as hyperbolic processes. We derive the abstract theory for\nthe time-dependent and time-independent operator-valued Riccati equations in\nthe first part of this work. In the second part, we derive optimal error\nestimates for the finite element approximation of the functional gain\nassociated with model weakly damped wave and thermal LQR control systems. These\ntheoretical claims are then corroborated with computational evidence.\n', 'Riccati equations and LQ-optimal control for a class of hyperbolic PDEs   We derive an explicit solution to the operator Riccati equation solving the\nLinear-Quadratic (LQ) optimal control problem for a class of boundary\ncontrolled hyperbolic partial differential equations (PDEs). Different\ndescriptions of the system are used to obtain different representations of the\noperator Riccati equation. By means of an example, we illustrate the importance\nof considering an extended operator Riccati equation to solve the LQ-optimal\ncontrol problem for our class of systems.\n', 'Unified Riccati theory for optimal permanent and sampled-data control\n  problems in finite and infinite time horizons   We revisit and extend the Riccati theory, unifying continuous-time\nlinear-quadratic optimal permanent and sampled-data control problems, in finite\nand infinite time horizons. In a nutshell, we prove that:-- when the time\nhorizon T tends to $+\\infty$, one passes from the Sampled-Data Difference\nRiccati Equation (SD-DRE) to the Sampled-Data Algebraic Riccati Equation\n(SD-ARE), and from the Permanent Differential Riccati Equation (P-DRE) to the\nPermanent Algebraic Riccati Equation (P-ARE);-- when the maximal step of the\ntime partition $\\Delta$ tends to $0$, one passes from (SD-DRE) to (P-DRE), and\nfrom (SD-ARE) to (P-ARE).Our notations and analysis provide a unified framework\nin order to settle all corresponding results.\n']","[('riccati equations', 0.6137946248054504), ('algebraic riccati equations', 0.6098012924194336), ('differential riccati', 0.5525162220001221), ('quadratic optimal control', 0.5451856255531311), ('algebraic riccati', 0.5449851155281067), ('unique optimal control', 0.5377346873283386), ('optimal boundary control', 0.5175909996032715), ('linear quadratic control', 0.5012218356132507), ('optimal control', 0.4960232377052307), ('lq optimal control', 0.4943777620792389)]"
1472,1472,20,1472_ample line bundles_smooth projective varieties_projective varieties_ample line bundle,"['ample line bundles', 'smooth projective varieties', 'projective varieties', 'ample line bundle', 'projective variety dimension', 'projective variety', 'smooth projective variety', 'projective scheme', 'complex projective varieties', 'ample line']","[""Construction of varieties of low codimension with applications to moduli\n  spaces of varieties of general type   In this article we develop a new way of systematically constructing\ninfinitely many families of smooth subvarieties $X$ of any given dimension $m$,\n$m \\geq 3$, and any given codimension in $\\mathbb P^N$, embedded by complete\nsubcanonical linear series, and, in particular, in the range of Hartshorne's\nconjecture. We accomplish this by showing the existence of everywhere\nnon--reduced schemes called ropes, embedded in $\\mathbb P^N$, and by smoothing\nthem. In the range $3 \\leq m < N/2$, we construct smooth subvarieties, embedded\nby complete subcanonical linear series, that are not complete intersections. We\nalso go beyond a question of Enriques on constructing simple canonical surfaces\nin projective spaces, and construct simple canonical varieties in all\ndimensions. The canonical map of infinitely many of these simple canonical\nvarieties is finite birational but not an embedding. Finally, we show the\nexistence of components of moduli spaces of varieties of general type (in all\ndimensions $m$, $m \\geq 3$) that are analogues of the moduli space of curves of\ngenus $g > 2$ with respect to the behavior of the canonical map and its\ndeformations. In many cases, the general elements of these components are\ncanonically embedded and their codimension is in the range of Hartshorne's\nconjecture.\n"", 'Positivity of double point divisors   The non-isomorphic locus of a general projection from an embedded smooth\nprojective variety to a hypersurface moves in a linear system of an effective\ndivisor which we call the double point divisor. David Mumford proved that the\ndouble point divisor from outer projection is always base point free, and Bo\nIlic proved that it is ample except for a Roth variety. The first aim of this\npaper is to show that the double point divisor from outer projection is very\nample except in the Roth case. This answers a question of Bo Ilic. Unlike the\ncase of outer projection, the double point divisor from inner projection may\nnot be base point free nor ample. However, Atsushi Noma proved that it is\nsemiample except when a variety is neither a Roth variety, a scroll over a\ncurve, nor the second Veronese surface. In this paper, we investigate when the\ndouble point divisor from inner projection is base point free or big.\n', 'Cactus varieties of sufficiently ample embeddings of projective schemes\n  have determinantal equations   For a fixed projective scheme X, a property P of line bundles is satisfied by\nsufficiently ample line bundles if there exists a line bundle L_0 on X such\nthat P(L) holds for any L with (L - L_0) ample. As an example, sufficiently\nample line bundles are very ample, moreover, for a normal variety X, the\nembedding corresponding to sufficiently ample line bundle is projectively\nnormal. The grandfather of such properties and a basic ingredient used to study\nthis concept is Fujita vanishing theorem, which is a strengthening of Serre\nvanishing to sufficiently ample line bundles. The r-th cactus variety of X is\nan analogue of secant variety and it is defined using linear spans of finite\nschemes of degree r. In this article we show that cactus varieties of\nsufficiently ample embeddings of X are set-theoretically defined by minors of\nmatrices with linear entries. The topic is closely related to conjectures of\nEisenbud-Koh-Stillman, which was proved by Ginensky in the case X a smooth\ncurve. On the other hand Sidman-Smith proved that the ideal of sufficiently\nample embedding of any projective scheme X is generated by 2 x 2 minors of a\nmatrix with linear entries.\n']","[('ample line bundles', 0.65248042345047), ('smooth projective varieties', 0.6483500599861145), ('projective varieties', 0.6481868028640747), ('ample line bundle', 0.6333032250404358), ('projective variety dimension', 0.6294220089912415), ('projective variety', 0.6284605860710144), ('smooth projective variety', 0.6212118864059448), ('projective scheme', 0.6153520941734314), ('complex projective varieties', 0.5986247658729553), ('ample line', 0.5861525535583496)]"
1473,1473,20,1473_extreme learning machines_extreme learning_forward neural network_randomized neural networks,"['extreme learning machines', 'extreme learning', 'forward neural network', 'randomized neural networks', 'trained linear', 'neural networks', 'forward neural', 'feed forward neural', 'neural network', 'neural networks single']","['Numerical Computation of Partial Differential Equations by Hidden-Layer\n  Concatenated Extreme Learning Machine   The extreme learning machine (ELM) method can yield highly accurate solutions\nto linear/nonlinear partial differential equations (PDEs), but requires the\nlast hidden layer of the neural network to be wide to achieve a high accuracy.\nIf the last hidden layer is narrow, the accuracy of the existing ELM method\nwill be poor, irrespective of the rest of the network configuration. In this\npaper we present a modified ELM method, termed HLConcELM (hidden-layer\nconcatenated ELM), to overcome the above drawback of the conventional ELM\nmethod. The HLConcELM method can produce highly accurate solutions to\nlinear/nonlinear PDEs when the last hidden layer of the network is narrow and\nwhen it is wide. The new method is based on a type of modified feedforward\nneural networks (FNN), termed HLConcFNN (hidden-layer concatenated FNN), which\nincorporates a logical concatenation of the hidden layers in the network and\nexposes all the hidden nodes to the output-layer nodes. HLConcFNNs have the\ninteresting property that, given a network architecture, when additional hidden\nlayers are appended to the network or when extra nodes are added to the\nexisting hidden layers the representation capacity of the HLConcFNN associated\nwith the new architecture is guaranteed to be not smaller than that of the\noriginal network architecture. Here representation capacity refers to the set\nof all functions that can be exactly represented by the neural network of a\ngiven architecture. We present ample benchmark tests with linear/nonlinear PDEs\nto demonstrate the computational accuracy and performance of the HLConcELM\nmethod and the superiority of this method to the conventional ELM from previous\nworks.\n', 'Local Extreme Learning Machines and Domain Decomposition for Solving\n  Linear and Nonlinear Partial Differential Equations   We present a neural network-based method for solving linear and nonlinear\npartial differential equations, by combining the ideas of extreme learning\nmachines (ELM), domain decomposition and local neural networks. The field\nsolution on each sub-domain is represented by a local feed-forward neural\nnetwork, and $C^k$ continuity is imposed on the sub-domain boundaries. Each\nlocal neural network consists of a small number of hidden layers, while its\nlast hidden layer can be wide. The weight/bias coefficients in all hidden\nlayers of the local neural networks are pre-set to random values and are fixed,\nand only the weight coefficients in the output layers are training parameters.\nThe overall neural network is trained by a linear or nonlinear least squares\ncomputation, not by the back-propagation type algorithms. We introduce a block\ntime-marching scheme together with the presented method for long-time dynamic\nsimulations. The current method exhibits a clear sense of convergence with\nrespect to the degrees of freedom in the neural network. Its numerical errors\ntypically decrease exponentially or nearly exponentially as the number of\ndegrees of freedom increases. Extensive numerical experiments have been\nperformed to demonstrate the computational performance of the presented method.\nWe compare the current method with the deep Galerkin method (DGM) and the\nphysics-informed neural network (PINN) in terms of the accuracy and\ncomputational cost. The current method exhibits a clear superiority, with its\nnumerical errors and network training time considerably smaller (typically by\norders of magnitude) than those of DGM and PINN. We also compare the current\nmethod with the classical finite element method (FEM). The computational\nperformance of the current method is on par with, and oftentimes exceeds, the\nFEM performance.\n', 'A Nonoverlapping Domain Decomposition Method for Extreme Learning\n  Machines: Elliptic Problems   Extreme learning machine (ELM) is a methodology for solving partial\ndifferential equations (PDEs) using a single hidden layer feed-forward neural\nnetwork. It presets the weight/bias coefficients in the hidden layer with\nrandom values, which remain fixed throughout the computation, and uses a linear\nleast squares method for training the parameters of the output layer of the\nneural network. It is known to be much faster than Physics informed neural\nnetworks. However, classical ELM is still computationally expensive when a high\nlevel of representation is desired in the solution as this requires solving a\nlarge least squares system. In this paper, we propose a nonoverlapping domain\ndecomposition method (DDM) for ELMs that not only reduces the training time of\nELMs, but is also suitable for parallel computation. In numerical analysis,\nDDMs have been widely studied to reduce the time to obtain finite element\nsolutions for elliptic PDEs through parallel computation. Among these\napproaches, nonoverlapping DDMs are attracting the most attention. Motivated by\nthese methods, we introduce local neural networks, which are valid only at\ncorresponding subdomains, and an auxiliary variable at the interface. We\nconstruct a system on the variable and the parameters of local neural networks.\nA Schur complement system on the interface can be derived by eliminating the\nparameters of the output layer. The auxiliary variable is then directly\nobtained by solving the reduced system after which the parameters for each\nlocal neural network are solved in parallel. A method for initializing the\nhidden layer parameters suitable for high approximation quality in large\nsystems is also proposed. Numerical results that verify the acceleration\nperformance of the proposed method with respect to the number of subdomains are\npresented.\n']","[('extreme learning machines', 0.6447048187255859), ('extreme learning', 0.5981588363647461), ('forward neural network', 0.4940992295742035), ('randomized neural networks', 0.46727314591407776), ('trained linear', 0.45372748374938965), ('neural networks', 0.426000714302063), ('forward neural', 0.4218418300151825), ('feed forward neural', 0.4191663861274719), ('neural network', 0.41785088181495667), ('neural networks single', 0.4168676435947418)]"
1474,1474,20,1474_bifurcation theory_solutions bifurcation_global bifurcation theory_bifurcation points,"['bifurcation theory', 'solutions bifurcation', 'global bifurcation theory', 'bifurcation points', 'bifurcations', 'bifurcation point', 'bifurcation', 'bifurcation results', 'global bifurcation', 'hopf bifurcation']","['Parameterized splitting theorems and bifurcations for potential\n  operators, Part II: Applications to quasi-linear elliptic equations and\n  systems   This is the second part of a series devoting to the generalizations and\napplications of common theorems in variational bifurcation theory. Using\nabstract theorems in the first part we obtain many new bifurcation results for\nquasi-linear elliptic boundary value problems of higher order.\n', ""Bifurcation Theory for a Class of Periodic Superlinear Problems   We analyze, mainly using bifurcation methods, an elliptic superlinear problem\nin one-dimension with periodic boundary conditions. One of the main novelties\nis that we follow for the first time a bifurcation approach, relying on a\nLyapunov-Schmidt reduction and some recent global bifurcation results, that\nallows us to study the local and global structure of non-trivial solutions at\nbifurcation points where the linearized operator has a two-dimensional kernel.\nIndeed, at such points the classical tools in bifurcation theory, like the\nCrandall-Rabinowitz theorem or some generalizations of it, cannot be applied\nbecause the multiplicity of the eigenvalues is not odd, and a new approach is\nrequired. We apply this analysis to specific examples, obtaining new existence\nand multiplicity results for the considered periodic problems, going beyond the\ninformation variational and fixed point methods like Poincar\\'e-Birkhoff\ntheorem can provide.\n"", 'Parameterized splitting theorems and bifurcations for potential\n  operators, Part I: Abstract theory   This is the first part of a series devoting to the generalizations and\napplications of common theorems in variational bifurcation theory. Using\nparameterized versions of splitting theorems in Morse theory we generalize some\nfamous bifurcation theorems for potential operators by weakening standard\nassumptions on the differentiability of the involved functionals, which opens\nup a way of bifurcation studies for quasi-linear elliptic boundary value\nproblems.\n']","[('bifurcation theory', 0.6566445827484131), ('solutions bifurcation', 0.6254898905754089), ('global bifurcation theory', 0.6210013628005981), ('bifurcation points', 0.6145238280296326), ('bifurcations', 0.6106367707252502), ('bifurcation point', 0.5842716097831726), ('bifurcation', 0.5807368755340576), ('bifurcation results', 0.5773276090621948), ('global bifurcation', 0.5692720413208008), ('hopf bifurcation', 0.5093734860420227)]"
1475,1475,20,1475_port hamiltonian formulation_port hamiltonian systems_port hamiltonian framework_port hamiltonian structure,"['port hamiltonian formulation', 'port hamiltonian systems', 'port hamiltonian framework', 'port hamiltonian structure', 'port hamiltonian', 'hamiltonian formulations', 'dimensional hamiltonian systems', 'hamiltonian formulation', 'hamiltonian framework', 'hamiltonian systems']","['Port-Hamiltonian Modeling of Ideal Fluid Flow: Part II. Compressible and\n  Incompressible Flow   Part I of this paper presented a systematic derivation of the Stokes Dirac\nstructure underlying the port-Hamiltonian model of ideal fluid flow on\nRiemannian manifolds. Starting from the group of diffeomorphisms as a\nconfiguration space for the fluid, the Stokes Dirac structure is derived by\nPoisson reduction and then augmented by boundary ports and distributed ports.\nThe additional boundary ports have been shown to appear naturally as surface\nterms in the pairings of dual maps, always neglected in standard Hamiltonian\ntheory. The port-Hamiltonian model presented in Part I corresponded only to the\nkinetic energy of the fluid and how its energy variables evolve such that the\nenergy is conserved.\n  In Part II, we utilize the distributed port of the kinetic energy\nport-Hamiltonian system for representing a number of fluid-dynamical systems.\nBy adding internal energy we model compressible flow, both adiabatic and\nisentropic, and by adding constraint forces we model incompressible flow. The\nkey tools used are the interconnection maps relating the dynamics of fluid\nmotion to the dynamics of advected quantities.\n', 'A geometric framework for discrete time port-Hamiltonian systems   Port-Hamiltonian systems provide an energy-based formulation with a model\nclass that is closed under structure preserving interconnection.\n  For continuous-time systems these interconnections are constructed by\ngeometric objects called Dirac structures. In this paper, we derive this\ngeometric formulation and the interconnection properties for scattering passive\ndiscrete-time port-Hamiltonian systems.\n', ""Moving-Boundary Port-Hamiltonian Systems   In this paper, we consider linear boundary port-Hamiltonian distributed\nparameter systems on a time-varying spatial domain. We derive the specific\ntime-varying Dirac structure that these systems give rise to and use it to\nformally introduce a new class of moving-boundary port-Hamiltonian systems by\nshowing that these distributed parameter systems on a time-varying spatial\ndomain admit a port-Hamiltonian representation. We demonstrate that our results\ncan be leveraged to develop a spatial discretization scheme with dynamic\nmeshing for approximating the telegrapher's equations on a time-varying spatial\ndomain, which we subsequently verify numerically.\n""]","[('port hamiltonian formulation', 0.7675387263298035), ('port hamiltonian systems', 0.7476687431335449), ('port hamiltonian framework', 0.727231502532959), ('port hamiltonian structure', 0.7026283144950867), ('port hamiltonian', 0.6991578340530396), ('hamiltonian formulations', 0.5790098309516907), ('dimensional hamiltonian systems', 0.5567852854728699), ('hamiltonian formulation', 0.5348711013793945), ('hamiltonian framework', 0.5249298810958862), ('hamiltonian systems', 0.5196822881698608)]"
1476,1476,20,1476_nonlinear oscillations_nonlinear oscillators_oscillations_bifurcations,"['nonlinear oscillations', 'nonlinear oscillators', 'oscillations', 'bifurcations', 'vibration', 'period doubling bifurcations', 'bifurcation', 'dynamics hybrid', 'coupled oscillator', 'doubling bifurcations']","['Analysis of Dry Friction Dynamics in a Vibro-Impact Energy Harvester   Vibro-impact (VI) systems provide a promising nonlinear mechanism for energy\nharvesting (EH) in many engineering applications. Here, we consider a VI-EH\nsystem that consists of an inclined cylindrical capsule that is externally\nforced and a bullet that is allowed to move inside the capsule, and analyze its\ndynamics under the presence of dry friction. Dry friction introduces a\nswitching manifold corresponding to zero relative velocity where the bullet\nsticks to the capsule, appearing as sliding in the model. We identify\nanalytical conditions for the occurrence of non-stick and sliding motions, and\nconstruct a series of nonlinear maps that capture model solutions and their\ndynamics on the switching and impacting manifolds. An interplay of smooth\n(period-doubling) and non-smooth (grazing) bifurcations characterizes the\ntransition from periodic solutions with alternating impacts to solutions with\nan additional impact on one end of the capsule per period. This transition is\npreceded by a sequence of grazing-sliding, switching-sliding and\ncrossing-sliding bifurcations on the switching manifold that may reverse period\ndoubling bifurcations for larger values of the dry friction coefficient. In\ngeneral, a larger dry friction coefficient also results in larger sliding\nintervals, lower impact velocities yielding lower average energy outputs, and a\nshift in the location of some bifurcations. Surprisingly, we identify parameter\nregimes in which higher dry friction maintains higher energy output levels, as\nit shifts the location of grazing bifurcations.\n', ""Stability of a Parametrically Driven, Coupled Oscillator System: An\n  Auxillary Function Method Approach   Coupled, nonlinear oscillators are often studied in applied biology, physics,\nfluids, and many other disciplines. In this paper, we study a parametrically\ndriven, coupled oscillator system where the individual oscillators are\nsubjected to varying frequency and phase with a focus on the influence of the\ndamping and coupling parameters away from parametric resonance frequencies. In\nparticular, we study the key long-term statistics of the oscillator system's\ntrajectories and stability. We present a novel, robust and computationally\nefficient method come to be known as an auxillary function method for long-time\naverages, and we pair this method with classical, perturbative-asymptotic\nanalysis to corroborate the results of this auxillary function method. These\npaired methods are then used to compute the regions of stability for a coupled\noscillator system. The objective is to explore the influence of higher order,\ncoupling effects on the stability boundary across a broad range of modulation\nfrequencies, including frequencies away from parametric resonances. We show\nthat both simplified and more general asymptotic methods can be dangerously\nun-conservative in predicting the true regions of stability due to high order\neffects caused by coupling parameters. The differences between the true\nstability boundary and the approximate stability boundary can occur at\nphysically relevant parameter values in regions away from parametric resonance.\nThe differences between the solutions depends on the specific parameters of the\nsystem, as explained in the results section. As an alternative to asymptotic\nmethods, we show that the auxillary function method for long-time averages is\nan efficient and robust means of computing true regions of stability across all\npossible initial conditions.\n"", ""Suppressing parametric resonance of a Hyperloop vehicle using a\n  parametric force   In this paper, we study the stability of a simple model of a Hyperloop\nvehicle resulting from the interaction between electromagnetic and aeroelastic\nforces for both constant and periodically varying coefficients (i.e.,\nparametric excitation). For the constant coefficients, through linear stability\nanalysis, we analytically identify three distinct regions for the physically\nsignificant equilibrium point. Further inspection reveals that the system\nexhibits limit-cycle vibrations in one of these regions. Using the harmonic\nbalance method, we determine the properties of the limit cycle, thereby\nunravelling the frequency and amplitude that characterize the periodic\noscillations of the system's variables. For the varying coefficients case, the\nstability is studied using Floquet analysis and Hills determinant method. The\npart of the stability boundary related to parametric resonance has an\nelliptical shape, while the remaining part remains unchanged. One of the major\nfindings is that a linear parametric force, can suppress or amplify the\nparametric resonance induced by another parametric force depending on the\namplitude of the former. In the context of the Hyperloop system, this means\nthat parametric resonance caused by base excitation-in other words by the\nlinearized parametric electromagnetic force can be suppressed by modulating the\ncoefficient of the aeroelastic force in the same frequency. The effectiveness\nis highly dependent on the phase difference between the modulation and the base\nexcitation. The origin of the suppression is attributed to the stabilizing\ncharacter of the parametric aeroelastic force as revealed through energy\nanalysis. We provide analytical expressions for the stability boundaries and\nfor the stability's dependence on the phase shift of the modulation.\n""]","[('nonlinear oscillations', 0.597947359085083), ('nonlinear oscillators', 0.5673474669456482), ('oscillations', 0.506835401058197), ('bifurcations', 0.48702555894851685), ('vibration', 0.4867440462112427), ('period doubling bifurcations', 0.48494279384613037), ('bifurcation', 0.4828035831451416), ('dynamics hybrid', 0.4752293825149536), ('coupled oscillator', 0.47336673736572266), ('doubling bifurcations', 0.46964818239212036)]"
1477,1477,20,1477_toda equations_toda lattice_lie algebra structures_toda type,"['toda equations', 'toda lattice', 'lie algebra structures', 'toda type', 'lie algebra structure', 'toda hierarchy', 'lie algebras', 'lie algebra type', 'affine lie algebra', 'affine weyl group']","['Total masses of solutions to general Toda systems with singular sources   In this article we obtain total masses of solutions to the Toda system\nassociated to a general simple Lie algebra with singular sources at the origin.\nThe determination of such total masses is one of the important steps towards\nestablishing the a priori bound for solutions to the mean field type of Toda\nsystem on compact surfaces. The total mass is found to be related to the\nlongest element $\\kappa$ in the Weyl group of the corresponding Lie algebra.\nThis is the foundation to future work relating the local blowup masses (from\nanalysis) with the Weyl group.\n  This work generalizes the previous works in Lin et al. (2012), Ao et al.\n(2015) and Nie (20160 for Toda systems of types $A, G_2$ and $B, C$. However, a\nmore Lie-theoretic method is needed here for the general case, and the method\nrelies heavily on the DPW method, Drinfeld-Sokolov gauge and the\n$W$-invariants. The last crucial step for the total masses is obtained by\napplying the work of Kostant (1979) on the one dimensional Toda lattice.\n', 'Affine Toda system of $\\mathbf{A}$ and $\\mathbf{C}^t$ type: compactness\n  and affine Weyl group   The local mass is a fundamental quantized information that characterizes the\nblow-up solution to the Toda system and has a profound relationship with its\nunderlying algebraic structure. In \\cite{Lin-Yang-Zhong-2020}, it was observed\nthat the associated Weyl group can be employed to represent this information\nfor the $\\mathbf{A}_n$, $\\mathbf{B}_n$, $\\mathbf{C}_n$ and $\\mathbf{G}_2$ type\nToda systems. The relationship between the local mass of blow-up solution and\nthe corresponding affine Weyl group is further explored for some affine\n$\\mathbf{B}$ type Toda systems in \\cite{Cui-Wei-Yang-Zhang-2022}, where the\npossible local masses are explicitly expressed in terms of $8$ types. The\ncurrent work presents a comprehensive study of the general affine $\\mathbf{A}$\nand $\\mathbf{C}^t$ type Toda systems with arbitrary rank. At each stage of the\nblow-up process (via scaling), we can employ certain elements (known as ""set\nchains"") in the corresponding affine Weyl group to measure the variation of\nlocal mass. Consequently, we obtain the a priori estimate of the affine\n$\\mathbf{A}$ and $\\mathbf{C}^t$ type Toda systems with arbitrary number of\nsingularities.\n', 'The Blow-up Analysis on $\\mathbf{B}_2^{(1)}$ Affine Toda system: Local\n  mass and Affine Weyl group   It has been established that the local mass of blow-up solutions to Toda\nsystems associated with the simple Lie algebras\n$\\mathbf{A}_n,~\\mathbf{B}_n,~\\mathbf{C}_n$ and $\\mathbf{G}_2$ can be\nrepresented by a finite Weyl group. In particular, at each blow-up point, after\na sequence of bubbling steps (via scaling) is performed, the transformation of\nthe local mass at each step corresponds to the action of an element in the Weyl\ngroup. In this article, we present the results in the same spirit for the\naffine $\\mathbf{B}_2^{(1)}$ Toda system with singularities. Compared with the\nToda system with simple Lie algebras, the computation of local masses is more\nchallenging due to the infinite number of elements of the {affine Weyl group of\ntype $\\mathbf{B}_{2}^{(1)}$}. In order to give an explicit expression for the\nlocal mass formula we introduce two free integers and write down all the\npossibilities into 8 types. This shows a striking difference to previous\nresults on Toda systems with simple Lie algebras. The main result of this\narticle seems to provide the first major advance in understanding the relation\nbetween the blow-up analysis of affine Toda system and the {affine Weyl group}\nof the associated Lie algebras.\n']","[('toda equations', 0.5947203040122986), ('toda lattice', 0.5544192790985107), ('lie algebra structures', 0.5469045639038086), ('toda type', 0.5280199646949768), ('lie algebra structure', 0.5077033042907715), ('toda hierarchy', 0.4994847774505615), ('lie algebras', 0.49365919828414917), ('lie algebra type', 0.4870322346687317), ('affine lie algebra', 0.4736989140510559), ('affine weyl group', 0.4589725434780121)]"
1478,1478,20,1478_number electrons_bound states_ground state density_thomas fermi,"['number electrons', 'bound states', 'ground state density', 'thomas fermi', 'electrons', 'particle number', 'atom', 'atomic systems', 'coulomb systems', 'atoms']","['On the excess charge of a relativistic statistical model of molecules\n  with an inhomogeneity correction   We show that the molecular relativistic Thomas-Fermi-Weizs\\""acker functional\nconsisting of atoms of atomic numbers $Z_1,...,Z_k$ has a minimizer, if the\nparticle number $N$ is constrained to a number less or equal to the total\nnuclear charge $Z:=Z_1+...+Z_K$. Moreover, there is no minimizer, if the\nparticle number exceeds $2.56 Z$. This gives lower and upper bounds on the\nmaximal ionization of heavy atoms.\n', 'Thomas-Fermi approximation to electronic density   In heavy atoms and molecules, on the distances $a \\gg Z^{-1}$ from all of the\nnuclei (with a charge $Z_m$) we prove that $\\rho_\\Psi (x)$ is approximated in\n$L^p$-norm, by the Thomas-Fermi density.\n', 'The Atomic Density on the Thomas--Fermi Length Scale for the\n  Chandrasekhar Hamiltonian   We consider a large neutral atom of atomic number $Z$, modeled by a\npseudo-relativistic Hamiltonian of Chandrasekhar. We study its suitably\nrescaled one-particle ground state density on the Thomas--Fermi length scale\n$Z^{-1/3}$. Using an observation by Fefferman and Seco (1989), we find that the\ndensity on this scale converges to the minimizer of the Thomas--Fermi\nfunctional of hydrogen as $Z\\to\\infty$ when $Z/c$ is fixed to a value not\nexceeding $2/\\pi$. This shows that the electron density on the Thomas--Fermi\nlength scale does not exhibit any relativistic effects.\n']","[('number electrons', 0.40373507142066956), ('bound states', 0.3933621346950531), ('ground state density', 0.37546348571777344), ('thomas fermi', 0.35862356424331665), ('electrons', 0.35212862491607666), ('particle number', 0.35132208466529846), ('atom', 0.34241825342178345), ('atomic systems', 0.3365154266357422), ('coulomb systems', 0.33611157536506653), ('atoms', 0.3353351354598999)]"
1479,1479,20,1479_zeros dirichlet functions_zeros dirichlet_dirichlet functions_values dirichlet functions,"['zeros dirichlet functions', 'zeros dirichlet', 'dirichlet functions', 'values dirichlet functions', 'geq dirichlet', 'distribution dirichlet', 'derivatives dirichlet functions', 'generalized riemann hypothesis', 'values dirichlet', 'critical zeros']","['The positivity technique and low-lying zeros of Dirichlet $L$-functions   Assuming the generalized Riemann hypothesis, we rediscover and sharpen some\nof the best known results regarding the distribution of low-lying zeros of\nDirichlet $L$-functions. This builds upon earlier work of Omar, which relies on\nthe classical positivity technique of explicit formulas. In addition, we\ngeneralize some of our results to a larger class of $L$-functions and provide\neffective conditional estimates for the lowest zeros of Dirichlet\n$L$-functions.\n', 'Zeros of Dirichlet $L$-functions near the critical line   We prove an upper bound on the density of zeros very close to the critical\nline of the family of Dirichlet $L$-functions of modulus $q$ at height $T$. To\ndo this, we derive an asymptotic for the twisted second moment of Dirichlet\n$L$-functions uniformly in $q$ and $t$. As a second application of the\nasymptotic formula we prove that, for every integer $q$, at least $38.2\\%$ of\nzeros of the primitive Dirichlet $L$-functions of modulus $q$ lie on the\ncritical line.\n', ""Zeros of Dirichlet $L$-functions on the critical line   In this paper, we estimate the proportion of zeros of Dirichlet $L$-functions\non the critical line. Using Feng's mollifier and an asymptotic formula for the\nmean square of Dirichlet $L$-functions, we prove that averaged over primitive\ncharacters and conductors, at least 61.07 % of zeros of Dirichlet $L$-functions\nare on the critical line, and at least 60.44 % of zeros are simple and on the\ncritical line. These results improve the work of Conrey, Iwaniec and\nSoundararajan.\n""]","[('zeros dirichlet functions', 0.735079288482666), ('zeros dirichlet', 0.6607958078384399), ('dirichlet functions', 0.6347460746765137), ('values dirichlet functions', 0.597739040851593), ('geq dirichlet', 0.5041996240615845), ('distribution dirichlet', 0.5005351901054382), ('derivatives dirichlet functions', 0.492412269115448), ('generalized riemann hypothesis', 0.48066747188568115), ('values dirichlet', 0.46998879313468933), ('critical zeros', 0.46946704387664795)]"
1480,1480,20,1480_quantum contextuality_interpretation quantum_quantum measurements_quantum measurement,"['quantum contextuality', 'interpretation quantum', 'quantum measurements', 'quantum measurement', 'theory quantum', 'quantum', 'quantum theory', 'quantum probability', 'quantum mechanics', 'quantum statistical']","['Quantum collapse as undecidable proposition in an Everettian multiverse   Our representation of the Universe is built with sequences of symbols,\nnumbers, operators, rules and undecidable propositions defining our\nmathematical truths, represented either by classical, quantum and probabilistic\nTuring Machines containing intrinsic randomness. Each representation is at all\neffects a physical subset of the Universe, a metastructure of events in space\nand time, which actively participate to the evolution of the Universe as we are\ninternal observers. The evolution is a deterministic sequence of local events,\nquantum measurements, originated from the local wavefunction collapse of the\ncomplementary set of the observers that generate the local events in the\nUniverse. With these assumptions, the Universe and its evolution are described\nin terms of a semantically closed structure without a global object-environment\nloss of decoherence as a von Neumann\'s universal constructor with a semantical\nabstract whose structure cannot be decided deterministically a-priori from an\ninternal observer. In a semantically closed structure the realization of a\nspecific event writing the semantical abstract of the constructor is a problem\nthat finds a ""which way"" for the evolution of the Universe in terms of a choice\nof the constructor\'s state in a metastructure, the many-world Everett scenario\nfrom the specific result of a quantum measurement, a classical G\\""odel\nundecidable proposition for an internal observer, exposing the limits of our\ndescription and possible simulation of the Universe.\n', ""Quantum Measurement Without Collapse or Many Worlds: The Branched Hilbert Subspace Interpretation The interpretation of quantum measurements remains contested between collapse-based frameworks like the Copenhagen Interpretation and no-collapse approaches like the Many-Worlds Interpretation (MWI). We propose the Branched Hilbert Subspace Interpretation (BHSI) as a minimalist alternative that preserves unitarity while avoiding both wavefunction collapse and ontological excess. BHSI models measurement as the unitary branching of a system's local Hilbert space into decoherent subspaces, formalized through causal state updates using branching and disengaging operators. Unlike MWI, BHSI avoids parallel worlds by maintaining a single-world ontology in which branching is confined to observable subspaces; unlike Copenhagen, it eliminates collapse while recovering the Born rule through branch weights. Through physically meaningful subspace records, the framework resolves quantum paradoxes such as particle-wave duality, Wigner and his friend, black hole radiation, etc. It remains consistent with interference patterns, entanglement correlations, and information preservation. By comparing BHSI with QBism, Relational Quantum Mechanics, and modal interpretations, as well as analyzing quantum teleportation (where locally decoherent Hilbert subspaces are observed), we demonstrate its advantages as a causally sound and empirically grounded approach that reconciles unitary evolution with definite measurement outcomes without metaphysical proliferation."", ""Quantum Immortality and Non-Classical Logic   The Everett Box is a device in which an observer and a lethal quantum\napparatus are isolated from the rest of the universe. On a regular basis,\nsuccessive trials occur, in each of which an automatic measurement of a quantum\nsuperposition inside the apparatus either causes instant death or does nothing\nto the observer. From the observer's perspective, the chances of surviving $m$\ntrials monotonically decreases with increasing $m$. As a result, if the\nobserver is still alive for sufficiently large $m$ she must reject any\ninterpretation of quantum mechanics which is not the many-worlds interpretation\n(MWI), since surviving $m$ trials becomes vanishingly unlikely in a single\nworld, whereas a version of the observer will necessarily survive in the\nbranching MWI universe. Here we ask whether this conclusion still holds if\nrather than a classical understanding of limits built on classical logic we\ninstead require our physics to satisfy a computability requirement by\ninvestigating the Everett Box in a model of a computational universe running on\na variety of constructive logic, Recursive Constructive Mathematics. We show\nthat although the standard Everett argument rejecting non-MWI interpretations\nis no longer valid, we can show that Everett's conclusion still holds within a\ncomputable universe. Thus we argue that Everett's argument is strengthened and\nany counter-argument must be strengthened, since it holds not only in classical\nlogic (with embedded notions of continuity and infinity) but also in a\ncomputable logic.\n""]","[('quantum contextuality', 0.6455812454223633), ('interpretation quantum', 0.638550341129303), ('quantum measurements', 0.5984289050102234), ('quantum measurement', 0.5853363275527954), ('theory quantum', 0.5575242042541504), ('quantum', 0.5543314814567566), ('quantum theory', 0.5507369041442871), ('quantum probability', 0.5379374623298645), ('quantum mechanics', 0.5277025699615479), ('quantum statistical', 0.5103850960731506)]"
1481,1481,20,1481_convex hamilton jacobi_periodic homogenization_hamilton jacobi equations_hamiltonian periodic,"['convex hamilton jacobi', 'periodic homogenization', 'hamilton jacobi equations', 'hamiltonian periodic', 'viscous hamilton jacobi', 'convex hamiltonians', 'convergence rate periodic', 'convergence homogenization', 'homogenization nonlinear', 'convex hamilton']","['Slow periodic homogenization for Hamilton-Jacobi equations   Capuzzo-Dolcetta and Ishii proved that the rate of periodic homogenization\nfor coercive Hamilton-Jacobi equations is $O(\\varepsilon^{1/3})$. We complement\nthis result by constructing examples of coercive nonconvex Hamiltonians whose\nrate of periodic homogenization is $\\Omega(\\varepsilon^{1/2})$.\n', 'Rate of Convergence in Periodic Homogenization for Convex\n  Hamilton-Jacobi Equations with Multiscales   We study the rate of convergence in periodic homogenization for convex\nHamilton--Jacobi equations with multiscales, where the Hamiltonian $H=H(x, y,\np): \\mathbb{R}^n \\times \\mathbb{T}^n \\times \\mathbb{R}^n \\to \\mathbb{R }$\ndepends on both of the spatial variable and the oscillatory variable. In\nparticular, we show that for the Cauchy problem, the rate of convergence is\n$O(\\sqrt{\\epsilon})$ by optimal control formulas, scale separations and curve\ncutting techniques. We also show the rate $O(\\sqrt{\\epsilon})$ of\nhomogenization for the static problem based on the same idea. Additionally, we\nprovide examples that illustrate the rate of convergence for the Cauchy problem\nis optimal.\n', 'Optimal convergence rate for periodic homogenization of convex\n  Hamilton-Jacobi equations   In this paper, we show that the rate of convergence in periodic\nhomogenization of convex Hamilton-Jacobi equations is always $O(\\varepsilon)$,\nwhich is optimal. This is a natural extension of a result concerning stable\nnorms in metric geometry [4] that is essentially equivalent to the\nhomogenization of convex static Hamilton-Jacobi equations. Another extremely\ninteresting question in this direction is whether the $O(\\varepsilon)$ rate\nholds in the nonconvex setting. We present a special nonconvex example with\n$O(\\varepsilon)$ convergence rate, which relies on identifying the shape of the\neffective Hamiltonian and game theory interpretation formulas.\n']","[('convex hamilton jacobi', 0.5924562811851501), ('periodic homogenization', 0.5906884670257568), ('hamilton jacobi equations', 0.5709293484687805), ('hamiltonian periodic', 0.5529066920280457), ('viscous hamilton jacobi', 0.5527694821357727), ('convex hamiltonians', 0.5287250876426697), ('convergence rate periodic', 0.5210480093955994), ('convergence homogenization', 0.5040297508239746), ('homogenization nonlinear', 0.5032979249954224), ('convex hamilton', 0.49764958024024963)]"
1482,1482,20,1482_symmetric directed graph_directed cycles length_complete graph k_n_symmetric directed,"['symmetric directed graph', 'directed cycles length', 'complete graph k_n', 'symmetric directed', 'edge disjoint cycles', 'disjoint union cycles', 'directed cycles', 'directed graph', 'graph k_n', 'cycle lengths']","['Completing the solution of the directed Oberwolfach problem with two\n  tables   We address the last outstanding case of the directed Oberwolfach problem with\ntwo tables of different lengths. Specifically, we show that the complete\nsymmetric directed graph $K^*_n$ admits a decomposition into spanning\nsubdigraphs comprised of two vertex-disjoint directed cycles of length $t_1$\nand $t_2$, respectively, where $t_1\\in \\{4,6\\}$, $t_2$ is even, and\n$t_1+t_2\\geqslant 14$. In conjunction with recent results of Kadri and\n\\v{S}ajna, this gives a complete solution to the directed Oberwolfach problem\nwith two tables of different lengths.\n', 'The directed Oberwolfach problem with variable cycle lengths: a\n  recursive construction   The directed Oberwolfach problem OP$^\\ast(m_1,\\ldots,m_k)$ asks whether the\ncomplete symmetric digraph $K_n^\\ast$, assuming $n=m_1+\\ldots +m_k$, admits a\ndecomposition into spanning subdigraphs, each a disjoint union of $k$ directed\ncycles of lengths $m_1,\\ldots,m_k$. We hereby describe a method for\nconstructing a solution to OP$^\\ast(m_1,\\ldots,m_k)$ given a solution to\nOP$^\\ast(m_1,\\ldots,m_\\ell)$, for some $\\ell<k$, if certain conditions on\n$m_1,\\ldots,m_k$ are satisfied. This approach enables us to extend a solution\nfor OP$^\\ast(m_1,\\ldots,m_\\ell)$ into a solution for\nOP$^\\ast(m_1,\\ldots,m_\\ell,t)$, as well as into a solution for\nOP$^\\ast(m_1,\\ldots,m_\\ell,2^{\\langle t \\rangle})$, where $2^{\\langle t\n\\rangle}$ denotes $t$ copies of 2, provided $t$ is sufficiently large.\n  In particular, our recursive construction allows us to effectively address\nthe two-table directed Oberwolfach problem. We show that OP$^\\ast(m_1,m_2)$ has\na solution for all $2 \\le m_1\\le m_2$, with a definite exception of $m_1=m_2=3$\nand a possible exception in the case that $m_1 \\in \\{ 4,6 \\}$, $m_2$ is even,\nand $m_1+m_2 \\ge 14$. It has been shown previously that OP$^\\ast(m_1,m_2)$ has\na solution if $m_1+m_2$ is odd, and that OP$^\\ast(m,m)$ has a solution if and\nonly if $m \\ne 3$.\n  In addition to solving many other cases of OP$^\\ast$, we show that when $2\n\\le m_1+\\ldots +m_k \\le 13$, OP$^\\ast(m_1,\\ldots,m_k)$ has a solution if and\nonly if $(m_1,\\ldots,m_k) \\not\\in \\{ (4),(6),(3,3) \\}$.\n', 'On the Directed Oberwolfach Problem with variable cycle lengths   The Directed Oberwolfach Problem can be considered as the directed version of\nthe well-known Oberwolfach Problem, first mentioned by Ringel at a conference\nin Oberwolfach, Germany in 1967. In this paper, we describe some new partial\nresults on the Directed Oberwolfach Problem with variable cycle lengths. In\nparticular, we show that the complete symmetric digraph $K_n^{*}$ admits a $(\n\\vec{C}_2, ..., \\vec{C}_2, \\vec{C}_3) $-factorization for all $ n\\equiv 1, 3,$\nor $ 7\\pmod{8}$. We also show that $K_n^{*}$ admits a $(\\vec{C}_2,\n\\vec{C}_{n-2})$-factorization for any integer $n \\geq 5$.\n']","[('symmetric directed graph', 0.5501456260681152), ('directed cycles length', 0.5314946174621582), ('complete graph k_n', 0.5043923854827881), ('symmetric directed', 0.502176821231842), ('edge disjoint cycles', 0.48683595657348633), ('disjoint union cycles', 0.46894022822380066), ('directed cycles', 0.4631488621234894), ('directed graph', 0.45266300439834595), ('graph k_n', 0.4393994212150574), ('cycle lengths', 0.43568873405456543)]"
1483,1483,20,1483_existence optimal control_distributed optimal control_optimal control_sparse optimal control,"['existence optimal control', 'distributed optimal control', 'optimal control', 'sparse optimal control', 'optimal controls', 'optimality conditions optimal', 'optimality conditions', 'reaction diffusion', 'coupled reaction diffusion', 'necessary optimality conditions']","['Optimal control theory and advanced optimality conditions for a diffuse\n  interface model of tumor growth   In this paper, we study a distributed optimal control problem for a diffuse\ninterface model for tumor growth. The model consists of a Cahn-Hilliard type\nequation for the phase field variable coupled to a reaction diffusion equation\nfor the nutrient and a Brinkman type equation for the velocity. The system is\nequipped with homogeneous Neumann boundary conditions for the tumor variable,\nthe chemical potential and the nutrient as well as a ""no-friction"" boundary\ncondition for the velocity. The control acts as a medication by cytotoxic drugs\nand enters the phase field equation. The cost functional is of standard\ntracking type and is designed to track the phase field variable during the\nevolution and at some fixed final time. We prove that the model satisfies the\nbasics for calculus of variations and we establish first-order and second-order\nconditions for local optimality. Moreover, we present a globality condition for\ncritical controls and we show that the optimal control is unique on small time\nintervals.\n', ""Long-time Dynamics and Optimal Control of a Diffuse Interface Model for\n  Tumor Growth   We investigate the long-time dynamics and optimal control problem of a\ndiffuse interface model that describes the growth of a tumor in presence of a\nnutrient and surrounded by host tissues. The state system consists of a\nCahn-Hilliard type equation for the tumor cell fraction and a\nreaction-diffusion equation for the nutrient. The possible medication that\nserves to eliminate tumor cells is in terms of drugs and is introduced into the\nsystem through the nutrient. In this setting, the control variable acts as an\nexternal source in the nutrient equation. First, we consider the problem of\n`long-time treatment' under a suitable given source and prove the convergence\nof any global solution to a single equilibrium as $t\\to+\\infty$. Then we\nconsider the `finite-time treatment' of a tumor, which corresponds to an\noptimal control problem. Here we also allow the objective cost functional to\ndepend on a free time variable, which represents the unknown treatment time to\nbe optimized. We prove the existence of an optimal control and obtain first\norder necessary optimality conditions for both the drug concentration and the\ntreatment time. One of the main aim of the control problem is to realize in the\nbest possible way a desired final distribution of the tumor cells, which is\nexpressed by the target function $\\phi_\\Omega$. By establishing the Lyapunov\nstability of certain equilibria of the state system (without external source),\nwe see that $\\phi_{\\Omega}$ can be taken as a stable configuration, so that the\ntumor will not grow again once the finite-time treatment is completed.\n"", 'Optimal medication for tumors modeled by a Cahn-Hilliard-Brinkman\n  equation   In this paper, we study a distributed optimal control problem for a diffuse\ninterface model for tumor growth. The model consists of a Cahn-Hilliard type\nequation for the phase field variable coupled to a reaction diffusion equation\nfor the nutrient and a Brinkman type equation for the velocity. The system is\nequipped with homogeneous Neumann boundary conditions for the tumor variable\nand the chemical potential, Robin boundary conditions for the nutrient and a\n""no-friction"" boundary condition for the velocity. The control acts as a\nmedication by cytotoxic drugs and enters the phase field equation. The cost\nfunctional is of standard tracking type and is designed to track the variables\nof the state equation during the evolution and the distribution of tumor cells\nat some fixed final time. We prove that the model satisfies the basics for\ncalculus of variations and we establish first-order necessary optimality\nconditions for the optimal control problem.\n']","[('existence optimal control', 0.5799016952514648), ('distributed optimal control', 0.5663267970085144), ('optimal control', 0.5661488175392151), ('sparse optimal control', 0.5429407954216003), ('optimal controls', 0.5362972021102905), ('optimality conditions optimal', 0.4335988163948059), ('optimality conditions', 0.4304574429988861), ('reaction diffusion', 0.4204567074775696), ('coupled reaction diffusion', 0.4121127426624298), ('necessary optimality conditions', 0.3958982527256012)]"
1484,1484,20,1484_independent component analysis_blind source separation_component analysis ica_source separation,"['independent component analysis', 'blind source separation', 'component analysis ica', 'source separation', 'component analysis', 'independent component', 'source signals', 'analysis ica', 'mixing matrix', 'independent sources']","['Cumulant Tensors in Partitioned Independent Component Analysis   In this work, we explore Partitioned Independent Component Analysis (PICA),\nan extension of the well-established Independent Component Analysis (ICA)\nframework. Traditionally, ICA focuses on extracting a vector of independent\nsource signals from a linear combination of them defined by a mixing matrix. We\naim to provide a comprehensive understanding of the identifiability of this\nmixing matrix in ICA. Significant to our investigation, recent developments by\nMesters and Zwiernik relax these strict independence requirements, studying the\nidentifiability of the mixing matrix from zero restrictions on cumulant\ntensors. In this paper, we assume alternative independence conditions, in\nparticular, the PICA case, where only partitions of the sources are mutually\nindependent. We study this case from an algebraic perspective, and our primary\nresult generalizes previous results on the identifiability of the mixing\nmatrix.\n', ""Nonparametric Evaluation of Noisy ICA Solutions   Independent Component Analysis (ICA) was introduced in the 1980's as a model\nfor Blind Source Separation (BSS), which refers to the process of recovering\nthe sources underlying a mixture of signals, with little knowledge about the\nsource signals or the mixing process. While there are many sophisticated\nalgorithms for estimation, different methods have different shortcomings. In\nthis paper, we develop a nonparametric score to adaptively pick the right\nalgorithm for ICA with arbitrary Gaussian noise. The novelty of this score\nstems from the fact that it just assumes a finite second moment of the data and\nuses the characteristic function to evaluate the quality of the estimated\nmixing matrix without any knowledge of the parameters of the noise\ndistribution. In addition, we propose some new contrast functions and\nalgorithms that enjoy the same fast computability as existing algorithms like\nFASTICA and JADE but work in domains where the former may fail. While these\nalso may have weaknesses, our proposed diagnostic, as shown by our simulations,\ncan remedy them. Finally, we propose a theoretical framework to analyze the\nlocal and global convergence properties of our algorithms.\n"", 'Nonparametric Independent Component Analysis for the Sources with Mixed\n  Spectra   Independent component analysis (ICA) is a blind source separation method to\nrecover source signals of interest from their mixtures. Most existing ICA\nprocedures assume independent sampling. Second-order-statistics-based source\nseparation methods have been developed based on parametric time series models\nfor the mixtures from the autocorrelated sources. However, the\nsecond-order-statistics-based methods cannot separate the sources accurately\nwhen the sources have temporal autocorrelations with mixed spectra. To address\nthis issue, we propose a new ICA method by estimating spectral density\nfunctions and line spectra of the source signals using cubic splines and\nindicator functions, respectively. The mixed spectra and the mixing matrix are\nestimated by maximizing the Whittle likelihood function. We illustrate the\nperformance of the proposed method through simulation experiments and an EEG\ndata application. The numerical results indicate that our approach outperforms\nexisting ICA methods, including SOBI algorithms. In addition, we investigate\nthe asymptotic behavior of the proposed method.\n']","[('independent component analysis', 0.7173891663551331), ('blind source separation', 0.6253902316093445), ('component analysis ica', 0.6025832295417786), ('source separation', 0.5470215082168579), ('component analysis', 0.5183255672454834), ('independent component', 0.4712055027484894), ('source signals', 0.4589090347290039), ('analysis ica', 0.4493844211101532), ('mixing matrix', 0.437775582075119), ('independent sources', 0.41538846492767334)]"
1485,1485,20,1485_harmonic mappings_holomorphic mappings_harmonic functions unit_quasiregular mappings,"['harmonic mappings', 'holomorphic mappings', 'harmonic functions unit', 'quasiregular mappings', 'harmonic functions', 'preserving harmonic', 'mappings banach', 'schwarz type', 'type harmonic', 'classical schwarz']","['Some sharp Schwarz-Pick type estimates and their applications of\n  harmonic and pluriharmonic functions   The purpose of this paper is to study the Schwarz-Pick type inequalities for\nharmonic or pluriharmonic functions. By analogy with the generalized Khavinson\nconjecture, we first give some sharp estimates of the norm of harmonic\nfunctions from the Euclidean unit ball in $\\mathbb{R}^n$ into the unit ball of\nthe real Minkowski space. Next, we give several sharp Schwarz-Pick type\ninequalities for pluriharmonic functions from the Euclidean unit ball in\n$\\mathbb{C}^n$ or from the unit polydisc in $\\mathbb{C}^n$ into the unit ball\nof the Minkowski space. Furthermore, we establish some sharp coefficient type\nSchwarz-Pick inequalities for pluriharmonic functions defined in the Minkowski\nspace. Finally, we use the obtained Schwarz-Pick type inequalities to discuss\nthe Lipschitz continuity, the Schwarz-Pick type lemmas of arbitrary order and\nthe Bohr phenomenon of harmonic or pluriharmonic functions.\n', 'The Boundary Schwarz lemma for harmonic and pluriharmonic mappings and\n  some generalisations   The main purpose of this paper is to develop some methods to investigate the\nSchwarz type lemmas of holomorphic mappings and pluriharmonic mappings in\nHilbert and Banach spaces. Initially, we extend the classical Schwarz lemmas of\nholomorphic mappings to Hilbert and Banach spaces. Furthermore, we improve and\ngeneralize the classical Schwarz lemmas of planar harmonic mappings into the\nsharp forms of Banach spaces, and present some applications to sharp boundary\nSchwarz type lemmas for pluriharmonic mappings in Hilbert and Banach spaces and\nthe obtained results provide the improvements and generalizations of some\nlatest corresponding results in this subject. In the last section we studied\nharmonic and hyperbolical-harmonic function mapping unit ball in Euclidial\nn-space, to unit ball in Euclidial m-space, taking prescribed value in the\norigin, which improved some previous results.\n', 'Schwarz type lemmas and their applications in Banach spaces   The main purpose of this paper is to develop some methods to investigate the\nSchwarz type lemmas of holomorphic mappings and pluriharmonic mappings in\nBanach spaces. Initially, we extend the classical Schwarz lemmas of holomorphic\nmappings to Banach spaces, and then we apply these extensions to establish a\nsharp Bloch type theorem for pluriharmonic mappings on homogeneous unit balls\nof $\\C^n$ and to obtain some sharp boundary Schwarz type lemmas for holomorphic\nmappings in Banach spaces. Furthermore, we improve and generalize the classical\nSchwarz lemmas of planar harmonic mappings into the sharp forms of Banach\nspaces, and present some applications to sharp boundary Schwarz type lemmas for\npluriharmonic mappings in Banach spaces. Additionally, using a relatively\nsimple method of proof, we prove some sharp Schwarz-Pick type estimates of\npluriharmonic mappings in JB$^*$-triples, and the obtained results provide the\nimprovements and generalizations of the corresponding results in \\cite{CH20}.\n']","[('harmonic mappings', 0.6014350056648254), ('holomorphic mappings', 0.5379160046577454), ('harmonic functions unit', 0.4692497253417969), ('quasiregular mappings', 0.45607927441596985), ('harmonic functions', 0.45460206270217896), ('preserving harmonic', 0.4352612793445587), ('mappings banach', 0.41885754466056824), ('schwarz type', 0.41587093472480774), ('type harmonic', 0.4147700369358063), ('classical schwarz', 0.4145715534687042)]"
1486,1486,19,1486_seiberg witten invariants_seiberg witten invariant_witten invariants_seiberg witten theory,"['seiberg witten invariants', 'seiberg witten invariant', 'witten invariants', 'seiberg witten theory', 'witten invariant', 'invariants manifolds', 'seiberg witten equations', 'invariants manifold', 'invariants families', 'four manifold']","['Surgery formulas for Seiberg-Witten invariants and family Seiberg-Witten\n  invariants   We prove a surgery formula for the ordinary Seiberg-Witten invariants, and\nsurgery formulas for the families Seiberg-Witten invariants of families of\n$4$-manifolds obtained through fibrewise surgery. Our formula expresses the\nSeiberg-Witten invariants of the manifold after the surgery, in terms of the\noriginal Seiberg-Witten moduli space cut down by a cohomology class in the\nconfiguration space. We use these surgery formulas to study how a surgery can\npreserve or produce exotic phenomena.\n', 'On the Bauer-Furuta and Seiberg-Witten invariants of families of\n  $4$-manifolds   We show how the families Seiberg-Witten invariants of a family of smooth\n$4$-manifolds can be recovered from the families Bauer-Furuta invariant via a\ncohomological formula. We use this formula to deduce several properties of the\nfamilies Seiberg-Witten invariants. We give a formula for the Steenrod squares\nof the families Seiberg-Witten invariants leading to a series of mod $2$\nrelations between these invariants and the Chern classes of the spin$^c$ index\nbundle of the family. As a result we discover a new aspect of the ordinary\nSeiberg-Witten invariants of a $4$-manifold $X$: they obstruct the existence of\ncertain families of $4$-manifolds with fibres diffeomorphic to $X$. As a\nconcrete geometric application, we shall detect a non-smoothable family of $K3$\nsurfaces. Our formalism also leads to a simple new proof of the families wall\ncrossing formula. Lastly, we introduce $K$-theoretic Seiberg-Witten invariants\nand give a formula expressing the Chern character of the $K$-theoretic\nSeiberg-Witten invariants in terms of the cohomological Seiberg-Witten\ninvariants. This leads to new divisibility properties of the families\nSeiberg-Witten invariants.\n', 'A gluing formula for families Seiberg-Witten invariants   We prove a gluing formula for the families Seiberg-Witten invariants of\nfamilies of $4$-manifolds obtained by fibrewise connected sum. Our formula\nexpresses the families Seiberg-Witten invariants of such a connected sum family\nin terms of the ordinary Seiberg-Witten invariants of one of the summands,\nunder certain assumptions on the families. We construct some variants of the\nfamilies Seiberg-Witten invariants and prove the gluing formula also for these\nvariants. One variant incorporates a twist of the families moduli space using\nthe charge conjugation symmetry of the Seiberg-Witten equations. The other\nvariant is an equivariant Seiberg-Witten invariant of smooth group actions. We\nconsider several applications of the gluing formula including: obstructions to\nsmooth isotopy of diffeomorpihsms, computation of the mod $2$ Seiberg-Witten\ninvariants of spin structures, relations between mod $2$ Seiberg-Witten\ninvariants of $4$-manifolds and obstructions to the existence of invariant\nmetrics of positive scalar curvature for smooth group actions on $4$-manifolds.\n']","[('seiberg witten invariants', 0.8119807839393616), ('seiberg witten invariant', 0.7825695872306824), ('witten invariants', 0.7119279503822327), ('seiberg witten theory', 0.6801872849464417), ('witten invariant', 0.6746529340744019), ('invariants manifolds', 0.6009199023246765), ('seiberg witten equations', 0.5985626578330994), ('invariants manifold', 0.5785855054855347), ('invariants families', 0.5467647910118103), ('four manifold', 0.5272125601768494)]"
1487,1487,19,1487_optimization pareto_multi objective optimization_optimization multi objective_single objective optimization,"['optimization pareto', 'multi objective optimization', 'optimization multi objective', 'single objective optimization', 'pareto optimal', 'bi objective optimization', 'multiobjective optimization', 'pareto optimality', 'objective optimization problems', 'pareto optimal points']","['Optimization Over the Pareto Front of Nonconvex Multi-objective Optimal\n  Control Problems   Simultaneous optimization of multiple objective functions results in a set of\ntrade-off, or Pareto, solutions. Choosing a, in some sense, best solution in\nthis set is in general a challenging task: In the case of three or more\nobjectives the Pareto front is usually difficult to view, if not impossible,\nand even in the case of just two objectives constructing the whole Pareto front\nso as to visually inspect it might be very costly. Therefore, optimization over\nthe Pareto (or efficient) set has been an active area of research. Although\nthere is a wealth of literature involving finite dimensional optimization\nproblems in this area, there is a lack of problem formulation and numerical\nmethods for optimal control problems, except for the convex case. In this\npaper, we formulate the problem of optimizing over the Pareto front of\nnonconvex constrained and time-delayed optimal control problems as a bi-level\noptimization problem. Motivated by existing solution differentiability results,\nwe propose an algorithm incorporating (i) the Chebyshev scalarization, (ii) a\nconcept of the essential interval of weights, and (iii) the simple but\neffective bisection method, for optimal control problems with two objectives.\nWe illustrate the working of the algorithm on two example problems involving an\nelectric circuit and treatment of tuberculosis and discuss future lines of\nresearch for new computational methods.\n', 'Hypervolume-Optimal $\\mu$-Distributions on Line/Plane-based Pareto\n  Fronts in Three Dimensions   Hypervolume is widely used in the evolutionary multi-objective optimization\n(EMO) field to evaluate the quality of a solution set. For a solution set with\n$\\mu$ solutions on a Pareto front, a larger hypervolume means a better solution\nset. Investigating the distribution of the solution set with the largest\nhypervolume is an important topic in EMO, which is the so-called hypervolume\noptimal $\\mu$-distribution. Theoretical results have shown that the $\\mu$\nsolutions are uniformly distributed on a linear Pareto front in two dimensions.\nHowever, the $\\mu$ solutions are not always uniformly distributed on a\nsingle-line Pareto front in three dimensions. They are only uniform when the\nsingle-line Pareto front has one constant objective. In this paper, we further\ninvestigate the hypervolume optimal $\\mu$-distribution in three dimensions. We\nconsider the line- and plane-based Pareto fronts. For the line-based Pareto\nfronts, we extend the single-line Pareto front to two-line and three-line\nPareto fronts, where each line has one constant objective. For the plane-based\nPareto fronts, the linear triangular and inverted triangular Pareto fronts are\nconsidered. First, we show that the $\\mu$ solutions are not always uniformly\ndistributed on the line-based Pareto fronts. The uniformity depends on how the\nlines are combined. Then, we show that a uniform solution set on the\nplane-based Pareto front is not always optimal for hypervolume maximization. It\nis locally optimal with respect to a $(\\mu+1)$ selection scheme. Our results\ncan help researchers in the community to better understand and utilize the\nhypervolume indicator.\n', 'A Trust Region Method for Pareto Front Approximation   In this paper, we consider black-box multiobjective optimization problems in\nwhich all objective functions are not given analytically. In multiobjective\noptimization, it is important to produce a set of uniformly distributed\ndiscrete solutions over the Pareto front to build a good approximation. In\nblack-box biobjective optimization, one can evaluate distances between\nsolutions with the ordering property of the Pareto front. These distances allow\nto be able to evaluate distribution of all solution points, so it is not\ndifficult to maintain uniformity of solutions distribution. However, problems\nwith more than two objectives do not have ordering property, so it is noted\nthat these problems require other techniques to measure the coverage and\nmaintain uniformity of solutions distribution. In this paper, we propose an\nalgorithm based on a trust region method for the Pareto front approximation in\nblack-box multiobjective optimization. In the algorithm, we select a reference\npoint in the set of non-dominated points by employing the density function and\nexplore area around this point. This ensures uniformity of solutions\ndistribution even for problems with more than two objective functions. We also\nprove that the iteration points of the algorithm converge to Pareto critical\npoints. Finally, we present numerical results suggesting that the algorithm\ngenerates the set of well-distributed solutions approximating the Pareto front,\neven in the case for the problems with three objective functions.\n']","[('optimization pareto', 0.7236133217811584), ('multi objective optimization', 0.6950056552886963), ('optimization multi objective', 0.6860713958740234), ('single objective optimization', 0.6628181338310242), ('pareto optimal', 0.6512640118598938), ('bi objective optimization', 0.6455113887786865), ('multiobjective optimization', 0.642799973487854), ('pareto optimality', 0.6370107531547546), ('objective optimization problems', 0.6356148719787598), ('pareto optimal points', 0.6312907338142395)]"
1488,1488,19,1488_z_2 graded_mathbb _2 graded_supersymmetric quantum mechanics_supersymmetric quantum,"['z_2 graded', 'mathbb _2 graded', 'supersymmetric quantum mechanics', 'supersymmetric quantum', 'supersymmetry algebra', 'supersymmetric', 'quantum super', 'bosons fermions', 'supersymmetry', 'superalgebras']","['New aspects of the Z$_{\\textrm 2}$ $\\times$ Z$_{\\textrm 2}$-graded 1D\n  superspace: induced strings and 2D relativistic models   A novel feature of the ${\\mathbb Z}_2\\times {\\mathbb Z}_2$-graded\nsupersymmetry which finds no counterpart in ordinary supersymmetry is the\npresence of $11$-graded exotic bosons (implied by the existence of two classes\nof parafermions). Their interpretation, both physical and mathematical,\npresents a challenge. The role of the ""exotic bosonic coordinate"" was not\nconsidered by previous works on the one-dimensional ${\\mathbb Z}_2\\times\n{\\mathbb Z}_2$-graded superspace (which was restricted to produce\npoint-particle models). By treating this coordinate at par with the other\ngraded superspace coordinates new consequences are obtained. The graded\nsuperspace calculus of the ${\\mathbb Z}_2\\times {\\mathbb Z}_2$-graded worldline\nsuper-Poincar\\\'e algebra induces two-dimensional ${\\mathbb Z}_2\\times {\\mathbb\nZ}_2$-graded relativistic models; they are invariant under a new ${\\mathbb\nZ}_2\\times {\\mathbb Z}_2$-graded $2D$ super-Poincar\\\'e algebra which differs\nfrom the previous two ${\\mathbb Z}_2\\times {\\mathbb Z}_2$-graded $2D$ versions\nof super-Poincar\\\'e introduced in the literature. In this new superalgebra the\nsecond translation generator and the Lorentz boost are $11$-graded.\nFurthermore, if the exotic coordinate is compactified on a circle ${\\bf S}^1$,\na ${\\mathbb Z}_2\\times {\\mathbb Z}_2$-graded closed string with periodic\nboundary conditions is derived. The analysis of the irreducibility conditions\nof the $2D$ supermultiplet implies that a larger $(\\beta$-deformed, where\n$\\beta\\geq 0$ is a real parameter) class of point-particle models than the ones\ndiscussed so far in the literature (recovered at $\\beta=0$) is obtained. While\nthe spectrum of the $\\beta=0$ point-particle models is degenerate (due to its\nrelation with an ${\\cal N}=2$ supersymmetry), this is no longer the case for\nthe $\\beta> 0$ models.\n', '${\\mathbb Z}_2\\times {\\mathbb Z}_2$-graded mechanics: the quantization   In the previous paper arXiv:2003.06470 we introduced the notion of ${\\mathbb\nZ}_2\\times{\\mathbb Z}_2$-graded classical mechanics and presented a general\nframework to construct, in the Lagrangian setting, the worldline sigma models\ninvariant under a ${\\mathbb Z}_2\\times{\\mathbb Z}_2$-graded superalgebra. In\nthis work we discuss at first the classical Hamiltonian formulation of some of\nthese models and later present their canonical quantization. As the simplest\napplication of the construction we recover the ${\\mathbb Z}_2\\times{\\mathbb\nZ}_2$-graded quantum Hamiltonian introduced by Bruce and Duplij in\narXiv:1904.06975. We prove that this is the first example of a large class of\n${\\mathbb Z}_2\\times{\\mathbb Z}_2$-graded quantum models. We derive in\nparticular interacting multiparticle quantum Hamiltonians given by Hermitian,\nmatrix, differential operators. The interacting terms appear as non-diagonal\nentries in the matrices. The construction of the Noether charges, both\nclassical and quantum, is presented. A comprehensive discussion of the\ndifferent ${\\mathbb Z}_2\\times{\\mathbb Z}_2$-graded symmetries possessed by the\nquantum Hamiltonians is given.\n', '${\\mathbb Z}_2\\times {\\mathbb Z}_2$-graded parastatistics in\n  multiparticle quantum Hamiltonians   The recent surge of interest in ${\\mathbb Z}_2\\times {\\mathbb Z}_2$-graded\ninvariant mechanics poses the challenge of understanding the physical\nconsequences of a ${\\mathbb Z}_2\\times{\\mathbb Z}_2$-graded symmetry. In this\npaper it is shown that non-trivial physics can be detected in the multiparticle\nsector of a theory, being induced by the ${\\mathbb Z}_2\\times{\\mathbb\nZ}_2$-graded parastatistics obeyed by the particles. The toy model of the\n${\\cal N}=4$ supersymmetric/ ${\\mathbb Z}_2\\times {\\mathbb Z}_2$-graded\noscillator is used. In this set-up the one-particle energy levels and their\ndegenerations are the same for both supersymmetric and ${\\mathbb\nZ}_2\\times{\\mathbb Z}_2$-graded versions. Nevertheless, in the multiparticle\nsector, a measurement of an observable operator on suitable states can\ndiscriminate whether the system under consideration is composed by ordinary\nbosons/fermions or by ${\\mathbb Z}_2\\times {\\mathbb Z}_2$-graded particles.\nTherefore, ${\\mathbb Z}_2\\times {\\mathbb Z}_2$-graded mechanics has\nexperimentally testable consequences. Furthermore, the ${\\mathbb Z}_2\\times\n{\\mathbb Z}_2$-grading constrains the observables to obey a superselection\nrule. As a technical tool, the multiparticle sector is encoded in the coproduct\nof a Hopf algebra defined on a Universal Enveloping Algebra of a graded Lie\nsuperalgebra with a braided tensor product.\n']","[('z_2 graded', 0.5722174644470215), ('mathbb _2 graded', 0.5333623290061951), ('supersymmetric quantum mechanics', 0.5248712301254272), ('supersymmetric quantum', 0.513267993927002), ('supersymmetry algebra', 0.47966426610946655), ('supersymmetric', 0.4651738405227661), ('quantum super', 0.45530104637145996), ('bosons fermions', 0.4527559280395508), ('supersymmetry', 0.4518311023712158), ('superalgebras', 0.4377736449241638)]"
1489,1489,19,1489_lie conformal algebras_conformal algebras_lie conformal_conformal algebra,"['lie conformal algebras', 'conformal algebras', 'lie conformal', 'conformal algebra', 'dimensional lie algebras', 'superconformal algebra', 'conformal', 'mathbb graded lie', 'virasoro conformal', 'graded lie']","['Finite irreducible conformal modules of rank two Lie conformal algebras   In the present paper, we prove that any finite non-trivial irreducible module\nover a rank two Lie conformal algebra $\\mathcal{H}$ is of rank one. We also\ndescribe the actions of $\\mathcal{H}$ on its finite irreducible modules\nexplicitly. Moreover, we show that all finite non-trivial irreducible modules\nof finite Lie conformal algebras whose semisimple quotient is the Virasoro Lie\nconformal algebra are of rank one.\n', 'Finite irreducible modules of a class of $\\mathbb{Z}^+$-graded Lie\n  conformal algebras   In this paper, we introduce the notion of completely non-trivial module of a\nLie conformal algebra. By this notion, we classify all finite irreducible\nmodules of a class of $\\mathbb{Z}^+$-graded Lie conformal algebras\n$\\mathcal{L}=\\bigoplus_{i=0}^{\\infty} \\mathbb{C}[\\partial]L_i$ satisfying $\n[{L_0}_\\lambda L_0]=(\\partial+2\\lambda)L_0,$ and $[{L_1}_\\lambda L_i]\\neq 0$\nfor any $i\\in \\mathbb{Z}^+$. These Lie conformal algebras include Block type\nLie conformal algebra $\\mathcal{B}(p)$ and map Virasoro Lie conformal algebra\n$\\mathcal{V}(\\mathbb{C}[T])=Vir\\otimes \\mathbb{C}[T]$. As a result, we show\nthat all non-trivial finite irreducible modules of these algebras are free of\nrank one as a $\\mathbb{C}[\\partial]$-module.\n', 'Another class of simple graded Lie conformal algebras that cannot be\n  embedded into general Lie conformal algebras   In a previous paper by the authors, we obtain the first example of a finitely\nfreely generated simple $\\mathbb Z$-graded Lie conformal algebra of linear\ngrowth that cannot be embedded into any general Lie conformal algebra. In this\npaper, we obtain, as a byproduct, another class of such Lie conformal algebras\nby classifying $\\mathbb Z$-graded simple Lie conformal algebras ${\\cal\nG}=\\oplus_{i=-1}^\\infty{\\cal G}_i$ satisfying the following, (1) ${\\cal\nG}_0\\cong{\\rm Vir}$, the Virasoro conformal algebra; (2) Each ${\\cal G}_i$ for\n$i\\ge-1$ is a ${\\rm Vir}$-module of rank one. These algebras include some Lie\nconformal algebras of Block type.\n']","[('lie conformal algebras', 0.8335814476013184), ('conformal algebras', 0.7174398303031921), ('lie conformal', 0.6708136200904846), ('conformal algebra', 0.6529389023780823), ('dimensional lie algebras', 0.6017197966575623), ('superconformal algebra', 0.48243725299835205), ('conformal', 0.4814334809780121), ('mathbb graded lie', 0.47324034571647644), ('virasoro conformal', 0.4694805443286896), ('graded lie', 0.4469289481639862)]"
1490,1490,19,1490_knapsack_knapsack problems_binary knapsack_multidimensional knapsack,"['knapsack', 'knapsack problems', 'binary knapsack', 'multidimensional knapsack', 'dimensional knapsack', 'choice knapsack', 'integer programming', 'integer programming problems', 'combinatorial optimization', 'programming formulation']","['Genetic Algorithm for the 0/1 Multidimensional Knapsack Problem   The 0/1 multidimensional knapsack problem is the 0/1 knapsack problem with m\nconstraints which makes it difficult to solve using traditional methods like\ndynamic programming or branch and bound algorithms. We present a genetic\nalgorithm for the multidimensional knapsack problem with Java and C++ code that\nis able to solve publicly available instances in a very short computational\nduration. Our algorithm uses iteratively computed Lagrangian multipliers as\nconstraint weights to augment the greedy algorithm for the multidimensional\nknapsack problem and uses that information in a greedy crossover in a genetic\nalgorithm. The algorithm uses several other hyperparameters which can be set in\nthe code to control convergence. Our algorithm improves upon the algorithm by\nChu and Beasley in that it converges to optimum or near optimum solutions much\nfaster.\n', 'The Product Knapsack Problem: Approximation and Complexity   We consider the product knapsack problem, which is the variant of the\nclassical 0-1 knapsack problem where the objective consists of maximizing the\nproduct of the profits of the selected items. These profits are allowed to be\npositive or negative. We show that this recently introduced variant of the\nknapsack problem is weakly NP-hard and present a fully polynomial-time\napproximation scheme (FPTAS) for the problem. Moreover, we analyze the\napproximation quality achieved by a natural extension of the classical greedy\nprocedure to the product knapsack problem.\n', 'Preemptive Two-stage Goal-Programming Formulation of a Strict Version of\n  the Unbounded Knapsack Problem with Bounded Weights   The unbounded knapsack problem with bounded weights is a variant of the\nwell-studied variant of the traditional binary knapsack problem; key changes\nbeing the relaxation of the binary constraint and allowing the unit weights of\neach item to fall within a range. In this paper, we formulate a variant of this\nproblem, which we call the strict unbounded knapsack problem with bounded\nweights, by replacing the inequality constraint on the total weight with an\nequality. We show that this problem can be decomposed into a two-stage,\npre-emptive goal programming problem, with the first stage being a\n2-dimensional knapsack problem and the second being either a linear feasibility\nprogram (per canonical formulation) or simply a linearly-constrained program in\nthe general case. This reformulation is shown to be equivalent to the original\nformulation but allows the use of well-studied, efficient algorithms for\nmultidimensional knapsack problems. In addition, it separates the modeling\neffort around what to put in the knapsack from considerations around what unit\nweight one should assign to each item type, providing substantially more\nflexibility to the modeler without adding complexity to the choice of knapsack\nconfiguration. Finally, we show that for the feasibility version of the second\nstage, one can immediately get a feasible solution to the first stage solution.\n']","[('knapsack', 0.7807870507240295), ('knapsack problems', 0.77587890625), ('binary knapsack', 0.7715046405792236), ('multidimensional knapsack', 0.7502995729446411), ('dimensional knapsack', 0.7312968373298645), ('choice knapsack', 0.7194426655769348), ('integer programming', 0.5318805575370789), ('integer programming problems', 0.5161920785903931), ('combinatorial optimization', 0.5098671913146973), ('programming formulation', 0.4952754080295563)]"
1491,1491,19,1491_varieties kodaira dimension_kodaira dimension_kodaira dimension zero_varieties kodaira,"['varieties kodaira dimension', 'kodaira dimension', 'kodaira dimension zero', 'varieties kodaira', 'dimension algebraic', 'abelian varieties', 'dimensions algebraic', 'spaces abelian varieties', 'abelian varieties give', 'dimension zero']","['Estimates on the Kodaira dimension for fibrations over abelian varieties   We give estimates on the Kodaira dimension for fibrations over abelian\nvarieties, and give some applications. One of the results strengthens the\nsubadditivity of Kodaira dimension of fibrations over abelian varieties.\n', 'Kodaira dimension of fibrations over abelian varieties   We prove an additivity result for the log Kodaira dimension of algebraic\nfiber spaces over abelian varieties, a superadditivity result for fiber spaces\nover varieties of maximal Albanese dimension, as well as a subadditivity result\nfor log pairs.\n', 'On the Kodaira dimension   We discuss the behavior of the Kodaira dimension under smooth morphisms.\n']","[('varieties kodaira dimension', 0.7836287617683411), ('kodaira dimension', 0.7284473180770874), ('kodaira dimension zero', 0.7018783092498779), ('varieties kodaira', 0.5354172587394714), ('dimension algebraic', 0.5329737067222595), ('abelian varieties', 0.4847576320171356), ('dimensions algebraic', 0.4768693149089813), ('spaces abelian varieties', 0.4714484214782715), ('abelian varieties give', 0.46798598766326904), ('dimension zero', 0.46293914318084717)]"
1492,1492,19,1492_renewal processes_renewal theory_stochastic resetting_continuous time random,"['renewal processes', 'renewal theory', 'stochastic resetting', 'continuous time random', 'renewal process', 'poissonian resetting', 'branching processes random', 'time random walks', 'renewal', 'arbitrary stochastic']","['A solvable class of renewal processes   When the distribution of the inter-arrival times of a renewal process is a\nmixture of geometric laws, we prove that the renewal function of the process is\ngiven by the moments of a probability measure which is explicitly related to\nthe mixture distribution. We also present an analogous result in the continuous\ncase when the inter-arrival law is a mixture of exponential laws. We then\nobserve that the above discrete class of renewal processes provides a solvable\nfamily of random polymers. Namely, we obtain an exact representation of the\npartition function of polymers pinned at sites of the aforementioned renewal\nprocesses. In the particular case where the mixture measure is a generalized\nArcsine law, the computations can be explicitly handled.\n', 'Statistics of the number of renewals, occupation times and correlation\n  in ordinary, equilibrium and aging alternating renewal processes   Renewal process is a point process where an inter-event time between\nsuccessive renewals is an independent and identically distributed random\nvariable. Alternating renewal process is a dichotomous process and a slight\ngeneralization of the renewal process, where the inter-event time distribution\nalternates between two distributions. We investigate statistical properties of\nthe number of renewals and occupation times for one of the two states in\nalternating renewal processes. When both means of the inter-event times are\nfinite, the alternating renewal process can reach an equilibrium. On the other\nhand, an alternating renewal process shows aging when one of the means\ndiverges. We provide analytical calculations for the moments of the number of\nrenewals, occupation time statistics, and the correlation function for several\ncase studies in the inter-event-time distributions. We show anomalous\nfluctuations for the number of renewals and occupation times when the second\nmoment of inter-event time diverges. When the mean inter-event time diverges,\ndistributional limit theorems for the number of events and occupation times are\nshown analytically. These are known as the Mittag-Leffler distribution and the\ngeneralized arcsine law in probability theory.\n', ""Replicating a renewal process at random times   We replicate a renewal process at random times, which is equivalent to\nnesting two renewal processes, or considering a renewal process subject to\nstochastic resetting. We investigate the consequences on the statistical\nproperties of the model of the intricate interplay between the two probability\nlaws governing the distribution of time intervals between renewals, on the one\nhand, and of time intervals between resettings, on the other hand. In\nparticular, the total number ${\\mathcal N}_t$ of renewal events occurring\nwithin a specified observation time exhibits a remarkable range of behaviours,\ndepending on the exponents characterising the power-law decays of the two\nprobability distributions. Specifically, ${\\mathcal N}_t$ can either grow\nlinearly in time and have relatively negligible fluctuations, or grow\nsubextensively over time while continuing to fluctuate. These behaviours\nhighlight the dominance of the most regular process across all regions of the\nphase diagram. In the presence of Poissonian resetting, the statistics of\n${\\mathcal N}_t$ is described by a unique `dressed' renewal process, which is a\ndeformation of the renewal process without resetting. We also discuss the\nrelevance of the present study to first passage under restart and to continuous\ntime random walks subject to stochastic resetting.\n""]","[('renewal processes', 0.658123791217804), ('renewal theory', 0.6224223375320435), ('stochastic resetting', 0.5986221432685852), ('continuous time random', 0.5472010970115662), ('renewal process', 0.5374804735183716), ('poissonian resetting', 0.5276764035224915), ('branching processes random', 0.49304071068763733), ('time random walks', 0.4796862006187439), ('renewal', 0.47901615500450134), ('arbitrary stochastic', 0.46539172530174255)]"
1493,1493,19,1493_perverse sheaves_simple perverse sheaves_perverse sheaf_category perverse sheaves,"['perverse sheaves', 'simple perverse sheaves', 'perverse sheaf', 'category perverse sheaves', 'sheaves', 'sheaf', 'category sheaves', 'category perverse', 'sheaves stack', 'sheaves semi']","['New description of perverse sheaves on a disc   There is a connection between the category of perverse sheaves on a disc and\ndifferent notions related to spherical functors. We introduce a category whose\nobjects are analogous to 4-periodic semiorthogonal decompositions and prove\nthat it is equivalent to the category of perverse sheaves on a disc stratified\nby the origin and its complement.\n', 'On Perverse sheaves of a Coxeter hyperplane arrangement of type\n  $\\mathcal{A}_n$   Kapranov and schechtman gave quiver description of perverse sheaves on real\nhyperplane arrangements. We used this description to relate the perverse\nsheaves on Coxeter hyperplane arrangements of type $\\mathcal A_n$ for different\nvalues of $n$. As a consequence we prove that the simple perverse sheaves whose\nstalk on open cells are zero are induced from the perverse sheaves on lower\ndimension arrangements.\n', 'Perverse sheaves on smooth toric varieties and stacks   It is usually not straightforward to work with the category of perverse\nsheaves on a variety using only its definition as a heart of a $t$-structure.\nIn this paper, the category of perverse sheaves on a smooth toric variety with\nits orbit stratification is described explicitly as a category of\nfinite-dimensional modules over an algebra. An analogous result is also\nestablished for various categories of equivariant perverse sheaves, which in\nparticular gives a description of perverse sheaves on toric orbifolds, and we\nalso compare the derived category of the category of perverse sheaves to the\nderived category of constructible sheaves.\n']","[('perverse sheaves', 0.8779028058052063), ('simple perverse sheaves', 0.8641195297241211), ('perverse sheaf', 0.8534758687019348), ('category perverse sheaves', 0.8463547229766846), ('sheaves', 0.6132123470306396), ('sheaf', 0.5950289368629456), ('category sheaves', 0.5913228392601013), ('category perverse', 0.5888972282409668), ('sheaves stack', 0.5859276652336121), ('sheaves semi', 0.5793047547340393)]"
1494,1494,19,1494_storage computation_coded storage_computing distributed computing_distributed computing,"['storage computation', 'coded storage', 'computing distributed computing', 'distributed computing', 'heterogeneous computing', 'cloud computing', 'coded computing', 'straggler mitigation', 'coded computation', 'virtual machines']","[""Dual-Lagrange Encoding for Storage and Download in Elastic Computing for\n  Resilience   Coded elastic computing enables virtual machines to be preempted for\nhigh-priority tasks while allowing new virtual machines to join ongoing\ncomputation seamlessly. This paper addresses coded elastic computing for\nmatrix-matrix multiplications with straggler tolerance by encoding both storage\nand download using Lagrange codes. In 2018, Yang et al. introduced the first\ncoded elastic computing scheme for matrix-matrix multiplications, achieving a\nlower computational load requirement. However, this scheme lacks straggler\ntolerance and suffers from high upload cost. Zhong et al. (2023) later tackled\nthese shortcomings by employing uncoded storage and Lagrange-coded download.\nHowever, their approach requires each machine to store the entire dataset. This\npaper introduces a new class of elastic computing schemes that utilize Lagrange\ncodes to encode both storage and download, achieving a reduced storage size.\nThe proposed schemes efficiently mitigate both elasticity and straggler\neffects, with a storage size reduced to a fraction $\\frac{1}{L}$ of Zhong et\nal.'s approach, at the expense of doubling the download cost. Moreover, we\nevaluate the proposed schemes on AWS EC2 by measuring computation time under\ntwo different tasks allocations: heterogeneous and cyclic assignments. Both\nassignments minimize computation redundancy of the system while distributing\nvarying computation loads across machines.\n"", 'A New Design Framework for Heterogeneous Uncoded Storage Elastic\n  Computing   Elasticity is one important feature in modern cloud computing systems and can\nresult in computation failure or significantly increase computing time. Such\nelasticity means that virtual machines over the cloud can be preempted under a\nshort notice (e.g., hours or minutes) if a high-priority job appears; on the\nother hand, new virtual machines may become available over time to compensate\nthe computing resources. Coded Storage Elastic Computing (CSEC) introduced by\nYang et al. in 2018 is an effective and efficient approach to overcome the\nelasticity and it costs relatively less storage and computation load. However,\none of the limitations of the CSEC is that it may only be applied to certain\ntypes of computations (e.g., linear) and may be challenging to be applied to\nmore involved computations because the coded data storage and approximation are\noften needed. Hence, it may be preferred to use uncoded storage by directly\ncopying data into the virtual machines. In addition, based on our own\nmeasurement, virtual machines on Amazon EC2 clusters often have heterogeneous\ncomputation speed even if they have exactly the same configurations (e.g., CPU,\nRAM, I/O cost). In this paper, we introduce a new optimization framework on\nUncoded Storage Elastic Computing (USEC) systems with heterogeneous computing\nspeed to minimize the overall computation time. Under this framework, we\npropose optimal solutions of USEC systems with or without straggler tolerance\nusing different storage placements. Our proposed algorithms are evaluated using\npower iteration applications on Amazon EC2.\n', ""Decentralized Uncoded Storage Elastic Computing with Heterogeneous\n  Computation Speeds   Elasticity plays an important role in modern cloud computing systems. Elastic\ncomputing allows virtual machines (i.e., computing nodes) to be preempted when\nhigh-priority jobs arise, and also allows new virtual machines to participate\nin the computation. In 2018, Yang et al. introduced Coded Storage Elastic\nComputing (CSEC) to address the elasticity using coding technology, with lower\nstorage and computation load requirements. However, CSEC is limited to certain\ntypes of computations (e.g., linear) due to the coded data storage based on\nlinear coding. Then Centralized Uncoded Storage Elastic Computing (CUSEC) with\nheterogeneous computation speeds was proposed, which directly copies parts of\ndata into the virtual machines. In all existing works in elastic computing, the\nstorage assignment is centralized, meaning that the number and identity of all\nvirtual machines possible used in the whole computation process are known\nduring the storage assignment. In this paper, we consider Decentralized Uncoded\nStorage Elastic Computing (DUSEC) with heterogeneous computation speeds, where\nany available virtual machine can join the computation which is not predicted\nand thus coordination among different virtual machines' storage assignments is\nnot allowed. Under a decentralized storage assignment originally proposed in\ncoded caching by Maddah-Ali and Niesen, we propose a computing scheme with\nclosed-form optimal computation time. We also run experiments over MNIST\ndataset with Softmax regression model through the Tencent cloud platform, and\nthe experiment results demonstrate that the proposed DUSEC system approaches\nthe state-of-art best storage assignment in the CUSEC system in computation\ntime.\n""]","[('storage computation', 0.5657134056091309), ('coded storage', 0.533085286617279), ('computing distributed computing', 0.48091500997543335), ('distributed computing', 0.4690943658351898), ('heterogeneous computing', 0.44657421112060547), ('cloud computing', 0.4460219442844391), ('coded computing', 0.43755701184272766), ('straggler mitigation', 0.41121339797973633), ('coded computation', 0.3942814767360687), ('virtual machines', 0.3921641707420349)]"
1495,1495,19,1495_cyclotomic polynomials_th cyclotomic polynomial_cyclotomic polynomial_conjecture cyclotomic,"['cyclotomic polynomials', 'th cyclotomic polynomial', 'cyclotomic polynomial', 'conjecture cyclotomic', 'generalized cyclotomic', 'th cyclotomic', 'cyclotomic', 'integers polynomials', 'integers coefficients', 'integers generalized']","['An Identity involving the Cyclotomic Polynomials   We present an elementary identity for the cyclotomic polynomials $\\Phi_n(X)$\nwhich reflects a kind of multiplicative property of $\\Phi_n(X)$ as a function\nof $n$, and we explore its connections with the properties of other\narithmetical functions.\n  Important Note: In the first version of this article uploaded to the arXiv,\nit is said that this result seemed to be new. However, after that, I have\nlearned that this identity (in Theorem 1.1) has previously appeared in\n  Cheng, C. C. A., McKay, J. H., & Wang, S. S. S. (1995). Resultants of\ncyclotomic polynomials. Proceedings of the American Mathematical Society,\n123(4), 1053-1059.\n  (with a different proof).\n', 'Generalized cyclotomic polynomials associated with regular systems of\n  divisors and arbitrary sets of positive integers   We introduce and study the generalized cyclotomic polynomials\n$\\Phi_{A,S,n}(x)$ associated with a regular system $A$ of divisors and an\narbitrary set $S$ of positive integers. We show that all of these polynomials\nhave integer coefficients, they can be expressed as the product of certain\nclassical cyclotomic polynomials $\\Phi_d(x)$ with $d\\mid n$, and enjoy many\nother properties which are similar to the classical and unitary cases. We also\npoint out some related Menon-type identities. One of them seems to be new even\nfor the cyclotomic polynomials $\\Phi_n(x)$.\n', 'Non-Beiter ternary cyclotomic polynomials with an optimally large set of\n  coefficients   Let l>=1 be an arbitrary odd integer and p,q and r primes. We show that there\nexist infinitely many ternary cyclotomic polynomials \\Phi_{pqr}(x) with\nl^2+3l+5<= p<q<r such that the set of coefficients of each of them consists of\nthe p integers in the interval [-(p-l-2)/2,(p+l+2)/2]. It is known that no\nlarger coefficient range is possible. The Beiter conjecture states that the\ncyclotomic coefficients a_{pqr}(k) of \\Phi_{pqr} satisfy |a_{pqr}(k)|<= (p+1)/2\nand thus the above family contradicts the Beiter conjecture. The two already\nknown families of ternary cyclotomic polynomials with an optimally large set of\ncoefficients (found by G. Bachman) satisfy the Beiter conjecture.\n']","[('cyclotomic polynomials', 0.8219469785690308), ('th cyclotomic polynomial', 0.7618408203125), ('cyclotomic polynomial', 0.7577782273292542), ('conjecture cyclotomic', 0.7415415048599243), ('generalized cyclotomic', 0.6959949135780334), ('th cyclotomic', 0.6249384880065918), ('cyclotomic', 0.5948110222816467), ('integers polynomials', 0.53565514087677), ('integers coefficients', 0.47775304317474365), ('integers generalized', 0.44068652391433716)]"
1496,1496,19,1496_maxwell boltzmann_limit vlasov_poisson boltzmann_hydrodynamic limit,"['maxwell boltzmann', 'limit vlasov', 'poisson boltzmann', 'hydrodynamic limit', 'vlasov poisson', 'boltzmann operator', 'boltzmann system', 'global maxwellian', 'boltzmann', 'incompressible navier stokes']","['Diffusive Limit of the Vlasov-Poisson-Boltzmann System for the Full\n  Range of Cutoff Potentials   Diffusive limit of the Vlasov-Poisson-Boltzmann system with cutoff soft\npotentials $-3<\\gamma<0$ in the perturbative framework around global Maxwellian\nstill remains open. By introducing a new weighted $H_{x,v}^2$-$W_{x,v}^{2,\n\\infty}$ approach with time decay, we solve this problem for the full range of\ncutoff potentials $-3<\\gamma\\leq 1$. The core of this approach lies in the\ninterplay between the velocity weighted $H_{x,v}^2$ energy estimate with time\ndecay and the time-velocity weighted $W_{x,v}^{2,\\infty}$ estimate with time\ndecay for the Vlasov-Poisson-Boltzmann system, which leads to the uniform\nestimate with respect to the Knudsen number $\\varepsilon\\in (0,1]$ globally in\ntime. As a result, global strong solution is constructed and incompressible\nNavier-Stokes-Fourier-Poisson limit is rigorously justified for both hard and\nsoft potentials. Meanwhile, this uniform estimate with respect to\n$\\varepsilon\\in (0,1]$ also yields optimal $L^2$ time decay rate and $L^\\infty$\ntime decay rate for the Vlasov-Poisson-Boltzmann system and its incompressible\nNavier-Stokes-Fourier-Poisson limit. This newly introduced weighted\n$H_{x,v}^2$-$W_{x,v}^{2, \\infty}$ approach with time decay is flexible and\nrobust, as it can deal with both optimal time decay problems and hydrodynamic\nlimit problems in a unified framework for the Boltzmann equation as well as the\nVlasov-Poisson-Boltzmann system for the full range of cutoff potentials. It is\nalso expected to shed some light on the more challenging hydrodynamic limit of\nthe Landau equation and the Vlasov-Poisson-Landau system.\n', ""Diffusive Limit of the Vlasov-Maxwell-Boltzmann System without Angular\n  Cutoff   Diffusive limit of the non-cutoff Vlasov-Maxwell-Boltzmann system in\nperturbation framework still remains open. By employing a new weight function\nand making full use of the anisotropic dissipation property of the non-cutoff\nlinearized Boltzmann operator, we solve this problem with some novel treatments\nfor non-cutoff potentials $\\gamma > \\max\\{-3, -\\frac{3}{2}-2s\\}$, including\nboth strong angular singularity $\\frac{1}{2} \\leq s <1$ and weak angular\nsingularity $0 < s < \\frac{1}{2}$. Uniform estimate with respect to the Knudsen\nnumber $\\varepsilon\\in (0,1]$ is established globally in time, which eventually\nleads to the global existence of solutions to the non-cutoff\nVlasov-Maxwell-Boltzmann system as well as hydrodynamic limit to the two-fluid\nincompressible Navier-Stokes-Fourier-Maxwell system with Ohm's law. The\nindicators $\\gamma > \\max\\{-3, -\\frac{3}{2}-2s\\}$ and $0 < s <1$ in this paper\ncover all ranges that can be achieved by the previously established global\nsolutions to the non-cutoff Vlasov-Maxwell-Boltzmann system in perturbation\nframework.\n"", ""Diffusive Limit of the Vlasov-Poisson-Boltzmann System without Angular\n  Cutoff   Diffusive limit of the Vlasov-Poisson-Boltzmann system without angular cutoff\nin the framework of perturbation around global Maxwellian still remains open.\nBy employing the weighted energy method with a newly introduced weight function\n$w_l(\\alpha,\\beta)$ and some novel treatments, we solve this problem for the\nfull range of non-cutoff potentials $\\gamma>-3$ and $0<s<1$. Uniform estimate\nwith respect to the Knudsen number $\\varepsilon \\in (0,1]$ is established\nglobally in time, which eventually leads to the global existence of solutions\nto the Vlasov-Poisson-Boltzmann system without angular cutoff for the full\nrange of non-cutoff potentials and hydrodynamic limit to the two-fluid\nincompressible Navier-Stokes-Fourier-Poisson system with Ohm's law. As a\nbyproduct, this approach also extends the global existence results of previous\nstudies on the Vlasov-Poisson-Boltzmann system without angular cutoff to the\nfull range of non-cutoff potentials $\\gamma>-3$ and $0<s<1$.\n""]","[('maxwell boltzmann', 0.548107385635376), ('limit vlasov', 0.538611650466919), ('poisson boltzmann', 0.4914814531803131), ('hydrodynamic limit', 0.47554829716682434), ('vlasov poisson', 0.4488907754421234), ('boltzmann operator', 0.448557049036026), ('boltzmann system', 0.4116700291633606), ('global maxwellian', 0.3908138573169708), ('boltzmann', 0.3743312656879425), ('incompressible navier stokes', 0.37093544006347656)]"
1497,1497,19,1497_diffusion posterior sampling_image prior_langevin sampling_bayesian inversion,"['diffusion posterior sampling', 'image prior', 'langevin sampling', 'bayesian inversion', 'imaging inverse', 'posterior sampling', 'image reconstruction', 'gaussian priors', 'prior bayesian', 'diffusion posterior']","['Provably Robust Score-Based Diffusion Posterior Sampling for\n  Plug-and-Play Image Reconstruction   In a great number of tasks in science and engineering, the goal is to infer\nan unknown image from a small number of measurements collected from a known\nforward model describing certain sensing or imaging modality. Due to resource\nconstraints, this task is often extremely ill-posed, which necessitates the\nadoption of expressive prior information to regularize the solution space.\nScore-based diffusion models, due to its impressive empirical success, have\nemerged as an appealing candidate of an expressive prior in image\nreconstruction. In order to accommodate diverse tasks at once, it is of great\ninterest to develop efficient, consistent and robust algorithms that\nincorporate unconditional score functions of an image prior distribution in\nconjunction with flexible choices of forward models.\n  This work develops an algorithmic framework for employing score-based\ndiffusion models as an expressive data prior in general nonlinear inverse\nproblems. Motivated by the plug-and-play framework in the imaging community, we\nintroduce a diffusion plug-and-play method (DPnP) that alternatively calls two\nsamplers, a proximal consistency sampler based solely on the likelihood\nfunction of the forward model, and a denoising diffusion sampler based solely\non the score functions of the image prior. The key insight is that denoising\nunder white Gaussian noise can be solved rigorously via both stochastic (i.e.,\nDDPM-type) and deterministic (i.e., DDIM-type) samplers using the unconditional\nscore functions. We establish both asymptotic and non-asymptotic performance\nguarantees of DPnP, and provide numerical experiments to illustrate its promise\nin solving both linear and nonlinear image reconstruction tasks. To the best of\nour knowledge, DPnP is the first provably-robust posterior sampling method for\nnonlinear inverse problems using unconditional diffusion priors.\n', 'NF-ULA: Langevin Monte Carlo with Normalizing Flow Prior for Imaging\n  Inverse Problems   Bayesian methods for solving inverse problems are a powerful alternative to\nclassical methods since the Bayesian approach offers the ability to quantify\nthe uncertainty in the solution. In recent years, data-driven techniques for\nsolving inverse problems have also been remarkably successful, due to their\nsuperior representation ability. In this work, we incorporate data-based models\ninto a class of Langevin-based sampling algorithms for Bayesian inference in\nimaging inverse problems. In particular, we introduce NF-ULA (Normalizing\nFlow-based Unadjusted Langevin algorithm), which involves learning a\nnormalizing flow (NF) as the image prior. We use NF to learn the prior because\na tractable closed-form expression for the log prior enables the\ndifferentiation of it using autograd libraries. Our algorithm only requires a\nnormalizing flow-based generative network, which can be pre-trained\nindependently of the considered inverse problem and the forward operator. We\nperform theoretical analysis by investigating the well-posedness and\nnon-asymptotic convergence of the resulting NF-ULA algorithm. The efficacy of\nthe proposed NF-ULA algorithm is demonstrated in various image restoration\nproblems such as image deblurring, image inpainting, and limited-angle X-ray\ncomputed tomography (CT) reconstruction. NF-ULA is found to perform better than\ncompeting methods for severely ill-posed inverse problems.\n', 'Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie   Since the seminal work of Venkatakrishnan et al. in 2013, Plug & Play (PnP)\nmethods have become ubiquitous in Bayesian imaging. These methods derive\nMinimum Mean Square Error (MMSE) or Maximum A Posteriori (MAP) estimators for\ninverse problems in imaging by combining an explicit likelihood function with a\nprior that is implicitly defined by an image denoising algorithm. The PnP\nalgorithms proposed in the literature mainly differ in the iterative schemes\nthey use for optimisation or for sampling. In the case of optimisation schemes,\nsome recent works guarantee the convergence to a fixed point, albeit not\nnecessarily a MAP estimate. In the case of sampling schemes, to the best of our\nknowledge, there is no known proof of convergence. There also remain important\nopen questions regarding whether the underlying Bayesian models and estimators\nare well defined, well-posed, and have the basic regularity properties required\nto support these numerical schemes. To address these limitations, this paper\ndevelops theory, methods, and provably convergent algorithms for performing\nBayesian inference with PnP priors. We introduce two algorithms: 1) PnP-ULA\n(Unadjusted Langevin Algorithm) for Monte Carlo sampling and MMSE inference;\nand 2) PnP-SGD (Stochastic Gradient Descent) for MAP inference. Using recent\nresults on the quantitative convergence of Markov chains, we establish detailed\nconvergence guarantees for these two algorithms under realistic assumptions on\nthe denoising operators used, with special attention to denoisers based on deep\nneural networks. We also show that these algorithms approximately target a\ndecision-theoretically optimal Bayesian model that is well-posed. The proposed\nalgorithms are demonstrated on several canonical problems such as image\ndeblurring, inpainting, and denoising, where they are used for point estimation\nas well as for uncertainty visualisation and quantification.\n']","[('diffusion posterior sampling', 0.6170844435691833), ('image prior', 0.5810057520866394), ('langevin sampling', 0.5588621497154236), ('bayesian inversion', 0.5558667778968811), ('imaging inverse', 0.5551425814628601), ('posterior sampling', 0.5416978597640991), ('image reconstruction', 0.501410186290741), ('gaussian priors', 0.48574724793434143), ('prior bayesian', 0.47911036014556885), ('diffusion posterior', 0.4734068214893341)]"
1498,1498,19,1498_circular arc graphs_graphs circular_arc graphs_chordal graphs,"['circular arc graphs', 'graphs circular', 'arc graphs', 'chordal graphs', 'arc graph', 'minimal graphs', 'graph can represented', 'graphs', 'graphs interval graphs', 'various graph classes']","['Characterization of Chordal Circular-arc Graphs: I. Split Graphs   The most elusive problem around the class of circular-arc graphs is\nidentifying all minimal graphs that are not in this class. The main obstacle is\nthe lack of a systematic way of enumerating these minimal graphs. McConnell\n[FOCS 2001] presented a transformation from circular-arc graphs to interval\ngraphs with certain patterns of representations. We fully characterize these\ninterval patterns for circular-arc graphs that are split graphs, thereby\nbuilding a connection between minimal split graphs that are not circular-arc\ngraphs and minimal non-interval graphs. This connection enables us to identify\nall minimal split graphs that are not circular-arc graphs. As a byproduct, we\ndevelop a linear-time certifying recognition algorithm for circular-arc graphs\nwhen the input is a split graph.\n', 'Essential obstacles to Helly circular-arc graphs   A Helly circular-arc graph is the intersection graph of a set of arcs on a\ncircle having the Helly property. We introduce essential obstacles, which are a\nrefinement of the notion of obstacles, and prove that essential obstacles are\nprecisely the minimal forbidden induced circular-arc subgraphs for the class of\nHelly circular-arc graphs. We show that it is possible to find in linear time,\nin any given obstacle, some minimal forbidden induced subgraph for the class of\nHelly circular-arc graphs contained as an induced subgraph. Moreover, relying\non an existing linear-time algorithm for finding induced obstacles in\ncircular-arc graphs, we conclude that it is possible to find in linear time an\ninduced essential obstacle in any circular-arc graph that is not a Helly\ncircular-arc graph. The problem of finding a forbidden induced subgraph\ncharacterization, not restricted only to circular-arc graphs, for the class of\nHelly circular-arc graphs remains unresolved. As a partial answer to this\nproblem, we find the minimal forbidden induced subgraph characterization for\nthe class of Helly circular-arc graphs restricted to graphs containing no\ninduced claw and no induced 5-wheel. Furthermore, we show that there is a\nlinear-time algorithm for finding, in any given graph that is not a Helly\ncircular-arc graph, an induced subgraph isomorphic to claw, 5-wheel, or some\nminimal forbidden induced subgraph for the class of Helly circular-arc graphs.\n', 'On the bend number of circular-arc graphs as edge intersection graphs of\n  paths on a grid   Golumbic, Lipshteyn and Stern \\cite{Golumbic-epg} proved that every graph can\nbe represented as the edge intersection graph of paths on a grid (EPG graph),\ni.e., one can associate with each vertex of the graph a nontrivial path on a\nrectangular grid such that two vertices are adjacent if and only if the\ncorresponding paths share at least one edge of the grid. For a nonnegative\ninteger $k$, $B_k$-EPG graphs are defined as EPG graphs admitting a model in\nwhich each path has at most $k$ bends. Circular-arc graphs are intersection\ngraphs of open arcs of a circle. It is easy to see that every circular-arc\ngraph is a $B_4$-EPG graph, by embedding the circle into a rectangle of the\ngrid. In this paper, we prove that every circular-arc graph is $B_3$-EPG, and\nthat there exist circular-arc graphs which are not $B_2$-EPG. If we restrict\nourselves to rectangular representations (i.e., the union of the paths used in\nthe model is contained in a rectangle of the grid), we obtain EPR (edge\nintersection of path in a rectangle) representations. We may define $B_k$-EPR\ngraphs, $k\\geq 0$, the same way as $B_k$-EPG graphs. Circular-arc graphs are\nclearly $B_4$-EPR graphs and we will show that there exist circular-arc graphs\nthat are not $B_3$-EPR graphs. We also show that normal circular-arc graphs are\n$B_2$-EPR graphs and that there exist normal circular-arc graphs that are not\n$B_1$-EPR graphs. Finally, we characterize $B_1$-EPR graphs by a family of\nminimal forbidden induced subgraphs, and show that they form a subclass of\nnormal Helly circular-arc graphs.\n']","[('circular arc graphs', 0.7383167743682861), ('graphs circular', 0.6942147612571716), ('arc graphs', 0.6583229899406433), ('chordal graphs', 0.5911024808883667), ('arc graph', 0.5715813636779785), ('minimal graphs', 0.5588590502738953), ('graph can represented', 0.5471213459968567), ('graphs', 0.5297622084617615), ('graphs interval graphs', 0.5254186391830444), ('various graph classes', 0.5136886239051819)]"
1499,1499,19,1499_null lagrangians_lagrangian systems_singular lagrangians_euler lagrange equations,"['null lagrangians', 'lagrangian systems', 'singular lagrangians', 'euler lagrange equations', 'eulerian lagrangian', 'lagrangian', 'lagrangian formalism', 'lagrangian invariant', 'lagrangians', 'lagrange equations']","[""Nonstandard Null Lagrangians and Gauge Functions and Dissipative Forces\n  in Dynamics   Standard and non-standard Lagrangians that give the same equation of motion\nare significantly different in their forms, as the latter do not have terms\nthat clearly discernable energy-like expressions. A special family of these\nLagrangians are null Lagrangians and their gauge functions. It is shown that\nnon-standard null Lagrangians and their gauge functions can be used to\nintroduce dissipative forces to dynamical systems. With standard null\nLagrangians being known for introducing non-dissipative forces, the presented\nresults allow for a complete picture of novel roles played by null Lagrangians\nin introducing forces to dynamics. Applications of the results to Newton's laws\nare presented and their Galilean invariance is discussed.\n"", 'General Null Lagrangians and Their Novel Role in Classical Dynamics   A method for constructing general null Lagrangians and their higher harmonics\nis presented for dynamical systems with one degree of freedom. It is shown that\nthese Lagrangians can be used to obtain non-standard Lagrangians, which give\nequations of motion for the law of inertia and some dissipative dynamical\nsystems. The necessary condition for deriving equations of motion by using null\nLagrangians is presented, and it is demonstrated that this condition plays the\nsame role for null Lagrangians as the Euler-Lagrange equation plays for\nstandard and non-standard Lagrangians. The obtained results and their\napplications establish a novel role of null Lagrangians in classical dynamics.\n', 'Null Lagrangians and Invariance of Action: Exact Gauge Functions   Null Lagrangians and their gauge functions are derived for given standard and\nnon-standard Lagrangians. The obtained standard null Lagrangians generalize\nthose previously found but the non-standard null Lagrangians are new. The gauge\nfunctions are used to make the action invariant and introduce the exact null\nLagrangians, which form a new family of null Lagrangians. The conditions\nrequired for the action to be invariant are derived for all null Lagrangians\npresented in this paper, thus, making them exact. As a specific application,\nthe exact null Lagrangians are derived for a second-order ordinary differential\nequation. The application shows that the exact null Lagrangians can be obtained\nfor any ordinary differential equation with known Lagrangian.\n']","[('null lagrangians', 0.7274386286735535), ('lagrangian systems', 0.6048735976219177), ('singular lagrangians', 0.5610779523849487), ('euler lagrange equations', 0.5577903985977173), ('eulerian lagrangian', 0.5499478578567505), ('lagrangian', 0.5293614864349365), ('lagrangian formalism', 0.5293048024177551), ('lagrangian invariant', 0.5244942903518677), ('lagrangians', 0.5053107738494873), ('lagrange equations', 0.4936991035938263)]"
1500,1500,19,1500_metric lie group_left invariant metrics_dimensional lie groups_invariant riemannian metrics,"['metric lie group', 'left invariant metrics', 'dimensional lie groups', 'invariant riemannian metrics', 'lie groups dimension', 'left invariant metric', 'dimensional lie group', 'lie groups', 'invariant metrics', 'invariant riemannian metric']","['Invariant Einstein metrics on SU(N) and complex Stiefel manifolds   We study existence of invariant Einstein metrics on complex Stiefel manifolds\n$G/K = \\SU(\\ell+m+n)/\\SU(n) $ and the special unitary groups $G =\n\\SU(\\ell+m+n)$. We decompose the Lie algebra $\\frak g$ of $G$ and the tangent\nspace $\\frak p$ of $G/K$, by using the generalized flag manifolds $G/H =\n\\SU(\\ell+m+n)/\\s(\\U(\\ell)\\times\\U(m)\\times\\U(n))$.\n  We parametrize scalar products on the 2-dimensional center of the Lie algebra\nof $H$, and we consider $G$-invariant and left invariant metrics determined by\n$\\Ad(\\s(\\U(\\ell)\\times\\U(m)\\times\\U(n))$-invariant scalar products on $\\frak g$\nand $\\frak p$ respectively. Then we compute their Ricci tensor for such\nmetrics.\n  We prove existence of $\\Ad(\\s(\\U(1)\\times\\U(2)\\times\\U(2))$-invariant\nEinstein metrics on $V_3\\bb{C}^{5}=\\SU(5)/\\SU(2)$,\n$\\Ad(\\s(\\U(2)\\times\\U(2)\\times\\U(2))$-invariant Einstein metrics on\n$V_4\\bb{C}^{6}=\\SU(6)/\\SU(2)$, and\n$\\Ad(\\s(\\U(m)\\times\\U(m)\\times\\U(n))$-invariant Einstein metrics on\n$V_{2m}\\bb{C}^{2m+n}=\\SU(2m+n)/\\SU(n)$. We also prove existence of\n$\\Ad(\\s(\\U(1)\\times\\U(2)\\times\\U(2))$-invariant Einstein metrics on the compact\nLie group $\\SU(5)$, which are not naturally reductive. The Lie group $\\SU(5)$\nis the special unitary group of smallest rank known for the moment, admitting\nnon naturally reductive Einstein metrics. Finally, we show that the compact Lie\ngroup $\\SU(4+n)$ admits two non naturally reductive\n$\\Ad(\\s(\\U(2)\\times\\U(2)\\times\\U(n)))$-invariant Einstein metrics for $ 2 \\leq\nn \\leq 25$, and four non naturally reductive Einstein metrics for $n\\ge 26$.\nThis extends previous results of K.~ Mori about non naturally reductive\nEinstein metrics on $\\SU(4+n)$ ($n \\geq 2$).\n', 'A classification of left-invariant pseudo-Riemannian metrics on some\n  nilpotent Lie groups   It is known that a connected and simply-connected Lie group admits only one\nleft-invariant Riemannian metric up to scaling and isometry if and only if it\nis isomorphic to the Euclidean space, the Lie group of the real hyperbolic\nspace, or the direct product of the three dimensional Heisenberg group and the\nEuclidean space of dimension $n-3$. In this paper, we give a classification of\nleft-invariant pseudo-Riemannian metrics of an arbitrary signature for the\nthird Lie groups with $n \\geq 4$ up to scaling and automorphisms. This\ncompletes the classifications of left-invariant pseudo-Riemannian metrics for\nthe above three Lie groups up to scaling and automorphisms.\n', 'The index of symmetry for a left-invariant metric on a solvable\n  three-dimensional Lie group   We find the index of symmetry for all solvable three-dimensional Lie groups\nwith a left-invariant metric. When combined with the work of Reggiani on\nunimodular three-dimensional Lie groups, the index of symmetry is then known\nfor all three-dimensional Lie groups with a left-invariant metric. Similar to\nthe unimodular case, for every solvable three-dimensional Lie algebra there is\nat least one left-invariant metric for which the index of symmetry is positive.\nAlso, the index is never equal to 2.\n']","[('metric lie group', 0.7331143617630005), ('left invariant metrics', 0.6981147527694702), ('dimensional lie groups', 0.6772543787956238), ('invariant riemannian metrics', 0.6671539545059204), ('lie groups dimension', 0.6669746041297913), ('left invariant metric', 0.6579381823539734), ('dimensional lie group', 0.6452913880348206), ('lie groups', 0.6395912170410156), ('invariant metrics', 0.6383697390556335), ('invariant riemannian metric', 0.6324954628944397)]"
1501,1501,19,1501_categorical quantum mechanics_categorical quantum_foundations quantum_quantum programming,"['categorical quantum mechanics', 'categorical quantum', 'foundations quantum', 'quantum programming', 'quantum foundations', 'category hilbert', 'features quantum', 'category theory', 'category finite dimensional', 'finite dimensional quantum']","['Why FHilb is Not an Interesting (Co)Differential Category   Differential categories provide an axiomatization of the basics of\ndifferentiation and categorical models of differential linear logic. As\ndifferentiation is an important tool throughout quantum mechanics and quantum\ninformation, it makes sense to study applications of the theory of differential\ncategories to categorical quantum foundations. In categorical quantum\nfoundations, compact closed categories (and therefore traced symmetric monoidal\ncategories) are one of the main objects of study, in particular the category of\nfinite-dimensional Hilbert spaces FHilb. In this paper, we will explain why the\nonly differential category structure on FHilb is the trivial one. This follows\nfrom a sort of in-compatibility between the trace of FHilb and possible\ndifferential category structure. That said, there are interesting non-trivial\nexamples of traced/compact closed differential categories, which we also\ndiscuss.\n  The goal of this paper is to introduce differential categories to the broader\ncategorical quantum foundation community and hopefully open the door to further\nwork in combining these two fields. While the main result of this paper may\nseem somewhat ""negative"" in achieving this goal, we discuss interesting\npotential applications of differential categories to categorical quantum\nfoundations.\n', 'Dagger linear logic and categorical quantum mechanics   This thesis develops the categorical proof theory for the non-compact\nmultiplicative dagger linear logic, and investigates its applications to\nCategorical Quantum Mechanics (CQM). The existing frameworks of CQM are\ncategorical proof theories of compact dagger linear logic, and are motivated by\nthe interpretation of quantum systems in the category of finite dimensional\nHilbert spaces. This thesis describes a new non-compact framework called Mixed\nUnitary Categories which can accommodate infinite dimensional systems, and\ndevelops models for the framework. To this end, it builds on linearly\ndistributive categories, and $*$-autonomous categories which are categorical\nproof theories of (non-compact) multiplicative linear logic. The proof theory\nof non-compact dagger-linear logic is obtained from the basic setting of an LDC\nby adding a dagger functor satisfying appropriate coherences to give a\ndagger-LDC. From every (isomix) dagger-LDC one can extract a canonical ""unitary\ncore"" which up to equivalence is the traditional CQM framework of\ndagger-monoidal categories. This leads to the framework of Mixed Unitary\nCategories (MUCs): every MUC contains a (compact) unitary core which is\nextended by a (non-compact) isomix dagger-LDC. Various models of MUCs based on\nFiniteness Spaces, Chu spaces, Hopf modules, etc., are developed in this\nthesis. This thesis also generalizes the key algebraic structures of CQM, such\nas observables, measurement, and complementarity, to MUC framework.\nFurthermore, using the MUC framework, this thesis establishes a connection\nbetween the complementary observables of quantum mechanics and the exponential\nmodalities of linear logic.\n', 'Dagger linear logic for categorical quantum mechanics   Categorical quantum mechanics exploits the dagger compact closed structure of\nfinite dimensional Hilbert spaces, and uses the graphical calculus of string\ndiagrams to facilitate reasoning about finite dimensional processes. A\nsignificant portion of quantum physics, however, involves reasoning about\ninfinite dimensional processes, and it is well-known that the category of all\nHilbert spaces is not compact closed. Thus, a limitation of using dagger\ncompact closed categories is that one cannot directly accommodate reasoning\nabout infinite dimensional processes.\n  A natural categorical generalization of compact closed categories, in which\ninfinite dimensional spaces can be modelled, is *-autonomous categories and,\nmore generally, linearly distributive categories. This article starts the\ndevelopment of this direction of generalizing categorical quantum mechanics. An\nimportant first step is to establish the behaviour of the dagger in these more\ngeneral settings. Thus, these notes simultaneously develop the categorical\nsemantics of multiplicative dagger linear logic.\n  The notes end with the definition of a mixed unitary category. It is this\nstructure which is subsequently used to extend the key features of categorical\nquantum mechanics.\n']","[('categorical quantum mechanics', 0.7633236646652222), ('categorical quantum', 0.7547377347946167), ('foundations quantum', 0.5455237627029419), ('quantum programming', 0.5266899466514587), ('quantum foundations', 0.5264583230018616), ('category hilbert', 0.5206470489501953), ('features quantum', 0.5198203921318054), ('category theory', 0.5037181973457336), ('category finite dimensional', 0.5031097531318665), ('finite dimensional quantum', 0.4940386712551117)]"
1502,1502,19,1502_dependent convection diffusion_admits asymptotic expansion_asymptotic expansions_asymptotic expansion,"['dependent convection diffusion', 'admits asymptotic expansion', 'asymptotic expansions', 'asymptotic expansion', 'convection diffusion', 'varepsilon diffusion', 'admits asymptotic', 'asymptotic behavior', 'convection dominated', 'diffusion coefficients']","[""Asymptotic expansion for convection-dominated transport in a thin\n  graph-like junction   We consider for a small parameter $\\varepsilon >0$ a parabolic\nconvection-diffusion problem with P\\'eclet number of order\n$\\mathcal{O}(\\varepsilon^{-1})$ in a three-dimensional graph-like junction\nconsisting of thin curvilinear cylinders with radii of order\n$\\mathcal{O}(\\varepsilon)$ connected through a domain (node) of diameter\n$\\mathcal{O}(\\varepsilon).$ Inhomogeneous Neumann type boundary conditions,\nthat involve convective and diffusive fluxes, are prescribed both on the\nlateral surfaces of the thin cylinders and the boundary of the node.\n  The asymptotic behaviour of the solution is studied as $\\varepsilon \\to 0,$\ni.e., when the diffusion coefficients are eliminated and the thin junction is\nshrunk into a three-part graph connected in a single vertex. A rigorous\nprocedure for the construction of the complete asymptotic expansion of the\nsolution is developed and the corresponding energetic and uniform pointwise\nestimates are proven. Depending on the directions of the limit convective\nfluxes, the corresponding limit problems $(\\varepsilon = 0)$ are derived in the\nform of first-order hyperbolic differential equations on the one-dimensional\nbranches with novel gluing conditions at the vertex. These generalize the\nclassical Kirchhoff transmission conditions and might require the solution of a\nthree-dimensional cell-like problem associated with the vertex to account for\nthe local geometric inhomogeneity of the node and the physical processes in the\nnode. The asymptotic ansatz consists of three parts, namely, the regular part,\nnode-layer part, and boundary-layer one. Their coefficients are classical\nsolutions to mixed-dimensional limit problems. The existence and other\nproperties of those solutions are analyzed.\n"", ""Puiseux asymptotic expansions for convection-dominated transport\n  problems in thin graph-like networks: strong boundary interactions   This article completes the study of the influence of the intensity parameter\n$\\alpha$ in the boundary condition $\\varepsilon\n\\partial_{\\boldsymbol{\\nu}_\\varepsilon} u_\\varepsilon - u_\\varepsilon \\,\n\\overrightarrow{V_\\varepsilon}\\boldsymbol{\\cdot}\\boldsymbol{\\nu}_\\varepsilon =\n\\varepsilon^{\\alpha} \\varphi_\\varepsilon $ given on the boundary of a thin\nthree-dimensional graph-like network consisting of thin cylinders that are\ninterconnected by small domains (nodes) with diameters of order\n$\\mathcal{O}(\\varepsilon).$ Inside of the thin network a time-dependent\nconvection-diffusion equation with high P\\'eclet number of order\n$\\mathcal{O}(\\varepsilon^{-1})$ is considered. The novelty of this article is\nthe case of $\\alpha <1,$ which indicates a strong intensity of physical\nprocesses on the boundary, described by the inhomogeneity $\\varphi_\\varepsilon$\n(the cases $\\alpha =1$ and $\\alpha >1$ were previously studied by the same\nauthors).\n  A complete Puiseux asymptotic expansion is constructed for the solution\n$u_\\varepsilon$ as $\\varepsilon \\to 0,$ i.e., when the diffusion coefficients\nare eliminated and the thin network shrinks into a graph. Furthermore, the\ncorresponding uniform pointwise and energy estimates are proved, which provide\nan approximation of the solution with a given accuracy in terms of the\nparameter $\\varepsilon.$\n"", ""Asymptotic approximations for semilinear parabolic convection-dominated\n  transport problems in thin graph-like networks   We consider time-dependent convection-diffusion problems with high P\\'eclet\nnumber of order $\\mathcal{O}(\\varepsilon^{-1})$ in thin three-dimensional\ngraph-like networks consisting of cylinders that are interconnected by small\ndomains (nodes) with diameters of order $\\mathcal{O}(\\varepsilon).$ On the\nlateral surfaces of the thin cylinders and the boundaries of the nodes we\naccount for solution-dependent inhomogeneous Robin boundary conditions which\ncan render the associated initial-boundary problem to be nonlinear. The\nstrength of the inhomogeneity is controlled by an intensity factor of order\n${\\mathcal{O}} (\\varepsilon^\\alpha)$, $\\alpha >0$.\n  The asymptotic behaviour of the solution is studied as $\\varepsilon \\to 0,$\ni.e., when the diffusion coefficients are eliminated and the thin\nthree-diemnsional network is shrunk into a graph. There are three qualitatively\ndifferent cases in the asymptotic behaviour of the solution depending on the\nvalue of the intensity parameter $\\alpha:$ $\\alpha =1,$ $\\alpha > 1,$ and\n$\\alpha \\in (0, 1).$ We construct the asymptotic approximation of the solution,\nwhich provides us with the hyperbolic limit model for $\\varepsilon \\to 0$ for\nthe first two cases, and prove the corresponding uniform pointwise estimates\nand energy estimates. As the main result, we derive uniform pointwise estimates\nfor the difference between the solutions of the convection-diffusion problem\nand the zero-order approximation that includes the solution of the\ncorresponding hyperbolic limit problem.\n""]","[('dependent convection diffusion', 0.5354464650154114), ('admits asymptotic expansion', 0.5298795104026794), ('asymptotic expansions', 0.5196520090103149), ('asymptotic expansion', 0.5005151629447937), ('convection diffusion', 0.4996759295463562), ('varepsilon diffusion', 0.47971096634864807), ('admits asymptotic', 0.4727458953857422), ('asymptotic behavior', 0.46946024894714355), ('convection dominated', 0.4693649709224701), ('diffusion coefficients', 0.4414069354534149)]"
1503,1503,19,1503_differential galois theory_differential galois_theory galois theory_theory galois,"['differential galois theory', 'differential galois', 'theory galois theory', 'theory galois', 'galois theory', 'algebras differential', 'central simple algebras', 'differential field', 'field characteristic', 'galois']","['Differential Galois Groups of Differential Central Simple Algebras and\n  their Projective Representations   Let $F$ be a $\\delta-$field (differential field) of characteristic zero with\nan algebraically closed field of constants $F^\\delta$, $A$ be a\n$\\delta-F-$central simple algebra, $K$ be a Picard-Vessiot extension for the\n$\\delta-F-$module $A$ and $\\mathscr G(K|F)$ be the $\\delta-$Galois group of $K$\nover $F.$ We prove that a $\\delta-$field extension $L$ of $F,$ having\n$F^\\delta$ as its field of constants, splits the $\\delta-F-$central simple\nalgebra $A$ if and only if the $\\delta-$field $K$ embeds in $L.$\n  We then extend the theory of $\\delta-F-$matrix algebras over a $\\delta-$field\n$F,$ put forward by Magid & Juan (2008), to arbitrary $\\delta-F-$central simple\nalgebras. In particular, we establish a natural bijective correspondence\nbetween the isomorphism classes of $\\delta-F-$central simple algebras of\ndimension $n^2$ over $F$ that are split by the $\\delta-$field $K$ and the\nclasses of inequivalent representations of the algebraic group $\\mathscr\nG(K|F)$ in $\\mathrm{PGL}_n(F^\\delta).$ We show that $\\mathscr G(K|F)$ is a\nreductive or a solvable algebraic group if and only if $A$ has certain kinds of\n$\\delta-$right ideals.\n', 'A categorical approach to Picard-Vessiot theory   Picard-Vessiot rings are present in many settings like differential Galois\ntheory, difference Galois theory and Galois theory of Artinian simple module\nalgebras. In this article we set up an abstract framework in which we can prove\ntheorems on existence and uniqueness of Picard-Vessiot rings, as well as on\nGalois groups corresponding to the Picard-Vessiot rings. As the present\napproach restricts to the categorical properties which all the categories of\ndifferential modules resp. difference modules etc. share, it gives unified\nproofs for all these Galois theories (and maybe more general ones).\n', 'Picard-Vessiot theory of differentially simple rings   In Picard-Vessiot theory, the Galois theory for linear differential\nequations, the Picard-Vessiot ring plays an important role, since it is the\nPicard-Vessiot ring which is a torsor (principal homogeneous space) for the\nGalois group (scheme). Like fields are simple rings having only (0) and (1) as\nideals, the Picard-Vessiot ring is a differentially simple ring, i.e. a\ndifferential ring having only (0) and (1) as differential ideals. Having in\nmind that the classical Galois theory is a theory of extensions of fields, i.e.\nof simple rings, it is quite natural to ask whether one can also set up a\nPicard-Vessiot theory where the base is not a differential field, but more\ngeneral a differentially simple ring. It is the aim of this article to give a\npositive answer to this question, i.e. to set up such a differential Galois\ntheory.\n']","[('differential galois theory', 0.6380136013031006), ('differential galois', 0.5750481486320496), ('theory galois theory', 0.49527549743652344), ('theory galois', 0.47782102227211), ('galois theory', 0.4639602601528168), ('algebras differential', 0.4352251887321472), ('central simple algebras', 0.4192425310611725), ('differential field', 0.39543119072914124), ('field characteristic', 0.3781193196773529), ('galois', 0.37250033020973206)]"
1504,1504,19,1504_g_2 manifolds_solvable lie groups_shrinking solitons_g_2 structures,"['g_2 manifolds', 'solvable lie groups', 'shrinking solitons', 'g_2 structures', 'solitons', 'g_2 structure', 'invariant g_2', 'structures lie groups', 'soliton', 'lie groups']","['Quadratic closed G2-structures   This article studies closed G2-structures satisfying the quadratic condition,\na second-order PDE system introduced by Bryant involving a parameter $\\lambda.$\nFor certain special values of $\\lambda$ the quadratic condition is equivalent\nto the Einstein condition for the metric induced by the closed G2-structure\n(for $\\lambda = 1/2$), the extremally Ricci-pinched (ERP) condition (for\n$\\lambda=1/6$), and the condition that the closed G2-structure be an eigenform\nfor the Laplace operator (for $\\lambda = 0$). Prior to the work in this\narticle, solutions to the quadratic system were known only for $\\lambda = 1/6,$\n$-1/8,$ and $2/5,$ and for these values only a handful of solutions were known.\n  In this article, we produce infinitely many new examples of ERP\nG2-structures, including the first example of a complete inhomogeneous ERP\nG2-structure and a new example of a compact ERP G2-structure. We also give a\nclassification of homogeneous ERP G2-structures. We provide the first examples\nof quadratic closed G2-structures for $\\lambda = -1,$ $1/3,$ and $3/4,$ as well\nas infinitely many new examples for $\\lambda = -1/8$ and $2/5.$ Our\nconstructions involve the notion of special torsion for closed G2-structures, a\nnew concept that is likely to have wider applicability.\n  In the final section of the article, we provide two large families of\ninhomogeneous complete steady gradient solitons for the Laplacian flow, the\nfirst known such examples.\n', ""Uniqueness of Asymptotically Conical Gradient Shrinking Solitons in\n  G_2-Laplacian Flow   We prove a uniqueness result for asymptotically conical (AC) gradient\nshrinking solitons for the Laplacian flow of closed G_2-structures: If two\ngradient shrinking solitons to Laplacian flow are asymptotic to the same closed\nG_2-cone, then their G_2-structures are equivalent, and in particular, the two\nsolitons are isometric. The proof extends Kotschwar and Wang's argument for\nuniqueness of AC gradient shrinking Ricci solitons. We additionally show that\nthe symmetries of the G_2-structure of an AC shrinker end are inherited from\nits asymptotic cone; under a mild assumption on the fundamental group, the\nsymmetries of the asymptotic cone extend to global symmetries.\n"", ""Cohomogeneity-one solitons in Laplacian flow: local, smoothly-closing\n  and steady solitons   We initiate a systematic study of cohomogeneity-one solitons in Bryant's\nLaplacian flow of closed G_2-structures on a 7-manifold, motivated by the\nproblem of understanding finite-time singularities of that flow. Here we focus\non solitons with symmetry groups Sp(2) and SU(3); in both cases we prove the\nexistence of continuous families of local cohomogeneity-one gradient Laplacian\nsolitons and characterise which of these local solutions extend smoothly over\ntheir unique singular orbits. The main questions are then to determine which of\nthese smoothly-closing solutions extend to complete solitons and furthermore to\nunderstand the asymptotic geometry of these complete solitons.\n  We provide complete answers to both questions in the case of steady solitons.\nUp to the actions of scaling and discrete symmetries, we show that the set of\nall smoothly-closing SU(3)-invariant steady Laplacian solitons defined on a\nneighbourhood of the zero-section of the anti-self-dual bundle of CP^2 is\nparametrised by the set of nonnegative reals. An open interval I=(0,c)\ncorresponds to complete nontrivial gradient solitons that are asymptotic to the\nunique SU(3)-invariant torsion-free G_2 cone. The boundary point 0 of I\ncorresponds to the well-known Bryant--Salamon asymptotically conical\nG_2-manifold, while the other boundary point c corresponds to an explicit\ncomplete gradient steady soliton with exponential volume growth and novel\nasymptotic geometry. The open interval (c, oo) consists entirely of incomplete\nsolutions.\n  In addition, we find an explicit complete gradient shrinking soliton on the\nanti-self-dual bundle of S^4 and CP^2. Both these shrinkers are asymptotic to\nclosed but non-torsion-free G_2 cones. Like the nontrivial AC gradient steady\nsolitons on the anti-self-dual bundle of CP^2, these shrinkers appear to be\npotential singularity models for finite-time singularities of Laplacian flow.\n""]","[('g_2 manifolds', 0.567780613899231), ('solvable lie groups', 0.5285710096359253), ('shrinking solitons', 0.5280371904373169), ('g_2 structures', 0.5155497193336487), ('solitons', 0.5114765167236328), ('g_2 structure', 0.510421872138977), ('invariant g_2', 0.5009415745735168), ('structures lie groups', 0.4672420024871826), ('soliton', 0.4536653757095337), ('lie groups', 0.4480949640274048)]"
1505,1505,19,1505_topological complexity_higher topological complexity_complexity digital_topological methods,"['topological complexity', 'higher topological complexity', 'complexity digital', 'topological methods', 'topological', 'topological complexities', 'higher topological', 'digital images', 'topological spaces', 'topology']","['Certain topological methods for computing digital topological complexity   In this paper, we examine the relations of two closely related concepts, the\ndigital Lusternik-Schnirelmann category and the digital higher topological\ncomplexity, with each other in digital images. For some certain digital images,\nwe introduce $\\kappa-$topological groups in the digital topological manner for\nhaving stronger ideas about the digital higher topological complexity. Our aim\nis to improve the understanding of the digital higher topological complexity.\nWe present examples and counterexamples for $\\kappa-$topological groups.\n', 'Topological Complexities of Finite Digital Images   Digital topological methods are often used on computing the topological\ncomplexity of digital images. We give new results on the relation between\nreducibility and digital contractibility in order to determine the topological\ncomplexity of a digitally connected finite digital image. We present all\npossible cases of the topological complexity TC of a finite digital image in Z\nand Z^2$. Finally, we determine the higher topological complexity TC_{n} of\nfinite irreducible digital images independently of the number of points for n >\n1.\n', ""Essential concepts of digital topology\\\\ (digital $k$-connectivity and\n  $k$-adjacencis for digital products)   The paper refers to several concepts which are essential to studying digital\nobjects from the viewpoint of digital topology: digital $k$-connectivity or\ndigital $k$-adjacency, $C$-compatible and normal $k$-adjacency for a digital\nproduct.\n  Since L. Boxer has often mentioned the origins of these concepts in an\ninaccurate way, we discuss something incorrectly cited or mentioned in Boxer's\npapers according to the facts.\n""]","[('topological complexity', 0.7337669134140015), ('higher topological complexity', 0.7211492657661438), ('complexity digital', 0.6274954080581665), ('topological methods', 0.5606959462165833), ('topological', 0.5570417642593384), ('topological complexities', 0.5558891892433167), ('higher topological', 0.5334446430206299), ('digital images', 0.4847293496131897), ('topological spaces', 0.47455838322639465), ('topology', 0.456412136554718)]"
1506,1506,19,1506_communication complexity_shared randomness_mutual information_information theoretic,"['communication complexity', 'shared randomness', 'mutual information', 'information theoretic', 'kolmogorov complexity', 'shared secret', 'secret key agreement', 'information leakage', 'shared secret key', 'protocol']","[""Secret key agreement from correlated data, with no prior information   A fundamental question that has been studied in cryptography and in\ninformation theory is whether two parties can communicate confidentially using\nexclusively an open channel. We consider the model in which the two parties\nhold inputs that are correlated in a certain sense. This model has been studied\nextensively in information theory, and communication protocols have been\ndesigned which exploit the correlation to extract from the inputs a shared\nsecret key. However, all the existing protocols are not universal in the sense\nthat they require that the two parties also know some attributes of the\ncorrelation. In other words, they require that each party knows something about\nthe other party's input. We present a protocol that does not require any prior\nadditional information. It uses space-bounded Kolmogorov complexity to measure\ncorrelation and it allows the two legal parties to obtain a common key that\nlooks random to an eavesdropper that observes the communication and is\nrestricted to use a bounded amount of space for the attack. Thus the protocol\nachieves complexity-theoretical security, but it does not use any unproven\nresult from computational complexity. On the negative side, the protocol is not\nefficient in the sense that the computation of the two legal parties uses more\nspace than the space allowed to the adversary.\n"", ""Spectral approach to the communication complexity of multi-party key\n  agreement   We propose a linear algebraic method, rooted in the spectral properties of\ngraphs, that can be used to prove lower bounds in communication complexity. Our\nproof technique effectively marries spectral bounds with information-theoretic\ninequalities. The key insight is the observation that, in specific settings,\neven when data sets $X$ and $Y$ are closely correlated and have high mutual\ninformation, the owner of $X$ cannot convey a reasonably short message that\nmaintains substantial mutual information with $Y$. In essence, from the\nperspective of the owner of $Y$, any sufficiently brief message $m=m(X)$ would\nappear nearly indistinguishable from a random bit sequence.\n  We employ this argument in several problems of communication complexity. Our\nmain result concerns cryptographic protocols. We establish a lower bound for\ncommunication complexity of multi-party secret key agreement with\nunconditional, i.e., information-theoretic security. Specifically, for\none-round protocols (simultaneous messages model) of secret key agreement with\nthree participants we obtain an asymptotically tight lower bound. This bound\nimplies optimality of the previously known omniscience communication protocol\n(this result applies to a non-interactive secret key agreement with three\nparties and input data sets with an arbitrary symmetric information profile).\n  We consider communication problems in one-shot scenarios when the parties'\ninputs are not produced by any i.i.d. sources, and there are no ergodicity\nassumptions on the input data. In this setting, we found it natural to present\nour results using the framework of Kolmogorov complexity.\n"", 'Communication Complexity of the Secret Key Agreement in Algorithmic\n  Information Theory   It is known that the mutual information, in the sense of Kolmogorov\ncomplexity, of any pair of strings x and y is equal to the length of the\nlongest shared secret key that two parties can establish via a probabilistic\nprotocol with interaction on a public channel, assuming that the parties hold\nas their inputs x and y respectively. We determine the worst-case communication\ncomplexity of this problem for the setting where the parties can use private\nsources of random bits. We show that for some x, y the communication complexity\nof the secret key agreement does not decrease even if the parties have to agree\non a secret key whose size is much smaller than the mutual information between\nx and y. On the other hand, we discuss examples of x, y such that the\ncommunication complexity of the protocol declines gradually with the size of\nthe derived secret key. The proof of the main result uses spectral properties\nof appropriate graphs and the expander mixing lemma, as well as information\ntheoretic techniques.\n']","[('communication complexity', 0.615010142326355), ('shared randomness', 0.5606260895729065), ('mutual information', 0.5109899640083313), ('information theoretic', 0.509270429611206), ('kolmogorov complexity', 0.48429134488105774), ('shared secret', 0.48058193922042847), ('secret key agreement', 0.4592552185058594), ('information leakage', 0.4528331160545349), ('shared secret key', 0.4162693917751312), ('protocol', 0.41352614760398865)]"
1507,1507,19,1507_turbulence theory_turbulent flows_hydrodynamic turbulence_turbulence,"['turbulence theory', 'turbulent flows', 'hydrodynamic turbulence', 'turbulence', 'turbulent', 'developed turbulence', 'fully developed turbulence', 'anomalous dissipation', 'anomalous diffusion', 'navier stokes equations']","[""Anomalous dissipation and lack of selection in the Obukhov-Corrsin\n  theory of scalar turbulence   The Obukhov-Corrsin theory of scalar turbulence [Obu49, Cor51] advances\nquantitative predictions on passive-scalar advection in a turbulent regime and\ncan be regarded as the analogue for passive scalars of Kolmogorov's K41 theory\nof fully developed turbulence [Kol41]. The scaling analysis of Obukhov and\nCorrsin from 1949-1951 identifies a critical regularity threshold for the\nadvection-diffusion equation and predicts anomalous dissipation in the limit of\nvanishing diffusivity in the supercritical regime. In this paper we provide a\nfully rigorous mathematical validation of this prediction by constructing a\nvelocity field and an initial datum such that the unique bounded solution of\nthe advection-diffusion equation is bounded uniformly-in-diffusivity within any\nfixed supercritical Obukhov-Corrsin regularity regime while also exhibiting\nanomalous dissipation. Our approach relies on a fine quantitative analysis of\nthe interaction between the spatial scale of the solution and the scale of the\nBrownian motion which represents diffusion in a stochastic Lagrangian setting.\nThis provides a direct Lagrangian approach to anomalous dissipation which is\nfundamental in order to get detailed insight on the behavior of the solution.\nExploiting further this approach, we also show that for a velocity field in\n$C^{\\alpha}$ of space and time (for an arbitrary $0 \\leq \\alpha < 1$) neither\nvanishing diffusivity nor regularization by convolution provide a selection\ncriterion for bounded solutions of the advection equation. This is motivated by\nthe fundamental open problem of the selection of solutions of the Euler\nequations as vanishing-viscosity limit of solutions of the Navier-Stokes\nequations and provides a complete negative answer in the case of passive\nadvection.\n"", 'Interior and H$^\\infty$ feedback stabilization for sabra Shell model of\n  turbulence   Shell models of turbulence are representation of turbulence equations in\nFourier domain. Various shell models along with numerical simulations have been\nstudied earlier. One of the most suitable shell model of turbulence is so\ncalled sabra shell model. The existence, uniqueness and regularity property of\nthis model are extensively studied in \\cite{PBT}. In this paper we have\naddressed stabilization problems related to sabra shell model of turbulence. We\nhave studied internal stabilization via finite dimensional controller. Moreover\nwe have also studied optimal robust control problem by solving an infinite time\nhorizon max-min control problem. We first prove the $H^ \\infty$ stabilization\nof the linearized system and charatarize it in terms of a feedback operator by\nsolving an algebric ricatti equation. Finally we show that the control will\nasymptotically stabilize the nonlinear system.\n', ""Dynamics of vorticity moments in shell models of turbulence: A\n  comparison with the Navier-Stokes equations   Shell models allow much greater scale separations than those presently\nachievable with direct numerical simulations of the Navier-Stokes equations.\nConsequently, they are an invaluable tool for testing new concepts and ideas in\nthe theory of fully developed turbulence. They also successfully display energy\ncascades and intermittency in homogeneous and isotropic turbulent flows.\nMoreover, they are also of great interest to mathematical analysts because,\nwhile retaining some of the key features of the Euler and the Navier-Stokes\nequations, they are much more tractable. A comparison of the mathematical\nproperties of shell models and of the three-dimensional Navier-Stokes equations\nis therefore essential in understanding the correspondence between the two\nsystems. Here we focus on the temporal evolution of the moments, or\n$L^{2m}$-norms, of the vorticity. Specifically, differential inequalities for\nthe moments of the vorticity in shell models are derived. The contribution of\nthe nonlinear term turns out to be much weaker than its equivalent for the\nthree-dimensional Navier-Stokes equations. Consequently, pointwise-in-time\nestimates are shown to exist for the vorticity moments for shell models of any\norder. This result is also recovered via a high-low frequency slaving argument\nthat highlights the scaling relations between vorticity moments of different\norders. Finally, it is shown that the estimates for shell models formally\ncorrespond to those for the Navier-Stokes equations 'on a point'.\n""]","[('turbulence theory', 0.6302657127380371), ('turbulent flows', 0.5304688811302185), ('hydrodynamic turbulence', 0.5280720591545105), ('turbulence', 0.5252424478530884), ('turbulent', 0.4905046224594116), ('developed turbulence', 0.4793682098388672), ('fully developed turbulence', 0.47561776638031006), ('anomalous dissipation', 0.43922173976898193), ('anomalous diffusion', 0.38659003376960754), ('navier stokes equations', 0.3830048739910126)]"
1508,1508,19,1508_berezin toeplitz quantization_deformation quantization_toeplitz quantization_ahler manifolds,"['berezin toeplitz quantization', 'deformation quantization', 'toeplitz quantization', 'ahler manifolds', 'geometric quantization', 'space quantization', 'quantizations', 'quantization', 'quantization case', 'type quantization']","['Symmetry in Deformation quantization and Geometric quantization   In this paper, we explore the quantization of K\\""ahler manifolds, focusing on\nthe relationship between deformation quantization and geometric quantization.\nWe provide a classification of degree 1 formal quantizable functions in the\nBerezin-Toeplitz deformation quantization, establishing that these formal\nfunctions are of the form $f = f_0 - \\frac{\\hbar}{4\\pi}(\\Delta f_0 + c)$ for a\ncertain smooth (non-formal) function $f_0$. If $f_0$ is real-valued then $f_0$\ncorresponds to a Hamiltonian Killing vector field. In the presence of\nHamiltonian $G$-symmetry, we address the compatibility between the\ninfinitesimal symmetry for deformation quantization via quantum moment map and\ninfinitesimal symmetry on geometric quantization acting on Hilbert spaces of\nholomorphic sections via Berezin-Toeplitz quantization.\n', 'Quantization of K\\""ahler manifolds   This is a survey on our recent works which reveal new relationships among\ndeformation quantization, geometric quantization, Berezin-Toeplitz quantization\nand BV quantization on K\\""ahler manifolds.\n', 'Deformation quantization via Toeplitz operators on geometric\n  quantization in real polarizations   In this paper, we study quantization on a compact integral symplectic\nmanifold $X$ with transversal real polarizations. In the case of complex\npolarizations, namely $X$ is K\\""ahler equipped with transversal complex\npolarizations $T^{1, 0}X, T^{0, 1}X$, geometric quantization gives $H^0(X,\nL^{\\otimes k})$\'s. They are acted upon by $\\mathcal{C}^\\infty(X, \\mathbb{C})$\nvia Toeplitz operators as $\\hbar = \\tfrac{1}{k} \\to 0^+$, determining a\ndeformation quantization $(\\mathcal{C}^\\infty(X, \\mathbb{C})[[\\hbar]], \\star)$\nof $X$.\\par We investigate the real analogue to these, comparing deformation\nquantization, geometric quantization and Berezin-Toeplitz quantization. The\ntechniques used are different from the complex case as distributional sections\nsupported on Bohr-Sommerfeld fibres are involved.\\par By switching the roles of\nthe two real polarizations, we obtain Fourier-type transforms for both\ndeformation quantization and geometric quantization, and they are compatible\nasymptotically as $\\hbar \\to 0^+$. We also show that the asymptotic expansion\nof traces of Toeplitz operators realizes a trace map on deformation\nquantization.\n']","[('berezin toeplitz quantization', 0.7089244723320007), ('deformation quantization', 0.6972548961639404), ('toeplitz quantization', 0.647778332233429), ('ahler manifolds', 0.6331930756568909), ('geometric quantization', 0.6210612654685974), ('space quantization', 0.6129419207572937), ('quantizations', 0.6020848751068115), ('quantization', 0.5802571177482605), ('quantization case', 0.5691584944725037), ('type quantization', 0.5493983626365662)]"
1509,1509,19,1509_random graph models_random graphs_graph models_random graph,"['random graph models', 'random graphs', 'graph models', 'random graph', 'random geometric graphs', 'bipartite networks', 'sparse graph', 'graphs sampled', 'exponential random graph', 'network analysis']","['Sparse graphs using exchangeable random measures   Statistical network modeling has focused on representing the graph as a\ndiscrete structure, namely the adjacency matrix, and considering the\nexchangeability of this array. In such cases, the Aldous-Hoover representation\ntheorem (Aldous, 1981;Hoover, 1979} applies and informs us that the graph is\nnecessarily either dense or empty. In this paper, we instead consider\nrepresenting the graph as a measure on $\\mathbb{R}_+^2$. For the associated\ndefinition of exchangeability in this continuous space, we rely on the\nKallenberg representation theorem (Kallenberg, 2005). We show that for certain\nchoices of such exchangeable random measures underlying our graph construction,\nour network process is sparse with power-law degree distribution. In\nparticular, we build on the framework of completely random measures (CRMs) and\nuse the theory associated with such processes to derive important network\nproperties, such as an urn representation for our analysis and network\nsimulation. Our theoretical results are explored empirically and compared to\ncommon network models. We then present a Hamiltonian Monte Carlo algorithm for\nefficient exploration of the posterior distribution and demonstrate that we are\nable to recover graphs ranging from dense to sparse--and perform associated\ntests--based on our flexible CRM-based formulation. We explore network\nproperties in a range of real datasets, including Facebook social circles, a\npolitical blogosphere, protein networks, citation networks, and world wide web\nnetworks, including networks with hundreds of thousands of nodes and millions\nof edges.\n', 'Higher-Order Graphon Theory: Fluctuations, Degeneracies, and Inference   Exchangeable random graphs, which include some of the most widely studied\nnetwork models, have emerged as the mainstay of statistical network analysis in\nrecent years. Graphons, which are the central objects in graph limit theory,\nprovide a natural way to sample exchangeable random graphs. It is well known\nthat network moments (motif/subgraph counts) identify a graphon (up to an\nisomorphism), hence, understanding the sampling distribution of subgraph counts\nin random graphs sampled from a graphon is pivotal for nonparametric network\ninference. In this paper, we derive the joint asymptotic distribution of any\nfinite collection of network moments in random graphs sampled from a graphon,\nthat includes both the non-degenerate case (where the distribution is Gaussian)\nas well as the degenerate case (where the distribution has both Gaussian or\nnon-Gaussian components). This provides the higher-order fluctuation theory for\nsubgraph counts in the graphon model. We also develop a novel multiplier\nbootstrap for graphons that consistently approximates the limiting distribution\nof the network moments (both in the Gaussian and non-Gaussian regimes). Using\nthis and a procedure for testing degeneracy, we construct joint confidence sets\nfor any finite collection of motif densities. This provides a general framework\nfor statistical inference based on network moments in the graphon model. To\nillustrate the broad scope of our results we also consider the problem of\ndetecting global structure (that is, testing whether the graphon is a constant\nfunction) based on small subgraphs. We propose a consistent test for this\nproblem, invoking celebrated results on quasi-random graphs, and derive its\nlimiting distribution both under the null and the alternative.\n', 'Network Representation Using Graph Root Distributions   Exchangeable random graphs serve as an important probabilistic framework for\nthe statistical analysis of network data. In this work we develop an\nalternative parameterization for a large class of exchangeable random graphs,\nwhere the nodes are independent random vectors in a linear space equipped with\nan indefinite inner product, and the edge probability between two nodes equals\nthe inner product of the corresponding node vectors. Therefore, the\ndistribution of exchangeable random graphs in this subclass can be represented\nby a node sampling distribution on this linear space, which we call the graph\nroot distribution. We study existence and identifiability of such\nrepresentations, the topological relationship between the graph root\ndistribution and the exchangeable random graph sampling distribution, and\nestimation of graph root distributions.\n']","[('random graph models', 0.6906726360321045), ('random graphs', 0.6099583506584167), ('graph models', 0.5757418870925903), ('random graph', 0.5310153365135193), ('random geometric graphs', 0.5202296376228333), ('bipartite networks', 0.5026520490646362), ('sparse graph', 0.49232059717178345), ('graphs sampled', 0.4903157651424408), ('exponential random graph', 0.48969417810440063), ('network analysis', 0.4868161380290985)]"
1510,1510,19,1510_carleson measure condition_carleson measure_rectifiable boundary_elliptic operators,"['carleson measure condition', 'carleson measure', 'rectifiable boundary', 'elliptic operators', 'elliptic divergence', 'elliptic divergence form', 'divergence form elliptic', 'measure estimates', 'boundary equivalent', 'constant estimates']","['Uniform rectifiability and elliptic operators satisfying a Carleson\n  measure condition. Part II: The large constant case   The present paper, along with its companion [Hofmann, Martell, Mayboroda,\nToro, Zhao, arXiv:1710.06157], establishes the correspondence between the\nproperties of the solutions of a class of PDEs and the geometry of sets in\nEuclidean space. We settle the question of whether (quantitative) absolute\ncontinuity of the elliptic measure with respect to the surface measure and\nuniform rectifiability of the boundary are equivalent, in an optimal class of\ndivergence form elliptic operators satisfying a suitable Carleson measure\ncondition. The result can be viewed as a quantitative analogue of the Wiener\ncriterion adapted to the singular $L^p$ data case.\n  The first step in this direction was taken in our previous paper [Hofmann,\nMartell, Mayboroda, Toro, Zhao, arXiv:1710.06157], where we considered the case\nin which the desired Carleson measure condition on the coefficients holds with\nsufficiently small constant. In this paper we establish the final, general\nresult, that is, the ""large constant case"". The key elements of our approach\nare a powerful extrapolation argument, which provides a general pathway to\nself-improve scale-invariant small constant estimates, as well as a new\nmechanism to transfer quantitative absolute continuity of elliptic measure\nbetween a domain and its subdomains.\n', 'Uniform rectifiability and elliptic operators satisfying a Carleson\n  measure condition. Part I: The small constant case   The present paper, along with its sequel, establishes the correspondence\nbetween the properties of the solutions of a class of PDEs and the geometry of\nsets in Euclidean space. We settle the question of whether (quantitative)\nabsolute continuity of the elliptic measure with respect to the surface measure\nand uniform rectifiability of the boundary are equivalent, in an optimal class\nof divergence form elliptic operators satisfying a suitable Carleson measure\ncondition. The result can be viewed as a quantitative analogue of the Wiener\ncriterion adapted to the singular $L^p$ data case.\n  This paper addresses the free boundary problem under the assumption of\nsmallness of the Carleson measure of the coefficients. Part II of this work\ndevelops an extrapolation argument to bootstrap this result to the general\ncase. The ideas in Part I constitute a novel application of techniques\ndeveloped in geometric measure theory. They highlight the synergy between\nseveral areas. The ideas developed in this paper are well suited to study\nsingularities arising in variational problems in a geometric setting.\n', 'Uniform rectifiability and elliptic operators satisfying a Carleson\n  measure condition   The present paper establishes the correspondence between the properties of\nthe solutions of a class of PDEs and the geometry of sets in Euclidean space.\nWe settle the question of whether (quantitative) absolute continuity of the\nelliptic measure with respect to the surface measure and uniform rectifiability\nof the boundary are equivalent, in an optimal class of divergence form elliptic\noperators satisfying a suitable Carleson measure condition. The result can be\nviewed as a quantitative analogue of the Wiener criterion adapted to the\nsingular $L^p$ data case.\n  We split our proof on two main steps. In the first one we considered the case\nin which the desired Carleson measure condition on the coefficients holds with\n""sufficiently small constant"", using a novel application of techniques\ndeveloped in geometric measure theory. In the second step we establish the\nfinal result, that is, the ""large constant case"". The key elements are a\npowerful extrapolation argument, which provides a general pathway to\nself-improve scale-invariant small constant estimates, and a new mechanism to\ntransfer quantitative absolute continuity of elliptic measure between a domain\nand its subdomains.\n']","[('carleson measure condition', 0.6498627066612244), ('carleson measure', 0.5893197059631348), ('rectifiable boundary', 0.5261080265045166), ('elliptic operators', 0.4862402677536011), ('elliptic divergence', 0.46700602769851685), ('elliptic divergence form', 0.4279748201370239), ('divergence form elliptic', 0.4257398545742035), ('measure estimates', 0.4233191907405853), ('boundary equivalent', 0.408757746219635), ('constant estimates', 0.40757808089256287)]"
1511,1511,19,1511_wasserstein gradient flows_wasserstein gradient_normalizing flows_gradient flows,"['wasserstein gradient flows', 'wasserstein gradient', 'normalizing flows', 'gradient flows', 'normalizing flow', 'learning generative', 'generative models', 'generative modeling', 'flow', 'optimal transport']","['Taming Hyperparameter Tuning in Continuous Normalizing Flows Using the\n  JKO Scheme   A normalizing flow (NF) is a mapping that transforms a chosen probability\ndistribution to a normal distribution. Such flows are a common technique used\nfor data generation and density estimation in machine learning and data\nscience. The density estimate obtained with a NF requires a change of variables\nformula that involves the computation of the Jacobian determinant of the NF\ntransformation. In order to tractably compute this determinant, continuous\nnormalizing flows (CNF) estimate the mapping and its Jacobian determinant using\na neural ODE. Optimal transport (OT) theory has been successfully used to\nassist in finding CNFs by formulating them as OT problems with a soft penalty\nfor enforcing the standard normal distribution as a target measure. A drawback\nof OT-based CNFs is the addition of a hyperparameter, $\\alpha$, that controls\nthe strength of the soft penalty and requires significant tuning. We present\nJKO-Flow, an algorithm to solve OT-based CNF without the need of tuning\n$\\alpha$. This is achieved by integrating the OT CNF framework into a\nWasserstein gradient flow framework, also known as the JKO scheme. Instead of\ntuning $\\alpha$, we repeatedly solve the optimization problem for a fixed\n$\\alpha$ effectively performing a JKO update with a time-step $\\alpha$. Hence\nwe obtain a ""divide and conquer"" algorithm by repeatedly solving simpler\nproblems instead of solving a potentially harder problem with large $\\alpha$.\n', ""Efficient Gradient Flows in Sliced-Wasserstein Space   Minimizing functionals in the space of probability distributions can be done\nwith Wasserstein gradient flows. To solve them numerically, a possible approach\nis to rely on the Jordan-Kinderlehrer-Otto (JKO) scheme which is analogous to\nthe proximal scheme in Euclidean spaces. However, it requires solving a nested\noptimization problem at each iteration, and is known for its computational\nchallenges, especially in high dimension. To alleviate it, very recent works\npropose to approximate the JKO scheme leveraging Brenier's theorem, and using\ngradients of Input Convex Neural Networks to parameterize the density\n(JKO-ICNN). However, this method comes with a high computational cost and\nstability issues. Instead, this work proposes to use gradient flows in the\nspace of probability measures endowed with the sliced-Wasserstein (SW)\ndistance. We argue that this method is more flexible than JKO-ICNN, since SW\nenjoys a closed-form differentiable approximation. Thus, the density at each\nstep can be parameterized by any generative model which alleviates the\ncomputational burden and makes it tractable in higher dimensions.\n"", 'Convergence of flow-based generative models via proximal gradient\n  descent in Wasserstein space   Flow-based generative models enjoy certain advantages in computing the data\ngeneration and the likelihood, and have recently shown competitive empirical\nperformance. Compared to the accumulating theoretical studies on related\nscore-based diffusion models, analysis of flow-based models, which are\ndeterministic in both forward (data-to-noise) and reverse (noise-to-data)\ndirections, remain sparse. In this paper, we provide a theoretical guarantee of\ngenerating data distribution by a progressive flow model, the so-called JKO\nflow model, which implements the Jordan-Kinderleherer-Otto (JKO) scheme in a\nnormalizing flow network. Leveraging the exponential convergence of the\nproximal gradient descent (GD) in Wasserstein space, we prove the\nKullback-Leibler (KL) guarantee of data generation by a JKO flow model to be\n$O(\\varepsilon^2)$ when using $N \\lesssim \\log (1/\\varepsilon)$ many JKO steps\n($N$ Residual Blocks in the flow) where $\\varepsilon $ is the error in the\nper-step first-order condition. The assumption on data density is merely a\nfinite second moment, and the theory extends to data distributions without\ndensity and when there are inversion errors in the reverse process where we\nobtain KL-$W_2$ mixed error guarantees. The non-asymptotic convergence rate of\nthe JKO-type $W_2$-proximal GD is proved for a general class of convex\nobjective functionals that includes the KL divergence as a special case, which\ncan be of independent interest. The analysis framework can extend to other\nfirst-order Wasserstein optimization schemes applied to flow-based generative\nmodels.\n']","[('wasserstein gradient flows', 0.6757268309593201), ('wasserstein gradient', 0.5681596994400024), ('normalizing flows', 0.5643447637557983), ('gradient flows', 0.5458934903144836), ('normalizing flow', 0.541107714176178), ('learning generative', 0.4846664071083069), ('generative models', 0.46887797117233276), ('generative modeling', 0.46761247515678406), ('flow', 0.46437394618988037), ('optimal transport', 0.46388188004493713)]"
1512,1512,19,1512_equivariant cohomology_equivariant theory_group action equivariant_theory equivariant,"['equivariant cohomology', 'equivariant theory', 'group action equivariant', 'theory equivariant', 'equivariant elliptic cohomology', 'equivariant cohomology ring', 'equivariant formality', 'action equivariant', 'characterization equivariant', 'equivariant version']","['The equivariant K-theory of a cohomogeneity-one action   We compute the equivariant complex K-theory ring of a cohomogeneity-one\naction of a compact Lie group at the level of generators and relations and\nderive a characterization of K-theoretic equivariant formality for these\nactions. Less explicit expressions survive for a range of equivariant\ncohomology theories including Bredon cohomology and Borel complex cobordism.\nThe proof accordingly involves elements of equivariant homotopy theory,\nrepresentation theory, and Lie theory.\n  Aside from analysis of maps of representation rings and heavy use of the\nstructure theory of compact Lie groups, a more curious feature is the essential\nneed for a basic structural fact about the Mayer--Vietoris sequence for any\nmultiplicative cohomology theory which seems to be otherwise unremarked in the\nliterature, and a similarly unrecognized basic lemma governing the equivariant\ncohomology of the orbit space of a finite group action.\n', ""Equivariant K-theory and Resolution II: Non-Abelian actions   The smooth action of a compact Lie group on a compact manifold can be\nresolved to an iterated space, as made explicit by Pierre Albin and the second\nauthor. On the resolution the lifted action has fixed isotropy type\ncorresponding to the open stratum and also in an iterated sense, with\nconnecting equivariant fibrations over the boundary hypersurfaces covering the\nresolutions of the other strata. This structure descends to a resolution of the\nquotient as a stratified space. For an Abelian group action the equivariant\nK-theory can then be described in terms of bundles over the bases `dressed' by\nthe representations of the isotropy types with morphisms covering the\nconnecting maps. A similar model is given here covering the non-Abelian case.\nNow the reduced objects are torsion-twisted bundles over finite covers of the\nbases, corresponding to the projective action of the normalizers on the\nrepresentations of the isotropy groups, again with morphisms over all the\nboundaries. This leads to a closely related iterated deRham model for\nequivariant cohomology and, now with values in forms twisted by flat bundles of\nrepresentation rings over the bases, for delocalized equivariant cohomology. We\nshow, as envisioned by Baum, Brylinksi and MacPherson, that the usual\nequivariant Chern character, mapping to equivariant cohomology, factors through\na natural Chern character from equivariant K-theory to delocalized equivariant\ncohomology with the latter giving an Atiyah-Hirzebruch isomorphism.\n"", 'Equivariant formality of istropy actions   Let $G$ be a compact connected Lie group and $K$ a connected Lie subgroup. In\nthis paper, we collect an assortment of results on equivariant formality of the\nisotropy action of $K$ on $G/K$. If the isotropy action of $K$ on $G/K$ is\nequivariantly formal, then $G/K$ is formal in the sense of rational homotopy\ntheory. This enables us to strengthen a theorem of Shiga--Takahashi to a\ncharacterization of equivariant formality in this case. Using a K-theoretic\nanalogue of equivariant formality introduced and shown by the second-named\nauthor to be equivalent to equivariant formality in the usual sense, we provide\na representation-theoretic characterization for equivariant formality of the\nisotropy action and give a new, uniform proof of equivariant formality for some\nclasses of homogeneous spaces for which it was previously known.\n']","[('equivariant cohomology', 0.7248339056968689), ('equivariant theory', 0.7014938592910767), ('group action equivariant', 0.678191065788269), ('theory equivariant', 0.6738071441650391), ('equivariant elliptic cohomology', 0.6697313785552979), ('equivariant cohomology ring', 0.6691774725914001), ('equivariant formality', 0.6526831984519958), ('action equivariant', 0.644944429397583), ('characterization equivariant', 0.6434914469718933), ('equivariant version', 0.6035508513450623)]"
1513,1513,19,1513_stochastic variational inequalities_stochastic variational inequality_stochastic variational_variational inequalities variational,"['stochastic variational inequalities', 'stochastic variational inequality', 'stochastic variational', 'variational inequalities variational', 'variational inequalities', 'inequalities variational inequalities', 'monotone variational inequality', 'inequalities variational', 'stochastic formulation', 'variational inequality problems']","['Simple and optimal methods for stochastic variational inequalities, I:\n  operator extrapolation   In this paper we first present a novel operator extrapolation (OE) method for\nsolving deterministic variational inequality (VI) problems. Similar to the\ngradient (operator) projection method, OE updates one single search sequence by\nsolving a single projection subproblem in each iteration. We show that OE can\nachieve the optimal rate of convergence for solving a variety of VI problems in\na much simpler way than existing approaches. We then introduce the stochastic\noperator extrapolation (SOE) method and establish its optimal convergence\nbehavior for solving different stochastic VI problems. In particular, SOE\nachieves the optimal complexity for solving a fundamental problem, i.e.,\nstochastic smooth and strongly monotone VI, for the first time in the\nliterature. We also present a stochastic block operator extrapolations (SBOE)\nmethod to further reduce the iteration cost for the OE method applied to\nlarge-scale deterministic VIs with a certain block structure. Numerical\nexperiments have been conducted to demonstrate the potential advantages of the\nproposed algorithms. In fact, all these algorithms are applied to solve\ngeneralized monotone variational inequality (GMVI) problems whose operator is\nnot necessarily monotone. We will also discuss optimal OE-based policy\nevaluation methods for reinforcement learning in a companion paper.\n', 'Optimal Analysis of Method with Batching for Monotone Stochastic\n  Finite-Sum Variational Inequalities   Variational inequalities are a universal optimization paradigm that is\ninteresting in itself, but also incorporates classical minimization and saddle\npoint problems. Modern realities encourage to consider stochastic formulations\nof optimization problems. In this paper, we present an analysis of a method\nthat gives optimal convergence estimates for monotone stochastic finite-sum\nvariational inequalities. In contrast to the previous works, our method\nsupports batching and does not lose the oracle complexity optimality. The\neffectiveness of the algorithm, especially in the case of small but not single\nbatches is confirmed experimentally.\n', 'Smooth Monotone Stochastic Variational Inequalities and Saddle Point\n  Problems: A Survey   This paper is a survey of methods for solving smooth (strongly) monotone\nstochastic variational inequalities. To begin with, we give the deterministic\nfoundation from which the stochastic methods eventually evolved. Then we review\nmethods for the general stochastic formulation, and look at the finite sum\nsetup. The last parts of the paper are devoted to various recent (not\nnecessarily stochastic) advances in algorithms for variational inequalities.\n']","[('stochastic variational inequalities', 0.7973536849021912), ('stochastic variational inequality', 0.7346110939979553), ('stochastic variational', 0.6252184510231018), ('variational inequalities variational', 0.6065483689308167), ('variational inequalities', 0.5951167345046997), ('inequalities variational inequalities', 0.5819372534751892), ('monotone variational inequality', 0.5814576148986816), ('inequalities variational', 0.5657070279121399), ('stochastic formulation', 0.5652583837509155), ('variational inequality problems', 0.561025083065033)]"
1514,1514,19,1514_convergence wasserstein distance_wasserstein distance empirical_wasserstein convergence_wasserstein distance,"['convergence wasserstein distance', 'wasserstein distance empirical', 'wasserstein convergence', 'wasserstein distance', 'convergence wasserstein', 'quadratic wasserstein distance', 'entropy wasserstein', 'invariant measure process', 'diffusion processes', 'convergence rate empirical']","['Limit Theorems in Warsserstein Distance for Empirical Measures of\n  Diffusion Processes on Riemannian Manifolds   Let $M$ be a compact connected Riemannian manifold possibly with a boundary,\nlet $V\\in C^2(M)$ such that $\\mu(d x):=e^{V(x)}d x$ is a probability measure,\nand let\n  $\\{\\lambda_i\\}_{i\\ge 1} $ be all non-trivial eigenvalues of $-L$ with Neumann\nboundary condition if the boundary exists. Then the empirical measures\n$\\{\\mu_t\\}_{t>0}$ of the diffusion process generated by $L$ (with reflecting\nboundary if the boundary exists) satisfy $$ \\lim_{t\\to \\infty} \\big\\{t \\mathbb\nE^x [W_2(\\mu_{t},\\mu)^2]\\big\\}= \\sum_{i=1}^\\infty\\frac 2 {\\lambda_i^2}\\ \\text{\nuniformly\\ in\\ } x\\in M,$$ where $\\mathbb E^x$ denotes the expectation for the\ndiffusion process starting at point $x$, $W_2$ is the $L^2$-Warsserstein\ndistance induced by the Riemannian metric. The limit is finite if and only if\n$d\\le 3$, and in this case we derive the following central limit theorem:\n  $$\\lim_{t\\to\\infty} \\sup_{x\\in M} \\Big|\\mathbb P^x(t W_2(\\mu_{t},\\mu)^2<a)-\n\\mathbb P\\Big( \\sum_{k=1}^\\infty \\frac{2\\xi_k^2}{\\lambda_k^2}<a\\Big)\\Big|=0, \\\n\\ a\\ge 0,$$ where $\\mathbb P^x$ is the probability with respect to $\\mathbb\nE^x$, and $\\{\\xi_k\\}_{k\\ge 1}$ are i.i.d. standard Gaussian random variables.\nMoreover, when $d\\ge 4$ we prove that the main order of $\\mathbb\nE^x[W_2(\\mu_{t},\\mu)^2]$ is $t^{-\\frac 2 {d-2}}$ as $t\\to\\infty$. Moreover,\nwhen $d\\ge 4$ the main order of $\\mathbb E^x[W_2(\\mu_{t},\\mu)^2]$ is $t^{-\\frac\n2 {d-2}}$ as $t\\to\\infty$.\n  Finally, we establish the long-time large deviation principle for\n$\\{W_2(\\mu_t,\\mu)^2\\}_{t\\ge 0}$ with a good rate function given by the\ninformation with respect to $\\mu$.\n', 'Precise Limit in Wasserstein Distance for Conditional Empirical Measures\n  of Dirichlet Diffusion Processes   Let $M$ be a $d$-dimensional connected compact Riemannian manifold with\nboundary $\\partial M$, let $V\\in C^2(M)$ such that $\\mu(dx):=e^{V(x)} d x$ is a\nprobability measure, and let $X_t$ be the diffusion process generated by\n$L:=\\Delta+\\nabla V$ with $\\tau:=\\inf\\{t\\ge 0: X_t\\in\\partial M\\}$. Consider\nthe conditional empirical measure\n  $\\mu_t^\\nu:= \\mathbb E^\\nu\\big(\\frac 1 t \\int_0^t \\delta_{X_s}d\ns\\big|t<\\tau\\big)$ for the diffusion process with initial distribution $\\nu$\nsuch that $\\nu(\\partial M)<1$. Then $$\\lim_{t\\to\\infty} \\big\\{t\\mathbb\nW_2(\\mu_t^\\nu,\\mu_0)\\big\\}^2 = \\frac 1 {\\{\\mu(\\phi_0)\\nu(\\phi_0)\\}^2}\n\\sum_{m=1}^\\infty \\frac{\\{\\nu(\\phi_0)\\mu(\\phi_m)+ \\mu(\\phi_0)\n\\nu(\\phi_m)\\}^2}{(\\lambda_m-\\lambda_0)^3},$$ where $\\nu(f):=\\int_Mf {d} \\nu$\nfor a measure $\\nu$ and $f\\in L^1(\\nu)$, $\\mu_0:=\\phi_0^2\\mu$,\n$\\{\\phi_m\\}_{m\\ge 0}$ is the eigenbasis of $-L$ in $L^2(\\mu)$ with the\nDirichlet boundary,\n  $\\{\\lambda_m\\}_{m\\ge 0}$ are the corresponding Dirichlet eigenvalues, and\n$\\mathbb W_2$ is the $L^2$-Wasserstein distance induced by the Riemannian\nmetric.\n', 'Convergence in Wasserstein Distance for Empirical Measures of Dirichlet\n  Diffusion Processes on Manifolds   Let $M$ be a $d$-dimensional connected compact Riemannian manifold with\nboundary $\\partial M$, let $V\\in C^2(M)$ such that $\\mu({\\rm d} x):={\\rm\ne}^{V(x)}{\\rm d} x$ is a probability measure, and let $X_t$ be the diffusion\nprocess generated by $L:=\\Delta+\\nabla V$ with $\\tau:=\\inf\\{t\\ge 0:\nX_t\\in\\partial M\\}$. Consider the empirical measure $\\mu_t:=\\frac 1 t \\int_0^t\n\\delta_{X_s}{\\rm d} s$ under the condition $t<\\tau$ for the diffusion process.\nIf $d\\le 3$, then for any initial distribution not fully supported on $\\partial\nM$, \\begin{align*} &c\\sum_{m=1}^\\infty \\frac{2}{(\\lambda_m-\\lambda_0)^2} \\le\n\\liminf_{t\\to \\infty} \\inf_{T\\ge t} \\Big\\{t {\\mathbb E}\\big[\\mathbb W_2(\\mu_t,\n\\mu_0)^2\\big|T<\\tau\\big]\\Big\\} \\\\ &\\le \\limsup_{t\\to \\infty} \\sup_{T\\ge t}\n\\Big\\{ t \\mathbb E\\big[\\mathbb W_2(\\mu_t, \\mu_0)^2\\big|T<\\tau\\big] \\Big\\}\\le\n\\sum_{m=1}^\\infty \\frac{2}{(\\lambda_m-\\lambda_0)^2}\\end{align*} holds for some\nconstant $c\\in (0,1]$ with $c=1$ when $\\partial M$ is convex, where $\\mu_0:=\n\\phi_0^2\\mu$ for the first Dirichet eigenfunction $\\phi_0$ of $L$,\n$\\{\\lambda_m\\}_{m\\ge 0}$ are the Dirichlet eigenvalues of $-L$ listed in the\nincreasing order counting multiplicities, and the upper bound is finite if and\nonly if $d\\le 3$. When $d=4$, $\\sup_{T\\ge t} \\mathbb E\\big[\\mathbb W_2(\\mu_t,\n\\mu_0)^2\\big|T<\\tau\\big] $ decays in the order $t^{-1}\\log t$, while for $d\\ge\n5$ it behaves like $t^{-\\frac 2 {d-2}}$, as $t\\to\\infty$.\n']","[('convergence wasserstein distance', 0.6464295983314514), ('wasserstein distance empirical', 0.6292976140975952), ('wasserstein convergence', 0.5619423389434814), ('wasserstein distance', 0.5284950733184814), ('convergence wasserstein', 0.5228320360183716), ('quadratic wasserstein distance', 0.5223147869110107), ('entropy wasserstein', 0.4566884934902191), ('invariant measure process', 0.44849997758865356), ('diffusion processes', 0.3965469300746918), ('convergence rate empirical', 0.3936295211315155)]"
1515,1515,19,1515_spherical harmonics_harmonic functions_harmonics_functions harmonic,"['spherical harmonics', 'harmonic functions', 'harmonics', 'functions harmonic', 'fundamental laplace', 'solutions laplace', 'legendre functions', 'laplace', 'case laplace', 'expansion fundamental']","[""Prolate spheroidal operator and Zeta   In this paper we describe a remarkable new property of the self-adjoint\nextension W of the prolate spheroidal operator introduced in\n\\cite{college98},\\cite{CMbook}. The restriction of this operator to the\ninterval J whose characteristic function commutes with it is well known, has\ndiscrete positive spectrum and is well understood. What we have discovered is\nthat the restriction of W to the complement of J admits (besides a replica of\nthe above positive spectrum) negative eigenvalues whose ultraviolet behavior\nreproduce that of the squares of zeros of the Riemann zeta function.\nFurthermore, their corresponding eigenfunctions belong to the Sonin space. This\nfeature fits with the proof \\cite{weilpos} of Weil's positivity at the\narchimedean place, which uses the compression of the scaling action to the\nSonin space. As a byproduct we construct an isospectral family of Dirac\noperators whose spectra have the same ultraviolet behavior as the zeros of the\nRiemann zeta function.\n"", ""Internal and external harmonics in bi-cyclide coordinates   The Laplace equation in three dimensional Euclidean space is $R$-separable in\nbi-cyclide coordinates leading to harmonic functions expressed in terms of\nLam\\'e-Wangerin functions called internal and external bi-cyclide harmonics. An\nexpansion for the fundamental solution of Laplace's equation in products of\ninternal and external bi-cyclide harmonics is derived. In limiting cases this\nexpansion reduces to known expansion in bi-spherical and prolate spheroidal\ncoordinates.\n"", ""Peanut harmonic expansion for a fundamental solution of Laplace's\n  equation in flat-ring coordinates   We derive an expansion for the fundamental solution of Laplace's equation in\nflat-ring cyclide coordinates in three-dimensional Euclidean space. This\nexpansion is a double series of products of functions that are harmonic in the\ninterior and exterior of coordinate surfaces which are peanut shaped and\northogonal to surfaces which are flat-rings. These internal and external peanut\nharmonic functions are expressed in terms of Lam\\'e-Wangerin functions. Using\nthe expansion for the fundamental solution, we derive an addition theorem for\nthe azimuthal Fourier component in terms of the odd-half-integer degree\nLegendre function of the second kind as an infinite series in Lam\\'e-Wangerin\nfunctions. We also derive integral identities over the Legendre function of the\nsecond kind for a product of three Lam\\'e-Wangerin functions. In a limiting\ncase we obtain the expansion of the fundamental solution in spherical\ncoordinates.\n""]","[('spherical harmonics', 0.6114858388900757), ('harmonic functions', 0.49703165888786316), ('harmonics', 0.43565377593040466), ('functions harmonic', 0.4326038360595703), ('fundamental laplace', 0.4256385266780853), ('solutions laplace', 0.41412651538848877), ('legendre functions', 0.4122796654701233), ('laplace', 0.3981119990348816), ('case laplace', 0.3955480456352234), ('expansion fundamental', 0.39232102036476135)]"
1516,1516,19,1516_outerplanar graphs_embeddable graphs_planar graphs_embedding graph,"['outerplanar graphs', 'embeddable graphs', 'planar graphs', 'embedding graph', 'graphs clique', 'class planar graphs', 'graphs require', 'graphs', 'graphs determined', 'regular graphs admitting']","['Bipartite cubic planar graphs are dispersable   The book embedding of a graph $G$ is to place the vertices of $G$ on the\nspine and draw the edges to the pages so that the edges in the same page do not\ncross with each other. A book embedding is matching if the vertices in the same\npage have maximum degree at most 1. The matching book thickness is the minimum\nnumber of pages in which a graph can be matching book embedded. A graph $G$ is\ndispersable if and only if $mbt(G)=\\Delta(G)$. In this paper, we prove that\nbipartite cubic planar graphs are dispersable.\n', 'Matching Book Thickness of Halin Graphs   The \\emph{matching book embedding} of a graph $G$ is to arrange its vertices\non the spine, and draw its edges into the pages so that the edges on every page\ndo not intersect each other and the maximum degree of vertices on every page is\none. The \\emph{matching book thickness} is the minimum number of pages in which\nthe graph $G$ can be matching embedded. In this paper, the matching book\nthickness of Halin graphs is determined.\n', 'Four Pages Are Indeed Necessary for Planar Graphs   An embedding of a graph in a book consists of a linear order of its vertices\nalong the spine of the book and of an assignment of its edges to the pages of\nthe book, so that no two edges on the same page cross. The book thickness of a\ngraph is the minimum number of pages over all its book embeddings. Accordingly,\nthe book thickness of a class of graphs is the maximum book thickness over all\nits members. In this paper, we address a long-standing open problem regarding\nthe exact book thickness of the class of planar graphs, which previously was\nknown to be either three or four. We settle this problem by demonstrating\nplanar graphs that require four pages in any of their book embeddings, thus\nestablishing that the book thickness of the class of planar graphs is four.\n']","[('outerplanar graphs', 0.5717170238494873), ('embeddable graphs', 0.5590940713882446), ('planar graphs', 0.5193981528282166), ('embedding graph', 0.5119941830635071), ('graphs clique', 0.493523508310318), ('class planar graphs', 0.47726550698280334), ('graphs require', 0.46687012910842896), ('graphs', 0.45888131856918335), ('graphs determined', 0.44602155685424805), ('regular graphs admitting', 0.44409582018852234)]"
1517,1517,19,1517_splitting methods_order splitting methods_operator splitting methods_numerical splitting,"['splitting methods', 'order splitting methods', 'operator splitting methods', 'numerical splitting', 'high order splitting', 'operator splitting scheme', 'splitting scheme', 'operator splitting', 'splitting schemes', 'order splitting']","['Overcoming the order barrier two in splitting methods when applied to\n  semilinear parabolic problems with non-periodic boundary conditions   In general, high order splitting methods suffer from an order reduction\nphenomena when applied to the time integration of partial differential\nequations with non-periodic boundary conditions. In the last decade, there were\nintroduced several modifications to prevent the second order Strang Splitting\nmethod from such a phenomena. In this article, inspired by these recent\ncorrector techniques, we introduce a splitting method of order three for a\nclass of semilinear parabolic problems that avoids order reduction in the\ncontext of non-periodic boundary conditions. We give a proof for the third\norder convergence of the method in a simplified linear setting and confirm the\nresult by numerical experiments. Moreover, we show numerically that the high\norder convergence persists for an order four variant of a splitting method, and\nalso for a nonlinear source term.\n', ""An initial-corrected splitting approach for\n  convection-diffusion-reaction problems   Splitting methods constitute a well-established class of numerical schemes\nfor solving convection-diffusion-reaction problems. They have been shown to be\neffective in solving problems with periodic boundary conditions. However, in\nthe case of Dirichlet boundary conditions, order reduction has been observed\neven with homogeneous boundary conditions. In this paper, we propose a novel\nsplitting approach, the so-called `initial-corrected splitting method', which\nsucceeds in overcoming order reduction. A convergence analysis is performed to\ndemonstrate second-order convergence of this modified Strang splitting method.\nFurthermore, we conduct numerical experiments to illustrate the performance of\nthe newly developed splitting approach.\n"", 'Improving the stability and efficiency of high-order operator-splitting\n  methods   Operator-splitting methods are widely used to solve differential equations,\nespecially those that arise from multi-scale or multi-physics models, because a\nmonolithic (single-method) approach may be inefficient or even infeasible. The\nmost common operator-splitting methods are the first-order Lie--Trotter (or\nGodunov) and the second-order Strang (Strang--Marchuk) splitting methods.\nHigh-order splitting methods with real coefficients require backward-in-time\nintegration in each operator and hence may be adversely impacted by instability\nfor certain operators such as diffusion. However, besides the method\ncoefficients, there are many other ancillary aspects to an overall\noperator-splitting method that are important but often overlooked. For example,\nthe operator ordering and the choice of sub-integration methods can\nsignificantly affect the stability and efficiency of an operator-splitting\nmethod. In this paper, we investigate some design principles for the\nconstruction of operator-splitting methods, including minimization of local\nerror measure, choice of sub-integration method, maximization of linear\nstability, and minimization of overall computational cost. We propose a new\nfour-stage, third-order, 2-split operator-splitting method with seven\nsub-integrations per step and optimized linear stability for a benchmark\nproblem from cardiac electrophysiology. We then propose a general principle to\nfurther improve stability and efficiency of such operator-splitting methods by\nusing low-order, explicit sub-integrators for unstable sub-integrations. We\ndemonstrate an almost 30\\% improvement in the performance of methods derived\nfrom these design principles compared to the best-known third-order methods.\n']","[('splitting methods', 0.6846630573272705), ('order splitting methods', 0.6657071113586426), ('operator splitting methods', 0.6566407680511475), ('numerical splitting', 0.6335259079933167), ('high order splitting', 0.5969434380531311), ('operator splitting scheme', 0.5337594747543335), ('splitting scheme', 0.4766593277454376), ('operator splitting', 0.47043272852897644), ('splitting schemes', 0.46091872453689575), ('order splitting', 0.46024733781814575)]"
1518,1518,19,1518_finite element methods_convection diffusion equations_convection diffusion_finite element time,"['finite element methods', 'convection diffusion equations', 'convection diffusion', 'finite element time', 'nonlinear convection diffusion', 'dependent convection diffusion', 'discretizations', 'element methods', 'space time formulation', 'advection diffusion']","[""Time-Continuous and Time-Discontinuous Space-Time Finite Elements for\n  Advection-Diffusion Problems   We construct four variants of space-time finite element discretizations based\non linear tensor-product and simplex-type finite elements. The resulting\ndiscretizations are continuous in space, and continuous or discontinuous in\ntime. In a first test run, all four methods are applied to a linear scalar\nadvection-diffusion model problem. Then, the convergence properties of the\ntime-discontinuous space-time finite element discretizations are studied in\nnumerical experiments. Advection velocity and diffusion coefficient are varied,\nsuch that the parabolic case of pure diffusion (heat equation), as well as, the\nhyperbolic case of pure advection (transport equation) are included in the\nstudy. For each model parameter set, the L2 error at the final time is computed\nfor spatial and temporal element lengths ranging over several orders of\nmagnitude to allow for an individual evaluation of the methods' spatial,\ntemporal, and spacetime accuracy. In the parabolic case, particular attention\nis paid to the influence of time-dependent boundary conditions. Key findings\ninclude a spatial accuracy of second order and a temporal accuracy between\nsecond and third order. The temporal accuracy tends towards third order\ndepending on how advection-dominated the test case is, on the choice of the\nspecific discretization method, and on the time-(in)dependence and treatment of\nthe boundary conditions. Additionally, the potential of time-continuous simplex\nspace-time finite elements for heat flux computations is demonstrated with a\npiston ring pack test case.\n"", 'Finite element methods respecting the discrete maximum principle for\n  convection-diffusion equations   Convection-diffusion-reaction equations model the conservation of scalar\nquantities. From the analytic point of view, solution of these equations\nsatisfy under certain conditions maximum principles, which represent physical\nbounds of the solution. That the same bounds are respected by numerical\napproximations of the solution is often of utmost importance in practice. The\nmathematical formulation of this property, which contributes to the physical\nconsistency of a method, is called Discrete Maximum Principle (DMP). In many\napplications, convection dominates diffusion by several orders of magnitude. It\nis well known that standard discretizations typically do not satisfy the DMP in\nthis convection-dominated regime. In fact, in this case, it turns out to be a\nchallenging problem to construct discretizations that, on the one hand, respect\nthe DMP and, on the other hand, compute accurate solutions. This paper presents\na survey on finite element methods, with a main focus on the\nconvection-dominated regime, that satisfy a local or a global DMP. The concepts\nof the underlying numerical analysis are discussed. The survey reveals that for\nthe steady-state problem there are only a few discretizations, all of them\nnonlinear, that at the same time satisfy the DMP and compute reasonably\naccurate solutions, e.g., algebraically stabilized schemes. Moreover, most of\nthese discretizations have been developed in recent years, showing the enormous\nprogress that has been achieved lately. Methods based on algebraic\nstabilization, nonlinear and linear ones, are currently as well the only finite\nelement methods that combine the satisfaction of the global DMP and accurate\nnumerical results for the evolutionary equations in the convection-dominated\nsituation.\n', 'Automatic Variationally Stable Analysis for Finite Element Computations:\n  Transient Convection-Diffusion Problems   We establish stable finite element (FE) approximations of\nconvection-diffusion initial boundary value problems using the automatic\nvariationally stable finite element (AVS-FE) method. The transient\nconvection-diffusion problem leads to issues in classical FE methods as the\ndifferential operator can be considered singular perturbation in both space and\ntime. The unconditional stability of the AVS-FE method, regardless of the\nunderlying differential operator, allows us significant flexibility in the\nconstruction of FE approximations. We take two distinct approaches to the FE\ndiscretization of the convection-diffusion problem: i) considering a space-time\napproach in which the temporal discretization is established using finite\nelements, and ii) a method of lines approach in which we employ the AVS-FE\nmethod in space whereas the temporal domain is discretized using the\ngeneralized-alpha method. In the generalized-alpha method, we discretize the\ntemporal domain into finite sized time-steps and adopt the generalized-alpha\nmethod as time integrator. Then, we derive a corresponding norm for the\nobtained operator to guarantee the temporal stability of the method.\n  We present numerical verifications for both approaches, including numerical\nasymptotic convergence studies highlighting optimal convergence properties.\nFurthermore, in the spirit of the discontinuous Petrov-Galerkin method by\nDemkowicz and Gopalakrishnan, the AVS-FE method also leads to readily available\na posteriori error estimates through a Riesz representer of the residual of the\nAVS-FE approximations. Hence, the norm of the resulting local restrictions of\nthese estimates serve as error indicators in both space and time for which we\npresent multiple numerical verifications adaptive strategies.\n']","[('finite element methods', 0.6394194960594177), ('convection diffusion equations', 0.5257400274276733), ('convection diffusion', 0.49095529317855835), ('finite element time', 0.48963016271591187), ('nonlinear convection diffusion', 0.48515555262565613), ('dependent convection diffusion', 0.4758681356906891), ('discretizations', 0.4663132429122925), ('element methods', 0.4626365005970001), ('space time formulation', 0.46189090609550476), ('advection diffusion', 0.45016321539878845)]"
1519,1519,19,1519_cost markov_markov decision processes_markov decision process_observable markov decision,"['cost markov', 'markov decision processes', 'markov decision process', 'observable markov decision', 'partially observable markov', 'markov decision', 'optimal policies optimal', 'optimal policies', 'horizon markov decision', 'policies optimal']","['Average Cost Markov Decision Processes with Semi-Uniform Feller\n  Transition Probabilities   This paper studies average-cost Markov decision processes with semi-uniform\nFeller transition probabilities. This class of MDPs was recently introduced by\nthe authors to study MDPs with incomplete information. This paper studies the\nvalidity of optimality inequalities, the existence of optimal policies, and the\napproximations of optimal policies by policies optimizing total discounted\ncosts.\n', ""On the Minimum Pair Approach for Average-Cost Markov Decision Processes\n  with Countable Discrete Action Spaces and Strictly Unbounded Costs   We consider average-cost Markov decision processes (MDPs) with Borel state\nspaces, countable, discrete action spaces, and strictly unbounded one-stage\ncosts. For the minimum pair approach, we introduce a new majorization condition\non the state transition stochastic kernel, in place of the commonly required\ncontinuity conditions on the MDP model. We combine this majorization condition\nwith Lusin's theorem to prove the existence of a stationary minimum pair, i.e.,\na stationary policy paired with an invariant probability measure induced on the\nstate space, with the property that the pair attains the minimum long-run\naverage cost over all policies and initial distributions. We also establish\nother optimality properties of a stationary minimum pair, and for the\nstationary policy in such a pair, under additional recurrence or regularity\nconditions, we prove its pathwise optimality and strong optimality. Our results\ncan be applied to a class of countable action space MDPs in which the dynamics\nand one-stage costs are discontinuous with respect to the state variable.\n"", ""On Linear Programming for Constrained and Unconstrained Average-Cost\n  Markov Decision Processes with Countable Action Spaces and Strictly Unbounded\n  Costs   We consider the linear programming approach for constrained and unconstrained\nMarkov decision processes (MDPs) under the long-run average cost criterion,\nwhere the class of MDPs in our study have Borel state spaces and discrete\ncountable action spaces. Under a strict unboundedness condition on the\none-stage costs and a recently introduced majorization condition on the state\ntransition stochastic kernel, we study infinite-dimensional linear programs for\nthe average-cost MDPs and prove the absence of a duality gap and other\noptimality results. Our results do not require a lower-semicontinuous MDP\nmodel. Thus, they can be applied to countable action space MDPs where the\ndynamics and one-stage costs are discontinuous in the state variable. Our\nproofs make use of the continuity property of Borel measurable functions\nasserted by Lusin's theorem.\n""]","[('cost markov', 0.675635814666748), ('markov decision processes', 0.6351323127746582), ('markov decision process', 0.622826337814331), ('observable markov decision', 0.6180061101913452), ('partially observable markov', 0.5981683731079102), ('markov decision', 0.5895238518714905), ('optimal policies optimal', 0.5722628235816956), ('optimal policies', 0.5698366761207581), ('horizon markov decision', 0.5622768402099609), ('policies optimal', 0.5609598159790039)]"
1520,1520,19,1520_quantum field theories_algebraic quantum field_algebraic quantum_quantum field theory,"['quantum field theories', 'algebraic quantum field', 'algebraic quantum', 'quantum field theory', 'field theories', 'quantum fields', 'theory algebraic', 'quantum field', 'category algebras', 'field theory']","[""Operads for algebraic quantum field theory   We construct a colored operad whose category of algebras is the category of\nalgebraic quantum field theories. This is achieved by a construction that\ndepends on the choice of a category, whose objects provide the operad colors,\nequipped with an additional structure that we call an orthogonality relation.\nThis allows us to describe different types of quantum field theories, including\ntheories on a fixed Lorentzian manifold, locally covariant theories and also\nchiral conformal and Euclidean theories. Moreover, because the colored operad\ndepends functorially on the orthogonal category, we obtain adjunctions between\ncategories of different types of quantum field theories. These include novel\nand interesting constructions, such as time-slicification and local-to-global\nextensions of quantum field theories. We compare the latter to Fredenhagen's\nuniversal algebra.\n"", 'Lorentzian bordisms in algebraic quantum field theory   It is shown that every algebraic quantum field theory has an underlying\nfunctorial field theory which is defined on a suitable globally hyperbolic\nLorentzian bordism pseudo-category. This means that globally hyperbolic\nLorentzian bordisms between Cauchy surfaces arise naturally in the context of\nalgebraic quantum field theory. The underlying functorial field theory encodes\nthe time evolution of the original theory, but not its spatially local\nstructure. As an illustrative application of these results, the algebraic and\nfunctorial descriptions of a free scalar quantum field are compared in detail.\n', 'Homotopical Quantum Field Theory   Algebraic quantum field theory and prefactorization algebra are two\nmathematical approaches to quantum field theory. In this monograph, using a new\ncoend definition of the Boardman-Vogt construction of a colored operad, we\ndefine homotopy algebraic quantum field theories and homotopy prefactorization\nalgebras and investigate their homotopy coherent structures. Homotopy coherent\ndiagrams, homotopy inverses, A-infinity-algebras, E-infinity-algebras, and\nE-infinity-modules arise naturally in this context. In particular, each\nhomotopy algebraic quantum field theory has the structure of a homotopy\ncoherent diagram of A-infinity-algebras and satisfies a homotopy coherent\nversion of the causality axiom. When the time-slice axiom is defined for\nalgebraic quantum field theory, a homotopy coherent version of the time-slice\naxiom is satisfied by each homotopy algebraic quantum field theory. Over each\ntopological space, every homotopy prefactorization algebra has the structure of\na homotopy coherent diagram of E-infinity-modules over an E-infinity-algebra.\nTo compare the two approaches, we construct a comparison morphism from the\ncolored operad for (homotopy) prefactorization algebras to the colored operad\nfor (homotopy) algebraic quantum field theories and study the induced\nadjunctions on algebras.\n']","[('quantum field theories', 0.6556194424629211), ('algebraic quantum field', 0.6317195296287537), ('algebraic quantum', 0.6001908779144287), ('quantum field theory', 0.5960256457328796), ('field theories', 0.5695972442626953), ('quantum fields', 0.5589460730552673), ('theory algebraic', 0.5296276807785034), ('quantum field', 0.5144070982933044), ('category algebras', 0.5080576539039612), ('field theory', 0.4936482310295105)]"
1521,1521,19,1521_randomized approximation_optimal sampling_adaptive randomized_randomized adaptive,"['randomized approximation', 'optimal sampling', 'adaptive randomized', 'randomized adaptive', 'information approximation', 'sampling approximation', 'least squares approximation', 'non adaptive methods', 'best approximation', 'adaptive methods']","['Optimal sampling and Christoffel functions on general domains   We consider the problem of reconstructing an unknown function $u\\in\nL^2(D,\\mu)$ from its evaluations at given sampling points $x^1,\\dots,x^m\\in D$,\nwhere $D\\subset \\mathbb R^d$ is a general domain and $\\mu$ a probability\nmeasure. The approximation is picked from a linear space $V_n$ of interest\nwhere $n=\\dim(V_n)$. Recent results have revealed that certain weighted\nleast-squares methods achieve near best approximation with a sampling budget\n$m$ that is proportional to $n$, up to a logarithmic factor\n$\\ln(2n/\\varepsilon)$, where $\\varepsilon>0$ is a probability of failure. The\nsampling points should be picked at random according to a well-chosen\nprobability measure $\\sigma$ whose density is given by the inverse Christoffel\nfunction that depends both on $V_n$ and $\\mu$. While this approach is greatly\nfacilitated when $D$ and $\\mu$ have tensor product structure, it becomes\nproblematic for domains $D$ with arbitrary geometry since the optimal measure\ndepends on an orthonormal basis of $V_n$ in $L^2(D,\\mu)$ which is not\nexplicitly given, even for simple polynomial spaces. Therefore sampling\naccording to this measure is not practically feasible. In this paper, we\ndiscuss practical sampling strategies, which amount to using a perturbed\nmeasure $\\widetilde \\sigma$ that can be computed in an offline stage, not\ninvolving the measurement of $u$. We show that near best approximation is\nattained by the resulting weighted least-squares method at near-optimal\nsampling budget and we discuss multilevel approaches that preserve optimality\nof the cumulated sampling budget when the spaces $V_n$ are iteratively\nenriched. These strategies rely on the knowledge of a-priori upper bounds on\nthe inverse Christoffel function. We establish such bounds for spaces $V_n$ of\nmultivariate algebraic polynomials, and for general domains $D$.\n', 'Randomized approximation of summable sequences -- adaptive and\n  non-adaptive   We prove lower bounds for the randomized approximation of the embedding\n$\\ell_1^m \\rightarrow \\ell_\\infty^m$ based on algorithms that use arbitrary\nlinear (hence non-adaptive) information provided by a (randomized) measurement\nmatrix $N \\in \\mathbb{R}^{n \\times m}$. These lower bounds reflect the\nincreasing difficulty of the problem for $m \\to \\infty$, namely, a term\n$\\sqrt{\\log m}$ in the complexity $n$. This result implies that non-compact\noperators between arbitrary Banach spaces are not approximable using\nnon-adaptive Monte Carlo methods. We also compare these lower bounds for\nnon-adaptive methods with upper bounds based on adaptive, randomized methods\nfor recovery for which the complexity $n$ only exhibits a $(\\log\\log\nm)$-dependence. In doing so we give an example of linear problems where the\nerror for adaptive vs. non-adaptive Monte Carlo methods shows a gap of order\n$n^{1/2} ( \\log n)^{-1/2}$.\n', 'Weighted least-squares approximation with determinantal point processes\n  and generalized volume sampling   We consider the problem of approximating a function from $L^2$ by an element\nof a given $m$-dimensional space $V_m$, associated with some feature map\n$\\varphi$, using evaluations of the function at random points $x_1,\\dots,x_n$.\nAfter recalling some results on optimal weighted least-squares using\nindependent and identically distributed points, we consider weighted\nleast-squares using projection determinantal point processes (DPP) or volume\nsampling. These distributions introduce dependence between the points that\npromotes diversity in the selected features $\\varphi(x_i)$. We first provide a\ngeneralized version of volume-rescaled sampling yielding quasi-optimality\nresults in expectation with a number of samples $n = O(m\\log(m))$, that means\nthat the expected $L^2$ error is bounded by a constant times the best\napproximation error in $L^2$. Also, further assuming that the function is in\nsome normed vector space $H$ continuously embedded in $L^2$, we further prove\nthat the approximation is almost surely bounded by the best approximation error\nmeasured in the $H$-norm. This includes the cases of functions from $L^\\infty$\nor reproducing kernel Hilbert spaces. Finally, we present an alternative\nstrategy consisting in using independent repetitions of projection DPP (or\nvolume sampling), yielding similar error bounds as with i.i.d. or volume\nsampling, but in practice with a much lower number of samples. Numerical\nexperiments illustrate the performance of the different strategies.\n']","[('randomized approximation', 0.6032230257987976), ('optimal sampling', 0.5271466374397278), ('adaptive randomized', 0.5244091153144836), ('randomized adaptive', 0.5180137753486633), ('information approximation', 0.5063377022743225), ('sampling approximation', 0.5029577612876892), ('least squares approximation', 0.4563600718975067), ('non adaptive methods', 0.4250185489654541), ('best approximation', 0.4012100398540497), ('adaptive methods', 0.40115121006965637)]"
1522,1522,19,1522_mathbb character varieties_character varieties_mathbb character variety_representation variety,"['mathbb character varieties', 'character varieties', 'mathbb character variety', 'representation variety', 'representation varieties', 'sl_2 mathbb character', 'character variety', 'variety torus', 'torus knot groups', 'varieties generalized']","['Character varieties of odd classical pretzel knots   We determine the ${\\rm SL}(2,\\mathbb{C})$-character variety for each odd\nclassical pretzel knot $P(2k_1+1,2k_2+1,2k_3+1)$, and present a method for\ncomputing its A-polynomial.\n', 'The ${\\rm SL}(2,\\mathbb{C})$-character variety of the Borromean link   For the Borromean link, we determine its irreducible ${\\rm\nSL}(2,\\mathbb{C})$-character variety, and find a formula for the twisted\nAlexander polynomial as a function on the character variety.\n', 'The symmetric slice of ${\\rm SL}(3,\\mathbb{C})$-character variety of the\n  Whitehead link   We give a nice description for a Zariski open subset of the ${\\rm\nSL}(3,\\mathbb{C})$-character variety of the Whitehead link.\n']","[('mathbb character varieties', 0.5934813618659973), ('character varieties', 0.5913481712341309), ('mathbb character variety', 0.5490700602531433), ('representation variety', 0.5294322371482849), ('representation varieties', 0.5237315893173218), ('sl_2 mathbb character', 0.5063398480415344), ('character variety', 0.49308866262435913), ('variety torus', 0.46221911907196045), ('torus knot groups', 0.4552939236164093), ('varieties generalized', 0.45274990797042847)]"
1523,1523,19,1523_greedy approximation_sum reciprocals_reciprocals_sequence positive integers,"['greedy approximation', 'sum reciprocals', 'reciprocals', 'sequence positive integers', 'integers b_n', 'fraction representation', 'frac a_i', 'integer sequence', 'fractions', 'theta sum_']","[""A Threshold for the Best Two-term Underapproximation by Egyptian\n  Fractions   Let $\\mathcal{G}$ be the greedy algorithm that, for each $\\theta\\in (0,1]$,\nproduces an infinite sequence of positive integers $(a_n)_{n=1}^\\infty$\nsatisfying $\\sum_{n=1}^\\infty 1/a_n = \\theta$. For natural numbers $p < q$, let\n$\\Upsilon(p,q)$ denote the smallest positive integer $j$ such that $p$ divides\n$q+j$. Continuing Nathanson's study of two-term underapproximations, we show\nthat whenever $\\Upsilon(p,q) \\leqslant 3$, $\\mathcal{G}$ gives the (unique)\nbest two-term underapproximation of $p/q$; i.e., if $1/x_1 + 1/x_2 < p/q$ for\nsome $x_1, x_2\\in \\mathbb{N}$, then $1/x_1 + 1/x_2 \\leqslant 1/a_1+1/a_2$.\nHowever, the same conclusion fails for every $\\Upsilon(p,q)\\geqslant 4$.\n  Next, we study stepwise underapproximation by $\\mathcal{G}$. Let $e_{m} =\n\\theta - \\sum_{n=1}^{m}1/a_n$ be the $m$th error term. We compare $1/a_m$ to a\nsuperior underapproximation of $e_{m-1}$, denoted by $N/b_m$ ($N\n\\in\\mathbb{N}_{\\geqslant 2}$), and characterize when $1/a_m = N/b_m$. One\ncharacterization is $a_{m+1} \\geqslant N a_m^2 - a_m + 1$. Hence, for rational\n$\\theta$, we only have $1/a_m = N/b_m$ for finitely many $m$. However, there\nare irrational numbers such that $1/a_m = N/b_m$ for all $m$. Along the way,\nvarious auxiliary results are encountered.\n"", 'Weighted real Egyptian numbers   Let $\\mathcal A = (A_1,\\ldots, A_n)$ be a sequence of nonempty finite sets of\npositive real numbers, and let $\\mathcal{B} = (B_1,\\ldots, B_n)$ be a sequence\nof infinite discrete sets of positive real numbers. A weighted real Egyptian\nnumber with numerators $\\mathcal{A}$ and denominators $\\mathcal{B}$ is a real\nnumber $c$ that can be represented in the form \\[ c = \\sum_{i=1}^n\n\\frac{a_i}{b_i} \\] with $a_i \\in A_i$ and $b_i \\in B_i$ for $i \\in \\{1,\\ldots,\nn\\}$. In this paper, classical results of Sierpinski for Egyptian fractions are\nextended to the set of weighted real Egyptian numbers.\n', 'An algorithm for Egyptian fraction representations with restricted\n  denominators   A unit fraction representation of a rational number $r$ is a finite sum of\nreciprocals of positive integers that equals $r$. Of particular interest is the\ncase when all denominators in the representation are distinct, resulting in an\nEgyptian fraction representation of $r$. Common algorithms for computing\nEgyptian fraction representations of a given rational number tend to result in\nextremely large denominators and cannot be adapted to restrictions on the\nallowed denominators. We describe an algorithm for finding all unit fraction\nrepresentations of a given rational number using denominators from a given\nfinite multiset of positive integers. The freely available algorithm,\nimplemented in Scheme, is particularly well suited to computing dense Egyptian\nfraction representations, where the allowed denominators have a prescribed\nmaximum.\n']","[('greedy approximation', 0.4274255633354187), ('sum reciprocals', 0.41219520568847656), ('reciprocals', 0.4007924497127533), ('sequence positive integers', 0.37263205647468567), ('integers b_n', 0.3725050985813141), ('fraction representation', 0.3631789982318878), ('frac a_i', 0.34742680191993713), ('integer sequence', 0.34343066811561584), ('fractions', 0.337832510471344), ('theta sum_', 0.33427128195762634)]"
1524,1524,19,1524_rankin selberg functions_selberg eigenvalue conjecture_selberg functions_pi cuspidal automorphic,"['rankin selberg functions', 'selberg eigenvalue conjecture', 'selberg functions', 'pi cuspidal automorphic', 'rankin selberg', 'cuspidal automorphic representations', 'cuspidal automorphic representation', 'automorphic representations pi', 'selberg eigenvalue', 'automorphic representation mathrm']","['Moments of $L$-functions via the relative trace formula   We prove an asymptotic formula for the second moment of the\n$\\mathrm{GL}(n)\\times\\mathrm{GL}(n+1)$ Rankin--Selberg central $L$-values\n$L(1/2,\\Pi\\otimes\\pi)$, where $\\pi$ is a fixed cuspidal representation of\n$\\mathrm{GL}(n)$ that is tempered and unramified at every place, while $\\Pi$\nvaries over a family of automorphic representations of $\\mathrm{PGL}(n+1)$\nordered by (archimedean or non-archimedean) conductor. As another application\nof our method, we prove the existence of infinitely many cuspidal\nrepresentations $\\Pi$ of $\\mathrm{PGL}(n+1)$ such that $L(1/2,\\Pi\\otimes\\pi_1)$\nand $L(1/2,\\Pi\\otimes\\pi_2)$ do not vanish simultaneously where $\\pi_1$ and\n$\\pi_2$ are cuspidal representations of $\\mathrm{GL}(n)$ that are unramified\nand tempered at every place and have trivial central characters.\n', 'Spectral Reciprocity and Hybrid Subconvexity Bound for triple product\n  $L$-functions   Let $F$ be a number field with adele ring $\\mathbb{A}_F$, $\\pi_1, \\pi_2$ be\ntwo unitary cuspidal automorphic representations of\n$\\mathrm{PGL}_2(\\mathbb{A}_F)$ with finite analytic conductor. We study the\ntwisted first moment of the triple product $L$-function $L(\\frac{1}{2}, \\pi\n\\otimes \\pi_1 \\otimes \\pi_2)$ and the Hecke eigenvalues $\\lambda_\\pi\n(\\mathfrak{l})$, where $\\pi$ is a unitary automorphic representation of\n$\\mathrm{PGL}_2(\\mathbb{A}_F)$ and $\\mathfrak{l}$ is an integral ideal coprimes\nwith the finite analytic conductor $C(\\pi \\otimes \\pi_1 \\otimes \\pi_2)$. The\nestimation becomes a reciprocity formula between different moments of\n$L$-functions. Combining with the ideas and estimations established in [HMN23]\nand [MV10], we study the subconvexity problem for the triple product\n$L$-function in the level aspect and give a new explicit hybrid subconvexity\nbound for $L(\\frac{1}{2}, \\pi \\otimes \\pi_1 \\otimes \\pi_2)$, allowing joint\nramifications and conductor dropping range.\n', 'Spectral reciprocity for $\\mathrm{GL}(n)$ and simultaneous non-vanishing\n  of central $L$-values   Let $F$ be a totally real number field and $n\\ge 3$. Let $\\Pi$ and $\\pi$ be\ncuspidal automorphic representations for $\\mathrm{PGL}_{n+1}(F)$ and\n$\\mathrm{PGL}_{n-1}(F)$, respectively, that are unramified and tempered at all\nfinite places. We prove simultaneous non-vanishing of the Rankin--Selberg\n$L$-values $L(1/2,\\Pi\\otimes\\widetilde{\\sigma})$ and\n$L(1/2,\\sigma\\otimes\\widetilde{\\pi})$ for certain sequences of $\\sigma$ varying\nover cuspidal automorphic representations for $\\mathrm{PGL}_n(F)$ with\nconductor tending to infinity in the level aspect and bearing certain local\nconditions. Along the way, we also prove a reciprocity formula for the average\nof the product of Rankin--Selberg $L$-functions\n$L(1/2,\\Pi\\otimes\\widetilde{\\sigma})L(1/2,\\sigma\\otimes\\widetilde{\\pi})$ over a\nconductor aspect family of $\\sigma$.\n']","[('rankin selberg functions', 0.6430793404579163), ('selberg eigenvalue conjecture', 0.5471691489219666), ('selberg functions', 0.5388874411582947), ('pi cuspidal automorphic', 0.5303295254707336), ('rankin selberg', 0.5300617814064026), ('cuspidal automorphic representations', 0.5257407426834106), ('cuspidal automorphic representation', 0.5217684507369995), ('automorphic representations pi', 0.5116270780563354), ('selberg eigenvalue', 0.48294365406036377), ('automorphic representation mathrm', 0.4783964455127716)]"
1525,1525,19,1525_basic hypergeometric series_hypergeometric identities_hypergeometric functions also_hypergeometric functions,"['basic hypergeometric series', 'hypergeometric identities', 'hypergeometric functions also', 'hypergeometric functions', 'hypergeometric series', 'classical hypergeometric', 'elliptic hypergeometric', 'basic hypergeometric', 'expansion formulas', 'hypergeometric']","[""Several transformation formulas involving bilateral basic hypergeometric\n  series   In terms of the analytic continuation method, we prove three transformation\nformulas involving bilateral basic hypergeometric series. One of them is\nequivalent to Jouhet's result involving two $_8\\psi_8$ series and two\n$_8\\phi_7$ series.\n"", ""The generalized Zwegers' $\\mu$-function and transformation formulas for\n  the bilateral basic hypergeometric series   By applying Slater's transformation formulas for the bilateral basic\nhypergeometric series ${}_2\\psi_{2}$, we derive three type translation formulas\nfor the generalized Zwegers' $\\mu$-function (``continuous $q$-Hermite\nfunction'') which was introduced by Shibukawa--Tsuchimi (SIGMA, 2023). From\nsome Bailey's transformation formula of ${}_2\\psi_{2}$, we also give a formula\nfor the expression of the generalized Zwegers' $\\mu$-function by some\nvery-well-poised bilateral basic hypergeometric series ${}_4\\psi_{8}$. As an\napplication of this new expression formula for the generalized Zwegers'\n$\\mu$-function, we obtain some new Fourier expansions for the Weierstrass and\nJacobi elliptic functions.\n"", ""Transformations and summations for bilateral basic hypergeometric series   We derive transformation and summation formulas for bilateral basic\nhypergeometric series. As a starting point, we use two transformations of\nbilateral basic very-well-poised ${}_8\\Psi_8$. The first transformation is\ngiven as a sum of two nonterminating ${}_8W_7$'s and the second is given in\nterms of a sum of a ${}_4\\psi_4$ and two balanced ${}_4\\phi_3$'s. From these\ntransformations we derive limiting transformations with vanishing denominator\nelements which shed light on the transformation properties of these bilateral\nbasic hypergeometric series. We also study tuple product identities, namely\ntriple, quintuple, sextuple, septuple, octuple, nonuple and undecuple, which\nare given in terms of sums of bilateral basic hypergeometric series.\n""]","[('basic hypergeometric series', 0.6830437779426575), ('hypergeometric identities', 0.6754735708236694), ('hypergeometric functions also', 0.6719394326210022), ('hypergeometric functions', 0.6663894057273865), ('hypergeometric series', 0.6663066744804382), ('classical hypergeometric', 0.6228405833244324), ('elliptic hypergeometric', 0.5749362707138062), ('basic hypergeometric', 0.5609728097915649), ('expansion formulas', 0.5245581269264221), ('hypergeometric', 0.5214913487434387)]"
1526,1526,19,1526_regularized optimization_sparse optimization_minimization nonconvex_regularized sparse,"['regularized optimization', 'sparse optimization', 'minimization nonconvex', 'regularized sparse', 'proximal majorization minimization', 'algorithms convex optimization', 'regularized newton', 'loss minimization', 'regularization problems', 'norm regularized']","['Convergence Rate Analysis of Proximal Iteratively Reweighted $\\ell_1$\n  Methods for $\\ell_p$ Regularization Problems   In this paper, we focus on the local convergence rate analysis of the\nproximal iteratively reweighted $\\ell_1$ algorithms for solving $\\ell_p$\nregularization problems, which are widely applied for inducing sparse\nsolutions. We show that if the Kurdyka-Lojasiewicz (KL) property is satisfied,\nthe algorithm converges to a unique first-order stationary point; furthermore,\nthe algorithm has local linear convergence or local sublinear convergence. The\ntheoretical results we derived are much stronger than the existing results for\niteratively reweighted $\\ell_1$ algorithms.\n', 'A proximal MM method for the zero-norm regularized PLQ composite\n  optimization problem   This paper is concerned with a class of zero-norm regularized piecewise\nlinear-quadratic (PLQ) composite minimization problems, which covers the\nzero-norm regularized $\\ell_1$-loss minimization problem as a special case. For\nthis class of nonconvex nonsmooth problems, we show that its equivalent MPEC\nreformulation is partially calm on the set of global optima and make use of\nthis property to derive a family of equivalent DC surrogates. Then, we propose\na proximal majorization-minimization (MM) method, a convex relaxation approach\nnot in the DC algorithm framework, for solving one of the DC surrogates which\nis a semiconvex PLQ minimization problem involving three nonsmooth terms. For\nthis method, we establish its global convergence and linear rate of\nconvergence, and under suitable conditions show that the limit of the generated\nsequence is not only a local optimum but also a good critical point in a\nstatistical sense. Numerical experiments are conducted with synthetic and real\ndata for the proximal MM method with the subproblems solved by a dual\nsemismooth Newton method to confirm our theoretical findings, and numerical\ncomparisons with a convergent indefinite-proximal ADMM for the partially\nsmoothed DC surrogate verify its superiority in the quality of solutions and\ncomputing time.\n', 'Group zero-norm regularized robust loss minimization: proximal MM method and statistical error bound This study focuses on solving group zero-norm regularized robust loss minimization problems. We propose a proximal Majorization-Minimization (PMM) algorithm to address a class of equivalent Difference-of-Convex (DC) surrogate optimization problems. First, we present the core principles and iterative framework of the PMM method. Under the Kurdyka-{\\L}ojasiewicz (KL) property assumption of the potential function, we establish the global convergence of the algorithm and characterize its local (sub)linear convergence rate. Furthermore, for linear observation models with design matrices satisfying restricted eigenvalue conditions, we derive statistical estimation error bounds between the PMM-generated iterates (including their limit points) and the ground truth solution. These bounds not only rigorously quantify the approximation accuracy of the algorithm but also extend previous results on element-wise sparse composite optimization from reference [57]. To efficiently implement the PMM framework, we develop a proximal dual semismooth Newton method for solving critical subproblems. Extensive numerical experiments on both synthetic data and the UCI benchmark demonstrate the superior computational efficiency of our PMM method compared to the proximal Alternating Direction Method of Multipliers (pADMM).']","[('regularized optimization', 0.6649693250656128), ('sparse optimization', 0.6549964547157288), ('minimization nonconvex', 0.6412442922592163), ('regularized sparse', 0.6145914196968079), ('proximal majorization minimization', 0.5964226722717285), ('algorithms convex optimization', 0.5524237751960754), ('regularized newton', 0.5344008803367615), ('loss minimization', 0.5285618305206299), ('regularization problems', 0.5263557434082031), ('norm regularized', 0.5166217088699341)]"
1527,1527,19,1527_pid controller_pid controllers_control nonlinear systems_integral derivative pid,"['pid controller', 'pid controllers', 'control nonlinear systems', 'integral derivative pid', 'derivative pid', 'feedback control proposed', 'uncertain nonlinear systems', 'continuous control', 'control control', 'lyapunov based']","['Classical Stability Margins by PID Control   Proportional-Integral-Derivative (PID) control has been the workhorse of\ncontrol technology for about a century. Yet to this day, designing and tuning\nPID controllers relies mostly on either tabulated rules (Ziegler-Nichols) or on\nclassical graphical techniques (Bode). Our goal in this paper is to take a\nfresh look on PID control in the context of optimizing stability margins for\nlow-order (first- and second-order) linear time-invariant systems.\nSpecifically, we seek to derive explicit expressions for gain and phase margins\nthat are achievable using PID control, and thereby gain insights on the role of\nunstable poles and nonminimum-phase zeros in attaining robust stability. In\nparticular, stability margins attained by PID control for minimum-phase systems\nmatch those obtained by more general control, while for nonminimum-phase\nsystems, PID control achieves margins that are no worse than those of general\ncontrol modulo a predetermined factor. Furthermore, integral action does not\ncontribute to robust stabilization beyond what can be achieved by PD control\nalone.\n', 'A Rolling PID Control Approach and its Applications   The canonical proportional-integral-derivative (PID) control approach has\nbeen widely used in industrial application due to their simplicity and ease of\nuse. However, its corresponding controller parameters are hard to be adjusted,\nespecially for nonlinear systems. The optimization-based method provides a\ngeneral framework to find optimal PID controller parameters; nevertheless,\nseveral disadvantages exist, for example, it is nontrivial to select an\nappropriate sample size and it is necessary to obtain the global optimal\nsolution but the optimization problem is non-convex, making it hard to achieve.\nTo alleviate the aforementioned limitations, a rolling PID control approach is\nproposed in this study, in which, at each rolling period, the PID controller\nparameters are updated using observable data, which can be classified to\ndata-driven control method. The effectiveness of the proposed approach has been\nvalidated by experiments.\n', 'Tracking performance of PID for nonlinear stochastic systems   In this paper, we will consider a class of continuous-time stochastic control\nsystems with both unknown nonlinear structure and unknown disturbances, and\ninvestigate the capability of the classical\nproportional-integral-derivative(PID) controller in tracking time-varying\nreference signals. First, under some suitable conditions on system nonlinear\nfunctions, reference signals, and unknown disturbances, we will show that PID\ncontrollers can be designed to globally stabilize such systems and ensure the\nboundedness of the tracking error. Analytic design formulae for PID gain\nmatrices are also provided, which only involve some prior knowledge of the\npartial derivatives of system structural nonlinear functions. Besides, it will\nbe shown that the steady-state tracking error hinges on three critical factors:\ni) the change rate of reference signals and external disturbances; ii) the\nintensity of random noises; iii) the selection of PID gains, and can be made\narbitrarily small by choosing PID gains suitably large. Finally, by introducing\na desired transient process which is shaped from the reference signal, we will\npresent a new PID tuning rule, which can guarantee both nice steady-state and\nsuperior transient control performances.\n']","[('pid controller', 0.6499167084693909), ('pid controllers', 0.6222894787788391), ('control nonlinear systems', 0.5252538323402405), ('integral derivative pid', 0.5107219815254211), ('derivative pid', 0.5102871656417847), ('feedback control proposed', 0.4771376848220825), ('uncertain nonlinear systems', 0.43864595890045166), ('continuous control', 0.42174360156059265), ('control control', 0.41094115376472473), ('lyapunov based', 0.4055285155773163)]"
1528,1528,19,1528_representation variety_variety representations_character varieties_mathbb character variety,"['representation variety', 'variety representations', 'character varieties', 'mathbb character variety', 'representation character', 'mixed hodge structures', 'character variety', 'varieties finite fields', 'representations finitely generated', 'affine algebraic group']","['E-Polynomials of Generic $\\text{GL}_n\\rtimes\\!<\\!\\sigma\\!>\\!~$-Character\n  Varieties: Branched Case   For any branched double covering of compact Riemann surfaces, we consider the\nassociated character varieties that are unitary in the global sense, which we\ncall $\\text{GL}_n\\rtimes\\!<\\!\\sigma\\!>\\!~$-character varieties. We restrict the\nmonodromies around the ramification points to generic semi-simple conjugacy\nclasses contained in $\\text{GL}_n\\sigma$, and compute the E-polynomials of\nthese character varieties using the character table of\n$\\text{GL}_n(q)\\rtimes\\!<\\!\\sigma\\!>\\!$. The result is expressed as the inner\nproduct of certain symmetric functions associated to the wreath products\n$(\\mathbb{Z}/2\\mathbb{Z})^N\\rtimes\\mathfrak{S}_N$. We are then led to a\nconjectural formula for the mixed Hodge polynomial, which involves (modified)\nMacdonald polynomials and wreath Macdonald polynomials.\n', 'Asymptotic Dynamics on Character Varieties over Finite Fields   In this paper, we prove the lack of asymptotic transitivity of the outer\nautomorphism group action of $\\mathbb{Z}^r$ on\n$\\mathrm{SL}_n(\\mathbb{F}_q)$-character varieties of $\\mathbb{Z}^r$ for $n=2,3$\nand $r\\geq 2$. Along the way, we stratify the character varieties and compute\nthe $E$-polynomial, also known as the Hodge-Deligne polynomial or Serre\npolynomial, of these character varieties.\n', 'E-Polynomials of Generic $\\text{GL}_n\\rtimes\\!<\\!\\sigma\\!>\\!~$-Character\n  Varieties: Unbranched Case   For any unbranched double covering of compact Riemann surfaces, we study the\nassociated character varieties that are unitary in the global sense, which we\ncall $\\text{GL}_n\\rtimes\\!<\\!\\sigma\\!>\\!~$-character varieties. We introduce\n$k>0$ punctures on the surface, and restrict the monodromies around the\npunctures to generic semi-simple conjugacy classes in $\\text{GL}_n$, and\ncompute the E-polynomials of these character varieties using the character\ntable of $\\text{GL}_n(q)$. The result is expressed as the inner product of\ncertain symmetric functions. We are then led to a conjectural formula for the\nmixed Hodge polynomial, which is built out of (modified) Macdonald polynomials,\ntheir self-pairings, and self-pairings of wreath Macdonald polynomials.\n']","[('representation variety', 0.6497332453727722), ('variety representations', 0.6372950673103333), ('character varieties', 0.5827422142028809), ('mathbb character variety', 0.5368261337280273), ('representation character', 0.4850042760372162), ('mixed hodge structures', 0.4776954650878906), ('character variety', 0.44929176568984985), ('varieties finite fields', 0.44324782490730286), ('representations finitely generated', 0.4350810647010803), ('affine algebraic group', 0.4290177822113037)]"
1529,1529,19,1529_numerical integrators_transient simulation_power system transient_numerical integration,"['numerical integrators', 'transient simulation', 'power system transient', 'numerical integration', 'power system models', 'system simulation', 'integrators used', 'simulation scheme', 'transient stability', 'numerical stability']","['Efficient Power System Transient Simulation Based on Frequency Response\n  Optimized Integrators Considering Second Order Derivative   Frequency response optimized integrators considering second order derivative\nare proposed in this paper. Based on the proposed numerical integrators, and\nothers which also consider second order derivative, this paper puts forward a\nnovel power system transient simulation scheme. Instead of using a unique\nnumerical integrator, the proposed simulation scheme chooses proper ones\naccording to the dominant frequency component of the differential state\nvariables. With the proposed simulation scheme, computational efficiency is\nimproved by using large step sizes without sacrificing accuracy. Numerical case\nstudies demonstrate the validity and efficiency of the simulation scheme.\n', 'Proper Selection of Obreshkov-Like Numerical Integrators Used as\n  Numerical Differentiators for Power System Transient Simulation   Obreshkov-like numerical integrators have been widely applied to power system\ntransient simulation. Misuse of the numerical integrators as numerical\ndifferentiators may lead to numerical oscillation or bias. Criteria for\nObreshkov-like numerical integrators to be used as numerical differentiators\nare proposed in this paper to avoid these misleading phenomena. The\ncoefficients of a numerical integrator for the highest order derivative turn\nout to determine its suitability. Some existing Obreshkov-like numerical\nintegrators are examined under the proposed criteria. It is revealed that the\nnotorious numerical oscillations induced by the implicit trapezoidal method\ncannot always be eliminated by using the backward Euler method for a few time\nsteps. Guided by the proposed criteria, a frequency response optimized\nintegrator considering second order derivative is put forward which is suitable\nto be used as a numerical differentiator. Theoretical observations are\ndemonstrated in time domain via case studies. The paper points out how to\nproperly select the numerical integrators for power system transient simulation\nand helps to prevent their misuse.\n', 'Improved Method for Dealing with Discontinuities in Power System\n  Transient Simulation Based on Frequency Response Optimized Integrators\n  Considering Second Order Derivative   Potential disagreement in the result induced by discontinuities is revealed\nin this paper between a novel power system transient simulation scheme using\nnumerical integrators considering second order derivative and conventional ones\nusing numerical integrators considering first order derivative. The\ndisagreement is due to the formula of the different numerical integrators. An\nimproved method for dealing with discontinuities in the novel transient\nsimulation scheme is proposed to resolve the disagreement. The effectiveness of\nthe improved method is demonstrated and verified via numerical case studies.\nAlthough the disagreement is studied on and the improved method is proposed for\na particular transient simulation scheme, similar conclusions also apply to\nother ones using numerical integrators considering high order derivative.\n']","[('numerical integrators', 0.5325097441673279), ('transient simulation', 0.5127193331718445), ('power system transient', 0.40268707275390625), ('numerical integration', 0.3962787985801697), ('power system models', 0.3815244436264038), ('system simulation', 0.36439916491508484), ('integrators used', 0.3606085181236267), ('simulation scheme', 0.35363465547561646), ('transient stability', 0.35092252492904663), ('numerical stability', 0.34725484251976013)]"
1530,1530,19,1530_plurisubharmonic functions_compact convex sets_compact convex_optimal polynomials,"['plurisubharmonic functions', 'compact convex sets', 'compact convex', 'optimal polynomials', 'compact convex subset', 'convex sets', 'weighted extremal', 'extremal functions', 'polynomial map', 'convex subset']","['Polynomials with exponents in compact convex sets and associated\n  weighted extremal functions -- The Bernstein-Walsh-Siciak theorem   We generalize the Bernstein-Walsh-Siciak theorem on polynomial approximation\nin $\\mathbb{C}^n$ to the case where the polynomial ring\n$\\mathcal{P}(\\mathbb{C}^n)$ is replaced by a subring\n$\\mathcal{P}^S(\\mathbb{C}^n)$ consisting of all polynomials with exponents\nrestricted to sets $mS$, where $S$ is a compact convex subset of\n$\\mathbb{R}_+^n$ with $0 \\in S$ and $m = 0, 1, 2, 3, \\dots$, and uniform\nestimates of error in the approximation are replaced by weighted uniform\nestimates with respect to an admissible weight function.\n', ""Polynomials with exponents in compact convex sets and associated\n  weighted extremal functions -- Generalized product property   A famous result of Siciak is how the Siciak-Zakharyuta functions, sometimes\ncalled global extremal functions or pluricomplex Green functions with a pole at\ninfinity, of two sets relate to the Siciak-Zakharyuta function of their\ncartesian product. In this paper Siciak's result is generalized to the setting\nof Siciak-Zakharyuta functions with growth given by a compact convex set, along\nwith discussing why this generalization does not work in the weighted setting.\n"", 'Polynomials with exponents in compact convex sets and associated\n  weighted extremal functions -- The Siciak-Zakharyuta theorem   The classical Siciak-Zakharyuta theorem states that the Siciak-Zakharyuta\nfunction $V_{E}$ of a subset $E$ of $\\mathbb C^n$, also called a pluricomplex\nGreen function or global exremal function of $E$, equals the logarithm of the\nSiciak function $\\Phi_E$ if $E$ is compact. The Siciak-Zakharyuta function is\ndefined as the upper envelope of functions in the Lelong class that are\nnegative on $E$, and the Siciak function is the upper envelope of $m$-th roots\nof polynomials $p$ in $\\mathcal{P}_m(\\mathbb C^n)$ of degree $\\leq m$ such that\n$|p|\\leq 1$ on $E$. We generalize the Siciak-Zakharyuta theorem to the case\nwhere the polynomial space ${\\mathcal P}_m(\\mathbb C^n)$ is replaced by\n${\\mathcal P}_m^S(\\mathbb C^n)$ consisting of all polynomials with exponents\nrestricted to sets $mS$, where $S$ is a compact convex subset of $\\mathbb\nR^n_+$ with $0\\in S$. It states that if $q$ is an admissible weight on a closed\nset $E$ in $\\mathbb C^n$ then $V^S_{E,q}=\\log\\Phi^S_{E,q}$ on $\\mathbb C^{*n}$\nif and only if the rational points in $S$ form a dense subset of $S$.\n']","[('plurisubharmonic functions', 0.5087398290634155), ('compact convex sets', 0.4873232841491699), ('compact convex', 0.470612496137619), ('optimal polynomials', 0.4467301368713379), ('compact convex subset', 0.4421080946922302), ('convex sets', 0.40619415044784546), ('weighted extremal', 0.36590510606765747), ('extremal functions', 0.3531990647315979), ('polynomial map', 0.3442178964614868), ('convex subset', 0.3402523100376129)]"
1531,1531,19,1531_efficient federated learning_learning federated learning_federated learning_learning federated,"['efficient federated learning', 'learning federated learning', 'federated learning', 'learning federated', 'federated learning federated', 'hierarchical federated learning', 'federated learning however', 'federated learning fl', 'efficient federated', 'decentralized machine learning']","['FedPAQ: A Communication-Efficient Federated Learning Method with\n  Periodic Averaging and Quantization   Federated learning is a distributed framework according to which a model is\ntrained over a set of devices, while keeping data localized. This framework\nfaces several systems-oriented challenges which include (i) communication\nbottleneck since a large number of devices upload their local updates to a\nparameter server, and (ii) scalability as the federated network consists of\nmillions of devices. Due to these systems challenges as well as issues related\nto statistical heterogeneity of data and privacy concerns, designing a provably\nefficient federated learning method is of significant importance yet it remains\nchallenging. In this paper, we present FedPAQ, a communication-efficient\nFederated Learning method with Periodic Averaging and Quantization. FedPAQ\nrelies on three key features: (1) periodic averaging where models are updated\nlocally at devices and only periodically averaged at the server; (2) partial\ndevice participation where only a fraction of devices participate in each round\nof the training; and (3) quantized message-passing where the edge nodes\nquantize their updates before uploading to the parameter server. These features\naddress the communications and scalability challenges in federated learning. We\nalso show that FedPAQ achieves near-optimal theoretical guarantees for strongly\nconvex and non-convex loss functions and empirically demonstrate the\ncommunication-computation tradeoff provided by our method.\n', 'Dynamic Fair Federated Learning Based on Reinforcement Learning   Federated learning enables a collaborative training and optimization of\nglobal models among a group of devices without sharing local data samples.\nHowever, the heterogeneity of data in federated learning can lead to unfair\nrepresentation of the global model across different devices. To address the\nfairness issue in federated learning, we propose a dynamic q fairness federated\nlearning algorithm with reinforcement learning, called DQFFL. DQFFL aims to\nmitigate the discrepancies in device aggregation and enhance the fairness of\ntreatment for all groups involved in federated learning. To quantify fairness,\nDQFFL leverages the performance of the global federated model on each device\nand incorporates {\\alpha}-fairness to transform the preservation of fairness\nduring federated aggregation into the distribution of client weights in the\naggregation process. Considering the sensitivity of parameters in measuring\nfairness, we propose to utilize reinforcement learning for dynamic parameters\nduring aggregation. Experimental results demonstrate that our DQFFL outperforms\nthe state-of-the-art methods in terms of overall performance, fairness and\nconvergence speed.\n', 'Communication and Storage Efficient Federated Split Learning   Federated learning (FL) is a popular distributed machine learning (ML)\nparadigm, but is often limited by significant communication costs and edge\ndevice computation capabilities. Federated Split Learning (FSL) preserves the\nparallel model training principle of FL, with a reduced device computation\nrequirement thanks to splitting the ML model between the server and clients.\nHowever, FSL still incurs very high communication overhead due to transmitting\nthe smashed data and gradients between the clients and the server in each\nglobal round. Furthermore, the server has to maintain separate models for every\nclient, resulting in a significant computation and storage requirement that\ngrows linearly with the number of clients. This paper tries to solve these two\nissues by proposing a communication and storage efficient federated and split\nlearning (CSE-FSL) strategy, which utilizes an auxiliary network to locally\nupdate the client models while keeping only a single model at the server, hence\navoiding the communication of gradients from the server and greatly reducing\nthe server resource requirement. Communication cost is further reduced by only\nsending the smashed data in selected epochs from the clients. We provide a\nrigorous theoretical analysis of CSE-FSL that guarantees its convergence for\nnon-convex loss functions. Extensive experimental results demonstrate that\nCSE-FSL has a significant communication reduction over existing FSL techniques\nwhile achieving state-of-the-art convergence and model accuracy, using several\nreal-world FL tasks.\n']","[('efficient federated learning', 0.8109393119812012), ('learning federated learning', 0.7676061987876892), ('federated learning', 0.7387728095054626), ('learning federated', 0.7131357192993164), ('federated learning federated', 0.6983180046081543), ('hierarchical federated learning', 0.6901431679725647), ('federated learning however', 0.6761408448219299), ('federated learning fl', 0.6182279586791992), ('efficient federated', 0.5977281928062439), ('decentralized machine learning', 0.5602120161056519)]"
1532,1532,19,1532_boltzmann collision operator_boltzmann collision_boltzmann operator_linearized boltzmann,"['boltzmann collision operator', 'boltzmann collision', 'boltzmann operator', 'linearized boltzmann', 'boltzmann equations', 'homogeneous boltzmann', 'linearized collision operator', 'boltzmann', 'boltzmann system', 'collision operator']","['Linearized Boltzmann Collision Operator: I. Polyatomic Molecules Modeled\n  by a Discrete Internal Energy Variable and Multicomponent Mixtures   The linearized collision operator of the Boltzmann equation can in a natural\nway be written as a sum of a positive multiplication operator, the collision\nfrequency, and an integral operator. Compactness of the integral operator for\nmonatomic single species is a classical result, while corresponding result for\nmixtures is more recently obtained. In this work the compactness of the\noperator for polyatomic single species, where the polyatomicity is modeled by a\ndiscrete internal energy variable, is studied. With a probabilistic formulation\nof the collision operator as a starting point, compactness is obtained by\nproving that the integral operator is a sum of Hilbert-Schmidt integral\noperators and approximately Hilbert-Schmidt integral operators, under some\nassumptions on the collision kernel. Self-adjointness of the linearized\ncollision operator follows. Moreover, bounds on - including coercivity of - the\ncollision frequency are obtained for a hard sphere model. Then it follows that\nthe linearized collision operator is a Fredholm operator.\n  The results can be extended to mixtures. For brevity, only the case of\nmixtures for monatomic species is accounted for.\n', 'Compactness property of the linearized Boltzmann collision operator for\n  a mixture of monatomic and polyatomic species   The linearized Boltzmann collision operator has a central role in many\nimportant applications of the Boltzmann equation. Recently some important\nclassical properties of the linearized collision operator for monatomic single\nspecies were extended to multicomponent monatomic gases and polyatomic single\nspecies. For multicomponent polyatomic gases, the case where the polyatomicity\nis modelled by a discrete internal energy variable was considered lately. Here\nwe considers the corresponding case for a continuous internal energy variable.\nCompactness results, saying that the linearized operator can be decomposed into\na sum of a positive multiplication operator, the collision frequency, and a\ncompact operator, bringing e.g., self-adjointness, is extended from the\nclassical result for monatomic single species, under reasonable assumptions on\nthe collision kernel. With a probabilistic formulation of the collision\noperator as a starting point, the compactness property is shown by a\ndecomposition, such that the terms are, or at least are uniform limits of,\nHilbert-Schmidt integral operators and therefore are compact operators.\nMoreover, bounds on - including coercivity of - the collision frequency are\nobtained for a hard sphere like, as well as hard potentials with cutoff like,\nmodels, from which Fredholmness of the linearized collision operator follows,\nas well as its domain.\n', ""Compactness property of the linearized Boltzmann collision operator for\n  a multicomponent polyatomic gas   The linearized Boltzmann collision operator is fundamental in many studies of\nthe Boltzmann equation and its main properties are of substantial importance.\nThe decomposition into a sum of a positive multiplication operator, the\ncollision frequency, and an integral operator is trivial. Compactness of the\nintegral operator for monatomic single species is a classical result, while\ncorresponding results for monatomic mixtures and polyatomic single species are\nmore recently obtained. This work concerns the compactness of the operator for\na multicomponent mixture of polyatomic species, where the polyatomicity is\nmodeled by a discrete internal energy variable. With a probabilistic\nformulation of the collision operator as a starting point, compactness is\nobtained by proving that the integral operator is a sum of Hilbert-Schmidt\nintegral operators and operators, which are uniform limits of Hilbert-Schmidt\nintegral operators, under some assumptions on the collision kernel. The\nassumptions are essentially generalizations of the Grad's assumptions for\nmonatomic single species. Self-adjointness of the linearized collision operator\nfollows. Moreover, bounds on - including coercivity of - the collision\nfrequency are obtained for a hard sphere like model. Then it follows that the\nlinearized collision operator is a Fredholm operator, and its domain is also\nobtained.\n""]","[('boltzmann collision operator', 0.72713702917099), ('boltzmann collision', 0.6353542804718018), ('boltzmann operator', 0.5959392189979553), ('linearized boltzmann', 0.5801389813423157), ('boltzmann equations', 0.5548231601715088), ('homogeneous boltzmann', 0.5521554350852966), ('linearized collision operator', 0.515744149684906), ('boltzmann', 0.4927920699119568), ('boltzmann system', 0.4868848919868469), ('collision operator', 0.45745089650154114)]"
1533,1533,19,1533_curves genus_curves genus three_genus curves_genus two curves,"['curves genus', 'curves genus three', 'genus curves', 'genus two curves', 'hyperelliptic curves', 'smooth hyperelliptic curves', 'genus two curve', 'genus curve', 'abelian surfaces', 'curves prym']","['Hyperelliptic genus 3 curves with involutions and a Prym map   We characterise genus 3 complex smooth hyperelliptic curves that contain two\nadditional involutions as curves that can be build from five points in\n$\\mathbb{P}^1$ with a distinguished triple. We are able to write down explicit\nequations for the curves and all their quotient curves. We show that, fixing\none of the elliptic quotient curve, the Prym map becomes a 2:1 map and\ntherefore the hyperelliptic Klein Prym map, constructed recently by the first\nauthor with A. Ortega, is also 2:1 in this case. As a by-product we show an\nexplicit family of $(1, d)$ polarised abelian surfaces (for d > 1), such that\nany surface in the family satisfying a certain explicit condition is abstractly\nnon-isomorphic to its dual abelian surface.\n', 'On the Prym map for cyclic covers of genus two curves   The Prym map assigns to each covering of curves a polarized abelian variety.\nIn the case of unramified cyclic covers of curves of genus two, we show that\nthe Prym map is ramified precisely on the locus of bielliptic covers. The key\nobservation is that we can naturally associate to such a cover an abelian\nsurface with a cyclic polarization, and then the codifferential of the Prym map\ncan be interpreted in terms of multiplication of sections on the abelian\nsurface. Furthermore, we give a different proof of a result by Ramanan that a\ngenus two cyclic cover of degree sufficiently high is never hyperelliptic.\n', 'Pryms of $\\mathbb{Z}_3\\times\\mathbb{Z}_3$ coverings of genus 2 curves   We study unramified Galois $\\mathbb{Z}_3 \\times \\mathbb{Z}_3$ coverings of\ngenus 2 curves and the corresponding Prym varieties and Prym maps. In\nparticular, we prove that any such covering can be reconstructed from its Prym\nvariety, that is, the Prym-Torelli theorem holds for these coverings. We also\ninvestigate the Prym map of unramified $G$-coverings of genus 2 curves for an\narbitrary abelian group $G$. We show that the generic fiber of the Prym map is\nfinite unless $G$ is cyclic of order less than 6\n']","[('curves genus', 0.6507501602172852), ('curves genus three', 0.6461063623428345), ('genus curves', 0.6459097266197205), ('genus two curves', 0.6436315774917603), ('hyperelliptic curves', 0.6426100730895996), ('smooth hyperelliptic curves', 0.6253673434257507), ('genus two curve', 0.611862063407898), ('genus curve', 0.6069886684417725), ('abelian surfaces', 0.5898934006690979), ('curves prym', 0.5530099868774414)]"
1534,1534,19,1534_shrinkage estimators_shrinkage priors_linear estimators_estimators multivariate,"['shrinkage estimators', 'shrinkage priors', 'linear estimators', 'estimators multivariate', 'estimation multivariate', 'estimation matrix', 'mean covariance estimation', 'james stein estimator', 'improved estimation', 'adaptive minimax']","[""Matrix norm shrinkage estimators and priors   We develop a class of minimax estimators for a normal mean matrix under the\nFrobenius loss, which generalizes the James--Stein and Efron--Morris\nestimators. It shrinks the Schatten norm towards zero and works well for\nlow-rank matrices. We also propose a class of superharmonic priors based on the\nSchatten norm, which generalizes Stein's prior and the singular value shrinkage\nprior. The generalized Bayes estimators and Bayesian predictive densities with\nrespect to these priors are minimax. We examine the performance of the proposed\nestimators and priors in simulation.\n"", 'Mean and Covariance Estimation for Discretely Observed High-Dimensional\n  Functional Data: Rates of Convergence and Division of Observational Regimes   Estimation of the mean and covariance parameters for functional data is a\ncritical task, with local linear smoothing being a popular choice. In recent\nyears, many scientific domains are producing multivariate functional data for\nwhich $p$, the number of curves per subject, is often much larger than the\nsample size $n$. In this setting of high-dimensional functional data, much of\ndeveloped methodology relies on preliminary estimates of the unknown mean\nfunctions and the auto- and cross-covariance functions. This paper investigates\nthe convergence rates of local linear estimators in terms of the maximal error\nacross components and pairs of components for mean and covariance functions,\nrespectively, in both $L^2$ and uniform metrics. The local linear estimators\nutilize a generic weighting scheme that can adjust for differing numbers of\ndiscrete observations $N_{ij}$ across curves $j$ and subjects $i$, where the\n$N_{ij}$ vary with $n$. Particular attention is given to the equal weight per\nobservation (OBS) and equal weight per subject (SUBJ) weighting schemes. The\ntheoretical results utilize novel applications of concentration inequalities\nfor functional data and demonstrate that, similar to univariate functional\ndata, the order of the $N_{ij}$ relative to $p$ and $n$ divides\nhigh-dimensional functional data into three regimes (sparse, dense, and\nultra-dense), with the high-dimensional parametric convergence rate of\n$\\left\\{\\log(p)/n\\right\\}^{1/2}$ being attainable in the latter two.\n', ""Double shrinkage priors for a normal mean matrix   We consider estimation of a normal mean matrix under the Frobenius loss.\nMotivated by the Efron--Morris estimator, a generalization of Stein's prior has\nbeen recently developed, which is superharmonic and shrinks the singular values\ntowards zero. The generalized Bayes estimator with respect to this prior is\nminimax and dominates the maximum likelihood estimator. However, here we show\nthat it is inadmissible by using Brown's condition. Then, we develop two types\nof priors that provide improved generalized Bayes estimators and examine their\nperformance numerically. The proposed priors attain risk reduction by adding\nscalar shrinkage or column-wise shrinkage to singular value shrinkage. Parallel\nresults for Bayesian predictive densities are also given.\n""]","[('shrinkage estimators', 0.5713999271392822), ('shrinkage priors', 0.5469474196434021), ('linear estimators', 0.5053429007530212), ('estimators multivariate', 0.49281853437423706), ('estimation multivariate', 0.49149757623672485), ('estimation matrix', 0.487787663936615), ('mean covariance estimation', 0.4854218661785126), ('james stein estimator', 0.477165549993515), ('improved estimation', 0.4704229533672333), ('adaptive minimax', 0.4568040668964386)]"
1535,1535,19,1535_massey products_massey product_galois cohomology_conjecture fields,"['massey products', 'massey product', 'galois cohomology', 'conjecture fields', 'vanishing conjecture', 'massey', 'cohomological dimension', 'galois groups', 'type conjecture', 'cohomology algebra']","['The Massey Vanishing Conjecture for fourfold Massey products modulo 2   We prove the Massey Vanishing Conjecture for $n=4$ and $p=2$. That is, we\nshow that for all fields $F$, if a fourfold Massey product modulo $2$ is\ndefined over $F$, then it vanishes over $F$.\n', 'The symbol length for elementary type pro-$p$ groups and Massey products   For a prime number $p$ and an integer $m\\geq2$, we prove that the symbol\nlength of all elements of $m$-fold Massey products in $H^2(G,\\mathbb{F}_p)$,\nfor pro-$p$ groups $G$ of elementary type, is bounded by $(m^2/4)+m$. Assuming\nthe Elementary Type Conjecture, this applies to all finitely generated maximal\npro-$p$ Galois groups $G=G_F(p)$ of fields $F$ which contain a root of unity of\norder $p$. More generally, we provide such a uniform bound for the symbol\nlength of all pullbacks $\\rho^*(\\bar\\omega)$ of a given cohomology element\n$\\bar\\omega\\in H^n(\\bar G,\\mathbb{F}_p)$, where $\\bar G$ is a finite $p$-group,\n$n\\geq2$, and $\\rho\\colon G\\to \\bar G$ is a pro-$p$ group homomorphism.\n', ""Massey products in Galois cohomology and the Elementary Type Conjecture   Let $p$ be a prime. We prove that a positive solution to Efrat's Elementary\nType Conjecture implies a positive solution to the strengthened version of\nMina\\v{c}--T\\^an's Massey Vanishing Conjecture in the case of finitely\ngenerated maximal pro-$p$ Galois groups whose pro-$p$ cyclotomic character has\ntorsion-free image. Consequently, the maximal pro-$p$ Galois group of a field\n$\\mathbb{K}$ containing a root of 1 of order $p$ (and also \\sqrt{-1} if $p=2$)\nsatisfies the strong $n$-Massey vanishing property for every $n>2$ (which is\nequivalent to the cup-defining $n$-Massey product property for every $n>2$, as\ndefined by Mina\\v{c}--T\\^an) in several relevant cases.\n""]","[('massey products', 0.5575289726257324), ('massey product', 0.5530337691307068), ('galois cohomology', 0.4800110161304474), ('conjecture fields', 0.473331093788147), ('vanishing conjecture', 0.4592756927013397), ('massey', 0.45675718784332275), ('cohomological dimension', 0.4251859784126282), ('galois groups', 0.3960306644439697), ('type conjecture', 0.38700470328330994), ('cohomology algebra', 0.38403525948524475)]"
1536,1536,19,1536_compact lie groups_compact lie group_lie groups_lie group,"['compact lie groups', 'compact lie group', 'lie groups', 'lie group', 'semilinear heat equations', 'lie groups let', 'unimodular lie groups', 'compact lie', 'stratified lie groups', 'associated sobolev']","['Results of existence and uniqueness for the Cauchy problem of semilinear\n  heat equations on stratified Lie groups   The aim of this paper is to give existence and uniqueness results for\nsolutions of the Cauchy problem for semilinear heat equations on stratified Lie\ngroups $\\mathbb{G}$ with the homogeneous dimension $N$. We consider the\nnonlinear function behaves like $|u|^{\\alpha}$ or $|u|^{\\alpha-1}u$\n$(\\alpha>1)$ and the initial data $u_0$ belongs to the Sobolev spaces\n$L^p_s(\\mathbb{G})$ for $1<p<\\infty$ and $0<s<N/p$. Since stratified Lie groups\n$\\mathbb{G}$ include the Euclidean space ${\\mathbb R}^n$ as an example, our\nresults are an extension of the existence and uniqueness results obtained by F.\nRibaud on ${\\mathbb R}^n$ to $\\mathbb{G}$. It should be noted that our proof is\nvery different from it given by Ribaud on ${\\mathbb R}^n$. We adopt the\ngeneralized fractional chain rule on $\\mathbb{G}$ to obtain the estimate for\nthe nonlinear term, which is very different from the paracomposition technique\nadopted by Ribaud on ${\\mathbb R}^n$. By using the generalized fractional chain\nrule on $\\mathbb{G}$, we can avoid the discussion of Fourier analysis on\n$\\mathbb{G}$ and make the proof more simple.\n', 'Nonlinear fractional wave equation on compact Lie groups   Let $G$ be a compact Lie group. In this article, we consider the initial\nvalue fractional wave equation with power-type nonlinearity on $G$. Mainly, we\ninvestigate some $L^{2}-L^{2}$ estimates of the solutions to the homogeneous\nfractional wave equation on $G$ with the help of the group Fourier transform on\n$G$. Further, using the Fourier analysis on compact Lie groups, we prove a\nlocal in-time existence result in the energy space. Moreover, under certain\nconditions on the initial data, a finite time blow-up result is established. We\nalso derive a sharp lifespan for local (in-time) solutions. Finally, we\nconsider the space-fractional wave equation with a regular mass term depending\non the position and study the well-posedness of the fractional Klein-Gordon\nequation on compact Lie groups.\n', 'Nonlinear fractional damped wave equation on compact Lie groups   In this paper, we deal with the initial value fractional damped wave equation\non $G$, a compact Lie group, with power-type nonlinearity. The aim of this\nmanuscript is twofold. First, using the Fourier analysis on compact Lie groups,\nwe prove a local in-time existence result in the energy space for the\nfractional damped wave equation on $G$. Moreover, a finite time blow-up result\nis established under certain conditions on the initial data. In the next part\nof the paper, we consider fractional wave equation with lower order terms, that\nis, damping and mass with the same power type nonlinearity on compact Lie\ngroups, and prove the global in-time existence of small data solutions in the\nenergy evolution space.\n']","[('compact lie groups', 0.5548768043518066), ('compact lie group', 0.5472068786621094), ('lie groups', 0.4915950298309326), ('lie group', 0.4812968373298645), ('semilinear heat equations', 0.4569815695285797), ('lie groups let', 0.45174258947372437), ('unimodular lie groups', 0.4352928102016449), ('compact lie', 0.4327276647090912), ('stratified lie groups', 0.4237993657588959), ('associated sobolev', 0.42220062017440796)]"
1537,1537,19,1537_globally hyperbolic lorentzian_lorentzian manifold_lorentzian manifolds_dirichlet neumann map,"['globally hyperbolic lorentzian', 'lorentzian manifold', 'lorentzian manifolds', 'dirichlet neumann map', 'riemannian manifolds boundary', 'hyperbolic lorentzian', 'lorentzian metrics', 'riemannian manifolds', 'dirichlet neumann', 'riemannian']","['The Dirichlet-to-Neumann map for a semilinear wave equation on\n  Lorentzian manifolds   We consider the semilinear wave equation $\\Box_g u+a u^4=0$, $a\\neq 0$, on a\nLorentzian manifold $(M,g)$ with timelike boundary. We show that from the\nknowledge of the Dirichlet-to-Neumann map one can recover the metric $g$ and\nthe coefficient $a$ up to natural obstructions. Our proof rests on the analysis\nof the interaction of distorted plane waves together with a scattering control\nargument, as well as Gaussian beam solutions.\n', ""Rigidity in the Lorentzian Calder\\'on problem with formally determined\n  data   We study the Lorentzian Calder\\'on problem, where the objective is to\ndetermine a globally hyperbolic Lorentzian metric up to a boundary fixing\ndiffeomorphism from boundary measurements given by the hyperbolic\nDirichlet-to-Neumann map. This problem is a wave equation analogue of the\nCalder\\'on problem on Riemannian manifolds. We prove that if a globally\nhyperbolic metric agrees with the Minkowski metric outside a compact set and\nhas the same hyperbolic Dirichlet-to-Neumann map as the Minkowski metric, then\nit must be the Minkowski metric up to diffeomorphism. In fact we prove the same\nresult with a much smaller amount of measurements, thus solving a formally\ndetermined inverse problem. To prove these results we introduce a new method\nfor geometric hyperbolic inverse problems. The method is based on distorted\nplane wave solutions and on a combination of geometric, topological and unique\ncontinuation arguments.\n"", 'Reconstruction of a Lorentzian manifold from its Dirichlet-to-Neumann\n  map   We prove that the Dirichlet-to-Neumann map of the linear wave equation\ndetermines the topological, differentiable and conformal structure of the\nunderlying Lorentzian manifold, under mild technical assumptions. With more\nstringent geometric assumptions, the full Lorentzian structure of the manifold\ncan be recovered as well. The key idea of the proof is to show that the\nsingular support of the Schwartz kernel of the Dirichlet-to-Neumann map of a\nmanifold completely determines the so-called boundary light observation set of\nthe manifold together with its natural causal structure.\n']","[('globally hyperbolic lorentzian', 0.5987824201583862), ('lorentzian manifold', 0.590350866317749), ('lorentzian manifolds', 0.5802465081214905), ('dirichlet neumann map', 0.5744107961654663), ('riemannian manifolds boundary', 0.5675668120384216), ('hyperbolic lorentzian', 0.561511218547821), ('lorentzian metrics', 0.5275015830993652), ('riemannian manifolds', 0.5213881731033325), ('dirichlet neumann', 0.510452926158905), ('riemannian', 0.4950428307056427)]"
1538,1538,19,1538_porous medium equations_transport equations_diffusion system_pressure gradient,"['porous medium equations', 'transport equations', 'diffusion system', 'pressure gradient', 'free boundary problems', 'cross diffusion system', 'cross diffusion systems', 'free boundary', 'diffusion systems', 'medium equations']","['Convergence of Free Boundaries in the Incompressible Limit of Tumor\n  Growth Models   We investigate the general Porous Medium Equations with drift and source\nterms that model tumor growth. Incompressible limit of such models has been\nwell-studied in the literature, where convergence of the density and pressure\nvariables are established, while it remains unclear whether the free boundaries\nof the solutions exhibit convergence as well. In this paper, we provide an\naffirmative result by showing that the free boundaries converge in the\nHausdorff distance in the incompressible limit. To achieve this, we quantify\nthe relation between the free boundary motion and spatial average of the\npressure, and establish a uniform-in-$m$ strict expansion property of the\npressure supports. As a corollary, we derive upper bounds for the Hausdorff\ndimensions of the free boundaries and show that the limiting free boundary has\nfinite $(d-1)$-dimensional Hausdorff measure.\n', ""Free boundary limit of tumor growth model with nutrient   Both compressible and incompressible porous medium models are used in the\nliterature to describe the mechanical properties of living tissues. These two\nclasses of models can be related using a stiff pressure law. In the\nincompressible limit, the compressible model generates a free boundary problem\nof Hele-Shaw type where incompressibility holds in the saturated phase. Here we\nconsider the case with a nutrient. Then, a badly coupled system of equations\ndescribes the cell density number and the nutrient concentration. For that\nreason, the derivation of the free boundary (incompressible) limit was an open\nproblem, in particular a difficulty is to establish the so-called\ncomplementarity relation which allows to recover the pressure using an elliptic\nequation. To establish the limit, we use two new ideas. The first idea, also\nused recently for related problems, is to extend the usual Aronson-B\\'enilan\nestimates in $L^\\infty$ to an $L^2$ setting. The second idea is to derive a\nsharp uniform $L^4$ estimate on the pressure gradient, independently of space\ndimension.\n"", 'Phenotypic heterogeneity in a model of tumor growth: existence of\n  solutions and incompressible limit   We consider a (degenerate) cross-diffusion model of tumor growth structured\nby phenotypic trait. We prove the existence of weak solutions and the\nincompressible limit as the pressure becomes stiff extending methods recently\nintroduced in the context of two-species cross-diffusion systems. In the\nstiff-pressure limit, the compressible model generates a free boundary problem\nof Hele-Shaw type. Moreover, we prove a new L4-bound on the pressure gradient.\n']","[('porous medium equations', 0.5378955602645874), ('transport equations', 0.45164409279823303), ('diffusion system', 0.44646790623664856), ('pressure gradient', 0.43703004717826843), ('free boundary problems', 0.4277043342590332), ('cross diffusion system', 0.4182300567626953), ('cross diffusion systems', 0.4167974293231964), ('free boundary', 0.4167180359363556), ('diffusion systems', 0.4139203429222107), ('medium equations', 0.4056563079357147)]"
1539,1539,19,1539_operator harmonic_operator theory_cauchy riemann operator_functions operators,"['operator harmonic', 'operator theory', 'cauchy riemann operator', 'functions operators', 'riemann operator', 'holomorphic functions', 'spectral theory', 'generalized cauchy', 'hyperholomorphic', 'mathcal functional']","['On the harmonic generalized Cauchy-Kovalevskaya extension and its\n  connection with the Fueter-Sce theorem   One of the primary objectives of this paper is to establish a generalized\nCauchy-Kovalevskaya extension for axially harmonic functions. We demonstrate\nthat the result can be expressed as a power series involving Bessel-type\nfunctions of specific differential operators acting on two initial functions.\nAdditionally, we analyze the decomposition of the harmonic CK extension in\nterms of integrals over the sphere $ \\mathbb{S}^{m-1} $ involving functions of\nplane wave type.\n  Another key goal of this paper is to explore the relationship between the\nharmonic Cauchy-Kovalevskaya extension and the Fueter-Sce theorem. The\nFueter-Sce theorem outlines a two-step process for constructing axially\nmonogenic functions in $ \\mathbb{R}^{m+1}$ starting from holomorphic functions\nin one complex variable. The first step generates the class of slice monogenic\nfunctions, while the second step produces axially monogenic functions by\napplying the pointwise differential operator $\n\\Delta_{\\mathbb{R}{^{m+1}}}^{\\frac{m-1}{2}} $ with $m$ being odd, known as the\nFueter-Sce map, to a slice monogenic function.\n  By suitably factorizing the Fueter-Sce map, we introduce the set of axially\nharmonic functions, which serves as an intermediate class between slice\nmonogenic and axially monogenic functions. In this paper, we establish a\nconnection between the harmonic CK extension and the factorization of the\nFueter-Sce map. This connection leads to a new notion of harmonic polynomials,\nwhich we show to form a basis for the Riesz potential. Finally, we also\nconstruct a basis for the space of axially harmonic functions.\n', 'An introduction to the fine structures on the $S$-spectrum   Holomorphic functions are fundamental in operator theory and their Cauchy\nformula is a crucial tool for defining functions of operators. The Fueter-Sce\nextension theorem (often called Fueter-Sce mapping theorem) provides a two-step\nprocedure for extending holomorphic functions to hyperholomorphic functions. In\nthe first step, slice hyperholomorphic functions are obtained, and their\nassociated Cauchy formula establishes the $S$-functional calculus for\nnoncommuting operators on the $S$-spectrum. The second step produces axially\nmonogenic functions, which lead to the development of the monogenic functional\ncalculus. In this review paper we discuss the second operator in the Fueter-Sce\nmapping theorem that takes slice hyperholomorphic to axially monogenic\nfunctions. This operator admits several factorizations which generate various\nfunction spaces and their corresponding functional calculi, thereby forming the\nso-called fine structures of spectral theories on the $S$-spectrum.\n', 'The Fueter-Sce mapping and the Clifford-Appell polynomials   The Fueter-Sce theorem provides a procedure to obtain axially monogenic\nfunctions, which are in the kernel of generalized Cauchy-Riemann operator in $\n\\mathbb{R}^{n+1}$. This result is obtained by using two operators. The first\none is the slice operator, which extends holomorphic functions of one complex\nvariable to slice monogenic functions in $ \\mathbb{R}^{n+1}$. The second one is\na suitable power of the Laplace operator in $n+1$ variables. Another way to get\naxially monogenic functions is the generalized Cauchy-Kovalevskaya (CK)\nextension. This characterizes axial monogenic functions by their restriction to\nthe real line. In this paper, using the connection between the Fueter-Sce map\nand the generalized CK-extension, we explicitly compute the actions\n$\\Delta_{\\mathbb{R}^{n+1}}^{\\frac{n-1}{2}} x^k$, where $x \\in\n\\mathbb{R}^{n+1}$. The expressions obtained is related to a well-known class of\nClifford-Appell polynomials. These are the building blocks to write a Taylor\nseries for axially monogenic functions. Moreover, we focus on some elementary\naxially monogenic functions, where the action of the Fueter-Sce map and the\ngeneralized CK-extension coincide. In order to get algebraic relations between\nthe elementary functions, as in complex analysis, we define a new product\nbetween axially monogenic functions. By using the connections between the\nFueter-Sce map and the generalized CK extension we characterize the range and\nthe kernel of the Fueter-Sce map. Furthermore, we focus on studying the\nClifford-Appell-Fock space and the Clifford-Appell-Hardy space. Finally, using\nthe polyanalytic Fueter-Sce theorems we obtain a new family of polyanalytic\nmonogenic polynomials, which extends to higher dimensions the Clifford-Appell\npolynomials.\n']","[('operator harmonic', 0.4562351405620575), ('operator theory', 0.45112207531929016), ('cauchy riemann operator', 0.45068395137786865), ('functions operators', 0.4495086371898651), ('riemann operator', 0.4472147524356842), ('holomorphic functions', 0.43647539615631104), ('spectral theory', 0.430364727973938), ('generalized cauchy', 0.42983317375183105), ('hyperholomorphic', 0.4253844916820526), ('mathcal functional', 0.42125123739242554)]"
1540,1540,19,1540_spectral singularities_spectral properties_spectral flow_spectral,"['spectral singularities', 'spectral properties', 'spectral flow', 'spectral', 'perturbed operator', 'sturm liouville operators', 'singular sturm liouville', 'liouville operators', 'sturm liouville operator', 'spectrum']","['Spectral flow inside essential spectrum II: resonance set and its\n  structure   This paper is a continuation of the study of spectral flow inside essential\nspectrum initiated in \\cite{AzSFIES}. Given a point $\\lambda$ outside the\nessential spectrum of a self-adjoint operator $H_0,$ the resonance set,\n$\\mathcal R(\\lambda),$ is an analytic variety which consists of self-adjoint\nrelatively compact perturbations $H_0+V$ of $H_0,$ for which $\\lambda$ is an\neigenvalue. One may ask for criteria for the vector $V$ to be tangent to the\nresonance set. Such criteria were given in \\cite{AzSFnRI}.\n  In this paper we study similar criteria for the case of $\\lambda$ inside the\nessential spectrum of $H_0.$ For the case $\\lambda \\in \\sigma_{ess}(H_0)$ the\nresonance set is defined in terms of the well-known limiting absorption\nprinciple. Among the results of this paper is that the resonance set contains\nplenty of straight lines, moreover, given any regular relatively compact\nperturbation $V$ there exists a finite rank self-adjoint operator, $\\tilde V,$\nsuch that the straight line $H_0 + \\mathbb R(V-\\tilde V)$ belongs to the\nresonance set.\n  Another result of this paper is that inside the essential spectrum there\nexist plenty of transversal to the resonance set perturbations $V$ which have\norder $\\geq 2,$ in contrast to what happens outside the essential spectrum,\n\\cite{AzSFnRI}.\n', 'Singular Boundary Conditions for Sturm--Liouville Operators via\n  Perturbation Theory   We show that all self-adjoint extensions of semi-bounded Sturm--Liouville\noperators with general limit-circle endpoint(s) can be obtained via an additive\nsingular form bounded self-adjoint perturbation of rank equal to the deficiency\nindices, say $d\\in\\{1,2\\}$. This characterization generalizes the well-known\nanalog for semi-bounded Sturm--Liouville operators with regular endpoints.\nExplicitly, every self-adjoint extension of the minimal operator can be written\nas \\begin{align*}\n  \\boldsymbol{A}_\\Theta=\\boldsymbol{A}_0+{\\bf B}\\Theta{\\bf B}^*, \\end{align*}\nwhere $\\boldsymbol{A}_0$ is a distinguished self-adjoint extension and $\\Theta$\nis a self-adjoint linear relation in $\\mathbb{C}^d$. The perturbation is\nsingular in the sense that it does not belong to the underlying Hilbert space\nbut is form bounded with respect to $\\boldsymbol{A}_0$, i.e. it belongs to\n$\\mathcal{H}_{-1}(\\boldsymbol{A}_0)$. The construction of a boundary triple and\ncompatible boundary pair for the symmetric operator ensure that the\nperturbation is well-defined and self-adjoint extensions are in a one-to-one\ncorrespondence with self-adjoint relations $\\Theta$.\n  As an example, self-adjoint extensions of the classical symmetric Jacobi\ndifferential equation (which has two limit-circle endpoints) are obtained and\ntheir spectra are analyzed with tools both from the theory of boundary triples\nand perturbation theory.\n', 'Spectral flow inside essential spectrum IV: $F^*F$ is a regular\n  direction   Let~$H_0$ and~$V$ be self-adjoint operators such that~$V$ admits a\nfactorisation $V = F^*JF$ with bounded self-adjoint $J$ and\n$|H_0|^{1/2}$-compact~$F.$ Flow of singular spectrum of the path of\nself-adjoint operators $H_0 + rV,$ $r \\in \\mathbb R,$ -- also called spectral\nflow, through a point $\\lambda$ outside the essential spectrum of~$H_0$ is well\nstudied, and appears in such diverse areas as differential geometry and\ncondensed matter physics. Inside the essential spectrum the spectral flow\nthrough $\\lambda$ for such a path is well-defined if the norm limit $$\n  \\lim_{y \\to 0^+} F (H_0 + r V - \\lambda - iy)^{-1} F^* $$ exists for at least\none value of the coupling variable $r \\in \\mathbb R$. This raises the question:\ngiven a self-adjoint operator~$H_0$ and $|H_0|^{1/2}$-compact operator $F,$ for\nwhich real numbers $\\lambda$ there exists a bounded self-adjoint operator $J$\nsuch that the limit above exists? Real numbers $\\lambda$ for which this\nstatement is true we call semi-regular and the operator $V = F^*JF$ we call a\nregular direction for~$H_0$ at $\\lambda.$ In this paper we prove that $\\lambda$\nis semi-regular for~$H_0$ if and only if the direction $F^*F$ is regular.\n']","[('spectral singularities', 0.6375836730003357), ('spectral properties', 0.5166769027709961), ('spectral flow', 0.4985375702381134), ('spectral', 0.49175116419792175), ('perturbed operator', 0.4837392568588257), ('sturm liouville operators', 0.4682108461856842), ('singular sturm liouville', 0.4614509046077728), ('liouville operators', 0.438103586435318), ('sturm liouville operator', 0.4354356825351715), ('spectrum', 0.407383531332016)]"
1541,1541,19,1541_holomorphic mappings_complex banach space_complex banach_holomorphically,"['holomorphic mappings', 'complex banach space', 'complex banach', 'holomorphically', 'holomorphic', 'analytic functions unit', 'bounded analytic functions', 'bounded analytic', 'unit ball complex', 'banach space']","['Nonlinear resolvents: distortion and order of starlikeness   This paper presents a new approach to studying nonlinear resolvents of\nholomorphically accretive mappings on the open unit ball of a complex Banach\nspace. We establish a distortion theorem and apply it to address problems in\ngeometric function theory concerning the class of resolvents. Specifically, we\nprove the accretivity of resolvents and provide estimates for the squeezing\nratio. Further, we show that nonlinear resolvents are starlike mappings of\ncertain order and determine lower bounds for this order.\n', 'Multidimensional analogs of the Fekete--Szeg\\""{o} functional   In this paper we introduce the Fekete--Szeg\\""{o} type mapping in the open\nunit ball of a complex Banach space. % and study its geometric and analytical\nproperties. All previously studied modifications of the Fekete--Szeg\\""{o}\nfunctional are either special cases or `components\' of the mapping we\nintroduce.\n  The study involves the examination of transforms of the Fekete--Szeg\\""o\nmapping under specific transformations applied to given holomorphic mappings.\n  We show that for a mapping $f$, the third order Fr\\\'eshet derivative of the\ninverse mapping $f^{-1}$ and of elements of the semigroup generated by $f$ can\nbe expressed in terms of the Fekete--Szeg\\""{o} mapping. Estimates of the\nFekete--Szeg\\""o mapping over some subclasses of semigroup generators and of\nstarlike mappings are also presented.\n', 'The Fekete--Szeg\\""{o} problem for spirallike mappings and non-linear\n  resolvents in Banach spaces   We study the Fekete--Szeg\\""{o} problem on the open unit ball of a complex\nBanach space. Namely, the Fekete--Szeg\\""{o} inequalities are proved for the\nclass of spirallike mappings relative to an arbitrary strongly accretive\noperator, and some of its subclasses. Next, we consider families of non-linear\nresolvents for holomorphically accretive mappings vanishing at the origin. We\nsolve the Fekete--Szeg\\""{o} problem over these families.\n']","[('holomorphic mappings', 0.6594766974449158), ('complex banach space', 0.5918171405792236), ('complex banach', 0.5850280523300171), ('holomorphically', 0.5091519951820374), ('holomorphic', 0.47203516960144043), ('analytic functions unit', 0.46269986033439636), ('bounded analytic functions', 0.4490315914154053), ('bounded analytic', 0.43862083554267883), ('unit ball complex', 0.4367048144340515), ('banach space', 0.4198266863822937)]"
1542,1542,19,1542_univalent polynomials_inequalities polynomials_well known polynomial_polynomial inequalities,"['univalent polynomials', 'inequalities polynomials', 'well known polynomial', 'polynomial inequalities', 'known polynomial', 'polynomials real coefficients', 'complex polynomial', 'type polynomials', 'polynomials real', 'zeros polynomial']","[""Annular bounds for the zeros of a polynomial from companion matrix   Let $p(z)=z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+\\ldots+a_1z+a_0$ be a complex\npolynomial with $a_0\\neq 0$ and $n\\geq 3$. Several new upper bounds for the\nmoduli of the zeros of $p$ are developed. In particular, if\n$\\alpha=\\sqrt{\\sum_{j=0}^{n-1}|a_j|^2}$ and $z$ is any zero of $p$, then we\nshow that \\begin{eqnarray*}\n  |z|^2 &\\leq & \\cos^2 \\frac{\\pi}{n+1}+|a_{n-2}|+ \\frac{1}{4} \\left (\n|a_{n-1}|+ { \\alpha} \\right)^2 + \\frac{1}{2}\\sqrt{\\alpha^2-|a_{n-1}|^2} +\n\\frac{1}{2}{\\alpha}, \\end{eqnarray*} which is sharper than the Abu-Omar and\nKittaneh's bound \\begin{eqnarray*}\n  |z|^2 &\\leq & \\cos^2 \\frac{\\pi}{n+1}+ \\frac{1}{4} \\left ( |a_{n-1}|+ {\n\\alpha}\\right)^2 + {\\alpha} \\end{eqnarray*} if and only if $2|a_{n-2}|<\n\\sqrt{\\sum_{j=0}^{n-1}|a_j|^2}-\\sqrt{\\sum_{j=0}^{n-2}|a_j|^2}. $ The upper\nbounds obtained here enable us to describe smaller annuli in the complex plane\ncontaining all the zeros of $p$.\n"", ""An extremal problem for odd univalent polynomials   For the univalent polynomials $F(z) = \\sum\\limits_{j=1}^{N} a_j z^{2j-1}$\nwith real coefficients and normalization \\(a_1 = 1\\) we solve the extremal\nproblem \\[\n  \\min_{a_j:\\,a_1=1} \\left( -iF(i) \\right) = \\min_{a_j:\\,a_1=1}\n\\sum\\limits_{j=1}^{N} {(-1)^{j+1} a_j}. \\] We show that the solution is\n$\\frac12 \\sec^2{\\frac{\\pi}{2N+2}},$ and the extremal polynomial \\[\n  \\sum_{j = 1}^N \\frac{U'_{2(N-j+1)} \\left(\n\\cos\\left(\\frac{\\pi}{2N+2}\\right)\\right)}{U'_{2N} \\left(\n\\cos\\left(\\frac{\\pi}{2N+2}\\right)\\right)}z^{2j-1} \\] is unique and univalent,\nwhere the $U_j(x)$ are the Chebyshev polynomials of the second kind and\n$U'_j(x)$ denotes the derivative. As an application, we obtain the estimate of\nthe Koebe radius for the odd univalent polynomials in $\\mathbb D$ and formulate\nseveral conjectures.\n"", ""Koebe's theorem for trinomials with fold symmetry   The Koebe problem for univalent polynomials with real coefficients is fully\nsolved only for trinomials, which means that in this case the Koebe radius and\nthe extremal polynomial (extremizer) have been found. The general case remains\nopen, but conjectures have been formulated. The corresponding conjectures have\nalso been hypothesized for univalent polynomials with real coefficients and\n$T$-fold rotational symmetry. This paper provides confirmation of these\nhypotheses for trinomials $z + az^{T + 1} + bz^{2T + 1}$. Namely, the Koebe\nradius is $r=4\\cos^2 \\frac{\\pi(1+T)}{2+3T}$, and the only extremizer of the\nKoebe problem is the trinomial \\begin{gather*}\nB^{(T)}(z)=z+\\frac2{2+3T}\\left(-T+(2+2T)\\cos\\frac{\\pi T}{2+3T}\\right)z^{1+T}+\\\\\n+\\frac1{2+3T}\\left(2+T-2T\\cos\\frac{\\pi T}{2+3T}\\right)z^{1+2T}. \\end{gather*}\n  Key words and phrases: Koebe one-quarter theorem, Koebe radius, univalent\npolynomial, trinomials with fold symmetry.\n""]","[('univalent polynomials', 0.5118004083633423), ('inequalities polynomials', 0.5088222026824951), ('well known polynomial', 0.4746941924095154), ('polynomial inequalities', 0.4707393944263458), ('known polynomial', 0.4645637273788452), ('polynomials real coefficients', 0.43318724632263184), ('complex polynomial', 0.428219735622406), ('type polynomials', 0.3959599435329437), ('polynomials real', 0.3930774927139282), ('zeros polynomial', 0.39125174283981323)]"
1543,1543,19,1543_adic hodge theory_adic cohomology_adic hodge_adic sheaves,"['adic hodge theory', 'adic cohomology', 'adic hodge', 'adic sheaves', 'hodge theory', 'adic etale', 'etale cohomology', 'hodge structures', 'hodge structure', 'adic field']","['Linear relations of p-adic periods of 1-motives (thesis)   In this thesis, we aim to develop p-adic analogs of known results for\nclassical periods, focusing specifically on 1-motives. We establish an\nintegration theory for 1-motives with good reductions, which generalizes the\nColmez-Fontaine-Messing p-adic integration for abelian varieties with good\nreductions. We also compare the integration pairing with other pairings such as\nthose induced by crystalline theory. Additionally, we introduce a formalism for\nperiods and formulate p-adic period conjectures related to p-adic periods\narising from this integration pairing. Broadly, our p-adic period conjecture\noperates at different depths, with each depth revealing distinct relations\namong the p-adic periods. Notably, the classical period conjecture\n(Kontsevich-Zanier conjecture over $\\bar{\\mathbb{Q}}$) for 1-periods fits\nwithin our framework, and, according to the classical subgroup theorem of\nHuber-W\\""ustholz for 1-motives, the conjecture for classical periods of\n1-motives holds true at depth 1. Finally, we identify three\n$\\mathbb{Q}$-structures arising from $\\bar{\\mathbb{Q}}$-rational points of the\nformal p-divisible group associated with a 1-motive $M$ with a good reduction\nat $p$, and we prove p-adic period conjectures at depths 2 and 1, relative to\nperiods induced by the p-adic integration of $M$ and these\n$\\mathbb{Q}$-structures. Our proof involves a p-adic version of the subgroup\ntheorem that we obtain for 1-motives with good reductions.\n', ""Nilpotent orbit theorem in $p$-adic Hodge theory   We state and prove three orbit theorems on the period domains for the\n$p$-adic Hodge structure analogous to the complex case. We shall consider the\nvariation of de Rham (resp. \\'etale) cohomology in a family of projective\nvarieties $f:\\mathfrak{X} \\to S$ defined over a p-adic field. First, we show\nthat any nilpotent orbit in the period domain of p-adic Hodge structures\nconverges to a semistable point (filtration) in the period domain of the p-adic\nHodge structure. Furthermore, the nilpotent orbits of the limit point are\nasymptotic to the twisted period map [Theorem \\ref{thm:nilpotent-orbit}]. The\norbit theorems come with some estimates of the distance between the nilpotent\norbit and the twisted period map. The distance estimate in the p-adic nilpotent\norbit theorem is given concerning the non-archimedean metric and is based on\nthe p-adic Fourier analysis of Amice-Schneider. The result is analogous to the\norbit theorems of W. Schmid [\\cite{Sch}-1973] on complex Hodge structures. Our\nproof is based on a \\textit{Geometric Invariant Theory} (GIT) criterion for\nsemi-stability (Kempf-Ness theorem) and estimates from the (Amice-Schneider)\np-adic Fourier theory. We also state the $SL_2$-orbit theorem in the p-adic\ncase, [Theorem \\ref{th:homomorphism}]. Finally, we explain how the nilpotent\norbit theorem should be modified and stated for a variation of the mixed Hodge\nstructure [Theorem \\ref{thm:mixed-orbit}].}\n"", ""On the $p$-adic pro-\\'etale cohomology of Drinfeld symmetric spaces   Via the relative fundamental exact sequence of $p$-adic Hodge theory, we\ndetermine the geometric $p$-adic pro-\\'etale cohomology of the Drinfeld\nsymmetric spaces defined over a $p$-adic field, thus giving an alternative\nproof of a theorem of Colmez-Dospinescu-Niziol. Along the way, we describe, in\nterms of differential forms, the geometric pro-\\'etale cohomology of the\npositive de Rham period sheaf on any connected, paracompact, smooth\nrigid-analytic variety over a $p$-adic field, and we do it with coefficients. A\nkey new ingredient is the condensed mathematics recently developed by\nClausen-Scholze.\n""]","[('adic hodge theory', 0.7063412070274353), ('adic cohomology', 0.5977701544761658), ('adic hodge', 0.5648791790008545), ('adic sheaves', 0.5597797632217407), ('hodge theory', 0.5511614680290222), ('adic etale', 0.5215464234352112), ('etale cohomology', 0.5198260545730591), ('hodge structures', 0.5156510472297668), ('hodge structure', 0.49168217182159424), ('adic field', 0.46931329369544983)]"
1544,1544,19,1544_thz wireless_thz communications_terahertz thz wireless_thz frequency,"['thz wireless', 'thz communications', 'terahertz thz wireless', 'thz frequency', 'thz communication', 'wireless link', 'rf wireless', 'channel fading', 'wireless system', 'wireless']","[""Fixed-Gain AF Relaying for RF-THz Wireless System over\n  $\\alpha$-$\\kappa$-$\\mu$ Shadowed and $\\alpha$-$\\mu$ Channels   Recent research investigates the decode-and-forward (DF) relaying for mixed\nradio frequency (RF) and terahertz (THz) wireless links with zero-boresight\npointing errors. In this letter, we analyze the performance of a fixed-gain\namplify-and-forward (AF) relaying for the RF-THz link to interface the access\nnetwork on the RF technology with wireless THz transmissions. We develop\nprobability density function (PDF) and cumulative distribution function (CDF)\nof the end-to-end SNR for the relay-assisted system in terms of bivariate Fox's\nH function considering $\\alpha$-$\\mu$ fading for the THz system with non-zero\nboresight pointing errors and $\\alpha$-$\\kappa$-$\\mu$ shadowed ($\\alpha$-KMS)\nfading model for the RF link. Using the derived PDF and CDF, we present exact\nanalytical expressions of the outage probability, average bit-error-rate (BER),\nand ergodic capacity of the considered system. We also analyze the outage\nprobability and average BER asymptotically for a better insight into the system\nbehavior at high SNR. We use simulations to compare the performance of the AF\nrelaying having a semi-blind gain factor with the recently proposed DF relaying\nfor THz-RF transmissions.\n"", ""Performance Analysis of Cooperative Relaying for Multi-Antenna RF\n  Transmissions over THz Wireless Link   Recent research has focused on single antenna radio-frequency (RF) and\nterahertz (THz) wireless systems to mix the access link with the backhaul. In\nthis paper, we evaluate the performance of a mixed RF-THz system employing\nmultiple antenna-assisted access point (AP) for the RF link and single-antenna\nTHz transmissions. We employ an equal gain combining (EGC) receiver at the AP\nand use the fixed-gain amplify and forward (AF) relaying protocol to interface\nthe RF and THz links. We derive analytical expressions for probability density\nfunction (PDF) and cumulative distribution function (CDF) of the end-to-end SNR\nfor the considered system assuming independent and non-identically distributed\n(i.ni.d.) $\\alpha$-$\\mu$ distribution to model for both RF and THz channels and\npointing errors in the THz link. We analyze the system performance using the\noutage probability, average bit error rate (BER), and ergodic capacity\ninvolving bivariate Fox's H-function. We use the residue method to develop\nasymptotic analysis using Gamma functions to show the impact of the various\nchannel and system parameters on the outage probability and average BER in the\nhigh SNR regime. We use computer simulations to depict the scaling of the\nperformance with an increase in the number of antennas at the AP for signal\nreception in the access link.\n"", 'Performance of Hybrid THz and Multi-Antenna RF System with Diversity\n  Combining   Recent studies investigate single-antenna radio frequency (RF) systems mixed\nwith terahertz (THz) wireless communications. This paper considers a two-tier\nsystem of THz for backhaul and multiple-antenna assisted RF for the access\nnetwork. We analyze the system performance by employing both selection\ncombining (SC) and maximal ratio combining (MRC) receivers for the RF link\nintegrated with the THz using the fixed-gain amplify and forward (AF) protocol.\nWe develop the probability density function (PDF) and cumulative distribution\nfunction (CDF) of the end-to-end signal-to-noise (SNR) of the dual-hop system\nover independent and non-identically distributed (i.ni.d.) $\\alpha$-$\\mu$\nfading channels with a statistical model for misalignment errors in the THz\nwireless link. We use the derived statistical results to develop analytical\nexpressions of the outage probability, average bit error rate (BER), and\nergodic capacity for the performance assessment of the considered system. We\ndevelop diversity order of the system using asymptotic analysis in the high SNR\nregion, demonstrating the scaling of system performance with the number of\nantennas. We use computer simulations to show the effect of system and channel\nparameters on the performance of the hybrid THz-RF link with multi-antenna\ndiversity schemes.\n']","[('thz wireless', 0.5380759239196777), ('thz communications', 0.53730309009552), ('terahertz thz wireless', 0.5274506211280823), ('thz frequency', 0.46237602829933167), ('thz communication', 0.4589943289756775), ('wireless link', 0.4423834979534149), ('rf wireless', 0.43084004521369934), ('channel fading', 0.424466997385025), ('wireless system', 0.36367058753967285), ('wireless', 0.35009393095970154)]"
1545,1545,19,1545_equiangular tight frames_tight frames etfs_orthogonal frames_equiangular tight frame,"['equiangular tight frames', 'tight frames etfs', 'orthogonal frames', 'equiangular tight frame', 'tight frames', 'frames', 'orthogonal designs', 'equi dimensional', 'tight frame', 'frames can']","[""Frames over finite fields: Basic theory and equiangular lines in unitary\n  geometry   We introduce the study of frames and equiangular lines in classical\ngeometries over finite fields. After developing the basic theory, we give\nseveral examples and demonstrate finite field analogs of equiangular tight\nframes (ETFs) produced by modular difference sets, and by translation and\nmodulation operators. Using the latter, we prove that Gerzon's bound is\nattained in each unitary geometry of dimension $d = 2^{2l+1}$ over the field\n$\\mathbb{F}_{3^2}$. We also investigate interactions between complex ETFs and\nthose in finite unitary geometries, and we show that every complex ETF implies\nthe existence of ETFs with the same size over infinitely many finite fields.\n"", ""$k$-Homogeneous Equiangular Tight Frames   Equiangular tight frames (ETFs) are optimal packings in projective space\nwhich also yield useful decompositions of signals. Paley ETFs are constructed\nusing number theory. In this article, we present the doubly homogeneous\nautomorphism groups of the Paley ETFs of prime order. We also prove some\nproperties of doubly homogeneous frames, namely that they are always ETFs and\nthat their short circuits -- i.e., dependent subsets of minimum size -- form a\nbalanced incomplete block design. We additionally characterize all\n$k$-homogeneous ETFs for $3 \\leq k \\leq 5$. Finally, we revisit David Larson's\nAMS Memoirs \\emph{Frames, Bases, and Group Representations} coauthored with\nDeguang Han and \\emph{Wandering Vectors for Unitary Systems and Orthogonal\nWavelets} coauthored with Xingde Dai with a modern eye and focus on\nfinite-dimensional Hilbert spaces.\n"", 'Mutually Unbiased Equiangular Tight Frames   An equiangular tight frame (ETF) yields a type of optimal packing of lines in\na Euclidean space. ETFs seem to be rare, and all known infinite families of\nthem arise from some type of combinatorial design. In this paper, we introduce\na new method for constructing ETFs. We begin by showing that it is sometimes\npossible to construct multiple ETFs for the same space that are ""mutually\nunbiased"" in a way that is analogous to the quantum-information-theoretic\nconcept of mutually unbiased bases. We then show that taking certain tensor\nproducts of these mutually unbiased ETFs with other ETFs sometimes yields\ninfinite families of new complex ETFs.\n']","[('equiangular tight frames', 0.5598608255386353), ('tight frames etfs', 0.5199734568595886), ('orthogonal frames', 0.5021650195121765), ('equiangular tight frame', 0.49195680022239685), ('tight frames', 0.48165857791900635), ('frames', 0.43431490659713745), ('orthogonal designs', 0.43046054244041443), ('equi dimensional', 0.4145970642566681), ('tight frame', 0.4085429906845093), ('frames can', 0.3846092224121094)]"
1546,1546,19,1546_intersection homology_intersection cohomology_homotopy cohomology_poincar duality,"['intersection homology', 'intersection cohomology', 'homotopy cohomology', 'poincar duality', 'cohomology', 'poincare duality', 'homotopy homology', 'homology groups', 'homology', 'cohomology groups']","['Topological invariance of torsion sensitive intersection homology   Torsion sensitive intersection homology was introduced to unify several\nversions of Poincare duality for stratified spaces into a single theorem. This\nunified duality theorem holds with ground coefficients in an arbitrary PID and\nwith no local cohomology conditions on the underlying space. In this paper we\nconsider for torsion sensitive intersection homology analogues of another\nimportant property of classical intersection homology: topological invariance.\nIn other words, we consider to what extent the defining sheaf complexes of the\ntheory are independent (up to quasi-isomorphism) of choice of stratification.\nIn addition to providing torsion sensitive versions of the existing invariance\ntheorems for classical intersection homology, our techniques provide some new\nresults even in the classical setting.\n', ""Poincar\\'e duality, cap product and Borel-Moore intersection Homology   Using a cap product, we construct an explicit Poincar\\'e duality isomorphism\nbetween the blown-up intersection cohomology and the Borel-Moore intersection\nhomology, for any commutative ring of coefficients and second-countable,\noriented pseudomanifolds.\n"", 'Variations on Poincar\\\'e duality for intersection homology   Intersection homology with coefficients in a field restores Poincar\\\'e\nduality for some spaces with singularities, as pseudomanifolds. But, with\ncoefficients in a ring, the behaviours of manifolds and pseudomanifolds are\ndifferent. This work is an overview, with proofs and explicit examples, of\nvarious possible situations with their properties.\n  We first set up a duality, defined from a cap product, between two\nintersection cohomologies: the first one arises from a linear dual and the\nsecond one from a simplicial blow up. Moreover, from this property, Poincar\\\'e\nduality in intersection homology looks like the Poincar\\\'e-Lefschetz duality of\na manifold with boundary. Besides that, an investigation of the coincidence of\nthe two previous cohomologies reveals that the only obstruction to the\nexistence of a Poincar\\\'e duality is the homology of a well defined complex.\nThis recovers the case of the peripheral sheaf introduced by Goresky and Siegel\nfor compact PL-pseudomanifolds. We also list a series of explicit computations\nof peripheral intersection cohomology. In particular, we observe that\nPoincar\\\'e duality can exist in the presence of torsion in the ""critical\ndegree"" of the intersection homology of the links of a pseudomanifold.\n']","[('intersection homology', 0.7267652153968811), ('intersection cohomology', 0.7116141319274902), ('homotopy cohomology', 0.5432268381118774), ('poincar duality', 0.5414657592773438), ('cohomology', 0.5273357033729553), ('poincare duality', 0.5214402675628662), ('homotopy homology', 0.5200220346450806), ('homology groups', 0.5176812410354614), ('homology', 0.5155259370803833), ('cohomology groups', 0.5018049478530884)]"
1547,1547,19,1547_hyperbolic spacetimes_globally hyperbolic spacetimes_globally hyperbolic spacetime_hyperbolic spacetime,"['hyperbolic spacetimes', 'globally hyperbolic spacetimes', 'globally hyperbolic spacetime', 'hyperbolic spacetime', 'hyperbolic operators', 'lorentzian manifolds', 'quantum field theory', 'de sitter spacetime', 'static spacetimes', 'minkowski spacetime']","['Paracausal deformations of Lorentzian metrics and M{\\o}ller isomorphisms\n  in algebraic quantum field theory   Given a pair of normally hyperbolic operators over (possibily different)\nglobally hyperbolic spacetimes on a given smooth manifold, the existence of a\ngeometric isomorphism, called {\\em M{\\o}ller operator}, between the space of\nsolutions is studied. This is achieved by exploiting a new equivalence relation\nin the space of globally hyperbolic metrics, called {\\em paracausal relation}.\nIn particular, it is shown that the M{\\o}ller operator associated to a pair of\nparacausally related metrics and normally hyperbolic operators also intertwines\nthe respective causal propagators of the normally hyperbolic operators and it\npreserves the natural symplectic forms on the space of (smooth) initial data.\nFinally, the M{\\o}ller map is lifted to a $*$-isomorphism between (generally\noff-shell) $CCR$-algebras. It is shown that the Wave Front set of a Hadamard\nbidistribution (and of a Hadamard state in particular) is preserved by the\npull-back action of this $*$-isomorphism.\n', 'The quantization of Proca fields on globally hyperbolic spacetimes:\n  Hadamard states and M{\\o}ller operators   This paper deals with several issues concerning the algebraic quantization of\nthe real Proca field in a globally hyperbolic spacetime and the definition and\nexistence of Hadamard states for that field. In particular, extending previous\nwork, we construct the so-called M\\o ller $*$-isomorphism between the algebras\nof Proca observables on paracausally related spacetimes, proving that the\npullback of these isomorphisms preserves the Hadamard property of corresponding\nquasifree states defined on the two spacetimes. Then, we pull-back a natural\nHadamard state constructed on ultrastatic spacetimes of bounded geometry, along\nthis $*$-isomorphism, to obtain a Hadamard state on a general globally\nhyperbolic spacetime. We conclude the paper, by comparing the definition of a\nHadamard state, here given in terms of wavefront set, with the one proposed by\nFewster and Pfenning, which makes use of a supplementary Klein-Gordon Hadamard\nform. We establish an (almost) complete equivalence of the two definitions.\n', 'On microlocalisation and the construction of Feynman Propagators for\n  normally hyperbolic operators   This article gives global microlocalisation constructions for normally\nhyperbolic operators on a vector bundle over a globally hyperbolic spacetime in\ngeometric terms. As an application, this is used to generalise the\nDuistermaat-H\\""{o}rmander construction of Feynman propagators, therefore\nincorporating the most important non-scalar geometric operators. It is shown\nthat for normally hyperbolic operators that are selfadjoint with respect to a\nhermitian bundle metric, the Feynman propagators can be constructed to satisfy\na positivity property that reflects the existence of Hadamard states in quantum\nfield theory on curved spacetimes. We also give a more direct construction of\nthe Feynman propagators for Dirac-type operators on a globally hyperbolic\nspacetime. Even though the natural bundle metric on spinors is not\npositive-definite, in this case, we can give a direct microlocal construction\nof a Feynman propagator that satisfies positivity.\n']","[('hyperbolic spacetimes', 0.611045777797699), ('globally hyperbolic spacetimes', 0.6056047677993774), ('globally hyperbolic spacetime', 0.5777244567871094), ('hyperbolic spacetime', 0.5750951766967773), ('hyperbolic operators', 0.5564970970153809), ('lorentzian manifolds', 0.4547402560710907), ('quantum field theory', 0.45030608773231506), ('de sitter spacetime', 0.4492942690849304), ('static spacetimes', 0.4489617943763733), ('minkowski spacetime', 0.4374839663505554)]"
1548,1548,19,1548_kantorovich operators_representation approximation_operators orlicz_type sampling,"['kantorovich operators', 'representation approximation', 'operators orlicz', 'type sampling', 'approximation properties', 'estimates approximation', 'orlicz spaces', 'kantorovich type', 'certain approximation', 'sampling type']","['Quantitative estimates for nonlinear sampling Kantorovich operators   In this paper, we establish quantitative estimates for nonlinear sampling\nKantorovich operators in terms of the modulus of continuity in the setting of\nOrlicz spaces. This general frame allows us to directly deduce some\nquantitative estimates of approximation in $L^{p}$-spaces, $1\\leq p<\\infty $,\nand in other well-known instances of Orlicz spaces, such as the Zygmung and the\nexponential spaces. Further, the qualitative order of approximation has been\nobtained assuming $f$ in suitable Lipschitz classes. The above estimates\nachieved in the general setting of Orlicz spaces, have been also improved in\nthe $L^p$-case, using a direct approach suitable to this context. At the end,\nwe consider the particular cases of the nonlinear sampling Kantorovich\noperators constructed by using some special kernels.\n', 'Convergence results in Orlicz spaces for sequences of max-product\n  Kantorovich sampling operators   In this paper, we provide a unifying theory concerning the convergence\nproperties of the so-called max-product Kantorovich sampling operators based\nupon generalized kernels in the setting of Orlicz spaces. The approximation of\nfunctions defined on both bounded intervals and on the whole real axis has been\nconsidered. Here, under suitable assumptions on the kernels, considered in\norder to define the operators, we are able to establish a modular convergence\ntheorem for these sampling-type operators. As a direct consequence of the main\ntheorem of this paper, we obtain that the involved operators can be\nsuccessfully used for approximation processes in a wide variety of functional\nspaces, including the well-known interpolation and exponential spaces. This\nmakes the Kantorovich variant of max-product sampling operators suitable for\nreconstructing not necessarily continuous functions (signals) belonging to a\nwide range of functional spaces. Finally, several examples of Orlicz spaces and\nof kernels for which the above theory can be applied are presented.\n', 'Max-product Kantorovich sampling operators: quantitative estimates in\n  functional spaces   In this paper, we study the order of approximation for max-product\nKantorovich sampling operators based upon generalized kernels in the setting of\nOrlicz spaces. We establish a quantitative estimate for the considered family\nof sampling-type operators using the Orlicz-type modulus of smoothness, which\ninvolves the modular functional of the space. From this result, it is possible\nto obtain the qualitative order of convergence when functions belonging to\nsuitable Lipschitz classes are considered. On the other hand, in the compact\ncase, we exploit a suitable definition of K-functional in Orlicz spaces in\norder to provide an upper bound for the approximation error of the involved\noperators. The treatment in the general framework of Orlicz spaces allows one\nto obtain a unifying theory on the rate of convergence, as the proved results\ncan be deduced for a wide range of functional spaces, such as $L^{p}$-spaces,\ninterpolation spaces and exponential spaces.\n']","[('kantorovich operators', 0.5883272886276245), ('representation approximation', 0.4523935914039612), ('operators orlicz', 0.4377955496311188), ('type sampling', 0.4110579490661621), ('approximation properties', 0.40875181555747986), ('estimates approximation', 0.40392428636550903), ('orlicz spaces', 0.40241649746894836), ('kantorovich type', 0.4008708894252777), ('certain approximation', 0.3809318542480469), ('sampling type', 0.36569005250930786)]"
1549,1549,19,1549_quantum hamiltonians_invariant hamiltonians_quantum harmonic oscillator_quantum harmonic,"['quantum hamiltonians', 'invariant hamiltonians', 'quantum harmonic oscillator', 'quantum harmonic', 'quantum models', 'new quantum', 'free quantum', 'quantum', 'hamiltonians', 'dynamical symmetry']","['Hamiltonians for the quantised Volterra hierarchy   This paper builds upon our recent work, published in Lett. Math. Phys., 112:\n94, 2022, where we established that the integrable Volterra lattice on a free\nassociative algebra and the whole hierarchy of its symmetries admits a\nquantisation dependent on a parameter $\\omega$. We also uncovered an intriguing\naspect: all odd-degree symmetries of the hierarchy admits an alternative,\nnon-deformation quantisation, resulting in a non-commutative algebra for any\nchoice of the quantisation parameter $\\omega$. In this study, we demonstrate\nthat each equation within the quantum Volterra hierarchy can be expressed in\nthe Heisenberg form. We provide explicit expressions for all quantum\nHamiltonians and establish their commutativity. In the classical limit, these\nquantum Hamiltonians yield explicit expressions for the classical ones of the\ncommutative Volterra hierarchy. Furthermore, we present Heisenberg equations\nand their Hamiltonians in the case of non-deformation quantisation. Finally, we\ndiscuss commuting first integrals, central elements of the quantum algebra, and\nthe integrability problem for periodic reductions of the Volterra lattice in\nthe context of both quantisations.\n', ""Quantum Painlev\\'e II Lax Pair and Quantum (Matrix) Analogues of\n  Classical Painlev\\'e II equation   In this article, we present a new quantum Painlev\\'e II Lax pair which\nexplicitly involves the Planck constant $ \\hbar $ and an arbitrary field\nvariable $v$ so these two objects make this new pair different from\nFlaschka-Newell Painlev\\'e II Lax pair and that pair appears as particular case\nof our's pair which consolidates the Painlev\\'e II equation from quantum\nmechanical point of view. It is shown that the compatibility of quantum\nPainlev\\'e II Lax pair simultaneously yields a quantum Painlev\\'e II equation\nand a quantum commutation relation between field variable $v $ and independent\nvariable $z$. We manifest that with the different choices of arbitrary field\nvariable system reduces to its classical version, matrix Painlev\\'e II equation\nand derivative matrix Painlev\\'e II equation. Further, we construct the gauge\nequivalence of quantum Painlev\\'e II Lax pair whose compatibility condition\ngives rise to quantum p34 equation that involves $\\hbar $ with power $+1$ which\nmakes our system more quantized as compared to the existed one that carries\n$\\hbar $ with power $+2$.\n"", 'Deformation of the Heisenberg-Weyl algebra and the Lie superalgebra\n  $\\mathfrak{osp}\\left( {1|2} \\right)$: exact solution for the quantum harmonic\n  oscillator with a position-dependent mass   We propose a new deformation of the quantum harmonic oscillator\nHeisenberg-Weyl algebra with a parameter $a>-1$. This parameter is introduced\nthrough the replacement of the homogeneous mass $m_0$ in the definition of the\nmomentum operator $\\hat p_x$ as well as in the creation-annihilation operators\n$\\hat a^\\pm$ with a mass varying with position $x$. The realization of such a\ndeformation is shown through the exact solution of the corresponding\nSchr\\""odinger equation for the non-relativistic quantum harmonic oscillator\nwithin the canonical approach. The obtained analytical expression of the energy\nspectrum consists of an infinite number of equidistant levels, whereas the\nwavefunctions of the stationary states of the problem under construction are\nexpressed through the Hermite polynomials. Then, the Heisenberg-Weyl algebra\ndeformation is generalized to the case of the Lie superalgebra\n$\\mathfrak{osp}\\left( {1|2} \\right)$. It is shown that the realization of such\na generalized superalgebra can be performed for the parabose quantum harmonic\noscillator problem, the mass of which possesses a behavior completely\noverlapping with the position-dependent mass of the canonically deformed\nharmonic oscillator problem. This problem is solved exactly for both even and\nodd stationary states. It is shown that the energy spectrum of the deformed\nparabose oscillator is still equidistant, however, both even and odd state\nwavefunctions are now expressed through the Laguerre polynomials. Some basic\nlimit relations recovering the canonical harmonic oscillator with constant mass\nare also discussed briefly.\n']","[('quantum hamiltonians', 0.6359636783599854), ('invariant hamiltonians', 0.5661707520484924), ('quantum harmonic oscillator', 0.5260791778564453), ('quantum harmonic', 0.5170146822929382), ('quantum models', 0.5122741460800171), ('new quantum', 0.5064113140106201), ('free quantum', 0.4954746663570404), ('quantum', 0.47222715616226196), ('hamiltonians', 0.45893263816833496), ('dynamical symmetry', 0.45530399680137634)]"
1550,1550,19,1550_colored graph_vertex colored_color graph_colors graph,"['colored graph', 'vertex colored', 'color graph', 'colors graph', 'connected graphs', 'connection graphs', 'coloring', 'monochromatic', 'connected graph', 'distinct colors']","['Some results on the rainbow vertex-disconnection colorings of graphs   Let $G$ be a nontrivial connected and vertex-colored graph. A vertex subset\n$X$ is called rainbow if any two vertices in $X$ have distinct colors. The\ngraph $G$ is called \\emph{rainbow vertex-disconnected} if for any two vertices\n$x$ and $y$ of $G$, there exists a vertex subset $S$ such that when $x$ and $y$\nare nonadjacent, $S$ is rainbow and $x$ and $y$ belong to different components\nof $G-S$; whereas when $x$ and $y$ are adjacent, $S+x$ or $S+y$ is rainbow and\n$x$ and $y$ belong to different components of $(G-xy)-S$. For a connected graph\n$G$, the \\emph{rainbow vertex-disconnection number} of $G$, $rvd(G)$, is the\nminimum number of colors that are needed to make $G$ rainbow\nvertex-disconnected.\n  In this paper, we prove for any $K_4$-minor free graph, $rvd(G)\\leq\n\\Delta(G)$ and the bound is sharp. We show it is $NP$-complete to determine the\nrainbow vertex-disconnection number for bipartite graphs and split graphs.\nMoreover, we show for every $\\epsilon>0$, it is impossible to efficiently\napproximate the rainbow vertex-disconnection number of any bipartite graph and\nsplit graph within a factor of $n^{\\frac{1}{3}-\\epsilon}$ unless $ZPP=NP$.\n', 'Further results on the rainbow vertex-disconnection of graphs   Let $G$ be a nontrivial connected and vertex-colored graph. A subset $X$ of\nthe vertex set of $G$ is called rainbow if any two vertices in $X$ have\ndistinct colors. The graph $G$ is called \\emph{rainbow vertex-disconnected} if\nfor any two vertices $x$ and $y$ of $G$, there exists a vertex subset $S$ such\nthat when $x$ and $y$ are nonadjacent, $S$ is rainbow and $x$ and $y$ belong to\ndifferent components of $G-S$; whereas when $x$ and $y$ are adjacent, $S+x$ or\n$S+y$ is rainbow and $x$ and $y$ belong to different components of $(G-xy)-S$.\nSuch a vertex subset $S$ is called a \\emph{rainbow vertex-cut} of $G$. For a\nconnected graph $G$, the \\emph{rainbow vertex-disconnection number} of $G$,\ndenoted by $rvd(G)$, is the minimum number of colors that are needed to make\n$G$ rainbow vertex-disconnected.\n  In this paper, we obtain bounds of the rainbow vertex-disconnection number of\na graph in terms of the minimum degree and maximum degree of the graph. We give\na tighter upper bound for the maximum size of a graph $G$ with $rvd(G)=k$ for\n$k\\geq\\frac{n}{2}$. We then characterize the graphs of order $n$ with rainbow\nvertex-disconnection number $n-1$ and obtain the maximum size of a graph $G$\nwith $rvd(G)=n-1$. Moreover, we get a sharp threshold function for the property\n$rvd(G(n,p))=n$ and prove that almost all graphs $G$ have\n$rvd(G)=rvd(\\overline{G})=n$. Finally, we obtain some Nordhaus-Gaddum-type\nresults: $n-5\\leq rvd(G)+rvd(\\overline{G})\\leq 2n$ and $n-1\\leq rvd(G)\\cdot\nrvd(\\overline{G})\\leq n^2$ for the rainbow vertex-disconnection numbers of\nnontrivial connected graphs $G$ and $\\overline{G}$ with order $n\\geq 24$.\n', 'The rainbow vertex-disconnection in graphs   Let $G$ be a nontrivial connected and vertex-colored graph. A subset $X$ of\nthe vertex set of $G$ is called rainbow if any two vertices in $X$ have\ndistinct colors. The graph $G$ is called \\emph{rainbow vertex-disconnected} if\nfor any two vertices $x$ and $y$ of $G$, there exists a vertex subset $S$ of\n$G$ such that when $x$ and $y$ are nonadjacent, $S$ is rainbow and $x$ and $y$\nbelong to different components of $G-S$; whereas when $x$ and $y$ are adjacent,\n$S+x$ or $S+y$ is rainbow and $x$ and $y$ belong to different components of\n$(G-xy)-S$. For a connected graph $G$, the \\emph{rainbow vertex-disconnection\nnumber} of $G$, denoted by $rvd(G)$, is the minimum number of colors that are\nneeded to make $G$ rainbow vertex-disconnected.\n  In this paper, we characterize all graphs of order $n$ with rainbow\nvertex-disconnection number $k$ for $k\\in\\{1,2,n\\}$, and determine the rainbow\nvertex-disconnection numbers of some special graphs. Moreover, we study the\nextremal problems on the number of edges of a connected graph $G$ with order\n$n$ and $rvd(G)=k$ for given integers $k$ and $n$ with $1\\leq k\\leq n$.\n']","[('colored graph', 0.5486957430839539), ('vertex colored', 0.5440016984939575), ('color graph', 0.5179247856140137), ('colors graph', 0.5170668959617615), ('connected graphs', 0.5079834461212158), ('connection graphs', 0.5031055212020874), ('coloring', 0.4492039084434509), ('monochromatic', 0.4473765790462494), ('connected graph', 0.4347982406616211), ('distinct colors', 0.4337836503982544)]"
1551,1551,19,1551_water distribution networks_water distribution_distribution networks_distribution network,"['water distribution networks', 'water distribution', 'distribution networks', 'distribution network', 'water flow', 'integer nonlinear programming', 'optimal design', 'compute feasible', 'network design', 'hydraulic']","['Optimal Pump Control for Water Distribution Networks via Data-based\n  Distributional Robustness   In this paper, we propose a data-based methodology to solve a multi-period\nstochastic optimal water flow (OWF) problem for water distribution networks\n(WDNs). The framework explicitly considers the pump schedule and water network\nhead level with limited information of demand forecast errors for an extended\nperiod simulation. The objective is to determine the optimal feedback decisions\nof network-connected components, such as nominal pump schedules and tank head\nlevels and reserve policies, which specify device reactions to forecast errors\nfor accommodation of fluctuating water demand. Instead of assuming the\nuncertainties across the water network are generated by a prescribed certain\ndistribution, we consider ambiguity sets of distributions centered at an\nempirical distribution, which is based directly on a finite training data set.\nWe use a distance-based ambiguity set with the Wasserstein metric to quantify\nthe distance between the real unknown data-generating distribution and the\nempirical distribution. This allows our multi-period OWF framework to trade off\nsystem performance and inherent sampling errors in the training dataset. Case\nstudies on a three-tank water distribution network systematically illustrate\nthe tradeoff between pump operational cost, risks of constraint violation, and\nout-of-sample performance.\n', 'Optimal design-for-control of self-cleaning water distribution networks\n  using a convex multi-start algorithm   The provision of self-cleaning velocities has been shown to reduce the risk\nof discolouration in water distribution networks (WDNs). Despite these\nfindings, control implementations continue to be focused primarily on pressure\nand leakage management. This paper considers the control of diurnal flow\nvelocities to maximize the self-cleaning capacity (SCC) of WDNs. We formulate a\nnew optimal design-for-control problem where locations and operational settings\nof pressure control and automatic flushing valves are jointly optimized. The\nproblem formulation includes a nonconvex objective function, nonconvex\nhydraulic conservation law constraints, and binary variables for modelling\nvalve placement, resulting in a nonconvex mixed integer nonlinear programming\n(MINLP) optimization problem. Considering the challenges with solving nonconvex\nMINLP problems, we propose a heuristic algorithm which combines convex\nrelaxations (with domain reduction), a randomization technique, and a\nmulti-start strategy to compute feasible solutions. We evaluate the proposed\nalgorithm on case study networks with varying size and degrees of complexity,\nincluding a large-scale operational network in the UK. The convex multi-start\nalgorithm is shown to be a more robust solution method compared to an\noff-the-shelf genetic algorithm, finding good-quality feasible solutions to all\ndesign-for-control numerical experiments. Moreover, we demonstrate the\nimplemented multi-start strategy to be a fast and scalable method for computing\nfeasible solutions to the nonlinear SCC control problem. The proposed method\nextends the control capabilities and benefits of dynamically adaptive networks\nto improve water quality in WDNs.\n', 'Novel Spanning-Tree Matrix Approach to Model and Optimize Large-Scale,\n  Tree-Shaped Water Distribution Networks   There exist many criteria for the optimal design of water distribution\nnetworks. One of the most common criteria is to design the optimal cost water\ndistribution network while satisfying the hydraulic design constraints. This\nstudy was carried out to propose a novel computational method named\nSpanning-Tree Matrix Approach that can model large-scale tree-shaped water\ndistribution networks. A case study was tested to demonstrate the use of the\nSpanning-Tree Matrix Approach model coupled with the Honey-Bee Mating\nOptimization algorithm to find the combination of pipe diameters that minimizes\nthe cost of the network. The results show that the Spanning-Tree Matrix\nApproach is successful in modeling a tree-shaped water distribution network of\nany size. Moreover, proposed Spanning-Tree Matrix Approach has the flexibility\nto be adapted to any desirable governing equation or design criteria being\nimposed, and the element of simplicity to output desired constraint evaluations\ninto a modern stochastic optimization algorithm (i.e., Genetic Algorithm,\nSimulated Annealing, Ant-Colony Optimization, Honey-Bee Mating Optimization,\netc.) for the network optimization purpose.\n']","[('water distribution networks', 0.6897041201591492), ('water distribution', 0.47944164276123047), ('distribution networks', 0.4547725021839142), ('distribution network', 0.4087940454483032), ('water flow', 0.4067575931549072), ('integer nonlinear programming', 0.34415289759635925), ('optimal design', 0.30846506357192993), ('compute feasible', 0.30684417486190796), ('network design', 0.3029668927192688), ('hydraulic', 0.29982051253318787)]"
1552,1552,19,1552_optimization pareto_pareto optimal_single objective optimization_multi objective optimization,"['optimization pareto', 'pareto optimal', 'single objective optimization', 'multi objective optimization', 'approximate pareto', 'multi objective evolutionary', 'objective optimization', 'objective learning', 'multiobjective optimization', 'pareto sets']","['A Framework for Controllable Pareto Front Learning with Completed\n  Scalarization Functions and its Applications   Pareto Front Learning (PFL) was recently introduced as an efficient method\nfor approximating the entire Pareto front, the set of all optimal solutions to\na Multi-Objective Optimization (MOO) problem. In the previous work, the mapping\nbetween a preference vector and a Pareto optimal solution is still ambiguous,\nrendering its results. This study demonstrates the convergence and completion\naspects of solving MOO with pseudoconvex scalarization functions and combines\nthem into Hypernetwork in order to offer a comprehensive framework for PFL,\ncalled Controllable Pareto Front Learning. Extensive experiments demonstrate\nthat our approach is highly accurate and significantly less computationally\nexpensive than prior methods in term of inference time.\n', ""Preference-Optimized Pareto Set Learning for Blackbox Optimization   Multi-Objective Optimization (MOO) is an important problem in real-world\napplications. However, for a non-trivial problem, no single solution exists\nthat can optimize all the objectives simultaneously. In a typical MOO problem,\nthe goal is to find a set of optimum solutions (Pareto set) that trades off the\npreferences among objectives. Scalarization in MOO is a well-established method\nfor finding a finite set approximation of the whole Pareto set (PS). However,\nin real-world experimental design scenarios, it's beneficial to obtain the\nwhole PS for flexible exploration of the design space. Recently Pareto set\nlearning (PSL) has been introduced to approximate the whole PS. PSL involves\ncreating a manifold representing the Pareto front of a multi-objective\noptimization problem. A naive approach includes finding discrete points on the\nPareto front through randomly generated preference vectors and connecting them\nby regression. However, this approach is computationally expensive and leads to\na poor PS approximation. We propose to optimize the preference points to be\ndistributed evenly on the Pareto front. Our formulation leads to a bilevel\noptimization problem that can be solved by e.g. differentiable cross-entropy\nmethods. We demonstrated the efficacy of our method for complex and difficult\nblack-box MOO problems using both synthetic and real-world benchmark data.\n"", 'Pareto Front Shape-Agnostic Pareto Set Learning in Multi-Objective\n  Optimization   Pareto set learning (PSL) is an emerging approach for acquiring the complete\nPareto set of a multi-objective optimization problem. Existing methods\nprimarily rely on the mapping of preference vectors in the objective space to\nPareto optimal solutions in the decision space. However, the sampling of\npreference vectors theoretically requires prior knowledge of the Pareto front\nshape to ensure high performance of the PSL methods. Designing a sampling\nstrategy of preference vectors is difficult since the Pareto front shape cannot\nbe known in advance. To make Pareto set learning work effectively in any Pareto\nfront shape, we propose a Pareto front shape-agnostic Pareto Set Learning\n(GPSL) that does not require the prior information about the Pareto front. The\nfundamental concept behind GPSL is to treat the learning of the Pareto set as a\ndistribution transformation problem. Specifically, GPSL can transform an\narbitrary distribution into the Pareto set distribution. We demonstrate that\ntraining a neural network by maximizing hypervolume enables the process of\ndistribution transformation. Our proposed method can handle any shape of the\nPareto front and learn the Pareto set without requiring prior knowledge.\nExperimental results show the high performance of our proposed method on\ndiverse test problems compared with recent Pareto set learning algorithms.\n']","[('optimization pareto', 0.718235433101654), ('pareto optimal', 0.6499180197715759), ('single objective optimization', 0.6362498998641968), ('multi objective optimization', 0.5946375131607056), ('approximate pareto', 0.5703973770141602), ('multi objective evolutionary', 0.5601404309272766), ('objective optimization', 0.5537423491477966), ('objective learning', 0.5512290000915527), ('multiobjective optimization', 0.5491127967834473), ('pareto sets', 0.5426002144813538)]"
1553,1553,19,1553_oriented graphs_every oriented graph_acyclic digraph_oriented graph,"['oriented graphs', 'every oriented graph', 'acyclic digraph', 'oriented graph', 'digraph obtained', 'inversions', 'number inversions', 'inversion number', 'digraph', 'graphs']","[""On the inversion number of oriented graphs   Let $D$ be an oriented graph. The inversion of a set $X$ of vertices in $D$\nconsists in reversing the direction of all arcs with both ends in $X$. The\ninversion number of $D$, denoted by ${\\rm inv}(D)$, is the minimum number of\ninversions needed to make $D$ acyclic. Denoting by $\\tau(D)$, $\\tau' (D)$, and\n$\\nu(D)$ the cycle transversal number, the cycle arc-transversal number and the\ncycle packing number of $D$ respectively, one shows that ${\\rm inv}(D) \\leq\n\\tau' (D)$, ${\\rm inv}(D) \\leq 2\\tau(D)$ and there exists a function $g$ such\nthat ${\\rm inv}(D)\\leq g(\\nu(D))$. We conjecture that for any two oriented\ngraphs $L$ and $R$, ${\\rm inv}(L\\rightarrow R) ={\\rm inv}(L) +{\\rm inv}(R)$\nwhere $L\\rightarrow R$ is the dijoin of $L$ and $R$. This would imply that the\nfirst two inequalities are tight. We prove this conjecture when ${\\rm\ninv}(L)\\leq 1$ and ${\\rm inv}(R)\\leq 2$ and when ${\\rm inv}(L) ={\\rm inv}(R)=2$\nand $L$ and $R$ are strongly connected. We also show that the function $g$ of\nthe third inequality satisfies $g(1)\\leq 4$.\n  We then consider the complexity of deciding whether ${\\rm inv}(D)\\leq k$ for\na given oriented graph $D$. We show that it is NP-complete for $k=1$, which\ntogether with the above conjecture would imply that it is NP-complete for every\n$k$. This contrasts with a result of Belkhechine et al. which states that\ndeciding whether ${\\rm inv}(T)\\leq k$ for a given tournament $T$ is\npolynomial-time solvable.\n"", 'The inversion number of dijoins and blow-up digraphs   For an oriented graph $D$, the $inversion$ of $X \\subseteq V(D)$ in $D$ is\nthe digraph obtained from $D$ by reversing the direction of all arcs with both\nends in $X$. The inversion number of $D$, denoted by $inv(D)$, is the minimum\nnumber of inversions needed to transform $D$ into an acyclic digraph. In this\npaper, we first show that $inv (\\overrightarrow{C_3} \\Rightarrow D)= inv(D) +1$\nfor any oriented graph $\\textit{D}$ with even inversion number $inv(D)$, where\nthe dijoin $\\overrightarrow{C_3} \\Rightarrow D$ is the oriented graph obtained\nfrom the disjoint union of $\\overrightarrow{C_3}$ and $D$ by adding all arcs\nfrom $\\overrightarrow{C_3}$ to $D$. Thus we disprove the conjecture of Aubian\nel at. \\cite{2212.09188} and the conjecture of Alon el at. \\cite{2212.11969}.\nWe also study the blow-up graph which is an oriented graph obtained from a\ntournament by replacing all vertices into oriented graphs. We construct a\ntournament $T$ with order $n$ and $inv(T)=\\frac{n}{3}+1$ using blow-up graphs.\n', 'Problems, proofs, and disproofs on the inversion number   The {\\it inversion} of a set $X$ of vertices in a digraph $D$ consists in\nreversing the direction of all arcs of $D\\langle X\\rangle$. The {\\it inversion\nnumber} of an oriented graph $D$, denoted by ${\\rm inv}(D)$, is the minimum\nnumber of inversions needed to transform $D$ into an acyclic oriented graph. In\nthis paper, we study a number of problems involving the inversion number of\noriented graphs. Firstly, we give bounds on ${\\rm inv}(n)$, the maximum of the\ninversion numbers of the oriented graphs of order $n$. We show $n -\n\\mathcal{O}(\\sqrt{n\\log n}) \\ \\leq \\ {\\rm inv}(n) \\ \\leq \\ n - \\lceil \\log\n(n+1) \\rceil$. Secondly, we disprove a conjecture of Bang-Jensen et al.\nasserting that, for every pair of oriented graphs $L$ and $R$, we have ${\\rm\ninv}(L\\Rightarrow R) ={\\rm inv}(L) + {\\rm inv}(R)$, where $L\\Rightarrow R$ is\nthe oriented graph obtained from the disjoint union of $L$ and $R$ by adding\nall arcs from $L$ to $R$. Finally, we investigate whether, for all pairs of\npositive integers $k_1,k_2$, there exists an integer $f(k_1,k_2)$ such that if\n$D$ is an oriented graph with ${\\rm inv}(D) \\geq f(k_1,k_2)$ then there is a\npartition $(V_1, V_2)$ of $V(D)$ such that ${\\rm inv}(D\\langle V_i\\rangle) \\geq\nk_i$ for $i=1,2$. We show that $f(1,k)$ exists and $f(1,k)\\leq k+10$ for all\npositive integers $k$. Further, we show that $f(k_1,k_2)$ exists for all pairs\nof positive integers $k_1,k_2$ when the oriented graphs in consideration are\nrestricted to be tournaments.\n']","[('oriented graphs', 0.5675836801528931), ('every oriented graph', 0.5645049214363098), ('acyclic digraph', 0.5459972023963928), ('oriented graph', 0.5205422639846802), ('digraph obtained', 0.48476171493530273), ('inversions', 0.45020726323127747), ('number inversions', 0.42525148391723633), ('inversion number', 0.42457833886146545), ('digraph', 0.41829004883766174), ('graphs', 0.4182247817516327)]"
1554,1554,19,1554_rota baxter algebras_rota baxter algebra_algebras rota baxter_rota baxter operators,"['rota baxter algebras', 'rota baxter algebra', 'algebras rota baxter', 'rota baxter operators', 'rota baxter operator', 'baxter algebras', 'baxter operators weight', 'baxter operator weight', 'baxter algebra', 'baxter operators nonzero']","['Monomial Rota-Baxter operators of weight zero and averaging operators on\n  the polynomial algebra   Starting with the work S.H. Zheng, L. Guo and M. Rosenkranz (2015),\nRota-Baxter operators are studied on the polynomial algebra. Injective\nRota-Baxter operators of weight zero on $F[x]$ were described in 2021. We\nclassify the following classes of monomial Rota-Baxter operators of weight zero\non the polynomial algebra $F[x,y]$ and its augmentation ideal $F_0[x,y]$: 1)\nnon-increasing in degree that do not contain monomials in the kernel, 2)\nmapping all monomials to themselves with a coefficient. In the context of these\nsets of operators, we show how one may define a monomial averaging operator by\na given RB-operator and vice versa.\n', 'Rota-Baxter operators of weight zero on Cayley-Dickson algebra   All Rota-Baxter operators of weight zero on split octonion algebra over\na~field of characteristic not 2 are classified up to conjugation by\nautomorphisms and antiautomorphisms. Thus, the classification of Rota-Baxter\noperators on composition algebras is finished. There are two descriptions:\na~common description over arbitratry field of characteristic not 2 and more\naccurate description over a~quadratically closed field of characteristic not 2.\n', 'Rota-Baxter operators on unital algebras   We state that all Rota-Baxter operators of nonzero weight on Grassmann\nalgebra over a field of characteristic zero are projections on a subalgebra\nalong another one. We show the one-to-one correspondence between the solutions\nof associative Yang-Baxter equation and Rota-Baxter operators of weight zero on\nthe matrix algebra $M_n(F)$ (joint with P. Kolesnikov). We prove that all\nRota-Baxter operators of weight zero on a unital associative (alternative,\nJordan) algebraic algebra over a field of characteristic zero are nilpotent.\nFor an algebra $A$, we introduce its new invariant the rb-index\n$\\mathrm{rb}(A)$ as the nilpotency index for Rota-Baxter operators of weight\nzero on $A$. We show that $\\mathrm{rb}(M_n(F)) = 2n-1$ provided that\ncharacteristic of $F$ is zero.\n']","[('rota baxter algebras', 0.8182979226112366), ('rota baxter algebra', 0.7981550693511963), ('algebras rota baxter', 0.7604145407676697), ('rota baxter operators', 0.7365821003913879), ('rota baxter operator', 0.6998555660247803), ('baxter algebras', 0.6927300095558167), ('baxter operators weight', 0.6768867373466492), ('baxter operator weight', 0.660081684589386), ('baxter algebra', 0.6561705470085144), ('baxter operators nonzero', 0.6158961653709412)]"
1555,1555,19,1555_bose einstein condensates_bose einstein condensate_einstein condensate bec_bose einstein,"['bose einstein condensates', 'bose einstein condensate', 'einstein condensate bec', 'bose einstein', 'states bose', 'ground states spin', 'einstein condensates', 'einstein condensate', 'morse indices', 'discrete minimizers']","['A normalized gradient flow method for computing ground states of spin-2\n  Bose-Einstein condensates   We propose and analyze an efficient and accurate numerical method for\ncomputing ground states of spin-2 Bose-Einstein condensates (BECs) by using the\nnormalized gradient flow (NGF). In order to successfully extend the NGF to\nspin-2 BECs which has five components in the vector wave function but with only\ntwo physical constraints on total mass conservation and magnetization\nconservation, two important techniques are introduced for designing the\nproposed numerical method. The first one is to systematically investigate the\nground state structure and property of spin-2 BECs within a spatially uniform\nsystem, which can be used on how to properly choose initial data in the NGF for\ncomputing ground states of spin-2 BECs. The second one is to introduce three\nadditional projection conditions based on the relations between the chemical\npotentials, together with the two existing physical constraints, such that the\nfive projection parameters used in the projection step of the NGF can be\nuniquely determined. Then a backward-forward Euler finite difference method is\nadapted to discretize the NGF. We prove rigorously that there exists a unique\nsolution of the nonlinear system for determining the five projection parameters\nin the full discretization of the NGF under a mild condition on the time step\nsize. Extensive numerical results on ground states of spin-2 BECs with\ndifferent types of phases and under different potentials are reported to show\nthe efficiency and accuracy of the proposed numerical method and to demonstrate\nseveral interesting physical phenomena on ground states of spin-2 BECs.\n', 'Newton-based alternating methods for the ground state of a class of\n  multi-component Bose-Einstein condensates   The computation of the ground states of special multi-component Bose-Einstein\ncondensates (BECs) can be formulated as an energy functional minimization\nproblem with spherical constraints. It leads to a nonconvex quartic-quadratic\noptimization problem after suitable discretizations. First, we generalize the\nNewton-based methods for single-component BECs to the alternating minimization\nscheme for multi-component BECs. Second, the global convergent alternating\nNewton-Noda iteration (ANNI) is proposed. In particular, we prove the\npositivity preserving property of ANNI under mild conditions. Finally, our\nanalysis is applied to a class of more general ""multi-block"" optimization\nproblems with spherical constraints. Numerical experiments are performed to\nevaluate the performance of proposed methods for different multi-component\nBECs, including pseudo spin-1/2, anti-ferromagnetic spin-1 and spin-2 BECs.\nThese results support our theory and demonstrate the efficiency of our\nalgorithms.\n', 'On discrete ground states of rotating Bose-Einstein condensates   The ground states of Bose-Einstein condensates in a rotating frame can be\ndescribed as constrained minimizers of the Gross-Pitaevskii energy functional\nwith an angular momentum term. In this paper we consider the corresponding\ndiscrete minimization problem in Lagrange finite element spaces of arbitrary\npolynomial order and we investigate the approximation properties of discrete\nground states. In particular, we prove a priori error estimates of optimal\norder in the $L^2$- and $H^1$-norm, as well as for the ground state energy and\nthe corresponding chemical potential. A central issue in the analysis of the\nproblem is the missing uniqueness of ground states, which is mainly caused by\nthe invariance of the energy functional under complex phase shifts. Our error\nanalysis is therefore based on an Euler-Lagrange functional that we restrict to\ncertain tangent spaces in which we have local uniqueness of ground states. This\ngives rise to an error decomposition that is ultimately used to derive the\ndesired a priori error estimates. We also present numerical experiments to\nillustrate various aspects of the problem structure.\n']","[('bose einstein condensates', 0.5240538716316223), ('bose einstein condensate', 0.5161107778549194), ('einstein condensate bec', 0.4242720901966095), ('bose einstein', 0.3896152377128601), ('states bose', 0.3884808123111725), ('ground states spin', 0.3843146562576294), ('einstein condensates', 0.38400912284851074), ('einstein condensate', 0.3764011859893799), ('morse indices', 0.3731285631656647), ('discrete minimizers', 0.3705204129219055)]"
1556,1556,19,1556_moduli spaces_hodge theory_adic representations_adic formal scheme,"['moduli spaces', 'hodge theory', 'adic representations', 'adic formal scheme', 'abelian hodge', 'moduli theoretic', 'varieties adic', 'adic formal', 'morphism moduli', 'non abelian hodge']","['Moduli spaces in $p$-adic non-abelian Hodge theory   We propose a new moduli-theoretic approach to the $p$-adic Simpson\ncorrespondence for a smooth proper rigid space $X$ over $\\mathbb C_p$ with\ncoefficients in any rigid analytic group $G$, in terms of a comparison of\nmoduli stacks. For its formulation, we introduce the class of ""smoothoid\nspaces"" which are perfectoid families of smooth rigid spaces, well-suited for\nstudying relative $p$-adic Hodge theory. For any smoothoid space $Y$, we then\nconstruct a ""sheafified non-abelian Hodge correspondence"", namely a canonical\nisomorphism \\[R^1\\nu_{\\ast}G\\xrightarrow{\\sim} \\mathrm{Higgs}_G\\] where\n$\\nu:Y_{v}\\to Y_{et}$ is the natural morphism of sites, and where\n$\\mathrm{Higgs}_G$ is the sheaf of isomorphism classes of $G$-Higgs bundles on\n$Y_{et}$. We also prove a generalisation of Faltings\' local $p$-adic Simpson\ncorrespondence to $G$-bundles and to perfectoid families.\n  We apply these results to deduce $v$-descent criteria for \\\'etale $G$-bundles\nwhich show that $G$-Higgs bundles on $X$ form a small $v$-stack $\\mathscr\nHiggs_G$. As a second application, we construct an analogue of the Hitchin\nmorphism on the Betti side: a morphism $\\mathscr Bun_{G,v}\\to \\mathcal A_G$\nfrom the small $v$-stack of $v$-topological $G$-bundles on $X$ to the Hitchin\nbase. This allows us to give a conjectural reformulation of the $p$-adic\nSimpson correspondence for $X$ in a more geometric and more canonical way,\nnamely in terms of a comparison of Hitchin morphisms.\n', ""Correspondance de Simpson p-adique II : fonctorialit\\'e par image\n  directe propre et syst\\`emes locaux de Hodge-Tate   Faltings initiated in 2005 a p-adic analogue of the (complex) Simpson\ncorrespondence whose construction has been taken up by various authors,\naccording to several approaches. Following the one we initiated previously, we\ndevelop in this new monograph new features of the p-adic Simpson\ncorrespondence, inspired by our construction of the relative Hodge-Tate\nspectral sequence. First, we address the connection to Hodge-Tate local\nsystems. Second, we establish the functoriality of the p-adic Simpson\ncorrespondence by proper direct image. Along the way, we expand the scope of\nour original construction.\n  Faltings a d\\'egag\\'e en 2005 un analogue p-adique de la correspondance de\nSimpson (complexe) dont la construction a \\'et\\'e reprise par diff\\'erents\nauteurs, selon plusieurs approches. Poursuivant celle que nous avons initi\\'ee\npr\\'ec\\'edemment, nous d\\'eveloppons dans la pr\\'esente monographie de nouveaux\naspects de la correspondance de Simpson p-adique, inspir\\'es par notre\nconstruction de la suite spectrale de Hodge-Tate relative. Nous traitons tout\nd'abord du lien avec les syst\\`emes locaux de Hodge-Tate. Nous \\'etablissons\nensuite la fonctorialit\\'e de la correspondance de Simpson p-adique par image\ndirecte propre. Chemin faisant, nous \\'elargissons la port\\'ee de notre\nconstruction initiale.\n"", 'The p-adic Simpson Correspondence II: Functoriality by proper direct\n  image and Hodge-Tate local systems -- an overview   Faltings initiated in 2005 a p-adic analogue of the (complex) Simpson\ncorrespondence whose construction has been taken up by various authors,\naccording to several approaches. Following the one we initiated previously, we\npresent an overview of a new monograph developing new features of the p-adic\nSimpson correspondence, inspired by our construction of the relative Hodge-Tate\nspectral sequence. First, we address the connection to Hodge-Tate local\nsystems. Second, we establish the functoriality of the p-adic Simpson\ncorrespondence by proper direct image. Along the way, we expand the scope of\nour original construction.\n']","[('moduli spaces', 0.551238477230072), ('hodge theory', 0.5401561856269836), ('adic representations', 0.5177493691444397), ('adic formal scheme', 0.49780207872390747), ('abelian hodge', 0.4944469928741455), ('moduli theoretic', 0.49142175912857056), ('varieties adic', 0.4729313552379608), ('adic formal', 0.44773080945014954), ('morphism moduli', 0.44152697920799255), ('non abelian hodge', 0.43687573075294495)]"
1557,1557,19,1557_beamforming optimization_power allocation beamforming_massive mimo_downlink beamforming,"['beamforming optimization', 'power allocation beamforming', 'massive mimo', 'downlink beamforming', 'optimal beamforming', 'allocation beamforming design', 'coordinated beamforming', 'mimo cellular', 'multicast beamforming', 'deep learning']","['Model-driven Learning for Generic MIMO Downlink Beamforming With Uplink\n  Channel Information   Accurate downlink channel information is crucial to the beamforming design,\nbut it is difficult to obtain in practice. This paper investigates a deep\nlearning-based optimization approach of the downlink beamforming to maximize\nthe system sum rate, when only the uplink channel information is available. Our\nmain contribution is to propose a model-driven learning technique that exploits\nthe structure of the optimal downlink beamforming to design an effective hybrid\nlearning strategy with the aim to maximize the sum rate performance. This is\nachieved by jointly considering the learning performance of the downlink\nchannel, the power and the sum rate in the training stage. The proposed\napproach applies to generic cases in which the uplink channel information is\navailable, but its relation to the downlink channel is unknown and does not\nrequire an explicit downlink channel estimation. We further extend the\ndeveloped technique to massive multiple-input multiple-output scenarios and\nachieve a distributed learning strategy for multicell systems without an\ninter-cell signalling overhead. Simulation results verify that our proposed\nmethod provides the performance close to the state of the art numerical\nalgorithms with perfect downlink channel information and significantly\noutperforms existing data-driven methods in terms of the sum rate.\n', 'Deep Learning Based Joint Multi-User MISO Power Allocation and\n  Beamforming Design   The evolution of fifth generation (5G) wireless communication networks has\nled to an increased need for wireless resource management solutions that\nprovide higher data rates, wide coverage, low latency, and power efficiency.\nYet, many of existing traditional approaches remain non-practical due to\ncomputational limitations, and unrealistic presumptions of static network\nconditions and algorithm initialization dependencies. This creates an important\ngap between theoretical analysis and real-time processing of algorithms. To\nbridge this gap, deep learning based techniques offer promising solutions with\ntheir representational capabilities for universal function approximation. We\npropose a novel unsupervised deep learning based joint power allocation and\nbeamforming design for multi-user multiple-input single-output (MU-MISO)\nsystem. The objective is to enhance the spectral efficiency by maximizing the\nsum-rate with the proposed joint design framework, NNBF-P while also offering\ncomputationally efficient solution in contrast to conventional approaches. We\nconduct experiments for diverse settings to compare the performance of NNBF-P\nwith zero-forcing beamforming (ZFBF), minimum mean square error (MMSE)\nbeamforming, and NNBF, which is also our deep learning based beamforming design\nwithout joint power allocation scheme. Experiment results demonstrate the\nsuperiority of NNBF-P compared to ZFBF, and MMSE while NNBF can have lower\nperformances than MMSE and ZFBF in some experiment settings. It can also\ndemonstrate the effectiveness of joint design framework with respect to NNBF.\n', 'A Deep Learning Framework for Optimization of MISO Downlink Beamforming   Beamforming is an effective means to improve the quality of the received\nsignals in multiuser multiple-input-single-output (MISO) systems.\nTraditionally, finding the optimal beamforming solution relies on iterative\nalgorithms, which introduces high computational delay and is thus not suitable\nfor real-time implementation. In this paper, we propose a deep learning\nframework for the optimization of downlink beamforming. In particular, the\nsolution is obtained based on convolutional neural networks and exploitation of\nexpert knowledge, such as the uplink-downlink duality and the known structure\nof optimal solutions. Using this framework, we construct three beamforming\nneural networks (BNNs) for three typical optimization problems, i.e., the\nsignal-to-interference-plus-noise ratio (SINR) balancing problem, the power\nminimization problem, and the sum rate maximization problem. For the former two\nproblems the BNNs adopt the supervised learning approach, while for the sum\nrate maximization problem a hybrid method of supervised and unsupervised\nlearning is employed. Simulation results show that the BNNs can achieve\nnear-optimal solutions to the SINR balancing and power minimization problems,\nand a performance close to that of the weighted minimum mean squared error\nalgorithm for the sum rate maximization problem, while in all cases enjoy\nsignificantly reduced computational complexity. In summary, this work paves the\nway for fast realization of optimal beamforming in multiuser MISO systems.\n']","[('beamforming optimization', 0.49852389097213745), ('power allocation beamforming', 0.476365327835083), ('massive mimo', 0.4739173948764801), ('downlink beamforming', 0.46784913539886475), ('optimal beamforming', 0.45663294196128845), ('allocation beamforming design', 0.4554295539855957), ('coordinated beamforming', 0.4486355483531952), ('mimo cellular', 0.42887094616889954), ('multicast beamforming', 0.4271986782550812), ('deep learning', 0.42460787296295166)]"
1558,1558,19,1558_extended kalman filtering_kalman filtering_kalman filter_kalman filter based,"['extended kalman filtering', 'kalman filtering', 'kalman filter', 'kalman filter based', 'extended kalman filter', 'unscented kalman filter', 'extended kalman', 'unscented kalman', 'state estimation methods', 'state estimation continuous']","['State Estimation Methods for Continuous-Discrete Nonlinear Systems\n  involving Stochastic Differential Equations   In this work, we present methods for state estimation in continuous-discrete\nnonlinear systems involving stochastic differential equations. We present the\nextended Kalman filter, the unscented Kalman filter, the ensemble Kalman\nfilter, and a particle filter. We implement the state estimation methods in\nMatlab. We evaluate the performance of the methods on a simulation of the\nmodified four-tank system. We implement the state estimation methods for\nnon-stiff systems, i.e., using an explicit numerical integration scheme. The\nimplementation of the extended Kalman filter utilises the Joseph stabilising\nform for numerical stability. We evaluate the accuracy of the state estimation\nmethods in terms of the mean absolute percentage error over the simulation\nhorizon. We show that each method successfully estimates the states and\nunmeasured disturbances of the simulated modified four-tank system. Finally, we\npresent conclusions.\n', 'MATLAB-based general approach for square-root extended-unscented and\n  fifth-degree cubature Kalman filtering methods   A stable square-root approach has been recently proposed for the unscented\nKalman filter (UKF) and fifth-degree cubature Kalman filter (5D-CKF) as well as\nfor the mixed-type methods consisting of the extended Kalman filter (EKF) time\nupdate and the UKF/5D-CKF measurement update steps. The mixed-type estimators\nprovide a good balance in trading between estimation accuracy and computational\ndemand because of the EKF moment differential equations involved. The key\nbenefit is a consolidation of reliable state mean and error covariance\npropagation by using delicate discretization error control while solving the\nEKF moment differential equations and an accurate measurement update according\nto the advanced UKF and/or 5D-CKF filtering strategies. Meanwhile the drawback\nof the previously proposed estimators is an utilization of sophisticated\nnumerical integration scheme with the built-in discretization error control\nthat is, in fact, a complicated and computationally costly tool. In contrast,\nwe design here the mixed-type methods that keep the same estimation quality but\nreduce a computational time significantly. The novel estimators elegantly\nutilize any MATLAB-based numerical integration scheme developed for solving\nordinary differential equations (ODEs) with the required accuracy tolerance\npre-defined by users. In summary, a simplicity of the suggested estimators,\ntheir numerical robustness with respect to roundoff due to the square-root form\nutilized as well as their estimation accuracy due to the MATLAB ODEs solvers\nwith discretization error control involved are the attractive features of the\nnovel estimators. The numerical experiments are provided for illustrating a\nperformance of the suggested methods in comparison with the existing ones.\n', 'On derivative-free extended Kalman filtering and its Matlab-oriented\n  square-root implementations for state estimation in continuous-discrete\n  nonlinear stochastic systems   Recent research in nonlinear filtering and signal processing has suggested an\nefficient derivative-free Extended Kalman filter (EKF) designed for\ndiscrete-time stochastic systems. Such approach, however, has failed to address\nthe estimation problem for continuous-discrete models. In this paper, we\ndevelop a novel continuous-discrete derivative-free EKF methodology by deriving\nthe related moment differential equations (MDEs) and sample point differential\nequations (SPDEs). Additionally, we derive their Cholesky-based square-root\nMDEs and SPDEs and obtain several numerically stable derivative-free EKF\nmethods. Finally, we propose the MATLAB-oriented implementations for all\ncontinuous-discrete derivative-free EKF algorithms derived. They are easy to\nimplement because of the built-in fashion of the MATLAB numerical integrators\nutilized for solving either the MDEs or SPDEs in use, which are the ordinary\ndifferential equations (ODEs). More importantly, these are accurate\nderivative-free EKF implementations because any built-in MATLAB ODE solver\nincludes the discretization error control that bounds the discretization error\narisen and makes the implementation methods accurate. Besides, this is done in\nautomatic way and no extra coding is required from users. The new filters are\nparticularly effective for working with stochastic systems with highly\nnonlinear and/or nondifferentiable drift and observation functions, i.e. when\nthe calculation of Jacobian matrices are either problematical or questionable.\nThe performance of the novel filtering methods is demonstrated on several\nnumerical tests.\n']","[('extended kalman filtering', 0.635546863079071), ('kalman filtering', 0.6312622427940369), ('kalman filter', 0.6309724450111389), ('kalman filter based', 0.6278190612792969), ('extended kalman filter', 0.6255495548248291), ('unscented kalman filter', 0.610805869102478), ('extended kalman', 0.5548620223999023), ('unscented kalman', 0.5363174080848694), ('state estimation methods', 0.4992533028125763), ('state estimation continuous', 0.4952676296234131)]"
1559,1559,19,1559_weighted banach spaces_operator norm_operators weighted_multiplication operators,"['weighted banach spaces', 'operator norm', 'operators weighted', 'multiplication operators', 'spaces tree', 'weighted composition operators', 'operators', 'estimates operator norm', 'composition operators', 'operators discrete']","['Multiplication operators on weighted Banach spaces of a tree   We study multiplication operators on the weighted Banach spaces of an\ninfinite tree. We characterize the bounded and the compact operators, as well\nas determine the operator norm. In addition, we determine the spectrum of the\nbounded multiplication operators and characterize the isometries. Finally, we\nstudy the multiplication operators between the weighted Banach spaces and the\nLipschitz space by characterizing the bounded and the compact operators,\ndetermine estimates on the operator norm, and show there are no isometries.\n', 'Multiplication operators on the weighted Lipschitz space of a tree   We study the multiplication operators on the weighted Lipschitz space\n$\\mathcal{L}_{\\textbf{w}}$ consisting of the complex-valued functions $f$ on\nthe set of vertices of an infinite tree $T$ rooted at $o$ such that\n$\\sup_{v\\neq o}|v||f(v)-f(v^-)|<\\infty$, where $|v|$ denotes the distance\nbetween $o$ and $v$ and $v^-$ is the neighbor of $v$ closest to $o$. For the\nmultiplication operator, we characterize boundedness, compactness, provide\nestimates on the operator norm and the essential norm, and determine the\nspectrum. We prove that there are no isometric multiplication operators or\nisometric zero divisors on $\\mathcal{L}_{\\textbf{w}}$.\n', 'Multiplication operators between iterated logarithmic Lipschitz spaces\n  of a tree   In this article, we characterize the bounded and the compact multiplication\noperators between distinct iterated logarithmic Lipschitz spaces, and between\nthe Lipschitz space and an iterated logarithmic Lipschitz space of an infinite\ntree. In addition, we provide operator norm estimates and show that there are\nno isometries among such operators. %We obtain a new characterization of the\nbounded multiplication operators acting on an iterated logarithmic Lipschitz\nspace and the compact multiplication operators between the weighted Lipschitz\nspace and the Lipschitz space.\n']","[('weighted banach spaces', 0.5092034339904785), ('operator norm', 0.4657127559185028), ('operators weighted', 0.45159873366355896), ('multiplication operators', 0.45111599564552307), ('spaces tree', 0.4472975432872772), ('weighted composition operators', 0.44254907965660095), ('operators', 0.4409436285495758), ('estimates operator norm', 0.4399702250957489), ('composition operators', 0.43132296204566956), ('operators discrete', 0.4198421239852905)]"
1560,1560,19,1560_boundary controllability_exact boundary controllability_controllability nonlinear_controllability results,"['boundary controllability', 'exact boundary controllability', 'controllability nonlinear', 'controllability results', 'local controllability', 'controllability trajectories', 'controllability', 'boundary controls', 'exact controllability', 'exact controllability trajectories']","['Internal controllability of the Korteweg-de Vries equation on a bounded\n  domain   This paper is concerned with the control properties of the Korteweg-de Vries\n(KdV) equation posed on a bounded interval with a distributed control. When the\ncontrol region is an arbitrary open subdomain, we prove the null\ncontrollability of the KdV equation by means of a new Carleman inequality. As a\nconsequence, we obtain a regional controllability result, the state function\nbeing controlled on the left part of the complement of the control region.\nFinally, when the control region is a neighborhood of the right endpoint, an\nexact controllability result in a weighted L2 space is also established.\n', 'Neumann boundary controllability of the Korteweg-de Vries equation on a\n  bounded domain   In this paper we study boundary controllability of the Korteweg-de Vries\n(KdV) equation posed on a finite domain $(0,L)$ with the Neumann boundary\nconditions:\n  u_t+u_x+uu_x+u_{xxx}=0 in (0,L)x(0,T),\n  u_{xx}(0,t)=0, u_x(L,t)=h(t), u_{xx}(L,t)=0 in (0,T),\n  u(x,0)=u_0(x) in (0,L).\n  We show that the associated linearized system\n  u_t+(1+\\beta)u_x+u_{xxx}=0 in (0,L)x(0,T),\n  u_{xx}(0,t)=0, u_x(L,t)=h(t), u_{xx}(L,t)=0 in (0,T),\n  u(x,0)=u_0(x) in (0,L)\n  is exactly controllable if and only if the length $L$ of the spatial domain\n$(0,L)$ does not equal to $-1$ or does not belong to set\n  R_{\\beta}:={\\frac{2\\pi}{\\sqrt{3(1+\\beta)}}\\sqrt{k^{2}+kl+l^{2}}:k,l\\in\\mathbb{N}^{\\ast}}\\cup{\\frac{k\\pi}{\\sqrt{1+\\beta}}:k\\in\\mathbb{N}^{\\ast}}\n  and the nonlinear system is locally exactly controllable around a constant\nsteady state $\\beta$ if the associated linear system is exactly controllable.\n', 'Boundary controllability of a nonlinear coupled system of two\n  Korteweg-de Vries equations with critical size restrictions on the spatial\n  domain   This article is dedicated to improve the controllability results obtained by\nCerpa et al. in Commun. Contemp. Math 13 (2011) and by Micu et al. in Commun.\nContemp. Math 11 (5) (2009) for a nonlinear coupled system of two Korteweg-de\nVries (KdV) equations posed on a bounded interval. Initially, in Micu et al.,\nthe authors proved that the nonlinear system is exactly controllable by using\nfour boundary controls without any restriction on the length L of the interval.\nLater on, in Cerpa et al., two boundary controls were considered to prove that\nthe same system is exactly controllable for small values of the length L and\nlarge time of control T. Here, we use the ideas contained in Capistrano-Filho\net al. (arXiv 1508.07525) to prove that, with another configuration of four\ncontrols, it is possible to prove the existence of the so-called critical\nlength phenomenon for the nonlinear system, i. e., whether the system is\ncontrollable depends on the length of the spatial domain. In addition, when we\nconsider only one control input, the boundary controllability still holds for\nsuitable values of the length L and time of control T. In both cases, the\ncontrol spaces are sharp due a technical lemma which reveals a hidden\nregularity for the solution of the adjoint system.\n']","[('boundary controllability', 0.6819846034049988), ('exact boundary controllability', 0.6634947061538696), ('controllability nonlinear', 0.6019960641860962), ('controllability results', 0.5353420376777649), ('local controllability', 0.526168704032898), ('controllability trajectories', 0.5143738389015198), ('controllability', 0.5082280039787292), ('boundary controls', 0.5009803175926208), ('exact controllability', 0.49147582054138184), ('exact controllability trajectories', 0.48750919103622437)]"
1561,1561,18,1561_burnside ring_ring finite group_groups field characteristic_burnside,"['burnside ring', 'ring finite group', 'groups field characteristic', 'burnside', 'rings finite', 'coefficients commutative ring', 'ring finite', 'compute ring', 'rings connected', 'rings']","[""Blocks of Fibered Burnside Rings   In this article, we provide bases for the indecomposable factors of fibered\nBurnside rings in finite rank, and we give further characterizations of these\nas solvable components of fibered Burnside rings for certain Weyl groups. We\nrevisit Dress' construction of prime spectra of fibered Burnside rings and its\nconnected components for some rings of characteristic zero.\n"", 'Simplicial Burnside ring   This paper develops links between the Burnside ring of a finite group $G$ and\nthe slice Burnside ring}. The goal is to gain a better understanding of ghost\nmaps, idempotents, prime spectrum of these Burnside rings and connections\nbetween them.\n', 'The $A$-fibered Burnside ring as $A$-fibered biset functor in\n  characteristic zero   Let $A$ be an abelian group such that $\\mathrm{Hom}(G,A)$ is finite for all\nfinite groups $G$, and let $\\mathbb{K}$ be a field of characteristic zero\ncontaining roots of unity of all orders equal to finite element orders in $A$.\nIn this paper we prove foundational properties of the $A$-fibered Burnside ring\nfunctor $B_{\\mathbb{K}}^A$ as an $A$-fibered biset functor over $\\mathbb{K}$.\nThis includes the determination of the lattice of subfunctors of\n$B_{\\mathbb{K}}^A$ and the determination of the composition factors of\n$B_{\\mathbb{K}}^A$. The results of the paper extend results of Co\\c{s}kun and\nY\\i lmaz for the $A$-fibered Burnside ring functor restricted to $p$-groups and\nresults of Bouc in the case that $A$ is trivial, i.e., the case of the Burnside\nring functor over fields of characteristic zero.\n']","[('burnside ring', 0.6328104734420776), ('ring finite group', 0.5146500468254089), ('groups field characteristic', 0.4527515769004822), ('burnside', 0.42525726556777954), ('rings finite', 0.3980538547039032), ('coefficients commutative ring', 0.39401596784591675), ('ring finite', 0.3858652114868164), ('compute ring', 0.378431499004364), ('rings connected', 0.3756887912750244), ('rings', 0.3739399015903473)]"
1562,1562,18,1562_integer matrices_matrices integer_matrices finite_number matrices,"['integer matrices', 'matrices integer', 'matrices finite', 'number matrices', 'matrix polynomials', 'matrices fixed', 'matrices entries', 'matrices ranks', 'matrices rank', 'circulant matrices']","['Counting integer matrices with square-free determinants   We consider the set $\\mathcal M_n\\left(\\mathbb Z; H\\right)$ of $n\\times\nn$-matrices with integer elements of size at most $H$ and obtain and asymptotic\nformula on the number of matrices from $\\mathcal M_n\\left(\\mathbb Z; H\\right)$\nwith square-free determinants. We also use our approach with some further\nenhancements, to obtain an asymptotic formula for the sum of the Euler function\nwith determinants of matrices from $\\mathcal M_n\\left(\\mathbb Z; H\\right)$.\n', 'Integer matrices with a given characteristic polynomial and\n  multiplicative dependence of matrices   We consider the set $\\mathcal{M}_n(\\mathbb Z; H)$ of $n\\times n$-matrices\nwith integer elements of size at most $H$ and obtain a new upper bound on the\nnumber of matrices from $\\mathcal{M}_n(\\mathbb Z; H)$ with a given\ncharacteristic polynomial $f \\in \\mathbb Z[X]$, which is uniform with respect\nto $f$. This complements the asymptotic formula of A. Eskin, S. Mozes and N.\nShah (1996) in which $f$ has to be fixed and irreducible.\n  Using this result, among others, we obtain upper and lower bounds on the\nnumber of $s$-tuples of matrices from $\\mathcal{M}_n(\\mathbb Z; H)$, satisfying\nvarious multiplicative relations, including multiplicative dependence and\nbounded generation of a subgroup of $\\mathrm{GL}_n(\\mathbb Q)$. These problems\ngeneralise those studied in the scalar case $n=1$ by F. Pappalardi, M. Sha, I.\nE. Shparlinski and C. L. Stewart (2018) with an obvious distinction due to the\nnon-commutativity of matrices.\n  Motivated by these problems, we also prove various properties of the variety\nof complex matrices with fixed characteristic polynomial, including computing\nthe degree of this variety.\n', 'On the sparsity of non-diagonalisable integer matrices and matrices with\n  a given discriminant   We consider the set $\\mathcal M_n(\\mathbb Z; H)$ of $n\\times n$-matrices with\ninteger elements of size at most $H$ and obtain upper bounds on the number of\nmatrices from $\\mathcal M_n(\\mathbb Z; H)$, for which the characteristic\npolynomial has a fixed discriminant $d$. When $d=0$, this corresponds to\ncounting matrices with a repeated eigenvalue, and thus is related to counting\nnon-diagonalisable matrices. For $d\\ne 0$, this problem seems not to have been\nstudied previously, while for $d=0$, both our approach and the final result\nimprove on those of A. J. Hetzel, J. S. Liew and K. Morrison (2007).\n']","[('integer matrices', 0.6167662739753723), ('matrices integer', 0.5576868057250977), ('matrices finite', 0.531114399433136), ('number matrices', 0.5048562288284302), ('matrix polynomials', 0.4541923999786377), ('matrices fixed', 0.44492390751838684), ('matrices entries', 0.43502718210220337), ('matrices ranks', 0.40618735551834106), ('matrices rank', 0.38968923687934875), ('circulant matrices', 0.3835614025592804)]"
1563,1563,18,1563_wavelets_wavelet functions_functions wavelets_wavelet theory,"['wavelets', 'wavelet functions', 'functions wavelets', 'wavelet theory', 'wavelet', 'wavelet frames', 'wavelet system', 'multiresolution analysis', 'multiresolution', 'signals moreover']","['Wavelet sets on Cantor Dyadic Group   W. C. Lang determined wavelets on Cantor dyadic group by using\nMultiresolution analysis method. In this paper we have given characterization\nof wavelet sets on Cantor dyadic group providing another method for the\nconstruction of wavelets. All the wavelets originating from wavelet sets are\nnot necessarily associated with a multiresolution analysis. Relation between\nmultiresolution analysis and, wavelets determined from wavelet sets is\nestablished along with relevant examples.\n', 'Wavelet Sets and Generalized Scaling Sets on Vilenkin Group   For Vilenkin group only the existence of multiwavelets associated with\nmultiresolution analysis (MRA) is known. In this paper, we have shown that by\nusing wavelet sets we can also construct single wavelet in case of Vilenkin\ngroup which are not associated with MRA.We have given characterization of\nsingle and multi-wavelet sets on Vilenkin group. Further, we have studied\ngeneralized scaling sets, some of their properties and relation between wavelet\nsets and generalized scaling sets.\n', 'A characterization of wavelet sets on Vilenkin groups with its\n  application to construction of MRA wavelets   Let $G$ be a Vilenkin group. In 2008, Y. A. Farkov constructed wavelets on\n$G$ via the multiresolution analysis method. In this article, a\ncharacterization of wavelet sets on $G$ is established, which provides another\nmethod for the construction of wavelets. As an application, the relation\nbetween multiresolution analyses and wavelets determined from wavelet sets is\nalso presented. To some extent, these results positively answer a question\nmentioned by P. Mahapatra and D. Singh in [Bull. Sci. Math. 167 (2021), Paper\nNo. 102945, 20 pp].\n']","[('wavelets', 0.6790218949317932), ('wavelet functions', 0.6497677564620972), ('functions wavelets', 0.6488965749740601), ('wavelet theory', 0.634869396686554), ('wavelet', 0.6268848776817322), ('wavelet frames', 0.6025747656822205), ('wavelet system', 0.5784580707550049), ('multiresolution analysis', 0.555718183517456), ('multiresolution', 0.4930480718612671), ('signals moreover', 0.29440706968307495)]"
1564,1564,18,1564_infinitesimals_infinitesimal_infinities_leibniz,"['infinitesimals', 'infinitesimal', 'infinities', 'leibniz', 'unlike infinite', 'mathematicians', 'mathematical', 'mathematics', 'notions context', 'leibnitz']","[""19th century real analysis, forward and backward   19th century real analysis received a major impetus from Cauchy's work.\nCauchy mentions variable quantities, limits, and infinitesimals, but the\nmeaning he attached to these terms is not identical to their modern meaning.\n  Some Cauchy historians work in a conceptual scheme dominated by an assumption\nof a teleological nature of the evolution of real analysis toward a preordained\noutcome. Thus, Gilain and Siegmund-Schultze assume that references to limite in\nCauchy's work necessarily imply that Cauchy was working with an Archi-medean\ncontinuum, whereas infinitesimals were merely a convenient figure of speech,\nfor which Cauchy had in mind a complete justification in terms of Archimedean\nlimits. However, there is another formalisation of Cauchy's procedures\nexploiting his limite, more consistent with Cauchy's ubiquitous use of\ninfinitesimals, in terms of the standard part principle of modern infinitesimal\nanalysis.\n  We challenge a misconception according to which Cauchy was allegedly forced\nto teach infinitesimals at the Ecole Polytechnique. We show that the debate\nthere concerned mainly the issue of rigor, a separate one from infinitesimals.\nA critique of Cauchy's approach by his contemporary de Prony sheds light on the\nmeaning of rigor to Cauchy and his contemporaries. An attentive reading of\nCauchy's work challenges received views on Cauchy's role in the history of\nanalysis, and indicates that he was a pioneer of infinitesimal techniques as\nmuch as a harbinger of the Epsilontik.\n"", ""Cauchy's work on integral geometry, centers of curvature, and other\n  applications of infinitesimals   Like his colleagues de Prony, Petit, and Poisson at the Ecole Polytechnique,\nCauchy used infinitesimals in the Leibniz-Euler tradition both in his research\nand teaching. Cauchy applied infinitesimals in an 1826 work in differential\ngeometry where infinitesimals are used neither as variable quantities nor as\nsequences but rather as numbers. He also applied infinitesimals in an 1832\narticle on integral geometry, similarly as numbers. We explore these and other\napplications of Cauchy's infinitesimals as used in his textbooks and research\narticles.\n  An attentive reading of Cauchy's work challenges received views on Cauchy's\nrole in the history of analysis and geometry. We demonstrate the viability of\nCauchy's infinitesimal techniques in fields as diverse as geometric\nprobability, differential geometry, elasticity, Dirac delta functions,\ncontinuity and convergence.\n  Keywords: Cauchy--Crofton formula; center of curvature; continuity;\ninfinitesimals; integral geometry; limite; standard part; de Prony; Poisson\n"", ""Evolution of Leibniz's thought in the matter of fictions and\n  infinitesimals   In this paper we offer a reconstruction of the evolution of Leibniz's thought\nconcerning the problem of the infinite divisibility of bodies, the tension\nbetween actuality, unassignability and syncategorematicity, and the closely\nrelated question of the possibility of infinitesimal quantities, both in\nphysics and in mathematics.\n  Some scholars have argued that syncategorematicity is a mature acquisition,\nto which Leibniz resorts to solve the question of his infinitesimals namely the\nidea that infinitesimals are just signs for Archimedean exhaustions, and their\nunassignability is a nominalist maneuver. On the contrary, we show that\nsycategorematicity, as a traditional idea of classical scholasticism, is a\nfeature of young Leibniz's thinking, from which he moves away in order to solve\nthe same problem, as he gains mathematical knowledge.\n  We have divided Leibniz's path toward his mature view of infinitesimals into\nfive phases, which are especially significant for reconstructing the entire\nevolution. In our reconstruction, an important role is played by Leibniz's text\nDe Quadratura Arithmetica. Based on this and other texts we dispute the thesis\nthat fictionality coincides with syncategorematicity, and that unassignability\ncan be bypassed. On the contrary, we maintain that unassignability, as\nincompatible with the principle of harmony, is the ultimate reason for the\nfictionality of infinitesimals.\n""]","[('infinitesimals', 0.5972924828529358), ('infinitesimal', 0.5265169143676758), ('infinities', 0.4461539387702942), ('leibniz', 0.4092860519886017), ('unlike infinite', 0.405917227268219), ('mathematicians', 0.38570740818977356), ('mathematical', 0.3798181414604187), ('mathematics', 0.3693366050720215), ('notions context', 0.32567980885505676), ('leibnitz', 0.3243463337421417)]"
1565,1565,18,1565_solutions klein gordon_spectrum eigenfunctions_yukawa potential_relativistic quantum,"['solutions klein gordon', 'spectrum eigenfunctions', 'yukawa potential', 'relativistic quantum', 'relativistic schr odinger', 'klein gordon dirac', 'energy spectrum', 'coulomb potential', 'delta potentials', 'energy eigenvalues']","['Nonlinear PDE models in semi-relativistic quantum physics   We present the self-consistent Pauli equation, a semi-relativistic model for\ncharged spin-$1/2$-particles with self-interaction with the electromagnetic\nfield. The Pauli equation arises as the $O(1/c)$ approximation of the\nrelativistic Dirac equation. The fully relativistic self-consistent model is\nthe Dirac-Maxwell equation where the description of spin and the magnetic field\narises naturally. In the non-relativistic setting the correct self-consistent\nequation is the Schr\\""odinger-Poisson equation which does not describe spin and\nthe magnetic field and where the self-interaction is with the electric field\nonly.\n  The Schr\\""odinger-Poisson equation also arises as the mean field limit of the\n$N$-body Schr\\""odinger equation with Coulomb interaction. We propose that the\nPauli-Poisson equation arises as the mean field limit $N \\rightarrow \\infty$ of\nthe linear $N$-body Pauli equation with Coulomb interaction where one has to\npay extra attention to the fermionic nature of the Pauli equation.\n  We present the semiclassical limit of the Pauli-Poisson equation by the\nWigner method to the Vlasov equation with Lorentz force coupled to the Poisson\nequation which is also consistent with the hierarchy in $1/c$ of the\nself-consistent Vlasov equation. This is a non-trivial extension of the\ngroundbreaking works by Lions & Paul and Markowich & Mauser, where we need\nmethods like magnetic Lieb-Thirring estimates.\n', ""Analytical bound-state solutions of the Klein-Fock-Gordon equation for\n  the sum of Hulth\\'en and Yukawa potential within SUSY quantum mechanics   The relativistic wave equations determine the dynamics of quantum fields in\nthe context of quantum field theory. One of the conventional tools for dealing\nwith the relativistic bound-state problem is the Klein-Fock-Gordon equation. In\nthis work, using a developed scheme, we present how to surmount the centrifugal\npart and solve the modified Klein-Fock-Gordon equation for the linear\ncombination of Hulth\\'en and Yukawa potentials. In particular, we show that the\nrelativistic energy eigenvalues and corresponding radial wave functions are\nobtained from supersymmetric quantum mechanics by applying the shape invariance\nconcept. Here, both scalar potential conditions, which are whether equal and\nnon-equal to vector potential, are considered in the calculation. The energy\nlevels and corresponding normalized eigenfunctions are represented as a\nrecursion relation regarding the Jacobi polynomials for arbitrary $l$ states.\nBeyond that, a closed-form of the normalization constant of the wave functions\nis found. Furthermore, we state that the energy eigenvalues are quite sensitive\nwith potential parameters for the quantum states. The non-relativistic and\nrelativistic results obtained within SUSY QM overlap entirely with the results\nobtained by ordinary quantum mechanics, and it displays that the mathematical\nimplementation of SUSY quantum mechanics is quite perfect.\n"", 'Arbitrary $\\ell$-state solutions of the Klein-Gordon equation with the\n  Eckart plus a class of Yukawa potential and its non-relativistic thermal\n  properties   We report bound state solutions of the Klein Gordon equation with a novel\ncombined potential, the Eckart plus a class of Yukawa potential, by means of\nthe parametric Nikiforov-Uvarov method. To deal the centrifugal and the\ncoulombic behavior terms, we apply the Greene-Aldrich approximation scheme. We\npresent any $\\ell$-state energy eigenvalues and the corresponding normalized\nwave functions of a mentioned system in a closed form. We discuss various\nspecial cases related to our considered potential which are utility for other\nphysical systems and show that these are consistent with previous reports in\nliterature. Moreover, we calculate the non-relativistic thermodynamic\nquantities (partition function, mean energy, free energy, specific heat and\nentropy) for the potential model in question, and investigate them for a few\ndiatomic molecules. We find that the energy eigenvalues are sensitive with\nregard to the quantum numbers $n_r$ and $\\ell$ as well as the parameter\n$\\delta$. Our results show that energy eigenvalues are more bounded at either\nsmaller quantum number $\\ell$ or smaller parameter $\\delta$.\n']","[('solutions klein gordon', 0.4894888997077942), ('spectrum eigenfunctions', 0.4613206386566162), ('yukawa potential', 0.4597790241241455), ('relativistic quantum', 0.45849645137786865), ('relativistic schr odinger', 0.44241783022880554), ('klein gordon dirac', 0.423172265291214), ('energy spectrum', 0.4160185158252716), ('coulomb potential', 0.41469958424568176), ('delta potentials', 0.41217881441116333), ('energy eigenvalues', 0.4054442048072815)]"
1566,1566,18,1566_inverse scattering_gaussian random field_scattering random_isotropic gaussian,"['inverse scattering', 'gaussian random field', 'scattering random', 'isotropic gaussian', 'elastic scattering', 'potential scattering', 'gaussian random', 'wave field', 'covariance operator', 'scattering biharmonic']","['Inverse Elastic Scattering for a Random Potential   This paper is concerned with an inverse scattering problem for the\ntime-harmonic elastic wave equation with a random potential. Interpreted as a\ndistribution, the potential is assumed to be a microlocally isotropic\ngeneralized Gaussian random field with the covariance operator being described\nby a classical pseudo-differential operator. The goal is to determine the\nprincipal symbol of the covariance operator from the scattered wave measured in\na bounded domain which has a positive distance from the domain of the\npotential. For such a rough potential, the well-posedness of the direct\nscattering problem in the distribution sense is established by studying an\nequivalent Lippmann--Schwinger integral equation. For the inverse scattering\nproblem, it is shown with probability one that the principal symbol of the\ncovariance operator can be uniquely determined by the amplitude of the\nscattered waves averaged over the frequency band from a single realization of\nthe random potential. The analysis employs the Born approximation in high\nfrequency, asymptotics of the Green tensor for the elastic wave equation, and\nmicrolocal analysis for the Fourier integral operators.\n', 'An inverse random source problem for the one-dimensional Helmholtz\n  equation with attenuation   This paper is concerned with an inverse random source problem for the\none-dimensional stochastic Helmholtz equation with attenuation. The source is\nassumed to be a microlocally isotropic Gaussian random field with its\ncovariance operator being a classical pseudo-differential operator. The random\nsources under consideration are equivalent to the generalized fractional\nGaussian random fields which include rough fields and can be even rougher than\nthe white noise, and hence should be interpreted as distributions. The\nwell-posedness of the direct source scattering problem is established in the\ndistribution sense. The micro-correlation strength of the random source, which\nappears to be the strength in the principal symbol of the covariance operator,\nis proved to be uniquely determined by the wave field in an open measurement\nset. Numerical experiments are presented for the white noise model to\ndemonstrate the validity and effectiveness of the proposed method.\n', 'An inverse random source problem for the biharmonic wave equation   This paper is concerned with an inverse source problem for the stochastic\nbiharmonic operator wave equation. The driven source is assumed to be a\nmicrolocally isotropic Gaussian random field with its covariance operator being\na classical pseudo-differential operator. The well-posedness of the direct\nproblem is examined in the distribution sense and the regularity of the\nsolution is discussed for the given rough source. For the inverse problem, the\nstrength of the random source, involved in the principal symbol of its\ncovariance operator, is shown to be uniquely determined by a single realization\nof the magnitude of the wave field averaged over the frequency band with\nprobability one. Numerical experiments are presented to illustrate the validity\nand effectiveness of the proposed method for the case that the random source is\nthe white noise.\n']","[('inverse scattering', 0.5516213774681091), ('gaussian random field', 0.5272305011749268), ('scattering random', 0.49922844767570496), ('isotropic gaussian', 0.46567386388778687), ('elastic scattering', 0.4619753360748291), ('potential scattering', 0.4609701931476593), ('gaussian random', 0.4517252445220947), ('wave field', 0.4377739131450653), ('covariance operator', 0.40763792395591736), ('scattering biharmonic', 0.402404248714447)]"
1567,1567,18,1567_random unitary_random quantum_quantum circuits_quantum gates,"['random unitary', 'random quantum', 'quantum circuits', 'quantum gates', 'quantum information', 'random unitaries', 'applications quantum', 'quantum channel', 'qubits', 'depth random']","['Local random quantum circuits form approximate designs on arbitrary\n  architectures   We consider random quantum circuits (RQC) on arbitrary connected graphs whose\nedges determine the allowed $2$-qudit interactions. Prior work has established\nthat such $n$-qudit circuits with local dimension $q$ on 1D, complete, and\n$D$-dimensional graphs form approximate unitary designs, that is, they generate\nunitaries from distributions close to the Haar measure on the unitary group\n$U(q^n)$ after polynomially many gates. Here, we extend those results by\nproving that RQCs comprised of $O(\\mathrm{poly}(n,k))$ gates on a wide class of\ngraphs form approximate unitary $k$-designs. We prove that RQCs on graphs with\nspanning trees of bounded degree and height form $k$-designs after\n$O(|E|n\\,\\mathrm{poly}(k))$ gates, where $|E|$ is the number of edges in the\ngraph. Furthermore, we identify larger classes of graphs for which RQCs\ngenerate approximate designs in polynomial circuit size. For $k \\leq 4$, we\nshow that RQCs on graphs of certain maximum degrees form designs after\n$O(|E|n)$ gates, providing explicit constants. We determine our circuit size\nbounds from the spectral gaps of local Hamiltonians. To that end, we extend the\nfinite-size (or Knabe) method for bounding gaps of frustration-free\nHamiltonians on regular graphs to arbitrary connected graphs. We further\nintroduce a new method based on the Detectability Lemma for determining the\nspectral gaps of Hamiltonians on arbitrary graphs. Our methods have wider\napplicability as the first method provides a succinct alternative proof of\n[Commun. Math. Phys. 291, 257 (2009)] and the second method proves that RQCs on\nany connected architecture form approximate designs in quasi-polynomial circuit\nsize.\n', 'Random unitaries in extremely low depth   We prove that random quantum circuits on any geometry, including a 1D line,\ncan form approximate unitary designs over $n$ qubits in $\\log n$ depth. In a\nsimilar manner, we construct pseudorandom unitaries (PRUs) in 1D circuits in\n$\\text{poly}(\\log n)$ depth, and in all-to-all-connected circuits in\n$\\text{poly}(\\log \\log n)$ depth. In all three cases, the $n$ dependence is\noptimal and improves exponentially over known results. These shallow quantum\ncircuits have low complexity and create only short-range entanglement, yet are\nindistinguishable from unitaries with exponential complexity. Our construction\nglues local random unitaries on $\\log n$-sized or $\\text{poly}(\\log n)$-sized\npatches of qubits to form a global random unitary on all $n$ qubits. In the\ncase of designs, the local unitaries are drawn from existing constructions of\napproximate unitary $k$-designs, and hence also inherit an optimal scaling in\n$k$. In the case of PRUs, the local unitaries are drawn from existing PRU\nconstructions. Applications of our results include proving that classical\nshadows with 1D log-depth Clifford circuits are as powerful as those with deep\ncircuits, demonstrating superpolynomial quantum advantage in learning\nlow-complexity physical systems, and establishing quantum hardness for\nrecognizing phases of matter with topological order.\n', ""Random quantum circuits are approximate unitary $t$-designs in depth\n  $O\\left(nt^{5+o(1)}\\right)$   The applications of random quantum circuits range from quantum computing and\nquantum many-body systems to the physics of black holes. Many of these\napplications are related to the generation of quantum pseudorandomness: Random\nquantum circuits are known to approximate unitary $t$-designs. Unitary\n$t$-designs are probability distributions that mimic Haar randomness up to\n$t$th moments. In a seminal paper, Brand\\~{a}o, Harrow and Horodecki prove that\nrandom quantum circuits on qubits in a brickwork architecture of depth $O(n\nt^{10.5})$ are approximate unitary $t$-designs. In this work, we revisit this\nargument, which lower bounds the spectral gap of moment operators for local\nrandom quantum circuits by $\\Omega(n^{-1}t^{-9.5})$. We improve this lower\nbound to $\\Omega(n^{-1}t^{-4-o(1)})$, where the $o(1)$ term goes to $0$ as\n$t\\to\\infty$. A direct consequence of this scaling is that random quantum\ncircuits generate approximate unitary $t$-designs in depth $O(nt^{5+o(1)})$.\nOur techniques involve Gao's quantum union bound and the unreasonable\neffectiveness of the Clifford group. As an auxiliary result, we prove fast\nconvergence to the Haar measure for random Clifford unitaries interleaved with\nHaar random single qubit unitaries.\n""]","[('random unitary', 0.593514621257782), ('random quantum', 0.5920584797859192), ('quantum circuits', 0.4972614049911499), ('quantum gates', 0.4656941592693329), ('quantum information', 0.42232978343963623), ('random unitaries', 0.4179765284061432), ('applications quantum', 0.4165491461753845), ('quantum channel', 0.41591671109199524), ('qubits', 0.4006562829017639), ('depth random', 0.37984389066696167)]"
1568,1568,18,1568_combinatorial optimization_airline_flights_integer programming,"['combinatorial optimization', 'airline', 'flights', 'integer programming', 'crew', 'pilots', 'pairings', 'pairing', 'flight', 'aviation']","[""Real-World Airline Crew Pairing Optimization: Customized Genetic\n  Algorithm versus Column Generation Method   Airline crew pairing optimization problem (CPOP) aims to find a set of flight\nsequences (crew pairings) that cover all flights in an airline's highly\nconstrained flight schedule at minimum cost. Since crew cost is second only to\nthe fuel cost, CPOP solutioning is critically important for an airline.\nHowever, CPOP is NP-hard, and tackling it is quite challenging. The literature\nsuggests, that when the CPOP's scale and complexity is reasonably limited, and\nan enumeration of all crew pairings is possible, then Metaheuristics are used,\npredominantly Genetic Algorithms (GAs). Else, Column Generation (CG) based\nMixed Integer Programming techniques are used. Notably, as per the literature,\na maximum of 45,000 crew pairings have been tackled by GAs. In a significant\ndeparture, this paper considers over 800 flights of a US-based large airline\n(with a monthly network of over 33,000 flights), and tests the efficacy of GAs\nby enumerating all 400,000+ crew pairings, apriori. Towards it, this paper\nproposes a domain-knowledge-driven customized-GA. The utility of incorporating\ndomain-knowledge in GA operations, particularly initialization and crossover,\nis highlighted through suitable experiments. Finally, the proposed GA's\nperformance is compared with a CG-based approach (developed in-house by the\nauthors). Though the latter is found to perform better in terms of solution's\ncost-quality and run time, it is hoped that this paper will help in better\nunderstanding the strengths and limitations of domain-knowledge-driven\ncustomizations in GAs, for solving combinatorial optimization problems,\nincluding CPOPs.\n"", ""A Novel Column Generation Heuristic for Airline Crew Pairing\n  Optimization with Large-scale Complex Flight Networks   Crew Pairing Optimization (CPO) is critical for an airlines' business\nviability, given that the crew operating cost is second only to the fuel cost.\nCPO aims at generating a set of flight sequences (crew pairings) to cover all\nscheduled flights, at minimum cost, while satisfying several legality\nconstraints. The state-of-the-art heavily relies on relaxing the underlying\nInteger Programming Problem into a Linear Programming Problem, which in turn is\nsolved through the Column Generation (CG) technique. However, with the\nalarmingly expanding airlines' operations, CPO is marred by the curse of\ndimensionality, rendering the exact CG-implementations obsolete, and\nnecessitating the heuristic-based CG-implementations. Yet, in literature, the\nmuch prevalent large-scale complex flight networks involving multiple { crew\nbases and/or hub-and-spoke sub-networks, largely remain uninvestigated. This\npaper proposes a novel CG heuristic, which has enabled the in-house development\nof an Airline Crew Pairing Optimizer (AirCROP). The efficacy of the\nheuristic/AirCROP has been tested on real-world, large-scale, complex network\ninstances with over 4,200 flights, 15 crew bases, and multiple hub-and-spoke\nsub-networks (resulting in billion-plus possible pairings). Notably, this paper\nhas a dedicated focus on the proposed CG heuristic (not the entire AirCROP\nframework) based on balancing random exploration of pairings; exploitation of\ndomain knowledge (on optimal solution features); and utilization of the past\ncomputational & search effort through archiving. Though this paper has an\nairline context, the proposed CG heuristic may find wider applications across\ndifferent domains, by serving as a template on how to utilize domain knowledge\nto better tackle combinatorial optimization problems.\n"", ""Airline Crew Pairing Optimization Framework for Large Networks with\n  Multiple Crew Bases and Hub-and-Spoke Subnetworks   Crew Pairing Optimization aims at generating a set of flight sequences (crew\npairings), covering all flights in an airline's flight schedule, at minimum\ncost, while satisfying several legality constraints. CPO is critically\nimportant for airlines' business viability, considering that the crew operating\ncost is their second-largest expense. It poses an NP-hard combinatorial\noptimization problem, to tackle which, the state-of-the-art relies on relaxing\nthe underlying Integer Programming Problem (IPP) into a Linear Programming\nProblem (LPP), solving the latter through Column Generation (CG) technique, and\nintegerization of the resulting LPP solution. However, with the growing scale\nand complexity of the flight networks (those with a large number of flights,\nmultiple crew bases and/or multiple hub-and-spoke subnetworks), the utility of\nthe conventional CG-practices has become questionable. This paper proposed an\nAirline Crew Pairing Optimization Framework, AirCROP, whose constitutive\nmodules include the Legal Crew Pairing Generator, Initial Feasible Solution\nGenerator, and an Optimization Engine built on heuristic-based\nCG-implementation. In this paper, besides the design of AirCROP's modules,\ninsights into important questions related to how these modules interact, which\nthe literature is otherwise silent on, have been shared. These relate to the\nsensitivity of AirCROP's performance towards: sources of variability over\nmultiple runs for a given problem, initialization method, and termination\nparameters for LPP-solutioning and IPP-solutioning. The efficacy of the AirCROP\nhas been demonstrated on real-world large-scale and complex flight networks\n(with over 4200 flights, 15 crew bases, and billion-plus pairings). It is hoped\nthat with the emergence of such complex flight networks, this paper shall serve\nas an important milestone for affiliated research and applications.\n""]","[('combinatorial optimization', 0.541743278503418), ('airline', 0.4485376477241516), ('flights', 0.43417492508888245), ('integer programming', 0.43042242527008057), ('crew', 0.41991281509399414), ('pilots', 0.4022640287876129), ('pairings', 0.3851449191570282), ('pairing', 0.3713845908641815), ('flight', 0.368168443441391), ('aviation', 0.36751309037208557)]"
1569,1569,18,1569_hyperk ahler manifolds_ahler manifolds_hyperk ahler metric_compact hyperk ahler,"['hyperk ahler manifolds', 'ahler manifolds', 'hyperk ahler metric', 'compact hyperk ahler', 'ahler metric', 'hyperk ahler', 'space ahler', 'hermitian manifolds', 'hler manifold', 'fully nonlinear elliptic']","['Fully nonlinear elliptic equations on compact manifolds with a flat\n  hyperK\\""ahler metric   Mainly motivated by a conjecture of Alesker and Verbitsky, we study a class\nof fully non-linear elliptic equations on certain compact hyperhermitian\nmanifolds. By adapting the approach of Sz\\\'{e}kelyhidi to the hypercomplex\nsetting, we prove some a priori estimates for solutions to such equations under\nthe assumption of existence of $\\mathcal{C}$-subsolutions. In the estimate of\nthe quaternionic Laplacian, we need to further assume the existence of a flat\nhyperk\\""ahler metric. As an application of our results we prove that the\nquaternionic analogue of the Hessian equation and Monge-Amp\\`ere equation for\n$(n-1)$-plurisubharmonic functions can always be solved on compact flat\nhyperk\\""ahler manifolds.\n', 'Fully non-linear elliptic equations on compact hyperk\\""ahler manifolds   We consider a general class of elliptic equations on hypercomplex manifolds\nwhich includes the quaternionic Monge-Amp\\`ere equation, the quaternionic\nHessian equation and the Monge-Amp\\`ere equation for quaternionic\n$(n-1)$-plurisubharmonic functions. We prove that under suitable assumptions\nthe solutions to these equations on hyperk\\""ahler manifolds satisfy a\n$C^{2,\\alpha}$ a priori estimate.\n', 'The parabolic quaternionic Calabi-Yau equation on hyperk\\""ahler\n  manifolds   We show that the parabolic quaternionic Monge-Amp\\`ere equation on a compact\nhyperk\\""ahler manifold has always a long-time solution which once normalized\nconverges smoothly to a solution of the quaternionic Monge-Amp\\`ere equation.\nThis is the same setting in which Dinew and Sroka prove the conjecture of\nAlesker and Verbitsky. We also introduce an analogue of the Chern-Ricci flow in\nhyperhermitian manifolds.\n']","[('hyperk ahler manifolds', 0.7504304647445679), ('ahler manifolds', 0.667629063129425), ('hyperk ahler metric', 0.6449100375175476), ('compact hyperk ahler', 0.6370552182197571), ('ahler metric', 0.5595778226852417), ('hyperk ahler', 0.507981538772583), ('space ahler', 0.44053471088409424), ('hermitian manifolds', 0.43595612049102783), ('hler manifold', 0.42577147483825684), ('fully nonlinear elliptic', 0.4238293766975403)]"
1570,1570,18,1570_contextuality_context dependent_contexts_contextual,"['contextuality', 'context dependent', 'contexts', 'contextual', 'noncontextuality', 'context independent', 'context', 'arbitrary systems', 'deterministic systems', 'causality']","[""Contextuality with disturbance and without: Neither can violate\n  substantive requirements the other satisfies   Contextuality was originally defined only for consistently connected systems\nof random variables (those without disturbance/signaling).\nContextuality-by-Default theory (CbD) offers an extension of the notion of\ncontextuality to inconsistently connected systems (those with disturbance), by\ndefining it in terms of the systems' couplings subject to certain constraints.\nSuch extensions are sometimes met with skepticism. We pose the question of\nwhether it is possible to develop a set of substantive requirements (i.e.,\nthose addressing a notion itself rather than its presentation form) such that\n(1) for any consistently connected system these requirements are satisfied, but\n(2) they are violated for some inconsistently connected systems. We show that\nno such set of requirements is possible, not only for CbD but for all possible\nCbD-like extensions of contextuality. This follows from the fact that any\nextended contextuality theory \\T is contextually equivalent to a theory \\T' in\nwhich all systems are consistently connected. The contextual equivalence means\nthe following: there is a bijective correspondence between the systems in \\T\nand \\T' such that the corresponding systems in \\T and \\T' are, in a\nwell-defined sense, mere reformulations of each other, and they are contextual\nor noncontextual together.\n"", 'A note on the relation between the Contextual Fraction and CNT2   Contextuality (or lack thereof) is a property of systems of random variables.\nAmong the measures of the degree of contextuality, two have played important\nroles. One of them, Contextual Fraction ($\\text{CNTF}$) was proposed within the\nframework of the sheaf-theoretic approach to contextuality, and extended to\narbitrary systems in the Contextuality-by-Default approach. The other, denoted\n$\\text{CNT}_{2}$, was proposed as one of the measures within the\nContextuality-by-Default approach. In this note, I prove that\n$\\text{CNTF}=2\\text{CNT}_{2}$ within a class of systems, called cyclic, that\nhave played a prominent role in contextuality research.\n', 'Contextuality and Noncontextuality Measures and Generalized Bell\n  Inequalities for Cyclic Systems   Cyclic systems of dichotomous random variables have played a prominent role\nin contextuality research, describing such experimental paradigms as the\nKlyachko-Can-Binicoglu-Shumovky, Einstein-Podolsky-Rosen-Bell, and Leggett-Garg\nones in physics, as well as conjoint binary choices in human decision making.\nHere, we understand contextuality within the framework of the\nContextuality-by-Default (CbD) theory, based on the notion of probabilistic\ncouplings satisfying certain constraints. CbD allows us to drop the commonly\nmade assumption that systems of random variables are consistently connected.\nConsistently connected systems constitute a special case in which CbD\nessentially reduces to the conventional understanding of contextuality. We\npresent a theoretical analysis of the degree of contextuality in cyclic systems\n(if they are contextual) and the degree of noncontextuality in them (if they\nare not). By contrast, all previously proposed measures of contextuality are\nconfined to consistently connected systems, and most of them cannot be extended\nto measures of noncontextuality. Our measures of (non)contextuality are defined\nby the L_{1}-distance between a point representing a cyclic system and the\nsurface of the polytope representing all possible noncontextual cyclic systems\nwith the same single-variable marginals. We completely characterize this\npolytope, as well as the polytope of all possible probabilistic couplings for\ncyclic systems with given single-variable marginals.[...]\n']","[('contextuality', 0.6005847454071045), ('context dependent', 0.5271548628807068), ('contexts', 0.5262406468391418), ('contextual', 0.5250336527824402), ('noncontextuality', 0.5246880650520325), ('context independent', 0.49655309319496155), ('context', 0.4366315007209778), ('arbitrary systems', 0.4016592502593994), ('deterministic systems', 0.3993411958217621), ('causality', 0.3938787281513214)]"
1571,1571,18,1571_lozenge tilings_tilings_tilings two_number tilings,"['lozenge tilings', 'tilings', 'tilings two', 'number tilings', 'hexagons', 'tiling', 'lattice paths', 'triangular lattice', 'intersecting lattice paths', 'hexagon']","[""Lozenge tilings of hexagons with holes on three crossing lines   The enumeration of lozenge tilings of hexagons with holes has received much\nattention during the last three decades. One notable feature is that a lot of\nthe recent development involved Kuo's graphical condensation. Motivated by\nCiucu, Lai and Rohatgi's work on tilings of hexagons with a removed triad of\nbowties, in this paper, we show that the ratio of numbers of lozenge tilings of\ntwo more general regions is expressed as a simple product formula. Our proof\ndoes not involve the graphical condensation method. The proof is short and\ndirect. We also provide a corresponding formula for cyclically symmetric\nlozenge tilings. Several previous results can be easily deduced from our\ngeneralization.\n"", 'The quotient of generating functions of lozenge tilings for certain\n  regions derived from hexagons, obtained with non--intersecting lattice paths   In a recent preprint, Lai showed that the quotient of generating functions of\nweighted lozenge tilings of two ""half hexagons with lateral dents"", which\ndiffer only in width, factors nicely, and the same is true for the quotient of\ngenerating functions of weighted lozenge tilings of two ""quarter hexagons with\nlateral dents"". Lai achieved this by using ""graphical condensation"" (i.e.,\napplication of a certain Pfaffian identity to the weighted enumeration of\nmatchings).\n  The purpose of this note is to exhibit how this can be done by the\nLindstr\\""om--Gessel--Viennot method for nonintersecting lattice paths. For the\ncase of ""half hexagons"", basically the same observation, but restricted to mere\nenumeration (i.e., all weights of lozenge tilings are equal to $1$), is\ncontained in a recent preprint of Condon.\n', 'A certain ratio of generating functions of lozenge tilings, obtained\n  with non--intersecting lattice paths   In a recent preprint, Lai worked out the quotient of generating functions of\nweighted lozenge tilings of two ""half hexagons with lateral dents"" which differ\nonly in width. Lai achieved this by using ""graphical condensation"" (i.e.,\napplication of a certain Pfaffian identity to the weighted enumeration of\nmatchings).\n  The purpose of this note is to exhibit how this can be done by the\nLindstr\\""om--Gessel--Viennot method for nonintersecting lattice paths in a\nquite simple way. Basically the same observation, but restricted to mere\nenumeration (i.e., all weights of lozenge tilings are equal to $1$), is\ncontained in a recent preprint of Condon.\n']","[('lozenge tilings', 0.6346507668495178), ('tilings', 0.6046542525291443), ('tilings two', 0.5876247882843018), ('number tilings', 0.5766039490699768), ('hexagons', 0.5242584943771362), ('tiling', 0.4918866753578186), ('lattice paths', 0.4891705811023712), ('triangular lattice', 0.47128674387931824), ('intersecting lattice paths', 0.46910548210144043), ('hexagon', 0.42575469613075256)]"
1572,1572,18,1572_tate shafarevich groups_shafarevich groups_tate shafarevich group_tate conjecture,"['tate shafarevich groups', 'shafarevich groups', 'tate shafarevich group', 'tate conjecture', 'shafarevich group', 'abelian varieties', 'varieties abelian', 'ordinary abelian varieties', 'abelian variety', 'abelian varieties abelian']","['On Tate--Shafarevich groups of one-dimensional families of commutative\n  group schemes over number fields   Given a smooth geometrically connected curve $C$ over a field $k$ and a\nsmooth commutative group scheme $G$ of finite type over the function field $K$\nof $C$ we study the Tate--Shafarevich groups given by elements of $H^1(K,G)$\nlocally trivial at completions of $K$ associated with closed points of $C$.\nWhen $G$ comes from a $k$-group scheme and $k$ is a number field (or $k$ is a\nfinitely generated field and $C$ has a $k$-point) we prove that the\nTate--Shafarevich group is finite, generalizing a result of Sa\\""idi and\nTamagawa for abelian varieties. We also give examples of nontrivial\nTate--Shafarevich groups in the case when $G$ is a torus and prove other\nrelated statements.\n', ""Finitude du groupe de Tate-Shafarevich pour les groupes de type\n  multiplicatif constants sur des corps des fonctions   Let $k_0$ be a number field, $K$ be a finite extension of\n$k_0(\\!(x_1,...,x_n)\\!)$ and let $R$ be the integral closure of\n$k_0[[x_1,...,x_n]]$ in $K$. Consider a group of multiplicative type $G$\ndefined over $K$. We study the Tate-Shafarevich group given by elements of\n$H^1(K,G)$ locally trivial at completions of $K$ with respect to the points of\ncodimension $1$ of $Spec(R)$. We show the finiteness of the Tate-Shafarevich\ngroup when $G$ comes from a group of multiplicative type $G_{k_0}$ defined over\n$k_0$ provided that two technical conditions are satisfied. We then prove that\nthe Tate-Shafarevich group is trivial when the ring of integers $R$ is regular.\n  --\n  Soient $k_0$ un corps de nombres, $K$ une extension finie de\n$k_0(\\!(x_1,...,x_n)\\!)$ et soit $R$ la cl\\^oture int\\'egrale de\n$k_0[[x_1,...,x_n]]$ dans $K$. Soit $G$ un groupe de type multiplicatif\nd\\'efini sur $k_0$. On \\'etudie le groupe de Tate-Shafarevich donn\\'e par les\n\\'el\\'ements de $H^1(K,G)$ localement triviaux aux compl\\'etions de $K$ par\nrapport aux points de codimension $1$ de $Spec(R)$. On \\'etablit la finitude du\ngroupe de Tate-Shafarevich lorsque $G$ provient d'un groupe de type\nmultiplicatif $G_{k_0}$ d\\'efini sur $k_0$ sous r\\'eserve que deux hypoth\\`eses\ntechniques soient satisfaites. On montre que le groupe de Tate-Shafarevich est\ntrivial lorsque l'anneau des entiers $R$ est r\\'egulier.\n"", 'On geometric Brauer groups and Tate-Shafarevich groups   Let $X$ be a smooth projective variety over a finitely generated field $K$ of\ncharacteristic $p>0$. We proved that the finiteness of the $\\ell$-primary part\nof $\\mathrm{Br}(X_{K^s})^{G_K}$ for a single prime $\\ell\\neq p$ will imply the\nfiniteness of the prime-to-$p$ part of $\\mathrm{Br}(X_{K^s})^{G_K}$,\ngeneralizing a theorem of Tate and Lichtenbaum for varieties over finite\nfields. For an abelian variety $A$ over $K$, we proved a similar result for the\nTate-Shafarevich group of $A$, generalizing a theorem of Schneider for abelian\nvarieties over global function fields.\n']","[('tate shafarevich groups', 0.691504716873169), ('shafarevich groups', 0.6224671006202698), ('tate shafarevich group', 0.6092822551727295), ('tate conjecture', 0.5727142095565796), ('shafarevich group', 0.5527767539024353), ('abelian varieties', 0.5423074960708618), ('varieties abelian', 0.5342299938201904), ('ordinary abelian varieties', 0.5170314311981201), ('abelian variety', 0.5120946168899536), ('abelian varieties abelian', 0.49141448736190796)]"
1573,1573,18,1573_policy asymptotically optimal_bandit problems_multi armed bandits_optimal policies,"['policy asymptotically optimal', 'bandit problems', 'multi armed bandits', 'optimal policies', 'optimal policy', 'near optimality', 'asymptotic optimality', 'bandits', 'optimal policy can', 'near optimal']","[""Low-Complexity Algorithm for Restless Bandits with Imperfect\n  Observations   We consider a class of restless bandit problems that finds a broad\napplication area in reinforcement learning and stochastic optimization. We\nconsider $N$ independent discrete-time Markov processes, each of which had two\npossible states: 1 and 0 (`good' and `bad'). Only if a process is both in state\n1 and observed to be so does reward accrue. The aim is to maximize the expected\ndiscounted sum of returns over the infinite horizon subject to a constraint\nthat only $M$ $(<N)$ processes may be observed at each step. Observation is\nerror-prone: there are known probabilities that state 1 (0) will be observed as\n0 (1). From this one knows, at any time $t$, a probability that process $i$ is\nin state 1. The resulting system may be modeled as a restless multi-armed\nbandit problem with an information state space of uncountable cardinality.\nRestless bandit problems with even finite state spaces are PSPACE-HARD in\ngeneral. We propose a novel approach for simplifying the dynamic programming\nequations of this class of restless bandits and develop a low-complexity\nalgorithm that achieves a strong performance and is readily extensible to the\ngeneral restless bandit model with observation errors. Under certain\nconditions, we establish the existence (indexability) of Whittle index and its\nequivalence to our algorithm. When those conditions do not hold, we show by\nnumerical experiments the near-optimal performance of our algorithm in the\ngeneral parametric space. Furthermore, we theoretically prove the optimality of\nour algorithm for homogeneous systems.\n"", 'Restless Bandits with Many Arms: Beating the Central Limit Theorem   We consider finite-horizon restless bandits with multiple pulls per period,\nwhich play an important role in recommender systems, active learning, revenue\nmanagement, and many other areas. While an optimal policy can be computed, in\nprinciple, using dynamic programming, the computation required scales\nexponentially in the number of arms $N$. Thus, there is substantial value in\nunderstanding the performance of index policies and other policies that can be\ncomputed efficiently for large $N$. We study the growth of the optimality gap,\ni.e., the loss in expected performance compared to an optimal policy, for such\npolicies in a classical asymptotic regime proposed by Whittle in which $N$\ngrows while holding constant the fraction of arms that can be pulled per\nperiod. Intuition from the Central Limit Theorem and the tightest previous\ntheoretical bounds suggest that this optimality gap should grow like\n$O(\\sqrt{N})$. Surprisingly, we show that it is possible to outperform this\nbound. We characterize a non-degeneracy condition and a wide class of novel\npractically-computable policies, called fluid-priority policies, in which the\noptimality gap is $O(1)$. These include most widely-used index policies. When\nthis non-degeneracy condition does not hold, we show that fluid-priority\npolicies nevertheless have an optimality gap that is $O(\\sqrt{N})$,\nsignificantly generalizing the class of policies for which convergence rates\nare known. We demonstrate that fluid-priority policies offer state-of-the-art\nperformance on a collection of restless bandit problems in numerical\nexperiments.\n', 'Near-optimality for infinite-horizon restless bandits with many arms   Restless bandits are an important class of problems with applications in\nrecommender systems, active learning, revenue management and other areas. We\nconsider infinite-horizon discounted restless bandits with many arms where a\nfixed proportion of arms may be pulled in each period and where arms share a\nfinite state space. Although an average-case-optimal policy can be computed via\nstochastic dynamic programming, the computation required grows exponentially\nwith the number of arms $N$. Thus, it is important to find scalable policies\nthat can be computed efficiently for large $N$ and that are near optimal in\nthis regime, in the sense that the optimality gap (i.e. the loss of expected\nperformance against an optimal policy) per arm vanishes for large $N$. However,\nthe most popular approach, the Whittle index, requires a hard-to-verify\nindexability condition to be well-defined and another hard-to-verify condition\nto guarantee a $o(N)$ optimality gap. We present a method resolving these\ndifficulties. By replacing a global Lagrange multiplier used by the Whittle\nindex with a sequence of Lagrangian multipliers, one per time period up to a\nfinite truncation point, we derive a class of policies, called fluid-balance\npolicies, that have a $O(\\sqrt{N})$ optimality gap. Unlike the Whittle index,\nfluid-balance policies do not require indexability to be well-defined and their\n$O(\\sqrt{N})$ optimality gap bound holds universally without sufficient\nconditions. We also demonstrate empirically that fluid-balance policies provide\nstate-of-the-art performance on specific problems.\n']","[('policy asymptotically optimal', 0.6348870992660522), ('bandit problems', 0.6251485347747803), ('multi armed bandits', 0.6027236580848694), ('optimal policies', 0.5713021755218506), ('optimal policy', 0.5554718971252441), ('near optimality', 0.5528209805488586), ('asymptotic optimality', 0.5463099479675293), ('bandits', 0.5377699136734009), ('optimal policy can', 0.5340976119041443), ('near optimal', 0.5107086896896362)]"
1574,1574,18,1574_air computation aircomp_computation air computation_computation aircomp_air computation,"['air computation aircomp', 'computation air computation', 'computation aircomp', 'air computation', 'wireless aggregation', 'wireless multiple access', 'multiple access channel', 'wireless multiple', 'aircomp systems', 'multiple access channels']","['Worst-case Design for RIS-aided Over-the-air Computation with Imperfect\n  CSI   Over-the-air computation (AirComp) enables fast wireless data aggregation at\nthe receiver through concurrent transmission by sensors in the application of\nInternet-of-Things (IoT). To further improve the performance of AirComp under\nunfavorable propagation channel conditions, we consider the problem of\ncomputation distortion minimization in a reconfigurable intelligent surface\n(RIS)-aided AirComp system. In particular, we take into account an additive\nbounded uncertainty of the channel state information (CSI) and the total power\nconstraint, and jointly optimize the transceiver (Tx-Rx) and the RIS phase\ndesign from the perspective of worst-case robustness by minimizing the mean\nsquared error (MSE) of the computation. To solve this intractable nonconvex\nproblem, we develop an efficient alternating algorithm where both solutions to\nthe robust sub-problem and to the joint design of Tx-Rx and RIS are obtained in\nclosed forms. Simulation results demonstrate the effectiveness of the proposed\nmethod.\n', 'Over-the-Air Computation Systems: Optimal Design with Sum-Power\n  Constraint   Over-the-air computation (AirComp), which leverages the superposition\nproperty of wireless multiple-access channel (MAC) and the mathematical tool of\nfunction representation, has been considered as a promising technique for\neffective collection and computation of massive sensor data in wireless Big\nData applications. In most of the existing work on AirComp, optimal\nsystem-parameter design is commonly considered under the peak-power constraint\nof each sensor. In this paper, we propose an optimal transmitter-receiver\n(Tx-Rx) parameter design problem to minimize the computation mean-squared error\n(MSE) of an AirComp system under the sum-power constraint of the sensors. We\nsolve the non-convex problem and obtain a closed-form solution. Also, we\ninvestigate another problem that minimizes the sum power of the sensors under\nthe constraint of computation MSE. Our results show that in both of the\nproblems, the sensors with poor and good channel conditions should use less\npower than the ones with moderate channel conditions.\n', 'Over-the-Air Computation with Spatial-and-Temporal Correlated Signals   Over-the-air computation (AirComp) leveraging the superposition property of\nwireless multiple-access channel (MAC), is a promising technique for effective\ndata collection and computation of large-scale wireless sensor measurements in\nInternet of Things applications. Most existing work on AirComp only considered\ncomputation of spatial-and-temporal independent sensor signals, though in\npractice different sensor measurement signals are usually correlated. In this\nletter, we propose an AirComp system with spatial-and-temporal correlated\nsensor signals, and formulate the optimal AirComp policy design problem for\nachieving the minimum computation mean-squared error (MSE). We develop the\noptimal AirComp policy with the minimum computation MSE in each time step by\nutilizing the current and the previously received signals. We also propose and\noptimize a low-complexity AirComp policy in closed form with the performance\napproaching to the optimal policy.\n']","[('air computation aircomp', 0.5335244536399841), ('computation air computation', 0.5164493322372437), ('computation aircomp', 0.5140156149864197), ('air computation', 0.5006730556488037), ('wireless aggregation', 0.4895508289337158), ('wireless multiple access', 0.4676971733570099), ('multiple access channel', 0.4621082842350006), ('wireless multiple', 0.45617902278900146), ('aircomp systems', 0.455814003944397), ('multiple access channels', 0.45489636063575745)]"
1575,1575,18,1575_stochastic maximum principle_stochastic control_mean field stochastic_mean field control,"['stochastic maximum principle', 'stochastic control', 'mean field stochastic', 'mean field control', 'field stochastic differential', 'stochastic maximum', 'principle mean field', 'optimal control', 'field stochastic', 'control variational']","['Constrained mean-field control with singular control: Existence,\n  stochastic maximum principle and constrained FBSDE   This paper studies some mean-field control (MFC) problems with singular\ncontrol under general dynamic state-control-law constraints. We first propose a\ncustomized relaxed control formulation to cope with the dynamic mixed\nconstraints and establish the existence of an optimal control using some\ncompactification arguments in the proper canonical spaces to accommodate the\nsingular control. To characterize the optimal pair of regular and singular\ncontrols, we treat the controlled McKean-Vlasov process as an\ninfinite-dimensional equality constraint and recast the MFC problem as an\noptimization problem on canonical spaces with constraints on Banach space,\nallowing us to derive the stochastic maximum principle (SMP) and a constrained\nBSDE using a novel Lagrange multipliers method. In addition, we further\ninvestigate the uniqueness and the stability result of the solution to the\nconstrained FBSDE associated to the constrained MFC problem with singular\ncontrol.\n', 'Extended mean field control problems with constraints: The generalized\n  Fritz-John conditions and Lagrangian method   This paper studies the extended mean field control problems under general\ndynamic expectation constraints and/or dynamic pathwise state-control and law\nconstraints. We aim to pioneer the establishment of the stochastic maximum\nprinciple (SMP) and the derivation of the backward SDE (BSDE) from the\nperspective of the constrained optimization using the method of Lagrangian\nmultipliers. To this end, we first propose to embed the constrained extended\nmean-field control (C-MFC) problems into some abstract optimization problems\nwith constraints on Banach spaces, for which we develop the generalized\nFritz-John (FJ) optimality conditions. We then prove the stochastic maximum\nprinciple (SMP) for C-MFC problems by transforming the FJ type conditions into\nan equivalent stochastic first-order condition associated with a general type\nof constrained forward-backward SDEs (FBSDEs). Contrary to the existing\nliterature, we treat the controlled Mckean-Vlasov SDE as an\ninfinite-dimensional equality constraint such that the BSDE induced by the FJ\nfirst-order optimality condition can be interpreted as the generalized Lagrange\nmultiplier to cope with the SDE constraint. Finally, we also present the SMP\nfor stochastic control problems and mean field game problems under similar\ntypes of constraints as consequences of our main result for C-MFC problems.\n', 'A stochastic maximum principle of mean-field type with monotonicity\n  conditions   The objective of this paper is to weaken the Lipschitz condition to a\nmonotonicity condition and to study the corresponding Pontryagin stochastic\nmaximum principle (SMP) for a mean-field optimal control problem under\nmonotonicity conditions.The dynamics of the controlled state process is\ngoverned by a mean-field stochastic differential equation (SDE) whose\ncoefficients depend not only on the control, the controlled state process\nitself but also on its law, and in particular, these coefficients satisfy the\nmonotonicity condition with respect to both the controlled state process and\nits distribution. The associated cost functional is also of mean-field type.\nUnder the assumption of a convex control domain we derive the SMP, which\nprovides a necessary optimality condition for control processes. Under\nadditional convexity assumptions on the Hamiltonian, we further prove that this\nnecessary condition is also a sufficient one. To achieve this, we first address\nthe challenges related to the existence and the uniqueness of solutions for\nmean-field backward stochastic differential equations and mean-field SDEs whose\ncoefficients satisfy monotonicity conditions with respect to both the solution\nas well as its distribution. On the other hand we also construct several\nillustrative examples demonstrating the generality of our results compared to\nexisting literature.\n']","[('stochastic maximum principle', 0.6405139565467834), ('stochastic control', 0.6006765961647034), ('mean field stochastic', 0.5946360230445862), ('mean field control', 0.5857744216918945), ('field stochastic differential', 0.5374908447265625), ('stochastic maximum', 0.5242226719856262), ('principle mean field', 0.5054675936698914), ('optimal control', 0.5041412115097046), ('field stochastic', 0.49799251556396484), ('control variational', 0.46538010239601135)]"
1576,1576,18,1576_graph local_infinite graphs_gradient flows_dynamical networks,"['graph local', 'infinite graphs', 'gradient flows', 'dynamical networks', 'graphs converges', 'non local approximation', 'viscosity solutions', 'limit gradient flow', 'local approximation', 'uniformly viscosity']","['Graph-to-local limit for the nonlocal interaction equation   We study a class of nonlocal partial differential equations presenting a\ntensor-mobility, in space, obtained asymptotically from nonlocal dynamics on\nlocalising infinite graphs. Our strategy relies on the variational structure of\nboth equations, being a Riemannian and Finslerian gradient flow, respectively.\nMore precisely, we prove that weak solutions of the nonlocal interaction\nequation on graphs converge to weak solutions of the aforementioned class of\nnonlocal interaction equation with a tensor-mobility in the Euclidean space.\nThis highlights an interesting property of the graph, being a potential\nspace-discretisation for the equation under study.\n', 'Limits of non-local approximations to the Eikonal equation on manifolds   In this paper, we consider a non-local approximation of the time-dependent\nEikonal equation defined on a Riemannian manifold. We show that the local and\nthe non-local problems are well-posed in the sense of viscosity solutions and\nwe prove regularity properties of these solutions in time and space. If the\nkernel is properly scaled, we then derive error bounds between the solution to\nthe non-local problem and the one to the local problem, both in continuous-time\nand Forward Euler discretization. Finally, we apply these results to a sequence\nof random weighted graphs with n vertices. In particular, we establish that the\nsolution to the problem on graphs converges almost surely uniformly to the\nviscosity solution of the local problem as the kernel scale parameter decreases\nat an appropriate rate when the number of vertices grows and the time step\nvanishes.\n', 'Limits and consistency of non-local and graph approximations to the\n  Eikonal equation   In this paper, we study a non-local approximation of the time-dependent\n(local) Eikonal equation with Dirichlet-type boundary conditions, where the\nkernel in the non-local problem is properly scaled. Based on the theory of\nviscosity solutions, we prove existence and uniqueness of the viscosity\nsolutions of both the local and non-local problems, as well as regularity\nproperties of these solutions in time and space. We then derive error bounds\nbetween the solution to the non-local problem and that of the local one, both\nin continuous-time and Backward Euler time discretization. We then turn to\nstudying continuum limits of non-local problems defined on random weighted\ngraphs with $n$ vertices. In particular, we establish that if the kernel scale\nparameter decreases at an appropriate rate as $n$ grows, then almost surely,\nthe solution of the problem on graphs converges uniformly to the viscosity\nsolution of the local problem as the time step vanishes and the number vertices\n$n$ grows large.\n']","[('graph local', 0.4610252380371094), ('infinite graphs', 0.43854430317878723), ('gradient flows', 0.4319189786911011), ('dynamical networks', 0.4272879660129547), ('graphs converges', 0.4264967143535614), ('non local approximation', 0.42418184876441956), ('viscosity solutions', 0.4161199927330017), ('limit gradient flow', 0.40536925196647644), ('local approximation', 0.401868611574173), ('uniformly viscosity', 0.39983129501342773)]"
1577,1577,18,1577_conformal mappings_conformal mapping_compute conformal_conformal modulus,"['conformal mappings', 'conformal mapping', 'compute conformal', 'conformal modulus', 'conformal invariants', 'conformal', 'polygonal domains', 'polygonal domain', 'domains complex plane', 'conformal capacity']","['Laplace--Beltrami Equations and Numerical Conformal Mappings on Surfaces   The conjugate function method is an algorithm for numerical computation of\nconformal mappings for simply and multiply connected domains. In this paper,\nthe conjugate function method is extended to cover conformal mappings between\nRiemannian surfaces. The main challenge addressed here is the connection\nbetween Laplace--Beltrami equations on surfaces and the computation of the\nconformal modulus of a quadrilateral. We consider mappings of simply, doubly,\nand multiply connected domains. The numerical computation is based on an\n$hp$-adaptive finite element method. The key advantage of our approach is that\nit allows highly accurate computations of mappings on surfaces, including\ndomains of complex boundary geometry involving strong singularities and cusps.\nThe efficacy of the proposed method is illustrated via an extensive set of\nnumerical experiments including error estimates.\n', 'PlgCirMap: A MATLAB toolbox for computing conformal mappings from\n  polygonal multiply connected domains onto circular domains   This paper presents a MATLAB toolbox for computing the conformal mapping from\na given polygonal multiply connected domain onto a circular multiply connected\ndomain and its inverse. The toolbox can be used for multiply connected domains\nwith high connectivity and complex geometry. It can be employed also for simply\nconnected domains.\n', 'One Parameter Families of Conformal Mappings of Bounded Doubly Connected\n  Polygonal Domains   We suggest an approximate method of finding a conformal mapping of an annulus\nonto an arbitrary bounded doubly connected polygonal domain. The method is\nbased on the parametric Loewner--Komatu method. We consider smooth one\nparameter families $\\mathcal{F}(z,t)$ of conformal mappings of concentric\nannuli onto doubly connected polygonal domains $\\mathcal{D}(t)$ which are\nobtained from a fixed doubly connected polygonal domain $\\mathcal{D}$ by making\na finite number of rectilinear slits of variable lengths; meanwhile we do not\nrequire the family of domains $\\mathcal{D}(t)$ to be monotonous. The integral\nrepresentation for the conformal mappings $\\mathcal{F}(z,t)$ has unknown\n(accessory) parameters. We find a PDE for this family and then deduce a system\nof PDEs describing dynamics of accessory parameters and conformal modulus of\n$\\mathcal{D}(t)$ when changing the parameter $t$. We note that the right-hand\nsides of equations in the system of ODEs involve functions standing for speeds\nof movement of the end points of the slits. This allows us to control\ncompletely dynamics of the slits and to seek their agreed change, if we have\nmore than one slit. We also give some results of numerical calculations which\nshow the efficiency of the suggested method.\n']","[('conformal mappings', 0.7072650194168091), ('conformal mapping', 0.7053071856498718), ('compute conformal', 0.6556667685508728), ('conformal modulus', 0.5914669632911682), ('conformal invariants', 0.5389226078987122), ('conformal', 0.5341658592224121), ('polygonal domains', 0.517536461353302), ('polygonal domain', 0.4796595573425293), ('domains complex plane', 0.44560348987579346), ('conformal capacity', 0.43931853771209717)]"
1578,1578,18,1578_polytope graph_edge polytopes_lattice polytopes_edge polytope,"['polytope graph', 'edge polytopes', 'lattice polytopes', 'edge polytope', 'polytopes associated', 'polytopes arising', 'root polytopes', 'polytopes particular', 'polytopes', 'symmetric edge']","['Symmetric edge polytopes and matching generating polynomials   Symmetric edge polytopes $\\mathcal{A}_G$ of type A are lattice polytopes\narising from the root system $A_n$ and finite simple graphs $G$. There is a\nconnection between $\\mathcal{A}_G$ and the Kuramoto synchronization model in\nphysics. In particular, the normalized volume of $\\mathcal {A}_G$ plays a\ncentral role. In the present paper, we focus on a particular class of graphs.\nIn fact, for any cactus graph $G$, we give a formula for the $h^*$-polynomial\nof $\\mathcal{A}_{\\widehat{G}}$ by using matching generating polynomials, where\n$\\widehat{G}$ is the suspension of $G$. This gives also a formula for the\nnormalized volume of $\\mathcal{A}_{\\widehat{G}}$. Moreover, via the chemical\ngraph theory, we show that for any cactus graph $G$, the $h^*$-polynomial of\n$\\mathcal{A}_{\\widehat{G}}$ is real-rooted. Finally, we extend the discussion\nto symmetric edge polytopes of type $B$, which are lattice polytopes arising\nfrom the root system $B_n$ and finite simple graphs.\n', 'Many faces of symmetric edge polytopes   Symmetric edge polytopes are a class of lattice polytopes constructed from\nfinite simple graphs. In the present paper we highlight their connections to\nthe Kuramoto synchronization model in physics -- where they are called\nadjacency polytopes -- and to Kantorovich--Rubinstein polytopes from finite\nmetric space theory. Each of these connections motivates the study of symmetric\nedge polytopes of particular classes of graphs. We focus on such classes and\napply algebraic-combinatorial methods to investigate invariants of the\nassociated symmetric edge polytopes.\n', ""Facets and facet subgraphs of symmetric edge polytopes   Symmetric edge polytopes, a.k.a. PV-type adjacency polytopes, associated with\nundirected graphs have been defined and studied in several seemingly\nindependent areas including number theory, discrete geometry, and dynamical\nsystems. In particular, the authors are motivated by the study of the algebraic\nKuramoto equations of unmixed form whose Newton polytopes are the symmetric\nedge polytopes.\n  The interplay between the geometric structure of symmetric edge polytopes and\nthe topological structure of the underlying graphs has been a recurring theme\nin recent studies. In particular, ``facet/face subgraphs'' have emerged as one\nof the central concepts in describing this symmetry. Continuing along this line\nof inquiry we provide a complete description of the correspondence between\nfacets/faces of a symmetric edge polytope and maximal bipartite subgraphs of\nthe underlying connected graph.\n""]","[('polytope graph', 0.6693865060806274), ('edge polytopes', 0.6569781303405762), ('lattice polytopes', 0.5973155498504639), ('edge polytope', 0.5970640182495117), ('polytopes associated', 0.5907450318336487), ('polytopes arising', 0.5742628574371338), ('root polytopes', 0.5644333362579346), ('polytopes particular', 0.5635105967521667), ('polytopes', 0.5479267835617065), ('symmetric edge', 0.5460763573646545)]"
1579,1579,18,1579_stochastic mirror descent_mirror descent_stochastic convex optimization_mirror descent primal,"['stochastic mirror descent', 'mirror descent', 'stochastic convex optimization', 'mirror descent primal', 'stochastic mirror', 'smooth convex optimization', 'stochastic approximation algorithms', 'convex optimization', 'accelerated stochastic', 'stochastic convex']","['Mirrorless Mirror Descent: A Natural Derivation of Mirror Descent   We present a primal only derivation of Mirror Descent as a ""partial""\ndiscretization of gradient flow on a Riemannian manifold where the metric\ntensor is the Hessian of the Mirror Descent potential. We contrast this\ndiscretization to Natural Gradient Descent, which is obtained by a ""full""\nforward Euler discretization. This view helps shed light on the relationship\nbetween the methods and allows generalizing Mirror Descent to general\nRiemannian geometries, even when the metric tensor is {\\em not} a Hessian, and\nthus there is no ""dual.""\n', 'Investigating Variance Definitions for Mirror Descent with Relative\n  Smoothness   Mirror Descent is a popular algorithm, that extends Gradients Descent (GD)\nbeyond the Euclidean geometry. One of its benefits is to enable strong\nconvergence guarantees through smooth-like analyses, even for objectives with\nexploding or vanishing curvature. This is achieved through the introduction of\nthe notion of relative smoothness, which holds in many of the common use-cases\nof Mirror descent. While basic deterministic results extend well to the\nrelative setting, most existing stochastic analyses require additional\nassumptions on the mirror, such as strong convexity (in the usual sense), to\nensure bounded variance. In this work, we revisit Stochastic Mirror Descent\n(SMD) proofs in the (relatively-strongly-) convex and relatively-smooth\nsetting, and introduce a new (less restrictive) definition of variance which\ncan generally be bounded (globally) under mild regularity assumptions. We then\ninvestigate this notion in more details, and show that it naturally leads to\nstrong convergence guarantees for stochastic mirror descent. Finally, we\nleverage this new analysis to obtain convergence guarantees for the Maximum\nLikelihood Estimator of a Gaussian with unknown mean and variance.\n', 'Stochastic Mirror Descent: Convergence Analysis and Adaptive Variants\n  via the Mirror Stochastic Polyak Stepsize   We investigate the convergence of stochastic mirror descent (SMD) under\ninterpolation in relatively smooth and smooth convex optimization. In\nrelatively smooth convex optimization we provide new convergence guarantees for\nSMD with a constant stepsize. For smooth convex optimization we propose a new\nadaptive stepsize scheme -- the mirror stochastic Polyak stepsize (mSPS).\nNotably, our convergence results in both settings do not make bounded gradient\nassumptions or bounded variance assumptions, and we show convergence to a\nneighborhood that vanishes under interpolation. Consequently, these results\ncorrespond to the first convergence guarantees under interpolation for the\nexponentiated gradient algorithm for fixed or adaptive stepsizes. mSPS\ngeneralizes the recently proposed stochastic Polyak stepsize (SPS) (Loizou et\nal. 2021) to mirror descent and remains both practical and efficient for modern\nmachine learning applications while inheriting the benefits of mirror descent.\nWe complement our results with experiments across various supervised learning\ntasks and different instances of SMD, demonstrating the effectiveness of mSPS.\n']","[('stochastic mirror descent', 0.7901339530944824), ('mirror descent', 0.6205441951751709), ('stochastic convex optimization', 0.6081722974777222), ('mirror descent primal', 0.5814460515975952), ('stochastic mirror', 0.5674105882644653), ('smooth convex optimization', 0.5263281464576721), ('stochastic approximation algorithms', 0.5137606263160706), ('convex optimization', 0.5119320750236511), ('accelerated stochastic', 0.4833887815475464), ('stochastic convex', 0.475883424282074)]"
1580,1580,18,1580_turbulence theory_isotropic turbulence_2d turbulence_decaying turbulence,"['turbulence theory', 'isotropic turbulence', '2d turbulence', 'decaying turbulence', 'turbulence', 'fully developed turbulence', 'turbulent', 'developed turbulence', 'euler navier stokes', 'forced navier stokes']","['Onsager\'s ""Ideal Turbulence"" Theory   Lars Onsager in 1945-1949 made an exact analysis of the high Reynolds-number\nlimit for individual turbulent flow realizations modeled by incompressible\nNavier-Stokes equations, motivated by experimental observations that\ndissipation of kinetic energy does not vanish. I review here developments\nspurred by his key idea, that such flows are well-described by distributional\nor ""weak"" solutions of ideal Euler equations. 1/3 H\\""older singularities of the\nvelocity field were predicted by Onsager and since observed. His theory\ndescribes turbulent energy cascade without probabilistic assumptions and yields\na local, deterministic version of the Kolmogorov 4/5th law. The approach is\nclosely related to renormalization group methods in physics and envisages\n""conservation-law anomalies"", as discovered later in quantum field theory.\nThere are also deep connections with Large-Eddy Simulation modeling. More\nrecently, dissipative Euler solutions of the type conjectured by Onsager have\nbeen constructed and his 1/3 H\\""older singularity proved to be the sharp\nthreshold for anomalous dissipation. This progress has been achieved by an\nunexpected connection with work of John Nash on isometric embeddings of low\nregularity or ""convex integration"" techniques. The dissipative Euler solutions\nyielded by this method are wildly non-unique for fixed initial data, suggesting\n""spontaneously stochastic"" behavior of high-Reynolds number solutions. I focus\nin particular on applications to wall-bounded turbulence, leading to novel\nconcepts of spatial cascades of momentum, energy and vorticity to or from the\nwall as deterministic, space-time local phenomena. This theory thus makes\ntestable predictions and offers new perspectives on Large-Eddy Simulation in\npresence of solid walls.\n', ""Scaling laws and exact results in turbulence   In this note, we address the validity of certain exact results from\nturbulence theory in the deterministic setting. The main tools, inspired by the\nwork of Duchon-Robert (Inertial energy dissipation for weak solutions of\nincompressible Euler and Navier-Stokes equations, Nonlinearity, 13(249), 2000)\nand Eyink (Local 4/5-law and energy dissipation anomaly in turbulence,\nNonlinearity, 16(137), 2003), are a number of energy balance identities for\nweak solutions of the incompressible Euler and Navier-Stokes equations. As a\nconsequence, we show that certain weak solutions of the Euler and Navier-Stokes\nequations satisfy deterministic versions of Kolmogorov's 4/5, 4/3, 4/15 laws.\nWe apply these computations to improve a recent result of Hofmanova et al.\n(Kolmogorov 4/5 law for the forced 3D Navier-Stokes equations,\narXiv:2304.14470), which shows that a construction of solutions of forced\nNavier-Stokes due to Bru\\`e et al. (Onsager critical solutions of the forced\nNavier-Stokes equations, arXiv:2212.08413) and exhibiting a form of anomalous\ndissipation satisfies asymptotic versions of Kolmogorov's laws. In addition, we\nshow that the globally dissipative 3D Euler flows recently constructed by Giri,\nKwon, and the author (The $L^3$-based strong Onsager theorem, arXiv:2305.18509)\nsatisfy the local versions of Kolmogorov's laws.\n"", ""Self-Regularization in turbulence from the Kolmogorov 4/5-Law and\n  Alignment   A defining feature of 3D hydrodynamic turbulence is that the rate of energy\ndissipation is bounded away from zero as viscosity is decreased (Reynolds\nnumber increased). This phenomenon - anomalous dissipation - is sometimes\ncalled the `zeroth law of turbulence' as it underpins many celebrated\ntheoretical predictions. Another robust feature observed in turbulence is that\nvelocity structure functions $S_p(\\ell) :=\\langle |\\delta_\\ell u|^p\\rangle$\nexhibit persistent power-law scaling in the inertial range, namely $S_p(\\ell)\n\\sim |\\ell|^{\\zeta_p}$ for exponents $\\zeta_p>0$ over an ever-increasing (with\nReynolds) range of scales. This behavior indicates that the velocity field\nretains some fractional differentiability uniformly in the Reynolds number. The\nKolmogorov 1941 theory of turbulence predicts that $\\zeta_p=p/3$ for all $p$\nand Onsager's 1949 theory establishes the requirement that $\\zeta_p\\leq p/3$\nfor $p\\geq 3$ for consistency with the zeroth law. Empirically, $\\zeta_2\n\\gtrapprox 2/3$ and $\\zeta_3 \\lessapprox 1$, suggesting that turbulent\nNavier-Stokes solutions approximate dissipative weak solutions of the Euler\nequations possessing (nearly) the minimal degree of singularity required to\nsustain anomalous dissipation. In this note, we adopt an experimentally\nsupported hypothesis on the anti-alignment of velocity increments with their\nseparation vectors and demonstrate that the inertial dissipation provides a\nregularization mechanism via the Kolmogorov 4/5-law.\n""]","[('turbulence theory', 0.6496209502220154), ('isotropic turbulence', 0.5439906716346741), ('2d turbulence', 0.5417124629020691), ('decaying turbulence', 0.537423849105835), ('turbulence', 0.5283268094062805), ('fully developed turbulence', 0.5089750289916992), ('turbulent', 0.50874924659729), ('developed turbulence', 0.5064995288848877), ('euler navier stokes', 0.4841756522655487), ('forced navier stokes', 0.46819204092025757)]"
1581,1581,18,1581_boltzmann bgk_classical boltzmann_quantum boltzmann_boltzmann,"['boltzmann bgk', 'classical boltzmann', 'quantum boltzmann', 'boltzmann', 'kinetic fokker planck', 'kinetic theory', 'solutions relativistic', 'gas mixtures', 'polyatomic gases', 'transport coefficients']","['Stationary solutions to the relativistic BGK model for gas mixtures in a\n  slab   In a recent paper [16], the authors proposed a BGK model for relativistic gas\nmixtures based on the Marle-type approximation, which satisfies the fundamental\nkinetic properties: non-negativity of distribution functions, conservation\nlaws, H-theorem, and indifferentiability principle. In this paper, we are\nconcerned with the stationary problems to the relativistic BGK model for gas\nmixtures in slab geometry. We establish the existence of a unique mild solution\nwith the fixed inflow boundary data when the collision frequencies for each\nspecies are sufficiently small.\n', 'Relativistic BGK model for gas mixtures   Unlike the case for classical particles, the literature on BGK type models\nfor relativistic gas mixture is extremely limited. There are a few results\n%\\cite{Kremer,Kremer3,KP} in which such relativistic BGK models for gas mixture\nare employed to compute transport coefficients. However, to the best knowledge\nof authors, relativistic BGK models for gas mixtures with complete presentation\nof the relaxation operators are missing in the literature.\n  In this paper, we fill this gap by suggesting a BGK model for relativistic\ngas mixtures for which the existence of each equilibrium coefficients in the\nrelaxation operator is rigorously guaranteed in a way that all the essential\nphysical properties are satisfied such as the conservation laws, the H-theorem,\nthe capturing of the correct equilibrium state, the indifferentiability\nprinciple, and the recovery of the classical BGK model in the Newtonian limit.\n', 'On a relativistic BGK model for polyatomic gases near equilibrium   Recently, a novel relativistic polyatomic BGK model was suggested by Pennisi\nand Ruggeri [J. of Phys. Conf. Series, 1035, (2018)] to overcome drawbacks of\nthe Anderson-Witting model and Marle model.In this paper, we prove the unique\nexistence and asymptotic behavior of classical solutions to the relativistic\npolyatomic BGK model when the initial data is sufficiently close to a global\nequilibrium.\n']","[('boltzmann bgk', 0.5794975161552429), ('classical boltzmann', 0.5756776928901672), ('quantum boltzmann', 0.45482519268989563), ('boltzmann', 0.4547247290611267), ('kinetic fokker planck', 0.4515167772769928), ('kinetic theory', 0.44169577956199646), ('solutions relativistic', 0.43644750118255615), ('gas mixtures', 0.43103277683258057), ('polyatomic gases', 0.43027234077453613), ('transport coefficients', 0.40936800837516785)]"
1582,1582,18,1582_positive definite kernels_positive kernels_radial kernels_definite kernels,"['positive definite kernels', 'positive kernels', 'radial kernels', 'definite kernels', 'kernel positive', 'gaussian kernels', 'positive definiteness', 'kernels studied', 'invariant kernels', 'preserving positive definiteness']","['Strict positive definiteness of convolutional and axially symmetric\n  kernels on d-dimensional spheres   The paper introduces new sufficient conditions of strict positive\ndefiniteness for kernels on d-dimensional spheres which are not radially\nsymmetric but possess specific coefficient structures. The results use the\nseries expansion of the kernel in spherical harmonics. The kernels either have\na convolutional form or are axially symmetric with respect to one axis. The\ngiven results on convolutional kernels generalise the result derived by Chen et\nal. [8] for radial kernels. Keywords: strictly positive definite kernels,\ncovariance functions, sphere\n', 'Strictly positive definite non-isotropic kernels on two-point\n  homogeneous manifolds: The asymptotic approach   We present sufficient condition for a family of positive definite kernels on\na compact two-point homogeneous space to be strictly positive definite based on\ntheir representation as a series of spherical harmonics. The family analyzed is\na generalization of the isotropic kernels and the case of a real sphere is\nanalyzed in details.\n', 'Strictly positive definite kernels on compact Riemannian manifolds   The paper studies strictly positive definite kernels on compact Riemannian\nmanifolds. We state new conditions to ensure strict positive definiteness for\ngeneral kernels and kernels with certain convolutional structure. We also state\nconditions for such kernels on product manifolds. As an example conditions for\nproducts of two-point homogeneous spaces are presented.\n']","[('positive definite kernels', 0.7133401036262512), ('positive kernels', 0.6777722835540771), ('radial kernels', 0.6742792129516602), ('definite kernels', 0.6136854290962219), ('kernel positive', 0.598004937171936), ('gaussian kernels', 0.5813611149787903), ('positive definiteness', 0.555461585521698), ('kernels studied', 0.5553756356239319), ('invariant kernels', 0.5330725312232971), ('preserving positive definiteness', 0.5329453945159912)]"
1583,1583,18,1583_ptychography_ptychographic_computational imaging_phase retrieval,"['ptychography', 'ptychographic', 'computational imaging', 'phase retrieval', 'imaging technique', 'imaging', 'phase contrast', 'diffraction patterns', 'microscopy', 'spatial resolution']","['Background Denoising for Ptychography via Wigner Distribution\n  Deconvolution   Ptychography is a computational imaging technique that aims to reconstruct\nthe object of interest from a set of diffraction patterns. Each of these is\nobtained by a localized illumination of the object, which is shifted after each\nillumination to cover its whole domain. As in the resulting measurements the\nphase information is lost, ptychography gives rise to solving a phase retrieval\nproblem. In this work, we consider ptychographic measurements corrupted with\nbackground noise, a type of additive noise that is independent of the shift,\ni.e., it is the same for all diffraction patterns. Two algorithms are provided,\nfor arbitrary objects and for so-called phase objects that do not absorb the\nlight but only scatter it. For the second type, a uniqueness of reconstruction\nis established for almost every object. Our approach is based on the Wigner\nDistribution Deconvolution, which lifts the object to a higher-dimensional\nmatrix space where the recovery can be reformulated as a linear problem.\nBackground noise only affects a few equations of the linear system that are\ntherefore discarded. The lost information is then restored using redundancy in\nthe higher-dimensional space.\n  Keywords: phase retrieval, ptychography, background noise, Wigner\nDistribution Deconvolution, uniqueness of reconstruction.\n', 'Image Recovery for Blind Polychromatic Ptychography   Ptychography is a lensless imaging technique, which considers reconstruction\nfrom a set of far-field diffraction patterns obtained by illuminating small\noverlapping regions of the specimen. In many cases, a distribution of light\ninside the illuminated region is unknown and has to be estimated along with the\nobject of interest. This problem is referred to as blind ptychography. While in\nptychography the illumination is commonly assumed to have a point spectrum, in\nthis paper we consider an alternative scenario with non-trivial light spectrum\nknown as blind polychromatic ptychography.\n  Firstly, we show that non-blind polychromatic ptychography can be seen as a\nrecovery from quadratic measurements. Then, a reconstruction from such\nmeasurements can be performed by a variant of Amplitude Flow algorithm, which\nhas guaranteed sublinear convergence to a critical point. Secondly, we address\nrecovery from blind polychromatic ptychographic measurements by devising an\nalternating minimization version of Amplitude Flow and showing that it\nconverges to a critical point at a sublinear rate.\n  Keywords: ptychography, phase retrieval, blind, alternating minimization,\ngradient descent.\n', 'Iterative X-ray Spectroscopic Ptychography   Spectroscopic ptychography is a powerful technique to determine the chemical\ncomposition of a sample with high spatial resolution. In spectro-ptychography,\na sample is rastered through a focused x-ray beam with varying photon energy so\nthat a series of phaseless diffraction data are recorded. Each chemical\ncomponent in the material under investigation has a characteristic absorption\nand phase contrast as a function of photon energy. Using a dictionary formed by\nthe set of contrast functions of each energy for each chemical component, it is\npossible to obtain the chemical composition of the material from high\nresolution multi-spectral images. This paper presents SPA (Spectroscopic\nPtychography with ADMM), a novel algorithm to iteratively solve the\nspectroscopic blind ptychography problem. We design first a nonlinear\nspectro-ptychography model based on Poisson maximum likelihood, and construct\nthen the proposed method based on fast iterative splitting operators. SPA can\nbe used to retrieve spectral contrast when considering both a known or an\nincomplete (partially known) dictionary of reference spectra. By coupling the\nredundancy across different spectral measurements, the proposed algorithm can\nachieve higher reconstruction quality when compared to standard\nstate-of-the-art two-step methods. We demonstrate how SPA can recover accurate\nchemical maps from Poisson-noised measurements, and also show its enhanced\nrobustness when reconstructing reduced redundancy ptychography data using large\nscanning stepsizes.\n']","[('ptychography', 0.6115227341651917), ('ptychographic', 0.5978177785873413), ('computational imaging', 0.5316058993339539), ('phase retrieval', 0.5012145042419434), ('imaging technique', 0.45200788974761963), ('imaging', 0.43729710578918457), ('phase contrast', 0.41423657536506653), ('diffraction patterns', 0.3866000175476074), ('microscopy', 0.38025468587875366), ('spatial resolution', 0.3741106688976288)]"
1584,1584,18,1584_twisted conjugacy classes_residually finite group_twisted conjugacy_conjugacy classes,"['twisted conjugacy classes', 'residually finite group', 'twisted conjugacy', 'conjugacy classes', 'group automorphism', 'finite groups', 'representations fixed', 'wreath products', 'group infinite rank', 'metacyclic groups']","['Twisted Burnside-Frobenius Theorem and $R_\\infty$-Property for\n  Lamplighter-Type Groups   We prove that the restricted wreath product ${\\mathbb{Z}_n\n\\mathbin{\\mathrm{wr}} \\mathbb{Z}^k}$ has the $R_\\infty$-property, i. e. every\nits automorphism $\\varphi$ has infinite Reidemeister number $R(\\varphi)$, in\nexactly two cases: (1) for any $k$ and even $n$; (2) for odd $k$ and $n$\ndivisible by 3. In the remaining cases there are automorphisms with finite\nReidemeister number, for which we prove the finite-dimensional twisted\nBurnside--Frobenius theorem (TBFT): $R(\\varphi)$ is equal to the number of\nequivalence classes of finite-dimensional irreducible unitary representations\nfixed by the action ${[\\rho]\\mapsto[\\rho\\circ\\varphi]}$.\n', 'Twisted conjugacy in residually finite groups of finite Pr\\""ufer rank   Suppose, $G$ is a residually finite group of finite upper rank admitting an\nautomorphism $\\varphi$ with finite Reidemeister number $R(\\varphi)$ (the number\nof $\\varphi$-twisted conjugacy classes). We prove that such $G$ is\nsoluble-by-finite (in other words, any residually finite group of finite upper\nrank, which is not soluble-by-finite, has the $R_\\infty$ property).\n  This reduction is the first step in the proof of the second main theorem of\nthe paper: suppose, $G$ is a residually finite group of finite Pr\\""ufer rank\nand $\\varphi$ is its automorphism with $R(\\varphi)<\\infty$; then $R(\\varphi)$\nis equal to the number of equivalence classes of finite-dimensional irreducible\nunitary representations of $G$, which are fixed points of the dual map\n$\\widehat{\\varphi}:[\\rho]\\mapsto [\\rho\\circ \\varphi]$ (i.e., we prove the\nTBFT$_f$, the finite version of the conjecture about the twisted\nBurnside-Frobenius theorem, for such groups).\n', 'Reidemeister classes in some wreath products by $\\mathbb Z^k$   Among restricted wreath products $G\\wr \\mathbb Z^k $, where $G$ is a finite\nAbelian group, we find three large classes of groups admitting an automorphism\n$\\varphi$ with finite Reidemeister number $R(\\varphi)$ (number of\n$\\varphi$-twisted conjugacy classes). In other words, groups from these classes\ndo not have the $R_\\infty$ property.\n  If a general automorphism $\\varphi$ of $G\\wr \\mathbb Z^k$ has a finite order\n(this is the case for $\\varphi$ detected in the first part of the paper) and\n$R(\\varphi)<\\infty$, we prove that $R(\\varphi)$ coincides with the number of\nequivalence classes of finite-dimensional irreducible unitary representations\nof $G\\wr \\mathbb Z^k$, which are fixed by the dual map $[\\rho]\\mapsto\n[\\rho\\circ \\varphi]$ (i.e. we prove the conjecture about finite twisted\nBurnside-Frobenius theorem, TBFT$_f$, for these $\\varphi$).\n']","[('twisted conjugacy classes', 0.5490121841430664), ('residually finite group', 0.48896563053131104), ('twisted conjugacy', 0.4811301529407501), ('conjugacy classes', 0.43049320578575134), ('group automorphism', 0.42303961515426636), ('finite groups', 0.41779181361198425), ('representations fixed', 0.41530510783195496), ('wreath products', 0.40936240553855896), ('group infinite rank', 0.40772053599357605), ('metacyclic groups', 0.4011198878288269)]"
1585,1585,18,1585_extensions fields_algebraic extensions_finite extensions_valued fields,"['extensions fields', 'algebraic extensions', 'finite extensions', 'valued fields', 'field positive characteristic', 'extension mathbb _p', 'decidability', 'undecidability', 'fields mathbb', 'fields']","[""Decidability of positive characteristic tame Hahn fields in\n  $\\mathcal{L}_t$   We show that any positive characteristic tame Hahn field\n$\\mathbb{F}((t^\\Gamma))$ containing $t$ is decidable in $\\mathcal{L}_t$, the\nlanguage of valued fields with a constant symbol for $t$, if $\\mathbb{F}$ and\n$\\Gamma$ are decidable. In particular, we obtain decidability of\n$\\mathbb{F}_p((t^{1/p^{\\infty}}))$ and $\\mathbb{F}_p((t^{\\mathbb{Q}}))$ in\n$\\mathcal{L}_t$. This uses a new AKE-principle for equal characteristic tame\nfields in $\\mathcal{L}_t$, building on work by Kuhlmann, together with\nKedlaya's work on finite automata and algebraic extensions of function fields.\nIn the process, we obtain an AKE-principle for tame fields in mixed\ncharacteristic.\n"", ""First-order definitions of rings of integral functions over algebraic\n  extensions of function fields and undecidability   In this paper, we study questions of definability and decidability for\ninfinite algebraic extensions ${\\bf K}$ of $\\mathbb{F}_p(t)$ and their subrings\nof $\\mathcal{S}$-integral functions. We focus on fields ${\\bf K}$ satisfying a\nlocal property which we call $q$-boundedness. This can be considered a function\nfield analogue of prior work of the first author which considered algebraic\nextensions of $\\mathbb{Q}$. One simple consequence of our work states that if\n${\\bf K}$ is a $q$-bounded Galois extension of $\\mathbb{F}_p(t)$, then for\ninfinitely many non-constant $u$ the integral closure $\\mathcal{O}_{\\bf K}$ of\n$\\mathbb{F}_p[u]$ inside ${\\bf K}$ is first-order definable in ${\\bf K}$. Under\nthe additional assumption that the constant subfield of ${\\bf K}$ is infinite,\nit follows that both $\\mathcal{O}_{\\bf K}$ and ${\\bf K}$ have undecidable\nfirst-order theories, and that $\\mathbb{F}_p[w]$ is definable in ${\\bf K}$ for\nevery non-constant $w$ in ${\\bf K}$. Our primary tools are norm equations and\nthe Hasse Norm Principle, in the spirit of Rumely. Our paper has an\nintersection with a recent arXiv preprint by Mart\\'inez-Ranero, Salcedo, and\nUtreras, although our definability results are more extensive and\nundecidability results are much stronger.\n"", 'Decidability via the tilting correspondence   We prove a relative decidability result for perfectoid fields. This applies\nto show that the fields $\\mathbb{Q}_p(p^{1/p^{\\infty}})$ and\n$\\mathbb{Q}_p(\\zeta_{p^{\\infty}})$ are (existentially) decidable relative to\nthe perfect hull of $ \\mathbb{F}_p(\\!(t)\\!)$ and $\\mathbb{Q}_p^{ab}$ is\n(existentially) decidable relative to the perfect hull of $\\overline{\n\\mathbb{F}}_p(\\!(t)\\!)$. We also prove some unconditional decidability results\nin mixed characteristic via reduction to characteristic $p$.\n']","[('extensions fields', 0.5164466500282288), ('algebraic extensions', 0.4612056016921997), ('finite extensions', 0.46111080050468445), ('valued fields', 0.44805291295051575), ('field positive characteristic', 0.4453153610229492), ('extension mathbb _p', 0.442752867937088), ('decidability', 0.42304548621177673), ('undecidability', 0.41482651233673096), ('fields mathbb', 0.40801557898521423), ('fields', 0.40716639161109924)]"
1586,1586,18,1586_cayley digraphs_representations finite groups_dihedral groups_cayley digraph,"['cayley digraphs', 'representations finite groups', 'dihedral groups', 'cayley digraph', 'representations groups', 'classify finite groups', 'classification finite groups', 'finite simple groups', 'finite groups', 'finite groups admitting']","['A conjecture on bipartite graphical regular representations   In this paper we are concerned with the classification of the finite groups\nadmitting a bipartite DRR and a bipartite GRR.\n  First, we find a natural obstruction in a finite group for not admitting a\nbipartite GRR. Then we give a complete classification of the finite groups\nsatisfying this natural obstruction and hence not admitting a bipartite GRR.\nBased on these results and on some extensive computer computations, we state a\nconjecture aiming to give a complete classification of the finite groups\nadmitting a bipartite GRR.\n  Next, we prove the existence of bipartite DRRs for most of the finite groups\nnot admitting a bipartite GRR found in this paper. Actually, we prove a much\nstronger result: we give an asymptotic enumeration of the bipartite DRRs over\nthese groups. Again, based on these results and on some extensive computer\ncomputations, we state a conjecture aiming to give a complete classification of\nthe finite groups admitting a bipartite DRR.\n', 'On oriented $m$-semiregular representations of finite groups   A finite group $G$ admits an {\\em oriented regular representation} if there\nexists a Cayley digraph of $G$ such that it has no digons and its automorphism\ngroup is isomorphic to $G$. Let $m$ be a positive integer. In this paper, we\nextend the notion of oriented regular representations to oriented\n$m$-semiregular representations using $m$-Cayley digraphs. Given a finite group\n$G$, an {\\em $m$-Cayley digraph} of $G$ is a digraph that has a group of\nautomorphisms isomorphic to $G$ acting semiregularly on the vertex set with $m$\norbits. We say that a finite group $G$ admits an {\\em oriented $m$-semiregular\nrepresentation} if there exists a regular $m$-Cayley digraph of $G$ such that\nit has no digons and $G$ is isomorphic to its automorphism group. In this\npaper, we classify finite groups admitting an oriented $m$-semiregular\nrepresentation for each positive integer $m$.\n', 'Dihedral groups with the $m$-DCI property   A Cayley digraph $\\rm{Cay}(G,S)$ of a group $G$ with respect to a subset $S$\nof $G$ is called a CI-digraph if for any Cayley digraph $\\rm{Cay}(G,T)$\nisomorphic to $\\rm{Cay}(G,S)$, there is an $\\alpha\\in \\rm{Aut}(G)$ such that\n$S^\\alpha=T$. For a positive integer $m$, $G$ is said to have the $m$-DCI\nproperty if all Cayley digraphs of $G$ with out-valency $m$ are CI-digraphs. Li\n[The Cyclic groups with the $m$-DCI Property, European J. Combin. 18 (1997)\n655-665] characterized cyclic groups with the $m$-DCI property, and in this\npaper, we characterize dihedral groups with the $m$-DCI property. For a\ndihedral group $\\mathrm{D}_{2n}$ of order $2n$, assume that $\\mathrm{D}_{2n}$\nhas the $m$-DCI property for some $1 \\leq m\\leq n-1$. Then it is shown that $n$\nis odd, and if further $p+1\\leq m\\leq n-1$ for an odd prime divisor $p$ of $n$,\nthen $p^2\\nmid n$. Furthermore, if $n$ is a power of a prime $q$, then\n$\\mathrm{D}_{2n}$ has the $m$-DCI property if and only if either $n=q$, or $q$\nis odd and $1\\leq m\\leq q$.\n']","[('cayley digraphs', 0.5862393379211426), ('representations finite groups', 0.5786780714988708), ('dihedral groups', 0.5446524620056152), ('cayley digraph', 0.5438580513000488), ('representations groups', 0.5280339121818542), ('classify finite groups', 0.5125550627708435), ('classification finite groups', 0.5070887804031372), ('finite simple groups', 0.4958305358886719), ('finite groups', 0.4902467429637909), ('finite groups admitting', 0.4890967905521393)]"
1587,1587,18,1587_gradient descent sgd_stochastic gradient descent_shuffle_finite sum optimization,"['gradient descent sgd', 'stochastic gradient descent', 'shuffle', 'finite sum optimization', 'gradient descent ascent', 'shuffling', 'sgd random', 'gradient descent', 'finite sum minimization', 'sgd solving']","['SMG: A Shuffling Gradient-Based Method with Momentum   We combine two advanced ideas widely used in optimization for machine\nlearning: shuffling strategy and momentum technique to develop a novel\nshuffling gradient-based method with momentum, coined Shuffling Momentum\nGradient (SMG), for non-convex finite-sum optimization problems. While our\nmethod is inspired by momentum techniques, its update is fundamentally\ndifferent from existing momentum-based methods. We establish state-of-the-art\nconvergence rates of SMG for any shuffling strategy using either constant or\ndiminishing learning rate under standard assumptions (i.e.$L$-smoothness and\nbounded variance). When the shuffling strategy is fixed, we develop another new\nalgorithm that is similar to existing momentum methods, and prove the same\nconvergence rates for this algorithm under the $L$-smoothness and bounded\ngradient assumptions. We demonstrate our algorithms via numerical simulations\non standard datasets and compare them with existing shuffling methods. Our\ntests have shown encouraging performance of the new algorithms.\n', ""Shuffling Momentum Gradient Algorithm for Convex Optimization   The Stochastic Gradient Descent method (SGD) and its stochastic variants have\nbecome methods of choice for solving finite-sum optimization problems arising\nfrom machine learning and data science thanks to their ability to handle\nlarge-scale applications and big datasets. In the last decades, researchers\nhave made substantial effort to study the theoretical performance of SGD and\nits shuffling variants. However, only limited work has investigated its\nshuffling momentum variants, including shuffling heavy-ball momentum schemes\nfor non-convex problems and Nesterov's momentum for convex settings. In this\nwork, we extend the analysis of the shuffling momentum gradient method\ndeveloped in [Tran et al (2021)] to both finite-sum convex and strongly convex\noptimization problems. We provide the first analysis of shuffling\nmomentum-based methods for the strongly convex setting, attaining a convergence\nrate of $O(1/nT^2)$, where $n$ is the number of samples and $T$ is the number\nof training epochs. Our analysis is a state-of-the-art, matching the best rates\nof existing shuffling stochastic gradient algorithms in the literature.\n"", ""Nesterov Accelerated Shuffling Gradient Method for Convex Optimization   In this paper, we propose Nesterov Accelerated Shuffling Gradient (NASG), a\nnew algorithm for the convex finite-sum minimization problems. Our method\nintegrates the traditional Nesterov's acceleration momentum with different\nshuffling sampling schemes. We show that our algorithm has an improved rate of\n$\\mathcal{O}(1/T)$ using unified shuffling schemes, where $T$ is the number of\nepochs. This rate is better than that of any other shuffling gradient methods\nin convex regime. Our convergence analysis does not require an assumption on\nbounded domain or a bounded gradient condition. For randomized shuffling\nschemes, we improve the convergence bound further. When employing some initial\ncondition, we show that our method converges faster near the small neighborhood\nof the solution. Numerical simulations demonstrate the efficiency of our\nalgorithm.\n""]","[('gradient descent sgd', 0.5237061977386475), ('stochastic gradient descent', 0.5053864121437073), ('shuffle', 0.500701367855072), ('finite sum optimization', 0.4885476529598236), ('gradient descent ascent', 0.4852667450904846), ('shuffling', 0.4848281145095825), ('sgd random', 0.4418327212333679), ('gradient descent', 0.4392217993736267), ('finite sum minimization', 0.4136973023414612), ('sgd solving', 0.40830060839653015)]"
1588,1588,18,1588_conjectured least_conjecture_special polynomials_conjecture begin,"['conjectured least', 'conjecture', 'special polynomials', 'conjecture begin', 'integer coefficients', 'horn conjecture', 'free polynomial', 'irreducible polynomials', 'polynomials explicit', 'many prime']","['A lower bound on the LCM of polynomial sequences   Let $f$ be a polynomial $f$ of degree $d\\ge 2$ with integer coefficients\nwhich is irreducible over the rationals. Cilleruelo conjectured that the least\ncommon multiple of the values of the polynomial at the first $N$ integers\nsatisfies $\\log lcm(f(1),\\dots, f(N)) \\sim (d-1) N\\log N$ as $N\\to \\infty$.\nThis is only known for degree $d=2$. In this note we give a simple lower bound\nfor all degrees $d\\geq 2$ which is consistent with the conjecture: $\\log lcm\n(f(1),\\dots, f(N)) \\gg N\\log N$.\n', ""An average version of Cilleruelo's conjecture for families of\n  $S_n$-polynomials over a number field   For $ f\\in\\mathbb{Z}[X] $ an irreducible polynomial of degree $ n $, the\nCilleruelo's conjecture states\nthat$$\\log(\\mbox{lcm}(f(1),\\dots,f(M)))\\sim(n-1)M\\log M$$as $\nM\\rightarrow+\\infty $, where $ \\mbox{lcm}(f(1),\\dots,f(M)) $ is the least\ncommon multiple of $f(1),\\dots,f(M)$. It's well-known for $ n=1 $ as a\nconsequence of Dirichlet's Theorem for primes in arithmetic progression, and it\nwas proved by Cilleruelo for quadratic polynomials. Recently the conjecture was\nshown by Rudnick and Zehavi for a large family of polynomials of any degree. We\nwant to investigate an average version of the conjecture for $S_n$-polynomials\nwith integral coefficients over a fixed extension $K/\\mathbb{Q}$ by considering\nthe least common multiple of ideals of $\\mathcal{O}_K$.\n"", 'The Least Common Multiple of Polynomial Values over Function Fields   Cilleruelo conjectured that for an irreducible polynomial $f \\in\n\\mathbb{Z}[X]$ of degree $d \\geq 2$ one has\n$$\\log\\left[\\mathrm{lcm}(f(1),f(2),\\ldots f(N))\\right]\\sim(d-1)N\\log N$$ as $N\n\\to \\infty$. He proved it in the case $d=2$ but it remains open for every\npolynomial with $d>2$. We investigate the function field analogue of the\nproblem by considering polynomials over the ring $\\mathbb F_q[T]$. We state an\nanalog of Cilleruelo\'s conjecture in this setting: denoting by $$L_f(n) :=\n\\mathrm{lcm} \\left(f\\left(Q\\right)\\ : \\ Q \\in \\mathbb F_q[T]\\mbox{ monic},\\,\n\\mathrm{deg}\\,Q = n\\right)$$ we conjecture that\n\\begin{equation}\\label{eq:conjffabs}\\mathrm{deg}\\, L_f(n) \\sim c_f\n\\left(d-1\\right) nq^n,\\ n \\to \\infty\\end{equation} ($c_f$ is an explicit\nconstant dependent only on $f$, typically $c_f=1$). We give both upper and\nlower bounds for $L_f(n)$ and show that the conjectured asymptotic holds for a\nclass of ``special"" polynomials, initially considered by Leumi in this context,\nwhich includes all quadratic polynomials and many other examples as well. We\nfully classify these special polynomials. We also show that $\\mathrm{deg}\\,\nL_f(n) \\sim \\mathrm{deg}\\,\\mathrm{rad}\\left(L_f(n)\\right)$ (in other words the\ncorresponding LCM is close to being squarefree), which is not known over\n$\\mathbb Z$.\n']","[('conjectured least', 0.48052075505256653), ('conjecture', 0.462331086397171), ('special polynomials', 0.4285838007926941), ('conjecture begin', 0.4049496650695801), ('integer coefficients', 0.4011520445346832), ('horn conjecture', 0.39899304509162903), ('free polynomial', 0.39012426137924194), ('irreducible polynomials', 0.3830031752586365), ('polynomials explicit', 0.373891144990921), ('many prime', 0.36786985397338867)]"
1589,1589,18,1589_wave spacetimes_gravitational waves_gravitational wave_spacetime models,"['wave spacetimes', 'gravitational waves', 'gravitational wave', 'spacetime models', 'general theory relativity', 'theory general relativity', 'spacetime', 'spacetimes', 'cosmological models', 'equations cosmological']","[""Type I Shapovalov wave spacetimes in the Brans-Dicke scalar-tensor\n  theory of gravity   Exact solutions for Shapovalov wave spacetimes of type I in the scalar-tensor\ntheory of gravity of Brans-Dicke are constructed. Shapovalov's wave spacetimes\ndescribe gravitational-wave models that allow the separation of wave variables\nin privileged coordinate systems. In contrast to the general theory of\nrelativity, the vacuum field equations of the Brans-Dicke scalar-tensor theory\nof gravity lead to exact solutions for type I Shapovalov spaces, which makes it\npossible to construct observational checks for detecting such wave\ndisturbances. For the models under consideration, equations for the\ntrajectories of test particles are obtained.\n"", ""Gravitational Waves of Type III Shapovalov Spacetimes: Particle\n  Trajectories, Geodesic Deviation and Tidal Accelerations   For gravitational-wave spacetimes of Shapovalov type III, exact general\nsolutions of geodesic deviation equations and equations of motion of test\nparticles are obtained. Solutions are found in a privileged coordinate system,\nwhere the metric of the considered spacetime models depends on the wave\nvariable. The exact form of tidal accelerations of the gravitational wave is\nobtained. In the considered wave models of spacetime, the complete integral of\nthe Hamilton-Jacobi equations of test particles can be constructed. An explicit\nform of the equations for the transition to a synchronous coordinate system is\nfound, where the proper time of a test particle on the base geodesic is chosen\nas the time variable, and the time and space variables are separated. In the\nsynchronous coordinate system, the form of the metric of the considered wave\nspacetime is presented, the form of the geodesic deviation vector and the tidal\nacceleration vector are obtained. The methods used in the paper and the results\nobtained are applicable to gravitational waves both in the general theory of\nrelativity and in modified theories of gravity. The proposed approaches are\napplied to the case of Einstein's vacuum equations.\n"", ""Deviation of geodesics and particle trajectories in a gravitational wave\n  of the Bianchi type VI universe   For the Bianchi type VI universe, exact solutions of the equation of geodesic\ndeviation in a strong primordial gravitational wave in a privileged coordinate\nsystem are obtained. The solutions refer to Shapovalov's gravitational-wave\nmodels of spacetime and allow the existence of complete integrals of the\nHamilton-Jacobi equation for test particles. For all the solutions obtained,\nthe analytical form of the tidal acceleration vector in a strong primordial\ngravitational wave is obtained. An explicit form of the coordinate\ntransformation, an explicit form of the metric of the primordial gravitational\nwave of the Bianchi type VI universe, and the form of the tidal acceleration\nvector in the laboratory synchronous coordinate system are obtained. The\nsynchronous coordinate system is associated with a freely falling observer and\nallows the observer to separate time and spatial coordinates, as well as to\nsynchronize time at different points in space. The presented mathematical\napproach can be applied both in the general theory of relativity and in\nmodified theories of gravity.\n""]","[('wave spacetimes', 0.6413630247116089), ('gravitational waves', 0.6107459664344788), ('gravitational wave', 0.59815514087677), ('spacetime models', 0.566189706325531), ('general theory relativity', 0.556896448135376), ('theory general relativity', 0.5405353307723999), ('spacetime', 0.49632325768470764), ('spacetimes', 0.4860643744468689), ('cosmological models', 0.48143789172172546), ('equations cosmological', 0.47685134410858154)]"
1590,1590,18,1590_stochastic games_stochastic game_tug war games_tug war,"['stochastic games', 'stochastic game', 'tug war games', 'tug war', 'viscosity solutions', 'boundary regularity', 'laplace equations', 'game theory', 'weighted laplace', 'game theoretical']","['Time-dependent tug-of-war games and normalized parabolic $p$-Laplace\n  equations   This paper concerns value functions of time-dependent tug-of-war games. We\nfirst prove the existence and uniqueness of value functions and verify that\nthese game values satisfy a dynamic programming principle. Using the arguments\nin the proof of existence of game values, we can also deduce asymptotic\nbehavior of game values when $T \\to \\infty$. Furthermore, we investigate\nboundary regularity for game values. Thereafter, based on the regularity\nresults for value functions, we deduce that game values converge to viscosity\nsolutions of the normalized parabolic $p$-Laplace equation.\n', 'Regularity for tug-of-war games associated with Robin type boundary\n  value conditions in nondivergence form   In this paper, we study a certain type of noisy tug-of-war game which can be\nregarded as an interpretation of a certain type of boundary value problem for\nthe normalized $p$-Laplace equation, where $1<p<2$. More precisely, we will\ninvestigate the boundary regularity of the value function to the game and its\nconvergence to a viscosity solution of the model problem.\n', 'Tug-of-war with Kolmogorov   We introduce a new class of strongly degenerate nonlinear parabolic PDEs\n$$((p-2)\\Delta_{\\infty,X}^N+\\Delta_X)u(X,Y,t)+(m+p)(X\\cdot\\nabla_Yu(X,Y,t)-\\partial_tu(X,Y,t))=0,$$\n$(X,Y,t)\\in\\mathbb R^m\\times \\mathbb R^m\\times \\mathbb R$, $p\\in (1,\\infty)$,\ncombining the classical PDE of Kolmogorov and the normalized $p$-Laplace\noperator. We characterize solutions in terms of an asymptotic mean value\nproperty and the results are connected to the analysis of certain tug-of-war\ngames with noise. The value functions for the games introduced approximate\nsolutions to the stated PDE when the parameter that controls the size of the\npossible steps goes to zero. Existence and uniqueness of viscosity solutions to\nthe Dirichlet problem is established. The asymptotic mean value property, the\nassociated games and the geometry underlying the Dirichlet problem, all reflect\nthe family of dilation and the Lie group underlying operators of Kolmogorov\ntype and this makes our setting different from the context of standard\nparabolic dilations and Euclidean translations applicable in the context of the\nheat operator and the normalized parabolic infinity Laplace operator.\n']","[('stochastic games', 0.5572742223739624), ('stochastic game', 0.55428147315979), ('tug war games', 0.5132418274879456), ('tug war', 0.4452575147151947), ('viscosity solutions', 0.43860188126564026), ('boundary regularity', 0.43345358967781067), ('laplace equations', 0.42078813910484314), ('game theory', 0.4174202084541321), ('weighted laplace', 0.4027772843837738), ('game theoretical', 0.4011795222759247)]"
1591,1591,18,1591_utility theory_social welfare_utility representation_social choice theory,"['utility theory', 'social welfare', 'utility representation', 'social choice theory', 'preference relations', 'welfare', 'partial orders', 'equitable', 'choice theory', 'utility']","['Equitable preference relations on infinite utility streams   We propose generalized versions of strong equity and Pigou-Dalton transfer\nprinciple. We study the existence and the real valued representation of social\nwelfare relations satisfying these two generalized equity principles. Our\nresults characterize the restrictions on one period utility domains for the\nequitable social welfare relation (i) to exist; and (ii) to admit real-valued\nrepresentations.\n', 'On the Representation and Construction of Equitable Social Welfare\n  Orders   This paper examines the representation and explicit description of social\nwelfare orders on infinite utility streams. It is assumed that the social\nwelfare orders under investigation satisfy upper asymptotic Pareto and\nanonymity axioms. We prove that there exists no real-valued representation of\nsuch social welfare orders. In addition, we establish that the existence of a\nsocial welfare order satisfying the anonymity and upper asymptotic Pareto\naxioms implies the existence of a non-Ramsey set, which is a non-constructive\nobject. Thus, we conclude that the social welfare orders under study do not\nadmit explicit description.\n', 'On social welfare orders satisfying anonymity and asymptotic density-one\n  Pareto   We study the nature (i.e., constructive as opposed to non-constructive) of\nsocial welfare orders on infinite utility streams, and their representability\nby means of real-valued functions. We assume finite anonymity and introduce a\nnew efficiency concept we refer to as asymptotic density-one Pareto. We\ncharacterize the existence of representable and constructive social welfare\norders (satisfying the above properties) in terms of easily verifiable\nconditions on the feasible set of one-period utilities.\n']","[('utility theory', 0.46272796392440796), ('social welfare', 0.46108555793762207), ('utility representation', 0.4583044946193695), ('social choice theory', 0.43572095036506653), ('preference relations', 0.43260300159454346), ('welfare', 0.40702539682388306), ('partial orders', 0.38357558846473694), ('equitable', 0.37479421496391296), ('choice theory', 0.37321293354034424), ('utility', 0.35410845279693604)]"
1592,1592,18,1592_riemannian geometry_differential geometry_riemannian metrics_methods differential geometry,"['riemannian geometry', 'differential geometry', 'riemannian metrics', 'methods differential geometry', 'tensor fields', 'metric tensor', 'riemannian', 'theory curvature', 'metric tensor g_', 'differential forms']","['Riemannian Geometry to Higher Order in the Infinitesimals   Differential geometry may be generalized to allow infinitesimals to any\norder. The purpose of the present contribution is to show that the theory so\ndeveloped expands received geometrical ideas in an interesting way, rich in\npotential for future exploration. The first order of business is to furnish the\nnotion of a higher tangent vector, as defined abstractly by means of\ncommutative algebra, with a workable interpretation in terms of spatial\nintuition. Then we introduce the differential calculus of the so-called jet\nconnection, viz., an extension of the usual affine connection that takes higher\ntangent vectors as its arguments -- thereby enabling us to give a sense to\nparallel transport in the direction of a higher tangent, what has (to our\nknowledge) never been entertained before. After generalizing the Riemannian\nmetric tensor to include a dependence up to any order in the infinitesimals, we\narrive at natural analogues of the Levi-Civita connection and the Riemannian\ncurvature tensor which display novel phenomena rooted in interactions among\ninfinitesimals differing in order. Finally on the integral side, an intrinsic\ntheory of integration adapted to integrands possibly of higher than first order\nin the differentials is developed, with a view towards eventually defining an\naction functional that will be applicable in the general theory of relativity.\n', 'Geometrical methods in mathematical physics   We give detailed exposition of modern differential geometry from global\ncoordinate independent point of view as well as local coordinate description\nsuited for actual computations. In introduction, we consider Euclidean spaces\nand different structures on it; rotational, Lorentz, and Poincare groups;\nspecial relativity. The main body of the manuscript includes manifolds, tensor\nfields, differential forms, integration, Riemannian and Lorentzian metrics,\nconnection on vector and frame fiber bundles, affine geometry, Lie groups,\ntransformation groups, homotopy and fundamental group, coverings, principal and\nassociated fiber bundles, connections on fiber bundles, Killing vector fields,\ngeodesics and extremals, symplectic and Poisson manifolds, Clifford algebras,\nprinciple of least action, canonical formalism for constrained systems.\nApplications of differential geometry in quantum theory (adiabatic theorem,\nBerry phase, Aharonov-Bohm effect), general relativity and geometric theory of\ndefects are described. We give introduction to general relativity and its\nHamiltonian formulation; describe scalar, spinor, electromagnetic and\nYang-Mills fields. Riemannian and Lorentzian surfaces with one Killing vector\nfield are discussed in detail, and their global structure is described using\nconformal block method. We also classified all global vacuum solutions of the\nEinstein equations, which have the form of warped product metrics of two\nsurfaces. The manuscript is not a textbook, and intended for efficient reader.\n', 'A nonlinear theory of distributional geometry   This paper builds on the theory of generalised functions begun in [1]. The\nColombeau theory of generalised scalar fields on manifolds is extended to a\nnonlinear theory of generalised tensor fields which is diffeomorphism invariant\nand has the sheaf property. The generalised Lie derivative for generalised\ntensor fields is introduced and it is shown that this commutes with the\nembedding of distributional tensor fields. It is also shown that the covariant\nderivative of generalised tensor fields commutes with the embedding at the\nlevel of association. The concept of generalised metric is introduced and used\nto develop a nonsmooth theory of differential geometry. It is shown that the\nembedding of a continuous metric results in a generalised metric with well\ndefined connection and curvature. It is also shown that a twice continuously\ndifferentiable metric which is a solution of the vacuum Einstein equations may\nbe embedded into the algebra of generalised tensor fields and has generalised\nRicci curvature associated to zero. Thus, the embedding preserves the Einstein\nequations at the level of association. Finally, we consider an example of a\nmetric which lies outside the Geroch-Traschen class and show that in our\ndiffeomorphism invariant theory the curvature of a cone is associated to a\ndelta function.\n']","[('riemannian geometry', 0.696810245513916), ('differential geometry', 0.6546017527580261), ('riemannian metrics', 0.6078945398330688), ('methods differential geometry', 0.6058882474899292), ('tensor fields', 0.6029467582702637), ('metric tensor', 0.5912091732025146), ('riemannian', 0.5875006318092346), ('theory curvature', 0.5771957039833069), ('metric tensor g_', 0.5727128386497498), ('differential forms', 0.5474692583084106)]"
1593,1593,18,1593_ginzburg landau equations_landau vortices_solutions ginzburg landau_ginzburg landau functional,"['ginzburg landau equations', 'landau vortices', 'solutions ginzburg landau', 'ginzburg landau functional', 'dimensional ginzburg landau', 'vortex solutions', 'ginzburg landau energy', 'landau equations', 'ginzburg landau type', 'landau theory']","['Quantization effects for multi-component Ginzburg-Landau vortices   In this paper, we are concerned with $n$-component Ginzburg-Landau equations\non $\\rtwo$.By introducing a diffusion constant for each component, we discuss\nthat the $n$-component equations are different from $n$-copies of the single\nGinzburg-Landau equations.Then, the results of Brezis-Merle-Riviere for the\nsingle Ginzburg-Landau equation can be nontrivially extended to the\nmulti-component case.First, we show that if the solutions have their gradients\nin $L^2$ space, they are trivial solutions.Second, we prove that if the\npotential is square summable, then it has quantized integrals, i.e., there\nexists one-to-one correspondence between the possible values of the potential\nenergy and $\\nat^n$.Third, we show that different diffusion coefficients in the\nsystem are important to obtain nontrivial solutions of $n$-component equations.\n', 'Vortices for the magnetic Ginzburg-Landau theory in curved space   Since the Ginzburg-Landau theory is concerned with macroscopic phenomena, and\ngravity affects how objects interact at the macroscopic level. It becomes\nrelevant to study the Ginzburg-Landau theory in curved space, that is, in the\npresence of gravity. In this paper, some existence theorems are established for\nthe vortex solutions of the magnetic Ginzburg-Landau theory coupled to the\nEinstein equations. First, when the coupling constant \\lambda=1, we get a\nself-dual structure from the Ginzburg-Landau theory, then a partial\ndifferential equation with a gravitational term that has power-type\nsingularities is deduced from the coupled system. To overcome the difficulty\narising from the orders of singularities at the vortices, a constraint\nminimization method and a monotone iteration method are employed. We also show\nthat the quantized flux and total curvature are determined by the number of\nvortices. Second, when the coupling constant \\lambda>0, we use a suitable\nansatz to get the radially symmetric case for the magnetic Ginzburg-Landau\ntheory in curved space. The existence of the symmetric vortex solutions are\nobtained through combining a two-step iterative shooting argument and a\nfixed-point theorem approach. Some fundamental properties of the solutions are\nestablished via applying a series of analysis techniques.\n', 'On the stability of the Ginzburg-Landau vortex   We introduce a functional framework taylored to investigate the minimality\nand stability properties of the Ginzburg-Landau vortex of degree one on the\nwhole plane. We prove that a renormalized Ginzburg-Landau energy is\nwell-defined in that framework and that the vortex is its unique global\nminimizer up to the invariances by translation and phase shift. Our main result\nis a nonlinear coercivity estimate for the renormalized energy around the\nvortex, from which we can deduce its orbital stability as a solution to the\nGross-Pitaevskii equation, the natural Hamiltonian evolution equation\nassociated to the Ginzburg-Landau energy.\n']","[('ginzburg landau equations', 0.7058535218238831), ('landau vortices', 0.6528065204620361), ('solutions ginzburg landau', 0.6077888607978821), ('ginzburg landau functional', 0.6074702739715576), ('dimensional ginzburg landau', 0.5690183043479919), ('vortex solutions', 0.5673239827156067), ('ginzburg landau energy', 0.5368219614028931), ('landau equations', 0.5110253095626831), ('ginzburg landau type', 0.5086922645568848), ('landau theory', 0.48277702927589417)]"
1594,1594,18,1594_manifolds two_topological manifolds_manifolds_manifolds arising,"['manifolds two', 'topological manifolds', 'manifolds', 'manifolds arising', 'manifolds homeomorphic', 'manifolds fundamental', 'connected manifolds', 'smooth manifolds', 'diffeomorphism groups', 'two manifolds']","['Families of diffeomorphisms, embeddings, and positive scalar curvature\n  metrics via Seiberg-Witten theory   We construct infinite rank summands isomorphic to $\\mathbb{Z}^\\infty$ in the\nhigher homotopy and homology groups of the diffeomorphism groups of certain\n$4$-manifolds. These spherical families become trivial in the homotopy and\nhomology groups of the homeomorphism group; an infinite rank subgroup becomes\ntrivial after a single stabilization by connected sum with $S^2 \\times S^2$.\nThe stabilization result gives rise to an inductive construction, starting from\nnon-isotopic but pseudoisotopic diffeomorphisms constructed by the second\nauthor in 1998. The spherical families give $\\mathbb{Z}^\\infty$ summands in the\nhomology of the classifying spaces of specific subgroups of those\ndiffeomorphism groups.\n  The non-triviality is shown by computations with family Seiberg-Witten\ninvariants, including a gluing theorem adapted to our inductive construction.\nAs applications, we we obtain infinite generation for higher homotopy and\nhomology groups of spaces of embeddings of surfaces and $3$-manifolds in\nvarious $4$-manifolds, and for the space of positive scalar curvature metrics\non standard PSC $4$-manifolds.\n', 'Algorithms in 4-manifold topology   We show that there exists an algorithm that takes as input two closed, simply\nconnected, topological 4-manifolds and decides whether or not these 4-manifolds\nare homeomorphic. In particular, we explain in detail how closed, simply\nconnected, topological 4-manifolds can be naturally represented by a Kirby\ndiagram consisting only of 2-handles. This representation is used as input for\nour algorithm. Along the way, we develop an algorithm to compute the\nKirby-Siebenmann invariant of a closed, simply connected, topological\n4-manifold from any of its Kirby diagrams and describe an algorithm that\ndecides whether or not two intersection forms are isometric.\n  In a slightly different direction, we discuss the decidability of the stable\nclassification of smooth manifolds with more general fundamental groups. Here\nwe show that there exists an algorithm that takes as input two closed,\noriented, smooth 4-manifolds with fundamental groups isomorphic to a finite\ngroup with cyclic Sylow 2-subgroup, an infinite cyclic group, or a group of\ngeometric dimension at most 3 (in the latter case we additionally assume that\nthe universal covers of both 4-manifolds are not spin), and decides whether or\nnot these two 4-manifolds are orientation-preserving stably diffeomorphic.\n', 'On Watanabe\'s theta graph diffeomorphism in the 4-sphere   Watanabe\'s theta graph diffeomorphism, constructed using Watanabe\'s clasper\nsurgery construction which turns trivalent graphs in 4-manifolds into\nparameterized families of diffeomorphisms of 4-manifolds, is a diffeomorphism\nof $S^4$ representing a potentially nontrivial smooth mapping class of $S^4$.\nThe ""(1,2)-subgroup"" of the smooth mapping class group of $S^4$ is the subgroup\nrepresented by diffeomorphisms which are pseudoisotopic to the identity via a\nCerf family with only index 1 and 2 critical points. This author and Hartman\nshowed that this subgroup is either trivial or has order 2 and explicitly\nidentified a diffeomorphism that would represent the nontrivial element if this\nsubgroup is nontrivial. Here we show that the theta graph diffeomorphism is\nisotopic to this one possibly nontrivial element of the (1,2)-subgroup. To\nprove this relation we develop a diagrammatic calculus for working in the\nsmooth mapping class group of $S^4$.\n']","[('manifolds two', 0.5937663912773132), ('topological manifolds', 0.5902242064476013), ('manifolds', 0.5782567858695984), ('manifolds arising', 0.5740451216697693), ('manifolds homeomorphic', 0.5715078115463257), ('manifolds fundamental', 0.5508963465690613), ('connected manifolds', 0.5484936833381653), ('smooth manifolds', 0.5394706726074219), ('diffeomorphism groups', 0.5340011119842529), ('two manifolds', 0.5328760743141174)]"
1595,1595,18,1595_exponential integrators_dynamics magnetic_preserving integrators_time integrators,"['exponential integrators', 'dynamics magnetic', 'preserving integrators', 'time integrators', 'particle dynamics', 'dynamics charged particles', 'integrators used', 'integrators', 'integrator', 'strong magnetic field']","['A filtered two-step variational integrator for charged-particle dynamics\n  in a normal or strong magnetic field   This article is concerned with a new filtered two-step variational integrator\nfor solving the charged-particle dynamics in a mildly non-homogeneous normal or\nstrong magnetic field with a dimensionless parameter $\\epsilon$ inversely\nproportional to the strength of the magnetic field. In the case of a normal\nmagnetic field ($\\epsilon \\approx 1$), second-order error bounds and long time\nenergy and momentum conservations are obtained. Moreover, the proof of the\nlong-term analysis is accomplished by the backward error analysis. For the\nstrong magnetic field ($0<\\epsilon \\ll1$), this paper clarifies the behaviour\nof the filtered variational integrator for both a large stepsize $h^2 \\geq\n\\epsilon$ and a smaller stepsize $ h \\sim \\epsilon$. The approach to analysing\nthe error bounds for these two stepsizes is based on comparing the modulated\nFourier expansions of the exact and the numerical solutions. It is shown that\nthe proposed integrator achieves a second-order accuracy $\\mathcal{O}(h^2)$ in\nthe position and in the parallel velocity for a large step size and an\n$\\mathcal{O}(\\epsilon)$ accuracy for a smaller stepsize. This paper also yields\nthe long time energy and magnetic moment conservations for the strong magnetic\nfield by developing the modulated Fourier expansion of the proposed scheme. All\nthe theoretical results of the error behaviour and long-term conservations are\nnumerically demonstrated by two numerical experiments.\n', ""Two-scale exponential integrators with uniform accuracy for\n  three-dimensional charged-particle dynamics under strong magnetic field   The numerical simulation of three-dimensional charged-particle dynamics (CPD)\nunder strong magnetic field is a basic and challenging algorithmic task in\nplasma physics. In this paper, we introduce a new methodology to design\ntwo-scale exponential integrators for three-dimensional CPD whose magnetic\nfield's strength is inversely proportional to a dimensionless and small\nparameter $0<\\varepsilon \\ll 1$. By dealing with the transformed form of\nthree-dimensional CPD, we linearize the magnetic field and put the residual\ncomponent in a new nonlinear function which is shown to be uniformly bounded.\nBased on this foundation and the proposed two-scale exponential integrators, a\nclass of novel integrators is formulated and studied. The corresponding uniform\naccuracy of the proposed $r$-th order integrator is shown to be\n$\\mathcal{O}(h^r)$, where $r=1,2,3,4$ and the constant symbolized by\n$\\mathcal{O}$, the time stepsize $h$ and the computation cost are all\nindependent of $\\varepsilon$. Moreover, in the case of maximal ordering strong\nmagnetic field, improved error bound $\\mathcal{O}(\\varepsilon^r h^r)$ is\nobtained for the proposed $r$-th order integrator. A rigorous proof of these\nuniform and improved error bounds is presented, and a numerical test is\nperformed to illustrate the error and efficiency behaviour of the proposed\nintegrators.\n"", 'Large-stepsize integrators for charged-particle dynamics over multiple\n  time scales   The Boris algorithm, a closely related variational integrator and a newly\nproposed filtered variational integrator are studied when they are used to\nnumerically integrate the equations of motion of a charged particle in a\nnon-uniform strong magnetic field, taking step sizes that are much larger than\nthe period of the Larmor rotations. For the Boris algorithm and the standard\n(unfiltered) variational integrator, satisfactory behaviour is only obtained\nwhen the component of the initial velocity orthogonal to the magnetic field is\nfiltered out. The particle motion shows varying behaviour over multiple time\nscales: fast Larmor rotation, guiding centre motion, slow perpendicular drift,\nnear-conservation of the magnetic moment over very long times and conservation\nof energy for all times. Using modulated Fourier expansions of the exact and\nnumerical solutions, it is analysed to which extent this behaviour is\nreproduced by the three numerical integrators used with large step sizes.\n']","[('exponential integrators', 0.49128636717796326), ('dynamics magnetic', 0.49063053727149963), ('preserving integrators', 0.4689772427082062), ('time integrators', 0.46612969040870667), ('particle dynamics', 0.44780662655830383), ('dynamics charged particles', 0.4460920989513397), ('integrators used', 0.4456033706665039), ('integrators', 0.4448532164096832), ('integrator', 0.4173267185688019), ('strong magnetic field', 0.39178022742271423)]"
1596,1596,18,1596_radially symmetric solutions_liouville type theorems_existence radially symmetric_elliptic systems bounded,"['radially symmetric solutions', 'liouville type theorems', 'existence radially symmetric', 'elliptic systems bounded', 'bounded solutions', 'existence radially', 'elliptic systems', 'radial solutions', 'also weak solutions', 'lane emden']","['On a fully nonlinear k-Hessian system of Lane-Emden type   In this manuscript we prove the existence of solutions to a fully nonlinear\nsystem of (degenerate) elliptic equations of Lane-Emden type and discuss a\ninhomogeneous generalization.\n', 'Liouville-type theorems for the Lane-Emden equation in the half-space\n  and cones   We prove that 0 the only classical solution of the Lane-Emden equation in the\nhalf-space which is stable outside a compact set. We also consider weak\nsolutions and the case of general cones.\n', 'Nonradial sign changing solutions to Lane Emden equation   In this paper we prove the existence of continua of nonradial solutions for\nthe Lane-Emden equation. In a first result we show that there are infinitely\nmany global continua detaching from the curve of radial solutions with any\nprescribed number of nodal zones. Next, using the fixed point index in cone, we\nproduce nonradial solutions with a new type of symmetry. This result also\napplies to solutions with fixed signed, showing that the set of solutions to\nthe Lane Emden problem has a very rich and complex structure.\n']","[('radially symmetric solutions', 0.5307807922363281), ('liouville type theorems', 0.5225175023078918), ('existence radially symmetric', 0.5091242790222168), ('elliptic systems bounded', 0.5083761811256409), ('bounded solutions', 0.5020464658737183), ('existence radially', 0.49555692076683044), ('elliptic systems', 0.47135019302368164), ('radial solutions', 0.4646465480327606), ('also weak solutions', 0.45531973242759705), ('lane emden', 0.4346216022968292)]"
1597,1597,18,1597_high order quadrature_quadrature scheme_boundary element methods_high order numerical,"['high order quadrature', 'quadrature scheme', 'boundary element methods', 'high order numerical', 'quadrature rules', 'additive schwarz methods', 'quadrature points', 'boundary numerical experiments', 'order quadrature', 'numerical integration']","[""On the linear convergence of additive Schwarz methods for the\n  $p$-Laplacian   We consider additive Schwarz methods for boundary value problems involving\nthe $p$-Laplacian. While existing theoretical estimates suggest a sublinear\nconvergence rate for these methods, empirical evidence from numerical\nexperiments demonstrates a linear convergence rate. In this paper, we narrow\nthe gap between these theoretical and empirical results by presenting a novel\nconvergence analysis. Firstly, we present a new convergence theory for additive\nSchwarz methods written in terms of a quasi-norm. This quasi-norm exhibits\nbehavior akin to the Bregman distance of the convex energy functional\nassociated with the problem. Secondly, we provide a quasi-norm version of the\nPoincar'{e}--Friedrichs inequality, which plays a crucial role in deriving a\nquasi-norm stable decomposition for a two-level domain decomposition setting.\nBy utilizing these key elements, we establish the asymptotic linear convergence\nof additive Schwarz methods for the $p$-Laplacian.\n"", 'High-accuracy mesh-free quadrature for trimmed parametric surfaces and\n  volumes   This work presents a high-accuracy, mesh-free, generalized Stokes\ntheorem-based numerical quadrature scheme for integrating functions over\ntrimmed parametric surfaces and volumes. The algorithm relies on two\nfundamental steps: (1) We iteratively reduce the dimensionality of integration\nusing the generalized Stokes theorem to line integrals over trimming curves,\nand (2) we employ numerical antidifferentiation in the generalized Stokes\ntheorem using high-order quadrature rules. The scheme achieves exponential\nconvergence up to trimming curve approximation error and has applications to\ncomputation of geometric moments, immersogeometric analysis, conservative field\ntransfer between high-order curvilinear meshes, and initialization of\nmulti-material simulations. We compare the quadrature scheme to commonly-used\nquadrature schemes in the literature and show that our scheme is much more\nefficient in terms of number of quadrature points used. We provide an\nopen-source implementation of the scheme in MATLAB as part of QuaHOG, a\nsoftware package for Quadrature of High-Order Geometries.\n', 'Quadrature Rules on Triangles and Tetrahedra for Multidimensional\n  Summation-By-Parts Operators   Multidimensional diagonal-norm summation-by-parts (SBP) operators with\ncollocated volume and facet nodes, known as diagonal-$ \\mathsf{E} $ operators,\nare attractive for entropy-stable discretizations from an efficiency\nstandpoint. However, there is a limited number of such operators, and those\ncurrently in existence often have a relatively high node count for a given\npolynomial order due to a scarcity of suitable quadrature rules. We present\nseveral new symmetric positive-weight quadrature rules on triangles and\ntetrahedra that are suitable for construction of diagonal-$ \\mathsf{E} $ SBP\noperators. For triangles, quadrature rules of degree one through twenty with\nfacet nodes that correspond to the Legendre-Gauss-Lobatto (LGL) and\nLegendre-Gauss (LG) quadrature rules are derived. For tetrahedra, quadrature\nrules of degree one through ten are presented along with the corresponding\nfacet quadrature rules. All of the quadrature rules are provided in a\nsupplementary data repository. The quadrature rules are used to construct novel\nSBP diagonal-$ \\mathsf{E} $ operators, whose accuracy and maximum timestep\nrestrictions are studied numerically.\n']","[('high order quadrature', 0.589597225189209), ('quadrature scheme', 0.5349472165107727), ('boundary element methods', 0.5323427319526672), ('high order numerical', 0.4691287875175476), ('quadrature rules', 0.46000000834465027), ('additive schwarz methods', 0.44723016023635864), ('quadrature points', 0.4126366376876831), ('boundary numerical experiments', 0.41209876537323), ('order quadrature', 0.39846518635749817), ('numerical integration', 0.3878783881664276)]"
1598,1598,18,1598_temporal graphs_temporal graph_algorithms temporal_vertex time,"['temporal graphs', 'temporal graph', 'algorithms temporal', 'vertex time', 'times edges', 'directed graph', 'temporal', 'discrete time steps', 'static graphs', 'time solvable']","['Algorithms and complexity for path covers of temporal DAGs: when is\n  Dilworth dynamic?   In this paper, we study a dynamic analogue of the Path Cover problem, which\ncan be solved in polynomial-time in directed acyclic graphs. A temporal digraph\nhas an arc set that changes over discrete time-steps, if the underlying digraph\n(the union of all the arc sets) is acyclic, then we have a temporal DAG. A\ntemporal path is a directed path in the underlying digraph, such that the\ntime-steps of arcs are strictly increasing along the path. Two temporal paths\nare temporally disjoint if they do not occupy any vertex at the same time. A\ntemporal (resp. temporally disjoint) path cover is a collection of (resp.\ntemporally disjoint) temporal paths that covers all vertices. In this paper, we\nstudy the computational complexities of the problems of finding a temporal\n(disjoint) path cover with minimum cardinality, denoted as Temporal Path Cover\n(TPC) and Temporally Disjoint Path Cover (TD-PC). We show that both problems\nare NP-hard even when the underlying DAG is planar, bipartite, subcubic, and\nthere are only two arc-disjoint time-steps. Moreover, TD-PC remains NP-hard\neven on temporal oriented trees. In contrast, we show that TPC is\npolynomial-time solvable on temporal oriented trees by a reduction to Clique\nCover for (static undirected) weakly chordal graphs (a subclass of perfect\ngraphs for which Clique Cover admits an efficient algorithm). This highlights\nan interesting algorithmic difference between the two problems. Although it is\nNP-hard on temporal oriented trees, TD-PC becomes polynomial-time solvable on\ntemporal oriented lines and temporal rooted directed trees. We also show that\nTPC (resp. TD-PC) admits an XP (resp. FPT) time algorithm with respect to\nparameter tmax + tw, where tmax is the maximum time-step, and tw is the\ntreewidth of the underlying static undirected graph.\n', 'Resolving Sets in Temporal Graphs   A \\emph{resolving set} $R$ in a graph $G$ is a set of vertices such that\nevery vertex of $G$ is uniquely identified by its distances to the vertices of\n$R$. Introduced in the 1970s, this concept has been since then extensively\nstudied from both combinatorial and algorithmic points of view. We propose a\ngeneralization of the concept of resolving sets to temporal graphs,\n\\emph{i.e.}, graphs with edge sets that change over discrete time-steps. In\nthis setting, the \\emph{temporal distance from $u$ to $v$} is the earliest\npossible time-step at which a journey with strictly increasing time-steps on\nedges leaving $u$ reaches $v$, \\emph{i.e.}, the first time-step at which $v$\ncould receive a message broadcast from $u$. A \\emph{temporal resolving set} of\na temporal graph $\\mathcal{G}$ is a subset $R$ of its vertices such that every\nvertex of $\\mathcal{G}$ is uniquely identified by its temporal distances from\nvertices of $R$.\n  We study the problem of finding a minimum-size temporal resolving set, and\nshow that it is NP-complete even on very restricted graph classes and with\nstrong constraints on the time-steps: temporal complete graphs where every edge\nappears in either time-step~1 or~2, temporal trees where every edge appears in\nat most two consecutive time-steps, and even temporal subdivided stars where\nevery edge appears in at most two (not necessarily consecutive) time-steps. On\nthe other hand, we give polynomial-time algorithms for temporal paths and\ntemporal stars where every edge appears in exactly one time-step, and give a\ncombinatorial analysis and algorithms for several temporal graph classes where\nthe edges appear in periodic time-steps.\n', 'Structural Parameters for Dense Temporal Graphs   Temporal graphs provide a useful model for many real-world networks.\nUnfortunately the majority of algorithmic problems we might consider on such\ngraphs are intractable. There has been recent progress in defining structural\nparameters which describe tractable cases by simultaneously restricting the\nunderlying structure and the times at which edges appear in the graph. These\nall rely on the temporal graph being sparse in some sense. We introduce\ntemporal analogues of three increasingly restrictive static graph parameters --\ncliquewidth, modular-width and neighbourhood diversity -- which take small\nvalues for highly structured temporal graphs, even if a large number of edges\nare active at each timestep. The computational problems solvable efficiently\nwhen the temporal cliquewidth of the input graph is bounded form a subset of\nthose solvable efficiently when the temporal modular-width is bounded, which is\nin turn a subset of problems efficiently solvable when the temporal\nneighbourhood diversity is bounded. By considering specific temporal graph\nproblems, we demonstrate that (up to standard complexity theoretic assumptions)\nthese inclusions are strict.\n']","[('temporal graphs', 0.7202598452568054), ('temporal graph', 0.6562671065330505), ('algorithms temporal', 0.6152921319007874), ('vertex time', 0.5394964218139648), ('times edges', 0.5186631083488464), ('directed graph', 0.509379506111145), ('temporal', 0.4809389114379883), ('discrete time steps', 0.45240792632102966), ('static graphs', 0.4479779005050659), ('time solvable', 0.4361737370491028)]"
1599,1599,18,1599_stochastic reaction diffusion_reaction diffusion systems_reaction diffusion processes_reaction diffusion,"['stochastic reaction diffusion', 'reaction diffusion systems', 'reaction diffusion processes', 'reaction diffusion', 'reaction diffusion system', 'stochastic reaction', 'reaction diffusion pde', 'diffusion systems', 'molecular simulations', 'models reaction']","['Macroscopic limit for stochastic chemical reactions involving diffusion\n  and spatial heterogeneity   To model bio-chemical reaction systems with diffusion one can either use\nstochastic, microscopic reaction-diffusion master equations or deterministic,\nmacroscopic reaction-diffusion system. The connection between these two models\nis not only theoretically important but also plays an essential role in\napplications. This paper considers the macroscopic limits of the chemical\nreaction-diffusion master equation for first-order chemical reaction systems in\nhighly heterogeneous environments. More precisely, the diffusion coefficients\nas well as the reaction rates are spatially inhomogeneous and the reaction\nrates may also be discontinuous. By carefully discretizing these\nheterogeneities within a reaction-diffusion master equation model, we show that\nin the limit we recover the macroscopic reaction-diffusion system with\ninhomogeneous diffusion and reaction rates.\n', 'How reaction-diffusion PDEs approximate the large-population limit of\n  stochastic particle models   Reaction-diffusion PDEs and particle-based stochastic reaction-diffusion\n(PBSRD) models are commonly-used approaches for modeling the spatial dynamics\nof chemical and biological systems. Standard reaction-diffusion PDE models\nignore the underlying stochasticity of spatial transport and reactions, and are\noften described as appropriate in regimes where there are large numbers of\nparticles in a system. Recent studies have proven the rigorous large-population\nlimit of PBSRD models, showing the resulting mean-field models (MFM) correspond\nto non-local systems of partial-integro differential equations. In this work we\nexplore the rigorous relationship between standard reaction-diffusion PDE\nmodels and the derived MFM. We prove that the former can be interpreted as an\nasymptotic approximation to the later in the limit that bimolecular reaction\nkernels are short-range and averaging. As the reactive interaction length scale\napproaches zero, we prove the MFMs converge at second order to standard\nreaction-diffusion PDE models. In proving this result we also establish local\nwell-posedness of the MFM model in time for general systems, and global\nwell-posedness for specific reaction systems and kernels. Finally, we\nillustrate the agreement and disagreement between the MFM, SM and the\nunderlying particle model for several numerical examples.\n', 'Revisit of macroscopic dynamics for some non-equilibrium chemical\n  reactions from a Hamiltonian viewpoint   Most biochemical reactions in living cells are open systems interacting with\nenvironment through chemostats to exchange both energy and materials. At a\nmesoscopic scale, the number of each species in those biochemical reactions can\nbe modeled by a random time-changed Poisson processes. To characterize\nmacroscopic behaviors in the large volume limit, the law of large numbers in\nthe path space determines a mean-field limit nonlinear reaction rate equation\ndescribing the dynamics of the concentration of species, while the WKB\nexpansion for the chemical master equation yields a Hamilton-Jacobi equation\n(HJE) and the Lagrangian gives the good rate function in the large deviation\nprinciple. We decompose a general macroscopic reaction rate equation into a\nconservative part and a dissipative part in terms of the stationary solution to\nHJE. This stationary solution is used to determine the energy landscape and\nthermodynamics for general chemical reactions, which particularly maintains a\npositive entropy production rate at a non-equilibrium steady state. The\nassociated energy dissipation law is proved together with the passage from the\nmesoscopic to macroscopic one. Furthermore, we use a reversible Hamiltonian to\nstudy a class of non-equilibrium enzyme reactions, which identifies a new\nconcept of balance within the same reaction vector due to flux grouping\ndegeneracy. This macroscopic reversibility, brought by the reversibility of the\nchemical reaction jumping process, gives an Onsager-type strong gradient flow.\nThe reversible Hamiltonian also yields a time reversal symmetry for the\ncorresponding Lagrangian. Thus a modified time reversed least action path\nserves as the transition paths with associated path affinities and energy\nbarriers.\n']","[('stochastic reaction diffusion', 0.720947265625), ('reaction diffusion systems', 0.6929048895835876), ('reaction diffusion processes', 0.666363000869751), ('reaction diffusion', 0.6612609624862671), ('reaction diffusion system', 0.6299283504486084), ('stochastic reaction', 0.6170169115066528), ('reaction diffusion pde', 0.6067373156547546), ('diffusion systems', 0.5237868428230286), ('molecular simulations', 0.5009709000587463), ('models reaction', 0.4973379373550415)]"
1600,1600,18,1600_matrix completion_rank matrix completion_completion algorithms_rank matrix estimation,"['matrix completion', 'rank matrix completion', 'completion algorithms', 'rank matrix estimation', 'matrix estimation', 'completion methods', 'low rank matrix', 'noisy matrix', 'missingness probabilities', 'completion']","['Truncated Matrix Completion - An Empirical Study   Low-rank Matrix Completion (LRMC) describes the problem where we wish to\nrecover missing entries of partially observed low-rank matrix. Most existing\nmatrix completion work deals with sampling procedures that are independent of\nthe underlying data values. While this assumption allows the derivation of nice\ntheoretical guarantees, it seldom holds in real-world applications. In this\npaper, we consider various settings where the sampling mask is dependent on the\nunderlying data values, motivated by applications in sensing, sequential\ndecision-making, and recommender systems. Through a series of experiments, we\nstudy and compare the performance of various LRMC algorithms that were\noriginally successful for data-independent sampling patterns.\n', 'Matrix Completion under Low-Rank Missing Mechanism   Matrix completion is a modern missing data problem where both the missing\nstructure and the underlying parameter are high dimensional. Although missing\nstructure is a key component to any missing data problems, existing matrix\ncompletion methods often assume a simple uniform missing mechanism. In this\nwork, we study matrix completion from corrupted data under a novel low-rank\nmissing mechanism. The probability matrix of observation is estimated via a\nhigh dimensional low-rank matrix estimation procedure, and further used to\ncomplete the target matrix via inverse probabilities weighting. Due to both\nhigh dimensional and extreme (i.e., very small) nature of the true probability\nmatrix, the effect of inverse probability weighting requires careful study. We\nderive optimal asymptotic convergence rates of the proposed estimators for both\nthe observation probabilities and the target matrix.\n', ""An Adaptation for Iterative Structured Matrix Completion   The task of predicting missing entries of a matrix, from a subset of known\nentries, is known as \\textit{matrix completion}. In today's data-driven world,\ndata completion is essential whether it is the main goal or a pre-processing\nstep. Structured matrix completion includes any setting in which data is not\nmissing uniformly at random. In recent work, a modification to the standard\nnuclear norm minimization (NNM) for matrix completion has been developed to\ntake into account \\emph{sparsity-based} structure in the missing entries. This\nnotion of structure is motivated in many settings including recommender\nsystems, where the probability that an entry is observed depends on the value\nof the entry. We propose adjusting an Iteratively Reweighted Least Squares\n(IRLS) algorithm for low-rank matrix completion to take into account\nsparsity-based structure in the missing entries. We also present an iterative\ngradient-projection-based implementation of the algorithm that can handle\nlarge-scale matrices. Finally, we present a robust array of numerical\nexperiments on matrices of varying sizes, ranks, and level of structure. We\nshow that our proposed method is comparable with the adjusted NNM on\nsmall-sized matrices, and often outperforms the IRLS algorithm in structured\nsettings on matrices up to size $1000 \\times 1000$.\n""]","[('matrix completion', 0.775566577911377), ('rank matrix completion', 0.7515085339546204), ('completion algorithms', 0.589091420173645), ('rank matrix estimation', 0.549059271812439), ('matrix estimation', 0.532931387424469), ('completion methods', 0.5323327779769897), ('low rank matrix', 0.5286771655082703), ('noisy matrix', 0.4907275438308716), ('missingness probabilities', 0.46645012497901917), ('completion', 0.4356650710105896)]"
1601,1601,18,1601_algebraic integers_integer irreducible_conjectures note_algebraic integer,"['algebraic integers', 'integer irreducible', 'conjectures note', 'algebraic integer', 'algebraic numbers', 'integer coefficients', 'random polynomial', 'conjecture olya', 'positive algebraic', 'complexity uniform']","['Irreducibility of random polynomials: general measures   Let $\\mu$ be a probability measure on $\\mathbb{Z}$ that is not a Dirac mass\nand that has finite support. We prove that if the coefficients of a monic\npolynomial $f(x)\\in\\mathbb{Z}[x]$ of degree $n$ are chosen independently at\nrandom according to $\\mu$ while ensuring that $f(0)\\neq0$, then there is a\npositive constant $\\theta=\\theta(\\mu)$ such that $f(x)$ has no divisors of\ndegree $\\le \\theta n$ with probability that tends to 1 as $n\\to\\infty$.\n  Furthermore, in certain cases, we show that a random polynomial $f(x)$ with\n$f(0)\\neq0$ is irreducible with probability tending to 1 as $n\\to\\infty$. In\nparticular, this is the case if $\\mu$ is the uniform measure on a set of at\nleast 35 consecutive integers, or on a subset of $[-H,H]\\cap\\mathbb{Z}$ of\ncardinality $\\ge H^{4/5}(\\log H)^2$ with $H$ sufficiently large. In addition,\nin all of these settings, we show that the Galois group of $f(x)$ is either\n$\\mathcal{A}_n$ or $\\mathcal{S}_n$ with high probability.\n  Finally, when $\\mu$ is the uniform measure on a finite arithmetic progression\nof at least two elements, we prove a random polynomial $f(x)$ as above is\nirreducible with probability $\\ge\\delta$ for some constant\n$\\delta=\\delta(\\mu)>0$. In fact, if the arithmetic progression has step 1, we\nprove the stronger result that the Galois group of $f(x)$ is $\\mathcal{A}_n$ or\n$\\mathcal{S}_n$ with probability $\\ge\\delta$.\n', ""Limiting distributions of conjugate algebraic integers   Let $\\Sigma \\subset \\mathbb{C}$ be a compact subset of the complex plane, and\n$\\mu$ be a probability distribution on $\\Sigma$. We give necessary and\nsufficient conditions for $\\mu$ to be the weak* limit of a sequence of uniform\nprobability measures on a complete set of conjugate algebraic integers lying\neventually in any open set containing $\\Sigma$. Given $n\\geq 0$, any\nprobability measure $\\mu$ satisfying our necessary conditions, and any open set\n$D$ containing $\\Sigma$, we develop and implement a polynomial time algorithm\nin $n$ that returns an integral monic irreducible polynomial of degree $n$ such\nthat all of its roots are inside $D$ and their root distributions converge\nweakly to $\\mu$ as $n\\to \\infty$. We also prove our theorem for $\\Sigma\\subset\n\\mathbb{R}$ and open sets inside $\\mathbb{R}$ that recovers Smith's main\ntheorem \\cite{Smith} as special case. Given any finite field $\\mathbb{F}_q$ and\nany integer $n$, our algorithm returns infinitely many abelian varieties over\n$\\mathbb{F}_q$ which are not isogenous to the Jacobian of any curve over\n$\\mathbb{F}_{q^n}$.\n"", ""A quantitative converse of Fekete's theorem   Given a compact subset $\\Sigma \\subset \\mathbb{R}$ (or $\\mathbb{C}$) with\nlogarithmic capacity greater than zero, we construct an explicit family of\nprobability measures supported on $\\Sigma$ such that their closure is all the\npossible weak limit measures of complete sets of conjugate algebraic integers\nlying inside $\\Sigma$. We give an asymptotic formula for the number of\nalgebraic integers with given degree and prescribed distribution. We exploit\nthe algorithmic nature of our approach to give a family of upper bounds that\nconverges to the smallest limiting trace-to-degree ratio of totally positive\nalgebraic integers and improve the best previously known upper bound on the\nSchur-Siegel-Smyth trace problem to 1.8216.\n""]","[('algebraic integers', 0.4156222343444824), ('integer irreducible', 0.3891753554344177), ('conjectures note', 0.3819599747657776), ('algebraic integer', 0.3718373775482178), ('algebraic numbers', 0.3485938310623169), ('integer coefficients', 0.33985280990600586), ('random polynomial', 0.33470699191093445), ('conjecture olya', 0.31963086128234863), ('positive algebraic', 0.31645524501800537), ('complexity uniform', 0.31267213821411133)]"
1602,1602,18,1602_tamari lattices_tamari lattice_nu tamari lattices_lattice order,"['tamari lattices', 'tamari lattice', 'nu tamari lattices', 'lattice order', 'lattices', 'lattice', 'lattices also', 'lattices three', 'lattice isomorphic', 'lattice paths']","['The Pop-Stack Operator on Ornamentation Lattices   Each rooted plane tree $\\mathsf{T}$ has an associated ornamentation lattice\n$\\mathcal{O}(\\mathsf{T})$. The ornamentation lattice of an $n$-element chain is\nthe $n$-th Tamari lattice. We study the pop-stack operator\n$\\mathsf{Pop}\\colon\\mathcal{O}(\\mathsf{T})\\to\\mathcal{O}(\\mathsf{T})$, which\nsends each element $\\delta$ to the meet of the elements covered by or equal to\n$\\delta$. We compute the maximum size of a forward orbit of $\\mathsf{Pop}$ on\n$\\mathcal{O}(\\mathsf{T})$, generalizing a result of Defant for Tamari lattices.\nWe also characterize the image of $\\mathsf{Pop}$ on $\\mathcal{O}(\\mathsf{T})$,\ngeneralizing a result of Hong for Tamari lattices. For each integer $k\\geq 0$,\nwe provide necessary conditions for an element of $\\mathcal{O}(\\mathsf{T})$ to\nbe in the image of $\\mathsf{Pop}^k$. This allows us to completely characterize\nthe image of $\\mathsf{Pop}^k$ on a Tamari lattice.\n', ""The Pop-stack-sorting Operator on Tamari Lattices   Motivated by the pop-stack-sorting map on the symmetric groups, Defant\ndefined an operator $\\mathsf{Pop}_M : M \\to M$ for each complete\nmeet-semilattice $M$ by $$\\mathsf{Pop}_M(x)=\\bigwedge(\\{y\\in M: y\\lessdot\nx\\}\\cup \\{x\\}).$$ This paper concerns the dynamics of\n$\\mathsf{Pop}_{\\mathrm{Tam}_n}$, where $\\mathrm{Tam}_n$ is the $n$-th Tamari\nlattice.\n  We say an element $x\\in \\mathrm{Tam}_n$ is $t$-$\\mathsf{Pop}$-sortable if\n$\\mathsf{Pop}_M^t (x)$ is the minimal element and we let $h_t(n)$ denote the\nnumber of $t$-$\\mathsf{Pop}$-sortable elements in $\\mathrm{Tam}_n$. We find an\nexplicit formula for the generating function $\\sum_{n\\ge 1}h_t(n)z^n$ and\nverify Defant's conjecture that it is rational. We furthermore prove that the\nsize of the image of $\\mathsf{Pop}_{\\mathrm{Tam}_n}$ is the Motzkin number\n$M_n$, settling a conjecture of Defant and Williams.\n"", 'Meeting Covered Elements in $\\nu$-Tamari Lattices   For each complete meet-semilattice $M$, we define an operator\n$\\mathsf{Pop}_M:M\\to M$ by \\[\\mathsf{Pop}_M(x)=\\bigwedge(\\{y\\in M:y\\lessdot\nx\\}\\cup\\{x\\}).\\] When $M$ is the right weak order on a symmetric group,\n$\\mathsf{Pop}_M$ is the pop-stack-sorting map. We prove some general properties\nof these operators, including a theorem that describes how they interact with\ncertain lattice congruences. We then specialize our attention to the dynamics\nof $\\mathsf{Pop}_{\\text{Tam}(\\nu)}$, where $\\text{Tam}(\\nu)$ is the\n$\\nu$-Tamari lattice. We determine the maximum size of a forward orbit of\n$\\mathsf{Pop}_{\\text{Tam}(\\nu)}$. When $\\text{Tam}(\\nu)$ is the $n^\\text{th}$\n$m$-Tamari lattice, this maximum forward orbit size is $m+n-1$; in this case,\nwe prove that the number of forward orbits of size $m+n-1$ is\n\\[\\frac{1}{n-1}\\binom{(m+1)(n-2)+m-1}{n-2}.\\] Motivated by the recent\ninvestigation of the pop-stack-sorting map, we define a lattice path\n$\\mu\\in\\text{Tam}(\\nu)$ to be $t$-$\\mathsf{Pop}$-sortable if\n$\\mathsf{Pop}_{\\text{Tam}(\\nu)}^t(\\mu)=\\nu$. We enumerate\n$1$-$\\mathsf{Pop}$-sortable lattice paths in $\\text{Tam}(\\nu)$ for arbitrary\n$\\nu$. We also give a recursive method to generate $2$-$\\mathsf{Pop}$-sortable\nlattice paths in $\\text{Tam}(\\nu)$ for arbitrary $\\nu$; this allows us to\nenumerate $2$-$\\mathsf{Pop}$-sortable lattice paths in a large variety of\n$\\nu$-Tamari lattices that includes the $m$-Tamari lattices.\n']","[('tamari lattices', 0.6709170341491699), ('tamari lattice', 0.6342507004737854), ('nu tamari lattices', 0.6277156472206116), ('lattice order', 0.5617207884788513), ('lattices', 0.5534108877182007), ('lattice', 0.524850606918335), ('lattices also', 0.5221338868141174), ('lattices three', 0.5172461867332458), ('lattice isomorphic', 0.48900023102760315), ('lattice paths', 0.48804476857185364)]"
1603,1603,18,1603_pdes spatial_pde systems_linear pdes_analysis pdes,"['pdes spatial', 'pde systems', 'linear pdes', 'analysis pdes', 'coupled pdes', 'linear pde', 'stability analysis', 'pde system', 'equations pdes one', 'pdes']","[""A Computational Method for $H_2$-optimal Estimator and State Feedback\n  Controller Synthesis for PDEs   In this paper, we present solvable, convex formulations of $H_2$-optimal\nstate estimation and state-feedback control problems for a general class of\nlinear Partial Differential Equations (PDEs) with one spatial dimension. These\nconvex formulations are derived by using an analysis and control framework\ncalled the `Partial Integral Equation' (PIE) framework, which utilizes the PIE\nrepresentation of infinite-dimensional systems. Since PIEs are parameterized by\nPartial Integral (PI) operators that form an algebra, $H_2$-optimal estimation\nand control problems for PIEs can be formulated as Linear PI Inequalities\n(LPIs). Furthermore, if a PDE admits a PIE representation, then the stability\nand $H_2$ performance of the PIE system implies that of the PDE system.\nConsequently, the optimal estimator and controller obtained for a PIE using\nLPIs provide the same stability and performance when applied to the\ncorresponding PDE. These LPI optimization problems can be solved\ncomputationally using semi-definite programming solvers because such problems\ncan be formulated using Linear Matrix Inequalities by using positive matrices\nto parameterize a cone of positive PI operators. We illustrate the application\nof these methods by constructing observers and controllers for some standard\nPDE examples.\n"", 'Representation of linear PDEs with spatial integral terms as Partial\n  Integral Equations   In this paper, we present the Partial Integral Equation (PIE) representation\nof linear Partial Differential Equations (PDEs) in one spatial dimension, where\nthe PDE has spatial integral terms appearing in the dynamics and the boundary\nconditions. The PIE representation is obtained by performing a change of\nvariable where every PDE state is replaced by its highest, well-defined\nderivative using the Fundamental Theorem of Calculus to obtain a new equation\n(a PIE). We show that this conversion from PDE representation to PIE\nrepresentation can be written in terms of explicit maps from the PDE parameters\nto PIE parameters. Lastly, we present numerical examples to demonstrate the\napplication of the PIE representation by performing stability analysis of PDEs\nvia convex optimization methods.\n', 'A PIE Representation of Coupled Linear 2D PDEs and Stability Analysis\n  using LPIs   We introduce a Partial Integral Equation (PIE) representation of Partial\nDifferential Equations (PDEs) in two spatial variables. PIEs are an algebraic\nstate-space representation of infinite-dimensional systems and have been used\nto model 1D PDEs and time-delay systems without continuity constraints or\nboundary conditions -- making these PIE representations amenable to stability\nanalysis using convex optimization. To extend the PIE framework to 2D PDEs, we\nfirst construct an algebra of Partial Integral (PI) operators on the function\nspace L_2[x,y], providing formulae for composition, adjoint, and inversion. We\nthen extend this algebra to R^n x L_2[x] x L_2[y] x L_2[x,y] and demonstrate\nthat, for any suitable coupled, linear PDE in 2 spatial variables, there exists\nan associated PIE whose solutions bijectively map to solutions of the original\nPDE -- providing conversion formulae between these representations. Next, we\nuse positive matrices to parameterize the convex cone of 2D PI operators --\nallowing us to optimize PI operators and solve Linear PI Inequality (LPI)\nfeasibility problems. Finally, we use the 2D LPI framework to provide\nconditions for stability of 2D linear PDEs. We test these conditions on 2D heat\nand wave equations and demonstrate that the stability condition has little to\nno conservatism.\n']","[('pdes spatial', 0.4502308666706085), ('pde systems', 0.44402918219566345), ('linear pdes', 0.41812804341316223), ('analysis pdes', 0.3901921808719635), ('coupled pdes', 0.38380593061447144), ('linear pde', 0.3804780840873718), ('stability analysis', 0.37399935722351074), ('pde system', 0.37128719687461853), ('equations pdes one', 0.3677358627319336), ('pdes', 0.366767555475235)]"
1604,1604,18,1604_corresponding extremal graphs_extremal graphs_mathcal free graphs_maximum spectral,"['corresponding extremal graphs', 'extremal graphs', 'mathcal free graphs', 'maximum spectral', 'graphs maximum', 'extremal graph', 'graphs maximum number', 'free graphs', 'maximum spectral radius', 'mathcal free graph']","[""Tur\\'an-type problems on $[a,b]$-factors of graphs, and beyond   Given a set of graphs $\\mathcal{H}$, we say that a graph $G$ is\n\\textit{$\\mathcal{H}$-free} if it does not contain any member of $\\mathcal{H}$\nas a subgraph. Let $\\text{ex}(n,\\mathcal{H})$ (resp.\n$\\text{ex}_{sp}(n,\\mathcal{H})$) denote the maximum size (resp. spectral\nradius) of an $n$-vertex $\\mathcal{H}$-free graph. Denote by $\\text{Ex}(n,\n\\mathcal{H})$ the set of all $n$-vertex $\\mathcal{H}$-free graphs with\n$\\text{ex}(n, \\mathcal{H})$ edges. Similarly, let\n$\\mathrm{Ex}_{sp}(n,\\mathcal{H})$ be the set of all $n$-vertex\n$\\mathcal{H}$-free graphs with spectral radius $\\text{ex}_{sp}(n,\n\\mathcal{H})$. For positive integers $a, b$ with $a\\leqslant b$, an\n$[a,b]$-factor of a graph $G$ is a spanning subgraph $F$ of $G$ such that\n$a\\leqslant d_F(v)\\leqslant b$ for all $v\\in V(G)$, where $d_F(v)$ denotes the\ndegree of the vertex $v$ in $F.$ Let $\\mathcal{F}_{a,b}$ be the set of all the\n$[a,b]$-factors of an $n$-vertex complete graph $K_n$. In this paper, we\ndetermine the Tur\\'an number $\\text{ex}(n,\\mathcal{F}_{a,b})$ and the spectral\nTur\\'an number $\\text{ex}_{sp}(n,\\mathcal{F}_{a,b}),$ respectively.\nFurthermore, the bipartite analogue of $\\text{ex}(n,\\mathcal{F}_{a,b})$ (resp.\n$\\text{ex}_{sp}(n,\\mathcal{F}_{a,b})$) is also obtained. All the corresponding\nextremal graphs are identified. Consequently, one sees that\n$\\mathrm{Ex}_{sp}(n,\\mathcal{F}_{a,b})\\subseteq \\text{Ex}(n,\n\\mathcal{F}_{a,b})$ holds for graphs and bipartite graphs. This partially\nanswers an open problem proposed by Liu and Ning \\cite{LN2023}. Our results may\ndeduce a main result of Fan and Lin \\cite{FL2022}.\n"", ""Tur\\'an numbers for non-bipartite graphs and applications to spectral\n  extremal problems   Given a graph family $\\mathcal{H}$ with $\\min_{H\\in\n\\mathcal{H}}\\chi(H)=r+1\\geq 3$. Let ${\\rm ex}(n,\\mathcal{H})$ and ${\\rm\nspex}(n,\\mathcal{H})$ be the maximum number of edges and the maximum spectral\nradius of the adjacency matrix over all $\\mathcal{H}$-free graphs of order $n$,\nrespectively. Denote by ${\\rm EX}(n,\\mathcal{H})$ (resp. ${\\rm\nSPEX}(n,\\mathcal{H})$) the set of extremal graphs with respect to ${\\rm\nex}(n,\\mathcal{H})$ (resp. ${\\rm spex}(n,\\mathcal{H})$).\n  In this paper, we use a decomposition family defined by Simonovits to give a\ncharacterization of which graph families $\\mathcal{H}$ satisfy ${\\rm\nex}(n,\\mathcal{H})<e(T_{n,r})+\\lfloor \\frac{n}{2r} \\rfloor$. Furthermore, we\ncompletely determine ${\\rm EX}\\big(n,\\mathbb{G}(F_1,\\ldots,F_k)\\big)$ for $n$\nsufficiently large, where $\\mathbb{G}(F_1,\\ldots,F_k)$ denotes a finite graph\nfamily which consists of $k$ edge-disjoint $(r+1)$-chromatic color-critical\ngraphs $F_1,\\ldots,F_k$. This result strengthens a theorem of Gy\\H{o}ri, who\nsettled the case that $F_1=\\cdots =F_k = K_{r+1}$.\n  Wang, Kang and Xue %[J. Combin. Theory Ser. B 159 (2023) 20--41] proved that\n${\\rm SPEX}(n,H)\\subseteq {\\rm EX}(n,H)$ for $n$ sufficiently large and any\ngraph $H$ with ${\\rm ex}(n,H)=e(T_{n,r})+O(1)$. As an application of our first\ntheorem, we show that ${\\rm SPEX}(n,\\mathcal{H})\\subseteq {\\rm\nEX}(n,\\mathcal{H})$ for $n$ sufficiently large and any finite family\n$\\mathcal{H}$ with ${\\rm ex}(n,\\mathcal{H})<e(T_{n,r})+\\lfloor\n\\frac{n}{2r}\\rfloor$. As an application of our second theorem we completely\ndetermine ${\\rm SPEX}\\big(n,\\mathbb{G}(F_1,\\ldots,F_k)\\big)$ for $n$\nsufficiently large.\n  Finally, related problems are proposed for further research.\n"", ""A sharp spectral extremal result for general non-bipartite graphs For a graph family $\\mathcal F$, let $\\mathrm{ex}(n,\\mathcal F)$ and $\\mathrm{spex}(n,\\mathcal F)$ denote the maximum number of edges and maximum spectral radius of an $n$-vertex $\\mathcal F$-free graph, respectively, and let $\\mathrm{EX}(n,\\mathcal F)$ and $\\mathrm{SPEX}(n,\\mathcal F)$ denote the corresponding sets of extremal graphs. Wang, Kang, and Xue showed that if $\\mathrm{EX}(n,\\mathcal F)$ consists of Tur\\'an graphs $T_{n,r}$ plus $O(1)$ edges, then $\\mathrm{SPEX}(n,\\mathcal F)\\subseteq\\mathrm{EX}(n,\\mathcal F)$ for $n$ large enough. Fang, Tait, and Zhai extended this result by showing if $e(T_{n,r})\\le\\mathrm{ex}(n,\\mathcal F) < e(T_{n,r})+\\lfloor n/2r\\rfloor$ then $\\mathrm{SPEX}(n,\\mathcal F)\\subseteq\\mathrm{EX}(n,\\mathcal F)$ for $n$ large enough. In this paper we extend the result further and for many values of $r$ we can show that our result is best possible, answering a question of Fang, Tait, and Zhai.""]","[('corresponding extremal graphs', 0.6040093302726746), ('extremal graphs', 0.5612576007843018), ('mathcal free graphs', 0.4689424932003021), ('maximum spectral', 0.46264010667800903), ('graphs maximum', 0.4606121778488159), ('extremal graph', 0.45843008160591125), ('graphs maximum number', 0.4341287314891815), ('free graphs', 0.4243212044239044), ('maximum spectral radius', 0.42400071024894714), ('mathcal free graph', 0.416981965303421)]"
1605,1605,18,1605_binary optimization qubo_ising machines_unconstrained binary optimization_binary optimization,"['binary optimization qubo', 'ising machines', 'unconstrained binary optimization', 'binary optimization', 'optimization qubo', 'ising', 'based ising', 'quadratic unconstrained binary', 'unconstrained binary', 'computationally hard']","['Design of General Purpose Minimal-Auxiliary Ising Machines   Ising machines are a form of quantum-inspired processing-in-memory computer\nwhich has shown great promise for overcoming the limitations of traditional\ncomputing paradigms while operating at a fraction of the energy use. The\nprocess of designing Ising machines is known as the reverse Ising problem.\nUnfortunately, this problem is in general computationally intractable: it is a\nnonconvex mixed-integer linear programming problem which cannot be naively\nbrute-forced except in the simplest cases due to exponential scaling of runtime\nwith number of spins. We prove new theoretical results which allow us to reduce\nthe search space to one with quadratic scaling. We utilize this theory to\ndevelop general purpose algorithmic solutions to the reverse Ising problem. In\nparticular, we demonstrate Ising formulations of 3-bit and 4-bit integer\nmultiplication which use fewer total spins than previously known methods by a\nfactor of more than three. Our results increase the practicality of\nimplementing such circuits on modern Ising hardware, where spins are at a\npremium.\n', 'Self-contained relaxation-based dynamical Ising machines   Dynamical Ising machines are based on continuous dynamical systems evolving\nfrom a generic initial state to a state strongly related to the ground state of\nthe classical Ising model on a graph. Reaching the ground state is equivalent\nto finding the maximum (weighted) cut of the graph, which presents the Ising\nmachines as an alternative way to solving and investigating NP-complete\nproblems. Among the dynamical models, relaxation-based models are distinguished\nby their relations with guarantees of performance achieved in time scaling\npolynomially with the problem size. However, the terminal states of such\nmachines are essentially non-binary, necessitating special post-processing\nrelying on disparate computing. We show that an Ising machine implementing a\nspecial continuous dynamical system (called the V${}_2$ model) solves the\nrounding problem dynamically. We prove that the V${}_2$ model, starting from an\narbitrary non-binary state, terminates in a state that trivially rounds to a\nbinary state with the cut at least as big as obtained by optimal rounding of\nthe initial state. Besides showing that relaxation-based dynamical Ising\nmachines can be made self-contained, this result presents a non-Boolean\nrealization of solving a non-trivial information processing task on Ising\nmachines. Moreover, we prove that if the initial state of the V${}_2$-machine\nis a random limited amplitude perturbation of a binary state, the machine\nprogresses to a state with at least as high cut as that of the initial binary\nstate. Since the probability of improving the cut is finite, this shows that\nthe V${}_2$-machine with random agitations converges to a maximum cut state\nalmost surely.\n', 'Linearizing Binary Optimization Problems Using Variable Posets for Ising\n  Machines   Ising machines are next-generation computers expected to efficiently sample\nnear-optimal solutions of combinatorial optimization problems. Combinatorial\noptimization problems are modeled as quadratic unconstrained binary\noptimization (QUBO) problems to apply an Ising machine. However, current\nstate-of-the-art Ising machines still often fail to output near-optimal\nsolutions due to the complicated energy landscape of QUBO problems.\nFurthermore, the physical implementation of Ising machines severely restricts\nthe size of QUBO problems to be input as a result of limited hardware graph\nstructures. In this study, we take a new approach to these challenges by\ninjecting auxiliary penalties preserving the optimum, which reduces quadratic\nterms in QUBO objective functions. The process simultaneously simplifies the\nenergy landscape of QUBO problems, allowing the search for near-optimal\nsolutions, and makes QUBO problems sparser, facilitating encoding into Ising\nmachines with restriction on the hardware graph structure. We propose\nlinearization of QUBO problems using variable posets as an outcome of the\napproach. By applying the proposed method to synthetic QUBO instances and to\nmulti-dimensional knapsack problems, we empirically validate the effects on\nenhancing minor-embedding of QUBO problems and the performance of Ising\nmachines.\n']","[('binary optimization qubo', 0.5768764615058899), ('ising machines', 0.5673750638961792), ('unconstrained binary optimization', 0.5139539241790771), ('binary optimization', 0.4982205033302307), ('optimization qubo', 0.49386927485466003), ('ising', 0.44885358214378357), ('based ising', 0.4317641258239746), ('quadratic unconstrained binary', 0.41936978697776794), ('unconstrained binary', 0.39688071608543396), ('computationally hard', 0.392299085855484)]"
1606,1606,18,1606_del pezzo surfaces_pezzo surfaces_pezzo surfaces degree_del pezzo surface,"['del pezzo surfaces', 'pezzo surfaces', 'pezzo surfaces degree', 'del pezzo surface', 'pezzo surface degree', 'pezzo surface', 'algebraic surfaces', 'smooth cubic surfaces', 'cubic surfaces', 'surfaces rational']","['Boundedness of regular del Pezzo surfaces over imperfect fields   For a regular del Pezzo surface $X$, we prove that $|-12K_X|$ is very ample.\nFurthermore, we also give an explicit upper bound for the volume $K_X^2$ which\ndepends only on $[k : k^p]$ for the base field $k$. As a consequence, we obtain\nthe boundedness of geometrically integral regular del Pezzo surfaces.\n', 'Interpolation Problems: Del Pezzo Surfaces   We consider the problem of interpolating projective varieties through points\nand linear spaces. We show that del Pezzo surfaces satisfy weak interpolation.\n', 'Bounding geometrically integral del Pezzo surfaces   We prove several boundedness statements for geometrically integral normal del\nPezzo surfaces $X$ over arbitrary fields. We give an explicit sharp bound on\nthe irregularity if $X$ is canonical or regular. In particular, we show that\nwild canonical del Pezzo surfaces exist only in characteristic 2. As an\napplication, we deduce that canonical del Pezzo surfaces form a bounded family\nover $\\mathbb{Z}$, generalising work of Tanaka. More generally, we prove the\nBAB conjecture on the boundedness of $\\varepsilon$-klt del Pezzo surfaces over\narbitrary fields of characteristic different from 2, 3, and 5.\n']","[('del pezzo surfaces', 0.7801184058189392), ('pezzo surfaces', 0.764850914478302), ('pezzo surfaces degree', 0.7609304785728455), ('del pezzo surface', 0.719312846660614), ('pezzo surface degree', 0.7106019258499146), ('pezzo surface', 0.7076383233070374), ('algebraic surfaces', 0.6084501147270203), ('smooth cubic surfaces', 0.6068426370620728), ('cubic surfaces', 0.6009489893913269), ('surfaces rational', 0.5961675047874451)]"
1607,1607,18,1607_ohsawa takegoshi extension_extension theorems_extension holomorphic_extension estimates,"['ohsawa takegoshi extension', 'extension theorems', 'extension holomorphic', 'extension estimates', 'plurisubharmonic functions', 'extension singular', 'takegoshi extension', 'holomorphic sections', 'analytic singularities', 'sharp estimates']","['On the Ohsawa-Takegoshi $L^2$ extension theorem and removable\n  singularities of plurisubharmonic functions   The celebrated Ohsawa--Takegoshi extension theorem for $L^2$ holomorphic\nfunctions on bounded pseudoconvex domains in $\\mathbb C^n$ is a fundamental\nresult in several complex variables and complex geometry. Ohsawa conjectured in\n1995 that the same theorem still holds for more general bounded complete\nK\\""ahler domains in $\\mathbb C^n$. Recently, Chen--Wu--Wang confirmed this\nconjecture in a special case. In this paper we extend their result to the case\nof holomorphic sections of twisted canonical bundles over relatively compact\ncomplete K\\""{a}hler domains in Stein manifolds. As an application we prove a\nHartogs type extension theorem for plurisubharmonic functions across a compact\ncomplete pluripolar set, which is complementary to a classical result of\nShiffman and can be seen as an analogue of the Skoda--El Mir extension theorem\nfor plurisubharmonic functions -- a result that has been vacant since at least\n1985.\n', 'Minimal $L^2$ and $L^p$ Ohsawa-Takegoshi extensions   We find a precise relationship between the minimal extensions in $L^2$ and\n$L^p$ Ohsawa-Takegoshi extension theorems. This relationship also gives another\nproof to the $L^p$ version of the Ohsawa-Takegoshi extension theorem, which is\ndifferent from the original proof due to Berndtsson-P\\u{a}un.\n', 'Extension with log-canonical measures and an improvement to the plt\n  extension of Demailly--Hacon--Paun   With a view to proving the conjecture of ""dlt extension"" related to the\nabundance conjecture, a sequence of potential candidates for replacing the\nOhsawa measure in the Ohsawa-Takegoshi $L^2$ extension theorem, called the\n""lc-measures"", which hopefully could provide the $L^2$ estimate of a\nholomorphic extension of any suitable holomorphic section on a subvariety with\nsingular locus, are introduced in the first half of the paper. Based on the\nversion of $L^2$ extension theorem proved by Demailly, a proof is provided to\nshow that the lc-measure can replace the Ohsawa measure in the case where the\nclassical Ohsawa-Takegoshi $L^2$ extension works, with some improvements on the\nassumptions on the metrics involved. The second half of the paper provides a\nsimplified proof of the result of Demailly-Hacon-Paun on the ""plt extension""\nwith the superfluous assumption ""$\\operatorname{supp} D \\subset\n\\operatorname{supp}(S+B)$"" in their result removed. Most arguments in the proof\nare readily adopted to the ""dlt extension"" once the $L^2$ estimates with\nrespect to the lc-measures of holomorphic extensions of sections on\nsubvarieties with singular locus are ready.\n']","[('ohsawa takegoshi extension', 0.5250588059425354), ('extension theorems', 0.5020766258239746), ('extension holomorphic', 0.4939034879207611), ('extension estimates', 0.49175581336021423), ('plurisubharmonic functions', 0.45771241188049316), ('extension singular', 0.43373456597328186), ('takegoshi extension', 0.4025488793849945), ('holomorphic sections', 0.3772939145565033), ('analytic singularities', 0.35048916935920715), ('sharp estimates', 0.3440527021884918)]"
1608,1608,18,1608_monotone variational inequalities_variational inequality problems_variational inequalities_monotone variational inequality,"['monotone variational inequalities', 'variational inequality problems', 'variational inequalities', 'monotone variational inequality', 'variational inequality', 'methods variational', 'class variational inequalities', 'variational inequality vi', 'monotone variational', 'solving variational']","['Some Adaptive First-order Methods for Variational Inequalities with\n  Relatively Strongly Monotone Operators and Generalized Smoothness   In this paper, we introduce some adaptive methods for solving variational\ninequalities with relatively strongly monotone operators. Firstly, we focus on\nthe modification of the recently proposed, in smooth case [1], adaptive\nnumerical method for generalized smooth (with H\\""older condition) saddle point\nproblem, which has convergence rate estimates similar to accelerated methods.\nWe provide the motivation for such an approach and obtain theoretical results\nof the proposed method. Our second focus is the adaptation of widespread\nrecently proposed methods for solving variational inequalities with relatively\nstrongly monotone operators. The key idea in our approach is the refusal of the\nwell-known restart technique, which in some cases causes difficulties in\nimplementing such algorithms for applied problems. Nevertheless, our algorithms\nshow a comparable rate of convergence with respect to algorithms based on the\nabove-mentioned restart technique. Also, we present some numerical experiments,\nwhich demonstrate the effectiveness of the proposed methods.\n  [1] Jin, Y., Sidford, A., & Tian, K. (2022). Sharper rates for separable\nminimax and finite sum optimization via primal-dual extragradient methods.\narXiv preprint arXiv:2202.04640.\n', 'Adaptive Methods or Variational Inequalities with Relatively Smooth and\n  Reletively Strongly Monotone Operators   The article is devoted to some adaptive methods for variational inequalities\nwith relatively smooth and relatively strongly monotone operators. Starting\nfrom the recently proposed proximal variant of the extragradient method for\nthis class of problems, we investigate in detail the method with adaptively\nselected parameter values. An estimate of the convergence rate of this method\nis proved. The result is generalized to a class of variational inequalities\nwith relatively strongly monotone generalized smooth variational inequality\noperators. Numerical experiments have been performed for the problem of ridge\nregression and variational inequality associated with box-simplex games.\n', 'Some Methods for Relatively Strongly Monotone Variational Inequalities   The article is devoted to the development of numerical methods for solving\nvariational inequalities with relatively strongly monotone operators. We\nconsider two classes of variational inequalities related to some analogs of the\nLipschitz condition of the operator that appeared several years ago. One of\nthese classes is associated with the relative boundedness of the operator, and\nthe other one with the analog of the Lipschitz condition (namely, relative\nsmoothness). For variational inequalities with relatively bounded and\nrelatively strongly monotone operators, we introduce a modification of the\nMirror Descent method, which optimizes the convergence rate. We also propose\nthe adaptive Proximal Pirror algorithm and its restarted version with a linear\nconvergence rate for problems with relatively smooth and relatively strongly\nmonotone operators.\n']","[('monotone variational inequalities', 0.66677325963974), ('variational inequality problems', 0.6495981216430664), ('variational inequalities', 0.6393502950668335), ('monotone variational inequality', 0.6281837224960327), ('variational inequality', 0.5937941670417786), ('methods variational', 0.5483214259147644), ('class variational inequalities', 0.5433566570281982), ('variational inequality vi', 0.5407083630561829), ('monotone variational', 0.5387420654296875), ('solving variational', 0.5285091996192932)]"
1609,1609,18,1609_triangulation manifold_triangulations_triangulation_dimensional simplicial complex,"['triangulation manifold', 'triangulations', 'triangulation', 'dimensional simplicial complex', 'dimensional simplicial', 'symmetric simplicial', 'simplicial complexes', 'complex projective plane', 'manifolds like', 'projective plane']","['New examples and partial classification of 15-vertex triangulations of\n  the quaternionic projective plane   Brehm and K\\""uhnel (1992) constructed three 15-vertex combinatorial\n8-manifolds `like the quaternionic projective plane\' with symmetry groups\n$\\mathrm{A}_5$, $\\mathrm{A}_4$, and $\\mathrm{S}_3$, respectively. Gorodkov\n(2016) proved that these three manifolds are in fact PL homeomorphic to\n$\\mathbb{HP}^2$. Note that 15 is the minimal number of vertices of a\ncombinatorial 8-manifold that is not PL homeomorphic to $S^8$. In the present\npaper we construct a lot of new 15-vertex triangulations of $\\mathbb{HP}^2$. A\nsurprising fact is that such examples are found for very different symmetry\ngroups, including those not in any way related to the group $\\mathrm{A}_5$.\nNamely, we find 19 triangulations with symmetry group $\\mathrm{C}_7$, one\ntriangulation with symmetry group $\\mathrm{C}_6\\times\\mathrm{C}_2$, 14\ntriangulations with symmetry group $\\mathrm{C}_6$, 26 triangulations with\nsymmetry group $\\mathrm{C}_5$, one new triangulation with symmetry group\n$\\mathrm{A}_4$, and 11 new triangulations with symmetry group $\\mathrm{S}_3$.\nFurther, we obtain the following classification result. We prove that, up to\nisomorphism, there are exactly 75 triangulations of $\\mathbb{HP}^2$ with 15\nvertices and symmetry group of order at least 4: the three Brehm-K\\""uhnel\ntriangulations and the 72 new triangulations listed above. On the other hand,\nwe show that there are plenty of triangulations with symmetry groups\n$\\mathrm{C}_3$ and $\\mathrm{C}_2$, as well as the trivial symmetry group.\n', '634 vertex-transitive and more than $10^{103}$ non-vertex-transitive\n  27-vertex triangulations of manifolds like the octonionic projective plane   In 1987 Brehm and K\\""uhnel showed that any combinatorial $d$-manifold with\nless than $3d/2+3$ vertices is PL homeomorphic to the sphere and any\ncombinatorial $d$-manifold with exactly $3d/2+3$ vertices is PL homeomorphic to\neither the sphere or a manifold like a projective plane in the sense of Eells\nand Kuiper. The latter possibility may occur for $d\\in\\{2,4,8,16\\}$ only. There\nexist a unique $6$-vertex triangulation of $\\mathbb{RP}^2$, a unique $9$-vertex\ntriangulation of $\\mathbb{CP}^2$, and at least three $15$-vertex triangulations\nof $\\mathbb{HP}^2$. However, until now, the question of whether there exists a\n$27$-vertex triangulation of a manifold like the octonionic projective plane\nhas remained open. We solve this problem by constructing a lot of examples of\nsuch triangulations. Namely, we construct $634$ vertex-transitive $27$-vertex\ncombinatorial $16$-manifolds like the octonionic projective plane. Four of them\nhave symmetry group $\\mathrm{C}_3^3\\rtimes \\mathrm{C}_{13}$ of order $351$, and\nthe other $630$ have symmetry group $\\mathrm{C}_3^3$ of order $27$. Further, we\nconstruct more than $10^{103}$ non-vertex-transitive $27$-vertex combinatorial\n$16$-manifolds like the octonionic projective plane. Most of them have trivial\nsymmetry group, but there are also symmetry groups $\\mathrm{C}_3$,\n$\\mathrm{C}_3^2$, and $\\mathrm{C}_{13}$. We conjecture that all the\ntriangulations constructed are PL homeomorphic to the octonionic projective\nplane $\\mathbb{OP}^2$. Nevertheless, we have no proof of this fact so far.\n', 'On possible symmetry groups of 27-vertex triangulations of manifolds\n  like the octonionic projective plane   In 1987 Brehm and K\\""uhnel showed that any triangulation of a $d$-manifold\n(without boundary) that is not homeomorphic to the sphere has at least $3d/2+3$\nvertices. Moreover, triangulations with exactly $3d/2+3$ vertices may exist\nonly for `manifolds like projective planes\', which can have dimensions $2$,\n$4$, $8$, and $16$ only. There is a $6$-vertex triangulation of the real\nprojective plane $\\mathbb{RP}^2$, a $9$-vertex triangulation of the complex\nprojective plane $\\mathbb{CP}^2$, and $15$-vertex triangulations of the\nquaternionic projective plane $\\mathbb{HP}^2$. Recently, the author has\nconstructed first examples of $27$-vertex triangulations of manifolds like the\noctonionic projective plane $\\mathbb{OP}^2$. The four most symmetrical have\nsymmetry group $\\mathrm{C}_3^3\\rtimes \\mathrm{C}_{13}$ of order $351$. These\ntriangulations were constructed using a computer program after the symmetry\ngroup was guessed. However, it remained unclear why exactly this group is\nrealized as the symmetry group and whether $27$-vertex triangulations of\nmanifolds like $\\mathbb{OP}^2$ exist with other (possibly larger) symmetry\ngroups. In this paper we find strong restrictions on symmetry groups of such\n$27$-vertex triangulations. Namely, we present a list of $26$ subgroups of\n$\\mathrm{S}_{27}$ containing all possible symmetry groups of $27$-vertex\ntriangulations of manifolds like the octonionic projective plane. (We do not\nknow whether all these subgroups can be realized as symmetry groups.) The group\n$\\mathrm{C}_3^3\\rtimes \\mathrm{C}_{13}$ is the largest group in this list, and\nthe orders of all other groups do not exceed $52$. A key role in our approach\nis played by the use of Smith and Bredon\'s results on the topology of fixed\npoint sets of finite transformation groups.\n']","[('triangulation manifold', 0.6599432229995728), ('triangulations', 0.6185158491134644), ('triangulation', 0.5659748315811157), ('dimensional simplicial complex', 0.5168549418449402), ('dimensional simplicial', 0.49556851387023926), ('symmetric simplicial', 0.4590497612953186), ('simplicial complexes', 0.4589274525642395), ('complex projective plane', 0.420111745595932), ('manifolds like', 0.4100518226623535), ('projective plane', 0.4002113342285156)]"
1610,1610,18,1610_multi objective optimization_integer linear programming_multiobjective optimization_pareto optimal solutions,"['multi objective optimization', 'integer linear programming', 'multiobjective optimization', 'pareto optimal solutions', 'objective optimization problems', 'multi objective', 'objective optimization', 'mixed integer programming', 'pareto optimal', 'integer programming']","['An outer approximation algorithm for multi-objective mixed-integer\n  linear and non-linear programming   In this paper, we present the first outer approximation algorithm for\nmulti-objective mixed-integer linear programming problems with any number of\nobjectives. The algorithm also works for certain classes of non-linear\nprogramming problems. It produces the non-dominated extreme points as well as\nthe facets of the convex hull of these points. The algorithm relies on an\noracle which solves single-objective weighted-sum problems and we show that the\nrequired number of oracle calls is polynomial in the number of facets of the\nconvex hull of the non-dominated extreme points in the case of multiobjective\nmixed-integer programming (MOMILP). Thus, for MOMILP problems for which the\nweighted-sum problem is solvable in polynomial time, the facets can be computed\nwith incremental-polynomial delay. From a practical perspective, the algorithm\nstarts from a valid lower bound set for the non-dominated extreme points and\niteratively improves it. Therefore it can be used in multi-objective\nbranch-and-bound algorithms and still provide a valid bound set at any stage,\neven if interrupted before converging. Moreover, the oracle produces Pareto\noptimal solutions, which makes the algorithm also attractive from the primal\nside in a multi-objective branch-and-bound context. Finally, the oracle can\nalso be called with any relaxation of the primal problem, and the obtained\npoints and facets still provide a valid lower bound set. A computational study\non a set of benchmark instances from the literature and new non-linear\nmulti-objective instances is provided.\n', 'An Extension of the Non-Inferior Set Estimation Algorithm for Many\n  Objectives   This work proposes a novel multi-objective optimization approach that\nglobally finds a representative non-inferior set of solutions, also known as\nPareto-optimal solutions, by automatically formulating and solving a sequence\nof weighted sum method scalarization problems. The approach is called MONISE\n(Many-Objective NISE) because it represents an extension of the well-known\nnon-inferior set estimation (NISE) algorithm, which was originally conceived to\ndeal with two-dimensional objective spaces. The proposal is endowed with the\nfollowing characteristics: (1) uses a mixed-integer linear programming\nformulation to operate in two or more dimensions, thus properly supporting many\n(i.e., three or more) objectives; (2) relies on an external algorithm to solve\nthe weighted sum method scalarization problem to optimality; and (3) creates a\nfaithful representation of the Pareto frontier in the case of convex problems,\nand a useful approximation of it in the non-convex case. Moreover, when dealing\nspecifically with two objectives, some additional properties are portrayed for\nthe estimated non-inferior set. Experimental results validate the proposal and\nindicate that MONISE is competitive, in convex and non-convex (combinatorial)\nproblems, both in terms of computational cost and the overall quality of the\nnon-inferior set, measured by the acquired hypervolume.\n', 'An Extension of the Non-Inferior Set Estimation Algorithm for Many\n  Objectives   This work proposes a novel multi-objective optimization approach that\nglobally finds a representative non-inferior set of solutions, also known as\nPareto-optimal solutions, by automatically formulating and solving a sequence\nof weighted sum method scalarization problems. The approach is called MONISE\n(Many-Objective NISE) because it represents an extension of the well-known\nnon-inferior set estimation (NISE) algorithm, which was originally conceived to\ndeal with two-dimensional objective spaces. The proposal is endowed with the\nfollowing characteristics: (1) uses a mixed-integer linear programming\nformulation to operate in two or more dimensions, thus properly supporting many\n(i.e., three or more) objectives; (2) relies on an external algorithm to solve\nthe weighted sum method scalarization problem to optimality; and (3) creates a\nfaithful representation of the Pareto frontier in the case of convex problems,\nand a useful approximation of it in the non-convex case. Moreover, when dealing\nspecifically with two objectives, some additional properties are portrayed for\nthe estimated non-inferior set. Experimental results validate the proposal and\nindicate that MONISE is competitive, in convex and non-convex (combinatorial)\nproblems, both in terms of computational cost and the overall quality of the\nnon-inferior set, measured by the acquired hypervolume.\n']","[('multi objective optimization', 0.6423717141151428), ('integer linear programming', 0.6371331810951233), ('multiobjective optimization', 0.5885855555534363), ('pareto optimal solutions', 0.5856372117996216), ('objective optimization problems', 0.5849742293357849), ('multi objective', 0.5776746273040771), ('objective optimization', 0.5630518794059753), ('mixed integer programming', 0.5629011392593384), ('pareto optimal', 0.5535382628440857), ('integer programming', 0.5465387105941772)]"
1611,1611,18,1611_delta conjecture_conjecture generalized_conjectures_conjecture formula,"['delta conjecture', 'conjecture generalized', 'conjectures', 'conjecture formula', 'symmetric delta', 'conjecture', 'extended delta', 'catalan numbers', 'version delta', 'case delta']","[""A proof of the compositional Delta conjecture   We prove a compositional refinement of the Delta conjecture (rise version) of\nHaglund, Remmel and Wilson (2018) for $\\Delta_{e_{n-k-1}}'e_n$ which was stated\nby D'Adderio, Iraci and Vanden Wyngaerd (2020) in terms of Theta operators.\n"", 'Some consequences of the valley Delta conjectures   In (Haglund, Remmel, Wilson 2018) Haglund, Remmel and Wilson introduced their\nDelta conjectures, which give two different combinatorial interpretations of\nthe symmetric function $\\Delta\'_{e_{n-k-1}} e_n$ in terms of rise-decorated or\nvalley-decorated labelled Dyck paths respectively. While the rise version has\nbeen recently proved (D\'Adderio, Mellit 2021; Blasiak, Haiman, Morse, Pun,\nSeelinger preprint 2021), not much is known about the valley version. In this\nwork we prove the Schr\\""oder case of the valley Delta conjecture, the\nSchr\\""oder case of its square version (Iraci, Vanden Wyngaerd 2021), and the\nCatalan case of its extended version (Qiu, Wilson 2020). Furthermore, assuming\nthe symmetry of (a refinement of) the combinatorial side of the extended valley\nDelta conjecture, we deduce also the Catalan case of its square version (Iraci,\nVanden Wyngaerd 2021).\n', ""The valley version of the Extended Delta Conjecture   The Shuffle Theorem of Carlsson and Mellit gives a combinatorial expression\nfor the bigraded Frobenius characteristic of the ring of diagonal harmonics,\nand the Delta Conjecture of Haglund, Remmel and the second author provides two\ngeneralizations of the Shuffle Theorem to the delta operator expression\n$\\Delta'_{e_k} e_n$. Haglund et al. also propose the Extended Delta Conjecture\nfor the delta operator expression $\\Delta'_{e_k} \\Delta_{h_r}e_n$, which is\nanalogous to the rise version of the Delta Conjecture. Recently, D'Adderio,\nIraci and Wyngaerd proved the rise version of the Extended Delta Conjecture at\nthe case when $t=0$. In this paper, we propose a new valley version of the\nExtended Delta Conjecture. Then, we work on the combinatorics of extended\nordered multiset partitions to prove that the two conjectures for\n$\\Delta'_{e_k} \\Delta_{h_r}e_n$ are equivalent when $t$ or $q$ equals 0, thus\nproving the valley version of the Extended Delta Conjecture when $t$ or $q$\nequals 0.\n""]","[('delta conjecture', 0.7086639404296875), ('conjecture generalized', 0.529731273651123), ('conjectures', 0.48150837421417236), ('conjecture formula', 0.4790554344654083), ('symmetric delta', 0.4671841561794281), ('conjecture', 0.4520544409751892), ('extended delta', 0.43079912662506104), ('catalan numbers', 0.40340057015419006), ('version delta', 0.39834633469581604), ('case delta', 0.3953225314617157)]"
1612,1612,18,1612_equivariant theory_twisted equivariant_equivariant theories_equivariant cohomology,"['equivariant theory', 'twisted equivariant', 'equivariant theories', 'equivariant cohomology', 'characterization equivariant', 'theory groups', 'equivariant', 'equivariant formality', 'cohomology theory', 'valued equivariant']","['Scissors congruence K-theory for equivariant manifolds   We introduce a scissors congruence $K$-theory spectrum which lifts the\nequivariant scissors congruence groups for compact $G$-manifolds with boundary,\nand we show that on $\\pi_0$ this is the source of a spectrum level lift of the\nBurnside ring valued equivariant Euler characteristic of a compact\n$G$-manifold. We also show that the equivariant scissors congruence groups for\nvarying subgroups assemble into a Mackey functor, which is a shadow of a\nconjectural higher genuine equivariant structure.\n', ""Magnetic Equivariant K-theory   We present the fundamental properties of the K-theory groups of complex\nvector bundles endowed with actions of magnetic groups. In this work we show\nthat the magnetic equivariant K-theory groups define an equivariant cohomology\ntheory, we determine its coefficients, we show Bott's, Thom's and the degree\nshift isomorphism, we present the Atiyah-Hirzeburh spectral sequence, and we\nexplicitly calculate two magnetic equivariant K-theory groups in order to\nshowcase its applicability. These magnetic equivariant K-theory groups are\nrelevant in condensed matter physics since they provide topological invariants\nof gapped Hamiltonians in magnetic crystals.\n"", 'Rational magnetic equivariant K-theory   We introduce the magnetic equivariant K-theory groups as the K-theory groups\nassociated to magnetic groups and their respective magnetic equivariant complex\nbundles. We restrict the magnetic group to its subgroup of elements that act\ncomplex linearly, and we show that this restriction induces a rational\nisomorphism with the conjugation invariant part of the complex equivariant\nK-theory of the restricted group. This isomorphism allows to calculate the\ntorsion free part of the magnetic equivariant K-theory groups reducing it to\nknown calculations in complex equivariant K-theory\n']","[('equivariant theory', 0.6221608519554138), ('twisted equivariant', 0.6195222735404968), ('equivariant theories', 0.6189700961112976), ('equivariant cohomology', 0.6107681393623352), ('characterization equivariant', 0.5444583892822266), ('theory groups', 0.5224947929382324), ('equivariant', 0.5213744640350342), ('equivariant formality', 0.5201768279075623), ('cohomology theory', 0.4672464430332184), ('valued equivariant', 0.4601733684539795)]"
1613,1613,18,1613_reasoning tasks_language models llms_large language models_artificial general intelligence,"['reasoning tasks', 'language models llms', 'large language models', 'artificial general intelligence', 'language models', 'modeling solving', 'ai', 'models optimization', 'artificial intelligence', 'artificial intelligence ai']","['OR-LLM-Agent: Automating Modeling and Solving of Operations Research\n  Optimization Problem with Reasoning Large Language Model   Operations Research (OR) has been widely applied in various fields such as\nresource allocation, production planning, and supply chain management. However,\naddressing real-world OR problems requires OR experts to perform mathematical\nmodeling and programmers to develop solution algorithms. This traditional\nmethod, heavily reliant on experts, is costly and has long development cycles,\nseverely limiting the widespread adoption of OR techniques. Few have considered\nusing Artificial Intelligence (AI) to replace professionals to achieve fully\nautomated solutions for OR problems. We propose OR-LLM-Agent, the first AI\nagent that enables end-to-end automation for solving real-world OR problems.\nOR-LLM-Agent leverages the Chain-of-Thought (CoT) reasoning capabilities of\nLarge Language Models (LLMs) to translate natural language problem descriptions\ninto formal mathematical models and automatically generate Gurobi solver code.\nIn OR-LLM-Agent, OR-CodeAgent is designed to automate code execution and repair\nwithin a sandbox environment, facilitating the derivation of the final\nsolution. Due to the lack of dedicated benchmark datasets for evaluating the\nautomated solving of OR problems, we construct a benchmark dataset comprising\n83 real-world OR problems described in natural language. We conduct comparative\nexperiments with state-of-the-art (SOTA) reasoning LLMs, including GPT-o3-mini,\nDeepSeek-R1, and Gemini 2.0 Flash Thinking. The OR-LLM-Agent achieved the\nhighest pass rate of 100% and the highest solution accuracy of 85%,\ndemonstrating the feasibility of automated OR problem-solving. Data and code\nhave been publicly available at https://github.com/bwz96sco/or_llm_agent.\n', 'From Good to Great: Improving Math Reasoning with Tool-Augmented\n  Interleaf Prompting   This paper investigates the performance of Large Language Models (LLMs) and\nTool-augmented LLMs in tackling complex mathematical reasoning tasks. We\nintroduce IMP-TIP: Improving Math Reasoning with Tool-augmented Interleaf\nPrompting, a framework that combines the strengths of both LLMs and\nTool-augmented LLMs. IMP-TIP follows the ``From Good to Great"" concept,\ncollecting multiple potential solutions from both LLMs and their Tool-Augmented\ncounterparts for the same math problem, and then selecting or re-generating the\nmost accurate answer after cross-checking these solutions via tool-augmented\ninterleaf prompting. The framework incorporates two key aspects: self-prompt\nand tool-augmented interleaf prompting (TIP). The former allows LLMs to\nautonomously refine and improve an initial prompt related to tool usage, while\nthe latter enables LLMs to derive the final answer by dynamically analyzing the\nproblem, cross-checking potential solutions, and revising previous reasoning\nhints in an interleaved manner. Experimental analysis shows that IMP-TIP\nachieves enhanced mathematical capabilities and outperforms traditional LLMs\nand tool-augmented LLMs in accuracy and reasoning diversity on math reasoning\ntasks. For instance, IMP-TIP can improve Tool-augmented ChatGPT on GSM8K-Hard\nfrom 56.0% to 65.2%.\n', 'From Large Language Models and Optimization to Decision Optimization\n  CoPilot: A Research Manifesto   Significantly simplifying the creation of optimization models for real-world\nbusiness problems has long been a major goal in applying mathematical\noptimization more widely to important business and societal decisions. The\nrecent capabilities of Large Language Models (LLMs) present a timely\nopportunity to achieve this goal. Therefore, we propose research at the\nintersection of LLMs and optimization to create a Decision Optimization CoPilot\n(DOCP) - an AI tool designed to assist any decision maker, interacting in\nnatural language to grasp the business problem, subsequently formulating and\nsolving the corresponding optimization model. This paper outlines our DOCP\nvision and identifies several fundamental requirements for its implementation.\nWe describe the state of the art through a literature survey and experiments\nusing ChatGPT. We show that a) LLMs already provide substantial novel\ncapabilities relevant to a DOCP, and b) major research challenges remain to be\naddressed. We also propose possible research directions to overcome these gaps.\nWe also see this work as a call to action to bring together the LLM and\noptimization communities to pursue our vision, thereby enabling much more\nwidespread improved decision-making.\n']","[('reasoning tasks', 0.5186280608177185), ('language models llms', 0.5018630623817444), ('large language models', 0.4958750605583191), ('artificial general intelligence', 0.4794963002204895), ('language models', 0.4705997407436371), ('modeling solving', 0.4532855749130249), ('ai', 0.42800432443618774), ('models optimization', 0.4161006510257721), ('artificial intelligence', 0.4086783528327942), ('artificial intelligence ai', 0.40658435225486755)]"
1614,1614,18,1614_martingale transforms_valued martingales_valued martingale_martingale theory,"['martingale transforms', 'valued martingales', 'valued martingale', 'martingale theory', 'martingale concentration', 'martingale differences', 'normalized martingales', 'martingales', 'martingale', 'self normalized martingales']","[""Optimal range of Haar martingale transforms and its applications   Let $(\\mathcal{F}_n)_{n\\ge 0}$ be the standard dyadic filtration on $[0,1]$.\nLet $\\mathbb{E}_{\\mathcal{F}_n}$ be the conditional expectation from $\nL_1=L_1[0,1]$ onto $\\mathcal{F} _n$, $n\\ge 0$, and let $\\mathbb{E}_{\\mathcal{F}\n_{-1}} =0$. We present the sharp estimate for the distribution function of the\nmartingale transform $T$ defined by \\begin{align*} Tf=\\sum_{m=0}^\\infty \\left(\n\\mathbb{E}_{\\mathcal{F}_{2m}} f-\\mathbb{E}_{\\mathcal{F}_{2m-1}}f \\right), ~f\\in\nL_1, \\end{align*} in terms of the classical Calder\\'{o}n operator. As an\napplication, for a given symmetric function space $E$ on $[0,1]$, we identify\nthe symmetric space $\\mathcal{S}_E$, the optimal Banach symmetric range of\nmartingale transforms/Haar basis projections acting on $E$.\n"", 'A Note on Some Martingale Inequalities   We derive inequalities for time-discrete and time-continuous martingales that\nare similar to the well-known Burkholder inequalities. For the time-discrete\ncase arbitrary martingales in $L^p(\\Omega)$ are treated, whereas in the\ntime-continuous case martingales defined by It\\^o integrals w.r.t. a\nmulti-dimensional Wiener process are considered. The estimates for the\ntime-discrete martingales are related to the more general results by I. Pinelis\n(1994) and are proved to be sharp by a different and more elementary proof for\nthis special setting. Further, for time-continuous martingales the presented\ninequalities are generalizations of similar estimates proved by M. Zakai (1967)\nand E. Rio (2009) to the general multi-dimensional case. Especially, these\ninequalities possess smaller constants compared to the ones that result if the\noriginal Burkholder inequalities would be applied for such estimates.\nTherefore, the presented inequalities are highly valuable in, e.g., stochastic\nanalysis and stochastic numerics.\n', ""A note on concentration inequality for vector-valued martingales with\n  weak exponential-type tails   We present novel martingale concentration inequalities for martingale\ndifferences with finite Orlicz-$\\psi_\\alpha$ norms. Such martingale differences\nwith weak exponential-type tails scatters in many statistical applications and\ncan be heavier than sub-exponential distributions. In the case of one\ndimension, we prove in general that for a sequence of scalar-valued\nsupermartingale difference, the tail bound depends solely on the sum of squared\nOrlicz-$\\psi_\\alpha$ norms instead of the maximal Orlicz-$\\psi_\\alpha$ norm,\ngeneralizing the results of Lesigne & Voln\\'y (2001) and Fan et al. (2012). In\nthe multidimensional case, using a dimension reduction lemma proposed by\nKallenberg & Sztencel (1991) we show that essentially the same concentration\ntail bound holds for vector-valued martingale difference sequences.\n""]","[('martingale transforms', 0.7062259912490845), ('valued martingales', 0.6997286081314087), ('valued martingale', 0.6865350604057312), ('martingale theory', 0.6594642400741577), ('martingale concentration', 0.6536524295806885), ('martingale differences', 0.6518557071685791), ('normalized martingales', 0.629177987575531), ('martingales', 0.6210116147994995), ('martingale', 0.6186957359313965), ('self normalized martingales', 0.615939199924469)]"
1615,1615,18,1615_flow manifolds_asymptotically flat manifold_asymptotically flat manifolds_yamabe flow,"['flow manifolds', 'asymptotically flat manifold', 'asymptotically flat manifolds', 'yamabe flow', 'flow asymptotically', 'yamabe metrics', 'flow singular', 'complete riemannian manifold', 'yamabe invariant', 'riemannian manifold']","['Global Yamabe flow on asymptotically flat manifolds   In this paper, we study the existence of global Yamabe flow on asymptotically\nflat (in short, AF or ALE) manifolds. Note that the ADM mass is preserved in\ndimensions 3,4 and 5. We present a new general local existence of Yamabe flow\non a complete Riemannian manifold with the initial metric quasi-isometric to a\nbackground metric of bounded scalar curvature. Asymptotic behaviour of the\nYamabe flow on ALE manifolds is also addressed provided the initial scalar\ncurvature is non-negative and there is a bounded subsolution to the\ncorresponding Poisson equation. We also present a maximum principle for a very\ngeneral parabolic equations on the complete Riemannian manifolds.\n', 'Convergence rate of the weighted Yamabe flow   The weighted Yamabe flow was the geometric flow introduced to study the\nweighted Yamabe problem on smooth metric measure spaces. Carlotto, Chodosh and\nRubinstein have studied the convergence rate of the Yamabe flow. Inspired by\ntheir result, we study in this paper the convergence rate of the weighted\nYamabe flow.\n', 'The Yamabe flow on asymptotically Euclidean manifolds with nonpositive\n  Yamabe constant   We study the Yamabe flow on asymptotically flat manifolds with non-positive\nYamabe constant $Y\\leq 0$. Previous work by the second and third named authors\n\\cite{ChenWang} showed that while the Yamabe flow always converges in a global\nweighted sense when $Y>0$, the flow must diverge when $Y\\leq 0$. We show here\nin the $Y\\leq 0$ case however that after suitable rescalings, the Yamabe flow\nstarting from any asymptotically flat manifold must converge to the unique\npositive function which solves the Yamabe problem on a compactification of the\noriginal manifold.\n']","[('flow manifolds', 0.5829977989196777), ('asymptotically flat manifold', 0.5726295709609985), ('asymptotically flat manifolds', 0.5652822852134705), ('yamabe flow', 0.5520456433296204), ('flow asymptotically', 0.5337123274803162), ('yamabe metrics', 0.5205048322677612), ('flow singular', 0.49874386191368103), ('complete riemannian manifold', 0.4650368392467499), ('yamabe invariant', 0.45343056321144104), ('riemannian manifold', 0.4429986774921417)]"
1616,1616,18,1616_bose einstein condensates_ground states exist_bose einstein condensate_dimensional bose,"['bose einstein condensates', 'ground states exist', 'bose einstein condensate', 'dimensional bose', 'bose gases', 'einstein condensates', 'instability properties', 'ground states two', 'stability instability properties', 'states rotating']","['The Nonexistence of Vortices for Rotating Bose-Einstein Condensates with\n  Attractive Interactions   This article is devoted to studying the model of two-dimensional attractive\nBose-Einstein condensates in a trap $V(x)$ rotating at the velocity $\\Omega $.\nThis model can be described by the complex-valued Gross-Pitaevskii energy\nfunctional. It is shown that there exists a critical rotational velocity\n$0<\\Omega^*:=\\Omega^*(V)\\leq \\infty$, depending on the general trap $V(x)$,\nsuch that for any rotational velocity $0\\leq \\Omega <\\Omega ^*$, minimizers\n(i.e., ground states) exist if and only if $a<a^*=\\|w\\|^2_2$, where $a>0$\ndenotes the absolute product for the number of particles times the scattering\nlength, and $w>0$ is the unique positive solution of $\\Delta w-w+w^3=0$ in\n$\\mathbb{R}^2$. If $V(x)=|x|^2$ and $ 0<\\Omega <\\Omega^*(=2)$ is fixed, we\nprove that, up to a constant phase, all minimizers must be real-valued, unique\nand free of vortices as $a \\nearrow a^*$, by analyzing the refined limit\nbehavior of minimizers and employing the non-degenerancy of $w$.\n', 'Local Uniqueness of Ground States for Rotating Bose-Einstein Condensates\n  with Attractive Interactions   We study ground states of two-dimensional Bose-Einstein condensates with\nattractive interactions in a trap $V(x)$ rotating at the velocity $\\Omega $. It\nis known that there exist a critical rotational velocity $0<\\Omega\n^*:=\\Omega^*(V)\\leq \\infty$ and a critical number $0<a^*<\\infty$ such that for\nany rotational velocity $0\\le \\Omega <\\Omega ^*$, ground states exist if and\nonly if the coupling constant $a$ satisfies $a<a^*$. For a general class of\ntraps $V(x)$, which may not be symmetric, we prove in this paper that up to a\nconstant phase, there exists a unique ground state as $a\\nearrow a^*$, where\n$\\Omega\\in(0,\\Omega^*)$ is fixed. This result extends essentially our recent\nuniqueness result, where only the radially symmetric traps $V(x)$ could be\nhandled with.\n', 'Existence and Asymptotic Behavior of Ground States for Rotating\n  Bose-Einstein Condensates   We study ground states of two-dimensional Bose-Einstein condensates with\nrepulsive ($a>0$) or attractive ($a<0$) interactions in a trap $V (x)$ rotating\nat the velocity $\\Omega $. It is known that there exist critical parameters\n$a^*>0$ and $\\Omega ^*:=\\Omega^*(V(x))>0$ such that if $\\Omega>\\Omega^*$, then\nthere is no ground state for any $a\\in\\R$; if $0\\le \\Omega <\\Omega ^*$, then\nground states exist if and only if $a\\in(-a^*,+\\infty)$. As a completion of the\nexisting results, in this paper, we focus on the critical case where\n$0<\\Omega=\\Omega^*<+\\infty$ and classify the existence and nonexistence of\nground states for $a\\in\\R$. Moreover, for a suitable class of radially\nsymmetric traps $V(x)$, employing the inductive symmetry method, we prove that\nup to a constant phase, the ground states must be real-valued, unique and free\nof vortices as $\\Omega \\searrow 0$, no matter whether the interactions of the\ncondensates are repulsive or not.\n']","[('bose einstein condensates', 0.4789269268512726), ('ground states exist', 0.46212056279182434), ('bose einstein condensate', 0.4437791407108307), ('dimensional bose', 0.40661370754241943), ('bose gases', 0.37621986865997314), ('einstein condensates', 0.3730272650718689), ('instability properties', 0.3689674437046051), ('ground states two', 0.35075104236602783), ('stability instability properties', 0.34861379861831665), ('states rotating', 0.34438058733940125)]"
1617,1617,18,1617_graph admits_biregular graphs_every graph_almost every graph,"['graph admits', 'biregular graphs', 'every graph', 'almost every graph', 'every connected graph', 'labelings graphs', 'graph bijection', 'labeling graph', 'connected graph', 'graph edges']","['Every connected graph admits a local antimagic orientation and almost\n  every graph admits an antimagic orientation   An undirected graph $G$ is said to admit an antimagic orientation if there\nexist an orientation $D$ and a bijection between $E(G)$ and\n$\\{1,2,\\ldots,|E(G)|\\}$ such that any two vertices have distinct vertex sums,\nwhere the vertex sum of a vertex is the sum of the labels of the in-edges minus\nthat of the out-edges incident to the vertex. It is conjectured by Hefetz,\nM\\""{u}tze, and Schwartz that every connected graph admits an antimagic\norientation. A weak version of this problem is to require the distinct vertex\nsums only for the adjacent vertices. In that case, we say the graph admits a\nlocal antimagic orientation. Chang, Jing, and Wang~\\cite{CJW20} conjectured\nthat every connected graph admits a local antimagic orientation. In this paper,\nwe give an affirmative answer to the conjecture of Chang et al., and show that\nalmost every graph satisfies the conjecture of Hefetz et al.\n', 'Caterpillars are Antimagic   An antimagic labeling of a graph $G$ is an injection from $E(G)$ to\n$\\{1,2,\\dots,|E(G)|\\}$ such that all vertex sums are pairwise distinct, where\nthe vertex sum at vertex $u$ is the sum of the labels assigned to edges\nincident to $u$. A graph is called antimagic when it has an antimagic labeling.\nHartsfield and Ringel conjectured that every simple connected graph other than\n$K_2$ is antimagic and the conjecture remains open even for trees. Here we\nprove that caterpillars are antimagic by means of an $O(n \\log n)$ algorithm.\n', 'Antimagic Orientation of Forests   An antimagic labeling of a digraph $D$ with $n$ vertices and $m$ arcs is a\nbijection from the set of arcs of $D$ to $\\{1,2,\\cdots,m\\}$ such that all $n$\noriented vertex-sums are pairwise distinct, where the oriented vertex-sum of a\nvertex is the sum of labels of all arcs entering that vertex minus the sum of\nlabels of all arcs leaving it. A graph $G$ admits an antimagic orientation if\n$G$ has an orientation $D$ such that $D$ has an antimagic labeling. Hefetz,\nM{\\""{u}}tze and Schwartz conjectured every connected graph admits an antimagic\norientation. In this paper, we support this conjecture by proving that any\nforest obtained from a given forest with at most one isolated vertex by\nsubdividing each edge at least once admits an antimagic orientation.\n']","[('graph admits', 0.5506689548492432), ('biregular graphs', 0.5286457538604736), ('every graph', 0.5282544493675232), ('almost every graph', 0.5146164298057556), ('every connected graph', 0.5109925270080566), ('labelings graphs', 0.4975859522819519), ('graph bijection', 0.47617819905281067), ('labeling graph', 0.4291122257709503), ('connected graph', 0.4200558066368103), ('graph edges', 0.4192729890346527)]"
1618,1618,18,1618_stochastic dynamics_dynamics deterministic_stochastic agent_time propagation chaos,"['stochastic dynamics', 'dynamics deterministic', 'stochastic agent', 'time propagation chaos', 'propagation chaos', 'classical boltzmann', 'stochastic agent based', 'martingale convergence', 'equilibrium distribution', 'chaos']","['Uniform propagation of chaos for a dollar exchange econophysics model   We study the poor-biased model for money exchange introduced in [2]: agents\nare being randomly picked at a rate proportional to their current wealth, and\nthen the selected agent gives a dollar to another agent picked uniformly at\nrandom. Simulations of a stochastic system of finitely many agents as well as a\nrigorous analysis carried out in [2,16] suggest that, when both the number of\nagents and time become large enough, the distribution of money among the agents\nconverges to a Poisson distribution. In this manuscript, we establish a\nuniform-in-time propagation of chaos result as the number of agents goes to\ninfinity, which justifies the validity of the mean-field deterministic infinite\nsystem of ordinary differential equations as an approximation of the underlying\nstochastic agent-based dynamics.\n', 'Explicit decay rate for the Gini index in the repeated averaging model   We investigate the repeated averaging model for money exchanges: two agents\npicked uniformly at random share half of their wealth to each other. It is\nintuitively convincing that a Dirac distribution of wealth (centered at the\ninitial average wealth) will be the long time equilibrium for this dynamics. In\nother words, the Gini index should converge to zero. To better understand this\ndynamics, we investigate its limit as the number of agents goes to infinity by\nproving the so-called propagation of chaos, which links the stochastic\nagent-based dynamics to a (limiting) nonlinear partial differential equation\n(PDE). This deterministic description has a flavor of the classical Boltzmann\nequation arising from statistical mechanics of dilute gases. We prove its\nconvergence toward its Dirac equilibrium distribution by showing that the\nassociated Gini index of the wealth distribution converges to zero with an\nexplicit rate.\n', 'Uncovering a two-phase dynamics from a dollar exchange model with bank\n  and debt   We investigate the unbiased model for money exchanges with collective debt\nlimit: agents give at random time a dollar to one another as long as they have\nat least one dollar or they can borrow a dollar from a central bank if the bank\nis not empty. Surprisingly, this dynamics eventually leads to an asymmetric\nLaplace distribution of wealth (conjectured in [22] and shown formally in a\nrecent work [18]). In this manuscript, we carry out a formal mean-field limit\nas the number of agents goes to infinity where we uncover a two-phase (ODE)\ndynamics. Convergence towards the unique equilibrium (two-sided geometric)\ndistribution in the large time limit is also shown and the role played by the\nbank and debt (in terms of Gini index or wealth inequality) will be explored\nnumerically as well.\n']","[('stochastic dynamics', 0.47925713658332825), ('dynamics deterministic', 0.4519597589969635), ('stochastic agent', 0.45144060254096985), ('time propagation chaos', 0.40837037563323975), ('propagation chaos', 0.40131866931915283), ('classical boltzmann', 0.3959881067276001), ('stochastic agent based', 0.38454243540763855), ('martingale convergence', 0.36377254128456116), ('equilibrium distribution', 0.363282710313797), ('chaos', 0.35591262578964233)]"
1619,1619,18,1619_algebraic curves_two galois_galois groups_rational curves,"['algebraic curves', 'two galois', 'galois groups', 'rational curves', 'galois group', 'algebraic curve', 'whose galois group', 'galois', 'exist galois', 'galois extension']","['Plane curves possessing two outer Galois points   We classify plane curves $\\mathcal{C}$ possessing two Galois points $P_1$ and\n$P_2 \\in \\mathbb{P}^2 \\setminus \\mathcal{C}$ such that the associated Galois\ngroups $G_{P_1}$ and $G_{P_2}$ generate the semidirect product $G_{P_1}\\rtimes\nG_{P_2}$. New examples of plane curves with two Galois points are also\npresented.\n', 'Algebraic curves with collinear Galois points   A criterion for the existence of a birational embedding into a projective\nplane with three collinear Galois points for algebraic curves is presented. The\nextendability of an automorphism induced by a Galois point to a linear\ntransformation of the projective plane is also discussed, under the assumption\nthat two Galois points exist.\n', 'A birational embedding with two Galois points for quotient curves   A criterion for the existence of a birational embedding with two Galois\npoints for quotient curves is presented. We apply our criterion to several\ncurves, for example, some cyclic subcovers of the Giulietti-Korchmaros curve or\nof the curves constructed by Skabelund. They are new examples of plane curves\nwith two Galois points.\n']","[('algebraic curves', 0.6538633704185486), ('two galois', 0.6169561743736267), ('galois groups', 0.5925667881965637), ('rational curves', 0.5881099104881287), ('galois group', 0.5639814138412476), ('algebraic curve', 0.5572715997695923), ('whose galois group', 0.551843523979187), ('galois', 0.5440922379493713), ('exist galois', 0.5419241189956665), ('galois extension', 0.535335898399353)]"
1620,1620,18,1620_spectral measures_spectral measure_measures spectral_mathcal spectral,"['spectral measures', 'spectral measure', 'measures spectral', 'mathcal spectral', 'spectrality', 'affine measures', 'spectral', 'self affine measures', 'classification spectral', 'affine measure']","['The spectrality of self-affine measure under the similarity\n  transformation of $GL_n(p)$   Let $\\mu_{M,D}$ be the self-affine measure generated by an expanding integer\nmatrix $M\\in M_n(\\mathbb{Z})$ and a finite digit set $D\\subset\\mathbb{Z}^n$. It\nis well known that the two measures $\\mu_{M,D}$ and $\\mu_{\\tilde{M},\\tilde{D}}$\nhave the same spectrality if $\\tilde{M}=B^{-1}MB$ and $\\tilde{D}=B^{-1}D$,\nwhere $B\\in M_n(\\mathbb{R})$ is a nonsingular matrix. This fact is usually used\nto simplify the digit set $D$ or the expanding matrix $M$. However, it often\ntransforms integer digit set $D$ or expanding matrix $M$ into real, which\nbrings many difficulties to study the spectrality of\n$\\mu_{\\tilde{M},\\tilde{D}}$. In this paper, we introduce a similarity\ntransformation of general linear group $GL_n(p)$ for some self-affine measures,\nand discuss their spectrality. This kind of similarity transformation can keep\nthe integer properties of $D$ and $M$ simultaneously, which leads to many\nadvantages in discussing the spectrality of self-affine measures. As an\napplication, we extend some well-known spectral self-affine measures to more\ngeneral forms.\n', 'Fourier bases of a class of planar self-affine measures   Let $\\mu_{M,D}$ be the planar self-affine measure generated by an expansive\ninteger matrix $M\\in M_2(\\mathbb{Z})$ and a non-collinear integer digit set\n$D=\\left\\{\\begin{pmatrix} 0\\\\0\\end{pmatrix},\\begin{pmatrix} \\alpha_{1}\\\\\n\\alpha_{2} \\end{pmatrix}, \\begin{pmatrix} \\beta_{1}\\\\ \\beta_{2} \\end{pmatrix},\n\\begin{pmatrix} -\\alpha_{1}-\\beta_{1}\\\\ -\\alpha_{2}-\\beta_{2}\n\\end{pmatrix}\\right\\}$. In this paper, we show that $\\mu_{M,D}$ is a spectral\nmeasure if and only if there exists a matrix $Q\\in M_2(\\mathbb{R})$ such that\n$(\\tilde{M},\\tilde{D})$ is admissible, where $\\tilde{M}=QMQ^{-1}$ and\n$\\tilde{D}=QD$. In particular, when $\\alpha_1\\beta_2-\\alpha_2\\beta_1\\notin\n2\\Bbb Z$, $\\mu_{M,D}$ is a spectral measure if and only if $M\\in\nM_2(2\\mathbb{Z})$.\n', 'Spectrality of a class of moran measures on $\\mathbb{R}^2$   Let $\\mu_{\\{M_n\\},\\{D_n\\}}$ be a Moran measure on $\\mathbb{R}^2$ generated by\na sequence of expanding matrices $\\{M_n\\}\\subset GL(2, \\mathbb{Z})$ and a\nsequence of integer digit sets $\\{D_n\\}$ where $D_n=\\left\\{\\begin{pmatrix} 0 \\\\\n0 \\end{pmatrix},\\begin{pmatrix} \\alpha_{n_1} \\\\ \\alpha_{n_2}\n\\end{pmatrix},\\begin{pmatrix} \\beta_{n_1} \\\\ \\beta_{n_2}\n\\end{pmatrix},\\begin{pmatrix} -\\alpha_{n_1}-\\beta_{n_1} \\\\\n-\\alpha_{n_2}-\\beta_{n_2} \\end{pmatrix} \\right\\}$ with\n$\\alpha_{n_1}\\beta_{n_2}-\\alpha_{n_2}\\beta_{n_1}\\notin2\\mathbb{Z}$. If\n$|\\det(M_n)|>4$ for $n\\geq1$, $\\sup\\limits_{n\\ge 1}\\Vert M_n^{-1}\\Vert<1$ and\n$\\#\\{D_n: n\\ge 1\\}<\\infty$, then we show that $\\mu_{\\{M_n\\},\\{D_n\\}}$ is a\nspectral measure if and only if $M_n\\in GL(2, 2\\mathbb{Z})$ for $n\\geq2$. If\n$|\\det(M_n)| =4$ for $n\\geq1$, we also establish a necessary and sufficient\ncondition for a class of special Moran measures to be spectral measures.\n']","[('spectral measures', 0.6223564743995667), ('spectral measure', 0.6102303266525269), ('measures spectral', 0.6100502610206604), ('mathcal spectral', 0.4898469150066376), ('spectrality', 0.46737608313560486), ('affine measures', 0.45871448516845703), ('spectral', 0.4546626806259155), ('self affine measures', 0.45003947615623474), ('classification spectral', 0.4210081696510315), ('affine measure', 0.413404256105423)]"
1621,1621,18,1621_interior point methods_convex quadratic programming_convex optimization_quadratic programming,"['interior point methods', 'convex quadratic programming', 'convex optimization', 'quadratic programming', 'composite optimization problems', 'definite optimization', 'semi definite optimization', 'linear optimization', 'quadratic programming problems', 'linear programming problems']","[""An infeasible interior-point arc-search method with Nesterov's\n  restarting strategy for linear programming problems   An arc-search interior-point method is a type of interior-point methods that\napproximates the central path by an ellipsoidal arc, and it can often reduce\nthe number of iterations. In this work, to further reduce the number of\niterations and computation time for solving linear programming problems, we\npropose two arc-search interior-point methods using Nesterov's restarting\nstrategy that is well-known method to accelerate the gradient method with a\nmomentum term. The first one generates a sequence of iterations in the\nneighborhood, and we prove that the convergence of the generated sequence to an\noptimal solution and the computation complexity is polynomial time. The second\none incorporates the concept of the Mehrotra-type interior-point method to\nimprove numerical performance. The numerical experiments demonstrate that the\nsecond one reduced the number of iterations and computational time. In\nparticular, the average number of iterations was reduced compared to existing\ninterior-point methods due to the momentum term.\n"", 'An Interior Point-Proximal Method of Multipliers for Positive\n  Semi-Definite Programming   In this paper we generalize the Interior Point-Proximal Method of Multipliers\n(IP-PMM) presented in [An Interior Point-Proximal Method of Multipliers for\nConvex Quadratic Programming, Computational Optimization and Applications, 78,\n307--351 (2021)] for the solution of linear positive Semi-Definite Programming\n(SDP) problems, allowing inexactness in the solution of the associated Newton\nsystems. In particular, we combine an infeasible Interior Point Method (IPM)\nwith the Proximal Method of Multipliers (PMM) and interpret the algorithm\n(IP-PMM) as a primal-dual regularized IPM, suitable for solving SDP problems.\nWe apply some iterations of an IPM to each sub-problem of the PMM until a\nsatisfactory solution is found. We then update the PMM parameters, form a new\nIPM neighbourhood, and repeat this process. Given this framework, we prove\npolynomial complexity of the algorithm, under mild assumptions, and without\nrequiring exact computations for the Newton directions. We furthermore provide\na necessary condition for lack of strong duality, which can be used as a basis\nfor constructing detection mechanisms for identifying pathological cases within\nIP-PMM.\n', 'An Interior Point-Proximal Method of Multipliers for Convex Quadratic\n  Programming   In this paper we combine an infeasible Interior Point Method (IPM) with the\nProximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is\ninterpreted as a primal-dual regularized IPM, suitable for solving linearly\nconstrained convex quadratic programming problems. We apply few iterations of\nthe interior point method to each sub-problem of the proximal method of\nmultipliers. Once a satisfactory solution of the PMM sub-problem is found, we\nupdate the PMM parameters, form a new IPM neighbourhood and repeat this\nprocess. Given this framework, we prove polynomial complexity of the algorithm,\nunder standard assumptions. To our knowledge, this is the first polynomial\ncomplexity result for a primal-dual regularized IPM. The algorithm is guided by\nthe use of a single penalty parameter; that of the logarithmic barrier. In\nother words, we show that IP-PMM inherits the polynomial complexity of IPMs, as\nwell as the strict convexity of the PMM sub-problems. The updates of the\npenalty parameter are controlled by IPM, and hence are well-tuned, and do not\ndepend on the problem solved. Furthermore, we study the behavior of the method\nwhen it is applied to an infeasible problem, and identify a necessary condition\nfor infeasibility. The latter is used to construct an infeasibility detection\nmechanism. Subsequently, we provide a robust implementation of the presented\nalgorithm and test it over a set of small to large scale linear and convex\nquadratic programming problems. The numerical results demonstrate the benefits\nof using regularization in IPMs as well as the reliability of the method.\n']","[('interior point methods', 0.5644954442977905), ('convex quadratic programming', 0.5304011702537537), ('convex optimization', 0.5287936925888062), ('quadratic programming', 0.5067355632781982), ('composite optimization problems', 0.49444618821144104), ('definite optimization', 0.48496538400650024), ('semi definite optimization', 0.48398491740226746), ('linear optimization', 0.4798612594604492), ('quadratic programming problems', 0.4676332473754883), ('linear programming problems', 0.44589075446128845)]"
1622,1622,18,1622_conic line arrangements_arrangements complex projective_arrangements projective_combinatorial algebraic geometry,"['conic line arrangements', 'arrangements complex projective', 'arrangements projective', 'combinatorial algebraic geometry', 'complex projective plane', 'associated conic', 'projective plane', 'singularities note', 'conics', 'line arrangements']","['Bounds for characteristic numbers of conic-line arrangements in the\n  plane   The main aim of the note is to provide an upper-bound for the characteristic\nnumber of conic-line arrangements with ordinary singularities in the complex\nprojective plane.\n', 'Weak Ziegler pairs of conic-line arrangements with ordinary\n  singularities   In the present note we focus on conic line arrangements in the plane with\nquasihomogeneous ordinary singularities from the perspective of weak Ziegler\npairs. The foundations of this article come from an active area of research\ndevoted to the freeness and nearly freeness of curve arrangements in the\ncomplex projective plane and the socalled Numerical Terao s Conjecture. This\nconjecture boils down to a very fundamental problem in combinatorial algebraic\ngeometry, namely whether the weak combinatorics of a given arrangement\ndetermines the freeness.\n', 'Conic-line arrangements in the complex projective plane   The main goal of this note is to begin a systematic study on conic-line\narrangements in the complex projective plane. We show a de\nBruijn-Erd\\H{o}s-type inequality and Hirzebruch-type inequality for a certain\nclass of conic-line arrangements having ordinary singularities. We will also\nstudy, in detail, certain conic-line arrangements in the context of the\ngeography of log-surfaces and free divisors in the sense of Saito.\n']","[('conic line arrangements', 0.6890292763710022), ('arrangements complex projective', 0.6761893033981323), ('arrangements projective', 0.5765098333358765), ('combinatorial algebraic geometry', 0.571312665939331), ('complex projective plane', 0.5252959132194519), ('associated conic', 0.4891572594642639), ('projective plane', 0.4874727129936218), ('singularities note', 0.48662838339805603), ('conics', 0.4859553277492523), ('line arrangements', 0.4805879592895508)]"
1623,1623,18,1623_6g technologies_6g network_technologies 6g_6g applications,"['6g technologies', '6g network', 'technologies 6g', '6g applications', '6g wireless systems', '6g wireless', '6g systems', 'towards 6g', 'generation 6g wireless', '6g']","['Perspectives on 6G Architectures   Mobile communications have been undergoing a generational change every ten\nyears. While 5G network deployments are maturing, significant efforts are being\nmade to standardize 6G, which is expected to be commercially introduced by\n2030. This paper provides unique perspectives on the 6G network (radio and\ncore) architecture(s) from the anticipated 6G use cases to meet the necessary\nperformance requirements. To cater for the key 6G use cases, the 6G\narchitecture must integrate different network-level functions in a multiplicity\nof virtual cloud environments, leveraging the advancements of distributed\nprocessing, artificial intelligence, and securely integrating different\nsub-networks e.g., terrestrial, and non-terrestrial networks into the overall\n6G network. This paper characterizes the impact of 6G architectures from a\ndeployment perspective with backwards compatibility in mind.\n', '6G: The Intelligent Network of Everything   The global 6G vision has taken its shape after years of international\nresearch and development efforts. This work culminated in ITU-R Recommendation\non ""IMT-2030 Framework"". While the definition phase of technological\nrequirements is currently ongoing, 3GPP standardization process on 6G networks\nis expected to start in 2025 and worldwide commercialization around 2029-2030.\nThis article serves as a comprehensive guide to 6G by providing an overall\nvision, a contemporary survey of the main literature, and an informative\ntutorial-type presentation style. In our vision, 6G will be based on three\nfundamental elements: wireless, artificial intelligence, and Internet of\nEverything. Consequently, 6G can ultimately become the Intelligent Network of\nEverything while serving as an enabling platform for the next major disruption\nin mobile communication, called mobile intelligence. The potential of mobile\nintelligence is that anything can be made connected, intelligent, and aware of\nits environment. This will revolutionize the way how devices, systems, and\napplications are designed; how they operate and interact with humans and each\nother; and how they can be used for the benefit of people, society, and the\nworld in general. After high-level visioning, the main details of 6G are\ndiscussed, including fundamental elements, disruptive applications, key use\ncases, main performance requirements, potential technologies, and defining\nfeatures. A special focus is given to a comprehensive set of potential 6G\ntechnologies, each of which is introduced in a tutorial manner. Finally, we\nspeculate on what comes after 6G and sketch the first high-level vision of 7G.\nAll in all, the objective of this article is to provide a thorough guide to 6G\nin order to serve as a source of knowledge and inspiration for further research\nand development work in academia, industry, and standardization bodies.\n', '6G Takes Shape   The contours of 6G -- its key technical components and driving requirements\n-- are finally coming into focus. Through twenty questions and answers, this\narticle defines the important aspects of 6G across four categories. First, we\nidentify the key themes and forces driving the development of 6G, and what will\nmake 6G unique. We argue that 6G requirements and system design will be driven\nby (i) the tenacious pursuit of spectral (bits/Hz/area), energy (bits/Joule),\nand cost (bits/dollar) efficiencies, and (ii) three new service enhancements:\nsensing/localization/awareness, compute, and global broadband/emergency\nconnectivity. Second, we overview the important role of spectrum in 6G, what\nnew spectrum to expect in 6G, and outline how the different bands will be used\nto provide 6G services. Third, we focus our attention on the 6G physical layer,\nincluding waveforms, MIMO advancements, and the potential use of deep learning.\nFinally, we explore how global connectivity will be achieved in 6G, through\nnon-terrestrial networks as well as low-cost network expansion via\ndisaggregation and O-RAN. Although 6G standardization activities will not begin\nuntil late 2025, meaning this article is by definition speculative, our\npredictions are informed by several years of intensive research and\ndiscussions. Our goal is to provide a grounded perspective that will be helpful\nto both researchers and engineers as we move into the 6G era.\n']","[('6g technologies', 0.8034356236457825), ('6g network', 0.7993571162223816), ('technologies 6g', 0.7955998182296753), ('6g applications', 0.7902648448944092), ('6g wireless systems', 0.7843310832977295), ('6g wireless', 0.7670663595199585), ('6g systems', 0.7658146023750305), ('towards 6g', 0.7599874138832092), ('generation 6g wireless', 0.7310277223587036), ('6g', 0.6967345476150513)]"
1624,1624,18,1624_random interlacements_random walks_random walk critical_dynamical percolation,"['random interlacements', 'random walks', 'random walk critical', 'dynamical percolation', 'passage percolation', 'random walk', 'biased random walk', 'one dimensional random', 'random walk random', 'simple random walk']","['Finite range interlacements and couplings   In this article, we consider the interlacement set $\\mathcal{I}^u$ at level\n$u>0$ on $\\mathbb{Z}^d$, $d \\geq3$, and its finite range version\n$\\mathcal{I}^{u,L}$ for $L >0$, given by the union of the ranges of a Poisson\ncloud of random walks on $\\mathbb{Z}^d$ having intensity $u/L$ and killed after\n$L$ steps. As $L\\to \\infty$, the random set $\\mathcal{I}^{u,L}$ has a\nnon-trivial (local) limit, which is precisely $\\mathcal{I}^u$. A natural\nquestion is to understand how the sets $\\mathcal{I}^{u,L}$ and\n$\\mathcal{I}^{{u}}$ can be related, if at all, in such a way that their\nintersections with a box of large radius $R$ almost coincide. We address this\nquestion, which depends sensitively on $R$, by developing couplings allowing\nfor a similar comparison to hold with very high probability for\n$\\mathcal{I}^{u,L}$ and $\\mathcal{I}^{{u\'},2L}$, with $u\' \\approx u$. In\nparticular, for the vacant set $\\mathcal{V}^u=\\mathbb{Z}^d \\setminus\n\\mathcal{I}^u$ with values of $u$ near the critical threshold, our couplings\nremain effective at scales $R \\gg \\sqrt{L}$, which corresponds to a natural\nbarrier across which the walks of length $L$ comprised in $\\mathcal{I}^{u,L}$\nde-solidify inside $B_R$, i.e. lose their intrinsic long-range structure to\nbecome increasingly ""dust-like"". These mechanisms are complementary to the\nsolidification effects recently exhibited in arXiv:1706.07229. By iterating the\nresulting couplings over dyadic scales $L$, the models $\\mathcal{I}^{u,L}$ are\nseen to constitute a stationary finite range approximation of $\\mathcal{I}^u$\nat large spatial scales near the critical point $u_*$. Among others, these\ncouplings are important ingredients for the characterization of the phase\ntransition for percolation of the vacant sets of random walk and random\ninterlacements in two upcoming companion articles.\n', 'Quenched large deviations for simple random walks on percolation models\n  including long-range correlations   We prove a {\\it{quenched}} large deviation principle (LDP) for a simple\nrandom walk on a supercritical percolation cluster (SRWPC) on $\\mathbb Z^d$\n($d\\geq 2$). The models under interest include classical Bernoulli bond and\nsite percolation as well as models that exhibit long range correlations, like\nthe random cluster model, the random interlacement and {the vacant set of\nrandom interlacements} (for $d\\geq 3$) and the level sets of the Gaussian free\nfield ($d\\geq 3$).\n  Inspired by the methods developed by Kosygina, Rezakhanlou and Varadhan\n([KRV06]) for proving quenched LDP for elliptic diffusions with a random drift,\nand by Yilmaz ([Y08]) and Rosenbluth ([R06]) for similar results regarding\nelliptic random walks in random environment, we take the point of view of the\nmoving particle and prove a large deviation principle for the quenched\ndistribution of the {\\it{pair empirical measures}} of the environment Markov\nchain in the non-elliptic case of SRWPC . Via a contraction principle, this\nreduces easily to a quenched LDP for the distribution of the mean velocity of\nthe random walk and both rate functions admit explicit variational formulas.\n  The main difficulty in our set up lies in the inherent non-ellipticity as\nwell as the lack of {\\it{translation-invariance}} stemming from conditioning on\nthe fact that the origin belongs to the infinite cluster. We develop a unifying\napproach for proving quenched large deviations for SRWPC based on exploiting\ncoercivity properties of the relative entropies in the context of convex\nvariational analysis, combined with input from ergodic theory and invoking\ngeometric properties of the supercritical percolation cluster.\n', 'Phase transition for the vacant set of random walk and random\n  interlacements   We consider the set of points visited by the random walk on the discrete\ntorus $(\\mathbb{Z}/N\\mathbb{Z})^d$, for $d \\geq 3$, at times of order $uN^d$,\nfor a parameter $u>0$ in the large-$N$ limit. We prove that the vacant set left\nby the walk undergoes a phase transition across a non-degenerate critical value\n$u_* = u_*(d)$, as follows. For all $u< u_*$, the vacant set contains a giant\nconnected component with high probability, which has a non-vanishing asymptotic\ndensity and satisfies a certain local uniqueness property. In stark contrast,\nfor all $u> u_*$ the vacant set scatters into tiny connected components. Our\nresults further imply that the threshold $u_*$ precisely equals the critical\nvalue, introduced by Sznitman in arXiv:0704.2560, which characterizes the\npercolation transition of the corresponding local limit, the vacant set of\nrandom interlacements on $\\mathbb{Z}^d$. Our findings also yield the analogous\ninfinite-volume result, i.e. the long purported equality of three critical\nparameters $\\bar u$, $u_*$ and $u_{**}$ naturally associated to the vacant set\nof random interlacements.\n']","[('random interlacements', 0.5907055139541626), ('random walks', 0.5728186964988708), ('random walk critical', 0.5332452058792114), ('dynamical percolation', 0.5269100666046143), ('passage percolation', 0.498991459608078), ('random walk', 0.4837948977947235), ('biased random walk', 0.4803965985774994), ('one dimensional random', 0.47971248626708984), ('random walk random', 0.47069603204727173), ('simple random walk', 0.4686974883079529)]"
1625,1625,18,1625_gaussian process priors_gaussian process regression_posterior contraction rates_process priors,"['gaussian process priors', 'gaussian process regression', 'posterior contraction rates', 'process priors', 'posterior contraction rate', 'gaussian processes', 'deep gaussian', 'posterior contraction', 'bayesian nonparametric', 'approximate posterior']","['Equivalence of Convergence Rates of Posterior Distributions and Bayes\n  Estimators for Functions and Nonparametric Functionals   We study the posterior contraction rates of a Bayesian method with Gaussian\nprocess priors in nonparametric regression and its plug-in property for\ndifferential operators. For a general class of kernels, we establish\nconvergence rates of the posterior measure of the regression function and its\nderivatives, which are both minimax optimal up to a logarithmic factor for\nfunctions in certain classes. Our calculation shows that the rate-optimal\nestimation of the regression function and its derivatives share the same choice\nof hyperparameter, indicating that the Bayes procedure remarkably adapts to the\norder of derivatives and enjoys a generalized plug-in property that extends\nreal-valued functionals to function-valued functionals. This leads to a\npractically simple method for estimating the regression function and its\nderivatives, whose finite sample performance is assessed using simulations.\n  Our proof shows that, under certain conditions, to any convergence rate of\nBayes estimators there corresponds the same convergence rate of the posterior\ndistributions (i.e., posterior contraction rate), and vice versa. This\nequivalence holds for a general class of Gaussian processes and covers the\nregression function and its derivative functionals, under both the $L_2$ and\n$L_{\\infty}$ norms. In addition to connecting these two fundamental large\nsample properties in Bayesian and non-Bayesian regimes, such equivalence\nenables a new routine to establish posterior contraction rates by calculating\nconvergence rates of nonparametric point estimators.\n  At the core of our argument is an operator-theoretic framework for kernel\nridge regression and equivalent kernel techniques. We derive a range of sharp\nnon-asymptotic bounds that are pivotal in establishing convergence rates of\nnonparametric point estimators and the equivalence theory, which may be of\nindependent interest.\n', 'On the inability of Gaussian process regression to optimally learn\n  compositional functions   We rigorously prove that deep Gaussian process priors can outperform Gaussian\nprocess priors if the target function has a compositional structure. To this\nend, we study information-theoretic lower bounds for posterior contraction\nrates for Gaussian process regression in a continuous regression model. We show\nthat if the true function is a generalized additive function, then the\nposterior based on any mean-zero Gaussian process can only recover the truth at\na rate that is strictly slower than the minimax rate by a factor that is\npolynomially suboptimal in the sample size $n$.\n', 'Posterior contraction for deep Gaussian process priors   We study posterior contraction rates for a class of deep Gaussian process\npriors applied to the nonparametric regression problem under a general\ncomposition assumption on the regression function. It is shown that the\ncontraction rates can achieve the minimax convergence rate (up to $\\log n$\nfactors), while being adaptive to the underlying structure and smoothness of\nthe target function. The proposed framework extends the Bayesian nonparametric\ntheory for Gaussian process priors.\n']","[('gaussian process priors', 0.680902361869812), ('gaussian process regression', 0.5776471495628357), ('posterior contraction rates', 0.568271279335022), ('process priors', 0.5397200584411621), ('posterior contraction rate', 0.5370562672615051), ('gaussian processes', 0.5322496294975281), ('deep gaussian', 0.528671145439148), ('posterior contraction', 0.5231916308403015), ('bayesian nonparametric', 0.5085722804069519), ('approximate posterior', 0.5061543583869934)]"
1626,1626,18,1626_trust region optimization_optimization trust_hessian approximations_hessian approximation,"['trust region optimization', 'optimization trust', 'hessian approximations', 'hessian approximation', 'nonsmooth optimization', 'trust region methods', 'nonconvex optimization', 'smooth optimization', 'approximate minimizers', 'nonconvex optimization problems']","['First- and Second-Order High Probability Complexity Bounds for\n  Trust-Region Methods with Noisy Oracles   In this paper, we present convergence guarantees for a modified trust-region\nmethod designed for minimizing objective functions whose value and gradient and\nHessian estimates are computed with noise. These estimates are produced by\ngeneric stochastic oracles, which are not assumed to be unbiased or consistent.\nWe introduce these oracles and show that they are more general and have more\nrelaxed assumptions than the stochastic oracles used in prior literature on\nstochastic trust-region methods. Our method utilizes a relaxed step acceptance\ncriterion and a cautious trust-region radius updating strategy which allows us\nto derive exponentially decaying tail bounds on the iteration complexity for\nconvergence to points that satisfy approximate first- and second-order\noptimality conditions. Finally, we present two sets of numerical results. We\nfirst explore the tightness of our theoretical results on an example with\nadversarial zeroth- and first-order oracles. We then investigate the\nperformance of the modified trust-region algorithm on standard noisy\nderivative-free optimization problems.\n', 'A Proximal Quasi-Newton Trust-Region Method for Nonsmooth Regularized\n  Optimization   We develop a trust-region method for minimizing the sum of a smooth term $f$\nand a nonsmooth term $h$), both of which can be nonconvex. Each iteration of\nour method minimizes a possibly nonconvex model of $f + h$ in a trust region.\nThe model coincides with $f + h$ in value and subdifferential at the center. We\nestablish global convergence to a first-order stationary point when $f$\nsatisfies a smoothness condition that holds, in particular, when it has\nLipschitz-continuous gradient, and $h$ is proper and lower semi-continuous. The\nmodel of $h$ is required to be proper, lower-semi-continuous and prox-bounded.\nUnder these weak assumptions, we establish a worst-case $O(1/\\epsilon^2)$\niteration complexity bound that matches the best known complexity bound of\nstandard trust-region methods for smooth optimization. We detail a special\ninstance, named TR-PG, in which we use a limited-memory quasi-Newton model of\n$f$ and compute a step with the proximal gradient method, resulting in a\npractical proximal quasi-Newton method. We establish similar convergence\nproperties and complexity bound for a quadratic regularization variant, named\nR2, and provide an interpretation as a proximal gradient method with adaptive\nstep size for nonconvex problems. R2 may also be used to compute steps inside\nthe trust-region method, resulting in an implementation named TR-R2. We\ndescribe our Julia implementations and report numerical results on inverse\nproblems from sparse optimization and signal processing. Both TR-PG and TR-R2\nexhibit promising performance and compare favorably with two linesearch\nproximal quasi-Newton methods based on convex models.\n', 'A consistently adaptive trust-region method   Adaptive trust-region methods attempt to maintain strong convergence\nguarantees without depending on conservative estimates of problem properties\nsuch as Lipschitz constants. However, on close inspection, one can show\nexisting adaptive trust-region methods have theoretical guarantees with\nseverely suboptimal dependence on problem properties such as the Lipschitz\nconstant of the Hessian. For example, TRACE developed by Curtis et al. obtains\na $O(\\Delta_f L^{3/2} \\epsilon^{-3/2}) + \\tilde{O}(1)$ iteration bound where\n$L$ is the Lipschitz constant of the Hessian. Compared with the optimal\n$O(\\Delta_f L^{1/2} \\epsilon^{-3/2})$ bound this is suboptimal with respect to\n$L$. We present the first adaptive trust-region method which circumvents this\nissue and requires at most $O( \\Delta_f L^{1/2} \\epsilon^{-3/2}) +\n\\tilde{O}(1)$ iterations to find an $\\epsilon$-approximate stationary point,\nmatching the optimal iteration bound up to an additive logarithmic term. Our\nmethod is a simple variant of a classic trust-region method and in our\nexperiments performs competitively with both ARC and a classical trust-region\nmethod.\n']","[('trust region optimization', 0.6061794757843018), ('optimization trust', 0.5765558481216431), ('hessian approximations', 0.5715683698654175), ('hessian approximation', 0.5517522096633911), ('nonsmooth optimization', 0.5278554558753967), ('trust region methods', 0.5183653235435486), ('nonconvex optimization', 0.49244460463523865), ('smooth optimization', 0.488903284072876), ('approximate minimizers', 0.4856272041797638), ('nonconvex optimization problems', 0.47288915514945984)]"
1627,1627,18,1627_communication localization_localization performance_localization accuracy_joint localization,"['communication localization', 'localization performance', 'localization accuracy', 'joint localization', 'intelligent surface ris', 'localization', 'wireless communication', 'reconfigurable intelligent surfaces', 'reconfigurable intelligent surface', 'intelligent surfaces riss']","['Reconfigurable Intelligent Surface Aided Integrated Communication and\n  Localization with a Single Access Point   Reconfigurable intelligent surfaces (RISs) not only assist communication but\nalso help the localization of user equipment (UE). This study focuses on the\nindoor localization of UE with a single access point (AP) aided by multiple\nRISs. First, we propose a two-stage channel estimation scheme where the phase\nshifts of RIS elements are tuned to obtain multiple channel soundings. In the\nfirst stage, the newtonized orthogonal matching pursuit algorithm extracts the\nparameters of multiple paths from the received signals. Then, the LOS path and\nRIS-reflected paths are identified. In the second stage, the estimated path\ngains of RIS-reflected paths with different phase shifts are utilized to\ndetermine the angle of arrival (AOA) at the RIS by obtaining the angular pseudo\nspectrum. Consequently, by taking the AP and RISs as reference points, the\nlinear least squares estimator can locate UE with the estimated AOAs.\nSimulation results show that the proposed algorithm can realize\ncentimeter-level localization accuracy in the discussed scenarios. Moreover,\nthe higher accuracy of pseudo spectrum, a larger number of channel soundings,\nand a larger number of reference points can realize higher localization\naccuracy of UE.\n', 'Reconfigurable Intelligent Surfaces for Localization: Position and\n  Orientation Error Bounds   Next-generation cellular networks will witness the creation of smart radio\nenvironments (SREs), where walls and objects can be coated with reconfigurable\nintelligent surfaces (RISs) to strengthen the communication and localization\ncoverage by controlling the reflected multipath. In fact, RISs have been\nrecently introduced not only to overcome communication blockages due to\nobstacles but also for high-precision localization of mobile users in GPS\ndenied environments, e.g., indoors. Towards this vision, this paper presents\nthe localization performance limits for communication scenarios where a single\nnext-generation NodeB base station (gNB), equipped with multiple-antennas,\ninfers the position and the orientation of the user equipment(UE) in a\nRIS-assisted SRE. We consider a signal model that is valid also for near-field\npropagation conditions, as the usually adopted far-field assumption does not\nalways hold, especially for large RISs. For the considered scenario, we derive\nthe Cramer-Rao lower bound (CRLB) for assessing the ultimate localization and\norientation performance of synchronous and asynchronous signaling schemes. In\naddition, we propose a closed-form RIS phase profile that well suits joint\ncommunication and localization. We perform extensive numerical results to\nassess the performance of our scheme for various localization scenarios and RIS\nphase design. Numerical results show that the proposed scheme can achieve\nremarkable performance, even in asynchronous signaling and that the proposed\nphase design approaches the numerical optimal phase design that minimizes the\nCRLB.\n', 'RIS-Aided Localization under Position and Orientation Offsets in the\n  Near and Far Field   This paper presents a rigorous Bayesian analysis of the information in the\nsignal (consisting of both the line-of-sight (LOS) path and reflections from\nmultiple reconfigurable intelligent surfaces (RISs)) that originate from a\nsingle base station (BS) and is received by a user equipment (UE). For a\ncomprehensive Bayesian analysis, both near and far field regimes are\nconsidered. The Bayesian analysis views both the location of the RISs and\nprevious information about the UE as {\\em a priori} information for UE\nlocalization. With outdated {\\em a priori} information, the position and\norientation offsets of the RISs become parameters that need to be estimated and\nfed back to the BS for correction. We first show that when the RIS elements\nhave a half wavelength spacing, this RIS orientation offset is a factor in the\npathloss of the RIS paths. Subsequently, we show through the Bayesian\nequivalent Fisher information matrix (EFIM) for the channel parameters that the\nRIS orientation offset cannot be corrected when there is an unknown phase\noffset in the received signal in the far-field regime. However, the\ncorresponding EFIM for the channel parameters in the received signal observed\nin the near-field shows that this unknown phase offset does not hinder the\nestimation of the RIS orientation offset when the UE has more than one receive\nantenna. Furthermore, we use the EFIM for the UE location parameters to present\nbounds for UE localization in the presence of RIS uncertainty.\n']","[('communication localization', 0.5397770404815674), ('localization performance', 0.5315364003181458), ('localization accuracy', 0.5088731050491333), ('joint localization', 0.47069811820983887), ('intelligent surface ris', 0.4132052958011627), ('localization', 0.3957829773426056), ('wireless communication', 0.3930983543395996), ('reconfigurable intelligent surfaces', 0.3744475841522217), ('reconfigurable intelligent surface', 0.3711811602115631), ('intelligent surfaces riss', 0.3450743854045868)]"
1628,1628,18,1628_transitive subshifts_subshifts satisfying_complexity measure_unique ergodicity,"['transitive subshifts', 'subshifts satisfying', 'complexity measure', 'unique ergodicity', 'measure theoretic dynamical', 'free subshifts', 'structure low complexity', 'low complexity', 'complexity grows', 'sets complexity']","[""The Jacobs--Keane theorem from the $\\cS$-adic viewpoint   In the light of recent developments of the ${\\mathcal S}$-adic study of\nsubshifts, we revisit, within this framework, a well-known result on Toeplitz\nsubshifts due to Jacobs--Keane giving a sufficient combinatorial condition to\nensure discrete spectrum.We show that the notion of coincidences, originally\nintroduced in the '$70$s for the study of the discrete spectrum of substitution\nsubshifts, together with the ${\\mathcal S}$-adic structure of the subshift\nallow to go deeper in the study of Toeplitz subshifts. We characterize spectral\nproperties of the factor maps onto the maximal equicontinuous topological\nfactors by means of coincidences density.We also provide an easy to check\nnecessary and sufficient condition to ensure unique ergodicity for constant\nlength ${\\mathcal S}$-adic subshifts.\n"", 'Dynamics of $\\mathscr{B}$-free systems generated by Behrend sets. I   We study the complexity of $\\mathscr{B}$-free subshifts which are proximal\nand of zero entropy. Such subshifts are generated by Behrend sets. The\ncomplexity is shown to achieve any subexponential growth and is estimated for\nsome classical subshifts (prime and semiprime subshifts). We also show that\n$\\mathscr{B}$-admissible subshifts are transitive only for coprime sets\n$\\mathscr{B}$ which allows one to characterize dynamically the subshifts\ngenerated by the Erd\\""os sets.\n', ""On minimal subshifts of linear word complexity with slope less than 3/2   We prove that every infinite minimal subshift with word complexity $p(q)$\nsatisfying $\\limsup p(q)/q < 3/2$ is measure-theoretically isomorphic to its\nmaximal equicontinuous factor; in particular, it has measurably discrete\nspectrum. Among other applications, this provides a proof of Sarnak's\nconjecture for all subshifts with $\\limsup p(q)/q < 3/2$ (which can be thought\nof as a much stronger version of zero entropy).\n  As in \\cite{creutzpavlov}, our main technique is proving that all\nlow-complexity minimal subshifts have a specific type of representation via a\nsequence $\\{\\tau_k\\}$ of substitutions, usually called an S-adic decomposition.\nThe maximal equicontinuous factor is the product of an odometer with a rotation\non a compact abelian connected one-dimensional group, for which we can give an\nexplicit description in terms of the substitutions $\\tau_k$. We also prove that\nall such odometers and groups may appear for minimal subshifts with $\\limsup\np(q)/q = 1$, demonstrating that lower complexity thresholds do not further\nrestrict the possible structure.\n""]","[('transitive subshifts', 0.4904375672340393), ('subshifts satisfying', 0.4535943567752838), ('complexity measure', 0.45068296790122986), ('unique ergodicity', 0.44759663939476013), ('measure theoretic dynamical', 0.44552212953567505), ('free subshifts', 0.43611839413642883), ('structure low complexity', 0.4015343487262726), ('low complexity', 0.39683985710144043), ('complexity grows', 0.3833436667919159), ('sets complexity', 0.3784772753715515)]"
1629,1629,18,1629_dynamic traffic_flows time_network congestion_queueing networks,"['dynamic traffic', 'flows time', 'network congestion', 'queueing networks', 'congestion games', 'flow time', 'dynamic flow', 'time flow', 'flow networks', 'congestion']","['Dynamic Flows with Adaptive Route Choice   We study dynamic network flows and introduce a notion of instantaneous\ndynamic equilibrium (IDE) requiring that for any positive inflow into an edge,\nthis edge must lie on a currently shortest path towards the respective sink. We\nmeasure current shortest path length by current waiting times in queues plus\nphysical travel times. As our main results, we show: 1. existence and\nconstructive computation of IDE flows for single-source single-sink networks\nassuming constant network inflow rates, 2. finite termination of IDE flows for\nmulti-source single-sink networks assuming bounded and finitely lasting inflow\nrates, 3. the existence of IDE flows for multi-source multi-sink instances\nassuming general measurable network inflow rates, 4. the existence of a complex\nsingle-source multi-sink instance in which any IDE flow is caught in cycles and\nflow remains forever in the network.\n', ""Multi-Source Multi-Sink Nash Flows Over Time   Nash flows over time describe the behavior of selfish users eager to reach\ntheir destination as early as possible while traveling along the arcs of a\nnetwork with capacities and transit times. Throughout the past decade, they\nhave been thoroughly studied in single-source single-sink networks for the\ndeterministic queuing model, which is of particular relevance and frequently\nused in the context of traffic and transport networks. In this setting there\nexist Nash flows over time that can be described by a sequence of static flows\nfeaturing special properties, so-called `thin flows with resetting'. This\ninsight can also be used algorithmically to compute Nash flows over time. We\npresent an extension of these result to networks with multiple sources and\nsinks which are much more relevant in practical applications. In particular, we\ncome up with a subtle generalization of thin flows with resetting which yields\na compact description as well as an algorithmic approach for computing\nmulti-terminal Nash flows over time.\n"", 'Dynamic Equilibria in Time-Varying Networks   Predicting selfish behavior in public environments by considering Nash\nequilibria is a central concept of game theory. For the dynamic traffic\nassignment problem modeled by a flow over time game, in which every particle\ntries to reach its destination as fast as possible, the dynamic equilibria are\ncalled Nash flows over time. So far, this model has only been considered for\nnetworks in which each arc is equipped with a constant capacity, limiting the\noutflow rate, and with a transit time, determining the time it takes for a\nparticle to traverse the arc. However, real-world traffic networks can be\naffected by temporal changes, for example, caused by construction works or\nspecial speed zones during some time period. To model these traffic scenarios\nappropriately, we extend the flow over time model by time-dependent capacities\nand time-dependent transit times. Our first main result is the characterization\nof the structure of Nash flows over time. Similar to the static-network model,\nthe strategies of the particles in dynamic equilibria can be characterized by\nspecific static flows, called thin flows with resetting. The second main result\nis the existence of Nash flows over time, which we show in a constructive\nmanner by extending a flow over time step by step by these thin flows.\n']","[('dynamic traffic', 0.5642625093460083), ('flows time', 0.5632086992263794), ('network congestion', 0.5494306683540344), ('queueing networks', 0.5344521999359131), ('congestion games', 0.522297739982605), ('flow time', 0.5194514393806458), ('dynamic flow', 0.5174951553344727), ('time flow', 0.5112007856369019), ('flow networks', 0.5049401521682739), ('congestion', 0.5048421025276184)]"
1630,1630,18,1630_quantum games_quantum advantage_optimal quantum_classical game,"['quantum games', 'quantum advantage', 'optimal quantum', 'classical game', 'game theory', 'quantum resource', 'cooperative games', 'quantum', 'qubit quantum', 'game theoretic']","[""Optimal, and approximately optimal, quantum strategies for\n  $\\mathrm{XOR}^{*}$ and $\\mathrm{FFL}$ games   We analyze optimal, and approximately optimal, quantum strategies for a\nvariety of non-local XOR games. Building upon previous arguments due to Ostrev\nin 2016, which characterized approximately optimal, and optimal, strategies\nthat players Alice and Bob can adopt for maximizing a linear functional to win\nnon-local games after a Referee party examines each answer to a question drawn\nfrom some probability distribution, we identify additional applications of the\nframework for analyzing the performance of a broader class of quantum\nstrategies in which it is possible for Alice and Bob to realize quantum\nadvantage if the two players adopt strategies relying upon quantum\nentanglement, two-dimensional resource systems, and reversible transformations.\nFor the Fortnow-Feige-Lovasz (FFL) game, the 2016 framework is directly\napplicable, which consists of five steps, including: (1) constructing a\nsuitable, nonzero, linear transformation for the intertwining operations, (2)\ndemonstrating that the operator has unit Frobenius norm, (3) constructing error\nbounds, and corresponding approximate operations, for $\\big( A_k \\otimes\n\\textbf{I} \\big) \\ket{\\psi}$, and $\\big( \\textbf{I} \\otimes \\big( \\frac{\\pm\nB_{kl} + B_{lk}}{\\sqrt{2}} \\big) \\big) \\ket{\\psi}$, (4) constructing additional\nbounds for permuting the order in which $A^{j_i}_i$ operators are applied, (5)\nobtaining Frobenius norm upper bounds for Alice and Bob's strategies. We draw\nthe attention of the reader to applications of this framework in other games\nwith less regular structure.\n"", 'Quantum strategies, error bounds, optimality, and duality gaps for multiplayer XOR, $\\mathrm{XOR}^{*}$, compiled XOR, $\\mathrm{XOR}^{*}$, and strong parallel repetiton of XOR, $\\mathrm{XOR}^{*}$, and FFL games We characterize exact, and approximate, optimality of games that players can interact with using quantum strategies. In comparison to a previous work of the author, arXiv: 2311.12887, which applied a 2016 framework due to Ostrev for constructing error bounds beyond CHSH and XOR games, in addition to the existence of well-posed semidefinite programs for determining primal feasible solutions, along with quantum-classical duality gaps, it continues to remain of interest to further develop the construction of error bounds, and related objects, to game-theoretic settings with several participants. In such settings, one encounters a rich information theoretic landscape, not only from the fact that there exists a significantly larger combinatorial space of possible strategies for each player, but also several opportunities for pronounced quantum advantage. We conclude this effort by describing other variants of other possible strategies, as proposed sources for quantum advantage, in $\\mathrm{XOR}^{*}$, compiled $\\mathrm{XOR}^{*}$, and strong parallel repetition variants of $\\mathrm{XOR}^{*}$ games.', 'Four-Qubit CHSH Games   In this paper, the CHSH quantum game is extended to four players. This is\nachieved by exploring all possible 4-variable Boolean functions to identify\nthose that yield a game scenario with a quantum advantage using a specific\nentangled state. Notably, two new four-player quantum games are presented. In\none game, the optimal quantum strategy is achieved when players share a\n$GHZ$-state, breaking the traditional 10\\% gain observed in 2 and 3 qubit CHSH\ngames and achieving a 22.5\\% gap. In the other game, players gain a greater\nadvantage using a $W$-state as their quantum resource. Quantum games with other\nfour-qubit entangled states are also explored. To demonstrate the results,\nthese game scenarios are implemented on an online quantum computer, and the\nadvantage of the respective quantum resource for each game is experimentally\nverified.\n']","[('quantum games', 0.7952113747596741), ('quantum advantage', 0.6393189430236816), ('optimal quantum', 0.6119801998138428), ('classical game', 0.5579482316970825), ('game theory', 0.5390633344650269), ('quantum resource', 0.5176455974578857), ('cooperative games', 0.5017054677009583), ('quantum', 0.4863376021385193), ('qubit quantum', 0.4830789268016815), ('game theoretic', 0.482962042093277)]"
1631,1631,18,1631_free multiplicative convolution_free additive convolution_multiplicative convolution_convolutions measures,"['free multiplicative convolution', 'free additive convolution', 'multiplicative convolution', 'convolutions measures', 'convolution measure', 'convolution semigroups', 'free convolution', 'free convolutions', 'additive convolution', 'convolutions']","['Max-convolution semigroups and extreme values in limit theorems for the\n  free multiplicative convolution   We investigate relations between additive convolution semigroup and\nmax-convolution semigroup through the law of large numbers for the free\nmultiplicative convolution. Based on the relation, we give a formula related\nwith Belinschi-Nica semigroup and max-Belinschi-Nica semigroup. Finally, we\ngive several limit theorems for classical, free and Boolean extreme values.\n', 'Regularity for free multiplicative convolution on the unit circle   It is shown that the free multiplicative convolution of two nondegenerate\nprobability measures on the unit circle has no continuous singular part\nrelative to arclength measure. Analogous results have long been known for free\nadditive convolutions on the line and free multiplicative convolution on the\npositive half-line.\n', 'On the support of free convolutions   We extend to arbitrary measures results of Bao, Erd\\""os, Schnelli, Moreillon,\nand Ji on the connectedness of the supports of additive convolutions of\nmeasures on \\mathbb{R} and of free multiplicative convolutions of measures on\n\\mathbb{R}_+. More precisely, the convolution of two measures with connected\nsupports also has connected support. The result holds without any absolute\ncontinuity or bounded support hypotheses on the measures being convolved. We\nalso show that the results of Moreillon and Schnelli concerning the number of\ncomponents of the support of a free additive convolution hold for arbitrary\nmeasures with bounded supports. Finally, we provide an approach to the\ncorresponding results in the case of free multiplicative convolutions of\nprobability measures on the unit circle.\n']","[('free multiplicative convolution', 0.7151567935943604), ('free additive convolution', 0.6699192523956299), ('multiplicative convolution', 0.6467763185501099), ('convolutions measures', 0.6440292596817017), ('convolution measure', 0.6386756896972656), ('convolution semigroups', 0.6352803111076355), ('free convolution', 0.6317304372787476), ('free convolutions', 0.6260714530944824), ('additive convolution', 0.5897226929664612), ('convolutions', 0.5451292991638184)]"
1632,1632,18,1632_finite quivers_quivers type_acyclic quivers_quivers,"['finite quivers', 'quivers type', 'acyclic quivers', 'quivers', 'quiver', 'valued quiver', 'mutation invariant', 'mutation finite', 'mutation', 'mutations']","['New Hereditary and Mutation-Invariant Properties Arising from Forks   A hereditary property of quivers is a property preserved by restriction to\nany full subquiver. Similarly, a mutation-invariant property of quivers is a\nproperty preserved by mutation. Using forks, a class of quivers developed by M.\nWarkentin, we introduce a new hereditary and mutation-invariant property. We\nprove that a quiver being mutation-equivalent to a finite number of non-forks\n-- defined as having a finite forkless part -- is this new property, using only\nelementary methods. Additionally, we show that a more general property --\nhaving a finite pre-forkless part -- is also a new hereditary and\nmutation-invariant property in much the same manner.\n', 'Unrestricted Red Size and Sign-Coherence   The unrestricted red size of a quiver is the maximal number of red vertices\nin its framed quiver after any given mutation sequence. In a 2023 paper by E.\nBucher and J. Machacek, it was shown that connected, mutation-finite quivers\neither have an unrestricted red size of $n-1$ or $n$, where $n$ is the number\nof vertices in the quiver. We prove here that the same holds for the connected,\nmutation-infinite case using forks. As such, the unrestricted red size for any\nquiver equals $n-c$, where $c$ is the number of connected components of the\nquiver that do not admit a reddening sequence. Additionally, we prove a result\non the $c$-vectors of forks that allows us to show that the $c$-vectors of both\nabundant acyclic quivers on any number of vertices and mutation-cyclic quivers\non three vertices are sign-coherent with only elementary methods.\n', 'A topology on the poset of quiver mutation classes   To better understand mutation-invariant and hereditary properties of quivers\n(and more generally skew-symmetrizable matrices), we have constructed a\ntopology on the set of all mutation classes of quivers which we call the\nmutation class topology. This topology is the Alexandrov topology induced by\nthe poset structure on the set of mutation classes of quivers from the partial\norder of quiver embedding. The closed sets of our topology -- equivalently, the\nlower sets of the poset -- are in bijective correspondence with\nmutation-invariant and hereditary properties of quivers. We show that this\nspace is strictly $T_0$, connected, non-Noetherian, and that every open set is\ndense. We close by providing open questions from cluster algebra theory in the\nsetting of the mutation class topology and some directions for future research.\n']","[('finite quivers', 0.7271146774291992), ('quivers type', 0.6678182482719421), ('acyclic quivers', 0.6634328961372375), ('quivers', 0.6169602870941162), ('quiver', 0.606067955493927), ('valued quiver', 0.5901519656181335), ('mutation invariant', 0.579179048538208), ('mutation finite', 0.5086865425109863), ('mutation', 0.4173346161842346), ('mutations', 0.40530699491500854)]"
1633,1633,18,1633_kahler manifold_ahler manifolds_ahler manifold_complex manifold,"['kahler manifold', 'ahler manifolds', 'ahler manifold', 'complex manifold', 'ahler forms', 'ahler structures', 'ahler geometry', 'locally conformally ahler', 'structures symplectic', 'manifold invariant']","['Construction of special Lagrangian submanifolds of the Taub-NUT manifold\n  and the Atiyah-Hitchin manifold   We construct special Lagrangian submanifolds of the Taub-NUT manifold and the\nAtiyah-Hitchin manifold by combining the generalized Legendre transform\napproach and the moment map technique. The generalized Legendre transform\napproach provides a formulation to construct hyperk\\""ahler manifolds and can\nmake their Calabi-Yau structures manifest. In this approach, the K\\""ahler\n$2$-forms and the holomorphic volume forms can be written in terms of\nholomorphic coordinates, which are convenient to employ the moment map\ntechnique. This technique derives the condition that a submanifold in the\nCalabi-Yau manifold is special Lagrangian. For the Taub-NUT manifold and the\nAtiyah-Hitchin manifold, by the moment map technique, special Lagrangian\nsubmanifolds are obtained as a one-parameter family of the orbits corresponding\nto Hamiltonian action with respect to their K\\""ahler 2-forms. The resultant\nspecial Lagrangian submanifolds have cohomogeneity-one symmetry. To demonstrate\nthat our method is useful, we recover the conditions for the special Lagrangian\nsubmanifold of the Taub-NUT manifold which is invariant under the\ntri-holomorphic $U(1)$ symmetry. As new applications of our method, we\nconstruct special Lagrangian submanifolds of the Taub-NUT manifold and the\nAtiyah-Hitchin manifold which are invariant under the action of a Lie subgroup\nof $SO(3)$. In these constructions, our conditions for being special Lagrangian\nare expressed by ordinary differential equations (ODEs) with respect to the\none-parameters. We numerically give solution curves for the ODEs which specify\nthe special Lagrangian submanifolds for the above cases.\n', 'Matsushima-Lichnerowicz type theorems of Lie algebra of automorphisms of\n  generalized K\\""ahler manifolds of symplectic type   In K\\""ahler geometry, Fujiki--Donaldson show that the scalar curvature arises\nas the moment map for Hamiltonian diffeomorphisms. In generalized K\\""ahler\ngeometry, one does not have suitable notions of Levi-Civita connection and\ncurvature, however there still exists a precise framework for a moment map and\nthe scalar curvature is defined as the moment map. Then a fundamental question\nis to understand the existence or non-existence of generalized K\\""ahler\nstructures with constant scalar curvature. In the paper, we study the Lie\nalgebra of automorphisms of a generalized complex manifold. We assume that\n$H^{1}(M)=0$. Then we show that the Lie algebra of the automorphisms is a\nreductive Lie algebra if a generalized complex manifold admits a generalized\nK\\""ahler structure of symplectic type with constant scalar curvature. This is a\ngeneralization of Matsushima and Lichnerowicz theorem in K\\""ahler geometry. We\nexplicitly calculate the Lie algebra of the automorphisms of a generalized\ncomplex structure given by a cubic curve on $\\Bbb C P^2$. Cubic curves are\nclassified into nine cases (see Figure.$1 -- 9$). In the three cases as in\nFigures. 7, 8 and 9, the Lie algebra of the automorphisms is not reductive and\nthere is an obstruction to the existence of generalized K\\""ahler structures of\nsymplectic type with constant scalar curvature in the three cases. We also\ndiscuss deformations starting from an ordinary K\\""ahler manifold $(X,\\omega)$\nwith constant scalar curvature and show that nontrivial generalized K\\""ahler\nstructures of symplectic type with constant scalar curvature arise as\ndeformations if the Lie algebra of automorphisms of $X$ is trivial.\n', 'Scalar curvature and the moment map in generalized Kahler geometry   We introduce a notion of scalar curvature of a twisted generalized Kahler\nmanifold in terms of pure spinors formalism. A moment map framework with a\nmodified action of generalized Hamiltonians on an arbitrary compact generalized\nKahler manifold is developed. Then it turns out that a moment map is given by\nthe scalar curvature, which is a generalization of the result of the scalar\ncurvature as a moment map in the ordinary Kahler geometry, due to Fujiki and\nDonaldson.\n  A noncommutative compact Lie group $G$ does not have any Kahler structure.\nHowever, we show that every compact Lie group admits generalized Kahler\nstructures with constant scalar curvature. In particular, generalized Kahler\nstructures with constant scalar curvature on the standard Hopf surface are\nexplicitly given.\n']","[('kahler manifold', 0.6856569647789001), ('ahler manifolds', 0.6769678592681885), ('ahler manifold', 0.6464176774024963), ('complex manifold', 0.5578498840332031), ('ahler forms', 0.557272732257843), ('ahler structures', 0.5564124584197998), ('ahler geometry', 0.551562488079071), ('locally conformally ahler', 0.5035218000411987), ('structures symplectic', 0.49358072876930237), ('manifold invariant', 0.4815515875816345)]"
1634,1634,17,1634_neural network approximation_solving hamilton jacobi_dimensional stochastic control_optimal control problems,"['neural network approximation', 'solving hamilton jacobi', 'dimensional stochastic control', 'optimal control problems', 'optimal control', 'jacobi bellman equations', 'stochastic optimal control', 'dimensional hamilton jacobi', 'deep galerkin', 'hamilton jacobi theory']","['Deep neural network approximation for high-dimensional parabolic\n  Hamilton-Jacobi-Bellman equations   The approximation of solutions to second order Hamilton--Jacobi--Bellman\n(HJB) equations by deep neural networks is investigated. It is shown that for\nHJB equations that arise in the context of the optimal control of certain\nMarkov processes the solution can be approximated by deep neural networks\nwithout incurring the curse of dimension. The dynamics is assumed to depend\naffinely on the controls and the cost depends quadratically on the controls.\nThe admissible controls take values in a bounded set.\n', 'SOC-MartNet: A Martingale Neural Network for the Hamilton-Jacobi-Bellman\n  Equation without Explicit inf H in Stochastic Optimal Controls   In this paper, we propose a martingale-based neural network, SOC-MartNet, for\nsolving high-dimensional Hamilton-Jacobi-Bellman (HJB) equations where no\nexplicit expression is needed for the infimum of the Hamiltonian, $\\inf_{u \\in\nU} H(t,x,u, z,p)$, and stochastic optimal control problems (SOCPs) with\ncontrols on both drift and volatility. We reformulate the HJB equations for the\nvalue function by training two neural networks, one for the value function and\none for the optimal control with the help of two stochastic processes - a\nHamiltonian process and a cost process. The control and value networks are\ntrained such that the associated Hamiltonian process is minimized to satisfy\nthe minimum principle of a feedback SOCP, and the cost process becomes a\nmartingale, thus, ensuring the value function network as the solution to the\ncorresponding HJB equation. Moreover, to enforce the martingale property for\nthe cost process, we employ an adversarial network and construct a loss\nfunction characterizing the projection property of the conditional expectation\ncondition of the martingale. Numerical results show that the proposed\nSOC-MartNet is effective and efficient for solving HJB-type equations and SOCPs\nwith a dimension up to 10,000 in a small number of iteration steps (less than\n6000) of training.\n', ""Adaptive Deep Learning for High-Dimensional Hamilton-Jacobi-Bellman\n  Equations   Computing optimal feedback controls for nonlinear systems generally requires\nsolving Hamilton-Jacobi-Bellman (HJB) equations, which are notoriously\ndifficult when the state dimension is large. Existing strategies for\nhigh-dimensional problems often rely on specific, restrictive problem\nstructures, or are valid only locally around some nominal trajectory. In this\npaper, we propose a data-driven method to approximate semi-global solutions to\nHJB equations for general high-dimensional nonlinear systems and compute\ncandidate optimal feedback controls in real-time. To accomplish this, we model\nsolutions to HJB equations with neural networks (NNs) trained on data generated\nwithout discretizing the state space. Training is made more effective and\ndata-efficient by leveraging the known physics of the problem and using the\npartially-trained NN to aid in adaptive data generation. We demonstrate the\neffectiveness of our method by learning solutions to HJB equations\ncorresponding to the attitude control of a six-dimensional nonlinear rigid\nbody, and nonlinear systems of dimension up to 30 arising from the\nstabilization of a Burgers'-type partial differential equation. The trained NNs\nare then used for real-time feedback control of these systems.\n""]","[('neural network approximation', 0.5010032653808594), ('solving hamilton jacobi', 0.4949028789997101), ('dimensional stochastic control', 0.47656533122062683), ('optimal control problems', 0.47521865367889404), ('optimal control', 0.474826842546463), ('jacobi bellman equations', 0.4727517366409302), ('stochastic optimal control', 0.46908852458000183), ('dimensional hamilton jacobi', 0.46657848358154297), ('deep galerkin', 0.46244877576828003), ('hamilton jacobi theory', 0.46075505018234253)]"
1635,1635,17,1635_diffusion scaling_advection reaction diffusion_nonlinear drift diffusion_diffusion large,"['diffusion scaling', 'advection reaction diffusion', 'nonlinear drift diffusion', 'diffusion large', 'reaction diffusion convection', 'reaction diffusion', 'diffusion coupled', 'diffusion convection', 'diffusion', 'reaction diffusion processes']","['Scaling effects on the periodic homogenization of a\n  reaction-diffusion-convection problem posed in homogeneous domains connected\n  by a thin composite layer   We study the question of periodic homogenization of a variably scaled\nreaction-diffusion problem with non-linear drift posed for a domain crossed by\na flat composite thin layer. The structure of the non-linearity in the drift\nwas obtained in earlier works as hydrodynamic limit of a totally asymmetric\nsimple exclusion process (TASEP) process for a population of interacting\nparticles crossing a domain with obstacle.\n  Using energy-type estimates as well as concepts like thin-layer convergence\nand two-scale convergence, we derive the homogenized evolution equation and the\ncorresponding effective model parameters for a regularized problem. Special\nattention is paid to the derivation of the effective transmission conditions\nacross the separating limit interface in essentially two different situations:\n(i) finitely thin layer and (ii) infinitely thin layer.\n  This study should be seen as a preliminary step needed for the investigation\nof averaging fast non-linear drifts across material interfaces -- a topic with\ndirect applications in the design of thin composite materials meant to be\nimpenetrable to high-velocity impacts.\n', ""Rigorous derivation of an effective model for coupled Stokes advection,\n  reaction and diffusion with freely evolving microstructure   We consider the homogenisation of a coupled Stokes flow and\nadvection-reaction-diffusion problem in a perforated domain with an evolving\nmicrostructure of size $\\varepsilon$. Reactions at the boundaries of the\nmicroscopic interfaces lead to the formation of a solid layer having a\nvariable, a priori unknown thickness. This results in a growth or shrinkage of\nthe solid phase and, thus, the domain evolution is not known a priori but\ninduced by the advection-reaction-diffusion process. The achievements of this\nwork are the existence and uniqueness of a weak microscopic solution and the\nrigorous derivation of an effective model for $\\varepsilon \\to 0$, based on\n$\\varepsilon$-uniform a priori estimates. As a result of the limit passage, the\nprocesses on the macroscale are described by an advection-reaction-diffusion\nproblem coupled to Darcy's equation with effective coefficients (porosity,\ndiffusivity and permeability) depending on local cell problems. These local\nproblems are formulated on cells, which depend on the macroscopic position and\nevolve in time. In particular, the evolution of these cells depends on the\nmacroscopic concentration. Thus, the cell problems (respectively the effective\ncoefficients) are coupled to the macroscopic unknowns and vice versa, leading\nto a strongly coupled micro-macro model. For pure reactive-diffusive transport\ncoupled with microscopic domain evolution but without advective transport,\nhomogenisation results have recently been presented. We extend these models by\nadvective transport which is driven by the Stokes equation in the a priori\nunknown evolving pore domain.\n"", 'Homogenization of a reaction-diffusion problem with large nonlinear\n  drift and Robin boundary data   We study the periodic homogenization of a reaction-diffusion problem with\nlarge nonlinear drift and Robin boundary condition posed in an unbounded\nperforated domain. The nonlinear problem is associated with the hydrodynamic\nlimit of a totally asymmetric simple exclusion process (TASEP) governing a\npopulation of interacting particles crossing a domain with obstacle. We are\ninterested in deriving rigorously the upscaled model equations and the\ncorresponding effective coefficients for the case when the microscopic dynamics\nare linked to a particular choice of characteristic length and time scales that\nlead to an exploding nonlinear drift. The main mathematical difficulty lies in\nproving the two-scale compactness and strong convergence results needed for the\npassage to the homogenization limit. To cope with the situation, we use the\nconcept of two-scale compactness with drift, which is similar to the more\nclassical two-scale compactness result but it is defined now in moving\ncoordinates. We provide as well a strong convergence result for the corrector\nfunction, starting this way the search for the order of the convergence rate of\nthe homogenization process for our target nonlinear drift problem.\n']","[('diffusion scaling', 0.576266884803772), ('advection reaction diffusion', 0.5683452486991882), ('nonlinear drift diffusion', 0.558528482913971), ('diffusion large', 0.5467299818992615), ('reaction diffusion convection', 0.5313398838043213), ('reaction diffusion', 0.5116523504257202), ('diffusion coupled', 0.5022463202476501), ('diffusion convection', 0.4919120967388153), ('diffusion', 0.4834705889225006), ('reaction diffusion processes', 0.4791695177555084)]"
1636,1636,17,1636_vortex dynamics_vortex filaments_vortex_vortex like,"['vortex dynamics', 'vortex filaments', 'vortex', 'vortex like', 'vortex lines', 'vortex filament', 'vortex core', 'point vortex', 'vortices', 'quantum fluid']","['Quantized vortex dynamics of the nonlinear Schr\\""{o}dinger equation on\n  torus with non-vanishing momentum   We derive rigorously the reduced dynamical laws for quantized vortex dynamics\nof the nonlinear Schr\\""{o}dinger equation on the torus with non-vanishing\nmomentum when the vortex core size {\\epsilon} \\to 0. The reduced dynamical laws\nare governed by a Hamiltonian flow driven by a renormalized energy. A key\ningredient is to construct a new canonical harmonic map to include the effect\nfrom the non-vanishing momentum into the dynamics. Finally, some properties of\nthe reduced dynamical law are discussed.\n', 'Quantized Vortex Dynamics of the Coupled Nonlinear Schr\\""odinger\n  Equation   We derive rigorously the reduced dynamical law for quantized vortex dynamics\nof the coupled nonlinear Schr\\""odinger equation without Josephson junction\n(CNLS) when the core size of vortex $\\varepsilon\\to 0$. It is proved that when\n$\\varepsilon\\to 0$, the vortex motion of one component won\'t affect the vortex\nmotion on the other component. Moreover, the motion of vortices of each\ncomponent follows the vortex motion law for the nonlinear Schr\\""odinger.\n', 'Quantized Vortex Dynamics of the Nonlinear Wave Equation on the Torus   We derive rigorously the reduced dynamical laws for quantized vortex dynamics\nof the nonlinear wave equation on the torus when the core size of vortex\n$\\varepsilon\\to 0$. It is proved that the reduced dynamical laws are\nsecond-order nonlinear ordinary differential equations which are driven by the\nrenormalized energy on the torus, and the initial data of the reduced dynamical\nlaws are determined by the positions of vortices and the momentum. We will also\ninvestigate the effect of the momentum on the vortex dynamics.\n']","[('vortex dynamics', 0.6568956971168518), ('vortex filaments', 0.5189006328582764), ('vortex', 0.5031092762947083), ('vortex like', 0.48393484950065613), ('vortex lines', 0.47275683283805847), ('vortex filament', 0.47149229049682617), ('vortex core', 0.4702928066253662), ('point vortex', 0.4468418061733246), ('vortices', 0.4405581057071686), ('quantum fluid', 0.4330790042877197)]"
1637,1637,17,1637_fisher information metric_fisher metric_fisher information_metric probabilistic,"['fisher information metric', 'fisher metric', 'fisher information', 'metric probabilistic', 'statistical manifold', 'fisher rao', 'geodesic distance', 'riemannian metric', 'gaussian measures', 'information metric']","['On Closed-Form Expressions for the Fisher-Rao Distance   The Fisher-Rao distance is the geodesic distance between probability\ndistributions in a statistical manifold equipped with the Fisher metric, which\nis a natural choice of Riemannian metric on such manifolds. It has recently\nbeen applied to supervised and unsupervised problems in machine learning, in\nvarious contexts. Finding closed-form expressions for the Fisher-Rao distance\nis generally a non-trivial task, and those are only available for a few\nfamilies of probability distributions. In this survey, we collect examples of\nclosed-form expressions for the Fisher-Rao distance of both discrete and\ncontinuous distributions, aiming to present them in a unified and accessible\nlanguage. In doing so, we also: illustrate the relation between negative\nmultinomial distributions and the hyperbolic model, include a few new examples,\nand write a few more in the standard form of elliptical distributions.\n', 'Approximation and bounding techniques for the Fisher-Rao distances\n  between parametric statistical models   The Fisher-Rao distance between two probability distributions of a\nstatistical model is defined as the Riemannian geodesic distance induced by the\nFisher information metric. In order to calculate the Fisher-Rao distance in\nclosed-form, we need (1) to elicit a formula for the Fisher-Rao geodesics, and\n(2) to integrate the Fisher length element along those geodesics. We consider\nseveral numerically robust approximation and bounding techniques for the\nFisher-Rao distances: First, we report generic upper bounds on Fisher-Rao\ndistances based on closed-form 1D Fisher-Rao distances of submodels. Second, we\ndescribe several generic approximation schemes depending on whether the\nFisher-Rao geodesics or pregeodesics are available in closed-form or not. In\nparticular, we obtain a generic method to guarantee an arbitrarily small\nadditive error on the approximation provided that Fisher-Rao pregeodesics and\ntight lower and upper bounds are available. Third, we consider the case of\nFisher metrics being Hessian metrics, and report generic tight upper bounds on\nthe Fisher-Rao distances using techniques of information geometry.\nUniparametric and biparametric statistical models always have Fisher Hessian\nmetrics, and in general a simple test allows to check whether the Fisher\ninformation matrix yields a Hessian metric or not. Fourth, we consider\nelliptical distribution families and show how to apply the above techniques to\nthese models. We also propose two new distances based either on the Fisher-Rao\nlengths of curves serving as proxies of Fisher-Rao geodesics, or based on the\nBirkhoff/Hilbert projective cone distance. Last, we consider an alternative\ngroup-theoretic approach for statistical transformation models based on the\nnotion of maximal invariant which yields insights on the structures of the\nFisher-Rao distance formula which may be used fruitfully in applications.\n', 'Fisher-Rao distances between finite energy signals in noise This paper proposes to represent finite-energy signals observed in agiven bandwidth as parameters of a probability distribution, and use the information geometrical framework to compute the Fisher-Rao distance between these signals, seen as distributions. The observations are represented by their discrete Fourier transform, which are modeled as complex Gaussian vectors with fixed diagonal covariance matrix and parametrized means. The parameters define the coordinate system of a statistical manifold. This work investigates the possibility of obtaining closed-form expressions for the Fisher-Rao distance. We study two cases: the general case representing any finite energy signal observed in a given bandwidth and a parametrized example of observing an attenuated signal with a known magnitude spectrum and unknown phase spectrum, and we calculate the Fisher-Rao distances for both cases. The finite energy signal manifold corresponds to the manifold of the Gaussian distribution with a known covariance matrix, and the manifold of known magnitude spectrum signals is a submanifold. We derive the expressions for the Christoffel symbols and the tensorial equations of the geodesics. This leads to geodesic equations expressed as second order differential equations. We show that the tensor differential equations can be transformed into matrix equations. These equations depend on the parametric model but simplify to only two vectorial equations, which combine the magnitude and phase of the signal and their gradients with respect to the parameters. We compute closed-form expressions of the Fisher-Rao distances for both studied cases and show that the submanifold is non-geodesic, indicating that the Fisher-Rao distance measured within the submanifold is greater than in the full manifold.']","[('fisher information metric', 0.6857677698135376), ('fisher metric', 0.6733174324035645), ('fisher information', 0.560793936252594), ('metric probabilistic', 0.5200868844985962), ('statistical manifold', 0.5043964982032776), ('fisher rao', 0.4925231337547302), ('geodesic distance', 0.4653540849685669), ('riemannian metric', 0.463571161031723), ('gaussian measures', 0.4362718164920807), ('information metric', 0.4156458079814911)]"
1638,1638,17,1638_field optimal control_mean field control_mean field neural_mean field optimal,"['field optimal control', 'mean field control', 'mean field neural', 'mean field optimal', 'optimal control', 'field optimal transport', 'field neural', 'forward backward stochastic', 'optimal control second', 'mean field games']","['A deep learning algorithm for computing mean field control problems via forward-backward score dynamics We propose a deep learning approach to compute mean field control problems with individual noises. The problem consists of the Fokker-Planck (FP) equation and the Hamilton-Jacobi-Bellman (HJB) equation. Using the differential of the entropy, namely the score function, we first formulate the deterministic forward-backward characteristics for the mean field control system, which is different from the classical forward-backward stochastic differential equations (FBSDEs). We further apply the neural network approximation to fit the proposed deterministic characteristic lines. Numerical examples, including the control problem with entropy potential energy, the linear quadratic regulator, and the systemic risks, demonstrate the effectiveness of the proposed method.', 'Variational conditional normalizing flows for computing second-order\n  mean field control problems   Mean field control (MFC) problems have vast applications in artificial\nintelligence, engineering, and economics, while solving MFC problems accurately\nand efficiently in high-dimensional spaces remains challenging. This work\nintroduces variational conditional normalizing flow (VCNF), a neural\nnetwork-based variational algorithm for solving general MFC problems based on\nflow maps. Formulating MFC problems as optimal control of Fokker-Planck (FP)\nequations with suitable constraints and cost functionals, we use VCNF to model\nthe Lagrangian formulation of the MFC problems. In particular, VCNF builds upon\nconditional normalizing flows and neural spline flows, allowing efficient\ncalculations of the inverse push-forward maps and score functions in MFC\nproblems. We demonstrate the effectiveness of VCNF through extensive numerical\nexamples, including optimal transport, regularized Wasserstein proximal\noperators, and flow matching problems for FP equations.\n', 'Convergence Analysis of Machine Learning Algorithms for the Numerical\n  Solution of Mean Field Control and Games: II -- The Finite Horizon Case   We propose two numerical methods for the optimal control of McKean-Vlasov\ndynamics in finite time horizon. Both methods are based on the introduction of\na suitable loss function defined over the parameters of a neural network. This\nallows the use of machine learning tools, and efficient implementations of\nstochastic gradient descent in order to perform the optimization. In the first\nmethod, the loss function stems directly from the optimal control problem. The\nsecond method tackles a generic forward-backward stochastic differential\nequation system (FBSDE) of McKean-Vlasov type, and relies on suitable\nreformulation as a mean field control problem. To provide a guarantee on how\nour numerical schemes approximate the solution of the original mean field\ncontrol problem, we introduce a new optimization problem, directly amenable to\nnumerical computation, and for which we rigorously provide an error rate.\nSeveral numerical examples are provided. Both methods can easily be applied to\ncertain problems with common noise, which is not the case with the existing\ntechnology. Furthermore, although the first approach is designed for mean field\ncontrol problems, the second is more general and can also be applied to the\nFBSDE arising in the theory of mean field games.\n']","[('field optimal control', 0.6266335844993591), ('mean field control', 0.6093593835830688), ('mean field neural', 0.5949927568435669), ('mean field optimal', 0.5543820858001709), ('optimal control', 0.4955616891384125), ('field optimal transport', 0.4804162383079529), ('field neural', 0.4646396338939667), ('forward backward stochastic', 0.45734933018684387), ('optimal control second', 0.4532775580883026), ('mean field games', 0.426520437002182)]"
1639,1639,17,1639_quantum programming_categorical quantum_quantum computing_quantum circuits,"['quantum programming', 'categorical quantum', 'quantum computing', 'quantum circuits', 'quantum operations', 'control quantum', 'models quantum', 'quantum circuit', 'quantum', 'monad']","['The Quantum Monadology   The modern theory of functional programming languages uses monads for\nencoding computational side-effects and side-contexts, beyond bare-bone program\nlogic. Even though quantum computing is intrinsically side-effectful (as in\nquantum measurement) and context-dependent (as on mixed ancillary states),\nlittle of this monadic paradigm has previously been brought to bear on quantum\nprogramming languages.\n  Here we systematically analyze the (co)monads on categories of parameterized\nmodule spectra which are induced by Grothendieck\'s ""motivic yoga of operations""\n-- for the present purpose specialized to HC-modules and further to set-indexed\ncomplex vector spaces. Interpreting an indexed vector space as a collection of\nalternative possible quantum state spaces parameterized by quantum measurement\nresults, as familiar from Proto-Quipper-semantics, we find that these\n(co)monads provide a comprehensive natural language for functional quantum\nprogramming with classical control and with ""dynamic lifting"" of quantum\nmeasurement results back into classical contexts.\n  We close by indicating a domain-specific quantum programming language (QS)\nexpressing these monadic quantum effects in transparent do-notation, embeddable\ninto the recently constructed Linear Homotopy Type Theory (LHoTT) which\ninterprets into parameterized module spectra. Once embedded into LHoTT, this\nshould make for formally verifiable universal quantum programming with linear\nquantum types, classical control, dynamic lifting, and notably also with\ntopological effects.\n', 'Proto-Quipper with dynamic lifting   Quipper is a functional programming language for quantum computing.\nProto-Quipper is a family of languages aiming to provide a formal foundation\nfor Quipper. In this paper, we extend Proto-Quipper-M with a construct called\ndynamic lifting, which is present in Quipper. By virtue of being a circuit\ndescription language, Proto-Quipper has two separate runtimes: circuit\ngeneration time and circuit execution time. Values that are known at circuit\ngeneration time are called parameters, and values that are known at circuit\nexecution time are called states. Dynamic lifting is an operation that enables\na state, such as the result of a measurement, to be lifted to a parameter,\nwhere it can influence the generation of the next portion of the circuit. As a\nresult, dynamic lifting enables Proto-Quipper programs to interleave classical\nand quantum computation. We describe the syntax of a language we call\nProto-Quipper-Dyn. Its type system uses a system of modalities to keep track of\nthe use of dynamic lifting. We also provide an operational semantics, as well\nas an abstract categorical semantics for dynamic lifting based on enriched\ncategory theory. We prove that both the type system and the operational\nsemantics are sound with respect to our categorical semantics. Finally, we give\nsome examples of Proto-Quipper-Dyn programs that make essential use of dynamic\nlifting.\n', 'A Biset-Enriched Categorical Model for Proto-Quipper with Dynamic\n  Lifting   Quipper and Proto-Quipper are a family of quantum programming languages that,\nby their nature as circuit description languages, involve two runtimes: one at\nwhich the program generates a circuit and one at which the circuit is executed,\nnormally with probabilistic results due to measurements. Accordingly, the\nlanguage distinguishes two kinds of data: parameters, which are known at\ncircuit generation time, and states, which are known at circuit execution time.\nSometimes, it is desirable for the results of measurements to control the\ngeneration of the next part of the circuit. Therefore, the language needs to\nturn states, such as measurement outcomes, into parameters, an operation we\ncall dynamic lifting. The goal of this paper is to model this interaction\nbetween the runtimes by providing a general categorical structure enriched in\nwhat we call ""bisets"". We demonstrate that the biset-enriched structure\nachieves a proper semantics of the two runtimes and their interaction, by\nshowing that it models a variant of Proto-Quipper with dynamic lifting. The\npresent paper deals with the concrete categorical semantics of this language,\nwhereas a companion paper deals with the syntax, type system, operational\nsemantics, and abstract categorical semantics.\n']","[('quantum programming', 0.6343641877174377), ('categorical quantum', 0.624212384223938), ('quantum computing', 0.5317238569259644), ('quantum circuits', 0.4984463155269623), ('quantum operations', 0.49023711681365967), ('control quantum', 0.48297467827796936), ('models quantum', 0.4824701249599457), ('quantum circuit', 0.46538040041923523), ('quantum', 0.4596584737300873), ('monad', 0.4562155604362488)]"
1640,1640,17,1640_predictive control mpc_predictive control scheme_predictive control_distributed control,"['predictive control mpc', 'predictive control scheme', 'predictive control', 'distributed control', 'distributed optimization', 'distributed predictive', 'control mpc', 'mpc control', 'system level synthesis', 'closed loop control']","['Explicit Distributed and Localized Model Predictive Control via System\n  Level Synthesis   An explicit Model Predictive Control algorithm for large-scale structured\nlinear systems is presented. We base our results on Distributed and Localized\nModel Predictive Control (DLMPC), a closed-loop model predictive control scheme\nbased on the System Level Synthesis (SLS) framework wherein only local state\nand model information needs to be exchanged between subsystems for the\ncomputation and implementation of control actions. We provide an explicit\nsolution for each of the subproblems resulting from the distributed MPC scheme.\nWe show that given the separability of the problem, the explicit solution is\nonly divided into three regions per state and input instantiation, making the\npoint location problem very efficient. Moreover, given the locality\nconstraints, the subproblems are of much smaller dimension than the full\nproblem, which significantly reduces the computational overhead of explicit\nsolutions. We conclude with numerical simulations to demonstrate the\ncomputational advantages of our method, in which we show a large improvement in\nruntime per MPC iteration as compared with the results of computing the\noptimization with a solver online.\n', 'Distributed and Localized Model Predictive Control via System Level\n  Synthesis   We present the Distributed and Localized Model Predictive Control (DLMPC)\nalgorithm for large-scale structured linear systems, wherein only local state\nand model information needs to be exchanged between subsystems for the\ncomputation and implementation of control actions. We use the System Level\nSynthesis (SLS) framework to reformulate the MPC problem as an optimization\nproblem over closed loop system responses, and show that this allows us to\nnaturally impose localized communication constraints between sub-controllers,\nsuch that only local state and system model information needs to be exchanged\nfor both computation and implementation of closed loop MPC control policies. In\nparticular, we show that the structure of the resulting optimization problem\ncan be exploited to develop an Alternating Direction Method of Multipliers\n(ADMM) based algorithm that allows for distributed and localized computation of\ncontrol decisions. Moreover, our approach can accommodate constraints and\nobjective functions that couple the behavior of different subsystems, so long\nas the coupled systems are able to communicate directly with each other,\nallowing for a broader class of MPC problems to be solved via distributed\noptimization. We conclude with numerical simulations to demonstrate the\nusefulness of our method, and in particular, we demonstrate that the\ncomputational complexity of the subproblems solved by each subsystem in DLMPC\nis independent of the size of the global system.\n', 'Distributed and Localized Model Predictive Control. Part I: Synthesis\n  and Implementation   The increasing presence of large-scale distributed systems highlights the\nneed for scalable control strategies where only local communication is\nrequired. Moreover, in safety-critical systems it is imperative that such\ncontrol strategies handle constraints in the presence of disturbances. In\nresponse to this need, we present the Distributed and Localized Model\nPredictive Control (DLMPC) algorithm for large-scale linear systems. DLMPC is a\ndistributed closed-loop model predictive control (MPC) scheme wherein only\nlocal state and model information needs to be exchanged between subsystems for\nthe computation and implementation of control actions. We use the System Level\nSynthesis (SLS) framework to reformulate the centralized MPC problem, and show\nthat this allows us to naturally impose localized communication constraints\nbetween sub-controllers. The structure of the resulting problem can be\nexploited to develop an Alternating Direction Method of Multipliers (ADMM)\nbased algorithm that allows for distributed and localized computation of\nclosed-loop control policies. We demonstrate that computational complexity of\nthe subproblems solved by each subsystem in DLMPC is independent of the size of\nthe global system. To the best of our knowledge, DLMPC is the first MPC\nalgorithm that allows for the scalable distributed computation as well as\nimplementation of distributed closed-loop control policies, and seemingly deals\nwith additive disturbances. In our companion paper, we show that this approach\nenjoys recursive feasibility and asymptotic stability.\n']","[('predictive control mpc', 0.5632503628730774), ('predictive control scheme', 0.5589521527290344), ('predictive control', 0.48326388001441956), ('distributed control', 0.4713558256626129), ('distributed optimization', 0.4546263813972473), ('distributed predictive', 0.4382738471031189), ('control mpc', 0.4010283648967743), ('mpc control', 0.3998377025127411), ('system level synthesis', 0.39932313561439514), ('closed loop control', 0.38100665807724)]"
1641,1641,17,1641_gamma functions_monotonic functions_monotonicity logarithmic_complete monotonicity,"['gamma functions', 'monotonic functions', 'monotonicity logarithmic', 'complete monotonicity', 'results monotonicity', 'finite gamma', 'monotonicity properties', 'monotonicity certain', 'monotonicity two', 'monotonicity']","['An application of a moment problem to completely monotonic functions   We consider the following question: if a function of the form\n$\\int_0^{\\infty}\\varphi(t)\\, e^{-xt}dt$ is completely monotonic, is it then\n$\\varphi\\ge0$? It turns out that the question is related to a moment problem.\nIn the end we apply those results to answer some questions concerning complete\nmonotonicity of certain functions raised in F. Qi and R. Agarwal, \\textit{On\ncomplete monotonicity for several classes of functions related to ratios of\ngamma functions}, J. Inequal. Appl. (2019).\n', 'Logarithmically complete monotonicity of reciprocal arctan function   We prove the conjecture stated in F. Qi and R. Agarwal, \\textit{On complete\nmonotonicity for several classes of functions related to ratios of gamma\nfunctions}, J. Inequal. Appl. (2019), 1-42, that the function $1/\\arctan$ is\nlogarithmically completely monotonic on $(0,\\infty)$, but not a Stieltjes\ntransform.\n', 'From inequalities involving exponential functions and sums to\n  logarithmically complete monotonicity of ratios of gamma functions   In the paper, the authors review origins, motivations, and generalizations of\na series of inequalities involving several exponential functions and sums,\nestablish three new inequalities involving finite exponential functions and\nsums by finding convexity of a function related to the generating function of\nthe Bernoulli numbers, survey the history, backgrounds, generalizations,\nlogarithmically complete monotonicity, and applications of a series of ratios\nof finite gamma functions, present complete monotonicity of a linear\ncombination of finite trigamma functions, construct a new ratio of finite gamma\nfunctions, derives monotonicity, logarithmic convexity, concavity, complete\nmonotonicity, and the Bernstein function property of the newly constructed\nratio of finite gamma functions, and suggest two linear combinations of finite\ntrigamma functions and two ratios of finite gamma functions to be investigated.\n']","[('gamma functions', 0.5370917916297913), ('monotonic functions', 0.5015228390693665), ('monotonicity logarithmic', 0.4846227169036865), ('complete monotonicity', 0.47640568017959595), ('results monotonicity', 0.47394412755966187), ('finite gamma', 0.47376778721809387), ('monotonicity properties', 0.47155043482780457), ('monotonicity certain', 0.46725478768348694), ('monotonicity two', 0.4591553211212158), ('monotonicity', 0.45497140288352966)]"
1642,1642,17,1642_fractional diffusion equations_preconditioned matrix_discretization fractional_fractional diffusion,"['fractional diffusion equations', 'preconditioned matrix', 'discretization fractional', 'fractional diffusion', 'preconditioning technique', 'multigrid preconditioning', 'preconditioned conjugate gradient', 'space fractional diffusion', 'proposed preconditioner', 'preconditioner based']","['A {\\tau} Matrix Based Approximate Inverse Preconditioning for Tempered\n  Fractional Diffusion Equations   Tempered fractional diffusion equations are a crucial class of equations\nwidely applied in many physical fields. In this paper, the Crank-Nicolson\nmethod and the tempered weighted and shifts Gr\\""unwald formula are firstly\napplied to discretize the tempered fractional diffusion equations. We then\nobtain that the coefficient matrix of the discretized system has the structure\nof the sum of the identity matrix and a diagonal matrix multiplied by a\nsymmetric positive definite(SPD) Toeplitz matrix. Based on the properties of\nSPD Toeplitz matrices, we use $\\tau$ matrix approximate it and then propose a\nnovel approximate inverse preconditioner to approximate the coefficient matrix.\nThe $\\tau$ matrix based approximate inverse preconditioner can be efficiently\ncomputed using the discrete sine transform(DST). In spectral analysis, the\neigenvalues of the preconditioned coefficient matrix are clustered around 1,\nensuring fast convergence of Krylov subspace methods with the new\npreconditioner. Finally, numerical experiments demonstrate the effectiveness of\nthe proposed preconditioner.\n', 'A preconditioner based on sine transform for two-dimensional Riesz space\n  factional diffusion equations in convex domains   In this paper, we develop a fast numerical method for solving the\ntime-dependent Riesz space fractional diffusion equations with a nonlinear\nsource term in the convex domain. An implicit finite difference method is\nemployed to discretize the Riesz space fractional diffusion equations with a\npenalty term in a rectangular region by the volume-penalization approach. The\nstability and the convergence of the proposed method are studied. As the\ncoefficient matrix is with the Toeplitz-like structure, the generalized minimum\nresidual method with a preconditioner based on the sine transform is exploited\nto solve the discretized linear system, where the preconditioner is constructed\nin view of the combination of two approximate inverse ${\\tau}$ matrices, which\ncan be diagonalized by the sine transform. The spectrum of the preconditioned\nmatrix is also investigated. Numerical experiments are carried out to\ndemonstrate the efficiency of the proposed method.\n', 'On $\\tau$-preconditioners for a quasi-compact difference scheme to Riesz\n  fractional diffusion equations with variable coefficients   In the present study, we consider the numerical method for Toeplitz-like\nlinear systems arising from the $d$-dimensional Riesz space fractional\ndiffusion equations (RSFDEs). We apply the Crank-Nicolson (CN) technique to\ndiscretize the temporal derivative and apply a quasi-compact finite difference\nmethod to discretize the Riesz space fractional derivatives. For the\n$d$-dimensional problem, the corresponding coefficient matrix is the sum of a\nproduct of a (block) tridiagonal matrix multiplying a diagonal matrix and a\n$d$-level Toeplitz matrix. We develop a sine transform based preconditioner to\naccelerate the convergence of the GMRES method. Theoretical analyses show that\nthe upper bound of relative residual norm of the preconditioned GMRES method\nwith the proposed preconditioner is mesh-independent, which leads to a linear\nconvergence rate. Numerical results are presented to confirm the theoretical\nresults regarding the preconditioned matrix and to illustrate the efficiency of\nthe proposed preconditioner.\n']","[('fractional diffusion equations', 0.55631422996521), ('preconditioned matrix', 0.5475896000862122), ('discretization fractional', 0.5471652150154114), ('fractional diffusion', 0.4966844916343689), ('preconditioning technique', 0.4772043228149414), ('multigrid preconditioning', 0.4748381972312927), ('preconditioned conjugate gradient', 0.4643089175224304), ('space fractional diffusion', 0.4631231129169464), ('proposed preconditioner', 0.4563406705856323), ('preconditioner based', 0.451509952545166)]"
1643,1643,17,1643_boltzmann hard_derivation boltzmann_boltzmann kinetic_linearized boltzmann,"['boltzmann hard', 'derivation boltzmann', 'boltzmann kinetic', 'linearized boltzmann', 'boltzmann', 'boltzmann type', 'classical statistical mechanics', 'kinetic theory', 'hard spheres', 'hard sphere']","[""A Rigorous Derivation of a Boltzmann System for a Mixture of Hard-Sphere\n  Gases   In this paper, we rigorously derive a Boltzmann equation for mixtures from\nthe many body dynamics of two types of hard sphere gases. We prove that the\nmicroscopic dynamics of two gases with different masses and diameters is well\ndefined, and introduce the concept of a two parameter BBGKY hierarchy to handle\nthe non-symmetric interaction of these gases. As a corollary of the derivation,\nwe prove Boltzmann's propagation of chaos assumption for the case of a mixtures\nof gases.\n"", ""Long time derivation of the Boltzmann equation from hard sphere dynamics   We provide a rigorous derivation of Boltzmann's kinetic equation from the\nhard-sphere system for rarefied gas, which is valid for arbitrarily long time\nas long as the solution to the Boltzmann equation exists. This extends\nLanford's landmark theorem (1975) which justifies such derivation for\nsufficiently short time, and is a crucial step towards resolving Hilbert's\nsixth problem.\n  The general strategy follows the paradigm introduced by the first two authors\nfor the long-time derivation of the wave kinetic equation in wave turbulence\ntheory. This is based on propagating a long-time cumulant ansatz, which keeps\nmemory of the full collision history of the relevant particles. The heart of\nthe matter is proving the smallness of these cumulants in L1, which can be\nreduced to combinatorial properties for the associated Feynman diagrams, called\ncollision history (CH) molecules. The latter is then proved by devising an\nelaborate cutting algorithm, which is a major novelty of this work.\n"", 'Approaches to Derivation of the Boltzmann Equation with Hard Sphere\n  Collisions   In the paper the possible approaches to the rigorous derivation of the\nBoltzmann kinetic equation with hard sphere collisions from underlying dynamics\nare considered. In particular, a formalism for the description of the evolution\nof infinitely many hard spheres within the framework of marginal observables in\nthe Boltzmann--Grad scaling limit is developed. Also we give consideration to\none more approach of the description of the kinetic evolution of hard spheres\nin terms of a one-particle distribution function governed by the non-Markovian\ngeneralization of the Enskog equation and the Boltzmann--Grad asymptotic\nbehavior of its non-perturbative solution is established.\n']","[('boltzmann hard', 0.6663643717765808), ('derivation boltzmann', 0.6413082480430603), ('boltzmann kinetic', 0.6017391085624695), ('linearized boltzmann', 0.5901765823364258), ('boltzmann', 0.5753926038742065), ('boltzmann type', 0.5576373934745789), ('classical statistical mechanics', 0.4975404739379883), ('kinetic theory', 0.44482895731925964), ('hard spheres', 0.43968427181243896), ('hard sphere', 0.41272619366645813)]"
1644,1644,17,1644_lagrangian field theory_gauge symmetries_gauge transformations_gauge theories,"['lagrangian field theory', 'gauge symmetries', 'gauge transformations', 'gauge theories', 'gauge symmetry', 'lagrangian systems', 'gauge invariance', 'constrained hamiltonian systems', 'constrained hamiltonian', 'lagrangian field']","['Gauge symmetry and partially Lagrangian systems   We consider a classical field theory whose equations of motion follow from\nthe least action principle, but the class of admissible trajectories is\nrestricted by differential equations. The key element of the proposed\nconstruction is the complete gauge symmetry of these additional equations. The\nunfree variation of the trajectories reduces to the infinitesimal gauge\nsymmetry transformation of the equations, restricting the trajectories. We\nexplicitly derive the equations that follow from the requirement that this\ngauge variation of the action vanishes. The system of equations for conditional\nextrema is not a Lagrangian system as such, but it admits an equivalent\nHamiltonian formulation with a non-canonical Poisson bracket. The bracket is\ndegenerate, in general. Alternatively, the equations restricting the dynamics\ncould be added to the action with Lagrange multipliers with unrestricted\nvariation of the original variables. In this case, we would arrive at the\nLagrangian equations for the original variables involving Lagrange multipliers\nand for Lagrange multipliers themselves. In general, these two methods are not\nequivalent because the multipliers can bring extra degrees of freedom compared\nto the case of equations derived by unfree variation of the action. We\nillustrate the general method with two examples. The first example is a\nparticle in a central field with varying trajectories restricted by the\nequation of conservation of angular momentum. The phase space acquires one more\ndimension, and there is an extra conserved quantity $K$ which is responsible\nfor the precession of trajectories. The second example is linearized gravity\nwith the Einstein-Hilbert action, and the class of varying fields is restricted\nby the linearized Nordstr\\""om equation. This conditional extrema problem is\nshown to lead to the linearized Cotton gravity equations.\n', 'Integrable Non-Holonomic Constraints and Gauge Fixing in Classical Field Theory We show how the usual derivation of the equations of motion for a classical field theory with non-holonomic constraints, constraints that depend on the derivatives of the field, fails. As a result, the usual method for gauge fixing in classical and quantum field theories fails for general gauges that depend on the derivatives of the fields, such as the Coulomb and Lorenz gauges. The point of failure occurs at the use of the transposition rule, $\\delta(\\partial_\\nu A^\\mu)=\\partial_\\nu(\\delta A^\\mu)$, in the derivation of the equations of motion from the extremization of the action; we show that the transposition rule does not hold for general non-holonomic constraints. We define the concept of integrability of non-holonomic constraints in field theory and prove that the usual transposition rule holds for theories with these constraints. We are thus able to recover the usual treatment of gauge fixing for gauges of this type. We apply our formalism to the specific examples of the Coulomb and Lorenz gauges.', 'Singular Lagrangians, Constrained Hamiltonian Systems and Gauge\n  Invariance: An Example of the Dirac-Bergmann Algorithm   The Dirac-Bergmann algorithm is a recipe for converting a theory with a\nsingular Lagrangian into a constrained Hamiltonian system. Constrained\nHamiltonian systems include gauge theories -- general relativity,\nelectromagnetism, Yang Mills, string theory, etc. The Dirac-Bergmann algorithm\nis elegant but at the same time rather complicated. It consists of a large\nnumber of logical steps linked together by a subtle chain of reasoning.\nExamples of the Dirac-Bergmann algorithm found in the literature are designed\nto isolate and illustrate just one or two of those logical steps. In this paper\nI analyze a finite-dimensional system that exhibits all of the major steps in\nthe algorithm. The system includes primary and secondary constraints, first and\nsecond class constraints, restrictions on Lagrange multipliers, and both\nphysical and gauge degrees of freedom. This relatively simple system provides a\nplatform for discussing the Dirac conjecture, constructing Dirac brackets, and\napplying gauge conditions.\n']","[('lagrangian field theory', 0.6067768335342407), ('gauge symmetries', 0.5652772784233093), ('gauge transformations', 0.5600631237030029), ('gauge theories', 0.558476448059082), ('gauge symmetry', 0.5490770936012268), ('lagrangian systems', 0.5475845336914062), ('gauge invariance', 0.5377058386802673), ('constrained hamiltonian systems', 0.5374393463134766), ('constrained hamiltonian', 0.5168979167938232), ('lagrangian field', 0.5141922235488892)]"
1645,1645,17,1645_optimal decay estimates_decay estimates_time decay estimates_decay rates solutions,"['optimal decay estimates', 'decay estimates', 'time decay estimates', 'decay rates solutions', 'decay estimates large', 'optimal decay', 'optimal time decay', 'establish optimal decay', 'optimal decay rate', 'global weak solutions']","['Global well-posedness and large time behavior of solutions to the\n  compressible Oldroyd-B model without stress diffusion   We consider the Cauchy problem ($\\mathbb{R}^d, d=2,3$) and the initial\nboundary values problem ($\\mathbb{T}^d, d=2,3$)associated to the compressible\nOldroyd-B model which is first derived by Barrett, Lu and S\\""{u}li [Existence\nof large-data finite-energy global weak solutions to a compressible Oldroyd-B\nmodel, Commun. Math. Sci., 15 (2017), 1265--1323] through micro-macro-analysis\nof the compressible Navier-Stokes-Fokker-Planck system.Due to lack of stress\ndiffusion, the problems considered here are very difficult. Exploiting tools\nfrom harmonic analysis,notably the Littlewood Paley theory,we first establish\nthe global well-posedness and time-decay rates for solutions of the model with\nsmall initial data in Besov spaces with critical regularity.Then, through\ndeeply exploring and fully utilizing the structure of the perturbation\nsystem,we obtain the global well-posedness and exponential decay rates for\nsolutions of the model with small initial data in the Soboles spaces\n$H^3(\\mathbb{T}^d)$.Our obtained results improve considerably the recent\nresults by Lu, Pokorn\\\'{y} [Anal. Theory Appl., 36 (2020), 348--372],Wang, Wen\n[Math. Models Methods Appl. Sci., 30 (2020), 139--179],and Liu, Lu, Wen [SIAM\nJ. Math. Anal., 53 (2021), 6216--6242].\n', 'Optimal decay rate for the generalized Oldroyd-B model with only stress\n  tensor diffusion in $\\mathbb{R}^2$   In this paper, we are concerned with optimal decay rate for the 2-D\ngeneralized Oldroyd-B model with only stress tensor diffusion\n$(-\\Delta)^{\\beta}\\tau$. In the case $\\beta=1$, we first establish optimal\ndecay rate in $H^1$ framework and remove the smallness assumption of low\nfrequencies by virtue of the Fourier splitting method and the Littlewood-Paley\ndecomposition theory. Furthermore, we prove optimal decay rate for the highest\nderivative of the solution by a different method combining time frequency\ndecomposition and the time weighted energy estimate. In the case $\\frac 1 2\\leq\n\\beta <1$, we study optimal decay rate for the highest derivative of the\nsolution by the improved Fourier splitting method.\n', 'Global existence and optimal decay rate of weak solutions to some\n  inviscid Oldroyd-B models   This paper is devoted to global existence and optimal decay rate of weak\nsolutions to some inviscid Oldroyd-B models with center diffusion. By virtue of\nthe properties of Calderon-Zygmund operator and the Littlewood-Paley\ndecomposition theory, we firstly prove that the 2-D co-rotation inviscid\nOldroyd-B model admits global weak solutions with some large data under\ndifferent integrability conditions. Furthermore, we prove the energy\nconservation of weak solutions for the co-rotation case. These obtained results\ngeneralize and cover the classical results for the Euler equation. Moreover, we\nestablish global weak solutions with small data for the 2-D noncorotation\ninviscid Oldroyd-B model without damping. Finally, we prove optimal decay rate\nof global weak solutions for the noncorotation case by the improved Fourier\nsplitting method.\n']","[('optimal decay estimates', 0.5703230500221252), ('decay estimates', 0.5338508486747742), ('time decay estimates', 0.520382821559906), ('decay rates solutions', 0.5187353491783142), ('decay estimates large', 0.5158166885375977), ('optimal decay', 0.5114337205886841), ('optimal time decay', 0.5068356990814209), ('establish optimal decay', 0.5040388703346252), ('optimal decay rate', 0.47576212882995605), ('global weak solutions', 0.45569273829460144)]"
1646,1646,17,1646_covering maps_branched covering_hyperbolic orbifold_maps sphere,"['covering maps', 'branched covering', 'hyperbolic orbifold', 'maps sphere', 'thurston', 'rational maps', 'finite rational maps', 'riemann sphere', 'maps four', 'maps topological']","['On the rank of the Thurston pullback map   Under some mild assumptions, an orientation-preserving branched covering map\nof marked $2$-spheres induces a pullback map between the corresponding\nTeichm\\""uller spaces. By analyzing the associated pushforward operator acting\non integrable quadratic differentials, we obtain a global lower bound on the\nrank of the derivative of the pullback map in terms of the action of the cover\non the marked points. In the dynamical context, the two sets of marked points\nin the target and source coincide with the postcritical set. Investigating the\nresulting pullback map is the central part of Thurston\'s topological\ncharacterization of postcritically finite rational maps. Postcritically finite\nmaps with constant pullback have been studied by various authors. In that\ndirection, our approach provides upper bounds on the size of the postcritical\nset of a map with constant pullback, and shows that the postcritical dynamics\nis highly restricted.\n', 'Eliminating Thurston obstructions and controlling dynamics on curves   Every Thurston map $f\\colon S^2\\rightarrow S^2$ on a $2$-sphere $S^2$ induces\na pull-back operation on Jordan curves $\\alpha\\subset S^2\\setminus P_f$, where\n$P_f$ is the postcritical set of $f$. Here the isotopy class $[f^{-1}(\\alpha)]$\n(relative to $P_f$) only depends on the isotopy class $[\\alpha]$. We study this\noperation for Thurston maps with four postcritical points. In this case a\nThurston obstruction for the map $f$ can be seen as a fixed point of the\npull-back operation.\n  We show that if a Thurston map $f$ with a hyperbolic orbifold and four\npostcritical points has a Thurston obstruction, then one can ""blow up"" suitable\narcs in the underlying $2$-sphere and construct a new Thurston map $\\widehat f$\nfor which this obstruction is eliminated. We prove that no other obstruction\narises and so $\\widehat f$ is realized by a rational map. In particular, this\nallows for the combinatorial construction of a large class of rational Thurston\nmaps with four postcritical points.\n  We also study the dynamics of the pull-back operation under iteration. We\nexhibit a subclass of our rational Thurston maps with four postcritical points\nfor which we can give positive answer to the global curve attractor problem.\n', 'Prime orbit theorems for expanding Thurston maps: Latt\\`es maps and\n  split Ruelle operators   We obtain an analog of the prime number theorem for a class of branched\ncovering maps on the $2$-sphere $S^2$ called expanding Thurston maps, which are\ntopological models of some non-uniformly expanding rational maps without any\nsmoothness or holomorphicity assumption. More precisely, we show that the\nnumber of primitive periodic orbits, ordered by a weight on each point induced\nby a non-constant (eventually) positive real-valued H\\""{o}lder continuous\nfunction on $S^2$ satisfying the $\\alpha$-strong non-integrability condition,\nis asymptotically the same as the well-known logarithmic integral, with an\nexponential error bound. In particular, our results apply to\npostcritically-finite rational maps for which the Julia set is the whole\nRiemann sphere. Moreover, a stronger result is obtained for Latt\\`{e}s maps.\n']","[('covering maps', 0.5163981318473816), ('branched covering', 0.48221611976623535), ('hyperbolic orbifold', 0.4733005464076996), ('maps sphere', 0.4726423919200897), ('thurston', 0.4510786235332489), ('rational maps', 0.4423006772994995), ('finite rational maps', 0.4254970848560333), ('riemann sphere', 0.42299506068229675), ('maps four', 0.4114551544189453), ('maps topological', 0.4062912166118622)]"
1647,1647,17,1647_projective varieties_smooth projective varieties_projective variety_homogeneous varieties,"['projective varieties', 'smooth projective varieties', 'projective variety', 'homogeneous varieties', 'projective scheme', 'projective schemes', 'birational maps', 'smooth projective', 'varieties picard', 'smooth varieties']","['Toric non-equalized flips associated to $\\mathbb{C}^*$-actions   Starting from $\\mathbb{C}^*$-actions on complex projective varieties, we\nconstruct and investigate birational maps among the corresponding extremal\nfixed point components. We study the case in which such birational maps are\nlocally described by toric flips, either of Atiyah type or so called\nnon-equalized. We relate this notion of toric flip with the property of the\naction being non-equalized. Moreover, we find explicit examples of rational\nhomogeneous varieties admitting a $\\mathbb{C}^*$-action whose weighted blow-up\nat the extremal fixed point components gives a birational map among two\nprojective varieties that is locally a toric non-equalized flip.\n', 'Characterizing rational homogeneous spaces via $\\mathbb{C}^*$-actions   We study smooth varieties of Picard number one admitting a special dominating\nfamily of rational curves and an equalized $\\mathbb{C}^*$-action. In particular\nwe show that $X$ is a smooth variety of Picard number one with nef tangent\nbundle admitting an equalized $\\mathbb{C}^*$-action with an isolated extremal\nfixed point if and only if $X$ is an irreducible Hermitian symmetric space.\n', 'Small modifications of Mori dream spaces arising from ${\\mathbb\n  C}^*$-actions   We link small modifications of projective varieties with a ${\\mathbb\nC}^*$-action to their GIT quotients. Namely, using flips with centers in\nclosures of Bia{\\l}ynicki-Birula cells, we produce a system of birational\nequivariant modifications of the original variety, which includes those on\nwhich a quotient map extends from a set of semistable points to a regular\nmorphism.\n  The structure of the modifications is completely described for the blowup\nalong the sink and the source of smooth varieties with Picard number one with a\n${\\mathbb C}^*$-action which has no finite isotropy for any point. Examples can\nbe constructed upon homogeneous varieties with a ${\\mathbb C}^*$-action\nassociated to short grading of their Lie algebras.\n']","[('projective varieties', 0.5486997961997986), ('smooth projective varieties', 0.5384360551834106), ('projective variety', 0.5324152112007141), ('homogeneous varieties', 0.4875462055206299), ('projective scheme', 0.48101943731307983), ('projective schemes', 0.47348085045814514), ('birational maps', 0.4734678268432617), ('smooth projective', 0.4609745442867279), ('varieties picard', 0.44399356842041016), ('smooth varieties', 0.4427606165409088)]"
1648,1648,17,1648_warehouses_aisles_warehouse_order selection,"['warehouses', 'aisles', 'warehouse', 'order selection', 'batching', 'orders', 'programming formulation', 'picking', 'grocery', 'multi depot']","['Order batching using an approximation for the distance travelled by\n  pickers   In this paper we investigate the problem of order batching for picker\nrouting. Our approach is applicable to warehouses (storage areas) arranged in\nthe standard rectangular grid layout, so with parallel aisles and two or more\ncross-aisles. The motivation underlying our work is online grocery shopping in\nwhich orders may be composed of dozens of items. The approach presented\ndirectly addresses order batching, but uses a distance approximation to\ninfluence the batching of orders without directly addressing the routing\nproblem.\n  We present a basic formulation based on deciding the orders to be batched\ntogether so as to optimise an objective that approximates the picker routing\ndistance travelled. We extend our formulation by improving the approximation\nfor cases where we have more than one block in the warehouse. We present\nconstraints to remove symmetry in order to lessen the computational effort\nrequired, as well as constraints that significantly improve the value of the\nlinear programming relaxation of our formulation. A heuristic algorithm based\non partial integer optimisation of our mathematical formulation is also\npresented. Once order batching has been decided we optimally route each\nindividual picker using a previous approach presented in the literature.\n  Extensive computational results for publicly available test problems\ninvolving up to 75 orders are given for both single and multiple block\nwarehouse configurations.\n', 'Improved formulations of the joint order batching and picker routing\n  problem   Order picking is the process of retrieving ordered products from storage\nlocations in warehouses. In picker-to-parts order picking systems, two or more\ncustomer orders may be grouped and assigned to a single picker. Then routing\ndecision regarding the visiting sequence of items during a picking tour must be\nmade. (J.Won and S.Olafsson 2005) found that solving the integrated problem of\nbatching and routing enables warehouse managers to organize order picking\noperations more efficiently compared with solving the two problems separately\nand sequentially. We therefore investigate the mathematical programming\nformulation of this integrated problem. We present several improved\nformulations for the problem based on the findings of (Valle, Beasley, and da\nCunha 2017), that can significantly improve computational results. More\nspecifically, we reconstruct the connectivity constraints and generate new\ncutting planes in our branch-and-cut framework. We also discuss some problem\nproperties by studying the structure of the graphical representation, and we\npresent two types of additional constraints. We also consider the no-reversal\ncase of this problem. We present efficient formulations by building different\nauxiliary graphs. Finally, we present computational results for publicly\navailable test problems for single-block and multiple-block warehouse\nconfigurations\n', 'Dynamic AGV Task Allocation in Intelligent Warehouses   This paper explores the integration of Automated Guided Vehicles (AGVs) in\nwarehouse order picking, a crucial and cost-intensive aspect of warehouse\noperations. The booming AGV industry, accelerated by the COVID-19 pandemic, is\nwitnessing widespread adoption due to its efficiency, reliability, and\ncost-effectiveness in automating warehouse tasks. This paper focuses on\nenhancing the picker-to-parts system, prevalent in small to medium-sized\nwarehouses, through the strategic use of AGVs. We discuss the benefits and\napplications of AGVs in various warehouse tasks, highlighting their\ntransformative potential in improving operational efficiency. We examine the\ndeployment of AGVs by leading companies in the industry, showcasing their\nvaried functionalities in warehouse management. Addressing the gap in research\non optimizing operational performance in hybrid environments where humans and\nAGVs coexist, our study delves into a dynamic picker-to-parts warehouse\nscenario. We propose a novel approach Neural Approximate Dynamic Programming\napproach for coordinating a mixed team of human and AGV workers, aiming to\nmaximize order throughput and operational efficiency. This involves innovative\nsolutions for non-myopic decision making, order batching, and battery\nmanagement. We also discuss the integration of advanced robotics technology in\nautomating the complete order-picking process. Through a comprehensive\nnumerical study, our work offers valuable insights for managing a heterogeneous\nworkforce in a hybrid warehouse setting, contributing significantly to the\nfield of warehouse automation and logistics.\n']","[('warehouses', 0.539483904838562), ('aisles', 0.5273107886314392), ('warehouse', 0.5105981826782227), ('order selection', 0.4389106333255768), ('batching', 0.3909628987312317), ('orders', 0.37763679027557373), ('programming formulation', 0.37724801898002625), ('picking', 0.37293851375579834), ('grocery', 0.3599902093410492), ('multi depot', 0.3528974652290344)]"
1649,1649,17,1649_interacting diffusions_propagation chaos mean_chaos mean field_quantitative propagation chaos,"['interacting diffusions', 'propagation chaos mean', 'chaos mean field', 'quantitative propagation chaos', 'mean field dynamics', 'time propagation chaos', 'propagation chaos', 'entropy estimates', 'mean field interacting', 'log sobolev inequalities']","['Hierarchies, entropy, and quantitative propagation of chaos for mean\n  field diffusions   This paper develops a non-asymptotic, local approach to quantitative\npropagation of chaos for a wide class of mean field diffusive dynamics. For a\nsystem of $n$ interacting particles, the relative entropy between the marginal\nlaw of $k$ particles and its limiting product measure is shown to be\n$O((k/n)^2)$ at each time, as long as the same is true at time zero. A simple\nGaussian example shows that this rate is optimal. The main assumption is that\nthe limiting measure obeys a certain functional inequality, which is shown to\nencompass many potentially irregular but not too singular finite-range\ninteractions, as well as some infinite-range interactions. This unifies the\npreviously disparate cases of Lipschitz versus bounded measurable interactions,\nimproving the best prior bounds of $O(k/n)$ which were deduced from global\nestimates involving all $n$ particles. We also cover a class of models for\nwhich qualitative propagation of chaos and even well-posedness of the\nMcKean-Vlasov equation were previously unknown. At the center of a new approach\nis a differential inequality, derived from a form of the BBGKY hierarchy, which\nbounds the $k$-particle entropy in terms of the $(k+1)$-particle entropy.\n', 'Sharp uniform-in-time propagation of chaos   We prove the optimal rate of quantitative propagation of chaos, uniformly in\ntime, for interacting diffusions. Our main examples are interactions governed\nby convex potentials and models on the torus with small interactions. We show\nthat the distance between the $k$-particle marginal of the $n$-particle system\nand its limiting product measure is $O((k/n)^2)$, uniformly in time, with\ndistance measured either by relative entropy, squared quadratic Wasserstein\nmetric, or squared total variation. Our proof is based on an analysis of\nrelative entropy through the BBGKY hierarchy, adapting prior work of the first\nauthor to the time-uniform case by means of log-Sobolev inequalities.\n', ""Phase transitions, logarithmic Sobolev inequalities, and uniform-in-time\n  propagation of chaos for weakly interacting diffusions   In this article, we study the mean field limit of weakly interacting\ndiffusions for confining and interaction potentials that are not necessarily\nconvex. We explore the relationship between the large $N$ limit of the constant\nin the logarithmic Sobolev inequality (LSI) for the $N$-particle system and the\npresence or absence of phase transitions for the mean field limit. The\nnon-degeneracy of the LSI constant is shown to have far reaching consequences,\nespecially in the context of uniform-in-time propagation of chaos and the\nbehaviour of equilibrium fluctuations. Our results extend previous results\nrelated to unbounded spin systems and recent results on propagation of chaos\nusing novel coupling methods. As incidentals, we provide concise and, to our\nknowledge, new proofs of a generalised form of Talagrand's inequality and of\nquantitative propagation of chaos by employing techniques from the theory of\ngradient flows, specifically the Riemannian calculus on the space of\nprobability measures.\n""]","[('interacting diffusions', 0.5738732218742371), ('propagation chaos mean', 0.5613532066345215), ('chaos mean field', 0.525854229927063), ('quantitative propagation chaos', 0.508549690246582), ('mean field dynamics', 0.5056114196777344), ('time propagation chaos', 0.5054916143417358), ('propagation chaos', 0.5019072890281677), ('entropy estimates', 0.46879711747169495), ('mean field interacting', 0.4658162295818329), ('log sobolev inequalities', 0.4469532072544098)]"
1650,1650,17,1650_harmonic maps_harmonic mappings_harmonic map_harmonic mapping,"['harmonic maps', 'harmonic mappings', 'harmonic map', 'harmonic mapping', 'maps dirichlet', 'singular harmonic', 'boundary map', 'minimizing harmonic', 'maps spheres', 'boundary regularity']","[""The Dirichlet Principle for Inner Variations   We are concerned with the Dirichlet energy of mappings defined on domains in\nthe complex plane. The motivation behind our questions, however, comes from\nmore general energy integrals of mathematical models of Hyperelasticity. The\nDirichlet Principle, the name coined by Riemann, tells us that the outer\nvariation of a harmonic mapping increases its energy. Surprisingly, when one\njumps into details about inner variations, which are just a change of\nindependent variables, new equations and related questions start to matter. The\ninner variational equation, called the Hopf Laplace equation, is no longer the\nLaplace equation. Its solutions are generally not harmonic; we refer to them as\nHopf harmonics. The natural question that arises is how does a change of\nvariables in the domain of a Hopf harmonic map affect its energy? We show,\namong other results, that in case of a simply connected domain the energy\nincreases. This should be viewed as Riemann's Dirichlet Principle for Hopf\nharmonics.\n  The Dirichlet Principle for Hopf harmonics in domains of higher connectivity\nis not completely solved. What complicates the matter is the insufficient\nknowledge of global structure of trajectories of the associated Hopf quadratic\ndifferentials, mainly because of the presence of recurrent trajectories.\nNevertheless, we have established the Dirichlet Principle whenever the Hopf\ndifferential admits closed trajectories and crosscuts. Regardless of these\nassumptions, we established the so-called Infinitesimal Dirichlet Principle for\nall domains and all Hopf harmonics. Precisely, the second order term of inner\nvariation of a Hopf harmonic map is always nonnegative.\n"", ""Stationary $p$-harmonic maps approaching planar singular harmonic maps to the circle Given a bounded planar domain $\\Omega \\subset \\mathbb{R}^2$, we show that any singular harmonic map into the circle $\\mathbb{S}^1$ corresponding to a topologically nondegenerate critical point of the renormalised energy in the sense of Bethuel, Brezis and H\\'elein is a limit of stationary $p$-harmonic maps for $p < 2$ as $p \\to 2$"", 'Limiting behavior of minimizing $p$-harmonic maps in 3d as $p$ goes to\n  $2$ with finite fundamental group   We study the limiting behavior of minimizing $p$-harmonic maps from a bounded\nLipschitz domain $\\Omega \\subset \\mathbb{R}^{3}$ to a compact connected\nRiemannian manifold without boundary and with finite fundamental group as $p\n\\nearrow 2$. We prove that there exists a closed set $S_{*}$ of finite length\nsuch that minimizing $p$-harmonic maps converge to a locally minimizing\nharmonic map in $\\Omega \\setminus S_{*}$. We prove that locally inside $\\Omega$\nthe singular set $S_{*}$ is a finite union of straight line segments, and it\nminimizes the mass in the appropriate class of admissible chains. Furthermore,\nwe establish local and global estimates for the limiting singular harmonic map.\nUnder additional assumptions, we prove that globally in $\\overline{\\Omega}$ the\nset $S_{*}$ is a finite union of straight line segments, and it minimizes the\nmass in the appropriate class of admissible chains, which is defined by a given\nboundary datum and $\\Omega$.\n']","[('harmonic maps', 0.6979523301124573), ('harmonic mappings', 0.6657776236534119), ('harmonic map', 0.6495885252952576), ('harmonic mapping', 0.6138946413993835), ('maps dirichlet', 0.5838996767997742), ('singular harmonic', 0.4977688193321228), ('boundary map', 0.49494311213493347), ('minimizing harmonic', 0.46492281556129456), ('maps spheres', 0.4598979651927948), ('boundary regularity', 0.4582592844963074)]"
1651,1651,17,1651_brownian motion poissonian_wiener process_process brownian motion_reflecting brownian motion,"['brownian motion poissonian', 'wiener process', 'process brownian motion', 'reflecting brownian motion', 'brownian motion', 'homogeneous poisson process', 'like brownian motion', 'first passage time', 'drifted brownian motion', 'absorbing boundary condition']","['Approximation convergence in the inverse first-passage time problem   The inverse first-passage time problem determines a boundary such that the\nfirst-passage time of a Wiener process to this boundary has a given\ndistribution. An approximation which is based on the starting value of the\nboundary to a smooth boundary by a piecewise linear boundary is given by\nequating the probability of the first-passage time to a linear boundary and the\nincrement of the distribution on each interval. We propose a modification of\nthat approximation which also approximates the starting value of the boundary.\nFirst, we show that the approximation is well-defined when assuming that the\nboundary is absolutely continuous. Second, we show that a subsequence of this\nnew approximation uniformly converges to the boundary when the length of each\ninterval of linear approximation goes to 0 asymptotically. The results are\nobtained using Arzela-Ascoli theorem on any compact space on which we further\nassume that the boundary admits uniformly dominated derivative. As the starting\nvalue of the boundary is unknown, this makes the new approximation more\nsuitable for applications. The results are also proved in the first-passage\ntime problem of a reflected Wiener process.\n', 'The Inverse First Passage Time Problem for killed Brownian motion   The classical inverse first passage time problem asks whether, for a Brownian\nmotion $(B_t)_{t\\geq 0}$ and a positive random variable $\\xi$, there exists a\nbarrier $b:\\mathbb{R}_+\\to\\mathbb{R}$ such that $\\mathbb{P}\\{B_s>b(s), 0\\leq s\n\\leq t\\}=\\mathbb{P}\\{\\xi>t\\}$, for all $t\\geq 0$. We study a variant of the\ninverse first passage time problem for killed Brownian motion. We show that if\n$\\lambda>0$ is a killing rate parameter and $\\mathbb{1}_{(-\\infty,0]}$ is the\nindicator of the set $(-\\infty,0]$ then, under certain compatibility\nassumptions, there exists a unique continuous function\n$b:\\mathbb{R}_+\\to\\mathbb{R}$ such that $\\mathbb{E}\\left[-\\lambda \\int_0^t\n\\mathbb{1}_{(-\\infty,0]}(B_s-b(s))\\,ds\\right] = \\mathbb{P}\\{\\zeta>t\\}$ holds\nfor all $t\\geq 0$. This is a significant improvement of a result of the first\ntwo authors (Annals of Applied Probability 24(1):1--33, 2014).\n  The main difficulty arises because $\\mathbb{1}_{(-\\infty,0]}$ is\ndiscontinuous. We associate a semi-linear parabolic partial differential\nequation (PDE) coupled with an integral constraint to this version of the\ninverse first passage time problem. We prove the existence and uniqueness of\nweak solutions to this constrained PDE system. In addition, we use the recent\nFeynman-Kac representation results of Glau (Finance and Stochastics\n20(4):1021--1059, 2016) to prove that the weak solutions give the correct\nprobabilistic interpretation.\n', 'Inverse first-passage problems of a diffusion with resetting   We address some inverse problems for the first-passage place and the\nfirst-passage time of a one-dimensional diffusion process $\\mathcal X(t)$ with\nstochastic resetting, starting from an initial position $\\mathcal X(0)= \\eta ;$\nthis type of diffusion $\\mathcal X(t)$ is characterized by the fact that a\nreset to the position $x_R $ can occur according to a homogeneous Poisson\nprocess with rate $r>0.$ As regards the inverse first-passage place problem,\nfor random $\\eta \\in (0,b), \\ b < + \\infty$ (and fixed $r$ and $x_R \\in\n(0,b))$, let $\\tau_{0,b}$ be the first time at which $\\mathcal X(t)$ exits the\ninterval $(0,b),$ and $\\pi _0 = P(\\mathcal X(\\tau_{0,b}) = 0)$ the probability\nof exit from the left end of $(0,b);$ given a probability $q \\in (0,1),$ the\ninverse first-passage place problem consists in finding the density $g$ of\n$\\eta ,$ if it exists, such that $\\pi _0 = q.$ Concerning the inverse\nfirst-passage time problem, for random $\\eta \\in (0, + \\infty)$ (and fixed $r$\nand $x_R >0)$, let $\\tau$ be the first-passage time of $\\mathcal X(t)$ through\nzero; for a given distribution function $F(t)$ on the positive real axis, the\ninverse first-passage time problem consists in finding the density $g$ of\n$\\eta,$ if it exists, such that $P(\\tau \\le t ) = F(t), \\ t >0.$ In addition to\nthe case of random initial position $\\eta,$ we also study the case when the\ninitial position $\\eta$ and the resetting rate $r$ are fixed, whereas the reset\nposition $x_R$ is random. For all types of inverse problems considered, several\nexplicit examples of solutions are reported.\n']","[('brownian motion poissonian', 0.49676504731178284), ('wiener process', 0.4864494204521179), ('process brownian motion', 0.4853714108467102), ('reflecting brownian motion', 0.45204728841781616), ('brownian motion', 0.4402649402618408), ('homogeneous poisson process', 0.41557031869888306), ('like brownian motion', 0.41306304931640625), ('first passage time', 0.41232118010520935), ('drifted brownian motion', 0.41052788496017456), ('absorbing boundary condition', 0.4088825285434723)]"
1652,1652,17,1652_hopf algebras_bundles quantum_principal bundles_hopf algebra,"['hopf algebras', 'bundles quantum', 'principal bundles', 'hopf algebra', 'hopf algebra symmetry', 'hopf algebra mathbb', 'principal bundle', 'hopf galois extensions', 'hopf fibration', 'crossed product algebras']","['Differential calculi on quantum principal bundles in the Durdevic\n  approach   In this thesis we study the Durdevic theory of differential calculi on\nquantum principal bundles within the domain of noncommutative geometry.\nThroughout the exposition, an algebraic approach based on Hopf algebras is\nemployed. We begin by briefly recalling the foundational concepts of Hopf\nalgebras and comodule algebras. Hopf-Galois extensions are introduced, along\nwith an important correspondence result which relates crossed product algebras\nand cleft extensions. Differential calculus over algebras is reviewed, with a\nparticular focus on the covariant case. The Durdevic theory is presented in a\nmodern language. We compare this theory to existing literature on the topic. We\nextend the Durdevic theory and provide explicit realisations of quantum\nprincipal bundles and complete differential calculi on the noncommutative\nalgebraic 2-torus, the quantum Hopf fibration and on crossed product algebras,\nresulting in an original contribution within this thesis.\n', 'The Gauge Group of a Noncommutative Principal Bundle and Twist\n  Deformations   We study noncommutative principal bundles (Hopf-Galois extensions) in the\ncontext of coquasitriangular Hopf algebras and their monoidal category of\ncomodule algebras. When the total space is quasi-commutative, and thus the base\nspace subalgebra is central, we define the gauge group as the group of vertical\nautomorphisms or equivalently as the group of equivariant algebra maps. We\nstudy Drinfeld twist (2-cocycle) deformations of Hopf-Galois extensions and\nshow that the gauge group of the twisted extension is isomorphic to the gauge\ngroup of the initial extension. In particular, noncommutative principal bundles\narising via twist deformation of commutative principal bundles have classical\ngauge group. We illustrate the theory with a few examples.\n', ""Gauge transformations on quantum principal bundles We understand quantum principal bundle as faithfully flat Hopf--Galois extensions, with a structure Hopf algebra coacting on a total space algebra and with base algebra given by the coinvariant elements. To endow such bundles with a compatible differential structure, one requires the coaction to extend as a morphism of differential graded algebras. This leads to an exact noncommutative Atiyah sequence, a graded Hopf--Galois extension of differential forms and a canonical braiding on total space forms such that the latter are graded-braided commutative. We recall this approach to noncommutative differential geometry and further discuss the extension of quantum gauge transformations, in the sense of Brzezi\\'nski, to differential forms. In this way we obtain an action of quantum gauge transformations on connections of the quantum principal bundle and their curvature. Explicit examples, such as the noncommutative 2-torus, the quantum Hopf fibration and smash product algebras are discussed.""]","[('hopf algebras', 0.6210423707962036), ('bundles quantum', 0.6106422543525696), ('principal bundles', 0.577938437461853), ('hopf algebra', 0.5685757994651794), ('hopf algebra symmetry', 0.5423516631126404), ('hopf algebra mathbb', 0.5364381074905396), ('principal bundle', 0.533054530620575), ('hopf galois extensions', 0.5127447843551636), ('hopf fibration', 0.5104893445968628), ('crossed product algebras', 0.5034931898117065)]"
1653,1653,17,1653_groups polynomial time_isomorphism testing_isomorphic groups_groups isomorphic,"['groups polynomial time', 'isomorphism testing', 'isomorphic groups', 'groups isomorphic', 'non isomorphic groups', 'isomorphism groups', 'groups corresponding', 'groups extensions', 'isomorphism test', 'groups abelian groups']","['Efficient Isomorphism Testing for a Class of Group Extensions   The group isomorphism problem asks whether two given groups are isomorphic or\nnot. Whereas the case where both groups are abelian is well understood and can\nbe solved efficiently, very little is known about the complexity of isomorphism\ntesting for nonabelian groups. In this paper we study this problem for a class\nof groups corresponding to one of the simplest ways of constructing nonabelian\ngroups from abelian groups: the groups that are extensions of an abelian group\nA by a cyclic group of order m. We present an efficient algorithm solving the\ngroup isomorphism problem for all the groups of this class such that the order\nof A is coprime with m. More precisely, our algorithm runs in time almost\nlinear in the orders of the input groups and works in the general setting where\nthe groups are given as black-boxes.\n', 'Count-Free Weisfeiler--Leman and Group Isomorphism   We investigate the power of counting in Group Isomorphism. We first leverage\nthe count-free variant of the Weisfeiler--Leman Version I algorithm for groups\n(Brachter & Schweitzer, LICS 2020) in tandem with limited non-determinism and\nlimited counting to improve the parallel complexity of isomorphism testing for\nseveral families of groups. These families include:\n  - Direct products of non-Abelian simple groups.\n  - Coprime extensions, where the normal Hall subgroup is Abelian and the\ncomplement is an $O(1)$-generated solvable group with solvability class\n$\\text{poly} \\log \\log n$. This notably includes instances where the complement\nis an $O(1)$-generated nilpotent group. This problem was previously known to be\nin $\\textsf{P}$ (Qiao, Sarma, & Tang, STACS 2011), and the complexity was\nrecently improved to $\\textsf{L}$ (Grochow & Levet, FCT 2023).\n  - Graphical groups of class $2$ and exponent $p > 2$ (Mekler, J. Symb. Log.,\n1981) arising from the CFI and twisted CFI graphs (Cai, F\\""urer, & Immerman,\nCombinatorica 1992) respectively. In particular, our work improves upon\nprevious results of Brachter & Schweitzer (LICS 2020).\n  We finally show that the $q$-ary count-free pebble game is unable to\ndistinguish even Abelian groups. This extends the result of Grochow & Levet\n(ibid), who established the result in the case of $q = 1$. The general theme is\nthat some counting appears necessary to place Group Isomorphism into\n$\\textsf{P}$.\n', ""On the Parallel Complexity of Group Isomorphism via Weisfeiler-Leman   In this paper, we show that the constant-dimensional Weisfeiler-Leman\nalgorithm for groups (Brachter & Schweitzer, LICS 2020) can be fruitfully used\nto improve parallel complexity upper bounds on isomorphism testing for several\nfamilies of groups. In particular, we show:\n  - Groups with an Abelian normal Hall subgroup whose complement is\n$O(1)$-generated are identified by constant-dimensional Weisfeiler-Leman using\nonly a constant number of rounds. This places isomorphism testing for this\nfamily of groups into $\\textsf{L}$; the previous upper bound for isomorphism\ntesting was $\\textsf{P}$ (Qiao, Sarma, & Tang, STACS 2011).\n  - We use the individualize-and-refine paradigm to obtain an isomorphism test\nfor groups without Abelian normal subgroups by $\\textsf{SAC}$ circuits of depth\n$O(\\log n)$ and size $n^{O(\\log \\log n)}$, previously only known to be in\n$\\textsf{P}$ (Babai, Codenotti, \\& Qiao, ICALP 2012) and $\\mathsf{quasiSAC}^1$\n(Chattopadhyay, Tor\\'an, \\& Wagner, ACM Trans. Comput. Theory, 2013).\n  - We extend a result of Brachter \\& Schweitzer (ESA, 2022) on direct products\nof groups to the parallel setting. Namely, we also show that Weisfeiler--Leman\ncan identify direct products in parallel, provided it can identify each of the\nindecomposable direct factors in parallel. They previously showed the analogous\nresult for $\\textsf{P}$.\n  We finally consider the count-free Weisfeiler--Leman algorithm, where we show\nthat count-free WL is unable to even distinguish Abelian groups in\npolynomial-time. Nonetheless, we use count-free WL in tandem with bounded\nnon-determinism and limited counting to obtain a new upper bound of\n$\\beta_{1}\\textsf{MAC}^{0}(\\textsf{FOLL})$ for isomorphism testing of Abelian\ngroups. This improves upon the previous $\\textsf{TC}^{0}(\\textsf{FOLL})$ upper\nbound due to Chattopadhyay, Tor\\'an, \\& Wagner (ibid.).\n""]","[('groups polynomial time', 0.5860987901687622), ('isomorphism testing', 0.5635915994644165), ('isomorphic groups', 0.5609478950500488), ('groups isomorphic', 0.5542173385620117), ('non isomorphic groups', 0.5311180949211121), ('isomorphism groups', 0.5194455981254578), ('groups corresponding', 0.5170578956604004), ('groups extensions', 0.5073601603507996), ('isomorphism test', 0.5007146000862122), ('groups abelian groups', 0.4936803877353668)]"
1654,1654,17,1654_benford law_benford_concrete examples presented_law distribution,"['benford law', 'benford', 'concrete examples presented', 'law distribution', 'numbers often', 'generalized law', 'well known sequences', 'base invariant', 'sequences well known', 'distribution obeys']","[""The Mathematics of Benford's Law -- A Primer   This article provides a concise overview of the main mathematical theory of\nBenford's law in a form accessible to scientists and students who have had\nfirst courses in calculus and probability. In particular, one of the main\nobjectives here is to aid researchers who are interested in applying Benford's\nlaw, and need to understand general principles clarifying when to expect the\nappearance of Benford's law in real-life data and when not to expect it. A\nsecond main target audience is students of statistics or mathematics, at all\nlevels, who are curious about the mathematics underlying this surprising and\nrobust phenomenon, and may wish to delve more deeply into the subject. This\nsurvey of the fundamental principles behind Benford's law includes many basic\nexamples and theorems, but does not include the proofs or the most general\nstatements of the theorems; rather it provides precise references where both\nmay be found.\n"", 'Base Dependence of Benford Random Variables   A random variable X that is base b Benford will not in general be base c\nBenford when c is not equal to b. This paper builds on two of my earlier papers\nand is an attempt to cast some light on the issue of base dependence. Following\nsome introductory material, the ""Benford spectrum"" of a positive random\nvariable is introduced and known analytic results about Benford spectra are\nsummarized. Some standard machinery for a ""Benford analysis"" is introduced and\ncombined with my method of ""seed functions"" to yield tools to analyze the base\nc Benford properties of a base b Benford random variable. Examples are\ngenerated by applying these general methods to several families of Benford\nrandom variables. Berger and Hill\'s concept of ""base-invariant significant\ndigits"" is discussed. Some potential extensions are sketched.\n', 'A local Benford Law for a class of arithmetic sequences   It is well-known that sequences such as the Fibonacci numbers and the\nfactorials satisfy Benford\'s Law, that is, leading digits in these sequences\noccur with frequencies given by $P(d)=\\log_{10}(1+1/d)$, $d=1,2,\\dots,9$. In\nthis paper, we investigate leading digit distributions of arithmetic sequences\nfrom a local point of view. We call a sequence locally Benford distributed of\norder $k$ if, roughly speaking, $k$-tuples of consecutive leading digits behave\nlike $k$ independent Benford-distributed digits. This notion refines that of a\nBenford distributed sequence, and it provides a way to quantify the extent to\nwhich the Benford distribution persists at the local level. Surprisingly, most\nsequences known to satisfy Benford\'s Law have rather poor local distribution\nproperties. In our main result we establish, for a large class of arithmetic\nsequences, a ""best-possible"" local Benford Law, that is, we determine the\nmaximal value $k$ such that the sequence is locally Benford distributed of\norder $k$. The result applies, in particular, to sequences of the form\n$\\{a^n\\}$, $\\{a^{n^d}\\}$, and $\\{n^{\\beta} a^{n^\\alpha}\\}$, as well as the\nsequence of factorials $\\{n!\\}$ and similar iterated product sequences.\n']","[('benford law', 0.6783125996589661), ('benford', 0.5376490354537964), ('concrete examples presented', 0.32919952273368835), ('law distribution', 0.3237725496292114), ('numbers often', 0.31047970056533813), ('generalized law', 0.30655890703201294), ('well known sequences', 0.29782426357269287), ('base invariant', 0.291079580783844), ('sequences well known', 0.2900848984718323), ('distribution obeys', 0.28079813718795776)]"
1655,1655,17,1655_generalized chern simons_solutions chern simons_chern simons higgs_generalized chern,"['generalized chern simons', 'solutions chern simons', 'chern simons higgs', 'generalized chern', 'solutions chern', 'simons higgs', 'graph laplacian', 'chern simons', 'finite connected graph', 'connected finite graph']","['Existence of solutions to a generalized self-dual Chern-Simons equation\n  on finite graphs   Let $G=(V,E)$ be a connected finite graph. We study the existence of\nsolutions for the following generalized Chern-Simons equation on $G$\n\\begin{equation*}\n  \\Delta u=\\lambda \\mathrm{e}^{u}\\left(\\mathrm{e}^{u}-1\\right)^{5}+4 \\pi\n\\sum_{s=1}^{N} \\delta_{p_{s}} \\quad , \\end{equation*} where $\\lambda>0$,\n$\\delta_{p_{s}}$ is the Dirac mass at the vetex $p_s$, and $p_1, p_2,\\dots,\np_N$ are arbitrarily chosen distinct vertices on the graph. We show that there\nexists a critial value $\\hat{\\lambda}$ such that when $\\lambda >\n\\hat{\\lambda}$, the generalized Chern-Simons equation has at least two\nsolutions, when $\\lambda = \\hat{\\lambda}$, the generalized Chern-Simons\nequation has a solution, and when $\\lambda < \\hat\\lambda$, the generalized\nChern-Simons equation has no solution.\n', 'Brouwer degree for Chern-Simons Higgs models on finite graphs   Let $G=(V, E)$ be a finite connected graph, where $V$ denotes the set of\nvertices and $E$ denotes the set of edges. We revisit the following\nChern-Simons Higgs\n  model,\n  \\begin{equation*}\n  \\Delta u=\\lambda \\mathrm{e}^u\\left(\\mathrm{e}^u-1\\right)+f \\ \\text {in} \\ V,\n  \\end{equation*}\n  where $\\Delta$ is the graph Laplacian, $\\lambda$ is a real number and $f$ is\na function defined on $V$. Firstly, when $\\lambda \\int_V f \\mathrm{d} \\mu \\neq\n0$, we find that the odevity of the number of vertices in the graph affects the\nnumber of solutions. Then by calculating the topological degree and using the\nrelationship between the degree and the critical group of a related functional,\nwe obtain the existence of multiple solutions. Also we study the existence of\nsolutions when $\\lambda \\int_V f \\mathrm{d} \\mu=0$. These findings extend the\nwork of Huang\n  et al. [Comm Math Phys 377:613-621 (2020)], Hou and Sun [Calc Var 61:139\n(2022)] and Li et al. [Calc Var 63:81 (2024)]. Similarly, for the generalized\nChern-Simons Higgs model, we obtain the same results. Moreover, this method is\nalso applied to the Chern-Simons Higgs system, yielding partial results for the\nexistence of multiple solutions. To our knowledge, this is the first instance\nwhere it has been concluded that an equation on graphs can have at least three\ndistinct solutions. We think that our results will be valuable for studying the\nmultiplicity of solutions to analogous equations on graphs.\n', 'Existence of solutions to Chern-Simons-Higgs equations on graphs   Let $G=(V,E)$ be a finite graph. We consider the existence of solutions to a\ngeneralized Chern-Simons-Higgs equation $$ \\Delta u=-\\lambda e^{g(u)}\\left(\ne^{g(u)}-1\\right)^2+4\\pi\\sum\\limits_{j=1}^{N}\\delta_{p_j} $$ on $G$, where\n$\\lambda$ is a positive constant; $g(u)$ is the inverse function of\n$u=f(\\upsilon)=1+\\upsilon-e^{\\upsilon}$ on $(-\\infty, 0]$; $N$ is a positive\ninteger; $p_1, p_2, \\cdot\\cdot\\cdot, p_N$ are distinct vertices of $V$ and\n$\\delta_{p_j}$ is the Dirac delta mass at $p_j$. We prove that there is\ncritical value $\\lambda_c$ such that the generalized Chern-Simons-Higgs\nequation has a solution if and only if $\\lambda\\geq \\lambda_c$ . We also prove\nthe existence of solutions to the Chern-Simons-Higgs equation\n  $$ \\Delta u=\\lambda e^{u}(e^{u}-1)+4\\pi\\sum\\limits_{j=1}^{N}\\delta_{p_j} $$\non $G$ when $\\lambda$ takes the critical value $\\lambda_c$ and this completes\nthe results of An Huang, Yong Lin and Shing-Tung Yau (Commun. Math. Phys. 377,\n613-621 (2020)).\n']","[('generalized chern simons', 0.6018987894058228), ('solutions chern simons', 0.598074734210968), ('chern simons higgs', 0.554308295249939), ('generalized chern', 0.4666554927825928), ('solutions chern', 0.46035847067832947), ('simons higgs', 0.45757150650024414), ('graph laplacian', 0.4341464638710022), ('chern simons', 0.41937899589538574), ('finite connected graph', 0.36018866300582886), ('connected finite graph', 0.3594607710838318)]"
1656,1656,17,1656_riemannian orbifold_hodge laplacians_orbifolds discuss_orbifolds,"['riemannian orbifold', 'hodge laplacians', 'orbifolds discuss', 'orbifolds', 'singularities manifolds', 'hodge laplacian', 'orbifold', 'laplacian forms', 'harmonic forms', 'manifolds long']","['Approximating orbifold spectra using collapsing connected sums   For a closed Riemannian orbifold $O$, we compare the spectra of the\nLaplacian, acting on functions or differential forms, to the Neumann spectra of\nthe orbifold with boundary given by a domain $U$ in $O$ whose boundary is a\nsmooth manifold. Generalizing results of several authors, we prove that the\nmetric of $O$ can be perturbed to ensure that the first $N$ eigenvalues of $U$\nand $O$ are arbitrarily close to one another. This involves a generalization of\nthe Hodge decomposition to the case of orbifolds with manifold boundary. Using\nthese results, we study the behavior of the Laplace spectrum on functions or\nforms of a connected sum of two Riemannian orbifolds as one orbifold in the\npair is collapsed to a point. We show that the limits of the eigenvalues of the\nconnected sum are equal to those of the non-collapsed orbifold in the pair. In\ndoing so, we prove the existence of a sequence of orbifolds with singular\npoints whose eigenvalue spectra come arbitrarily close to the spectrum of a\nmanifold, and a sequence of manifolds whose eigenvalue spectra come arbitrarily\nclose to the eigenvalue spectrum of an orbifold with singular points. We also\nconsider the question of prescribing the first part of the spectrum of an\norientable orbifold.\n', 'Do the Hodge spectra distinguish orbifolds from manifolds? Part 2   In \\cite{GGKM-SSS} we examined the relationship between the singular set of a\ncompact Riemannian orbifold and the spectrum of the Hodge Laplacian on\n$p$-forms by computing the heat invariants associated to the $p$-spectrum. We\nshowed that the heat invariants of the $0$-spectrum together with those of the\n$1$-spectrum for the corresponding Hodge Laplacians are sufficient to\ndistinguish orbifolds from manifolds as long as the singular sets have\ncodimension $\\le 3.$ This is enough to distinguish orbifolds from manifolds for\ndimension $\\le 3.$ Here we give both positive and negative inverse spectral\nresults for the individual $p$-spectra considered separately. For example, we\ngive conditions on the codimension of the singular set which guarantee that the\nvolume of the singular set is determined, and in many cases we show by\nproviding counterexamples that the conditions are sharp.\n', 'Do the Hodge spectra distinguish orbifolds from manifolds? Part 1   We examine the relationship between the singular set of a compact Riemannian\norbifold and the spectrum of the Hodge Laplacian on $p$-forms by computing the\nheat invariants associated to the $p$-spectrum. We show that the heat\ninvariants of the $0$-spectrum together with those of the $1$-spectrum for the\ncorresponding Hodge Laplacians are sufficient to distinguish orbifolds with\nsingularities from manifolds as long as the singular sets have codimension $\\le\n3.$ This is enough to distinguish orbifolds from manifolds for dimension $\\le\n3.$\n']","[('riemannian orbifold', 0.6773965358734131), ('hodge laplacians', 0.5527163147926331), ('orbifolds discuss', 0.5349484086036682), ('orbifolds', 0.5303100347518921), ('singularities manifolds', 0.49953213334083557), ('hodge laplacian', 0.4942259192466736), ('orbifold', 0.48316094279289246), ('laplacian forms', 0.4758460223674774), ('harmonic forms', 0.46080705523490906), ('manifolds long', 0.4605547785758972)]"
1657,1657,17,1657_riemannian manifolds boundary_riemannian manifold boundary_riemannian metrics_gromov hausdorff convergence,"['riemannian manifolds boundary', 'riemannian manifold boundary', 'riemannian metrics', 'gromov hausdorff convergence', 'spaces riemannian manifolds', 'riemannian manifolds', 'gromov hausdorff limits', 'riemannian manifold', 'oriented riemannian manifold', 'spaces riemannian']","['Intrinsic Flat Stability of Manifolds with Boundary where Volume\n  Converges and Distance is Bounded Below   Given a compact, connected, and oriented manifold with boundary $M$ and a\nsequence of smooth Riemannian metrics defined on it, $g_j$, we prove volume\npreserving intrinsic flat convergence of the sequence to the smooth Riemannian\nmetric $g_0$ provided $g_j$ always measures vectors strictly larger than or\nequal to $g_0$, the diameter of $g_j$ is uniformly bounded, the volume of $g_j$\nconverges to the volume of $g_0$, and $L^{\\frac{m-1}{2}}$ convergence of the\nmetrics restricted to the boundary. Many examples are reviewed which justify\nand explain the intuition behind these hypotheses. These examples also show\nthat uniform, Lipschitz, and Gromov-Hausdorff convergence are not appropriate\nin this setting. Our results provide a new rigorous method of proving some\nspecial cases of the intrinsic flat stability of the positive mass theorem.\n', 'Volume Above Distance Below with Boundary II   It was shown by B. Allen, R. Perales, and C. Sormani that on a closed\nmanifold where the diameter of a sequence of Riemannian metrics is bounded, if\nthe volume converges to the volume of a limit manifold, and the sequence of\nRiemannian metrics are $C^0$ converging from below then one can conclude volume\npreserving Sormani-Wenger Intrinsic Flat convergence. The result was extended\nto manifolds with boundary by B. Allen and R. Perales by a doubling with necks\nprocedure which produced a closed manifold and reduced the case with boundary\nto the case without boundary. The consequence of the doubling with necks\nprocedure was requiring a stronger condition than necessary on the boundary.\nUsing the estimates for the Sormani-Wenger Intrinsic Flat distance on manifolds\nwith boundary developed by B. Allen and R. Perales, we show that only a bound\non the area of the boundary is needed in order to conclude volume preserving\nintrinsic flat convergence for manifolds with boundary. We also provide an\nexample which shows that one should not expect convergence without a bound on\narea.\n', 'Convergence of Manifolds and Metric Spaces with Boundary   We study sequences of oriented Riemannian manifolds with boundary and, more\ngenerally, integral current spaces and metric spaces with boundary.\n{\\color{blue}For a metric space, we define its boundary to be the completion of\nthe space minus the space. We impose conditions on these spaces in order to get\nGromov-Hausdorff (GH) subconvergence. By adding some other conditions} we prove\ntheorems demonstrating that the Gromov-Hausdorff (GH) and Sormani-Wenger\nIntrinsic Flat (SWIF) limits of sequences of such metric spaces agree. Thus in\nparticular the limit spaces we get are countably $\\mathcal{H}^n$ rectifiable\nspaces. From these we derive GH compactness theorems for sequences of\nRiemannian manifolds with boundary where both the GH and SWIF limits agree.\n  For sequences of Riemannian manifolds with boundary we only require\nnonnegative Ricci curvature, upper bounds on volume, noncollapsing conditions\non the interior of the manifold and diameter controls on the level sets near\nthe boundary.\n']","[('riemannian manifolds boundary', 0.5938604474067688), ('riemannian manifold boundary', 0.5800509452819824), ('riemannian metrics', 0.560027003288269), ('gromov hausdorff convergence', 0.5599774718284607), ('spaces riemannian manifolds', 0.5576145052909851), ('riemannian manifolds', 0.5547784566879272), ('gromov hausdorff limits', 0.5374077558517456), ('riemannian manifold', 0.5269143581390381), ('oriented riemannian manifold', 0.5152053833007812), ('spaces riemannian', 0.5151768922805786)]"
1658,1658,17,1658_chern simons theory_simons theory_gauge theories_abelian gauge theories,"['chern simons theory', 'simons theory', 'gauge theories', 'abelian gauge theories', 'knots manifolds', 'chern simons', 'su chern simons', 'gauge theories mathbb', 'hyperbolic knot', 'invariants manifolds']","[""Peacock patterns and resurgence in complex Chern-Simons theory   The partition function of complex Chern-Simons theory on a 3-manifold with\ntorus boundary reduces to a finite dimensional state-integral which is a\nholomorphic function of a complexified Planck's constant $\\tau$ in the complex\ncut plane and an entire function of a complex parameter $u$. This gives rise to\na vector of factorially divergent perturbative formal power series whose Stokes\nrays form a peacock-like pattern in the complex plane.\n  We conjecture that these perturbative series are resurgent, their\ntrans-series involve two non-perturbative variables, their Stokes automorphism\nsatisfies a unique factorization property and that it is given explicitly in\nterms of a fundamental matrix solution to a (dual) linear $q$-difference\nequation. We further conjecture that entries of the Stokes automorphism matrix\nare the 3D-indices of Dimofte-Gaiotto-Gukov. We provide proofs of our\nstatements regarding the $q$-difference equations and their properties of their\nfundamental solutions and illustrate our conjectures regarding the Stokes\nmatrices with numerical calculations for the two simplest hyperbolic $4_1$ and\n$5_2$ knots.\n"", 'Lie groups and Chern-Simons Theory   Witten introduced classical Chern-Simons theory to topology in 1989, when he\ndefined an invariant for knots in 3-manifolds by an integral over a certain\ninfinite-dimensional space, which up to today have not been entirely\nunderstood. However, they motivated lots of interesting questions and results\nin knot theory and low-dimensional topology, as well as the development of\nentirely new fields.\n  These are lecture notes for a course in Lie groups and Chern-Simons Theory\naimed at graduate students.\n', 'Going to the Other Side via the Resurgent Bridge   Using resurgent analysis we offer a novel mathematical perspective on a\ncurious bijection (duality) that has many potential applications ranging from\nthe theory of vertex algebras to the physics of SCFTs in various dimensions, to\nq-series invariants in low-dimensional topology that arise, e.g. in Vafa-Witten\ntheory and in non-perturbative completion of complex Chern-Simons theory. In\nparticular, we introduce explicit numerical algorithms that efficiently\nimplement this bijection. This bijection is founded on preservation of\nrelations, a fundamental property of resurgent functions. Using resurgent\nanalysis we find new structures and patterns in complex Chern-Simons theory on\nclosed hyperbolic 3-manifolds obtained by surgeries on hyperbolic twist knots.\nThe Borel plane exhibits several intriguing hints of a new form of\nintegrability. An important role in this analysis is played by the twisted\nAlexander polynomials and the adjoint Reidemeister torsion, which help us\ndetermine the Stokes data. The method of singularity elimination enables\nextraction of geometric data even for very distant Borel singularities, leading\nto detailed non-perturbative information from perturbative data. We also\nintroduce a new double-scaling limit to probe 0-surgeries from the limiting\n$r\\to\\infty$ behavior of 1/r surgeries, and apply it to the family of\nhyperbolic twist knots.\n']","[('chern simons theory', 0.6655904054641724), ('simons theory', 0.5430595278739929), ('gauge theories', 0.5158005952835083), ('abelian gauge theories', 0.4744856059551239), ('knots manifolds', 0.4654366075992584), ('chern simons', 0.45781317353248596), ('su chern simons', 0.44336700439453125), ('gauge theories mathbb', 0.4387955367565155), ('hyperbolic knot', 0.42873042821884155), ('invariants manifolds', 0.41437339782714844)]"
1659,1659,17,1659_well posedness solutions_posedness solutions_posed sobolev_prandtl boundary layer,"['well posedness solutions', 'posedness solutions', 'posed sobolev', 'prandtl boundary layer', 'prandtl boundary', 'local well posedness', 'posed sobolev spaces', 'global well posedness', 'boundary layer equations', 'shear flow']","['Quantitative aspects on the ill-posedness of the Prandtl and hyperbolic\n  Prandtl equations   We address a physically-meaningful extension of the Prandtl system, also\nknown as hyperbolic Prandtl equations. We show that the linearised model around\na non-monotonic shear flow is ill-posed in any Sobolev spaces. Indeed, shortly\nin time, we generate solutions that experience a dispersion relation of order\nk^(1/3) in the frequencies of the tangential direction, akin the pioneering\nresult of Gerard-Varet and Dormy in [10] for Prandtl (where the dispersion was\nof order k^(1/2)). We emphasise however that this growth rate does not imply\nill-posedness in Gevrey-class m, with m > 3 and we relate also these aspects to\nthe original Prandtl equations in Gevrey-class m, with m > 2. By relaxing\ncertain assumptions on the shear flow and on the solutions, namely allowing for\nunbounded flows in the vertical direction, we however determine a suitable\nshear flow for the mentioned ill-posedness in Gevrey spaces.\n', 'Global Well-posedness of a Prandtl Model from MHD in Gevrey Function\n  Spaces   We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime\nthat has a damping term due to the effect of the Hartmann boundary layer. A\nglobal-in-time well-posedness is obtained in the Gevrey function space with the\noptimal index $2$. The proof is based on a cancellation mechanism through some\nauxiliary functions from the study of the Prandtl equation and an observation\nabout the structure of the loss of one order tangential derivatives through\ntwice operations of the Prandtl operator\n', 'Prandtl Equations and Related Boundary Layer Equations   This book aims to present some recent results on Prandtl equations and MHD\nboundary layer equations.\n  This book is essentially divided into two parts. Chapter 1 as the first part\nsystematically surveys the results till 2020 on Prandtl equations and MHD\nboundary layer equations. Chapter 2 to 6 are the main part of the book, which\npresents the local and the global well-posedness of solutions to the Prandtl\nequations and MHD boundary layer equations. In detail, Chapter 2 is concerned\nwith global well-posedness of solutions to the 2D Prandtl-Hartmann equations in\nan analytic framework. Chapter 3 investigates the local existence of solutions\nto the 2D Prandtl equations in a weighted Sobolev space. Chapter 4 studies the\nlocal well-posedness of solutions to the 2D mixed Prandtl equations in a\nSobolev space without monotonicity and lower bound. Chapter 5 is concerned with\nglobal existence of solutions to the 2D magnetic Prandtl equations in the\nPrandtl-Hartmann regime. Chapter 6 proves the local existence of solutions to\nthe 3D Prandtl equations with a special structure.\n  Mathematicians and physicists who are interested in fluid dynamics will find\nthis book helpful.\n']","[('well posedness solutions', 0.5375322103500366), ('posedness solutions', 0.5088574886322021), ('posed sobolev', 0.5052890181541443), ('prandtl boundary layer', 0.4999767541885376), ('prandtl boundary', 0.48841241002082825), ('local well posedness', 0.4810272753238678), ('posed sobolev spaces', 0.4737415015697479), ('global well posedness', 0.47284165024757385), ('boundary layer equations', 0.4568966031074524), ('shear flow', 0.44248464703559875)]"
1660,1660,17,1660_interacting fermions_fermionic systems_random phase approximation_fermi gas,"['interacting fermions', 'fermionic systems', 'random phase approximation', 'fermi gas', 'hartree fock theory', 'fermions', 'fock theory', 'strongly interacting', 'fermionic', 'correlation energy']","['The Random Phase Approximation for Interacting Fermi Gases in the\n  Mean-Field Regime   We present a general approach to justify the random phase approximation for\nthe homogeneous Fermi gas in three dimensions in the mean-field scaling regime.\nWe consider a system of $N$ fermions on a torus, interacting via a two-body\nrepulsive potential proportional to $N^{-\\frac{1}{3}}$. In the limit\n$N\\to\\infty$, we derive the exact leading order of the correlation energy and\nthe bosonic elementary excitations of the system, which are consistent with the\nprediction of the random phase approximation in the physics literature.\n', 'Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the\n  Mean-Field Regime   While Hartree-Fock theory is well established as a fundamental approximation\nfor interacting fermions, it has been unclear how to describe corrections to it\ndue to many-body correlations. In this paper we start from the Hartree-Fock\nstate given by plane waves and introduce collective particle-hole pair\nexcitations. These pairs can be approximately described by a bosonic quadratic\nHamiltonian. We use Bogoliubov theory to construct a trial state yielding a\nrigorous Gell-Mann-Brueckner-type upper bound to the ground state energy. Our\nresult justifies the random phase approximation in the mean-field scaling\nregime, for repulsive, regular interaction potentials.\n', 'Correlation Energy of a Weakly Interacting Fermi Gas   We derive rigorously the leading order of the correlation energy of a Fermi\ngas in a scaling regime of high density and weak interaction. The result\nverifies the prediction of the random-phase approximation. Our proof refines\nthe method of collective bosonization in three dimensions. We approximately\ndiagonalize an effective Hamiltonian describing approximately bosonic\ncollective excitations around the Hartree-Fock state, while showing that\ngapless and non-collective excitations have only a negligible effect on the\nground state energy.\n']","[('interacting fermions', 0.6513094902038574), ('fermionic systems', 0.5510376691818237), ('random phase approximation', 0.4676695764064789), ('fermi gas', 0.4666144549846649), ('hartree fock theory', 0.42978936433792114), ('fermions', 0.4250379204750061), ('fock theory', 0.4056689143180847), ('strongly interacting', 0.40067338943481445), ('fermionic', 0.39635637402534485), ('correlation energy', 0.3905358910560608)]"
1661,1661,17,1661_optimal stopping problems_deep neural_deep learning_novel deep learning,"['optimal stopping problems', 'deep neural', 'deep learning', 'novel deep learning', 'high dimensional optimal', 'deep neural networks', 'optimal stopping', 'randomized neural networks', 'option pricing', 'backward stochastic differential']","['DNN Expression Rate Analysis of High-dimensional PDEs: Application to\n  Option Pricing   We analyze approximation rates by deep ReLU networks of a class of\nmulti-variate solutions of Kolmogorov equations which arise in option pricing.\nKey technical devices are deep ReLU architectures capable of efficiently\napproximating tensor products. Combining this with results concerning the\napproximation of well behaved (i.e. fulfilling some smoothness properties)\nunivariate functions, this provides insights into rates of deep ReLU\napproximation of multi-variate functions with tensor structures. We apply this\nin particular to the model problem given by the price of a European maximum\noption on a basket of $d$ assets within the Black-Scholes model for European\nmaximum option pricing. We prove that the solution to the $d$-variate option\npricing problem can be approximated up to an $\\varepsilon$-error by a deep ReLU\nnetwork with depth $\\mathcal{O}\\big(\\ln(d)\\ln(\\varepsilon^{-1})+\\ln(d)^2\\big)$\nand $\\mathcal{O}\\big(d^{2+\\frac{1}{n}}\\varepsilon^{-\\frac{1}{n}}\\big)$ non-zero\nweights, where $n\\in \\mathbb{N}$ is arbitrary (with the constant implied in\n$\\mathcal{O}(\\cdot)$ depending on $n$). The techniques developed in the\nconstructive proof are of independent interest in the analysis of the\nexpressive power of deep neural networks for solution manifolds of PDEs in high\ndimension.\n', 'Solving high-dimensional optimal stopping problems using deep learning   Nowadays many financial derivatives, such as American or Bermudan options,\nare of early exercise type. Often the pricing of early exercise options gives\nrise to high-dimensional optimal stopping problems, since the dimension\ncorresponds to the number of underlying assets. High-dimensional optimal\nstopping problems are, however, notoriously difficult to solve due to the\nwell-known curse of dimensionality. In this work, we propose an algorithm for\nsolving such problems, which is based on deep learning and computes, in the\ncontext of early exercise option pricing, both approximations of an optimal\nexercise strategy and the price of the considered option. The proposed\nalgorithm can also be applied to optimal stopping problems that arise in other\nareas where the underlying stochastic process can be efficiently simulated. We\npresent numerical results for a large number of example problems, which include\nthe pricing of many high-dimensional American and Bermudan options, such as\nBermudan max-call options in up to 5000 dimensions. Most of the obtained\nresults are compared to reference values computed by exploiting the specific\nproblem design or, where available, to reference values from the literature.\nThese numerical results suggest that the proposed algorithm is highly effective\nin the case of many underlyings, in terms of both accuracy and speed.\n', ""Deep neural network expressivity for optimal stopping problems   This article studies deep neural network expression rates for optimal\nstopping problems of discrete-time Markov processes on high-dimensional state\nspaces. A general framework is established in which the value function and\ncontinuation value of an optimal stopping problem can be approximated with\nerror at most $\\varepsilon$ by a deep ReLU neural network of size at most\n$\\kappa d^{\\mathfrak{q}} \\varepsilon^{-\\mathfrak{r}}$. The constants\n$\\kappa,\\mathfrak{q},\\mathfrak{r} \\geq 0$ do not depend on the dimension $d$ of\nthe state space or the approximation accuracy $\\varepsilon$. This proves that\ndeep neural networks do not suffer from the curse of dimensionality when\nemployed to solve optimal stopping problems. The framework covers, for example,\nexponential L\\'evy models, discrete diffusion processes and their running\nminima and maxima. These results mathematically justify the use of deep neural\nnetworks for numerically solving optimal stopping problems and pricing American\noptions in high dimensions.\n""]","[('optimal stopping problems', 0.47027909755706787), ('deep neural', 0.4695504903793335), ('deep learning', 0.4666104018688202), ('novel deep learning', 0.4663047790527344), ('high dimensional optimal', 0.46573367714881897), ('deep neural networks', 0.45041435956954956), ('optimal stopping', 0.4352826774120331), ('randomized neural networks', 0.42907631397247314), ('option pricing', 0.41173914074897766), ('backward stochastic differential', 0.4042169749736786)]"
1662,1662,17,1662_moore penrose inverses_moore penrose inverse_penrose inverses_tensor generalized,"['moore penrose inverses', 'moore penrose inverse', 'penrose inverses', 'tensor generalized', 'decomposition tensors', 'tensors', 'tensors product', 'order tensors', 'square tensor', 'product tensor']","['Weighted Moore-Penrose inverses of arbitrary-order tensors   Within the field of multilinear algebra, inverses and generalized inverses of\ntensors based on the Einstein product have been investigated over the past few\nyears. In this paper, we explore the singular value decomposition and full-rank\ndecomposition of arbitrary-order tensors using {\\it reshape} operation.\nApplying range and null space of tensors along with the reshape operation; we\nfurther study the Moore-Penrose inverse of tensors and their cancellation\nproperties via the Einstein product. Then we discuss weighted Moore-Penrose\ninverses of arbitrary-order tensors using such product. Following a specific\nalgebraic approach, a few characterizations and representations of these\ninverses are explored. In addition to this, we obtain a few necessary and\nsufficient conditions for the reverse-order law to hold for weighted\nMoore-Penrose inverses of arbitrary-order tensors.\n', 'On reverse-order law of tensors and its application to additive results\n  on Moore-Penrose inverse   The equality $(\\mc{A}\\n\\mc{B})^\\dagger = \\mc{B}^\\dagger \\n \\mc{A}^\\dagger$\nfor any two complex tensors $\\mc{A}$ and $\\mc{B}$ of arbitrary order, is called\nas the {\\it reverse-order law} for the Moore-Penrose inverse of arbitrary order\ntensors via the Einstein product. Panigrahy {\\it et al.} [Linear Multilinear\nAlgebra; 68 (2020), 246-264.] obtained several necessary and sufficient\nconditions to hold the reverse-order law for the Moore-Penrose inverse of\neven-order tensors via the Einstein product, very recently. This notion is\nrevisited here among other results. In this context, we present several new\ncharacterizations of the reverse-order law of arbitrary order tensors via the\nsame product. More importantly, we illustrate a result on the Moore-Penrose\ninverse of a sum of two tensors as an application of the reverse-order law\nwhich leaves an open problem. We recall the definition of the Frobenius norm\nand the spectral norm to illustrate a result for finding the additive\nperturbation bounds of the Moore-Penrose inverse under the Frobenius norm. We\nconclude our paper with the introduction of the notion of sub-proper splitting\nfor tensors which may help to find an iterative solution of a tensor\nmultilinear system.\n', 'The generalized inverses of tensors via the C-Product   This paper studies the issues about the generalized inverses of tensors under\nthe C-Product. The aim of this paper is threefold. Firstly, this paper present\nthe definition of the Moore-Penrose inverse, Drazin inverse of tensors under\nthe C-Product. Moreover, the inverse along a tensor is also introduced.\nSecondly, this paper gives some other expressions of the generalized inverses\nof tensors by using several decomposition forms of tensors. Finally, the\nalgorithms for the Moore-Penrose inverse, Drazin inverse of tensors and the\ninverse along a tensor are established.\n']","[('moore penrose inverses', 0.6767613887786865), ('moore penrose inverse', 0.6313438415527344), ('penrose inverses', 0.6278499364852905), ('tensor generalized', 0.6143368482589722), ('decomposition tensors', 0.6057254672050476), ('tensors', 0.6029298305511475), ('tensors product', 0.595966637134552), ('order tensors', 0.5934553742408752), ('square tensor', 0.5886436104774475), ('product tensor', 0.580403745174408)]"
1663,1663,17,1663_tychonoff spaces_locally convex spaces_locally convex space_spaces locally convex,"['tychonoff spaces', 'locally convex spaces', 'locally convex space', 'spaces locally convex', 'banach spaces', 'banach space', 'space banach space', 'tychonoff space', 'wallach spaces', 'convex spaces']","[""On complemented copies of the space $c_0$ in spaces $C_p(X,E)$   We study the question for which Tychonoff spaces $X$ and locally convex\nspaces $E$ the space $C_p(X,E)$ of continuous $E$-valued functions on $X$\ncontains a complemented copy of the space\n$(c_0)_p=\\{x\\in\\mathbb{R}^\\omega\\colon x(n)\\to0\\}$, both endowed with the\npointwise topology. We provide a positive answer for a vast class of spaces,\nextending classical theorems of Cembranos, Freniche, and Doma\\'nski and\nDrewnowski, proved for the case of Banach and Fr\\'echet spaces $C_k(X,E)$.\nAlso, for given infinite Tychonoff spaces $X$ and $Y$, we show that\n$C_p(X,C_p(Y))$ contains a complemented copy of $(c_0)_p$ if and only if any of\nthe spaces $C_p(X)$ and $C_p(Y)$ contains such a subspace.\n"", 'Locally convex spaces with the strong Gelfand-Phillips property   We introduce the strong Gelfand-Phillips property for locally convex spaces\nand give several characterizations of this property. We characterize the strong\nGelfand-Phillips property among locally convex spaces admitting a stronger\nBanach space topology. If $C_{\\mathcal T}(X)$ is a space of continuous\nfunctions on a Tychonoff space $X$, endowed with a locally convex topology\n$\\mathcal T$ between the pointwise topology and the compact-open topology,\nthen: (a) the space $C_{\\mathcal T}(X)$ has the strong Gelfand-Phillips\nproperty iff $X$ contains a compact countable subspace $K\\subseteq X$ of finite\nscattered height such that for every functionally bounded set $B\\subseteq X$\nthe complement $B\\setminus K$ is finite, (b) the subspace $C^b_{\\mathcal T}(X)$\nof $C_{\\mathcal T}(X)$ consisting of all bounded functions on $X$ has the\nstrong Gelfand-Phillips property iff $X$ is a compact countable space of finite\nscattered height.\n', 'Josefson-Nissenzweig property for $C_p$-spaces   The famous Rosenthal-Lacey theorem asserts that for each infinite compact\nspace $K$ the Banach space $C(K)$ admits a quotient which is either a copy of\n$c_{0}$ or $\\ell_{2}$. The aim of the paper is to study a natural variant of\nthis result for the space $C_{p}(K)$ of continuous real-valued maps on $K$ with\nthe pointwise topology. Following famous Josefson-Nissenzweig theorem for\ninfinite-dimensional Banach spaces we introduce a corresponding property\n(called Josefson-Nissenzweig property, briefly, the JNP) for $C_{p}$-spaces. We\nprove: For a Tychonoff space $X$ the space $C_p(X)$ satisfies the JNP if and\nonly if $C_p(X)$ has a quotient isomorphic to $c_{0}$ (with the product\ntopology of $\\mathbb R^\\mathbb{N}$) if and only if $C_{p}(X)$ contains a\ncomplemented subspace, isomorphic to $c_0$. For a pseudocompact space $X$ the\nspace $C_p(X)$ has the JNP if and only if $C_p(X)$ has a complemented\nmetrizable infinite-dimensional subspace. This applies to show that for a\nTychonoff space $X$ the space $C_p(X)$ has a complemented subspace isomorphic\nto $\\mathbb R^{\\mathbb N}$ or $c_0$ if and only if $X$ is not pseudocompact or\n$C_p(X)$ has the JNP. The space $C_{p}(\\beta\\mathbb{N})$ contains a subspace\nisomorphic to $c_0$ and admits a quotient isomorphic to $\\ell_{\\infty}$ but\nfails to have a quotient isomorphic to $c_{0}$. An example of a compact space\n$K$ without infinite convergent sequences with $C_{p}(K)$ containing a\ncomplemented subspace isomorphic to $c_{0}$ is constructed.\n']","[('tychonoff spaces', 0.6265951991081238), ('locally convex spaces', 0.6204878687858582), ('locally convex space', 0.5899201035499573), ('spaces locally convex', 0.5790086388587952), ('banach spaces', 0.5769381523132324), ('banach space', 0.5505716800689697), ('space banach space', 0.5413163900375366), ('tychonoff space', 0.5318831205368042), ('wallach spaces', 0.5117529630661011), ('convex spaces', 0.5005996227264404)]"
1664,1664,17,1664_threshold conjecture_perceptrons_algorithmic threshold_perceptron,"['threshold conjecture', 'perceptrons', 'algorithmic threshold', 'perceptron', 'statistical computational gap', 'satisfiability threshold', 'sharp threshold', 'threshold', 'computational gap', 'statistical computational']","['Critical Window of The Symmetric Perceptron   We study the critical window of the symmetric binary perceptron, or\nequivalently, combinatorial discrepancy. Consider the problem of finding a\nbinary vector $\\sigma$ satisfying $\\|A\\sigma\\|_\\infty \\le K$, where $A$ is an\n$\\alpha n \\times n$ matrix with iid Gaussian entries. For fixed $K$, at which\ndensities $\\alpha$ is this constraint satisfaction problem (CSP) satisfiable? A\nsharp threshold was recently established by Perkins and Xu, and Abbe, Li, and\nSly , answering this to first order. Namely, for each $K$ there exists an\nexplicit critical density $\\alpha_c$ so that for any fixed $\\epsilon > 0$, with\nhigh probability the CSP is satisfiable for $\\alpha n < (\\alpha_c - \\epsilon )\nn$ and unsatisfiable for $\\alpha n > (\\alpha_c + \\epsilon) n$. This corresponds\nto a bound of $o(n)$ on the size of the critical window.\n  We sharpen these results significantly, as well as provide exponential tail\nbounds. Our main result is that, perhaps surprisingly, the critical window is\nactually at most $O(\\log n)$. More precisely, with high probability the CSP is\nsatisfiable for $\\alpha n < \\alpha_c n -O(\\log n)$ and unsatisfiable for any\n$\\alpha n > \\alpha_c n + \\omega(1)$. This implies the symmetric perceptron has\nnearly the ""sharpest possible transition,"" adding it to a short list of CSP for\nwhich the critical window is rigorously known to be of near-constant width.\n', ""Binary perceptron: efficient algorithms can find solutions in a rare\n  well-connected cluster   It was recently shown that almost all solutions in the symmetric binary\nperceptron are isolated, even at low constraint densities, suggesting that\nfinding typical solutions is hard. In contrast, some algorithms have been shown\nempirically to succeed in finding solutions at low density. This phenomenon has\nbeen justified numerically by the existence of subdominant and dense connected\nregions of solutions, which are accessible by simple learning algorithms. In\nthis paper, we establish formally such a phenomenon for both the symmetric and\nasymmetric binary perceptrons. We show that at low constraint density\n(equivalently for overparametrized perceptrons), there exists indeed a\nsubdominant connected cluster of solutions with almost maximal diameter, and\nthat an efficient multiscale majority algorithm can find solutions in such a\ncluster with high probability, settling in particular an open problem posed by\nPerkins-Xu '21. In addition, even close to the critical threshold, we show that\nthere exist clusters of linear diameter for the symmetric perceptron, as well\nas for the asymmetric perceptron under additional assumptions.\n"", 'Distribution of the threshold for the symmetric perceptron   We derive an explicit distribution for the threshold sequence of the\nsymmetric binary perceptron with Gaussian disorder, proving that the critical\nwindow is of constant width.\n']","[('threshold conjecture', 0.4750823676586151), ('perceptrons', 0.469392329454422), ('algorithmic threshold', 0.4667651057243347), ('perceptron', 0.4332923889160156), ('statistical computational gap', 0.41108593344688416), ('satisfiability threshold', 0.3913330137729645), ('sharp threshold', 0.3816961646080017), ('threshold', 0.37301623821258545), ('computational gap', 0.3567962348461151), ('statistical computational', 0.32753321528434753)]"
1665,1665,17,1665_pricing american options_american option pricing_american options_finite difference scheme,"['pricing american options', 'american option pricing', 'american options', 'finite difference scheme', 'american option', 'option pricing', 'temporal discretization', 'difference scheme', 'pricing american', 'policy iteration']","['A note on the numerical approximation of Greeks for American-style\n  options   In this note we consider the approximation of the Greeks Delta and Gamma of\nAmerican-style options through the numerical solution of time-dependent partial\ndifferential complementarity problems (PDCPs). This approach is very attractive\nas it can yield accurate approximations to these Greeks at essentially no\nadditional computational cost during the numerical solution of the PDCP for the\npertinent option value function. For the temporal discretization, the\nCrank-Nicolson method is arguably the most popular method in computational\nfinance. It is well-known, however, that this method can have an undesirable\nconvergence behaviour in the approximation of the Greeks Delta and Gamma for\nAmerican-style options, even when backward Euler damping (Rannacher smoothing)\nis employed.\n  In this note we study for the temporal discretization an interesting family\nof diagonally implicit Runge-Kutta (DIRK) methods together with the two-stage\nLobatto IIIC method. Through ample numerical experiments for one- and two-asset\nAmerican-style options, it is shown that these methods can yield a regular\nsecond-order convergence behaviour for the option value as well as for the\nGreeks Delta and Gamma. A mutual comparison reveals that the DIRK method with\nsuitably chosen parameter $\\theta$ is preferable.\n', 'Pricing European and American Options under Heston Model using\n  Discontinuous Galerkin Finite Elements   This paper deals with pricing of European and American options, when the\nunderlying asset price follows Heston model, via the interior penalty\ndiscontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM\nspace discretization with Rannacher smoothing as time integrator with nonsmooth\ninitial and boundary conditions are illustrated for European vanilla options,\ndigital call and American put options. The convection dominated Heston model\nfor vanishing volatility is efficiently solved utilizing the adaptive dGFEM.\nFor fast solution of the linear complementary problem of the American options,\na projected successive over relaxation (PSOR) method is developed with the norm\npreconditioned dGFEM. We show the efficiency and accuracy of dGFEM for option\npricing by conducting comparison analysis with other methods and numerical\nexperiments.\n', ""An efficient numerical method for American options and their Greeks\n  under the two-asset Kou jump-diffusion model   In this paper we consider the numerical solution of the two-dimensional\ntime-dependent partial integro-differential complementarity problem (PIDCP)\nthat holds for the value of American-style options under the two-asset Kou\njump-diffusion model. Following the method of lines (MOL), we derive an\nefficient numerical method for the pertinent PIDCP. Here, for the\ndiscretization of the nonlocal double integral term, an extension is employed\nof the fast algorithm by Toivanen (2008) in the case of the one-asset Kou\njump-diffusion model. For the temporal discretization, we study a useful family\nof second-order diagonally implicit Runge-Kutta (DIRK) methods. Their\nadaptation to the semidiscrete two-dimensional Kou PIDCP is obtained by means\nof an effective iteration introduced by d'Halluin, Forsyth & Labahn (2004) and\nd'Halluin, Forsyth & Vetzal (2005).\n  Ample numerical experiments are presented showing that the proposed numerical\nmethod achieves a favourable, second-order convergence behaviour to the\nAmerican two-asset option value as well as to its Greeks Delta and Gamma.\n""]","[('pricing american options', 0.5529504418373108), ('american option pricing', 0.5075145959854126), ('american options', 0.4735385477542877), ('finite difference scheme', 0.4518924951553345), ('american option', 0.4293283522129059), ('option pricing', 0.4217897951602936), ('temporal discretization', 0.4162352681159973), ('difference scheme', 0.36001867055892944), ('pricing american', 0.3500504493713379), ('policy iteration', 0.34741827845573425)]"
1666,1666,17,1666_differential galois groups_differential galois theory_differential galois group_differential galois,"['differential galois groups', 'differential galois theory', 'differential galois group', 'differential galois', 'linear differential algebraic', 'differential algebraic', 'galois theory linear', 'galois groups', 'linear algebraic group', 'groups galois']","['Calculating differential Galois groups of parametrized differential\n  equations, with applications to hypertranscendence   The main motivation of our work is to create an efficient algorithm that\ndecides hypertranscendence of solutions of linear differential equations, via\nthe parameterized differential and Galois theories. To achieve this, we expand\nthe representation theory of linear differential algebraic groups and develop\nnew algorithms that calculate unipotent radicals of parameterized differential\nGalois groups for differential equations whose coefficients are rational\nfunctions. P. Berman and M.F. Singer presented an algorithm calculating the\ndifferential Galois group for differential equations without parameters whose\ndifferential operator is a composition of two completely reducible differential\noperators. We use their algorithm as a part of our algorithm. As a result, we\nfind an effective criterion for the algebraic independence of the solutions of\nparameterized differential equations and all of their derivatives with respect\nto the parameter.\n', 'Computing the Lie algebra of the differential Galois group: the\n  reducible case   In this paper, we explain how to compute the Lie algebra of the differential\nGalois group of a reducible linear differential system. We achieve this by\nshowing how to transform a block-triangular linear differential system into a\nKolchin-Kovacic reduced form. We combine this with other reduction results to\npropose a general algorithm for computing a reduced form of a general linear\ndifferential system. In particular, this provides directly the Lie algebra of\nthe differential Galois group without an a priori computation of this Galois\ngroup.\n', 'Connections whose differential Galois groups are reductive of maximal\n  degree   The differential Galois group of an $n^\\mathrm{th}$ order linear differential\nequation is the symmetry group of its solutions; it is an algebraic subgroup of\n$\\mathrm{GL}_n(\\mathbb{C})$. More generally, if $G$ is a simple complex\nalgebraic group, the differential Galois group of a $G$-connection is an\nalgebraic subgroup of $G$. A connected reductive subgroup of $G$ is said to\nhave maximal degree if it has a fundamental degree equal to the Coxeter number\nof $G$. We give a complete classification of these subgroups and generalise a\ntheorem of Katz on linear differential equations by giving a criterion for the\ndifferential Galois group of a $G$-connection to be reductive of maximal\ndegree. As an application, we determine the differential Galois groups of\ncertain $G$-connections that play an important role in recent work on the\ngeometric Langlands program: connections on $\\mathbb{G}_m$ with an (irregular)\n""Coxeter"" singularity and possibly an additional regular singular point.\n']","[('differential galois groups', 0.7207979559898376), ('differential galois theory', 0.7184397578239441), ('differential galois group', 0.7070220112800598), ('differential galois', 0.6688104271888733), ('linear differential algebraic', 0.6040526032447815), ('differential algebraic', 0.6021969318389893), ('galois theory linear', 0.5647444128990173), ('galois groups', 0.5280278325080872), ('linear algebraic group', 0.5249897837638855), ('groups galois', 0.5170046091079712)]"
1667,1667,17,1667_algebraic groups_algebraic group algebraically_algebraic group_automorphism,"['algebraic groups', 'algebraic group algebraically', 'algebraic group', 'automorphism', 'variety algebraically closed', 'algebraic varieties', 'linear cellular automata', 'algebraically closed', 'cellular automata', 'morphism algebraic']","['LEF-groups and endomorphisms of symbolic varieties   Let $G$ be a group and let $X$ be an algebraic variety over an algebraically\nclosed field $k$ of characteristic zero. Denote $A=X(k)$ the set of rational\npoints of $X$. We investigate invertible algebraic cellular automata $\\tau\n\\colon A^G \\to A^G$ whose local defining map is induced by some morphism of\nalgebraic varieties $X^M \\to X$ where $M$ is a finite memory. When $G$ is\nlocally embeddable into finite groups (LEF), then we show that the inverses of\nreversible algebraic cellular automata are automatically algebraic cellular\nautomata. Generalizations are also obtained for finite product Hopfian pointed\nobject alphabets in concrete categories.\n', ""On symbolic group varieties and dual surjunctivity   Let $G$ be a group. Let $X$ be an algebraic group over an algebraically\nclosed field $K$. Denote by $A=X(K)$ the set of rational points of $X$. We\nstudy algebraic group cellular automata $\\tau \\colon A^G \\to A^G$ whose local\ndefining map is induced by a homomorphism of algebraic groups $X^M \\to X$ where\n$M$ is a finite memory. When $G$ is sofic and $K$ is uncountable, we show that\nif $\\tau$ is post-surjective then it is weakly pre-injective. Our result\nextends the dual version of Gottschalk's Conjecture for finite alphabets\nproposed by Capobianco, Kari, and Taati. When $G$ is amenable, we prove that if\n$\\tau$ is surjective then it is weakly pre-injective, and conversely, if $\\tau$\nis pre-injective then it is surjective. Hence, we obtain a complete answer to a\nquestion of Gromov on the Garden of Eden theorem in the case of algebraic group\ncellular automata.\n"", ""On sofic groups, Kaplansky's conjectures, and endomorphisms of\n  pro-algebraic groups   Let $G$ be a group. Let $X$ be a connected algebraic group over an\nalgebraically closed field $K$. Denote by $A=X(K)$ the set of $K$-points of\n$X$. We study a class of endomorphisms of pro-algebraic groups, namely\nalgebraic group cellular automata over $(G,X,K)$. They are cellular automata\n$\\tau \\colon A^G \\to A^G$ whose local defining map is induced by a homomorphism\nof algebraic groups $X^M \\to X$ where $M\\subset G$ is a finite memory set of\n$\\tau$. Our first result is that when $G$ is sofic, such an algebraic group\ncellular automaton $\\tau$ is invertible whenever it is injective and\n$\\text{char}(K)=0$. As an application, we prove that if $G$ is sofic and the\ngroup $X$ is commutative then the group ring $R[G]$, where $R=\\text{End}(X)$ is\nthe endomorphism ring of $X$, is stably finite. When $G$ is amenable, we show\nthat an algebraic group cellular automaton $\\tau$ is surjective if and only if\nit satisfies a weak form of pre-injectivity called $(\\bullet)$-pre-injectivity.\nThis yields an analogue of the classical Moore-Myhill Garden of Eden theorem.\nWe also introduce the near ring $R(K,G)$ which is $K[X_g: g \\in G]$ as an\nadditive group but the multiplication is induced by the group law of $G$. The\nnear ring $R(K,G)$ contains naturally the group ring $K[G]$ and we extend\nKaplansky's conjectures to this new setting. Among other results, we prove that\nwhen $G$ is an orderable group, then all one-sided invertible elements of\n$R(K,G)$ are trivial, i.e., of the form $aX_g+b$ for some $g\\in G$, $a\\in K^*$,\n$b\\in K$. This allows us to show that when $G$ is locally residually finite and\norderable (e.g. $\\mathbb{Z}^d$ or a free group), and $\\text{char}(K)=0$, all\ninjective algebraic cellular automata $\\tau \\colon \\mathbb{C}^G \\to\n\\mathbb{C}^G$ are of the form $\\tau(x)(h)= a x(g^{-1}h) +b$ for all $x\\in\n\\mathbb{C}^G, h \\in G$ for some $g\\in G$, $a\\in \\mathbb{C}^*$, $b\\in\n\\mathbb{C}$.\n""]","[('algebraic groups', 0.5374630093574524), ('algebraic group algebraically', 0.5014230608940125), ('algebraic group', 0.4946554899215698), ('automorphism', 0.4814382493495941), ('variety algebraically closed', 0.4692246615886688), ('algebraic varieties', 0.45697152614593506), ('linear cellular automata', 0.4550570249557495), ('algebraically closed', 0.4495154917240143), ('cellular automata', 0.4448563754558563), ('morphism algebraic', 0.4354005455970764)]"
1668,1668,17,1668_finite difference methods_finite difference schemes_finite difference scheme_methods elliptic,"['finite difference methods', 'finite difference schemes', 'finite difference scheme', 'methods elliptic', 'elliptic interface problems', 'elliptic interface', 'grid finite difference', 'difference schemes', 'linear elliptic equations', 'elliptic equations']","['Sixth-Order Hybrid Finite Difference Methods for Elliptic Interface\n  Problems with Mixed Boundary Conditions   In this paper, we develop sixth-order hybrid finite difference methods (FDMs)\nfor the elliptic interface problem $-\\nabla \\cdot( a\\nabla u)=f$ in\n$\\Omega\\backslash \\Gamma$, where $\\Gamma$ is a smooth interface inside\n$\\Omega$. The variable scalar coefficient $a>0$ and source $f$ are possibly\ndiscontinuous across $\\Gamma$. The hybrid FDMs utilize a $9$-point compact\nstencil at any interior regular points of the grid and a $13$-point stencil at\nirregular points near $\\Gamma$. For interior regular points away from $\\Gamma$,\nwe obtain a sixth-order $9$-point compact FDM satisfying the sign and sum\nconditions for ensuring the M-matrix property. We also derive sixth-order\ncompact ($4$-point for corners and $6$-point for edges) FDMs satisfying the\nsign and sum conditions for the M-matrix property at any boundary point subject\nto (mixed) Dirichlet/Neumann/Robin boundary conditions. Thus, for the elliptic\nproblem without interface (i.e., $\\Gamma$ is empty), our compact FDM has the\nM-matrix property for any mesh size $h>0$ and consequently, satisfies the\ndiscrete maximum principle, which guarantees the theoretical sixth-order\nconvergence. For irregular points near $\\Gamma$, we propose fifth-order\n$13$-point FDMs, whose stencil coefficients can be effectively calculated by\nrecursively solving several small linear systems. Theoretically, the proposed\nhigh order FDMs use high order (partial) derivatives of the coefficient $a$,\nthe source term $f$, the interface curve $\\Gamma$, the two jump functions along\n$\\Gamma$, and the functions on $\\partial \\Omega$. Numerically, we always use\nfunction values to approximate all required high order (partial) derivatives in\nour hybrid FDMs without losing accuracy. Our numerical experiments confirm the\nsixth-order convergence in the $l_{\\infty}$ norm of the proposed hybrid FDMs\nfor the elliptic interface problem.\n', 'A High Order Compact Finite Difference Scheme for Elliptic Interface\n  Problems with Discontinuous and High-Contrast Coefficients   The elliptic interface problems with discontinuous and high-contrast\ncoefficients appear in many applications and often lead to huge condition\nnumbers of the corresponding linear systems. Thus, it is highly desired to\nconstruct high order schemes to solve the elliptic interface problems with\ndiscontinuous and high-contrast coefficients. Let $\\Gamma$ be a smooth curve\ninside a rectangular region $\\Omega$. In this paper, we consider the elliptic\ninterface problem $-\\nabla\\cdot (a \\nabla u)=f$ in $\\Omega\\setminus \\Gamma$\nwith Dirichlet boundary conditions, where the coefficient $a$ and the source\nterm $f$ are smooth in $\\Omega\\setminus \\Gamma$ and the two nonzero jump\ncondition functions $[u]$ and $[a\\nabla u\\cdot \\vec{n}]$ across $\\Gamma$ are\nsmooth along $\\Gamma$. To solve such elliptic interface problems, we propose a\nhigh order compact finite difference scheme for numerically computing both the\nsolution $u$ and the gradient $\\nabla u$ on uniform Cartesian grids without\nchanging coordinates into local coordinates. Our numerical experiments confirm\nthe fourth order accuracy for computing the solution $u$, the gradient $\\nabla\nu$ and the velocity $a \\nabla u$ of the proposed compact finite difference\nscheme on uniform meshes for the elliptic interface problems with discontinuous\nand high-contrast coefficients.\n', 'Hybrid Finite Difference Schemes for Elliptic Interface Problems with\n  Discontinuous and High-Contrast Variable Coefficients   For elliptic interface problems with discontinuous coefficients, the maximum\naccuracy order for compact 9-point finite difference scheme in irregular points\nis three [7]. The discontinuous coefficients usually have abrupt jumps across\nthe interface curve in the porous medium of realistic problems, causing the\npollution effect of numerical methods. So, to obtain a reasonable numerical\nsolution of the above problem, the higher order scheme and its effective\nimplementation are necessary. In this paper, we propose an efficient and\nflexible way to achieve the implementation of a hybrid (9-point scheme with\nsixth order accuracy for interior regular points and 13-point scheme with fifth\norder accuracy for interior irregular points) finite difference scheme in\nuniform meshes for the elliptic interface problems with discontinuous and\nhigh-contrast piecewise smooth coefficients in a rectangle $\\Omega$. We also\nderive the $6$-point and $4$-point finite difference schemes in uniform meshes\nwith sixth order accuracy for the side points and corner points of various\nmixed boundary conditions (Dirichlet, Neumann and Robin) of elliptic equations\nin a rectangle. Our numerical experiments confirm the flexibility and the sixth\norder accuracy in $l_2$ and $l_{\\infty}$ norms of the proposed hybrid scheme.\n']","[('finite difference methods', 0.6133086681365967), ('finite difference schemes', 0.6045148968696594), ('finite difference scheme', 0.597637414932251), ('methods elliptic', 0.5739365816116333), ('elliptic interface problems', 0.543512225151062), ('elliptic interface', 0.4949650466442108), ('grid finite difference', 0.4791824221611023), ('difference schemes', 0.47316691279411316), ('linear elliptic equations', 0.4584302008152008), ('elliptic equations', 0.4525662064552307)]"
1669,1669,17,1669_steiner trees_tree connectivity_steiner tree_edge disjoint,"['steiner trees', 'tree connectivity', 'steiner tree', 'edge disjoint', 'edge connectivity', 'steiner', 'internally disjoint paths', 'disjoint paths', 'number edge disjoint', 'connected graph']","[""Constructing disjoint Steiner trees in Sierpi\\'{n}ski graphs   Let $G$ be a graph and $S\\subseteq V(G)$ with $|S|\\geq 2$. Then the trees\n$T_1, T_2, \\cdots, T_\\ell$ in $G$ are \\emph{internally disjoint Steiner trees}\nconnecting $S$ (or $S$-Steiner trees) if $E(T_i) \\cap E(T_j )=\\emptyset$ and\n$V(T_i)\\cap V(T_j)=S$ for every pair of distinct integers $i,j$, $1 \\leq i, j\n\\leq \\ell$. Similarly, if we only have the condition $E(T_i) \\cap E(T_j\n)=\\emptyset$ but without the condition $V(T_i)\\cap V(T_j)=S$, then they are\n\\emph{edge-disjoint Steiner trees}. The \\emph{generalized $k$-connectivity},\ndenoted by $\\kappa_k(G)$, of a graph $G$, is defined as\n$\\kappa_k(G)=\\min\\{\\kappa_G(S)|S \\subseteq V(G) \\ \\textrm{and} \\ |S|=k \\}$,\nwhere $\\kappa_G(S)$ is the maximum number of internally disjoint $S$-Steiner\ntrees. The \\emph{generalized local edge-connectivity} $\\lambda_{G}(S)$ is the\nmaximum number of edge-disjoint Steiner trees connecting $S$ in $G$. The {\\it\ngeneralized $k$-edge-connectivity} $\\lambda_k(G)$ of $G$ is defined as\n$\\lambda_k(G)=\\min\\{\\lambda_{G}(S)\\,|\\,S\\subseteq V(G) \\ and \\ |S|=k\\}$. These\nmeasures are generalizations of the concepts of connectivity and\nedge-connectivity, and they and can be used as measures of vulnerability of\nnetworks. It is, in general, difficult to compute these generalized\nconnectivities. However, there are precise results for some special classes of\ngraphs. In this paper, we obtain the exact value of $\\lambda_{k}(S(n,\\ell))$\nfor $3\\leq k\\leq \\ell^n$, and the exact value of $\\kappa_{k}(S(n,\\ell))$ for\n$3\\leq k\\leq \\ell$, where $S(n, \\ell)$ is the Sierpi\\'{n}ski graphs with order\n$\\ell^n$. As a direct consequence, these graphs provide additional interesting\nexamples when $\\lambda_{k}(S(n,\\ell))=\\kappa_{k}(S(n,\\ell))$. We also study the\nsome network properties of Sierpi\\'{n}ski graphs.\n"", ""$k$-tree connectivity of line graphs   For a graph $G=(V,E)$ and a set $S\\subseteq V(G)$ of size at least $2$, an\n$S$-Steiner tree $T$ is a subgraph of $G$ that is a tree with $S\\subseteq\nV(T)$. Two $S$-Steiner trees $T$ and $T'$ are internally disjoint (resp.\nedge-disjoint) if $E(T)\\cap E(T')=\\emptyset$ and $V(T)\\cap V(T')=S$ (resp. if\n$E(T)\\cap E(T')=\\emptyset$). Let $\\kappa_G (S)$ (resp. $\\lambda_G (S)$) denote\nthe maximum number of internally disjoint (resp. edge-disjoint) $S$-Steiner\ntrees in $G$. The $k$-tree connectivity $\\kappa_k(G)$ (resp. $k$-tree\nedge-connectivity $\\lambda_k(G)$) of $G$ is then defined as the minimum\n$\\kappa_G (S)$ (resp. $\\lambda_G (S)$), where $S$ ranges over all $k$-subsets\nof $V(G)$. In [H. Li, B. Wu, J. Meng, Y. Ma, Steiner tree packing number and\ntree connectivity, Discrete Math. 341(2018), 1945--1951], the authors\nconjectured that if a connected graph $G$ has at least $k$ vertices and at\nleast $k$ edges, then $\\kappa_k(L(G))\\geq \\lambda_k(G)$ for any $k\\geq 2$,\nwhere $L(G)$ is the line graph of $G$. In this paper, we confirm this\nconjecture and prove that the bound is sharp.\n"", ""Pendant 3-tree Connectivity of Augmented Cubes   The Steiner tree problem in graphs has applications in network design or\ncircuit layout. Given a set $S$ of vertices, $|S| \\geq 2,$ a tree connecting\nall vertices of $S$ is called an $S$-Steiner tree (tree connecting $S$). The\nreliability of a network $G$ to connect any $S$ vertices ($|S|$ number of\nvertices) in $G$ can be measure by this parameter. For an $S$-Steiner tree, if\nthe degree of each vertex in $S$ is equal to one, then that tree is called a\npendant S-Steiner tree. Two pendant $S$-Steiner trees $T$ and $T'$ are said to\nbe internally disjoint if $E(T) \\cap E(T') = \\emptyset$ and $V(T) \\cap V(T') =\nS.$ The local pendant tree-connectivity $\\tau_{G}(S)$ is the maximum number of\ninternally disjoint pendant $S$-Steiner trees in $G.$ For an integer $k$ with\n$2 \\leq k \\leq n,$ the pendant k-tree-connectivity is defined as $\\tau_{k}(G) =\nmin\\{ \\tau_{G}(S) : S \\subseteq V(G), |S| = k\\}.$ In this paper, we study the\npendant $3$-tree connectivity of Augmented cubes which are modifications of\nhypercubes invented to increase the connectivity and decrease the diameter\nhence superior to hypercubes. We show that $\\tau_3(AQ_n) = 2n-3.$ , which\nattains the upper bound of $\\tau_3(G)$ given by Hager, for $G = AQ_n$.\n""]","[('steiner trees', 0.6133039593696594), ('tree connectivity', 0.5774517059326172), ('steiner tree', 0.5724525451660156), ('edge disjoint', 0.4848109781742096), ('edge connectivity', 0.45999425649642944), ('steiner', 0.43085312843322754), ('internally disjoint paths', 0.42272019386291504), ('disjoint paths', 0.42026031017303467), ('number edge disjoint', 0.4030861258506775), ('connected graph', 0.37599244713783264)]"
1670,1670,17,1670_systems quantized_optimal quantizer_quantized measurements_quantization schemes,"['systems quantized', 'optimal quantizer', 'quantized measurements', 'quantization schemes', 'quantization', 'quantizer', 'quantized', 'quantization error', 'quantizers', 'optimal controller']","['Self-triggered Stabilization of Contracting Systems under Quantization   We propose self-triggered control schemes for nonlinear systems with\nquantized state measurements. Our focus lies on scenarios where both the\ncontroller and the self-triggering mechanism receive only the quantized state\nat each sampling time. We assume that the ideal closed-loop system without\nquantization or self-triggered sampling is contracting. Moreover, an upper\nbound on the growth rate of the open-loop system is assumed to be known. We\npresent two control schemes that achieve closed-loop stability without Zeno\nbehavior. The first scheme is implemented under logarithmic quantization and\nuses the quantized state for the threshold in the triggering condition. The\nsecond one is a joint design of zooming quantization and self-triggered\nsampling, where the adjustable zoom parameter for quantization changes based on\ninter-sampling times and is also used for the threshold of self-triggered\nsampling. In both schemes, the self-triggering mechanism predicts the future\nstate from the quantized data for the computation of the next sampling time. We\nemploy a trajectory-based approach for stability analysis, where contraction\ntheory plays a key role.\n', 'Optimal Controller and Quantizer Selection for Partially Observable\n  Linear-Quadratic-Gaussian Systems   In networked control systems, often the sensory signals are quantized before\nbeing transmitted to the controller. Consequently, performance is affected by\nthe coarseness of this quantization process. Modern communication technologies\nallow users to obtain resolution-varying quantized measurements based on the\nprices paid. In this paper, we consider joint optimal controller synthesis and\nquantizer scheduling for a partially observed Quantized-Feedback\nLinear-Quadratic-Gaussian (QF-LQG) system, where the measurements are quantized\nbefore being sent to the controller. The system is presented with several\nchoices of quantizers, along with the cost of using each quantizer. The\nobjective is to jointly select the quantizers and synthesize the controller to\nstrike an optimal balance between control performance and quantization cost.\nWhen the innovation signal is quantized instead of the measurement, the problem\nis decoupled into two optimization problems: one for optimal controller\nsynthesis, and the other for optimal quantizer selection. The optimal\ncontroller is found by solving a Riccati equation and the optimal quantizer\nselection policy is found by solving a linear program (LP)- both of which can\nbe solved offline.\n', 'Optimal Controller Synthesis and Dynamic Quantizer Switching for\n  Linear-Quadratic-Gaussian Systems   In networked control systems, often the sensory signals are quantized before\nbeing transmitted to the controller. Consequently, performance is affected by\nthe coarseness of this quantization process. Modern communication technologies\nallow users to obtain resolution-varying quantized measurements based on the\nprices paid. In this paper, we consider optimal controller synthesis of a\nQuantized-Feedback Linear-Quadratic-Gaussian (QF-LQG) system where the\nmeasurements are to be quantized before being transmitted to the controller.\nThe system is presented with several choices of quantizers, along with the cost\nof operating each quantizer. The objective is to jointly select the quantizers\nand the controller that would maintain an optimal balance between control\nperformance and quantization cost. Under certain assumptions, this problem can\nbe decoupled into two optimization problems: one for optimal controller\nsynthesis and the other for optimal quantizer selection. We show that,\nsimilarly to the classical LQG problem, the optimal controller synthesis\nsubproblem is characterized by Riccati equations. On the other hand, the\noptimal quantizer selection policy is found by solving a certain\nMarkov-Decision-Process (MDP).\n']","[('systems quantized', 0.6380689740180969), ('optimal quantizer', 0.590207040309906), ('quantized measurements', 0.525361955165863), ('quantization schemes', 0.5038331747055054), ('quantization', 0.496660977602005), ('quantizer', 0.48572060465812683), ('quantized', 0.45826131105422974), ('quantization error', 0.43748098611831665), ('quantizers', 0.43619364500045776), ('optimal controller', 0.4215244650840759)]"
1671,1671,17,1671_bounds tail probabilities_exponential tail bounds_lower tail bounds_tail bounds random,"['bounds tail probabilities', 'exponential tail bounds', 'lower tail bounds', 'tail bounds random', 'concentration inequalities', 'concentration inequality', 'tail bounds', 'high dimensional statistics', 'gaussian sub exponential', 'approximation bounds']","['On the Non-asymptotic and Sharp Lower Tail Bounds of Random Variables   The non-asymptotic tail bounds of random variables play crucial roles in\nprobability, statistics, and machine learning. Despite much success in\ndeveloping upper bounds on tail probability in literature, the lower bounds on\ntail probabilities are relatively fewer. In this paper, we introduce systematic\nand user-friendly schemes for developing non-asymptotic lower bounds of tail\nprobabilities. In addition, we develop sharp lower tail bounds for the sum of\nindependent sub-Gaussian and sub-exponential random variables, which match the\nclassic Hoeffding-type and Bernstein-type concentration inequalities,\nrespectively. We also provide non-asymptotic matching upper and lower tail\nbounds for a suite of distributions, including gamma, beta, (regular, weighted,\nand noncentral) chi-square, binomial, Poisson, Irwin-Hall, etc. We apply the\nresult to establish the matching upper and lower bounds for extreme value\nexpectation of the sum of independent sub-Gaussian and sub-exponential random\nvariables. A statistical application of signal identification from sparse\nheterogeneous mixtures is finally considered.\n', 'Moving Beyond Sub-Gaussianity in High-Dimensional Statistics:\n  Applications in Covariance Estimation and Linear Regression   Concentration inequalities form an essential toolkit in the study of high\ndimensional (HD) statistical methods. Most of the relevant statistics\nliterature in this regard is based on sub-Gaussian or sub-exponential tail\nassumptions. In this paper, we first bring together various probabilistic\ninequalities for sums of independent random variables under much more general\nexponential type (namely sub-Weibull) tail assumptions. These results extract a\npart sub-Gaussian tail behavior in finite samples, matching the asymptotics\ngoverned by the central limit theorem, and are compactly represented in terms\nof a new Orlicz quasi-norm - the Generalized Bernstein-Orlicz norm - that\ntypifies such tail behaviors.\n  We illustrate the usefulness of these inequalities through the analysis of\nfour fundamental problems in HD statistics. In the first two problems, we study\nthe rate of convergence of the sample covariance matrix in terms of the maximum\nelementwise norm and the maximum k-sub-matrix operator norm which are key\nquantities of interest in bootstrap, HD covariance matrix estimation and HD\ninference. The third example concerns the restricted eigenvalue condition,\nrequired in HD linear regression, which we verify for all sub-Weibull random\nvectors through a unified analysis, and also prove a more general result\nrelated to restricted strong convexity in the process. In the final example, we\nconsider the Lasso estimator for linear regression and establish its rate of\nconvergence under much weaker than usual tail assumptions (on the errors as\nwell as the covariates), while also allowing for misspecified models and both\nfixed and random design. To our knowledge, these are the first such results for\nLasso obtained in this generality. The common feature in all our results over\nall the examples is that the convergence rates under most exponential tails\nmatch the usual ones under sub-Gaussian assumptions.\n', ""Sharper Sub-Weibull Concentrations   Constant-specified and exponential concentration inequalities play an\nessential role in the finite-sample theory of machine learning and\nhigh-dimensional statistics area. We obtain sharper and constants-specified\nconcentration inequalities for the sum of independent sub-Weibull random\nvariables, which leads to a mixture of two tails: sub-Gaussian for small\ndeviations and sub-Weibull for large deviations from the mean. These bounds are\nnew and improve existing bounds with sharper constants. In addition, a new\nsub-Weibull parameter if the italic should be retained. Please check the whole\ntext. is also proposed, which enables recovering the tight concentration\ninequality for a random variable (vector). For statistical applications, we\ngive an $\\ell_2$-error of estimated coefficients in negative binomial\nregressions when the heavy-tailed covariates are sub-Weibull distributed with\nsparse structures, which is a new result for negative binomial regressions. In\napplying random matrices, we derive non-asymptotic versions of Bai-Yin's\ntheorem for sub-Weibull entries with exponential tail bounds. Finally, by\ndemonstrating a sub-Weibull confidence region for a log-truncated Z-estimator\nwithout the second-moment condition, we discuss and define the sub-Weibull type\nrobust estimator for independent observations $\\{X_i\\}_{i=1}^{n}$ without\nexponential-moment conditions.\n""]","[('bounds tail probabilities', 0.5507788062095642), ('exponential tail bounds', 0.5406970381736755), ('lower tail bounds', 0.5222486257553101), ('tail bounds random', 0.52025306224823), ('concentration inequalities', 0.4806581437587738), ('concentration inequality', 0.4740898311138153), ('tail bounds', 0.4690176844596863), ('high dimensional statistics', 0.4600204825401306), ('gaussian sub exponential', 0.4599284529685974), ('approximation bounds', 0.45910778641700745)]"
1672,1672,17,1672_moduli space genus_curves genus_dimension moduli space_dimension moduli,"['moduli space genus', 'curves genus', 'dimension moduli space', 'dimension moduli', 'moduli space', 'moduli space mathcal', 'moduli space overline', 'hyperelliptic curves', 'strata moduli', 'covers curves']","['Moduli of $G$-covers of curves: geometry and singularities   In a recent paper Chiodo and Farkas described the singular locus and the\nlocus of non-canonical singularities of the moduli space of level curves. In\nthis work we generalize their results to the moduli space $\\overline{\\mathcal\nR}_{g,G}$ of curves with a $G$-cover for any finite group $G$. We show that\nnon-canonical singularities are of two types: $T$-curves, that is singularities\nlifted from the moduli space $\\overline{\\mathcal M}_g$ of stable curves, and\n$J$-curves, that is new singularities entirely characterized by the dual graph\nof the cover. Finally, we prove that in the case $G=S_3$, the $J$-locus is\nempty, which is the first fundamental step in evaluating the Kodaira dimension\nof $\\overline{\\mathcal R}_{g,S_3}$.\n', 'Pencils on surfaces with normal crossings and the Kodaira dimension of\n  $\\overline{\\mathcal{M}}_{g,n}$   We study smoothing of pencils of curves on surfaces with normal crossings. As\na consequence we show that the canonical divisor of\n$\\overline{\\mathcal{M}}_{g,n}$ is not pseudo-effective in some range, implying\nthat\n$\\overline{\\mathcal{M}}_{12,6},\\overline{\\mathcal{M}}_{12,7},\\overline{\\mathcal{M}}_{13,4}$\nand $\\overline{\\mathcal{M}}_{14,3}$ are uniruled. We provide upper bounds for\nthe Kodaira dimension of $\\overline{\\mathcal{M}}_{12,8}$ and\n$\\overline{\\mathcal{M}}_{16}$. We also show that the moduli of $(4g+5)$-pointed\nhyperelliptic curves $\\mathcal{H}_{g,4g+5}$ is uniruled. Together with a recent\nresult of Schwarz, this concludes the Kodaira classification for moduli of\npointed hyperelliptic curves.\n', 'The birational geometry of $\\overline{\\mathcal{R}}_{g,2}$ and\n  Prym-canonical divisorial strata   We prove that the moduli space of double covers ramified at two points\n$\\mathcal{R}_{g,2}$ is uniruled for $3\\leq g\\leq 6$ and of general type for\n$g\\geq 16$. Furthermore, we consider Prym-canonical divisorial strata in the\nmoduli space $\\overline{\\mathcal{C}^n\\mathcal{R}}_g$ parametrizing $n$-pointed\nPrym curves, and we compute their classes in\n$\\mathrm{Pic}_\\mathbb{Q}(\\overline{\\mathcal{C}^n\\mathcal{R}}_g)$.\n']","[('moduli space genus', 0.6301777958869934), ('curves genus', 0.5921878814697266), ('dimension moduli space', 0.5880528688430786), ('dimension moduli', 0.5726622939109802), ('moduli space', 0.5666910409927368), ('moduli space mathcal', 0.5613852739334106), ('moduli space overline', 0.5501987338066101), ('hyperelliptic curves', 0.5484746098518372), ('strata moduli', 0.5409695506095886), ('covers curves', 0.536440372467041)]"
1673,1673,17,1673_constrained optimal control_pontryagin maximum principle_parabolic optimal control_optimal control problems,"['constrained optimal control', 'pontryagin maximum principle', 'parabolic optimal control', 'optimal control problems', 'optimal control', 'problems optimal control', 'maximum principle pontryagin', 'optimal controls', 'optimality conditions', 'differential constraints']","['On the Pontryagin Maximum Principle under differential constraints of\n  higher order   Exploiting our previous results on higher order controlled Lagrangians in\n[Nonlinear Anal. {\\bf 207} (2021), 112263], we derive here an analogue of the\nclassical first order Pontryagin Maximum Principle (PMP) for cost minimising\nproblems subjected to higher order differential constraints $\\frac{d^k\nx^j}{dt^k} = f^j\\big(t, x(t), \\frac{d x}{dt}(t), \\ldots, \\frac{d^{k-1}\nx}{dt^{k-1}}(t), u(t)\\big)$, $t \\in [0,T]$, where $u(t)$ is a control curve in\na compact set $K \\subset \\mathbb R^m$. This result and its proof can be\nconsidered as a detailed illustration of one of the claims of that previous\npaper, namely that the results of that paper, originally established in a\nsmooth differential geometric framework, yield directly properties holding\nunder much weaker and more common assumptions. In addition, for further\nclarifying our motivations, in the last section we display a couple of quick\nindications on how the two-step approach of this paper (i.e., a preliminary\neasy-to-get differential geometric discussion followed by a refining analysis\nto weaken the regularity assumptions) might be fruitfully exploited also in the\ncontext of control problems governed by partial differential equations or in\nstudies on the dynamics of controlled mechanical systems.\n', 'Goh conditions for minima of nonsmooth problems with unbounded controls   Higher order necessary conditions for a minimizer of an optimal control\nproblem are generally obtained for systems whose dynamics is continuously\ndifferentiable in the state variable. Here, by making use of the notion of\nset-valued Lie bracket we obtain a Goh-type condition for a control affine\nsystem with Lipschitz continuous dynamics and unbounded controls. In order to\nmanage the simultaneous lack of smoothness of the adjoint equation and of the\nLie bracket-like variations we make use of the notion of Quasi Differential\nQuotient. We conclude the paper with a worked out example where the established\nhigher order condition is capable to rule out the optimality of a control\nverifying the standard maximum principle.\n', 'Goh and Legendre-Clebsh conditions for nonsmooth control systems   Higher order necessary conditions for a minimizer of an optimal control\nproblem are generally obtained for systems whose dynamics is at least\ncontinuously differentiable in the state variable. Here, by making use of the\nnotion of set-valued Lie bracket introduced in ""Set-valued differentials and a\nnonsmooth version of Chow-Rashevski\'s theorem"" by F. Rampazzo and H.J.Sussmann\nand extended in ""Iterated Lie brackets for nonsmooth vector fields"" by E.\nFeleqi and F.Rampazzo , we obtain Goh and Legendre-Clebsh type conditions for a\ncontrol affine system with Lipschitz continuous dynamics. In order to manage\nthe simultaneous lack of smoothness of the adjoint equation and of the Lie\nbracket-like variations, we will exploit the notion of Quasi Differential\nQuotient, introduced in ""A geometrically based criterion to avoid infimum-gaps\nin Optimal Control"" by M. Palladino and F.Rampazzo. We finally exhibit an\nexample where the established higher order condition is capable to rule out the\noptimality of a control verifying a first order Maximum Principle.\n']","[('constrained optimal control', 0.679058849811554), ('pontryagin maximum principle', 0.6520861387252808), ('parabolic optimal control', 0.6424238085746765), ('optimal control problems', 0.6388636231422424), ('optimal control', 0.6224397420883179), ('problems optimal control', 0.608939528465271), ('maximum principle pontryagin', 0.6025647521018982), ('optimal controls', 0.5949504971504211), ('optimality conditions', 0.5528768301010132), ('differential constraints', 0.5452852249145508)]"
1674,1674,17,1674_post quantum cryptography_quantum cryptography_code based cryptography_quantum algorithms,"['post quantum cryptography', 'quantum cryptography', 'code based cryptography', 'quantum algorithms', 'cryptosystems', 'cryptographic systems', 'cryptosystem', 'cryptography', 'cryptographic', 'homomorphic encryption']","['SPANSE: combining sparsity with density for efficient one-time\n  code-based digital signatures   The use of codes defined by sparse characteristic matrices, like QC-LDPC and\nQC-MDPC codes, has become an established solution to design secure and\nefficient code-based public-key encryption schemes, as also witnessed by the\nongoing NIST post-quantum cryptography standardization process. However,\nsimilar approaches have been less fortunate in the context of code-based\ndigital signatures, since no secure and efficient signature scheme based on\nthese codes is available to date. The main limitation of previous attempts in\nthis line of research has been the use of sparse signatures, which produces\nsome leakage of information about the private key. In this paper, we propose a\nnew code-based digital signature scheme that overcomes such a problem by\npublishing signatures that are abnormally dense, rather than sparse. This\neliminates the possibility of deducing information from the sparsity of\nsignatures, and follows a recent trend in code-based cryptography exploiting\nthe hardness of the decoding problem for large-weight vectors, instead of its\nclassical version based on small-weight vectors. In this study we focus on\none-time use and provide some preliminary instances of the new scheme, showing\nthat it achieves very fast signature generation and verification with\nreasonably small public keys.\n', ""Post-Quantum Homomorphic Encryption: A Case for Code-Based Alternatives   Homomorphic Encryption (HE) allows secure and privacy-protected computation\non encrypted data without the need to decrypt it. Since Shor's algorithm\nrendered prime factorisation and discrete logarithm-based ciphers insecure with\nquantum computations, researchers have been working on building post-quantum\nhomomorphic encryption (PQHE) algorithms. Most of the current PQHE algorithms\nare secured by Lattice-based problems and there have been limited attempts to\nbuild ciphers based on error-correcting code-based problems. This review\npresents an overview of the current approaches to building PQHE schemes and\njustifies code-based encryption as a novel way to diversify post-quantum\nalgorithms. We present the mathematical underpinnings of existing code-based\ncryptographic frameworks and their security and efficiency guarantees. We\ncompare lattice-based and code-based homomorphic encryption solutions\nidentifying challenges that have inhibited the progress of code-based schemes.\nWe finally propose five new research directions to advance post-quantum\ncode-based homomorphic encryption.\n"", 'Lattice-Based Vulnerabilities in Lee Metric Post-Quantum Cryptosystems   Post-quantum cryptography has gained attention due to the need for secure\ncryptographic systems in the face of quantum computing. Code-based and\nlattice-based cryptography are two prominent approaches, both heavily studied\nwithin the NIST standardization project. Code-based cryptography -- most\nprominently exemplified by the McEliece cryptosystem -- is based on the\nhardness of decoding random linear error-correcting codes. Despite the McEliece\ncryptosystem having been unbroken for several decades, it suffers from large\nkey sizes, which has led to exploring variants using metrics than the Hamming\nmetric, such as the Lee metric. This alternative metric may allow for smaller\nkey sizes, but requires further analysis for potential vulnerabilities to\nlattice-based attack techniques. In this paper, we consider a generic Lee\nmetric based McEliece type cryptosystem and evaluate its security against\nlattice-based attacks.\n']","[('post quantum cryptography', 0.7614653706550598), ('quantum cryptography', 0.7240182757377625), ('code based cryptography', 0.5873239636421204), ('quantum algorithms', 0.5820955038070679), ('cryptosystems', 0.5596096515655518), ('cryptographic systems', 0.5496683120727539), ('cryptosystem', 0.5368106961250305), ('cryptography', 0.5330290794372559), ('cryptographic', 0.5238034129142761), ('homomorphic encryption', 0.5227366089820862)]"
1675,1675,17,1675_kolmogorov complexity_algorithmic complexity_bounded kolmogorov_complexity theory,"['kolmogorov complexity', 'algorithmic complexity', 'bounded kolmogorov', 'complexity theory', 'complexity', 'complexity space', 'complexity combinatorial', 'kolmogorov', 'complexity approaches', 'algorithmic information theory']","['Kolmogorov Complexity of Attractive Degrees   This paper proves a Kolmogorov-complexity-flavored sufficient condition for a\nset to be attractive and discusses some consequences of this condition.\n', 'How incomputable is Kolmogorov complexity?   Kolmogorov complexity is the length of the ultimately compressed version of a\nfile (that is, anything which can be put in a computer). Formally, it is the\nlength of a shortest program from which the file can be reconstructed. We\ndiscuss the incomputabilty of Kolmogorov complexity, which formal loopholes\nthis leaves us, recent approaches to compute or approximate Kolmogorov\ncomplexity, which approaches are problematic and which approaches are viable.\n', 'Theory and Applications of Probabilistic Kolmogorov Complexity   Diverse applications of Kolmogorov complexity to learning [CIKK16], circuit\ncomplexity [OPS19], cryptography [LP20], average-case complexity [Hir21], and\nproof search [Kra22] have been discovered in recent years. Since the running\ntime of algorithms is a key resource in these fields, it is crucial in the\ncorresponding arguments to consider time-bounded variants of Kolmogorov\ncomplexity. While fruitful interactions between time-bounded Kolmogorov\ncomplexity and different areas of theoretical computer science have been known\nfor quite a while (e.g., [Sip83, Ko91, ABK+06, AF09], to name a few), the\naforementioned results have led to a renewed interest in this topic.\n  The theory of Kolmogorov complexity is well understood, but many useful\nresults and properties of Kolmogorov complexity are not known to hold in\ntime-bounded settings. This creates technical difficulties or leads to\nconditional results when applying methods from time-bounded Kolmogorov\ncomplexity to algorithms and complexity theory. Perhaps even more importantly,\nin many cases it is necessary to consider randomised algorithms. Since random\nstrings have high complexity, the classical theory of time-bounded Kolmogorov\ncomplexity might be inappropriate in such contexts.\n  To mitigate these issues and develop a theory of time-bounded Kolmogorov\ncomplexity that survives in the setting of randomised computations, some recent\npapers [Oli19, LO21, LOS21, GKLO22, LOZ22] have explored probabilistic notions\nof time-bounded Kolmogorov complexity, such as $\\mathsf{rKt}$ complexity\n[Oli19], $\\mathsf{rK}^t$ complexity [LOS21], and $\\mathsf{pK}^t$ complexity\n[GKLO22]. These measures consider different ways of encoding an object via a\nprobabilistic representation. In this survey, we provide an introduction to\nprobabilistic time-bounded Kolmogorov complexity and its applications,\nhighlighting many open problems and research directions.\n']","[('kolmogorov complexity', 0.8724332451820374), ('algorithmic complexity', 0.652844250202179), ('bounded kolmogorov', 0.6383351683616638), ('complexity theory', 0.6351571083068848), ('complexity', 0.6279702186584473), ('complexity space', 0.6078153252601624), ('complexity combinatorial', 0.5896112322807312), ('kolmogorov', 0.5710980296134949), ('complexity approaches', 0.5478047132492065), ('algorithmic information theory', 0.5254051685333252)]"
1676,1676,17,1676_bandit algorithms_linear bandits_differential privacy_contextual bandits,"['bandit algorithms', 'linear bandits', 'differential privacy', 'contextual bandits', 'bandit problems', 'differentially private', 'privacy regime', 'bandits', 'privacy constraints', 'optimal regret']","['Optimal Regret of Bernoulli Bandits under Global Differential Privacy As sequential learning algorithms are increasingly applied to real life, ensuring data privacy while maintaining their utilities emerges as a timely question. In this context, regret minimisation in stochastic bandits under $\\epsilon$-global Differential Privacy (DP) has been widely studied. Unlike bandits without DP, there is a significant gap between the best-known regret lower and upper bound in this setting, though they ""match"" in order. Thus, we revisit the regret lower and upper bounds of $\\epsilon$-global DP algorithms for Bernoulli bandits and improve both. First, we prove a tighter regret lower bound involving a novel information-theoretic quantity characterising the hardness of $\\epsilon$-global DP in stochastic bandits. Our lower bound strictly improves on the existing ones across all $\\epsilon$ values. Then, we choose two asymptotically optimal bandit algorithms, i.e. DP-KLUCB and DP-IMED, and propose their DP versions using a unified blueprint, i.e., (a) running in arm-dependent phases, and (b) adding Laplace noise to achieve privacy. For Bernoulli bandits, we analyse the regrets of these algorithms and show that their regrets asymptotically match our lower bound up to a constant arbitrary close to 1. This refutes the conjecture that forgetting past rewards is necessary to design optimal bandit algorithms under global DP. At the core of our algorithms lies a new concentration inequality for sums of Bernoulli variables under Laplace mechanism, which is a new DP version of the Chernoff bound. This result is universally useful as the DP literature commonly treats the concentrations of Laplace noise and random variables separately, while we couple them to yield a tighter bound.', 'Concentrated Differential Privacy for Bandits   Bandits serve as the theoretical foundation of sequential learning and an\nalgorithmic foundation of modern recommender systems. However, recommender\nsystems often rely on user-sensitive data, making privacy a critical concern.\nThis paper contributes to the understanding of Differential Privacy (DP) in\nbandits with a trusted centralised decision-maker, and especially the\nimplications of ensuring zero Concentrated Differential Privacy (zCDP). First,\nwe formalise and compare different adaptations of DP to bandits, depending on\nthe considered input and the interaction protocol. Then, we propose three\nprivate algorithms, namely AdaC-UCB, AdaC-GOPE and AdaC-OFUL, for three bandit\nsettings, namely finite-armed bandits, linear bandits, and linear contextual\nbandits. The three algorithms share a generic algorithmic blueprint, i.e. the\nGaussian mechanism and adaptive episodes, to ensure a good privacy-utility\ntrade-off. We analyse and upper bound the regret of these three algorithms. Our\nanalysis shows that in all of these settings, the prices of imposing zCDP are\n(asymptotically) negligible in comparison with the regrets incurred oblivious\nto privacy. Next, we complement our regret upper bounds with the first minimax\nlower bounds on the regret of bandits with zCDP. To prove the lower bounds, we\nelaborate a new proof technique based on couplings and optimal transport. We\nconclude by experimentally validating our theoretical results for the three\ndifferent settings of bandits.\n', 'When Privacy Meets Partial Information: A Refined Analysis of\n  Differentially Private Bandits   We study the problem of multi-armed bandits with $\\epsilon$-global\nDifferential Privacy (DP). First, we prove the minimax and problem-dependent\nregret lower bounds for stochastic and linear bandits that quantify the\nhardness of bandits with $\\epsilon$-global DP. These bounds suggest the\nexistence of two hardness regimes depending on the privacy budget $\\epsilon$.\nIn the high-privacy regime (small $\\epsilon$), the hardness depends on a\ncoupled effect of privacy and partial information about the reward\ndistributions. In the low-privacy regime (large $\\epsilon$), bandits with\n$\\epsilon$-global DP are not harder than the bandits without privacy. For\nstochastic bandits, we further propose a generic framework to design a\nnear-optimal $\\epsilon$ global DP extension of an index-based optimistic bandit\nalgorithm. The framework consists of three ingredients: the Laplace mechanism,\narm-dependent adaptive episodes, and usage of only the rewards collected in the\nlast episode for computing private statistics. Specifically, we instantiate\n$\\epsilon$-global DP extensions of UCB and KL-UCB algorithms, namely AdaP-UCB\nand AdaP-KLUCB. AdaP-KLUCB is the first algorithm that both satisfies\n$\\epsilon$-global DP and yields a regret upper bound that matches the\nproblem-dependent lower bound up to multiplicative constants.\n']","[('bandit algorithms', 0.6255204677581787), ('linear bandits', 0.6181410551071167), ('differential privacy', 0.5973632335662842), ('contextual bandits', 0.5781199932098389), ('bandit problems', 0.5329623818397522), ('differentially private', 0.5177110433578491), ('privacy regime', 0.5062328577041626), ('bandits', 0.500851035118103), ('privacy constraints', 0.4819974899291992), ('optimal regret', 0.46480974555015564)]"
1677,1677,17,1677_compressible navier stokes_incompressible navier stokes_navier stokes equations_navier stokes system,"['compressible navier stokes', 'incompressible navier stokes', 'navier stokes equations', 'navier stokes system', 'viscous compressible', 'viscous compressible fluid', 'navier stokes', 'homogeneous incompressible', 'navier stokes fourier', 'incompressible navier']","[""Homogenization problems for the compressible Navier-Stokes system in 2D\n  perforated domains   In this paper, we study the homogenization problems for the stationary\ncompressible Navier-Stokes system in a bounded 2D domain, where the domain is\nperforated with very tiny holes (or obstacles) whose diameters are much smaller\nthan their mutual distances. We obtain that the process of homogenization\ndoesn't change the motion of the fluids. From another point of view, we obtain\nthe same system of equations in the asymptotic limit. It is the first result of\nhomogenization problem in the compressible case in 2 dimensions.\n"", ""Homogenization of the full compressible Navier-Stokes-Fourier system in\n  randomly perforated domains   We consider the homogenization of the compressible Navier-Stokes-Fourier\nequations in a randomly perforated domain in $\\mathbb{R}^3$. Assuming that the\nparticle size scales like $\\varepsilon^\\alpha$, where $\\varepsilon>0$ is their\nmutual distance and $\\alpha>3$, we show that in the limit $\\varepsilon\\to 0$,\nthe velocity, density, and temperature converge to a solution of the same\nsystem. We follow the methods of Lu and Pokorn\\'{y}\n[https://doi.org/10.1016/j.jde.2020.10.032], where they considered the full\nsystem in periodically perforated domains.\n"", 'Homogenization of the two-dimensional evolutionary compressible\n  Navier-Stokes equations   We consider the evolutionary compressible Navier-Stokes equations in a\ntwo-dimensional perforated domain, and show that in the subcritical case of\nvery tiny holes, the density and velocity converge to a solution of the\nevolutionary compressible Navier-Stokes equations in the non-perforated domain.\n']","[('compressible navier stokes', 0.7010465860366821), ('incompressible navier stokes', 0.6649144887924194), ('navier stokes equations', 0.6093897223472595), ('navier stokes system', 0.6083946824073792), ('viscous compressible', 0.6010719537734985), ('viscous compressible fluid', 0.5857884883880615), ('navier stokes', 0.567561149597168), ('homogeneous incompressible', 0.5506914258003235), ('navier stokes fourier', 0.5501347780227661), ('incompressible navier', 0.5312975645065308)]"
1678,1678,17,1678_hopf bifurcations_homoclinic bifurcations_hopf bifurcation_bifurcations,"['hopf bifurcations', 'homoclinic bifurcations', 'hopf bifurcation', 'bifurcations', 'bifurcation', 'takens bifurcations', 'bogdanov takens bifurcations', 'saddle node bifurcation', 'bogdanov takens bifurcation', 'takens bifurcation']","[""On the pitchfork bifurcation of the folded node and other unbounded\n  time-reversible connection problems in $\\mathbb R^3$   In this paper, we revisit the folded node and the bifurcations of secondary\ncanards at resonances $\\mu\\in \\mathbb N$. In particular, we prove for the first\ntime that pitchfork bifurcations occur at all even values of $\\mu$. Our\napproach relies on a time-reversible version of the Melnikov approach in\n\\cite{wechselberger2002a}, used in \\cite{wechselberger_existence_2005} to prove\nthe transcritical bifurcations for all odd values of $\\mu$. It is known that\nthe secondary canards produced by the transcritical and the pitchfork\nbifurcations only reach the Fenichel slow manifolds on one side of each\ntranscritical bifurcation for all $0<\\epsilon\\ll 1$. In this paper, we provide\na new geometric explanation for this fact, relying on the symmetry of the\nnormal form and a separate blowup of the fold lines. We also show that our\napproach for evaluating the Melnikov integrals of the folded node -- based upon\nlocal characterization of the invariant manifolds by higher order variational\nequations and reducing these to an inhomogeneous Weber equation -- applies to\ngeneral, quadratic, time-reversible, unbounded connection problems in $\\mathbb\nR^3$. We conclude the paper by using our approach to present a new proof of the\nbifurcation of periodic orbits from infinity in the Falkner-Skan equation and\nthe Nos\\'e equations.\n"", 'Singularly Perturbed Boundary-Equilibrium Bifurcations   Boundary equilibria bifurcation (BEB) arises in piecewise-smooth systems when\nan equilibrium collides with a discontinuity set under parameter variation.\nSingularly perturbed BEB refers to a bifurcation arising in singular\nperturbation problems which limit as some $\\epsilon \\to 0$ to piecewise-smooth\n(PWS) systems which undergo a BEB. This work completes a classification for\ncodimension-1 singularly perturbed BEB in the plane initiated by the present\nauthors in [19], using a combination of tools from PWS theory, geometric\nsingular perturbation theory (GSPT) and a method of geometric desingularization\nknown as blow-up. After deriving a local normal form capable of generating all\n12 singularly perturbed BEBs, we describe the unfolding in each case. Detailed\nquantitative results on saddle-node, Andronov-Hopf, homoclinic and\ncodimension-2 Bogdanov-Takens bifurcations involved in the unfoldings and\nclassification are presented. Each bifurcation is singular in the sense that it\noccurs within a domain which shrinks to zero as $\\epsilon \\to 0$ at a rate\ndetermined by the rate at which the system loses smoothness. Detailed\nasymptotics for a distinguished homoclinic connection which forms the boundary\nbetween two singularly perturbed BEBs in parameter space are also given.\nFinally, we describe the explosive onset of oscillations arising in the\nunfolding of a particular singularly perturbed boundary-node (BN) bifurcation.\nWe prove the existence of the oscillations as perturbations of PWS cycles, and\nderive a growth rate which is polynomial in $\\epsilon$ and dependent on the\nrate at which the system loses smoothness. For all the results presented\nherein, corresponding results for regularized PWS systems are obtained via the\nlimit $\\epsilon \\to 0$.\n', 'Symmetry-breaking singular controller design for Bogdanov-Takens\n  bifurcations with an application to Chua system   We provide a complete symmetry-breaking bifurcation control for equivariant\nsmooth differential systems with Bogdanov-Takens singularities. Controller\ncoefficient space is partitioned by critical controller sets into different\nconnected regions. The connected regions provide a classification for all\nqualitatively different dynamics of the controlled system. Hence, a state\nfeedback controller design with four small controller coefficients is proposed\nfor an efficient and full singular symmetry-breaking control. Our approach\nworks well for nonlinear control systems with both controllable and\nuncontrollable linearizations. Origin is a primary equilibrium for the\nuncontrolled system. This gives rise to two secondary local equilibria for the\ncontrolled system. These equilibria further experience tertiary fold and\nhysteresis type bifurcations. The secondary and primary equilibria experience\nHopf and Bautin bifurcations leading to the appearance of one limit cycle from\nprimary equilibrium, and either one or two from each secondary equilibria. The\ncollisions of limit cycles with equilibria lead to either a heteroclinic cycle\nor four different homoclinic cycles. Each pair of limit cycles may respectively\nmerge together and disappear. This is a saddle-node bifurcation of limit\ncycles. Different combinations of these give rise to a rich list of bifurcation\nscenarios. Finite determinacy of each of these bifurcations has been thoroughly\ninvestigated. This greatly influences their stabilization potential in\napplications. We consider Chua system with a quadratic state-feedback\ncontroller. Controlled Chua system experiences a pitchfork bifurcation, three\nHopf bifurcations and two homoclinic bifurcations. There exist two different\nregions of controller coefficient choices for feedback regularization and two\nnearby regions for supercritical Hopf stabilization approach.\n']","[('hopf bifurcations', 0.7742345929145813), ('homoclinic bifurcations', 0.7519301772117615), ('hopf bifurcation', 0.742787778377533), ('bifurcations', 0.7014982104301453), ('bifurcation', 0.677812397480011), ('takens bifurcations', 0.6722109317779541), ('bogdanov takens bifurcations', 0.6661090850830078), ('saddle node bifurcation', 0.6603080034255981), ('bogdanov takens bifurcation', 0.6571536660194397), ('takens bifurcation', 0.6492587327957153)]"
1679,1679,17,1679_quantum hypothesis testing_quantum hypothesis_quantum state discrimination_quantum relative entropy,"['quantum hypothesis testing', 'quantum hypothesis', 'quantum state discrimination', 'quantum relative entropy', 'arbitrary quantum', 'random quantum', 'quantum correlations', 'generalised quantum', 'cost quantum', 'bounds entanglement']","[""Error bounds for composite quantum hypothesis testing and a new\n  characterization of the weighted Kubo-Ando geometric means   The optimal error exponents of binary composite i.i.d. state discrimination\nare trivially bounded by the worst-case pairwise exponents of discriminating\nindividual elements of the sets representing the two hypotheses, and in the\nfinite-dimensional classical case, these bounds in fact give exact single-copy\nexpressions for the error exponents. In contrast, in the non-commutative case,\nthe optimal exponents are only known to be expressible in terms of regularized\ndivergences, resulting in formulas that, while conceptually relevant,\npractically not very useful. In this paper, we develop further an approach\ninitiated in [Mosonyi, Szil\\'agyi, Weiner, IEEE Trans. Inf. Th.\n68(2):1032--1067, 2022] to give improved single-copy bounds on the error\nexponents by comparing not only individual states from the two hypotheses, but\nalso various unnormalized positive semi-definite operators associated to them.\nHere, we show a number of equivalent characterizations of such operators giving\nvalid bounds, and show that in the commutative case, considering weighted\ngeometric means of the states, and in the case of two states per hypothesis,\nconsidering weighted Kubo-Ando geometric means, are optimal for this approach.\nAs a result, we give a new characterization of the weighted Kubo-Ando geometric\nmeans as the only $2$-variable operator geometric means that are block\nadditive, tensor multiplicative, and satisfy the arithmetic-geometric mean\ninequality. We also extend our results to composite quantum channel\ndiscrimination, and show an analogous optimality property of the weighted\nKubo-Ando geometric means of two quantum channels, a notion that seems to be\nnew. We extend this concept to defining the notion of superoperator perspective\nfunction and establish some of its basic properties, which may be of\nindependent interest.\n"", 'Interpolating between symmetric and asymmetric hypothesis testing   The task of binary quantum hypothesis testing is to determine the state of a\nquantum system via measurements on it, given the side information that it is in\none of two possible states, say $\\rho$ and $\\sigma$. This task is generally\nstudied in either the symmetric setting, in which the two possible errors\nincurred in the task (the so-called type I and type II errors) are treated on\nan equal footing, or the asymmetric setting in which one minimizes the type II\nerror probability under the constraint that the corresponding type I error\nprobability is below a given threshold. Here we define a one-parameter family\nof binary quantum hypothesis testing tasks, which we call $s$-hypothesis\ntesting, and in which the relative significance of the two errors are weighted\nby a parameter $s$. In particular, $s$-hypothesis testing interpolates\ncontinuously between the regimes of symmetric and asymmetric hypothesis\ntesting. Moreover, if arbitrarily many identical copies of the system are\nassumed to be available, then the minimal error probability of $s$-hypothesis\ntesting is shown to decay exponentially in the number of copies, with a decay\nrate given by a quantum divergence which we denote as $\\xi_s(\\rho\\|\\sigma)$,\nand which satisfies a host of interesting properties. Moreover, this\none-parameter family of divergences interpolates continuously between the\ncorresponding decay rates for symmetric hypothesis testing (the quantum\nChernoff divergence) for $s = 1$, and asymmetric hypothesis testing (the\nUmegaki relative entropy) for $s = 0$.\n', ""Postselected quantum hypothesis testing   We study a variant of quantum hypothesis testing wherein an additional\n'inconclusive' measurement outcome is added, allowing one to abstain from\nattempting to discriminate the hypotheses. The error probabilities are then\nconditioned on a successful attempt, with inconclusive trials disregarded. We\ncompletely characterise this task in both the single-shot and asymptotic\nregimes, providing exact formulas for the optimal error probabilities. In\nparticular, we prove that the asymptotic error exponent of discriminating any\ntwo quantum states $\\rho$ and $\\sigma$ is given by the Hilbert projective\nmetric $D_{\\max}(\\rho\\|\\sigma) + D_{\\max}(\\sigma \\| \\rho)$ in asymmetric\nhypothesis testing, and by the Thompson metric $\\max \\{ D_{\\max}(\\rho\\|\\sigma),\nD_{\\max}(\\sigma \\| \\rho) \\}$ in symmetric hypothesis testing. This endows these\ntwo quantities with fundamental operational interpretations in quantum state\ndiscrimination. Our findings extend to composite hypothesis testing, where we\nshow that the asymmetric error exponent with respect to any convex set of\ndensity matrices is given by a regularisation of the Hilbert projective metric.\nWe apply our results also to quantum channels, showing that no advantage is\ngained by employing adaptive or even more general discrimination schemes over\nparallel ones, in both the asymmetric and symmetric settings. Our state\ndiscrimination results make use of no properties specific to quantum mechanics\nand are also valid in general probabilistic theories.\n""]","[('quantum hypothesis testing', 0.631601095199585), ('quantum hypothesis', 0.5631243586540222), ('quantum state discrimination', 0.5458739399909973), ('quantum relative entropy', 0.510892391204834), ('arbitrary quantum', 0.4991553723812103), ('random quantum', 0.49529460072517395), ('quantum correlations', 0.4815831780433655), ('generalised quantum', 0.4778205156326294), ('cost quantum', 0.47475266456604004), ('bounds entanglement', 0.45274293422698975)]"
1680,1680,17,1680_testing rate_infection status_adaptive testing_epidemic outbreak,"['testing rate', 'infection status', 'adaptive testing', 'epidemic outbreak', 'hiv', 'infected cases', 'testing strategies', 'testing', 'infected individuals', 'infection recovery']","['Modeling and Control of Epidemics through Testing Policies   Testing is a crucial control mechanism in the beginning phase of an epidemic\nwhen the vaccines are not yet available. It enables the public health authority\nto detect and isolate the infected cases from the population, thereby limiting\nthe disease transmission to susceptible people. However, despite the\nsignificance of testing in epidemic control, the recent literature on the\nsubject lacks a control-theoretic perspective. In this paper, an epidemic model\nis proposed that incorporates the testing rate as a control input and\ndifferentiates the undetected infected from the detected infected cases, who\nare assumed to be removed from the disease spreading process in the population.\nAfter estimating the model on the data corresponding to the beginning phase of\nCOVID-19 in France, two testing policies are proposed: the so-called\nbest-effort strategy for testing (BEST) and constant optimal strategy for\ntesting (COST). The BEST policy is a suppression strategy that provides a\nminimum testing rate that stops the growth of the epidemic when implemented.\nThe COST policy, on the other hand, is a mitigation strategy that provides an\noptimal value of testing rate minimizing the peak value of the infected\npopulation when the total stockpile of tests is limited. Both testing policies\nare evaluated by their impact on the number of active intensive care unit (ICU)\ncases and the cumulative number of deaths for the COVID-19 case of France.\n', ""Using Timeliness in Tracking Infections   We consider real-time timely tracking of infection status (e.g., covid-19) of\nindividuals in a population. In this work, a health care provider wants to\ndetect infected people as well as people who have recovered from the disease as\nquickly as possible. In order to measure the timeliness of the tracking\nprocess, we use the long-term average difference between the actual infection\nstatus of the people and their real-time estimate by the health care provider\nbased on the most recent test results. We first find an analytical expression\nfor this average difference for given test rates, infection rates and recovery\nrates of people. Next, we propose an alternating minimization based algorithm\nto find the test rates that minimize the average difference. We observe that if\nthe total test rate is limited, instead of testing all members of the\npopulation equally, only a portion of the population may be tested in unequal\nrates calculated based on their infection and recovery rates. Next, we\ncharacterize the average difference when the test measurements are erroneous\n(i.e., noisy). Further, we consider the case where the infection status of\nindividuals may be dependent, which happens when an infected person spreads the\ndisease to another person if they are not detected and isolated by the health\ncare provider. Then, we consider an age of incorrect information based error\nmetric where the staleness metric increases linearly over time as long as the\nhealth care provider does not detect the changes in the infection status of the\npeople. In numerical results, we observe that an increased population size\nincreases diversity of people with different infection and recovery rates which\nmay be exploited to spend testing capacity more efficiently. Depending on the\nhealth care provider's preferences, test rate allocation can be adjusted to\ndetect either the infected people or the recovered people more quickly.\n"", ""Timely Tracking of Infection Status of Individuals in a Population   We consider real-time timely tracking of infection status (e.g., covid-19) of\nindividuals in a population. In this work, a health care provider wants to\ndetect infected people as well as people who recovered from the disease as\nquickly as possible. In order to measure the timeliness of the tracking\nprocess, we use the long-term average difference between the actual infection\nstatus of the people and their real-time estimate by the health care provider\nbased on the most recent test results. We first find an analytical expression\nfor this average difference for given test rates, and given infection and\nrecovery rates of people. Next, we propose an alternating minimization based\nalgorithm to minimize this average difference. We observe that if the total\ntest rate is limited, instead of testing all members of the population equally,\nonly a portion of the population is tested based on their infection and\nrecovery rates. We also observe that increasing the total test rate helps track\nthe infection status better. In addition, an increased population size\nincreases diversity of people with different infection and recovery rates,\nwhich may be exploited to spend testing capacity more efficiently, thereby\nimproving the system performance. Finally, depending on the health care\nprovider's preferences, test rate allocation can be altered to detect either\nthe infected people or the recovered people more quickly.\n""]","[('testing rate', 0.4721541404724121), ('infection status', 0.4222381114959717), ('adaptive testing', 0.4214427173137665), ('epidemic outbreak', 0.4095596671104431), ('hiv', 0.40520256757736206), ('infected cases', 0.3944353759288788), ('testing strategies', 0.39240917563438416), ('testing', 0.37393033504486084), ('infected individuals', 0.37120476365089417), ('infection recovery', 0.3707387149333954)]"
1681,1681,17,1681_fluid antenna systems_fluid antenna system_antenna systems_antenna system fas,"['fluid antenna systems', 'fluid antenna system', 'antenna systems', 'antenna system fas', 'antenna system', 'fluid antenna assisted', 'fluid antennas', 'fluid antenna', 'single antenna', 'antenna']","['Performance Analysis of Fluid Antenna System under Spatially-Correlated Rician Fading Channels Fluid antenna systems (FAS) are among the most promising technologies for the sixth generation (6G) mobile communication networks. Unlike traditional fixed-position multiple-input multiple-output (MIMO) systems, a FAS possesses position reconfigurability to switch on-demand among $N$ predefined ports over a prescribed space. This paper explores the performance of a single-input single-output (SISO) model with a fixed-position antenna transmitter and a single-antenna FAS receiver, referred to as the Rx-SISO-FAS model, under spatially-correlated Rician fading channels. Our contributions include exact expressions and closed-form bounds for the outage probability of the Rx-SISO-FAS model, as well as exact and closed-form lower bounds for the ergodic rate. Importantly, we also analyze the performance considering both uniform linear array (ULA) and uniform planar array (UPA) configurations for the ports of the FAS. To gain insights, we evaluate the diversity order of the proposed model and our analytical results indicate that with a fixed overall system size, increasing the number of ports, $N$, significantly decreases the outage performance of FAS under different Rician fading factors. Our numerical results further demonstrate that: $i)$ the Rx-SISO-FAS model can enhance performance under spatially-correlated Rician fading channels over the fixed-position antenna counterpart; $ii)$ the Rician factor negatively impacts performance in the low signal-to-noise ratio (SNR) regime; $iii$) FAS can outperform an $L$ branches maximum ratio combining (MRC) system under Rician fading channels; and $iv)$ when the number of ports is identical, UPA outperforms ULA.', 'Fluid Antenna System: New Insights on Outage Probability and Diversity\n  Gain   To enable innovative applications and services, both industry and academia\nare exploring new technologies for sixth generation (6G) communications. One of\nthe promising candidates is fluid antenna system (FAS). Unlike existing\nsystems, FAS is a novel communication technology where its antenna can freely\nchange its position and shape within a given space. Compared to the traditional\nsystems, this unique capability has the potential of providing higher diversity\nand interference-free communications. Nevertheless, the performance limits of\nFAS remain unclear as its system properties are difficult to analyze. To\naddress this, we approximate the outage probability and diversity gain of FAS\nin closed-form expressions. We then propose a suboptimal FAS with $N^{*}$\nports, where a significant gain can be obtained over FAS with $N^{*}-1$ ports\nwhilst FAS with $N^{*}+1$ ports only yields marginal improvement over the\nproposed suboptimal FAS. In this paper, we also provide analytical and\nsimulation results to unfold the key factors that affect the performance of\nFAS. Limited to systems with one active radio frequency (RF)-chain, we show\nthat the proposed suboptimal FAS outperforms single-antenna (SISO) system and\nselection combining (SC) system in terms of outage probability. Interestingly,\nwhen the given space is $\\frac{\\lambda}{2}$, the outage probability of the\nproposed suboptimal FAS with one active RF-chain achieves near to that of the\nmaximal ratio combining (MRC) system with multiple active RF-chains.\n', 'Performance Limits of Fluid Antenna Systems   Fluid antenna represents a concept where a mechanically flexible antenna can\nswitch its location freely within a given space. Recently, it has been reported\nthat even with a tiny space, a single-antenna fluid antenna system (FAS) can\noutperform an L-antenna maximum ratio combining (MRC) system in terms of outage\nprobability if the number of locations (or ports) the fluid antenna can be\nswitched to, is large enough. This letter aims to study if extraordinary\ncapacity can also be achieved by FAS with a small space. We do this by deriving\nthe ergodic capacity, and a capacity lower bound. This letter also derives the\nlevel crossing rate (LCR) and average fade duration (AFD) for the FAS.\n']","[('fluid antenna systems', 0.6419730186462402), ('fluid antenna system', 0.6057310700416565), ('antenna systems', 0.5887336730957031), ('antenna system fas', 0.5680448412895203), ('antenna system', 0.5591408014297485), ('fluid antenna assisted', 0.5575315952301025), ('fluid antennas', 0.5520773530006409), ('fluid antenna', 0.5274300575256348), ('single antenna', 0.510672390460968), ('antenna', 0.506255567073822)]"
1682,1682,17,1682_stochastic parabolic_parabolic stochastic_stochastic evolution equations_solutions stochastic,"['stochastic parabolic', 'parabolic stochastic', 'stochastic evolution equations', 'solutions stochastic', 'nonlinear stochastic', 'stochastic navier stokes', 'ergodicity stochastic', 'stochastic navier', 'stochastic evolution', 'local stochastic']","['Ergodicity for stochastic equation of Navier--Stokes type   In the first part of the note we analyze the long time behaviour of a two\ndimensional stochastic Navier--Stokes equations system on a torus with a\ndegenerate, one dimensional noise. In particular, for some initial data and\nnoises we identify the invariant probability measure for the system and give a\nsufficient condition under which it is unique and stochastically stable. In the\nsecond part of the note, we consider a simple example of a finite-dimensional\nsystem of stochastic differential equations driven by a one dimensional Wiener\nprocess with a drift, that displays some similarity with the stochastic N.S.E.,\nand investigate its ergodic properties depending on the strength of the drift.\nIf the latter is sufficiently small and lies below a critical threshold, then\nthe system admits a unique invariant probability measure which is Gaussian. If,\non the other hand, the strength of the noise drift is larger than the\nthreshold, then in addition to a Gaussian invariant probability measure, there\nexist another one. In particular, the generator of the system is not\nhypoelliptic.\n', 'Nonlinear parabolic stochastic evolution equations in critical spaces\n  Part I. Stochastic maximal regularity and local existence   In this paper we develop a new approach to nonlinear stochastic partial\ndifferential equations with Gaussian noise. Our aim is to provide an abstract\nframework which is applicable to a large class of SPDEs and includes many\nimportant cases of nonlinear parabolic problems which are of quasi- or\nsemilinear type. This first part is on local existence and well-posedness. A\nsecond part in preparation is on blow-up criteria and regularization. Our\ntheory is formulated in an $L^p$-setting, and because of this we can deal with\nnonlinearities in a very efficient way. Applications to several concrete\nproblems and their quasilinear variants are given. This includes Burger\'s\nequation, the Allen-Cahn equation, the Cahn-Hilliard equation,\nreaction-diffusion equations, and the porous media equation. The interplay of\nthe nonlinearities and the critical spaces of initial data leads to new results\nand insights for these SPDEs. The proofs are based on recent developments in\nmaximal regularity theory for the linearized problem for deterministic and\nstochastic evolution equations. In particular, our theory can be seen as a\nstochastic version of the theory of critical spaces due to\nPr\\""uss-Simonett-Wilke (2018). Sharp weighted time-regularity allow us to deal\nwith rough initial values and obtain instantaneous regularization results. The\nabstract well-posedness results are obtained by a combination of several\nsophisticated splitting and truncation arguments.\n', 'Nonlinear parabolic stochastic evolution equations in critical spaces\n  Part II. Blow-up criteria and instantaneous regularization   This paper is a continuation of Part I of this project, where we developed a\nnew local well-posedness theory for nonlinear stochastic PDEs with Gaussian\nnoise. In the current Part II we consider blow-up criteria and regularization\nphenomena. As in Part I we can allow nonlinearities with polynomial growth, and\nrough initial values from critical spaces.\n  In the first main result we obtain several new blow-up criteria for quasi-\nand semilinear stochastic evolution equations. In particular, for semilinear\nequations we obtain a Serrin type blow-up criterium, which extends a recent\nresult of Pr\\""uss-Simonett-Wilke (2018) to the stochastic setting. Blow-up\ncriteria can be used to prove global well-posedness for SPDEs. As in Part I,\nmaximal regularity techniques and weights in time play a central role in the\nproofs.\n  Our second contribution is a new method to bootstrap Sobolev and H\\""older\nregularity in time and space, which does not require smoothness of the initial\ndata. The blow-up criteria are at the basis of these new methods. Moreover, in\napplications the bootstrap results can be combined with our blow-up criteria,\nto obtain efficient ways to prove global existence. This gives new results even\nin classical $L^2$-settings, which we illustrate for a concrete SPDE.\n  In future works in preparation we apply the results of the current paper to\nobtain global well-posedness results, and regularity for several concrete\nSPDEs. These include stochastic Navier-Stokes, reaction diffusion equations,\nand Allen-Cahn equations. Our setting allows to put these SPDEs into a more\nflexible framework, where less restrictions on the nonlinearities are needed,\nand we are able to treat rough initial values from critical spaces. Moreover,\nwe will obtain higher order regularity results.\n']","[('stochastic parabolic', 0.6657612919807434), ('parabolic stochastic', 0.656446099281311), ('stochastic evolution equations', 0.6179160475730896), ('solutions stochastic', 0.6088553071022034), ('nonlinear stochastic', 0.5882018208503723), ('stochastic navier stokes', 0.5880392789840698), ('ergodicity stochastic', 0.5864304900169373), ('stochastic navier', 0.5808746218681335), ('stochastic evolution', 0.5580386519432068), ('local stochastic', 0.5359276533126831)]"
1683,1683,17,1683_droplets_dynamics_nonlinear dynamics_bouncing,"['droplets', 'dynamics', 'nonlinear dynamics', 'bouncing', 'hydrodynamic', 'emergent dynamics', 'fluid particle', 'vibrations', 'damped driven', 'droplet']","['Collective vibrations of a hydrodynamic active lattice   Recent experiments show that quasi-one-dimensional lattices of self-propelled\ndroplets exhibit collective instabilities in the form of out-of-phase\noscillations and solitary-like waves. This hydrodynamic lattice is driven by\nthe external forcing of a vertically vibrating fluid bath, which invokes a\nfield of subcritical Faraday waves on the bath surface, mediating the\nspatio-temporal droplet coupling.By modelling the droplet lattice as a\nmemory-endowed system with spatially nonlocal coupling, we herein rationalise\nthe form and onset of instability in this new class of dynamical oscillator. We\nidentify the memory-driven instability of the lattice as a function of the\nnumber of droplets, and determine equispaced lattice configurations precluded\nby geometrical constraints. Each memory-driven instability is then classified\nas either a super- or sub-critical Hopf bifurcation \\emph{via} a systematic\nweakly nonlinear analysis, rationalising experimental observations. We further\ndiscover a previously unreported symmetry-breaking instability, manifest as an\noscillatory-rotary motion of the lattice. Numerical simulations support our\nfindings and prompt further investigations of this nonlinear dynamical system.\n', ""Walking Droplets Through the Lens of Dynamical Systems   Over the past decade the study of fluidic droplets bouncing and skipping (or\n``walking'') on a vibrating fluid bath has gone from an interesting experiment\nto a vibrant research field. The field exhibits challenging fluids problems,\npotential connections with quantum mechanics, and complex nonlinear dynamics.\nWe detail advancements in the field of walking droplets through the lens of\nDynamical Systems Theory, and outline questions that can be answered using\ndynamical systems analysis. The article begins by discussing the history of the\nfluidic experiments and their resemblance to quantum experiments. With this\nphysics backdrop, we paint a portrait of the complex nonlinear dynamics present\nin physical models of various walking droplet systems. Naturally, these\ninvestigations lead to even more questions, and some unsolved problems that are\nbound to benefit from rigorous Dynamical Systems Analysis are outlined.\n"", 'Damped-driven system of bouncing droplets leading to deterministic\n  diffusive behavior   Damped-driven systems are ubiquitous in science, however the damping and\ndriving mechanisms are often quite convoluted. This manuscript presents an\nexperimental and theoretical investigation of a fluidic droplet on a vertically\nvibrating fluid bath as a damped-driven system. We study a fluidic droplet in\nan annular cavity with the fluid bath forced above the Faraday wave threshold.\nWe model the droplet as a kinematic point particle in air and as inelastic\ncollisions during impact with the bath. In both experiments and the model the\ndroplet is observed to chaotically change velocity with a Gaussian\ndistribution. Finally, the statistical distributions from experiments and\ntheory are analyzed. Incredibly, this simple deterministic interaction of\ndamping and driving of the droplet leads to more complex Brownian-like and\nLevy-like behavior.\n']","[('droplets', 0.532509982585907), ('dynamics', 0.5046894550323486), ('nonlinear dynamics', 0.45414191484451294), ('bouncing', 0.44616398215293884), ('hydrodynamic', 0.43003183603286743), ('emergent dynamics', 0.4258083999156952), ('fluid particle', 0.38826602697372437), ('vibrations', 0.38563284277915955), ('damped driven', 0.3815045654773712), ('droplet', 0.38001254200935364)]"
1684,1684,17,1684_multi soliton solutions_soliton solutions_kdv equations_kadomtsev petviashvili hierarchy,"['multi soliton solutions', 'soliton solutions', 'kdv equations', 'kadomtsev petviashvili hierarchy', 'multi soliton', 'integrable equations', 'solitons', 'integrable systems', 'coupled kdv', 'boussinesq equations']","['Kadomtsev-Petviashvili hierarchies of types B and C   This is a short review of the Kadomtsev-Petviashvili hierarchies of types B\nand C. The main objects are the $L$-operator, the wave operator, the auxiliary\nlinear problems for the wave function, the bilinear identity for the wave\nfunction and the tau-function. All of them are discussed in the paper. The\nconnections with the usual Kadomtsev-Petviashvili hierarchy (of the type A) are\nclarified. Examples of soliton solutions and the dispersionless limit of the\nhierarchies are also considered.\n', 'On a coupled Kadomtsev--Petviashvili system associated with an elliptic\n  curve   The coupled Kadomtsev--Petviashvili system associated with an elliptic curve,\nproposed by Date, Jimbo and Miwa [J. Phys. Soc. Jpn., 52:766--771, 1983], is\nreinvestigated within the direct linearisation framework, which provides us\nwith more insights into the integrability of this elliptic model from the\nperspective of a general linear integral equation. As a result, we successfully\nconstruct for the elliptic coupled Kadomtsev--Petviashvili system not only a\nLax pair composed of differential operators in $2\\times2$ matrix form but also\nmulti-soliton solutions with phases parametrised by points on the elliptic\ncurve. Dimensional reductions based on the direct linearisation, to the\nelliptic coupled Korteweg-de Vries and Boussinesq systems, are also discussed.\nIn addition, a novel class of solutions are obtained for the $D_\\infty$-type\nKadomtsev--Petviashvili equation with nonzero constant background as a\nbyproduct.\n', 'Common Hirota Form B\\""{a}cklund Transformation for the Unified Soliton\n  System   We study to unify soliton systems, KdV/mKdV/sinh-Gordon, through SO(2,1)\n$\\cong$ GL(2,$\\mathbb R$) $\\cong$ M\\""{o}bius group point of view, which might\nbe a keystone to exactly solve some special non-linear differential equations.\nIf we construct the $N$-soliton solutions through the KdV type B\\""{a}cklund\ntransformation, we can transform different KdV/mKdV/sinh-Gordon equations and\nthe B\\""{a}cklund transformations of the standard form into the same common\nHirota form and the same common B\\""{a}cklund transformation except the equation\nwhich has the time-derivative term. The difference is only the time-dependence\nand the main structure of the $N$-soliton solutions has same common form for\nKdV/mKdV/sinh-Gordon systems. Then the $N$-soliton solutions for the\nsinh-Gordon equation is obtained just by the replacement from KdV/mKdV\n$N$-soliton solutions. We also give general addition formulae coming from the\nKdV type B\\""{a}cklund transformation which plays not only an important role to\nconstruct the trigonometric/hyperbolic $N$-soliton solutions but also an\nessential role to construct the elliptic $N$-soliton solutions. In contrast to\nthe KdV type B\\""{a}cklund transformation, the well-known mKdV/sinh-Gordon type\nB\\""{a}cklund transformation gives the non-cyclic symmetric $N$-soliton\nsolutions. We give an explicit non-cyclic symmetric 3-soliton solution for\nKdV/mKdV/sinh-Gordon equations.\n']","[('multi soliton solutions', 0.5954300761222839), ('soliton solutions', 0.5811634063720703), ('kdv equations', 0.5683749914169312), ('kadomtsev petviashvili hierarchy', 0.558489203453064), ('multi soliton', 0.53936368227005), ('integrable equations', 0.5040083527565002), ('solitons', 0.48313021659851074), ('integrable systems', 0.46679067611694336), ('coupled kdv', 0.4657615125179291), ('boussinesq equations', 0.46494269371032715)]"
1685,1685,17,1685_ahler einstein metrics_fano manifolds_ahler einstein metric_fano manifold,"['ahler einstein metrics', 'fano manifolds', 'ahler einstein metric', 'fano manifold', 'smooth fano threefolds', 'kahler ricci', 'ahler ricci', 'ahler einstein', 'einstein metrics', 'fano threefolds']","['K\\""ahler-Einstein metrics on smooth Fano toroidal symmetric varieties of\n  type AIII   The wonderful compactification $X_m$ of a symmetric homogeneous space of type\nAIII$(2,m)$ for each $m \\geq 4$ is Fano, and its blowup $Y_m$ along the unique\nclosed orbit is Fano if $m \\geq 5$ and Calabi-Yau if $m = 4$. Using a\ncombinatorial criterion for K-polystability of smooth Fano spherical varieties\nobtained by Delcroix, we prove that $X_m$ admits a K\\""ahler-Einstein metric for\neach $m \\geq 4$ and $Y_m$ admits a K\\""ahler-Einstein metric if and only if $m =\n4, 5$.\n', 'K-Stability of Fano spherical varieties   We prove a criterion for K-stability of a $\\mathbb{Q}$-Fano spherical variety\nwith respect to equivariant special test configurations, in terms of its moment\npolytope and some combinatorial data associated to the open orbit. Combined\nwith the equivariant version of the Yau-Tian-Donaldson conjecture for Fano\nmanifolds proved by Datar and Sz\\\'ekelyhidi, it yields a criterion for the\nexistence of a K\\""ahler-Einstein metric on a spherical Fano manifold. The\nresults hold also for modified K-stability and existence of K\\""ahler-Ricci\nsolitons.\n', 'K\\""{a}hler-Einstein metrics on smooth Fano symmetric varieties with\n  Picard number one   Symmetric varieties are normal equivarient open embeddings of symmetric\nhomogeneous spaces, and they are interesting examples of spherical varieties.\nWe prove that all smooth Fano symmetric varieties with Picard number one admit\nK\\""{a}hler-Einstein metrics by using a combinatorial criterion for K-stability\nof Fano spherical varieties obtained by Delcroix. For this purpose, we present\ntheir algebraic moment polytopes and compute the barycenter of each moment\npolytope with respect to the Duistermaat-Heckman measure.\n']","[('ahler einstein metrics', 0.618696928024292), ('fano manifolds', 0.5977462530136108), ('ahler einstein metric', 0.5764334797859192), ('fano manifold', 0.5719650983810425), ('smooth fano threefolds', 0.516584575176239), ('kahler ricci', 0.47108855843544006), ('ahler ricci', 0.46656471490859985), ('ahler einstein', 0.4461486041545868), ('einstein metrics', 0.444161593914032), ('fano threefolds', 0.4406702518463135)]"
1686,1686,17,1686_sparsity regularization_regularization methods_regularization operator_regularization technique,"['sparsity regularization', 'regularization methods', 'regularization operator', 'regularization technique', 'regularization', 'regularization yields', 'regularization parameter', 'regularization procedure', 'tikhonov regularization', 'regularization can']","['Weighted sparsity regularization for source identification for elliptic\n  PDEs   This investigation is motivated by PDE-constrained optimization problems\narising in connection with electrocardiograms (ECGs) and electroencephalography\n(EEG). Standard sparsity regularization does not necessarily produce adequate\nresults for these applications because only boundary data/observations are\navailable for the identification of the unknown source, which may be interior.\nWe therefore study a weighted $\\ell^1$-regularization technique for solving\ninverse problems when the forward operator has a significant null space. In\nparticular, we prove that a sparse source, regardless of whether it is interior\nor located at the boundary, can be exactly recovered with this weighting\nprocedure as the regularization parameter $\\alpha$ tends to zero. Our analysis\nis supported by numerical experiments for cases with one and several local\nsources. The theory is developed in terms of Euclidean spaces, and our results\ncan therefore be applied to many problems.\n', 'Box constraints and weighted sparsity regularization for identifying\n  sources in elliptic PDEs   We explore the possibility for using boundary data to identify sources in\nelliptic PDEs. Even though the associated forward operator has a large null\nspace, it turns out that box constraints, combined with weighted sparsity\nregularization, can enable rather accurate recovery of sources with constant\nmagnitude/strength. In addition, for sources with varying strength, the support\nof the inverse solution will be a subset of the support of the true source. We\npresent both an analysis of the problem and a series of numerical experiments.\nOur work only addresses discretized problems.\n  The reason for introducing the weighting procedure is that standard\n(unweighted) sparsity regularization fails to provide adequate results for the\nsource identification task considered in this paper. This investigation is also\nmotivated by applications, e.g., recovering mass distributions from\nmeasurements of gravitational fields and inverse scattering. We develop the\nmethodology and the analysis in terms of Euclidean spaces, and our results can\ntherefore be applied to many problems. For example, the results are equally\napplicable to models involving the screened Poisson equation as to models using\nthe Helmholtz equation, with both large and small wave numbers.\n', ""A regularization operator for source identification for elliptic PDEs   We study a source identification problem for a prototypical elliptic PDE from\nDirichlet boundary data. This problem is ill-posed, and the involved forward\noperator has a significant nullspace. Standard Tikhonov regularization yields\nsolutions which approach the minimum $L^2$-norm least-squares solution as the\nregularization parameter tends to zero. We show that this approach 'always'\nsuggests that the unknown local source is very close to the boundary of the\ndomain of the PDE, regardless of the position of the true local source.\n  We propose an alternative regularization procedure, realized in terms of a\nnovel regularization operator, which is better suited for identifying local\nsources positioned anywhere in the domain of the PDE. Our approach is motivated\nby the classical theory for Tikhonov regularization and yields a standard\nquadratic optimization problem. Since the new methodology is derived for an\nabstract operator equation, it can be applied to many other source\nidentification problems. This paper contains several numerical experiments and\nan analysis of the new methodology.\n""]","[('sparsity regularization', 0.6229920387268066), ('regularization methods', 0.6081237196922302), ('regularization operator', 0.5940055251121521), ('regularization technique', 0.586001455783844), ('regularization', 0.5513755083084106), ('regularization yields', 0.5480333566665649), ('regularization parameter', 0.5472968816757202), ('regularization procedure', 0.5470151901245117), ('tikhonov regularization', 0.5157033205032349), ('regularization can', 0.458091676235199)]"
1687,1687,17,1687_minimizers non_local minimizers_minimizers_global minimizers,"['minimizers non', 'local minimizers', 'minimizers', 'global minimizers', 'nonlocal interaction', 'energy minimizers', 'dimensional periodic functions', 'one dimensional periodic', 'energy minimizer', 'radial symmetry']","['Periodic striped configurations in the large volume limit   We show striped pattern formation in the large volume limit for a class of\ngeneralized antiferromagnetic local/nonlocal interaction functionals in general\ndimension previously considered Goldman-Runa and Daneri-Runa and in\nGiuliani-Lieb-Lebowitz and Giuliani-Seiringer in the discrete setting. In such\na model the relative strength between the short range attractive term favouring\npure phases and the long range repulsive term favouring oscillations is\nmodulated by a parameter $\\tau$. For $\\tau<0$ minimizers are trivial uniform\nstates. It is conjectured that $\\forall\\,d\\geq2$ there exists\n$0<\\bar{\\tau}\\ll1$ such that for all $0<\\tau\\leq\\bar{\\tau}$ and for all $L>0$\nminimizers are striped/lamellar patterns. In Daneri-Runa arXiv:1702.07334 the\nauthors prove the above for $L=2kh^*_\\tau$, where $k\\in\\N$ and $h^*_\\tau$ is\nthe optimal period of stripes for a given $0<\\tau\\leq\\bar{\\tau}$. The purpose\nof this paper is to show the validity of the conjecture for generic $L$.\n', 'Exact periodic stripes for a local/nonlocal minimization problem with\n  volume constraint   We consider a class of generalized antiferromagnetic local/nonlocal\ninteraction functionals in general dimension, where a short range attractive\nterm of perimeter type competes with a long range repulsive term characterized\nby a reflection positive power law kernel. Breaking of symmetry with respect to\ncoordinate permutations and pattern formation for functionals in this class\nhave been shown in~\\cite{gr,dr_arma} and previously by~\\cite{gs_cmp} in the\ndiscrete setting, for a smaller range of exponents. Global minimizers of such\nfunctionals have been proved in~\\cite{dr_arma} to be given by periodic stripes\nof volume density $1/2$ in any cube having optimal period size, also in the\nlarge volume limit. In this paper we study the minimization problem with\narbitrarily prescribed volume constraint $\\alpha\\in(0,1)$. We show that, in the\nlarge volume limit, minimizers are periodic stripes of volume density $\\alpha$,\nnamely stripes whose one-dimensional slices in the direction orthogonal to\ntheir boundary are simple periodic with volume density $\\alpha$ in each period.\nResults of this type in the one-dimensional setting, where no symmetry breaking\noccurs, have been previously obtained in \\cite{muller1993singular,\nalberti2001new,ren2003energy,chen2005periodicity,giuliani2009modulated}.\n', 'One-dimensionality of the minimizers in the large volume limit for a\n  diffuse interface attractive/repulsive model in general dimension   In this paper we consider the diffuse interface generalized antiferromagnetic\nmodel with local/nonlocal attractive/repulsive terms in competition studied in\nDaneri-Kerschbaum-Runa arXiv:1907.06419. The parameters of the model are\ndenoted by $\\tau$ and $\\varepsilon$: the parameter $\\tau$ represents the\nrelative strength of the local term with respect to the nonlocal one, while the\nparameter $\\varepsilon$ describes the transition scale in the Modica-Mortola\ntype term.\n  Restricting to a periodic box of size $L$, with $L$ multiple of the period of\nthe minimal one-dimensional minimizers, in Daneri-Kerschbaum-Runa\narXiv:1907.06419 the authors prove that in any dimension $d\\geq1$ and for small\nbut positive $\\tau$ and $\\varepsilon$ (eventually depending on $L$), the\nminimizers are non-constant one-dimensional periodic functions.\n  In this paper we prove that periodicity and one-dimensionality of minimizers\noccurs also in the zero temperature analogue of the thermodynamic limit, namely\nas $L\\to+\\infty$.\n']","[('minimizers non', 0.46842941641807556), ('local minimizers', 0.46123218536376953), ('minimizers', 0.43679291009902954), ('global minimizers', 0.42716121673583984), ('nonlocal interaction', 0.4267708361148834), ('energy minimizers', 0.4236619472503662), ('dimensional periodic functions', 0.4224064350128174), ('one dimensional periodic', 0.40013572573661804), ('energy minimizer', 0.3869532644748688), ('radial symmetry', 0.36563733220100403)]"
1688,1688,17,1688_integral quadratic forms_quadratic forms_quadratic forms two_quaternary quadratic,"['integral quadratic forms', 'quadratic forms', 'quadratic forms two', 'quaternary quadratic', 'ternary quadratic', 'quadratic form', 'forms primitive', 'binary forms', 'forms prime', 'exists quadratic']","['Diagonal odd-regular ternary quadratic forms   A (positive definite primitive integral) quadratic form is called odd-regular\nif it represents every odd positive integer which is locally represented. In\nthis paper, we show that there are at most 147 diagonal odd-regular ternary\nquadratic forms and prove the odd-regularities of all but 6 candidates.\n', 'Primitively universal quaternary quadratic forms   A (positive definite and integral) quadratic form $f$ is said to be\n$\\textit{universal}$ if it represents all positive integers, and is said to be\n$\\textit{primitively universal}$ if it represents all positive integers\nprimitively. We also say $f$ is $\\textit{primitively almost universal}$ if it\nrepresents almost all positive integers primitively. Conway and Schneeberger\nproved (see [1]) that there are exactly $204$ equivalence classes of universal\nquaternary quadratic forms. Recently, Earnest and Gunawardana proved in [4]\nthat among $204$ equivalence classes of universal quaternary quadratic forms,\nthere are exactly $152$ equivalence classes of primitively almost universal\nquaternary quadratic forms. In this article, we prove that there are exactly\n$107$ equivalence classes of primitively universal quaternary quadratic forms.\nWe also determine the set of all positive integers that are not primitively\nrepresented by each of the remaining $152-107=45$ equivalence classes of\nprimitively almost universal quaternary quadratic forms.\n', 'Prime-universal diagonal quadratic forms   A (positive definite and integral) quadratic form is said to be\n$\\textit{prime-universal}$ if it represents all primes. Recently, Doyle and\nWilliams in [2] classified all prime-universal diagonal ternary quadratic\nforms, and all prime-universal diagonal quaternary quadratic forms under two\nconjectures proposed by themselves. In this article, we classify all\nprime-universal diagonal quadratic forms regardless of ranks. Furthermore, we\nprove, so called, $67$-Theorem for a diagonal quadratic form to be\nprime-universal.\n']","[('integral quadratic forms', 0.6747887134552002), ('quadratic forms', 0.6496520638465881), ('quadratic forms two', 0.5888949036598206), ('quaternary quadratic', 0.5776508450508118), ('ternary quadratic', 0.5661655068397522), ('quadratic form', 0.5319556593894958), ('forms primitive', 0.522087812423706), ('binary forms', 0.4686248302459717), ('forms prime', 0.4481598138809204), ('exists quadratic', 0.42034032940864563)]"
1689,1689,17,1689_vafa witten invariants_invariants virtual_witten invariants_perfect obstruction theory,"['vafa witten invariants', 'invariants virtual', 'witten invariants', 'perfect obstruction theory', 'invariants k3', 'obstruction theory', 'theoretic invariants', 'euler characteristic', 'structure sheaves', 'donaldson thomas invariants']","['Virtual Riemann-Roch Theorems for Almost Perfect Obstruction Theories   This is the third in a series of works devoted to constructing virtual\nstructure sheaves and $K$-theoretic invariants in moduli theory. The central\nobjects of study are almost perfect obstruction theories, introduced by Y.-H.\nKiem and the author as the appropriate notion in order to define invariants in\n$K$-theory for many moduli stacks of interest, including generalized\n$K$-theoretic Donaldson-Thomas invariants.\n  In this paper, we prove virtual Riemann-Roch theorems in the setting of\nalmost perfect obstruction theory in both the non-equivariant and equivariant\ncases, including cosection localized versions. These generalize and remove\ntechnical assumptions from the virtual Riemann-Roch theorems of\nFantechi-G\\""{o}ttsche and Ravi-Sreedhar. The main technical ingredients are a\ntreatment of the equivariant $K$-theory and equivariant Gysin map of sheaf\nstacks and a formula for the virtual Todd class.\n', 'Localizing Virtual Structure Sheaves for Almost Perfect Obstruction\n  Theories   Almost perfect obstruction theories were introduced in an earlier paper by\nthe authors as the appropriate notion in order to define virtual structure\nsheaves and $K$-theoretic invariants for many moduli stacks of interest,\nincluding $K$-theoretic Donaldson-Thomas invariants of sheaves and complexes on\nCalabi-Yau threefolds. The construction of virtual structure sheaves is based\non the $K$-theory and Gysin maps of sheaf stacks.\n  In this paper, we generalize the virtual torus localization and cosection\nlocalization formulas and their combination to the setting of almost perfect\nobstruction theory. To this end, we further investigate the $K$-theory of sheaf\nstacks and its functoriality properties. As applications of the localization\nformulas, we establish a $K$-theoretic wall crossing formula for simple\n$\\mathbb{C}^\\ast$-wall crossings and define $K$-theoretic invariants refining\nthe Jiang-Thomas virtual signed Euler characteristics.\n', 'Virtual signed Euler characteristics   Roughly speaking, to any space $M$ with perfect obstruction theory we\nassociate a space $N$ with symmetric perfect obstruction theory. It is a cone\nover $M$ given by the dual of the obstruction sheaf of $M$, and contains $M$ as\nits zero section. It is locally the critical locus of a function.\n  More precisely, in the language of derived algebraic geometry, to any\nquasi-smooth space $M$ we associate its $(-1)$-shifted cotangent bundle $N$.\n  By localising from $N$ to its $\\mathbb C^*$-fixed locus $M$ this gives five\nnotions of virtual signed Euler characteristic of $M$:\n  (1) The Ciocan-Fontanine-Kapranov/Fantechi-G\\""ottsche signed virtual Euler\ncharacteristic of $M$ defined using its own obstruction theory,\n  (2) Graber-Pandharipande\'s virtual Atiyah-Bott localisation of the virtual\ncycle of $N$ to $M$,\n  (3) Behrend\'s Kai-weighted Euler characteristic localisation of the virtual\ncycle of $N$ to $M$,\n  (4) Kiem-Li\'s cosection localisation of the virtual cycle of $N$ to $M$,\n  (5) $(-1)^{vd}$ times by the topological Euler characteristic of $M$.\n  Our main result is that (1)=(2) and (3)=(4)=(5). The first two are\ndeformation invariant while the last three are not.\n']","[('vafa witten invariants', 0.5293267965316772), ('invariants virtual', 0.5252640247344971), ('witten invariants', 0.49314022064208984), ('perfect obstruction theory', 0.4849918782711029), ('invariants k3', 0.4658730924129486), ('obstruction theory', 0.4610936939716339), ('theoretic invariants', 0.4595791697502136), ('euler characteristic', 0.43854764103889465), ('structure sheaves', 0.4353373646736145), ('donaldson thomas invariants', 0.43305739760398865)]"
1690,1690,17,1690_boltzmann equations_limit boltzmann_boundary layer equations_boltzmann theory,"['boltzmann equations', 'limit boltzmann', 'boundary layer equations', 'boltzmann theory', 'fluid boundary', 'hydrodynamic limits', 'boundary layers', 'specular boundary condition', 'hydrodynamic limit', 'boundary layer']","['Boltzmann boundary layer equation with Maxwell reflection boundary\n  condition and applications to fluid limits   This paper investigates the Knudsen layer equation in half-space, arising\nfrom the hydrodynamic limit of the Boltzmann equation to fluid dynamics. We\nconsider the Maxwell reflection boundary condition with accommodation\ncoefficient $0<\\alpha<1$. We restrict our attention to hard sphere collisions\nwith angular cutoff, proving the existence, uniqueness, and asymptotic behavior\nof the solution in $L^{\\infty}_{x,v}$. Additionally, we demonstrate the\napplication of our theorem to the hydrodynamic limit through a specific\nexample. In this expample, we derive the boundary conditions of the fluid\nequations using our theorem and the symmetric properties of the Knudsen layer\nequation for $\\alpha\\in(0,1]$ and $\\alpha=O(1)$. These derivations differs\nsignificantly from the cases of specular and almost specular reflection. This\nexplicitly characterizes the {\\em vanishing sources set} defined in\n\\cite{jiang2024knudsenboundarylayerequations}\n', 'Hilbert expansion of the Boltzmann equation in the incompressible Euler\n  level in a channel   The study of hydrodynamic limit of the Boltzmann equation with physical\nboundary is a challenging problem due to appearance of the viscous and Knudsen\nboundary layers. In this paper, the hydrodynamic limit from the Boltzmann\nequation with specular reflection boundary condition to the incompressible\nEuler in a channel is investigated. Based on the multiscaled Hilbert expansion,\nthe equations with boundary conditions and compatibility conditions for\ninterior solutions, viscous and Knudsen boundary layers are derived under\ndifferent scaling, respectively. Then some uniform estimates for the interior\nsolutions, viscous and Knudsen boundary layers are established. With the help\nof $L^2-L^\\infty$ framework and the uniform estimates obtained above, the\nsolutions to the Boltzmann equation are constructed by the truncated Hilbert\nexpansion with multiscales, and hence the hydrodynamic limit in the\nincompressible Euler level is justified.\n', 'Hilbert expansion of the Boltzmann equation on a 2-dimensional disk with\n  specular boundary condition   In the present paper, we concern the hydrodynamic limit of Boltzmann equation\nwith specular reflection boundary condition in a two-dimensional disk to the\ncompressible Euler equations. Due to the non-zero curvature and non-zero\ntangential velocity of compressible Euler solution on the boundary, new\ndifficulties arise in the construction of Knudsen boundary layer. By employing\nthe geometric correction, and an innovative and refined $L^2-L^\\infty$ method,\nwe establish the existence and space-decay for a truncated Knudsen boundary\nlayer. Then, by the Hilbert expansion of multi-scales, we successfully justify\nthe hydrodynamic limit of Boltzmann equation with specular reflection boundary\ncondition to the compressible Euler equations in the two-dimensional disk.\n']","[('boltzmann equations', 0.557727038860321), ('limit boltzmann', 0.5533711910247803), ('boundary layer equations', 0.5086411237716675), ('boltzmann theory', 0.49894580245018005), ('fluid boundary', 0.46554580330848694), ('hydrodynamic limits', 0.4578341245651245), ('boundary layers', 0.4561433494091034), ('specular boundary condition', 0.4479881823062897), ('hydrodynamic limit', 0.44674918055534363), ('boundary layer', 0.44568419456481934)]"
1691,1691,17,1691_projective toric_blow projective_toric surfaces_blow ups projective,"['projective toric', 'blow projective', 'toric surfaces', 'blow ups projective', 'projective plane mathbb', 'projective plane', 'projective', 'rational polyhedral fundamental', 'surfaces whose', 'weighted projective plane']","['On The Geometry Of Elliptic Pairs   An elliptic pair $(X, C)$ is a projective rational surface $X$ with log\nterminal singularities, and an irreducible curve $C$ contained in the smooth\nlocus of $X$, with arithmetic genus one and self-intersection zero. They are a\nuseful tool for determining whether the pseudo-effective cone of $X$ is\npolyhedral, and interesting algebraic and geometric objects in their own right.\nEspecially of interest are toric elliptic pairs, where $X$ is the blow-up of a\nprojective toric surface at the identity element of the torus. In this paper,\nwe classify all toric elliptic pairs of Picard number two. Strikingly, it turns\nout that there are only three of these. Furthermore, we study a class of\nnon-toric elliptic pairs coming from the blow-up of $\\mathbb{P}^2$ at nine\npoints on a nodal cubic, in characteristic $p$. This construction gives us\nexamples of surfaces where the pseudo-effective cone is non-polyhedral for a\nset of primes $p$ of positive density, and, assuming the generalized Riemann\nhypothesis, polyhedral for a set of primes $p$ of positive density.\n', 'Blown-up toric surfaces with non-polyhedral effective cone   We construct examples of projective toric surfaces whose blow-up at a general\npoint has a non-polyhedral pseudo-effective cone, both in characteristic $0$\nand in every prime characteristic $p$. As a consequence, we prove that the\npseudo-effective cone of the Grothendieck-Knudsen moduli space $\\overline\nM_{0,n}$ of stable rational curves is not polyhedral for $n\\geq 10$ in\ncharacteristic $0$ and in characteristic $p$, for all primes $p$. Many of these\ntoric surfaces are related to a very interesting class of arithmetic threefolds\nthat we call arithmetic elliptic pairs of infinite order. Their analysis in\ncharacteristic $p$ relies on tools of arithmetic geometry and Galois\nrepresentations in the spirit of the Lang-Trotter conjecture, producing toric\nsurfaces whose blow-up at a general point has a non-polyhedral pseudo-effective\ncone in characteristic $0$ and in characteristic $p$, for an infinite set of\nprimes $p$ of positive density.\n', ""Birational geometry of blow-ups of projective spaces along points and\n  lines   Consider the blow-up $X$ of $\\mathbb{P}^3$ at 6 points in very general\nposition and the 15 lines through the 6 points. We construct an infinite-order\npseudo-automorphism $\\phi_X$ on $X$, induced by the complete linear system of a\ndivisor of degree 13. The effective cone of $X$ has infinitely many extremal\nrays and hence, $X$ is not a Mori Dream Space. The threefold $X$ has a unique\nanticanonical section which is a Jacobian K3 Kummer surface $S$ of Picard\nnumber 17. The restriction of $\\phi_X$ on $S$ realizes one of Keum's 192\ninfinite-order automorphisms of Jacobian K3 Kummer surfaces. In general, we\nshow the blow-up of $\\mathbb{P}^n$ ($n\\geq 3$) at $(n+3)$ very general points\nand certain 9 lines through them is not Mori Dream, with infinitely many\nextremal effective divisors. As an application, for $n\\geq 7$, the blow-up of\n$\\overline{M}_{0,n}$ at a very general point has infinitely many extremal\neffective divisors.\n""]","[('projective toric', 0.6394093036651611), ('blow projective', 0.6165832281112671), ('toric surfaces', 0.6138467788696289), ('blow ups projective', 0.6007600426673889), ('projective plane mathbb', 0.4662206768989563), ('projective plane', 0.46593424677848816), ('projective', 0.4640357196331024), ('rational polyhedral fundamental', 0.45430782437324524), ('surfaces whose', 0.4492889940738678), ('weighted projective plane', 0.4264565706253052)]"
1692,1692,17,1692_limit navier stokes_incompressible navier stokes_navier stokes system_viscous incompressible,"['limit navier stokes', 'incompressible navier stokes', 'navier stokes system', 'viscous incompressible', 'viscous incompressible fluids', 'navier stokes', 'navier stokes allen', 'sharp interface limit', 'stokes allen cahn', 'stokes allen']","['Sharp Interface Limit for a Navier-Stokes/Allen-Cahn System in the Case\n  of a Vanishing Mobility   We consider the sharp interface limit of a Navier-Stokes/Allen Cahn equation\nin a bounded smooth domain in two space dimensions, in the case of vanishing\nmobility $m_\\varepsilon=\\sqrt{\\varepsilon}$, where the small parameter\n$\\varepsilon>0$ related to the thickness of the diffuse interface is sent to\nzero. For well-prepared initial data and sufficiently small times, we\nrigorously prove convergence to the classical two-phase Navier-Stokes system\nwith surface tension. The idea of the proof is to use asymptotic expansions to\nconstruct an approximate solution and to estimate the difference of the exact\nand approximate solutions with a spectral estimate for the (at the approximate\nsolution) linearized Allen-Cahn operator. In the calculations we use a\nfractional order ansatz and new ansatz terms in higher orders leading to a\nsuitable $\\varepsilon$-scaled and coupled model problem. Moreover, we apply the\nnovel idea of introducing $\\varepsilon$-dependent coordinates.\n', 'Sharp interface limit for inhomogeneous incompressible\n  Navier-Stokes/Allen-Cahn system in a bounded domain via a relative energy\n  method   This paper concerns the sharp interface limit of solutions to the\ninhomogeneous incompressible Navier-Stokes/Allen-Cahn coupled system in a\nbounded domain $\\Omega \\subset \\mathbb{R}^n,\\ n =2,3$. Based on a relative\nenergy method, we prove that the solutions to the Navier-Stokes/Allen-Cahn\nsystem converge to the corresponding solutions to a sharp interface model\nprovided that the thickness of the diffuse interfacial zone goes to zero. It is\nnoted that the relative energy method can avoid both the spectral estimates of\nthe linearized Allen-Cahn operator and the construction of approximate\nsolutions by the matched asymptotic expansion method in the study of the sharp\ninterface limit process. And some suitable functionals are designed and\nestimated by elaborated energy methods accordingly.\n', 'Sharp Interface Limit for a Navier-Stokes/Allen-Cahn System with\n  Different Viscosities   We discuss the sharp interface limit of a coupled Navier-Stokes/Allen-Cahn\nsystem in a two dimensional, bounded and smooth domain, when a parameter\n$\\varepsilon>0$ that is proportional to the thickness of the diffuse interface\ntends to zero rigorously. We prove convergence of the solutions of the\nNavier-Stokes/Allen-Cahn system to solutions of a sharp interface model, where\nthe interface evolution is given by the mean curvature flow with an additional\nconvection term coupled to a two-phase Navier-Stokes system with surface\ntension. This is done by constructing an approximate solution from the limiting\nsystem via matched asymptotic expansions together with a novel Ansatz for the\nhighest order term, and then estimating its difference with the real solution\nwith the aid of a refined spectral estimate of the linearized Allen-Cahn\noperator near the approximate solution.\n']","[('limit navier stokes', 0.5903369188308716), ('incompressible navier stokes', 0.5226598381996155), ('navier stokes system', 0.5002073049545288), ('viscous incompressible', 0.4621029198169708), ('viscous incompressible fluids', 0.4546760320663452), ('navier stokes', 0.451850950717926), ('navier stokes allen', 0.45019111037254333), ('sharp interface limit', 0.4489612281322479), ('stokes allen cahn', 0.44283702969551086), ('stokes allen', 0.4007619023323059)]"
1693,1693,17,1693_cluster varieties_grassmannian cluster algebras_grassmannian cluster_cluster algebras,"['cluster varieties', 'grassmannian cluster algebras', 'grassmannian cluster', 'cluster algebras', 'cluster algebra', 'cluster structures', 'plabic graphs', 'cluster structure', 'varieties description', 'grassmannian mathrm']","[""Quasi-coincidence of cluster structures on positroid varieties   By work of a number of authors, beginning with Scott and culminating with\nGalashin and Lam, the coordinate rings of positroid varieties in the\nGrassmannian carry cluster algebra structures. In fact, they typically carry\nmany such structures, the two best understood being the source-labelled and\ntarget-labelled structures, referring to how the initial cluster is computed\nfrom a Postnikov diagram or plabic graph. In this article we show that these\ntwo cluster algebra structures quasi-coincide, meaning in particular that a\ncluster variable in one structure may be expressed in the other structure as\nthe product of a cluster variable and a Laurent monomial in the frozen\nvariables. This resolves a conjecture attributed to Muller and Speyer from\n2017. The proof depends critically on categorification: of the relevant cluster\nalgebra structures by the author, of perfect matchings and twists by the author\nwith \\c{C}anak\\c{c}{\\i} and King, and of quasi-equivalences of cluster algebras\nby Fraser-Keller. By similar techniques, we also show that Muller-Speyer's left\ntwist map is a quasi-cluster equivalence from the target-labelled structure to\nthe source-labelled structure.\n"", 'Demazure weaves for reduced plabic graphs (with a proof that\n  Muller-Speyer twist is Donaldson-Thomas)   First, this article develops the theory of weaves and their cluster\nstructures for the affine cones of positroid varieties. In particular, we\nexplain how to construct a weave from a reduced plabic graph, show it is\nDemazure, compare their associated cluster structures, and prove that the\nconjugate surface of the graph is Hamiltonian isotopic to the Lagrangian\nfilling associated to the weave. The T-duality map for plabic graphs has a\nsurprising key role in the construction of these weaves. Second, we use the\nabove established bridge between weaves and reduced plabic graphs to show that\nthe Muller-Speyer twist map on positroid varieties is the Donaldson-Thomas\ntransformation. This latter statement implies that the Muller-Speyer twist is a\nquasi-cluster automorphism. An additional corollary of our results is that\ntarget labeled seeds and the source labeled seeds are related by a\nquasi-cluster transformation.\n', 'Positroid cluster structures from relabeled plabic graphs   The Grassmannian is a disjoint union of open positroid varieties $P_v$,\ncertain smooth irreducible subvarieties whose definition is motivated by total\npositivity. The coordinate ring of $P_v$ is a cluster algebra, and each reduced\nplabic graph $G$ for $P_v$ determines a cluster. We study the effect of\nrelabeling the boundary vertices of $G$ by a permutation $r$. Under suitable\nhypotheses on the permutation, we show that the relabeled graph $G^r$\ndetermines a cluster for a different open positroid variety $P_w$. As a key\nstep of the proof, we show that $P_v$ and $P_w$ are isomorphic by a nontrivial\ntwist isomorphism. Our constructions yield many cluster structures on each open\npositroid variety $P_w$, given by plabic graphs with appropriately relabeled\nboundary. We conjecture that the seeds in all of these cluster structures are\nrelated by a combination of mutations and Laurent monomial transformations\ninvolving frozen variables, and establish this conjecture for (open) Schubert\nand opposite Schubert varieties. As an application, we also show that for\ncertain reduced plabic graphs $G$, the ""source"" cluster and the ""target""\ncluster are related by mutation and Laurent monomial rescalings.\n']","[('cluster varieties', 0.672694206237793), ('grassmannian cluster algebras', 0.6471408009529114), ('grassmannian cluster', 0.6278406977653503), ('cluster algebras', 0.557532787322998), ('cluster algebra', 0.5200250744819641), ('cluster structures', 0.5083720684051514), ('plabic graphs', 0.4884777367115021), ('cluster structure', 0.47886717319488525), ('varieties description', 0.45598599314689636), ('grassmannian mathrm', 0.44664454460144043)]"
1694,1694,17,1694_laplacians random_laplacian random_spectral gap random_spectral statistics,"['laplacians random', 'laplacian random', 'spectral gap random', 'spectral statistics', 'compact hyperbolic surfaces', 'compact hyperbolic surface', 'spectral gaps', 'random matrix theory', 'closed hyperbolic surfaces', 'hyperbolic surfaces']","['Effective lower bounds for spectra of random covers and random unitary\n  bundles   Let $X$ be a finite-area non-compact hyperbolic surface. We study the\nspectrum of the Laplacian on random covering surfaces of X and on random\nunitary bundles over X. We show that there is a constant $c > 0$ such that,\nwith probability tending to 1 as $n \\to \\infty$, a uniformly random degree-$n$\nRiemannian covering surface $X_n$ of $X$ has no Laplacian eigenvalues below\n$\\frac{1}{4}-c\\frac{(\\log\\log\\log n)^2}{\\log \\log n}$ other than those of $X$\nand with the same multiplicities. We also show that with probability tending to\n1 as $n\\to \\infty$, a random unitary bundle $E_{\\phi}$ over $X$ of rank $n$ has\nno Laplacian eigenvalues below $\\frac{1}{4}-c\\frac{(\\log\\log n)^2}{\\log n}$.\n', 'Smooth linear eigenvalue statistics on random covers of compact\n  hyperbolic surfaces -- A central limit theorem and almost sure RMT statistics   We study smooth linear spectral statistics of twisted Laplacians on random\n$n$-covers of a fixed compact hyperbolic surface $X$. We consider two aspects\nof such statistics. The first is the fluctuations of such statistics in a small\nenergy window around a fixed energy level when averaged over the space of all\ndegree $n$ covers of $X$. The second is the energy variance of a typical\nsurface.\n  In the first case, we show a central limit theorem. Specifically, we show\nthat the distribution of such fluctuations tends to a Gaussian with variance\ngiven by the corresponding quantity for the Gaussian Orthogonal/Unitary\nEnsemble (GOE/GUE). In the second case, we show that the energy variance of a\ntypical random $n$-cover is that of the GOE/GUE. In both cases, we consider a\ndouble limit where first we let $n$, the covering degree, go to $\\infty$ then\nlet $L\\to \\infty$ where $1/L$ is the window length.\n', 'Spectral statistics of the Laplacian on random covers of a closed\n  negatively curved surface   Let $(X,g)$ be a closed, connected surface, with variable negative curvature.\nWe consider the distribution of eigenvalues of the Laplacian on random covers\n$X_n\\to X$ of degree $n$. We focus on the ensemble variance of the smoothed\nnumber of eigenvalues of the square root of the positive Laplacian\n$\\sqrt{\\Delta}$ in windows $[\\lambda-\\frac 1L,\\lambda+\\frac 1L]$, over the set\nof $n$-sheeted covers of $X$. We first take the limit of large degree $n\\to\n+\\infty$, then we let the energy $\\lambda$ go to $+\\infty$ while the window\nsize $\\frac 1L$ goes to $0$. In this ad hoc limit, local energy averages of the\nvariance converge to an expression corresponding to the variance of the same\nstatistic when considering instead spectra of large random matrices of the\nGaussian Orthogonal Ensemble (GOE). By twisting the Laplacian with unitary\nrepresentations, we are able to observe different statistics, corresponding to\nthe Gaussian Unitary Ensemble (GUE) when time reversal symmetry is broken.\nThese results were shown by F. Naud for the model of random covers of a\nhyperbolic surface.\n  For an individual cover $X_n\\to X$, we consider spectral fluctuations of the\ncounting function on $X_n$ around the ensemble average. In the large energy\nregime, for a typical cover $X_n\\to X$ of large degree, these fluctuations are\nshown to approach the GOE result, a phenomenon called ergodicity in Random\nMatrix Theory. An analogous result for random covers of hyperbolic surfaces was\nobtained by Y. Maoz.\n']","[('laplacians random', 0.6144744753837585), ('laplacian random', 0.5830680131912231), ('spectral gap random', 0.5568339824676514), ('spectral statistics', 0.4959268569946289), ('compact hyperbolic surfaces', 0.4942838251590729), ('compact hyperbolic surface', 0.4864555299282074), ('spectral gaps', 0.45828086137771606), ('random matrix theory', 0.4481889605522156), ('closed hyperbolic surfaces', 0.4455282688140869), ('hyperbolic surfaces', 0.4397347569465637)]"
1695,1695,17,1695_fuzzy sets_fuzzy relations_theory rough_fuzzy theory,"['fuzzy sets', 'fuzzy relations', 'theory rough', 'fuzzy theory', 'general rough', 'rough', 'called rough', 'fuzzy', 'granularity', 'sets']","['Relational correspondences for L-fuzzy rough approximations defined on\n  De Morgan Heyting algebras   We consider fuzzy rough sets defined on De Morgan Heyting algebras. We\npresent a theorem that can be used to obtain several correspondence results\nbetween fuzzy rough sets and fuzzy relations defining them. We characterize\nfuzzy rough approximation operators corresponding to compositions of reflexive,\ntransitive, mediate, Euclidean and adjoint fuzzy relations defined on De Morgan\nHeyting algebras by using only a single axiom.\n', 'Notes on the lattice of fuzzy rough sets with crisp reference sets   Since the theory of rough sets was introduced by Zdzislaw Pawlak, several\napproaches have been proposed to combine rough set theory with fuzzy set\ntheory. In this paper, we examine one of these approaches, namely fuzzy rough\nsets with crisp reference sets, from a lattice-theoretic point of view. We\nconnect the lower and upper approximations of a fuzzy relation $R$ to the\napproximations of the core and support of $R$. We also show that the lattice of\nfuzzy rough sets corresponding to a fuzzy equivalence relation $R$ and the\ncrisp subsets of its universe is isomorphic to the lattice of rough sets for\nthe (crisp) equivalence relation $E$, where $E$ is the core of $R$. We\nestablish a connection between the exact (fuzzy) sets of $R$ and the exact\n(crisp) sets of the support of $R$.\n', 'A novel axiomatic approach to L-valued rough sets within an L-universe\n  via inner product and outer product of L-subsets   The fuzzy rough approximation operator serves as the cornerstone of fuzzy\nrough set theory and its practical applications. Axiomatization is a crucial\napproach in the exploration of fuzzy rough sets, aiming to offer a clear and\ndirect characterization of fuzzy rough approximation operators. Among the\nfundamental tools employed in this process, the inner product and outer product\nof fuzzy sets stand out as essential components in the axiomatization of fuzzy\nrough sets. In this paper, we will develop the axiomatization of a\ncomprehensive fuzzy rough set theory, that is, the so-called L-valued rough\nsets with an L-set serving as the foundational universe (referred to as the\nL-universe) for defining L-valued rough approximation operators, where L\ntypically denotes a GL-quantale. Firstly, we give the notions of inner product\nand outer product of two L-subsets within an L-universe and examine their basic\nproperties. It is shown that these notions are extensions of the corresponding\nnotion of fuzzy sets within a classical universe. Secondly, leveraging the\ninner product and outer product of L-subsets, we respectively characterize\nL-valued upper and lower rough approximation operators generated by general,\nreflexive, transitive, symmetric, Euclidean, and median L-value relations on\nL-universe as well as their compositions. Finally, utilizing the provided\naxiomatic characterizations, we present the precise examples for the least and\nlargest equivalent L-valued upper and lower rough approximation operators.\nNotably, many existing axiom characterizations of fuzzy rough sets within\nclassical universe can be viewed as direct consequences of our findings.\n']","[('fuzzy sets', 0.6450253129005432), ('fuzzy relations', 0.5357996821403503), ('theory rough', 0.5345670580863953), ('fuzzy theory', 0.5278814435005188), ('general rough', 0.4991706311702728), ('rough', 0.43053075671195984), ('called rough', 0.42747819423675537), ('fuzzy', 0.41799241304397583), ('granularity', 0.4158487617969513), ('sets', 0.4142341911792755)]"
1696,1696,17,1696_compact ahler manifolds_compact ahler manifold_ahler manifold dimension_ahler manifolds,"['compact ahler manifolds', 'compact ahler manifold', 'ahler manifold dimension', 'ahler manifolds', 'ahler manifold', 'compact ahler', 'compact complex manifold', 'automorphisms compact', 'compact complex surfaces', 'compact hyperk ahler']","['Jordan property for groups of bimeromorphic automorphisms of compact\n  K\\""ahler threefolds   Let $X$ be a non-uniruled compact K\\""ahler space of dimension 3. We show that\nthe group of bimeromorphic automorphisms of $X$ is Jordan. More generally, the\nsame result holds for any compact K\\""ahler space admitting a quasi-minimal\nmodel.\n', 'Finite groups of bimeromorphic selfmaps of non-uniruled K\\""ahler\n  threefolds   We prove the Jordan property for groups of bimeromorphic selfmaps of\nthree-dimensional compact K\\""ahler varieties of non-negative Kodaira dimension\nand positive irregularity.\n', 'Finite groups of bimeromorphic selfmaps of uniruled K\\""ahler threefolds   We classify uniruled compact K\\""ahler threefolds whose groups of\nbimeromorphic selfmaps do not have Jordan property.\n']","[('compact ahler manifolds', 0.6641107201576233), ('compact ahler manifold', 0.6294183731079102), ('ahler manifold dimension', 0.6070355176925659), ('ahler manifolds', 0.606539785861969), ('ahler manifold', 0.5691626071929932), ('compact ahler', 0.5446392297744751), ('compact complex manifold', 0.5342738032341003), ('automorphisms compact', 0.5341326594352722), ('compact complex surfaces', 0.5226268172264099), ('compact hyperk ahler', 0.5044158101081848)]"
1697,1697,17,1697_phase synchronization_synchronization_synchronization problems_clock synchronization,"['phase synchronization', 'synchronization', 'synchronization problems', 'clock synchronization', 'synchronization first', 'synchronization via', 'spectral methods', 'convex relaxation', 'rotation group', 'orthogonal group']","['Near-Optimal Performance Bounds for Orthogonal and Permutation Group\n  Synchronization via Spectral Methods   Group synchronization asks to recover group elements from their pairwise\nmeasurements. It has found numerous applications across various scientific\ndisciplines. In this work, we focus on orthogonal and permutation group\nsynchronization which are widely used in computer vision such as object\nmatching and structure from motion. Among many available approaches, the\nspectral methods have enjoyed great popularity due to their efficiency and\nconvenience. We will study the performance guarantees of the spectral methods\nin solving these two synchronization problems by investigating how well the\ncomputed eigenvectors approximate each group element individually. We establish\nour theory by applying the recent popular~\\emph{leave-one-out} technique and\nderive a~\\emph{block-wise} performance bound for the recovery of each group\nelement via eigenvectors. In particular, for orthogonal group synchronization,\nwe obtain a near-optimal performance bound for the group recovery in presence\nof additive Gaussian noise. For permutation group synchronization under random\ncorruption, we show that the widely-used two-step procedure (spectral method\nplus rounding) can recover all the group elements exactly if the SNR\n(signal-to-noise ratio) is close to the information theoretical limit. Our\nnumerical experiments confirm our theory and indicate a sharp phase transition\nfor the exact group recovery.\n', 'Rotation Group Synchronization via Quotient Manifold   Rotation group $\\mathcal{SO}(d)$ synchronization is an important inverse\nproblem and has attracted intense attention from numerous application fields\nsuch as graph realization, computer vision, and robotics. In this paper, we\nfocus on the least-squares estimator of rotation group synchronization with\ngeneral additive noise models, which is a nonconvex optimization problem with\nmanifold constraints. Unlike the phase/orthogonal group synchronization, there\nare limited provable approaches for solving rotation group synchronization.\nFirst, we derive improved estimation results of the least-squares/spectral\nestimator, illustrating the tightness and validating the existing relaxation\nmethods of solving rotation group synchronization through the optimum of\nrelaxed orthogonal group version under near-optimal noise level for exact\nrecovery. Moreover, departing from the standard approach of utilizing the\ngeometry of the ambient Euclidean space, we adopt an intrinsic Riemannian\napproach to study orthogonal/rotation group synchronization. Benefiting from a\nquotient geometric view, we prove the positive definite condition of quotient\nRiemannian Hessian around the optimum of orthogonal group synchronization\nproblem, and consequently the Riemannian local error bound property is\nestablished to analyze the convergence rate properties of various Riemannian\nalgorithms. As a simple and feasible method, the sequential convergence\nguarantee of the (quotient) Riemannian gradient method for solving\northogonal/rotation group synchronization problem is studied, and we derive its\nglobal linear convergence rate to the optimum with the spectral initialization.\nAll results are deterministic without any probabilistic model.\n', ""The Noise-Sensitivity Phase Transition in Spectral Group Synchronization\n  Over Compact Groups   In Group Synchronization, one attempts to find a collection of unknown group\nelements from noisy measurements of their pairwise differences. Several\nimportant problems in vision and data analysis reduce to group synchronization\nover various compact groups. Spectral Group Synchronization is a commonly used,\nrobust algorithm for solving group synchronization problems, which relies on\ndiagonalization of a block matrix whose blocks are matrix representations of\nthe measured pairwise differences. Assuming uniformly distributed measurement\nerrors, we present a rigorous analysis of the accuracy and noise sensitivity of\nspectral group synchronization algorithms over any compact group, up to the\nrounding error. We identify a Baik-Ben Arous-P\\'ech\\'e type phase transition in\nthe noise level, beyond which spectral group synchronization necessarily fails.\nBelow the phase transition, spectral group synchronization succeeds in\nrecovering the unknown group elements, but its performance deteriorates with\nthe noise level. We provide asymptotically exact formulas for the accuracy of\nspectral group synchronization below the phase transition, up to the rounding\nerror. We also provide a consistent risk estimate, allowing practitioners to\nestimate the method's accuracy from available measurements.\n""]","[('phase synchronization', 0.47418728470802307), ('synchronization', 0.4586470127105713), ('synchronization problems', 0.4547581672668457), ('clock synchronization', 0.4460589289665222), ('synchronization first', 0.4378737807273865), ('synchronization via', 0.43677133321762085), ('spectral methods', 0.3730606138706207), ('convex relaxation', 0.371959924697876), ('rotation group', 0.35346564650535583), ('orthogonal group', 0.3456524908542633)]"
1698,1698,17,1698_tangent sheaves_sheaf_projective three_three dimensional projective,"['tangent sheaves', 'sheaf', 'projective three', 'three dimensional projective', 'singular schemes', 'sheaves', 'sheaves mathbb', 'dimensional projective space', 'tangent sheaf', 'projective space']","['Dimension two holomorphic distributions on four-dimensional projective\n  space   We study two-dimensional holomorphic distributions on $\\mathbb{P}^4$. We\nclassify dimension two distributions, of degree at most $2$, with either\nlocally free tangent sheaf or locally free conormal sheaf and whose singular\nscheme has pure dimension one. We show that the corresponding sheaves are\nsplit. Next, we investigate the geometry of such distributions, studying from\nmaximally non-integrable to integrable distributions. In the maximally\nnon-integrable case, we show that the distribution is either of Lorentzian type\nor a push-forward by a rational map of the Cartan prolongation of a singular\ncontact structure on a weighted projective 3-fold. We study distributions of\ndimension two in $\\mathbb{P}^4$ whose the conormal sheaves are the\nHorrocks-Mumford sheaves, describing the numerical invariants of their singular\nschemes which are smooth and connected. Such distributions are maximally\nnon-integrable, uniquely determined by their singular schemes and invariant by\na group $H_5 \\rtimes SL(2,\\mathbb{Z}_5) \\subset Sp(4, \\mathbb{Q})$, where $H_5$\nis the Heisenberg group of level $5$. We prove that the moduli spaces of\nHorrocks-Mumford distributions are irreducible quasi-projective varieties and\nwe determine their dimensions. Finally, we observe that the space of\ncodimension one distributions, of degree $d\\geq 6$, on $\\mathbb{P}^4$ have a\nfamily of degenerated flat holomorphic Riemannian metrics. Moreover, the\ndegeneracy divisors of such metrics consist of codimension one distributions\ninvariant by $H_5 \\rtimes SL(2,\\mathbb{Z}_5)$ and singular along a degenerate\nabelian surface with $(1,5)$-polarization and level-$5$-structure.\n', 'Codimension one distributions and stable rank 2 reflexive sheaves on\n  threefolds   We show that codimension one distributions with at most isolated\nsingularities on certain smooth projective threefolds with Picard rank one have\nstable tangent sheaves. The ideas in the proof of this fact are then applied to\nthe characterization of certain irreducible components of the moduli space of\nstable rank 2 reflexive sheaves on $\\mathbb{P}^3$, and to the construction of\nstable rank 2 reflexive sheaves with prescribed Chern classes on general\nthreefolds. We also prove that if $\\mathscr{G}$ is a subfoliation of a\ncodimension one distribution $\\mathscr{F}$ with isolated singularities, then\n$Sing(\\mathscr{G})$ is a curve. As a consequence, we give a criterion to decide\nwhether $\\mathscr{G}$ is globally given as the intersection of $\\mathscr{F}$\nwith another codimension one distribution. Turning our attention to codimension\none distributions with non isolated singularities, we determine the number of\nconnected components of the pure 1-dimensional component of the singular\nscheme.\n', ""Codimension one holomorphic distributions on the projective three-space   We study codimension one holomorphic distributions on the projective\nthree-space, analyzing the properties of their singular schemes and tangent\nsheaves. In particular, we provide a classification of codimension one\ndistributions of degree at most 2 with locally free tangent sheaves, and show\nthat codimension one distributions of arbitrary degree with only isolated\nsingularities have stable tangent sheaves. Furthermore, we describe the moduli\nspace of distributions in terms of Grothendieck's Quot-scheme for the tangent\nbundle. In certain cases, we show that the moduli space of codimension one\ndistributions on the projective space is an irreducible, nonsingular\nquasi-projective variety. Finally, we prove that every rational foliation, and\ncertain logarithmic foliations have stable tangent sheaves.\n""]","[('tangent sheaves', 0.5349258780479431), ('sheaf', 0.5145747661590576), ('projective three', 0.5142602324485779), ('three dimensional projective', 0.5101236701011658), ('singular schemes', 0.49914801120758057), ('sheaves', 0.4988649785518646), ('sheaves mathbb', 0.4985819160938263), ('dimensional projective space', 0.49351266026496887), ('tangent sheaf', 0.4916958510875702), ('projective space', 0.48938214778900146)]"
1699,1699,17,1699_operators trace_trace class perturbations_dissipative operators_spectral shift functions,"['operators trace', 'trace class perturbations', 'dissipative operators', 'spectral shift functions', 'operator integrals', 'valued spectral', 'self adjoint operators', 'double operator integrals', 'operator lipschitz', 'operator functions']","['Second order trace formulae   Koplienko \\cite{Ko} found a trace formula for perturbations of self-adjoint\noperators by operators of Hilbert-Schmidt class $\\mathcal{B}_2(\\mathcal{H})$.\nLater, Neidhardt introduced a similar formula in the case of pair of unitaries\n$(U,U_0)$ via multiplicative path in \\cite{NH}. In 2012, Potapov and Sukochev\n\\cite{PoSu} obtained a trace formula like the Koplienko trace formula for pairs\nof contractions by answering an open question posed by Gesztesy, Pushnitski,\nand Simon in \\cite[Open Question 11.2]{GePu}. In this article, we supply a new\nproof of the Koplienko trace formula in the case of pair of contractions\n$(T,T_0)$, where the initial operator $T_0$ is normal, via linear path by\nreducing the problem to a finite-dimensional one as in the proof of Krein\'s\ntrace formula by Voiculescu \\cite{Voi}, Sinha and Mohapatra\n\\cite{MoSi94,MoSi96}. Consequently, we obtain the Koplienko trace formula for a\nclass of pairs of contractions using the Sch\\""{a}ffer matrix unitary dilation.\nMoreover, we also obtain the Koplienko trace formula for a pair of self-adjoint\noperators and maximal dissipative operators using the Cayley transform. At the\nend, we extend the Koplienko-Neidhardt trace formula for a class of pair of\ncontractions $(T,T_0)$ via multiplicative path.\n', 'Functions of self-adjoint operators under relatively bounded and\n  relatively trace class perturbations. Relatively operator Lipschitz functions   We study the behaviour of functions of self-adjoint operators under\nrelatively bounded and relatively trace class perturbation We introduce and\nstudy the class of relatively operator Lipschitz functions. An essential role\nis played by double operator integrals. We also consider study the class of\nresolvent Lipschitz functions. Then we obtain a trace formula in the case of\nrelatively trace class perturbations and show that the maximal class of\nfunction for which the trace formula holds in the case of relatively trace\nclass perturbations coincides with the class of relatively operator Lipschitz\nfunctions. Our methods also gives us a new approach to the inequality\n$\\int|\\boldsymbol{\\xi}(t)|(1+|t|)^{-1}\\,{\\rm d}t<\\infty$ for the spectral shift\nfunction $\\boldsymbol{\\xi}$ in the case of relatively trace class\nperturbations.\n', 'Functions of dissipative operators under relatively bounded and\n  relatively trace class perturbations   We study the behaviour of functions of dissipative operators under relatively\nbounded and relatively trace class perturbation. We introduce and study the\nclass of analytic relatively operator Lipschitz functions. An essential role is\nplayed by double operator integrals with respect to semispectral measures. We\nalso study the class of analytic resolvent Lipschitz functions. Then we obtain\na trace formula in the case of relatively trace class perturbations and show\nthat the maximal class of function for which the trace formula holds in the\ncase of relatively trace class perturbations coincides with the class of\nanalytic relatively operator Lipschitz functions. We also establish the\ninequality $\\int|\\boldsymbol{\\xi}(t)|(1+|t|)^{-1}\\,{\\rm d}t<\\infty$ for the\nspectral shift function $\\boldsymbol\\xi$ in the case of relatively trace class\nperturbations.\n']","[('operators trace', 0.5774138569831848), ('trace class perturbations', 0.5626262426376343), ('dissipative operators', 0.5503910183906555), ('spectral shift functions', 0.5422648787498474), ('operator integrals', 0.5418525338172913), ('valued spectral', 0.5170779824256897), ('self adjoint operators', 0.5059460401535034), ('double operator integrals', 0.48946836590766907), ('operator lipschitz', 0.47064468264579773), ('operator functions', 0.45451438426971436)]"
1700,1700,17,1700_homology configuration spaces_stable homology_homology configuration_homological stability,"['homology configuration spaces', 'stable homology', 'homology configuration', 'homological stability', 'homology groups', 'homology', 'homology classes', 'cohomological dimension', 'th homology', 'homology twisted']","['Secondary representation stability and the ordered configuration space\n  of the once-punctured torus   In this paper we study stability patterns in the homology of the ordered\nconfiguration space of the once-punctured torus. In the last decade Church and\nChurch-Ellenberg-Farb proved that the homology groups of the ordered\nconfiguration space of a connected noncompact orientable manifold stabilize in\na representation theoretic sense as the number of points in the configuration\ngrows, with respect to a map that adds each new point ""at infinity."" Miller and\nWilson proved that there is a secondary representation stability pattern among\nthe unstable homology classes, with respect to adding a pair of orbiting points\n""near infinity."" This pattern is formalized by considering sequences of\nhomology classes as FIM$^{+}$-modules. We prove that, as FIM$^{+}$-modules, the\nsequence of ""new"" homology generators in the n-th homology of the ordered\nconfiguration space of 2n-2 points on the once-punctured torus is neither\n""free"" nor ""stably zero."" We also show that this sequence is generated by\nhomology classes on at most 4 points. Our proof uses Pagaria\'s work on the\nBetti numbers of the ordered configuration space of the torus to calculate the\ngrowth rate of the Betti numbers of the ordered configuration space of the\nonce-punctured torus. Our computations are the first to demonstrate that\nsecondary representation stability is a non-trivial phenomenon in\npositive-genus surfaces.\n', 'Arithmeticity for integral cohomological dimension of configuration\n  spaces of manifolds   Consider the configuration spaces of manifolds. We give a precise formula for\nthe integral cohomological dimension (the degree of top non-trivial integral\ncohomology group) of unordered configuration spaces of manifolds with\nnon-trivial co-dimension one cohomology group, and show that the the sequence\nof cohomological dimensions is arithmetic. This arithmeticity is not present in\nthe classical example of Arnold. Moreover, we show that the top integral\ncohomology group is infinite. Furthermore, We give a lower bound for the rank\nof top integral cohomology group. We also predict that the top integral\ncohomology group of configuration spaces of manifolds with non-trivial\nco-dimension one cohomology group is eventually finite. To the best of our\nknowledge, there is no rigorous bound for the cohomological dimension of\nordered configuration spaces. As an application of main results, we give a\nsharp lower bound for the cohomological dimension of ordered configuration\nspaces of manifolds. The first step of the proof of main results is to define a\nreduced Chevalley Eilenberg complex.\n', 'Homological monotonicity for configuration spaces of manifolds   Consider the configuration spaces of manifolds. An influential theorem of\nMcDuff, Segal and Church shows that the (co)homology of the unordered\nconfiguration space is independent of number of points in a range of degree\ncalled the stable range. We study the another important (and general) property\nof unordered configuration spaces of manifolds (not necessarily orientable, and\nnot necessarily admitting non-vanishing vector field) that is homological\nmonotonicity in unstable part. We show that the homological dimension of\nunordered configuration spaces of manifolds in each degree is monotonically\nincreasing. Our results show that the monotonicity property is not depend on\nthe differential structure and orientiability of manifold.\n']","[('homology configuration spaces', 0.7144370079040527), ('stable homology', 0.6635491251945496), ('homology configuration', 0.6208065748214722), ('homological stability', 0.6140412092208862), ('homology groups', 0.5918565988540649), ('homology', 0.5654404163360596), ('homology classes', 0.5640146136283875), ('cohomological dimension', 0.5559209585189819), ('th homology', 0.5541508197784424), ('homology twisted', 0.5490614175796509)]"
1701,1701,17,1701_bell polynomials_bell polynomial_bell numbers_charlier polynomials,"['bell polynomials', 'bell polynomial', 'bell numbers', 'charlier polynomials', 'moment generating', 'factorial moments', 'bell number', 'bernstein polynomials', 'poisson random variables', 'polynomials associated']","['Probabilistic central Bell polynomials   Let Y be a random variable whose moment generating function exists in a\nneighborhood of the origin. In this paper, we study the probabilistic central\nBell polynomials associated with random variable Y, as probabilistic extension\nof the central Bell polynomials. In addition, we investigate the probabilistic\ncentral factorial numbers of the second kind associated with Y and the\nprobabilistic central Fubini polynomials associated with Y. The aim of this\npaper is to derive some properties, explicit expressions, certain identities\nand recurrence relations for those polynomials and numbers.\n', 'Probabilistic Lah numbers and Lah-Bell polynomials   Let Y be a random variable whose moment generating function exists in some\nneighborhood of the origin. The aim of this paper is to study the probabilistic\nLah numbers associated with Y and the probabilistic Lah-Bell polynomials\nassociated with Y, as probabilistic versions of the Lah numbers and the\nLah-Bell polynomials, respectively. We derive some properties, explicit\nexpressions, recurrence relations and certain identities for those numbers and\npolynomials. In addition, we treat the special cases that Y is the Poisson\nrandom variable with parameter {\\alpha} > 0 and the Bernoulli random variable\nwith probability of success p.\n', 'Degenerate binomial and degenerate Poisson random variables   The aim of this paper is to study the Poisson random variables in relation to\nthe Lah-Bell polynomials and the degenerate binomial and degenerate Poisson\nrandom variables in connection\n  with the degenerate Lah-Bell polynomials. Among other things, we show that\nthe rising factorial moments of the degenerate Poisson random variable with\nparameter {\\alpha} are given by the degenerate Lah-Bell polynomials evaluated\nat {\\alpha}. We also show that the probability-generating function of the\ndegenerate Poisson random variable is equal to the generating function of the\ndegenerate Lah-Bell polynomials. Also, we show similar results for the Poisson\nrandom variables. Here the nth Lah-Bell number counts the number of ways a set\nof n elements can be partitioned into non-empty linearly ordered subsets, the\nLah-Bell polynomials are natural extensions of the Lah-Bell numbers and the\ndegenerate Lah-Bell polynomials are degenerate versions of the Lah-Bell\npolynomials.\n']","[('bell polynomials', 0.7176146507263184), ('bell polynomial', 0.6609019637107849), ('bell numbers', 0.47747862339019775), ('charlier polynomials', 0.47335171699523926), ('moment generating', 0.4732273519039154), ('factorial moments', 0.46156394481658936), ('bell number', 0.4353214502334595), ('bernstein polynomials', 0.42894500494003296), ('poisson random variables', 0.390217125415802), ('polynomials associated', 0.38990816473960876)]"
1702,1702,17,1702_optimal stochastic control_agent optimal_optimal stopping_stochastic control theory,"['optimal stochastic control', 'agent optimal', 'optimal stopping', 'stochastic control theory', 'continuous time optimal', 'optimal stochastic', 'stochastic differential games', 'stochastic control', 'optimal trading', 'stochastic differential']","[""Random horizon principal-agent problems   We consider a general formulation of the random horizon Principal-Agent\nproblem with a continuous payment and a lump-sum payment at termination. In the\nEuropean version of the problem, the random horizon is chosen solely by the\nprincipal with no other possible action from the agent than exerting effort on\nthe dynamics of the output process. We also consider the American version of\nthe contract, which covers the seminal Sannikov's model, where the agent can\nalso quit by optimally choosing the termination time of the contract. Our main\nresult reduces such non-zero-sum stochastic differential games to appropriate\nstochastic control problems which may be solved by standard methods of\nstochastic control theory. This reduction is obtained by following Sannikov's\napproach, further developed by Cvitanic, Possamai, and Touzi. We first\nintroduce an appropriate class of contracts for which the agent's optimal\neffort is immediately characterized by the standard verification argument in\nstochastic control theory. We then show that this class of contracts is dense\nin an appropriate sense so that the optimization over this restricted family of\ncontracts represents no loss of generality. The result is obtained by using the\nrecent well-posedness result of random horizon second-order backward SDE.\n"", 'Optimal stopping contract for Public Private Partnerships under moral\n  hazard   This paper studies optimal Public Private Partnerships contract between a\npublic entity and a consortium, in continuous-time and with a continuous\npayment, with the possibility for the public to stop the contract. The public\n(""she"") pays a continuous rent to the consortium (""he""), while the latter gives\na best response characterized by his effort. This effect impacts the drift of\nthe social welfare, until a terminal date decided by the public when she stops\nthe contract and gives compensation to the consortium. Usually, the public can\nnot observe the effort done by the consortium, leading to a principal agent\'s\nproblem with moral hazard. We solve this optimal stochastic control with\noptimal stopping problem in this context of moral hazard. The public value\nfunction is characterized by the solution of an associated Hamilton Jacobi\nBellman Variational Inequality. The public value function and the optimal\neffort and rent processes are computed numerically by using the Howard\nalgorithm. In particular, the impact of the social welfare\'s volatility on the\noptimal contract is studied.\n', 'The value of the information in the Moral Hazard setting   This article studies the problem of evaluating the information that a\nPrincipal lacks when establishing an incentive contract with an Agent whose\neffort is not observable. The Principal (""she"") pays a continuous rent to the\nAgent (""he""), while the latter gives a best response characterized by his\neffort, until a terminal date decided by the Principal when she stops the\ncontract and gives compensation to the Agent. The output process of the project\nis a diffusion process driven by a Brownian motion whose drift is impacted by\nthe Agent\'s effort. The first part of the paper investigates the optimal\nstochastic control problem when the Principal and the Agent share the same\ninformation. This situation, known as the first-best case, is solved by\ntackling the Lagrangian problem. In the second part, the Principal observes the\noutput process but she may not observe the drift and the Brownian motion\nseparately. This situation is known as the second-best case. We derive the best\nresponse of the Agent, then we solve the mixed optimal stopping/stochastic\ncontrol problem of the Principal under a fixed probability and on the\nfiltration generated by the Brownian motion, which is larger than the one\ngenerated by the output process (that corresponds to the information available\nfor the Principal). Under some regularity conditions, the Principal value\nfunction is characterized by solving the associated Hamilton Jacobi Bellman\nVariational Inequality. At the optimum, we prove that the two filtrations\ncoincide. Finally, we compute the value of the information for the Principal\nprovided by the observation of the Agent\'s effort. It is defined as the\ndifference between the principal value function in the first-best and\nsecond-best cases.\n']","[('optimal stochastic control', 0.5791910290718079), ('agent optimal', 0.5776549577713013), ('optimal stopping', 0.5738794207572937), ('stochastic control theory', 0.54071044921875), ('continuous time optimal', 0.5304229855537415), ('optimal stochastic', 0.5269723534584045), ('stochastic differential games', 0.5233405828475952), ('stochastic control', 0.5168876051902771), ('optimal trading', 0.417927086353302), ('stochastic differential', 0.3953622579574585)]"
1703,1703,17,1703_operadic algebras_homotopy theory_coalgebras_infty algebras,"['operadic algebras', 'homotopy theory', 'coalgebras', 'infty algebras', 'invariant homotopy', 'homotopy category', 'identity functor', 'homotopy classes maps', 'koszul duality', 'homotopical']","['E-infinity coalgebra structure on chain complexes with coefficients in\n  $\\mathbb{Z}$   The aim of this paper is to construct an $E_\\infty$-operad inducing an\n$E_\\infty$-coalgebra structure on chain complexes with coefficients in\n$\\mathbb{Z}$, which is an alternative description to the $E_\\infty$-coalgebra\nby the Barrat-Eccles operad.\n', ""Functor calculus completions for retractive operadic algebras in spectra   The aim of this paper is to study convergence of Bousfield-Kan completions\nwith respect to the 1-excisive approximation of the identity functor and exotic\nconvergence of the Taylor tower of the identity functor, for algebras over\noperads in spectra centered away from the null object. In Goodwillie's homotopy\nfunctor calculus, being centered away from the null object amounts to doing\nhomotopy theory and functor calculus in the retractive setting.\n"", '$E_n$-Hopf invariants   The classical Hopf invariant is an invariant of homotopy classes of maps from\n$S^{4n-1} $ to $S^{2n}$, and is an important invariant in homotopy theory. The\ngoal of this paper is to use the Koszul duality theory for $E_n$-operads to\ndefine a generalization of the classical Hopf invariant. One way of defining\nthe classical Hopf invariant is by defining a pairing between the cohomology of\nthe associative bar construction on the cochains of a space $X$ and the\nhomotopy groups of $X$. In this paper we will give a generalization of the\nclassical Hopf invariant by defining a pairing between the cohomology of the\n$E_n$-bar construction on the cochains of $X$ and the homotopy groups of $X$.\nThis pairing gives us a set of invariants of homotopy classes of maps from\n$S^m$ to a simplicial set $X$, this pairing can detect more homotopy classes of\nmaps than the classical Hopf invariant.\n  The second part of the paper is devoted to combining the $E_n$-Hopf\ninvariants with the Koszul duality theory for $E_n$-operads to get a relation\nbetween the $E_n$-Hopf invariants of a space $X$ and the $E_{n+1}$-Hopf\ninvariants of the suspension of $X$. This is done by studying the suspension\nmorphism for the $E_\\infty$-operad, which is a morphism from the\n$E_{\\infty}$-operad to the desuspension of the $E_\\infty$-operad. We show that\nit induces a functor from $E_\\infty$-algebras to $E_\\infty$-algebras, which has\nthe property that it sends an $E_\\infty$-model for a simplicial set $X$ to an\n$E_\\infty$-model for the suspension of $X$.\n  We use this result to give a relation between the $E_n$-Hopf invariants of\nmaps from $S^m$ into $X$ and the $E_{n+1}$-Hopf invariants of maps from\n$S^{m+1}$ into the suspension of $X$. One of the main results we show here, is\nthat this relation can be used to define invariants of stable homotopy classes\nof maps.\n']","[('operadic algebras', 0.5179116725921631), ('homotopy theory', 0.49139833450317383), ('coalgebras', 0.472874253988266), ('infty algebras', 0.4671333134174347), ('invariant homotopy', 0.46622687578201294), ('homotopy category', 0.43072351813316345), ('identity functor', 0.4300917387008667), ('homotopy classes maps', 0.42953094840049744), ('koszul duality', 0.42584821581840515), ('homotopical', 0.42272207140922546)]"
1704,1704,17,1704_cardiac electrophysiology_ecg_electrocardiogram_electrocardiograms,"['cardiac electrophysiology', 'ecg', 'electrocardiogram', 'electrocardiograms', 'cardiac', 'electrophysiology', 'models human', 'cardiovascular', 'myocardial', 'fidelity monte carlo']","['Digital twinning of cardiac electrophysiology models from the surface\n  ECG: a geodesic backpropagation approach   The eikonal equation has become an indispensable tool for modeling cardiac\nelectrical activation accurately and efficiently. In principle, by matching\nclinically recorded and eikonal-based electrocardiograms (ECGs), it is possible\nto build patient-specific models of cardiac electrophysiology in a purely\nnon-invasive manner. Nonetheless, the fitting procedure remains a challenging\ntask. The present study introduces a novel method, Geodesic-BP, to solve the\ninverse eikonal problem. Geodesic-BP is well-suited for GPU-accelerated machine\nlearning frameworks, allowing us to optimize the parameters of the eikonal\nequation to reproduce a given ECG. We show that Geodesic-BP can reconstruct a\nsimulated cardiac activation with high accuracy in a synthetic test case, even\nin the presence of modeling inaccuracies. Furthermore, we apply our algorithm\nto a publicly available dataset of a biventricular rabbit model, with promising\nresults. Given the future shift towards personalized medicine, Geodesic-BP has\nthe potential to help in future functionalizations of cardiac models meeting\nclinical time constraints while maintaining the physiological accuracy of\nstate-of-the-art cardiac models.\n', 'Accurate and Efficient Cardiac Digital Twin from surface ECGs: Insights\n  into Identifiability of Ventricular Conduction System   Digital twins for cardiac electrophysiology are an enabling technology for\nprecision cardiology. Current forward models are advanced enough to simulate\nthe cardiac electric activity under different pathophysiological conditions and\naccurately replicate clinical signals like torso electrocardiograms (ECGs). In\nthis work, we address the challenge of matching subject-specific QRS complexes\nusing anatomically accurate, physiologically grounded cardiac digital twins. By\nfitting the initial conditions of a cardiac propagation model, our non-invasive\nmethod predicts activation patterns during sinus rhythm. For the first time, we\ndemonstrate that distinct activation maps can generate identical surface ECGs.\nTo address this non-uniqueness, we introduce a physiological prior based on the\ndistribution of Purkinje-muscle junctions. Additionally, we develop a digital\ntwin ensemble for probabilistic inference of cardiac activation. Our approach\nmarks a significant advancement in the calibration of cardiac digital twins and\nenhances their credibility for clinical application.\n', 'Real-time whole-heart electromechanical simulations using Latent Neural\n  Ordinary Differential Equations   Cardiac digital twins provide a physics and physiology informed framework to\ndeliver predictive and personalized medicine. However, high-fidelity\nmulti-scale cardiac models remain a barrier to adoption due to their extensive\ncomputational costs and the high number of model evaluations needed for\npatient-specific personalization. Artificial Intelligence-based methods can\nmake the creation of fast and accurate whole-heart digital twins feasible. In\nthis work, we use Latent Neural Ordinary Differential Equations (LNODEs) to\nlearn the temporal pressure-volume dynamics of a heart failure patient. Our\nsurrogate model based on LNODEs is trained from 400 3D-0D whole-heart\nclosed-loop electromechanical simulations while accounting for 43 model\nparameters, describing single cell through to whole organ and cardiovascular\nhemodynamics. The trained LNODEs provides a compact and efficient\nrepresentation of the 3D-0D model in a latent space by means of a feedforward\nfully-connected Artificial Neural Network that retains 3 hidden layers with 13\nneurons per layer and allows for 300x real-time numerical simulations of the\ncardiac function on a single processor of a standard laptop. This surrogate\nmodel is employed to perform global sensitivity analysis and robust parameter\nestimation with uncertainty quantification in 3 hours of computations, still on\na single processor. We match pressure and volume time traces unseen by the\nLNODEs during the training phase and we calibrate 4 to 11 model parameters\nwhile also providing their posterior distribution. This paper introduces the\nmost advanced surrogate model of cardiac function available in the literature\nand opens new important venues for parameter calibration in cardiac digital\ntwins.\n']","[('cardiac electrophysiology', 0.5073026418685913), ('ecg', 0.42369508743286133), ('electrocardiogram', 0.4202415347099304), ('electrocardiograms', 0.4194352924823761), ('cardiac', 0.4153803288936615), ('electrophysiology', 0.39221492409706116), ('models human', 0.34990864992141724), ('cardiovascular', 0.3322746157646179), ('myocardial', 0.31194791197776794), ('fidelity monte carlo', 0.3082714080810547)]"
1705,1705,17,1705_nonholonomic systems_nonholonomic dynamics_physical constraints_constraints geometric,"['nonholonomic systems', 'nonholonomic dynamics', 'physical constraints', 'constraints geometric', 'control invariant', 'controlled invariant', 'affine constraints', 'constraints derive', 'constraints characterize', 'constraints illustrate']","['Virtual Constraints on Lie groups   This paper studies virtual constraints on Lie groups. Virtual constraints are\ninvariant relations imposed on a control system via feedback. In this work, we\nintroduce the notion of \\textit{virtual constraints on Lie groups}, in\nparticular, \\textit{virtual nonholonomic constraints on Lie groups}, in a\ngeometric framework. More precisely, this object is a controlled invariant\nsubspace associated with an affine connection mechanical control system on the\nLie algebra associated with the Lie group which is the configuration space of\nthe system. We demonstrate the existence and uniqueness of a control law\ndefining a virtual nonholonomic constraint and we characterize the trajectories\nof the closed-loop system as solutions of a mechanical system associated with\nan induced constrained connection. Moreover, we characterize the reduced\ndynamics for nonholonomic systems in terms of virtual nonholonomic constraints,\ni.e., we characterize when can we obtain reduced nonholonomic dynamics from\nvirtual nonholonomic constraints. We illustrate the theory with some examples\nand present simulation results for an application.\n', 'Virtual Affine Nonholonomic Constraints   Virtual constraints are relations imposed in a control system that become\ninvariant via feedback, instead of real physical constraints acting on the\nsystem. Nonholonomic systems are mechanical systems with non-integrable\nconstraints on the velocities. In this work, we introduce the notion of virtual\naffine nonholonomic constraints in a geometric framework. More precisely, it is\na controlled invariant affine distribution associated with an affine connection\nmechanical control system. We show the existence and uniqueness of a control\nlaw defining a virtual affine nonholonomic constraint.\n', 'Virtual Nonholonomic Constraints: A Geometric Approach   Virtual constraints are invariant relations imposed on a control system via\nfeedback as opposed to real physical constraints acting on the system.\nNonholonomic systems are mechanical systems with non-integrable constraints on\nthe velocities. In this work, we introduce the notion of virtual nonholonomic\nconstraints in a geometric framework. More precisely, it is a controlled\ninvariant distribution associated with an affine connection mechanical control\nsystem. We demonstrate the existence and uniqueness of a control law defining a\nvirtual nonholonomic constraint and we characterize the trajectories of the\nclosed-loop system as solutions of a mechanical system associated with an\ninduced constrained connection. Moreover, we characterize the dynamics for\nnonholonomic systems in terms of virtual nonholonomic constraints, i.e., we\ncharacterize when can we obtain nonholonomic dynamics from virtual nonholonomic\nconstraints.\n']","[('nonholonomic systems', 0.5531942248344421), ('nonholonomic dynamics', 0.5272839665412903), ('physical constraints', 0.5247572064399719), ('constraints geometric', 0.523747444152832), ('control invariant', 0.5137879252433777), ('controlled invariant', 0.5111469030380249), ('affine constraints', 0.475562185049057), ('constraints derive', 0.46690115332603455), ('constraints characterize', 0.46067672967910767), ('constraints illustrate', 0.4580102860927582)]"
1706,1706,17,1706_classification deep_softmax_entropy maximization_deep relu networks,"['classification deep', 'softmax', 'entropy maximization', 'deep relu networks', 'relu networks', 'deep neural', 'optimal learning', 'deep neural networks', 'classifiers', 'class deep']","['Statistical theory for image classification using deep convolutional\n  neural networks with cross-entropy loss under the hierarchical max-pooling\n  model   Convolutional neural networks (CNNs) trained with cross-entropy loss have\nproven to be extremely successful in classifying images. In recent years, much\nwork has been done to also improve the theoretical understanding of neural\nnetworks. Nevertheless, it seems limited when these networks are trained with\ncross-entropy loss, mainly because of the unboundedness of the target function.\nIn this paper, we aim to fill this gap by analyzing the rate of the excess risk\nof a CNN classifier trained by cross-entropy loss. Under suitable assumptions\non the smoothness and structure of the a posteriori probability, it is shown\nthat these classifiers achieve a rate of convergence which is independent of\nthe dimension of the image. These rates are in line with the practical\nobservations about CNNs.\n', 'Statistical learnability of smooth boundaries via pairwise binary\n  classification with deep ReLU networks   The topic of nonparametric estimation of smooth boundaries is extensively\nstudied in the conventional setting where pairs of single covariate and\nresponse variable are observed. However, this traditional setting often suffers\nfrom the cost of data collection. Recent years have witnessed the consistent\ndevelopment of learning algorithms for binary classification problems where one\ncan instead observe paired covariates and binary variable representing the\nstatistical relationship between the covariates. In this work, we theoretically\nstudy the question of whether multiple smooth boundaries are learnable if the\npairwise binary classification setting is considered. We investigate the\nquestion with the statistical dependence of paired covariates to develop a\nlearning algorithm using vector-valued functions. The main theorem shows that\nthere is an empirical risk minimization algorithm in a class of deep ReLU\nnetworks such that it produces a consistent estimator for indicator functions\ndefined with smooth boundaries. We also discuss how the pairwise binary\nclassification setting is different from the conventional settings, focusing on\nthe structural condition of function classes. As a by-product, we apply the\nmain theorem to a multiclass nonparametric classification problem where the\nestimation performance is measured by the excess risk in terms of\nmisclassification.\n', ""Minimax Optimal Deep Neural Network Classifiers Under Smooth Decision\n  Boundary   Deep learning has gained huge empirical successes in large-scale\nclassification problems. In contrast, there is a lack of statistical\nunderstanding about deep learning methods, particularly in the minimax\noptimality perspective. For instance, in the classical smooth decision boundary\nsetting, existing deep neural network (DNN) approaches are rate-suboptimal, and\nit remains elusive how to construct minimax optimal DNN classifiers. Moreover,\nit is interesting to explore whether DNN classifiers can circumvent the curse\nof dimensionality in handling high-dimensional data. The contributions of this\npaper are two-fold. First, based on a localized margin framework, we discover\nthe source of suboptimality of existing DNN approaches. Motivated by this, we\npropose a new deep learning classifier using a divide-and-conquer technique:\nDNN classifiers are constructed on each local region and then aggregated to a\nglobal one. We further propose a localized version of the classical Tsybakov's\nnoise condition, under which statistical optimality of our new classifier is\nestablished. Second, we show that DNN classifiers can adapt to low-dimensional\ndata structures and circumvent the curse of dimensionality in the sense that\nthe minimax rate only depends on the effective dimension, potentially much\nsmaller than the actual data dimension. Numerical experiments are conducted on\nsimulated data to corroborate our theoretical results.\n""]","[('classification deep', 0.6695908308029175), ('softmax', 0.5586211681365967), ('entropy maximization', 0.5219124555587769), ('deep relu networks', 0.5200232863426208), ('relu networks', 0.5187147259712219), ('deep neural', 0.513635516166687), ('optimal learning', 0.5058377385139465), ('deep neural networks', 0.5047576427459717), ('classifiers', 0.5044984221458435), ('class deep', 0.5024376511573792)]"
1707,1707,17,1707_simplicial volume_volume manifolds_fundamental groups manifolds_aspherical manifolds,"['simplicial volume', 'volume manifolds', 'fundamental groups manifolds', 'aspherical manifolds', 'simplicial', 'manifolds', 'manifolds fixed', 'manifolds whose', 'connected manifolds', 'volume arbitrary']","['Amenable covers and integral foliated simplicial volume   In analogy with ordinary simplicial volume, we show that integral foliated\nsimplicial volume of oriented closed connected aspherical $n$-manifolds that\nadmit an open amenable cover of multiplicity at most $n$ is zero. This implies\nthat the fundamental groups of such manifolds have fixed price and are cheap as\nwell as reproves some statements about homology growth.\n', 'Simplicial volume of manifolds fibering with connected structure group   In this note we investigate the simplicial volume of fiber bundles with\nconnected structure group. We are able to show that if the structure group is\neither compact or a Lie group, or if the fiber is aspherical that the\nsimplicial volume of the total space agrees with the simplicial volume of the\ntrivial bundle.\n', 'Stable integral simplicial volume of 3-manifolds   We show that non-elliptic prime 3-manifolds satisfy integral approximation\nfor the simplicial volume, i.e., that their simplicial volume equals the stable\nintegral simplicial volume. The proof makes use of integral foliated simplicial\nvolume and tools from ergodic theory.\n']","[('simplicial volume', 0.7081474661827087), ('volume manifolds', 0.6453778147697449), ('fundamental groups manifolds', 0.5081877112388611), ('aspherical manifolds', 0.4899941384792328), ('simplicial', 0.48168012499809265), ('manifolds', 0.47852522134780884), ('manifolds fixed', 0.4732590615749359), ('manifolds whose', 0.4694356322288513), ('connected manifolds', 0.4604508578777313), ('volume arbitrary', 0.4481390714645386)]"
1708,1708,17,1708_variations hodge structure_hodge structures_hodge structure_hodge theoretic,"['variations hodge structure', 'hodge structures', 'hodge structure', 'hodge theoretic', 'mixed hodge structures', 'variation hodge structure', 'mixed hodge structure', 'variation hodge', 'variations hodge', 'hodge number']","['Hodge Representations   Hodge representations were introduced by Green-Griffiths-Kerr to classify the\nHodge groups of polarized Hodge structures, and the corresponding Mumford-Tate\nsubdomains of a period domain. The purpose of this article is to provide an\nexposition of how, given a fixed period domain $\\mathcal{D}$, to enumerate the\nHodge representations corresponding to Mumford-Tate subdomains $D \\subset\n\\mathcal{D}$. After reviewing the well-known classical cases that $\\mathcal{D}$\nis Hermitian symmetric (weight $n=1$, and weight $n=2$ with $p_g = h^{2,0}=1$),\nwe illustrate this in the case that $\\mathcal{D}$ is the period domain\nparameterizing polarized Hodge structures of (effective) weight two Hodge\nstructures with first Hodge number $p_g = h^{2,0} = 2$. We also classify the\nHodge representations of Calabi-Yau type, and enumerate the horizontal\nrepresentations of CY 3-fold type. (The ""horizontal"" representations those with\nthe property that corresponding domain $D \\subset \\mathcal{D}$ satisfies the\ninfinitesimal period relation, a.k.a. Griffiths\' transversality, and is\ntherefore Hermitian.)\n', ""Degenerating complex variations of Hodge structure in dimension one   We analyze the behavior of polarized complex variations of Hodge structure on\nthe punctured unit disk. For integral variations of Hodge structure, this\nanalysis was first carried out by Wilfried Schmid. We get rid of the assumption\nthat the eigenvalues of the monodromy transformation are roots of unity. In\nthis generality, we give new (and, we think, more conceptual) proofs for all\nthe major results in Schmid's paper, such as the estimates for the rate of\ngrowth of the Hodge norm; the existence of a limiting mixed Hodge structure;\nthe nilpotent orbit theorem; and a simplified (but still sufficiently powerful)\nversion of the SL(2)-orbit theorem.\n"", ""Degenerations to secant cubic hypersurfaces and limiting Hodge structure   The secant variety of the Veronese surface is a singular cubic fourfold. The\ndegeneration of Hodge structures of one-parameter degenerations to this secant\ncubic fourfold is a key ingredient for B.~Hassett and R.~Laza in studying the\nmoduli space of cubic fourfolds via the period mapping. We generalize some of\ntheir results to the cubic hypersurface that is the secant variety of a Severi\nvariety. Specifically, we study the limit mixed Hodge structures associated to\none-parameter degenerations to the secant cubic hypersurface. Considering\nS.~Usui's partial compactification of a period domain for Hodge structures of\ngeneral weights, we apply the limit mixed Hodge structure to characterize a\nlocal extension of the period map for the corresponding cubic hypersurfaces.\n""]","[('variations hodge structure', 0.7585647702217102), ('hodge structures', 0.7564719915390015), ('hodge structure', 0.7402021288871765), ('hodge theoretic', 0.7344311475753784), ('mixed hodge structures', 0.7268387675285339), ('variation hodge structure', 0.7206779718399048), ('mixed hodge structure', 0.7055293917655945), ('variation hodge', 0.6801499128341675), ('variations hodge', 0.6791378855705261), ('hodge number', 0.644132137298584)]"
1709,1709,17,1709_epidemic models_dynamics epidemic_disease dynamics_disease outbreaks,"['epidemic models', 'dynamics epidemic', 'disease dynamics', 'disease outbreaks', 'epidemic', 'forecasting', 'predicting', 'outbreak', 'informed neural networks', 'epidemiological models']","['An Improved Mathematical Model of Sepsis: Modeling, Bifurcation\n  Analysis, and Optimal Control Study for Complex Nonlinear Infectious Disease\n  System   Sepsis is a life-threatening medical emergency, which is a major cause of\ndeath worldwide and the second highest cause of mortality in the United States.\nResearching the optimal control treatment or intervention strategy on the\ncomprehensive sepsis system is key in reducing mortality. For this purpose,\nfirst, this paper improves a complex nonlinear sepsis model proposed in our\nprevious work. Then, bifurcation analyses are conducted for each sepsis\nsubsystem to study the model behaviors under some system parameters. The\nbifurcation analysis results also further indicate the necessity of control\ntreatment and intervention therapy. If the sepsis system is without adding any\ncontrol under some parameter and initial system value settings, the system will\nperform persistent inflammation outcomes as time goes by. Therefore, we develop\nour complex improved nonlinear sepsis model into a sepsis optimal control\nmodel, and then use some effective biomarkers recommended in existing clinic\npractices as optimization objective function to measure the development of\nsepsis. Besides that, a Bayesian optimization algorithm by combining Recurrent\nneural network (RNN-BO algorithm) is introduced to predict the optimal control\nstrategy for the studied sepsis optimal control system. The difference between\nthe RNN-BO algorithm from other optimization algorithms is that once given any\nnew initial system value setting (initial value is associated with the initial\nconditions of patients), the RNN-BO algorithm is capable of quickly predicting\na corresponding time-series optimal control based on the historical optimal\ncontrol data for any new sepsis patient. To demonstrate the effectiveness and\nefficiency of the RNN-BO algorithm on solving the optimal control solution on\nthe complex nonlinear sepsis system, some numerical simulations are implemented\nby comparing with other optimization algorithms in this paper.\n', 'A Physics-Informed Neural Network approach for compartmental\n  epidemiological models   Compartmental models provide simple and efficient tools to analyze the\nrelevant transmission processes during an outbreak, to produce short-term\nforecasts or transmission scenarios, and to assess the impact of vaccination\ncampaigns. However, their calibration is not straightforward, since many\nfactors contribute to the rapid change of the transmission dynamics during an\nepidemic. For example, there might be changes in the individual awareness, the\nimposition of non-pharmacological interventions and the emergence of new\nvariants. As a consequence, model parameters such as the transmission rate are\ndoomed to change in time, making their assessment more challenging. Here, we\npropose to use Physics-Informed Neural Networks (PINNs) to track the temporal\nchanges in the model parameters and provide an estimate of the model state\nvariables. PINNs recently gained attention in many engineering applications\nthanks to their ability to consider both the information from data (typically\nuncertain) and the governing equations of the system. The ability of PINNs to\nidentify unknown model parameters makes them particularly suitable to solve\nill-posed inverse problems, such as those arising in the application of\nepidemiological models. Here, we develop a reduced-split approach for the\nimplementation of PINNs to estimate the temporal changes in the state variables\nand transmission rate of an epidemic based on the SIR model equation and\ninfectious data. The main idea is to split the training first on the\nepidemiological data, and then on the residual of the system equations. The\nproposed method is applied to five synthetic test cases and two real scenarios\nreproducing the first months of the COVID-19 Italian pandemic. Our results show\nthat the split implementation of PINNs outperforms the standard approach in\nterms of accuracy (up to one order of magnitude) and computational times (speed\nup of 20%).\n', ""Developing cholera outbreak forecasting through qualitative dynamics:\n  Insights into Malawi case study   Cholera, an acute diarrheal disease, is a serious concern in developing and\nunderdeveloped areas. A qualitative understanding of cholera epidemics aims to\nforesee transmission patterns based on reported data and mechanistic models.\nThe mechanistic model is a crucial tool for capturing the dynamics of disease\ntransmission and population spread. However, using real-time cholera cases is\nessential for forecasting the transmission trend. This prospective study seeks\nto furnish insights into transmission trends through qualitative dynamics\nfollowed by machine learning-based forecasting. The Monte Carlo Markov Chain\napproach is employed to calibrate the proposed mechanistic model. We identify\ncritical parameters that illustrate the disease's dynamics using partial rank\ncorrelation coefficient-based sensitivity analysis. The basic reproduction\nnumber as a crucial threshold measures asymptotic dynamics. Furthermore,\nforward bifurcation directs the stability of the infection state, and Hopf\nbifurcation suggests that trends in transmission may become unpredictable as\nsocietal disinfection rates rise. Further, we develop epidemic-informed machine\nlearning models by incorporating mechanistic cholera dynamics into\nautoregressive integrated moving averages and autoregressive neural networks.\nWe forecast short-term future cholera cases in Malawi by implementing the\nproposed epidemic-informed machine learning models to support this. We assert\nthat integrating temporal dynamics into the machine learning models can enhance\nthe capabilities of cholera forecasting models. The execution of this mechanism\ncan significantly influence future trends in cholera transmission. This\nevolving approach can also be beneficial for policymakers to interpret and\nrespond to potential disease systems. Moreover, our methodology is replicable\nand adaptable, encouraging future research on disease dynamics.\n""]","[('epidemic models', 0.6333726644515991), ('dynamics epidemic', 0.5801317095756531), ('disease dynamics', 0.5006738305091858), ('disease outbreaks', 0.48114272952079773), ('epidemic', 0.4619617760181427), ('forecasting', 0.42398956418037415), ('predicting', 0.4214320182800293), ('outbreak', 0.4194357693195343), ('informed neural networks', 0.4152125418186188), ('epidemiological models', 0.4111582636833191)]"
1710,1710,17,1710_associative memory_hopfield neural_memory networks_neural dynamics,"['associative memory', 'hopfield neural', 'memory networks', 'neural dynamics', 'memorization', 'term memory', 'memory', 'neural', 'memories', 'synapses']","['Mixed memories in Hopfield networks   We consider the class of Hopfield models of associative memory with\nactivation function $F$ and state space $\\{-1,1\\}^N$, where each vertex of the\ncube describes a configuration of $N$ binary neurons. $M$ randomly chosen\nconfigurations, called patterns, are stored using an energy function designed\nto make them local minima. If they are, which is known to depend on how $M$\nscales with $N$, then they can be retrieved using a dynamics that decreases the\nenergy. However, storing the patterns in the energy function also creates\nunintended local minima, and thus false memories. Although this has been known\nsince the earliest work on the subject, it has only been supported by numerical\nsimulations and non-rigorous calculations, except in elementary cases.\n  Our results are twofold. For a generic function $F$, we explicitly construct\na set of configurations, called mixed memories, whose properties are intended\nto characterise the local minima of the energy function. For three prominent\nmodels, namely the classical, the dense and the modern Hopfield models,\nobtained for quadratic, polynomial and exponential functions $F$ respectively,\nwe give conditions on the growth rate of $M$ which guarantee that, as $N$\ndiverges, mixed memories are fixed points of the retrieval dynamics and thus\nexact minima of the energy. We conjecture that in this regime, all local minima\nare mixed memories.\n', 'Firing Rate Models as Associative Memory: Excitatory-Inhibitory Balance\n  for Robust Retrieval   Firing rate models are dynamical systems widely used in applied and\ntheoretical neuroscience to describe local cortical dynamics in neuronal\npopulations. By providing a macroscopic perspective of neuronal activity, these\nmodels are essential for investigating oscillatory phenomena, chaotic behavior,\nand associative memory processes. Despite their widespread use, the application\nof firing rate models to associative memory networks has received limited\nmathematical exploration, and most existing studies are focused on specific\nmodels. Conversely, well-established associative memory designs, such as\nHopfield networks, lack key biologically-relevant features intrinsic to firing\nrate models, including positivity and interpretable synaptic matrices that\nreflect excitatory and inhibitory interactions. To address this gap, we propose\na general framework that ensures the emergence of re-scaled memory patterns as\nstable equilibria in the firing rate dynamics. Furthermore, we analyze the\nconditions under which the memories are locally and globally asymptotically\nstable, providing insights into constructing biologically-plausible and robust\nsystems for associative memory retrieval.\n', 'Enhanced Error-free Retrieval in Kuramoto-type Associative-memory Networks via Two-memory Configuration We study the associative-memory network of Kuramoto-type oscillators that stores a set of memorized patterns (memories). In [Phys. Rev. Lett., 92 (2004), 108101], Nishikawa, Lai and Hoppensteadt showed that the capacity of this system for pattern retrieval with small errors can be made as high as that of the Hopfield network. Some stability analysis efforts focus on mutually orthogonal memories; however, the theoretical results do not ensure error-free retrieval in general situations. In this paper, we present a route for using the model in pattern retrieval problems with small or large errors. We employ the eigenspectrum analysis of Jacobians and potential analysis of the gradient flow to derive the stability/instability of binary patterns. For two memories, the eigenspectrum of Jacobian at each pattern can be specified, which enables us to give the critical value of the parameter to distinguish the memories from all other patterns in stability. This setting of two memories substantially reduces the number of stable patterns and enlarges their basins, allowing us to recover defective patterns. We extend this approach to general cases and present a deterministic method for ensuring error-free retrieval across a general set of standard patterns. Numerical simulations and comparative analyses illustrate the approach.']","[('associative memory', 0.5971453785896301), ('hopfield neural', 0.5844635367393494), ('memory networks', 0.5666177272796631), ('neural dynamics', 0.5437549948692322), ('memorization', 0.47734498977661133), ('term memory', 0.45778176188468933), ('memory', 0.4413299262523651), ('neural', 0.40642017126083374), ('memories', 0.4045213758945465), ('synapses', 0.378074049949646)]"
1711,1711,16,1711_finite element methods_linearized elasticity_element methods linear_finite element approximations,"['finite element methods', 'linearized elasticity', 'element methods linear', 'finite element approximations', 'finite strain', 'finite element approximation', 'finite element based', 'element methods', 'nonlinear elasticity', 'strain tensor']","['A simple and efficient hybrid discretization approach to alleviate\n  membrane locking in isogeometric thin shells   This work presents a new hybrid discretization approach to alleviate membrane\nlocking in isogeometric finite element formulations for Kirchhoff-Love shells.\nThe approach is simple, and requires no additional dofs and no static\ncondensation. It does not increase the bandwidth of the tangent matrix and is\neffective for both linear and nonlinear problems. It combines isogeometric\nsurface discretizations with classical Lagrange-based surface discretizations,\nand can thus be run with existing isogeometric finite element codes. Also, the\nstresses can be recovered straightforwardly. The effectiveness of the proposed\napproach in alleviating, if not eliminating, membrane locking is demonstrated\nthrough the rigorous study of the convergence behavior of several classical\nbenchmark problems. Accuracy gains are particularly large in the membrane\nstresses. The approach is formulated here for quadratic NURBS, but an extension\nto other discretization types can be anticipated. The same applies to other\nconstraints and associated locking phenomena.\n', 'A robust finite strain isogeometric solid-beam element   In this work, an efficient and robust isogeometric three-dimensional\nsolid-beam finite element is developed for large deformations and finite\nrotations with merely displacements as degrees of freedom. The finite strain\ntheory and hyperelastic constitutive models are considered and B-Spline and\nNURBS are employed for the finite element discretization. Similar to finite\nelements based on Lagrange polynomials, also NURBS-based formulations are\naffected by the non-physical phenomena of locking, which constrains the field\nvariables and negatively impacts the solution accuracy and deteriorates\nconvergence behavior. To avoid this problem within the context of a Solid-Beam\nformulation, the Assumed Natural Strain (ANS) method is applied to alleviate\nmembrane and transversal shear locking and the Enhanced Assumed Strain (EAS)\nmethod against Poisson thickness locking. Furthermore, the Mixed Integration\nPoint (MIP) method is employed to make the formulation more efficient and\nrobust. The proposed novel isogeometric solid-beam element is tested on several\nsingle-patch and multi-patch benchmark problems, and it is validated against\nclassical solid finite elements and isoparametric solid-beam elements. The\nresults show that the proposed formulation can alleviate the locking effects\nand significantly improve the performance of the isogeometric solid-beam\nelement. With the developed element, efficient and accurate predictions of\nmechanical properties of lattice-based structured materials can be achieved.\nThe proposed solid-beam element inherits both the merits of solid elements e.g.\nflexible boundary conditions and of the beam elements i.e. higher computational\nefficiency.\n', 'Removing membrane locking in quadratic NURBS-based discretizations of\n  linear plane Kirchhoff rods: CAS elements   NURBS-based discretizations suffer from membrane locking when applied to\nprimal formulations of curved thin-walled structures. We consider linear plane\ncurved Kirchhoff rods as a model problem to study how to remove membrane\nlocking from NURBS-based discretizations. In this work, we propose\ncontinuous-assumed-strain (CAS) elements, an assumed strain treatment that\nremoves membrane locking from quadratic NURBS for an ample range of slenderness\nratios. CAS elements take advantage of the C1 inter-element continuity of the\ndisplacement vector given by quadratic NURBS to interpolate the membrane strain\nusing linear Lagrange polynomials while preserving the C0 inter-element\ncontinuity of the membrane strain. CAS elements are the first NURBS-based\nelement type able to remove membrane locking for a broad range of slenderness\nratios that combines the following characteristics: (1) No additional degrees\nof freedom are added, (2) No additional systems of algebraic equations need to\nbe solved, and (3) The nonzero pattern of the stiffness matrix is preserved.\nSince the only additional computations required by the proposed element type\nare to evaluate the derivatives of the basis functions and the unit tangent\nvector at the knots, the proposed scheme barely increases the computational\ncost with respect to the locking-prone NURBS-based discretization of the primal\nformulation. The benchmark problems show that the convergence of CAS elements\nis independent of the slenderness ratio while the convergence of quadratic\nNURBS elements, local Bbar elements, and local ANS elements depends heavily on\nthe slenderness ratio. The numerical examples also show how CAS elements remove\nthe spurious oscillations in stress resultants caused by membrane locking while\nquadratic NURBS elements, local Bbar elements, and local ANS elements suffer\nfrom large-amplitude spurious oscillations in stress resultants.\n']","[('finite element methods', 0.5830524563789368), ('linearized elasticity', 0.4815615117549896), ('element methods linear', 0.46929922699928284), ('finite element approximations', 0.4383845925331116), ('finite strain', 0.4169992208480835), ('finite element approximation', 0.41036635637283325), ('finite element based', 0.38807249069213867), ('element methods', 0.3760814368724823), ('nonlinear elasticity', 0.34110119938850403), ('strain tensor', 0.3360942602157593)]"
1712,1712,16,1712_optimal transport maps_log concave measures_optimal transport map_optimal transport,"['optimal transport maps', 'log concave measures', 'optimal transport map', 'optimal transport', 'gaussian isoperimetric inequality', 'concave measures', 'concave densities', 'transport maps', 'strongly log concave', 'log lipschitz']","['Heat flow, log-concavity, and Lipschitz transport maps   In this paper we derive estimates for the Hessian of the logarithm\n(log-Hessian) for solutions to the heat equation. For initial data in the form\nof log-Lipschitz perturbation of strongly log-concave measures, the log-Hessian\nadmits an explicit, uniform (in space) lower bound. This yields a new estimate\nfor the Lipschitz constant of a transport map pushing forward the standard\nGaussian to a measure in this class. Further connections are discussed with\nscore-based diffusion models and improved Gaussian logarithmic Sobolev\ninequalities. Finally, we show that assuming only fast decay of the tails of\nthe initial datum does not suffice to guarantee uniform log-Hessian upper\nbounds.\n', ""Optimal transport maps, majorization, and log-subharmonic measures   Caffarelli's contraction theorem bounds the derivative of the optimal\ntransport map between a log-convex measure and a strongly log-concave measure.\nWe show that an analogous phenomenon holds on the level of the trace: The trace\nof the derivative of the optimal transport map between a log-subharmonic\nmeasure and a strongly log-concave measure is bounded. We show that this trace\nbound has a number of consequences pertaining to volume-contracting transport\nmaps, majorization and its monotonicity along Wasserstein geodesics, growth\nestimates of log-subharmonic functions, the Wehrl conjecture for Glauber\nstates, and two-dimensional Coulomb gases. We also discuss volume-contraction\nproperties for the Kim-Milman transport map\n"", 'Transportation onto log-Lipschitz perturbations   We establish sufficient conditions for the existence of globally Lipschitz\ntransport maps between probability measures and their log-Lipschitz\nperturbations, with dimension-free bounds. Our results include Gaussian\nmeasures on Euclidean spaces and uniform measures on spheres as source\nmeasures. More generally, we prove results for source measures on manifolds\nsatisfying strong curvature assumptions. These seem to be the first examples of\ndimension-free Lipschitz transport maps in non-Euclidean settings, which are\nmoreover sharp on the sphere. We also present some applications to functional\ninequalities, including a new dimension-free Gaussian isoperimetric inequality\nfor log-Lipschitz perturbations of the standard Gaussian measure. Our proofs\nare based on the Langevin flow construction of transport maps of Kim and\nMilman.\n']","[('optimal transport maps', 0.596279501914978), ('log concave measures', 0.5912498235702515), ('optimal transport map', 0.5784353613853455), ('optimal transport', 0.5530928373336792), ('gaussian isoperimetric inequality', 0.5077527761459351), ('concave measures', 0.5060575604438782), ('concave densities', 0.48533710837364197), ('transport maps', 0.47363537549972534), ('strongly log concave', 0.4727259874343872), ('log lipschitz', 0.4601365923881531)]"
1713,1713,16,1713_planck navier stokes_navier stokes systems_case navier stokes_navier stokes system,"['planck navier stokes', 'navier stokes systems', 'case navier stokes', 'navier stokes system', 'navier stokes', 'nernst planck navier', 'planck navier', 'nernst planck equations', 'dirichlet boundary conditions', 'poisson nernst planck']","['Nernst-Planck-Navier-Stokes Systems Far From Equilibrium   We consider ionic electrodiffusion in fluids, described by the\nNernst-Planck-Navier-Stokes system. We prove that the system has global smooth\nsolutions for arbitrary smooth data: arbitrary positive Dirichlet boundary\nconditions for the ionic concentrations, arbitrary Dirichlet boundary\nconditions for the potential, arbitrary positive initial concentrations, and\narbitrary regular divergence-free initial velocities. The result holds for any\npositive diffusivities of ions, in bounded domains with smooth boundary in\nthree space dimensions, in the case of two ionic species, coupled to Stokes\nequations for the fluid. The result also holds in the case of Navier-Stokes\ncoupling, if the velocity is regular. The global smoothness of solutions is\nalso true for arbitrarily many ionic species, if all their diffusivities are\nthe same.\n', 'Interior Electroneutrality in Nernst-Planck-Navier-Stokes Systems   We consider the limit of vanishing Debye length for ionic diffusion in\nfluids, described by the Nernst-Planck-Navier-Stokes system. In the\nasymptotically stable cases of blocking (vanishing normal flux) and uniform\nselective (special Dirichlet) boundary conditions for the ionic concentrations,\nwe prove that the ionic charge density $\\rho$ converges in time to zero in the\ninterior of the domain, in the limit of vanishing Debye length ($\\epsilon\\to\n0$). For the unstable regime of Dirichlet boundary conditions for the ionic\nconcentrations, we prove bounds that are uniform in time and $\\epsilon$. We\nalso consider electroneutral boundary conditions, for which we prove that\nelectroneutrality $\\rho\\to 0$ is achieved at any fixed $\\epsilon> 0$,\nexponentially fast in time in $L^p$, for all $1\\le p<\\infty$. The results hold\nfor two oppositely charged ionic species with arbitrary ionic diffusivities, in\nbounded domains with smooth boundaries.\n', 'Global Regularity for Nernst-Planck-Navier-Stokes Systems with Mixed\n  Boundary Conditions   We consider electrodiffusion of ions in fluids, described by the\nNernst-Planck-Navier-Stokes system, in three dimensional bounded domains, with\nmixed blocking (no-flux) and selective (Dirichlet) boundary conditions for the\nionic concentrations and Robin boundary conditions for the electric potential,\nrepresenting the presence of an electrical double layer. We prove global\nexistence of strong solutions for large initial data in the case of two\noppositely charged ionic species. The result hold unconditionally in the case\nwhere fluid flow is described by the Stokes equations. In the case of\nNavier-Stokes coupling, the result holds conditionally on Navier-Stokes\nregularity. We use a simplified argument to also establish global regularity\nfor the case of purely blocking boundary conditions for the ionic\nconcentrations for two oppositely charged ionic species and also for more than\ntwo species if the diffusivities are equal and the magnitudes of the valences\nare also equal.\n']","[('planck navier stokes', 0.5941730737686157), ('navier stokes systems', 0.5634983777999878), ('case navier stokes', 0.5265589952468872), ('navier stokes system', 0.5143504738807678), ('navier stokes', 0.507244884967804), ('nernst planck navier', 0.4787815511226654), ('planck navier', 0.45686450600624084), ('nernst planck equations', 0.4566363990306854), ('dirichlet boundary conditions', 0.4561462998390198), ('poisson nernst planck', 0.4424830973148346)]"
1714,1714,16,1714_fractional diffusion_diffusion fractional_fractional laplacians_fractional laplacian,"['fractional diffusion', 'diffusion fractional', 'fractional laplacians', 'fractional laplacian', 'fractional reaction diffusion', 'spectral fractional laplacian', 'fractional parabolic', 'diffusion operators', 'solutions fractional', 'fractional porous medium']","[""Sharp Boundary Estimates and Harnack Inequalities for Fractional Porous\n  Medium type Equations   This paper provides sharp quantitative and constructive estimates of\nnonnegative solutions $u(t,x)\\geq 0$ to the nonlinear fractional diffusion\nequation, $$\\partial_t u +{\\mathcal L} F(u)=0,$$ also known as filtration\nequation, posed in a smooth bounded domain $x\\in \\Omega \\subset {\\mathbb R}^N$\nwith suitable homogeneous Dirichlet boundary conditions. Both the operator\n${\\mathcal L}$ and the nonlinearity $F$ belong to a general class. The\nassumption on ${\\mathcal L}$ are set in terms of the kernel of ${\\mathcal L}$\nand/or ${\\mathcal L}^{-1}$, and allow for operators with degenerate kernel at\nthe boundary of $\\Omega$. The main examples of ${\\mathcal L}$ are the three\ndifferent Dirichlet Fractional Laplacians on bounded domains, and the\nnonlinearity can be non-homogeneous, for instance, $F(u)=u^2+u^{10}$. Previous\nresult were known in the porous medium case, i.e. $F(u)=|u|^{m-1} u$ with\n$m>1$. Our aim here is to perform the next step: a delicate analysis of\nregularity through quantitative, constructive and sharp a priori estimates. Our\nmain results are global Harnack type inequalities $$H_0(t,u_0)\\, {\\rm dist}(x,\n\\partial \\Omega)^a\\leq F(u(t,x))\\leq H_1(t)\\, {\\rm dist}(x, \\partial\n\\Omega)^b\\qquad\\forall (t,x)\\in (0,\\infty)\\times \\overline{\\Omega},$$ where the\nexpressions of $H_0, H_1$ and $a,b$ are explicit and may change according to\n${\\mathcal L}$ and $F$. The sharpness of such estimates is proven by means of\nexamples and counterexamples: on the one hand, we can match the powers (i.e.\n$a=b$) when the operator has a non degenerate kernel. On the other hand, when\n${\\mathcal L}$ has a kernel that degenerates at the boundary $\\partial\\Omega$,\nthere appear an intriguing anomalous boundary behaviour: the size of the\ninitial data determines the sharp boundary behaviour of the solution, different\nfor ``small'' and ``large'' initial data. We conclude the paper with higher\nregularity results.\n"", 'A class of fractional parabolic reaction-diffusion systems with control\n  of total mass: theory and numerics   In this paper, we prove global-in-time existence of strong solutions to a\nclass of fractional parabolic reaction-diffusion systems posed in a bounded\ndomain of $\\mathbb{R}^N$. The nonlinear reactive terms are assumed to satisfy\nnatural structure conditions which provide non-negativity of the solutions and\nuniform control of the total mass. The diffusion operators are of type\n$u_i\\mapsto d_i(-\\Delta)^s u_i$ where $0<s<1$. Global existence of strong\nsolutions is proved under the assumption that the nonlinearities are at most of\npolynomial growth. Our results extend previous results obtained when the\ndiffusion operators are of type $u_i\\mapsto -d_i\\Delta u_i$. On the other hand,\nwe use numerical simulations to examine the global existence of solutions to\nsystems with exponentially growing right-hand sides, which remains so far an\nopen theoretical question even in the case $s=1$.\n', ""A class of parabolic reaction-diffusion systems governed by spectral\n  fractional Laplacians : Analysis and numerical simulations   In this paper, we prove the global-in-time existence of strong solutions to a\nclass of fractional parabolic reaction-diffusion systems set in a bounded open\nsubset of $\\mathbb{R}^N$. The diffusion operators are of the form $u_i \\mapsto\nd_i (-\\Delta)_{Sp}^{s_i} u_i$, where $0<s_i<1$. The operator\n$(-\\Delta)_{Sp}^{s}$ stands for the commonly called spectral fractional\nLaplacian. Moreover, the nonlinear reactive terms are assumed to fulfill\nnatural structural conditions that ensure the nonnegativity of the solutions\nand provide uniform control of the total mass. We establish the global\nexistence of strong solutions under the assumption that the nonlinearities\nexhibit at most polynomial growth. Our results extend previous results obtained\nwhen the diffusion operators are of the form $u_i\\mapsto d_i (-\\Delta)^s u_i$,\nwhere $(-\\Delta)^s$ denotes the widely known as regional fractional Laplacian.\nFurthermore, we use numerical simulations to investigate the global existence\nof solutions to the fractional version of the so-called ``Brusselator'' system,\na theoretical question that remains open to date.\n""]","[('fractional diffusion', 0.6722076535224915), ('diffusion fractional', 0.6664867997169495), ('fractional laplacians', 0.6598281264305115), ('fractional laplacian', 0.6377010345458984), ('fractional reaction diffusion', 0.6112645864486694), ('spectral fractional laplacian', 0.5954579710960388), ('fractional parabolic', 0.546790599822998), ('diffusion operators', 0.5100266933441162), ('solutions fractional', 0.5075089931488037), ('fractional porous medium', 0.5024040341377258)]"
1715,1715,16,1715_rational maps_two rational maps_rational map_maps rational,"['rational maps', 'two rational maps', 'rational map', 'maps rational', 'degree rational maps', 'maps integer', 'polynomial maps', 'maps periodic', 'rational field', 'map degree']","[""Entire or rational maps with integer multipliers   Let $\\mathcal{O}_{K}$ be the ring of integers of an imaginary quadratic field\n$K$. Recently, Ji and Xie proved that every rational map $f \\colon\n\\widehat{\\mathbb{C}} \\rightarrow \\widehat{\\mathbb{C}}$ of degree $d \\geq 2$\nwhose multipliers all lie in $\\mathcal{O}_{K}$ is a power map, a Chebyshev map\nor a Latt\\`{e}s map. Their proof relies on a result from non-Archimedean\ndynamics obtained by Rivera-Letelier. In the present note, we show that one can\navoid using this result by considering a differential equation instead. Our\nproof of Ji and Xie's result also applies to the case of entire maps. Thus, we\nalso show that every nonaffine entire map $f \\colon \\mathbb{C} \\rightarrow\n\\mathbb{C}$ whose multipliers all lie in $\\mathcal{O}_{K}$ is a power map or a\nChebyshev map.\n"", 'Quadratic rational maps with integer multipliers   In this article, we prove that every quadratic rational map whose multipliers\nall lie in the ring of integers of a given imaginary quadratic field is a power\nmap, a Chebyshev map or a Latt\\`{e}s map. In particular, this provides some\nevidence in support of a conjecture by Milnor concerning rational maps whose\nmultipliers are all integers.\n', 'Rational maps with rational multipliers   In this article, we show that every rational map whose multipliers all lie in\na given number field is a power map, a Chebyshev map or a Latt\\`{e}s map. This\nstrengthens a conjecture by Milnor concerning rational maps with integer\nmultipliers, which was recently proved by Ji and Xie.\n']","[('rational maps', 0.6790912747383118), ('two rational maps', 0.6645479202270508), ('rational map', 0.6569793224334717), ('maps rational', 0.651043176651001), ('degree rational maps', 0.6472686529159546), ('maps integer', 0.5395647287368774), ('polynomial maps', 0.5229616165161133), ('maps periodic', 0.4659247100353241), ('rational field', 0.46429121494293213), ('map degree', 0.43872180581092834)]"
1716,1716,16,1716_riemann sphere_riemann surface_conical singularities_conical metric,"['riemann sphere', 'riemann surface', 'conical singularities', 'conical metric', 'dirichlet laplacians', 'compact riemann surface', 'laplacians', 'laplacian dirichlet', 'formula conformal', 'laplacian']","['Polyakov-Alvarez Formula for Curvilinear Polygonal Domains with Slits   We consider the $\\zeta$-regularized determinant of the Friedrichs extension\nof the Dirichlet Laplace-Beltrami operator on curvilinear polygonal domains\nwith corners of arbitrary positive angles. In particular, this includes slit\ndomains. We obtain a short time asymptotic expansion of the heat trace using a\nclassical patchwork method. This allows us to define the $\\zeta$-regularized\ndeterminant of the Laplacian and prove a comparison formula of Polyakov-Alvarez\ntype for a smooth and conformal change of metric.\n', 'Polyakov formulas for conical singularities in two dimensions   We investigate the zeta-regularized determinant and its variation in the\npresence of conical singularities, boundaries, and corners. For surfaces with\nisolated conical singularities which may also have one or more smooth boundary\ncomponents, we demonstrate both a variational Polyakov formula as well as an\nintegrated Polyakov formula for the conformal variation of the Riemannian\nmetric with conformal factors which are smooth up to all singular points and\nboundary components. We demonstrate the analogous result for curvilinear\npolygonal domains in surfaces. We then specialize to finite circular sectors\nand cones and via two independent methods obtain variational Polyakov formulas\nfor the dependence of the determinant on the opening angle. Notably, this\nrequires the conformal factor to be logarithmically singular at the vertex. We\nfurther obtain explicit formulas for the determinant for finite circular\nsectors and cones.\n', 'Polyakov-Alvarez type comparison formulas for determinants of Laplacians\n  on Riemann surfaces with conical singularities   We present and prove Polyakov-Alvarez type comparison formulas for the\ndeterminants of Friederichs extensions of Laplacians corresponding to\nconformally equivalent metrics on a compact Riemann surface with conical\nsingularities. In particular, we find how the determinants depend on the orders\nof conical singularities. We also illustrate these general results with several\nexamples: based on our Polyakov-Alvarez type formulas we recover known and\nobtain new explicit formulas for determinants of Laplacians on singular\nsurfaces with and without boundary. In one of the examples we show that on the\nmetrics of constant curvature on a sphere with two conical singularities and\nfixed area $4\\pi$ the determinant of Friederichs Laplacian is unbounded from\nabove and attains its local maximum on the metric of standard round sphere. In\nanother example we deduce the famous Aurell-Salomonson formula for the\ndeterminant of Friederichs Laplacian on polyhedra with spherical topology, thus\nproviding the formula with mathematically rigorous proof.\n']","[('riemann sphere', 0.5497437119483948), ('riemann surface', 0.5404156446456909), ('conical singularities', 0.5249261260032654), ('conical metric', 0.5115847587585449), ('dirichlet laplacians', 0.4822896122932434), ('compact riemann surface', 0.46906042098999023), ('laplacians', 0.4653494954109192), ('laplacian dirichlet', 0.4458085000514984), ('formula conformal', 0.44575801491737366), ('laplacian', 0.42656993865966797)]"
1717,1717,16,1717_topics_language models_latent semantic_nonnegative matrix factorization,"['topics', 'language models', 'latent semantic', 'nonnegative matrix factorization', 'topic', 'research topics', 'models topic', 'semi supervised', 'corpus', 'matrix factorization']","['Improving the Inference of Topic Models via Infinite Latent State\n  Replications   In text mining, topic models are a type of probabilistic generative models\nfor inferring latent semantic topics from text corpus. One of the most popular\ninference approaches to topic models is perhaps collapsed Gibbs sampling (CGS),\nwhich typically samples one single topic label for each observed document-word\npair. In this paper, we aim at improving the inference of CGS for topic models.\nWe propose to leverage state augmentation technique by maximizing the number of\ntopic samples to infinity, and then develop a new inference approach, called\ninfinite latent state replication (ILR), to generate robust soft topic\nassignment for each given document-word pair. Experimental results on the\npublicly available datasets show that ILR outperforms CGS for inference of\nexisting established topic models.\n', 'Iterative Improvement of an Additively Regularized Topic Model   Topic modelling is fundamentally a soft clustering problem (of known objects\n-- documents, over unknown clusters -- topics). That is, the task is\nincorrectly posed. In particular, the topic models are unstable and incomplete.\nAll this leads to the fact that the process of finding a good topic model\n(repeated hyperparameter selection, model training, and topic quality\nassessment) can be particularly long and labor-intensive. We aim to simplify\nthe process, to make it more deterministic and provable. To this end, we\npresent a method for iterative training of a topic model. The essence of the\nmethod is that a series of related topic models are trained so that each\nsubsequent model is at least as good as the previous one, i.e., that it retains\nall the good topics found earlier. The connection between the models is\nachieved by additive regularization. The result of this iterative training is\nthe last topic model in the series, which we call the iteratively updated\nadditively regularized topic model (ITAR). Experiments conducted on several\ncollections of natural language texts show that the proposed ITAR model\nperforms better than other popular topic models (LDA, ARTM, BERTopic), its\ntopics are diverse, and its perplexity (ability to ""explain"" the underlying\ndata) is moderate.\n', ""Dynamic Topic Analysis in Academic Journals using Convex Non-negative\n  Matrix Factorization Method   With the rapid advancement of large language models, academic topic\nidentification and topic evolution analysis are crucial for enhancing AI's\nunderstanding capabilities. Dynamic topic analysis provides a powerful approach\nto capturing and understanding the temporal evolution of topics in large-scale\ndatasets. This paper presents a two-stage dynamic topic analysis framework that\nincorporates convex optimization to improve topic consistency, sparsity, and\ninterpretability. In Stage 1, a two-layer non-negative matrix factorization\n(NMF) model is employed to extract annual topics and identify key terms. In\nStage 2, a convex optimization algorithm refines the dynamic topic structure\nusing the convex NMF (cNMF) model, further enhancing topic integration and\nstability. Applying the proposed method to IEEE journal abstracts from 2004 to\n2022 effectively identifies and quantifies emerging research topics, such as\nCOVID-19 and digital twins. By optimizing sparsity differences in the\nclustering feature space between traditional and emerging research topics, the\nframework provides deeper insights into topic evolution and ranking analysis.\nMoreover, the NMF-cNMF model demonstrates superior stability in topic\nconsistency. At sparsity levels of 0.4, 0.6, and 0.9, the proposed approach\nimproves topic ranking stability by 24.51%, 56.60%, and 36.93%, respectively.\nThe source code (to be open after publication) is available at\nhttps://github.com/meetyangyang/CDNMF.\n""]","[('topics', 0.5576786398887634), ('language models', 0.4171188771724701), ('latent semantic', 0.4128616154193878), ('nonnegative matrix factorization', 0.4065272808074951), ('topic', 0.40228936076164246), ('research topics', 0.3957068920135498), ('models topic', 0.3843346834182739), ('semi supervised', 0.34789809584617615), ('corpus', 0.34486907720565796), ('matrix factorization', 0.3434174954891205)]"
1718,1718,16,1718_order fractional laplacian_fractional laplacian_integral fractional laplacian_spectral fractional laplacian,"['order fractional laplacian', 'fractional laplacian', 'integral fractional laplacian', 'spectral fractional laplacian', 'fractional diffusion equations', 'fractional pdes', 'fractional diffusion', 'space fractional diffusion', 'spectral fractional', 'multidimensional fractional']","['Fast implicit difference schemes for time-space fractional diffusion\n  equations with the integral fractional Laplacian   In this paper, we develop two fast implicit difference schemes for solving a\nclass of variable-coefficient time-space fractional diffusion equations with\nintegral fractional Laplacian (IFL). The proposed schemes utilize the graded\n$L1$ formula for the Caputo fractional derivative and a special finite\ndifference discretization for IFL, where the graded mesh can capture the model\nproblem with a weak singularity at initial time. The stability and convergence\nare rigorously proved via the $M$-matrix analysis, which is from the spatial\ndiscretized matrix of IFL. Moreover, the proposed schemes use the fast\nsum-of-exponential approximation and Toeplitz matrix algorithms to reduce the\ncomputational cost for the nonlocal property of time and space fractional\nderivatives, respectively. The fast schemes greatly reduce the computational\nwork of solving the discretized linear systems from $\\mathcal{O}(MN^3 + M^2N)$\nby a direct solver to $\\mathcal{O}(MN(\\log N + N_{exp}))$ per preconditioned\nKrylov subspace iteration and a memory requirement from $O(MN^2)$ to\n$O(NN_{exp})$, where $N$ and $(N_{exp} \\ll)~M$ are the number of spatial and\ntemporal grid nodes. The spectrum of preconditioned matrix is also given for\nensuring the acceleration benefit of circulant preconditioners. Finally,\nnumerical results are presented to show the utility of the proposed methods.\n', 'A simple and fast finite difference method for the integral fractional\n  Laplacian of variable order   For the fractional Laplacian of variable order, an efficient and accurate\nnumerical evaluation in multi-dimension is a challenge for the nature of a\nsingular integral. We propose a simple and easy-to-implement finite difference\nscheme for the multi-dimensional variable-order fractional Laplacian defined by\na hypersingular integral. We prove that the scheme is of second-order\nconvergence and apply the developed finite difference scheme to solve various\nequations with the variable-order fractional Laplacian. We present a fast\nsolver with quasi-linear complexity of the scheme for computing variable-order\nfractional Laplacian and corresponding PDEs. Several numerical examples\ndemonstrate the accuracy and efficiency of our algorithm and verify our theory.\n', 'Variable-order fractional Laplacian and its accurate and efficient\n  computations with meshfree methods   The variable-order fractional Laplacian plays an important role in the study\nof heterogeneous systems. In this paper, we propose the first numerical methods\nfor the variable-order Laplacian $(-\\Delta)^{\\alpha({\\bf x})/2}$ with $0 <\n\\alpha({\\bf x}) \\le 2$, which will also be referred as the variable-order\nfractional Laplacian if $\\alpha({\\bf x})$ is strictly less than 2. We present a\nclass of hypergeometric functions whose variable-order Laplacian can be\nanalytically expressed. Building on these analytical results, we design the\nmeshfree methods based on globally supported radial basis functions (RBFs),\nincluding Gaussian, generalized inverse multiquadric, and Bessel-type RBFs, to\napproximate the variable-order Laplacian $(-\\Delta)^{\\alpha({\\bf x})/2}$. Our\nmeshfree methods integrate the advantages of both pseudo-differential and\nhypersingular integral forms of the variable-order fractional Laplacian, and\nthus avoid numerically approximating the hypersingular integral. Moreover, our\nmethods are simple and flexible of domain geometry, and their computer\nimplementation remains the same for any dimension $d \\ge 1$. Compared to finite\ndifference methods, our methods can achieve a desired accuracy with much fewer\npoints. This fact makes our method much attractive for problems involving\nvariable-order fractional Laplacian where the number of points required is a\ncritical cost. We then apply our method to study solution behaviors of\nvariable-order fractional PDEs arising in different fields, including\ntransition of waves between classical and fractional media, and coexistence of\nanomalous and normal diffusion in both diffusion equation and the Allen-Cahn\nequation. These results would provide insights for further understanding and\napplications of variable-order fractional derivatives.\n']","[('order fractional laplacian', 0.5995664000511169), ('fractional laplacian', 0.5950145125389099), ('integral fractional laplacian', 0.5823440551757812), ('spectral fractional laplacian', 0.5793662071228027), ('fractional diffusion equations', 0.5698803663253784), ('fractional pdes', 0.5471394062042236), ('fractional diffusion', 0.5274574756622314), ('space fractional diffusion', 0.4706336259841919), ('spectral fractional', 0.4694449007511139), ('multidimensional fractional', 0.46726369857788086)]"
1719,1719,16,1719_empirical interpolation deim_discrete empirical interpolation_empirical interpolation_overlapping domain decomposition,"['empirical interpolation deim', 'discrete empirical interpolation', 'empirical interpolation', 'overlapping domain decomposition', 'co simulation', 'reduced basis functions', 'interpolation deim', 'coupled problems', 'finite volume schemes', 'reduced order rom']","['A Novel Partitioned Approach for Reduced Order Model -- Finite Element\n  Model (ROM-FEM) and ROM-ROM Coupling   Partitioned methods allow one to build a simulation capability for coupled\nproblems by reusing existing single-component codes. In so doing, partitioned\nmethods can shorten code development and validation times for multiphysics and\nmultiscale applications. In this work, we consider a scenario in which one or\nmore of the ""codes"" being coupled are projection-based reduced order models\n(ROMs), introduced to lower the computational cost associated with a particular\ncomponent. We simulate this scenario by considering a model interface problem\nthat is discretized independently on two non-overlapping subdomains. We then\nformulate a partitioned scheme for this problem that allows the coupling\nbetween a ROM ""code"" for one of the subdomains with a finite element model\n(FEM) or ROM ""code"" for the other subdomain. The ROM ""codes"" are constructed by\nperforming proper orthogonal decomposition (POD) on a snapshot ensemble to\nobtain a low-dimensional reduced order basis, followed by a Galerkin projection\nonto this basis. The ROM and/or FEM ""codes"" on each subdomain are then coupled\nusing a Lagrange multiplier representing the interface flux. To partition the\nresulting monolithic problem, we first eliminate the flux through a dual Schur\ncomplement. Application of an explicit time integration scheme to the\ntransformed monolithic problem decouples the subdomain equations, allowing\ntheir independent solution for the next time step. We show numerical results\nthat demonstrate the proposed method\'s efficacy in achieving both ROM-FEM and\nROM-ROM coupling.\n', 'A DEIM driven reduced basis method for the diffuse Stokes/Darcy model\n  coupled at parametric phase-field interfaces   In this article, we develop a reduced basis method for efficiently solving\nthe coupled Stokes/Darcy equations with parametric internal geometry. To\naccommodate possible changes in topology, we define the Stokes and Darcy\ndomains implicitly via a phase-field indicator function. In our reduced order\nmodel, we approximate the parameter-dependent phase-field function with a\ndiscrete empirical interpolation method (DEIM) that enables affine\ndecomposition of the associated linear and bilinear forms. In addition, we\nintroduce a modification of DEIM that leads to non-negativity preserving\napproximations, thus guaranteeing positive-semidefiniteness of the system\nmatrix. We also present a strategy for determining the required number of DEIM\nmodes for a given number of reduced basis functions. We couple reduced basis\nfunctions on neighboring patches to enable the efficient simulation of\nlarge-scale problems that consist of repetitive subdomains. We apply our\nreduced basis framework to efficiently solve the inverse problem of\ncharacterizing the subsurface damage state of a complete in-situ leach mining\nsite.\n', 'A reduced order model for domain decompositions with non-conforming\n  interfaces   In this paper, we propose a reduced-order modeling strategy for two-way\nDirichlet-Neumann parametric coupled problems solved with domain-decomposition\n(DD) sub-structuring methods. We split the original coupled differential\nproblem into two sub-problems with Dirichlet and Neumann interface conditions,\nrespectively. After discretization by, e.g., the finite element method, the\nfull-order model (FOM) is solved by Dirichlet-Neumann iterations between the\ntwo sub-problems until interface convergence is reached. We then apply the\nreduced basis (RB) method to obtain a low-dimensional representation of the\nsolution of each sub-problem. Furthermore, we apply the discrete empirical\ninterpolation method (DEIM) at the interface level to achieve a fully\nreduced-order representation of the DD techniques implemented. To deal with\nnon-conforming FE interface discretizations, we employ the INTERNODES method\ncombined with the interface DEIM reduction. The reduced-order model (ROM) is\nthen solved by sub-iterating between the two reduced-order sub-problems until\nthe convergence of the approximated high-fidelity interface solutions. The ROM\nscheme is numerically verified on both steady and unsteady coupled problems, in\nthe case of non-conforming FE interfaces.\n']","[('empirical interpolation deim', 0.42143014073371887), ('discrete empirical interpolation', 0.40666767954826355), ('empirical interpolation', 0.3885851800441742), ('overlapping domain decomposition', 0.3862170875072479), ('co simulation', 0.38419148325920105), ('reduced basis functions', 0.3713878095149994), ('interpolation deim', 0.3618898391723633), ('coupled problems', 0.3427186906337738), ('finite volume schemes', 0.33784252405166626), ('reduced order rom', 0.3348463773727417)]"
1720,1720,16,1720_elliptic operators_elliptic operator_ellipticity_elliptic systems divergence,"['elliptic operators', 'elliptic operator', 'ellipticity', 'elliptic systems divergence', 'carleson measure condition', 'dirichlet elliptic', 'vanishing carleson measure', 'uniformly elliptic', 'elliptic systems', 'carleson condition']","['Absolute continuity of degenerate elliptic measure   Let $\\Omega \\subset \\mathbb{R}^{n+1}$ be an open set whose boundary may be\ncomposed of pieces of different dimensions. Assume that $\\Omega$ satisfies the\nquantitative openness and connectedness, and there exist doubling measures $m$\non $\\Omega$ and $\\mu$ on $\\partial \\Omega$ with appropriate size conditions.\nLet $Lu=-\\mathrm{div}(A\\nabla u)$ be a real (not necessarily symmetric)\ndegenerate elliptic operator in $\\Omega$. Write $\\omega_L$ for the associated\ndegenerate elliptic measure. We establish the equivalence between the following\nproperties: (i) $\\omega_L \\in A_{\\infty}(\\mu)$, (ii) the Dirichlet problem for\n$L$ is solvable in $L^p(\\mu)$ for some $p \\in (1, \\infty)$, (iii) every bounded\nnull solution of $L$ satisfies Carleson measure estimates with respect to\n$\\mu$, (iv) the conical square function is controlled by the non-tangential\nmaximal function in $L^q(\\mu)$ for all $q \\in (0, \\infty)$ for any null\nsolution of $L$, and (v) the Dirichlet problem for $L$ is solvable in\n$\\mathrm{BMO}(\\mu)$. On the other hand, we obtain a qualitative analogy of the\nprevious equivalence. Indeed, we characterize the absolute continuity of\n$\\omega_L$ with respect to $\\mu$ in terms of local $L^2(\\mu)$ estimates of the\ntruncated conical square function for any bounded null solution of $L$. This is\nalso equivalent to the finiteness $\\mu$-almost everywhere of the truncated\nconical square function for any bounded null solution of $L$.\n', 'Perturbation of elliptic operators in 1-sided NTA domains satisfying the\n  capacity density condition   Let $\\Omega\\subset\\mathbb{R}^{n+1}$, $n\\ge 2$, be a 1-sided non-tangentially\naccessible domain (aka uniform domain), i.e., a set which satisfies the\ninterior Corkscrew and Harnack chain conditions, respectively\nscale-invariant/quantitative versions of openness and path-connectedness.\nAssume that $\\Omega$ satisfies the so-called capacity density condition. Let\n$L_0u=-\\mathrm{div}(A_0\\nabla u)$, $Lu=-\\mathrm{div}(A\\nabla u)$ be two real\n(non-necessarily symmetric) uniformly elliptic operators, and write\n$\\omega_{L_0}$, $\\omega_L$ for the associated elliptic measures. The goal of\nthis program is to find sufficient conditions guaranteeing that $\\omega_L$\nsatisfies an $A_\\infty$-condition or a $RH_q$-condition with respect to\n$\\omega_{L_0}$. We show that if the discrepancy of the two matrices satisfies a\nnatural Carleson measure condition with respect to $\\omega_{L_0}$, then\n$\\omega_L\\in A_\\infty(\\omega_{L_0})$. Moreover, $\\omega_L\\in\nRH_q(\\omega_{L_0})$ for any given $1<q<\\infty$ if the Carleson measure\ncondition is assumed to hold with a sufficiently small constant. This extends\nprevious work of Fefferman-Kenig-Pipher and Milakis-Pipher-Toro who considered\nLipschitz and chord-arc domains. Here we go beyond as the capacity density\ncondition is much weaker than the existence of exterior Corkscrew balls. The\n""large constant"" case, where the discrepancy satisfies a Carleson measure\ncondition, is new even for nice domains such as the unit ball, the upper\nhalf-space, or Lipschitz domains, and is obtained using the method of\nextrapolation of Carleson measure. Our domains do not have a nice surface\nmeasure: all the analysis is done with the underlying measure $\\omega_{L_0}$.\nWhen particularized to Lipschitz, chord-arc, or 1-sided chord-arc domains, we\nrecover previous results and extend some of them. Our arguments rely on the\nsquare function and non-tangential estimates proved in arXiv:2103.10046.\n', 'On the $A_\\infty$ condition for elliptic operators in 1-sided NTA\n  domains satisfying the capacity density condition   Let $\\Omega \\subset \\mathbb{R}^{n+1}$, $n\\ge 2$, be a 1-sided\nnon-tangentially accessible domain (i.e., quantitatively open and\npath-connected) satisfiying the capacity density condition. Let $L_0\nu=-\\mathrm{div}(A_0 \\nabla u)$, $Lu=-\\mathrm{div}(A\\nabla u)$ be two real\nuniformly elliptic operators in $\\Omega$, with $\\omega_{L_0}, \\omega_L$ the\nassociated elliptic measures. We establish the equivalence between the\nfollowing properties: (i) $\\omega_L \\in A_{\\infty}(\\omega_{L_0})$, (ii) $L$ is\n$L^p(\\omega_{L_0})$-solvable for some $p\\in (1,\\infty)$, (iii) bounded null\nsolutions of $L$ satisfy Carleson measure estimates with respect to\n$\\omega_{L_0}$, (iv) the conical square function is controlled by the\nnon-tangential maximal function in $L^q(\\omega_{L_0})$ for some (or for all)\n$q\\in (0,\\infty)$ for any null solution of $L$, and (v) $L$ is\n$\\mathrm{BMO}(\\omega_{L_0})$-solvable. Moreover, in each of the properties\n(ii)-(v) it is enough to consider the class of solutions $u(X)=\\omega_L^X(S)$\nwith arbitrary Borel sets $S\\subset\\partial\\Omega$.\n  Also, we characterize the absolute continuity of $\\omega_{L_0}$ with respect\nto $\\omega_L$ in terms of some qualitative local $L^2(\\omega_{L_0})$ estimates\nfor the truncated conical square function for any bounded null solution of $L$.\nThis is also equivalent to the finiteness $\\omega_{L_0}$-a.e. of the truncated\nconical square function for any bounded null solution of $L$. As applications,\nwe show that $\\omega_{L_0}\\ll\\omega_L$ if the disagreement of the coefficients\nsatisfies some qualitative quadratic estimate in truncated cones for\n$\\omega_{L_0}$-a.e. vertex. Finally, when $L_0$ is either the transpose of $L$\nor its symmetric part, we obtain the corresponding absolute continuity when the\nantisymmetric part of the coefficients has some controlled oscillation in\ntruncated cones for $\\omega_{L_0}$-a.e. vertex.\n']","[('elliptic operators', 0.5354153513908386), ('elliptic operator', 0.5185908675193787), ('ellipticity', 0.5109511017799377), ('elliptic systems divergence', 0.5025794506072998), ('carleson measure condition', 0.49456366896629333), ('dirichlet elliptic', 0.48546332120895386), ('vanishing carleson measure', 0.47868040204048157), ('uniformly elliptic', 0.43815967440605164), ('elliptic systems', 0.4115932583808899), ('carleson condition', 0.4104135036468506)]"
1721,1721,16,1721_chromatic polynomials_chromatic polynomial_graphs chromatic_colorings graph,"['chromatic polynomials', 'chromatic polynomial', 'graphs chromatic', 'colorings graph', 'chromatic number', 'list chromatic number', 'list chromatic', 'list colorings', 'analogue chromatic', 'color graph']","[""Shameful Inequalities for List and DP Coloring of Graphs   The chromatic polynomial of a graph is an important notion in algebraic\ncombinatorics that was introduced by Birkhoff in 1912; denoted $P(G,k)$, it\nequals the number of proper $k$-colorings of graph $G$. Enumerative analogues\nof the chromatic polynomial of a graph have been introduced for two\nwell-studied generalizations of ordinary coloring, namely, list colorings:\n$P_{\\ell}$, the list color function (1990); and DP colorings: $P_{DP}$, the DP\ncolor function (2019), and $P^*_{DP}$, the dual DP color function (2021). For\nany graph $G$ and $k \\in \\mathbb{N}$, $P_{DP}(G, k) \\leq P_\\ell(G,k) \\leq\nP(G,k) \\leq P_{DP}^*(G,k)$. In 2000, Dong settled a conjecture of Bartels and\nWelsh from 1995 known as the Shameful Conjecture by proving that for any\n$n$-vertex graph $G$, $P(G,k+1)/(k+1)^n \\geq P(G,k)/k^n$ for all $k \\in\n\\mathbb{N}$ satisfying $k \\geq n-1$. In contrast, for infinitely many positive\nintegers $n$, Seymour (1997) gave an example of an $n$-vertex graph for which\nthe above inequality does not hold for some $k = \\Theta(n/ \\log n)$. In this\npaper, we consider analogues of Dong's result for list and DP color functions.\nSpecifically, in contrast to the chromatic polynomial, we prove that for any\n$n$-vertex graph $G$, $P_{\\ell}(G,k+1)/(k+1)^n \\geq P_{\\ell}(G,k)/k^n$ and\n$P_{DP}(G,k+1)/(k+1)^n \\geq P_{DP}(G,k)/k^n$ for all $k \\in \\mathbb{N}$. For\nthe dual DP analogue of these inequalities, we show that there is a graph $G$\nand $k \\in \\mathbb{N}$ such that $P_{DP}^*(G,k+1)/(k+1)^n < P_{DP}^*(G,k)/k^n$,\nand we prove $P_{DP}^*(G,k+1)/(k+1)^n \\geq P_{DP}^*(G,k)/k^n$ for all $k \\in\n\\mathbb{N}$ satisfying $k \\geq n-1$ when $G$ is an $n$-vertex complete\nbipartite graph.\n"", ""Non-chromatic-adherence of the DP Color Function via Generalized Theta\n  Graphs   DP-coloring (also called correspondence coloring) is a generalization of list\ncoloring that has been widely studied in recent years after its introduction by\nDvo\\v{r}\\'{a}k and Postle in 2015. The chromatic polynomial of a graph is an\nextensively studied notion in combinatorics since its introduction by Birkhoff\nin 1912; denoted $P(G,m)$, it equals the number of proper $m$-colorings of\ngraph $G$. Counting function analogues of the chromatic polynomial have been\nintroduced and studied for list colorings: $P_{\\ell}$, the list color function\n(1990); DP colorings: $P_{DP}$, the DP color function (2019), and $P^*_{DP}$,\nthe dual DP color function (2021). For any graph $G$ and $m \\in \\mathbb{N}$,\n$P_{DP}(G, m) \\leq P_\\ell(G,m) \\leq P(G,m) \\leq P_{DP}^*(G,m)$. A function $f$\nis chromatic-adherent if for every graph $G$, $f(G,a) = P(G,a)$ for some $a\n\\geq \\chi(G)$ implies that $f(G,m) = P(G,m)$ for all $m \\geq a$. It is not\nknown if the list color function and the DP color function are\nchromatic-adherent. We show that the DP color function is not\nchromatic-adherent by studying the DP color function of Generalized Theta\ngraphs. The tools we develop along with the Rearrangement Inequality give a new\nmethod for determining the DP color function of all Theta graphs and the dual\nDP color function of all Generalized Theta graphs.\n"", ""On Polynomial Representations of Dual DP Color Functions   DP-coloring (also called correspondence coloring) is a generalization of list\ncoloring that was introduced by Dvo\\v{r}\\'{a}k and Postle in 2015. The\nchromatic polynomial of a graph is an important notion in algebraic\ncombinatorics that was introduced by Birkhoff in 1912; denoted $P(G,m)$, it\nequals the number of proper $m$-colorings of graph $G$. Counting function\nanalogues of chromatic polynomials have been introduced for list colorings:\n$P_{\\ell}$, list color functions (1990); DP colorings: $P_{DP}$, DP color\nfunctions (2019), and $P^*_{DP}$, dual DP color functions (2021). For any graph\n$G$ and $m \\in \\mathbb{N}$, $P_{DP}(G, m) \\leq P_\\ell(G,m) \\leq P(G,m) \\leq\nP_{DP}^*(G,m)$. In 2022 (improving on older results) Dong and Zhang showed that\nfor any graph $G$, $P_{\\ell}(G,m)=P(G,m)$ whenever $m \\geq |E(G)|-1$.\nConsequently, the list color function of a graph is a polynomial for\nsufficiently large $m$. One of the most important and longstanding open\nquestions on DP color functions asks: for every graph $G$ is there an $N \\in\n\\mathbb{N}$ and a polynomial $p(m)$ such that $P_{DP}(G,m) = p(m)$ whenever $m\n\\geq N$? We show that the answer to the analogue of this question for dual DP\ncolor functions is no. Our proof reveals a connection between a dual DP color\nfunction and the balanced chromatic polynomial of a signed graph introduced by\nZaslavsky in 1982.\n""]","[('chromatic polynomials', 0.665291428565979), ('chromatic polynomial', 0.6342723965644836), ('graphs chromatic', 0.6024770736694336), ('colorings graph', 0.5951533913612366), ('chromatic number', 0.5719569325447083), ('list chromatic number', 0.5620679259300232), ('list chromatic', 0.5605965256690979), ('list colorings', 0.5353195071220398), ('analogue chromatic', 0.5351890325546265), ('color graph', 0.5279829502105713)]"
1722,1722,16,1722_branching process_balls bins_hitting probabilities_random environment,"['branching process', 'balls bins', 'hitting probabilities', 'random environment', 'branching', 'occurs probability', 'occupancy', 'scheme random', 'bins', 'processes generalized']","[""On intermediate levels of nested occupancy scheme in random environment\n  generated by stick-breaking I   Consider a weighted branching process generated by the lengths of intervals\nobtained by stick-breaking of unit length (a.k.a. the residual allocation\nmodel) and associate with each weight a `box'. Given the weights `balls' are\nthrown independently into the boxes of the first generation with probability of\nhitting a box being equal to its weight. Each ball located in a box of the\n$j$th generation, independently of the others, hits a daughter box in the\n$(j+1)$th generation with probability being equal the ratio of the daughter\nweight and the mother weight. This is what we call nested occupancy scheme in\nrandom environment. Restricting attention to a particular generation one\nobtains the classical Karlin occupancy scheme in random environment.\n  Assuming that the stick-breaking factor has a uniform distribution on $[0,1]$\nand that the number of balls is $n$ we investigate occupancy of intermediate\ngenerations, that is, those with indices $\\lfloor j_n u\\rfloor$ for $u>0$,\nwhere $j_n$ diverges to infinity at a sublogarithmic rate as $n$ becomes large.\nDenote by $K_n(j)$ the number of occupied (ever hit) boxes in the $j$th\ngeneration. It is shown that the finite-dimensional distributions of the\nprocess $(K_n(\\lfloor j_n u\\rfloor))_{u>0}$, properly normalized and centered,\nconverge weakly to those of an integral functional of a Brownian motion. The\ncase of a more general stick-breaking is also analyzed.\n"", 'Late levels of nested occupancy scheme in random environment   Consider a weighted branching process generated by a point process on\n$[0,1]$, whose atoms sum up to one. Then the weights of all individuals in any\ngiven generation sum up to one, as well. We define a nested occupancy scheme in\nrandom environment as the sequence of balls-in-boxes schemes (with random\nprobabilities) in which boxes of the $j$th level, $j=1,2,\\ldots$ are identified\nwith the $j$th generation individuals and the hitting probabilities of boxes\nare identified with the corresponding weights. The collection of balls is the\nsame for all generations, and each ball starts at the root and moves along the\ntree of the weighted branching process according to the following rule:\ntransition from a mother box to a daughter box occurs with probability given by\nthe ratio of the daughter and mother weights.\n  Assuming that there are $n$ balls, we give a full classification of regimes\nof the a.s.\\ convergence for the number of occupied (ever hit) boxes in the\n$j$th level, properly normalized, as $n$ and $j=j_n$ grow to $\\infty$. Here,\n$(j_n)_{n\\in\\mathbb N}$ is a sequence of positive numbers growing\nproportionally to $\\log n$. We call such levels late, for the nested occupancy\nscheme gets extinct in the levels which grow super-logarithmically in $n$ in\nthe sense that each occupied box contains one ball. Also, in some regimes we\nprove the strong laws of large numbers (a) for the number of the $j$th level\nboxes which contain at least $k$ balls, $k\\geq 2$ and (b) under the assumption\nthat the mean number of the first level boxes is finite, for the number of\nempty boxes in the $j$th level.\n', 'On intermediate levels of nested occupancy scheme in random environment\n  generated by stick-breaking II   A nested occupancy scheme in random environment is a generalization of the\nclassical Karlin infinite balls-in-boxes occupancy scheme in random environment\n(with random probabilities). Unlike the Karlin scheme in which the collection\nof boxes is unique, there is a nested hierarchy of boxes, and the hitting\nprobabilities of boxes are defined in terms of iterated fragmentation of a unit\nmass. In the present paper we assume that the random fragmentation law is given\nby stick-breaking in which case the infinite occupancy scheme defined by the\nfirst level boxes is known as the Bernoulli sieve. Assuming that $n$ balls have\nbeen thrown, denote by $K_n(j)$ the number of occupied boxes in the $j$th level\nand call the level $j$ intermediate if $j=j_n\\to\\infty$ and $j_n=o(\\log n)$ as\n$n\\to\\infty$. We prove a multidimensional central limit theorem for the vector\n$(K_n(\\lfloor j_n u_1\\rfloor),\\ldots, K_n(\\lfloor j_n u_\\ell\\rfloor)$, properly\nnormalized and centered, as $n\\to\\infty$, where $j_n\\to\\infty$ and $j_n=o((\\log\nn)^{1/2})$. The present paper continues the line of investigation initiated in\nBuraczewski, Dovgay and Iksanov [Electron. J. Probab. 25: paper no. 123, 2020]\nin which the occupancy of intermediate levels $j_n\\to\\infty$, $j_n=o((\\log\nn)^{1/3})$ was analyzed.\n']","[('branching process', 0.4350391626358032), ('balls bins', 0.38984745740890503), ('hitting probabilities', 0.3815419673919678), ('random environment', 0.37909996509552), ('branching', 0.36339071393013), ('occurs probability', 0.32412394881248474), ('occupancy', 0.32254087924957275), ('scheme random', 0.31943991780281067), ('bins', 0.302049845457077), ('processes generalized', 0.29367560148239136)]"
1723,1723,16,1723_shimura varieties_shimura variety_unitary shimura varieties_shimura curves,"['shimura varieties', 'shimura variety', 'unitary shimura varieties', 'shimura curves', 'shimura curve', 'shimura type', 'abelian varieties', 'shimura', 'cm abelian varieties', 'unitary shimura']","[""Generalised Andr\\'e-Pink-Zannier Conjecture for Shimura varieties of\n  abelian type   In this paper, we prove the generalised Andr\\'e-Pink-Zannier conjecture (an\nimportant case of the Zilber-Pink conjecture) for all Shimura varieties of\nabelian type. Questions of this type were first asked by Y. Andr\\'e in 1989. We\nactually prove a general statement for all Shimura varieties, subject to\ncertain assumptions that are satisfied for Shimura varieties of abelian type\nand are expected to hold in general. We also prove another result, a p-adic\nKempf-Ness theorem, on the relation between good reduction of homogeneous\nspaces over p-adic integers with Mumford stability property in p-adic geometric\ninvariant theory.\n"", 'Lower bounds for Galois orbits of special points on Shimura varieties: a\n  point-counting approach   Let $S$ be a Shimura variety and let $h$ be a Weil height function on $S$. We\nconjecture that the heights of special points in $S$ are discriminant\nnegligible. Assuming this conjecture to be true, we prove that the sizes of the\nGalois orbits of special points grow as a fixed power of their discriminant (an\ninvariant we will define in the text). In the case of Shimura varieties of\nabelian type, the height bound holds by the recently proved averaged Colmez\nformula, and our theorem gives a new proof of Tsimerman\'s Galois lower bound in\nthis case. The main novelty is that our approach avoids the use of\nMasser-W\\""ustholz isogeny estimates, replacing them by a point-counting\nargument, and establishes lower bounds for Galois orbits conditional on height\nbounds for \\emph{arbitrary} Shimura varieties. In particular, following the\nPila-Zannier strategy (and Gao\'s work in the mixed case) this implies that the\nAndre-Oort conjecture for an arbitrary (mixed) Shimura variety follows from the\ncorresponding conjecture on heights of special points.\n', ""Heights on 'Hybrid orbits' in Shimura varieties   We prove the 'hybrid conjecture' which is a common generalisation of the\nAndre\\'e-Oort conjecture and the Andr\\'e-Pink-Zannier conjecture, in the case\nof Shimura varieties of abelian type.\n""]","[('shimura varieties', 0.7426624298095703), ('shimura variety', 0.7007952332496643), ('unitary shimura varieties', 0.6689208149909973), ('shimura curves', 0.6503204703330994), ('shimura curve', 0.5906414985656738), ('shimura type', 0.5838902592658997), ('abelian varieties', 0.5115022659301758), ('shimura', 0.5111908912658691), ('cm abelian varieties', 0.4868633449077606), ('unitary shimura', 0.4846012592315674)]"
1724,1724,16,1724_self similar measures_similar measures_conformal measures_spectral measures,"['self similar measures', 'similar measures', 'conformal measures', 'spectral measures', 'dimension measures', 'spectral measure', 'conformal measure', 'decay fourier', 'fourier decay', 'measures arbitrary']","['Van der Corput and metric theorems for geometric progressions for\n  self-similar measures   We prove a van der Corput lemma for non-atomic self-similar measures $\\mu$.\nAs an application, we show that the correlations of all finite orders of $( x^n\n\\mod 1 )_{n\\geq 1}$ converge to the Poissonian model for $\\mu$-a.e. $x$,\nassuming $x>1$. We also complete a recent result of Algom, Rodriguez Hertz, and\nWang (obtained simultaneously by Baker and Banaji), showing that any\nself-conformal measure with respect to a non-affine real analytic IFS has\npolynomial Fourier decay.\n', 'Fourier decay of self-similar measures and self-similar sets of\n  uniqueness   In this paper, we investigate the Fourier transform of self-similar measures\non R. We provide quantitative decay rates of Fourier transform of some\nself-similar measures. Our method is based on random walks on lattices and\nDiophantine approximation in number fields. We also completely identify all\nself-similar sets which are sets of uniqueness. This generalizes a classical\nresult of Salem and Zygmund.\n', 'Self-similar measures: asymptotic bounds for the dimension and Fourier\n  decay of smooth images   R. Kaufman and M. Tsujii proved that the Fourier transform of self-similar\nmeasures has a power decay outside of a sparse set of frequencies. We present a\nversion of this result for homogeneous self-similar measures, with quantitative\nestimates, and derive several applications: (1) non-linear smooth images of\nhomogeneous self-similar measures have a power Fourier decay, (2) convolving\nwith a homogeneous self-similar measure increases correlation dimension by a\nquantitative amount, (3) the dimension and Frostman exponent of (biased)\nBernoulli convolutions tend to $1$ as the contraction ratio tends to $1$, at an\nexplicit quantitative rate.\n']","[('self similar measures', 0.6509590744972229), ('similar measures', 0.5593674778938293), ('conformal measures', 0.5476754307746887), ('spectral measures', 0.5274246335029602), ('dimension measures', 0.5018688440322876), ('spectral measure', 0.4780842661857605), ('conformal measure', 0.47721630334854126), ('decay fourier', 0.47347426414489746), ('fourier decay', 0.46719858050346375), ('measures arbitrary', 0.46329405903816223)]"
1725,1725,16,1725_moment matching_higher order moment_least squares sense_least squares,"['moment matching', 'higher order moment', 'least squares sense', 'least squares', 'reduced order models', 'nonlinear reduction', 'matching linear', 'bilinear systems', 'order reduction nonlinear', 'time invariant systems']","['On Moment Matching for Stochastic Systems   In this paper we study the problem of model reduction by moment matching for\nstochastic systems. We characterize the mathematical object which generalizes\nthe notion of moment to stochastic differential equations and we find a class\nof models which achieve moment matching. However, differently from the\ndeterministic case, these reduced-order models cannot be considered ""simpler""\nbecause of the high computational cost paid to determine the moment. To\novercome this difficulty, we relax the moment matching problem in two different\nways and we present two classes of reduced-order models which, approximately\nmatching the stochastic moment, are computationally tractable.\n', 'Model reduction by least squares moment matching for linear and\n  nonlinear systems   The paper addresses the model reduction problem for linear and nonlinear\nsystems using the notion of least squares moment matching. For linear systems,\nthe main idea is to approximate a transfer function by ensuring that the\ninterpolation conditions imposed by moment matching are satisfied in a least\nsquares sense. The paper revisits this idea using tools from output regulation\ntheory to provide a new time-domain characterization of least squares moment\nmatching. It is shown that least squares moment matching can be characterized\nin terms of an optimization problem involving an invariance equation and in\nterms of the steady-state behavior of an error system. This characterization,\nin turn, is then used to define a nonlinear enhancement of the notion of least\nsquares moment matching and to develop a model reduction theory for nonlinear\nsystems based on the notion of least squares moment matching. Parameterized\nfamilies of models achieving least squares moment matching are determined both\nfor linear and nonlinear systems. The new parameterizations are shown to admit\nnatural geometric and system-theoretic interpretations. The theory is\nillustrated by worked-out numerical examples.\n', 'On model reduction by least squares moment matching   The paper addresses the model reduction problem by least squares moment\nmatching for continuous-time, linear, time-invariant systems. The basic idea\nbehind least squares moment matching is to approximate a transfer function by\nensuring that the interpolation conditions imposed by moment matching are\nsatisfied in a least squares sense. This idea is revisited using invariance\nequations and steady-state responses to provide a new time-domain\ncharacterization of least squares moment matching. The characterization, in\nturn, is then used to obtain a parameterized family of models achieving least\nsquares moment matching. The theory is illustrated by a worked-out numerical\nexample.\n']","[('moment matching', 0.6087645292282104), ('higher order moment', 0.41990044713020325), ('least squares sense', 0.41914889216423035), ('least squares', 0.41728323698043823), ('reduced order models', 0.4093240201473236), ('nonlinear reduction', 0.38410717248916626), ('matching linear', 0.38179853558540344), ('bilinear systems', 0.3742193281650543), ('order reduction nonlinear', 0.3694092035293579), ('time invariant systems', 0.3692052364349365)]"
1726,1726,16,1726_frobenius algebras_algebras groups_non associative algebras_associative algebras,"['frobenius algebras', 'algebras groups', 'non associative algebras', 'associative algebras', 'algebras arising', 'algebraic groups', 'jordan algebras', 'algebras constructed', 'algebras type', 'algebras rings']","['Albert Algebras over Rings and Related Torsors   We study exceptional Jordan algebras and related exceptional group schemes\nover commutative rings from a geometric point of view, using appropriate\ntorsors to parametrize and explain classical and new constructions, and proving\nthat over rings, they give rise to non-isomorphic structures.\n  We begin by showing that isotopes of Albert algebras are obtained as twists\nby a certain $\\mathrm F_4$-torsor with total space a group of type $\\mathrm\nE_6$, and using this, that Albert algebras over rings in general admit\nnon-isomorphic isotopes, even in the split case as opposed to the situation\nover fields. We then consider certain $\\mathrm D_4$-torsors constructed from\nreduced Albert algebras, and show how these give rise to a class of generalised\nreduced Albert algebras constructed from compositions of quadratic forms.\nShowing that this torsor is non-trivial, we conclude that the Albert algebra\ndoes not uniquely determine the underlying composition, even in the split case.\nIn a similar vein, we show that a given reduced Albert algebra can admit two\ncoordinate algebras which are non-isomorphic and have non-isometric quadratic\nforms, contrary, in a strong sense, to the case over fields, established by\nAlbert and Jacobson.\n', 'Non-associative Frobenius algebras of type $G_2$ and $F_4$   Very recently, Maurice Chayet and Skip Garibaldi have introduced a class of\ncommutative non-associative algebras, for each simple linear algebraic group\nover an arbitrary field (with some minor restriction on the characteristic).\n  We give an explicit description of these algebras for groups of type $G_2$\nand $F_4$ in terms of the octonion algebras and the Albert algebras,\nrespectively. As a byproduct, we determine all possible invariant commutative\nalgebra products on the representation with highest weight $2\\omega_1$ for\n$G_2$ and on the representation with highest weight $2\\omega_4$ for $F_4$.\n  It had already been observed by Chayet and Garibaldi that the automorphism\ngroup for the algebras for type $F_4$ is equal to the group of type $F_4$\nitself. Using our new description, we are able to show that the same result\nholds for type $G_2$.\n', 'Non-associative Frobenius algebras of type $^1E_6$ with trivial Tits\n  algebras   Very recently, Maurice Chayet and Skip Garibaldi have introduced a class of\ncommutative non-associative algebras, for each simple linear algebraic group\nover an arbitrary field (with some minor restriction on the characteristic).\n  In a previous paper, we gave an explicit description of these algebras for\ngroups of type $G_2$ and $F_4$ in terms of the octonion algebras and the Albert\nalgebras, respectively. In this paper, we attempt a similar approach for type\n$E_6$.\n']","[('frobenius algebras', 0.6494110822677612), ('algebras groups', 0.6377750635147095), ('non associative algebras', 0.6312332153320312), ('associative algebras', 0.6298909783363342), ('algebras arising', 0.5563439130783081), ('algebraic groups', 0.5484431385993958), ('jordan algebras', 0.5444918274879456), ('algebras constructed', 0.5313816070556641), ('algebras type', 0.5088285207748413), ('algebras rings', 0.5066763162612915)]"
1727,1727,16,1727_frequency representations_time frequency representations_time frequency representation_frequency representation,"['frequency representations', 'time frequency representations', 'time frequency representation', 'frequency representation', 'time fourier transform', 'wigner transforms', 'short time fourier', 'time fourier', 'fourier transform stft', 'modulation spaces']","['Symplectic Analysis of Time-Frequency Spaces   We present a different symplectic point of view in the definition of weighted\nmodulation spaces $M^{p,q}_m(\\mathbb{R}^d)$ and weighted Wiener amalgam spaces\n$W(\\mathcal{F} L^p_{m_1},L^q_{m_2})(\\mathbb{R}^d)$. All of the classical\ntime-frequency representations, such as the short-time Fourier transform\n(STFT), the $\\tau$-Wigner distributions and the ambiguity function, can be\nwritten as metaplectic Wigner distributions $\\mu(\\mathcal{A})(f\\otimes\n\\bar{g})$, where $\\mu(\\mathcal{A})$ is the metaplectic operator and\n$\\mathcal{A}$ is the associated symplectic matrix. Namely, time-frequency\nrepresentations can be represented as images of metaplectic operators, which\nbecome the real protagonists of time-frequency analysis. In [E. Cordero and L.\nRodino (2022) ""Characterization of Modulation Spaces by symplectic\nrepresentations and applications to Schr\\""odinger equations"",\narXiv:2204.14124], the authors suggest that any metaplectic Wigner distribution\nthat satisfies the so-called ""shift-invertibility"" condition can replace the\nSTFT in the definition of modulation spaces. In this work, we prove that\nshift-invertibility alone is not sufficient, but it has to be complemented by\nan upper-triangularity condition for this characterization to hold, whereas a\nlower-triangularity property comes in to play for Wiener amalgam spaces. The\nshift-invertibility property is necessary: Ryhaczek and and conjugate Ryhaczek\ndistributions are not shift-invertible and they fail the characterization of\nthe above spaces. We also exhibit examples of shift-invertible distributions\nwithout upper-tryangularity condition which do not define modulation spaces.\nFinally, we provide new families of time-frequency representations that\ncharacterize modulation spaces, with the purpose of replacing the\ntime-frequency shifts with other atoms that allow to decompose signals\ndifferently, with possible new outcomes in applications.\n', 'Metaplectic Gabor frames of Wigner-Decomposable Distributions   Metaplectic Wigner distributions generalize the most popular time-frequency\nrepresentations, such as the short-time Fourier transform (STFT) and\n$\\tau$-Wigner distributions, using metaplectic operators. However, in order for\na metaplectic Wigner distribution to measure local time-frequency concentration\nof signals, the additional property of shift-invertibility is fundamental. In\naddition, metaplectic atoms provide different ways to model signals. Namely,\nsignals can be written as discrete superpositions of these operators, providing\noriginal ways to represent signals, with applications to machine learning,\nsignal analysis, theory of pseudodifferential operators, to mention a few.\nAmong all shift-invertible distributions, Wigner-decomposable metaplectic\nWigner distributions provide the most straightforward generalization of the\nSTFT. In this work, we focus on metaplectic atoms of Wigner-decomposable\nshift-invertible metaplectic distributions and characterize the associated\nmetaplectic Gabor frames.\n', 'Benedicks-type uncertainty principle for metaplectic time-frequency\n  representations   Metaplectic Wigner distributions are joint time-frequency representations\nthat are parametrized by a symplectic matrix and generalize the short-time\nFourier transform and the Wigner distribution.\n  We investigate the question which metaplectic Wigner distributions satisfy an\nuncertainty principle in the style of Benedicks and Amrein-Berthier. That is,\nif the metaplectic Wigner distribution is supported on a set of finite measure,\nmust the functions then be zero? While this statement holds for the short-time\nFourier transform, it is false for some other natural time-frequency\nrepresentations. We provide a full characterization of the class of metaplectic\nWigner distributions which exhibit an uncertainty principle of this type, both\nfor sesquilinear and quadratic versions.\n']","[('frequency representations', 0.618506908416748), ('time frequency representations', 0.6053545475006104), ('time frequency representation', 0.5512616634368896), ('frequency representation', 0.5481929183006287), ('time fourier transform', 0.5009072422981262), ('wigner transforms', 0.49633342027664185), ('short time fourier', 0.4850313365459442), ('time fourier', 0.47337356209754944), ('fourier transform stft', 0.45958831906318665), ('modulation spaces', 0.45104488730430603)]"
1728,1728,16,1728_commutator subgroups_elementary subgroups_chevalley groups_exceptional groups,"['commutator subgroups', 'elementary subgroups', 'chevalley groups', 'exceptional groups', 'elementary groups', 'group algebras', 'subgroup phi', 'chevalley group', 'group elementary', 'commutators']","[""Commutators of relative and unrelative elementary unitary groups   In the present paper we find generators of the mixed commutator subgroups of\nrelative elementary groups and obtain unrelativised versions of commutator\nformulas in the setting of Bak's unitary groups. It is a direct sequel of our\nsimilar results were obtained for $GL(n,R)$ and for Chevalley groups over a\ncommutative ring with 1, respectively. Namely, let $(A,\\Lambda)$ be any form\nring and $n\\ge 3$. We consider Bak's hyperbolic unitary group\n$GU(2n,A,\\Lambda)$. Further, let $(I,\\Gamma)$ be a form ideal of $(A,\\Lambda)$.\nOne can associate with $(I,\\Gamma)$ the corresponding elementary subgroup\n$FU(2n,I,\\Gamma)$ and the relative elementary subgroup $EU(2n,I,\\Gamma)$ of\n$GU(2n,A,\\Lambda)$. Let $(J,\\Delta)$ be another form ideal of $(A,\\Lambda)$. In\nthe present paper we prove an unexpected result that the non-obvious type of\ngenerators for $\\big[EU(2n,I,\\Gamma),EU(2n,J,\\Delta)\\big]$, as constructed in\nour previous papers with Hazrat, are redundant and can be expressed as products\nof the obvious generators, the elementary conjugates\n$Z_{ij}(ab,c)=T_{ji}(c)T_{ij}(ab)T_{ji}(-c)$ and $Z_{ij}(ba,c)$, and the\nelementary commutators $Y_{ij}(a,b)=[T_{ji}(a),T_{ij}(b)]$, where\n$a\\in(I,\\Gamma)$, $b\\in(J,\\Delta)$, $c\\in(A,\\Lambda)$. It follows that\n$\\big[FU(2n,I,\\Gamma),FU(2n,J,\\Delta)\\big]=\n\\big[EU(2n,I,\\Gamma),EU(2n,J,\\Delta)\\big]$. In fact, we establish much more\nprecise generation results. In particular, even the elementary commutators\n$Y_{ij}(a,b)$ should be taken for one long root position and one short root\nposition. Moreover, $Y_{ij}(a,b)$ are central modulo\n$EU(2n,(I,\\Gamma)\\circ(J,\\Delta))$ and behave as symbols. This allows us to\ngeneralise and unify many previous results,including the multiple elementary\ncommutator formula, and dramatically simplify their proofs.\n"", 'Generation of relative commutator subgroups in Chevalley groups. II   In the present paper, which is a direct sequel of our paper [12] joint with\nRoozbeh Hazrat, we prove unrelativised version of the standard commutator\nformula in the setting of Chevalley groups. Namely, let $\\Phi$ be a reduced\nirreducible root system of rank $\\ge 2$, let $R$ be a commutative ring and let\n$I,J$ be two ideals of $R$. We consider subgroups of the Chevalley group\n$G(\\Phi,R)$ of type $\\Phi$ over $R$. The unrelativised elementary subgroup\n$E(\\Phi,I)$ of level $I$ is generated (as a group) by the elementary unipotents\n$x_{\\alpha}(\\xi)$, $\\alpha\\in\\Phi$, $\\xi\\in I$, of level $I$. Obviously, in\ngeneral $E(\\Phi,I)$ has no chances to be normal in $E(\\Phi,R)$, its normal\nclosure in the absolute elementary subgroup $E(\\Phi,R)$ is denoted by\n$E(\\Phi,R,I)$. The main results of [12] implied that the commutator\n$\\big[E(\\Phi,I),E(\\Phi,J)]$ is in fact normal in $E(\\Phi,R)$. In the present\npaper we prove an unexpected result that in fact\n$\\big[E(\\Phi,I),E(\\Phi,J)]=\\big[E(\\Phi,R,I),E(\\Phi,R,J)\\big]$. It follows that\nthe standard commutator formula also holds in the unrelativised form, namely\n$\\big[E(\\Phi,I),C(\\Phi,R,J)]=\\big[E(\\Phi,I),E(\\Phi,J)\\big]$, where\n$C(\\Phi,R,I)$ is the full congruence subgroup of level $I$. In particular,\n$E(\\Phi,I)$ is normal in $C(\\Phi,R,I)$.\n', 'Commutators of relative and unrelative elementary subgroups in Chevalley\n  groups   In the present paper, which is a direct sequel of our papers [10,11,35] joint\nwith Roozbeh Hazrat, we achieve a further dramatic reduction of the generating\nsets for commutators of relative elementary subgroups in Chevalley groups.\nNamely, let $\\Phi$ be a reduced irreducible root system of rank $\\ge 2$, let\n$R$ be a commutative ring and let $A,B$ be two ideals of $R$. We consider\nsubgroups of the Chevalley group $G(\\Phi,R)$ of type $\\Phi$ over $R$. The\nunrelative elementary subgroup $E(\\Phi,A)$ of level $A$ is generated (as a\ngroup) by the elementary unipotents $x_{\\alpha}(a)$, $\\alpha\\in\\Phi$, $a\\in A$,\nof level $A$. Its normal closure in the absolute elementary subgroup\n$E(\\Phi,R)$ is denoted by $E(\\Phi,R,A)$ and is called the relative elementary\nsubgroup of level $A$. The main results of [11,35] consisted in construction of\neconomic generator sets for the mutual commutator subgroups\n$[E(\\Phi,R,A),E(\\Phi,R,B)]$, where $A$ and $B$ are two ideals of $R$. It turned\nout that one can take Stein---Tits---Vaserstein generators of $E(\\Phi,R,AB)$,\nplus elementary commutators of the form\n$y_{\\alpha}(a,b)=[x_{\\alpha}(a),x_{-\\alpha}(b)]$, where $a\\in A$, $b\\in B$.\nHere we improve these results even further, by showing that in fact it suffices\nto engage only elementary commutators corresponding to {\\it one\\/} long root,\nand that modulo $E(\\Phi,R,AB)$ the commutators $y_{\\alpha}(a,b)$ behave as\nsymbols. We discuss also some further variations and applications of these\nresults.\n']","[('commutator subgroups', 0.5598858594894409), ('elementary subgroups', 0.5351778864860535), ('chevalley groups', 0.5233333110809326), ('exceptional groups', 0.5161451697349548), ('elementary groups', 0.507814884185791), ('group algebras', 0.4811079204082489), ('subgroup phi', 0.44478514790534973), ('chevalley group', 0.43616288900375366), ('group elementary', 0.40982821583747864), ('commutators', 0.3949345648288727)]"
1729,1729,16,1729_clifford algebras_associative algebras_clifford algebra_division algebras,"['clifford algebras', 'associative algebras', 'clifford algebra', 'division algebras', 'nonassociative algebras', 'algebras generalized', 'generalized cayley', 'algebra structure', 'group algebra structure', 'algebras obtained']","[""Octonions as Clifford-like algebras   The associative Cayley-Dickson algebras over the field of real numbers are\nalso Clifford algebras. The alternative but nonassociative real Cayley-Dickson\nalgebras, notably the octonions and split octonions, share with Clifford\nalgebras an involutary anti-automorphism and a set of mutually anticommutative\ngenerators. On the basis of these similarities, we introduce Kingdon algebras:\nalternative Clifford-like algebras over vector spaces equipped with a symmetric\nbilinear form. Over three-dimensional vector spaces, our construction quantizes\nan alternative non-associative analogue of the exterior algebra. The octonions\nand split octonions, along with other real generalized Cayley-Dickson algebras\nin Albert's sense, arise as Kingdon algebras. Our construction gives natural\ncharacterizations of the octonion and split octonion algebras by a universality\nproperty endowing them with a selected superalgebra structure.\n"", 'How to obtain division algebras from a generalized Cayley-Dickson\n  doubling process   New families of eight-dimensional real division algebras with large\nderivation algebra are presented: We generalize the classical Cayley-Dickson\ndoubling process starting with a unital algebra with involution over a field F\nby allowing the scalar in the doubling to be an invertible element in the\nalgebra. The resulting unital algebras are neither power-associative nor\nquadratic. Starting with a quaternion division algebra D, we obtain division\nalgebras A for all invertible scalars chosen in D outside of F. This is\nindependent on where the scalar is placed inside the product and three pairwise\nnon-isomorphic families of eight-dimensional division algebras are obtained.\nOver the reals, the derivation algebra of each such algebra A is isomorphic to\n$su(2)\\oplus F$ and the decomposition of A into irreducible su(2)-modules has\nthe form 1+1+3+3 (denoting an irreducible su(2)-module by its dimension). Their\nopposite algebras yield more classes of pairwise non-isomorphic families of\ndivision algebras of the same type. We thus give an affirmative answer to a\nquestion posed by Benkart and Osborn in 1981.\n', 'The twisted group algebra structure of the Cayley-Dickson algebra   The Cayley-Dickson algebra has long been a challenge due to the lack of an\nexplicit multiplication table. Despite being constructible through inductive\nconstruction, its explicit structure has remained elusive until now. In this\narticle, we propose a solution to this long-standing problem by revealing the\nCayley-Dickson algebra as a twisted group algebra with an explicit twist\nfunction $\\sigma(A,B)$. We show that this function satisfies the equation\n$$e_Ae_B=(-1)^{\\sigma(A,B)}e_{A\\oplus B}$$ and provide a formula for the\nrelationship between the Cayley-Dickson algebra and split Cayley-Dickson\nalgebra, thereby giving an explicit expression for the twist function of the\nsplit Cayley-Dickson algebra. Our approach not only resolves the lack of\nexplicit structure for the Cayley-Dickson algebra and split Cayley-Dickson\nalgebra but also sheds light on the algebraic structure underlying this\nfundamental mathematical object.\n']","[('clifford algebras', 0.6824262738227844), ('associative algebras', 0.6308569312095642), ('clifford algebra', 0.6233983039855957), ('division algebras', 0.585151731967926), ('nonassociative algebras', 0.5776594281196594), ('algebras generalized', 0.5619862675666809), ('generalized cayley', 0.554977297782898), ('algebra structure', 0.5511809587478638), ('group algebra structure', 0.550260603427887), ('algebras obtained', 0.5494407415390015)]"
1730,1730,16,1730_galerkin methods_acoustic wave propagation_discontinuous galerkin_acoustic wave,"['galerkin methods', 'acoustic wave propagation', 'discontinuous galerkin', 'acoustic wave', 'galerkin', 'wave propagation', 'wave piecewise', 'discontinuous petrov galerkin', 'order galerkin', 'plane wave']","[""A space-time quasi-Trefftz DG method for the wave equation with\n  piecewise-smooth coefficients   Trefftz methods are high-order Galerkin schemes in which all discrete\nfunctions are elementwise solution of the PDE to be approximated. They are\nviable only when the PDE is linear and its coefficients are piecewise constant.\nWe introduce a 'quasi-Trefftz' discontinuous Galerkin method for the\ndiscretisation of the acoustic wave equation with piecewise-smooth wavespeed:\nthe discrete functions are elementwise approximate PDE solutions. We show that\nthe new discretisation enjoys the same excellent approximation properties as\nthe classical Trefftz one, and prove stability and high-order convergence of\nthe DG scheme. We introduce polynomial basis functions for the new discrete\nspaces and describe a simple algorithm to compute them. The technique we\npropose is inspired by the generalised plane waves previously developed for\ntime-harmonic problems with variable coefficients; it turns out that in the\ncase of the time-domain wave equation under consideration the quasi-Trefftz\napproach allows for polynomial basis functions.\n"", 'A quasi-Trefftz discontinuous Galerkin method for the homogeneous\n  diffusion-advection-reaction equation with piecewise-smooth coefficients   We describe and analyze a quasi-Trefftz DG method for solving boundary value\nproblems for the homogeneous diffusion-advection-reaction equation with\npiecewise-smooth coefficients. Trefftz schemes are high-order Galerkin methods\nwhose discrete functions are elementwise exact solutions of the underlying PDE.\nTrefftz basis functions can be computed for many PDEs that are linear,\nhomogeneous and with piecewise-constant coefficients. However, if the equation\nhas varying coefficients, in general, exact solutions are unavailable, hence\nthe construction of discrete Trefftz spaces is impossible. Quasi-Trefftz\nmethods have been introduced to overcome this limitation, relying on discrete\nspaces of functions that are elementwise ""approximate solutions"" of the PDE. A\nspace-time quasi-Trefftz DG method for the acoustic wave equation with smoothly\nvarying coefficients has recently been studied; since it has shown excellent\nresults, we propose a related method that can be applied to second-order\nelliptic equations. The DG weak formulation is derived using an interior\npenalty parameter and the upwind numerical fluxes. We choose polynomial\nquasi-Trefftz basis functions, whose coefficients can be computed with a simple\nalgorithm based on the Taylor expansion of the PDE\'s coefficients. The main\nadvantage of Trefftz and quasi-Trefftz schemes over more classical ones is the\nhigher accuracy for comparable numbers of degrees of freedom. We prove that the\ndimension of the quasi-Trefftz space is smaller than the dimension of the full\npolynomial space of the same degree and that yields the same optimal\nconvergence rates. The quasi-Trefftz DG method is well-posed, consistent and\nstable and we prove its high-order convergence. We present some numerical\nexperiments in two dimensions that show excellent properties in terms of\napproximation and convergence rate.\n', 'Three types of quasi-Trefftz functions for the 3D convected Helmholtz\n  equation: construction and approximation properties   Trefftz methods are numerical methods for the approximation of solutions to\nboundary and/or initial value problems. They are Galerkin methods with\nparticular test and trial functions, which solve locally the governing partial\ndifferential equation (PDE). This property is called the Trefftz property.\nQuasi-Trefftz methods were introduced to leverage the advantages of Trefftz\nmethods for problems governed by variable coefficient PDEs, by relaxing the\nTrefftz property into a so-called quasi-Trefftz property: test and trial\nfunctions are not exact solutions but rather local approximate solutions to the\ngoverning PDE. In order to develop quassi-Trefftz methods for aero-acoustics\nproblems governed by the convected Helmholtz equation, the present work tackles\nthe question of the definition, construction and approximation properties of\nthree families of quasi-Trefftz functions: two based on generalizations on\nplane wave solutions, and one polynomial. The polynomial basis shows\nsignificant promise as it does not suffer from the ill-conditioning issue\ninherent to wave-like bases.\n']","[('galerkin methods', 0.6076334714889526), ('acoustic wave propagation', 0.4774601459503174), ('discontinuous galerkin', 0.46714308857917786), ('acoustic wave', 0.4435022175312042), ('galerkin', 0.4262806177139282), ('wave propagation', 0.42408403754234314), ('wave piecewise', 0.41948401927948), ('discontinuous petrov galerkin', 0.41346389055252075), ('order galerkin', 0.3992946147918701), ('plane wave', 0.39225873351097107)]"
1731,1731,16,1731_julia sets_polynomials mapping_laminations_symmetric polynomials,"['julia sets', 'polynomials mapping', 'laminations', 'symmetric polynomials', 'polynomials connected', 'algebraic correspondence', 'rational maps', 'cubic polynomials', 'locus space', 'quadratic invariant']","[""Unicritical Laminations   Thurston introduced \\emph{invariant (quadratic) laminations} in his 1984\npreprint as a vehicle for understanding the connected Julia sets and the\nparameter space of quadratic polynomials. Important ingredients of his analysis\nof the angle doubling map $\\sigma_2$ on the unit circle $\\mathbb{S}^1$ were the\nCentral Strip Lemma, non-existence of wandering polygons, the transitivity of\nthe first return map on vertices of periodic polygons, and the non-crossing of\nminors of quadratic invariant laminations. We use Thurston's methods to prove\nsimilar results for \\emph{unicritical} laminations of arbitrary degree $d$ and\nto show that the set of so-called \\emph{minors} of unicritical laminations\nthemselves form a \\emph{Unicritical Minor Lamination} $\\mathrm{UML}_d$. In the\nend we verify the \\emph{Fatou conjecture} for the unicritical laminations and\nextend the \\emph{Lavaurs algorithm} onto $\\mathrm{UML}_d$.\n"", 'Lavaurs algorithm for cubic symmetric polynomials   To investigate the degree $d$ connectedness locus, Thurston studied\n\\emph{$\\sigma_d$-invariant laminations}, where $\\sigma_d$ is the $d$-tupling\nmap on the unit circle, and built a topological model for the space of\nquadratic polynomials $f_c(z) = z^2 +c$. In the same spirit, we consider the\nspace of all \\emph{cubic symmetric polynomials} $f_\\lambda(z)=z^3+\\lambda^2 z$\nin three articles. In the first one we construct the lamination $C_sCL$\ntogether with the induced factor space $\\mathbb{S}/C_sCL$ of the unit circle\n$\\mathbb{S}$. As will be verified in the third paper, $\\mathbb{S}/C_sCL$ is a\nmonotone model of the \\emph{cubic symmetric connectedness locus}, i.e., the\nspace of all cubic symmetric polynomials with connected Julia sets. In the\npresent paper, the second in the series, we develop an algorithm for\nconstructing $C_sCL$ analogous to the Lavaurs algorithm for constructing a\ncombinatorial model $\\mathcal{M}^{comb}_2$ of the Mandelbrot set\n$\\mathcal{M}_2$.\n', ""Symmetric Cubic Laminations   To investigate the degree $d$ connectedness locus, Thur\\-ston studied\n\\emph{$\\sigma_d$-invariant laminations}, where $\\sigma_d$ is the $d$-tupling\nmap on the unit circle, and built a topological model for the space of\nquadratic polynomials $f(z) = z^2 +c$. In the spirit of Thurston's work, we\nconsider the space of all \\emph{cubic symmetric polynomials}\n$f_\\lambda(z)=z^3+\\lambda^2 z$ in a series of three articles. In the present\npaper, the first in the series, we construct a lamination $C_sCL$ together with\nthe induced factor space ${\\mathbb{S}}/C_sCL$ of the unit circle\n${\\mathbb{S}}$. As will be verified in the third paper of the series,\n${\\mathbb{S}}/C_sCL$ is a monotone model of the \\emph{cubic symmetric connected\nlocus}, i.e. the space of all cubic symmetric polynomials with connected Julia\nsets.\n""]","[('julia sets', 0.43687403202056885), ('polynomials mapping', 0.428580641746521), ('laminations', 0.4057253897190094), ('symmetric polynomials', 0.3995370864868164), ('polynomials connected', 0.38582754135131836), ('algebraic correspondence', 0.3826335370540619), ('rational maps', 0.3750123679637909), ('cubic polynomials', 0.3700253367424011), ('locus space', 0.3600095808506012), ('quadratic invariant', 0.3543607294559479)]"
1732,1732,16,1732_rational cherednik algebra_cherednik algebras_cherednik algebra_rational cherednik,"['rational cherednik algebra', 'cherednik algebras', 'cherednik algebra', 'rational cherednik', 'hecke algebras particular', 'complex reflection groups', 'representations rational', 'algebras positive characteristic', 'algebras particular', 'complex reflection group']","[""Twists of representations of complex reflection groups and rational\n  Cherednik algebras   Drinfeld twists, and the twists of Giaquinto and Zhang, allow for algebras\nand their modules to be deformed by a cocycle. We prove general results about\ncocycle twists of algebra factorisations and induced representations and apply\nthem to reflection groups and rational Cherednik algebras. In particular, we\ndescribe how a twist acts on characters of Coxeter groups of type $B_n$ and\n$D_n$ and relate them to characters of mystic reflection groups. This is used\nto characterise twists of standard modules of rational Cherednik algebras as\nstandard modules for certain braided Cherednik algebras. We introduce the\ncoinvariant algebra of a mystic reflection group and use a twist to show that\nan analogue of Chevalley's theorem holds for these noncommutative algebras. We\nalso discuss several cases where the negative braided Cherednik algebras are,\nand are not, isomorphic to rational Cherednik algebras.\n"", 'Towards a classification of finite-dimensional representations of\n  rational Cherednik algebras of type D   Using a combinatorial description due to Jacon and Lecouvey of the wall\ncrossing bijections for cyclotomic rational Cherednik algebras, we show that\nthe irreducible representations $L_c(\\lambda^\\pm)$ of the rational Cherednik\nalgebra $H_c(D_n, \\mathbb{C}^n)$ of type $D$ for symmetric bipartitions\n$\\lambda$ are infinite dimensional for all parameters $c$. In particular, all\nfinite-dimensional irreducible representations of rational Cherednik algebras\nof type $D$ arise as restrictions of finite-dimensional irreducible\nrepresentations of rational Cherednik algebras of type $B$.\n', 'The Rational Cherednik Algebra of Type $A_1$ with Divided Powers   Motivated by the recent developments of the theory of Cherednik algebras in\npositive characteristic, we study rational Cherednik algebras with divided\npowers. In our research we have started with the simplest case, the rational\nCherednik algebra of type $A_1$. We investigate its maximal divided power\nextensions over $R[c]$ and $R$ for arbitrary principal ideal domains $R$ of\ncharacteristic zero. In these cases, we prove that the maximal divided power\nextensions are free modules over the base rings, and construct an explicit\nbasis in the case of $R[c]$. In addition, we provide an abstract construction\nof the rational Cherednik algebra of type $A_1$ over an arbitrary ring, and\nprove that this generalization expands the rational Cherednik algebra to\ninclude all of the divided powers.\n']","[('rational cherednik algebra', 0.7817457318305969), ('cherednik algebras', 0.7806515693664551), ('cherednik algebra', 0.737401008605957), ('rational cherednik', 0.560310959815979), ('hecke algebras particular', 0.50672847032547), ('complex reflection groups', 0.47770991921424866), ('representations rational', 0.46369731426239014), ('algebras positive characteristic', 0.45585212111473083), ('algebras particular', 0.4508649408817291), ('complex reflection group', 0.4397898316383362)]"
1733,1733,16,1733_primal dual methods_primal dual formulations_lp solver_linear programming lp,"['primal dual methods', 'primal dual formulations', 'lp solver', 'linear programming lp', 'scale linear programming', 'hybrid gradient pdhg', 'linear programs lps', 'dual methods', 'dual hybrid gradient', 'linear programming']","['On the Infimal Sub-differential Size of Primal-Dual Hybrid Gradient\n  Method and Beyond   Primal-dual hybrid gradient method (PDHG, a.k.a. Chambolle and Pock method)\nis a well-studied algorithm for minimax optimization problems with a bilinear\ninteraction term. Recently, PDHG is used as the base algorithm for a new LP\nsolver PDLP that aims to solve large LP instances by taking advantage of modern\ncomputing resources, such as GPU and distributed system. Most of the previous\nconvergence results of PDHG are either on duality gap or on distance to the\noptimal solution set, which are usually hard to compute during the solving\nprocess. In this paper, we propose a new progress metric for analyzing PDHG,\nwhich we dub infimal sub-differential size (IDS), by utilizing the geometry of\nPDHG iterates. IDS is a natural extension of the gradient norm of smooth\nproblems to non-smooth problems, and it is tied with KKT error in the case of\nLP. Compared to traditional progress metrics for PDHG, IDS always has a finite\nvalue and can be computed only using information of the current solution. We\nshow that IDS monotonically decays, and it has an $\\mathcal O(\\frac{1}{k})$\nsublinear rate for solving convex-concave primal-dual problems, and it has a\nlinear convergence rate if the problem further satisfies a regularity condition\nthat is satisfied by applications such as linear programming, quadratic\nprogramming, TV-denoising model, etc. The simplicity of our analysis and the\nmonotonic decay of IDS suggest that IDS is a natural progress metric to analyze\nPDHG. As a by-product of our analysis, we show that the primal-dual gap has\n$\\mathcal O(\\frac{1}{\\sqrt{k}})$ convergence rate for the last iteration of\nPDHG for convex-concave problems. The analysis and results on PDHG can be\ndirectly generalized to other primal-dual algorithms, for example, proximal\npoint method (PPM), alternating direction method of multipliers (ADMM) and\nlinearized alternating direction method of multipliers (l-ADMM).\n', 'On the Geometry and Refined Rate of Primal-Dual Hybrid Gradient for\n  Linear Programming   We study the convergence behaviors of primal-dual hybrid gradient (PDHG) for\nsolving linear programming (LP). PDHG is the base algorithm of a new\ngeneral-purpose first-order method LP solver, PDLP, which aims to scale up LP\nby taking advantage of modern computing architectures. Despite its numerical\nsuccess, the theoretical understanding of PDHG for LP is still very limited;\nthe previous complexity result relies on the global Hoffman constant of the KKT\nsystem, which is known to be very loose and uninformative. In this work, we aim\nto develop a fundamental understanding of the convergence behaviors of PDHG for\nLP and to develop a refined complexity rate that does not rely on the global\nHoffman constant. We show that there are two major stages of PDHG for LP: in\nStage I, PDHG identifies active variables and the length of the first stage is\ndriven by a certain quantity which measures how close the non-degeneracy part\nof the LP instance is to degeneracy; in Stage II, PDHG effectively solves a\nhomogeneous linear inequality system, and the complexity of the second stage is\ndriven by a well-behaved local sharpness constant of the system. This finding\nis closely related to the concept of partial smoothness in non-smooth\noptimization, and it is the first complexity result of finite time\nidentification without the non-degeneracy assumption. An interesting\nimplication of our results is that degeneracy itself does not slow down the\nconvergence of PDHG for LP, but near-degeneracy does.\n', 'On the Relation Between LP Sharpness and Limiting Error Ratio and\n  Complexity Implications for Restarted PDHG   There has been a recent surge in development of first-order methods (FOMs)\nfor solving huge-scale linear programming (LP) problems. The attractiveness of\nFOMs for LP stems in part from the fact that they avoid costly matrix\nfactorization computation. However, the efficiency of FOMs is significantly\ninfluenced - both in theory and in practice - by certain instance-specific LP\ncondition measures. Xiong and Freund recently showed that the performance of\nthe restarted primal-dual hybrid gradient method (PDHG) is predominantly\ndetermined by two specific condition measures: LP sharpness and Limiting Error\nRatio. In this paper we examine the relationship between these two measures,\nparticularly in the case when the optimal solution is unique (which is generic\n- at least in theory), and we present an upper bound on the Limiting Error\nRatio involving the reciprocal of the LP sharpness. This shows that in LP\ninstances where there is a dual nondegenerate optimal solution, the\ncomputational complexity of restarted PDHG can be characterized solely in terms\nof LP sharpness and the distance to optimal solutions, and simplifies the\ntheoretical complexity upper bound of restarted PDHG for these instances.\n']","[('primal dual methods', 0.5740013718605042), ('primal dual formulations', 0.5677711367607117), ('lp solver', 0.5396823883056641), ('linear programming lp', 0.5312023758888245), ('scale linear programming', 0.521494448184967), ('hybrid gradient pdhg', 0.5138521790504456), ('linear programs lps', 0.5043755769729614), ('dual methods', 0.49156469106674194), ('dual hybrid gradient', 0.4909895062446594), ('linear programming', 0.4903998374938965)]"
1734,1734,16,1734_skyrmions_skyrmion_skyrme_self duality,"['skyrmions', 'skyrmion', 'skyrme', 'self duality', 'topological energy', 'self dual', 'conformal symmetry', 'topological charge', 'soliton solutions', 'duality equations']","['Background fields and self-dual Skyrmions   We show that a suitable background field can bring a non-BPS topological\nsoliton into its BPS, self-dual, counterpart. As an example we consider\nSkyrmions in the minimal Skyrme model. We prove the triviality of the\ncorresponding moduli space. This means that the resulting self-dual Skyrmion\ndoes statically interact with the background field. We also show that the\noriginally self-dual Skyrmions (e.g. solutions of the BPS Skyrme model) can\npreserve the self-duality after a coupling with a background field. In this\ncase, BPS Skyrmions can be effortless moved with respect to the background.\n', 'BPS Skyrmions of Generalized Skyrme Model In Higher Dimensions   In this work we consider the higher dimensional Skyrme model, with spatial\ndimension $d > 3$, focusing on its BPS submodels and their corresponding\nfeatures. To accommodate the cases with a higher topological degree, \\(B\\geq\n1\\), a modified generalized hedgehog ansatz is used where we assign an integer\n\\(n_i\\) for each rotational plane, resulting in a topological degree that\nproportional to product of these integers. It is found via BPS Lagrangian\nmethod that there are only two possible BPS submodels for this spherically\nsymmetric ansatz which shall be called as BPS Skyrme model and scale-invariant\nmodel. The properties of the higher dimensional version of both submodels are\nstudied and it is found that the BPS Skyrmions with \\(B\\geq1\\) exist in the\nfirst submodel but there is only \\(B=1\\) BPS Skyrmion in the second submodel.\nWe also study the higher dimensional version of self-duality conditions in\nterms of strain tensor eigenvalues and find that, in general, the\nscale-invariant model has a stronger self-duality condition than the BPS Skyrme\nmodel.\n', 'BPS Skyrme Submodels of The Five Dimensional Skyrme Model   In this paper, we search for the BPS skyrmions in some BPS submodels of the\ngeneralized Skyrme model in five-dimensional spacetime using the BPS Lagrangian\nmethod. We focus on the static solutions of the Bogomolny\'s equations and their\ncorresponding energies with topological charge $B>0$ is an integer. We consider\ntwo main cases based on the symmetry of the effective Lagrangian of the BPS\nsubmodels, i.e. the spherically symmetric and non-spherically symmetric cases.\nFor the spherically symmetric case, we find two BPS submodels. The first BPS\nsubmodels consist of a potential term and a term proportional to the square of\nthe topological current. The second BPS submodels consist of only the Skyrme\nterm. The second BPS submodel has BPS skyrmions with the same topological\ncharge $B>1$, but with different energies, that we shall call ""topological\ndegenerate"" BPS skyrmions. It also has the usual BPS skyrmions with equal\nenergies, if the topological charge is a prime number. Another interesting\nfeature of the BPS skyrmions, with $B>1$, in this BPS submodel, is that these\nBPS skyrmions have non-zero pressures in the angular direction. For the\nnon-spherically symmetric case, there is only one BPS submodel, which is\nsimilar to the first BPS submodel in the spherically symmetric case. We find\nthat the BPS skyrmions depend on a constant $k$ and for a particular value of\n$k$ we obtain the BPS skyrmions of the first BPS submodel in the spherically\nsymmetric case. The total static energy and the topological charge of these BPS\nskyrmions also depend on this constant. We also show that all the results found\nin this paper satisfy the full field equations of motions of the corresponding\nBPS submodels.\n']","[('skyrmions', 0.5398349165916443), ('skyrmion', 0.5128869414329529), ('skyrme', 0.44284260272979736), ('self duality', 0.3840290606021881), ('topological energy', 0.38026347756385803), ('self dual', 0.34857380390167236), ('conformal symmetry', 0.332419753074646), ('topological charge', 0.3212333023548126), ('soliton solutions', 0.3119862675666809), ('duality equations', 0.3102913498878479)]"
1735,1735,16,1735_constraint control_bayesian optimization bo_bayesian optimization_based bayesian optimization,"['constraint control', 'bayesian optimization bo', 'bayesian optimization', 'based bayesian optimization', 'black box optimization', 'constraint learning', 'optimization closed loop', 'constraints performance', 'real time optimization', 'constraint feasible']","['CONFIG: Constrained Efficient Global Optimization for Closed-Loop\n  Control System Optimization with Unmodeled Constraints   In this paper, the CONFIG algorithm, a simple and provably efficient\nconstrained global optimization algorithm, is applied to optimize the\nclosed-loop control performance of an unknown system with unmodeled\nconstraints. Existing Gaussian process based closed-loop optimization methods,\neither can only guarantee local convergence (e.g., SafeOPT), or have no known\noptimality guarantee (e.g., constrained expected improvement) at all, whereas\nthe recently introduced CONFIG algorithm has been proven to enjoy a theoretical\nglobal optimality guarantee. In this study, we demonstrate the effectiveness of\nCONFIG algorithm in the applications. The algorithm is first applied to an\nartificial numerical benchmark problem to corroborate its effectiveness. It is\nthen applied to a classical constrained steady-state optimization problem of a\ncontinuous stirred-tank reactor. Simulation results show that our CONFIG\nalgorithm can achieve performance competitive with the popular CEI (Constrained\nExpected Improvement) algorithm, which has no known optimality guarantee. As\nsuch, the CONFIG algorithm offers a new tool, with both a provable global\noptimality guarantee and competitive empirical performance, to optimize the\nclosed-loop control performance for a system with soft unmodeled constraints.\nLast, but not least, the open-source code is available as a python package to\nfacilitate future applications.\n', ""Violation-Aware Contextual Bayesian Optimization for Controller\n  Performance Optimization with Unmodeled Constraints   We study the problem of performance optimization of closed-loop control\nsystems with unmodeled dynamics. Bayesian optimization (BO) has been\ndemonstrated to be effective for improving closed-loop performance by\nautomatically tuning controller gains or reference setpoints in a model-free\nmanner. However, BO methods have rarely been tested on dynamical systems with\nunmodeled constraints and time-varying ambient conditions. In this paper, we\npropose a violation-aware contextual BO algorithm (VACBO) that optimizes\nclosed-loop performance while simultaneously learning constraint-feasible\nsolutions under time-varying ambient conditions. Unlike classical constrained\nBO methods which allow unlimited constraint violations, or 'safe' BO algorithms\nthat are conservative and try to operate with near-zero violations, we allow\nbudgeted constraint violations to improve constraint learning and accelerate\noptimization. We demonstrate the effectiveness of our proposed VACBO method for\nenergy minimization of industrial vapor compression systems under time-varying\nambient temperature and humidity.\n"", 'VABO: Violation-Aware Bayesian Optimization for Closed-Loop Control\n  Performance Optimization with Unmodeled Constraints   We study the problem of performance optimization of closed-loop control\nsystems with unmodeled dynamics. Bayesian optimization (BO) has been\ndemonstrated effective for improving closed-loop performance by automatically\ntuning controller gains or reference setpoints in a model-free manner. However,\nBO methods have rarely been tested on dynamical systems with unmodeled\nconstraints. In this paper, we propose a violation-aware BO algorithm (VABO)\nthat optimizes closed-loop performance while simultaneously learning\nconstraint-feasible solutions. Unlike classical constrained BO methods which\nallow an unlimited constraint violations, or safe BO algorithms that are\nconservative and try to operate with near-zero violations, we allow budgeted\nconstraint violations to improve constraint learning and accelerate\noptimization. We demonstrate the effectiveness of our proposed VABO method for\nenergy minimization of industrial vapor compression systems.\n']","[('constraint control', 0.5787711143493652), ('bayesian optimization bo', 0.5745681524276733), ('bayesian optimization', 0.5602638125419617), ('based bayesian optimization', 0.5521562695503235), ('black box optimization', 0.550045907497406), ('constraint learning', 0.5412639379501343), ('optimization closed loop', 0.5158258676528931), ('constraints performance', 0.5097275376319885), ('real time optimization', 0.5035213232040405), ('constraint feasible', 0.49086660146713257)]"
1736,1736,16,1736_group determinant_integer group_groups order 16_group order 4n,"['group determinant', 'integer group', 'groups order 16', 'group order 4n', 'group cyclic group', 'group order 16', 'order cyclic group', 'cyclic group order', 'cyclic group', 'group order two']","['Integer group determinants for ${\\rm C}_{4} \\rtimes {\\rm C}_{4}$   Let ${\\rm C}_{4}$ be the cyclic group of order $4$. We determine all possible\nvalues of the integer group determinant of ${\\rm C}_{4} \\rtimes {\\rm C}_{4}$.\n', 'Integer group determinants for ${\\rm C}_{4}^{2}$   We determine all possible values of the integer group determinant of ${\\rm\nC}_{4}^{2}$, where ${\\rm C}_{4}$ is the cyclic group of order $4$.\n', 'Integer group determinants for ${\\rm C}_{2}^{4}$   We determine all possible values of the integer group determinant of ${\\rm\nC}_{2}^{4}$, where ${\\rm C}_{2}$ is the cyclic group of order $2$.\n']","[('group determinant', 0.6351269483566284), ('integer group', 0.5430808663368225), ('groups order 16', 0.4901532530784607), ('group order 4n', 0.4677763283252716), ('group cyclic group', 0.46388307213783264), ('group order 16', 0.46027594804763794), ('order cyclic group', 0.45654717087745667), ('cyclic group order', 0.45098090171813965), ('cyclic group', 0.4401897192001343), ('group order two', 0.42582330107688904)]"
1737,1737,16,1737_quadratic regulator lqr_linear quadratic regulator_optimal state feedback_control linear quadratic,"['quadratic regulator lqr', 'linear quadratic regulator', 'optimal state feedback', 'control linear quadratic', 'optimal controller', 'quadratic regulator', 'optimal controllers', 'feedback control linear', 'optimal control nonlinear', 'optimal control']","['On the Relationship of Optimal State Feedback and Disturbance Response\n  Controllers   This paper studies the relationship between state feedback policies and\ndisturbance response policies for the standard Linear Quadratic Regulator\n(LQR). For open-loop stable plants, we establish a simple relationship between\nthe optimal state feedback controller $u_t=K_\\star x_t$ and the optimal\ndisturbance response controller\n$u_t=L^{(H)}_{\\star;1}w_{t-1}+\\cdots+L^{(H)}_{\\star;H}w_{t-H}$ with $H$-order.\nHere $x_t, w_t, u_t$ stands for the state, disturbance, control action of the\nsystem, respectively. Our result shows that $L_{\\star,1}^{(H)}$ is a good\napproximation of $K_\\star$ and the approximation error $\\|K_\\star -\nL_{\\star,1}^{(H)}\\|$ decays exponentially with $H$. We further extend this\nresult to LQR for open-loop unstable systems, when a pre-stabilizing controller\n$K_0$ is available.\n', 'A Note on Linear Quadratic Regulator and Kalman Filter   Two central problems in modern control theory are the controller design\nproblem: which deals with designing a control law for the dynamical system, and\nthe state estimation problem (observer design problem): which deals with\ncomputing an estimate of the states of the dynamical system. The Linear\nQuadratic Regulator (LQR) and Kalman Filter (KF) solves these problems\nrespectively for linear dynamical systems in an optimal manner, i.e., LQR is an\noptimal state feedback controller and KF is an optimal state estimator. In this\nnote, we will be discussing the basic concepts, derivation, steady-state\nanalysis, and numerical implementation of the LQR and KF.\n', 'Accelerated Optimization Landscape of Linear-Quadratic Regulator   Linear-quadratic regulator (LQR) is a landmark problem in the field of\noptimal control, which is the concern of this paper. Generally, LQR is\nclassified into state-feedback LQR (SLQR) and output-feedback LQR (OLQR) based\non whether the full state is obtained. It has been suggested in existing\nliterature that both SLQR and OLQR could be viewed as \\textit{constrained\nnonconvex matrix optimization} problems in which the only variable to be\noptimized is the feedback gain matrix. In this paper, we introduce a\nfirst-order accelerated optimization framework of handling the LQR problem, and\ngive its convergence analysis for the cases of SLQR and OLQR, respectively.\n  Specifically, a Lipschiz Hessian property of LQR performance criterion is\npresented, which turns out to be a crucial property for the application of\nmodern optimization techniques. For the SLQR problem, a continuous-time hybrid\ndynamic system is introduced, whose solution trajectory is shown to converge\nexponentially to the optimal feedback gain with Nesterov-optimal order\n$1-\\frac{1}{\\sqrt{\\kappa}}$ ($\\kappa$ the condition number). Then, the\nsymplectic Euler scheme is utilized to discretize the hybrid dynamic system,\nand a Nesterov-type method with a restarting rule is proposed that preserves\nthe continuous-time convergence rate, i.e., the discretized algorithm admits\nthe Nesterov-optimal convergence order. For the OLQR problem, a Hessian-free\naccelerated framework is proposed, which is a two-procedure method consisting\nof semiconvex function optimization and negative curvature exploitation. In a\ntime $\\mathcal{O}(\\epsilon^{-7/4}\\log(1/\\epsilon))$, the method can find an\n$\\epsilon$-stationary point of the performance criterion; this entails that the\nmethod improves upon the $\\mathcal{O}(\\epsilon^{-2})$ complexity of vanilla\ngradient descent. Moreover, our method provides the second-order guarantee of\nstationary point.\n']","[('quadratic regulator lqr', 0.6425834894180298), ('linear quadratic regulator', 0.620816707611084), ('optimal state feedback', 0.606671154499054), ('control linear quadratic', 0.6051264405250549), ('optimal controller', 0.5778530240058899), ('quadratic regulator', 0.5750263333320618), ('optimal controllers', 0.5735290050506592), ('feedback control linear', 0.5496081709861755), ('optimal control nonlinear', 0.5471357107162476), ('optimal control', 0.5456758737564087)]"
1738,1738,16,1738_modulation spaces_weighted modulation spaces_spaces modulation_fourier integral operators,"['modulation spaces', 'weighted modulation spaces', 'spaces modulation', 'fourier integral operators', 'wiener amalgam spaces', 'pseudodifferential operators', 'operators symbols', 'weighted modulation', 'localization operators', 'operators']","['Decay and Smoothness for Eigenfunctions of Localization Operators   We study decay and smoothness properties for eigenfunctions of compact\nlocalization operators. Operators with symbols a in the wide modulation space\nM^{p,\\infty} (containing the Lebesgue space L^p), p<\\infty, and windows\n\\f_1,\\f_2 in the Schwartz class are known to be compact. We show that their\nL^2-eigenfuctions with non-zero eigenvalues are indeed highly compressed onto a\nfew Gabor atoms. Similarly, for symbols a in the weighted modulation spaces\nM^{\\infty}_{v_s\\otimes 1} (\\rdd), s>0 (subspaces of M^{p,\\infty}(\\rdd), p>2d/s)\nthe L^2-eigenfunctions of the localization operator are actually Schwartz\nfunctions.\n  An important role is played by quasi-Banach Wiener amalgam and modulation\nspaces. As a tool, new convolution relations for modulation spaces and\nmultiplication relations for Wiener amalgam spaces in the quasi-Banach setting\nare exhibited.\n', 'Characterization of boundedness on weighted modulation spaces of\n  $\\tau$-Wigner distributions   This paper is devoted to give several characterizations on a more general\nlevel for the boundedness of $\\tau$-Wigner distributions acting from weighted\nmodulation spaces to weighted modulation and Wiener amalgam spaces. As\napplications, sharp exponents are obtained for the boundedness of $\\tau$-Wigner\ndistributions on modulation spaces with power weights. We also recapture the\nmain theorems of Wigner distribution obtained in\n\\cite{CorderoNicola2018IMRNI,Cordero2020a}. As consequences, the\ncharacterizations of the boundedness on weighted modulation spaces of several\ntypes of pseudodifferential operators are established. In particular, we give\nthe sharp exponents for the boundedness of pseudodifferential operators with\nsymbols in Sj\\""{o}strand\'s class and the corresponding Wiener amalgam spaces.\n', 'Localization Operators On Discrete Modulation Spaces   In this paper, we study a class of pseudo-differential operators known as\ntime-frequency localization operators on $\\mathbb Z^n$, which depend on a\nsymbol $\\varsigma$ and two windows functions $g_1$ and $g_2$. We define the\nshort-time Fourier transform on $ \\mathbb Z^n \\times \\mathbb T^n $ and\nmodulation spaces on $\\mathbb Z^n$, and present some basic properties. Then, we\nuse modulation spaces on $\\mathbb Z^n \\times \\mathbb T^n$ as appropriate\nclasses for symbols, and study the boundedness and compactness of the\nlocalization operators on modulation spaces on $\\mathbb Z^n$. Then, we show\nthat these operators are in the Schatten--von Neumann class. Also, we obtain\nthe relation between the Landau--Pollak--Slepian type operator and the\nlocalization operator on $\\mathbb Z^n$. Finally, under suitable conditions on\nthe symbols, we prove that the localization operators are paracommutators,\nparaproducts and Fourier multipliers.\n']","[('modulation spaces', 0.7105270624160767), ('weighted modulation spaces', 0.6837891340255737), ('spaces modulation', 0.584371030330658), ('fourier integral operators', 0.5418389439582825), ('wiener amalgam spaces', 0.5354904532432556), ('pseudodifferential operators', 0.5182405114173889), ('operators symbols', 0.49901020526885986), ('weighted modulation', 0.49069705605506897), ('localization operators', 0.48686331510543823), ('operators', 0.4824013411998749)]"
1739,1739,16,1739_holographic mimo_intelligent metasurfaces_transmit precoding_wireless communications,"['holographic mimo', 'intelligent metasurfaces', 'transmit precoding', 'wireless communications', 'channel estimator', 'domain channel', 'wireless communication', 'metasurface', 'mimo', 'ultra massive mimo']","['Channel Estimation for Stacked Intelligent Metasurface-Assisted Wireless\n  Networks   Emerging technologies, such as holographic multiple-input multiple-output\n(HMIMO) and stacked intelligent metasurface (SIM), are driving the development\nof wireless communication systems. Specifically, the SIM is physically\nconstructed by stacking multiple layers of metasurfaces and has an architecture\nsimilar to an artificial neural network (ANN), which can flexibly manipulate\nthe electromagnetic waves that propagate through it at the speed of light. This\narchitecture enables the SIM to achieve HMIMO precoding and combining in the\nwave domain, thus significantly reducing the hardware cost and energy\nconsumption. In this letter, we investigate the channel estimation problem in\nSIM-assisted multi-user HMIMO communication systems. Since the number of\nantennas at the base station (BS) is much smaller than the number of meta-atoms\nper layer of the SIM, it is challenging to acquire the channel state\ninformation (CSI) in SIM-assisted multi-user systems. To address this issue, we\ncollect multiple copies of the uplink pilot signals that propagate through the\nSIM. Furthermore, we leverage the array geometry to identify the subspace that\nspans arbitrary spatial correlation matrices. Based on partial CSI about the\nchannel statistics, a pair of subspace-based channel estimators are proposed.\nAdditionally, we compute the mean square error (MSE) of the proposed channel\nestimators and optimize the phase shifts of the SIM to minimize the MSE.\nNumerical results are illustrated to analyze the effectiveness of the proposed\nchannel estimation schemes.\n', 'Hybrid Digital-Wave Domain Channel Estimator for Stacked Intelligent\n  Metasurface Enabled Multi-User MISO Systems   Stacked intelligent metasurface (SIM) is an emerging programmable metasurface\narchitecture that can implement signal processing directly in the\nelectromagnetic wave domain, thereby enabling efficient implementation of\nultra-massive multiple-input multiple-output (MIMO) transceivers with a limited\nnumber of radio frequency (RF) chains. Channel estimation (CE) is challenging\nfor SIM-enabled communication systems due to the multi-layer architecture of\nSIM, and because we need to estimate large dimensional channels between the SIM\nand users with a limited number of RF chains. To efficiently solve this\nproblem, we develop a novel hybrid digital-wave domain channel estimator, in\nwhich the received training symbols are first processed in the wave domain\nwithin the SIM layers, and then processed in the digital domain. The wave\ndomain channel estimator, parametrized by the phase shifts applied by the\nmeta-atoms in all layers, is optimized to minimize the mean squared error (MSE)\nusing a gradient descent algorithm, within which the digital part is optimally\nupdated. For an SIM-enabled multi-user system equipped with 4 RF chains and a\n6-layer SIM with 64 meta-atoms each, the proposed estimator yields an MSE that\nis very close to that achieved by fully digital CE in a massive MIMO system\nemploying 64 RF chains. This high CE accuracy is achieved at the cost of a\ntraining overhead that can be reduced by exploiting the potential low rank of\nchannel correlation matrices.\n', 'Stacked Intelligent Metasurface-Based Transceiver Design for Near-Field\n  Wideband Systems   Intelligent metasurfaces may be harnessed for realizing efficient holographic\nmultiple-input and multiple-output (MIMO) systems, at a low hardware-cost and\nhigh energy-efficiency. As part of this family, we propose a hybrid beamforming\ndesign for stacked intelligent metasurfaces (SIM) aided wideband wireless\nsystems relying on the near-field channel model. Specifically, the holographic\nbeamformer is designed based on configuring the phase shifts in each layer of\nthe SIM for maximizing the sum of the baseband eigen-channel gains of all\nusers. To optimize the SIM phase shifts, we propose a layer-by-layer iterative\nalgorithm for optimizing the phase shifts in each layer alternately. Then, the\nminimum mean square error (MMSE) transmit precoding method is employed for the\ndigital beamformer to support multi-user access. Furthermore, the mitigation of\nthe SIM phase tuning error is also taken into account in the digital beamformer\nby exploiting its statistics. The power sharing ratio of each user is designed\nbased on the iterative waterfilling power allocation algorithm. Additionally,\nour analytical results indicate that the spectral efficiency attained saturates\nin the high signal-to-noise ratio (SNR) region due to the phase tuning error\nresulting from the imperfect SIM hardware quality. The simulation results show\nthat the SIM-aided holographic MIMO outperforms the state-of-the-art (SoA)\nsingle-layer holographic MIMO in terms of its achievable rate. We further\ndemonstrate that the near-field channel model allows the SIM-based transceiver\ndesign to support multiple users, since the spatial resources represented both\nby the angle domain and the distance domain can be exploited.\n']","[('holographic mimo', 0.4653930366039276), ('intelligent metasurfaces', 0.42469313740730286), ('transmit precoding', 0.4068889915943146), ('wireless communications', 0.40394484996795654), ('channel estimator', 0.3987133502960205), ('domain channel', 0.38877707719802856), ('wireless communication', 0.37157976627349854), ('metasurface', 0.366834431886673), ('mimo', 0.3659849464893341), ('ultra massive mimo', 0.3631766736507416)]"
1740,1740,16,1740_ahler manifold complex_bergman metrics_finsler manifolds_ahler manifold,"['ahler manifold complex', 'bergman metrics', 'finsler manifolds', 'ahler manifold', 'finsler manifold', 'finsler metrics', 'holomorphic sectional curvature', 'ahler einstein metric', 'finsler metric', 'bergman metric']","['Holomorphic invariant strongly pseudoconvex complex Finsler metrics   Let $B_n$ and $P_n$ be the unit ball and the unit polydisk in $\\mathbb{C}^n$\nwith $n\\geq 2$ respectively. Denote $\\mbox{Aut}(B_n)$ and $\\mbox{Aut}(P_n)$ the\nholomorphic automorphism group of $B_n$ and $P_n$ respectively. In this paper,\nwe prove that $B_n$ admits no $\\mbox{Aut}(B_n)$-invariant strongly pseudoconvex\ncomplex Finsler metric other than a constant multiple of the\nPoincar$\\acute{\\mbox{e}}$-Bergman metric, while $P_n$ admits infinite many\n$\\mbox{Aut}(P_n)$-invariant complete strongly convex complex Finsler metrics\nother than the Bergman metric. The $\\mbox{Aut}(P_n)$-invariant complex Finsler\nmetrics are explicitly constructed which depend on a real parameter $t\\in\n[0,+\\infty)$ and integer $k\\geq 2$. These metrics are proved to be strongly\nconvex K\\""ahler-Berwald metrics, and they posses very similar properties as\nthat of the Bergman metric on $P_n$. As applications, the existence of\n$\\mbox{Aut}(M)$-invariant strongly convex complex Finsler metrics is also\ninvestigated on some Siegel domains of the first and the second kind which are\nbiholomorphic equivalently to the unit polydisc in $\\mathbb{C}^n$. We also give\na characterization of strongly convex K\\""ahler-Berwald spaces and give a de\nRahm type decomposition theorem for strongly convex K\\""ahler-Berwald spaces.\n', 'A Schwarz lemma for weakly K\\""ahler-Finsler manifolds   In this paper, we first establish several theorems about the estimation of\ndistance function on real and strongly convex complex Finsler manifolds and\nthen obtain a Schwarz lemma from a strongly convex weakly K\\""ahler-Finsler\nmanifold into a strongly pseudoconvex complex Finsler manifold. As\napplications, we prove that a holomorphic mapping from a strongly convex weakly\nK\\""ahler-Finsler manifold into a strongly pseudoconvex complex Finsler manifold\nis necessary constant under an extra condition. In particular, we prove that a\nholomorphic mapping from a complex Minkowski space into a strongly pseudoconvex\ncomplex Finsler manifold such that its holomorphic sectional curvature is\nbounded from above by a negative constant is necessary constant.\n', 'Complete complex Finsler metrics and uniform equivalence of the\n  Kobayashi metric   In this paper, first of all, according to Lu\'s and Zhang\'s works about the\ncurvature of the Bergman metric on a bounded domain and the properties of the\nsqueezing functions, we obtain that Bergman curvature of the Bergman metric on\na bounded strictly pseudoconvex domain with $C^2$-boundary or bounded convex\ndomain is bounded. Secondly, by the property of curvature symmetry on a\nK\\""ahler manifold, we have the property: if holomorphic sectional curvature of\na K\\""ahler manifold is bounded, we can deduce that its sectional curvature is\nbounded. After that, applying to the Schwarz lemma from a complete K\\""ahler\nmanifold into a complex Finsler manifold, we get that a bounded strictly\npseudoconvex domain with $C^2$-boundary or bounded convex domain admit complete\nstrongly pseudoconvex complex Finsler metrics such that their holomorphic\nsectional curvature is bounded from above by a negative constant. Finally, by\nthe Schwarz lemma from a complete K\\""ahler manifold into a complex Finsler\nmanifold, we prove the uniform equivalences of the Kobayashi metric and\nCarath\\\'eodory metric on a bounded strongly convex domain with smooth boundary.\n']","[('ahler manifold complex', 0.6103784441947937), ('bergman metrics', 0.6090344786643982), ('finsler manifolds', 0.6077918410301208), ('ahler manifold', 0.6000245213508606), ('finsler manifold', 0.5936340689659119), ('finsler metrics', 0.5892699956893921), ('holomorphic sectional curvature', 0.5855253338813782), ('ahler einstein metric', 0.5786338448524475), ('finsler metric', 0.5772360563278198), ('bergman metric', 0.5736163258552551)]"
1741,1741,16,1741_random access memory_memory channel_access memory_memory cells,"['random access memory', 'memory channel', 'access memory', 'memory cells', 'memory', 'flash memory', 'detection decoding', 'random access', 'decoding', 'dram']","['Sneak Path Interference-Aware Adaptive Detection and Decoding for\n  Resistive Memory Arrays   Resistive random-access memory (ReRAM) is an emerging non-volatile memory\ntechnology for high-density and high-speed data storage. However, the sneak\npath interference (SPI) occurred in the ReRAM crossbar array seriously affects\nits data recovery performance. In this letter, we first propose a quantized\nchannel model of ReRAM, based on which we design both the one-bit and multi-bit\nchannel quantizers by maximizing the mutual information of the channel. A key\nchannel parameter that affects the quantizer design is the sneak path\noccurrence probability (SPOP) of the memory cell. We first use the average SPOP\ncalculated statistically to design the quantizer, which leads to the same\nchannel detector for different memory arrays. We then adopt the SPOP estimated\nseparately for each memory array for the quantizer design, which is generated\nby an effective channel estimator and through an iterative detection and\ndecoding scheme for the ReRAM channel. This results in an array-level SPI-aware\nadaptive detection and decoding approach. Moreover, since there is a strong\ncorrelation of the SPI that affects memory cells in the same rows/columns than\nthat affecting cells in different rows/columns, we further derive a\ncolumn-level scheme which outperforms the array-level scheme. We also propose a\nchannel decomposition method that enables effective ways for theoretically\nanalyzing the ReRAM channel. Simulation results show that the proposed\nSPI-aware adaptive detection and decoding schemes can approach the ideal\nperformance with three quantization bits, with only one decoding iteration.\n', 'Performance Limit and Coding Schemes for Resistive Random-Access Memory\n  Channels   Resistive random-access memory (ReRAM) is a promising candidate for the next\ngeneration non-volatile memory technology due to its simple read/write\noperations and high storage density. However, its crossbar array structure\ncauses a severe interference effect known as the ""sneak path."" In this paper,\nwe propose channel coding techniques that can mitigate both the sneak-path\ninterference and the channel noise. The main challenge is that the sneak-path\ninterference is data-dependent, and also correlated within a memory array, and\nhence the conventional error correction coding scheme will be inadequate. In\nthis work, we propose an across-array coding strategy that assigns a codeword\nto multiple independent memory arrays, and exploit a real-time channel\nestimation scheme to estimate the instantaneous status of the ReRAM channel.\nSince the coded bits from different arrays experience independent channels, a\n""diversity"" gain can be obtained during decoding, and when the codeword is\nadequately distributed over different memory arrays, the code actually performs\nas that over an uncorrelated channel. By performing decoding based on the\nscheme of treating-interference-as-noise (TIN), the ReRAM channel over\ndifferent memory arrays is equivalent to a block varying channel we defined,\nfor which we propose both the capacity bounds and a coding scheme. The proposed\ncoding scheme consists of a serial concatenation of an optimized error\ncorrection code with a data shaper, which enables the ReRAM system to achieve a\nnear capacity limit storage efficiency.\n', 'Constrained Coding and Deep Learning Aided Threshold Detection for\n  Resistive Memories   Resistive random access memory (ReRAM) is a promising emerging non-volatile\nmemory (NVM) technology that shows high potential for both data storage and\ncomputing. However, its crossbar array architecture leads to the sneak path\nproblem, which may severely degrade the reliability of data stored in the ReRAM\ncell. Due to the complication of memory physics and unique features of the\nsneak path induced interference (SPI), it is difficult to derive an accurate\nchannel model for it. The deep learning (DL)-based detection scheme\n\\cite{zhong2020sneakdl} can better mitigate the SPI, at the cost of additional\npower consumption and read latency. In this letter, we first propose a novel CC\nscheme which can not only reduce the SPI in the memory array, but also\neffectively differentiate the memory arrays into two categories of\nsneak-path-free and sneak-path-affected arrays. For the sneak-path-free arrays,\nwe can use a simple middle-point threshold detector to detect the low and high\nresistance cells of ReRAM. For the sneak-path-affected arrays, a DL detector is\nfirst trained off-line (prior to the data detection of ReRAM). To avoid the\nadditional power consumption and latency introduced by the DL detector, we\nfurther propose a DL-based threshold detector, whose detection threshold can be\nderived based on the outputs of the DL detector. It is then utilized for the\nonline data detection of all the identified sneak-path-affected arrays.\nSimulation results demonstrate that the above CC and DL aided threshold\ndetection scheme can effectively mitigate the SPI of the ReRAM array and\nachieve better error rate performance than the prior art detection schemes,\nwithout the prior knowledge of the channel.\n']","[('random access memory', 0.5804340243339539), ('memory channel', 0.579330563545227), ('access memory', 0.46350109577178955), ('memory cells', 0.4144314229488373), ('memory', 0.3704271912574768), ('flash memory', 0.35904014110565186), ('detection decoding', 0.3504248857498169), ('random access', 0.345818430185318), ('decoding', 0.3245507776737213), ('dram', 0.2945820391178131)]"
1742,1742,16,1742_controlled stochastic_stochastic dynamical_stochastic flows_schr odinger bridge,"['controlled stochastic', 'stochastic dynamical', 'stochastic flows', 'schr odinger bridge', 'schr odinger bridges', 'stochastic adaptive', 'state stochastic', 'odinger bridges', 'optimal mass transport', 'odinger bridge']","['On the Contraction Coefficient of the Schr\\""odinger Bridge for\n  Stochastic Linear Systems   Schr\\""{o}dinger bridge is a stochastic optimal control problem to steer a\ngiven initial state density to another, subject to controlled diffusion and\ndeadline constraints. A popular method to numerically solve the Schr\\""{o}dinger\nbridge problems, in both classical and in the linear system settings, is via\ncontractive fixed point recursions. These recursions can be seen as dynamic\nversions of the well-known Sinkhorn iterations, and under mild assumptions,\nthey solve the so-called Schr\\""{o}dinger systems with guaranteed linear\nconvergence. In this work, we study a priori estimates for the contraction\ncoefficients associated with the convergence of respective Schr\\""{o}dinger\nsystems. We provide new geometric and control-theoretic interpretations for the\nsame. Building on these newfound interpretations, we point out the possibility\nof improved computation for the worst-case contraction coefficients of linear\nSBPs by preconditioning the endpoint support sets.\n', 'Weyl Calculus and Exactly Solvable Schr\\""{o}dinger Bridges with\n  Quadratic State Cost   Schr\\""{o}dinger bridge--a stochastic dynamical generalization of optimal mass\ntransport--exhibits a learning-control duality. Viewed as a stochastic control\nproblem, the Schr\\""{o}dinger bridge finds an optimal control policy that steers\na given joint state statistics to another while minimizing the total control\neffort subject to controlled diffusion and deadline constraints. Viewed as a\nstochastic learning problem, the Schr\\""{o}dinger bridge finds the most-likely\ndistribution-valued trajectory connecting endpoint distributional observations,\ni.e., solves the two point boundary-constrained maximum likelihood problem over\nthe manifold of probability distributions. Recent works have shown that solving\nthe Schr\\""{o}dinger bridge problem with state cost requires finding the Markov\nkernel associated with a reaction-diffusion PDE where the state cost appears as\na state-dependent reaction rate. We explain how ideas from Weyl calculus in\nquantum mechanics, specifically the Weyl operator and the Weyl symbol, can help\ndetermine such Markov kernels. We illustrate these ideas by explicitly finding\nthe Markov kernel for the case of quadratic state cost via Weyl calculus,\nrecovering our earlier results but avoiding tedious computation with Hermite\npolynomials.\n', 'Schr\\""{o}dinger Bridge with Quadratic State Cost is Exactly Solvable   Schr\\""{o}dinger bridge is a diffusion process that steers a given\ndistribution to another in a prescribed time while minimizing the effort to do\nso. It can be seen as the stochastic dynamical version of the optimal mass\ntransport, and has growing applications in generative diffusion models and\nstochastic optimal control. {\\black{We say a Schr\\""{o}dinger bridge is\n``exactly solvable\'\' if the associated uncontrolled Markov kernel is available\nin closed form, since then the bridge can be numerically computed using dynamic\nSinkhorn recursion for arbitrary endpoint distributions with finite second\nmoments.}} In this work, we propose a regularized variant of the\nSchr\\""{o}dinger bridge with a quadratic state cost-to-go that incentivizes the\noptimal sample paths to stay close to a nominal level.\n  Unlike the conventional Schr\\""{o}dinger bridge, the regularization induces a\nstate-dependent rate of killing and creation of probability mass, and its\nsolution requires determining the Markov kernel of a reaction-diffusion partial\ndifferential equation. We derive this Markov kernel in closed form,\n{\\black{showing that the regularized Schr\\""{o}dinger bridge is exactly\nsolvable, even for non-Gaussian endpoints. This advances the state-of-the-art\nbecause closed form Markov kernel for the regularized Schr\\""{o}dinger bridge is\navailable in existing literature only for Gaussian endpoints}}. Our solution\nrecovers the heat kernel in the vanishing regularization (i.e., diffusion\nwithout reaction) limit, thereby recovering the solution of the conventional\nSchr\\""{o}dinger bridge {\\black{as a special case}}. We deduce properties of the\nnew kernel and explain its connections with certain exactly solvable models in\nquantum mechanics.\n']","[('controlled stochastic', 0.5082800984382629), ('stochastic dynamical', 0.4862319529056549), ('stochastic flows', 0.47515869140625), ('schr odinger bridge', 0.4522477090358734), ('schr odinger bridges', 0.44819414615631104), ('stochastic adaptive', 0.4269828200340271), ('state stochastic', 0.4232994318008423), ('odinger bridges', 0.4121244549751282), ('optimal mass transport', 0.40619322657585144), ('odinger bridge', 0.40420469641685486)]"
1743,1743,16,1743_port hamiltonian formulation_port hamiltonian systems_port hamiltonian framework_port hamiltonian,"['port hamiltonian formulation', 'port hamiltonian systems', 'port hamiltonian framework', 'port hamiltonian', 'operator splitting methods', 'hamiltonian systems', 'hamiltonian framework', 'hamiltonian formulation', 'hamiltonian differential', 'operator splitting based']","['Operator Splitting Based Dynamic Iteration for Linear Port-Hamiltonian\n  Systems   A dynamic iteration scheme for linear differential-algebraic\nport-Hamil\\-tonian systems based on Lions-Mercier-type operator splitting\nmethods is developed. The dynamic iteration is monotone in the sense that the\nerror is decreasing and no stability conditions are required. The developed\niteration scheme is even new for linear port-Hamiltonian systems. The obtained\nalgorithm is applied to multibody systems and electrical networks.\n', 'Dynamic iteration schemes and port-Hamiltonian formulation in coupled\n  DAE circuit simulation   Electric circuits are usually described by charge- and flux-oriented modified\nnodal analysis. In this paper, we derive models as port-Hamiltonian systems on\nseveral levels: overall systems, multiply coupled systems and systems within\ndynamic iteration procedures. To this end, we introduce new classes of\nport-Hamiltonian differential-algebraic equations. Thereby, we additionally\nallow for nonlinear dissipation on a subspace of the state space. Both, each\nsubsystem and the overall system, possess a port-Hamiltonian structure. A\nstructural analysis is performed for the new setups. Dynamic iteration schemes\nare investigated and we show that the Jacobi approach as well as an adapted\nGauss-Seidel approach lead to port-Hamiltonian differential-algebraic\nequations.\n', 'Discrete gradient methods for port-Hamiltonian differential-algebraic equations Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient methods to the system class of nonlinear port-Hamiltonian differential-algebraic equations - as they emerge from the port- and energy-based modeling of physical systems in various domains. We introduce a novel numerical scheme tailored for semi-explicit differential-algebraic equations and further address more general settings using the concepts of discrete gradient pairs and Dirac-dissipative structures. Additionally, the behavior under system transformations is investigated and we demonstrate that under suitable assumptions port-Hamiltonian differential-algebraic equations admit a representation which consists of a parametrized port-Hamiltonian semi-explicit system and an unstructured equation. Finally, we present the application to multibody system dynamics and discuss numerical results to demonstrate the capabilities of our approach.']","[('port hamiltonian formulation', 0.6360611915588379), ('port hamiltonian systems', 0.621764600276947), ('port hamiltonian framework', 0.6051701903343201), ('port hamiltonian', 0.5376669764518738), ('operator splitting methods', 0.45868200063705444), ('hamiltonian systems', 0.44943785667419434), ('hamiltonian framework', 0.44455599784851074), ('hamiltonian formulation', 0.4433441758155823), ('hamiltonian differential', 0.40367984771728516), ('operator splitting based', 0.39898940920829773)]"
1744,1744,16,1744_weighted banach spaces_complex banach spaces_weighted bergman spaces_holomorphic mappings,"['weighted banach spaces', 'complex banach spaces', 'weighted bergman spaces', 'holomorphic mappings', 'complex banach space', 'space bounded holomorphic', 'banach valued', 'operators weak', 'banach spaces mathcal', 'holomorphic mapping']","['On composition ideals and dual ideals of bounded holomorphic mappings   Applying a linearization theorem due to J. Mujica, we study the ideals of\nbounded holomorphic mappings $\\mathcal{H}^\\infty\\circ\\mathcal{I}$ generated by\ncomposition with an operator ideal $\\mathcal{I}$. The bounded-holomorphic dual\nideal of $\\mathcal{I}$ is introduced and its elements are characterized as\nthose that admit a factorization through $\\mathcal{I}^\\mathrm{dual}$. For\ncomplex Banach spaces $E$ and $F$, we also analyze new ideals of bounded\nholomorphic mappings from an open subset $U\\subseteq E$ to $F$ such as\n$p$-integral holomorphic mappings and $p$-nuclear holomorphic mappings with\n$1\\leq p<\\infty$. We prove that every $p$-integral ($p$-nuclear) holomorphic\nmapping from $U$ to $F$ has relatively weakly compact (compact) range.\n', 'On p-summability in weighted Banach spaces of holomorphic functions   Given an open subset $U$ of a complex Banach space $E$, a weight $v$ on $U$,\nand a complex Banach space $F$, let $\\mathcal{H}^\\infty_v(U,F)$ denote the\nBanach space of all weighted holomorphic mappings $f\\colon U\\to F$, under the\nweighted supremum norm\n$\\left\\|f\\right\\|_v:=\\sup\\left\\{v(x)\\left\\|f(x)\\right\\|\\colon x\\in U\\right\\}$.\nIn this paper, we introduce and study the class\n$\\Pi_p^{\\mathcal{H}^\\infty_v}(U,F)$ of $p$-summing weighted holomorphic\nmappings. We prove that it is an injective Banach ideal of weighted holomorphic\nmappings which is not generated by composition. Variants for weighted\nholomorphic mappings of Pietsch Domination Theorem, Pietsch Factorization\nTheorem and Maurey Extrapolation Theorem are presented. We also identify the\nspaces of $p$-summing weighted holomorphic mappings from $U$ into $F^*$ under\nthe norm $\\pi^{\\mathcal{H}^\\infty_v}_p$ with the duals of $F$-valued\n$\\mathcal{H}^\\infty_v$-molecules on $U$ under a suitable version\n$d^{\\mathcal{H}^\\infty_v}_{p^*}$ of the Chevet--Saphar tensor norms.\n', ""On holomorphic mappings with relatively $p$-compact range   Related to the concept of $p$-compact operator with $p\\in [1,\\infty]$\nintroduced by Sinha and Karn, this paper deals with the space\n$\\mathcal{H}^\\infty_{\\mathcal{K}_p}(U,F)$ of all Banach-valued holomorphic\nmappings on an open subset $U$ of a complex Banach space $E$ whose ranges are\nrelatively $p$-compact subsets of $F$. We characterize such holomorphic\nmappings as those whose Mujica's linearisations on the canonical predual of\n$\\mathcal{H}^\\infty(U)$ are $p$-compact operators. This fact allows us to make\na complete study of them. We show that $\\mathcal{H}^\\infty_{\\mathcal{K}_p}$ is\na surjective Banach ideal of bounded holomorphic mappings which is generated by\ncomposition with the ideal of $p$-compact operators and contains the Banach\nideal of all right $p$-nuclear holomorphic mappings. We also characterize\nholomorphic mappings with relatively $p$-compact ranges as those bounded\nholomorphic mappings which factorize through a quotient space of $\\ell_{p^*}$\nor as those whose transposes are quasi $p$-nuclear operators (respectively,\nfactor through a closed subspace of $\\ell_p$).\n""]","[('weighted banach spaces', 0.597223699092865), ('complex banach spaces', 0.5850374698638916), ('weighted bergman spaces', 0.5737716555595398), ('holomorphic mappings', 0.5609186291694641), ('complex banach space', 0.552383303642273), ('space bounded holomorphic', 0.5382190942764282), ('banach valued', 0.5333874821662903), ('operators weak', 0.5252096056938171), ('banach spaces mathcal', 0.5170608162879944), ('holomorphic mapping', 0.5162610411643982)]"
1745,1745,16,1745_anderson_motivic galois_finitely generated module_motives,"['anderson', 'motivic galois', 'finitely generated module', 'motives', 'modules relations', 'motivic galois group', 'frobenius endomorphism', 'motives let', 'modules', 'abelian varieties']","['$h^1$, $h_1$ of Anderson t-motives, systems of affine equations and\n  non-commutative determinants   The authors defined in ""$h^1\\ne h_1$ for Anderson t-motives"" the notion of an\naffine equation associated to a t-motive $M$. Here we define two systems of\naffine equations associated to a t-motive $M$, used for calculation of $H^1(M)$\nand $H_1(M)$. We describe the process of elimination of unknowns in these\nsystems. This is an analog of the corresponding theory of systems of linear\ndifferential equations. It gives us a notion of a non-commutative determinant\n$det_{i,c}(M)$ which belongs to the Anderson ring $\\Bbb C_\\infty[T,\\tau]$ of\nnon-commutative polynomials. Finally, we calculate $det_{i,c}(M)$ for $M=$ a\nDrinfeld module or its 1-dual. Also, some explicit calculations are made for\nAnderson t-motives of dimension $n$, rank $2n$. Some problems of future\nresearch are formulated.\n', ""Non-abelian Anderson A-modules: Comparison isomorphisms and Galois\n  representations   In this manuscript, we consider non-abelian Anderson $A$-modules $E$ (of\ngeneric characteristic). The main results are on the structure of their\nmotives, and on comparison isomorphisms between their cohomological\nrealizations. In the center of these comparison isomorphisms, there is the\nspace of special functions $\\mathfrak{sf}(E)$ as defined by Gazda and the\nauthor in arXiv:1903.07302. We also provide a generalization of Anderson's\nresult on the equivalence of uniformizability of the Anderson module and rigid\nanalytic triviality of its associated motive.\n  We contribute results that are new even in the case of abelian Anderson\nmodules. For every non-zero prime ideal $\\mathfrak{p}$ of $A$, the relation of\nthe space of special functions to the $\\mathfrak{p}$-adic Tate module provides\na way to obtain $\\mathfrak{p}^{n+1}$-torsion as special values of\nhyperderivatives of these special functions. Using this result for\nuniformizable Anderson modules, we are able to describe the $\\mathfrak{p}$-adic\nGalois representation via a rigid analytic trivialization, and hence give a\ndirect link between the image of the $\\mathfrak{p}$-adic Galois representation\nand the motivic Galois group. This generalizes results of various authors.\n"", ""Pairing Anderson motives via formal residues in the Frobenius\n  endomorphism   Anderson modules form a generalization of Drinfeld modules and are commonly\nunderstood as the counterpart of abelian varieties but with function field\ncoefficients. In an attempt to study their ``motivic theory'', two objects of\nsemilinear algebra are attached to an Anderson module: its motive and its dual\nmotive. While the former is better suited to follow the analogy with\nGrothendieck motives, the latter has proven much useful in the study of\ntranscendence questions in positive characteristic. Despite sharing similar\ndefinitions, the relationship between motives and dual motives has remained\nnebulous. Over perfect fields, it was only proved recently by the second author\nthat the finite generation of the motive is equivalent to the finite generation\nof the dual motive, answering a long-standing open question in function field\narithmetic (the ``abelian equals $A$-finite'' theorem). This work constructs a\nperfect pairing among the motive and the dual motive of an Anderson module,\nwith values in a module of differentials, thus answering a question raised by\nHartl and Juschka. Our construction involves taking the residue of certain\nformal power series in the Frobenius endomorphism. Although it may seem\npeculiar, this pairing is natural and compatible with base change. It also\ncomes with several new consequences in function field arithmetic; for example,\nwe generalize the ``abelian equals A-finite'' theorem to a large class of\nalgebras, including fields, perfect algebras and noetherian regular domains.\n""]","[('anderson', 0.3809981942176819), ('motivic galois', 0.36407941579818726), ('finitely generated module', 0.36011096835136414), ('motives', 0.3595718741416931), ('modules relations', 0.35884958505630493), ('motivic galois group', 0.35530510544776917), ('frobenius endomorphism', 0.3451017737388611), ('motives let', 0.33906620740890503), ('modules', 0.3336632549762726), ('abelian varieties', 0.3240942656993866)]"
1746,1746,16,1746_von neumann algebras_von neumann algebra_neumann algebras_l_p spaces,"['von neumann algebras', 'von neumann algebra', 'neumann algebras', 'l_p spaces', 'non commutative spaces', 'noncommutative', 'operator spaces', 'neumann algebra', 'mathrm spaces', 'orlicz spaces']","['Positive contractive projections on noncommutative $\\mathrm{L}^p$-spaces\n  and nonassociative $\\mathrm{L}^p$-spaces   We continue our investigation of contractive projections on noncommutative\n$\\mathrm{L}^p$-spaces where $1 < p < \\infty$ started in \\cite{ArR19}. We\nimprove the results of \\cite{ArR19} and we characterize precisely the positive\ncontractive projections on a noncommutative $\\mathrm{L}^p$-space associated\nwith a $\\sigma$-finite von Neumann algebra. We connect this topic to the theory\nof $\\mathrm{JW}^*$-algebras. More precisely, in large cases, we are able to\nshow that the range of a positive contractive projection is isometric to a\nnonassociative $\\mathrm{L}^p$-space associated to a $\\mathrm{JW}^*$-algebra.\n', ""2-positive contractive projections on noncommutative\n  $\\mathrm{L}^p$-spaces   We prove the first theorem on projections on general noncommutative\n$\\mathrm{L}^p$-spaces associated with non-type I von Neumann algebras where $1\n\\leqslant p < \\infty$. This is the first progress on this topic since the\nseminal work of Arazy and Friedman [Memoirs AMS 1992] where the problem of the\ndescription of contractively complemented subspaces of noncommutative\n$\\mathrm{L}^p$-spaces is explicitly raised. We show that the range of a\n2-positive contractive projection on an arbitrary noncommutative\n$\\mathrm{L}^p$-space is completely order isometrically isomorphic to some\nnoncommutative $\\mathrm{L}^p$-space. This result is sharp and is even new for\nSchatten spaces $S^p$. Our approach relies on non-tracial Haagerup's\nnoncommutative $\\mathrm{L}^p$-spaces in an essential way, even in the case of a\nprojection acting on a Schatten space and is unrelated to the methods of Arazy\nand Friedman.\n"", 'Nonassociative $\\mathrm{L}^p$-spaces and embeddings in noncommutative\n  $\\mathrm{L}^p$-spaces   We define a notion of nonassociative $\\mathrm{L}^p$-space associated to a\n$\\mathrm{JBW}^*$-algebra (Jordan von Neumann algebra) equipped with a normal\nfaithful state $\\varphi$. In the particular case of $\\mathrm{JW}^*$-algebras\nunderlying von Neumann algebras, we connect these spaces to a complex\ninterpolation theorem of Ricard and Xu on noncommutative $\\mathrm{L}^p$-spaces.\nWe also make the link with the nonassociative $\\mathrm{L}^p$-spaces of Iochum\nassociated to $\\mathrm{JBW}$-algebras and the investigation of contractively\ncomplemented subspaces of noncommutative $\\mathrm{L}^p$-spaces. More precisely,\nwe show that our nonassociative $\\mathrm{L}^p$-spaces contain isometrically the\n$\\mathrm{L}^p$-spaces of Iochum and that all tracial nonassociative\n$\\mathrm{L}^p$-spaces from $\\mathrm{JW}^*$-factors arise as positively\ncontractively complemented subspaces of noncommutative $\\mathrm{L}^p$-spaces.\n']","[('von neumann algebras', 0.6105507016181946), ('von neumann algebra', 0.5499734282493591), ('neumann algebras', 0.5457562804222107), ('l_p spaces', 0.5199744701385498), ('non commutative spaces', 0.5058336853981018), ('noncommutative', 0.4988039433956146), ('operator spaces', 0.4765931963920593), ('neumann algebra', 0.47431623935699463), ('mathrm spaces', 0.44623249769210815), ('orlicz spaces', 0.41239088773727417)]"
1747,1747,16,1747_average approximation stochastic_stochastic programs_stochastic approximation_stochastic programming,"['average approximation stochastic', 'stochastic programs', 'stochastic approximation', 'stochastic programming', 'approximation stochastic', 'stage stochastic programs', 'stochastic program', 'stochastic variational inequalities', 'risk averse stochastic', 'averse stochastic']","['Concentration inequalities for locally small increments of compound\n  empirical processes with applications to solutions of compound and risk\n  averse stochastical programming   The paper deals with concentration inequalities for locally small increments\nof compound empirical processes. In the asymptotic theory of $m$-estimation\nsuch inequalities play an essential role in deriving convergence rates for\nsolutions of the sample average approximation method to solve compound\nstochastic programs, and in particular for $m$-estimators. We develop\ninequalities dependent on the sample sizes with explicit terms instead of\nunspecified universal constants. They are applied to study the Sample Average\nApproximation method for compound stochastic programs. Nonasymptotic upper\nestimates for the deviation probabilities of the optimal solutions are derived\nwhich are dependent on the sample sizes. They allow to conclude immediately\nconvergence rates for the optimal solutions. In the special case of classical\nrisk neutral stochastic programs, we end up with upper estimates of deviation\nprobabilities for $m$-estimators, and their convergence rates. Moreover, we may\nalso demonstrate how to apply the results to sample average approximation of\nrisk averse stochastic programs. In this respect we consider stochastic\nprograms expressed in terms of absolute semideviations and Average Value at\nRisk. The investigations are based on concentration inequalities from the\nrecent contribution Kratschmer(2024).\n', 'First order asymptotics of the sample average approximation method to\n  solve risk averse stochastic progams   We investigate statistical properties of the optimal value of the Sample\nAverage Approximation of stochastic programs, continuing the study in\nKr\\""atschmer (2023). Central Limit Theorem type results are derived for the\noptimal value. As a crucial point the investigations are based on a new type of\nconditions from the theory of empirical processes which do not rely on pathwise\nanalytical properties of the goal functions. In particular, continuity in the\nparameter is not imposed in advance as usual in the literature on the Sample\nAverage Approximation method. It is also shown that the new condition is\nsatisfied if the paths of the goal functions are H\\""older continuous so that\nthe main results carry over in this case. Moreover, the main results are\napplied to goal functions whose paths are piecewise H\\""older continuous as e.g.\nin two stage mixed-integer programs. The main results are shown for classical\nrisk neutral stochastic programs, but we also demonstrate how to apply them to\nthe Sample Average Approximation of risk averse stochastic programs. In this\nrespect we consider stochastic programs expressed in terms of absolute\nsemideviations and divergence risk measures.\n', 'Nonasymptotic upper estimates for errors of the sample average\n  approximation method to solve risk averse stochastic programs   We study statistical properties of the optimal value of the Sample Average\nApproximation. The focus is on the tail function of the absolute error induced\nby the Sample Average Approximation, deriving upper estimates of its outcomes\ndependent on the sample size. The estimates allow to conclude immediately\nconvergence rates for the optimal value of the Sample Average Approximation. As\na crucial point the investigations are based on a new type of conditions from\nthe theory of empirical processes which do not rely on pathwise analytical\nproperties of the goal functions. In particular, continuity in the parameter is\nnot imposed in advance as often in the literature on the Sample Average\nApproximation method. It is also shown that the new condition is satisfied if\nthe paths of the goal functions are H\\""older continuous so that the main\nresults carry over in this case. Moreover, the main results are applied to goal\nfunctions whose paths are piecewise H\\""older continuous as e.g. in two stage\nmixed-integer programs. The main results are shown for classical risk neutral\nstochastic programs, but we also demonstrate how to apply them to the sample\naverage approximation of risk averse stochastic programs. In this respect we\nconsider stochastic programs expressed in terms of mean upper semideviations\nand divergence risk measures.\n']","[('average approximation stochastic', 0.6351161003112793), ('stochastic programs', 0.6279926896095276), ('stochastic approximation', 0.5992236733436584), ('stochastic programming', 0.595189094543457), ('approximation stochastic', 0.5843650102615356), ('stage stochastic programs', 0.5742368102073669), ('stochastic program', 0.5735443234443665), ('stochastic variational inequalities', 0.5646611452102661), ('risk averse stochastic', 0.5293074250221252), ('averse stochastic', 0.5036018490791321)]"
1748,1748,16,1748_energy saving_energy management_parallel hybrid_energy management system,"['energy saving', 'energy management', 'parallel hybrid', 'energy management system', 'fuel consumption', 'optimization power', 'hybrid', 'control energy', 'energy storage', 'electric vehicles']","[""Convex Optimization for Fuel Cell Hybrid Trains: Speed, Energy\n  Management System, and Battery Thermals   We optimize the operation of a fuel cell hybrid train using convex\noptimization. The main objective is to minimize hydrogen fuel consumption for a\ntarget journey time while considering battery thermal constraints. The state\ntrajectories: train speed, energy management system, and battery temperature,\nare all optimized concurrently within a single optimization problem. A novel\nthermal model is proposed in order to include battery temperature yet maintain\nformulation convexity. Simulations show fuel savings and better thermal\nmanagement when temperature is optimized concurrently with the other states\nrather than sequentially -- separately afterwards. The fuel reduction is caused\nby reduced cooling effort which is motivated by the formulation's awareness of\nactive cooling energy consumption. The benefit is more pronounced for warmer\nambient temperatures that require more cooling.\n"", 'Integrated Optimization of Power Split, Engine Thermal Management, and\n  Cabin Heating for Hybrid Electric Vehicles   Cabin heating demand and engine efficiency degradation in cold weather lead\nto considerable increase in fuel consumption of hybrid electric vehicles\n(HEVs), especially in congested traffic conditions. This paper presents an\nintegrated power and thermal management (i-PTM) scheme for the optimization of\npower split, engine thermal management, and cabin heating of HEVs. A\ncontrol-oriented model of a power split HEV, including power and thermal loops,\nis developed and experimentally validated against data collected from a 2017\nToyota Prius HEV. Based on this model, the dynamic programming (DP) technique\nis adopted to derive a bench-mark for minimal fuel consumption, using\n2-dimensional (power split and engine thermal management) and 3-dimensional\n(power split, engine thermal management, and cabin heating) formulations.\nSimulation results for a real-world congested driving cycle show that the\nengine thermal effect and the cabin heating requirement can significantly\ninfluence the optimal behavior for the power management, and substantial\npotential on fuel saving can be achieved by the i-PTM optimization as compared\nto conventional power and thermal management strategies.\n', 'Experimental Validation of Eco-Driving and Eco-Heating Strategies for\n  Connected and Automated HEVs   This paper presents experimental results that validate eco-driving and\neco-heating strategies developed for connected and automated vehicles (CAVs).\nBy exploiting vehicle-to-infrastructure (V2I) communications, traffic signal\ntiming, and queue length estimations, optimized and smoothed speed profiles for\nthe ego-vehicle are generated to reduce energy consumption. Next, the planned\neco-trajectories are incorporated into a real-time predictive optimization\nframework that coordinates the cabin thermal load (in cold weather) with the\nspeed preview, i.e., eco-heating. To enable eco-heating, the engine coolant (as\nthe only heat source for cabin heating) and the cabin air are leveraged as two\nthermal energy storages. Our eco-heating strategy stores thermal energy in the\nengine coolant and cabin air while the vehicle is driving at high speeds, and\nreleases the stored energy slowly during the vehicle stops for cabin heating\nwithout forcing the engine to idle to provide the heating source. To test and\nvalidate these solutions, a power-split hybrid electric vehicle (HEV) has been\ninstrumented for cabin thermal management, allowing to regulate heating,\nventilation, and air conditioning (HVAC) system inputs (cabin temperature\nsetpoint and blower flow rate) in real-time. Experiments were conducted to\ndemonstrate the energy-saving benefits of eco-driving and eco-heating\nstrategies over real-world city driving cycles at different cold ambient\ntemperatures. The data confirmed average fuel savings of 14.5% and 4.7%\nachieved by eco-driving and eco-heating, respectively, offering a combined\nenergy saving of more than 19% when comparing to the baseline vehicle driven by\na human driver with a constant-heating strategy.\n']","[('energy saving', 0.42812633514404297), ('energy management', 0.419426828622818), ('parallel hybrid', 0.3976166546344757), ('energy management system', 0.3919239938259125), ('fuel consumption', 0.3879653215408325), ('optimization power', 0.37459561228752136), ('hybrid', 0.3725363314151764), ('control energy', 0.3691950738430023), ('energy storage', 0.3671638071537018), ('electric vehicles', 0.3488844931125641)]"
1749,1749,16,1749_stochastic cahn hilliard_numerical approximation stochastic_stochastic cahn_numerical methods stochastic,"['stochastic cahn hilliard', 'numerical approximation stochastic', 'stochastic cahn', 'numerical methods stochastic', 'approximation stochastic', 'limit stochastic', 'noise diffusion', 'scheme stochastic', 'strong convergence rates', 'galerkin temporal']","['Improved estimates for the sharp interface limit of the stochastic\n  Cahn-Hilliard equation with space-time white noise   We study the sharp interface limit of the stochastic Cahn-Hilliard equation\nwith cubic double-well potential and additive space-time white noise\n$\\epsilon^{\\sigma}\\dot{W}$ where $\\epsilon>0$ is an interfacial width\nparameter. We prove that, for sufficiently large scaling constant $\\sigma >0$,\nthe stochastic Cahn-Hilliard equation converges to the deterministic\nMullins-Sekerka/Hele-Shaw problem for $\\epsilon\\rightarrow 0$. The convergence\nis shown in suitable fractional Sobolev norms as well as in the $L^p$-norm for\n$p\\in (2, 4]$ in spatial dimension $d=2,3$. This generalizes the existing\nresult for the space-time white noise to dimension $d=3$ and improves the\nexisting results for smooth noise, which were so far limited to $p\\in \\left(2,\n\\frac{2d+8}{d+2}\\right]$ in spatial dimension $d=2,3$. As a byproduct of the\nanalysis of the stochastic problem with space-time white noise, we identify\nminimal regularity requirements on the noise which allow convergence to the\nsharp interface limit in the $\\mathbb{H}^1$-norm and also provide improved\nconvergence estimates for the sharp interface limit of the deterministic\nproblem.\n', 'Absolute continuity and numerical approximation of stochastic\n  Cahn--Hilliard equation with unbounded noise diffusion   In this article, we develop and analyze a full discretization, based on the\nspatial spectral Galerkin method and the temporal drift implicit Euler scheme,\nfor the stochastic Cahn--Hilliard equation driven by multiplicative space-time\nwhite noise. By introducing an appropriate decomposition of the numerical\napproximation, we first use the factorization method to deduce the a priori\nestimate and regularity estimate of the proposed full discretization. With the\nhelp of the variation approach, we then obtain the sharp spatial and temporal\nconvergence rate in negative Sobolev space in mean square sense. Furthermore,\nthe sharp mean square convergence rates in both time and space are derived via\nthe Sobolev interpolation inequality and semigroup theory. To the best of our\nknowledge, this is the first result on the convergence rate of temporally and\nfully discrete numerical methods for the stochastic Cahn--Hilliard equation\ndriven by multiplicative space-time white noise.\n', 'Numerical approximation of the stochastic Cahn-Hilliard equation with\n  space-time white noise near the sharp interface limit   We consider the stochastic Cahn-Hilliard equation with additive space-time\nwhite noise $\\epsilon^{\\gamma}\\dot{W}$ in dimension $d=2,3$, where $\\epsilon>0$\nis an interfacial width parameter. We study numerical approximation of the\nequation which combines a structure preserving implicit time-discretization\nscheme with a discrete approximation of the space-time white noise. We derive a\nstrong error estimate for the considered numerical approximation which is\nrobust with respect to the inverse of the interfacial width parameter\n$\\epsilon$. Furthermore, by a splitting approach, we show that for sufficiently\nlarge scaling parameter $\\gamma$, the numerical approximation of the stochastic\nCahn-Hilliard equation converges uniformly to the deterministic\nHele-Shaw/Mullins-Sekerka problem in the sharp interface limit\n$\\epsilon\\rightarrow 0$.\n']","[('stochastic cahn hilliard', 0.67350834608078), ('numerical approximation stochastic', 0.5964006185531616), ('stochastic cahn', 0.5786569118499756), ('numerical methods stochastic', 0.5732355713844299), ('approximation stochastic', 0.5291284322738647), ('limit stochastic', 0.4924045503139496), ('noise diffusion', 0.4920254349708557), ('scheme stochastic', 0.42386746406555176), ('strong convergence rates', 0.41937631368637085), ('galerkin temporal', 0.4130724370479584)]"
1750,1750,16,1750_integer partitions_hook lengths_regular partitions_distinct partitions,"['integer partitions', 'hook lengths', 'regular partitions', 'distinct partitions', 'partitions distinct parts', 'partition maximum', 'restricted partitions', 'partitions', 'partitions distinct', 'hook length']","[""Hook length biases and general linear partition inequalities   Motivated in part by hook-content formulas for certain restricted partitions\nin representation theory, we consider the total number of hooks of fixed length\nin odd versus distinct partitions. We show that there are more hooks of length\n$2$, respectively $3$, in all odd partitions of $n$ than in all distinct\npartitions of $n$, and make the analogous conjecture for arbitrary hook length\n$t \\geq 2$. We also establish additional bias results on the number of gaps of\nsize $1,$ respectively $2$, in all odd versus distinct partitions of $n$. We\nconjecture similar biases and asymptotics, as well as congruences for the\nnumber of hooks of fixed length in odd distinct partitions versus\nself-conjugate partitions.\n  An integral component of the proof of our bias result for hooks of length $3$\nis a linear inequality involving $q(n)$, the number of distinct partitions of\n$n$. In this article we also establish effective linear inequalities for $q(n)$\nin great generality, a result which is of independent interest.\n  Our methods are both analytic and combinatorial, and our results and\nconjectures intersect the areas of representation theory, analytic number\ntheory, partition theory, and $q$-series. In particular, we use a\nRademacher-type exact formula for $q(n),$ Wright's circle method, modularity,\n$q$-series transformations, asymptotic methods, and combinatorial arguments.\n"", 'Inequalities and asymptotics for hook lengths in $\\ell$-regular\n  partitions and $\\ell$-distinct partitions   In this article, we study hook lengths in $\\ell$-regular partitions and\n$\\ell$-distinct partitions. More precisely, we establish hook length\ninequalities between $\\ell$-regular partitions and $\\ell$-distinct partitions\nfor hook lengths $2$ and $3$, by deriving asymptotic formulas for the total\nnumber of hooks of length $t$ in both partition classes, for $t = 1, 2, 3$.\nFrom these asymptotics, we show that the ratio of the total number of hooks of\nlength $t$ in $\\ell$-regular partitions to those in $\\ell$-distinct partitions\ntends to a constant that depends on $\\ell$ and $t$. We also provide hook length\ninequalities within $\\ell$-regular partitions and within $\\ell$-distinct\npartitions.\n', 'Hook length biases in ordinary and $t$-regular partitions   In this article, we study hook lengths of ordinary partitions and $t$-regular\npartitions. We establish hook length biases for the ordinary partitions and\nmotivated by them we find a few interesting hook length biases in $2$-regular\npartitions. For a positive integer $k$, let $p_{(k)}(n)$ denote the number of\nhooks of length $k$ in all the partitions of $n$. We prove that $p_{(k)}(n)\\geq\np_{(k+1)}(n)$ for all $n\\geq0$ and $n\\ne k+1$; and $p_{(k)}(k+1)-\np_{(k+1)}(k+1)=-1$ for $k\\geq 2$. For integers $t\\geq2$ and $k\\geq1$, let\n$b_{t,k}(n)$ denote the number of hooks of length $k$ in all the $t$-regular\npartitions of $n$. We find generating functions of $b_{t,k}(n)$ for certain\nvalues of $t$ and $k$. Exploring hook length biases for $b_{t,k}(n)$, we\nobserve that in certain cases biases are opposite to the biases for ordinary\npartitions. We prove that $b_{2,2}(n)\\geq b_{2,1}(n)$ for all $n>4$, whereas\n$b_{2,2}(n)\\geq b_{2,3}(n)$ for all $n\\geq 0$. We also propose some conjectures\non biases among $b_{t,k}(n)$.\n']","[('integer partitions', 0.49128615856170654), ('hook lengths', 0.4671398401260376), ('regular partitions', 0.4657852053642273), ('distinct partitions', 0.46499520540237427), ('partitions distinct parts', 0.46202191710472107), ('partition maximum', 0.4615422487258911), ('restricted partitions', 0.4553987979888916), ('partitions', 0.45320144295692444), ('partitions distinct', 0.4497261047363281), ('hook length', 0.436176061630249)]"
1751,1751,16,1751_gamma lattice_space lattices_dense orbits_periodic tori,"['gamma lattice', 'space lattices', 'dense orbits', 'periodic tori', 'gamma torsion free', 'measure equidistribution', 'moduli space rank', 'irreducible lattice', 'sl _3 mathbb', 'sl _2 mathbb']","['Equidistribution of lattice orbits in the space of homothety classes of\n  rank $2$ sublattices in $\\mathbb R^3$   We study the distribution of orbits of a lattice\n$\\Gamma\\leq\\text{SL}(3,\\mathbb R)$ in the moduli space $X_{2,3}$ of covolume\none rank-two discrete subgroups in $\\mathbb R^3$. Each orbit is dense, and our\nmain result is the limiting distribution of these orbits with respect to norm\nballs, where the norm is given by the sum of squares. Specifically, we consider\n$\\Gamma_T=\\{\\gamma\\in\\Gamma:\\|\\gamma\\|\\leq T\\}$ and show that, for any fixed\n$x_0\\in X_{2,3}$ and $\\varphi\\in C_c(X_{2,3})$,\n$$\\lim_{T\\to\\infty}\\frac{1}{\\#\\Gamma_T}\\sum_{\\gamma\\in\\Gamma_T}\\varphi(x_0\\cdot\\gamma)=\\int_{X_{2,3}}\\varphi(x)d\n\\tilde\\nu_{x_0}(x),$$ where $\\tilde\\nu_{x_0}$ is an explicit probability\nmeasure on $X_{2,3}$ depending on $x_0$. To prove our result, we use the\nduality principle developed by Gorodnik and Weiss which recasts the above\nproblem into the problem of computation of certain volume estimates of growing\nskewed balls in $H$ and proving ergodic theorems of the left action of the\nskewed balls on $\\text{SL}(3,\\mathbb{R})/\\Gamma$. The ergodic theorems are\nproven by applying theorems of Shah building on the linearisation technique.\nThe main contribution of the paper is the application of the duality principle\nin the case where $H$ has infinitely many non-compact connected components.\n', 'Equidistribution in the space of 3-lattices and Dirichlet-improvable\n  vectors on planar lines   Let $X=\\text{SL}_3(\\mathbb{R})/\\text{SL}_3(\\mathbb{Z})$, and\n$g_t=\\text{diag}(e^{2t}, e^{-t}, e^{-t})$. Let $\\nu$ denote the push-forward of\nthe normalized Lebesgue measure on a segment of a straight line in the\nexpanding horosphere of $\\{g_t\\}_{t>0}$, under the map $h\\mapsto\nh\\text{SL}_3(\\mathbb{Z})$ from $\\text{SL}_3(\\mathbb{R})$ to $X$. We give\nexplicit necessary and sufficient Diophantine conditions on the line for\nequidistribution of each of the following families of measures on $X$:\n  (1) $g_t$-translates of $\\nu$ as $t\\to\\infty$.\n  (2) averages of $g_t$-translates of $\\nu$ over $t\\in[0,T]$ as $T\\to\\infty$.\n  (3) $g_{t_i}$-translates of $\\nu$ for some $t_i\\to\\infty$.\n  We apply this dynamical result to show that Lebesgue-almost every point on\nthe planar line $y=ax+b$ is not Dirichlet-improvable if and only if\n$(a,b)\\notin\\mathbb{Q}^2$.\n', ""Equidistribution of polynomially bounded o-minimal curves in homogeneous\n  spaces   We extend Ratner's theorem on equidistribution of individual orbits of\nunipotent flows on finite volume homogeneous spaces of Lie groups to\ntrajectories of non-contracting curves definable in polynomially bounded\no-minimal structures.\n  To be precise, let $\\varphi:[0,\\infty)\\to \\text{SL}(n,\\mathbb R)$ be a\ncontinuous map whose coordinate functions are definable in a polynomially\nbounded o-minimal structure; for example, rational functions. Suppose that\n$\\varphi$ is non-contracting; that is, for any linearly independent vectors\n$v_1,\\ldots,v_k$ in $\\mathbb R^n$, $\\varphi(t).(v_1\\wedge\\cdots\\wedge\nv_k)\\not\\to0$ as $t\\to\\infty$. Then, there exists a unique smallest subgroup\n$H_\\varphi$ of $\\text{SL}(n,\\mathbb R)$ generated by unipotent one-parameter\nsubgroups such that $\\varphi(t)H_\\varphi\\to g_0H_\\varphi$ in\n$\\text{SL}(n,\\mathbb R)/H_\\varphi$ as $t\\to\\infty$ for some $g_0\\in\n\\text{SL}(n,\\mathbb R)$.\n  Let $G$ be a closed subgroup of $\\text{SL}(n,\\mathbb R)$ and $\\Gamma$ be a\nlattice in $G$. Suppose that $\\varphi([0,\\infty))\\subset G$. Then\n$H_\\varphi\\subset G$, and for any $x\\in G/\\Gamma$, the trajectory\n$\\{\\varphi(t)x:t\\in [0,T]\\}$ gets equidistributed with respect to the measure\n$g_0\\mu_{Lx}$ as $T\\to\\infty$, where $L$ is a closed subgroup of $G$ such that\n$\\overline{Hx}=Lx$ and $Lx$ admits a unique $L$-invariant probability measure,\ndenoted by $\\mu_{Lx}$.\n  A crucial new ingredient in this work is proving that for any\nfinite-dimensional representation $V$ of $\\text{SL}(n,\\mathbb R)$, there exist\n$T_0>0$, $C>0$, and $\\alpha>0$ such that for any $v\\in G$, the map $t\\mapsto\n\\|\\varphi(t)v\\|$ is $(C,\\alpha)$-good on $[T_0,\\infty)$.\n""]","[('gamma lattice', 0.42924025654792786), ('space lattices', 0.39786574244499207), ('dense orbits', 0.39339959621429443), ('periodic tori', 0.3693391680717468), ('gamma torsion free', 0.34996867179870605), ('measure equidistribution', 0.34235528111457825), ('moduli space rank', 0.33306169509887695), ('irreducible lattice', 0.3328477442264557), ('sl _3 mathbb', 0.3319586217403412), ('sl _2 mathbb', 0.3250117003917694)]"
1752,1752,16,1752_locally compact groups_locally compact group_compact groups_compact subgroups,"['locally compact groups', 'locally compact group', 'compact groups', 'compact subgroups', 'compact group', 'groups locally', 'subgroups locally', 'disconnected locally compact', 'compact abelian groups', 'compact totally disconnected']","['A new lattice invariant for lattices in totally disconnected locally\n  compact groups   We introduce and explore a natural rank for totally disconnected locally\ncompact groups called the bounded conjugacy rank. This rank is shown to be a\nlattice invariant for lattices in sigma compact totally disconnected locally\ncompact groups; that is to say, for a given sigma compact totally disconnected\nlocally compact group, some lattice has bounded conjugacy rank n if and only if\nevery lattice has bounded conjugacy rank n. Several examples are then\npresented.\n', 'Approximating simple locally compact groups by their dense locally\n  compact subgroups   The class, denoted by $\\mathscr{S}$, of totally disconnected locally compact\ngroups which are non-discrete, compactly generated, and topologically simple\ncontains many compelling examples. In recent years, a general theory for these\ngroups, which studies the interaction between the compact open subgroups and\nthe global structure, has emerged. In this article, we study the non-discrete\ntotally disconnected locally compact groups $H$ that admit a continuous\nembedding with dense image into some $G\\in \\mathscr{S}$; that is, we consider\nthe dense locally compact subgroups of groups $G\\in \\mathscr{S}$. We identify a\nclass $\\mathscr{R}$ of almost simple groups which properly contains\n$\\mathscr{S}$ and is moreover stable under passing to a non-discrete dense\nlocally compact subgroup. We show that $\\mathscr{R}$ enjoys many of the same\nproperties previously obtained for $\\mathscr{S}$ and establish various original\nresults for $\\mathscr{R}$ that are also new for the subclass $\\mathscr{S}$,\nnotably concerning the structure of the local Sylow subgroups and the full\nautomorphism group.\n', 'A totally disconnected invitation to locally compact groups   We present a selection of results contributing to a structure theory of\ntotally disconnected locally compact groups.\n']","[('locally compact groups', 0.8007674217224121), ('locally compact group', 0.7662967443466187), ('compact groups', 0.7212751507759094), ('compact subgroups', 0.6777799725532532), ('compact group', 0.6604048013687134), ('groups locally', 0.6563451290130615), ('subgroups locally', 0.5977137088775635), ('disconnected locally compact', 0.5961441993713379), ('compact abelian groups', 0.5894337296485901), ('compact totally disconnected', 0.5690297484397888)]"
1753,1753,16,1753_converges nash equilibrium_converges nash_matrix games_zero sum games,"['converges nash equilibrium', 'converges nash', 'matrix games', 'zero sum games', 'convergence learning', 'regret bounds', 'learning stable', 'general sum games', 'regret learning', 'multi agent learning']","['Tight last-iterate convergence rates for no-regret learning in\n  multi-player games   We study the question of obtaining last-iterate convergence rates for\nno-regret learning algorithms in multi-player games. We show that the\noptimistic gradient (OG) algorithm with a constant step-size, which is\nno-regret, achieves a last-iterate rate of $O(1/\\sqrt{T})$ with respect to the\ngap function in smooth monotone games. This result addresses a question of\nMertikopoulos & Zhou (2018), who asked whether extra-gradient approaches (such\nas OG) can be applied to achieve improved guarantees in the multi-agent\nlearning setting. The proof of our upper bound uses a new technique centered\naround an adaptive choice of potential function at each iteration. We also show\nthat the $O(1/\\sqrt{T})$ rate is tight for all $p$-SCLI algorithms, which\nincludes OG as a special case. As a byproduct of our lower bound analysis we\nadditionally present a proof of a conjecture of Arjevani et al. (2015) which is\nmore direct than previous approaches.\n', 'Finite-Time Last-Iterate Convergence for Multi-Agent Learning in Games   In this paper, we consider multi-agent learning via online gradient descent\nin a class of games called $\\lambda$-cocoercive games, a fairly broad class of\ngames that admits many Nash equilibria and that properly includes unconstrained\nstrongly monotone games. We characterize the finite-time last-iterate\nconvergence rate for joint OGD learning on $\\lambda$-cocoercive games; further,\nbuilding on this result, we develop a fully adaptive OGD learning algorithm\nthat does not require any knowledge of problem parameter (e.g. cocoercive\nconstant $\\lambda$) and show, via a novel double-stopping time technique, that\nthis adaptive algorithm achieves same finite-time last-iterate convergence rate\nas non-adaptive counterpart. Subsequently, we extend OGD learning to the noisy\ngradient feedback case and establish last-iterate convergence results -- first\nqualitative almost sure convergence, then quantitative finite-time convergence\nrates -- all under non-decreasing step-sizes. To our knowledge, we provide the\nfirst set of results that fill in several gaps of the existing multi-agent\nonline learning literature, where three aspects -- finite-time convergence\nrates, non-decreasing step-sizes, and fully adaptive algorithms have been\nunexplored before.\n', 'On Separation Between Best-Iterate, Random-Iterate, and Last-Iterate\n  Convergence of Learning in Games   Non-ergodic convergence of learning dynamics in games is widely studied\nrecently because of its importance in both theory and practice. Recent work\n(Cai et al., 2024) showed that a broad class of learning dynamics, including\nOptimistic Multiplicative Weights Update (OMWU), can exhibit arbitrarily slow\nlast-iterate convergence even in simple $2 \\times 2$ matrix games, despite many\nof these dynamics being known to converge asymptotically in the last iterate.\nIt remains unclear, however, whether these algorithms achieve fast non-ergodic\nconvergence under weaker criteria, such as best-iterate convergence. We show\nthat for $2\\times 2$ matrix games, OMWU achieves an $O(T^{-1/6})$ best-iterate\nconvergence rate, in stark contrast to its slow last-iterate convergence in the\nsame class of games. Furthermore, we establish a lower bound showing that OMWU\ndoes not achieve any polynomial random-iterate convergence rate, measured by\nthe expected duality gaps across all iterates. This result challenges the\nconventional wisdom that random-iterate convergence is essentially equivalent\nto best-iterate convergence, with the former often used as a proxy for\nestablishing the latter. Our analysis uncovers a new connection to dynamic\nregret and presents a novel two-phase approach to best-iterate convergence,\nwhich could be of independent interest.\n']","[('converges nash equilibrium', 0.5571871995925903), ('converges nash', 0.5298025608062744), ('matrix games', 0.5160300135612488), ('zero sum games', 0.496856153011322), ('convergence learning', 0.46746495366096497), ('regret bounds', 0.46045804023742676), ('learning stable', 0.4594334065914154), ('general sum games', 0.45147615671157837), ('regret learning', 0.44421088695526123), ('multi agent learning', 0.4355875551700592)]"
1754,1754,16,1754_finsler manifolds_riemannian finsler_finsler manifold_finsler metric,"['finsler manifolds', 'riemannian finsler', 'finsler manifold', 'finsler metric', 'ricci curvature bounds', 'ricci curvature bound', 'ricci curvature bounded', 'manifolds nonnegative ricci', 'weighted ricci curvature', 'curvature bounds']","[""Sufficient criteria for obtaining Hardy inequalities on Finsler\n  manifolds   We establish Hardy inequalities involving a weight function on complete, not\nnecessarily reversible Finsler manifolds. We prove that the superharmonicity of\nthe weight function provides a sufficient condition to obtain Hardy\ninequalities. Namely, if $\\rho$ is a nonnegative function and\n$-\\boldsymbol{\\Delta} \\rho \\geq 0$ in weak sense, where $\\boldsymbol{\\Delta}$\nis the Finsler-Laplace operator defined by $ \\boldsymbol{\\Delta} \\rho =\n\\mathrm{div}(\\boldsymbol{\\nabla} \\rho)$, then we obtain the generalization of\nsome Riemannian Hardy inequalities given in D'Ambrosio and Dipierro (Ann. Inst.\nH. Poincar\\'e, 2013).\n  By extending the results obtained, we prove a weighted Caccioppoli-type\ninequality, a Gagliardo-Nirenberg inequality and a Heisenberg-Pauli-Weyl\nuncertainty principle on complete Finsler manifolds. Furthermore, we present\nsome Hardy inequalities on Finsler-Hadamard manifolds with finite reversibility\nconstant, by defining the weight function with the help of the distance\nfunction. Finally, we extend a weighted Hardy-inequality to a class of Finsler\nmanifolds of bounded geometry.\n"", 'A semigroup approach to Finsler geometry: Bakry-Ledoux\'s isoperimetric\n  inequality   We develop the celebrated semigroup approach \\`a la Bakry et al on Finsler\nmanifolds, where natural Laplacian and heat semigroup are nonlinear, based on\nthe Bochner-Weitzenb\\""ock formula established by Sturm and the author. We show\nthe $L^1$-gradient estimate on Finsler manifolds (under some additional\nassumptions in the noncompact case), which is equivalent to a lower weighted\nRicci curvature bound and the improved Bochner inequality. As a geometric\napplication, we prove Bakry-Ledoux\'s Gaussian isoperimetric inequality, again\nunder some additional assumptions in the noncompact case. This extends\nCavalletti-Mondino\'s inequality on reversible Finsler manifolds to\nnon-reversible metrics, and improves the author\'s previous estimate, both based\non the localization (also called needle decomposition) method.\n', ""Some inequalities on Finsler manifolds with weighted Ricci curvature\n  bounded below   We establish some important inequalities under a lower weighted Ricci\ncurvature bound on Finsler manifolds. Firstly, we establish a relative volume\ncomparison of Bishop-Gromov type. As one of the applications, we obtain an\nupper bound for volumes of the Finsler manifolds. Further, when the S-curvature\nis bounded on the whole manifold, we obtain a theorem of Bonnet-Myers type on\nFinsler manifolds. Finally, we obtain a sharp Poincar\\'{e}-Lichnerowicz\ninequality by using integrated Bochner inequality, from which we obtain a sharp\nlower bound for the first eigenvalue on the Finsler manifolds.\n""]","[('finsler manifolds', 0.6830241084098816), ('riemannian finsler', 0.6825569272041321), ('finsler manifold', 0.6716024279594421), ('finsler metric', 0.6663026809692383), ('ricci curvature bounds', 0.6416893005371094), ('ricci curvature bound', 0.6347506046295166), ('ricci curvature bounded', 0.6330843567848206), ('manifolds nonnegative ricci', 0.5794348120689392), ('weighted ricci curvature', 0.5719615817070007), ('curvature bounds', 0.569411039352417)]"
1755,1755,16,1755_graph algebras_algebras brauer_graph algebra_symmetric algebras,"['graph algebras', 'algebras brauer', 'graph algebra', 'symmetric algebras', 'algebras symmetric', 'algebra associated', 'algebras type', 'algebras coincides', 'class algebras called', 'algebras called']","['Skew-Brauer graph algebras   In this work, we introduce a new class of algebras called skew-Brauer graph\nalgebras, which generalize the well-known Brauer graph algebras. We establish\nthat skew-Brauer graph algebras are symmetric and can be defined using a Brauer\ngraph with additional information. We show that the class of trivial extensions\nof skew-gentle algebras coincides with a subclass of skew-Brauer graph\nalgebras, where the associated skew-Brauer graph has multiplicity function\nidentically equal to one, generalizing a result over gentle algebras. We also\ncharacterize skew-Brauer algebras of finite representation type. Finally, we\nprovide a geometric interpretation of cut-sets and reflections of algebras\nusing orbifold dissections.\n', 'Generalized Kauer moves and derived equivalences of Brauer graph\n  algebras   Kauer moves are local moves of an edge in a Brauer graph that yield derived\nequivalences between Brauer graph algebras [Kau98]. These derived equivalences\nmay be interpreted in terms of silting mutations. In this paper, we generalize\nthe notion of Kauer moves to any finite number of edges. Their construction is\nbased on cutting and pasting actions on the Brauer graph. To define these\nactions, we use an alternative definition of Brauer graphs coming from\ncombinatorial topology [Laz14]. Using the link between Brauer graph algebras\nand gentle algebras via the trivial extension [Sch15], we show that the\ngeneralized Kauer moves also yield derived equivalences of Brauer graph\nalgebras and also may be interpreted in terms of silting mutations.\n', 'Tilting mutations as generalized Kauer moves for (skew) Brauer graph\n  algebras with multiplicity   Generalized Kauer moves are local moves of multiple edges in a Brauer graph\nthat yield derived equivalences between Brauer graph algebras of multiplicity\nidentically 1. Moreover, these derived equivalences are given by a tilting\nmutation. The goal of this paper is to generalize this result first for Brauer\ngraph algebras with arbitrary multiplicity and second for a generalization of\nBrauer graph algebras called skew Brauer graph algebras. In these contexts, we\nprove that the generalized Kauer moves induce derived equivalences via tilting\nmutations. We also show that skew Brauer graph algebras of multiplicity\nidentically 1 can be seen as the trivial extension of skew gentle algebras.\n']","[('graph algebras', 0.6253905892372131), ('algebras brauer', 0.6084384322166443), ('graph algebra', 0.5213944911956787), ('symmetric algebras', 0.48053449392318726), ('algebras symmetric', 0.44701260328292847), ('algebra associated', 0.42068371176719666), ('algebras type', 0.41256585717201233), ('algebras coincides', 0.4092123210430145), ('class algebras called', 0.40766385197639465), ('algebras called', 0.39577752351760864)]"
1756,1756,16,1756_hermitian yang mills_deformed hermitian yang_yang mills equations_hermitian yang,"['hermitian yang mills', 'deformed hermitian yang', 'yang mills equations', 'hermitian yang', 'hermitian manifolds', 'almost hermitian manifolds', 'compact ahler manifolds', 'compact ahler manifold', 'ahler manifolds', 'ahler manifold']","['The Cauchy-Dirichlet problem for parabolic deformed Hermitian-Yang-Mills\n  equation   The purpose of this paper is to investigate the parabolic deformed\nHermitian-Yang-Mills equation with hypercritical phase in a smooth domain\n$\\Omega\\subset \\mathbb{C}^{n}$. By using $J$-functional, we are able to prove\nthe convergence of solutions. As an application, we give an alternative proof\nof the Dirichlet problem for deformed Hermitian-Yang-Mills equation.\n', 'Hypercritical deformed Hermitian-Yang-Mills equation revisited   In this paper, we study the hypercritical deformed Hermitian-Yang-Mills\nequation on compact K\\""ahler manifolds and resolve two conjectures of\nCollins-Yau.\n', 'Hypercritical deformed Hermitian-Yang-Mills equation   In this work, we study the deformed Hermitian-Yang-Mills equation on compact\nK\\""ahler manifold. We introduce the notions of coerciveness and properness of\nthe $\\mathcal{J}$-functional on the space of almost calibrated $(1,1)$-forms\nand show that they are both equivalent to the existence of solutions to the\nhypercritical deformed Hermitian-Yang-Mills equation.\n']","[('hermitian yang mills', 0.6830807328224182), ('deformed hermitian yang', 0.6395098567008972), ('yang mills equations', 0.6069336533546448), ('hermitian yang', 0.5732197165489197), ('hermitian manifolds', 0.544465184211731), ('almost hermitian manifolds', 0.5325093865394592), ('compact ahler manifolds', 0.5043013095855713), ('compact ahler manifold', 0.4969361424446106), ('ahler manifolds', 0.49544990062713623), ('ahler manifold', 0.4833768606185913)]"
1757,1757,16,1757_discontinuous galerkin methods_galerkin hdg methods_discontinuous galerkin hdg_hybridized discontinuous galerkin,"['discontinuous galerkin methods', 'galerkin hdg methods', 'discontinuous galerkin hdg', 'hybridized discontinuous galerkin', 'hybrid discontinuous galerkin', 'hybridizable discontinuous galerkin', 'discontinuous galerkin dg', 'galerkin methods', 'discontinuous galerkin', 'galerkin approaches']","['Superconvergent interpolatory HDG methods for reaction diffusion\n  equations I: An HDG$_{k}$ method   In our earlier work [8], we approximated solutions of a general class of\nscalar parabolic semilinear PDEs by an interpolatory hybridizable discontinuous\nGalerkin (Interpolatory HDG) method. This method reduces the computational cost\ncompared to standard HDG since the HDG matrices are assembled once before the\ntime integration. Interpolatory HDG also achieves optimal convergence rates;\nhowever, we did not observe superconvergence after an element-by-element\npostprocessing. In this work, we revisit the Interpolatory HDG method for\nreaction diffusion problems, and use the postprocessed approximate solution to\nevaluate the nonlinear term. We prove this simple change restores the\nsuperconvergence and keeps the computational advantages of the Interpolatory\nHDG method. We present numerical results to illustrate the convergence theory\nand the performance of the method.\n', 'A Scharfetter-Gummerl stabilization scheme for HDG approximations of\n  convection-diffusion problems   We present a Scharfetter-Gummel (SG) stabilization scheme for high-order\nHybrid Discontinuous Galerkin (HDG) approximations of convection-diffusion\nproblems. The scheme is based on a careful choice of the stabilization\nparameters used to define the numerical flux in the HDG method. We show that,\nin one dimension, the SG-HDG scheme is equivalent to the Finite Volume method\nstabilized with the Scharfetter--Gummel on the dual grid, for all orders of HDG\nschemes.\n', 'eXtended Hybridizable Discontinous Galerkin (X-HDG) Method for Linear\n  Convection-Diffusion Equations on Unfitted Domains   In this work, we propose a novel strategy for the numerical solution of\nlinear convection diffusion equation (CDE) over unfitted domains. In the\nproposed numerical scheme, strategies from high order Hybridized Discontinuous\nGalerkin method and eXtended Finite Element method is combined with the level\nset definition of the boundaries. The proposed scheme and hence, is named as\neXtended Hybridizable Discontinuous Galerkin (XHDG) method. In this regard, the\nHybridizable Discontinuous Galerkin (HDG) method is eXtended to the unfitted\ndomains; i.e, the computational mesh does not need to fit to the domain\nboundary; instead, the boundary is defined by a level set function and cuts\nthrough the background mesh arbitrarily. The original unknown structure of HDG\nand its hybrid nature ensuring the local conservation of fluxes is kept, while\ndeveloping a modified bilinear form for the elements cut by the boundary. At\nevery cut element, an auxiliary nodal trace variable on the boundary is\nintroduced, which is eliminated afterwards while imposing the boundary\nconditions. Both stationary and time dependent CDEs are studied over a range of\nflow regimes from diffusion to convection dominated; using high order $(p \\leq\n4)$ XHDG through benchmark numerical examples over arbitrary unfitted domains.\nResults proved that XHDG inherits optimal $(p + 1)$ and super $(p + 2)$\nconvergence properties of HDG while removing the fitting mesh restriction.\n']","[('discontinuous galerkin methods', 0.756984293460846), ('galerkin hdg methods', 0.752333402633667), ('discontinuous galerkin hdg', 0.7374894022941589), ('hybridized discontinuous galerkin', 0.7034587860107422), ('hybrid discontinuous galerkin', 0.6999757885932922), ('hybridizable discontinuous galerkin', 0.6769042015075684), ('discontinuous galerkin dg', 0.6767436861991882), ('galerkin methods', 0.6596534848213196), ('discontinuous galerkin', 0.6438668966293335), ('galerkin approaches', 0.6266937255859375)]"
1758,1758,16,1758_homology groups_homology group_homology mathrm_integral homology,"['homology groups', 'homology group', 'homology mathrm', 'integral homology', 'dimensional homology', 'projective linear group', 'homology', 'sl _2 mathbb', 'exceptional lie groups', 'special linear group']","['On the connections between the low dimensional homology groups of\n  $\\textrm{SL}_2$ and $\\textrm{PSL}_2$   In this article we study the low dimensional homology groups of the special\nlinear group $\\textrm{SL}_2(A)$ and the projective special linear group\n$\\textrm{PSL}_2(A)$, $A$ a domain, through the natural surjective map\n$\\textrm{SL}_2(A) \\to \\textrm{PSL}_2(A)$. In particular, we study the\nconnection of the first, the second and the third homology groups of these\ngroups over euclidean domains $\\mathbb{Z}[\\frac{1}{m}]$, $m$ a square free\ninteger, and local domains.\n', 'A Refined scissors congruence group and the third homology of\n  $\\textrm{SL}_2$   There is a natural connection between the third homology of\n$\\textrm{SL}_2(A)$ and the refined Bloch group $\\mathcal{RB}(A)$ of a\ncommutative ring $A$. In this article we investigate this connection and as the\nmain result we show that if $A$ is a universal $\\textrm{GE}_2$-domain such that\n$-1 \\in A^{\\times 2}$, then we have the exact sequence\n$H_3(\\textrm{SM}_2(A),\\mathbb{Z}) \\to H_3(\\textrm{SL}_2(A),\\mathbb{Z}) \\to\n\\mathcal{RB}(A) \\to 0$, where $\\textrm{SM}_2(A)$ is the group of monomial\nmatrices in $\\textrm{SL}_2(A)$. Moreover we show that $\\mathcal{RP}_1(A)$, the\nrefined scissors congruence group of $A$, naturally is isomorph with the\nrelative homology group $H_3(\\textrm{SL}_2(A), \\textrm{SM}_2(A),\\mathbb{Z})$.\n', 'On the Vanishing Criterion for the Cohomology Groups of the Automorphism\n  Group of a finite Abelian $p$-Group   For a partition $\\underline{\\lambda} =\n(\\lambda_{1}^{\\rho_1}>\\lambda_{2}^{\\rho_2}>\\lambda_{3}^{\\rho_3}>\\ldots>\\lambda_{k}^{\\rho_k})$\nand its associated finite abelian $p$-group\n$\\mathcal{A}_{\\underline{\\lambda}}=\\underset{i=1}{\\overset{k}{\\oplus}}\n(\\mathbb{Z}/p^{\\lambda_i}\\mathbb{Z})^{\\rho_i}$, where $p$ is a prime, we\nconsider two actions of its automorphism group\n$\\mathcal{G}_{\\underline{\\lambda}}$ on $\\mathcal{A}_{\\underline{\\lambda}}$. The\nfirst action is the natural action $g\\bullet a=\\ ^ga$ for all\n$g\\in\\mathcal{G}_{\\underline{\\lambda}}$ and\n$a\\in\\mathcal{A}_{\\underline{\\lambda}}$ where the action map is denoted by\n$\\Lambda_1=Id_{\\mathcal{G}_{\\underline{\\lambda}}}:\\mathcal{G}_{\\underline{\\lambda}}\\longrightarrow\n\\mathcal{G}_{\\underline{\\lambda}}$ and the second action is the trivial action\n$g\\bullet a=a$ for all $g\\in\\mathcal{G}_{\\underline{\\lambda}}$ and\n$a\\in\\mathcal{A}_{\\underline{\\lambda}}$ where the action map is denoted by\n$\\Lambda_2:\\mathcal{G}_{\\underline{\\lambda}}\\longrightarrow\n\\{e\\}\\subset\\mathcal{G}_{\\underline{\\lambda}}$ the trivial map. For the natural\naction $\\Lambda_1$, we show that the first and second cohomology groups\n$H_{\\Lambda_1}^i(\\mathcal{G}_{\\underline{\\lambda}},\\mathcal{A}_{\\underline{\\lambda}}),i=1,2$\nvanish for any partition $\\underline{\\lambda}$ for an odd prime $p$. For the\ntrivial action $\\Lambda_2$ we show that, for an odd prime $p$, the first\ncohomology group\n$H_{\\Lambda_2}^1(\\mathcal{G}_{\\underline{\\lambda}},\\mathcal{A}_{\\underline{\\lambda}})$\nand for an odd prime $p\\neq 3$, the second cohomology group\n$H_{\\Lambda_2}^2(\\mathcal{G}_{\\underline{\\lambda}},\\mathcal{A}_{\\underline{\\lambda}})$\nvanish if and only if the difference between two successive parts of the\npartition $\\underline{\\lambda}$ is at most one. This is done by using the $mod\\\np$ cohomologies\n$H^i(\\mathcal{G}_{\\underline{\\lambda}},\\mathbb{Z}/p\\mathbb{Z}),i=1,2$.\n']","[('homology groups', 0.585728645324707), ('homology group', 0.5729328393936157), ('homology mathrm', 0.49285611510276794), ('integral homology', 0.4903968274593353), ('dimensional homology', 0.4837082326412201), ('projective linear group', 0.4696798622608185), ('homology', 0.46540406346321106), ('sl _2 mathbb', 0.4359343945980072), ('exceptional lie groups', 0.43493902683258057), ('special linear group', 0.40849539637565613)]"
1759,1759,16,1759_bochner laplacian_schr odinger operator_spectra operators_odinger operator h_,"['bochner laplacian', 'schr odinger operator', 'spectra operators', 'odinger operator h_', 'spectral parameter', 'hermitian line bundle', 'odinger operator', 'bochner', 'bundle riemannian', 'riemannian manifold bounded']","['Eigenvalue distribution in gaps of the essential spectrum of the\n  Bochner-Schr\\""odinger operator   The Bochner-Schr\\""odinger operator $H_{p}=\\frac 1p\\Delta^{L^p}+V$ on high\ntensor powers $L^p$ of a Hermitian line bundle $L$ on a Riemannian manifold $X$\nof bounded geometry is studied under the assumption of non-degeneracy of the\ncurvature form of $L$. For large $p$, the spectrum of $H_p$ asymptotically\ncoincides with the union of all local Landau levels of the operator at the\npoints of $X$. Moreover, if the union of the local Landau levels over the\ncomplement of a compact subset of $X$ has a gap, then the spectrum of $H_{p}$\nin the gap is discrete. The main result of the paper is the trace asymptotics\nformula associated with these eigenvalues. As a consequence, we get a Weyl type\nasymptotic formula for the eigenvalue counting function.\n', 'Semiclassical trace formula for the Bochner-Schr\\""odinger operator   We study the semiclassical Bochner-Schr\\""odinger operator\n$H_{p}=\\frac{1}{p^2}\\Delta^{L^p\\otimes E}+V$ on tensor powers $L^p$ of a\nHermitian line bundle $L$ twisted by a Hermitian vector bundle $E$ on a\nRiemannian manifold of bounded geometry. For any function $\\varphi\\in\nC^\\infty_c(\\mathbb R)$, we consider the bounded linear operator $\\varphi(H_p)$\nin $L^2(X,L^p\\otimes E)$ defined by the spectral theorem. We prove that its\nsmooth Schwartz kernel on the diagonal admits a complete asymptotic expansion\nin powers of $p^{-1}$ in the semiclassical limit $p\\to \\infty$. In particular,\nwhen the manifold is compact, we get a complete asymptotic expansion for the\ntrace of $\\varphi(H_p)$.\n', 'Exponential localization for eigensections of the Bochner-Schr\\""odinger\n  operator   We study asymptotic spectral properties of the Bochner-Schr\\""odinger operator\n$H_{p}=\\frac 1p\\Delta^{L^p\\otimes E}+V$ on high tensor powers of a Hermitian\nline bundle $L$ twisted by a Hermitian vector bundle $E$ on a Riemannian\nmanifold $X$ of bounded geometry under assumption that the curvature form of\n$L$ is non-degenerate. At an arbitrary point $x_0$ of $X$ the operator $H_p$\ncan be approximated by a model operator $\\mathcal H^{(x_0)}$, which is a\nSchr\\""odinger operator with constant magnetic field. For large $p$, the\nspectrum of $H_p$ asymptotically coincides, up to order $p^{-1/4}$, with the\nunion of the spectra of the model operators $\\mathcal H^{(x_0)}$ over $X$. We\nshow that, if the union of the spectra of $\\mathcal H^{(x_0)}$ over the\ncomplement of a compact subset of $X$ has a gap, then the spectrum of $H_{p}$\nin the gap is discrete and the corresponding eigensections decay exponentially\naway the compact subset.\n']","[('bochner laplacian', 0.5330587029457092), ('schr odinger operator', 0.5010240077972412), ('spectra operators', 0.49667099118232727), ('odinger operator h_', 0.491283655166626), ('spectral parameter', 0.46719256043434143), ('hermitian line bundle', 0.46451401710510254), ('odinger operator', 0.4629017412662506), ('bochner', 0.4611649215221405), ('bundle riemannian', 0.44006451964378357), ('riemannian manifold bounded', 0.4391344487667084)]"
1760,1760,16,1760_algebraic complexity_orbit closures_invariant theory_polynomial time reductions,"['algebraic complexity', 'orbit closures', 'invariant theory', 'polynomial time reductions', 'complexity theoretic', 'geometric complexity', 'polynomial time algorithms', 'orbit closure', 'representation theory algebraic', 'generators invariant']","[""Minimal length in an orbit closure as a semiclassical limit   Consider the action of a connected complex reductive group on a\nfinite-dimensional vector space. A fundamental result in invariant theory\nstates that the orbit closure of a vector v is separated from the origin if and\nonly if some homogeneous invariant polynomial is nonzero on v, i.e. v is not in\nthe null cone. Thus, efficiently finding the minimum distance between the orbit\nclosure and the origin can lead to deterministic algorithms for null cone\nmembership, an important polynomial identity testing problem including the\nnon-commutative Edmonds problem. This connection to optimization has recently\nled to efficient algorithms for many problems in invariant theory.\n  Here we explore a refinement of the famous duality between orbit closures and\ninvariant polynomials, which holds that the following two quantities coincide:\n(1) the logarithm of the Euclidean distance between the orbit closure and the\norigin and (2) the rate of exponential growth of the 'invariant part' of\n$v^{\\otimes k}$ in the semiclassical limit as k tends to infinity. This result\ncan be deduced from work of S. Zhang (Geometric reductivity at Archimedean\nplaces, 1994), which uses sophisticated tools in arithmetic geometry. We\nprovide a new and independent elementary proof inspired by the Fourier-analytic\nproof of the local central limit theorem. We generalize the result to\nprojections onto highest weight vectors and isotypical components, and explore\nconnections between such semiclassical limits and the asymptotic behavior of\nmultiplicities in representation theory, large deviations theory in classical\nand quantum statistics, and the Jacobian conjecture as reformulated by Mathieu.\nOur formulas imply that they can be computed, in many cases efficiently, to\narbitrary precision.\n"", 'Complexity theory of orbit closure intersection for tensors: reductions,\n  completeness, and graph isomorphism hardness   Many natural computational problems in computer science, mathematics,\nphysics, and other sciences amount to deciding if two objects are equivalent.\nOften this equivalence is defined in terms of group actions. A natural question\nis to ask when two objects can be distinguished by polynomial functions that\nare invariant under the group action. For finite groups, this is the usual\nnotion of equivalence, but for continuous groups like the general linear groups\nit gives rise to a new notion, called orbit closure intersection. It captures,\namong others, the graph isomorphism problem, noncommutative PIT, null cone\nproblems in invariant theory, equivalence problems for tensor networks, and the\nclassification of multiparty quantum states. Despite recent algorithmic\nprogress in celebrated special cases, the computational complexity of general\norbit closure intersection problems is currently quite unclear. In particular,\ntensors seem to give rise to the most difficult problems.\n  In this work we start a systematic study of orbit closure intersection from\nthe complexity-theoretic viewpoint. To this end, we define a complexity class\nTOCI that captures the power of orbit closure intersection problems for general\ntensor actions, give an appropriate notion of algebraic reductions that imply\npolynomial-time reductions in the usual sense, but are amenable to\ninvariant-theoretic techniques, identify natural tensor problems that are\ncomplete for TOCI, including the equivalence of 2D tensor networks with\nconstant physical dimension, and show that the graph isomorphism problem can be\nreduced to these complete problems, hence GI$\\subseteq$TOCI. As such, our work\nestablishes the first lower bound on the computational complexity of orbit\nclosure intersection problems, and it explains the difficulty of finding\nunconditional polynomial-time algorithms beyond special cases, as has been\nobserved in the literature.\n', 'Determination Problems for Orbit Closures and Matrix Groups   Computational problems concerning the orbit of a point under the action of a\nmatrix group occur in numerous subfields of computer science, including\ncomplexity theory, program analysis, quantum computation, and automata theory.\nIn many cases the focus extends beyond orbits proper to orbit closures under a\nsuitable topology. Typically one starts from a group and several points and\nasks questions about the orbit closure of the points under the action of the\ngroup, e.g., whether two given orbit closures intersect.\n  In this paper we consider a collection of what we call determination problems\nconcerning groups and orbit closures. These problems begin with a given variety\nand seek to understand whether and how it arises either as an algebraic group\nor as an orbit closure. The how question asks whether the underlying group is\n$s$-generated, meaning it is topologically generated by $s$ matrices for a\ngiven number $s$. Among other applications, problems of this type have recently\nbeen studied in the context of synthesising loops subject to certain specified\ninvariants on program variables.\n  Our main result is a polynomial-space procedure that inputs a variety $V$ and\na number $s$ and determines whether $V$ arises as an orbit closure of a point\nunder an $s$-generated commutative matrix group. The main tools in our approach\nare rooted in structural properties of commutative algebraic matrix groups and\nlattice theory. We leave open the question of determining whether a variety is\nan orbit closure of a point under an algebraic matrix group (without the\nrequirement of commutativity). In this regard, we note that a recent paper by\nNosan et al. [NPSHW2021] gives an elementary procedure to compute the orbit\nclosure of a point under finitely many matrices.\n']","[('algebraic complexity', 0.5679254531860352), ('orbit closures', 0.548846960067749), ('invariant theory', 0.5171507596969604), ('polynomial time reductions', 0.513745129108429), ('complexity theoretic', 0.5082208514213562), ('geometric complexity', 0.4976770877838135), ('polynomial time algorithms', 0.49575790762901306), ('orbit closure', 0.49574992060661316), ('representation theory algebraic', 0.46267884969711304), ('generators invariant', 0.455094575881958)]"
1761,1761,16,1761_simple lie algebras_lie algebras_complex lie algebras_lie algebras representation,"['simple lie algebras', 'lie algebras', 'complex lie algebras', 'lie algebras representation', 'classical lie algebras', 'simple lie algebra', 'lie algebra', 'complex lie algebra', 'lie algebra type', 'lie algebra isomorphic']","[""Canonical structure constants for simple Lie algebras   Let $\\mathfrak{g}$ be a finite-dimensional simple Lie algebra over\n$\\mathbb{C}$. In the 1950s Chevalley showed that $\\mathfrak{g}$ admits\nparticular bases, now called ``Chevalley bases'', for which the corresponding\nstructure constants are integers. Such bases are not unique but, using\nLusztig's theory of canonical bases, one can single out a ``canonical''\nChevalley basis which is unique up to a global sign. In this paper, we give\nexplicit formulae for the structure constants with respect to such a basis.\n"", 'The Table of the Structure Constants for the Complex Simple Lie Algebra\n  of Type E_6 and Chevalley Commutator Formulas in the Chevalley Group of Type\n  E_6 over a Field   This article is the third in the series. It is devoted the calculation of the\nstructure constants for the complex simple Lie algebra of type E_6 and\nChevalley commutator formulas.\n', 'The Table of the Structure Constants for the Complex Simple Lie Algebra\n  of Type G_2 and Chevalley Commutator Formulas in the Chevalley Group of Type\n  G_2 over a Field   This article is the second in the series and is devoted to the type G_2. The\nwork consists of two parts. In the first part we calculate the structure\nconstants of the complex simple Lie algebra of type G_2. All structure\nconstants are represented as functions of the structure constants corresponding\nto extraspecial pairs. The results obtained are used to calculate the\ncommutator Chevalley formulas for [x_r(u),x_s(y)], when the sum r+s is a root.\n  Further, in the second part there is a table of structure constants and\nChevalley commutator formulas in the special case, when all structure constants\ncorresponding to extraspecial pairs are positive.\n']","[('simple lie algebras', 0.712518036365509), ('lie algebras', 0.7079381346702576), ('complex lie algebras', 0.6901344060897827), ('lie algebras representation', 0.6894543170928955), ('classical lie algebras', 0.6884673833847046), ('simple lie algebra', 0.6745185852050781), ('lie algebra', 0.666386604309082), ('complex lie algebra', 0.6553865671157837), ('lie algebra type', 0.6446176767349243), ('lie algebra isomorphic', 0.612633228302002)]"
1762,1762,16,1762_hessian type equations_hessian quotient equations_hessian equations_hessian type,"['hessian type equations', 'hessian quotient equations', 'hessian equations', 'hessian type', 'hessian', 'hessian quotient', 'mixed hessian', 'class hessian', 'equations neumann', 'nonlinear elliptic equations']","['The Neumann problem for a class of Hessian quotient type equations   In this paper, we consider the Neumann problem for a class of Hessian\nquotient equations involving a gradient term on the right-hand side in\nEuclidean space. More precisely, we derive the interior gradient estimates for\nthe $(\\Lambda, k)$-convex solution of Hessian quotient equation\n$\\frac{\\sigma_k(\\Lambda(D^2 u))}{\\sigma_l(\\Lambda(D^2 u))}=\\psi(x,u,D u)$ with\n$0\\leq l<k\\leq C^{p-1}_{n-1}$ under the assumption of the growth condition. As\nan application, we obtain the global a priori estimates and the existence\ntheorem for the Neumann problem of this Hessian quotient type equation.\n', 'The Neumann Problem for Parabolic Hessian Quotient Equations   In this paper, we consider the Neumann problem for parabolic Hessian quotient\nequations. We show that the $k$-admissible solution of the parabolic Hessian\nquotient equation exists for all time and converges to the smooth solution of\nelliptic Hessian quotient equations. Also the solutions of the classical\nNeumann problem converge to a translating solution.\n', 'The Neumann problem of Hessian quotient equations   In this paper, we obtain some important inequalities of Hessian quotient\noperators, and global $C^2$ estimates of the Neumann problem of Hessian\nquotient equations. By the method of continuity, we establish the existence\ntheorem of $k$-admissible solutions of the Neumann problem of Hessian quotient\nequations.\n']","[('hessian type equations', 0.5978231430053711), ('hessian quotient equations', 0.5870493054389954), ('hessian equations', 0.5787274241447449), ('hessian type', 0.5724947452545166), ('hessian', 0.5578303337097168), ('hessian quotient', 0.5576364994049072), ('mixed hessian', 0.5257699489593506), ('class hessian', 0.5256864428520203), ('equations neumann', 0.4833005368709564), ('nonlinear elliptic equations', 0.47177624702453613)]"
1763,1763,16,1763_dynamical zeta_analytic torsion_zeta associated_hyperbolic manifolds,"['dynamical zeta', 'analytic torsion', 'zeta associated', 'hyperbolic manifolds', 'zeta defined', 'compact hyperbolic manifolds', 'zeta functions', 'fuchsian groups', 'zeta', 'compact hyperbolic']","['Analytic torsion, dynamical zeta function, and the Fried conjecture for\n  admissible twists   We show an equality between the analytic torsion and the absolute value at\nthe zero point of the Ruelle dynamical zeta function on a closed odd\ndimensional locally symmetric space twisted by an acyclic flat vector bundle\nobtained by the restriction of a representation of the underlying Lie group.\nThis generalises author\'s previous result for unitarily flat vector bundles,\nand the results of Br\\""ocker, M\\""uller, and Wotzke on closed hyperbolic\nmanifolds.\n', ""A Ruelle dynamical zeta function for equivariant flows   For proper group actions on smooth manifolds, with compact quotients, we\ndefine an equivariant version of the Ruelle dynamical $\\zeta$-function for\nequivariant flows satisfying a nondegeneracy condition. The construction is\nbased on an equivariant generalisation of Guillemin's trace formula, obtained\nin a companion paper. This formula implies several properties of the\nequivariant Ruelle $\\zeta$-function. We ask the question in what situations an\nequivariant generalisation of Fried's conjecture holds, relating the\nequivariant Ruelle $\\zeta$-function to equivariant analytic torsion. We compute\nthe equivariant Ruelle $\\zeta$-function in several examples, including examples\nwhere the classical Ruelle $\\zeta$-function is not defined. The equivariant\nFried conjecture holds in the examples where the condition of the conjecture\n(vanishing of the kernel of the Laplacian) is satisfied.\n"", 'Twisted Ruelle zeta function on hyperbolic manifolds and complex-valued\n  analytic torsion   In this paper, we study the twisted Ruelle zeta function associated with the\ngeodesic flow of a compact, hyperbolic, odd-dimensional manifold $X$. The\ntwisted Ruelle zeta function is associated with an acyclic representation\n$\\chi\\colon \\pi_{1}(X) \\rightarrow \\GL_{n}(\\C)$, which is close enough to an\nacyclic, unitary representation. In this case, the twisted Ruelle zeta function\nis regular at zero and equals the square of the refined analytic torsion, as it\nis introduced by Braverman and Kappeler in \\cite{BK2}, multiplied by an\nexponential, which involves the eta invariant of the even part of the\nodd-signature operator, associated with $\\chi$.\n']","[('dynamical zeta', 0.5407803654670715), ('analytic torsion', 0.5162624716758728), ('zeta associated', 0.5006606578826904), ('hyperbolic manifolds', 0.5004002451896667), ('zeta defined', 0.469499796628952), ('compact hyperbolic manifolds', 0.4694482088088989), ('zeta functions', 0.45028579235076904), ('fuchsian groups', 0.4453623294830322), ('zeta', 0.4194757342338562), ('compact hyperbolic', 0.41350415349006653)]"
1764,1764,16,1764_adams spectral sequence_adams spectral_spectral sequences_spectral sequence,"['adams spectral sequence', 'adams spectral', 'spectral sequences', 'spectral sequence', 'classical adams', 'novikov spectral', 'sphere spectrum', 'spectral', 'spectra', 'adams']","['Automated differential computation in the Adams spectral sequence   We describe an algorithm for the automated deduction of many $d_2$\ndifferentials in the Adams spectral sequence. We discuss our implementation and\nthe results of the computation.\n', 'The Borel and genuine $C_2$-equivariant Adams spectral sequences   We find out some relations between the classical Adams spectral sequences for\nstunted real projective spectra, the Borel $C_2$-equivariant Adams spectral\nsequence for the 2-completed sphere, and the genuine $C_2$-equivariant Adams\nspectral sequence for the 2-completed sphere. This allows us to understand the\ngenuine $C_2$-equivariant Adams spectral sequence from the Borel Adams spectral\nsequences. We show that the Borel Adams spectral sequence is computable as a\nclassical Adams spectral sequence.\n', ""An extension in the Adams spectral sequence in dimension 54   We establish a hidden extension in the Adams spectral sequence converging to\nthe stable homotopy groups of spheres at the prime 2 in the 54-stem. This\nextension is exceptional in that the only proof we know proceeds via\nPstragowski's category of synthetic spectra. This was the final unresolved\nhidden 2-extension in the Adams spectral sequence through dimension 80. We hope\nthis provides a concise demonstration of the computational leverage provided by\n$\\mathbb{F}_2$-synthetic spectra.\n""]","[('adams spectral sequence', 0.8006520867347717), ('adams spectral', 0.7371589541435242), ('spectral sequences', 0.5377950072288513), ('spectral sequence', 0.5188913941383362), ('classical adams', 0.5003986358642578), ('novikov spectral', 0.48577484488487244), ('sphere spectrum', 0.4367631673812866), ('spectral', 0.4202214181423187), ('spectra', 0.4194595217704773), ('adams', 0.41532838344573975)]"
1765,1765,16,1765_null controllability_hierarchical control_controllability coupled_solves optimal control,"['null controllability', 'hierarchical control', 'controllability coupled', 'solves optimal control', 'controllability', 'objective optimal control', 'approximate controllability', 'control existence uniqueness', 'controllability trajectories', 'exact controllability']","['Stackelberg-Nash null controllability for stochastic parabolic equations   We study a hierarchical control problem for stochastic parabolic equations\ninvolving gradient terms. We employ the Stackelberg-Nash strategy with two\nleaders and two followers. The leaders are responsible for selecting the policy\ntargeting null controllability, while the followers solve a bi-objective\noptimal control problem which consists of maintaining the solution process\nclose to prefixed targets. Once the Nash equilibrium is determined, the problem\nreduces to achieving null controllability of a coupled forward-backward\nstochastic system. To solve this problem, via Carleman estimates, we establish\na suitable observability inequality. Subsequently, we achieve the desired\ncontrollability result.\n', 'Stackelberg-Nash null controllability of heat equation with general\n  dynamic boundary conditions   This paper deals with the hierarchical control of the anisotropic heat\nequation with dynamic boundary conditions and drift terms. We use the\nStackelberg-Nash strategy with one leader and two followers. To each fixed\nleader, we find a Nash equilibrium corresponding to a bi-objective optimal\ncontrol problem for the followers. Then, by some new Carleman estimates, we\nprove a null controllability result.\n', ""Stackelberg-Nash null controllability for a non linear coupled\n  degenerate parabolic equations   The main purpose of this paper is to apply the notion of hierarchical control\nto a coupled degenerate non linear parabolic equations. We use the\nStackelberg-Nash strategy with one leader and two followers. The followers\nsolve a Nash equilibrium corresponding to a bi-objective optimal control\nproblem and the leader a null controllability problem. Since the considered\nproblem is non linear, the associated cost is non-convex. We first prove the\nexistence, uniqueness and the characterization of the Nash quasiequilibrium,\nwhich is a weak formulation of the Nash equilibrium because the cost associated\nto the non linear problem is non-convex. Next, we show that under suitable\nconditions, the Nash quasi-equilibrium is equivalent to the Nash equilibrium.\nFinally using some Carleman inequalities that we established, and the\nKakutani's fixed point Theorem, we brough the states of our system to the rest\nat final time T .\n""]","[('null controllability', 0.5322387218475342), ('hierarchical control', 0.509313702583313), ('controllability coupled', 0.5038352608680725), ('solves optimal control', 0.5013924837112427), ('controllability', 0.5013850331306458), ('objective optimal control', 0.49787643551826477), ('approximate controllability', 0.4956061542034149), ('control existence uniqueness', 0.4809386432170868), ('controllability trajectories', 0.47760921716690063), ('exact controllability', 0.4609293043613434)]"
1766,1766,16,1766_inequalities concentration_rademacher sums_concentration probability_rademacher random variables,"['inequalities concentration', 'rademacher sums', 'concentration probability', 'rademacher random variables', 'weighted sums', 'sums arbitrary', 'independent identically distributed', 'singular values random', 'infinitely divisible distributions', 'littlewood offord']","['A new bound in the Littlewood--Offord problem   The paper deals with studying a connection of the Littlewood--Offord problem\nwith estimating the concentration functions of some symmetric infinitely\ndivisible distributions.\n', ""Arak Inequalities for Concentration Functions and the Littlewood-Offord\n  Problem   Let $X,X_1,\\ldots,X_n$ be independent identically distributed random\nvariables. In this paper we study the behavior of concentration functions of\nweighted sums $\\sum_{k=1}^{n}a_k X_k$ with respect to the arithmetic structure\nof coefficients $a_k$ in the context of the Littlewood--Offord problem.\nConcentration results of this type received renewed interest in connection with\ndistributions of singular values of random matrices. Recently, Tao and Vu\nproposed an Inverse Principle in the Littlewood-Offord problem. We discuss the\nrelations between the Inverse Principle of Tao and Vu as well as that of Nguyen\nand Vu and a similar principle formulated for sums of arbitrary independent\nrandom variables in the work of Arak from the 1980's.\n"", ""Arak Inequalities for Concentration Functions and the Littlewood--Offord\n  Problem: a shortened version   Let $X,X_1,\\ldots,X_n$ be independent identically distributed random\nvariables. In this paper we study the behavior of concentration functions of\nweighted sums $\\sum_{k=1}^{n} X_k a_k$ with respect to the arithmetic structure\nof coefficients~$a_k$ in the context of the Littlewood--Offord problem.\nConcentration results of this type received renewed interest in connection with\ndistributions of singular values of random matrices. Recently, Tao and Vu\nproposed an Inverse Principle in the Littlewood--Offord problem. We discuss the\nrelations between the Inverse Principle of Tao and Vu as well as that of Nguyen\nand Vu and a similar principle formulated for sums of arbitrary independent\nrandom variables in the work of Arak from the 1980's. This paper is a shortened\nand edited version of the preprint arXiv:1506.09034. Here we present the\nresults without proofs.\n""]","[('inequalities concentration', 0.5826472640037537), ('rademacher sums', 0.4163186848163605), ('concentration probability', 0.4048500955104828), ('rademacher random variables', 0.3647421598434448), ('weighted sums', 0.3573157489299774), ('sums arbitrary', 0.3284391462802887), ('independent identically distributed', 0.32625511288642883), ('singular values random', 0.322434663772583), ('infinitely divisible distributions', 0.31854522228240967), ('littlewood offord', 0.31314119696617126)]"
1767,1767,16,1767_casimir operators_casimir operator_lie algebras_lie algebras terms,"['casimir operators', 'casimir operator', 'lie algebras', 'lie algebras terms', 'simple lie algebras', 'casimir', 'adjoint representations', 'symmetry algebra', 'adjoint representation', 'lie superalgebras']","['Split Casimir operator and universal formulation of the simple Lie\n  algebras   We construct characteristic identities for the split (polarized) Casimir\noperators of the simple Lie algebras in adjoint representation. By means of\nthese characteristic identities, for all simple Lie algebras we derive explicit\nformulae for invariant projectors onto irreducible subrepresentations in\nT^{\\otimes 2} in the case when T is the adjoint representation. These\nprojectors and characteristic identities are considered from the viewpoint of\nthe universal description of the simple Lie algebras in terms of the Vogel\nparameters.\n', 'Split Casimir operator for simple Lie algebras in the cube of\n  $\\mathsf{ad}$-representation and Vogel parameters   We constructed characteristic identities for the 3-split (polarized) Casimir\noperators of simple Lie algebras in the adjoint representations $\\mathsf{ad}$\nand deduced a certain class of subrepresentations in $\\mathsf{ad}^{\\otimes 3}$.\nThe projectors onto invariant subspaces for these subrepresentations were\ndirectly constructed from the characteristic identities for the 3-split Casimir\noperators. For all simple Lie algebras, universal expressions for the traces of\nhigher powers of the 3-split Casimir operators were found and dimensions of the\nsubrepresentations in $\\mathsf{ad}^{\\otimes 3}$ were calculated. All our\nformulas are in agreement with the universal description of (irreducible)\nsubrepresentations in $\\mathsf{ad}^{\\otimes 3}$ for simple Lie algebras in\nterms of the Vogel parameters.\n', 'Split Casimir operator for simple Lie algebras, solutions of Yang-Baxter\n  equations and Vogel parameters   We construct characteristic identities for the split (polarized) Casimir\noperators of the simple Lie algebras in defining (minimal fundamental) and\nadjoint representations. By means of these characteristic identities, for all\nsimple Lie algebras we derive explicit formulae for invariant projectors onto\nirreducible subrepresentations in T^{\\otimes 2} in two cases, when T is the\ndefining and the adjoint representation. In the case when T is the defining\nrepresentation, these projectors and the split Casimir operator are used to\nexplicitly write down invariant solutions of the Yang-Baxter equations. In the\ncase when T is the adjoint representation, these projectors and characteristic\nidentities are considered from the viewpoint of the universal description of\nthe simple Lie algebras in terms of the Vogel parameters.\n']","[('casimir operators', 0.7090505957603455), ('casimir operator', 0.6768007278442383), ('lie algebras', 0.6155568361282349), ('lie algebras terms', 0.609529435634613), ('simple lie algebras', 0.5978472828865051), ('casimir', 0.5340876579284668), ('adjoint representations', 0.508172333240509), ('symmetry algebra', 0.5005667805671692), ('adjoint representation', 0.49471911787986755), ('lie superalgebras', 0.47185924649238586)]"
1768,1768,16,1768_estimation sparse_sparse signals_sample complexity_sparse multi,"['estimation sparse', 'sparse signals', 'sample complexity', 'sparse multi', 'sufficiently sparse', 'sparse', 'phase retrieval', 'noisy observations', 'optimal estimation', 'signal recovery']","['Bispectrum Unbiasing for Dilation-Invariant Multi-reference Alignment   Motivated by modern data applications such as cryo-electron microscopy, the\ngoal of classic multi-reference alignment (MRA) is to recover an unknown signal\n$f: \\mathbb{R} \\to \\mathbb{R}$ from many observations that have been randomly\ntranslated and corrupted by additive noise. We consider a generalization of\nclassic MRA where signals are also corrupted by a random scale change, i.e.\ndilation. We propose a novel data-driven unbiasing procedure which can recover\nan unbiased estimator of the bispectrum of the unknown signal, given knowledge\nof the dilation distribution. Lastly, we invert the recovered bispectrum to\nachieve full signal recovery, and validate our methodology on a set of\nsynthetic signals.\n', 'Sparse Multi-Reference Alignment : Phase Retrieval, Uniform Uncertainty\n  Principles and the Beltway Problem   Motivated by cutting-edge applications like cryo-electron microscopy\n(cryo-EM), the Multi-Reference Alignment (MRA) model entails the learning of an\nunknown signal from repeated measurements of its images under the latent action\nof a group of isometries and additive noise of magnitude $\\sigma$. Despite\nsignificant interest, a clear picture for understanding rates of estimation in\nthis model has emerged only recently, particularly in the high-noise regime\n$\\sigma \\gg 1$ that is highly relevant in applications. Recent investigations\nhave revealed a remarkable asymptotic sample complexity of order $\\sigma^6$ for\ncertain signals whose Fourier transforms have full support, in stark contrast\nto the traditional $\\sigma^2$ that arise in regular models. Often prohibitively\nlarge in practice, these results have prompted the investigation of variations\naround the MRA model where better sample complexity may be achieved. In this\npaper, we show that sparse signals exhibit an intermediate $\\sigma^4$ sample\ncomplexity even in the classical MRA model. Further, we characterise the\ndependence of the estimation rate on the support size $s$ as $O_p(1)$ and\n$O_p(s^{3.5})$ in the dilute and moderate regimes of sparsity respectively. Our\ntechniques have implications for the problem of crystallographic phase\nretrieval, indicating a certain local uniqueness for the recovery of sparse\nsignals from their power spectrum. Our results explore and exploit connections\nof the MRA estimation problem with two classical topics in applied mathematics:\nthe beltway problem from combinatorial optimization, and uniform uncertainty\nprinciples from harmonic analysis. Our techniques include a certain enhanced\nform of the probabilistic method, which might be of general interest in its own\nright.\n', 'The sample complexity of sparse multi-reference alignment and\n  single-particle cryo-electron microscopy   Multi-reference alignment (MRA) is the problem of recovering a signal from\nits multiple noisy copies, each acted upon by a random group element. MRA is\nmainly motivated by single-particle cryo-electron microscopy (cryo-EM) that has\nrecently joined X-ray crystallography as one of the two leading technologies to\nreconstruct biological molecular structures. Previous papers have shown that in\nthe high noise regime, the sample complexity of MRA and cryo-EM is\n$n=\\omega(\\sigma^{2d})$, where $n$ is the number of observations, $\\sigma^2$ is\nthe variance of the noise, and $d$ is the lowest-order moment of the\nobservations that uniquely determines the signal. In particular, it was shown\nthat in many cases, $d=3$ for generic signals, and thus the sample complexity\nis $n=\\omega(\\sigma^6)$.\n  In this paper, we analyze the second moment of the MRA and cryo-EM models.\nFirst, we show that in both models the second moment determines the signal up\nto a set of unitary matrices, whose dimension is governed by the decomposition\nof the space of signals into irreducible representations of the group. Second,\nwe derive sparsity conditions under which a signal can be recovered from the\nsecond moment, implying sample complexity of $n=\\omega(\\sigma^4)$. Notably, we\nshow that the sample complexity of cryo-EM is $n=\\omega(\\sigma^4)$ if at most\none third of the coefficients representing the molecular structure are\nnon-zero; this bound is near-optimal. The analysis is based on tools from\nrepresentation theory and algebraic geometry. We also derive bounds on\nrecovering a sparse signal from its power spectrum, which is the main\ncomputational problem of X-ray crystallography.\n']","[('estimation sparse', 0.5315387845039368), ('sparse signals', 0.4819544851779938), ('sample complexity', 0.3973392844200134), ('sparse multi', 0.3849632441997528), ('sufficiently sparse', 0.38208162784576416), ('sparse', 0.3798336386680603), ('phase retrieval', 0.37859654426574707), ('noisy observations', 0.37285852432250977), ('optimal estimation', 0.34329330921173096), ('signal recovery', 0.33252689242362976)]"
1769,1769,16,1769_hessian estimates_estimate hessian_solutions hessian_estimates convex,"['hessian estimates', 'estimate hessian', 'solutions hessian', 'estimates convex', 'space hessian', 'estimate convex', 'class hessian', 'hessian', 'convex solutions', 'hessian equations']","['Pogorelov type estimates for a class of Hessian quotient equations in\n  Lorentz-Minkowski space $\\mathbb{R}^{n+1}_{1}$   Let $\\Omega$ be a bounded domain (with smooth boundary) on the hyperbolic\nplane $\\mathscr{H}^{n}(1)$, of center at origin and radius $1$, in the\n$(n+1)$-dimensional Lorentz-Minkowski space $\\mathbb{R}^{n+1}_{1}$. In this\npaper, by using a priori estimates, we can establish Pogorelov type estimates\nof $k$-convex solutions to a class of Hessian quotient equations defined over\n$\\Omega\\subset\\mathscr{H}^{n}(1)$ and with the vanishing Dirichlet boundary\ncondition.\n', 'Pogorelov type $C^2$ estimates for sum Hessian equations   In this paper, We establish Pogorelov type $C^2$ estimates for the admissible\nsolutions with $\\sigma_k(D^2u)$ bounded from below of Sum Hessian equations. We\nalso proved the lower bounded condition can be removed when $k = n$.\n', 'Pogorelov type $C^2$ estimates for Sum Hessian equations and a rigidity\n  theorem   We mainly study Pogorelov type $C^2$ estimates for solutions to the Dirichlet\nproblem of Sum Hessian equations. We establish respectively Pogorelov type\n$C^2$ estimates for $k$-convex solutions and admissible solutions under some\nconditions. Furthermore, we apply such estimates to obtain a rigidity theorem\nfor $k$-convex solutions of Sum Hessian equations in Euclidean space.\n']","[('hessian estimates', 0.6290463805198669), ('estimate hessian', 0.5944411754608154), ('solutions hessian', 0.5501425266265869), ('estimates convex', 0.5282801985740662), ('space hessian', 0.5196309685707092), ('estimate convex', 0.5080274939537048), ('class hessian', 0.5029329657554626), ('hessian', 0.5023739337921143), ('convex solutions', 0.5006046295166016), ('hessian equations', 0.4909520745277405)]"
1770,1770,16,1770_metric spaces provide_fuzzy sets_metric spaces_sets metric,"['metric spaces provide', 'fuzzy sets', 'metric spaces', 'sets metric', 'metric space results', 'metric space equipped', 'metric space', 'metric space compact', 'metric space introduced', 'setting metric spaces']","['Characterizations of compactness of fuzzy set space with endograph\n  metric   In this paper, we present the characterizations of total boundedness,\nrelative compactness and compactness in fuzzy set spaces equipped with the\nendograph metric. The conclusions in this paper significantly improve the\ncorresponding conclusions given in our previous paper [H. Huang,\nCharacterizations of endograph metric and $\\Gamma$-convergence on fuzzy sets,\nFuzzy Sets and Systems 350 (2018), 55-84]. The results in this paper are\napplicable to fuzzy sets in a general metric space. The results in our previous\npaper are applicable to fuzzy sets in the $m$-dimensional Euclidean space\n$\\mathbb{R}^m$, which is a special type of metric space. Furthermore, based on\nthe above results, we give the characterizations of relative compactness, total\nboundedness and compactness in a kind of common subspaces of general fuzzy sets\naccording to the endograph metric. As an application, we investigate some\nrelationship between the endograph metric and the $\\Gamma$-convergence on fuzzy\nsets.\n', 'Properties of several fuzzy set spaces   This paper discusses the properties the spaces of fuzzy sets in a metric\nspace equipped with the endograph metric and the sendograph metric,\nrespectively. We fist give some relations among the endograph metric, the\nsendograph metric and the $\\Gamma$-convergence, and then investigate the level\ncharacterizations of the endograph metric and the $\\Gamma$-convergence. By\nusing the above results, we give some relations among the endograph metric, the\nsendograph metric, the supremum metric and the $d_p^*$ metric, $p\\geq 1$. On\nthe basis of the above results, we present the characterizations of total\nboundedness, relative compactness and compactness in the space of compact\npositive $\\al$-cuts fuzzy sets equipped with the endograph metric, and in the\nspace of compact support fuzzy sets equipped with the sendograph metric,\nrespectively. Furthermore, we give completions of these metric spaces,\nrespectively.\n', 'Properties of several metric spaces of fuzzy sets   This paper discusses the properties the spaces of fuzzy sets in a metric\nspace equipped with the endograph metric and the sendograph metric,\nrespectively. We first give some relations among the endograph metric, the\nsendograph metric and the $\\Gamma$-convergence, and then investigate the level\ncharacterizations of the endograph metric and the $\\Gamma$-convergence. By\nusing the above results, we give some relations among the endograph metric, the\nsendograph metric, the supremum metric and the $d_p^*$ metric, $p\\geq 1$. On\nthe basis of the above results, we present the characterizations of total\nboundedness, relative compactness and compactness in the space of fuzzy sets\nwhose $\\alpha$-cuts are compact when $\\alpha>0$ equipped with the endograph\nmetric, and in the space of compact support fuzzy sets equipped with the\nsendograph metric, respectively. Furthermore, we give completions of these\nmetric spaces, respectively.\n']","[('metric spaces provide', 0.5852649211883545), ('fuzzy sets', 0.5687830448150635), ('metric spaces', 0.5564502477645874), ('sets metric', 0.5464515089988708), ('metric space results', 0.5360721349716187), ('metric space equipped', 0.5355128645896912), ('metric space', 0.5307087898254395), ('metric space compact', 0.5063899755477905), ('metric space introduced', 0.502670168876648), ('setting metric spaces', 0.49884477257728577)]"
1771,1771,16,1771_queueing system_queueing_server queue_queue,"['queueing system', 'queueing', 'server queue', 'queue', 'queues', 'single server queue', 'queue length', 'customer arrival', 'congestion', 'arrival rates']","[""Queue or lounge: strategic design for strategic customer   Considering an M/M/1 queue with an additional lounge facility (LF), the quest\nof this paper is to understand the instances when LF is an attractive option,\nfrom customer perspective as well as from system perspective: will the\ncustomers choose to join the queue or prefer to detour briefly to lounge? In\nreality, customers do not perform complex computations for such tasks, but\ninstead choose based on some heuristics. We further assume that the customers\npessimistically anticipate the future congestion while making the choice. Our\nanalysis reveals that the customers use the LF only when the queue is too\ncrowded, and the lounge is relatively empty; however, strikingly, the customer\nchoice is more inclined towards rejection for the LF in systems with higher\ntraffic (load).\n  We also explore an optimization problem where the system determines whether\nto implement an LF and what capacity it should have, while accounting for\ncustomers' behavioral responses. Under low load conditions, the system benefits\nfrom designing a high-capacity lounge, and the customers also prefer to use the\nLF actively. Surprisingly, neither the system prefers big LF, nor the customers\nprefer to use the LF profusely at high load conditions; optimal for either is\nto use the LF sparingly. Thus, importantly, the strategic system and the\nbounded-rational customers are not in a tug-of-war situation.\n"", 'Strategic arrivals to a queue with service rate uncertainty   We study the problem of strategic choice of arrival time to a single-server\nqueue with opening and closing times when there is uncertainty regarding\nservice speed. A Poisson population of customers choose their arrival time with\nthe goal of minimizing their expected waiting times and are served on a\nfirst-come first-served basis. There are two types of customers that differ in\ntheir beliefs regarding the service time distribution. The inconsistent beliefs\nmay arise from randomness in the server state along with noisy signals that\ncustomers observe. Customers are aware of the two types of populations with\ndiffering beliefs. We characterize the Nash equilibrium dynamics for\nexponentially distributed service times and show how they substantially differ\nfrom the model with homogeneous customers. We further provide an explicit\nsolution for a fluid approximation of the game. For general service time\ndistributions we provide an algorithm for computing the equilibrium in a\ndiscrete time setting. We find that in equilibrium customers with different\nbeliefs arrive during different (and often disjoint) time intervals. Numerical\nanalysis further shows that the mean waiting time increases with the\ncoefficient of variation of the service time. Furthermore, we present a\nlearning agent based model (ABM) in which customers make joining decisions\nbased solely on their signals and past experience. We numerically compare the\nlong-term average outcome of the ABM with that of the equilibrium and find that\nthe arrival distributions are quite close if we assume (for the equilibrium\nsolution) that customers are fully rational and have knowledge of the system\nparameters, while they may greatly differ if customers have limited information\nor computing abilities.\n', ""A survey of queueing systems with strategic timing of arrivals   Consider a population of customers each of which needs to decide\nindependently when to arrive to a facility that provides a service during a\nfixed period of time, say a day. This is a common scenario in many service\nsystems such as a bank, lunch at a cafeteria, music concert, flight check-in\nand many others. High demand for service at a specific time leads to congestion\nthat comes at a cost, e.g., for waiting, earliness or tardiness. Queueing\nTheory provides tools for the analysis of the waiting times and associated\ncosts. If customers have the option of deciding when to join the queue, they\nwill face a decision dilemma of when to arrive. The level of congestion one\nsuffers from depends on others behavior and not only that of the individual\nunder consideration. This fact leads customers to make strategic decisions\nregarding their time of arrival. In addition, multiple decision makers that\naffect each other's expected congestion, call for non-cooperative game\ntheoretic analysis of this strategic interaction. This common daily scenario\nhas prompted a research stream pioneered by the ?/M/1 model of Glazer and\nHassin (GH1983) that first characterized an arrival process to a queue as a\nNash equilibrium solution of a game. This survey provides an overview of the\nmain results and developments in the literature on queueing systems with\nstrategic timing of arrivals. Another issue is that of social optimality,\nnamely the strategy profile used by customers that optimizes their aggregate\nutility. In particular, we review results concerning the price of anarchy\n(PoA), which is the ratio between the socially optimal and the equilibrium\nutilities.\n""]","[('queueing system', 0.6666035652160645), ('queueing', 0.6629672050476074), ('server queue', 0.6339626312255859), ('queue', 0.6225968599319458), ('queues', 0.6153212189674377), ('single server queue', 0.6052248477935791), ('queue length', 0.5827205181121826), ('customer arrival', 0.5077903270721436), ('congestion', 0.48837050795555115), ('arrival rates', 0.46746039390563965)]"
1772,1772,16,1772_rational maps_degree rational maps_rational map_proper maps,"['rational maps', 'degree rational maps', 'rational map', 'proper maps', 'maps degree', 'maps proper', 'maps defined', 'maps', 'endomorphisms', 'complex rational']","['On the deck groups of iterates of bicritical rational maps   Given a rational map $f:\\widehat{\\mathbb C}\\to\\widehat{\\mathbb C}$ on the\nRiemann sphere, we define $\\mathrm{Deck}(f)$ to be the group of M\\""obius\ntransformations $\\mu$ satisfying $f \\circ \\mu = f$. In this note, we consider\nthe groups $\\mathrm{Deck}(f^k)$, where $f$ is a \\emph{bicritical} rational map\n(that is, a rational map with exactly two critical points) and $f^k$ denotes\nthe $k$th iterate of $f$. In particular, we give a complete description of\nwhich groups (up to isomorphism) arise as the groups $\\mathrm{Deck}(f^k)$ for\nbicritical rational maps $f$.\n', 'Bicritical rational maps with a common iterate   Let $f$ be a degree $d$ bicritical rational map with critical point set\n$\\mathcal{C}_f$ and critical value set $\\mathcal{V}_f$. Using the group\n$\\textrm{Deck}(f^k)$ of deck transformations of $f^k$, we show that if $g$ is a\nbicritical rational map which shares an iterate with $f$ then $\\mathcal{C}_f =\n\\mathcal{C}_g$ and $\\mathcal{V}_f = \\mathcal{V}_g$. Using this, we show that if\ntwo bicritical rational maps of even degree $d$ share an iterate then they\nshare a second iterate, and both maps belong to the symmetry locus of degree\n$d$ bicritical rational maps.\n', 'On Real and Pseudo-Real Rational Maps   The moduli space ${\\rm M}_{d}$, of complex rational maps of degree $d \\geq\n2$, is a connected complex orbifold which carries a natural real structure,\ncoming from usual complex conjugation. Its real points are the classes of\nrational maps admitting antiholomorphic automorphisms. The locus of the real\npoints ${\\rm M}_{d}({\\mathbb R})$ decomposes as a disjoint union of the loci\n${\\rm M}_{d}^{\\mathbb R}$, consisting of the real rational maps, and ${\\mathcal\nP}_{d}$, consisting of the pseudo-real ones. We obtain that, both ${\\rm\nM}_{d}^{\\mathbb R}$ and ${\\rm M}_{d}({\\mathbb R})$, are connected and that\n${\\mathcal P}_{d}$ is disconnected. We also observe that the group of\nholomorphic automorphisms of a pseudo-real rational map is either trivial or a\ncyclic group. For every $n \\geq 1$, we construct pseudo-real rational maps\nwhose group of holomorphic automorphisms is cyclic of order $n$. As the field\nof moduli of a pseudo-real rational map is contained in ${\\mathbb R}$, these\nmaps provide examples of rational maps which are not definable over their field\nof moduli. It seems that these are the only explicit examples in the literature\n(Silverman) of rational maps which cannot be defined over their field of\nmoduli. We provide explicit examples of real rational maps which cannot be\ndefined over their field of moduli. Finally, we also observe that every real\nrational map, which admits a model over the algebraic numbers, can be defined\nover the real algebraic numbers.\n']","[('rational maps', 0.6990227103233337), ('degree rational maps', 0.6637629866600037), ('rational map', 0.6481226086616516), ('proper maps', 0.4734502136707306), ('maps degree', 0.45300358533859253), ('maps proper', 0.42971161007881165), ('maps defined', 0.4202553629875183), ('maps', 0.4084239900112152), ('endomorphisms', 0.4022195339202881), ('complex rational', 0.39894649386405945)]"
1773,1773,16,1773_superconductivity_superconductors_superconducting_superconductor,"['superconductivity', 'superconductors', 'superconducting', 'superconductor', 'ginzburg landau parameter', 'ginzburg landau functional', 'bohm magnetic', 'landau theory', 'aharonov bohm magnetic', 'magnetic potential']","['The breakdown of superconductivity in the presence of magnetic steps   Many earlier works were devoted to the study of the breakdown of\nsuperconductivity in type-II superconducting bounded planar domains, submitted\nto smooth magnetic fields. In the present contribution, we consider a new\nsituation where the applied magnetic field is piecewise-constant, and the\ndiscontinuity jump occurs along a smooth curve meeting the boundary\ntransversely. To handle this situation, we perform a detailed spectral analysis\nof a new effective model. Consequently, we establish the monotonicity of the\ntransition from a superconducting to a normal state. Moreover, we determine the\nlocation of superconductivity in the sample just before it disappears\ncompletely. Interestingly, the study shows similarities with the case of corner\ndomains subjected to constant fields.\n', 'Magnetic steps on the threshold of the normal state   Superconductivity in the presence of a step magnetic field has been recently\nthe focus of many works. This contribution examines the behavior of a\ntwo-dimensional superconducting domain, when superconductivity is lost in the\nwhole domain except near the intersection points of the discontinuity edge and\nthe boundary. The problem involves its own effective energy. We provide local\nestimates of the minimizers in neighbourhoods of the intersection points.\nConsequently, we introduce new critical fields marking the loss of\nsuperconductivity in the vicinity of these points. The study is modelled by the\nGinzburg--Landau theory, and large Ginzburg--Landau parameters are considered.\n', 'On the existence of nematic-superconducting states in the\n  Ginzburg-Landau regime   In this article, we investigate the existence of nematic-superconducting\nstates in the Ginzburg-Landau regime, both analytically and numerically. From\nthe configurations considered, a slab and a cylinder with a circular\ncross-section, we demonstrate the existence of geometrical thresholds for the\nobtention of non-zero nematic order parameters. Within the frame of this\nconstraint, the numerical calculations on the slab reveal that the competition\nor collaboration between nematicity and superconductivity is a complex energy\nminimization problem, requiring the accommodation of the Ginzburg-Landau\nparameters of the decoupled individual systems, the sign of the bi-quadratic\npotential energy relating both order parameters and the magnitude of the\napplied magnetic field. Specifically, the numerical results show the existence\nof a parameter regime for which it is possible to find mixed\nnematic-superconducting states. These regimes depend strongly on both the\napplied magnetic field and the potential coupling parameter. Since the proposed\nmodel corresponds to the weak coupling regime, and since it is a condition on\nthese parameters, we design a test to decide whether this condition is\nfulfilled.\n']","[('superconductivity', 0.6623892188072205), ('superconductors', 0.5476447939872742), ('superconducting', 0.5243498086929321), ('superconductor', 0.49890628457069397), ('ginzburg landau parameter', 0.45767906308174133), ('ginzburg landau functional', 0.44157689809799194), ('bohm magnetic', 0.41810816526412964), ('landau theory', 0.4049372971057892), ('aharonov bohm magnetic', 0.4010990858078003), ('magnetic potential', 0.3760630786418915)]"
1774,1774,16,1774_lower semicontinuity_quasiconvex functions_regularity minimizers_integral functionals,"['lower semicontinuity', 'quasiconvex functions', 'regularity minimizers', 'integral functionals', 'lower semicontinuous', 'lower semi continuity', 'relaxed functional', 'semicontinuous envelope', 'semicontinuity', 'partial regularity']","['On the local everywhere H\\""older continuity of the minima of a class of\n  vectorial integral functionals of the calculus of variations   In this paper we study the everywhere H\\""oder continuity of the minima of a\nclass of vectorial integral funcionals\n', 'Cartesian convexity as the key notion in the variational existence\n  theory for nonlocal supremal functionals   Motivated by the direct method in the calculus of variations in $L^{\\infty}$,\nour main result identifies the notion of convexity characterizing the\nweakly$^*$ lower semicontinuity of nonlocal supremal functionals: Cartesian\nlevel convexity. This new concept coincides with separate level convexity in\nthe one-dimensional setting and is strictly weaker for higher dimensions. We\ndiscuss relaxation in the vectorial case, showing that the relaxed functional\nwill not generally maintain the supremal form. Apart from illustrating this\nfact with examples of multi-well type, we present precise criteria for\nstructure-preservation. When the structure is preserved, a representation\nformula is given in terms of the Cartesian level convex envelope of the\n(diagonalized) original supremand. This work does not only complete the picture\nof the analysis initiated in [Kreisbeck \\& Zappale, Calc.~Var.~PDE, 2020], but\nalso establishes a connection with double integrals. We relate the two classes\nof functionals via an $L^p$-approximation in the sense of $\\Gamma$-convergence\nfor diverging integrability exponents. The proofs exploit recent results on\nnonlocal inclusions and their asymptotic behavior, and use tools from Young\nmeasure theory and convex analysis.\n', ""Partial regularity for symmetric quasiconvex functionals on BD   We establish the first partial regularity results for (strongly) symmetric\nquasiconvex functionals of linear growth on BD, the space of functions of\nbounded deformation. By Rindler's foundational work (Lower semicontinuity for\nintegral functionals in the space of functions of bounded deformation via\nrigidity and Young measures, Arch. Ration. Mech. Anal. 202 (2011), no. 1,\n63-113), symmetric quasiconvexity is the foremost notion as to sequential\nweak*-lower semicontinuity of functionals on BD. The overarching main\ndifficulty here is Ornstein's Non-Inequality, implying that the BD-case is\ngenuinely different from the study of variational integrals on BV. In\nparticular, this paper extends the recent work of Kristensen and the author\n(Partial regularity for BV-Minimizers, Arch. Ration. Mech. Anal. 232 (2019),\nIssue 3, 1429-1473) from the BV- to the BD-situation. Alongside, we establish\npartial regularity results for strongly quasiconvex functionals of superlinear\ngrowth by reduction to the full gradient case, which might be of independent\ninterest.\n""]","[('lower semicontinuity', 0.6130234003067017), ('quasiconvex functions', 0.5907044410705566), ('regularity minimizers', 0.563004732131958), ('integral functionals', 0.5583041310310364), ('lower semicontinuous', 0.5547474026679993), ('lower semi continuity', 0.553772509098053), ('relaxed functional', 0.5338119864463806), ('semicontinuous envelope', 0.5273200869560242), ('semicontinuity', 0.5175989866256714), ('partial regularity', 0.47625356912612915)]"
1775,1775,16,1775_inventory management_inventory control_inventory_echelon inventory,"['inventory management', 'inventory control', 'inventory', 'echelon inventory', 'deep reinforcement learning', 'supply chain network', 'reinforcement learning', 'inventory levels', 'sequential decision making', 'supply chain']","['Comparing Deep Reinforcement Learning Algorithms in Two-Echelon Supply\n  Chains   In this study, we analyze and compare the performance of state-of-the-art\ndeep reinforcement learning algorithms for solving the supply chain inventory\nmanagement problem. This complex sequential decision-making problem consists of\ndetermining the optimal quantity of products to be produced and shipped across\ndifferent warehouses over a given time horizon. In particular, we present a\nmathematical formulation of a two-echelon supply chain environment with\nstochastic and seasonal demand, which allows managing an arbitrary number of\nwarehouses and product types. Through a rich set of numerical experiments, we\ncompare the performance of different deep reinforcement learning algorithms\nunder various supply chain structures, topologies, demands, capacities, and\ncosts. The results of the experimental plan indicate that deep reinforcement\nlearning algorithms outperform traditional inventory management strategies,\nsuch as the static (s, Q)-policy. Furthermore, this study provides detailed\ninsight into the design and development of an open-source software library that\nprovides a customizable environment for solving the supply chain inventory\nmanagement problem using a wide range of data-driven approaches.\n', 'Control of Dual-Sourcing Inventory Systems using Recurrent Neural\n  Networks   A key challenge in inventory management is to identify policies that\noptimally replenish inventory from multiple suppliers. To solve such\noptimization problems, inventory managers need to decide what quantities to\norder from each supplier, given the net inventory and outstanding orders, so\nthat the expected backlogging, holding, and sourcing costs are jointly\nminimized. Inventory management problems have been studied extensively for over\n60 years, and yet even basic dual-sourcing problems, in which orders from an\nexpensive supplier arrive faster than orders from a regular supplier, remain\nintractable in their general form. In addition, there is an emerging need to\ndevelop proactive, scalable optimization algorithms that can adjust their\nrecommendations to dynamic demand shifts in a timely fashion. In this work, we\napproach dual sourcing from a neural network--based optimization lens and\nincorporate information on inventory dynamics and its replenishment (i.e.,\ncontrol) policies into the design of recurrent neural networks. We show that\nthe proposed neural network controllers (NNCs) are able to learn near-optimal\npolicies of commonly used instances within a few minutes of CPU time on a\nregular personal computer. To demonstrate the versatility of NNCs, we also show\nthat they can control inventory dynamics with empirical, non-stationary demand\ndistributions that are challenging to tackle effectively using alternative,\nstate-of-the-art approaches. Our work shows that high-quality solutions of\ncomplex inventory management problems with non-stationary demand can be\nobtained with deep neural-network optimization approaches that directly account\nfor inventory dynamics in their optimization process. As such, our research\nopens up new ways of efficiently managing complex, high-dimensional inventory\ndynamics.\n', 'Deep Policy Iteration with Integer Programming for Inventory Management   We present a Reinforcement Learning (RL) based framework for optimizing\nlong-term discounted reward problems with large combinatorial action space and\nstate dependent constraints. These characteristics are common to many\noperations management problems, e.g., network inventory replenishment, where\nmanagers have to deal with uncertain demand, lost sales, and capacity\nconstraints that results in more complex feasible action spaces. Our proposed\nProgrammable Actor Reinforcement Learning (PARL) uses a deep-policy iteration\nmethod that leverages neural networks (NNs) to approximate the value function\nand combines it with mathematical programming (MP) and sample average\napproximation (SAA) to solve the per-step-action optimally while accounting for\ncombinatorial action spaces and state-dependent constraint sets. We show how\nthe proposed methodology can be applied to complex inventory replenishment\nproblems where analytical solutions are intractable. We also benchmark the\nproposed algorithm against state-of-the-art RL algorithms and commonly used\nreplenishment heuristics and find it considerably outperforms existing methods\nby as much as 14.7% on average in various complex supply chain settings. We\nfind that this improvement of PARL over benchmark algorithms can be directly\nattributed to better inventory cost management, especially in inventory\nconstrained settings. Furthermore, in the simpler setting where optimal\nreplenishment policy is tractable or known near optimal heuristics exist, we\nfind that the RL approaches can learn near optimal policies. Finally, to make\nRL algorithms more accessible for inventory management researchers, we also\ndiscuss the development of a modular Python library that can be used to test\nthe performance of RL algorithms with various supply chain structures and spur\nfuture research in developing practical and near-optimal algorithms for\ninventory management problems.\n']","[('inventory management', 0.6535516977310181), ('inventory control', 0.614733099937439), ('inventory', 0.5388941168785095), ('echelon inventory', 0.5228752493858337), ('deep reinforcement learning', 0.48754385113716125), ('supply chain network', 0.4786667227745056), ('reinforcement learning', 0.4754577875137329), ('inventory levels', 0.4722033143043518), ('sequential decision making', 0.4690884053707123), ('supply chain', 0.46487993001937866)]"
1776,1776,16,1776_hilliard navier stokes_stokes cahn hilliard_cahn hilliard phase_phase flows,"['hilliard navier stokes', 'stokes cahn hilliard', 'cahn hilliard phase', 'phase flows', 'two phase flows', 'hilliard phase field', 'hilliard phase', 'cahn hilliard system', 'navier stokes system', 'incompressible navier stokes']","[""Regularity Propagation of Global Weak Solutions to a\n  Navier-Stokes-Cahn-Hilliard System for Incompressible Two-phase Flows with\n  Chemotaxis and Active Transport   We analyze a diffuse interface model that describes the dynamics of\nincompressible viscous two-phase flows, incorporating mechanisms such as\nchemotaxis, active transport, and long-range interactions of Oono's type. The\nevolution system couples the Navier-Stokes equations for the volume-averaged\nfluid velocity $\\bm{v}$, a convective Cahn-Hilliard equation for the\nphase-field variable $\\varphi$, and an advection-diffusion equation for the\ndensity of a chemical substance $\\sigma$. For the initial-boundary value\nproblem with a physically relevant singular potential in three dimensions, we\ndemonstrate that every global weak solution $(\\bm{v}, \\varphi, \\sigma)$\nexhibits a propagation of regularity over time. Specifically, after an\narbitrary positive time, the phase-field $\\varphi$ transitions into a strong\nsolution, whereas the chemical density $\\sigma$ only partially regularizes.\nSubsequently, the velocity field $\\bm{v}$ becomes regular after a sufficiently\nlarge time, followed by a further regularization of the chemical density\n$\\sigma$, which in turn enhances the spatial regularity of $\\varphi$.\nFurthermore, we show that every global weak solution stabilizes towards a\nsingle equilibrium as $t\\to +\\infty$. Our analysis uncovers the influence of\nchemotaxis, active transport, and long-range interactions on the propagation of\nregularity at different stages of time. The proof relies on several key points,\nincluding a novel regularity result for a convective Cahn-Hilliard-diffusion\nsystem with minimal regularity requirements on the velocity field $\\bm{v}$, the\nstrict separation property of $\\varphi$ for large times, as well as two\nconditional uniqueness results pertaining to the full system and its subsystem\nfor $(\\varphi, \\sigma)$ with a given velocity, respectively.\n"", ""On the Stationary Nonlocal Cahn-Hilliard-Navier-Stokes System:\n  Existence, Uniqueness and Exponential Stability   Cahn-Hilliard-Navier-Stokes system describes the evolution of two isothermal,\nincompressible, immiscible fluids in a bounded domain. In this work, we\nconsider the stationary nonlocal Cahn-Hilliard-Navier-Stokes system in two and\nthree dimensions with singular potential. We prove the existence of a weak\nsolution for the system using pseudo-monotonicity arguments and Browder's\ntheorem. Further we establish the uniqueness and regularity results for the\nweak solution of the stationary nonlocal Cahn-Hilliard-Navier-Stokes system for\nconstant mobility parameter and viscosity. Finally, in two dimensions, we\nestablish that the stationary solution is exponentially stable under suitable\nconditions on mobility parameter and viscosity.\n"", ""On a Navier-Stokes-Cahn-Hilliard System for Viscous Incompressible\n  Two-phase Flows with Chemotaxis, Active Transport and Reaction   We analyze a Navier-Stokes-Cahn-Hilliard model for viscous incompressible\ntwo-phase flows where the mechanisms of chemotaxis, active transport and\nreaction are taken into account. The evolution system couples the Navier-Stokes\nequations for the volume-averaged fluid velocity, a convective Cahn-Hilliard\nequation for the phase-field variable, and an advection-diffusion equation for\nthe density of certain chemical substance. This system is thermodynamically\nconsistent and generalizes the well-known ``Model H'' for viscous\nincompressible binary fluids. For the initial-boundary value problem with a\nphysically relevant singular potential in a general bounded smooth domain\n$\\Omega\\subset \\mathbb{R}^3$, we first prove the existence and uniqueness of a\nlocal strong solution. When the initial velocity is small and the initial\nphase-field function as well as the initial chemical density are small\nperturbations of a local minimizer of the free energy, we establish the\nexistence of a unique global strong solution. Afterwards, we show the\nuniqueness of asymptotic limit for any global strong solution as time goes to\ninfinity and provide an estimate on the convergence rate. The proofs for global\nwell-posedness and long-time behavior are based on the dissipative structure of\nthe system and the Lojasiewicz-Simon approach. Our analysis reveals the effects\nof chemotaxis, active transport and a long-range interaction of Oono's type on\nthe global dynamics of the coupled system.\n""]","[('hilliard navier stokes', 0.6403286457061768), ('stokes cahn hilliard', 0.5802820920944214), ('cahn hilliard phase', 0.5440384149551392), ('phase flows', 0.5408675074577332), ('two phase flows', 0.5306801795959473), ('hilliard phase field', 0.5176936984062195), ('hilliard phase', 0.5146141052246094), ('cahn hilliard system', 0.5139198303222656), ('navier stokes system', 0.509022057056427), ('incompressible navier stokes', 0.5016127824783325)]"
1777,1777,16,1777_differential galois groups_differential galois group_differential galois theory_differential galois,"['differential galois groups', 'differential galois group', 'differential galois theory', 'differential galois', 'differential fields', 'galois correspondence', 'galois groups', 'differential algebraic', 'fields differential', 'algebraic groups']","['A Note on Liouvillian Picard-Vessiot Extensions   In this paper, we prove a new characterization theorem for Picard-Vessiot\nextensions whose differential Galois groups have solvable identity components.\n', 'Triviality of differential Galois cohomologies of linear differential\n  algebraic groups   We show that the triviality of the differential Galois cohomologies over a\npartial differential field K of a linear differential algebraic group is\nequivalent to K being algebraically, Picard-Vessiot, and linearly\ndifferentially closed. This former is also known to be equivalent to the\nuniqueness up to an isomorphism of a Picard-Vessiot extension of a linear\ndifferential equation with parameters.\n', 'The Complete Picard Vessiot Closure   Let F be a differential field with field of constants C. We assume C to be\nalgebraically closed and of characteristic 0. The complete Picard--Vessiot\nclosure of F is a differential field extension of F with the same constants C\nas F, which has no Picard--Vessiot extensions, and is minimal over F with these\nproperties. There is a correspondence between subfields of the complete\nPicard--Vessiot closure and subgroups of its differential automorphism group,\nwhich arises because the complete Picard--Vessiot closure comes from F via\nrepeated Picard--Vessiot extensions. This correspondence also obtains for\ncertain normal subfields of the complete Picard--Vessiot closure, fields which\ncan be characterized independently of their embedding in the complete\nPicard--Vessiot closure.\n']","[('differential galois groups', 0.6942265629768372), ('differential galois group', 0.6680389046669006), ('differential galois theory', 0.6671295762062073), ('differential galois', 0.6322760581970215), ('differential fields', 0.5510610342025757), ('galois correspondence', 0.527006983757019), ('galois groups', 0.523734986782074), ('differential algebraic', 0.5158145427703857), ('fields differential', 0.5138615965843201), ('algebraic groups', 0.5091310739517212)]"
1778,1778,16,1778_moduli stacks_moduli stack_moduli spaces_map moduli,"['moduli stacks', 'moduli stack', 'moduli spaces', 'map moduli', 'rapoport zink spaces', 'affine group scheme', 'moduli', 'group scheme mathcal', 'cohomology sheaves', 'spaces stacks']","[""On properness of moduli stacks of $D^{\\times}$-shtukas over ramified legs Given a maximal order $D$ of a central division algebra over a global function field $F$, we prove an explicit sufficient condition for moduli stacks of $D^\\times$-shtukas to be proper over a finite field in terms of the local invariants of $D$ and bounds. Our proof is a refinement of E.~Lau's result (Duke Math. J. 140 (2007)), which showed the properness of the leg morphism (or characteristic morphism) away from the ramification locus of $D$. We also establish non-emptiness of Newton and Kottwitz--Rapoport strata for moduli stacks of $B^\\times$-shtukas, where $B$ is a maximal order of a central simple algebra over $F$."", 'A Note On Two Fiber Bundles and The Manifestations Of ""Shtuka""   In this note we intend to look at the moduli stacks for global $G$-shtukas\nfrom a new perspective. We discuss a unifying interpretation of several moduli\nspaces (stacks) including moduli of global $G$-shtukas and (a variant of the)\nmoduli of Higgs bundles. We view these spaces (stacks) as different fibers of a\nfamily over a scheme (stack) locally of finite type. We discuss (a relative\nversion of) the local model theory for this family. We also consider the Hecke\nstacks over the moduli stack of $G$-shtukas and discuss the corresponding\n(motivic) Hecke operations.\n', ""Local Models For Rapoport-Zink Spaces For Local P-Shtukas   This article provides a ``local'' complementary to the previous results\nconcerning the local models for the moduli stacks of ``global'' $G$-shtukas.\nHere we study the geometry of Rapoport-Zink spaces for local $P$-shtukas by\nconstructing local models for them. We further discuss certain applications,\nincluding some results related to the theory of formal nearby cycles associated\nto these spaces and the semi-simple trace of Frobenius on the corresponding\nsheaves.\n""]","[('moduli stacks', 0.6299319267272949), ('moduli stack', 0.575960636138916), ('moduli spaces', 0.5574219226837158), ('map moduli', 0.4907256066799164), ('rapoport zink spaces', 0.46608102321624756), ('affine group scheme', 0.45934903621673584), ('moduli', 0.43484869599342346), ('group scheme mathcal', 0.4310029447078705), ('cohomology sheaves', 0.4257570505142212), ('spaces stacks', 0.39665547013282776)]"
1779,1779,16,1779_control architectures_formal verification_linear dynamical systems_contracts,"['control architectures', 'formal verification', 'linear dynamical systems', 'contracts', 'control architecture', 'dynamical control systems', 'dynamical control', 'controller synthesis', 'specification', 'dynamical systems']","['Contract Composition for Dynamical Control Systems: Definition and\n  Verification using Linear Programming   Designing large-scale control systems to satisfy complex specifications is\nhard in practice, as most formal methods are limited to systems of modest size.\nContract theory has been proposed as a modular alternative to formal methods in\ncontrol, in which specifications are defined by assumptions on the input to a\ncomponent and guarantees on its output. However, current contract-based methods\nfor control systems either prescribe guarantees on the state of the system,\ngoing against the spirit of contract theory, or can only support rudimentary\ncompositions.\n  In this paper, we present a contract-based modular framework for\ndiscrete-time dynamical control systems. We extend the definition of contracts\nby allowing the assumption on the input at a time $k$ to depend on outputs up\nto time $k-1$, which is essential when considering the feedback connection of\nan unregulated dynamical system and a controller. We also define contract\ncomposition for arbitrary interconnection topologies, under the pretence of\nwell-posedness, and prove that this notion supports modular design, analysis\nand verification. This is done using graph theory methods, and specifically\nusing the notions of topological ordering and backward-reachable nodes. Lastly,\nwe use $k$-induction to present an algorithm for verifying vertical contracts,\nwhich are claims of the form ""the conjugation of given component-level\ncontracts is a stronger specification than a given contract on the integrated\nsystem"". These algorithms are based on linear programming, and scale linearly\nwith the number of components in the interconnected network. A numerical\nexample is provided to demonstrate the scalability of the presented approach,\nas well as the modularity achieved by using it.\n', 'Behavioural contracts for linear dynamical systems: input assumptions\n  and output guarantees   We introduce contracts for linear dynamical systems with inputs and outputs.\nContracts are used to express formal specifications on the dynamic behaviour of\nsuch systems through two aspects: assumptions and guarantees. The assumptions\nare a linear system that captures the available knowledge about the dynamic\nbehaviour of the environment in which the system is supposed to operate. The\nguarantees are a linear system that captures the required dynamic behaviour of\nthe system when interconnected with its environment. In addition to contracts,\nwe also define and characterize notions of contract refinement and contract\nconjunction. Contract refinement allows one to determine if a contract\nexpresses a stricter specifications than another contract. On the other hand,\ncontract conjunction allows one to combine multiple contracts into a single\ncontract that fuses the specifications they express.\n', 'Series composition of simulation-based assume-guarantee contracts for\n  linear dynamical systems   We present assume-guarantee contracts for continuous-time linear dynamical\nsystems with inputs and outputs. These contracts are used to express\nspecifications on the dynamic behaviour of a system. Contrary to existing\napproaches, we use simulation to compare the dynamic behaviour of two systems.\nThis has the advantage of being supported by efficient numerical algorithms for\nverification as well as being related to the rich literature on (bi)simulation\nbased techniques for verification and control, such as those based on\n(discrete) abstractions. Using simulation, we define contract implementation\nand a notion of contract refinement. We also define a notion of series\ncomposition for contracts, which allows us to reason about the series\ninterconnection of systems on the basis of the contracts on its components.\nTogether, the notions of refinement and composition allow contracts to be used\nfor modular design and analysis of interconnected systems.\n']","[('control architectures', 0.47074589133262634), ('formal verification', 0.4469987750053406), ('linear dynamical systems', 0.4414324164390564), ('contracts', 0.43803489208221436), ('control architecture', 0.4340614676475525), ('dynamical control systems', 0.43313518166542053), ('dynamical control', 0.40022891759872437), ('controller synthesis', 0.3989637494087219), ('specification', 0.3976256251335144), ('dynamical systems', 0.3967960476875305)]"
1780,1780,16,1780_commutators_commutative operators_campbell hausdorff formula_fermionic operators,"['commutators', 'commutative operators', 'campbell hausdorff formula', 'fermionic operators', 'commutation relations', 'commutator', 'operators obtained', 'baker campbell hausdorff', 'hypergeometric operators', 'operators']","['A note on the Baker--Campbell--Hausdorff series in terms of right-nested\n  commutators   We get compact expressions for the Baker--Campbell--Hausdorff series $Z =\n\\log(\\e^X \\, \\e^Y)$ in terms of right-nested commutators. The reduction in the\nnumber of terms originates from two facts: (i) we use as a starting point an\nexplicit expression directly involving independent commutators and (ii) we\nderive a complete set of identities arising among right-nested commutators. The\nprocedure allows us to obtain the series with fewer terms than when expressed\nin the classical Hall basis at least up to terms of grade 10.\n', ""Closed forms of the Zassenhaus formula   The Zassenhaus formula finds many applications in theoretical physics or\nmathematics, from fluid dynamics to differential geometry. The\nnon-commutativity of the elements of the algebra implies that the exponential\nof a sum of operators cannot be expressed as the product of exponentials of\noperators. The exponential of the sum can then be decomposed as the product of\nthe exponentials multiplied by a supplementary term which takes generally the\nform of an infinite product of exponentials. Such a procedure is often referred\nto as ``disentanglement''. However, for some special commutators, closed forms\ncan be found. In this work, we propose a closed form for the Zassenhaus formula\nwhen the commutator of operators $\\hat{X}$ and $\\hat{Y}$ satisfy the relation\n$[\\hat{X},\\hat{Y}]=u\\hat{X}+v\\hat{Y}+c\\mathcal{I}$. Such an expression boils\ndown to three equivalent versions, a left-sided, a centered and a right-sided\nformula:\n  \\begin{equation*}\ne^{\\hat{X}+\\hat{Y}}=e^{\\hat{X}}e^{\\hat{Y}}e^{g_{r}(u,v)[\\hat{X},\\hat{Y}]}=e^{\\hat{X}}e^{g_{c}(u,v)[\\hat{X},\\hat{Y}]}e^{\\hat{Y}}=e^{g_{\\ell}(u,v)[\\hat{X},\\hat{Y}]}e^{\\hat{X}}e^{\\hat{Y}},\n\\end{equation*} with respective arguments, \\begin{eqnarray*}\ng_{r}(u,v)&=&g_{c}(v,u)e^{u}=g_{\\ell}(v,u)=\\frac{u\\left(e^{u-v}-e^{u}\\right)+v\\left(e^{u}-1\\right)}{vu(u-v)}\n\\end{eqnarray*} for $u\\ne v$ and \\begin{eqnarray*}\ng_{r}(u,u)=\\frac{u+1-e^u}{u^2}\\;\\;\\;\\;\\mathrm{with}\\;\\;\\;\\; g_r(0,0)=-1/2.\n\\end{eqnarray*} With additional special case \\begin{eqnarray*} g_{r}(0,v)=\n-\\frac{e^{-v}-1+v}{v^{2}}, \\quad & g_{r}(u,0)=\\frac{e^{u}(1-u)-1}{u^{2}}.\n\\end{eqnarray*}\n"", ""General ordering theorem   The problem of ordering operators has afflicted quantum mechanics since its\nfoundation. Several orderings have been devised, but a systematic procedure to\nmove from one ordering to another is still missing. The importance of\nestablishing relations among different orderings is demonstrated by Wick's\ntheorem (which relates time ordering to normal ordering), which played a\ncrucial role in the development of quantum field theory. We prove the General\nOrdering Theorem (GOT), which establishes a relation among any pair of\norderings, that act on operators satisfying generic (i.e. operatorial)\ncommutation relations. We expose the working principles of the GOT by simple\nexamples, and we demonstrate its potential by recovering two famous algebraic\ntheorems as special instances: the Magnus expansion and the\nBaker-Campbell-Hausdorff formula. Remarkably, the GOT establishes a formal\nrelation between these two theorems, and it provides compact expressions for\nthem, unlike the notoriously complicated ones currently known.\n""]","[('commutators', 0.5637720823287964), ('commutative operators', 0.5402655005455017), ('campbell hausdorff formula', 0.5117319226264954), ('fermionic operators', 0.5003645420074463), ('commutation relations', 0.49459704756736755), ('commutator', 0.4935457110404968), ('operators obtained', 0.4751495122909546), ('baker campbell hausdorff', 0.46547096967697144), ('hypergeometric operators', 0.4445754289627075), ('operators', 0.4314793050289154)]"
1781,1781,16,1781_meromorphic connections_irregular singularities_connection projective_regular singularity,"['meromorphic connections', 'irregular singularities', 'connection projective', 'regular singularity', 'meromorphic connection', 'moduli spaces', 'holomorphic connections', 'singularities', 'singular points', 'moduli space']","['Rigid connections on $\\mathbb{P}^1$ via the Bruhat-Tits building   We apply the theory of fundamental strata of Bremer and Sage to find\ncohomologically rigid $G$-connections on the projective line, generalising the\nwork of Frenkel and Gross. In this theory, one studies the leading term of a\nformal connection with respect to the Moy-Prasad filtration associated to a\npoint in the Bruhat-Tits building. If the leading term is regular semisimple\nwith centraliser a (not necessarily split) maximal torus $S$, then we have an\n$S$-toral connection. In this language, the irregular singularity of the\nFrenkel-Gross connection gives rise to the homogenous toral connection of\nminimal slope associated to the Coxeter torus $\\mathcal{C}$. In the present\npaper, we consider connections on $\\mathbb{G}_m$ which have an irregular\nhomogeneous $\\mathcal{C}$-toral singularity at zero of slope $i/h$, where $h$\nis the Coxeter number and $i$ is a positive integer coprime to $h$, and a\nregular singularity at infinity with unipotent monodromy. Our main result is\nthe characterisation of all such connections which are rigid.\n', ""Rigid connections and $F$-isocrystals   An irreducible integrable connection $(E,\\nabla)$ on a smooth projective\ncomplex variety $X$ is called rigid if it gives rise to an isolated point of\nthe corresponding moduli space $\\mathcal{M}_{dR}(X)$. According to Simpson's\nmotivicity conjecture, irreducible rigid flat connections are of geometric\norigin, that is, arise as subquotients of a Gau\\ss-Manin connection of a family\nof smooth projective varieties defined on an open dense subvariety of $X$. In\nthis article we study mod $p$ reductions of irreducible rigid connections and\nestablish results which confirm Simpson's prediction. In particular, for large\n$p$, we prove that $p$-curvatures of mod $p$ reductions of irreducible rigid\nflat connections are nilpotent, and building on this result, we construct an\n$F$-isocrystalline realization for {irreducible} rigid flat connections. More\nprecisely, we prove that there exist smooth models $X_R$ and $(E_R,\\nabla_R)$\nof $X$ and $(E,\\nabla)$, over a finite type ring $R$, such that for every Witt\nring $W(k)$ of a finite field $k$ and every homomorphism $R \\to W(k)$, the\n$p$-adic completion of the base change\n$(\\widehat{E}_{W(k)},\\widehat{\\nabla}_{W(k)})$ on $\\widehat{X}_{W(k)}$\nrepresents an $F$-isocrystal. Subsequently we show that {irreducible} rigid\nflat connections with vanishing $p$-curvatures are unitary. This allows us to\nprove new cases of the Grothendieck--Katz $p$-curvature conjecture. We also\nprove the existence of a complete companion correspondence for $F$-isocrystals\nstemming from irreducible cohomologically rigid connections.\n"", 'The Deligne-Simpson problem for connections on $\\mathbb{G}_m$ with a\n  maximally ramified singularity   The classical additive Deligne-Simpson problem is the existence problem for\nFuchsian connections with residues at the singular points in specified adjoint\norbits. Crawley-Boevey found the solution in 2003 by reinterpreting the problem\nin terms of quiver varieties. A more general version of this problem, solved by\nHiroe, allows additional unramified irregular singularities. We apply the\ntheory of fundamental and regular strata due to Bremer and Sage to formulate a\nversion of the Deligne-Simpson problem in which certain ramified singularities\nare allowed. These allowed singular points are called toral singularities; they\nare singularities whose leading term with respect to a lattice chain filtration\nis regular semisimple. We solve this problem in the important special case of\nconnections on $\\mathbb{G}_m$ with a maximally ramified singularity at $0$ and\npossibly an additional regular singular point at infinity. We also give a\ncomplete characterization of all such connections which are rigid, under the\nadditional hypothesis of unipotent monodromy at infinity.\n']","[('meromorphic connections', 0.561277449131012), ('irregular singularities', 0.5550386905670166), ('connection projective', 0.5415345430374146), ('regular singularity', 0.5409044027328491), ('meromorphic connection', 0.5130382776260376), ('moduli spaces', 0.4796290993690491), ('holomorphic connections', 0.4631800651550293), ('singularities', 0.4612502455711365), ('singular points', 0.4598059058189392), ('moduli space', 0.44604939222335815)]"
1782,1782,16,1782_numerical methods_analytical numerical_numerical oscillations_partial differential equations,"['numerical methods', 'analytical numerical', 'numerical oscillations', 'partial differential equations', 'differential equations piecewise', 'pdes second order', 'functional differential equations', 'solving nonlinear', 'solutions nonlinear partial', 'order time derivatives']","['Hamiltonian Boundary Value Methods (HBVMs) for functional differential\n  equations with piecewise continuous arguments   In this paper, a class of high-order methods to numerically solve Functional\nDifferential Equations with Piecewise Continuous Arguments (FDEPCAs) is\ndiscussed. The framework stems from the expansion of the vector field\nassociated with the reference differential equation along the shifted and\nscaled Legendre polynomial orthonormal basis, working on a suitable extension\nof Hamiltonian Boundary Value Methods. Within the design of the methods, a\nproper generalization of the perturbation results coming from the field of\nordinary differential equations is considered, with the aim of handling the\ncase of FDEPCAs. The error analysis of the devised family of methods is\nperformed, while a few numerical tests on Hamiltonian FDEPCAs are provided, to\ngive evidence to the theoretical findings and show the effectiveness of the\nobtained resolution strategy.\n', ""A novel analytic method for solving linear and nonlinear Telegraph\n  Equation   The modeling of many phenomena in various fields such as mathematics,\nphysics, chemistry, engineering, biology, and astronomy is done by the\nnonlinear partial differential equations (PDE). The hyperbolic telegraph\nequation is one of them, where it describes the vibrations of structures (e.g.,\nbuildings, beams, and machines) and are the basis for fundamental equations of\natomic physics. There are several analytical and numerical methods are used to\nsolve the telegraph equation. An analytical solution considers framing the\nproblem in a well-understood form and calculating the exact resolution. It also\nhelps to understand the answers to the problem in terms of accuracy and\nconvergence. These analytic methods have limitations with accuracy and\nconvergence. Therefore, a novel analytic approximate method is proposed to deal\nwith constraints in this paper. This method uses the Taylors' series in its\nderivation. The proposed method has used for solving the second-order,\nhyperbolic equation (Telegraph equation) with the initial condition. Three\nexamples have presented to check the effectiveness, accuracy, and convergence\nof the method. The solutions of the proposed method also compared with those\nobtained by the Adomian decomposition method (ADM), and the Homotopy analysis\nmethod (HAM). The technique is easy to implement and produces accurate results.\nIn particular, these results display that the proposed method is efficient and\nbetter than the other methods in terms of accuracy and convergence.\n"", 'The BLUES function method applied to partial differential equations and\n  analytic approximants for interface growth under shear   An iteration sequence based on the BLUES (beyond linear use of equation\nsuperposition) function method is presented for calculating analytic\napproximants to solutions of nonlinear partial differential equations. This\nextends previous work using this method for nonlinear ordinary differential\nequations with an external source term. Now, the initial condition plays the\nrole of the source. The method is tested on three examples: a\nreaction-diffusion-convection equation, the porous medium equation with growth\nor decay, and the nonlinear Black-Scholes equation. A comparison is made with\nthree other methods: the Adomian decomposition method (ADM), the variational\niteration method (VIM), and the variational iteration method with Green\nfunction (GVIM). As a physical application, a deterministic differential\nequation is proposed for interface growth under shear, combining Burgers and\nKardar- Parisi-Zhang nonlinearities. Thermal noise is neglected. This model is\nstudied with Gaussian and space-periodic initial conditions. A detailed Fourier\nanalysis is performed and the analytic coefficients are compared with those of\nADM, VIM, GVIM, and standard perturbation theory. The BLUES method turns out to\nbe a worthwhile alternative to the other methods. The advantages that it offers\nensue from the freedom of choosing judiciously the linear part, with associated\nGreen function, and the residual containing the nonlinear part of the\ndifferential operator at hand.\n']","[('numerical methods', 0.5706406831741333), ('analytical numerical', 0.5001326203346252), ('numerical oscillations', 0.4754910171031952), ('partial differential equations', 0.44879400730133057), ('differential equations piecewise', 0.441968709230423), ('pdes second order', 0.42517244815826416), ('functional differential equations', 0.4222251772880554), ('solving nonlinear', 0.42071276903152466), ('solutions nonlinear partial', 0.4059771001338959), ('order time derivatives', 0.3995213508605957)]"
1783,1783,16,1783_partial flag varieties_vector bundles flag_varieties cohomology_bundles flag,"['partial flag varieties', 'vector bundles flag', 'varieties cohomology', 'bundles flag', 'flag varieties', 'bundle grassmannian', 'flag variety', 'bundles rank', 'bundles characterize', 'oriented cohomology']","[""Chow-Witt rings and topology of flag varieties   The paper computes the Witt-sheaf cohomology rings of partial flag varieties\nin type A in terms of the Pontryagin classes of the subquotient bundles. The\nproof is based on a Leray-Hirsch-type theorem for Witt-sheaf cohomology for the\nmaximal rank cases, and a detailed study of cohomology ring presentations and\nannihilators of characteristic classes for the general case. The computations\nhave consequences for the topology of real flag manifolds: we show that all\ntorsion in the integral cohomology is 2-torsion, which was not known in full\ngenerality previously. This allows for example to compute the Poincar\\'e\npolynomials of complete flag varieties for cohomology with twisted integer\ncoefficients. The computations also allow to describe the Chow-Witt rings of\nflag varieties, and we sketch an enumerative application to counting flags\nsatisfying multiple incidence conditions to given hypersurfaces.\n"", 'Stable sheaf cohomology on flag varieties   We prove an effective stabilization result for the sheaf cohomology groups of\nline bundles on flag varieties parametrizing complete flags in k^n, as well as\nfor the sheaf cohomology groups of polynomial functors applied to the cotangent\nsheaf Omega on projective space. In characteristic zero, these are natural\nconsequences of the Borel-Weil-Bott theorem, but in characteristic p>0 they are\nnon-trivial. Unlike many important contexts in modular representation theory,\nwhere the prime characteristic p is assumed to be large relative to n, in our\nstudy we fix p and let n go to infinity. We illustrate the general theory by\nproviding explicit stable cohomology calculations in a number of cases of\ninterest. Our examples yield cohomology groups where the number of\nindecomposable summands has super-polynomial growth, and also show that the\ncohomological degrees where non-vanishing occurs do not form a connected\ninterval. In the case of polynomial functors of Omega, we prove a Kunneth\nformula for stable cohomology, and show the invariance of stable cohomology\nunder Frobenius, which combined with the Steinberg tensor product theorem\nyields calculations of stable cohomology for an interesting class of simple\npolynomial functors arising in the work of Doty. The results in the special\ncase of symmetric powers of Omega provide a nice application to commutative\nalgebra, yielding a sharp vanishing result for Koszul modules of finite length\nin all characteristics.\n', 'Vector Bundles on Flag varieties   We study vector bundles on flag varieties over an algebraically closed field\n$k$. In the first part, we suppose $G=G_k(d,n)$ $(2\\le d\\leq n-d)$ to be the\nGrassmannian manifold parameterizing linear subspaces of dimension $d$ in\n$k^n$, where $k$ is an algebraically closed field of characteristic $p>0$. Let\n$E$ be a uniform vector bundle over $G$ of rank $r\\le d$. We show that $E$ is\neither a direct sum of line bundles or a twist of a pull back of the universal\nbundle $H_d$ or its dual $H_d^{\\vee}$ by a series of absolute Frobenius maps.\nIn the second part, splitting properties of vector bundles on general flag\nvarieties $F(d_1,\\cdots,d_s)$ in characteristic zero are considered. We prove a\nstructure theorem for bundles over flag varieties which are uniform with\nrespect to the $i$-th component of the manifold of lines in\n$F(d_1,\\cdots,d_s)$. Furthermore, we generalize the\nGrauert-M$\\ddot{\\text{u}}$lich-Barth theorem to flag varieties. As a corollary,\nwe show that any strongly uniform $i$-semistable $(1\\le i\\le n-1)$ bundle over\nthe complete flag variety splits as a direct sum of special line bundles.\n']","[('partial flag varieties', 0.6409812569618225), ('vector bundles flag', 0.6136650443077087), ('varieties cohomology', 0.6097671985626221), ('bundles flag', 0.6037958860397339), ('flag varieties', 0.6014772057533264), ('bundle grassmannian', 0.6006324291229248), ('flag variety', 0.5815275311470032), ('bundles rank', 0.5142210721969604), ('bundles characterize', 0.513975203037262), ('oriented cohomology', 0.5131568312644958)]"
1784,1784,16,1784_graphs interval graphs_interval graphs_graph coloring_graphs interval,"['graphs interval graphs', 'interval graphs', 'graph coloring', 'graphs interval', 'colorable graphs', 'coloring graph', 'edge coloring graph', 'unit interval graphs', 'graph interval', 'edge colorings']","['Improper interval edge colorings of graphs   A $k$-improper edge coloring of a graph $G$ is a mapping\n$\\alpha:E(G)\\longrightarrow \\mathbb{N}$ such that at most $k$ edges of $G$ with\na common endpoint have the same color. An improper edge coloring of a graph $G$\nis called an improper interval edge coloring if the colors of the edges\nincident to each vertex of $G$ form an integral interval. In this paper we\nintroduce and investigate a new notion, the interval coloring impropriety (or\njust impropriety) of a graph $G$ defined as the smallest $k$ such that $G$ has\na $k$-improper interval edge coloring; we denote the smallest such $k$ by\n$\\mu_{\\mathrm{int}}(G)$. We prove upper bounds on $\\mu_{\\mathrm{int}}(G)$ for\ngeneral graphs $G$ and for particular families such as bipartite, complete\nmultipartite and outerplanar graphs; we also determine $\\mu_{\\mathrm{int}}(G)$\nexactly for $G$ belonging to some particular classes of graphs. Furthermore, we\nprovide several families of graphs with large impropriety; in particular, we\nprove that for each positive integer $k$, there exists a graph $G$ with\n$\\mu_{\\mathrm{int}}(G) =k$. Finally, for graphs with at least two vertices we\nprove a new upper bound on the number of colors used in an improper interval\nedge coloring.\n', 'Online coloring of short interval graphs and two-count interval graphs   We study the online coloring of $\\sigma$-interval graphs which are interval\ngraphs where the interval lengths are between 1 and $\\sigma$ and 2-count\ninterval graphs which are interval graphs that require at most $2$ distinct\ninterval lengths.\n  For online $\\sigma$-interval graph coloring, we focus on online algorithms\nthat do not have knowledge of the interval representation. The\nKierstead-Trotter algorithm has competitive ratio 3 for all $\\sigma$ and no\nonline algorithm has competitive ratio better than 2, even for $\\sigma=1$. In\nthis paper, we show that for every $\\epsilon>0$, there is a $\\sigma>1$ such\nthat there is no online algorithm for $\\sigma$-interval coloring with\ncompetitive ratio less than $3-\\epsilon$. Our strategy also improves the best\nknown lower bounds for the greedy algorithm First-Fit for many values of\n$\\sigma$.\n  For online 2-count interval graph coloring, we analyze the performance of\nFirst-Fit and algorithms under various scenarios. We consider algorithms that\nreceive the interval representation as input and algorithms that do not. We\nalso consider algorithms that have prior knowledge of the interval lengths and\nalgorithms that do not. We provide non-trivial lower bounds for each of the\nfour cases. In particular, we show that there is no online algorithm with\ncompetitive ratio less than $2.5$ when the interval lengths are known, there is\nno online algorithm with competitive ratio less than $2$ when the interval\nrepresentation is known, and there is no online algorithm with competitive\nratio less than $1.75$ when both the interval lengths and interval\nrepresentation are known.\n', 'On the interval coloring impropriety of graphs   An improper interval (edge) coloring of a graph $G$ is an assignment of\ncolors to the edges of $G$ satisfying the condition that, for every vertex $v\n\\in V(G)$, the set of colors assigned to the edges incident with $v$ forms an\nintegral interval. An interval coloring is $k$-improper if at most $k$ edges\nwith the same color all share a common endpoint. The minimum integer $k$ such\nthat there exists a $k$-improper interval coloring of the graph $G$ is the\ninterval coloring impropriety of $G$, denoted by $\\mu_{int}(G)$. In this paper,\nwe provide a construction of an interval coloring of a subclass of complete\nmultipartite graphs. This provides additional evidence to the conjecture by\nCasselgren and Petrosyan that $\\mu_{int}(G)\\leq 2$ for all complete\nmultipartite graphs $G$. Additionally, we determine improved upper bounds on\nthe interval coloring impropriety of several classes of graphs, namely 2-trees,\niterated triangulations, and outerplanar graphs. Finally, we investigate the\ninterval coloring impropriety of the corona product of two graphs, $G\\odot H$.\n']","[('graphs interval graphs', 0.626326858997345), ('interval graphs', 0.5993814468383789), ('graph coloring', 0.5944810509681702), ('graphs interval', 0.5806923508644104), ('colorable graphs', 0.5545054078102112), ('coloring graph', 0.5537604689598083), ('edge coloring graph', 0.553434431552887), ('unit interval graphs', 0.5452618598937988), ('graph interval', 0.5433393120765686), ('edge colorings', 0.537493884563446)]"
1785,1785,16,1785_varieties positive_surfaces positive characteristic_smooth projective surfaces_bridgeland stability conditions,"['varieties positive', 'surfaces positive characteristic', 'smooth projective surfaces', 'bridgeland stability conditions', 'stability conditions', 'bridgeland stability', 'explicit stability conditions', 'varieties positive characteristic', 'vanishing chern classes', 'vanishing chern']","['Bogomolov-Gieseker type inequalities on ruled threefolds   We strengthen a conjecture by the author. This conjecture is a\nBogomolov-Gieseker type inequality involving the third Chern character of mixed\ntilt-stable complexes on fibred threefolds. We extend it from complexes of\nmixed tilt-slope zero to arbitrary relative tilt-slope. We show that this\nstronger conjecture implies the support property of Bridgeland stability\nconditions, and the existence of explicit stability conditions. We prove our\nconjecture for ruled threefolds, hence improving a previous result by the\nauthor.\n', 'Stability conditions on fibred threefolds   We give a conjectural construction of Bridgeland stability conditions on the\nderived category of fibred threefolds. The construction depends on a\nconjectural Bogomolov-Gieseker type inequality for certain stable complexes. It\ncan be considered as a relative version of the construction of Bayer, Macr\\`i\nand Toda. We prove the conjectural Bogomolov-Gieseker type inequality in the\ncase of relative projective planes over curves. This gives the the existence of\nBridgeland stability conditions on such threefolds.\n', ""Bridgeland stability conditions on some threefolds of general type   We prove the Bogomolov-Gieseker type inequality conjectured by Bayer, Macri\nand Toda for some products of three curves. This gives the first examples of\nBridgeland stability conditions on some threefolds of general type. The key\ningredients are the spreading out technique, Frobenius morphism and Bogomolov's\ninequality for product type varieties in positive characteristic, proved by the\nauthor recently.\n""]","[('varieties positive', 0.4425700604915619), ('surfaces positive characteristic', 0.43217185139656067), ('smooth projective surfaces', 0.43037447333335876), ('bridgeland stability conditions', 0.42622146010398865), ('stability conditions', 0.4243593215942383), ('bridgeland stability', 0.42226147651672363), ('explicit stability conditions', 0.4217054545879364), ('varieties positive characteristic', 0.41331642866134644), ('vanishing chern classes', 0.41160959005355835), ('vanishing chern', 0.39216458797454834)]"
1786,1786,16,1786_forms rank_waring rank_binary forms_cubic forms,"['forms rank', 'waring rank', 'binary forms', 'cubic forms', 'powers linear forms', 'binary form', 'cubic form', 'mathbb rank', 'waring decomposition', 'linear forms']","['The Waring rank of binary binomial forms   We give an explicit formula for the Waring rank of every binary binomial form\nwith complex coefficients. We give several examples to illustrate this, and\ncompare the Waring rank and the real Waring rank for binary binomial forms.\n', 'Waring ranks of sextic binary forms via geometric invariant theory   We determine the Waring ranks of all sextic binary forms with complex\ncoefficients using a Geometric Invariant Theory approach. Using the five basic\ninvariants for sextic binary forms, our results give a rapid method to\ndetermine the Waring rank of any given sextic binary form. In particular, we\nshed new light on a claim by E. B. Elliott at the end of the 19th century\nconcerning the binary sextics with Waring rank 3. We show that for binary forms\nof arbitrary degree the cactus rank, a.k.a. scheme rank, is determined by the\ncorresponding Waring rank. Finally we determine the border ranks of all binary\nsextics.\n', 'On the Waring Rank of Binary Forms   The $K$-rank of a binary form $f$ in $K[x,y],~K\\subseteq \\mathbb{C},$ is the\nsmallest number of $d$-th powers of linear forms over $K$ of which $f$ is a\n$K$-linear combination. We provide lower bounds for the $\\mathbb{C}$-rank\n(Waring rank) and for the $\\mathbb{R}$-rank (real Waring rank) of binary forms\ndepending on their factorization. We completely classify binary forms of Waring\nrank 3.\n']","[('forms rank', 0.5909393429756165), ('waring rank', 0.5671233534812927), ('binary forms', 0.5621951222419739), ('cubic forms', 0.5293685793876648), ('powers linear forms', 0.4982505142688751), ('binary form', 0.4882742762565613), ('cubic form', 0.46846234798431396), ('mathbb rank', 0.46003055572509766), ('waring decomposition', 0.45800670981407166), ('linear forms', 0.4513722360134125)]"
1787,1787,16,1787_taylor series expansions_terms stirling numbers_series expansions_bell polynomials,"['taylor series expansions', 'terms stirling numbers', 'series expansions', 'bell polynomials', 'partial bell polynomials', 'stirling numbers', 'combinatorial identities', 'closed form formula', 'power series expansion', 'involving stirling']","['Uniform treatments of Bernoulli numbers, Stirling numbers, and their\n  generating functions   In this paper, by virtue of a determinantal formula for derivatives of the\nratio between two differentiable functions, in view of the Fa\\`a di Bruno\nformula, and with the help of several identities and closed-form formulas for\nthe partial Bell polynomials $\\operatorname{B}_{n,k}$, the author establishes\nthirteen Maclaurin series expansions of the functions \\begin{align*}\n&\\ln\\frac{\\operatorname{e}^x+1}{2}, && \\ln\\frac{\\operatorname{e}^x-1}{x}, &&\n\\ln\\cosh x, \\\\ &\\ln\\frac{\\sinh x}{x}, && \\biggl[\\frac{\\ln(1+x)}{x}\\biggr]^r, &&\n\\biggl(\\frac{\\operatorname{e}^x-1}{x}\\biggr)^r \\end{align*} for\n$r=\\pm\\frac{1}{2}$ and $r\\in\\mathbb{R}$ in terms of the Dirichlet eta function\n$\\eta(1-2k)$, the Riemann zeta function $\\zeta(1-2k)$, and the Stirling numbers\nof the first and second kinds $s(n,k)$ and $S(n,k)$. presents four\ndeterminantal expressions and three recursive relations for the Bernoulli\nnumbers $B_{2n}$. finds out three closed-form formulas for the Bernoulli\nnumbers $B_{2n}$ and the generalized Bernoulli numbers $B_n^{(r)}$ in terms of\nthe Stirling numbers of the second kind $S(n,k)$, and deduce two combinatorial\nidentities for the Stirling numbers of the second kind $S(n,k)$. acquires two\ncombinatorial identities, which can be regarded as diagonal recursive\nrelations, involving the Stirling numbers of the first and second kinds\n$s(n,k)$ and $S(n,k)$. recovers an integral representation and a closed-form\nformula, and establish an alternative explicit and closed-form formula, for the\nBernoulli numbers of the second kind $b_n$ in terms of the Stirling numbers of\nthe first kind $s(n,k)$. obtains three identities connecting the Stirling\nnumbers of the first and second kinds $s(n,k)$ and $S(n,k)$.\n', ""Maclaurin's series expansions for positive integer powers of inverse\n  (hyperbolic) sine and related functions, specific values of partial Bell\n  polynomials, and two applications   In the paper, the authors establish Maclaurin's series expansions and series\nidentities for positive integer powers of the inverse sine function, for\npositive integer powers of the inverse hyperbolic sine function, for the\ncomposite of incomplete gamma functions with the inverse hyperbolic sine\nfunction, for positive integer powers of the inverse tangent function, and for\npositive integer powers of the inverse hyperbolic tangent function, in terms of\nthe first kind Stirling numbers and binomial coefficients, apply the newly\nestablished Maclaurin's series expansion for positive integer powers of the\ninverse sine function to derive a closed-form formula for specific values of\npartial Bell polynomials and to derive a series representation of the\ngeneralized logsine function, and deduce several combinatorial identities\ninvolving the first kind Stirling numbers. Some of these results simplify and\nunify some known ones. All of these newly established Maclaurin's series\nexpansions of positive integer powers of the inverse (hyperbolic) sine and\ntangent functions can be used to derive infinite series representations of the\ncircular constant Pi and of positive integer powers of Pi.\n"", ""Taylor's series expansions for real powers of functions containing\n  squares of inverse (hyperbolic) cosine functions, explicit formulas for\n  special partial Bell polynomials, and series representations for powers of\n  circular constant   In the paper, by virtue of expansions of two finite products of finitely many\nsquare sums, with the aid of series expansions of composite functions of\n(hyperbolic) sine and cosine functions with inverse sine and cosine functions,\nand in the light of properties of partial Bell polynomials, the author\nestablishes Taylor's series expansions of real powers of two functions\ncontaining squares of inverse (hyperbolic) cosine functions in terms of the\nStirling numbers of the first kind, presents an explicit formula of specific\npartial Bell polynomials at a sequence of derivatives of a function containing\nthe square of inverse cosine function, derives several combinatorial identities\ninvolving the Stirling numbers of the first kind, demonstrates several series\nrepresentations of the circular constant Pi and its real powers, recovers\nseries expansions of positive integer powers of inverse (hyperbolic) sine\nfunctions in terms of the Stirling numbers of the first kind, and also deduces\nother useful, meaningful, and significant conclusions.\n""]","[('taylor series expansions', 0.505852997303009), ('terms stirling numbers', 0.49841058254241943), ('series expansions', 0.49203819036483765), ('bell polynomials', 0.4826180040836334), ('partial bell polynomials', 0.47440820932388306), ('stirling numbers', 0.4484419524669647), ('combinatorial identities', 0.4370053708553314), ('closed form formula', 0.4331182837486267), ('power series expansion', 0.4321885406970978), ('involving stirling', 0.42964398860931396)]"
1788,1788,16,1788_free nilpotent groups_nilpotent groups_finite nilpotent group_generated nilpotent group,"['free nilpotent groups', 'nilpotent groups', 'finite nilpotent group', 'generated nilpotent group', 'finitely generated group', 'groups finitely', 'nilpotent group', 'unipotent groups', 'finitely generated nilpotent', 'profinite groups']","['The Reidemeister spectrum of direct products of nilpotent groups   We investigate the Reidemeister spectrum of direct products of nilpotent\ngroups. More specifically, we prove that the Reidemeister spectra of the\nindividual factors yield complete information for the Reidemeister spectrum of\nthe direct product if all groups are finitely generated torsion-free nilpotent\nand have a directly indecomposable rational Malcev completion. We show this by\ndetermining the complete automorphism group of the direct product.\n', 'The product formula for Reidemeister numbers on nilpotent groups   We study the product formula for Reidemeister numbers on finitely generated\ntorsion-free nilpotent groups in two ways. On the one hand, we generalise the\nproduct formula to central extensions. On the other hand, we derive general\nresults for finitely generated (torsion-free) nilpotent groups from the product\nformula: we provide a strong tool to prove that an endomorphism on a finitely\ngenerated nilpotent group has infinite Reidemeister number and compute\nReidemeister numbers on finite index subgroups of finitely generated\ntorsion-free nilpotent groups. Using the latter, we provide an infinite family\nof groups with full Reidemeister spectrum.\n', 'Torsion-free nilpotent groups of small Hirsch length with isomorphic\n  finite quotients   Let $\\mathcal{T}$ denote the class of finitely generated torsion-free\nnilpotent groups. For a group $G$ let $F(G)$ be the set of isomorphism classes\nof finite quotients of $G$. Pickel proved that if $G \\in \\mathcal{T}$, then the\nset $\\mathfrak{g}(G)$ of isomorphism classes of groups $H \\in \\mathcal{T}$ with\n$F(G)=F(H)$ is finite. We give an explicit description of the sets\n$\\mathfrak{g}(G)$ for the $\\mathcal{T}$-groups $G$ of Hirsch length at most\n$5$. Based on this, we show that for each Hirsch length $n\\geq 4$ and for each\n$m \\in \\mathbb{N}$ there is a $\\mathcal{T}$-group $G$ of Hirsch length $n$ with\n$\\vert\\mathfrak{g}(G)\\vert\\geq m$.\n']","[('free nilpotent groups', 0.6947500109672546), ('nilpotent groups', 0.6254806518554688), ('finite nilpotent group', 0.6100374460220337), ('generated nilpotent group', 0.5996862053871155), ('finitely generated group', 0.5831403732299805), ('groups finitely', 0.5736724734306335), ('nilpotent group', 0.5731956958770752), ('unipotent groups', 0.5608712434768677), ('finitely generated nilpotent', 0.54507976770401), ('profinite groups', 0.5354287028312683)]"
1789,1789,16,1789_online convex optimization_online convex_convex optimization time_dynamic regret bound,"['online convex optimization', 'online convex', 'convex optimization time', 'dynamic regret bound', 'convex optimization', 'online primal dual', 'regret bounds', 'online algorithms', 'minimize network', 'constraints network']","['Regret and Cumulative Constraint Violation Analysis for Distributed\n  Online Constrained Convex Optimization   This paper considers the distributed online convex optimization problem with\ntime-varying constraints over a network of agents. This is a sequential\ndecision making problem with two sequences of arbitrarily varying convex loss\nand constraint functions. At each round, each agent selects a decision from the\ndecision set, and then only a portion of the loss function and a coordinate\nblock of the constraint function at this round are privately revealed to this\nagent. The goal of the network is to minimize the network-wide loss accumulated\nover time. Two distributed online algorithms with full-information and bandit\nfeedback are proposed. Both dynamic and static network regret bounds are\nanalyzed for the proposed algorithms, and network cumulative constraint\nviolation is used to measure constraint violation, which excludes the situation\nthat strictly feasible constraints can compensate the effects of violated\nconstraints. In particular, we show that the proposed algorithms achieve\n$\\mathcal{O}(T^{\\max\\{\\kappa,1-\\kappa\\}})$ static network regret and\n$\\mathcal{O}(T^{1-\\kappa/2})$ network cumulative constraint violation, where\n$T$ is the time horizon and $\\kappa\\in(0,1)$ is a user-defined trade-off\nparameter. Moreover, if the loss functions are strongly convex, then the static\nnetwork regret bound can be reduced to $\\mathcal{O}(T^{\\kappa})$. Finally,\nnumerical simulations are provided to illustrate the effectiveness of the\ntheoretical results.\n', ""Distributed Constrained Online Nonconvex Optimization with Compressed\n  Communication   This paper considers distributed online nonconvex optimization with\ntime-varying inequality constraints over a network of agents. For a\ntime-varying graph, we propose a distributed online primal-dual algorithm with\ncompressed communication to efficiently utilize communication resources. We\nshow that the proposed algorithm establishes an $\\mathcal{O}( {{T^{\\max \\{ {1 -\n{\\theta_1},{\\theta_1}} \\}}}} )$ network regret bound and an $\\mathcal{O}( {T^{1\n- {\\theta_1}/2}} )$ network cumulative constraint violation bound, where $T$ is\nthe number of iterations and ${\\theta_1} \\in ( {0,1} )$ is a user-defined\ntrade-off parameter. When Slater's condition holds (i.e, there is a point that\nstrictly satisfies the inequality constraints at all iterations), the network\ncumulative constraint violation bound is reduced to $\\mathcal{O}( {T^{1 -\n{\\theta_1}}} )$. These bounds are comparable to the state-of-the-art results\nestablished by existing distributed online algorithms with perfect\ncommunication for distributed online convex optimization with (time-varying)\ninequality constraints. Finally, a simulation example is presented to validate\nthe theoretical results.\n"", ""Distributed Online Convex Optimization with Adversarial Constraints:\n  Reduced Cumulative Constraint Violation Bounds under Slater's Condition   This paper considers distributed online convex optimization with adversarial\nconstraints. In this setting, a network of agents makes decisions at each\nround, and then only a portion of the loss function and a coordinate block of\nthe constraint function are privately revealed to each agent. The loss and\nconstraint functions are convex and can vary arbitrarily across rounds. The\nagents collaborate to minimize network regret and cumulative constraint\nviolation. A novel distributed online algorithm is proposed and it achieves an\n$\\mathcal{O}(T^{\\max\\{c,1-c\\}})$ network regret bound and an\n$\\mathcal{O}(T^{1-c/2})$ network cumulative constraint violation bound, where\n$T$ is the number of rounds and $c\\in(0,1)$ is a user-defined trade-off\nparameter. When Slater's condition holds (i.e, there is a point that strictly\nsatisfies the inequality constraints), the network cumulative constraint\nviolation bound is reduced to $\\mathcal{O}(T^{1-c})$. Moreover, if the loss\nfunctions are strongly convex, then the network regret bound is reduced to\n$\\mathcal{O}(\\log(T))$, and the network cumulative constraint violation bound\nis reduced to $\\mathcal{O}(\\sqrt{\\log(T)T})$ and $\\mathcal{O}(\\log(T))$ without\nand with Slater's condition, respectively. To the best of our knowledge, this\npaper is the first to achieve reduced (network) cumulative constraint violation\nbounds for (distributed) online convex optimization with adversarial\nconstraints under Slater's condition. Finally, the theoretical results are\nverified through numerical simulations.\n""]","[('online convex optimization', 0.6671718955039978), ('online convex', 0.5779625177383423), ('convex optimization time', 0.5653148889541626), ('dynamic regret bound', 0.5317519903182983), ('convex optimization', 0.5225643515586853), ('online primal dual', 0.4951647222042084), ('regret bounds', 0.45573729276657104), ('online algorithms', 0.45354723930358887), ('minimize network', 0.44389405846595764), ('constraints network', 0.4372636079788208)]"
1790,1790,16,1790_branched coverings_branched cover_branched covers_coverings sphere,"['branched coverings', 'branched cover', 'branched covers', 'coverings sphere', 'space branched', 'compactification', 'fold branched', 'coverings', 'hurwitz space', 'genus finitely']","['Non-manifold monodromy spaces of branched coverings between manifolds   By a construction of Berstein and Edmonds every proper branched cover f\nbetween manifolds is a factor of a branched covering orbit map from a locally\nconnected and locally compact Hausdorff space called the monodromy space of f\nto the target manifold. For proper branched covers between 2-manifolds the\nmonodromy space is known to be a manifold. We show that this does not\ngeneralize to dimension 3 by constructing a self-map of the 3-sphere for which\nthe monodromy space is not a locally contractible space.\n', ""A cell structure of the space of branched coverings of the\n  two-dimensional sphere   For a closed oriented surface $ \\Sigma $ let $X_{\\Sigma,n}$ be the space of\nisomorphism classes of orientation preserving $n$-fold branched coverings $\n\\Sigma\\rightarrow S^2 $ of the two-dimensional sphere. At a previous paper, the\nauthors constructed a compactification $\\bar{X}_{\\Sigma,n}$ of the space that\ncoincides with the Diaz-Edidin-Natanzon-Turaev compactification of the Hurwitz\nspace $H(\\Sigma,n)\\subset X_{\\Sigma,n}$ consisting of isomorphism classes of\nbranched coverings with all critical values being simple. Using Grothendieck's\ndessins d'enfants we construct a cell structure of the compactification. The\nobtained results are applied to the space of trigonal curves on a Hirzebruch\nsurface.\n"", 'Compactification of the space of branched coverings of the\n  two-dimensional sphere   For a closed oriented surface $ \\Sigma $ we define its degenerations into\nsingular surfaces that are locally homeomorphic to wedges of disks. Let\n$X_{\\Sigma,n}$ be the set of isomorphism classes of orientation preserving\n$n$-fold branched coverings $ \\Sigma\\rightarrow S^2 $ of the two-dimensional\nsphere. We complete $X_{\\Sigma,n}$ with the isomorphism classes of mappings\nthat cover the sphere by the degenerations of $ \\Sigma $. In case $\n\\Sigma=S^2$, the topology that we define on the obtained completion\n$\\bar{X}_{\\Sigma,n}$ coincides on $X_{S^2,n}$ with the topology induced by the\nspace of coefficients of rational functions $ P/Q $, where $ P,Q $ are\nhomogeneous polynomials of degree $ n $ on $ \\mathbb{C}\\mathrm{P}^1\\cong S^2$.\n  We prove that $\\bar{X}_{\\Sigma,n}$ coincides with the\nDiaz-Edidin-Natanzon-Turaev compactification of the Hurwitz space\n$H(\\Sigma,n)\\subset X_{\\Sigma,n}$ consisting of isomorphism classes of branched\ncoverings with all critical values being simple.\n']","[('branched coverings', 0.7457549571990967), ('branched cover', 0.6553082466125488), ('branched covers', 0.6457321643829346), ('coverings sphere', 0.5971092581748962), ('space branched', 0.551089882850647), ('compactification', 0.5440435409545898), ('fold branched', 0.528582751750946), ('coverings', 0.46893298625946045), ('hurwitz space', 0.43628644943237305), ('genus finitely', 0.43352001905441284)]"
1791,1791,16,1791_orlicz spaces_orlicz norms_orlicz space_orlicz norm,"['orlicz spaces', 'orlicz norms', 'orlicz space', 'orlicz norm', 'orlicz functions', 'lorentz spaces', 'orlicz lorentz', 'lorentz space', 'dual spaces', 'orlicz type']","['New Results in Analysis of Orlicz-Lorentz spaces   In this article, we investigate the existence of closed vector subspaces\n(i.e.spaceability) in various nonlinear subsets of Orlicz-Lorentz spaces\n$\\Lambda_{\\varphi,w}$, equipped with the Luxemburg norm. If a family of Orlicz\nfunctions $(\\varphi_n)_{n=1}^{\\infty}$ satisfies certain order relations with\nrespect to a given Orlicz function $\\varphi$, the subset of the\norder-continuous subspace $(\\Lambda_{\\varphi,w})_a$ whose elements do not\nbelong to $\\bigcup_{n=1}^{\\infty}\\Lambda_{\\varphi_n,w}$ is spaceable, and even\nmaximal-spaceable when $\\varphi$ satisfies the $\\Delta_2$-condition. We also\nshow that this subset is either residual or empty. In addition, sufficient\nconditions for this subset not being $(\\alpha, \\beta)$-spaceable are provided.\nA similar analysis is also performed on the subset $\\Lambda_{\\varphi,w}\n\\setminus (\\Lambda_{\\varphi,w})_a$ when $\\varphi$ does not satisfy the\n$\\Delta_2$-condition.\n  The comparison between different Orlicz-Lorentz spaces is characterized via\nthe generating pairs $(\\varphi,w)$. For a fixed Orlicz function that satisfies\nthe $\\Delta_2^{\\infty}$-condition, we provide a characterization of disjointly\nstrictly singular inclusion operators between Orlicz-Lorentz spaces with\ndifferent weights. As a consequence, there are certain subsets of\nOrlicz-Lorentz spaces on $[0,1]$ for which lineability problem is not valid.\nMoreover, various types of $(\\alpha,\\beta)$-lineability and pointwise\nlineability properties on other nonlinear subsets of Orlicz-Lorentz spaces are\nexamined. These results extend a number of previously known results in Orlicz\nand Lorentz spaces.\n', 'On K\\""othe duals of Orlicz-Lorentz spaces   In this article, we study a number of properties of the K\\""othe duals\n$\\mathcal{M}_{\\varphi,w}$ of Orlicz-Lorentz spaces. An explicit description of\nthe order-continuous subspace of $\\mathcal{M}_{\\varphi,w}$ is provided.\nMoreover, the separability of these spaces is characterized by the growth\ncondition $\\Delta_2$. Consequently, the K\\""othe dual space\n$\\mathcal{M}_{\\varphi,w}$ has the Radon-Nikod\\\'ym property if and only if the\nN-function at infinity $\\varphi$ satisfies the appropriate\n$\\Delta_2$-condition. The comparison between $\\mathcal{M}_{\\varphi,w}$ spaces\nis characterized via standard orders between Orlicz functions. As applications\nof these results, we provide sufficient conditions for M-embedded\norder-continuous subspaces of Orlicz-Lorentz spaces equipped with the Luxemburg\nnorm and prove the existence of a unique norm-preserving extension on\nOrlicz-Lorentz spaces equipped with the Orlicz norm.\n', 'Daugavet and diameter two properties in Orlicz-Lorentz spaces   In this article, we study the diameter two properties (D2Ps), the diametral\ndiameter two properties (diametral D2Ps), and the Daugavet property in\nOrlicz-Lorentz spaces equipped with the Luxemburg norm. First, we characterize\nthe Radon-Nikod\\\'ym property of Orlicz-Lorentz spaces in full generality by\nconsidering all finite real-valued Orlicz functions. To show this, the\nfundamental functions of their K\\""othe dual spaces defined by extended\nreal-valued Orlicz functions are computed. We also show that if an Orlicz\nfunction does not satisfy the appropriate $\\Delta_2$-condition, the\nOrlicz-Lorentz space and its order-continuous subspace have the strong diameter\ntwo property. Consequently, given that an Orlicz function is an N-function at\ninfinity, the same condition characterizes the diameter two properties of\nOrlicz-Lorentz spaces as well as the octahedralities of their K\\""othe dual\nspaces. The Orlicz-Lorentz function spaces with the Daugavet property and the\ndiametral D2Ps are isometrically isomorphic to $L_1$ when the weight function\nis regular. In the process, we observe that every locally uniformly nonsquare\npoint is not a $\\Delta$-point. This fact provides another class of real Banach\nspaces without $\\Delta$-points. As another application, it is shown that for\nOrlicz-Lorentz spaces equipped with the Luxemburg norm defined by an N-function\nat infinity, their K\\""othe dual spaces do not have the local diameter two\nproperty, and so as other (diametral) diameter two properties and the Daugavet\nproperty.\n']","[('orlicz spaces', 0.7382086515426636), ('orlicz norms', 0.6347668170928955), ('orlicz space', 0.6274493932723999), ('orlicz norm', 0.5844220519065857), ('orlicz functions', 0.5743957161903381), ('lorentz spaces', 0.5545819401741028), ('orlicz lorentz', 0.5167883634567261), ('lorentz space', 0.49594032764434814), ('dual spaces', 0.4553363025188446), ('orlicz type', 0.4541073739528656)]"
1792,1792,16,1792_regular algebras_koszul algebras_calabi yau algebras_graded algebras,"['regular algebras', 'koszul algebras', 'calabi yau algebras', 'graded algebras', 'algebras dimension', 'yau algebras', 'artin schelter regular', 'algebra dimension', 'algebras global', 'twisted tensor products']","['Group coactions on two-dimensional Artin-Schelter regular algebras   We describe all possible coactions of finite groups (equivalently, all group\ngradings) on two-dimensional Artin-Schelter regular algebras. We give necessary\nand sufficient conditions for the associated Auslander map to be an\nisomorphism, and determine precisely when the invariant ring for the coaction\nis Artin-Schelter regular. The proofs of our results are combinatorial and\nexploit the structure of the McKay quiver associated to the coaction.\n', 'Nakayama automorphisms of graded Ore extensions of Koszul Artin-Schelter\n  regular algebras   Let $A$ be a Koszul Artin-Schelter regular algebra, $\\sigma$ a graded\nautomorphism of $A$ and $\\delta$ a degree-one $\\sigma$-derivation of $A$. We\nintroduce an invariant for $\\delta$ called the $\\sigma$-divergence of $\\delta$.\nWe describe the Nakayama automorphism of the graded Ore extension\n$B=A[z;\\sigma,\\delta]$ explicitly using the $\\sigma$-divergence of $\\delta$,\nand construct a twisted superpotential $\\hat{\\omega}$ for $B$ so that it is a\nderivation quotient algebra defined by $\\hat{\\omega}$. We also determine all\ngraded Ore extensions of noetherian Artin-Schelter regular algebras of\ndimension 2 and compute their Nakayama automorphisms.\n', 'New Artin-Schelter regular and Calabi-Yau algebras via normal extensions   We introduce a new method to construct 4-dimensional Artin-Schelter regular\nalgebras as normal extensions of (not necessarily noetherian) 3-dimensional\nones. The method produces large classes of new 4-dimensional Artin-Schelter\nregular algebras. When applied to a 3-Calabi-Yau algebra our method produces a\nflat family of central extensions of it that are 4-Calabi-Yau, and all\n4-Calabi-Yau central extensions having the same generating set as the original\n3-Calabi-Yau algebra arise in this way. Each normal extension has the same\ngenerators as the original 3-dimensional algebra, and its relations consist of\nall but one of the relations for the original algebra and an equal number of\nnew relations determined by ""the missing one"" and a tuple of scalars satisfying\nsome numerical conditions. We determine the Nakayama automorphisms of the\n4-dimensional algebras obtained by our method and as a consequence show that\ntheir homological determinant is 1. This supports the conjecture by Mori-Smith\nthat the homological determinant of the Nakayama automorphism is 1 for all\nArtin-Schelter regular connected graded algebras. Reyes-Rogalski-Zhang proved\nthis is true in the noetherian case.\n']","[('regular algebras', 0.6421212553977966), ('koszul algebras', 0.6241147518157959), ('calabi yau algebras', 0.6118820905685425), ('graded algebras', 0.6100322008132935), ('algebras dimension', 0.5103706121444702), ('yau algebras', 0.4934366047382355), ('artin schelter regular', 0.47842109203338623), ('algebra dimension', 0.4701268672943115), ('algebras global', 0.4585631191730499), ('twisted tensor products', 0.4488977789878845)]"
1793,1793,16,1793_graph zeta_zeta functions associated_finite digraphs_ihara zeta,"['graph zeta', 'zeta functions associated', 'finite digraphs', 'ihara zeta', 'finite digraph', 'zeta generalized', 'zeta functions', 'graphs hypergraphs', 'zeta finite', 'formulas zeta']","['Ihara zeta functions for some simple graph families   The reciprocal of the Ihara zeta function of a graph is a polynomial\ninvariant introduced by Ihara in 1966. Scott and Storm gave a method to\ndetermine the coefficients of the polynomial. Here we simplify their\ncalculation and determine the zeta function for all graphs of rank two. We\nverify that it is a complete invariant for such graphs: If $G_1$ and $G_2$ are\nof rank two, then $G_1$ and $G_2$ are isomorphic if and only if they have the\nsame Ihara zeta function. We observe that the reciprocal of the zeta function\nis an even polynomial if the graph is bipartite. We also determine the zeta\nfunction for several graph families: complete graphs, complete bipartite\ngraphs, M\\""{o}bius ladders, cocktail party graphs, and all graphs of order five\nor less. We use the special value $u=1$ to count the spanning trees for these\nfamilies.\n', 'Artin-Ihara L-functions for hypergraphs   We generalize Artin-Ihara L-functions for graphs to hypergraphs by exploring\nseveral analogous notions, such as (unramified) Galois coverings and Frobenius\nelements. To a hypergraph $H$, one can naturally associate a bipartite graph\n$B_H$ encoding incidence relations of $H$. We study Artin-Ihara $L$-functions\nof hypergraphs $H$ by using Artin-Ihara $L$-functions of associated bipartite\ngraphs $B_H$. As a result, we prove various properties for Artin-Ihara\nL-functions for hypergraphs. For instance, we prove that the Ihara zeta\nfunction of a hypergraph $H$ can be written as a product of Artin-Ihara\n$L$-functions.\n', 'The Ihara expression for generalized weighted zeta functions of\n  Bartholdi type on finite digraphs   The Ihara expression of a weighted zeta function for a general finite digraph\nis given. It unifies all the Ihara expressions obtained for known zeta\nfunctions for finite digraphs. Any digraph in this paper permits multi-edges\nand multi-loops.\n']","[('graph zeta', 0.6594207882881165), ('zeta functions associated', 0.5484102368354797), ('finite digraphs', 0.5375519394874573), ('ihara zeta', 0.5226354002952576), ('finite digraph', 0.5088112950325012), ('zeta generalized', 0.5029227137565613), ('zeta functions', 0.49899545311927795), ('graphs hypergraphs', 0.47881174087524414), ('zeta finite', 0.4680008292198181), ('formulas zeta', 0.4612247049808502)]"
1794,1794,16,1794_fuzzy system_feasible solutions_linear optimization problems_equations optimization,"['fuzzy system', 'feasible solutions', 'linear optimization problems', 'equations optimization', 'linear optimization', 'feasible domain', 'objective optimization', 'linear objective', 'optimization whose objective', 'feasible region defined']","['A fast method for solving the linear optimization p roblem subjected to\n  simplified Dombi fuzzy relational equations   In this paper, an optimization model with a linear objective function\nsubjected to a system of fuzzy relation equations (FRE) is studied where the\nfeasible region is defined by the Dombi t-norm. Dombi family of t-norms\nincludes a parametric family of continuous strict t-norms, whose members are\nincreasing functions of the parameter. This family of t-norms covers the whole\nspectrum of t-norms when the parameter is changed from zero to infinity. Since\nthe feasible solutions set of FREs is non-convex and the finding of all minimal\nsolutions is an NP-hard problem, designing an efficient solution procedure for\nsolving such problems is not a trivial job. Firstly, the feasible domain is\ncharacterized and then, based on some theoretical properties of the problem, a\nmodified branch-and-bound solution technique is presented, which solves the\nproblem by considering a few number of feasible paths. After presenting our\nsolution procedure, a concrete example is included for illustration purpose.\n', 'On the nonlinear programming problems subject to a system of generalized\n  bipolar fuzzy relational equalities defined with continuous t-norms   This paper, in the first step, develops the system of bipolar fuzzy\nrelational equations (FRE) to the most general case where the bipolar FREs are\ndefined by an arbitrary continuous t-norm. Also, since fuzzy relational\nequations are special cases of the bipolar FREs, the proposed system can be\nalso interpreted as a generalization of traditional FREs where the fuzzy\ncompositions are generally defined by any continuous t-norm. The consistency of\nthe continuous bipolar FREs is initially investigated and some necessary and\nsufficient conditions are derived for determining the feasibility of the\nproposed system. Subsequently, the feasible solutions set of the problem is\ncompletely characterized. It is shown that unlike FREs and those bipolar FREs\ndefined by continuous Archimedean t-norms, the feasible solutions set of the\ngeneralized bipolar FREs is formed as the union of a finite number of compact\nsets that are not necessarily connected. Moreover, five techniques have also\nbeen introduced with the aim of simplifying the current problem, and then an\nalgorithm is accordingly presented to find the feasible region of the problem.\nIn the second step, a new class of optimization models is studied where the\nconstraints are defined by the continuous bipolar FREs and the objective\nfunction covers a wide range of (non)linear functions such as maximum function,\ngeometric mean function, log-sum-exp function, maximum eigenvalue of a\nsymmetric matrix, support function of a set, etc. It is proved that the problem\nhas a finite number of local optimal solutions and a global optimal solution\ncan always be obtained by choosing a point having the minimum objective value\ncompared to all the local optimal solutions. Finally, to illustrate the\ndiscussed study, a step-by-step example is described in several sections, whose\nconstraints are a system of the bipolar FRES defined by Dubois-Prade t-norm.\n', 'Resolution and simplification of Dombi-fuzzy relational equations and\n  latticized optimization programming on Dombi FREs   In this paper, we introduce a type of latticized optimization problem whose\nobjective function is the maximum component function and the feasible region is\ndefined as a system of fuzzy relational equalities (FRE) defined by the Dombi\nt-norm. Dombi family of t-norms includes a parametric family of continuous\nstrict t-norms, whose members are increasing functions of the parameter. This\nfamily of t-norms covers the whole spectrum of t-norms when the parameter is\nchanged from zero to infinity. Since the feasible solutions set of FREs is\nnon-convex and the finding of all minimal solutions is an NP-hard problem,\ndesigning an efficient solution procedure for solving such problems is not a\ntrivial job. Some necessary and sufficient conditions are derived to determine\nthe feasibility of the problem. The feasible solution set is characterized in\nterms of a finite number of closed convex cells. An algorithm is presented for\nsolving this nonlinear problem. It is proved that the algorithm can find the\nexact optimal solution and an example is presented to illustrate the proposed\nalgorithm.\n']","[('fuzzy system', 0.4874798357486725), ('feasible solutions', 0.4521304965019226), ('linear optimization problems', 0.4391517639160156), ('equations optimization', 0.43578505516052246), ('linear optimization', 0.430559366941452), ('feasible domain', 0.40428388118743896), ('objective optimization', 0.4034442603588104), ('linear objective', 0.39246460795402527), ('optimization whose objective', 0.3892369568347931), ('feasible region defined', 0.38176289200782776)]"
1795,1795,16,1795_gaussian process regression_gaussian processes_gaussian process gp_gaussian models,"['gaussian process regression', 'gaussian processes', 'gaussian process gp', 'gaussian models', 'kernel approximations', 'processes gaussian', 'gaussian process', 'sparse approximations', 'gaussian stochastic', 'gaussian stochastic process']","['Contraction rates for conjugate gradient and Lanczos approximate\n  posteriors in Gaussian process regression   Due to their flexibility and theoretical tractability Gaussian process (GP)\nregression models have become a central topic in modern statistics and machine\nlearning. While the true posterior in these models is given explicitly,\nnumerical evaluations depend on the inversion of the augmented kernel matrix $\nK + \\sigma^2 I $, which requires up to $ O(n^3) $ operations. For large sample\nsizes n, which are typically given in modern applications, this is\ncomputationally infeasible and necessitates the use of an approximate version\nof the posterior. Although such methods are widely used in practice, they\ntypically have very limtied theoretical underpinning.\n  In this context, we analyze a class of recently proposed approximation\nalgorithms from the field of Probabilistic numerics. They can be interpreted in\nterms of Lanczos approximate eigenvectors of the kernel matrix or a conjugate\ngradient approximation of the posterior mean, which are particularly\nadvantageous in truly large scale applications, as they are fundamentally only\nbased on matrix vector multiplications amenable to the GPU acceleration of\nmodern software frameworks. We combine result from the numerical analysis\nliterature with state of the art concentration results for spectra of kernel\nmatrices to obtain minimax contraction rates. Our theoretical findings are\nillustrated by numerical experiments.\n', 'Connections and Equivalences between the Nystr\\""om Method and Sparse\n  Variational Gaussian Processes   We investigate the connections between sparse approximation methods for\nmaking kernel methods and Gaussian processes (GPs) scalable to large-scale\ndata, focusing on the Nystr\\""om method and the Sparse Variational Gaussian\nProcesses (SVGP). While sparse approximation methods for GPs and kernel methods\nshare some algebraic similarities, the literature lacks a deep understanding of\nhow and why they are related. This may pose an obstacle to the communications\nbetween the GP and kernel communities, making it difficult to transfer results\nfrom one side to the other. Our motivation is to remove this obstacle, by\nclarifying the connections between the sparse approximations for GPs and kernel\nmethods. In this work, we study the two popular approaches, the Nystr\\""om and\nSVGP approximations, in the context of a regression problem, and establish\nvarious connections and equivalences between them. In particular, we provide an\nRKHS interpretation of the SVGP approximation, and show that the Evidence Lower\nBound of the SVGP contains the objective function of the Nystr\\""om\napproximation, revealing the origin of the algebraic equivalence between the\ntwo approaches. We also study recently established convergence results for the\nSVGP and how they are related to the approximation quality of the Nystr\\""om\nmethod.\n', 'On the Inference of Applying Gaussian Process Modeling to a\n  Deterministic Function   Gaussian process modeling is a standard tool for building emulators for\ncomputer experiments, which are usually used to study deterministic functions,\nfor example, a solution to a given system of partial differential equations.\nThis work investigates applying Gaussian process modeling to a deterministic\nfunction from prediction and uncertainty quantification perspectives, where the\nGaussian process model is misspecified. Specifically, we consider the case\nwhere the underlying function is fixed and from a reproducing kernel Hilbert\nspace generated by some kernel function, and the same kernel function is used\nin the Gaussian process modeling as the correlation function for prediction and\nuncertainty quantification. While upper bounds and the optimal convergence rate\nof prediction in the Gaussian process modeling have been extensively studied in\nthe literature, a comprehensive exploration of convergence rates and\ntheoretical study of uncertainty quantification is lacking. We prove that, if\none uses maximum likelihood estimation to estimate the variance in Gaussian\nprocess modeling, under different choices of the regularization parameter\nvalue, the predictor is not optimal and/or the confidence interval is not\nreliable. In particular, lower bounds of the prediction error under different\nchoices of the regularization parameter value are obtained. The results\nindicate that, if one directly applies Gaussian process modeling to a fixed\nfunction, the reliability of the confidence interval and the optimality of the\npredictor cannot be achieved at the same time.\n']","[('gaussian process regression', 0.6499967575073242), ('gaussian processes', 0.596840500831604), ('gaussian process gp', 0.5912504196166992), ('gaussian models', 0.5799259543418884), ('kernel approximations', 0.575109601020813), ('processes gaussian', 0.559329628944397), ('gaussian process', 0.5373706817626953), ('sparse approximations', 0.5176220536231995), ('gaussian stochastic', 0.5048603415489197), ('gaussian stochastic process', 0.5039570331573486)]"
1796,1796,16,1796_impulsive differential_conditions approximate controllability_approximate controllability_controllability linear,"['impulsive differential', 'conditions approximate controllability', 'approximate controllability', 'controllability linear', 'controllability semilinear', 'controllability obtained', 'class impulsive', 'controllability', 'controllability non', 'controllability results']","['Approximate Controllability of Linear Fractional Impulsive Evolution\n  Equations in Hilbert Spaces   In this paper, we investigate the approximate controllability of linear\nfractional impulsive evolution equations in Hilbert spaces. We provide a\nrepresentation of solutions utilizing impulsive operators. Necessary and\nsufficient conditions for the approximate controllability of linear fractional\nimpulsive evolution equations are established in terms of the impulsive\nresolvent operator. An example is presented to demonstrate the application of\nthe obtained theoretical results.\n', 'Existence and approximate controllability of non-autonomous functional\n  impulsive evolution inclusions in Banach spaces   In this paper, we are concerned with the approximate controllability results\nfor a class of impulsive functional differential control systems involving time\ndependent operators in Banach spaces. First, we show the existence of a mild\nsolution for non-autonomous functional impulsive evolution inclusions in\nseparable reflexive Banach spaces with the help of the evolution family and a\ngeneralization of the Leray-Schauder fixed point theorem for multi-valued maps.\nIn order to establish sufficient conditions for the approximate controllability\nof our problem, we first consider a linear-quadratic regulator problem and\nobtain the optimal control in the feedback form, which contains the resolvent\noperator consisting of duality mapping. With the help of this optimal control,\nwe prove the approximate controllability of the linear system and hence derive\nsufficient conditions for the approximate controllability of our problem.\nMoreover, in this paper, we rectify several shortcomings of the related works\navailable in the literature, namely, proper identification of resolvent\noperator in Banach spaces, characterization of phase space in the presence of\nimpulsive effects and lack of compactness of the operator $h(\\cdot)\\mapsto\n\\int_{0}^{\\cdot}\\mathrm{U}(\\cdot,s)h(s)\\mathrm{d} s :\n\\mathrm{L}^{1}([0,T];\\mathbb{Y}) \\rightarrow \\mathrm{C}([0,T];\\mathbb{Y}),$\nwhere $\\mathbb{Y}$ is a Banach space and $\\mathrm{U}(\\cdot,\\cdot)$ is the\nevolution family, etc. Finally, we provide a concrete example to illustrate the\nefficiency of our results.\n', ""Approximate controllability of non-autonomous second order impulsive\n  functional evolution equations in Banach spaces   This article investigates the approximate controllability of second order\nnon-autonomous functional evolution equations involving non-instantaneous\nimpulses and nonlocal conditions. First, we discuss the approximate\ncontrollability of second order linear system in detail, which lacks in the\nexisting literature. Then, we derive sufficient conditions for approximate\ncontrollability of our system in separable reflexive Banach spaces via linear\nevolution operator, resolvent operator conditions, and Schauder's fixed point\ntheorem. Moreover, in this paper, we define proper identification of resolvent\noperator in Banach spaces. Finally, we verify our results to examine the\napproximate controllability of the non-autonomous wave equation with\nnon-instantaneous impulses and finite delay in the application section.\n""]","[('impulsive differential', 0.5767647624015808), ('conditions approximate controllability', 0.5761476755142212), ('approximate controllability', 0.5680672526359558), ('controllability linear', 0.5029593706130981), ('controllability semilinear', 0.4926992356777191), ('controllability obtained', 0.47851893305778503), ('class impulsive', 0.4665387272834778), ('controllability', 0.45425909757614136), ('controllability non', 0.450210839509964), ('controllability results', 0.4473879933357239)]"
1797,1797,16,1797_learning control_control learning_safety controller_learning based control,"['learning control', 'control learning', 'safety controller', 'learning based control', 'safe learning', 'optimal control policies', 'safe control', 'control barrier functions', 'state control constraints', 'safety guarantees']","['Safe Model-Based Reinforcement Learning for Systems with Parametric\n  Uncertainties   Reinforcement learning has been established over the past decade as an\neffective tool to find optimal control policies for dynamical systems, with\nrecent focus on approaches that guarantee safety during the learning and/or\nexecution phases. In general, safety guarantees are critical in reinforcement\nlearning when the system is safety-critical and/or task restarts are not\npractically feasible. In optimal control theory, safety requirements are often\nexpressed in terms of state and/or control constraints. In recent years,\nreinforcement learning approaches that rely on persistent excitation have been\ncombined with a barrier transformation to learn the optimal control policies\nunder state constraints. To soften the excitation requirements, model-based\nreinforcement learning methods that rely on exact model knowledge have also\nbeen integrated with the barrier transformation framework. The objective of\nthis paper is to develop safe reinforcement learning method for deterministic\nnonlinear systems, with parametric uncertainties in the model, to learn\napproximate constrained optimal policies without relying on stringent\nexcitation conditions. To that end, a model-based reinforcement learning\ntechnique that utilizes a novel filtered concurrent learning method, along with\na barrier transformation, is developed in this paper to realize simultaneous\nlearning of unknown model parameters and approximate optimal state-constrained\ncontrol policies for safety-critical systems.\n', 'Learning Control Barrier Functions from Expert Demonstrations   Inspired by the success of imitation and inverse reinforcement learning in\nreplicating expert behavior through optimal control, we propose a learning\nbased approach to safe controller synthesis based on control barrier functions\n(CBFs). We consider the setting of a known nonlinear control affine dynamical\nsystem and assume that we have access to safe trajectories generated by an\nexpert - a practical example of such a setting would be a kinematic model of a\nself-driving vehicle with safe trajectories (e.g., trajectories that avoid\ncollisions with obstacles in the environment) generated by a human driver. We\nthen propose and analyze an optimization-based approach to learning a CBF that\nenjoys provable safety guarantees under suitable Lipschitz smoothness\nassumptions on the underlying dynamical system. A strength of our approach is\nthat it is agnostic to the parameterization used to represent the CBF, assuming\nonly that the Lipschitz constant of such functions can be efficiently bounded.\nFurthermore, if the CBF parameterization is convex, then under mild\nassumptions, so is our learning process. We end with extensive numerical\nevaluations of our results on both planar and realistic examples, using both\nrandom feature and deep neural network parameterizations of the CBF. To the\nbest of our knowledge, these are the first results that learn provably safe\ncontrol barrier functions from data.\n', 'Recursively Feasible Probabilistic Safe Online Learning with Control\n  Barrier Functions   Learning-based control has recently shown great efficacy in performing\ncomplex tasks for various applications. However, to deploy it in real systems,\nit is of vital importance to guarantee the system will stay safe. Control\nBarrier Functions (CBFs) offer mathematical tools for designing\nsafety-preserving controllers for systems with known dynamics. In this article,\nwe first introduce a model-uncertainty-aware reformulation of CBF-based\nsafety-critical controllers using Gaussian Process (GP) regression to close the\ngap between an approximate mathematical model and the real system, which\nresults in a second-order cone program (SOCP)-based control design. We then\npresent the pointwise feasibility conditions of the resulting safety\ncontroller, highlighting the level of richness that the available system\ninformation must meet to ensure safety. We use these conditions to devise an\nevent-triggered online data collection strategy that ensures the recursive\nfeasibility of the learned safety controller. Our method works by constantly\nreasoning about whether the current information is sufficient to ensure safety\nor if new measurements under active safe exploration are required to reduce the\nuncertainty. As a result, our proposed framework can guarantee the forward\ninvariance of the safe set defined by the CBF with high probability, even if it\ncontains a priori unexplored regions. We validate the proposed framework in two\nnumerical simulation experiments.\n']","[('learning control', 0.5795210003852844), ('control learning', 0.5550607442855835), ('safety controller', 0.551503598690033), ('learning based control', 0.5395585894584656), ('safe learning', 0.5065115094184875), ('optimal control policies', 0.5047518610954285), ('safe control', 0.4997451603412628), ('control barrier functions', 0.4915899336338043), ('state control constraints', 0.47306156158447266), ('safety guarantees', 0.4626506268978119)]"
1798,1798,16,1798_decompositions projective_semiorthogonal decompositions_category coherent sheaves_semiorthogonal decomposition,"['decompositions projective', 'semiorthogonal decompositions', 'category coherent sheaves', 'semiorthogonal decomposition', 'projective varieties', 'derived category coherent', 'coherent sheaves', 'derived categories', 'bounded derived categories', 'derived category']","['Semiorthogonal indecomposability of minimal irregular surfaces   We prove a relative version of the fact that semiorthogonal decompositions of\nthe bounded derived category of coherent sheaves are strongly constrained by\nthe base locus of the canonical linear system. As an application we prove that\nthe derived category of minimal surfaces $X$ with $H^1 (X,\\mathcal{O}_X) \\neq\n0$ are semiorthogonally indecomposable.\n', 'Derived categories of singular surfaces   We develop an approach that allows to construct semiorthogonal decompositions\nof derived categories of surfaces with cyclic quotient singularities whose\ncomponents are equivalent to derived categories of local finite dimensional\nalgebras. We first explain how to induce a semiorthogonal decomposition of a\nsurface $X$ with rational singularities from a semiorthogonal decomposition of\nits resolution. In the case when $X$ has cyclic quotient singularities, we\nintroduce the condition of adherence for the components of the semiorthogonal\ndecomposition of the resolution that allows to identify the components of the\ninduced decomposition with derived categories of local finite dimensional\nalgebras. Further, we present an obstruction in the Brauer group of $X$ to the\nexistence of such semiorthogonal decomposition, and show that in the presence\nof the obstruction a suitable modification of the adherence condition gives a\nsemiorthogonal decomposition of the twisted derived category of $X$. We\nillustrate the theory by exhibiting a semiorthogonal decomposition for the\nuntwisted or twisted derived category of any normal projective toric surface\ndepending on whether its Weil divisor class group is torsion-free or not. For\nweighted projective planes we compute the generators of the components\nexplicitly and relate our results to the results of Kawamata based on iterated\nextensions of reflexive sheaves of rank 1.\n', ""Moduli spaces of semiorthogonal decompositions in families   For a smooth projective family of schemes we prove that a semiorthogonal\ndecomposition of the bounded derived category of coherent sheaves of a fibre\nuniquely deforms over an \\'etale neighbourhood of the point. We do this using a\ncomparison theorem between semiorthogonal decompositions and decomposition\ntriangles of the structure sheaf of the diagonal. We then apply to the latter a\ndeformation theory for morphisms with a fixed lift of the target, which is\ndeveloped in the appendix.\n  Using this as a key ingredient we introduce a moduli space which classifies\nsemiorthogonal decompositions of the category of perfect complexes of a smooth\nprojective family. Using Artin's criterion, we show that this is an \\'etale\nalgebraic space over the base scheme of the family, which can be\nnon-quasicompact and non-separated.\n  We generalise this to families of geometric noncommutative schemes in the\nsense of Orlov. We also define a subfunctor classifying nontrivial\nsemiorthogonal decompositions only, and conjecture it is an open and closed\nsubspace.\n""]","[('decompositions projective', 0.5580639839172363), ('semiorthogonal decompositions', 0.5366138219833374), ('category coherent sheaves', 0.5117232203483582), ('semiorthogonal decomposition', 0.5090520977973938), ('projective varieties', 0.49765101075172424), ('derived category coherent', 0.49611175060272217), ('coherent sheaves', 0.4941169023513794), ('derived categories', 0.46007537841796875), ('bounded derived categories', 0.45395174622535706), ('derived category', 0.4395897686481476)]"
1799,1799,16,1799_compact quantum groups_quantum groups_compact quantum group_twisted tensor products,"['compact quantum groups', 'quantum groups', 'compact quantum group', 'twisted tensor products', 'hopf algebras', 'quantum group', 'tensor product algebras', 'twisted tensor product', 'algebraic quantum', 'hopf algebra']","['Quantum group-twisted tensor products of C*-algebras II   For a quasitriangular C*-quantum group, we enrich the twisted tensor product\nconstructed in the first part of this series to a monoidal structure on the\ncategory of its continuous coactions on C*-algebras. We define braided\nC*-quantum groups, where the comultiplication takes values in a twisted tensor\nproduct. We show that compact braided C*-quantum groups yield compact quantum\ngroups by a semidirect product construction.\n', 'Partial $*$-algebraic quantum groups and Drinfeld doubles of partial\n  compact quantum groups   We introduce a notion of partial algebraic quantum group. This is an\nimportant special case of a weak multiplier Hopf algebra with integrals, as\nintroduced in the work of Van Daele and Wang. At the same time, it generalizes\nthe notion of partial compact quantum group as introduced by De Commer and\nTimmermann. As an application, we show that the Drinfeld double of a partial\ncompact quantum group can be defined as a partial $*$-algebraic quantum group.\n', 'Algebraic quantum groups III. The modular and the analytic structure   This is the last part of a series of three papers on the subject. In the\nfirst part we have considered the duality of algebraic quantum groups. In that\npaper, we use the term algebraic quantum group for a regular multiplier Hopf\nalgebra with integrals. We treat the duality as studied in that theory. In the\nsecond part we have considered the duality for multiplier Hopf $^*$-algebras\nwith positive integrals. The main purpose of that paper is to explain how it\ngives rise to a locally compact quantum group in the sense of Kustermans and\nVaes. In a preliminary section of the second part we have mentioned the\nanalytic structure of such a $^*$-algebraic quantum group. We have not gone\ninto the details, except for that part needed to obtain that the scaling\nconstant is trivial and for proving that the composition of a positive left\nintegral with the antipode gives a right integral that is again positive. Also\nthe construction of the square root. of the modular element is discussed and\nused to obtain the two Haar weights on the associated locally compact quantum\ngroup. In this paper we treat the analytic structure of the $^*$-algebraic\nquantum group in detail. The analytic structure is intimately related with the\nmodular structure. We obtain a collection of interesting formulas, relating the\ntwo structures. Further we compare these results with formulas obtained in the\nframework of general locally compact quantum groups. As for the first two\npapers in this series, also here no new results are obtained. On the other hand\nthe approach is different, more direct and instructive. It might help the\nreader for understanding the more general theory of locally compact quantum\ngroups.\n']","[('compact quantum groups', 0.6258320212364197), ('quantum groups', 0.609168529510498), ('compact quantum group', 0.5925213694572449), ('twisted tensor products', 0.5615351796150208), ('hopf algebras', 0.5612486600875854), ('quantum group', 0.5567975044250488), ('tensor product algebras', 0.5567657351493835), ('twisted tensor product', 0.5380640625953674), ('algebraic quantum', 0.5339590311050415), ('hopf algebra', 0.4907475411891937)]"
1800,1800,16,1800_epidemic_epidemics_infection rates_random graphs,"['epidemic', 'epidemics', 'infection rates', 'random graphs', 'infection rate', 'extinction time', 'offspring distribution', 'process survives', 'contact process', 'mean extinction']","[""The contact process with fitness on random trees   The contact process is a simple model for the spread of an infection in a\nstructured population. We consider a variant of this process on\nBienaym\\'e-Galton-Watson trees, where vertices are equipped with a random\nfitness representing inhomogeneous transmission rates among individuals. In\nthis paper, we establish conditions under which this inhomogeneous contact\nprocess exhibits a phase transition. We first prove that if certain mixed\nmoments of the joint offspring and fitness distribution are finite, then the\nsurvival threshold is strictly positive. Further, we show that, if slightly\ndifferent mixed moments are infinite, then this implies that there is no phase\ntransition and the process survives with positive probability for any choice of\nthe infection parameter. A similar dichotomy is known for the contact process\non a Bienaym\\'e-Galton-Watson tree. However, we show that the introduction of\nfitness means that we have to take into account the combined effect of fitness\nand offspring distribution to decide which scenario occurs.\n"", 'On the One-Dimensional Contact Process with Enhancements   We study a one-dimensional contact process with two infection parameters, one\ngiving the infection rates at the boundaries of a finite infected region and\nthe other one the rates within that region. We prove that the critical value of\neach of these parameters is a strictly monotone continuous function of the\nother parameter. We also show that if one of these parameters is equal to the\ncritical value of the standard contact process and the other parameter is\nstrictly larger, then the infection starting from a single point has positive\nprobability of surviving. This is in contrast with another result also obtained\nhere, that the critical contact process on the half line with enhanced\ninfection rate at finitely many sites also dies out.\n', 'The effect of avoiding known infected neighbors on the persistence of a\n  recurring infection process   We study a generalization of the classical contact process (SIS epidemic\nmodel) in a directed graph $G$. Our model is a continuous-time interacting\nparticle system in which at every time, each vertex is either healthy or\ninfected, and each oriented edge is either active or inactive. Infected\nvertices become healthy at rate $1$, and pass the infection along each active\noutgoing edge at rate $\\lambda$. At rate $\\alpha$, healthy individuals\ndeactivate each incoming edge from their infected neighbors. We study the\npersistence time of this epidemic model on the lattice $\\mathbb{Z}$, the\n$n$-cycle $\\mathbb{Z}_n$, and the $n$-star graph. We show that on $\\mathbb{Z}$,\nfor every $\\alpha>0$, there is a phase transition in $\\lambda$ between almost\nsure extinction and positive probability of indefinite survival; on\n$\\mathbb{Z}_n$ we show that there is a phase transition between\npoly-logarithmic and exponential survival time as the size of the graph\nincreases. On the star graph, we show that the survival time is\n$n^{\\Delta+o(1)}$ for an explicit function $\\Delta(\\alpha,\\lambda)$ whenever\n$\\alpha>0$ and $\\lambda>0$. In the cases of $\\mathbb{Z}$ and $\\mathbb{Z}_n$,\nour results qualitatively match what has been shown for the classical contact\nprocess, while in the case of the star graph, the classical contact process\nexhibits exponential survival for all $\\lambda > 0$, which is qualitatively\ndifferent from our result. This model presents a challenge because, unlike the\nclassical contact process, it has not been shown to be monotonic in the\ninfection parameter $\\lambda$ or the initial infected set.\n']","[('epidemic', 0.4598323106765747), ('epidemics', 0.4580245018005371), ('infection rates', 0.4203612208366394), ('random graphs', 0.4130636751651764), ('infection rate', 0.41273289918899536), ('extinction time', 0.3986416161060333), ('offspring distribution', 0.3904571533203125), ('process survives', 0.3891266882419586), ('contact process', 0.38012728095054626), ('mean extinction', 0.3751738667488098)]"
1801,1801,16,1801_multiplier ideals_ideals associated_ideals_extension bernstein,"['multiplier ideals', 'ideals associated', 'ideals', 'extension bernstein', 'jacobian ideal', 'ideals upper', 'type bernstein', 'bernstein sato', 'polynomials commutative', 'ideal strongly']","['Estimates for zero loci of Bernstein-Sato ideals   We give estimates for the zero loci of Bernstein-Sato ideals. An upper bound\nis proved as a multivariate generalisation of the upper bound by Lichtin for\nthe roots of Bernstein-Sato polynomials. The lower bounds generalise the fact\nthat log-canonical thresholds, small jumping numbers of multiplier ideals, and\ntheir real versions provide roots of Bernstein-Sato polynomials.\n', 'Zero loci of Bernstein-Sato ideals -- II   We have recently proved a precise relation between Bernstein-Sato ideals of\ncollections of polynomials and monodromy of generalized nearby cycles. In this\narticle we extend this result to other ideals of Bernstein-Sato type.\n', ""A Note on Bernstein-Sato Varieties for Tame Divisors and Arrangements   For strongly Euler-homogeneous, Saito-holonomic, and tame analytic germs we\nconsider general types of multivariate Bernstein-Sato ideals associated to\narbitrary factorizations of our germ. We show the zero loci of these ideals are\npurely codimension one and the zero loci associated to different factorizations\nare related by a diagonal property. If, additionally, the divisor is a\nhyperplane arrangement, we show the Bernstein-Sato ideals attached to a\nfactorization into linear forms are principal. As an application, we\nindependently verify and improve an estimate of Maisonobe's regarding standard\nBernstein-Sato ideals for reduced, generic arrangements: we compute the\nBernstein-Sato ideal for a factorization into linear forms and we compute its\nzero locus for other factorizations.\n""]","[('multiplier ideals', 0.5272096395492554), ('ideals associated', 0.5119183659553528), ('ideals', 0.44262465834617615), ('extension bernstein', 0.424485981464386), ('jacobian ideal', 0.4204191267490387), ('ideals upper', 0.4019003212451935), ('type bernstein', 0.3875391483306885), ('bernstein sato', 0.3783227205276489), ('polynomials commutative', 0.37206947803497314), ('ideal strongly', 0.3556548058986664)]"
1802,1802,16,1802_tilings finite_tilings mathbb_tilings_tiling mathbb,"['tilings finite', 'tilings mathbb', 'tilings', 'tiling mathbb', 'tiling problems', 'tiles', 'tiling', 'tile', 'tiles mathbb', 'tile mathbb']","['Undecidability of Translational Tiling with Three Tiles   Is there a fixed dimension $n$ such that translational tiling of\n$\\mathbb{Z}^n$ with a monotile is undecidable? Several recent results support a\npositive answer to this question. Greenfeld and Tao disprove the periodic\ntiling conjecture by showing that an aperiodic monotile exists in sufficiently\nhigh dimension $n$ [Ann. Math. 200(2024), 301-363]. In another paper [to appear\nin J. Eur. Math. Soc.], they also show that if the dimension $n$ is part of the\ninput, then the translational tiling for subsets of $\\mathbb{Z}^n$ with one\ntile is undecidable. These two results are very strong pieces of evidence for\nthe conjecture that translational tiling of $\\mathbb{Z}^n$ with a monotile is\nundecidable, for some fixed $n$. This paper gives another supportive result for\nthis conjecture by showing that translational tiling of the $4$-dimensional\nspace with a set of three connected tiles is undecidable.\n', 'The structure of translational tilings in $\\mathbb{Z}^d$   We obtain structural results on translational tilings of periodic functions\nin $\\mathbb{Z}^d$ by finite tiles. In particular, we show that any level one\ntiling of a periodic set in $\\mathbb{Z}^2$ must be weakly periodic (the\ndisjoint union of sets that are individually periodic in one direction), but\npresent a counterexample of a higher level tiling of $\\mathbb{Z}^2$ that fails\nto be weakly periodic. We also establish a quantitative version of the\ntwo-dimensional periodic tiling conjecture which asserts that any finite tile\nin $\\mathbb{Z}^2$ that admits a tiling, must admit a periodic tiling, by\nproviding a polynomial bound on the period; this also gives an exponential-type\nbound on the computational complexity of the problem of deciding whether a\ngiven finite subset of $\\mathbb{Z}^2$ tiles or not. As a byproduct of our\nstructural theory, we also obtain an explicit formula for a universal period\nfor all tilings of a one-dimensional tile.\n', 'Undecidable translational tilings with only two tiles, or one nonabelian\n  tile   We construct an example of a group $G = \\mathbb{Z}^2 \\times G_0$ for a finite\nabelian group $G_0$, a subset $E$ of $G_0$, and two finite subsets $F_1,F_2$ of\n$G$, such that it is undecidable in ZFC whether $\\mathbb{Z}^2\\times E$ can be\ntiled by translations of $F_1,F_2$. In particular, this implies that this\ntiling problem is aperiodic, in the sense that (in the standard universe of\nZFC) there exist translational tilings of $E$ by the tiles $F_1,F_2$, but no\nperiodic tilings. Previously, such aperiodic or undecidable translational\ntilings were only constructed for sets of eleven or more tiles (mostly in\n$\\mathbb{Z}^2$). A similar construction also applies for $G = \\mathbb{Z}^d$ for\nsufficiently large $d$. If one allows the group $G_0$ to be non-abelian, a\nvariant of the construction produces an undecidable translational tiling with\nonly one tile $F$.\n  The argument proceeds by first observing that a single tiling equation is\nable to encode an arbitrary system of tiling equations, which in turn can\nencode an arbitrary system of certain functional equations once one has two or\nmore tiles. In particular, one can use two tiles to encode tiling problems for\nan arbitrary number of tiles.\n']","[('tilings finite', 0.6565556526184082), ('tilings mathbb', 0.5429906249046326), ('tilings', 0.5189284682273865), ('tiling mathbb', 0.5015541315078735), ('tiling problems', 0.48867109417915344), ('tiles', 0.4773291349411011), ('tiling', 0.4690118432044983), ('tile', 0.4641045033931732), ('tiles mathbb', 0.4505038559436798), ('tile mathbb', 0.4226452112197876)]"
1803,1803,15,1803_willmore flow_curvature flow_curvature flow two_inverse curvature flow,"['willmore flow', 'curvature flow', 'curvature flow two', 'inverse curvature flow', 'flow surfaces', 'mean curvature flow', 'flow arising', 'surfaces boundary', 'flow converges', 'parabolic initial boundary']","[""Global existence for the Willmore flow with boundary via Simon's Li-Yau\n  inequality   It is well-known that the Willmore flow of closed spherical immersions exists\nglobally in time and converges if the initial datum has Willmore energy below\n$8\\pi$ - exactly the Li-Yau energy threshold below which all closed immersions\nare embedded. Extending the Li-Yau inequality for closed surfaces via Simon's\nmonotonicity formula also for surfaces with boundary, given Dirichlet boundary\nconditions, one obtains an energy threshold $C_{\\mathrm{LY}}$ below which\nsurfaces with this boundary are embedded. By a slight modification, one obtains\na threshold $C_{\\mathrm{LY}}^{\\mathrm{rot}}$ below which surfaces of revolution\nsatisfying the boundary data have no self-intersections on the rotation axis.\n  With a new argument, using this modified Li-Yau inequality and tools from\ngeometric measure theory, we show that the Willmore flow with Dirichlet\nboundary data starting in cylindrical surfaces of revolution exists globally in\ntime if the energy of the initial datum is below\n$C_{\\mathrm{LY}}^{\\mathrm{rot}}$. Moreover, given Dirichlet boundary data, we\nalso obtain the existence of a Willmore minimizer in the class of cylindrical\nsurfaces of revolution if the corresponding infimum lies below\n$C_{\\mathrm{LY}}^{\\mathrm{rot}}$ which improves previous results for the\nstationary problem.\n"", 'The Willmore Flow of Tori of Revolution   We study long-time existence and asymptotic behavior for the $L^2$-gradient\nflow of the Willmore energy, under the condition that the initial datum is a\ntorus of revolution. We show that if an initial datum has Willmore energy below\n$8\\pi$ then the solution of the Willmore flow converges for $t \\rightarrow\n\\infty$ to the Clifford Torus, possibly rescaled and translated. The energy\nthreshold of $8\\pi$ turns out to be optimal for such a convergence result. We\ngive an application to the conformally constrained Willmore minimization\nproblem.\n', 'Willmore Flow of Complete Surfaces   We consider the Willmore flow equation for complete, properly immersed\nsurfaces in Rn. Given bounded geometry on the initial surface, we extend the\nresult by Kuwert and Sch\\""atzle in 2002 and prove short time existence and\nuniqueness of the Willmore flow. We also show that a complete Willmore surface\nwith low Willmore energy must be a plane, and that a Willmore flow with low\ninitial energy and Euclidean volume growth must converge smoothly to a plane.\n']","[('willmore flow', 0.5462814569473267), ('curvature flow', 0.5382236838340759), ('curvature flow two', 0.533074140548706), ('inverse curvature flow', 0.5151610374450684), ('flow surfaces', 0.4975452423095703), ('mean curvature flow', 0.4965015947818756), ('flow arising', 0.4800954759120941), ('surfaces boundary', 0.4797459542751312), ('flow converges', 0.4702593684196472), ('parabolic initial boundary', 0.44426873326301575)]"
1804,1804,15,1804_channel state information_dimensional channel_learning channel_high dimensional channel,"['channel state information', 'dimensional channel', 'learning channel', 'high dimensional channel', 'channel prediction', 'state art channel', 'channel vectors', 'mimo channel', 'channel state', 'global channel']","['Passive Channel Charting: Locating Passive Targets using Wi-Fi Channel\n  State Information   We propose passive channel charting, an extension of channel charting to\npassive target localization. As in conventional channel charting, we follow a\ndimensionality reduction approach to reconstruct a physically interpretable map\nof target positions from similarities in high-dimensional channel state\ninformation. We show that algorithms and neural network architectures developed\nin the context of channel charting with active mobile transmitters can be\nstraightforwardly applied to the passive case, where we assume a scenario with\nstatic transmitters and receivers and a mobile target. We evaluate our method\non a channel state information dataset collected indoors with a distributed\nsetup of ESPARGOS Wi-Fi sensing antenna arrays. This scenario can be\ninterpreted as either a multi-static or passive radar system. We demonstrate\nthat passive channel charting outperforms a baseline based on classical\ntriangulation in terms of localization accuracy. We discuss our results and\nhighlight some unsolved issues related to the proposed concept.\n', 'Augmenting Channel Charting with Classical Wireless Source Localization\n  Techniques   Channel Charting aims to construct a map of the radio environment by\nleveraging similarity relationships found in high-dimensional channel state\ninformation. Although resulting channel charts usually accurately represent\nlocal neighborhood relationships, even under conditions with strong multipath\npropagation, they often fall short in capturing global geometric features. On\nthe other hand, classical model-based localization methods, such as\ntriangulation and multilateration, can easily localize signal sources in the\nglobal coordinate frame. However, these methods rely heavily on the assumption\nof line-of-sight channels and distributed antenna deployments. Based on\nmeasured data, we compare classical source localization techniques to channel\ncharts with respect to localization performance. We suggest and evaluate\nmethods to enhance Channel Charting with model-based localization approaches:\nOne approach involves using information derived from classical localization\nmethods to map channel chart locations to physical positions after conventional\ntraining of the forward charting function. Foremost, though, we suggest to\nincorporate information from model-based approaches during the training of the\nforward charting function in what we call ""augmented Channel Charting"". We\ndemonstrate that Channel Charting can outperform classical localization methods\non the considered dataset.\n', 'Wireless Channel Charting: Theory, Practice, and Applications   Channel charting is a recently proposed framework that applies dimensionality\nreduction to channel state information (CSI) in wireless systems with the goal\nof associating a pseudo-position to each mobile user in a low-dimensional\nspace: the channel chart. Channel charting summarizes the entire CSI dataset in\na self-supervised manner, which opens up a range of applications that are tied\nto user location. In this article, we introduce the theoretical underpinnings\nof channel charting and present an overview of recent algorithmic developments\nand experimental results obtained in the field. We furthermore discuss concrete\napplication examples of channel charting to network- and user-related\napplications, and we provide a perspective on future developments and\nchallenges as well as the role of channel charting in next-generation wireless\nnetworks.\n']","[('channel state information', 0.5496636033058167), ('dimensional channel', 0.5462782382965088), ('learning channel', 0.5139912366867065), ('high dimensional channel', 0.5126778483390808), ('channel prediction', 0.5092295408248901), ('state art channel', 0.5004677772521973), ('channel vectors', 0.48076683282852173), ('mimo channel', 0.4721081852912903), ('channel state', 0.4657939374446869), ('global channel', 0.464414119720459)]"
1805,1805,15,1805_systems negative_nonlinear systems_imaginary_systems nonlinear,"['systems negative', 'nonlinear systems', 'imaginary', 'systems nonlinear', 'robust stability', 'state feedback control', 'uncertain system', 'class nonlinear systems', 'positive feedback', 'strictly negative']","['Converse negative imaginary theorems   Converse negative imaginary theorems for linear time-invariant systems are\nderived. In particular, we provide necessary and sufficient conditions for a\nfeedback system to be robustly stable against various types of negative\nimaginary (NI) uncertainty. Uncertainty classes of marginally stable NI systems\nand stable strictly NI systems with restrictions on their static or\ninstantaneous gains are considered. It is shown that robust stability against\nthe former class entails the strictly NI property, whereas the latter class\nentails the NI property. We also establish a non-existence result that no\nstable system can robustly stabilise all marginally stable NI uncertainty,\nthereby showing that the uncertainty class of NI systems is too large as far as\nrobust feedback stability is concerned, thus justifying the consideration of\nsubclasses of NI systems with constrained static or instantaneous gains.\n', 'Necessary and Sufficient Conditions for State Feedback Equivalence to\n  Negative Imaginary Systems   In this paper, we present necessary and sufficient conditions under which a\nlinear time-invariant (LTI) system is state feedback equivalent to a negative\nimaginary (NI) system. More precisely, we show that a minimal LTI strictly\nproper system can be rendered NI using full state feedback if and only if it\ncan be output transformed into a system, which has relative degree less than or\nequal to two and is weakly minimum phase. We also considered the problems of\nstate feedback equivalence to output strictly negative imaginary systems and\nstrongly strict negative imaginary systems. Then we apply the NI state feedback\nequivalence result to robustly stabilize an uncertain system with strictly\nnegative imaginary uncertainty. An example is provided to illustrate the\nproposed results, for the purpose of stabilizing an uncertain system.\n', 'Negative Imaginary State Feedback Equivalence for Systems of Relative\n  Degree One and Relative Degree Two   This paper presents necessary and sufficient conditions under which a linear\nsystem of relative degree either one or two is state feedback equivalent to a\nnegative imaginary (NI) system. More precisely, we show for a class of linear\ntime-invariant strictly proper systems, that such a system can be rendered\nminimal and NI using full state feedback if and only if it is controllable and\nweakly minimum phase. A strongly strict negative imaginary state feedback\nequivalence result is also provided. The NI state feedback equivalence result\nis then applied in a robust stabilization problem for an uncertain system with\na strictly negative imaginary uncertainty.\n']","[('systems negative', 0.5269278287887573), ('nonlinear systems', 0.42505455017089844), ('imaginary', 0.42323121428489685), ('systems nonlinear', 0.4220520853996277), ('robust stability', 0.41236117482185364), ('state feedback control', 0.4105636775493622), ('uncertain system', 0.3934114873409271), ('class nonlinear systems', 0.3833771347999573), ('positive feedback', 0.3514452278614044), ('strictly negative', 0.3460429608821869)]"
1806,1806,15,1806_symplectic matrices_symplectic matrix_symplectic subspaces_real symmetric matrices,"['symplectic matrices', 'symplectic matrix', 'symplectic subspaces', 'real symmetric matrices', 'positive definite matrices', 'symmetric positive definite', 'eigenvalues hermitian', 'symplectic', 'known symplectic', 'positive semidefinite matrices']","[""Orthosymplectic diagonalization in Williamson's theorem   In this paper, we provide an algebraic condition on any $2n \\times 2n$ real\nsymmetric positive definite matrix which is necessary and sufficient for the\nmatrix to be diagonalized by an orthosymplectic matrix in the sense of\nWilliamson's theorem.\n"", ""Block perturbation of symplectic matrices in Williamson's theorem   Williamson's theorem states that for any $2n \\times 2n$ real positive\ndefinite matrix $A$, there exists a $2n \\times 2n$ real symplectic matrix $S$\nsuch that $S^TAS=D \\oplus D$, where $D$ is an $n\\times n$ diagonal matrix with\npositive diagonal entries which are known as the symplectic eigenvalues of $A$.\nLet $H$ be any $2n \\times 2n$ real symmetric matrix such that the perturbed\nmatrix $A+H$ is also positive definite. In this paper, we show that any\nsymplectic matrix $\\tilde{S}$ diagonalizing $A+H$ in Williamson's theorem is of\nthe form $\\tilde{S}=S Q+\\mathcal{O}(\\|H\\|)$, where $Q$ is a $2n \\times 2n$ real\nsymplectic as well as orthogonal matrix. Moreover, $Q$ is in\n$\\textit{symplectic block diagonal}$ form with the block sizes given by twice\nthe multiplicities of the symplectic eigenvalues of $A$. Consequently, we show\nthat $\\tilde{S}$ and $S$ can be chosen so that\n$\\|\\tilde{S}-S\\|=\\mathcal{O}(\\|H\\|)$. Our results hold even if $A$ has repeated\nsymplectic eigenvalues. This generalizes the stability result of symplectic\nmatrices for non-repeated symplectic eigenvalues given by Idel, Gaona, and Wolf\n[$\\textit{Linear Algebra Appl., 525:45-58, 2017}$].\n"", ""On generalization of Williamson's theorem to real symmetric matrices   Williason's theorem states that if $A$ is a $2n \\times 2n$ real symmetric\npositive definite matrix then there exists a $2n \\times 2n$ real symplectic\nmatrix $M$ such that $M^T A M=D \\oplus D$, where $D$ is an $n \\times n$\ndiagonal matrix with positive diagonal entries known as the symplectic\neigenvalues of $A$. The theorem is known to be generalized to $2n \\times 2n$\nreal symmetric positive semidefinite matrices whose kernels are symplectic\nsubspaces of $\\mathbb{R}^{2n}$, in which case, some of the diagonal entries of\n$D$ are allowed to be zero. In this paper, we further generalize Williamson's\ntheorem to $2n \\times 2n$ real symmetric matrices by allowing the diagonal\nelements of $D$ to be any real numbers, and thus extending the notion of\nsymplectic eigenvalues to real symmetric matrices. Also, we provide an explicit\ndescription of symplectic eigenvalues, construct symplectic matrices achieving\nWilliamson's theorem type decomposition, and establish perturbation bounds on\nsymplectic eigenvalues for a class of $2n \\times 2n$ real symmetric matrices\ndenoted by $\\operatorname{EigSpSm}(2n)$. The set $\\operatorname{EigSpSm}(2n)$\ncontains $2n \\times 2n$ real symmetric positive semidefinite whose kernels are\nsymplectic subspaces of $\\mathbb{R}^{2n}$. Our perturbation bounds on\nsymplectic eigenvalues for $\\operatorname{EigSpSm}(2n)$ generalize known\nperturbation bounds on symplectic eigenvalues of positive definite matrices\ngiven by Bhatia and Jain \\textit{[J. Math. Phys. 56, 112201 (2015)]}.\n""]","[('symplectic matrices', 0.650741696357727), ('symplectic matrix', 0.6241223812103271), ('symplectic subspaces', 0.526611328125), ('real symmetric matrices', 0.5096653699874878), ('positive definite matrices', 0.5088382959365845), ('symmetric positive definite', 0.4915362596511841), ('eigenvalues hermitian', 0.48251354694366455), ('symplectic', 0.4816284477710724), ('known symplectic', 0.48154309391975403), ('positive semidefinite matrices', 0.4814663529396057)]"
1807,1807,15,1807_analytic half plane_holomorphic functions_univalent functions_quasiconformal,"['analytic half plane', 'holomorphic functions', 'univalent functions', 'quasiconformal', 'riemann mapping', 'sets holomorphic', 'analytic half', 'harmonic mappings', 'quasiconformality', 'sharp analytic']","['Criteria for univalence and quasiconformal extension for harmonic\n  mappings on planar domains   If $\\Omega$ is a simply connected domain in $\\overline{{\\mathbb C}}$ then,\naccording to the Ahlfors-Gehring theorem, $\\Omega$ is a quasidisk if and only\nif there exists a sufficient condition for the univalence of holomorphic\nfunctions in $\\Omega$ in relation to the growth of their Schwarzian derivative.\nWe extend this theorem to harmonic mappings by proving a univalence criterion\non quasidisks. We also show that the mappings satisfying this criterion admit a\nhomeomorphic extension to $\\overline{{\\mathbb C}}$ and, under the additional\nassumption of quasiconformality in $\\Omega$, they admit a quasiconformal\nextension to $\\overline{{\\mathbb C}}$.\n  The Ahlfors-Gehring theorem has been extended to finitely connected domains\n$\\Omega$ by Osgood, Beardon and Gehring, who showed that a Schwarzian criterion\nfor univalence holds in $\\Omega$ if and only if the components of\n$\\partial\\Omega$ are either points or quasicircles. We generalize this theorem\nto harmonic mappings.\n', ""Grunsky operator, Grinshpan's conjecture and universal Teichmuller space   A. Grinshpan posed a deep conjecture on the norm of the Grunsky operator\ngenerated by univalent functions in the disk. It gives a quantitative answer in\nterms of the Grunsky coefficients, to which extent a univalent function\ndetermines the bound of dilatations of its quasiconformal extensions. We\nprovide the proof of this conjecture and its various analytic, geometric and\npotential applications.\n  Another result concerns the model of universal Teichmuller space by Grunsky\ncoefficients.\n"", 'A Fermionic Grunsky operator   To a conformal map $f$ from the disk $\\mathbb{D}$ into the complex plane onto\na domain with rectifiable Ahlfors-regular boundary, we associate a new kind of\nGrunsky operator on the Hardy space of the unit disk. This is analogous to the\nclassical Grunsky operator, which itself can be viewed as an operator on\nBergman or Dirichlet space. We show that the pull-back of the Smirnov space of\nthe complement of $f(\\mathbb{D})$ by $f$ is the graph of the Grunsky operator.\nWe also characterize those domains with rectifiable Ahlfors-regular boundaries\nsuch that the Grunsky operator is Hilbert-Schmidt. In particular, we show that\nif the Grunsky operator is Hilbert-Schmidt, then $f(\\mathbb{D})$ is a\nWeil-Petersson quasidisk. The formulations of the results and proofs make\nessential use of a geometric treatment of Smirnov space as a space of\nhalf-order differentials.\n']","[('analytic half plane', 0.5080252289772034), ('holomorphic functions', 0.4876672923564911), ('univalent functions', 0.47151145339012146), ('quasiconformal', 0.4713428020477295), ('riemann mapping', 0.4671870172023773), ('sets holomorphic', 0.46441128849983215), ('analytic half', 0.4592535197734833), ('harmonic mappings', 0.4576879143714905), ('quasiconformality', 0.45686542987823486), ('sharp analytic', 0.4566642940044403)]"
1808,1808,15,1808_cloaking_elastic scattering_layer potential_scattered field,"['cloaking', 'elastic scattering', 'layer potential', 'scattered field', 'shielding', 'scattering coefficients', 'shields', 'elastic moduli', 'hydrodynamic', 'helmholtz']","['Far field broadband approximate cloaking for the Helmholtz equation with\n  a Drude-Lorentz refractive index   This paper concerns the analysis of a passive, broadband approximate cloaking\nscheme for the Helmholtz equation in ${\\mathbb R}^d$ for $d=2$ or $d=3$. Using\nideas from transformation optics, we construct an approximate cloak by\n``blowing up"" a small ball of radius $\\epsilon>0$ to one of radius $1$. In the\nanisotropic cloaking layer resulting from the ``blow-up"" change of variables,\nwe incorporate a Drude-Lorentz-type model for the index of refraction, and we\nassume that the cloaked object is a soft (perfectly conducting) obstacle. We\nfirst show that (for any fixed $\\epsilon$) there are no real transmission\neigenvalues associated with the inhomogeneity representing the cloak, which\nimplies that the cloaking devices we have created will not yield perfect\ncloaking at any frequency, even for a single incident time harmonic wave.\nSecondly, we establish estimates on the scattered field due to an arbitrary\ntime harmonic incident wave. These estimates show that, as $\\epsilon$\napproaches $0$, the $L^2$-norm of the scattered field outside the cloak, and\nits far field pattern, approach $0$ uniformly over any bounded band of\nfrequencies. In other words: our scheme leads to broadband approximate cloaking\nfor arbitrary incident time harmonic waves.\n', 'Simultaneously Cloaking Electric and Hydrodynamic Fields via\n  Electro-osmosis   In this paper, we develop a general mathematical framework for the\nelectro-osmosis problem to design simultaneous microscale electric and\nhydrodynamic cloaking in a Hele-Shaw configuration. A novel approach to\nachieving simultaneously cloaking both the electric and flow fields through a\ncombination of scattering-cancellation technology and an electro-osmosis effect\nis proposed. In the design, the electric field is manipulated with\nscattering-cancellation technology while the pressure with electro-osmosis\neffect. As proof of this concept, the perfect electric and hydrodynamic\ncloaking conditions are derived for the cloaks with the cross-sectional shape\nbeing annulus or confocal ellipses using the layer potential techniques.\nFurthermore, we also propose an optimization scheme for the design of\napproximate cloaks within general geometries and prove the well-posedness of\nthe optimization problem. In particular, the conditions that can ensure the\nsimultaneous occurrence of approximate cloaks for general geometries are also\nestablished. Our theoretical findings are validated by a variety of numerical\nresults and guide efficiently designing electric-related multiphysics cloaking.\n', 'Enhanced Microscale Hydrodynamic Near-cloaking using Electro-osmosis   In this paper, we develop a general mathematical framework for enhanced\nhydrodynamic near-cloaking of electro-osmotic flow for more complex shapes,\nwhich is obtained by simultaneously perturbing the inner and outer boundaries\nof the perfect cloaking structure. We first derive the asymptotic expansions of\nperturbed fields and obtain a first-order coupled system. We then establish the\nrepresentation formula of the solution to the first-order coupled system using\nthe layer potential techniques. Based on the asymptotic analysis, the enhanced\nhydrodynamic near-cloaking conditions are derived for the control region with\ngeneral cross-sectional shape. The conditions reveal the inner relationship\nbetween the shapes of the object and the control region. Especially, for the\nshape of a deformed annulus or confocal ellipses cylinder, the cloaking\nconditions and relationship of shapes are quantified more accurately. Our\ntheoretical findings are validated and supplemented by a variety of numerical\nresults. The results in this paper also provide a mathematical foundation for\nmore complex hydrodynamic cloaking.\n']","[('cloaking', 0.6027275323867798), ('elastic scattering', 0.42652779817581177), ('layer potential', 0.3112228810787201), ('scattered field', 0.30664199590682983), ('shielding', 0.29459914565086365), ('scattering coefficients', 0.27646347880363464), ('shields', 0.2555680572986603), ('elastic moduli', 0.24420315027236938), ('hydrodynamic', 0.24138575792312622), ('helmholtz', 0.24014349281787872)]"
1809,1809,15,1809_linearized boltzmann_solving boltzmann_neural networks approximating_radiative transfer,"['linearized boltzmann', 'solving boltzmann', 'neural networks approximating', 'radiative transfer', 'neural networks pinns', 'transfer equations', 'linear transport equations', 'micro macro decomposition', 'boltzmann', 'boltzmann bgk']","['A Micro-Macro Decomposition-Based Asymptotic-Preserving Random Feature Method for Multiscale Radiative Transfer Equations This paper introduces the Asymptotic-Preserving Random Feature Method (APRFM) for the efficient resolution of multiscale radiative transfer equations. The APRFM effectively addresses the challenges posed by stiffness and multiscale characteristics inherent in radiative transfer equations through the application of a micro-macro decomposition strategy. This approach decomposes the distribution function into equilibrium and non-equilibrium components, allowing for the approximation of both parts through the random feature method (RFM) within a least squares minimization framework. The proposed method exhibits remarkable robustness across different scales and achieves high accuracy with fewer degrees of freedom and collocation points than the vanilla RFM. Additionally, compared to the deep neural network-based method, our approach offers significant advantages in terms of parameter efficiency and computational speed. These benefits have been substantiated through numerous numerical experiments conducted on both one- and two-dimensional problems.', 'A model-data asymptotic-preserving neural network method based on\n  micro-macro decomposition for gray radiative transfer equations   We propose a model-data asymptotic-preserving neural network(MD-APNN) method\nto solve the nonlinear gray radiative transfer equations(GRTEs). The system is\nchallenging to be simulated with both the traditional numerical schemes and the\nvanilla physics-informed neural networks(PINNs) due to the multiscale\ncharacteristics. Under the framework of PINNs, we employ a micro-macro\ndecomposition technique to construct a new asymptotic-preserving(AP) loss\nfunction, which includes the residual of the governing equations in the\nmicro-macro coupled form, the initial and boundary conditions with additional\ndiffusion limit information, the conservation laws, and a few labeled data. A\nconvergence analysis is performed for the proposed method, and a number of\nnumerical examples are presented to illustrate the efficiency of MD-APNNs, and\nparticularly, the importance of the AP property in the neural networks for the\ndiffusion dominating problems. The numerical results indicate that MD-APNNs\nlead to a better performance than APNNs or pure data-driven networks in the\nsimulation of the nonlinear non-stationary GRTEs.\n', 'Asymptotic-Preserving Neural Networks based on Even-odd Decomposition\n  for Multiscale Gray Radiative Transfer Equations   We present a novel Asymptotic-Preserving Neural Network (APNN) approach\nutilizing even-odd decomposition to tackle the nonlinear gray radiative\ntransfer equations (GRTEs). Our AP loss demonstrates consistent stability\nconcerning the small Knudsen number, ensuring the neural network solution\nuniformly converges to the macro solution. This APNN method alleviates the\nrigorous conservation requirements while simultaneously incorporating an\nauxiliary deep neural network, distinguishing it from the APNN method based on\nmicro-macro decomposition for GRTE. Several numerical problems are examined to\ndemonstrate the effectiveness of our proposed APNN technique.\n']","[('linearized boltzmann', 0.4883483648300171), ('solving boltzmann', 0.4700050950050354), ('neural networks approximating', 0.4285590350627899), ('radiative transfer', 0.4241381287574768), ('neural networks pinns', 0.4039308428764343), ('transfer equations', 0.3848044276237488), ('linear transport equations', 0.3807010054588318), ('micro macro decomposition', 0.3727515637874603), ('boltzmann', 0.36993151903152466), ('boltzmann bgk', 0.3669246733188629)]"
1810,1810,15,1810_boundary thermal_insulation_robin boundary conditions_boundary conditions,"['boundary thermal', 'insulation', 'robin boundary conditions', 'boundary conditions', 'insulating', 'conditions free boundary', 'insulated', 'convection', 'nonlinear boundary conditions', 'heat content']","['Optimization of an eigenvalue arising in optimal insulation with a lower\n  bound   An eigenvalue problem arising in optimal insulation related to the\nminimization of the heat decay rate of an insulated body is adapted to enforce\na positive lower bound imposed on the distribution of insulating material. We\nprove the existence of optimal domains among a class of convex shapes and\npropose a numerical scheme to approximate the eigenvalue. The stability of the\nshape optimization among convex, bounded domains in $\\mathbb{R}^3$ is proven\nfor an approximation with polyhedral domains under a non-conformal convexity\nconstraint. We prove that on the ball, symmetry breaking of the optimal\ninsulation can be expected in general. To observe how the lower bound affects\nthe breaking of symmetry in the optimal insulation and the shape optimization,\nthe eigenvalue and optimal domains are approximated for several values of mass\n$m$ and lower bounds $\\ell_{\\min}\\ge0$. The numerical experiments suggest, that\nin general symmetry breaking still arises, unless $m$ is close to a critical\nvalue $m_0$, and $\\ell_{\\min}$ large enough such that almost all of the mass\n$m$ is fixed through the lower bound. For $\\ell_{\\min}=0$, the numerical\nresults are consistent with previous numerical experiments on shape\noptimization restricted to rotationally symmetric, convex domains.\n', 'Some remarks on optimal insulation with Robin boundary conditions   We consider an optimal insulation problem of a given domain in $\\mathbb R^N$.\nWe study a model of heat trasfer determined by convection; this corresponds,\nbefore insulation, to a Robin boundary value problem. We deal with a prototype\nwhich involves the first eigenvalue of an elliptic differential operator. Such\noptimization problem, if the convection heat transfer coefficient is\nsufficiently large and the total amount of insulation is small enough, presents\na symmetry breaking.\n', 'An optimization problem in thermal insulation with Robin boundary\n  conditions   We study thermal insulating of a bounded body $\\Omega\\subset \\mathbb{R}^n$.\nUnder a prescribed heat source $f\\geq 0$, we consider a model of heat transfer\nbetween $\\Omega$ and the environment determined by convection; this\ncorresponds, before insulation, to Robin boundary conditions. The body is then\nsurrounded by a layer of insulating material of thickness of size\n$\\varepsilon>0$, and whose conductivity is also proportional to $\\varepsilon$.\nThis corresponds to the case of a small amount of insulating material, with\nexcellent insulating properties. We then compute the $\\Gamma$-limit of the\nenergy functional $F_\\varepsilon$ and prove that this is a functional $F$ whose\nminimizers still satisfy an elliptic PDEs system with a non uniform Robin\nboundary condition depending on the distribution of insulating layer around\n$\\Omega$. In a second step we study the maximization of heat content (which\nmeasures the goodness of the insulation) among all the possible distributions\nof insulating material with fixed mass, and prove an optimal upper bound in\nterms of geometric properties. Eventually we prove a conjecture which states\nthat the ball surrounded by a uniform distribution of insulating material\nmaximizes the heat content.\n']","[('boundary thermal', 0.5998234152793884), ('insulation', 0.5280824899673462), ('robin boundary conditions', 0.5000699162483215), ('boundary conditions', 0.4910004138946533), ('insulating', 0.46391716599464417), ('conditions free boundary', 0.4626697897911072), ('insulated', 0.4536760449409485), ('convection', 0.41799911856651306), ('nonlinear boundary conditions', 0.40858909487724304), ('heat content', 0.40597695112228394)]"
1811,1811,15,1811_semigroups_semigroup_mathbb semigroup_semigroups main,"['semigroups', 'semigroup', 'mathbb semigroup', 'semigroups main', 'solutions functional', 'semigroups first', 'semigroups let', 'semigroup generated', 'topological semigroups', 'functional equations']","['A generalization of the Cosine-Sine functional equation on a semigroup   Given a semigroup $S$ equipped with an involutive automorphism $\\sigma$, we\ndetermine the complex-valued solutions $f,g,h$ of the functional equation\n\\begin{equation*}f(x\\sigma(y))=f(x)g(y)+g(x)f(y)+h(x)h(y),\\,\\,x,y\\in\nS,\\end{equation*} in terms of multiplicative functions and solutions of the\nspecial cases of sine and cosine-sine functional equations.\n', 'Integral Kannappan-Sine subtraction and addition law on semigroups   Let $S$ be a semigroup, $\\mu$ a discrete measure on $S$ and $\\sigma:S\n\\longrightarrow S$ is an involutive automorphism. We determine the\ncomplex-valued solutions of the integral Kannappan-Sine subtraction law\n$$\\int_{S}f(x\\sigma(y)t)d\\mu(t)=f(x)g(y)-f(y)g(x),\\; x,y \\in S,$$ and the\nintegral Kannappan-Sine addition law\n$$\\int_{S}f(x\\sigma(y)t)d\\mu(t)=f(x)g(y)+f(y)g(x),\\; x,y \\in S.$$\n  We express the solutions by means of exponentials on S, the solutions of the\nspecial sine addition law $f(xy)=f(x)\\chi(y)+f(y)\\chi(x),$ $x,y\\in S$ and the\nsolutions of of the special case of the integral Kannappan-Sine addition law\n$\\int_{S}f(x\\sigma(y)t)d\\mu(t)=[f(x)\\chi(y)+f(y)\\chi(x)]\\int_{S}\\chi(t)d\\mu(t),\n$ $x,y\\in S$, and where $\\chi$: $S\\longrightarrow \\mathbb{C}$ is an\nexponential. The continuous solutions on topological semigroups are also given.\n', 'A Kannappan-sine addition law on semigroups   Let $S$ be a semigroup and $z_{0}$ a fixed element in $S.$ We determine the\ncomplex-valued solutions of the following Kannappan-sine addition law\n$f(xyz_{0})=f(x)g(y)+f(y)g(x),x,y\\in S.$\n']","[('semigroups', 0.5138638615608215), ('semigroup', 0.4940444827079773), ('mathbb semigroup', 0.48205888271331787), ('semigroups main', 0.48046252131462097), ('solutions functional', 0.4764723777770996), ('semigroups first', 0.46900564432144165), ('semigroups let', 0.4500599503517151), ('semigroup generated', 0.4470311999320984), ('topological semigroups', 0.43084293603897095), ('functional equations', 0.41723504662513733)]"
1812,1812,15,1812_fano threefolds_fano varieties_chow ring_chow group zero,"['fano threefolds', 'fano varieties', 'chow ring', 'chow group zero', 'gushel mukai fourfolds', 'chow groups', 'fourfolds k3 type', 'fourfolds k3', 'varieties k3', 'chow group']","['Some more Fano threefolds with a multiplicative Chow-K\\""unneth\n  decomposition   We exhibit several families of Fano threefolds with a multiplicative\nChow-K\\""unneth decomposition, in the sense of Shen-Vial. As a consequence, a\ncertain tautological subring of the Chow ring of powers of these threefolds\ninjects into cohomology. As a by-product of the argument, we observe that\ndouble covers of projective spaces admit a multiplicative Chow-K\\""unneth\ndecomposition.\n', 'On the Chow Ring of Fano Fourfolds of K3 type   We show that a wide range of Fano varieties of K3 type, recently constructed\nby Bernardara, Fatighenti, Manivel and Tanturri, have a multiplicative\nChow-K\\""unneth decomposition, in the sense of Shen-Vial. It follows that the\nChow ring of these Fano varieties behaves like that of K3 surfaces. As a side\nresult, we obtain some criteria for the Franchetta property of blown-up\nprojective varieties.\n', 'Algebraic cycles and Gushel-Mukai fivefolds   We show that Gushel-Mukai fivefolds admit a multiplicative Chow-K\\""unneth\ndecomposition, in the sense of Shen-Vial. As a consequence, a certain\ntautological subring of the Chow ring of powers of these varieties injects into\ncohomology.\n']","[('fano threefolds', 0.5675146579742432), ('fano varieties', 0.5540570020675659), ('chow ring', 0.5222380757331848), ('chow group zero', 0.5085343718528748), ('gushel mukai fourfolds', 0.49963951110839844), ('chow groups', 0.49950510263442993), ('fourfolds k3 type', 0.4969913065433502), ('fourfolds k3', 0.46853068470954895), ('varieties k3', 0.4577051103115082), ('chow group', 0.4538213908672333)]"
1813,1813,15,1813_neuromorphic computing_drift diffusion equations_drift diffusion_synaptic coupling,"['neuromorphic computing', 'drift diffusion equations', 'drift diffusion', 'synaptic coupling', 'dissipative dynamics', 'synapses', 'dynamics diffusive', 'electronic circuits', 'neuromorphic', 'synaptic']","['Evaluating the transport properties of interface-type, analog memristors   Interface-type, analog memristors have quite a reputation for real-time\napplications in edge sensorics, edge computing, and neuromorphic computing. The\nn-type conducting BiFeO3 (BFO) is such an interface-type, analog memristor\nwhich is also nonlinear and can therefore not only store, but also process data\nin the same memristor cell without data transfer between the data storage unit\nand the data processing unit. Here we present a physical memristor model which\ndescribes the hysteretic current-voltage curves of the BFO memristor in the\nsmall and large current-voltage range. Extracted internal state variables are\nreconfigured by the ion drift in the two write branches and are determining the\nelectron transport in the two read branches. Simulation of electronic circuits\nwith the BFO interface-type, analog memristors was not possible so far because\nprevious physical memristor models have not captured the full range of internal\nstate variables. We show quantitative agreement between modeled and\nexperimental current-voltage curves exemplarily of three different BFO\nmemristors in the small and large current-voltage ranges. Extracted dynamic and\nstatic internal state variables in the two full write branches and in the two\nfull read branches, respectively, can be used for simulating electronic\ncircuits with BFO memristors, e.g. in edge sensorics, edge computing, and\nneuromorphic computing.\n', 'Dynamics and Synchronization of Weakly Coupled Memristive\n  Reaction-Diffusion Neural Networks   A new mathematical model of memristive neural networks described by the\npartly diffusive reaction-diffusion equations with weak synaptic coupling is\nproposed and investigated. Under rather general conditions it is proved that\nthere exists an absorbing set showing the dissipative dynamics of the solution\nsemiflow in the energy space and multiple ultimate bounds. Through uniform\nestimates and maneuver of integral inequalities and sharp interpolation\ninequalities on the interneuron differencing equations, it is rigorously proved\nthat exponential synchronization of the neural network solutions at a uniform\nconvergence rate occurs if the coupling strength satisfies a threshold\ncondition expressed by the system parameters. Applications with numerical\nsimulation to the memristive diffusive Hindmarsh-Rose neural networks and\nFitzHugh-Nagumo neural networks are also shown.\n', 'Three-species drift-diffusion models for memristors   A system of drift-diffusion equations for the electron, hole, and oxygene\nvacancy densities in a semiconductor, coupled to the Poisson equation for the\nelectric potential, is analyzed in a bounded domain with mixed\nDirichlet-Neumann boundary conditions. This system describes the dynamics of\ncharge carriers in a memristor device. Memristors can be seen as nonlinear\nresistors with memory, mimicking the conductance response of biological\nsynapses. In the fast-relaxation limit, the system reduces to a drift-diffusion\nsystem for the oxygene vacancy density and electric potential, which is often\nused in neuromorphic applications. The following results are proved: the global\nexistence of weak solutions to the full system in any space dimension; the\nuniform-in-time boundedness of the solutions to the full system and the\nfast-relaxation limit in two space dimensions; the global existence and\nweak-strong uniqueness analysis of the reduced system. Numerical experiments in\none space dimension illustrate the behavior of the solutions and reproduce\nhysteresis effects in the current-voltage characteristics.\n']","[('neuromorphic computing', 0.4533078372478485), ('drift diffusion equations', 0.4036167562007904), ('drift diffusion', 0.37008902430534363), ('synaptic coupling', 0.3574844002723694), ('dissipative dynamics', 0.3441542088985443), ('synapses', 0.3420303463935852), ('dynamics diffusive', 0.3298410475254059), ('electronic circuits', 0.3186848759651184), ('neuromorphic', 0.2715326249599457), ('synaptic', 0.2600213587284088)]"
1814,1814,15,1814_resistance two vertices_graphs_certain graphs_resistance distance,"['resistance two vertices', 'graphs', 'certain graphs', 'resistance distance', 'resistance corresponding', 'graphs give', 'constructing graphs', 'graph complete graph', 'graph complete', 'graph cycle']","['On the resistance regular graphs   For a connected graph $G$, its resistance matrix is denoted by $R(G)$. If all\nthe row(column) sums of $R(G)$ are equal, then $G$ is said to be resistance\nregular. We provide some necessary and sufficient conditions for a simple\nconnected graph to be a resistance regular graph. Also, we determine various\nbounds for the resistance energy and resistance spectral radius of $G.$\nFurthermore, we compute the resistance spectrum and resistance energies of some\nresistance regular graphs.\n', ""Resistance distance in $k$-coalescence of certain graphs   Any graph can be considered as a network of resistors, each of which has a\nresistance of $1 \\Omega.$ The resistance distance $r_{ij}$ between a pair of\nvertices $i$ and $j$ in a graph is defined as the effective resistance between\n$i$ and $j$. This article deals with the resistance distance in the\n$k$-coalescence of complete graphs. We also present its results in connection\nwith the Kemeny's constant, Kirchhoff index, additive degree-Kirchhoff index,\nmultiplicative degree-Kirchhoff index and mixed degree-Kirchhoff index.\nMoreover, we obtain the resistance distance in the $k$-coalescence of a\ncomplete graph with particular graphs. As an application, we provide the\nresistance distance of certain graphs such as the vertex coalescence of a\ncomplete bipartite graph with a complete graph, a complete bipartite graph with\na star graph, the windmill graph, pineapple graph, etc.\n"", 'A method for constructing graphs with the same resistance spectrum   Let $G=(V(G),E(G))$ be a graph with vertex set $V(G)$ and edge set $E(G)$.\nThe resistance distance $R_G(x,y)$ between two vertices $x,y$ of $G$ is defined\nto be the effective resistance between the two vertices in the corresponding\nelectrical network in which each edge of $G$ is replaced by a unit resistor.\nThe resistance spectrum $\\mathrm{RS}(G)$ of a graph $G$ is the multiset of the\nresistance distances of all pairs of vertices in the graph. This paper presents\na method for constructing graphs with the same resistance spectrum. It is\nobtained that for any positive integer $k$, there exist at least $2^k$ graphs\nwith the same resistance spectrum. Furthermore, it is shown that for $n \\geq\n10$, there are at least $2(n-9) p(n-9)$ pairs of graphs of order $n$ with the\nsame resistance spectrum, where $p(n-9)$ is the number of partitions of the\ninteger $n-9$.\n']","[('resistance two vertices', 0.6269429922103882), ('graphs', 0.5454738736152649), ('certain graphs', 0.5420585870742798), ('resistance distance', 0.5307009220123291), ('resistance corresponding', 0.5125863552093506), ('graphs give', 0.5048097968101501), ('constructing graphs', 0.5024535655975342), ('graph complete graph', 0.5023806095123291), ('graph complete', 0.4897570013999939), ('graph cycle', 0.48813390731811523)]"
1815,1815,15,1815_holographic dual_string field theory_string theory_symmetric tensors,"['holographic dual', 'string field theory', 'string theory', 'symmetric tensors', 'space scattering', 'ads cft', 'quantum deformation', 'conformal', 'holographic', 'field theory']","[""Flat limit of AdS/CFT from AdS geodesics: scattering amplitudes and\n  antipodal matching of Li\\'enard-Wiechert fields   We revisit the flat limit of AdS/CFT from the point of view of geodesics in\nAdS. We show that the flat space scattering amplitudes can be constructed from\noperator insertions where the geodesics of the particles corresponding to the\noperators hit the conformal boundary of AdS. Further, we compute the\nLi\\'enard-Wiechert solutions in AdS by boosting a static charge using AdS\nisometries and show that the solutions are antipodally matched between two\nregions, separated by a global time difference of $\\Delta\\tau=\\pi$. Going to\nthe boundary of AdS along null geodesics, in the flat limit, this antipodal\nmatching leads to the flat space antipodal matching near spatial infinity.\n"", 'A Celestial Route to AdS Bulk Locality   We prove a precise form of AdS bulk locality by deriving analytical two-sided\nbounds on bulk Wilson coefficients. Our bounds are on the Wilson coefficients\nthemselves, rather than their ratios, as is typically found in the literature.\nInspired by the Celestial amplitudes program in flat space, we perform a\nCelestial transform of the CFT Mellin amplitude of four identical scalars.\nUsing the crossing symmetric dispersion relation (CSDR), we express the\nresulting amplitude in terms of crossing symmetric conformal partial waves. The\npartial waves satisy remarkable positivity properties which along with the\nunitarity of the CFT prove sufficient to derive the bounds. We then employ our\nmethods in the limit of large AdS radius and recover known bounds on flat space\nWilson coefficients and new bounds on their large radius corrections. We check\nthat the planar Mellin amplitude of four stress-tensor multiplets in\n$\\mathcal{N} = 4$ SYM satisfies our bounds. Finally, using null constraints, we\nderive a form of low-spin dominance in AdS EFTs. We find that the low-spin\ndominance is strongest in flat space and weakens as we move away from flat\nspace towards higher AdS curvature.\n', ""Bounds on Regge growth of flat space scattering from bounds on chaos   We study four-point functions of scalars, conserved currents, and stress\ntensors in a conformal field theory, generated by a local contact term in the\nbulk dual description, in two different causal configurations. The first of\nthese is the standard Regge configuration in which the chaos bound applies. The\nsecond is the `causally scattering configuration' in which the correlator\ndevelops a bulk point singularity. We find an expression for the coefficient of\nthe bulk point singularity in terms of the bulk S matrix of the bulk dual\nmetric, gauge fields and scalars, and use it to determine the Regge scaling of\nthe correlator on the causally scattering sheet in terms of the Regge growth of\nthis S matrix. We then demonstrate that the Regge scaling on this sheet is\ngoverned by the same power as in the standard Regge configuration, and so is\nconstrained by the chaos bound, which turns out to be violated unless the bulk\nflat space S matrix grows no faster than $s^2$ in the Regge limit. It follows\nthat in the context of the AdS/CFT correspondence, the chaos bound applied to\nthe boundary field theory implies that the S matrices of the dual bulk scalars,\ngauge fields, and gravitons obey the Classical Regge Growth (CRG) conjecture.\n""]","[('holographic dual', 0.5341368317604065), ('string field theory', 0.520044207572937), ('string theory', 0.4586368799209595), ('symmetric tensors', 0.4362736940383911), ('space scattering', 0.4205544888973236), ('ads cft', 0.4131668210029602), ('quantum deformation', 0.4090658128261566), ('conformal', 0.39382147789001465), ('holographic', 0.3925679326057434), ('field theory', 0.3657251298427582)]"
1816,1816,15,1816_partition functions_partitions positive integer_partitions positive_partition numbers,"['partition functions', 'partitions positive integer', 'partitions positive', 'partition numbers', 'number partitions', 'partitions whose', 'partitions', 'partition', 'regular partition', 'overpartitions']","[""Inequalities for the $k$-Regular Overpartitions   Bessenrodt and Ono, Chen, Wang and Jia, DeSalvo and Pak were the first to\ndiscover the log-subadditivity, log-concavity, and the third-order Tur\\'{a}n\ninequality of partition function, respectively. Many other important partition\nstatistics are proved to enjoy similar properties. This paper focuses on the\npartition function $\\overline{p}_k(n)$, which counts the number of\noverpartitions of $n$ with no parts divisible by $k$. We provide a\ncombinatorial proof to establish that for any $k\\geq2$, the partition function\n$\\overline{p}_k(n)$ exhibits strict log-subadditivity. Specifically, we show\nthat $\\overline{p}_k(a)\\overline{p}_k(b)>\\overline{p}_k(a+b)$ for integers\n$a\\geq b\\geq1$ and $a+b\\geq k$. Furthermore, we investigate the log-concavity\nand the satisfaction of the third-order Tur\\'{a}n inequality for\n$\\overline{p}_k(n)$, where $2\\leq k\\leq9$.\n"", 'Bounds on the M\\""obius-signed partition numbers   For $n \\in \\mathbb{N}$ let $\\Pi[n]$ denote the set of partitions of $n$,\ni.e., the set of positive integer tuples $(x_1,x_2,\\ldots,x_k)$ such that $x_1\n\\geq x_2 \\geq \\cdots \\geq x_k$ and $x_1 + x_2 + \\cdots + x_k = n$. Fixing\n$f:\\mathbb{N}\\to\\{0,\\pm 1\\}$, for $\\pi = (x_1,x_2,\\ldots,x_k) \\in \\Pi[n]$ let\n$f(\\pi) := f(x_1)f(x_2)\\cdots f(x_k)$. In this way we define the {signed\npartition numbers} \\[ p(n,f) = \\sum_{\\pi\\in\\Pi[n]} f(\\pi). \\] Following work of\nVaughan and Gafni on partitions into primes and prime powers, we derive\nasymptotic formulae for quantities $p(n,\\mu)$ and $p(n,\\lambda)$, where $\\mu$\nand $\\lambda$ denote the M\\""obius and Liouville functions from prime number\ntheory, respectively. In addition we discuss how quantities $p(n,f)$ generalize\nthe classical notion of restricted partitions.\n', 'Biasymptotics of the M\\""obius- and Liouville-signed partition numbers   For $n \\in \\mathbb{N}$ let $\\Pi[n]$ denote the set of partitions of $n$,\ni.e., the set of positive integer tuples $(x_1,x_2,\\ldots,x_k)$ such that $x_1\n\\geq x_2 \\geq \\cdots \\geq x_k$ and $x_1 + x_2 + \\cdots + x_k = n$. Fixing\n$f:\\mathbb{N}\\to\\{0,\\pm 1\\}$, for $\\pi = (x_1,x_2,\\ldots,x_k) \\in \\Pi[n]$ let\n$f(\\pi) := f(x_1)f(x_2)\\cdots f(x_k)$. In this way we define the {signed\npartition numbers} \\[ p(n,f) = \\sum_{\\pi\\in\\Pi[n]} f(\\pi). \\]\n  Building on the author\'s previous work on the quantities $p(n,\\mu)$ and\n$p(n,\\lambda)$, where $\\mu$ and $\\lambda$ are the M\\""obius and Liouville\nfunctions of prime number theory, respectively, on assumptions about the zeros\nof the Riemann zeta function we establish an alternation of the terms\n$p(n,\\mu)$ between two asymptotic behaviors as $n\\to\\infty$. Similar results\nfor the quantities $p(n,\\lambda)$ are established. However, it is also\ndemonstrated that if the Riemann Hypothesis (RH) holds, then it is possible\nthat the quantities $p(n,\\lambda)$ maintain a single asymptotic behavior as\n$n\\to\\infty$. In particular, this stable asymptotic behavior occurs if, in\naddition to RH, it holds that all zeros of $\\zeta(s)$ in the critical strip\n$\\{0 < \\Re(s) < 1\\}$ are simple and the residues of $1/\\zeta(s)$ at these zeros\nare not too large.\n  To formally describe these stable and alternating behaviors, the notions of\nasymptotic and biasymptotic sequences are introduced using a modification of\nthe real logarithm.\n']","[('partition functions', 0.5471985936164856), ('partitions positive integer', 0.5434843897819519), ('partitions positive', 0.540316641330719), ('partition numbers', 0.48794981837272644), ('number partitions', 0.48374277353286743), ('partitions whose', 0.4305821359157562), ('partitions', 0.4158283472061157), ('partition', 0.3839179575443268), ('regular partition', 0.34994643926620483), ('overpartitions', 0.33377963304519653)]"
1817,1817,15,1817_parabolic convection diffusion_parabolic convection_convection diffusion problems_singularly perturbed boundary,"['parabolic convection diffusion', 'parabolic convection', 'convection diffusion problems', 'singularly perturbed boundary', 'convection diffusion', 'perturbed boundary value', 'perturbed boundary', 'boundary value problems', 'approximated numerically', 'diffusion boundary']","['A parameter uniform method for two-parameter singularly perturbed\n  boundary value problems with discontinuous data   A two-parameter singularly perturbed problem with discontinuous source and\nconvection coefficient is considered in one dimension. Both convection\ncoefficient and source term are discontinuous at a point in the domain. The\npresence of perturbation parameters results in boundary layers at the\nboundaries. Also, an interior layer occurs due to the discontinuity of data at\nan interior point. An upwind scheme on an appropriately defined\nShishkin-Bakhvalov mesh is used to resolve the boundary layers and interior\nlayers. A three-point formula is used at the point of discontinuity. The\nproposed method has first-order parameter uniform convergence. Theoretical\nerror estimates derived are verified using the numerical method on some test\nproblems. Numerical results authenticate the claims made. The use of the\nShiskin-Bakhvalov mesh helps achieve the first-order convergence, unlike the\nShishkin mesh, where the order of convergence deteriorates due to a logarithmic\nterm.\n', 'Parameter-uniform approximations for a singularly perturbed\n  convection-diffusion problem with a discontinuous initial condition   A singularly perturbed parabolic problem of convection-diffusion type with a\ndiscontinuous initial condition is examined. A particular complimentary error\nfunction is identified which matches the discontinuity in the initial\ncondition. The difference between this analytical function and the solution of\nthe parabolic problem is approximated numerically. A co-ordinate transformation\nis used so that a layer-adapted mesh can be aligned to the interior layer\npresent in the solution. Numerical analysis is presented for the associated\nnumerical method, which establishes that the numerical method is a\nparameter-uniform numerical method. Numerical results are presented to\nillustrate the pointwise error bounds established in the paper.\n', 'Numerical approximations to a singularly perturbed convection-diffusion\n  problem with a discontinuous initial condition   A singularly perturbed parabolic problem of convection-diffusion type with a\ndiscontinuous initial condition is examined. An analytic function is identified\nwhich matches the discontinuity in the initial condition and also satisfies the\nhomogenous parabolic differential equation associated with the problem. The\ndifference between this analytical function and the solution of the parabolic\nproblem is approximated numerically, using an upwind finite difference operator\ncombined with an appropriate layer-adapted mesh. The numerical method is shown\nto be parameter-uniform. Numerical results are presented to illustrate the\ntheoretical error bounds established in the paper.\n']","[('parabolic convection diffusion', 0.5786318182945251), ('parabolic convection', 0.5662187933921814), ('convection diffusion problems', 0.5554599761962891), ('singularly perturbed boundary', 0.5075975656509399), ('convection diffusion', 0.5005977749824524), ('perturbed boundary value', 0.4997994601726532), ('perturbed boundary', 0.47193118929862976), ('boundary value problems', 0.4433107078075409), ('approximated numerically', 0.44193151593208313), ('diffusion boundary', 0.4137805104255676)]"
1818,1818,15,1818_multiple robots_agent optimal_multi robot_optimal coverage,"['multiple robots', 'agent optimal', 'multi robot', 'optimal coverage', 'multi agent systems', 'control multi agent', 'multi agent', 'bandit feedback', 'robot', 'robots']","['Online Submodular Coordination with Bounded Tracking Regret: Theory,\n  Algorithm, and Applications to Multi-Robot Coordination   We enable efficient and effective coordination in unpredictable environments,\ni.e., in environments whose future evolution is unknown a priori and even\nadversarial. We are motivated by the future of autonomy that involves multiple\nrobots coordinating in dynamic, unstructured, and adversarial environments to\ncomplete complex tasks such as target tracking, environmental mapping, and area\nmonitoring. Such tasks are often modeled as submodular maximization\ncoordination problems. We introduce the first submodular coordination algorithm\nwith bounded tracking regret, i.e., with bounded suboptimality with respect to\noptimal time-varying actions that know the future a priori. The bound\ngracefully degrades with the environments\' capacity to change adversarially. It\nalso quantifies how often the robots must re-select actions to ""learn"" to\ncoordinate as if they knew the future a priori. The algorithm requires the\nrobots to select actions sequentially based on the actions selected by the\nprevious robots in the sequence. Particularly, the algorithm generalizes the\nseminal Sequential Greedy algorithm by Fisher et al. to unpredictable\nenvironments, leveraging submodularity and algorithms for the problem of\ntracking the best expert. We validate our algorithm in simulated scenarios of\ntarget tracking.\n', ""Leveraging Untrustworthy Commands for Multi-Robot Coordination in\n  Unpredictable Environments: A Bandit Submodular Maximization Approach   We study the problem of multi-agent coordination in unpredictable and\npartially-observable environments with untrustworthy external commands. The\ncommands are actions suggested to the robots, and are untrustworthy in that\ntheir performance guarantees, if any, are unknown. Such commands may be\ngenerated by human operators or machine learning algorithms and, although\nuntrustworthy, can often increase the robots' performance in complex\nmulti-robot tasks. We are motivated by complex multi-robot tasks such as target\ntracking, environmental mapping, and area monitoring. Such tasks are often\nmodeled as submodular maximization problems due to the information overlap\namong the robots. We provide an algorithm, Meta Bandit Sequential Greedy\n(MetaBSG), which enjoys performance guarantees even when the external commands\nare arbitrarily bad. MetaBSG leverages a meta-algorithm to learn whether the\nrobots should follow the commands or a recently developed submodular\ncoordination algorithm, Bandit Sequential Greedy (BSG) [1], which has\nperformance guarantees even in unpredictable and partially-observable\nenvironments. Particularly, MetaBSG asymptotically can achieve the better\nperformance out of the commands and the BSG algorithm, quantifying its\nsuboptimality against the optimal time-varying multi-robot actions in\nhindsight. Thus, MetaBSG can be interpreted as robustifying the untrustworthy\ncommands. We validate our algorithm in simulated scenarios of multi-target\ntracking.\n"", ""Bandit Submodular Maximization for Multi-Robot Coordination in\n  Unpredictable and Partially Observable Environments   We study the problem of multi-agent coordination in unpredictable and\npartially observable environments, that is, environments whose future evolution\nis unknown a priori and that can only be partially observed. We are motivated\nby the future of autonomy that involves multiple robots coordinating actions in\ndynamic, unstructured, and partially observable environments to complete\ncomplex tasks such as target tracking, environmental mapping, and area\nmonitoring. Such tasks are often modeled as submodular maximization\ncoordination problems due to the information overlap among the robots. We\nintroduce the first submodular coordination algorithm with bandit feedback and\nbounded tracking regret -- bandit feedback is the robots' ability to compute in\nhindsight only the effect of their chosen actions, instead of all the\nalternative actions that they could have chosen instead, due to the partial\nobservability; and tracking regret is the algorithm's suboptimality with\nrespect to the optimal time-varying actions that fully know the future a\npriori. The bound gracefully degrades with the environments' capacity to change\nadversarially, quantifying how often the robots should re-select actions to\nlearn to coordinate as if they fully knew the future a priori. The algorithm\ngeneralizes the seminal Sequential Greedy algorithm by Fisher et al. to the\nbandit setting, by leveraging submodularity and algorithms for the problem of\ntracking the best action. We validate our algorithm in simulated scenarios of\nmulti-target tracking.\n""]","[('multiple robots', 0.5103556513786316), ('agent optimal', 0.48969393968582153), ('multi robot', 0.47979736328125), ('optimal coverage', 0.43764030933380127), ('multi agent systems', 0.43065255880355835), ('control multi agent', 0.4267157316207886), ('multi agent', 0.41484811902046204), ('bandit feedback', 0.4123631715774536), ('robot', 0.406654417514801), ('robots', 0.38506239652633667)]"
1819,1819,15,1819_mixed hodge modules_hodge modules_hodge filtrations_mixed hodge module,"['mixed hodge modules', 'hodge modules', 'hodge filtrations', 'mixed hodge module', 'hodge module', 'hodge filtration', 'hodge theory', 'hodge structures', 'formula hodge', 'mixed hodge']","[""A description of monodromic mixed Hodge modules   For a smooth algebraic variety $X$, a monodromic $D$-module on $X\\times\n\\mathbb{C}$ is decomposed into a direct sum of some $D$-modules on $X$. We show\nthat the Hodge filtration of a mixed Hodge module on $X\\times \\mathbb{C}$ whose\nunderlying $D$-module is monodromic is also decomposed. Moreover, we show that\nthere is an equivalence of categories between the category of monodromic mixed\nHodge modules on $X\\times \\mathbb{C}$ and the category of ``gluing data''. As\nan application, we endow the Fourier-Laplace transformation of the underlying\n$D$-module of a monodromic mixed Hodge module with a mixed Hodge module\nstructure.\n"", 'The Hodge filtration of a monodromic mixed Hodge module and the\n  irregular Hodge filtration   For an algebraic vector bundle $E$ over a smooth algebraic variety $X$, a\nmonodromic $D$-module on $E$ is decomposed into a direct sum of some\n$O$-modules on $X$. We show that the Hodge filtration of a monodromic mixed\nHodge module is decomposed with respect to the decomposition of the underlying\n$D$-module. By using this result, we endow the Fourier-Laplace transform\n$M^{\\wedge}$ of the underlying $D$-module $M$ of a monodromic mixed Hodge\nmodule with a mixed Hodge module structure. Moreover, we describe the irregular\nHodge filtration on $M^{\\wedge}$ concretely and show that it coincides with the\nHodge filtration at all integer indices.\n', ""On $V$-filtration, Hodge filtration and Fourier transform   For $i : Z \\to X$ a closed immersion of smooth varieties, we study how the\n$V$-filtration along $Z$ and the Hodge filtration on a mixed Hodge module $M$\non $X$ interact with each other. We also give a formula for the functors $i^*$,\n$i^!$ in terms of this $V$-filtration. As applications, we obtain results on\nthe Hodge filtration of monodromic mixed Hodge modules and we give a Hodge\ntheoretic proof of Skoda's theorem on multiplier ideals. Finally, we use the\nresults to study the Fourier-Laplace transform of a monodromic mixed Hodge\nmodule.\n""]","[('mixed hodge modules', 0.7581576108932495), ('hodge modules', 0.7467056512832642), ('hodge filtrations', 0.7427472472190857), ('mixed hodge module', 0.7340031266212463), ('hodge module', 0.7184890508651733), ('hodge filtration', 0.6815480589866638), ('hodge theory', 0.67922443151474), ('hodge structures', 0.6579464077949524), ('formula hodge', 0.5637800693511963), ('mixed hodge', 0.5514997243881226)]"
1820,1820,15,1820_cyclic ldpc codes_ldpc codes constructed_parity check matrices_tanner graph,"['cyclic ldpc codes', 'ldpc codes constructed', 'parity check matrices', 'tanner graph', 'parity check matrix', 'based ldpc codes', 'ldpc codes', 'qc ldpc codes', 'check ldpc codes', 'cyclic ldpc']","['Necessary and Sufficient Girth Conditions for Tanner Graphs of\n  Quasi-Cyclic LDPC Codes   This paper revisits the connection between the girth of a protograph-based\nLDPC code given by a parity-check matrix and the properties of powers of the\nproduct between the matrix and its transpose in order to obtain the necessary\nand sufficient conditions for a code to have given girth between 6 and 12, and\nto show how these conditions can be incorporated into simple algorithms to\nconstruct codes of that girth. To this end, we highlight the role that certain\nsubmatrices that appear in these products have in the construction of codes of\ndesired girth. In particular, we show that imposing girth conditions on a\nparity-check matrix is equivalent to imposing conditions on a square submatrix\nobtained from it and we show how this equivalence is particularly strong for a\nprotograph based parity-check matrix of variable node degree 2, where the\ncycles in its Tanner graph correspond one-to-one to the cycles in the Tanner\ngraph of a square submatrix obtained by adding the permutation matrices (or\nproducts of these) in the composition of the parity-check matrix. We end the\npaper with exemplary constructions of codes with various girths and computer\nsimulations. Although, we mostly assume the case of fully connected protographs\nof variable node degree 2 and 3, the results can be used for any parity-check\nmatrix/protograph-based Tanner graph.\n', 'Necessary and Sufficient Girth Conditions for LDPC Tanner Graphs with\n  Denser Protographs   This paper gives necessary and sufficient conditions for the Tanner graph of\na quasi-cyclic (QC) low-density parity-check (LDPC) code based on the all-one\nprotograph to have girth 6, 8, 10, and 12, respectively, in the case of\nparity-check matrices with column weight 4. These results are a natural\nextension of the girth results of the already-studied cases of column weight 2\nand 3, and it is based on the connection between the girth of a Tanner graph\ngiven by a parity-check matrix and the properties of powers of the product\nbetween the matrix and its transpose. The girth conditions can be easily\nincorporated into fast algorithms that construct codes of desired girth between\n6 and 12; our own algorithms are presented for each girth, together with\nconstructions obtained from them and corresponding computer simulations. More\nimportantly, this paper emphasizes how the girth conditions of the Tanner graph\ncorresponding to a parity-check matrix composed of circulants relate to the\nmatrix obtained by adding (over the integers) the circulant columns of the\nparity-check matrix. In particular, we show that imposing girth conditions on a\nparity-check matrix is equivalent to imposing conditions on a square circulant\nsubmatrix of size 4 obtained from it.\n', 'A Unifying Framework to Construct QC-LDPC Tanner Graphs of Desired Girth   This paper presents a unifying framework to construct low-density\nparity-check (LDPC) codes with associated Tanner graphs of desired girth.\nTowards this goal, we highlight the role that a certain square matrix that\nappears in the product of the parity-check matrix with its transpose has in the\nconstruction of codes with graphs of desired girth and further explore it in\norder to generate the set of necessary and sufficient conditions for a Tanner\ngraph to have a given girth between 6 and 12. For each such girth, we present\nalgorithms to construct codes of the desired girth and we show how to use them\nto compute the minimum necessary value of the lifting factor. For girth larger\nthan 12, we show how to use multi-step graph lifting methods to\ndeterministically modify codes in order to increase their girth. We also give a\nnew perspective on LDPC protograph-based parity-check matrices by viewing them\nas rows of a parity-check matrix equal to the sum of certain permutation\nmatrices and obtain an important connection between all protographs and those\nwith variable nodes of degree 2. We also show that the results and methodology\nthat we develop for the all-one protograph can be used and adapted to analyze\nthe girth of the Tanner graph of any parity-check matrix and demonstrate how\nthis can be done using a well-known irregular, multi-edge protograph specified\nby the NASA Consultative Committee for Space Data Systems (CCSDS). Throughout\nthe paper, we exemplify our theoretical results with constructions of LDPC\ncodes with Tanner graphs of any girth between 6 and 14 and give sufficient\nconditions for a multi-step lifted parity-check matrix to have girth between 14\nand 22.\n']","[('cyclic ldpc codes', 0.5985028743743896), ('ldpc codes constructed', 0.5801704525947571), ('parity check matrices', 0.5492621660232544), ('tanner graph', 0.5415962338447571), ('parity check matrix', 0.5231733322143555), ('based ldpc codes', 0.516305685043335), ('ldpc codes', 0.49648046493530273), ('qc ldpc codes', 0.4889325499534607), ('check ldpc codes', 0.48363736271858215), ('cyclic ldpc', 0.47793635725975037)]"
1821,1821,15,1821_circulant graphs_circulant graph_graph adjacency matrix_adjacency matrix,"['circulant graphs', 'circulant graph', 'graph adjacency matrix', 'adjacency matrix', 'whose adjacency', 'graphs exist', 'simple graph whose', 'graph whose', 'graph nontrivial', 'adjacency']","['On $12$-regular nut graphs   A nut graph is a simple graph whose adjacency matrix is singular with\n$1$-dimensional kernel such that the corresponding eigenvector has no zero\nentries. In 2020, Fowler et al. characterised for each $d \\in\n\\{3,4,\\ldots,11\\}$ all values $n$ such that there exists a $d$-regular nut\ngraph of order $n$. In the present paper, we determine all values $n$ for which\na $12$-regular nut graph of order $n$ exists. We also present a result by which\nthere are infinitely many circulant nut graphs of degree $d \\equiv 0 \\pmod 4$\nand no circulant nut graph of degree $d \\equiv 2 \\pmod 4$.\n', 'On cubic polycirculant nut graphs   A nut graph is a nontrivial simple graph whose adjacency matrix contains a\none-dimensional null space spanned by a vector without zero entries. Moreover,\nan $\\ell$-circulant graph is a graph that admits a cyclic group of\nautomorphisms having $\\ell$ vertex orbits of equal size. It is not difficult to\nobserve that there exists no cubic $1$-circulant nut graph or cubic\n$2$-circulant nut graph, while the full classification of all the cubic\n$3$-circulant nut graphs was recently obtained [Electron. J. Comb. 31(2)\n(2024), #2.31]. Here, we investigate the existence of cubic $\\ell$-circulant\nnut graphs for $\\ell \\ge 4$ and show that there is no cubic $4$-circulant nut\ngraph or cubic $5$-circulant nut graph by using a computer-assisted proof.\nFurthermore, we rely on a construction based approach in order to demonstrate\nthat there exist infinitely many cubic $\\ell$-circulant nut graphs for any\nfixed $\\ell \\in \\{6, 7 \\}$ or $\\ell \\ge 9$.\n', 'Nut digraphs   A nut graph is a simple graph whose kernel is spanned by a single full vector\n(i.e. the adjacency matrix has a single zero eigenvalue and all non-zero kernel\neigenvectors have no zero entry). We classify generalisations of nut graphs to\nnut digraphs: a digraph whose kernel (resp. co-kernel) is spanned by a full\nvector is dextro-nut (resp. laevo-nut); a bi-nut digraph is both laevo- and\ndextro-nut; an ambi-nut digraph is a bi-nut digraph where kernel and co-kernel\nare spanned by the same vector; a digraph is inter-nut if the intersection of\nthe kernel and co-kernel is spanned by a full vector. It is known that a nut\ngraph is connected, leafless and non-bipartite. It is shown here that an\nambi-nut digraph is strongly connected, non-bipartite (i.e. has a non-bipartite\nunderlying graph) and has minimum in-degree and minimum out-degree of at least\n$2$. Refined notions of core and core-forbidden vertices apply to singular\ndigraphs. Infinite families of nut digraphs and systematic coalescence,\ncross-over and multiplier constructions are introduced. Relevance of nut\ndigraphs to topological physics is discussed.\n']","[('circulant graphs', 0.6284980177879333), ('circulant graph', 0.5582777857780457), ('graph adjacency matrix', 0.5273696780204773), ('adjacency matrix', 0.5087728500366211), ('whose adjacency', 0.5013824105262756), ('graphs exist', 0.4917986989021301), ('simple graph whose', 0.4891246259212494), ('graph whose', 0.48172861337661743), ('graph nontrivial', 0.4787255823612213), ('adjacency', 0.47871243953704834)]"
1822,1822,15,1822_helfrich functional_existence minimisers_spontaneous curvature_minimizers generalized,"['helfrich functional', 'existence minimisers', 'spontaneous curvature', 'minimizers generalized', 'surfaces boundaries', 'principal curvatures', 'characterization free boundary', 'curvatures', 'minimizers', 'lower semicontinuity']","['Boundary value problems for a special Helfrich functional for surfaces\n  of revolution   The central object of this article is (a special version of) the Helfrich\nfunctional which is the sum of the Willmore functional and the area functional\ntimes a weight factor $\\varepsilon\\ge 0$. We collect several results concerning\nthe existence of solutions to a Dirichlet boundary value problem for Helfrich\nsurfaces of revolution and cover some specific regimes of boundary conditions\nand weight factors $\\varepsilon\\ge 0$. These results are obtained with the help\nof different techniques like an energy method, gluing techniques and the use of\nthe implicit function theorem close to Helfrich cylinders. In particular,\nconcerning the regime of boundary values, where a catenoid exists as a global\nminimiser of the area functional, existence of minimisers of the Helfrich\nfunctional is established for \\emph{all} weight factors $\\varepsilon\\ge 0$. For\nthe singular limit of weight factors $ \\varepsilon \\nearrow \\infty $ they\nconverge uniformly to the catenoid which minimises the surface area in the\nclass of surfaces of revolution.\n', 'Minimizers of Generalized Willmore Functionals   We introduce a notion of generalized Willmore functionals motivated by the\nHawking energy of General Relativity and bending energies of membranes. An\nexample of a bending energy is discussed in detail. Using results of Y. Chen\nand J. Li, we present a compactness result for branched, immersed, haunted,\nstratified surface with bounded area and Willmore energy. This allows us to\nprove the existence of area constrained minimizers for generalized Willmore\nfunctionals in the class of haunted, branched, immersed bubble trees by direct\nminimization. Here a haunted, stratified surfaces are introduced, in order to\naccount for bubbling and vanishing components along the minimization process.\nSimilarly, we obtain the existence of area and volume constrained, minimal,\nclosed membranes for the discussed bending energy. Moreover, we argue that the\nregularity results of A. Mondino and T. Rivi\\`ere for Willmore surfaces can be\ncarried over to the setting of generalized Willmore surfaces. In particular,\nthis means that critical points of a generalized Willmore functional are smooth\naway from finitely many points.\n', 'Existence and Regularity of Spheres Minimising the Canham-Helfrich\n  Energy   We prove existence and regularity of minimisers for the Canham-Helfrich\nenergy in the class of weak (possibly branched and bubbled) immersions of the\n$2$-sphere. This solves (the spherical case) of the minimisation problem\nproposed by Helfrich in 1973, modelling lipid bilayer membranes. On the way to\nprove the main results we establish the lower semicontinuity of the\nCanham-Helfrich energy under weak convergence of (possibly branched and\nbubbled) weak immersions.\n']","[('helfrich functional', 0.5155003070831299), ('existence minimisers', 0.4677183926105499), ('spontaneous curvature', 0.45622578263282776), ('minimizers generalized', 0.44689682126045227), ('surfaces boundaries', 0.4437235891819), ('principal curvatures', 0.4258613884449005), ('characterization free boundary', 0.41991373896598816), ('curvatures', 0.39755967259407043), ('minimizers', 0.3939734399318695), ('lower semicontinuity', 0.39355969429016113)]"
1823,1823,15,1823_zeros polynomials_polynomials p_n_sequence polynomials_polynomial sequence,"['zeros polynomials', 'polynomials p_n', 'sequence polynomials', 'polynomial sequence', 'polynomials associated', 'polynomials generated', 'polynomials polynomial', 'polynomials', 'real zeros', 'z_0 z_0']","['On the location of ratios of zeros of special trinomials   Given coprime integers $k, \\ell$ with $k > \\ell \\geqslant 1$ and arbitrary\ncomplex polynomials $A(z), B(z)$ with $\\deg(A(z)B(z))\\geqslant 1$, we consider\nthe polynomial sequence $\\{P_n(z)\\}$ satisfying a three-term recurrence\n$P_n(z)+B(z)P_{n-\\ell}(z)+A(z)P_{n-k}(z)=0$ subject to the initial conditions\n$P_0(z)=1$, $P_{-1}(z)=\\cdots=P_{1-k}(z)=0$ and fully characterize the real\nalgebraic curve $\\Gamma$ on which the zeros of the polynomials in $\\{P_n(z)\\}$\nlie. In addition, we show that, for any (randomly chosen) $n\\in\n\\mathbb{Z}_{\\geqslant 1}$ and zero $z_0$ of $P_n(z)$ with $A(z_0)\\neq 0$,\nat-least two of the distinct zeros of the trinomial $D(t;z_0):={A(z_0)t^{k}+\nB(z_0)t^{\\ell}+1} $ have a ratio that lies on the real line and / or on the\nunit circle centred at the origin. This reveals a previously unknown geometric\nproperty exhibited by the zeros of trinomials of the form $t^k+at^{\\ell}+1$\nwhere $a\\in \\mathbb{C}-\\{0\\}$ is such that $a^k\\in \\mathbb{R}$.\n', ""Generalizing Tran's Conjecture   A conjecture of Khang Tran [6] claims that for an arbitrary pair of\npolynomials $A(z)$ and $B(z)$, every zero of every polynomial in the sequence\n$\\{P_n(z)\\}_{n=1}^\\infty$ satisfying the three-term recurrence relation of\nlength $k$ $$P_n(z)+B(z)P_{n-1}(z)+A(z)P_{n-k}(z)=0 $$ with the standard\ninitial conditions $P_0(z)=1$, $P_{-1}(z)=\\dots=P_{-k+1}(z)=0$ which is not a\nzero of $A(z)$ lies on the real (semi)-algebraic curve $\\mathcal C \\subset\n\\mathbb {C}$ given by $$\\Im \\left(\\frac{B^k(z)}{A(z)}\\right)=0\\quad {\\rm\nand}\\quad 0\\le (-1)^k\\Re \\left(\\frac{B^k(z)}{A(z)}\\right)\\le\n\\frac{k^k}{(k-1)^{k-1}}.$$ In this short note, we show that for the recurrence\nrelation (generalizing the latter recurrence of Tran) given by\n$$P_n(z)+B(z)P_{n-\\ell}(z)+A(z)P_{n-k}(z)=0, $$\n  with coprime $k$ and $\\ell$ and the same standard initial conditions as\nabove, every root of $P_n(z)$ which is not a zero of $A(z)B(z)$ belongs to the\nreal algebraic curve $\\mathcal C_{\\ell,k}$ given by $$\\Im\n\\left(\\frac{B^k(z)}{A^\\ell(z)}\\right)=0.$$\n"", 'Non-real zeros of polynomials in a polynomial sequence satisfying a\n  three-term recurrence relation   This paper discusses the location of zeros of polynomials in a polynomial\nsequence $\\{P_n(z)\\}$ generated by a three-term recurrence relation of the form\n$P_n(z)+ B(z)P_{n-1}(z) +A(z) P_{n-k}(z)=0$ with $k>2$ and the standard initial\nconditions $P_{0}(z)=1, P_{-1}(z)=\\ldots=P_{-k+1}(z)=0,$ where $A(z)$ and\n$B(z)$ are arbitrary coprime real polynomials. We show that there always exist\npolynomials in $\\{P_n(z)\\}$ with non-real zeros.\n']","[('zeros polynomials', 0.5462173819541931), ('polynomials p_n', 0.5398942828178406), ('sequence polynomials', 0.5044362545013428), ('polynomial sequence', 0.46524664759635925), ('polynomials associated', 0.43718644976615906), ('polynomials generated', 0.42580127716064453), ('polynomials polynomial', 0.4101569652557373), ('polynomials', 0.4074622094631195), ('real zeros', 0.3940712511539459), ('z_0 z_0', 0.38780102133750916)]"
1824,1824,15,1824_beta dynamical_dynamical systems beta_ergodic theory_beta critical,"['beta dynamical', 'dynamical systems beta', 'ergodic theory', 'beta critical', 'beta beta leq', 'beta leq beta', 't_ beta', 'beta leq', 'beta_1', 'beta_2']","[""Entropy plateaus, transitivity and bifurcation sets for the\n  $\\beta$-transformation with a hole at $0$   Given $\\beta\\in(1,2]$, let $T_\\beta$ be the $\\beta$-transformation on the\nunit circle $[0,1)$ such that $T_\\beta(x)=\\beta x\\pmod 1$. For each $t\\in[0,1)$\nlet $K_\\beta(t)$ be the survivor set consisting of all $x\\in[0,1)$ whose orbit\n$\\{T^n_\\beta(x): n\\ge 0\\}$ never enters the interval $[0,t)$. Letting\n$\\mathscr{E}_\\beta$ denote the bifurcation set of the set-valued map $t\\mapsto\nK_\\beta(t)$, Kalle et al. [Ergodic Theory Dynam. Systems, 40 (9): 2482--2514,\n2020] conjectured that \\[ \\dim_H\\big(\\mathscr{E}_\\beta\\cap[t,1]\\big)=\\dim_H\nK_\\beta(t) \\qquad \\forall\\,t\\in(0,1). \\] The main purpose of this article is to\nprove this conjecture. We do so by investigating dynamical properties of the\nsymbolic equivalent of the survivor set $K_\\beta(t)$, in particular its entropy\nand topological transitivity. In addition, we compare $\\mathscr{E}_\\beta$ with\nthe bifurcation set $\\mathscr{B}_\\beta$ of the map $t\\mapsto \\dim_H K_\\beta(t)$\n(which is a decreasing devil's staircase by a theorem of Kalle et al.), and\nshow that, for Lebesgue-almost every $\\beta\\in(1,2]$, the difference\n$\\mathscr{E}_\\beta\\backslash\\mathscr{B}_\\beta$ has positive Hausdorff\ndimension, but for every $k\\in\\{0,1,2,\\dots\\}\\cup\\{\\aleph_0\\}$, there are\ninfinitely many values of $\\beta$ such that the cardinality of\n$\\mathscr{E}_\\beta\\backslash\\mathscr{B}_\\beta$ is exactly $k$. For a countable\nbut dense subset of $\\beta$'s, we also determine the intervals of constancy of\nthe function $t\\mapsto \\dim_H K_\\beta(t)$.\n  Some connections with other topics in dynamics, such as kneading invariants\nof Lorenz maps and the doubling map with an arbitrary hole, are also discussed.\n"", ""The $\\beta$-transformation with a hole at $0$: the general case   Given $\\beta>1$, let $T_\\beta$ be the $\\beta$-transformation on the unit\ncircle $[0,1)$, defined by $T_\\beta(x)=\\beta x\\pmod 1$. For each $t\\in[0,1)$\nlet $K_\\beta(t)$ be the survivor set consisting of all $x\\in[0,1)$ whose orbit\n$\\{T^n_\\beta(x): n\\ge 0\\}$ never hits the interval $[0,t)$. Kalle et al.~[{\\em\nErgodic Theory Dynam. Systems} {\\bf 40} (2020), no.~9, 2482--2514] considered\nthe case $\\beta\\in(1,2]$. They studied the set-valued bifurcation set\n$\\mathscr{E}_\\beta:=\\{t\\in[0,1): K_\\beta(t')\\ne K_\\beta(t)~\\forall t'>t\\}$ and\nproved that the Hausdorff dimension function $t\\mapsto\\dim_H K_\\beta(t)$ is a\nnon-increasing Devil's staircase. In a previous paper [{\\em Ergodic Theory\nDynam. Systems} {\\bf 43} (2023), no.~6, 1785--1828] we determined, for all\n$\\beta\\in(1,2]$, the critical value $\\tau(\\beta):=\\min\\{t>0:\n\\eta_\\beta(t)=0\\}$. The purpose of the present article is to extend these\nresults to all $\\beta>1$. In addition to calculating $\\tau(\\beta)$, we show\nthat (i) the function $\\tau: \\beta\\mapsto\\tau(\\beta)$ is left continuous on\n$(1,\\infty)$ with right-hand limits everywhere, but has countably infinitely\nmany discontinuities; (ii) $\\tau$ has no downward jumps; and (iii) there exists\nan open set $O\\subset(1,\\infty)$, whose complement $(1,\\infty)\\backslash O$ has\nzero Hausdorff dimension, such that $\\tau$ is real-analytic, strictly convex\nand strictly decreasing on each connected component of $O$. We also prove\nseveral topological properties of the bifurcation set $\\mathscr{E}_\\beta$. The\nkey to extending the results from $\\beta\\in(1,2]$ to all $\\beta>1$ is an\nappropriate generalization of the Farey words that are used to parametrize the\nconnected components of the set $O$. Some of the original proofs from the\nabove-mentioned papers are simplified.\n"", ""Critical values for the $\\beta$-transformation with a hole at $0$   Given $\\beta\\in(1,2]$, let $T_\\beta$ be the $\\beta$-transformation on the\nunit circle $[0,1)$ such that $T_\\beta(x)=\\beta x\\pmod 1$. For each $t\\in[0,1)$\nlet $K_\\beta(t)$ be the survivor set consisting of all $x\\in[0,1)$ whose orbit\n$\\{T^n_\\beta(x): n\\ge 0\\}$ never hits the open interval $(0,t)$. Kalle et al.\nproved in [Ergodic Theory Dynam. Systems, 40 (9): 2482--2514, 2020] that the\nHausdorff dimension function $t\\mapsto\\dim_H K_\\beta(t)$ is a non-increasing\nDevil's staircase. So there exists a critical value $\\tau(\\beta)$ such that\n$\\dim_H K_\\beta(t)>0$ if and only if $t<\\tau(\\beta)$. In this paper we\ndetermine the critical value $\\tau(\\beta)$ for all $\\beta\\in(1,2]$, answering a\nquestion of Kalle et al. (2020). For example, we find that for the\nKomornik-Loreti constant $\\beta\\approx 1.78723$ we have\n$\\tau(\\beta)=(2-\\beta)/(\\beta-1)$. Furthermore, we show that (i) the function\n$\\tau: \\beta\\mapsto\\tau(\\beta)$ is left continuous on $(1,2]$ with right-hand\nlimits everywhere, but has countably infinitely many discontinuities; (ii)\n$\\tau$ has no downward jumps, with $\\tau(1+)=0$ and $\\tau(2)=1/2$; and (iii)\nthere exists an open set $O\\subset(1,2]$, whose complement $(1,2]\\setminus O$\nhas zero Hausdorff dimension, such that $\\tau$ is real-analytic, convex and\nstrictly decreasing on each connected component of $O$. Consequently, the\ndimension $\\dim_H K_\\beta(t)$ is not jointly continuous in $\\beta$ and $t$. Our\nstrategy to find the critical value $\\tau(\\beta)$ depends on certain\nsubstitutions of Farey words and a renormalization scheme from dynamical\nsystems.\n""]","[('beta dynamical', 0.4686622619628906), ('dynamical systems beta', 0.4579644501209259), ('ergodic theory', 0.45267748832702637), ('beta critical', 0.3863917589187622), ('beta beta leq', 0.3443114161491394), ('beta leq beta', 0.3369227945804596), ('t_ beta', 0.33518779277801514), ('beta leq', 0.3185955286026001), ('beta_1', 0.31155335903167725), ('beta_2', 0.3079531192779541)]"
1825,1825,15,1825_resolvent bound_resolvent estimates_resolvent estimate_resolvent bounds,"['resolvent bound', 'resolvent estimates', 'resolvent estimate', 'resolvent bounds', 'radial potentials', 'real valued potentials', 'odinger operator delta', 'valued potentials', 'bound form', 'schr odinger operators']","['Improved resolvent bounds for radial potentials. II   We prove semiclassical resolvent estimates for the Schr{\\""o}dinger operator\nin R d , d $\\ge$ 3, with real-valued radial potentials V $\\in$ L $\\infty$ (R\nd). We show that if V (x) = O x --$\\delta$ with $\\delta$ > 4, then the\nresolvent bound is of the form exp Ch -- $\\delta$ $\\delta$--1 log(h --1) 1\n$\\delta$--1 with some constant C > 0. If V (x) = O e -- C x $\\alpha$ with C,\n$\\alpha$ > 0, we get better resolvent bounds of the form exp Ch --1 log(h --1\n', 'Improved Resolvent Bounds for Radial Potentials   We prove semiclassical resolvent estimates for the Schr{\\""o}dinger operator\nin R d , d $\\ge$ 3, with real-valued radial potentials V $\\in$ L $\\infty$ (R\nd). In particular, we show that if V (x) = O x --$\\delta$ with $\\delta$ > 2,\nthen the resolvent bound is of the form e Ch --4/3 with some constant C > 0. We\nalso get resolvent bounds when 1 < $\\delta$ $\\le$ 2. For slowly decaying\n$\\alpha$-H{\\""o}lder potentials we get better resolvent bounds of the form e Ch\n--4/($\\alpha$+3) .\n', 'Semiclassical resolvent estimates for the magnetic Schr \\""odinger\n  operator   We obtain semiclassical resolvent estimates for the Schr{\\""o}dinger operator\n(ih$\\nabla$ + b)^2 + V in R^d , d $\\ge$ 3, where h is a semiclassical\nparameter, V and b are real-valued electric and magnetic potentials independent\nof h.Under quite general assumptions, we prove that the norm of the weighted\nresolvent is bounded by exp(Ch^{-2} log(h^{ -1} )) . We get better resolvent\nbounds for electric potentials which are H{\\""o}lder with respect to the radial\nvariable and magnetic potentials which are H{\\""o}lder with respect to the space\nvariable. For long-range electric potentials which are Lipschitz with respect\nto the radial variable and long-range magnetic potentials which are Lipschitz\nwith respect to the space variable we obtain a resolvent bound of the form\nexp(Ch^{-1}) .\n']","[('resolvent bound', 0.5894463062286377), ('resolvent estimates', 0.5652740001678467), ('resolvent estimate', 0.5579836964607239), ('resolvent bounds', 0.5573828816413879), ('radial potentials', 0.4841073751449585), ('real valued potentials', 0.43961480259895325), ('odinger operator delta', 0.4347931444644928), ('valued potentials', 0.4268155097961426), ('bound form', 0.42492029070854187), ('schr odinger operators', 0.41830378770828247)]"
1826,1826,15,1826_lie bialgebra_lie algebra_lie bracket_group surface,"['lie bialgebra', 'lie algebra', 'lie bracket', 'group surface', 'categorical symmetries', 'bialgebra', 'free homotopy classes', 'oriented surface', 'universal enveloping algebra', 'structure lie']","['A generalization of the Center Theorem of the Thurston-Wolpert-Goldman\n  Lie algebra   The Goldman Lie algebra of an oriented surface was defined by Goldman. By the\nnatural involution that opposes the orientation of curves, the Goldman Lie\nalgebra becomes a $\\mathbb{Z}_{2}$-graded Lie algebra. Its even part is\nisomorphic to the Thurston-Wolpert-Goldman Lie algebra or, briefly, the TWG Lie\nalgebra. Chas and Kabiraj proved the center of the TWG Lie algebra is generated\nby the class of the unoriented trivial loop and the classes of unoriented loops\nparallel to boundary components or punctures. The center of the even part can\nbe rephrased as the set of elements of the even part annihilated by all the\nelements of the even part. We also prove some similar statements for the\nremaining 3 cases involving the odd part. Moreover, we compute the elements of\nthe symmetric algebra and the universal enveloping algebra of the Goldman Lie\nalgebra annihilated by all the even elements of the Goldman Lie algebra, and\nthose annilated by all the odd elements.\n', 'Lie algebras of curves and loop-bundles on surfaces   W. Goldman and V. Turaev defined a Lie bialgebra structure on the $\\mathbb\nZ$-module generated by free homotopy classes of loops of an oriented surface\n(i.e. the conjugacy classes of its fundamental group). We develop a\ngeneralization of this construction replacing homotopies by thin homotopies,\nbased on the combinatorial approach given by M. Chas. We use it to give a\ngeometric proof of a characterization of simple curves in terms of the\nGoldman-Turaev bracket, which was conjectured by Chas.\n', 'The Goldman-Turaev Lie bialgebra and the Kashiwara-Vergne problem in\n  higher genera   For a compact oriented surface $\\Sigma$ of genus $g$ with $n+1$ boundary\ncomponents, the space $\\mathfrak{g}(\\Sigma)$ spanned by free homotopy classes\nof loops in $\\Sigma$ carries the structure of a Lie bialgebra equipped with a\nnatural decreasing filtration, whose structure morphisms are called the Goldman\nbracket and the (framed) Turaev cobracket.\n  We address the following Goldman-Turaev (GT) formality problem: construct a\nLie bialgebra homomorphism $\\theta$ from $\\mathfrak{g}(\\Sigma)$ to its\nassociated graded ${\\rm gr}\\, \\mathfrak{g}(\\Sigma)$ such that ${\\rm gr} \\,\n\\theta = {\\rm id}$. In order to solve it, we define a family of higher genus\nKashiwara-Vergne (KV) problems for an element $F\\in {\\rm Aut}(L)$, where $L$ is\na free Lie algebra. In the case of $g=0$ and $n=2$, it is the classical KV\nproblem from Lie theory. For $g>0$, these KV problems are new.\n  We show that an element $F$ induces a GT formality map if and only if it is a\nsolution of the KV problem. A crucial step in solving the higher genus KV\nproblem is to construct solutions for the case of $g=1$ and $n=1$ in terms of\ncertain elliptic associators following Enriquez. By solving the KV problem, we\nestablish the GT formality for every $g$ and $n$, with the exception of some\nframings for $g=1$ in which case the GT formality actually does not hold.\nFurthermore, we introduce pro-unipotent groups ${\\rm KV}$ and ${\\rm KRV}$ which\nact on the space of solutions of the KV problem freely and transitively. There\nare injective maps ${\\rm GT}_1\\to {\\rm KV}, {\\rm GRT}_1\\to {\\rm KRV}$ from\nGrothendieck-Teichm\\""uller groups.\n  As an application, we show that the Johnson obstruction given by the Turaev\ncobracket coincides with the one given by the Enomoto-Satoh trace. As part of\nour study, we prove a uniqueness theorem for non-commutative divergence\ncocycles on the group algebra of a free group which is of independent value.\n']","[('lie bialgebra', 0.5418314337730408), ('lie algebra', 0.47446125745773315), ('lie bracket', 0.44821831583976746), ('group surface', 0.42639580368995667), ('categorical symmetries', 0.41119641065597534), ('bialgebra', 0.4109960198402405), ('free homotopy classes', 0.3969784677028656), ('oriented surface', 0.3896988034248352), ('universal enveloping algebra', 0.3814789950847626), ('structure lie', 0.37863314151763916)]"
1827,1827,15,1827_flows compact_flows surfaces_flows manifolds_flows flows,"['flows compact', 'flows surfaces', 'flows manifolds', 'flows flows', 'flows', 'flows time', 'dynamical systems', 'closed surfaces', 'compact surfaces', 'topological characterizations']","[""Topological characterizations of recurrence, Poisson stability, and\n  isometric property of flows on surfaces   The long-time behavior is one of the most fundamental properties of dynamical\nsystems. Poincar\\'e studied the Poisson stability to capture the property of\nwhether points return arbitrarily near the initial positions. Birkhoff studied\nthe concept of recurrent points. Hilbert introduced distal property to describe\na rigid group of motions. We show that Poisson stability, recurrence, and\ndistal property of flows on surfaces are topological properties. In fact, a\nflow on a connected compact surface is Poisson stable (resp. recurrent) if and\nonly if the Kolmogorov quotient of the orbit space satisfies $T_{1}$ (resp.\n$T_{1/2}$) separation axiom. Moreover, Poisson stability for such flows is\nequivalent to distal property. In addition, $T_2$ separation axiom corresponds\nto the isometric property. In addition, we construct ``Lakes of Wada continua''\nwhich are the singular point sets of recurrent non-Poisson-stable flows and\nPoisson stable distal non-equicontinuous flows on surfaces.\n"", ""Generalization of Poincar\\'e recurrence theorem for flows on surfaces\n  and characterization of minimal flows on compact surfaces   Poincar\\'e recurrence theorem implies the density of recurrent points for\nvolume-preserving dynamical systems on compact domains. The density of closed\norbits in the non-wandering set is one of the essential properties of Axiom A\nand chaos. The minimal flows are one of the most fundamental objects in\ntopological dynamics. To analyze minimality, recurrence, and density in this\npaper, we introduce a strict limit circuit and a circuit with wandering\nholonomy. Using these concepts, we classify non-recurrent non-wandering orbits\nof flows on compact surfaces with finitely many singular points, characterize\nthe minimality of flows on compact surfaces, and generalize the Poincar\\'e\nrecurrence theorem for flows on surfaces. Moreover, we characterize the density\nof closed orbits in the non-wandering set under finiteness of singular points.\nFurthermore, we demonstrate the necessity of finiteness of singular points and\ncompactness of surfaces. In addition, the analogous results hold for flows with\nfinitely many connected components of the singular point set on non-compact\nsurfaces using the end compactification and collapsing singular points.\n"", ""Dependency of the positive and negative long-time behaviors of flows on\n  surfaces   Long-time behavior is one of the most fundamental properties in dynamical\nsystems. The limit behaviors of flows on surfaces are captured by the\nPoincar\\'e-Bendixson theorem using the $\\omega$-limit sets. This paper\ndemonstrates that the positive and negative long-time behaviors are not\nindependent. In fact, we show the dependence between the $\\omega$-limit sets\nand the $\\alpha$-limit sets of points of flows on surfaces, which partially\ngeneralizes the Poincar\\'e-Bendixson theorem. Applying the dependency result to\nsolve what kinds of the $\\omega$-limit sets appear in the area-preserving (or,\nmore generally, non-wandering) flows on compact surfaces, we show that the\n$\\omega$-limit set of any non-closed orbit of such a flow with arbitrarily many\nsingular points on a compact surface is either a subset of singular points or a\nlocally dense Q-set. Moreover, we show the wildness of surgeries to add totally\ndisconnected singular points and the tameness of those to add finitely many\nsingular points for flows on surfaces.\n""]","[('flows compact', 0.5820032954216003), ('flows surfaces', 0.5590839982032776), ('flows manifolds', 0.5582209825515747), ('flows flows', 0.4992452561855316), ('flows', 0.4735175371170044), ('flows time', 0.4469379782676697), ('dynamical systems', 0.44630345702171326), ('closed surfaces', 0.43196362257003784), ('compact surfaces', 0.4211917221546173), ('topological characterizations', 0.4147990942001343)]"
1828,1828,15,1828_covering systems_covering system_systems covering_existence covering,"['covering systems', 'covering system', 'systems covering', 'existence covering', 'covering', 'number minimal', 'every covering', 'number fields', 'minimum modulus', 'integers finite']","[""Bounds for Erd\\H{o}s covering systems in global function fields   Covering systems of the integers were introduced by Erd\\H{o}s in 1950. Since\nthen, many beautiful questions and conjectures about these objects have been\nposed. Most famously, Erd\\H{o}s asked whether the minimum modulus of a covering\nsystem with distinct moduli is arbitrarily large. This problem was resolved in\n2015 by Hough, who proved that the minimum modulus is bounded. In 2022,\nBalister et al. developed Hough's method and gave a simpler but more versatile\nproof of Hough's result. Their technique has many applications in a number of\nvariants on Erd\\H{o}s' minimum modulus problem. In this paper, we show that\nthere is no covering system of multiplicity $s$ in any global function field of\ngenus $g$ over $\\mathbb{F}_q$ for $q\\geq(82.26+18.88g)e^{0.95g}s^2$. Moreover,\nwe obtain that there is no covering system of $\\mathbb{F}_q[x]$ with distinct\nmoduli for $q>73$. This improves the results in the previous work of the author\njoint with Li, Wang and Yi.\n"", ""On covering systems of polynomial rings over finite fields   In 1950, Erd\\H{o}s posed a question known as the minimum modulus problem on\ncovering systems for $\\mathbb{Z}$, which asked whether the minimum modulus of a\ncovering system with distinct moduli is bounded. This long-standing problem was\nfinally resolved by Hough in 2015, as he proved that the minimum modulus of any\ncovering system with distinct moduli does not exceed $10^{16}$. Recently,\nBalister, Bollob\\'as, Morris, Sahasrabudhe, and Tiba developed a versatile\nmethod called the distortion method and significantly reduced Hough's bound to\n$616,000$. In this paper, we apply this method to present a proof that the\nsmallest degree of the moduli in any covering system for $\\mathbb{F}_q[x]$ of\nmultiplicity $s$ is bounded by a constant depending only on $s$ and $q$.\nConsequently, we successfully resolve the minimum modulus problem for\n$\\mathbb{F}_q[x]$ and disprove a conjecture by Azlin.\n"", ""On Erd\\H{o}s covering systems in global function fields   A covering system of the integers is a finite collection of arithmetic\nprogressions whose union is the set of integers. A well-known problem on\ncovering systems is the minimum modulus problem posed by Erd\\H{o}s in 1950, who\nasked whether the minimum modulus in such systems with distinct moduli can be\narbitrarily large. This problem was resolved by Hough in 2015, who showed that\nthe minimum modulus is at most $10^{16}$. In 2022, Balister, Bollob\\'as,\nMorris, Sahasrabudhe and Tiba reduced Hough's bound to $616,000$ by developing\nHough's method. They call it the distortion method. In this paper, by applying\nthis method, we mainly prove that there does not exist any covering system of\nmultiplicity $s$ in any global function field of genus $g$ over $\\mathbb{F}_q$\nfor $q\\geq (1.14+0.16g)e^{6.5+0.97g}s^2$. In particular, there is no covering\nsystem of $\\mathbb{F}_q[x]$ with distinct moduli for $q\\geq 759$.\n""]","[('covering systems', 0.5191321969032288), ('covering system', 0.5102412104606628), ('systems covering', 0.467949777841568), ('existence covering', 0.41440173983573914), ('covering', 0.40780436992645264), ('number minimal', 0.40096315741539), ('every covering', 0.3689984977245331), ('number fields', 0.3479578197002411), ('minimum modulus', 0.327616810798645), ('integers finite', 0.3251531720161438)]"
1829,1829,15,1829_random fields_random field_random fields investigate_strong law large,"['random fields', 'random field', 'random fields investigate', 'strong law large', 'functionals random', 'sequences random variables', 'stationary random', 'law large numbers', 'stationary ergodic', 'almost sure convergence']","['Strong Law of Large Numbers for Functionals of Random Fields With\n  Unboundedly Increasing Covariances   The paper proves the Strong Law of Large Numbers for integral functionals of\nrandom fields with unboundedly increasing covariances. The case of functional\ndata and increasing domain asymptotics is studied. Conditions to guarantee that\nthe Strong Law of Large Numbers holds true are provided. The considered\nscenarios include wide classes of non-stationary random fields. The discussion\nabout application to weak and long-range dependent random fields and numerical\nexamples are given.\n', 'On Rio\'s proof of limit theorems for dependent random fields   This paper presents an exposition of Rio\'s proof of the strong law of large\nnumbers and extends his method to random fields. In addition to considering the\nrate of convergence in the Marcinkiewicz--Zygmund strong law of large numbers,\nwe go a step further by establishing (i) the\nHsu--Robbins--Erd\\""{o}s--Spitzer--Baum--Katz theorem, (ii) the Feller weak law\nof large numbers, and (iii) the Pyke--Root theorem on mean convergence for\ndependent random fields. These results significantly improve several particular\ncases in the literature. The proof is based on new maximal inequalities that\nhold for random fields satisfying a very general dependence structure.\n', 'Weak and strong law of large numbers for strictly stationary\n  Banach-valued random fields   In this paper, we investigate the law of large numbers for strictly\nstationary random fields, that is, we provide sufficient conditions on the\nmoments and the dependence of the random field in order to guarantee the almost\nsure convergence to $0$ and the convergence in $\\mathbb L^p$ of partials sums\nover squares or rectangles of $\\mathbb Z^d$. Approximation by multi-indexed\nmartingales as well as by $m$-dependent random fields are investigated.\nApplications to functions of $d$-independent Bernoulli shifts and to\nfunctionals of i.i.d.\\ random fields are also provided.\n']","[('random fields', 0.577365517616272), ('random field', 0.5284257531166077), ('random fields investigate', 0.5085099935531616), ('strong law large', 0.43779364228248596), ('functionals random', 0.4294431507587433), ('sequences random variables', 0.4042024314403534), ('stationary random', 0.3989855945110321), ('law large numbers', 0.39898404479026794), ('stationary ergodic', 0.39725416898727417), ('almost sure convergence', 0.39528414607048035)]"
1830,1830,15,1830_siegel modular forms_siegel modular_siegel cusp forms_modular forms,"['siegel modular forms', 'siegel modular', 'siegel cusp forms', 'modular forms', 'modular forms also', 'holomorphic siegel', 'modular form', 'valued modular forms', 'modular curves', 'valued siegel']","['Siegel modular forms of degree two and level five   We construct a ring of meromorphic Siegel modular forms of degree 2 and level\n5, with singularities supported on an arrangement of Humbert surfaces, which is\ngenerated by four singular theta lifts of weights 1, 1, 2, 2 and their\nJacobian. We use this to prove that the ring of holomorphic Siegel modular\nforms of degree 2 and level $\\Gamma_0(5)$ is minimally generated by eighteen\nmodular forms of weights 2, 4, 4, 4, 4, 4, 6, 6, 6, 6, 10, 11, 11, 11, 13, 13,\n13, 15.\n', 'Formal Siegel modular forms for arithmetic subgroups   The notion of formal Siegel modular forms for an arithmetic subgroup $\\Gamma$\nof the symplectic group of genus $n$ is a generalization of symmetric formal\nFourier-Jacobi series. Assuming an upper bound on the affine covering number of\nthe Siegel modular variety associated with $\\Gamma$, we prove that all formal\nSiegel modular forms are given by Fourier-Jacobi expansions of classical\nholomorphic Siegel modular forms. We also show that the required upper bound is\nalways met if $2\\leq n \\leq 4$. As an application we consider the case of the\nparamodular group of squarefree level and genus $2$.\n', 'On the existence of Siegel modular forms with extra twists   In this paper, we study Siegel modular forms with extra twists. We provide\nconditions on the level and genus of the forms that is necessary for the\nexistence of extra twists for Siegel modular forms. We also give explicit\nexamples of Siegel modular forms with extra twists that are different from the\ncomplex conjugation\n']","[('siegel modular forms', 0.8710287809371948), ('siegel modular', 0.7584134936332703), ('siegel cusp forms', 0.718938946723938), ('modular forms', 0.7025258541107178), ('modular forms also', 0.658743143081665), ('holomorphic siegel', 0.6392965912818909), ('modular form', 0.6377094388008118), ('valued modular forms', 0.6278539299964905), ('modular curves', 0.622559130191803), ('valued siegel', 0.5941312909126282)]"
1831,1831,15,1831_magnetic geodesic_geodesic flows_strong magnetic fields_magnetic systems,"['magnetic geodesic', 'geodesic flows', 'strong magnetic fields', 'magnetic systems', 'pseudo riemannian', 'magnetic fields', 'riemannian', 'curvature non', 'curvature non positive', 'constant magnetic field']","[""Beltrami fields with nonconstant proportionality factor   We consider the question raised by Enciso and Peralta-Salas in [4] (see\narXiv:1402.6825): What nonconstant functions $f$ can occur as the\nproportionality factor for a Beltrami field $\\mathbf{u}$ on an open subset $U\n\\subset \\mathbb{R}^3$? We also consider the related question: For any such $f$,\nhow large is the space of associated Beltrami fields? By applying Cartan's\nmethod of moving frames and the theory of exterior differential systems, we are\nable to improve upon the results given in [4]. In particular, the answer to the\nsecond question depends crucially upon the geometry of the level surfaces of\n$f$. We conclude by giving a complete classification of Beltrami fields that\npossess either a translation symmetry or a rotation symmetry.\n"", ""Zoll magnetic systems on the two-torus: a Nash-Moser construction   We construct an infinite-dimensional family of smooth integrable magnetic\nsystems on the two-torus which are Zoll, meaning that all the unit-speed\nmagnetic geodesics are periodic. The metric and the magnetic field of such\nsystems are arbitrarily close to the flat metric and to a given constant\nmagnetic field. This extends to the magnetic setting a famous result by\nGuillemin on the two-sphere. We characterize Zoll magnetic systems as zeros of\na suitable action functional $S$, and then look for its zeros by means of a\nNash-Moser implicit function theorem. This requires showing the\nright-invertibility of the linearized operator $\\mathrm{d} S$ in a neighborhood\nof the flat metric and constant magnetic field, and establishing tame estimates\nfor the right inverse. As key step we prove the invertibility of the normal\noperator $\\mathrm{d} S\\circ \\mathrm{d} S^*$ which, unlike in Guillemin's case,\nis pseudo-differential only at the highest order. We overcome this difficulty\nnoting that, by the asymptotic properties of Bessel functions, the lower order\nexpansion of $\\mathrm{d} S \\circ \\mathrm{d}S^*$ is a sum of Fourier integral\noperators. We then use a resolvent identity decomposition which reduces the\nproblem to the invertibility of $\\mathrm{d} S \\circ \\mathrm{d} S^*$ restricted\nto the subspace of functions corresponding to high Fourier modes. The inversion\nof such a restricted operator is finally achieved by making the crucial\nobservation that lower order Fourier integral operators satisfy asymmetric tame\nestimates.\n"", ""On Ma\\~n\\'e's critical value for the two-component Hunter-Saxton system\n  and a infnite dimensional magnetic Hopf-Rinow theorem   In this paper, we introduce a nonlinear system of partial differential\nequations, the magnetic two-component Hunter-Saxton system (M2HS). This system\nis formulated as a magnetic geodesic equation on an infinite-dimensional Lie\ngroup equipped with a right-invariant metric, the $\\dot{H}^1$ -metric, which is\nclosely related to the infinite-dimensional Fisher-Rao metric, and the\nderivative of an infinite-dimensional contact-type form as the magnetic field.\nWe define Ma\\~n\\'e's critical value for exact magnetic systems on Hilbert\nmanifolds in full generality and compute it explicitly for the (M2HS).\nMoreover, we establish an infinite-dimensional Hopf-Rinow theorem for this\nmagnetic system, where Ma\\~n\\'e's critical value serves as the threshold beyond\nwhich the Hopf-Rinow theorem no longer holds. This geometric framework enables\nus to thoroughly analyze the blow-up behavior of solutions to the (M2HS). Using\nthis insight, we extend solutions beyond blow-up by introducing and proving the\nexistence of global conservative weak solutions. This extension is facilitated\nby extending the Madelung transform from an isometry into a magnetomorphism,\nembedding the magnetic system into a magnetic system on an infinite-dimensional\nsphere equipped with the derivative of the standard contact form as the\nmagnetic field. Crucially, this setup can always be reduced, via a dynamical\nreduction theorem, to a totally magnetic three-sphere, providing a deeper\nunderstanding of the underlying dynamics.\n""]","[('magnetic geodesic', 0.604069709777832), ('geodesic flows', 0.5096849799156189), ('strong magnetic fields', 0.47812333703041077), ('magnetic systems', 0.46887555718421936), ('pseudo riemannian', 0.44727203249931335), ('magnetic fields', 0.43857714533805847), ('riemannian', 0.4348045289516449), ('curvature non', 0.42826297879219055), ('curvature non positive', 0.4174764156341553), ('constant magnetic field', 0.3985104560852051)]"
1832,1832,15,1832_toric varieties_projective toric variety_toric variety_projective toric,"['toric varieties', 'projective toric variety', 'toric variety', 'projective toric', 'type toric', 'toric variety fan', 'proper toric', 'smooth toric', 'torus equivariant', 'toric']","['Local cohomology and singular cohomology of toric varieties via mixed Hodge modules Given an affine toric variety $X$ embedded in a smooth variety, we prove a general result about the mixed Hodge module structure on the local cohomology sheaves of $X$. As a consequence, we prove that the singular cohomology of a proper toric variety is mixed of Hodge-Tate type. Additionally, using these Hodge module techniques, we derive a purely combinatorial result on rational polyhedral cones that has consequences regarding the depth of reflexive differentials on a toric variety.\n  We then study in detail two important subclasses of toric varieties: those corresponding to cones over simplicial polytopes and those corresponding to cones over simple polytopes. Here, we give a comprehensive description of the local cohomology in terms of the combinatorics of the associated cones, and calculate the Betti numbers (or more precisely, the Hodge-Du Bois diamond) of a projective toric variety associated to a simple polytope.', ""Toric vector bundles over a discrete valuation ring and Bruhat-Tits\n  buildings   We give a classification of rank $r$ torus equivariant vector bundles\n$\\mathcal{E}$ on a toric scheme $\\mathfrak{X}$ over a discrete valuation ring\n$\\mathcal{O}$, in terms of graded piecewise linear maps $\\Phi$ from the fan of\n$\\mathfrak{X}$ to the (extended) building of $GL(r)$. This is an extension of\nKlyachko's classification of torus equivariant vector bundles on toric\nvarieties over a field on one hand, and Mumford's classification of equivariant\nline bundles on toric schemes over $\\mathcal{O}$ on the other hand. We also\ngive a simple criterion for equivariant splitting of $\\mathcal{E}$ into a sum\nof toric line bundles in terms of its piecewise linear map. Among other things,\nthis work lays the foundations for study of arithmetic geometry of toric vector\nbundles.\n"", 'Fibered toric varieties   A toric variety is called fibered if it can be represented as a total space\nof fibre bundle over toric base and with toric fiber. Fibered toric varieties\nform a special case of toric variety bundles. In this note we first give an\nintroduction to the class of fibered toric varieties. Then we use them to\nillustrate some known and conjectural results on topology and intersection\ntheory of general toric variety bundles. Finally, using the language of fibered\ntoric varieties, we compute the equivariant cohomology rings of smooth complete\ntoric varieties.\n']","[('toric varieties', 0.7969136834144592), ('projective toric variety', 0.7581773400306702), ('toric variety', 0.7489020228385925), ('projective toric', 0.7297411561012268), ('type toric', 0.6376567482948303), ('toric variety fan', 0.6258988976478577), ('proper toric', 0.6258288025856018), ('smooth toric', 0.6092005968093872), ('torus equivariant', 0.5630630850791931), ('toric', 0.5563623309135437)]"
1833,1833,15,1833_coloring_colorings_colourings_four colour,"['coloring', 'colorings', 'colourings', 'four colour', 'colouring', 'edge colouring', 'four color', 'colors', 'colorable', 'colour']","['A Mathematical Proof of the Four-Color Conjecture (1): Transformation\n  Step   The four-color conjecture has puzzled mathematicians for over 170 years and\nhas yet to be proven by purely mathematical methods. This series of articles\nprovides a purely mathematical proof of the four-color conjecture, consisting\nof two parts: the transformation step and the decycle step. The transformation\nstep uses two innovative tools, contracting and extending operations and\nunchanged bichromatic cycles, to transform the proof of the four-color\nconjecture into the decycle problem of 4-base modules. Moreover, the decycle\nstep solves the decycle problem of 4-base modules using two other innovative\ntools: the color-connected potential and the pocket operations. This article\npresents the proof of the transformation step.\n', ""A renewal approach to prove the Four Color Theorem unplugged, Part II:\n  R/G/B Kempe chains in an extremum non-4-colorable MPG   This is the second part of three episodes to demonstrate a renewal approach\nfor proving the Four Color Theorem without checking by a computer. The first\nand the third episodes have subtitles: ``RGB-tilings on maximal planar graphs''\nand ``Diamond routes, canal lines and $\\Sigma$-adjustments,'' where R/G/B stand\nfor red, green and blue colors to paint on edges and an MPG stands for a\nmaximal planar graph. We focus on an extremum non-4-colorable MPG $EP$ in the\nwhole paper. In this second part, we refresh the false proof on $EP$ by Kempe\nfor the Four Color Theorem. And then using single color tilings or RGB-tilings\non $EP$, we offer a renewal point of view through R/G/B Kempe chains to enhance\nour coloring skill, either in vertex-colorings or in edge-colorings. We\ndiscover many fundamental theorems associated with R-/RGB-tilings and\n4-colorability; an adventure study on One Piece, which is either an MPG or an\n$n$-semi-MPG; many if-and-only-if statements for $EP-\\{e\\}$ by using Type A or\nType B $e$-diamond and Kempe chains. This work started on May 31, 2018 and was\nfirst announced by the author~\\cite{Liu2020} on Jan.\\ 22, 2020, when the\npandemic just occurred.\n"", ""A renewal approach to prove the Four Color Theorem unplugged, Part III:\n  Diamond routes, canal lines and $\\Sigma$-adjustments   This is the last part of three episodes to demonstrate a renewal approach for\nproving the Four Color Theorem without checking by a computer. The first and\nthe second episodes have subtitles: ``RGB-tilings on maximal planar graphs''\nand ``R/G/B Kempe chains in an extremum non-4-colorable MPG,'' where R/G/B\nstand for red, green and blue colors to paint on edges and an MPG stands for a\nmaximal planar graph. We focus on an extremum non-4-colorable MPG $EP$ in the\nwhole paper. In this part we introduce three tools based on RGB-tilings. They\nare diamond routes, normal and generalized canal lines or rings and\n$\\Sigma$-adjustments. Using these tools, we show a major result of this paper:\nno four vertices of degree 5 form a diamond in any extremum $EP$.\n""]","[('coloring', 0.6089817881584167), ('colorings', 0.6036657691001892), ('colourings', 0.5985265374183655), ('four colour', 0.5638440251350403), ('colouring', 0.5535502433776855), ('edge colouring', 0.5448533892631531), ('four color', 0.5421841740608215), ('colors', 0.5056231617927551), ('colorable', 0.46237561106681824), ('colour', 0.446530282497406)]"
1834,1834,15,1834_conjecture holds groups_spectral conjecture_finite abelian groups_elementary abelian groups,"['conjecture holds groups', 'spectral conjecture', 'finite abelian groups', 'elementary abelian groups', 'finite abelian', 'conjecture', 'abelian groups', 'conjecture fails', 'conjecture verified', 'conjecture holds']","[""Fuglede's conjecture holds in $\\mathbb{Z}_{p}\\times\\mathbb{Z}_{p^{n}}$   Fuglede's conjecture states that for a subset $\\Omega$ of a locally compact\nabelian group $G$ with positive and finite Haar measure, there exists a subset\nof the dual group of $G$ which is an orthogonal basis of $L^{2}(\\Omega)$ if and\nonly if it tiles the group by translation. In this paper, we prove a\ndivisibility property for a set in $\\mathbb{Z}_{p}\\times\\mathbb{Z}_{p^{n}}$.\nThen using the divisibility property and equi-distributed property, we prove\nthat Fuglede's conjecture holds in the group\n$\\mathbb{Z}_{p}\\times\\mathbb{Z}_{p^{n}}$.\n"", ""Spectral sets and tiles in $\\mathbb{Z}_p^2 \\times \\mathbb{Z}_q^2$   In this paper we study Fuglede's conjecture on the direct product of two\ncyclic groups. After collecting the known results we prove that Fuglede's\nconjecture holds on $\\mathbb{Z}_{pq} \\times \\mathbb{Z}_{pq} \\cong\n\\mathbb{Z}_p^2 \\times \\mathbb{Z}_q^2$.\n"", ""Fuglede's conjecture holds on $\\mathbb{Z}_p^2 \\times \\mathbb{Z}_q$   The study of Fuglede's conjecture on the direct product of elementary abelian\ngroups was initiated by Iosevich et al. For the product of two elementary\nabelian groups the conjecture holds. For $\\mathbb{Z}_p^3$ the problem is still\nopen if $p\\ge 11$. In connection we prove that Fuglede's conjecture holds on\n$\\mathbb{Z}_{p}^2\\times \\mathbb{Z}_q$ by developing a method based on ideas\nfrom discrete geometry.\n""]","[('conjecture holds groups', 0.5208019614219666), ('spectral conjecture', 0.46620261669158936), ('finite abelian groups', 0.45734360814094543), ('elementary abelian groups', 0.4237913489341736), ('finite abelian', 0.42300543189048767), ('conjecture', 0.4139906167984009), ('abelian groups', 0.4099837839603424), ('conjecture fails', 0.4071061313152313), ('conjecture verified', 0.4059297442436218), ('conjecture holds', 0.39592915773391724)]"
1835,1835,15,1835_federated learning_decentralized federated learning_devices federated learning_federated learning fl,"['federated learning', 'decentralized federated learning', 'devices federated learning', 'federated learning fl', 'distributed learning', 'wireless federated', 'learning wireless communications', 'learning wireless', 'network computation', 'devices federated']","['Federated Learning and Wireless Communications   Federated learning becomes increasingly attractive in the areas of wireless\ncommunications and machine learning due to its powerful functions and potential\napplications. In contrast to other machine learning tools that require no\ncommunication resources, federated learning exploits communications between the\ncentral server and the distributed local clients to train and optimize a\nmachine learning model. Therefore, how to efficiently assign limited\ncommunication resources to train a federated learning model becomes critical to\nperformance optimization. On the other hand, federated learning, as a brand new\ntool, can potentially enhance the intelligence of wireless networks. In this\narticle, we provide a comprehensive overview on the relationship between\nfederated learning and wireless communications, including basic principle of\nfederated learning, efficient communications for training a federated learning\nmodel, and federated learning for intelligent wireless applications. We also\nidentify some future research challenges and directions at the end of this\narticle.\n', ""In-network Computation for Large-scale Federated Learning over Wireless\n  Edge Networks   Most conventional Federated Learning (FL) models are using a star network\ntopology where all users aggregate their local models at a single server (e.g.,\na cloud server). That causes significant overhead in terms of both\ncommunications and computing at the server, delaying the training process,\nespecially for large scale FL systems with straggling nodes. This paper\nproposes a novel edge network architecture that enables decentralizing the\nmodel aggregation process at the server, thereby significantly reducing the\ntraining delay for the whole FL network. Specifically, we design a\nhighly-effective in-network computation protocol (INC) consisting of a user\nscheduling mechanism, an in-network aggregation process (INA) which is designed\nfor both primal- and primal-dual methods in distributed machine learning\nproblems, and a network routing algorithm. Under the proposed INA, we then\nformulate a joint routing and resource optimization problem, aiming to minimize\nthe aggregation latency. The problem is NP-hard, and thus we propose a\npolynomial time routing algorithm which can achieve near optimal performance\nwith a theoretical bound. Simulation results showed that the proposed INC\nframework can not only help reduce the FL training latency, up to 5.6 times,\nbut also significantly decrease cloud's traffic and computing overhead. This\ncan enable large-scale FL.\n"", ""Enabling Large-Scale Federated Learning over Wireless Edge Networks   Major bottlenecks of large-scale Federated Learning(FL) networks are the high\ncosts for communication and computation. This is due to the fact that most of\ncurrent FL frameworks only consider a star network topology where all local\ntrained models are aggregated at a single server (e.g., a cloud server). This\ncauses significant overhead at the server when the number of users are huge and\nlocal models' sizes are large. This paper proposes a novel edge network\narchitecture which decentralizes the model aggregation process at the server,\nthereby significantly reducing the aggregation latency of the whole network. In\nthis architecture, we propose a highly-effective in-network computation\nprotocol consisting of two components. First, an in-network aggregation process\nis designed so that the majority of aggregation computations can be offloaded\nfrom cloud server to edge nodes. Second, a joint routing and resource\nallocation optimization problem is formulated to minimize the aggregation\nlatency for the whole system at every learning round. The problem turns out to\nbe NP-hard, and thus we propose a polynomial time routing algorithm which can\nachieve near optimal performance with a theoretical bound. Numerical results\nshow that our proposed framework can dramatically reduce the network latency,\nup to 4.6 times. Furthermore, this framework can significantly decrease cloud's\ntraffic and computing overhead by a factor of K/M, where K is the number of\nusers and M is the number of edge nodes, in comparison with conventional\nbaselines.\n""]","[('federated learning', 0.6635602712631226), ('decentralized federated learning', 0.6342055201530457), ('devices federated learning', 0.6092756390571594), ('federated learning fl', 0.5838451385498047), ('distributed learning', 0.5260396003723145), ('wireless federated', 0.5238260626792908), ('learning wireless communications', 0.44157326221466064), ('learning wireless', 0.4290309250354767), ('network computation', 0.39537733793258667), ('devices federated', 0.3916032314300537)]"
1836,1836,15,1836_semidefinite programming_solving semidefinite programming_semidefinite programs_semidefinite programming problems,"['semidefinite programming', 'solving semidefinite programming', 'semidefinite programs', 'semidefinite programming problems', 'semidefinite optimization', 'semidefinite programs sdps', 'sparse semidefinite', 'constrained polynomial optimization', 'solving semidefinite', 'sdp solver']","['Decomposed Structured Subsets for Semidefinite and Sum-of-Squares\n  Optimization   Semidefinite programs (SDPs) are standard convex problems that are frequently\nfound in control and optimization applications. Interior-point methods can\nsolve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the\nsize of matrix variables and the number of constraints increases. To improve\nscalability, SDPs can be approximated with lower and upper bounds through the\nuse of structured subsets (e.g., diagonally-dominant and scaled-diagonally\ndominant matrices). Meanwhile, any underlying sparsity or symmetry structure\nmay be leveraged to form an equivalent SDP with smaller positive semidefinite\nconstraints. In this paper, we present a notion of decomposed structured\nsubsets}to approximate an SDP with structured subsets after an equivalent\nconversion. The lower/upper bounds found by approximation after conversion\nbecome tighter than the bounds obtained by approximating the original SDP\ndirectly. We apply decomposed structured subsets to semidefinite and\nsum-of-squares optimization problems with examples of H-infinity norm\nestimation and constrained polynomial optimization. An existing basis pursuit\nmethod is adapted into this framework to iteratively refine bounds.\n', 'Fast ADMM for Semidefinite Programs with Chordal Sparsity   Many problems in control theory can be formulated as semidefinite programs\n(SDPs). For large-scale SDPs, it is important to exploit the inherent sparsity\nto improve the scalability. This paper develops efficient first-order methods\nto solve SDPs with chordal sparsity based on the alternating direction method\nof multipliers (ADMM). We show that chordal decomposition can be applied to\neither the primal or the dual standard form of a sparse SDP, resulting in\nscaled versions of ADMM algorithms with the same computational cost. Each\niteration of our algorithms consists of a projection on the product of small\npositive semidefinite cones, followed by a projection on an affine set, both of\nwhich can be carried out efficiently. Our techniques are implemented in CDCS,\nan open source add-on to MATLAB. Numerical experiments on large-scale sparse\nproblems in SDPLIB and random SDPs with block-arrow sparse patterns show\nspeedups compared to some common state-of-the-art software packages.\n', 'Chordal decomposition in operator-splitting methods for sparse\n  semidefinite programs   We employ chordal decomposition to reformulate a large and sparse\nsemidefinite program (SDP), either in primal or dual standard form, into an\nequivalent SDP with smaller positive semidefinite (PSD) constraints. In\ncontrast to previous approaches, the decomposed SDP is suitable for the\napplication of first-order operator-splitting methods, enabling the development\nof efficient and scalable algorithms. In particular, we apply the alternating\ndirection method of multipliers (ADMM) to solve decomposed primal- and\ndual-standard-form SDPs. Each iteration of such ADMM algorithms requires a\nprojection onto an affine subspace, and a set of projections onto small PSD\ncones that can be computed in parallel. We also formulate the homogeneous\nself-dual embedding (HSDE) of a primal-dual pair of decomposed SDPs, and extend\na recent ADMM-based algorithm to exploit the structure of our HSDE. The\nresulting HSDE algorithm has the same leading-order computational cost as those\nfor the primal or dual problems only, with the advantage of being able to\nidentify infeasible problems and produce an infeasibility certificate. All\nalgorithms are implemented in the open-source MATLAB solver CDCS. Numerical\nexperiments on a range of large-scale SDPs demonstrate the computational\nadvantages of the proposed methods compared to common state-of-the-art solvers.\n']","[('semidefinite programming', 0.6781073808670044), ('solving semidefinite programming', 0.6753634810447693), ('semidefinite programs', 0.6689030528068542), ('semidefinite programming problems', 0.6680299639701843), ('semidefinite optimization', 0.6498627066612244), ('semidefinite programs sdps', 0.6480270028114319), ('sparse semidefinite', 0.6123284101486206), ('constrained polynomial optimization', 0.5230873227119446), ('solving semidefinite', 0.5217955112457275), ('sdp solver', 0.4809480905532837)]"
1837,1837,15,1837_quantum harmonic oscillator_quantum harmonic_harmonic oscillator_anharmonic oscillators,"['quantum harmonic oscillator', 'quantum harmonic', 'harmonic oscillator', 'anharmonic oscillators', 'energy spectrum', 'quantum well', 'discrete spectrum', 'schrodinger', 'energy spectra', 'non relativistic quantum']","['On the exactly-solvable semi-infinite quantum well of the\n  non-rectangular step-harmonic profile   An exactly-solvable model of the non-relativistic harmonic oscillator with a\nposition-dependent effective mass is constructed. The model behaves itself as a\nsemi-infinite quantum well of the non-rectangular profile. Such a form of the\nprofile looks like a step-harmonic potential as a consequence of the certain\nanalytical dependence of the effective mass from the position and\nsemiconfinement parameter $a$. Both states of the discrete and continuous\nspectrum are studied. In the case of the discrete spectrum, wavefunctions of\nthe oscillator model are expressed through the Bessel polynomials. The discrete\nenergy spectrum is non-equidistant and finite as a consequence of its\ndependence on parameter $a$, too. In the case of the continuous spectrum,\nwavefunctions of the oscillator model are expressed through the $_1F_1$\nhypergeometric functions. At the limit, when the parameter $a$ goes to\ninfinity, both wavefunctions, and the energy spectrum of the model under\nconstruction correctly reduce to corresponding results of the usual\nnon-relativistic harmonic oscillator with a constant effective mass. Namely,\nwavefunctions of the discrete spectrum recover wavefunctions in terms of the\nHermite polynomials, and wavefunctions of the continuous spectrum simply\nvanish. We also present a new limit relation that reduces Bessel polynomials\ndirectly to Hermite polynomials and prove its correctness using the\nmathematical induction technique.\n', 'Comment on `Exact solution of the position-dependent effective mass and\n  angular frequency Schr\\""odinger equation: harmonic oscillator model with\n  quantized confinement parameter\'   In a recent paper by Jafarov, Nagiyev, Oste and Van der Jeugt (2020 {\\sl J.\\\nPhys.\\ A} {\\bf 53} 485301), a confined model of the non-relativistic quantum\nharmonic oscillator, where the effective mass and the angular frequency are\ndependent on the position, was constructed and it was shown that the\nconfinement parameter gets quantized. By using a point canonical transformation\nstarting from the constant-mass Schr\\""odinger equation for the Rosen-Morse II\npotential, it is shown here that similar results can be easily obtained without\nquantizing the confinement parameter. In addition, an extension to a confined\nshifted harmonic oscillator directly follows from the same point canonical\ntransformation.\n', 'Exact solution of the position-dependent effective mass and angular\n  frequency Schr\\""odinger equation: harmonic oscillator model with quantized\n  confinement parameter   We present an exact solution of a confined model of the non-relativistic\nquantum harmonic oscillator, where the effective mass and the angular frequency\nare dependent on the position. The free Hamiltonian of the proposed model has\nthe form of the BenDaniel--Duke kinetic energy operator. The\nposition-dependency of the mass and the angular frequency is such that the\nhomogeneous nature of the harmonic oscillator force constant $k$ and hence the\nregular harmonic oscillator potential is preserved. As a consequence thereof, a\nquantization of the confinement parameter is observed. It is shown that the\ndiscrete energy spectrum of the confined harmonic oscillator with\nposition-dependent mass and angular frequency is finite, has a non-equidistant\nform and depends on the confinement parameter. The wave functions of the\nstationary states of the confined oscillator with position-dependent mass and\nangular frequency are expressed in terms of the associated Legendre or\nGegenbauer polynomials. In the limit where the confinement parameter tends to\n$\\infty$, both the energy spectrum and the wave functions converge to the\nwell-known equidistant energy spectrum and the wave functions of the stationary\nnon-relativistic harmonic oscillator expressed in terms of Hermite polynomials.\nThe position-dependent effective mass and angular frequency also become\nconstant under this limit.\n']","[('quantum harmonic oscillator', 0.5849626064300537), ('quantum harmonic', 0.5134957432746887), ('harmonic oscillator', 0.45987680554389954), ('anharmonic oscillators', 0.42346441745758057), ('energy spectrum', 0.420216828584671), ('quantum well', 0.41911807656288147), ('discrete spectrum', 0.4060938060283661), ('schrodinger', 0.39331990480422974), ('energy spectra', 0.3759938180446625), ('non relativistic quantum', 0.37511545419692993)]"
1838,1838,15,1838_kk theory_theory algebras_ko theory_category equivariant,"['kk theory', 'theory algebras', 'ko theory', 'category equivariant', 'theory group', 'homological algebra', 'kasparov product', 'theory graded', 'bivariant theory', 'tensor category']","[""Controlled KK-theory, and a Milnor exact sequence   We introduce controlled $KK$-theory groups associated to a pair $(A,B)$ of\nseparable $C^*$-algebras. Roughly, these consist of elements of the usual\n$K$-theory group $K_0(B)$ that approximately commute with elements of $A$. Our\nmain results show that these groups are related to Kasparov's $KK$-groups by a\nMilnor exact sequence, in such a way that R\\o{}rdam's $KL$-group is identified\nwith an inverse limit of our controlled $KK$-groups.\n  In the case that the $C^*$-algebras involved satisfy the UCT, our Milnor\nexact sequence agrees with the Milnor sequence associated to a $KK$-filtration\nin the sense of Schochet, although our results are independent of the UCT.\nApplications to the UCT will be pursued in subsequent work.\n"", ""Tensor category equivariant KK-theory   In this paper, we introduce Kasparov's bivariant K-theory that is equivariant\nunder symmetries of a C*-tensor category. It is motivated by some dualities in\nquantum group equivariant KK-theory, and the classification theory of\ninclusions of C*-algebras. The fundamental properties of the KK-theory, i.e.,\nthe existence of the Kasparov product, Cuntz's picture, universality, and\ntriangulated category structure, hold true in this generalization as well.\nMoreover, we further prove a new property specific to this theory; the\ninvariance of KK-theory under weak Morita equivalence of the tensor categories.\nAs an example, we study the Baum-Connes type property for $3$-cocycle twists of\ndiscrete groups.\n"", 'On the Unbounded Picture of $KK$-Theory   In the founding paper on unbounded $KK$-theory it was established by Baaj and\nJulg that the bounded transform, which associates a class in $KK$-theory to any\nunbounded Kasparov module, is a surjective homomorphism (under a separability\nassumption). In this paper, we provide an equivalence relation on unbounded\nKasparov modules and we thereby describe the kernel of the bounded transform.\nThis allows us to introduce a notion of topological unbounded $KK$-theory,\nwhich becomes isomorphic to $KK$-theory via the bounded transform. The\nequivalence relation is formulated entirely at the level of unbounded Kasparov\nmodules and consists of homotopies together with an extra degeneracy condition.\nOur degenerate unbounded Kasparov modules are called spectrally decomposable\nsince they admit a decomposition into a part with positive spectrum and a part\nwith negative spectrum.\n']","[('kk theory', 0.5803091526031494), ('theory algebras', 0.4904228746891022), ('ko theory', 0.44748446345329285), ('category equivariant', 0.42941129207611084), ('theory group', 0.4153275787830353), ('homological algebra', 0.41401952505111694), ('kasparov product', 0.4031004309654236), ('theory graded', 0.39161548018455505), ('bivariant theory', 0.3859117031097412), ('tensor category', 0.3833081126213074)]"
1839,1839,15,1839_matrix noise_linear spectral statistics_spectral statistics_high dimensional noise,"['matrix noise', 'linear spectral statistics', 'spectral statistics', 'high dimensional noise', 'non gaussian noise', 'dimensional noise', 'gaussian noise', 'spiked eigenvalues', 'rank signal', 'covariance matrix high']","[""Detection of Signals in Colored Noise: Roy's Largest Root Test for\n  Non-central $F$-matrices   This paper investigates the signal detection problem in colored noise with an\nunknown covariance matrix. In particular, we focus on detecting a non-random\nsignal by capitalizing on the leading eigenvalue (a.k.a. Roy's largest root) of\nthe whitened sample covariance matrix as the test statistic. To this end, the\nwhitened sample covariance matrix is constructed via \\(m\\)-dimensional \\(p \\)\nplausible signal-bearing samples and \\(m\\)-dimensional \\(n \\) noise-only\nsamples. Since the signal is non-random, the whitened sample covariance matrix\nturns out to have a {\\it non-central} \\(F\\)-distribution with a rank-one\nnon-centrality parameter. Therefore, the performance of the test entails the\nstatistical characterization of the leading eigenvalue of the non-central\n\\(F\\)-matrix, which we address by deriving its cumulative distribution function\n(c.d.f.) in closed-form by leveraging the powerful orthogonal polynomial\napproach in random matrix theory. This new c.d.f. has been instrumental in\nanalyzing the receiver operating characteristic (ROC) of the detector. We also\nextend our analysis into the high dimensional regime in which \\(m,n\\), and\n\\(p\\) diverge such that \\(m/n\\) and \\(m/p\\) remain fixed. It turns out that,\nwhen \\(m=n\\) and fixed, the power of the test improves if the signal-to-noise\nratio (SNR) is of at least \\(O(p)\\), whereas the corresponding SNR in the high\ndimensional regime is of at least \\(O(p^2)\\). Nevertheless, more intriguingly,\nfor \\(m<n\\) with the SNR of order \\(O(p)\\), the leading eigenvalue does not\nhave power to detect {\\it weak} signals in the high dimensional regime.\n"", ""Detection problems in the spiked matrix models   We study the statistical decision process of detecting the low-rank signal\nfrom various signal-plus-noise type data matrices, known as the spiked random\nmatrix models. We first show that the principal component analysis can be\nimproved by entrywise pre-transforming the data matrix if the noise is\nnon-Gaussian, generalizing the known results for the spiked random matrix\nmodels with rank-1 signals. As an intermediate step, we find out sharp phase\ntransition thresholds for the extreme eigenvalues of spiked random matrices,\nwhich generalize the Baik-Ben Arous-P\\'{e}ch\\'{e} (BBP) transition. We also\nprove the central limit theorem for the linear spectral statistics for the\nspiked random matrices and propose a hypothesis test based on it, which does\nnot depend on the distribution of the signal or the noise. When the noise is\nnon-Gaussian noise, the test can be improved with an entrywise transformation\nto the data matrix with additive noise. We also introduce an algorithm that\nestimates the rank of the signal when it is not known a priori.\n"", 'Weak detection in the spiked Wigner model   We consider the weak detection problem in a rank-one spiked Wigner data\nmatrix where the signal-to-noise ratio is small so that reliable detection is\nimpossible. We propose a hypothesis test on the presence of the signal by\nutilizing the linear spectral statistics of the data matrix. The test is\ndata-driven and does not require prior knowledge about the distribution of the\nsignal or the noise. When the noise is Gaussian, the proposed test is optimal\nin the sense that its error matches that of the likelihood ratio test, which\nminimizes the sum of the Type-I and Type-II errors. If the density of the noise\nis known and non-Gaussian, the error of the test can be lowered by applying an\nentrywise transformation to the data matrix. We establish a central limit\ntheorem for the linear spectral statistics of general rank-one spiked Wigner\nmatrices as an intermediate step.\n']","[('matrix noise', 0.5910914540290833), ('linear spectral statistics', 0.5588194131851196), ('spectral statistics', 0.5262788534164429), ('high dimensional noise', 0.48180583119392395), ('non gaussian noise', 0.4774712324142456), ('dimensional noise', 0.46801233291625977), ('gaussian noise', 0.4632245600223541), ('spiked eigenvalues', 0.4430272579193115), ('rank signal', 0.4371527135372162), ('covariance matrix high', 0.4334897994995117)]"
1840,1840,15,1840_depth functions_depth based_sets depth_depth random,"['depth functions', 'depth based', 'sets depth', 'depth random', 'depth', 'depth general', 'tukey depth', 'depths', 'medians', 'depth respect']","['Partial reconstruction of measures from halfspace depth   The halfspace depth of a $d$-dimensional point $x$ with respect to a finite\n(or probability) Borel measure $\\mu$ in $\\mathbb{R}^d$ is defined as the\ninfimum of the $\\mu$-masses of all closed halfspaces containing $x$. A natural\nquestion is whether the halfspace depth, as a function of $x \\in \\mathbb{R}^d$,\ndetermines the measure $\\mu$ completely. In general, it turns out that this is\nnot the case, and it is possible for two different measures to have the same\nhalfspace depth function everywhere in $\\mathbb{R}^d$. In this paper we show\nthat despite this negative result, one can still obtain a substantial amount of\ninformation on the support and the location of the mass of $\\mu$ from its\nhalfspace depth. We illustrate our partial reconstruction procedure in an\nexample of a non-trivial bivariate probability distribution whose atomic part\nis determined successfully from its halfspace depth.\n', 'Theoretical properties of angular halfspace depth   The angular halfspace depth (ahD) is a natural modification of the celebrated\nhalfspace (or Tukey) depth to the setup of directional data. It allows us to\ndefine elements of nonparametric inference, such as the median, the\ninter-quantile regions, or the rank statistics, for datasets supported in the\nunit sphere. Despite being introduced in 1987, ahD has never received ample\nrecognition in the literature, mainly due to the lack of efficient algorithms\nfor its computation. With the recent progress on the computational front, ahD\nhowever exhibits the potential for developing viable nonparametric statistics\ntechniques for directional datasets. In this paper, we thoroughly treat the\ntheoretical properties of ahD. We show that similarly to the classical\nhalfspace depth for multivariate data, also ahD satisfies many desirable\nproperties of a statistical depth function. Further, we derive uniform\ncontinuity/consistency results for the associated set of directional medians,\nand the central regions of ahD, the latter representing a depth-based analogue\nof the quantiles for directional data.\n', 'Halfspace depth for general measures: The ray basis theorem and its\n  consequences   The halfspace depth is a prominent tool of nonparametric multivariate\nanalysis. The upper level sets of the depth, termed the trimmed regions of a\nmeasure, serve as a natural generalization of the quantiles and inter-quantile\nregions to higher-dimensional spaces. The smallest non-empty trimmed region,\ncoined the halfspace median of a measure, generalizes the median. We focus on\nthe (inverse) ray basis theorem for the halfspace depth, a crucial theoretical\nresult that characterizes the halfspace median by a covering property. First, a\nnovel elementary proof of that statement is provided, under minimal assumptions\non the underlying measure. The proof applies not only to the median, but also\nto other trimmed regions. Motivated by the technical development of the amended\nray basis theorem, we specify connections between the trimmed regions, floating\nbodies, and additional equi-affine convex sets related to the depth. As a\nconsequence, minimal conditions for the strict monotonicity of the depth are\nobtained. Applications to the computation of the depth and robust estimation\nare outlined.\n']","[('depth functions', 0.5512997508049011), ('depth based', 0.5271989703178406), ('sets depth', 0.507244884967804), ('depth random', 0.48982933163642883), ('depth', 0.47023719549179077), ('depth general', 0.4400217831134796), ('tukey depth', 0.4261517822742462), ('depths', 0.42489147186279297), ('medians', 0.42317450046539307), ('depth respect', 0.42013469338417053)]"
1841,1841,15,1841_waves reaction diffusion_perturbed reaction diffusion_stochastic phase_stochastic perturbations,"['waves reaction diffusion', 'perturbed reaction diffusion', 'stochastic phase', 'stochastic perturbations', 'stability traveling wave', 'stochastically perturbed', 'solutions stochastic', 'stochastic landau', 'reaction diffusion systems', 'diffusion systems']","['Travelling Waves for Reaction-Diffusion Equations Forced by Translation\n  Invariant Noise   Inspired by applications, we consider reaction-diffusion equations on\n$\\mathbb{R}$ that are stochastically forced by a small multiplicative noise\nterm that is white in time, coloured in space and invariant under translations.\nWe show how these equations can be understood as a stochastic partial\ndifferential equation (SPDE) forced by a cylindrical Q-Wiener process and\nsubsequently explain how to study stochastic travelling waves in this setting.\nIn particular, we generalize the phase tracking framework that was developed in\n[Hamster & Hupkes 2017] and [Hamster & Hupkes 2018] for noise processes driven\nby a single Brownian motion. The main focus lies on explaining how this\nframework naturally leads to long term approximations for the stochastic wave\nprofile and speed. We illustrate our approach by two fully worked-out examples,\nwhich highlight the predictive power of our expansions.\n', 'Stability of Traveling Waves for Systems of Reaction-Diffusion Equations\n  with Multiplicative Noise   We consider reaction-diffusion equations that are stochastically forced by a\nsmall multiplicative noise term. We show that spectrally stable traveling wave\nsolutions to the deterministic system retain their orbital stability if the\namplitude of the noise is sufficiently small.\n  By applying a stochastic phase-shift together with a time-transform, we\nobtain a quasi-linear SPDE that describes the fluctuations from the primary\nwave. We subsequently follow the semigroup approach developed by Hamster and\nHupkes in 2017 to handle the nonlinear stability question. The main novel\nfeature is that we no longer require the diffusion coefficients to be equal.\n', 'Stability of Travelling Waves for Reaction-Diffusion Equations with\n  Multiplicative Noise   We consider reaction-diffusion equations that are stochastically forced by a\nsmall multiplicative noise term. We show that spectrally stable travelling wave\nsolutions to the deterministic system retain their orbital stability if the\namplitude of the noise is sufficiently small.\n  By applying a stochastic phase-shift together with a time-transform, we\nobtain a semilinear sPDE that describes the fluctuations from the primary wave.\nWe subsequently develop a semigroup approach to handle the nonlinear stability\nquestion in a fashion that is closely related to modern deterministic methods.\n']","[('waves reaction diffusion', 0.5924002528190613), ('perturbed reaction diffusion', 0.5796821117401123), ('stochastic phase', 0.5434332489967346), ('stochastic perturbations', 0.5404955148696899), ('stability traveling wave', 0.5391874313354492), ('stochastically perturbed', 0.5343167185783386), ('solutions stochastic', 0.51214599609375), ('stochastic landau', 0.5058701634407043), ('reaction diffusion systems', 0.5018182396888733), ('diffusion systems', 0.49124789237976074)]"
1842,1842,15,1842_boundary integral equations_domain decomposition methods_boundary integrals_elliptic problems,"['boundary integral equations', 'domain decomposition methods', 'boundary integrals', 'elliptic problems', 'elliptic partial', 'solving elliptic', 'laplacian operator', 'decomposition methods', 'helmholtz problems', 'elliptic partial differential']","[""A GPU-accelerated Cartesian grid method is proposed for solving the\n  heat, wave, and Schrodinger equations on irregular domains   This paper introduces a second-order method for solving general elliptic\npartial differential equations (PDEs) on irregular domains using GPU\nacceleration, based on Ying's kernel-free boundary integral (KFBI) method. The\nmethod addresses limitations imposed by CFL conditions in explicit schemes and\naccuracy issues in fully implicit schemes for the Laplacian operator. To\novercome these challenges, the paper employs a series of second-order time\ndiscrete schemes and splits the Laplacian operator into explicit and implicit\ncomponents. Specifically, the Crank-Nicolson method discretizes the heat\nequation in the temporal dimension, while the implicit scheme is used for the\nwave equation. The Schrodinger equation is treated using the Strang splitting\nmethod. By discretizing the temporal dimension implicitly, the heat, wave, and\nSchrodinger equations are transformed into a sequence of elliptic equations.\nThe Laplacian operator on the right-hand side of the elliptic equation is\nobtained from the numerical scheme rather than being discretized and corrected\nby the five-point difference method. A Cartesian grid-based KFBI method is\nemployed to solve the resulting elliptic equations. GPU acceleration, achieved\nthrough a parallel Cartesian grid solver, enhances the computational efficiency\nby exploiting high degrees of parallelism. Numerical results demonstrate that\nthe proposed method achieves second-order accuracy for the heat, wave, and\nSchrodinger equations. Furthermore, the GPU-accelerated solvers for the three\ntypes of time-dependent equations exhibit a speedup of 30 times compared to\nCPU-based solvers.\n"", ""Kernel Free Boundary Integral Method for 3D Stokes and Navier Equations\n  on Irregular Domains   A second-order accurate kernel-free boundary integral method is presented for\nStokes and Navier boundary value problems on three-dimensional irregular\ndomains. It solves equations in the framework of boundary integral equations,\nwhose corresponding discrete forms are well-conditioned and solved by the GMRES\nmethod. A notable feature of this approach is that the boundary or volume\nintegrals encountered in BIEs are indirectly evaluated by a Cartesian\ngrid-based method, which includes discretizing corresponding simple interface\nproblems with a MAC scheme, correcting discrete linear systems to reduce large\nlocal truncation errors near the interface, solving the modified system by a CG\nmethod together with an FFT-based Poisson solver. No extra work or special\nquadratures are required to deal with singular or hyper-singular boundary\nintegrals and the dependence on the analytical expressions of Green's functions\nfor the integral kernels is completely eliminated. Numerical results are given\nto demonstrate the efficiency and accuracy of the Cartesian grid-based method.\n"", 'A correction function-based kernel-free boundary integral method for\n  elliptic PDEs with implicitly defined interfaces   This work addresses a novel version of the kernel-free boundary integral\n(KFBI) method for solving elliptic PDEs with implicitly defined irregular\nboundaries and interfaces. We focus on boundary value problems and interface\nproblems, which are reformulated into boundary integral equations and solved\nwith the matrix-free GMRES method. In the KFBI method, evaluating boundary and\nvolume integrals only requires solving equivalent but much simpler interface\nproblems in a bounding box, for which fast solvers such as FFTs and geometric\nmultigrid methods are applicable. For the simple interface problem, a\ncorrection function is introduced for both the evaluation of right-hand side\ncorrection terms and the interpolation of a non-smooth potential function. A\nmesh-free collocation method is proposed to compute the correction function\nnear the interface. The new method avoids complicated derivation for derivative\njumps of the solution and is easy to implement, especially for the fourth-order\nmethod in three space dimensions. Various numerical examples are presented,\nincluding challenging cases such as high-contrast coefficients, arbitrarily\nclose interfaces and heterogeneous interface problems. The reported numerical\nresults verify that the proposed method is both accurate and efficient.\n']","[('boundary integral equations', 0.4891434907913208), ('domain decomposition methods', 0.4739990830421448), ('boundary integrals', 0.4208235740661621), ('elliptic problems', 0.411686509847641), ('elliptic partial', 0.39246565103530884), ('solving elliptic', 0.390377938747406), ('laplacian operator', 0.3751744329929352), ('decomposition methods', 0.37204858660697937), ('helmholtz problems', 0.3717111051082611), ('elliptic partial differential', 0.36662983894348145)]"
1843,1843,15,1843_functions manifolds_smooth functions manifolds_manifolds_manifold equivalent,"['functions manifolds', 'smooth functions manifolds', 'manifolds', 'manifold equivalent', 'manifolds may', 'closed manifolds', 'manifold', 'dimensional closed manifolds', 'dimensional manifolds', 'graphs smooth']","[""Real algebraic functions on closed manifolds whose Reeb spaces are given\n  graphs   In our paper, we construct a real-algebraic function whose Reeb\n(Kronrod-Reeb) graph is a graph respecting some algebraic domain: a graph for\nthis is called Poincar\\'e-Reeb graph. The Reeb graph of a smooth function is\ndefined as a natural graph which is the quotient space of the manifold of the\ndomain under a natural equivalence relation for some wide and nice class of\nsmooth functions. The vertex set is defined as the set of all connected\ncomponents containing some singular points of the function: a singular point of\na smooth function is a point where the differential vanishes. Morse-Bott\nfunctions give very specific cases. The relation is\n  to contract each connected component of each preimage to a point.\n  Sharko has asked a natural and important problem: can we construct a nice\nsmooth function whose Reeb graph is a given graph? Explicit answers have been\ngiven first by Masumoto-Saeki in a generalized manner for closed surfaces.\nAfter that various answers have been presented by various researchers and most\nof them are essentially for functions on closed surfaces and Morse functions\nsuch that connected components of preimages containing no singular points are\nspheres. Recently the author has also considered questions and solved in cases\nthe preimages are general manifolds.\n"", 'On Reeb graphs induced from smooth functions on 3-dimensional closed\n  manifolds which may not be orientable   The Reeb space of a smooth function is a topological and combinatoric object\nand fundamental and important in understanding topological and geometric\nproperties of the manifold of the domain. It is the graph and a topological\nspace endowed with a natural topology. This is defined as the quotient space of\nthe manifold of the domain where the equivalence relation is as follows: two\npoints in the manifold are equivalent if and only if they are in a same\nconnected component of a level set or a preimage. In considerable cases they\nare graphs (Reeb graphs): if the function is a so-called Morse(-Bott) functions\nfor example, then this is the graph such that a point is a vertex if and only\nif the corresponding connected component of the level set contains some\nsingular points.\n  The author previously constructed explicit smooth functions on suitable\n3-dimensional connected, closed and orientable manifolds whose Reeb graphs are\nisomorphic to prescribed graphs and whose preimages are as prescribed types.\nThis gives a new answer to so-called realization problems of graphs as Reeb\ngraphs of smooth functions of suitable classes. The present paper concerns a\nvariant in the case where the 3-dimensional manifolds may not be non-orientable\nextending the result before. \\end{abstract}\n', 'Smooth functions with simple structures on 3-dimensional closed\n  manifolds with prescribed Reeb graphs and preimages   We give a new answer to so-called realization problems of graphs as Reeb\ngraphs of smooth functions with prescribed preimages of regular values having\nnice structures. We present a best possible answer for functions on\n3-dimensional closed manifolds.\n  The Reeb space of a smooth function is the quotient space of the manifold of\nthe domain induced from the following equivalence relation; two points in the\nmanifold are equivalent if and only if they are points of a same connected\ncomponent of some preimage. They are in considerable cases graphs (Reeb\ngraphs).\n  Reeb spaces with preimages represent the manifolds well and are important\ntools in geometry. Recently they play important roles in applications of\nmathematics such as visualizations. Realization problems ask us whether we can\nconstruct smooth functions with prescribed Reeb graphs and preimages. Studies\non construction respecting preimages were essentially started by the author.\n']","[('functions manifolds', 0.6385890245437622), ('smooth functions manifolds', 0.5913346409797668), ('manifolds', 0.5523279309272766), ('manifold equivalent', 0.5326564311981201), ('manifolds may', 0.5298649072647095), ('closed manifolds', 0.5252799391746521), ('manifold', 0.5242165923118591), ('dimensional closed manifolds', 0.517589271068573), ('dimensional manifolds', 0.5156846642494202), ('graphs smooth', 0.5145507454872131)]"
1844,1844,15,1844_dimensional hypercube q_n_hypercube q_n_cycle decompositions_hypercube graph,"['dimensional hypercube q_n', 'hypercube q_n', 'cycle decompositions', 'hypercube graph', 'hypercubes', 'hamilton cycle', 'hamiltonian cycles', 'hamilton paths', 'dimensional hypercube', 'cycle lengths']","['Hamiltonian cycles and paths in hypercubes with disjoint faulty edges   We consider hypercubes with pairwise disjoint faulty edges. An\n$n$-dimensional hypercube $Q_n$ is an undirected graph with $2^n$ nodes, each\nlabeled with a distinct binary strings of length $n$. The parity of the vertex\nis 0 if the number of ones in its labels is even, and is 1 if the number of\nones is odd. Two vertices $a$ and $b$ are connected by the edge iff $a$ and $b$\ndiffer in one position. If $a$ and $b$ differ in position $i$, then we say that\nthe edge $(a,b)$ goes in direction $i$ and we define the parity of the edge as\nthe parity of the end with 0 on the position $i$. It was already known that\n$Q_n$ is not Hamiltonian if all edges going in one direction and of the same\nparity are faulty.\n  In this paper we show that if $n\\ge4$ then all other hypercubes are\nHamiltonian. In other words, every cube $Q_n$, with $n\\ge4$ and disjoint faulty\nedges is Hamiltonian if and only if for each direction there are two healthy\ncrossing edges of different parity.\n', 'Matchings in Hypercubes Extend to Long Cycles   The $n$-dimensional hypercube graph $Q_n$ has as vertices all subsets of\n$\\{1, \\ldots, n\\}$, and an edge between any two sets that differ in a single\nelement. The Ruskey-Savage conjecture states that every matching of the\n$n$-dimensional hypercube $Q_n$ can be extended into a Hamilton cycle. We prove\nthat matchings of $Q_n$ containing edges spanning at most $d = 5$ directions\ncan be extended into a Hamilton cycle. We also characterize when these\nmatchings of most $d = 5$ directions can be extended into a Hamilton path\nbetween two prescribed vertices. Our proofs work for arbitrary $d$ and $n$\nwhere $d \\le n$ assuming some extension properties hold in $Q_d$ which we\nverified by a computer for $d=5$.\n', 'Generalization of Cycle Decompositions of Even Dimensional Hypercubes on\n  $d$-Dimensional Toruses   We consider cycle decompositions of even, $2an$-dimensional hypercubes\n$Q_{2an},$ where $a \\geq 3$ is odd and $n \\geq 1.$ Prior work done by\nAxenovich, Offner, and Tompkins focused on obtaining the existence of cycle\ndecompositions for even-dimensional hypercubes using long cycles of a given\nform, leaving out cycles of shorter lengths and, in fact, cycles of even longer\nlengths than those obtained there, such as $C_{7 \\cdot 2^{11}}$ in the case of\n$Q_{14}.$ In this paper, we provide two novel methods for explicitly\nconstructing cycle decompositions of virtually all possible cycle lengths,\nusing cycles of a given form, on Cartesian products of cycles up to those known\nby the work of Axenovich, Offner, and Tompkins. In particular, we show that we\ncan explicitly obtain cycle decompositions of even dimensional hypercubes\n$Q_{2an}$ for all lengths mentioned above while on the same Cartesian product\nof cycles. With this, the current understanding of cycle decompositions of even\ndimensional hypercubes is furthered constructively and is featured with some\ninteresting consequences for when $a$ is a positive, even integer.\nAdditionally, progress is made towards obtaining cycle decompositions using the\nlongest admissible cycle lengths with the incorporation of a more explicit\nstarting point from which such decompositions of $Q_{2an}$ can be studied\nfurther.\n']","[('dimensional hypercube q_n', 0.5874426960945129), ('hypercube q_n', 0.5606904029846191), ('cycle decompositions', 0.47404158115386963), ('hypercube graph', 0.47398120164871216), ('hypercubes', 0.4714936912059784), ('hamilton cycle', 0.4590703547000885), ('hamiltonian cycles', 0.45712438225746155), ('hamilton paths', 0.45494359731674194), ('dimensional hypercube', 0.4439345598220825), ('cycle lengths', 0.4323755204677582)]"
1845,1845,15,1845_gkz hypergeometric_hypergeometric solutions_hypergeometric functions_transformations hypergeometric,"['gkz hypergeometric', 'hypergeometric solutions', 'hypergeometric functions', 'transformations hypergeometric', 'mathbb f_p', 'equations finite field', 'hypergeometric system', 'hypergeometric', 'finite field mathbb', 'finite field']","[""Notes on solutions of KZ equations modulo $p^s$ and $p$-adic limit\n  $s\\to\\infty$   We consider the KZ equations over $\\mathbb C$ in the case, when the\nhypergeometric solutions are hyperelliptic integrals of genus $g$. Then the\nspace of solutions is a $2g$-dimensional complex vector space. We also consider\nthe same equations modulo $p^s$, where $p$ is an odd prime and $s$ is a\npositive integer, and over the field $\\mathbb Q_p$ of $p$-adic numbers. We\nconstruct polynomial solutions of the KZ equations modulo $p^s$ and study the\nspace $\\mathcal M_{p^s}$ of all constructed solutions. We show that the\n$p$-adic limit of $\\mathcal M_{p^s}$ as $s\\to\\infty$ gives us a $g$-dimensional\nvector space of solutions of the KZ equations over $\\mathbb Q_p$. The solutions\nover $\\mathbb Q_p$ are power series at a certain asymptotic zone of the KZ\nequations.\n  In the appendix written jointly with Steven Sperber we consider all\nasymptotic zones of the KZ equations in the case $g=1$ of elliptic integrals.\nThe $p$-adic limit of $\\mathcal M_{p^s}$ as $s\\to \\infty$ gives us a\none-dimensional space of solutions over $\\mathbb Q_p$ at every asymptotic zone.\nWe apply Dwork's theory and show that our germs of solutions over $\\mathbb Q_p$\ndefined at different asymptotic zones analytically continue into a single\nglobal invariant line subbundle of the associated KZ connection. Notice that\nthe corresponding KZ connection over $\\mathbb C$ does not have proper\nnontrivial invariant subbundles, and therefore our invariant line subbundle is\na new feature of the KZ equations over $\\mathbb Q_p$. We describe the Frobenius\ntransformations of solutions of the KZ equations for $g =1$ and then recover\nthe unit roots of the zeta functions of the elliptic curves defined by the\nequations $y^2= \\beta \\,x(x-1)(x-\\alpha)$ over the finite field $\\mathbb F_p$.\nHere $\\alpha,\\beta\\in\\mathbb F_p^\\times, \\alpha \\ne 1$.\n"", 'An invariant subbundle of the KZ connection mod $p$ and reducibility of\n  $\\hat{sl}_2$ Verma modules mod $p$   We consider the KZ differential equations over $\\mathbb C$ in the case, when\nits multidimensional hypergeometric solutions are one-dimensional integrals. We\nalso consider the same differential equations over a finite field $\\mathbb\nF_p$. We study the space of polynomial solutions of these differential\nequations over $\\mathbb F_p$, constructed in a previous work by V. Schechtman\nand the author. The module of these polynomial solutions defines an invariant\nsubbundle of the associated KZ connection modulo $p$. We describe the algebraic\nequations for that subbundle and argue that the equations correspond to highest\nweight vectors of the associated $\\hat{sl}_2$ Verma modules over the field\n$\\mathbb F_p$.\n', 'Determinant of $\\mathbb F_p$-hypergeometric solutions under ample\n  reduction   We consider the KZ differential equations over $\\mathbb C$ in the case, when\nthe hypergeometric solutions are one-dimensional integrals. We also consider\nthe same differential equations over a finite field $\\mathbb F_p$. We study the\npolynomial solutions of these differential equations over $\\mathbb F_p$,\nconstructed in a previous work joint with V.\\,Schechtman and called the\n$\\mathbb F_p$-hypergeometric solutions.\n  The dimension of the space of $\\mathbb F_p$-hypergeometric solutions depends\non the prime number $p$. We say that the KZ equations have ample reduction for\na prime $p$, if the dimension of the space of $\\mathbb F_p$-hypergeometric\nsolutions is maximal possible, that is, equal to the dimension of the space of\nsolutions of the corresponding KZ equations over $\\mathbb C$. Under the\nassumption of ample reduction, we prove a determinant formula for the matrix of\ncoordinates of basis $\\mathbb F_p$-hypergeometric solutions. The formula is\nanalogous to the corresponding formula for the determinant of the matrix of\ncoordinates of basis complex hypergeometric solutions, in which binomials\n$(z_i-z_j)^{M_i+M_j}$ are replaced with $(z_i-z_j)^{M_i+M_j-p}$ and the Euler\ngamma function $\\Gamma(x)$ is replaced with a suitable $\\mathbb F_p$-analog\n$\\Gamma_{\\mathbb F_p}(x)$ defined on $\\mathbb F_p$.\n']","[('gkz hypergeometric', 0.5203197002410889), ('hypergeometric solutions', 0.5083141326904297), ('hypergeometric functions', 0.4638858139514923), ('transformations hypergeometric', 0.44790026545524597), ('mathbb f_p', 0.4361444115638733), ('equations finite field', 0.42364639043807983), ('hypergeometric system', 0.4114609360694885), ('hypergeometric', 0.3782729208469391), ('finite field mathbb', 0.3192465603351593), ('finite field', 0.31874990463256836)]"
1846,1846,15,1846_scattered linear sets_scattered linear_polynomials finite fields_mathbb f_q,"['scattered linear sets', 'scattered linear', 'polynomials finite fields', 'mathbb f_q', 'linearized polynomials', 'scattered mathbb', 'finite fields', '_q linear', 'polynomials finite', 'polynomials properties']","['Scattered polynomials: an overview on their properties, connections and\n  applications   The aim of this survey is to outline the state of the art in research on a\nclass of linearized polynomials with coefficients over finite fields, known as\nscattered polynomials. These have been studied in several contexts, such as in\n[A. Blokhuis, M. Lavrauw. Scattered spaces with respect to a spread in\n$\\mathrm{PG}(n, q)$. Geometriae Dedicata 81(1) (2000), 231-243] and [G.\nLunardon, O. Polverino. Blocking sets and derivable partial spreads. J.\nAlgebraic Combin. 14 (2001), 49-56]. Recently, their connection to maximum\nrank-metric codes was brought to light in [J. Sheekey. MRD codes: Constructions\nand connections. In K.-U. Schmidt and A. Winterhof, editors, Combinatorics and\nFinite Fields, De Gruyter (2019), 255-286]. This link has significantly\nadvanced their study and investigation, sparking considerable interest in\nrecent years. Here, we will explore their relationship with certain subsets of\nthe finite projective line $\\mathrm{PG}(1, q^n)$ known as maximum scattered\nlinear sets, as well as with codes made up of square matrices of order $n$\nequipped with the rank metric. We will review the known examples of scattered\npolynomials up to date and discuss some of their key properties. We will also\naddress the classification of maximum scattered linear sets of the finite\nprojective line $\\mathrm{PG}(1, q^n)$ for small values of $n$ and discuss\ncharacterization results for the examples known so far. Finally, we will\nretrace how each scattered polynomial gives rise to a translation plane, as\ndiscussed in [V. Casarino, G. Longobardi, C. Zanella. Scattered linear sets in\na finite projective line and translation planes, Linear Algebra Appl. 650\n(2022), 286-298] and in [G. Longobardi, C. Zanella, A standard form for\nscattered linearized polynomials and properties of the related translation\nplanes, J. Algebr. Comb. 59(4) (2024), 917-937].\n', 'Partially scattered linearized polynomials and rank metric codes   A linearized polynomial $f(x)\\in\\mathbb F_{q^n}[x]$ is called scattered if\nfor any $y,z\\in\\mathbb F_{q^n}$, the condition $zf(y)-yf(z)=0$ implies that $y$\nand $z$ are $\\mathbb F_{q}$-linearly dependent. In this paper two\ngeneralizations of the notion of a scattered linearized polynomial are defined\nand investigated. Let $t$ be a nontrivial positive divisor of $n$. By weakening\nthe property defining a scattered linearized polynomial, L-$q^t$-partially\nscattered and R-$q^t$-partially scattered linearized polynomials are introduced\nin such a way that the scattered linearized polynomials are precisely those\nwhich are both L-$q^t$- and R-$q^t$-partially scattered. Also, connections\nbetween partially scattered polynomials, linear sets and rank metric codes are\nexhibited.\n', 'Investigating the exceptionality of scattered polynomials   Scattered polynomials over a finite field $\\mathbb{F}_{q^n}$ have been\nintroduced by Sheekey in 2016, and a central open problem regards the\nclassification of those that are exceptional. So far, only two families of\nexceptional scattered polynomials are known. Very recently, Longobardi and\nZanella weakened the property of being scattered by introducing the notion of\nL-$q^t$-partially scattered and R-$q^t$-partially scattered polynomials, for\n$t$ a divisor of $n$. Indeed, a polynomial is scattered if and only if it is\nboth L-$q^t$-partially scattered and R-$q^t$-partially scattered. In this\npaper, by using techniques from algebraic geometry over finite fields and\nfunction fields theory, we show that the property which is is the hardest to be\npreserved is the L-$q^t$-partially scattered one. On the one hand, we are able\nto extend the classification results of exceptional scattered polynomials to\nexceptional L-$q^t$-partially scattered polynomials. On the other hand, the\nR-$q^t$-partially scattered property seems more stable. We present a large\nfamily of R-$q^t$-partially scattered polynomials, containing examples of\nexceptional R-$q^t$-partially scattered polynomials, which turn out to be\nconnected with linear sets of so-called pseudoregulus type. In order to detect\nnew examples of polynomials which are R-$q^t$-partially scattered, we introduce\ntwo different notions of equivalence preserving this property and concerning\nnatural actions of the groups ${\\rm \\Gamma L}(2,q^n)$ and ${\\rm \\Gamma\nL}(2n/t,q^t)$. In particular, our family contains many examples of inequivalent\npolynomials, and geometric arguments are used to determine the equivalence\nclasses under the action of ${\\rm \\Gamma L}(2n/t,q^t)$.\n']","[('scattered linear sets', 0.529488205909729), ('scattered linear', 0.5204452276229858), ('polynomials finite fields', 0.49734967947006226), ('mathbb f_q', 0.4424023926258087), ('linearized polynomials', 0.4333535134792328), ('scattered mathbb', 0.4080254137516022), ('finite fields', 0.4044763743877411), ('_q linear', 0.4027617573738098), ('polynomials finite', 0.3892473876476288), ('polynomials properties', 0.3882259428501129)]"
1847,1847,15,1847_ornstein uhlenbeck semigroup_ornstein uhlenbeck operator_uhlenbeck semigroup_uhlenbeck operator,"['ornstein uhlenbeck semigroup', 'ornstein uhlenbeck operator', 'uhlenbeck semigroup', 'uhlenbeck operator', 'operator weak', 'invariant measure', 'ornstein uhlenbeck', 'noise operator', 'semigroup', 'maximal operator']","['On the variation operator for the Ornstein-Uhlenbeck semigroup in\n  dimension one   Consider the variation seminorm of the Ornstein-Uhlenbeck semigroup $H_t$ in\ndimension one, taken with respect to $t$. We show that this seminorm defines an\noperator of weak type $(1,1)$ for the relevant Gaussian measure. The analogous\n$L^p$ estimates for $1<p<\\infty$ were already known.\n', 'Riesz transforms of a general Ornstein--Uhlenbeck semigroup   We consider Riesz transforms of any order associated to an\nOrnstein--Uhlenbeck operator $\\mathcal L$, with covariance $Q$ given by a real,\nsymmetric and positive definite matrix, and with drift $B$ given by a real\nmatrix whose eigenvalues have negative real parts. In this general Gaussian\ncontext, we prove that a Riesz transform is of weak type $(1,1)$ with respect\nto the invariant measure if and only if its order is at most $2$.\n', 'On the maximal operator of a general Ornstein-Uhlenbeck semigroup   If $Q$ is a real, symmetric and positive definite $n\\times n$ matrix, and $B$\na real $n\\times n$ matrix whose eigenvalues have negative real parts, we\nconsider the Ornstein--Uhlenbeck semigroup on $\\mathbb{R}^n$ with covariance\n$Q$ and drift matrix $B$. Our main result says that the associated maximal\noperator is of weak type $(1,1)$ with respect to the invariant measure. The\nproof has a geometric gist and hinges on the ""forbidden zones method""\npreviously introduced by the third author.\n']","[('ornstein uhlenbeck semigroup', 0.7172982692718506), ('ornstein uhlenbeck operator', 0.6788185238838196), ('uhlenbeck semigroup', 0.6420409083366394), ('uhlenbeck operator', 0.5820622444152832), ('operator weak', 0.4748300611972809), ('invariant measure', 0.4477531611919403), ('ornstein uhlenbeck', 0.43451717495918274), ('noise operator', 0.4102216362953186), ('semigroup', 0.3988952040672302), ('maximal operator', 0.39852869510650635)]"
1848,1848,15,1848_moduli spaces parabolic_parabolic bundles_moduli space parabolic_moduli spaces,"['moduli spaces parabolic', 'parabolic bundles', 'moduli space parabolic', 'moduli spaces', 'moduli space mathcal', 'moduli spaces mathcal', 'structures moduli spaces', 'moduli space', 'moduli space higgs', 'picard group moduli']","['Picard group of moduli of parabolic Higgs bundles   Let $X$ be a compact Riemann surface of genus $g\\geq 3$ and let\n$\\mathcal{M}_{\\mathrm{par}}$ be the moduli space of semistable parabolic\nbundles over $X$. Let $\\mathcal{M}_{\\mathrm{parH}}$ denote the moduli space of\nsemistable parabolic Higgs bundles over $X$. In this article, we study the\nPicard group of $\\mathcal{M}_{\\mathrm{par}}$ and $\\mathcal{M}_{\\mathrm{parH}}$.\n', 'Topology of moduli of parabolic connections with fixed determinant   Let $X$ be a compact Riemann surface of genus $g \\geq 2$ and $D\\subset X$ be\na fixed finite subset. Let $\\xi$ be a line bundle of degree $d$ over $X$. Let\n$\\mathcal{M}(\\alpha, r, \\xi)$ (respectively,\n$\\mathcal{M}_{\\mathrm{conn}}(\\alpha, r, \\xi)$) denote the moduli space of\nstable parabolic bundles (respectively, parabolic connections) of rank $r$\n$(\\geq 2)$, determinant $\\xi$ and full flag generic rational parabolic weight\ntype $\\alpha$. We show that $\n  \\pi_k(\\mathcal{M}_{\\mathrm{conn}}(\\alpha, r, \\xi)) \\cong\n\\pi_k(\\mathcal{M}(\\alpha, r, \\xi)) $ for $k \\leq2(r-1)(g-1)-1$. As a\nconsequence, we deduce that the moduli space\n$\\mathcal{M}_{\\mathrm{conn}}(\\alpha, r, \\xi)$ is simply connected. We also show\nthat the Hodge structures on the torsion-free parts of both the cohomologies\n$H^k(\\mathcal{M}_{\\mathrm{conn}}(\\alpha, r, \\xi),\\mathbb{Z})$ and\n$H^k(\\mathcal{M}(\\alpha, r, \\xi),\\mathbb{Z})$ are isomorphic for all $k\\leq\n2(r-1)(g-1)+1$.\n', ""Line bundles on the moduli space of parabolic connections over a compact\n  Riemann surface   Let $X$ be a compact Riemann surface of genus $g \\geq 3$ and $S$ a finite\nsubset of $X$. Let $\\xi$ be fixed a holomorphic line bundle over $X$ of degree\n$d$. Let $\\mathcal{M}_{pc}(r, d, \\alpha)$ (respectively, $\\mathcal{M}_{pc}(r,\n\\alpha, \\xi)$ ) denote the moduli space of parabolic connections of rank $r$,\ndegree $d$ and full flag rational generic weight system $\\alpha$,\n(respectively, with the fixed determinant $\\xi$) singular over the parabolic\npoints $S \\subset X$.\n  Let $\\mathcal{M}'_{pc}(r, d, \\alpha)$ (respectively, $\\mathcal{M}'_{pc}(r,\n\\alpha, \\xi)$) be the Zariski dense open subset of $\\mathcal{M}_{pc}(r, d,\n\\alpha)$ (respectively, $\\mathcal{M}_{pc}(r, \\alpha, \\xi)$ )parametrizing all\nparabolic connections such that the underlying parabolic bundle is stable. We\nshow that there is a natural compactification of the moduli spaces\n$\\mathcal{M}'_{pc}(r, d, \\alpha)$, and $\\mathcal{M}'_{pc}(r, \\alpha, \\xi)$ by\nsmooth divisors.\n  We describe the numerically effectiveness of these divisors at infinity. We\ndetermine the Picard group of the moduli spaces $\\mathcal{M}_{pc}(r, d,\n\\alpha)$, and $\\mathcal{M}_{pc}(r, \\alpha, \\xi)$. Let $\\mathcal{C}(L)$ denote\nthe space of holomorphic connections on an ample line bundle $L$ over the\nmoduli space $\\mathcal{M}(r, d, \\alpha)$ of parabolic bundles. We show that\n$\\mathcal{C}(L)$ does not admit any non-constant algebraic function.\n""]","[('moduli spaces parabolic', 0.6906052827835083), ('parabolic bundles', 0.6764586567878723), ('moduli space parabolic', 0.6659908294677734), ('moduli spaces', 0.5780183672904968), ('moduli space mathcal', 0.556326150894165), ('moduli spaces mathcal', 0.5555987358093262), ('structures moduli spaces', 0.5520216226577759), ('moduli space', 0.5435093641281128), ('moduli space higgs', 0.5270984172821045), ('picard group moduli', 0.5233265161514282)]"
1849,1849,15,1849_hankel determinants_hankel determinant_discrete painlev equations_painlev equations,"['hankel determinants', 'hankel determinant', 'discrete painlev equations', 'painlev equations', 'unitary ensemble', 'riccati equations', 'perturbed gaussian', 'monic orthogonal polynomials', 'orthogonal polynomials', 'coefficients orthogonal']","[""Painlev\\'{e} VI, Painlev\\'{e} III and the Hankel Determinant Associated\n  with a Degenerate Jacobi Unitary Ensemble   This paper studies the Hankel determinant generated by a perturbed Jacobi\nweight, which is closely related to the largest and smallest eigenvalue\ndistribution of the degenerate Jacobi unitary ensemble. By using the ladder\noperator approach for the orthogonal polynomials, we find that the logarithmic\nderivative of the Hankel determinant satisfies a nonlinear second-order\ndifferential equation, which turns out to be the Jimbo-Miwa-Okamoto\n$\\sigma$-form of the Painlev\\'{e} VI equation by a translation transformation.\nWe also show that, after a suitable double scaling, the differential equation\nis reduced to the Jimbo-Miwa-Okamoto $\\sigma$-form of the Painlev\\'{e} III. In\nthe end, we obtain the asymptotic behavior of the Hankel determinant as\n$t\\rightarrow1^{-}$ and $t\\rightarrow0^{+}$ in two important cases,\nrespectively.\n"", ""Gaussian Unitary Ensembles with Jump Discontinuities, PDEs and the\n  Coupled Painlev\\'{e} IV System   We study the Hankel determinant generated by the Gaussian weight with jump\ndiscontinuities at $t_1,\\cdots,t_m$. By making use of a pair of ladder\noperators satisfied by the associated monic orthogonal polynomials and three\nsupplementary conditions, we show that the logarithmic derivative of the Hankel\ndeterminant satisfies a second order partial differential equation which is\nreduced to the $\\sigma$-form of a Painlev\\'{e} IV equation when $m=1$.\nMoreover, under the assumption that $t_k-t_1$ is fixed for $k=2,\\cdots,m$, by\nconsidering the Riemann-Hilbert problem for the orthogonal polynomials, we\nconstruct direct relationships between the auxiliary quantities introduced in\nthe ladder operators and solutions of a coupled Painlev\\'{e} IV system.\n"", ""Painlev\\'{e} V, Painlev\\'{e} XXXIV and the Degenerate Laguerre Unitary\n  Ensemble   In this paper, we study the Hankel determinant associated with the degenerate\nLaguerre unitary ensemble. This problem originates from the largest or smallest\neigenvalue distribution of the degenerate Laguerre unitary ensemble. We derive\nthe ladder operators and its compatibility condition with respect to a general\nperturbed weight. By applying the ladder operators to our problem, we obtain\ntwo auxiliary quantities $R_n(t)$ and $r_n(t)$ and show that they satisfy the\ncoupled Riccati equations, from which we find that $R_n(t)$ satisfies the\nPainlev\\'{e} V equation. Furthermore, we prove that $\\sigma_{n}(t)$, a quantity\nrelated to the logarithmic derivative of the Hankel determinant, satisfies both\nthe continuous and discrete Jimbo-Miwa-Okamoto $\\sigma$-form of the\nPainlev\\'{e} V. In the end, by using Dyson's Coulomb fluid approach, we\nconsider the large $n$ asymptotic behavior of our problem at the soft edge,\nwhich gives rise to the Painlev\\'{e} XXXIV equation.\n""]","[('hankel determinants', 0.5849670171737671), ('hankel determinant', 0.559059202671051), ('discrete painlev equations', 0.4678271412849426), ('painlev equations', 0.45734238624572754), ('unitary ensemble', 0.44602227210998535), ('riccati equations', 0.43128013610839844), ('perturbed gaussian', 0.42828044295310974), ('monic orthogonal polynomials', 0.4250624477863312), ('orthogonal polynomials', 0.3915232717990875), ('coefficients orthogonal', 0.3884696066379547)]"
1850,1850,15,1850_vlasov fokker planck_fokker planck equations_nonlinear vlasov poisson_solutions vlasov poisson,"['vlasov fokker planck', 'fokker planck equations', 'nonlinear vlasov poisson', 'solutions vlasov poisson', 'poisson fokker planck', 'nonlinear vlasov', 'kinetic fokker planck', 'fokker planck operator', 'fokker planck system', 'planck equations']","['Well-posedness and trend to equilibrium for the\n  Vlasov-Poisson-Fokker-Planck system with a confining potential   We study well-posedness and long time behavior of the nonlinear\nVlasov-Poisson- Fokker-Planck system with an external confining potential. The\nsystem describes the time evolution of particles (e.g.$\\,\\,$in a plasma)\nundergoing diffusion, friction and Coulomb interaction. We prove existence and\nuniqueness of mild solutions in a weighted Sobolev space. Moreover, we prove\nthat the solutions converge to the global equilibrium exponentially. Our\nresults hold for a wide class of external potentials and the estimates on the\nrate of convergence are explicit and constructive. The technique is based on\nthe construction of Lyapunov functionals, new short and long time estimates for\nthe linearized system, and fixed point arguments.\n', ""Well-posedness and long-time behavior for self-consistent\n  Vlasov-Fokker-Planck equations with general potentials   We study the well-posedness, steady states and long time behavior of\nsolutions to Vlasov-Fokker-Planck equation with external confinement potential\nand nonlinear self-consistent interactions. Our analysis introduces newly\ncharacterized conditions on the interaction kernel that ensure the local\nasymptotic stability of the unique steady state. Compared to previous works on\nthis topic, our results allow for large, singular and non-symmetric\ninteractions. As a corollary of our main results, we show exponential decay of\nsolutions to the Vlasov-Poisson-Fokker-Planck equation in dimension $3$, for\nlow regularity initial data. In the repulsive case, the result holds in\nstrongly nonlinear regimes (\\emph{i.e.} for arbitrarily small Debye length).\nOur techniques rely on the design of new Lyapunov functionals based on\nhypocoercivity and hypoellipticity theories. We use norms which include part of\nthe interaction kernel, and carefully mix ``macroscopic quantities\nbased''--hypocoercivity with ``commutators based''--hypocoercivity.\n"", 'L2-Hypocoercivity and large time asymptotics of the linearized\n  Vlasov-Poisson-Fokker-Planck system   This paper is devoted to the linearized Vlasov-Poisson-Fokker-Planck system\nin presence of an external potential of confinement. We investigate the large\ntime behaviour of the solutions using hypocoercivity methods and a notion of\nscalar product adapted to the presence of a Poisson coupling. Our framework\nprovides estimates which are uniform in the diffusion limit. As an application\nin a simple case, we study the one-dimensional case and prove the exponential\nconvergence of the nonlinear Vlasov-Poisson-Fokker-Planck system without any\nsmall mass assumption.\n']","[('vlasov fokker planck', 0.6441611647605896), ('fokker planck equations', 0.6394183039665222), ('nonlinear vlasov poisson', 0.5966928601264954), ('solutions vlasov poisson', 0.561674952507019), ('poisson fokker planck', 0.5577041506767273), ('nonlinear vlasov', 0.5504921674728394), ('kinetic fokker planck', 0.5376933217048645), ('fokker planck operator', 0.5350351333618164), ('fokker planck system', 0.5328471660614014), ('planck equations', 0.5174773931503296)]"
1851,1851,15,1851_erd enyi graphs_adjacency laplacian matrices_spectrum adjacency matrix_spectrum adjacency,"['erd enyi graphs', 'adjacency laplacian matrices', 'spectrum adjacency matrix', 'spectrum adjacency', 'eigenvectors adjacency', 'edge eigenvalues', 'erd enyi graph', 'spectral edge', 'sparse erd enyi', 'enyi random graph']","[""Localized phase for the Erd\\H{o}s-R\\'enyi graph   We analyse the eigenvectors of the adjacency matrix of the Erd\\H{o}s-R\\'enyi\ngraph $\\mathbb G(N,d/N)$ for $\\sqrt{\\log N} \\ll d \\lesssim \\log N$. We show the\nexistence of a localized phase, where each eigenvector is exponentially\nlocalized around a single vertex of the graph. This complements the completely\ndelocalized phase previously established in [arXiv:2005.14180]. For large\nenough $d$, we establish a mobility edge by showing that the localized phase\nextends up to the boundary of the delocalized phase. We derive explicit\nasymptotics for the localization length up to the mobility edge and\ncharacterize its divergence near the phase boundary.\n  The proof is based on a rigorous verification of Mott's criterion for\nlocalization, comparing the tunnelling amplitude between localization centres\nwith the eigenvalue spacing. The first main ingredient is a new family of\nglobal approximate eigenvectors, for which sharp enough estimates on the\ntunnelling amplitude can be established. The second main ingredient is a lower\nbound on the spacing of approximate eigenvalues. It follows from an\nanticoncentration result for these discrete random variables, obtained by a\nrecursive application of a self-improving anticoncentration estimate due to\nKesten.\n"", ""The completely delocalized region of the Erd\\H{o}s-R\\'enyi graph   We analyse the eigenvectors of the adjacency matrix of the Erd\\H{o}s-R\\'enyi\ngraph on $N$ vertices with edge probability $\\frac{d}{N}$. We determine the\nfull region of delocalization by determining the critical values of\n$\\frac{d}{\\log N}$ down to which delocalization persists: for $\\frac{d}{\\log N}\n> \\frac{1}{\\log 4 - 1}$ all eigenvectors are completely delocalized, and for\n$\\frac{d}{\\log N} > 1$ all eigenvectors with eigenvalues away from the spectral\nedges are completely delocalized. Below these critical values, it is known\n[arXiv:2005.14180, arXiv:2106.12519] that localized eigenvectors exist in the\ncorresponding spectral regions.\n"", ""Poisson statistics and localization at the spectral edge of sparse\n  Erd\\H{o}s-R\\'enyi graphs   We consider the adjacency matrix $A$ of the Erd\\H{o}s-R\\'enyi graph on $N$\nvertices with edge probability $d/N$. For $(\\log \\log N)^4 \\ll d \\lesssim \\log\nN$, we prove that the eigenvalues near the spectral edge form asymptotically a\nPoisson process and the associated eigenvectors are exponentially localized. As\na corollary, at the critical scale $d \\asymp \\log N$, the limiting distribution\nof the largest nontrivial eigenvalue does not match with any previously known\ndistribution. Together with [arXiv:2005.14180], our result establishes the\ncoexistence of a fully delocalized phase and a fully localized phase in the\nspectrum of $A$. The proof relies on a three-scale rigidity argument, which\ncharacterizes the fluctuations of the eigenvalues in terms of the fluctuations\nof sizes of spheres of radius 1 and 2 around vertices of large degree.\n""]","[('erd enyi graphs', 0.5597661733627319), ('adjacency laplacian matrices', 0.5502210855484009), ('spectrum adjacency matrix', 0.5445799231529236), ('spectrum adjacency', 0.5396233201026917), ('eigenvectors adjacency', 0.528810441493988), ('edge eigenvalues', 0.5244291424751282), ('erd enyi graph', 0.5121082663536072), ('spectral edge', 0.4916483163833618), ('sparse erd enyi', 0.4701296091079712), ('enyi random graph', 0.46699535846710205)]"
1852,1852,15,1852_string topology_homology loop_homology space_homology free,"['string topology', 'homology loop', 'homology space', 'homology free', 'free loop space', 'spaces fiber bundles', 'homology classes', 'homology', 'loop spaces', 'loop space']","['Product and coproduct in string topology   Let M be a closed Riemannian manifold. We extend the product of\nGoresky-Hingston, on the cohomology of the free loop space of M relative to the\nconstant loops, to a nonrelative product. It is graded associative and\ncommutative, and compatible with the length filtration on the loop space, like\nthe original product. We prove the following new geometric property of the dual\nhomology coproduct: the nonvanishing of the k-th iterate of the coproduct on a\nhomology class ensures the existence of a loop with a (k+1)-fold\nself-intersection in every representative of the class. For spheres and\nprojective spaces, we show that this is sharp, in the sense that the k-th\niterated coproduct vanishes precisely on those classes that have support in the\nloops with at most k-fold self-intersections. We study the interactions between\nthis cohomology product and the more well-known Chas-Sullivan product. We give\nexplicit integral chain level constructions of these loop products and\ncoproduct, including a new construction of the Chas-Sullivan product, which\navoid the technicalities of infinite dimensional tubular neighborhoods and\ndelicate intersections of chains in loop spaces.\n', 'On the string topology of symmetric spaces of higher rank   The homology of the free and the based loop space of a compact globally\nsymmetric space can be studied through explicit cycles. We use cycles\nconstructed by Bott and Samelson and by Ziller to study the string topology\ncoproduct and the Chas-Sullivan product on compact symmetric spaces. We show\nthat the Chas-Sullivan product for compact symmetric spaces is highly\nnon-trivial for any rank and we prove that there are many non-nilpotent classes\nwhose powers correspond to the iteration of closed geodesics. Moreover, we show\nthat the based string topology coproduct is trivial for compact symmetric\nspaces of higher rank and we study the implications of this result for the\nstring topology coproduct on the free loop space.\n', 'Intersection Multiplicity in Loop Spaces and the String Topology\n  Coproduct   The string topology coproduct is often perceived as a counterpart in string\ntopology to the Chas-Sullivan product. However, in certain aspects the string\ntopology coproduct is much harder to understand than the Chas-Sullivan product.\nIn particular the coproduct is not homotopy-invariant and it seems much harder\nto compute. In this article we give an overview over the string topology\ncoproduct and use the notion of intersection multiplicity of homology classes\nin loop spaces to show that the string topology coproduct and the based string\ntopology coproduct are trivial for certain classes of manifolds. In particular\nwe show that the string topology coproduct vanishes on product manifolds where\nboth factors have vanishing Euler characteristic and we show that the based\ncoproduct is trivial for total spaces of fiber bundles with sections. We also\ndiscuss implications of these results.\n']","[('string topology', 0.6152934432029724), ('homology loop', 0.6097854375839233), ('homology space', 0.5365983247756958), ('homology free', 0.5284411311149597), ('free loop space', 0.5037404298782349), ('spaces fiber bundles', 0.4994981288909912), ('homology classes', 0.4887387454509735), ('homology', 0.48669975996017456), ('loop spaces', 0.47374385595321655), ('loop space', 0.46189233660697937)]"
1853,1853,15,1853_cone constraints_conic optimization problems_conic optimization_convex conic,"['cone constraints', 'conic optimization problems', 'conic optimization', 'convex conic', 'order conic optimization', 'convex cone', 'semidefinite programming', 'cone programming', 'conic programs', 'closed convex cone']","['Multiparametric analysis of conic linear optimization based on the\n  lift-and-project procedure   We study how the lift-and-project procedure applies to the multiparametric\nanalysis of conic linear optimization (CLO) problems. We first introduce the\nconcept of a pair of primal and dual conic representable sets and define the\nset-valued mappings between them. We then explore a novel kind of duality of\nmpCLOs, which allows us to generalize as well as treat previous results for the\nmulitparametric analysis in a unified framework. In particular, we discuss the\nbehavior of the optimal partition of a conic representable set. This leads to\nthe invariant region decomposition of a conic representable set that is more\ngeneral than the known results in the literatures. Finally, we study the\nproperties of the optimal objective values as a function of that parametric\nvectors. All results are corroborated by examples having correlation.\n', 'Further Development in Convex Conic Reformulation of Geometric Nonconvex\n  Conic Optimization Problems   A geometric nonconvex conic optimization problem (COP) was recently proposed\nby Kim, Kojima and Toh as a unified framework for convex conic reformulation of\na class of quadratic optimization problems and polynomial optimization\nproblems. The nonconvex COP minimizes a linear function over the intersection\nof a nonconvex cone $\\mathbb{K}$, a convex subcone $\\mathbb{J}$ of the convex\nhull co$\\mathbb{K}$ of $\\mathbb{K}$, and an affine hyperplane with a normal\nvector $H$. Under the assumption co$(\\mathbb{K} \\cap \\mathbb{J}) = \\mathbb{J}$,\nthe original nonconvex COP in their paper was shown to be equivalently\nformulated as a convex conic program by replacing the constraint set with the\nintersection of $\\mathbb{J}$ and the affine hyperplane. This paper further\nstudies some remaining issues, not fully investigated there, such as the key\nassumption co$(\\mathbb{K} \\cap \\mathbb{J}) = \\mathbb{J}$ in the framework. More\nspecifically, we provide three sets of necessary-sufficient conditions for the\nassumption. As an application, we propose a new wide class of quadratically\nconstrained quadratic programs with multiple nonconvex equality and inequality\nconstraints that can be solved exactly by their semidefinite relaxation.\n', 'Strong duality of a conic optimization problem with a single hyperplane\n  and two cone constraints   Strong (Lagrangian) duality of general conic optimization problems (COPs) has\nlong been studied and its profound and complicated results appear in different\nforms in a wide range of literatures. As a result, characterizing the known and\nunknown results can sometimes be difficult. The aim of this article is to\nprovide a unified and geometric view of strong duality of COPs for the known\nresults. For our framework, we employ a COP minimizing a linear function in a\nvector variable $x$ subject to a single hyperplane constraint $x \\in H$ and two\ncone constraints $x \\in K_1$, $x \\in K_2$. It can be identically reformulated\nas a simpler COP with the single hyperplane constraint $x \\in H$ and the single\ncone constraint $x \\in K_1 \\cap K_2$. This simple COP and its dual as well as\ntheir duality relation can be represented geometrically, and they have no\nduality gap without any constraint qualification. The dual of the original\ntarget COP is equivalent to the dual of the reformulated COP if the Minkowski\nsum of the duals of the two cones $K_1$ and $K_2$ is closed or if the dual of\nthe reformulated COP satisfies a certain Slater condition. Thus, these two\nconditions make it possible to transfer all duality results, including the\nexistence and/or boundedness of optimal solutions, on the reformulated COP to\nthe ones on the original target COP, and further to the ones on a standard\nprimal-dual pair of COPs with symmetry.\n']","[('cone constraints', 0.6443259119987488), ('conic optimization problems', 0.6330705881118774), ('conic optimization', 0.6292012333869934), ('convex conic', 0.5931563973426819), ('order conic optimization', 0.5763001441955566), ('convex cone', 0.5563932657241821), ('semidefinite programming', 0.5524516701698303), ('cone programming', 0.5447906851768494), ('conic programs', 0.5340964794158936), ('closed convex cone', 0.5137185454368591)]"
1854,1854,15,1854_gross prasad conjecture_prasad conjecture_conjecture unitary_definite unitary groups,"['gross prasad conjecture', 'prasad conjecture', 'conjecture unitary', 'definite unitary groups', 'unitary groups', 'eisenstein series', 'gan gross prasad', 'representations tau', 'conjecture general', 'cuspidal automorphic representations']","['Isolation of cuspidal spectrum, with application to the\n  Gan--Gross--Prasad conjecture   We introduce a new technique for isolating components on the spectral side of\nthe trace formula. By applying it to the Jacquet--Rallis relative trace\nformula, we complete the proof of the global Gan--Gross--Prasad conjecture and\nits refinement Ichino--Ikeda conjecture for\n$\\mathrm{U}(n)\\times\\mathrm{U}(n+1)$ in the stable case.\n', 'The global Gan-Gross-Prasad conjecture for unitary groups. II. From\n  Eisenstein series to Bessel periods   We state and prove an extension of the global Gan-Gross-Prasad conjecture and\nthe Ichino-Ikeda conjecture to the case of some Eisenstein series on unitary\ngroups $U_n\\times U_{n+1}$. Our theorems are based on a comparison of the\nJacquet-Rallis trace formulas. A new point is the expression of some\ninteresting spectral contributions in these formulas in terms of integrals of\nrelative characters. As an application of our mains theorems, we prove the\nglobal Gan-Gross-Prasad and the Ichino-Ikeda conjecture for Bessel periods of\nunitary groups.\n', 'The global Gan-Gross-Prasad conjecture for Fourier-Jacobi periods on\n  unitary groups   We prove the Gan-Gross-Prasad conjecture for Fourier-Jacobi periods on\nunitary groups and an Ichino-Ikeda type refinement. Our strategy is based on\nthe comparison of relative trace formulae formulated by Liu. We develop the\nfull coarse spectral and geometric expansions of the relative trace formulae,\nand compute relevant spectral terms via zeta integrals and truncated periods.\nWe compare all geometric terms and characterize the local geometric comparison\nin terms of spectral data.\n']","[('gross prasad conjecture', 0.6455455422401428), ('prasad conjecture', 0.6279847025871277), ('conjecture unitary', 0.5139710903167725), ('definite unitary groups', 0.4941214621067047), ('unitary groups', 0.45767688751220703), ('eisenstein series', 0.4291777014732361), ('gan gross prasad', 0.41381675004959106), ('representations tau', 0.4014407694339752), ('conjecture general', 0.39989951252937317), ('cuspidal automorphic representations', 0.39308062195777893)]"
1855,1855,15,1855_generalized hypergeometric functions_confluent hypergeometric functions_hypergeometric functions_hypergeometric differential,"['generalized hypergeometric functions', 'confluent hypergeometric functions', 'hypergeometric functions', 'hypergeometric differential', 'hypergeometric operators', 'generalized hypergeometric', 'hypergeometric series', 'hypergeometric systems', 'confluent hypergeometric', 'hypergeometric system']","[""A system of hypergeometric differential equations in $m$ variables of\n  rank $p^m$   We define a hypergeometric series in $m$ variables with $p+(p-1)m$\nparameters, which reduces to the generalized hypergeometric series $_pF_{p-1}$\nwhen $m=1$, and to Lauricella's hypergeometric series $F_C$ in $m$ variables\nwhen $p=2$. We give a system of hypergeometric differential equations\nannihilating the series. Under some non-integral conditions on parameters, we\ngive an Euler type integral representation of the series, and linearly\nindependent $p^m$ solutions to this system around a point near to the origin.\nWe show that this system is of rank $p^m$, and determine its singular locus.\n"", 'PDE-Systems associated with the hypergeometric functions in three\n  variables and their particular solutions near the origin   The great success of the theory of hypergeometric series in one variable has\nstimulated the development of a corresponding theory in two and more variables.\nHorn has investigated the convergence of 34 (14 complete and 20 confluent)\nhypergeometric series of two variables and established the systems of partial\ndifferential equations which they satisfy. At present, 600 (of which 205 are\ncomplete and 395 are confluent) hypergeometric functions of three second-order\nvariables are known. The present work is devoted to the composition of systems\nof partial differential equations satisfied by 600 confluent hypergeometric\nfunctions of three variables. In addition, a particular solutions (if such\nsolutions exist) of some systems of differential equations have been found near\nthe origin.\n', ""Logarithmic $A$-hypergeometric series ${\\textrm I}\\! {\\textrm I}\\!\n  {\\textrm I}$   This paper is the third in a series exploring Frobenius's method for\n$A$-hypergeometric systems. Frobenius's method is a classical technique for\nconstructing logarithmic series solutions of differential equations by\nperturbing exponents of generic series solutions. We show that all\n$A$-hypergeometric series solutions can be obtained via this method.\n  Building upon our prior studies, we develop a duality framework between\nformal power series and differential operators, introduce minimal vectors with\nrespect to a generic weight, and establish key results on logarithmic\ncoefficients of $A$-hypergeometric series. We extend Frobenius's method and\nprove its sufficiency in constructing all $A$-hypergeometric series solutions.\nFurthermore, we explore conditions under which the Frobenius method developed\nin our previous studies suffices and we pose an open question on the necessity\nof the extended one.\n""]","[('generalized hypergeometric functions', 0.7534876465797424), ('confluent hypergeometric functions', 0.7337811589241028), ('hypergeometric functions', 0.71201491355896), ('hypergeometric differential', 0.7024422883987427), ('hypergeometric operators', 0.6953709125518799), ('generalized hypergeometric', 0.6873128414154053), ('hypergeometric series', 0.6820071339607239), ('hypergeometric systems', 0.6775422692298889), ('confluent hypergeometric', 0.6613874435424805), ('hypergeometric system', 0.6287612915039062)]"
1856,1856,15,1856_cartan hadamard manifolds_hadamard manifolds_manifolds unbounded_manifold stationary,"['cartan hadamard manifolds', 'hadamard manifolds', 'manifolds unbounded', 'manifold stationary', 'unbounded curvature', 'manifolds investigate existence', 'manifolds investigate', 'free energy functional', 'banach manifold', 'gradient flows']","['Global minimizers for fast diffusion versus nonlocal interactions on\n  negatively curved manifolds   We investigate the existence of ground states for a free energy functional on\nCartan-Hadamard manifolds. The energy, which consists of an entropy and an\ninteraction term, is associated to a macroscopic aggregation model that\nincludes nonlinear diffusion and nonlocal interactions. We consider\nspecifically the regime of fast diffusion, and establish necessary and\nsufficient conditions on the behaviour of the interaction potential for global\nenergy minimizers to exist. We first consider the case of manifolds with\nconstant bounds of sectional curvatures, then extend the results to manifolds\nwith general curvature bounds. To establish our results we derive several new\nCarlson-Levin type inequalities for Cartan-Hadamard manifolds.\n', 'Ground states for aggregation-diffusion models on Cartan-Hadamard\n  manifolds   We consider a free energy functional on Cartan-Hadamard manifolds, and\ninvestigate the existence of its global minimizers. The energy functional\nconsists of two components: an entropy (or internal energy) and an interaction\nenergy modelled by an attractive potential. The two components have competing\neffects, as they favour spreading by linear diffusion and blow-up by nonlocal\nattractive interactions, respectively. We find necessary and sufficient\nconditions for existence of ground states for manifolds with sectional\ncurvatures bounded above and below, respectively. In particular, for general\nCartan-Hadamard manifolds, superlinear growth at infinity of the attractive\npotential prevents the spreading. The behaviour can be relaxed for homogeneous\nmanifolds, for which only linear growth of the potential is sufficient for this\npurpose.\n', 'Aggregation-diffusion energies on Cartan-Hadamard manifolds of unbounded\n  curvature   We consider an aggregation-diffusion energy on Cartan-Hadamard manifolds with\nsectional curvatures that can grow unbounded at infinity. The energy\ncorresponds to a macroscopic aggregation model that involves nonlocal\ninteractions and linear diffusion. We establish necessary and sufficient\nconditions on the growth at infinity of the attractive interaction potential\nfor ground states to exist. Specifically, we derive explicit conditions on the\nattractive potential in terms of the bounds on the sectional curvatures at\ninfinity. To prove our results we establish a new logarithmic Hardy-Littlewood\ninequality for Cartan-Hadamard manifolds of unbounded curvature.\n']","[('cartan hadamard manifolds', 0.550530195236206), ('hadamard manifolds', 0.5257750749588013), ('manifolds unbounded', 0.5072571635246277), ('manifold stationary', 0.4666374623775482), ('unbounded curvature', 0.4639092683792114), ('manifolds investigate existence', 0.4531721770763397), ('manifolds investigate', 0.44353508949279785), ('free energy functional', 0.4225122034549713), ('banach manifold', 0.42154422402381897), ('gradient flows', 0.40820860862731934)]"
1857,1857,15,1857_normalized graph laplacian_laplacian spectral_graph laplacian matrix_graph laplacian operator,"['normalized graph laplacian', 'laplacian spectral', 'graph laplacian matrix', 'graph laplacian operator', 'graph laplacians', 'weighted laplacian', 'graph laplacian', 'laplacian spectrum', 'spectral convergence', 'laplacians']","['Bi-stochastically normalized graph Laplacian: convergence to manifold\n  Laplacian and robustness to outlier noise   Bi-stochastic normalization provides an alternative normalization of graph\nLaplacians in graph-based data analysis and can be computed efficiently by\nSinkhorn-Knopp (SK) iterations. This paper proves the convergence of\nbi-stochastically normalized graph Laplacian to manifold (weighted-)Laplacian\nwith rates, when $n$ data points are i.i.d. sampled from a general\n$d$-dimensional manifold embedded in a possibly high-dimensional space. Under\ncertain joint limit of $n \\to \\infty$ and kernel bandwidth $\\epsilon \\to 0$,\nthe point-wise convergence rate of the graph Laplacian operator (under 2-norm)\nis proved to be $ O( n^{-1/(d/2+3)})$ at finite large $n$ up to log factors,\nachieved at the scaling of $\\epsilon \\sim n^{-1/(d/2+3)} $. When the manifold\ndata are corrupted by outlier noise, we theoretically prove the graph Laplacian\npoint-wise consistency which matches the rate for clean manifold data plus an\nadditional term proportional to the boundedness of the inner-products of the\nnoise vectors among themselves and with data vectors. Motivated by our\nanalysis, which suggests that not exact bi-stochastic normalization but an\napproximate one will achieve the same consistency rate, we propose an\napproximate and constrained matrix scaling problem that can be solved by SK\niterations with early termination. Numerical experiments support our\ntheoretical results and show the robustness of bi-stochastically normalized\ngraph Laplacian to high-dimensional outlier noise.\n', ""Convergence of Graph Laplacian with kNN Self-tuned Kernels   Kernelized Gram matrix $W$ constructed from data points $\\{x_i\\}_{i=1}^N$ as\n$W_{ij}= k_0( \\frac{ \\| x_i - x_j \\|^2} {\\sigma^2} )$ is widely used in\ngraph-based geometric data analysis and unsupervised learning. An important\nquestion is how to choose the kernel bandwidth $\\sigma$, and a common practice\ncalled self-tuned kernel adaptively sets a $\\sigma_i$ at each point $x_i$ by\nthe $k$-nearest neighbor (kNN) distance. When $x_i$'s are sampled from a\n$d$-dimensional manifold embedded in a possibly high-dimensional space, unlike\nwith fixed-bandwidth kernels, theoretical results of graph Laplacian\nconvergence with self-tuned kernels have been incomplete. This paper proves the\nconvergence of graph Laplacian operator $L_N$ to manifold (weighted-)Laplacian\nfor a new family of kNN self-tuned kernels $W^{(\\alpha)}_{ij} = k_0( \\frac{ \\|\nx_i - x_j \\|^2}{ \\epsilon \\hat{\\rho}(x_i)\n\\hat{\\rho}(x_j)})/\\hat{\\rho}(x_i)^\\alpha \\hat{\\rho}(x_j)^\\alpha$, where\n$\\hat{\\rho}$ is the estimated bandwidth function {by kNN}, and the limiting\noperator is also parametrized by $\\alpha$. When $\\alpha = 1$, the limiting\noperator is the weighted manifold Laplacian $\\Delta_p$. Specifically, we prove\nthe point-wise convergence of $L_N f $ and convergence of the graph Dirichlet\nform with rates. Our analysis is based on first establishing a $C^0$\nconsistency for $\\hat{\\rho}$ which bounds the relative estimation error\n$|\\hat{\\rho} - \\bar{\\rho}|/\\bar{\\rho}$ uniformly with high probability, where\n$\\bar{\\rho} = p^{-1/d}$, and $p$ is the data density function. Our theoretical\nresults reveal the advantage of self-tuned kernel over fixed-bandwidth kernel\nvia smaller variance error in low-density regions. In the algorithm, no prior\nknowledge of $d$ or data density is needed. The theoretical results are\nsupported by numerical experiments on simulated data and hand-written digit\nimage data.\n"", 'Eigen-convergence of Gaussian kernelized graph Laplacian by manifold\n  heat interpolation   This work studies the spectral convergence of graph Laplacian to the\nLaplace-Beltrami operator when the graph affinity matrix is constructed from\n$N$ random samples on a $d$-dimensional manifold embedded in a possibly high\ndimensional space. By analyzing Dirichlet form convergence and constructing\ncandidate approximate eigenfunctions via convolution with manifold heat kernel,\nwe prove that, with Gaussian kernel, one can set the kernel bandwidth parameter\n$\\epsilon \\sim (\\log N/ N)^{1/(d/2+2)}$ such that the eigenvalue convergence\nrate is $N^{-1/(d/2+2)}$ and the eigenvector convergence in 2-norm has rate\n$N^{-1/(d+4)}$; When $\\epsilon \\sim (\\log N/N)^{1/(d/2+3)}$, both eigenvalue\nand eigenvector rates are $N^{-1/(d/2+3)}$. These rates are up to a $\\log N$\nfactor and proved for finitely many low-lying eigenvalues. The result holds for\nun-normalized and random-walk graph Laplacians when data are uniformly sampled\non the manifold, as well as the density-corrected graph Laplacian (where the\naffinity matrix is normalized by the degree matrix from both sides) with\nnon-uniformly sampled data. As an intermediate result, we prove new point-wise\nand Dirichlet form convergence rates for the density-corrected graph Laplacian.\nNumerical results are provided to verify the theory.\n']","[('normalized graph laplacian', 0.641063392162323), ('laplacian spectral', 0.6186388731002808), ('graph laplacian matrix', 0.6167605519294739), ('graph laplacian operator', 0.6024783849716187), ('graph laplacians', 0.5892760157585144), ('weighted laplacian', 0.56529301404953), ('graph laplacian', 0.5607132315635681), ('laplacian spectrum', 0.5601741671562195), ('spectral convergence', 0.538650393486023), ('laplacians', 0.5290190577507019)]"
1858,1858,15,1858_learning missing_imputation_missingness_missing values,"['learning missing', 'imputation', 'missingness', 'missing values', 'missing completely random', 'missing entries', 'missing completely', 'predictors', 'prediction', 'imputed']","['On the consistency of supervised learning with missing values   In many application settings, the data have missing entries which make\nanalysis challenging. An abundant literature addresses missing values in an\ninferential framework: estimating parameters and their variance from incomplete\ntables. Here, we consider supervised-learning settings: predicting a target\nwhen missing values appear in both training and testing data. We show the\nconsistency of two approaches in prediction. A striking result is that the\nwidely-used method of imputing with a constant, such as the mean prior to\nlearning is consistent when missing values are not informative. This contrasts\nwith inferential settings where mean imputation is pointed at for distorting\nthe distribution of the data. That such a simple approach can be consistent is\nimportant in practice. We also show that a predictor suited for complete\nobservations can predict optimally on incomplete data, through multiple\nimputation. Finally, to compare imputation with learning directly with a model\nthat accounts for missing values, we analyze further decision trees. These can\nnaturally tackle empirical risk minimization with missing values, due to their\nability to handle the half-discrete nature of incomplete variables. After\ncomparing theoretically and empirically different missing values strategies in\ntrees, we recommend using the ""missing incorporated in attribute"" method as it\ncan handle both non-informative and informative missing values.\n', 'Naive imputation implicitly regularizes high-dimensional linear models   Two different approaches exist to handle missing values for prediction:\neither imputation, prior to fitting any predictive algorithms, or dedicated\nmethods able to natively incorporate missing values. While imputation is widely\n(and easily) use, it is unfortunately biased when low-capacity predictors (such\nas linear models) are applied afterward. However, in practice, naive imputation\nexhibits good predictive performance. In this paper, we study the impact of\nimputation in a high-dimensional linear model with MCAR missing data. We prove\nthat zero imputation performs an implicit regularization closely related to the\nridge method, often used in high-dimensional problems. Leveraging on this\nconnection, we establish that the imputation bias is controlled by a ridge\nbias, which vanishes in high dimension. As a predictor, we argue in favor of\nthe averaged SGD strategy, applied to zero-imputed data. We establish an upper\nbound on its generalization error, highlighting that imputation is benign in\nthe d $\\sqrt$ n regime. Experiments illustrate our findings.\n', ""What is Hiding in Medicine's Dark Matter? Learning with Missing Data in\n  Medical Practices   Electronic patient records (EPRs) produce a wealth of data but contain\nsignificant missing information. Understanding and handling this missing data\nis an important part of clinical data analysis and if left unaddressed could\nresult in bias in analysis and distortion in critical conclusions. Missing data\nmay be linked to health care professional practice patterns and imputation of\nmissing data can increase the validity of clinical decisions. This study\nfocuses on statistical approaches for understanding and interpreting the\nmissing data and machine learning based clinical data imputation using a single\ncentre's paediatric emergency data and the data from UK's largest clinical\naudit for traumatic injury database (TARN). In the study of 56,961 data points\nrelated to initial vital signs and observations taken on children presenting to\nan Emergency Department, we have shown that missing data are likely to be\nnon-random and how these are linked to health care professional practice\npatterns. We have then examined 79 TARN fields with missing values for 5,791\ntrauma cases. Singular Value Decomposition (SVD) and k-Nearest Neighbour (kNN)\nbased missing data imputation methods are used and imputation results against\nthe original dataset are compared and statistically tested. We have concluded\nthat the 1NN imputer is the best imputation which indicates a usual pattern of\nclinical decision making: find the most similar patients and take their\nattributes as imputation.\n""]","[('learning missing', 0.637417197227478), ('imputation', 0.6007676124572754), ('missingness', 0.5370135307312012), ('missing values', 0.4571289122104645), ('missing completely random', 0.38368090987205505), ('missing entries', 0.37405624985694885), ('missing completely', 0.3509412705898285), ('predictors', 0.34254392981529236), ('prediction', 0.33171141147613525), ('imputed', 0.33150044083595276)]"
1859,1859,15,1859_countable models_arithmetical structure_models theory_genericity,"['countable models', 'arithmetical structure', 'models theory', 'genericity', 'standard models', 'arithmetical', 'first order theories', 'models', 'generics', 'order theories']","[""On Non-standard Models of Arithmetic with Uncountable Standard Systems   In 1960s, Dana Scott gave a recursion theoretic characterization of standard\nsystems of countable non-standard models of arithmetic, i.e., collections of\nsets of standard natural numbers coded in non-standard models. Later, Knight\nand Nadel proved that Scott's characterization also applies to non-standard\nmodels of arithmetic with cardinality $\\aleph_1$. But the question, whether the\nlimit on cardinality can be removed from the above characterization, remains a\nlong standing question, known as the Scott Set Problem. This article presents\ntwo constructions of non-standard models of arithmetic with non-trivial\nuncountable standard systems. The first one leads to a new proof of the above\ntheorem of Knight and Nadel, and the second proves the existence of models with\nnon-trivial standard systems of cardinality the continuum. A partial answer to\nthe Scott Set Problem under certain set theoretic hypothesis also follows from\nthe second construction.\n"", 'The Pentagon as a Substructure Lattice of Models of Peano Arithmetic   Wilke proved in 1977 that every countable model ${\\mathcal M}$ of Peano\nArithmetic has an elementary end extension ${\\mathcal N}$ such that the\ninterstructure lattice Lt(${\\mathcal N} / {\\mathcal M}$) is the pentagon\nlattice ${\\mathbf N}_5$. This theorem implies that every countable nonstandard\n$\\mathcal M$ has an elementary cofinal extension such that Lt(${\\mathcal N} /\n{\\mathcal M}) \\cong {\\mathbf N}_5$. It is proved here that if ${\\mathcal M}\n\\prec {\\mathcal N}$ and Lt(${\\mathcal N} / {\\mathcal M}) \\cong {\\mathbf N}_5$,\nthen ${\\mathcal N}$ is either an end or a cofinal extension of ${\\mathcal M}$.\nIn contrast, there are ${\\mathcal M}^* \\prec {\\mathcal N}^* \\models {\\mathsf\nPA}^*$ such that Lt(${\\mathcal N} / {\\mathcal M}) \\cong {\\mathbf N}_5$ and\n${\\mathcal N}^*$ is neither an end nor a cofinal extension of ${\\mathcal M}^*$.\n', 'Not all Kripke models of $\\sf HA$ are locally $\\sf PA$   Let ${\\bf K}$ be an arbitrary Kripke model of Heyting Arithmetic, ${\\sf HA}$.\nFor every node $k$ in ${\\bf K}$, we can view the classical structure of $k$,\n${\\mathfrak M}_k$ as a model of some classical theory of arithmetic. Let ${\\sf\nT}$ be a classical theory in the language of arithmetic. We say ${\\bf K}$ is\nlocally ${\\sf T}$, iff for every $k$ in ${\\bf K}$, ${\\mathfrak M}_k\\models{\\sf\nT}$. One of the most important problems in the model theory of ${\\sf HA}$ is\nthe following question: {\\it Is every Kripke model of ${\\sf HA}$ locally ${\\sf\nPA}$?} We answer this question negatively. We introduce two new Kripke model\nconstructions to this end. The first construction actually characterizes the\narithmetical structures that can be the root of a Kripke model ${\\bf\nK}\\Vdash{\\sf HA}+{\\sf ECT_0}$ (${\\sf ECT_0}$ stands for Extended Church\nThesis). The characterization says that for every arithmetical structure\n${\\mathfrak M}$, there exists a rooted Kripke model ${\\bf K}\\Vdash{\\sf HA}+{\\sf\nECT_0}$ with the root $r$ such that ${\\mathfrak M}_r={\\mathfrak M}$ iff\n${\\mathfrak M}\\models{\\bf Th}_{\\Pi_2}({\\sf PA})$. One of the consequences of\nthis characterization is that there is a rooted Kripke model ${\\bf K}\\Vdash{\\sf\nHA}+{\\sf ECT_0}$ with the root $r$ such that ${\\mathfrak M}_r\\not\\models{\\bf\nI}\\Delta_1$ and hence ${\\bf K}$ is not even locally ${\\bf I}\\Delta_1$. The\nsecond Kripke model construction is an implicit way of doing the first\nconstruction which works for any reasonable consistent intuitionistic\narithmetical theory ${\\sf T}$ with a recursively enumerable set of axioms that\nhas the existence property. We get a sufficient condition from this\nconstruction that describes when for an arithmetical structure ${\\mathfrak M}$,\nthere exists a rooted Kripke model ${\\bf K}\\Vdash {\\sf T}$ with the root $r$\nsuch that ${\\mathfrak M}_r={\\mathfrak M}$.\n']","[('countable models', 0.601758599281311), ('arithmetical structure', 0.5073960423469543), ('models theory', 0.4887322187423706), ('genericity', 0.463206022977829), ('standard models', 0.44633814692497253), ('arithmetical', 0.42989328503608704), ('first order theories', 0.4170600473880768), ('models', 0.4146212637424469), ('generics', 0.4129902720451355), ('order theories', 0.40958601236343384)]"
1860,1860,15,1860_brin thompson groups_finitely generated group_orderable groups_thompson groups,"['brin thompson groups', 'finitely generated group', 'orderable groups', 'thompson groups', 'groups regular', 'simple groups', 'baumslag solitar groups', 'ordered groups', 'thompson group', 'braid groups']","['Finite presentability of twisted Brin-Thompson groups   Given a group $G$ acting faithfully on a set $S$, we characterize precisely\nwhen the twisted Brin-Thompson group $SV_G$ is finitely presented. The answer\nis that $SV_G$ is finitely presented if and only if we have the following: $G$\nis finitely presented, the action of $G$ on $S$ has finitely many orbits of\ntwo-element subsets of $S$, and the stabilizer in $G$ of any element of $S$ is\nfinitely generated. Since twisted Brin-Thompson groups are simple, a\nconsequence is that any subgroup of a group admitting an action as above\nsatisfies the Boone-Higman conjecture. In the course of proving this, we also\nestablish a sufficient condition for a group acting cocompactly on a simply\nconnected complex to be finitely presented, even if certain edge stabilizers\nare not finitely generated, which may be of independent interest.\n', 'Boone-Higman embeddings of $\\mathrm{Aut}(F_n)$ and mapping class groups\n  of punctured surfaces   We prove that the groups $\\mathrm{Aut}(F_n)$ satisfy the Boone-Higman\nconjecture for all $n$, meaning each $\\mathrm{Aut}(F_n)$ embeds in a finitely\npresented simple group. In fact, we prove that each $\\mathrm{Aut}(F_n)$\nsatisfies the ""permutational"" Boone-Higman conjecture, which means the simple\ngroup in question can be taken to be a twisted Brin-Thompson group. A\nfar-reaching consequence of our approach is that finitely presented twisted\nBrin-Thompson groups are universal among finitely presented simple groups that\nare highly transitive. This is evidence toward the Boone-Higman conjecture\nbeing equivalent to its permutational version. Proving the conjecture for\n$\\mathrm{Aut}(F_n)$ also confirms the conjecture for all groups (virtually)\nembedding into some $\\mathrm{Aut}(F_n)$, such as mapping class groups of\nnon-closed surfaces, braid groups, loop braid groups, ribbon braid groups and\ncertain Artin groups. This answers several questions of the first and fourth\nauthors with Bleak and Matucci. Yet another consequence of our approach is that\nsatisfying the permutational Boone-Higman conjecture is closed under free\nproducts.\n', ""Twisted Brin-Thompson groups   We construct a family of infinite simple groups that we call \\emph{twisted\nBrin-Thompson groups}, generalizing Brin's higher-dimensional Thompson groups\n$sV$ ($s\\in\\mathbb{N}$). We use twisted Brin-Thompson groups to prove a variety\nof results regarding simple groups. For example, we prove that every finitely\ngenerated group embeds quasi-isometrically as a subgroup of a two-generated\nsimple group, strengthening a result of Bridson. We also produce examples of\nsimple groups that contain every $sV$ and hence every right-angled Artin group,\nincluding examples of type $\\textrm{F}_\\infty$ and a family of examples of type\n$\\textrm{F}_{n-1}$ but not of type $\\textrm{F}_n$, for arbitrary\n$n\\in\\mathbb{N}$. This provides the second known infinite family of simple\ngroups distinguished by their finiteness properties.\n""]","[('brin thompson groups', 0.5826123952865601), ('finitely generated group', 0.5768774151802063), ('orderable groups', 0.5583807826042175), ('thompson groups', 0.5545225739479065), ('groups regular', 0.5237336754798889), ('simple groups', 0.5027104616165161), ('baumslag solitar groups', 0.4982157349586487), ('ordered groups', 0.4906693994998932), ('thompson group', 0.4793092906475067), ('braid groups', 0.4702906012535095)]"
1861,1861,15,1861_parallel hyperplanes_hyperplane arrangements_hyperplanes_hyperplanes projective,"['parallel hyperplanes', 'hyperplane arrangements', 'hyperplanes', 'hyperplanes projective', 'affine hyperplanes', 'hyperplane arrangement', 'affine hyperplane', 'bisections', 'hyperplane', 'many partitions']","['Equipartitions with Wedges and Cones   A famous result about mass partitions is the so called \\emph{Ham-Sandwich\ntheorem}. It states that any $d$ mass distributions in $\\mathbb{R}^d$ can be\nsimultaneously bisected by a single hyperplane. In this work, we study two\nrelated questions.\n  The first one is how many masses we can simultaneously partition with a\n$k$-fan, that is, $k$ half-hyperplanes in $\\mathbb{R}^d$, emanating from a\ncommon $(d-2)$-dimensional apex. This question was extensively studied in the\nplane, but in higher dimensions the only known results are for the case where\n$k$ is an odd prime. We extend these results to a larger family of values of\n$k$. We further present a new result for $k=2$, which generalizes to cones.\n  The second question considers bisections with double wedges or, equivalently,\nHam-Sandwich cuts after projective transformations. Here we prove that given\n$d$ families of $d+1$ point sets each, there is always a projective\ntransformation such that after the transformation, each family has a\nHam-Sandwich cut. We further prove a result on partitions with parallel\nhyperplanes after a projective transformation.\n', ""Mass partitions by parallel hyperplanes via Fadell-Husseini index   In this paper, we study a problem of mass partitions by parallel hyperplanes.\nTakahashi and Sober\\'on conjectured an extension of the classical ham sandwich\ntheorem: any $d+k-1$ measures in $\\mathbb{R}^d$ can be simultaneously\nequipartitioned by $k$ parallel hyperplanes. We construct a configuration space\n-- test map scheme and prove a new Borsuk-Ulam-type theorem to show that the\nconjecture is true in the case when the Stirling number of second kind\n$S(d+k-1, k)$ is odd. This recovers exactly the parity condition obtained by\nHubard and Sober\\'on via different methods, reinforcing the possibility that\nthis condition is both necessary and sufficient. Our proof relies on a novel\ncomputation of the Fadell-Husseini index.\n"", ""Bisecting masses with families of parallel hyperplanes   We prove a common generalization to several mass partition results using\nhyperplane arrangements to split $\\mathbb{R}^d$ into two sets. Our main result\nimplies the ham-sandwich theorem, the necklace splitting theorem for two\nthieves, a theorem about chessboard splittings with hyperplanes with fixed\ndirections, and all known cases of Langerman's conjecture about equipartitions\nwith $n$ hyperplanes.\n  Our main result also confirms an infinite number of previously unknown cases\nof the following conjecture of Takahashi and Sober\\'on:\n  For any $d+k-1$ measures in $\\mathbb{R}^d$, there exist an arrangement of $k$\nparallel hyperplanes that bisects each of the measures.\n  The general result follows from the case of measures that are supported on a\nfinite set with an odd number of points. The proof for this case is inspired by\nideas of differential and algebraic topology, but it is a completely elementary\nparity argument.\n""]","[('parallel hyperplanes', 0.5794727802276611), ('hyperplane arrangements', 0.5597283840179443), ('hyperplanes', 0.5191195607185364), ('hyperplanes projective', 0.5013116002082825), ('affine hyperplanes', 0.49535369873046875), ('hyperplane arrangement', 0.4923679828643799), ('affine hyperplane', 0.41810178756713867), ('bisections', 0.39094865322113037), ('hyperplane', 0.37845587730407715), ('many partitions', 0.3672732412815094)]"
1862,1862,15,1862_graphs twin_bounded twin width_width graphs_width graph,"['graphs twin', 'bounded twin width', 'width graphs', 'width graph', 'graphs bounded', 'graphs known', 'twin width', 'hereditary graph classes', 'bounded twin', 'graphs proper']","[""Twin-width VI: the lens of contraction sequences   A contraction sequence of a graph consists of iteratively merging two of its\nvertices until only one vertex remains. The recently introduced twin-width\ngraph invariant is based on contraction sequences. More precisely, if one puts\nred edges between two vertices representing non-homogeneous subsets, the\ntwin-width is the minimum integer $d$ such that a contraction sequence keeps\nred degree at most $d$. By changing the condition imposed on the trigraphs\n(i.e., graphs with some edges being red) and possibly slightly tweaking the\nnotion of contractions, we show how to characterize the well-established\nbounded rank-width, tree-width, linear rank-width, path-width, and proper\nminor-closed classes by means of contraction sequences. As an application we\ngive a transparent alternative proof of the celebrated Courcelle's theorem\n(actually of its generalization by Courcelle, Makowsky, and Rotics), that\nMSO$_2$ (resp. MSO$_1$) model checking on graphs with bounded tree-width (resp.\nbounded rank-width) is fixed-parameter tractable in the size of the input\nsentence.\n  We then explore new avenues along the general theme of contraction sequences\nboth in order to refine the landscape between bounded tree-width and bounded\ntwin-width (via spanning twin-width) and to capture more general classes than\nbounded twin-width. To this end, we define an oriented version of twin-width,\nwhere appearing red edges are oriented away from the newly contracted vertex,\nand the mere red out-degree should remain bounded. Surprisingly, classes of\nbounded oriented twin-width coincide with those of bounded twin-width. Finally\nwe examine, from an algorithmic standpoint, the concept of partial contraction\nsequences, where, instead of terminating on a single-vertex graph, the sequence\nends when reaching a particular target class.\n"", ""A SAT Approach to Twin-Width   The graph invariant twin-width was recently introduced by Bonnet, Kim,\nThomass\\'e, and Watrigan. Problems expressible in first-order logic, which\nincludes many prominent NP-hard problems, are tractable on graphs of bounded\ntwin-width if a certificate for the twin-width bound is provided as an input.\nComputing such a certificate, however, is an intrinsic problem, for which no\nnontrivial algorithm is known.\n  In this paper, we propose the first practical approach for computing the\ntwin-width of graphs together with the corresponding certificate. We propose\nefficient SAT-encodings that rely on a characterization of twin-width based on\nelimination sequences. This allows us to determine the twin-width of many\nfamous graphs with previously unknown twin-width. We utilize our encodings to\nidentify the smallest graphs for a given twin-width bound $d \\in\n\\{1,\\dots,4\\}$.\n"", 'Twin-Width is Linear in the Poset Width   Twin-width is a new parameter informally measuring how diverse are the\nneighbourhoods of the graph vertices, and it extends also to other binary\nrelational structures, e.g. to digraphs and posets. It was introduced just very\nrecently, in 2020 by Bonnet, Kim, Thomasse and Watrigant. One of the core\nresults of these authors is that FO model checking on graph classes of bounded\ntwin-width is in FPT. With that result, they also claimed that posets of\nbounded width have bounded twin-width, thus capturing prior result on FO model\nchecking of posets of bounded width in FPT. However, their translation from\nposet width to twin-width was indirect and giving only a very loose\ndouble-exponential bound. We prove that posets of width d have twin-width at\nmost 9d with a direct and elegant argument, and show that this bound is\nasymptotically tight. Specially, for posets of width 2 we prove that in the\nworst case their twin-width is also equal 2. These two theoretical results are\ncomplemented with straightforward algorithms to construct the respective\ncontraction sequence for a given poset.\n']","[('graphs twin', 0.6181727647781372), ('bounded twin width', 0.6009643077850342), ('width graphs', 0.5921115875244141), ('width graph', 0.5289068818092346), ('graphs bounded', 0.5277560949325562), ('graphs known', 0.525140643119812), ('twin width', 0.5111676454544067), ('hereditary graph classes', 0.5018603801727295), ('bounded twin', 0.5012965798377991), ('graphs proper', 0.5005143880844116)]"
1863,1863,15,1863_utility theory_expected utility theory_utility representation_random utility,"['utility theory', 'expected utility theory', 'utility representation', 'random utility', 'choice functions', 'utility functions', 'preference relations', 'expected utility', 'preference', 'utility']","['Aggregation of Models, Choices, Beliefs, and Preferences   A natural notion of rationality/consistency for aggregating models is that,\nfor all (possibly aggregated) models $A$ and $B$, if the output of model $A$ is\n$f(A)$ and if the output model $B$ is $f(B)$, then the output of the model\nobtained by aggregating $A$ and $B$ must be a weighted average of $f(A)$ and\n$f(B)$. Similarly, a natural notion of rationality for aggregating preferences\nof ensembles of experts is that, for all (possibly aggregated) experts $A$ and\n$B$, and all possible choices $x$ and $y$, if both $A$ and $B$ prefer $x$ over\n$y$, then the expert obtained by aggregating $A$ and $B$ must also prefer $x$\nover $y$. Rational aggregation is an important element of uncertainty\nquantification, and it lies behind many seemingly different results in economic\ntheory: spanning social choice, belief formation, and individual decision\nmaking. Three examples of rational aggregation rules are as follows. (1) Give\neach individual model (expert) a weight (a score) and use weighted averaging to\naggregate individual or finite ensembles of models (experts). (2) Order/rank\nindividual model (expert) and let the aggregation of a finite ensemble of\nindividual models (experts) be the highest-ranked individual model (expert) in\nthat ensemble. (3) Give each individual model (expert) a weight, introduce a\nweak order/ranking over the set of models/experts, aggregate $A$ and $B$ as the\nweighted average of the highest-ranked models (experts) in $A$ or $B$. Note\nthat (1) and (2) are particular cases of (3). In this paper, we show that all\nrational aggregation rules are of the form (3). This result unifies aggregation\nprocedures across different economic environments. Following the main\nrepresentation, we show applications and extensions of our representation in\nvarious separated economics topics such as belief formation, choice theory, and\nsocial welfare economics.\n', 'A Representation Theorem for Finite Best-Worst Random Utility Models   This paper investigates best-worst choice probabilities (picking the best and\nthe worst alternative from an offered set). It is shown that non-negativity of\nbest-worst Block-Marschak polynomials is necessary and sufficient for the\nexistence of a random utility representation. The representation theorem is\nobtained by extending proof techniques employed by Falmagne (1978) for a\ncorresponding result on best choices (picking the best alternative from an\noffered set).\n', 'A technical note on finite best-worst random utility model\n  representations   This paper investigates the random utility representation of best-worst\nchoice probabilities (picking the best and the worst alternative from an\noffered set). Doignon (2023) presented a complete characterization of the\nbest-worst-choice polytope on four alternatives. Moreover, using polytope\nmethods he showed that the Block-Marschak inequalities for best-worst choices\nare not sufficient for a random utility representation of best-worst choices\nfor sets of four or more alternatives. Following the approach of Falmagne\n(1978), we construct a probability measure on the set of rankings for a set of\nfour alternatives implying a random utility representation.\n']","[('utility theory', 0.6258159875869751), ('expected utility theory', 0.6227129101753235), ('utility representation', 0.5993524789810181), ('random utility', 0.5488578081130981), ('choice functions', 0.54193514585495), ('utility functions', 0.5281937718391418), ('preference relations', 0.5158518552780151), ('expected utility', 0.5106762647628784), ('preference', 0.42741668224334717), ('utility', 0.4166300594806671)]"
1864,1864,15,1864_polygons small_perimeters_convex polygon_perimeter convex,"['polygons small', 'perimeters', 'convex polygon', 'perimeter convex', 'polygons', 'polygons whose', 'perimeter', 'polygon', 'polygon polygon', 'minimal area']","['Tight bounds on the maximal perimeter and the maximal width of convex\n  small polygons   A small polygon is a polygon of unit diameter. The maximal perimeter and the\nmaximal width of a convex small polygon with $n=2^s$ vertices are not known\nwhen $s \\ge 4$. In this paper, we construct a family of convex small $n$-gons,\n$n=2^s$ and $s\\ge 3$, and show that the perimeters and the widths obtained\ncannot be improved for large $n$ by more than $a/n^6$ and $b/n^4$ respectively,\nfor certain positive constants $a$ and $b$. In addition, assuming that a\nconjecture of Mossinghoff is true, we formulate the maximal perimeter problem\nas a nonlinear optimization problem involving trigonometric functions and, for\n$n=2^s$ with $3 \\le s\\le 7$, we provide global optimal solutions.\n', 'Tight bounds on the maximal area of small polygons: Improved Mossinghoff\n  polygons   A small polygon is a polygon of unit diameter. The maximal area of a small\npolygon with $n=2m$ vertices is not known when $m \\ge 7$. In this paper, we\nconstruct, for each $n=2m$ and $m\\ge 3$, a small $n$-gon whose area is the\nmaximal value of a one-variable function. We show that, for all even $n\\ge 6$,\nthe area obtained improves by $O(1/n^5)$ that of the best prior small $n$-gon\nconstructed by Mossinghoff. In particular, for $n=6$, the small $6$-gon\nconstructed has maximal area.\n', ""Maximal perimeter and maximal width of a convex small polygon   A small polygon is a polygon of unit diameter. The maximal perimeter and the\nmaximal width of a convex small polygon with $n=2^s$ sides are unknown when $s\n\\ge 4$. In this paper, we propose an approach to construct convex small\n$n$-gons of large perimeter and large width when $n=2^s$ with $s\\ge 2$.\nAssuming the existence of an axis of symmetry, a convex small $n$-gon is\ndescribed as a composition of $n/2$ and both its perimeter and its width are\ngiven as functions of a single variable. By selecting the composition that\nminimizes the violation of a cycle constraint by a particular solution, the\n$n$-gons constructed outperform the best $n$-gons found in the literature. For\nexample, for $n=64$, the perimeter and the width obtained are within $10^{-22}$\nand $10^{-12}$ of the maximal perimeter and the maximal width, respectively.\nFrom our results, it appears that Mossinghoff's conjecture on the diameter\ngraph of a convex small $2^s$-gon with maximal perimeter is not true when $s\n\\ge 4$.\n""]","[('polygons small', 0.6332750916481018), ('perimeters', 0.55635005235672), ('convex polygon', 0.5505453944206238), ('perimeter convex', 0.5495465397834778), ('polygons', 0.5345749258995056), ('polygons whose', 0.5098108053207397), ('perimeter', 0.5036352872848511), ('polygon', 0.49201729893684387), ('polygon polygon', 0.4752751290798187), ('minimal area', 0.4673624634742737)]"
1865,1865,15,1865_iwahori hecke algebras_iwahori hecke algebra_hecke algebras associated_affine hecke algebras,"['iwahori hecke algebras', 'iwahori hecke algebra', 'hecke algebras associated', 'affine hecke algebras', 'hecke algebras', 'algebras kac moody', 'hecke algebra mathcal', 'hecke algebra', 'kac moody groups', 'representations algebras']","['Tits groups of Iwahori-Weyl groups and presentations of Hecke algebras   Let $G$ be a connected reductive group over a non-archimedean local field $F$\nand $I$ be an Iwahori subgroup of $G(F)$. Let $I_n$ is the $n$-th Moy-Prasad\nfiltration subgroup of $I$. The purpose of this paper is two-fold: to give some\nnice presentations of the Hecke algebra of connected, reductive groups with\n$I_n$-level structure; and to introduce the Tits group of the Iwahori-Weyl\ngroup of groups $G$ that split over an unramified extension of $F$.\n  The first main result of this paper is a presentation of the Hecke algebra\n$\\mathcal H(G(F),I_n)$, generalizing the previous work of Iwahori-Matsumoto on\nthe affine Hecke algebras. For split $GL_n$, Howe gave a refined presentation\nof the Hecke algebra $\\mathcal H(G(F),I_n)$. To generalize such a refined\npresentation to other groups requires the existence of some nice lifting of the\nIwahori-Weyl group $W$ to $G(F)$. The study of a certain nice lifting of $W$ is\nthe second main motivation of this paper, which we discuss below.\n  In 1966, Tits introduced a certain subgroup of $G(\\mathbf k)$, which is an\nextension of $W$ by an elementary abelian $2$-group. This group is called the\nTits group and provides a nice lifting of the elements in the finite Weyl\ngroup. The ""Tits group"" $\\mathcal T$ for the Iwahori-Weyl group $W$ is a\ncertain subgroup of $G(F)$, which is an extension of the Iwahori-Weyl group $W$\nby an elementary abelian $2$-group. The second main result of this paper is a\nconstruction of Tits group $\\mathcal T$ for $W$ when $G$ splits over an\nunramified extension of $F$. As a consequence, we generalize Howe\'s\npresentation to such groups. We also show that when $G$ is ramified over $F$,\nsuch a group $\\mathcal T$ of $W$ may not exist.\n', 'Principal series representations of Iwahori-Hecke algebras for Kac-Moody\n  groups over local fields   Recently, Iwahori-Hecke algebras were associated to Kac-Moody groups over\nnon-Archimedean local fields. We introduce principal series representations for\nthese algebras. We study these representations and partially generalize Kato\nand Matsumoto irreducibility criteria.\n', 'Completed Iwahori-Hecke algebras and parahoric Hecke algebras for\n  Kac-Moody groups over local fields   Let G be a split Kac-Moody group over a non-archimedean local field. We\ndefine a completion of the Iwahori-Hecke algebra of G. We determine its center\nand prove that it is isomorphic to the spherical Hecke algebra of G using the\nSatake isomorphism. This is thus similar to the situation of reductive groups.\nOur main tool is the masure I associated to this setting, which is the analogue\nof the Bruhat-Tits building for reductive groups. Then, for each special and\nspherical facet F , we associate a Hecke algebra. In the Kac-Moody setting,\nthis construction was known only for the spherical subgroup and for the Iwahori\nsubgroup.\n']","[('iwahori hecke algebras', 0.7500901222229004), ('iwahori hecke algebra', 0.701420247554779), ('hecke algebras associated', 0.6969228982925415), ('affine hecke algebras', 0.6393583416938782), ('hecke algebras', 0.6189826726913452), ('algebras kac moody', 0.5291722416877747), ('hecke algebra mathcal', 0.5264905095100403), ('hecke algebra', 0.5253831148147583), ('kac moody groups', 0.5054305791854858), ('representations algebras', 0.4976853132247925)]"
1866,1866,15,1866_cohomology operations_cohomology theory_cohomology_cohomology spaces,"['cohomology operations', 'cohomology theory', 'cohomology', 'cohomology spaces', 'cohomology groups', 'cohomology rings', 'homotopy type theory', 'homology theory', 'theory homotopy type', 'integral cohomology']","[""Cochain level May-Steenrod operations   Steenrod defined in 1947 the Steenrod squares on the mod 2 cohomology of\nspaces using explicit cochain formulae for the cup-$i$ products; a family of\ncoherent homotopies derived from the broken symmetry of Alexander--Whitney's\nchain approximation to the diagonal. He later defined his homonymous operations\nfor all primes using the homology of symmetric groups. This approach enhanced\nthe conceptual understanding of the operations and allowed for many advances,\nbut lacked the concreteness of their definition at the even prime. In recent\nyears, thanks to the development of new applications of cohomology, the need to\nhave an effectively computable definition of Steenrod operations has become a\nkey issue. Using the operadic viewpoint of May, this article provides such\ndefinitions at all primes introducing multioperations that generalize the\nSteenrod cup-$i$ products on the simplicial and cubical cochains of spaces.\n"", ""Computational Synthetic Cohomology Theory in Homotopy Type Theory   This paper discusses the development of synthetic cohomology in Homotopy Type\nTheory (HoTT), as well as its computer formalisation. The objectives of this\npaper are (1) to generalise previous work on integral cohomology in HoTT by the\ncurrent authors and Brunerie (2022) to cohomology with arbitrary coefficients\nand (2) to provide the mathematical details of, as well as extend, results\nunderpinning the computer formalisation of cohomology rings by the current\nauthors and Lamiaux (2023). With respect to objective (1), we provide new\ndirect definitions of the cohomology group operations and of the cup product,\nwhich, just as in (Brunerie et al., 2022), enable significant simplifications\nof many earlier proofs in synthetic cohomology theory. In particular, the new\ndefinition of the cup product allows us to give the first complete\nformalisation of the axioms needed to turn the cohomology groups into a graded\ncommutative ring. We also establish that this cohomology theory satisfies the\nHoTT formulation of the Eilenberg-Steenrod axioms for cohomology and study the\nclassical Mayer-Vietoris and Gysin sequences. With respect to objective (2), we\ncharacterise the cohomology groups and rings of various spaces, including the\nspheres, torus, Klein bottle, real/complex projective planes, and infinite real\nprojective space. All results have been formalised in Cubical Agda and we\nobtain multiple new numbers, similar to the famous `Brunerie number', which can\nbe used as benchmarks for computational implementations of HoTT. Some of these\nnumbers are infeasible to compute in Cubical Agda and hence provide new\ncomputational challenges and open problems which are much easier to define than\nthe original Brunerie number.\n"", ""The Steenrod squares via unordered joins   The Steenrod squares are cohomology operations with important applications in\nalgebraic topology. While these operations are well-understood classically,\nlittle is known about them in the setting of homotopy type theory. Although a\ndefinition of the Steenrod squares was put forward by Brunerie (2017), proofs\nof their characterising properties have remained elusive. In this paper, we\nrevisit Brunerie's definition and provide proofs of these properties, including\nstability, Cartan's formula and the Adem relations. This is done by studying a\nhigher inductive type called the unordered join. This approach is inherently\nsynthetic and, consequently, many of our proofs differ significantly from their\nclassical counterparts. Along the way, we discuss upshots and limitations of\nhomotopy type theory as a synthetic language for homotopy theory. The paper is\naccompanied by a computer formalisation in Cubical Agda.\n""]","[('cohomology operations', 0.6926977038383484), ('cohomology theory', 0.6132906079292297), ('cohomology', 0.5791135430335999), ('cohomology spaces', 0.5696688294410706), ('cohomology groups', 0.5568336248397827), ('cohomology rings', 0.5538184642791748), ('homotopy type theory', 0.548876166343689), ('homology theory', 0.5314984321594238), ('theory homotopy type', 0.5200163125991821), ('integral cohomology', 0.5134159922599792)]"
1867,1867,15,1867_quantum dynamical_discrete time quantum_quantum dynamics_dynamical maps,"['quantum dynamical', 'discrete time quantum', 'quantum dynamics', 'dynamical maps', 'non markovianity', 'non markovian', 'dynamical semigroups', 'completely positive maps', 'dynamical semigroup', 'time quantum']","['Decomposable dynamics on matrix algebras   We explore a notion of decomposably divisible (D-divisible) quantum evolution\nfamilies, recently introduced in J. Phys. A: Math. Theor. 56, 485202 (2023).\nBoth necessary and sufficient conditions are presented for highly-symmetric\nqubit and qudit dynamical maps. Through a restructurization of the evolution\ngenerators, we encode the decomposable divisibility into the positivity of\ntime-dependent coefficients that multiply generators of D-divisible dynamical\nmaps. This provides an analogy to the CP-divisibility property, which is\nequivalent to the positivity of decoherence rates that multiply Markovian\nsemigroup generators.\n', 'Infinite dimensional dynamical maps   Completely positive trace preserving maps are widely used in quantum\ninformation theory. These are mostly studied using the master equation\nperspective. A central part in this theory is to study whether a given system\nof dynamical maps $\\{\\Lambda_t: t \\ge 0\\}$ is Markovian or non-Markovian. We\nstudy the problem when the underlying Hilbert space is of infinite dimensional.\nWe construct a sufficient condition for checking P (resp. CP) divisibility of\ndynamical maps. We construct several examples where the underlying Hilbert\nspace may not be of finite dimensional. We also give a special emphasis on\nGaussian dynamical maps and get a version of our result in it.\n', 'Construction of propagators for divisible dynamical maps   Divisible dynamical maps play an important role in characterizing\nMarkovianity on the level of quantum evolution. Divisible maps provide\nimportant generalization of Markovian semigroups. Usually one analyzes either\ncompletely positive or just positive divisibility meaning that the\ncorresponding propagators are defined in terms of completely positive or\npositive maps, respectively. For maps which are invertible at any moment of\ntime the very existence of propagator is already guaranteed and hence the only\nissue is (complete) positivity and trace-preservation. However, for maps which\nare not invertible the problem is much more involved since even the existence\nof a propagator is not guaranteed. In this paper we propose a simple method to\nconstruct propagators of dynamical maps using the concept of generalized\ninverse. We analyze both time-continuous and time-discrete maps. Since the\ngeneralized inverse is not uniquely defined the same applies for the\ncorresponding propagator. In simple examples of qubit evolution we analyze it\nturns out that additional requirement of complete positivity possibly makes the\npropagator unique.\n']","[('quantum dynamical', 0.6341842412948608), ('discrete time quantum', 0.5680997371673584), ('quantum dynamics', 0.537121593952179), ('dynamical maps', 0.5300196409225464), ('non markovianity', 0.5179266333580017), ('non markovian', 0.5120070576667786), ('dynamical semigroups', 0.49573269486427307), ('completely positive maps', 0.48538678884506226), ('dynamical semigroup', 0.4797838628292084), ('time quantum', 0.4748299717903137)]"
1868,1868,15,1868_kaehler manifolds_kaehler manifold_manifold complex dimension_manifold complex,"['kaehler manifolds', 'kaehler manifold', 'manifold complex dimension', 'manifold complex', 'submanifolds', 'manifold 2n', 'submanifold', 'hypersurfaces complex', 'real hypersurfaces', 'submanifold can']","['Minimal real Kaehler submanifolds   We show that generic rank conditions on the second fundamental form of an\nisometric immersion $f\\colon M^{2n}\\to\\mathbb{R}^{2n+p}$ of a Kaehler manifold\nof complex dimension $n\\geq 2$ into Euclidean space with low codimension $p$\nimplies that the submanifold has to be minimal. If $M^{2n}$ if simply\nconnected, this amounts to the existence of a one-parameter associated family\nof isometric minimal immersions unless $f$ is holomorphic.\n', 'Real Kaehler submanifolds in codimension up to four   Let $f\\colon M^{2n}\\to\\mathbb{R}^{2n+4}$ be an isometric immersion of a\nKaehler manifold of complex dimension $n\\geq 5$ into Euclidean space with\ncomplex rank at least $5$ everywhere. Our main result is that, along each\nconnected component of an open dense subset of $M^{2n}$, either $f$ is\nholomorphic in $\\mathbb{R}^{2n+4}\\cong\\mathbb{C}^{n+2}$ or it is in a unique\nway a composition $f=F\\circ h$ of isometric immersions. In the latter case, we\nhave that $h\\colon M^{2n}\\to N^{2n+2}$ is holomorphic and $F\\colon\nN^{2n+2}\\to\\mathbb{R}^{2n+4}$ belongs to the class, by now quite well\nunderstood, of non-holomorphic Kaehler submanifold in codimension two.\nMoreover, the submanifold $F$ is minimal if and only if $f$ is minimal.\n', 'The second fundamental form of the real Kaehler submanifolds   Let $f\\colon M^{2n}\\to\\R^{2n+p}$, $2\\leq p\\leq n-1$, be an isometric\nimmersion of a Kaehler manifold into Euclidean space. Yan and Zheng conjectured\nin \\cite{YZ} that if the codimension is $p\\leq 11$ then, along any connected\ncomponent of an open dense subset of $M^{2n}$, the submanifold is as follows:\nit is either foliated by holomorphic submanifolds of dimension at least $2n-2p$\nwith tangent spaces in the kernel of the second fundamental form whose images\nare open subsets of affine vector subspaces, or it is embedded holomorphically\nin a Kaehler submanifold of $\\R^{2n+p}$ of larger dimension than $2n$. This\nbold conjecture was proved by Dajczer and Gromoll just for codimension three\nand then by Yan and Zheng for codimension four.\n  In this paper we prove that the second fundamental form of the submanifold\nbehaves pointwise as expected in case that the conjecture is true. This result\nis a first fundamental step for a possible classification of the\nnon-holomorphic Kaehler submanifolds lying with low codimension in Euclidean\nspace. A counterexample shows that our proof does not work for higher\ncodimension, indicating that proposing $p=11$ in the conjecture as the largest\ncodimension is appropriate.\n']","[('kaehler manifolds', 0.6992514729499817), ('kaehler manifold', 0.6930204033851624), ('manifold complex dimension', 0.561583936214447), ('manifold complex', 0.5549584031105042), ('submanifolds', 0.5439349412918091), ('manifold 2n', 0.5405404567718506), ('submanifold', 0.5226660370826721), ('hypersurfaces complex', 0.5076044797897339), ('real hypersurfaces', 0.49726980924606323), ('submanifold can', 0.4656177759170532)]"
1869,1869,15,1869_surfaces positive characteristic_surfaces positive_rational surfaces_algebraic surfaces,"['surfaces positive characteristic', 'surfaces positive', 'rational surfaces', 'algebraic surfaces', 'smooth projective surface', 'projective surface', 'hirzebruch surfaces', 'curves blow', 'rational curves', 'irreducible curves']","['Towards the weighted bounded negativity conjecture for blow-ups of\n  algebraic surfaces   In the present paper, we focus on a weighted version of the Bounded\nNegativity Conjecture which predicts that for every smooth projective surface\nin characteristic zero the self-intersection numbers of reduced and irreducible\ncurves are bounded from below by a global constant. We gather evidence for this\nconjecture by showing various bounds on the self-intersection number of curves\nin an algebraic surface. We focus our attention on blow-ups of algebraic\nsurfaces, which have so far been neglected.\n', 'On weighted bounded negativity for rational surfaces   The weighted bounded negativity conjecture considers a smooth projective\nsurface $X$ and looks for a common lower bound on the quotients $C^2/(D\\cdot\nC)^2$, where $C$ runs over the integral curves on $X$ and $D$ over the big and\nnef divisors on $X$ such that $D \\cdot C >0$. We focus our study on rational\nsurfaces $Z$. Setting $\\pi: Z \\rightarrow Z_0$ a composition of blowups giving\nrise to $Z$, where $Z_0$ is the projective plane or a Hirzebruch surface, we\ngive a common lower bound on $C^2/(H^* \\cdot C)^2$ whenever $H^*$ is the\npull-back of a nef divisor $H$ on $Z_0$. In addition, we prove that, only in\nthe case when a nef divisor $D$ on $Z$ approaches the boundary of the nef cone,\nthe quotients $C^2/(D\\cdot C)^2$ could tend to minus infinity.\n', 'Bounded negativity and Harbourne constants on ruled surfaces   Let $X$ be a smooth projective surface and let $\\mathcal{C}$ be an\narrangement of curves on $X$. The Harbourne constant of $\\mathcal{C}$ was\ndefined as a way to investigate the occurrence of curves of negative\nself-intersection on blow ups of $X$. This is related to the bounded negativity\nconjecture which predicts that the self-intersection number of all reduced\ncurves on a surface is bounded below by a constant. We consider a geometrically\nruled surface $X$ over a smooth curve and give lower bounds for the Harbourne\nconstants of transversal arrangements of curves on $X$.\n']","[('surfaces positive characteristic', 0.6169207096099854), ('surfaces positive', 0.594363272190094), ('rational surfaces', 0.5777977108955383), ('algebraic surfaces', 0.5740517973899841), ('smooth projective surface', 0.49321249127388), ('projective surface', 0.48139768838882446), ('hirzebruch surfaces', 0.4558342397212982), ('curves blow', 0.443327397108078), ('rational curves', 0.42222273349761963), ('irreducible curves', 0.4162718653678894)]"
1870,1870,15,1870_profinite groups_profinite group_residually finite groups_group words,"['profinite groups', 'profinite group', 'residually finite groups', 'group words', 'group word', 'finite groups', 'finite group', 'subgroup finite', 'subgroup finite group', 'groups']","['On profinite groups admitting a word with only few values   A group-word $w$ is called concise if the verbal subgroup $w(G)$ is finite\nwhenever $w$ takes only finitely many values in a group $G$. It is known that\nthere are words that are not concise. The problem whether every word is concise\nin the class of profinite groups remains wide open. Moreover, there is a\nconjecture that every word $w$ is strongly concise in profinite groups, that\nis, $w(G)$ is finite whenever $G$ is a profinite group in which $w$ takes less\nthan $2^{\\aleph_0}$ values. In this paper we show that if the word $w$ takes\nless than $2^{\\aleph_0}$ values in a profinite group $G$ then $w(w(G))$ is\nfinite.\n', ""On conciseness of the word in Olshanskii's example   A group-word $w$ is called concise if the verbal subgroup $w(G)$ is finite\nwhenever $w$ takes only finitely many values in a group $G$. It is known that\nthere are words that are not concise. In particular, Olshanskii gave an example\nof such a word, which we denote by $w_o$. The problem whether every word is\nconcise in the class of residually finite groups remains wide open. In this\nnote we observe that $w_o$ is concise in residually finite groups. Moreover, we\nshow that $w_o$ is strongly concise in profinite groups, that is, $w_o(G)$ is\nfinite whenever $G$ is a profinite group in which $w_o$ takes less than\n$2^{\\aleph_0}$ values.\n"", 'Strong conciseness in profinite groups   A group word $w$ is said to be strongly concise in a class $\\mathcal{C}$ of\nprofinite groups if, for every group $G$ in $\\mathcal{C}$ such that $w$ takes\nless than $2^{\\aleph_0}$ values in $G$, the verbal subgroup $w(G)$ is finite.\nDetomi, Morigi and Shumyatsky established that multilinear commutator words --\nand the particular words $x^2$ and $[x^2,y]$ -- have the property that the\ncorresponding verbal subgroup is finite in a profinite group $G$ whenever the\nword takes at most countably many values in $G$. They conjectured that, in\nfact, this should be true for every word. In particular, their conjecture\nincluded as open cases power words and Engel words.\n  In the present paper, we take a new approach via parametrised words that\nleads to stronger results. First we prove that multilinear commutator words are\nstrongly concise in the class of all profinite groups. Then we establish that\nevery group word is strongly concise in the class of nilpotent profinite\ngroups. From this we deduce, for instance, that, if $w$ is one of the group\nwords $x^2$, $x^3$, $x^6$, $[x^3,y]$ or $[x,y,y]$, then $w$ is strongly concise\nin the class of all profinite groups. Indeed, the same conclusion can be\nreached for all words of the infinite families $[x^m,z_1,\\ldots,z_r]$ and\n$[x,y,y,z_1,\\ldots,z_r]$, where $m \\in \\{2,3\\}$ and $r \\ge 1$.\n']","[('profinite groups', 0.6108585000038147), ('profinite group', 0.5720254182815552), ('residually finite groups', 0.5642380714416504), ('group words', 0.5396414399147034), ('group word', 0.5189731121063232), ('finite groups', 0.503078281879425), ('finite group', 0.45053550601005554), ('subgroup finite', 0.4414032995700836), ('subgroup finite group', 0.41361355781555176), ('groups', 0.4134632647037506)]"
1871,1871,15,1871_distributed learning_distributed optimization_distributed learning problems_distributed machine learning,"['distributed learning', 'distributed optimization', 'distributed learning problems', 'distributed machine learning', 'communication efficient distributed', 'efficient distributed', 'decentralized learning', 'decentralized optimization', 'decentralized sgd', 'online distributed']","['Exponential Graph is Provably Efficient for Decentralized Deep Training   Decentralized SGD is an emerging training method for deep learning known for\nits much less (thus faster) communication per iteration, which relaxes the\naveraging step in parallel SGD to inexact averaging. The less exact the\naveraging is, however, the more the total iterations the training needs to\ntake. Therefore, the key to making decentralized SGD efficient is to realize\nnearly-exact averaging using little communication. This requires a skillful\nchoice of communication topology, which is an under-studied topic in\ndecentralized optimization.\n  In this paper, we study so-called exponential graphs where every node is\nconnected to $O(\\log(n))$ neighbors and $n$ is the total number of nodes. This\nwork proves such graphs can lead to both fast communication and effective\naveraging simultaneously. We also discover that a sequence of $\\log(n)$\none-peer exponential graphs, in which each node communicates to one single\nneighbor per iteration, can together achieve exact averaging. This favorable\nproperty enables one-peer exponential graph to average as effective as its\nstatic counterpart but communicates more efficiently. We apply these\nexponential graphs in decentralized (momentum) SGD to obtain the\nstate-of-the-art balance between per-iteration communication and iteration\ncomplexity among all commonly-used topologies. Experimental results on a\nvariety of tasks and models demonstrate that decentralized (momentum) SGD over\nexponential graphs promises both fast and high-quality training. Our code is\nimplemented through BlueFog and available at\nhttps://github.com/Bluefog-Lib/NeurIPS2021-Exponential-Graph.\n', 'Online Distributed Learning with Quantized Finite-Time Coordination   In this paper we consider online distributed learning problems. Online\ndistributed learning refers to the process of training learning models on\ndistributed data sources. In our setting a set of agents need to cooperatively\ntrain a learning model from streaming data. Differently from federated\nlearning, the proposed approach does not rely on a central server but only on\npeer-to-peer communications among the agents. This approach is often used in\nscenarios where data cannot be moved to a centralized location due to privacy,\nsecurity, or cost reasons. In order to overcome the absence of a central\nserver, we propose a distributed algorithm that relies on a quantized,\nfinite-time coordination protocol to aggregate the locally trained models.\nFurthermore, our algorithm allows for the use of stochastic gradients during\nlocal training. Stochastic gradients are computed using a randomly sampled\nsubset of the local training data, which makes the proposed algorithm more\nefficient and scalable than traditional gradient descent. In our paper, we\nanalyze the performance of the proposed algorithm in terms of the mean distance\nfrom the online solution. Finally, we present numerical results for a logistic\nregression task.\n', 'GADMM: Fast and Communication Efficient Framework for Distributed\n  Machine Learning   When the data is distributed across multiple servers, lowering the\ncommunication cost between the servers (or workers) while solving the\ndistributed learning problem is an important problem and is the focus of this\npaper. In particular, we propose a fast, and communication-efficient\ndecentralized framework to solve the distributed machine learning (DML)\nproblem. The proposed algorithm, Group Alternating Direction Method of\nMultipliers (GADMM) is based on the Alternating Direction Method of Multipliers\n(ADMM) framework. The key novelty in GADMM is that it solves the problem in a\ndecentralized topology where at most half of the workers are competing for the\nlimited communication resources at any given time. Moreover, each worker\nexchanges the locally trained model only with two neighboring workers, thereby\ntraining a global model with a lower amount of communication overhead in each\nexchange. We prove that GADMM converges to the optimal solution for convex loss\nfunctions, and numerically show that it converges faster and more\ncommunication-efficient than the state-of-the-art communication-efficient\nalgorithms such as the Lazily Aggregated Gradient (LAG) and dual averaging, in\nlinear and logistic regression tasks on synthetic and real datasets.\nFurthermore, we propose Dynamic GADMM (D-GADMM), a variant of GADMM, and prove\nits convergence under the time-varying network topology of the workers.\n']","[('distributed learning', 0.6564909815788269), ('distributed optimization', 0.6494972109794617), ('distributed learning problems', 0.6427002549171448), ('distributed machine learning', 0.615623414516449), ('communication efficient distributed', 0.6132522821426392), ('efficient distributed', 0.5998425483703613), ('decentralized learning', 0.5802748203277588), ('decentralized optimization', 0.5457680821418762), ('decentralized sgd', 0.5101630687713623), ('online distributed', 0.5034592747688293)]"
1872,1872,15,1872_polymer chains_polymer models_polymers random_polymer chain,"['polymer chains', 'polymer models', 'polymers random', 'polymer chain', 'directed polymers', 'directed polymer', 'polymers', 'oriented percolation', 'polymer', 'polymeric']","[""Weak-disorder limit at criticality for directed polymers on hierarchical\n  graphs   We prove a distributional limit theorem conjectured in [Journal of\nStatistical Physics 174, No. 6, 1372-1403 (2019)] for partition functions\ndefining models of directed polymers on diamond hierarchical graphs with\ndisorder variables placed at the graphical edges. The limiting regime involves\na joint scaling in which the number of hierarchical layers, $n\\in \\mathbb{N}$,\nof the graphs grows as the inverse temperature, $\\beta\\equiv \\beta(n)$,\nvanishes with a fine-tuned dependence on $n$. The conjecture pertains to the\nmarginally relevant disorder case of the model wherein the branching parameter\n$b \\in \\{2,3,\\ldots\\}$ and the segmenting parameter $s \\in \\{2,3,\\ldots\\}$\ndetermining the hierarchical graphs are equal, which coincides with the diamond\nfractal embedding the graphs having Hausdorff dimension two. Unlike the\nanalogous weak-disorder scaling limit for random polymer models on hierarchical\ngraphs in the disorder relevant $b<s$ case (or for the (1+1)-dimensional\npolymer on the rectangular lattice), the distributional convergence of the\npartition function when $b=s$ cannot be approached through a term-by-term\nconvergence to a Wiener chaos expansion, which does not exist for the continuum\nmodel emerging in the limit. The analysis proceeds by controlling the\ndistributional convergence of the partition functions in terms of the\nWasserstein distance through a perturbative generalization of Stein's method at\na critical step. In addition, we prove that a similar limit theorem holds for\nthe analogous model with disorder variables placed at the vertices of the\ngraphs.\n"", 'Adsorption of Lattice Polymers with Quenched Topologies   We introduce a framework for adsorption of a single polymer in which the\ntopology of the polymer is quenched before adsorption, in contrast to more\nstandard adsorption models having annealed topology. Our ""topology"" refers\neither to the precise branching structure of a branched polymer (in any\ndimension), or else to the knot type of a ring polymer in three dimensions. The\nquenched topology is chosen uniformly at random from all lattice polymers of a\ngiven size in one of four classes (lattice animals, trees, combs, or rings),\nand we then consider adsorption of the subclass of configurations that have the\nquenched topology. When the polymer-surface attraction increases without bound,\nthe quenched topological structure keeps a macroscopic fraction of monomers off\nthe surface, in contrast with annealed models that asymptotically have 100% of\nmonomers in the surface. We prove properties of the limiting free energy and\nthe critical point in each model, although important open questions remain. We\npay special attention to the class of comb polymers, which admit some rigorous\nanswers to questions that otherwise remain open. Since the class of all combs\nwas not previously examined rigorously in full generality, we also prove the\nexistence of its growth constant and its limiting free energy for annealed\nadsorption.\n', ""Undirected polymers in random environment: path properties in the mean\n  field limit   We consider the problem of undirected polymers (tied at the endpoints) in\nrandom environment, also known as the unoriented first passage percolation on\nthe hypercube, in the limit of large dimensions. By means of the multiscale\nrefinement of the second moment method we obtain a fairly precise geometrical\ndescription of optimal paths, i.e. of polymers with minimal energy. The picture\nwhich emerges can be loosely summarized as follows. The energy of the polymer\nis, to first approximation, uniformly spread along the strand. The polymer's\nbonds carry however a lower energy than in the directed setting, and are\nreached through the following geometrical evolution. Close to the origin, the\npolymer proceeds in oriented fashion -- it is thus as stretched as possible.\nThe tension of the strand decreases however gradually, with the polymer\nallowing for more and more backsteps as it enters the core of the hypercube.\nBacksteps, although increasing the length of the strand, allow the polymer to\nconnect reservoirs of energetically favorable edges which are otherwise\nunattainable in a fully directed regime. These reservoirs lie at mesoscopic\ndistance apart, but in virtue of the high dimensional nature of the ambient\nspace, the polymer manages to connect them through approximate geodesics with\nrespect to the Hamming metric: this is the key strategy which leads to an\noptimal energy/entropy balance. Around halfway, the mirror picture sets in: the\npolymer tension gradually builds up again, until full orientedness close to the\nendpoint. The approach yields, as a corollary, a constructive proof of the\nresult by Martinsson [Ann. Appl. Prob. 26 (2016), Ann. Prob. 46 (2018)]\nconcerning the leading order of the ground state.\n""]","[('polymer chains', 0.5985441207885742), ('polymer models', 0.5845222473144531), ('polymers random', 0.5741194486618042), ('polymer chain', 0.5480431318283081), ('directed polymers', 0.535101056098938), ('directed polymer', 0.5266891121864319), ('polymers', 0.46586400270462036), ('oriented percolation', 0.4633881151676178), ('polymer', 0.4501567780971527), ('polymeric', 0.43432652950286865)]"
1873,1873,15,1873_kuramoto sivashinsky equations_sivashinsky equations_dimensional kuramoto_kuramoto sivashinsky,"['kuramoto sivashinsky equations', 'sivashinsky equations', 'dimensional kuramoto', 'kuramoto sivashinsky', 'solutions nonlinear parabolic', 'solutions two dimensional', 'global regular solutions', 'analyticity solutions', 'sivashinsky', 'solutions 2d']","['Global Existence for the Two-dimensional Kuramoto-Sivashinsky equation\n  with a Shear Flow   We consider the Kuramoto-Sivashinsky equation (KSE) on the two-dimensional\ntorus in the presence of advection by a given background shear flow. Under the\nassumption that the shear has a finite number of critical points and there are\nlinearly growing modes only in the direction of the shear, we prove global\nexistence of solutions with data in $L^2$, using a bootstrap argument. The\ninitial data can be taken arbitrarily large.\n', 'Time-Dependent Solutions to the 2D Kuramoto-Sivashinsky Equation via Pseudospectral Method on a Rectangular Domain This report provides an investigation into solving the Kuramoto-Sivashinsky equation in two spatial dimensions (2DKS) using a pseudo-spectral method on various rectangular periodic domains. The Kuramoto-Sivashinsky equation is a fluid dynamics model that exhibits dynamical features that are highly dependent on the length of the periodic domain. The goals of this report are to describe the mathematical problem; explain the details of the chosen numerical method; inspect solutions and dynamical features for varying grid sizes, step sizes, and domains; and summarize the findings.', 'Global solutions of the two-dimensional Kuramoto-Sivashinsky equation\n  with a linearly growing mode in each direction   In two spatial dimensions, there are very few global existence results for\nthe Kuramoto-Sivashinsky equation. The majority of the few results in the\nliterature are strongly anisotropic, i.e. are results of thin-domain type. In\nthe spatially periodic case, the dynamics of the Kuramoto-Sivashinsky equation\nare in part governed by the size of the domain, as this determines how many\nlinearly growing Fourier modes are present. The strongly anisotropic results\nallow linearly growing Fourier modes in only one of the spatial directions. We\nprovide here the first proof of global solutions for the two-dimensional\nKuramoto-Sivashinsky equation with a linearly growing mode in both spatial\ndirections. We develop a new method to this end, categorizing wavenumbers as\nlow (linearly growing modes), intermediate (linearly decaying modes which serve\nas energy sinks for the low modes), and high (strongly linearly decaying\nmodes). The low and intermediate modes are controlled by means of a Lyapunov\nfunction, while the high modes are controlled with operator estimates in\nfunction spaces based on the Wiener algebra.\n']","[('kuramoto sivashinsky equations', 0.750706136226654), ('sivashinsky equations', 0.660221517086029), ('dimensional kuramoto', 0.4841247797012329), ('kuramoto sivashinsky', 0.48404669761657715), ('solutions nonlinear parabolic', 0.48086032271385193), ('solutions two dimensional', 0.4070872366428375), ('global regular solutions', 0.3755801022052765), ('analyticity solutions', 0.37369006872177124), ('sivashinsky', 0.3711174428462982), ('solutions 2d', 0.3537895083427429)]"
1874,1874,15,1874_emergent dynamics_collective dynamics_dynamics_free flows,"['emergent dynamics', 'collective dynamics', 'dynamics', 'free flows', 'emergent behaviors', 'tensor models', 'state aggregation', 'dynamics proposed', 'unit sphere', 'sphere']","['Emergent behaviors of the kinetic Lohe Hermitian sphere model   We study a global well-posedness of measure-valued solutions to the kinetic\nLohe Hermitian sphere(LHS) model derived from the Lohe tensor(LT) model on the\nset of rank-1 complex tensors(i.e. complex vectors) with the same size and\ninvestigate emergent behaviors. The kinetic LHS model corresponds to a complex\nanalogue of the kinetic LS model which has been extensively studied in the\nliterature on the aggregation modeling of Lohe particles on the unit sphere in\nEuclidean space. In this paper, we provide several frameworks in terms of\nsystem parameters and initial data leading to the local and global\nwell-posedness of measure-valued solutions. In particular, we show emergent\nbehaviors of the kinetic LHS model with the same free flows by analyzing the\ntemporal evolution of the order parameter.\n', 'Emergent behaviors of homogeneous Lohe Hermitian sphere particles under\n  time-delayed interactions   We study emergent behaviors of the Lohe hermitian sphere(LHS) model with a\ntime-delay for a homogeneous ensemble. The LHS model is a complex counterpart\nof the Lohe sphere(LS) aggregation model on the unit sphere in Euclidean space,\nand it describes the aggregation of particles on the unit hermitian sphere in\n$\\mathbb{C}^d$ with $d \\geq 2$, Recently it has been introduced by two authors\nof this work as a special case of the Lohe tensor model [23]. When the coupling\ngain pair satisfies a specific linear relation, namely the Stuart-Landau(SL)\ncoupling gain pair, it can be embedded into the LS model on $\\mathbb{R}^{2d}$.\nIn this work, we show that if the coupling gain pair is close to the SL\ncoupling pair case, the dynamics of the LHS model exhibits an emergent\naggregate phenomenon via the interplay between time-delayed interactions and\nnonlinear coupling between states. For this, we present several frameworks for\ncomplete aggregation and practical aggregation in terms of initial data and\nsystem parameters using the Lyapunov functional approach.\n', 'From the Lohe tensor model to the Lohe Hermitian sphere model and\n  emergent dynamics   We study emergent behaviors of the Lohe hermitian sphere(LHS) model which is\nan aggregation model on ${\\mathbb C}^d$. The LHS model is a complex analog of\nthe Lohe sphere model on ${\\mathbb R}^d$, and hermitian spheres are invariant\nsets for the LHS dynamics. For the derivation of the LHS model, we use a\ntop-down approach, namely a reduction from a high-rank aggregation model,\n""$\\textit{the Lohe tensor model}$."" The Lohe tensor model is a first-order\naggregation model on the space of tensors with the same rank and sizes, and it\nwas first proposed by the authors in a recent work \\cite{H-P}. In this work, we\nstudy how the LHS model appears as a special case of the Lohe tensor model and\nfor the proposed model, we provide a cross-ratio like conserved quantity, a\nsufficient framework for the complete aggregation and a uniform\n$\\ell^p$-stability estimate with respect to initial data.\n']","[('emergent dynamics', 0.5271841287612915), ('collective dynamics', 0.41385704278945923), ('dynamics', 0.3830724060535431), ('free flows', 0.3524257242679596), ('emergent behaviors', 0.3519505560398102), ('tensor models', 0.34700196981430054), ('state aggregation', 0.3461063802242279), ('dynamics proposed', 0.33855417370796204), ('unit sphere', 0.33479833602905273), ('sphere', 0.3314116895198822)]"
1875,1875,15,1875_predictive control mpc_quadratic programming qp_quadratic programming_quadratic program qp,"['predictive control mpc', 'quadratic programming qp', 'quadratic programming', 'quadratic program qp', 'convex quadratic programming', 'linear mpc', 'linear predictive control', 'quadratic program', 'control mpc', 'predictive control']","['A Parallel Vector-form $LDL^\\top$ Decomposition for Accelerating\n  Execution-time-certified $\\ell_1$-penalty Soft-constrained MPC   Handling possible infeasibility and providing an execution time certificate\nare two pressing requirements of real-time Model Predictive Control (MPC). To\nmeet these two requirements simultaneously, this paper proposes an\n$\\ell_1$-penalty soft-constrained MPC formulation that is globally feasible and\nsolvable with an execution time certificate using our proposed algorithm. This\npaper proves for the first time that $\\ell_1$-penalty soft-constrained MPC\nproblems can be equivalently transformed into a box-constrained quadratic\nprogramming (Box-QP) and then our previous execution-time-certified algorithm\n\\cite{wu2023direct} (only limited to Box-QP) can be applied. However, our\nprevious Box-QP algorithm \\cite{wu2023direct}, which provides a theoretical\nexecution-time certificate, is conservative in its iteration analysis, thus\nsacrificing computation efficiency. To this end, this paper proposes a novel\n$LDL^\\top$ decomposition for the first time, to accelerate the computation of\nNewton step at each iteration. The speedup of our $LDL^\\top$ decomposition\ncomes from two-fold: \\textit{i)} exploitation of the fact that the number of\ninequality constraints is generally larger than the number of variables in\ncondensed MPC formulations, \\textit{ii)} vectorized and parallel implementation\nbased on based on its vector-wise operations, instead of element-wise\noperations of previous decomposition methods. Numerical experiments demonstrate\ngreat speedups of the proposed $LDL^\\top$ decomposition (even up to 1000-fold,\ncompared to the standard Choleksky method), which thus helps our solver achieve\ncomparable computation performance to the state-of-the-art solvers such as\nIPOPT and OSQP. Code is available at\n\\url{https://github.com/liangwu2019/L1-penalty-QP}.\n', ""imuQP: An Inverse-Matrix-Updates-Based Fast QP Solver Suitable for\n  Real-Time MPC   This paper presents a new fast active-set quadratic programming (QP) solver\nbased on inverse matrix updates, which is suitable for real-time model\npredictive control (MPC). This QP solver, called imuQP (inverse matrix update\nQP), is based on Karush-Kuhn-Tucker (KKT) conditions and is inspired by\nHildreth's QP solver. An extensive convergence and optimality analysis of\nimuQP, including infeasibility detection, is presented. The memory footprint\nand computational complexity of imuQP are analyzed and compared with qpOASES, a\nwell-known active-set QP solver in literature. Speed and accuracy of imuQP are\ncompared with state-of-the-art active-set QP solvers by simulating a chain of\nspring-connected masses in MATLAB. For illustration, MPC with integral action\nis used, to remove offset when tracking a constant reference, with a small\nsampling period of Ts = 4 ms. Simulation results show that imuQP is suitable\nfor fast systems - with small Ts - and is competitive with state-of-the-art\nactive-set QP solvers.\n"", 'Distributed MPC with ALADIN -- A Tutorial   This paper consists of a tutorial on the Augmented Lagrangian based\nAlternating Direction Inexact Newton method (ALADIN) and its application to\ndistributed model predictive control (MPC). The focus is - for simplicity of\npresentation - on convex quadratic programming (QP) formulations of MPC. It is\nexplained how ALADIN can be used to synthesize sparse QP solvers for\nlarge-scale linear-quadratic optimal control by combining ideas from augmented\nLagrangian methods, sequential quadratic programming, as well as barrier or\ninterior point methods. The highlight of this tutorial is a real-time ALADIN\nvariant that can be implemented with a few lines of code yet arriving at a\nsparse QP solver that can compete with mature open-source and commercial QP\nsolvers in terms of both run-time as well as numerical accuracy. It is\ndiscussed why this observation could have far reaching consequences on the\nfuture of algorithm and software development in the field of large-scale\noptimization and MPC.\n']","[('predictive control mpc', 0.6202458143234253), ('quadratic programming qp', 0.6016420722007751), ('quadratic programming', 0.5695914030075073), ('quadratic program qp', 0.5627073049545288), ('convex quadratic programming', 0.56244295835495), ('linear mpc', 0.5136910676956177), ('linear predictive control', 0.5097612738609314), ('quadratic program', 0.5059422254562378), ('control mpc', 0.4888148009777069), ('predictive control', 0.44896429777145386)]"
1876,1876,15,1876_fermion systems_fermion system_theory causal_quantum theory,"['fermion systems', 'fermion system', 'theory causal', 'quantum theory', 'causal', 'introduced causal', 'fermionic', 'physical theory', 'body quantum system', 'fermion']","['Causal Fermion Systems and the ETH Approach to Quantum Theory   After reviewing the theory of ""causal fermion systems"" (CFS theory) and the\n""Events, Trees, and Histories Approach"" to quantum theory (ETH approach), we\ncompare some of the mathematical structures underlying these two general\nframeworks and discuss similarities and differences. For causal fermion\nsystems, we introduce future algebras based on causal relations inherent to a\ncausal fermion system. These algebras are analogous to the algebras previously\nintroduced in the ETH approach. We then show that the spacetime points of a\ncausal fermion system have properties similar to those of ""events"", as defined\nin the ETH approach. Our discussion is underpinned by a survey of results on\ncausal fermion systems describing Minkowski space that show that an operator\nrepresenting a spacetime point commutes with the algebra in its causal future,\nup to tiny corrections that depend on a regularization length.\n', 'Causal Fermion Systems and Octonions   We compare the structures and methods in the theory of causal fermion systems\nwith approaches to fundamental physics based on division algebras, in\nparticular the octonions. We find that octonions and, more generally, tensor\nproducts of division algebras come up naturally to describe the symmetries of\nthe vacuum configuration of a causal fermion system. This is achieved by\nassociating the real and imaginary octonion basis elements with the neutrino\nand charged sectors of the vacuum fermionic projector, respectively.\nConversely, causal fermion systems provide octonionic theories with spacetime\nstructures and dynamical equations via the causal action principle. In this\nway, octonionic theories and causal fermion systems complement each other..\n', 'Introduction to Causal Fermion Systems   This paper is dedicated to give a concise introduction to the theory of\ncausal fermion systems. After putting the theory of causal fermion systems into\nthe historical context, we recall fundamental physical preliminaries.\nAfterwards, we enter the underlying ideas of the principle of the fermionic\nprojector and clarify its connection to causal fermion systems. We finally\noutline the main structures of the theory of causal fermion systems.\n']","[('fermion systems', 0.6110631823539734), ('fermion system', 0.55600506067276), ('theory causal', 0.518122673034668), ('quantum theory', 0.49598678946495056), ('causal', 0.4783915877342224), ('introduced causal', 0.46928995847702026), ('fermionic', 0.4476572573184967), ('physical theory', 0.42307206988334656), ('body quantum system', 0.41551321744918823), ('fermion', 0.40711840987205505)]"
1877,1877,15,1877_wind farms_wind farm_wind turbines_wind turbine,"['wind farms', 'wind farm', 'wind turbines', 'wind turbine', 'turbines', 'turbine', 'wind', 'flow control', 'control algorithms', 'control strategy']","['Feedforward-Feedback wake redirection for wind farm control   This work presents a combined feedforward-feedback wake redirection framework\nfor wind farm control. The FLORIS wake model, a control-oriented steady-state\nwake model is used to calculate optimal yaw angles for a given wind farm layout\nand atmospheric condition. The optimal yaw angles, which maximize the total\npower output, are applied to the wind farm. Further, the lidar-based\nclosed-loop wake redirection concept is used to realize a local feedback on\nturbine level. The wake center is estimated from lidar measurements \\unit[3]{D}\ndownwind of the wind turbines. The dynamical feedback controllers support the\nfeedforward controller and reject disturbances and adapt to model\nuncertainties. Altogether, the total framework is presented and applied to a\nnine turbine wind farm test case. In a high fidelity simulation study the\nconcept shows promising results and an increase in total energy production\ncompared to the baseline case and the feedforward-only case.\n', 'Collective wind farm operation based on a predictive model increases\n  utility-scale energy production   Wind turbines located in wind farms are operated to maximize only their own\npower production. Individual operation results in wake losses that reduce farm\nenergy. In this study, we operate a wind turbine array collectively to maximize\ntotal array production through wake steering. The selection of the farm control\nstrategy relies on the optimization of computationally efficient flow models.\nWe develop a physics-based, data-assisted flow control model to predict the\noptimal control strategy. In contrast to previous studies, we first design and\nimplement a multi-month field experiment at a utility-scale wind farm to\nvalidate the model over a range of control strategies, most of which are\nsuboptimal. The flow control model is able to predict the optimal yaw\nmisalignment angles for the array within +/- 5 degrees for most wind directions\n(11-32% power gains). Using the validated model, we design a control protocol\nwhich increases the energy production of the farm in a second multi-month\nexperiment by 2.7% and 1.0%, for the wind directions of interest and for wind\nspeeds between 6 and 8 m/s and all wind speeds, respectively. The developed and\nvalidated predictive model can enable a wider adoption of collective wind farm\noperation.\n', 'Particle swarm optimization of a wind farm layout with active control of\n  turbine yaws   Active yaw control (AYC) of wind turbines has been widely applied to increase\nthe annual energy production (AEP) of a wind farm. AYC efficiency depends on\nthe wind direction and the wind farm layout because an AYC method utilizes wake\ndeflection by yawing wind turbines. Conventional optimization of a wind farm\nlayout assumed that the swept areas of all wind turbines are aligned\nperpendicular to the wind direction, thereby allowing non-optimal utilization\nof an AYC method. Higher AEP can be obtained by joint optimization which\nconsiders an AYC method in the layout design stage. Joint optimization of the\nfarm layout and AYC has been difficult due to the non-convexity of the problem\nand the computational inefficiency. In the present study, a particle swarm\noptimization based method is developed for joint optimization. The layout is\noptimized with simultaneous consideration for yaw angles for all wind\nvelocities to obtain a globally optimal layout. A number of random initial\nparticles consisting of the layout and yaw angles of wind turbines reduce the\ninitial layout dependency on the optimized layout. To deal with the challenge\nof large-scale optimization, the adaptive granularity learning distributed\nparticle swarm optimization algorithm is implemented. The improvement in AEP\nwhen using a jointly optimized layout compared to a conventionally optimized\nlayout in a real wind farm is demonstrated using the present method.\n']","[('wind farms', 0.6023722887039185), ('wind farm', 0.5707414746284485), ('wind turbines', 0.5696773529052734), ('wind turbine', 0.5618424415588379), ('turbines', 0.428921639919281), ('turbine', 0.4078935980796814), ('wind', 0.37307626008987427), ('flow control', 0.34916308522224426), ('control algorithms', 0.32332292199134827), ('control strategy', 0.30453377962112427)]"
1878,1878,15,1878_invariant riemannian metrics_invariant riemannian metric_riemannian metrics_matrices riemannian,"['invariant riemannian metrics', 'invariant riemannian metric', 'riemannian metrics', 'matrices riemannian', 'invariant metrics', 'riemannian metric', 'invariant riemannian', 'definite spd matrices', 'invariant metric', 'spd matrices']","[""Theoretically and computationally convenient geometries on full-rank\n  correlation matrices   In contrast to SPD matrices, few tools exist to perform Riemannian statistics\non the open elliptope of full-rank correlation matrices. The quotient-affine\nmetric was recently built as the quotient of the affine-invariant metric by the\ncongruence action of positive diagonal matrices. The space of SPD matrices had\nalways been thought of as a Riemannian homogeneous space. In contrast, we view\nin this work SPD matrices as a Lie group and the affine-invariant metric as a\nleft-invariant metric. This unexpected new viewpoint allows us to generalize\nthe construction of the quotient-affine metric and to show that the main\nRiemannian operations can be computed numerically. However, the uniqueness of\nthe Riemannian logarithm or the Fr{\\'e}chet mean are not ensured, which is bad\nfor computing on the elliptope. Hence, we define three new families of\nRiemannian metrics on full-rank correlation matrices which provide Hadamard\nstructures, including two flat. Thus the Riemannian logarithm and the\nFr{\\'e}chet mean are unique. We also define a nilpotent group structure for\nwhich the affine logarithm and the group mean are unique. We provide the main\nRiemannian/group operations of these four structures in closed form.\n"", ""Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky\n  Decomposition   We present a new Riemannian metric, termed Log-Cholesky metric, on the\nmanifold of symmetric positive definite (SPD) matrices via Cholesky\ndecomposition. We first construct a Lie group structure and a bi-invariant\nmetric on Cholesky space, the collection of lower triangular matrices whose\ndiagonal elements are all positive. Such group structure and metric are then\npushed forward to the space of SPD matrices via the inverse of Cholesky\ndecomposition that is a bijective map between Cholesky space and SPD matrix\nspace. This new Riemannian metric and Lie group structure fully circumvent\nswelling effect, in the sense that the determinant of the Fr\\'echet average of\na set of SPD matrices under the presented metric, called Log-Cholesky average,\nis between the minimum and the maximum of the determinants of the original SPD\nmatrices. Comparing to existing metrics such as the affine-invariant metric and\nLog-Euclidean metric, the presented metric is simpler, more computationally\nefficient and numerically stabler. In particular, parallel transport along\ngeodesics under Log-Cholesky metric is given in a closed and easy-to-compute\nform.\n"", 'O(n)-invariant Riemannian metrics on SPD matrices   Symmetric Positive Definite (SPD) matrices are ubiquitous in data analysis\nunder the form of covariance matrices or correlation matrices. Several\nO(n)-invariant Riemannian metrics were defined on the SPD cone, in particular\nthe kernel metrics introduced by Hiai and Petz. The class of kernel metrics\ninterpolates between many classical O(n)-invariant metrics and it satisfies key\nresults of stability and completeness. However, it does not contain all the\nclassical O(n)-invariant metrics. Therefore in this work, we investigate\nsuper-classes of kernel metrics and we study which key results remain true. We\nalso introduce an additional key result called cometric-stability, a crucial\nproperty to implement geodesics with a Hamiltonian formulation. Our method to\nbuild intermediate embedded classes between O(n)-invariant metrics and kernel\nmetrics is to give a characterization of the whole class of O(n)-invariant\nmetrics on SPD matrices and to specify requirements on metrics one by one until\nwe reach kernel metrics. As a secondary contribution, we synthesize the\nliterature on the main O(n)-invariant metrics, we provide the complete formula\nof the sectional curvature of the affine-invariant metric and the formula of\nthe geodesic parallel transport between commuting matrices for the\nBures-Wasserstein metric.\n']","[('invariant riemannian metrics', 0.7048707604408264), ('invariant riemannian metric', 0.6754258275032043), ('riemannian metrics', 0.6499032974243164), ('matrices riemannian', 0.6454852819442749), ('invariant metrics', 0.621457576751709), ('riemannian metric', 0.6104266047477722), ('invariant riemannian', 0.6004018783569336), ('definite spd matrices', 0.5994920134544373), ('invariant metric', 0.5789709091186523), ('spd matrices', 0.5725528597831726)]"
1879,1879,15,1879_compact operator_generalized hilbert_positive borel measures_operator acting,"['compact operator', 'generalized hilbert', 'positive borel measures', 'operator acting', 'operator mathcal', 'space analytic', 'operator defined', 'mu positive borel', 'positive borel measure', 'hankel matrix']","['Generalized Hilbert Operator Acting on Bloch Type Spaces   Let $\\mu$ be a positive Borel measure on the interval [0,1). For $\\alpha>0$,\nthe Hankel matrix $\\mathcal{H}_{\\mu,\\alpha}=(\\mu_{n,k,\\alpha})_{n,k\\geq 0}$\nwith entries\n$\\mu_{n,k,\\alpha}=\\int_{[0,1)}\\frac{\\Gamma(n+\\alpha)}{n!\\Gamma(\\alpha)}t^{n+k}d\\mu(t)$\nformally induces the operator\n  $$\\mathcal{H}_{\\mu,\\alpha}(f)(z)=\\sum_{n=0}^{\\infty}\\left(\\sum_{k=0}^{\\infty}\n\\mu_{n, k,\\alpha} a_{k}\\right)z^{n} $$ on the space of all analytic functions\n$f(z)=\\sum_{k=0}^{\\infty}a_{k}z^{k}$ in the unit disc $\\mathbb{D}$. In this\npaper, we characterize the measures $\\mu$ for which $\\mathcal{H}_{\\mu,\\alpha}$\n($\\alpha\\geq 2$) is a bounded (resp., compact) operator from the Bloch type\nspace $\\mathscr{B}_{\\beta}$ ($0<\\beta<\\infty$) into $\\mathscr{B}_{\\alpha-1}$.\nWe also give a necessary condition for which $\\mathcal{H}_{\\mu,\\alpha}$ is a\nbounded operator by acting on Bloch type spaces for general cases.\n', 'A Derivative-Hilbert operator acting on BMOA space   Let $\\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel\nmatrix $\\mathcal{H}_{\\mu}=(\\mu_{n,k})_{n,k\\geq 0}$ with entries\n$\\mu_{n,k}=\\mu_{n+k}$, where $\\mu_{n}=\\int_{[0,1)}t^nd\\mu(t)$, induces,\nformally, the Derivative-Hilbert operator\n$$\\mathcal{DH}_\\mu(f)(z)=\\sum_{n=0}^\\infty\\left(\\sum_{k=0}^\\infty\n\\mu_{n,k}a_k\\right)(n+1)z^n , ~z\\in \\mathbb{D},$$ where $f(z)=\\sum_{n=0}^\\infty\na_nz^n$ is an analytic function in $\\mathbb{D}$. We characterize the measures\n$\\mu$ for which $\\mathcal{DH}_\\mu$ is a bounded operator on $BMOA$ space. We\nalso study the analogous problem from the $\\alpha$-Bloch space\n$\\mathcal{B}_\\alpha(\\alpha>0)$ into the $BMOA$ space.\n', 'A Derivative-Hilbert operator Acting on Dirichlet spaces   Let $\\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel\nmatrix $\\mathcal{H}_{\\mu}=(\\mu_{n,k})_{n,k\\geq 0}$ with entries\n$\\mu_{n,k}=\\mu_{n+k}$, where $\\mu_{n}=\\int_{[0,1)}t^nd\\mu(t)$, induces formally\nthe operator as\n$$\\mathcal{DH}_\\mu(f)(z)=\\sum_{n=0}^\\infty\\left(\\sum_{k=0}^\\infty\n\\mu_{n,k}a_k\\right)(n+1)z^n , z\\in \\mathbb{D},$$ where\n$f(z)=\\sum_{n=0}^{\\infty}a_nz^n$ is an analytic function in $\\mathbb{D}$. In\nthis paper, we characterize those positive Borel measures on $[0, 1)$ for which\n$\\mathcal{DH}_\\mu$ is bounded (resp. compact) from Dirichlet spaces\n$\\mathcal{D}_\\alpha ( 0<\\alpha\\leq2 )$ into $\\mathcal{D}_\\beta ( 2\\leq\\beta<4\n)$.\n']","[('compact operator', 0.38881418108940125), ('generalized hilbert', 0.3861745297908783), ('positive borel measures', 0.38098210096359253), ('operator acting', 0.3499956727027893), ('operator mathcal', 0.34086593985557556), ('space analytic', 0.33807533979415894), ('operator defined', 0.3170657157897949), ('mu positive borel', 0.3106135129928589), ('positive borel measure', 0.29861265420913696), ('hankel matrix', 0.2977437674999237)]"
1880,1880,15,1880_network reliability_networks binary_probability network_network structures,"['network reliability', 'networks binary', 'probability network', 'network structures', 'state network', 'performance network', 'binary addition', 'networks computer', 'scale network', 'state networks']","['A Cut-Based BAT-MCS Approach for Binary-State Network Reliability\n  Assessment   The BAT-MCS is an integrated Monte Carlo simulation method (MCS) that\ncombines a binary adaptation tree algorithm (BAT) with a self-regulating\nsimulation mechanism. The BAT algorithm operates deterministically, while the\nMonte Carlo simulation method is stochastic. By hybridizing these two\napproaches, BAT-MCS successfully reduces variance, increases efficiency, and\nimproves the quality of its binary-state network reliability. However, it has\ntwo notable weaknesses. First, the selection of the supervectors, sub-vectors\nthat form the core of BAT-MCS, is overly simplistic, potentially affecting\noverall performance. Second, the calculation of the approximate reliability is\ncomplicated, which limits its strength in reducing variance. In this study, a\nnew BAT-MCS called cBAT-MCS is proposed to enhance the performance of the\nBAT-MCS. The approach reduces the complexity of MCS. Selecting the super-vector\nbased on a novel layer-cut approach can reduce both runtime and variance.\nExtensive numerical experiments on large-scale binary-state network demonstrate\nthat the proposed new cBAT-MCS outperforms traditional MCS and original BAT-MCS\napproaches in terms of computational efficiency and accuracy.\n', 'Development of a Parallel BAT and Its Applications in Binary-state\n  Network Reliability Problems   Various networks are broadly and deeply applied in real-life applications.\nReliability is the most important index for measuring the performance of all\nnetwork types. Among the various algorithms, only implicit enumeration\nalgorithms, such as depth-first-search, breadth-search-first, universal\ngenerating function methodology, binary-decision diagram, and\nbinary-addition-tree algorithm (BAT), can be used to calculate the exact\nnetwork reliability. However, implicit enumeration algorithms can only be used\nto solve small-scale network reliability problems. The BAT was recently\nproposed as a simple, fast, easy-to-code, and flexible make-to-fit\nexact-solution algorithm. Based on the experimental results, the BAT and its\nvariants outperformed other implicit enumeration algorithms. Hence, to overcome\nthe above-mentioned obstacle as a result of the size problem, a new parallel\nBAT (PBAT) was proposed to improve the BAT based on compute multithread\narchitecture to calculate the binary-state network reliability problem, which\nis fundamental for all types of network reliability problems. From the analysis\nof the time complexity and experiments conducted on 20 benchmarks of\nbinary-state network reliability problems, PBAT was able to efficiently solve\nmedium-scale network reliability problems.\n', 'Novel Binary-Addition Tree Algorithm (BAT) for Binary-State Network\n  Reliability Problem   Network structures and models have been widely adopted, e.g., for Internet of\nThings, wireless sensor networks, smart grids, transportation networks,\ncommunication networks, social networks, and computer grid systems. Network\nreliability is an effective and popular technique to estimate the probability\nthat the network is still functioning. Networks composed of binary-state (e.g.,\nworking or failed) components (arcs and/or nodes) are called binary-state\nnetworks. The binary-state network is the fundamental type of network; thus,\nthere is always a need for a more efficient algorithm to calculate the network\nreliability. Thus, a novel binary-addition tree (BAT) algorithm that employs\nbinary addition for finding all the possible state vectors and the path-based\nlayered-search algorithm for filtering out all the connected vectors is\nproposed for calculating the binary-state network reliability. According to the\ntime complexity and numerical examples, the efficiency of the proposed BAT is\nhigher than those of traditional algorithms for solving the binary-state\nnetwork reliability problem.\n']","[('network reliability', 0.5594572424888611), ('networks binary', 0.5131414532661438), ('probability network', 0.4263095557689667), ('network structures', 0.3958691358566284), ('state network', 0.3767390847206116), ('performance network', 0.3605858385562897), ('binary addition', 0.356808066368103), ('networks computer', 0.35172805190086365), ('scale network', 0.3303387761116028), ('state networks', 0.3293655216693878)]"
1881,1881,15,1881_numerical homogenization_generalized multiscale_multiscale finite element_multiscale basis,"['numerical homogenization', 'generalized multiscale', 'multiscale finite element', 'multiscale basis', 'generalized multiscale finite', 'localized orthogonal decomposition', 'multiscale', 'multiscale finite', 'complex multiscale', 'numerical methods work']","['Multiscale simulations for upscaled multi-continuum flows   We consider in this paper a challenging problem of simulating fluid flows, in\ncomplex multiscale media possessing multi-continuum background. As an effort to\nhandle this obstacle, model reduction is employed. In \\cite{rh2},\nhomogenization was nicely applied, to find effective coefficients and\nhomogenized equations (for fluid flow pressures) of a dual-continuum system,\nwith new convection terms and negative interaction coefficients. However, some\ndegree of multiscale still remains. This motivates us to propose the\ngeneralized multiscale finite element method (GMsFEM), which is coupled with\nthe dual-continuum homogenized equations, toward speeding up the simulation,\nimproving the accuracy as well as clearly representing the interactions between\nthe dual continua. In our paper, globally, each continuum is viewed as a system\nand connected to the other throughout the domain. We take into consideration\nthe flow transfers between the dual continua and within each continuum itself.\nSuch multiscale flow dynamics are modeled by the GMsFEM, which systematically\ngenerates either uncoupled or coupled multiscale basis (to carry the local\ncharacteristics to the global ones), via establishing local snapshots and\nspectral decomposition in the snapshot space. As a result, we will work with a\nsystem of two equations coupled with some interaction terms, and each equation\ndescribes one of the dual continua on the fine grid. Convergence analysis of\nthe proposed GMsFEM is accompanied with the numerical results, which support\nthe favorable outcomes.\n', 'An algebraic multiscale method for spatial network models   In this work, we present a multiscale approach for the reliable coarse-scale\napproximation of spatial network models represented by a linear system of\nequations with respect to the nodes of a graph. The method is based on the\nideas of the Localized Orthogonal Decomposition (LOD) strategy and is\nconstructed in a fully algebraic way. This allows to apply the method to\ngeometrically challenging objects such as corrugated cardboard. In particular,\nthe method can also be applied to finite difference or finite element\ndiscretizations of elliptic partial differential equations, yielding an\napproximation with similar properties as the LOD in the continuous setting. We\npresent a rigorous error analysis of the proposed method under suitable\nassumptions on the network. Moreover, numerical examples are presented that\nunderline our theoretical results.\n', ""Super-localization of spatial network models   Spatial network models are used as a simplified discrete representation in a\nwide range of applications, e.g., flow in blood vessels, elasticity of fiber\nbased materials, and pore network models of porous materials. Nevertheless, the\nresulting linear systems are typically large and poorly conditioned and their\nnumerical solution is challenging.\n  This paper proposes a numerical homogenization technique for spatial network\nmodels which is based on the Super Localized Orthogonal Decomposition (SLOD),\nrecently introduced for elliptic multiscale partial differential equations. It\nprovides accurate coarse solution spaces with approximation properties\nindependent of the smoothness of the material data. A unique selling point of\nthe SLOD is that it constructs an almost local basis of these coarse spaces,\nrequiring less computations on the fine scale and achieving improved sparsity\non the coarse scale compared to other state-of-the-art methods. We provide an\na-posteriori analysis of the proposed method and numerically confirm the\nmethod's unique localization properties. In addition, we show its applicability\nalso for high-contrast channeled material data.\n""]","[('numerical homogenization', 0.5214704275131226), ('generalized multiscale', 0.4990428686141968), ('multiscale finite element', 0.4974895417690277), ('multiscale basis', 0.48861727118492126), ('generalized multiscale finite', 0.4675379991531372), ('localized orthogonal decomposition', 0.46325525641441345), ('multiscale', 0.45744478702545166), ('multiscale finite', 0.4294593930244446), ('complex multiscale', 0.41702336072921753), ('numerical methods work', 0.40945109724998474)]"
1882,1882,15,1882_dense graph limits_graphons_theory dense graph_graphon,"['dense graph limits', 'graphons', 'theory dense graph', 'graphon', 'random graphs', 'large graph limit', 'graph limits', 'graph sequences', 'graph limit', 'convergence graph']","['Probability-graphons: Limits of large dense weighted graphs   We introduce probability-graphons which are probability kernels that\ngeneralize graphons to the case of weighted graphs. Probability-graphons appear\nas the limit objects to study sequences of large weighted graphs whose\ndistribution of subgraph sampling converge. The edge-weights are taken from a\ngeneral Polish space, which also covers the case of decorated graphs. Here,\ngraphs can be either directed or undirected. Starting from a distance $d_m$\ninducing the weak topology on measures, we define a cut distance on\nprobability-graphons, making it a Polish space, and study the properties of\nthis cut distance. In particular, we exhibit a tightness criterion for\nprobability-graphons related to relative compactness in the cut distance. We\nalso prove that under some conditions on the distance $d_m$, which are\nsatisfied for some well-know distances like the Prohorov distance, and the\nFortet-Mourier and Kantorovitch-Rubinstein norms, the topology induced by the\ncut distance on the spaceof probability-graphons is independent from the choice\nof $d_m$. Eventually, we prove that this topology coincides with the topology\ninduced by the convergence in distribution of the sampled subgraphs.\n', 'Probability graphons and P-variables: two equivalent viewpoints for\n  dense weighted graph limits   We develop further the graph limit theory for dense weighted graph sequences.\nIn particular, we consider probability graphons, which have recently appeared\nin graph limit theory as continuum representations of weighted graphs, and we\nintroduce P-variables, which also appear in the context of the Aldous-Hoover\ntheorem for exchangeable infinite random arrays, as an alternative continuum\nrepresentation for weighted graphs. In particular, we explain how P-variables\nare related to probability graphons in a similar way in which random variables\nare related to probability measures. We define a metric for P-variables\n(inspired by action convergence in the graph limit theory of sparse graph\nsequences) and show that convergence of P-variables in this metric is\nequivalent to probability graphons convergence. We exploit this equivalence to\ntranslate several results from the theory of probability graphons to\nP-variables. In addition, we prove several properties of P-variables\nconvergence, thus showing new properties also for probability graphons\nconvergence and demonstrating the power of the connection between probability\ngraphons and P-variables. Furthermore, we show how P-variables convergence can\nbe easily modified and generalised to cover other combinatorial structures such\nas bipartite graphs and hypergraphs.\n', ""Probability graphons: the right convergence point of view   We extend the theory of probability graphons, continuum representations of\nedge-decorated graphs arising in graph limits theory, to the 'right\nconvergence' point of view. First of all, we generalise the notions of overlay\nfunctionals and quotient sets to the case of probability graphons. Furthermore,\nwe characterise the convergence of probability graphons in terms of these\nglobal quantities. In particular, we show the equivalence of these two notions\nof convergence with the unlabelled cut-metric convergence (and thus also with\nthe homomorphism densities convergence and the subgraph sampling convergence).\nIn other words, we prove the equivalence of the 'left convergence' and the\n'right convergence' views on probability graphons convergence, generalising the\ncorresponding result for (real-valued) graphons (the classical continuum\nrepresentation for simple graphs).\n""]","[('dense graph limits', 0.5760850310325623), ('graphons', 0.5685957074165344), ('theory dense graph', 0.5643714666366577), ('graphon', 0.553270697593689), ('random graphs', 0.5352932214736938), ('large graph limit', 0.5244631767272949), ('graph limits', 0.5156877636909485), ('graph sequences', 0.5115470290184021), ('graph limit', 0.49300023913383484), ('convergence graph', 0.48036402463912964)]"
1883,1883,15,1883_stochastic control_control stochastic_controlled stochastic_stochastic differential equations,"['stochastic control', 'control stochastic', 'controlled stochastic', 'stochastic differential equations', 'backward stochastic differential', 'stochastic differential', 'backward stochastic', 'optimal control', 'driven stochastic', 'optimal controls']","[""HJB and Fokker-Planck equations for river environmental management based\n  on stochastic impulse control with discrete and random observation   We formulate a new two-variable river environmental restoration problem based\non jump stochastic differential equations (SDEs) governing the sediment storage\nand nuisance benthic algae population dynamics in a dam-downstream river.\nControlling the dynamics is carried out through impulsive sediment\nreplenishment with discrete and random observation/intervention to avoid\nsediment depletion and thick algae growth. We consider a cost-efficient\nmanagement problem of the SDEs to achieve the objectives whose resolution\nreduces to solving a Hamilton-Jacobi-Bellman (HJB) equation. We also consider a\nFokker-Planck (FP) equation governing the probability density function of the\ncontrolled dynamics. The HJB equation has a discontinuous solution, while the\nFP equation has a Dirac's delta along boundaries. We show that the value\nfunction, the optimized objective function, is governed by the HJB equation in\nthe simplified case and further that a threshold-type control is optimal. We\ndemonstrate that simple numerical schemes can handle these equations. Finally,\nwe numerically analyze the optimal controls and the resulting probability\ndensity functions.\n"", 'Towards Control of Dam and Reservoir Systems with Forward-Backward\n  Stochastic Differential Equations Driven by Clustered Jumps   We deal with a new maximum principle-based stochastic control model for river\nmanagement through operating a dam and reservoir system. The model is based on\ncoupled forward-backward stochastic differential equations (FBSDEs) derived\nfrom jump-driven streamflow dynamics and reservoir water balance. A\ncontinuous-time branching process with immigration driven by a tempered stable\nsubordinator efficiently describes clustered inflow streamflow dynamics. This\nis a completely new attempt in hydrology and control engineering. Applying a\nstochastic maximum principle to the dynamics based on an objective functional\nfor designing cost-efficient control of dam and reservoir systems leads to the\nFBSDEs as a system of optimality equations. The FBSDEs under a linear-quadratic\nansatz lead to a tractable model, while they are solved numerically in the\nother cases using a least-squares Monte-Carlo method. Optimal controls are\nfound in the former, while only sub-optimal ones are computable in the latter\ndue to a hard state constraint. Model parameters are successfully identified\nfrom a real data of a river in Japan having a dam and reservoir system. We also\nshow that the linear-quadratic case can capture the real operation data of the\nsystem with underestimation of the outflow discharge. More complex cases with a\nrealistic time horizon are analyzed numerically to investigate impacts of\nconsidering the environmental flows and seasonal operational purposes. Key\nchallenges towards more sophisticated modeling and analysis with jump-driven\nFBSDEs are discussed as well.\n', 'River environmental restoration based on random observations of a\n  non-smooth stochastic dynamical system   Earth and soils are indispensable elements of river environment.\nDam-downstream environment and ecosystems have been severely affected by\nreduced or even stopped sediment supply from the upstream. Replenishing earth\nand soils from outside the river has been considered as an effective way to\nmitigate this issue. However, its cost-effective implementation has not been\nconsidered from a theoretical side. This paper presents a tractable new\nstochastic control model to deal with this issue. The sediment dynamics in the\nriver environment follow non-smooth and continuous-time piecewise deterministic\ndynamics. The model assumes that the observation of the sediment dynamics is\ncarried out only randomly and discretely, and that the sediment can be\nreplenished at each observation time with cost. This partial observation\nassumption is consistent with the fact that continuously obtaining the\nenvironmental information is difficult in applications. The performance index\nto penalize the sediment depletion has a non-smooth term as well. We\ndemonstrate that these non-smoothness factors harmonize with a dynamic\nprogramming principle, and derive the optimality equation in a degenerate\nelliptic form governing the most cost-efficient sediment replenishment policy.\nWe analytically derive and verify an exact solution under a simplified\ncondition for a discounted case, an Ergodic case, and a complete information\ncase. A more realistic case is handled using a high-resolution finite\ndifference scheme. We then provide the optimal sediment replenishment policy\nnumerically.\n']","[('stochastic control', 0.6000220775604248), ('control stochastic', 0.5753117203712463), ('controlled stochastic', 0.5573655962944031), ('stochastic differential equations', 0.5287933945655823), ('backward stochastic differential', 0.48988446593284607), ('stochastic differential', 0.46459272503852844), ('backward stochastic', 0.44564151763916016), ('optimal control', 0.4421520233154297), ('driven stochastic', 0.43667176365852356), ('optimal controls', 0.408332884311676)]"
1884,1884,15,1884_ideals local_filtrations mathcal_local ring mathfrak_regular local rings,"['ideals local', 'filtrations mathcal', 'local ring mathfrak', 'regular local rings', 'ideals regular', 'local rings', 'primary ideals', 'ideals noetherian', 'regular local ring', 'filtrations']","['The Minkowski Equality for Filtrations   Suppose that R is an analytically irreducible or excellent local domain with\nmaximal ideal m_R. We consider multiplicities and mixed multiplicities of R by\nfiltrations of m_R-primary ideals. We show that the theorem of Teissier, Rees\nand Sharp, and Katz, characterizing equality in the Minkowski inequality for\nmultiplicities of ideals, is true for divisorial filtrations, and for the\nlarger category of bounded filtrations. This theorem is not true for arbitrary\nfiltrations of m_R-primary ideals.\n', ""The Rees algebra and analytic spread of a divisorial filtration   In this paper we investigate some properties of Rees algebras of divisorial\nfiltrations and their analytic spread. A classical theorem of McAdam shows that\nthe analytic spread of an ideal $I$ in a formally equidimensional local ring is\nequal to the dimension of the ring if and only if the maximal ideal is an\nassociated prime of $R/\\overline{I^n}$ for some $n$. We show in Theorem 1.6\nthat McAdam's theorem holds for $\\mathbb Q$-divisorial filtrations in an\nequidimensional local ring which is essentially of finite type over a field.\nThis generalizes an earlier result for $\\mathbb Q$-divisorial filtrations in an\nequicharacteristic zero excellent local domain by the author. This theorem does\nnot hold for more general filtrations.\n  We consider the question of the asymptotic behavior of the function $n\\mapsto\n\\lambda_R(R/I_n)$ for a $\\mathbb Q$-divisorial filtration $\\mathcal I=\\{I_n\\}$\nof $m_R$-primary ideals on a $d$-dimensional normal excellent local ring. It is\nknown from earlier work of the author that the multiplicity $$ e(\\mathcal I)=d!\n\\lim_{n\\rightarrow\\infty}\\frac{\\lambda_R(R/I_n)}{n^d} $$ can be irrational. We\nshow in Lemma 4.1 that the limsup of the first difference function $$\n\\limsup_{n\\rightarrow\\infty}\\frac{\\lambda_R(I_n/I_{n+1})}{n^{d-1}} $$ is always\nfinite for a $\\mathbb Q$-divisorial filtration. We then give an example in\nSection 4 showing that this limsup may not exist as a limit.\n  In the final section, we give an example of a symbolic filtration\n$\\{P^{(n)}\\}$ of a prime ideal $P$ in a normal two dimensional excellent local\nring which has the property that the set of Rees valuations of all the symbolic\npowers $P^{(n)}$ of $P$ is infinite.\n"", 'Multiplicities and Mixed Multiplicities of arbitrary Filtrations   We develop a theory of multiplicities and mixed multiplicities of\nfiltrations, extending the theory for filtrations of $m$-primary ideals to\narbitrary (not necessarily Noetherian) filtrations. The mixed multiplicities of\n$r$ filtrations on an analytically unramified local ring $R$ come from the\ncoefficients of a suitable homogeneous polynomial in $r$ variables of degree\nequal to the dimension of the ring, analogously to the classical case of the\nmixed multiplicities of $m$-primary ideals in a local ring. We prove that the\nMinkowski inequalities hold for arbitrary filtrations. The characterization of\nequality in the Minkowski inequality for m-primary ideals in a local ring by\nTeissier, Rees and Sharp and Katz does not extend to arbitrary filtrations, but\nwe show that they are true in a large and important subcategory of filtrations.\nWe define divisorial and bounded filtrations. The filtration of powers of a\nfixed ideal is a bounded filtration, as is a divisorial filtration. We show\nthat in an excellent local domain, the characterization of equality in the\nMinkowski equality is characterized by the condition that the integral closures\nof suitable Rees like algebras are the same, strictly generalizing the theorem\nof Teissier, Rees and Sharp and Katz. We also prove that a theorem of Rees\ncharacterizing the inclusion of ideals with the same multiplicity generalizes\nto bounded filtrations in excellent local domains. We give a number of other\napplications, extending classical theorems for ideals.\n']","[('ideals local', 0.5663962364196777), ('filtrations mathcal', 0.49808382987976074), ('local ring mathfrak', 0.49514636397361755), ('regular local rings', 0.4802815914154053), ('ideals regular', 0.47915270924568176), ('local rings', 0.47719481587409973), ('primary ideals', 0.4681878983974457), ('ideals noetherian', 0.45777374505996704), ('regular local ring', 0.45679691433906555), ('filtrations', 0.4517419934272766)]"
1885,1885,15,1885_invariant borel_measure preserving system_ergodic measure_measure preserving,"['invariant borel', 'measure preserving system', 'ergodic measure', 'measure preserving', 'action countable', 'actions countable', 'invariant borel probability', 'topological dynamical', 'minimal systems', 'ergodic']","[""Strongly mixing systems are almost strongly mixing of all orders   We prove that any strongly mixing action of a countable abelian group on a\nprobability space has higher order mixing properties. This is achieved via\nintroducing and utilizing $\\mathcal R$-limits, a notion of convergence which is\nbased on the classical Ramsey Theorem. $\\mathcal R$-limits are intrinsically\nconnected with a new combinatorial notion of largeness which is similar to but\nhas stronger properties than the classical notions of uniform density one and\nIP$^*$. While the main goal of this paper is to establish a\n$\\textit{universal}$ property of strongly mixing actions of countable abelian\ngroups, our results, when applied to $\\mathbb Z$-actions, offer a new way of\ndealing with strongly mixing transformations. In particular, we obtain several\nnew characterizations of strong mixing for $\\mathbb Z$-actions, including a\nresult which can be viewed as the analogue of the weak mixing of all orders\nproperty established by Furstenberg in the course of his proof of Szemer\\'edi's\ntheorem. We also demonstrate the versatility of $\\mathcal R$-limits by\nobtaining new characterizations of higher order weak and mild mixing for\nactions of countable abelian groups.\n"", 'Independence and mean sensitivity in minimal systems under group actions   In this paper, we mainly study the relation between regularity, independence\nand mean sensitivity for minimal systems. In the first part, we show that if a\nminimal system is incontractible, or local Bronstein with an invariant Borel\nprobability measure, then the regularity is strictly bounded by the infinite\nindependence. In particular, the following two types of minimal systems are\napplicable to our result: (1) The acting group of the minimal system is a\nvirtually nilpotent group. (2) The minimal system is a proximal extension of\nits maximal equicontinuous factor and admits an invariant Borel probability\nmeasure. Items (1) and (2) correspond to Conjectures 1 and 2 from Huang, Lian,\nShao, and Ye (J. Funct. Anal., 2021); item (1) verifies Conjecture 1 in the\nvirtually nilpotent case, and item (2) gives an affirmative answer to\nConjecture 2.\n  In the second part, for a minimal system acting by an amenable group, under\nthe local Bronstein condition, we establish parallel results regarding weak\nmean sensitivity and establish that every mean-sensitive tuple is an IT-tuple.\n', ""Topological characteristic factors and independence along arithmetic\n  progressions   Let $\\pi: (X,T)\\rightarrow (Y,T)$ be a factor map of topological dynamics and\n$d\\in {\\mathbb {N}}$. $(Y,T)$ is said to be a $d$-step topological\ncharacteristic factor if there exists a dense $G_\\delta$ set $X_0$ of $X$ such\nthat for each $x\\in X_0$ the orbit closure $\\overline{\\mathcal O}((x,\n\\ldots,x), T\\times T^2\\times \\ldots \\times T^d)$ is $\\pi\\times \\ldots \\times\n\\pi$ ($d$ times) saturated. In 1994 Eli Glasner studied the topological\ncharacteristic factor for minimal systems. For example, it is shown that for a\ndistal minimal system, its largest distal factor of order $d-1$ is its $d$-step\ntopological characteristic factor. In this paper, we generalize Glasner's work\nto the product system of finitely many minimal systems and give its relative\nversion. To prove these results, we need to deal with $(X,T^m)$ for $m\\in\n{\\mathbb {N}}$. We will study the structure theorem of $(X,T^m)$. We show that\nthough for a minimal system $(X,T)$ and $m\\in {\\mathbb {N}}$, $(X,T^m)$ may not\nbe minimal, but we still can have PI-tower for $(X,T^m)$ and in fact it looks\nthe same as the PI tower of $(X,T)$. We give some applications of the results\ndeveloped. For example, we show that if a minimal system has no nontrivial\nindependent pair along arithmetic progressions of order $d$, then up to a\ncanonically defined proximal extension, it is PI of order $d$; if a minimal\nsystem $(X,T)$ has a nontrivial $d$-step topological characteristic factor,\nthen there exist ``many'' $\\Delta$-transitive sets of order $d$.\n""]","[('invariant borel', 0.5196681022644043), ('measure preserving system', 0.5023346543312073), ('ergodic measure', 0.4967033565044403), ('measure preserving', 0.45512571930885315), ('action countable', 0.4521169364452362), ('actions countable', 0.44822075963020325), ('invariant borel probability', 0.4364033043384552), ('topological dynamical', 0.42655909061431885), ('minimal systems', 0.420240193605423), ('ergodic', 0.41755664348602295)]"
1886,1886,15,1886_existence invariant measures_uniqueness invariant measures_stochastic functional differential_invariant measures,"['existence invariant measures', 'uniqueness invariant measures', 'stochastic functional differential', 'invariant measures', 'infinite dimensional stochastic', 'existence stochastic', 'degenerate stochastic', 'stochastic functional', 'invariant measure', 'stochastic evolution equations']","['Conservativeness and uniqueness of invariant measures related to\n  non-symmetric divergence type operators   We present conservativeness criteria for sub-Markovian semigroups generated\nby divergence type operators with specified infinitesimally invariant measures.\nThe conservativeness criteria in this article are derived by $L^1$-uniqueness\nand imply that a given infinitesimally invariant measure becomes an invariant\nmeasure. We explore further conditions on the coefficients of the partial\ndifferential operators that ensure the uniqueness of the invariant measure\nbeyond the case where the corresponding semigroups are recurrent. A main\nobservation is that for conservativeness and uniqueness of invariant measures\nin this article, no growth conditions are required for the partial derivatives\nrelated to the anti-symmetric matrix of functions $C=(c_{ij})_{1 \\leq i,j \\leq\nd}$ that determine a part of the drift coefficient. As stochastic counterparts,\nour results can be applied to show not only the existence of a pathwise unique\nand strong solution up to infinity to a corresponding It\\^{o}-SDE, but also the\nexistence and uniqueness of invariant measures for the family of strong\nsolutions.\n', 'The essential m-dissipativity for degenerate infinite dimensional\n  stochastic Hamiltonian systems and applications   We consider a degenerate infinite dimensional stochastic Hamiltonian system\nwith multiplicative noise and establish the essential m-dissipativity on\n$L^2(\\mu^{\\Phi})$ of the corresponding Kolmogorov (backwards) operator. Here,\n$\\Phi$ is the potential and $\\mu^{\\Phi}$ the invariant measure with density\n$e^{-\\Phi}$ with respect to an infinite dimensional non-degenerate Gaussian\nmeasure. The main difficulty, besides the non-sectorality of the Kolmogorov\noperator, is the coverage of a large class of potentials. We include potentials\nthat have neither a bounded nor a Lipschitz continuous gradient. The essential\nm-dissipativity is the starting point to establish the hypocoercivity of the\nstrongly continuous contraction semigroup $(T_t)_{t\\geq 0}$ generated by the\nKolmogorov operator. By using the refined abstract Hilbert space hypocoercivity\nmethod of Grothaus and Stilgenbauer, originally introduced by Dolbeault, Mouhot\nand Schmeiser, we construct a $\\mu^{\\Phi}$-invariant Hunt process with weakly\ncontinuous paths and infinite lifetime, whose transition semigroup is\nassociated with $(T_t)_{t\\geq 0}$. This process provides a stochastically and\nanalytically weak solution to the degenerate infinite dimensional stochastic\nHamiltonian system with multiplicative noise. The hypocoercivity of\n$(T_t)_{t\\geq 0}$ and the identification of $(T_t)_{t\\geq 0}$ with the\ntransition semigroup of the process leads to the exponential ergodicity.\nFinally, we apply our results to degenerate second order in time stochastic\nreaction-diffusion equations with multiplicative noise. A discussion of the\nclass of applicable potentials and coefficients governing these equations\ncompletes our analysis.\n', 'Hypocoercivity for infinite-dimensional non-linear degenerate stochastic\n  differential equations with multiplicative noise   We analyze infinite-dimensional non-linear degenerate stochastic differential\nequations with multiplicative noise. First, essential m-dissipativity of their\nassociated Kolmogorov backward generators on $L^2(\\mu^{\\Phi})$ defined on\nsmooth finitely based functions is established. Here $\\Phi$ is an appropriate\npotential and $\\mu^{\\Phi}$ is the invariant measure with density $e^{-\\Phi}$\nw.r.t. an infinite-dimensional non-degenerate Gaussian measure. Second, we use\nresolvent methods to construct corresponding right processes with infinite\nlifetime, solving the martingale problem for the Kolmogorov backward\ngenerators. They provide weak solutions, with weakly continuous paths, to the\nnon-linear degenerate stochastic partial differential equations. Moreover, we\nidentify the transition semigroup of such a process with the strongly\ncontinuous contraction semigroup $(T_t)_{t\\geq 0}$ generated by the\ncorresponding Kolmogorov backwards generator. Afterwards, we apply a refinement\nof the abstract Hilbert space hypocoercivity method, developed by Dolbeaut,\nMouhot and Schmeiser, to derive hypocoercivity of $(T_t)_{t\\geq 0}$. I.e. we\ntake domain issues into account and use the formulation in the Kolmogorov\nbackwards setting worked out by Grothaus and Stilgenbauer. The method enables\nus to explicitly compute the constants determining the exponential convergence\nrate to equilibrium of $(T_t)_{t\\geq 0}$. The identification between\n$(T_t)_{t\\geq 0}$ and the transition semigroup of the process yields\nexponential ergodicity of the latter. Finally, we apply our results to second\norder in time stochastic reaction-diffusion and Cahn-Hilliard type equations\nwith multiplicative noise. More generally, we analyze corresponding couplings\nof infinite-dimensional deterministic with stochastic differential equations.\n']","[('existence invariant measures', 0.5810831189155579), ('uniqueness invariant measures', 0.5597001314163208), ('stochastic functional differential', 0.556732714176178), ('invariant measures', 0.549335241317749), ('infinite dimensional stochastic', 0.5480265021324158), ('existence stochastic', 0.5255711674690247), ('degenerate stochastic', 0.5146414041519165), ('stochastic functional', 0.5137922763824463), ('invariant measure', 0.5005528926849365), ('stochastic evolution equations', 0.49338218569755554)]"
1887,1887,15,1887_network pruning_pruning based_pruning_based pruning,"['network pruning', 'pruning based', 'pruning', 'based pruning', 'networks iterative', 'prune', 'neural networks often', 'deep neural', 'pruned', 'large language models']","[""i-SpaSP: Structured Neural Pruning via Sparse Signal Recovery   We propose a novel, structured pruning algorithm for neural networks -- the\niterative, Sparse Structured Pruning algorithm, dubbed as i-SpaSP. Inspired by\nideas from sparse signal recovery, i-SpaSP operates by iteratively identifying\na larger set of important parameter groups (e.g., filters or neurons) within a\nnetwork that contribute most to the residual between pruned and dense network\noutput, then thresholding these groups based on a smaller, pre-defined pruning\nratio. For both two-layer and multi-layer network architectures with ReLU\nactivations, we show the error induced by pruning with i-SpaSP decays\npolynomially, where the degree of this polynomial becomes arbitrarily large\nbased on the sparsity of the dense network's hidden representations. In our\nexperiments, i-SpaSP is evaluated across a variety of datasets (i.e., MNIST,\nImageNet, and XNLI) and architectures (i.e., feed forward networks, ResNet34,\nMobileNetV2, and BERT), where it is shown to discover high-performing\nsub-networks and improve upon the pruning efficiency of provable baseline\nmethodologies by several orders of magnitude. Put simply, i-SpaSP is easy to\nimplement with automatic differentiation, achieves strong empirical results,\ncomes with theoretical convergence guarantees, and is efficient, thus\ndistinguishing itself as one of the few computationally efficient, practical,\nand provable pruning algorithms.\n"", ""SPAP: Structured Pruning via Alternating Optimization and Penalty\n  Methods   The deployment of large language models (LLMs) is often constrained by their\nsubstantial computational and memory demands. While structured pruning presents\na viable approach by eliminating entire network components, existing methods\nsuffer from performance degradation, reliance on heuristic metrics, or\nexpensive finetuning. To address these challenges, we propose SPAP (Structured\nPruning via Alternating Optimization and Penalty Methods), a novel and\nefficient structured pruning framework for LLMs grounded in optimization\ntheory. SPAP formulates the pruning problem through a mixed-integer\noptimization model, employs a penalty method that effectively makes pruning\ndecisions to minimize pruning errors, and introduces an alternating\nminimization algorithm tailored to the splittable problem structure for\nefficient weight updates and performance recovery. Extensive experiments on\nOPT, LLaMA-3/3.1/3.2, and Qwen2.5 models demonstrate SPAP's superiority over\nstate-of-the-art methods, delivering linear inference speedups (1.29$\\times$ at\n30% sparsity) and proportional memory reductions. Our work offers a practical,\noptimization-driven solution for pruning LLMs while preserving model\nperformance.\n"", 'An Operator Theoretic View on Pruning Deep Neural Networks   The discovery of sparse subnetworks that are able to perform as well as full\nmodels has found broad applied and theoretical interest. While many pruning\nmethods have been developed to this end, the na\\""ive approach of removing\nparameters based on their magnitude has been found to be as robust as more\ncomplex, state-of-the-art algorithms. The lack of theory behind magnitude\npruning\'s success, especially pre-convergence, and its relation to other\npruning methods, such as gradient based pruning, are outstanding open questions\nin the field that are in need of being addressed. We make use of recent\nadvances in dynamical systems theory, namely Koopman operator theory, to define\na new class of theoretically motivated pruning algorithms. We show that these\nalgorithms can be equivalent to magnitude and gradient based pruning, unifying\nthese seemingly disparate methods, and find that they can be used to shed light\non magnitude pruning\'s performance during the early part of training.\n']","[('network pruning', 0.6393842101097107), ('pruning based', 0.5719398260116577), ('pruning', 0.5617232322692871), ('based pruning', 0.5101487040519714), ('networks iterative', 0.4931489825248718), ('prune', 0.4659852087497711), ('neural networks often', 0.4461996257305145), ('deep neural', 0.4423317611217499), ('pruned', 0.4352334141731262), ('large language models', 0.4283982813358307)]"
1888,1888,15,1888_assembling_self assembly_genome_assembly,"['assembling', 'self assembly', 'genome', 'assembly', 'bioinformatics', 'assemble', 'complete algorithms', 'graph structure', 'rna', 'graph families']","[""Computational complexity and pragmatic solutions for flexible tile based\n  DNA self-assembly   Branched junction molecule assembly of DNA nanostructures, pioneered by\nSeeman's laboratory in the 1980s, has become increasingly sophisticated, as\nhave the assembly targets. A critical design step is finding minimal sets of\nbranched junction molecules that will self-assemble into target structures\nwithout unwanted substructures forming. We use graph theory, which is a natural\ndesign tool for self-assembling DNA complexes, to address this problem. After\ndetermining that finding optimal design strategies for this method is generally\nNP-complete, we provide pragmatic solutions in the form of programs for special\nsettings and provably optimal solutions for natural assembly targets such as\nplatonic solids, regular lattices, and nanotubes. These examples also\nillustrate the range of design challenges.\n"", 'The Hydrostructure: a Universal Framework for Safe and Complete\n  Algorithms for Genome Assembly   Genome assembly is a fundamental problem in Bioinformatics, requiring to\nreconstruct a source genome from an assembly graph built from a set of reads\n(short strings sequenced from the genome). A notion of genome assembly solution\nis that of an arc-covering walk of the graph. Since assembly graphs admit many\nsolutions, the goal is to find what is definitely present in all solutions, or\nwhat is safe. Most practical assemblers are based on heuristics having at their\ncore unitigs, namely paths whose internal nodes have unit in-degree and\nout-degree, and which are clearly safe. The long-standing open problem of\nfinding all the safe parts of the solutions was recently solved [RECOMB 2016]\nyielding a 60% increase in contig length. This safe and complete genome\nassembly algorithm was followed by other works improving the time bounds, as\nwell as extending the results for different notions of assembly solution. But\nit remained open whether one can be complete also for models of genome assembly\nof practical applicability.\n  In this paper we present a universal framework for obtaining safe and\ncomplete algorithms which unify the previous results, while also allowing for\neasy generalisations to assembly problems including many practical aspects.\nThis is based on a novel graph structure, called the hydrostructure of a walk,\nwhich highlights the reachability properties of the graph from the perspective\nof the walk. The hydrostructure allows for simple characterisations of the\nexisting safe walks, and of their new practical versions. Almost all of our\ncharacterisations are directly adaptable to optimal verification algorithms,\nand simple enumeration algorithms. Most of these algorithms are also improved\nto optimality using an incremental computation procedure and a previous optimal\nalgorithm of a specific model.\n', 'The Role of Sequence Information in Minimal Models of Molecular Assembly   Sequence-directed assembly processes - such as protein folding - allow the\nassembly of a large number of structures with high accuracy from only a small\nhandful of fundamental building blocks. We aim to explore how efficiently\nsequence information can be used to direct assembly by studying variants of the\ntemperature-1 abstract tile assembly model (aTAM). We ask whether, for each\nvariant, their exists a finite set of tile types that can deterministically\nassemble any shape producible by a given assembly model; we call such tile type\nsets ""universal assembly kits"". Our first model, which we call the ""backboned\naTAM"", generates backbone-assisted assembly by forcing tiles to be added to\nlattice positions neighbouring the immediately preceding tile, using a\npredetermined sequence of tile types. We demonstrate the existence of universal\nassembly kit for the backboned aTAM, and show that the existence of this set is\nmaintained even under stringent restrictions to the rules of assembly. We\ncompare these results to a less constrained model that we call sequenced aTAM,\nwhich also uses a predetermined sequence of tiles, but does not constrain a\ntile to neighbour the immediately preceding tiles. We prove that this model has\nno universal assembly kit in the stringent case. The lack of such a kit is\nsurprising, given that the number of tile sequences of length N scales faster\nthan both the number and worst-case Kolmogorov complexity of producible shapes\nof size N for a sufficiently large - but finite - set of tiles. Our results\ndemonstrate the importance of physical mechanisms, and specifically geometric\nconstraints, in facilitating efficient use of the information in molecular\nprograms for structure assembly.\n']","[('assembling', 0.4718848466873169), ('self assembly', 0.4613337218761444), ('genome', 0.44362661242485046), ('assembly', 0.4092196524143219), ('bioinformatics', 0.37825533747673035), ('assemble', 0.37579935789108276), ('complete algorithms', 0.35447046160697937), ('graph structure', 0.3502229154109955), ('rna', 0.3321084976196289), ('graph families', 0.33188050985336304)]"
1889,1889,15,1889_hyperbolic actions_affine actions_action lattice_affine action,"['hyperbolic actions', 'affine actions', 'action lattice', 'affine action', 'actions topological', 'local rigidity', 'lattice actions', 'boundary actions', 'algebraic actions', 'actions groups']","['Partially hyperbolic lattice actions on 2-step nilmanifolds   We prove global rigidity results for actions of higher rank lattices on\nnilmanifolds containing a partially hyperbolic element. We consider actions of\nhigher rank lattices on tori or on $2-$step nilpotent nilmanifolds, such that\nthe actions contain a partially hyperbolic element with $1-$dimensional center.\nIn this setting we prove, under a technical assumption on the partially\nhyperbolic element, that any such action must be by affine maps. This extends\nresults by Brown, Rodriguez Hertz, and Wang to certain lattice actions that are\nnot Anosov.\n', 'Global rigidity for some partially hyperbolic abelian actions with\n  1-dimensional center   We obtain a global rigidity result for abelian partially hyperbolic higher\nrank actions on certain $2-$step nilmanifolds $X_{\\Gamma}$. We show that, under\ncertain natural assumptions, all such actions are $C^{\\infty}-$conjugated to an\naffine model. As a consequence, we obtain a centralizer rigidity result,\nclassifying all possible centralizers for any $C^{1}-$small perturbation of an\nirreducible, affine partially hyperbolic map on $X_{\\Gamma}$. Along the way, we\nalso prove two results of independent interest. We describe fibered partially\nhyperbolic diffeomorphisms on $X_{\\Gamma}$ and we show that topological\nconjugacies between partially hyperbolic actions and higher rank affine actions\nare $C^{\\infty}$.\n', 'Local rigidity of higher rank partially hyperbolic algebraic actions   We give a complete solution to the local classification program of higher\nrank partially hyperbolic algebraic actions. We show $C^\\infty$ local rigidity\nof abelian ergodic algebraic actions for symmetric space examples, twisted\nsymmetric space examples and automorphisms on nilmanifolds. The method is a\ncombination of representation theory, harmonic analysis and a KAM iteration. A\nstriking feature of the method is no specific information from representation\ntheory is needed. It is the first time local rigidity for non-accessible\npartially hyperbolic actions has ever been obtained other than torus examples.\nEven for Anosov actions, our results are new: it is the first time twisted\nspaces with non-abelian nilradical have been treated in the literature.\n']","[('hyperbolic actions', 0.5789855718612671), ('affine actions', 0.570500373840332), ('action lattice', 0.5597898960113525), ('affine action', 0.5552017688751221), ('actions topological', 0.544707715511322), ('local rigidity', 0.5401315093040466), ('lattice actions', 0.5258160829544067), ('boundary actions', 0.5252810716629028), ('algebraic actions', 0.5223274827003479), ('actions groups', 0.4927283525466919)]"
1890,1890,15,1890_riesz basis_characterization riesz_riesz bases_bound riesz,"['riesz basis', 'characterization riesz', 'riesz bases', 'bound riesz', 'riesz', 'basis space', 'form basis space', 'orthogonal basis', 'lattice lambda', 'basis']","[""Exponential Riesz bases in $L^2$ on two interval   We give sufficient conditions for the exponential system to be a Riesz basis\nin $L^2(E)$, where $E$ is a union of two intervals. We show that these\nconditions are close to be necessary. In addition, we demonstrate ``extra point\neffect'' for such systems, i.e. it may happen that the Riesz basis in $L^2(E)$\ndiffers by one point from the Riesz basis on an interval.\n"", 'A set with no Riesz basis of exponentials   We show that there exists a bounded subset of R such that no system of\nexponentials can be a Riesz basis for the corresponding Hilbert space. An\nadditional result gives a lower bound for the Riesz constant of any putative\nRiesz basis of the two dimensional disk.\n', 'Riesz bases of exponentials for multi-tiling measures   Let $G$ be a closed subgroup of ${\\mathbb R}^d$ and let $\\nu$ be a Borel\nprobability measure admitting a Riesz basis of exponentials with frequency sets\nin the dual group $G^{\\perp}$. We form a multi-tiling measure $\\mu =\n\\mu_1+...+\\mu_N$ where $\\mu_i$ is translationally equivalent to $\\nu$ and\ndifferent $\\mu_i$ and $\\mu_j$ have essentially disjoint support. We obtain some\nnecessary and sufficient conditions for $\\mu$ to admit a Riesz basis of\nexponentials . As an application, the square boundary, after a rotation, is a\nunion of two fundamental domains of $G = {\\mathbb Z}\\times {\\mathbb R}$ and can\nbe regarded as a multi-tiling measure. We show that, unfortunately, the square\nboundary does not admit a Riesz basis of exponentials of the form as a union of\ntranslate of discrete subgroups ${\\mathbb Z}\\times \\{0\\}$. This rules out a\nnatural candidate of potential Riesz basis for the square boundary.\n']","[('riesz basis', 0.6760918498039246), ('characterization riesz', 0.5794658660888672), ('riesz bases', 0.5730609893798828), ('bound riesz', 0.519736111164093), ('riesz', 0.4328785240650177), ('basis space', 0.3888637125492096), ('form basis space', 0.358493447303772), ('orthogonal basis', 0.3551046848297119), ('lattice lambda', 0.35475441813468933), ('basis', 0.35350075364112854)]"
1891,1891,15,1891_random variables asymptotic_normal random variables_distributions product_distribution product,"['random variables asymptotic', 'normal random variables', 'distributions product', 'distribution product', 'two correlated', 'random variables zero', 'random variables non', 'moments variance', 'correlated', 'random variables']","['Asymptotic expansions relating to the distribution of the product of correlated normal random variables Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables. Asymptotic approximations are also given for the quantile function. Numerical results are given to test the performance of the asymptotic approximations.', 'Infinite Divisibility of the Product of Two Correlated Normal Random\n  Variables and Exact Distribution of the Sample Mean   We prove that the distribution of the product of two correlated normal random\nvariables with non-zero means and arbitrary variances is infinitely divisible.\nWe also obtain exact formulas for the probability density function of the sum\nof independent copies of such random variables.\n', 'A Stein characterisation of the distribution of the product of\n  correlated normal random variables   We obtain a Stein characterisation of the distribution of the product of two\ncorrelated normal random variables with non-zero means, and more generally the\ndistribution of the sum of independent copies of such random variables. Our\nStein characterisation is shown to naturally generalise a number of other Stein\ncharacterisations in the literature. From our Stein characterisation we derive\nrecursive formulas for the moments of the product of two correlated normal\nrandom variables, and more generally the sum of independent copies of such\nrandom variables, which allows for efficient computation of higher order\nmoments.\n']","[('random variables asymptotic', 0.5258226990699768), ('normal random variables', 0.4926080107688904), ('distributions product', 0.4889020025730133), ('distribution product', 0.4437325596809387), ('two correlated', 0.4323342442512512), ('random variables zero', 0.4317353665828705), ('random variables non', 0.40423819422721863), ('moments variance', 0.3969612717628479), ('correlated', 0.3901360332965851), ('random variables', 0.3841898739337921)]"
1892,1892,15,1892_rational homotopy theory_rational homotopy groups_rational homotopy_rational homology,"['rational homotopy theory', 'rational homotopy groups', 'rational homotopy', 'rational homology', 'rational homotopy type', 'maps rational', 'homotopy theory', 'spaces homological', 'homotopy equivalences', 'homotopy groups pi_']","[""Rational homotopy equivalences and singular chains   Bousfield and Kan's $\\mathbb{Q}$-completion and fiberwise\n$\\mathbb{Q}$-completion of spaces lead to two different approaches to the\nrational homotopy theory of non-simply connected spaces. In the first approach,\na map is a weak equivalence if it induces an isomorphism on rational homology.\nIn the second, a map of connected and pointed spaces is a weak equivalence if\nit induces an isomorphism between fundamental groups and higher rationalized\nhomotopy groups; we call these maps $\\pi_1$-rational homotopy equivalences. In\nthis paper, we compare these two notions and show that $\\pi_1$-rational\nhomotopy equivalences correspond to maps that induce\n$\\Omega$-quasi-isomorphisms on the rational singular chains, i.e. maps that\ninduce a quasi-isomorphism after applying the cobar functor to the dg\ncoassociative coalgebra of rational singular chains. This implies that both\nnotions of rational homotopy equivalence can be deduced from the rational\nsingular chains by using different algebraic notions of weak equivalences:\nquasi-isomorphism and $\\Omega$-quasi-isomorphisms. We further show that, in the\nsecond approach, there are no dg coalgebra models of the chains that are both\nstrictly cocommutative and coassociative.\n"", ""Baumslag rationalization of spaces   Using the functor of Baumslag rationalization of groups we construct a\nfunctor on the category of all (non necessarily simply connected) spaces that\nextends the classical rationalization of simply connected spaces. We study this\nfunctor and compare it with other extensions of the classical rationalization:\nBousfield-Kan $\\mathbb Q$-completion; Bousfield's homology rationalization;\nG\\'{o}mez-Tato--Halperin--Tantr\\'{e}'s $\\pi_1$-fiberwise rationalization; and\nthe localization with respect to the maps $n:S^1\\to S^1$ that we call\n$\\Omega$-rationalization.\n"", ""An overview of rationalization theories of non-simply connected spaces\n  and non-nilpotent groups   We give an overview of five rationalization theories for spaces\n(Bousfield-Kan's $\\mathbb Q$-completion; Sullivan's rationalization;\nBousfield's homology rationalization; Casacuberta-Peschke's\n$\\Omega$-rationalization; G\\'{o}mez-Tato-Halperin-Tanr\\'{e}'s $\\pi_1$-fiberwise\nrationalization) that extend the classical rationalization of simply connected\nspaces. We also give an overview of the corresponding rationalization theories\nfor groups ($\\mathbb Q$-completion; $H\\mathbb Q$-localization; Baumslag\nrationalization) that extend the classical Malcev completion.\n""]","[('rational homotopy theory', 0.7101938724517822), ('rational homotopy groups', 0.6552618145942688), ('rational homotopy', 0.6380209922790527), ('rational homology', 0.6347890496253967), ('rational homotopy type', 0.6327595710754395), ('maps rational', 0.5054725408554077), ('homotopy theory', 0.5003455281257629), ('spaces homological', 0.49208763241767883), ('homotopy equivalences', 0.45219364762306213), ('homotopy groups pi_', 0.4500844478607178)]"
1893,1893,15,1893_einstein equations_solutions einstein_curvature initial_general relativity,"['einstein equations', 'solutions einstein', 'curvature initial', 'general relativity', 'schwarzschild spacetime', 'constant mean curvature', 'solutions conformal', 'coupled einstein', 'mean curvature', 'spacetime smooth']","['A class of solutions to the conformal constraint equations on compact\n  manifolds with apparent horizon boundary conditions   This article is dedicated to solving the Einstein constraint equations with\napparent horizon boundaries and freely specified mean curvature. The main\nnovelty is that we study the conformal constraint equations assuming only low\nregularity.\n', 'A Phase Space Approach to the Conformal Construction of Non-Vacuum\n  Initial Data Sets in General Relativity   We present a uniform (and unambiguous) procedure for scaling the matter\nfields in implementing the conformal method to parameterize and construct\nsolutions of Einstein constraint equations with coupled matter sources. The\napproach is based on a phase space representation of the space-time matter\nfields after a careful $n+1$ decomposition into spatial fields $B$ and\nconjugate momenta $\\Pi_B$, which are specified directly and are conformally\ninvariant quantities. We show that if the Einstein-matter field theory is\nspecified by a Lagrangian which is diffeomorphism invariant and involves no\ndependence on derivatives of the space-time metric in the matter portion of the\nLagrangian, then fixing $B$ and $\\Pi_B$ results in conformal constraint\nequations that, for constant-mean curvature initial data, semi-decouple just as\nthey do for the vacuum Einstein conformal constraint equations. We prove this\nresult by establishing a structural property of the Einstein momentum\nconstraint that is independent of the conformal method: For an Einstein-matter\nfield theory which satisfies the conditions just stated, if $B$ and $\\Pi_B$\nsatisfy the matter Euler-Lagrange equations, then (in suitable form) the\nright-hand side of the momentum constraint on each spatial slice depends only\non $B$ and $\\Pi_B$ and is independent of the space-time metric. We discuss the\ndetails of our construction in the special cases of the following models:\nEinstein-Maxwell-charged scalar field, Einstein-Proca, Einstein-perfect fluid,\nand Einstein-Maxwell-charged dust. In these examples we find that our technique\ngives a theoretical basis for scaling rules, such as those for\nelectromagnetism, that have worked pragmatically in the past, but also\ngenerates new equations with advantageous features for perfect fluids that\nallow direct specification of total rest mass and total charge in any spatial\nregion.\n', 'Global regular null hypersurfaces in a perturbed Schwarzschild black\n  hole exterior   The spherically symmetric null hypersurfaces in a Schwarzschild spacetime are\nsmooth away from the singularities and foliate the spacetime. We prove the\nexistence of more general foliations by null hypersurfaces without the\nspherical symmetry condition. In fact we also relax the spherical symmetry of\nthe ambient spacetime and prove a more general result: in a perturbed\nSchwarzschild spacetime (not necessary being vacuum), nearly round null\nhypersurfaces can be extended regularly to the past null infinity, thus there\nexist many foliations by regular null hypersurfaces in the exterior region of a\nperturbed Schwarzschild black hole. A significant point of the result is that\nthe ambient spacetime metric is not required to be differentiable in all\ndirections.\n']","[('einstein equations', 0.5570436120033264), ('solutions einstein', 0.5223399996757507), ('curvature initial', 0.5140337944030762), ('general relativity', 0.503962516784668), ('schwarzschild spacetime', 0.5023018717765808), ('constant mean curvature', 0.4804559051990509), ('solutions conformal', 0.47680413722991943), ('coupled einstein', 0.4588562548160553), ('mean curvature', 0.4483316242694855), ('spacetime smooth', 0.4279290735721588)]"
1894,1894,15,1894_elliptic operators_general elliptic operators_elliptic systems divergence_order elliptic operators,"['elliptic operators', 'general elliptic operators', 'elliptic systems divergence', 'order elliptic operators', 'fractional laplacians', 'ellipticity', 'fractional laplacian', 'fractional dirichlet laplacian', 'second order elliptic', 'degenerate ellipticity']","['The Kato square root problem for weighted parabolic operators   We give a simplified and direct proof of the Kato square root estimate for\nparabolic operators with elliptic part in divergence form and coefficients\npossibly depending on space and time in a merely measurable way. The argument\nrelies on the nowadays classical reduction to a quadratic estimate and a\nCarleson-type inequality. The precise organization of the estimates is\ndifferent from earlier works. In particular, we succeed in separating space and\ntime variables almost completely despite the non-autonomous character of the\noperator. Hence, we can allow for degenerate ellipticity dictated by a spatial\n$A_2$-weight, which has not been treated before in this context.\n', 'The Kato Square Root Problem on locally uniform domains   We obtain the Kato square root estimate for second order elliptic operators\nin divergence form with mixed boundary conditions on an open and possibly\nunbounded set in $\\mathbb{R}^d$ under two simple geometric conditions: The\nDirichlet boundary part is Ahlfors--David regular and a quantitative\nconnectivity property in the spirit of locally uniform domains holds near the\nNeumann boundary part. This improves upon all existing results even in the case\nof pure Dirichlet or Neumann boundary conditions. We also treat elliptic\nsystems with lower order terms. As a side product we establish new regularity\nresults for the fractional powers of the Laplacian with boundary conditions in\nour geometric setup.\n', 'The Kato Square Root Problem follows from an Extrapolation Property of\n  the Laplacian   On a domain $\\Omega \\subseteq \\mathbb{R}^d$ we consider second order elliptic\nsystems in divergence form with bounded complex coefficients, realized via a\nsesquilinear form with domain $V \\subseteq H^1(\\Omega)$. Under very mild\nassumptions on $\\Omega$ and $V$ we show that the Kato Square Root Problem for\nsuch systems can be reduced to a regularity result for the fractional powers of\nthe negative Laplacian in the same geometric setting. This extends an earlier\nresult of McIntosh to non-smooth coefficients.\n']","[('elliptic operators', 0.625007152557373), ('general elliptic operators', 0.6159019470214844), ('elliptic systems divergence', 0.5780402421951294), ('order elliptic operators', 0.5720379948616028), ('fractional laplacians', 0.5707360506057739), ('ellipticity', 0.5458865761756897), ('fractional laplacian', 0.5402892827987671), ('fractional dirichlet laplacian', 0.5323206782341003), ('second order elliptic', 0.5206042528152466), ('degenerate ellipticity', 0.510834813117981)]"
1895,1895,15,1895_stability network_networks stability_stability infinite_finite networks,"['stability network', 'networks stability', 'stability infinite', 'finite networks', 'input state stability', 'infinite network', 'networks infinite', 'infinite dimensional systems', 'lyapunov based', 'input output stability']","['Nonlinear small-gain theorems for input-to-state stability of infinite\n  interconnections   We consider infinite heterogeneous networks, consisting of input-to-state\nstable subsystems of possibly infinite dimension. We show that the network is\ninput-to-state stable, provided that the gain operator satisfies a certain\nsmall-gain condition. We show that for finite networks of nonlinear systems\nthis condition is equivalent to the so-called strong small-gain condition of\nthe gain operator (and thus our results extend available results for finite\nnetworks), and for infinite networks with a linear gain operator they\ncorrespond to the condition that the spectral radius of the gain operator is\nless than one. We provide efficient criteria for input-to-state stability of\ninfinite networks with linear gains, governed by linear and homogeneous gain\noperators, respectively.\n', 'Small gain theorems for general networks of heterogeneous\n  infinite-dimensional systems   We prove a small-gain theorem for interconnections of $n$ nonlinear\nheterogeneous input-to-state stable (ISS) control systems of a general nature,\ncovering partial, delay and ordinary differential equations. Furthermore, for\nthe same class of control systems, we derive small-gain theorems for asymptotic\ngain, uniform global stability and weak input-to-state stability properties. We\nshow that our technique is applicable for different formulations of ISS\nproperty (summation, maximum, semimaximum) and discuss tightness of achieved\nsmall-gain theorems. Finally, we introduce variations of uniform asymptotic\ngain and uniform limit properties, which are particularly useful for small-gain\narguments and characterize ISS in terms of these notions.\n', 'Input-to-state stability meets small-gain theory   Input-to-state stability (ISS) unifies global asymptotic stability with\nrespect to variations of initial conditions with robustness with respect to\nexternal disturbances. First, we present Lyapunov characterizations for\ninput-to-state stability as well as ISS superpositions theorems showing\nrelations of ISS to other robust stability properties. Next, we present one of\nthe characteristic applications of the ISS framework - the design of\nevent-based control schemes for the stabilization of nonlinear systems. In the\nsecond half of the paper, we focus on small-gain theorems for stability\nanalysis of finite and infinite networks with input-to-state stable components.\nFirst, we present a classical small-gain theorem in terms of trajectories for\nthe feedback interconnection of 2 nonlinear systems. Finally, a recent\nLyapunov-based small-gain result for a network with infinitely many ISS\ncomponents is shown.\n']","[('stability network', 0.5759137868881226), ('networks stability', 0.5645571351051331), ('stability infinite', 0.54417484998703), ('finite networks', 0.508283257484436), ('input state stability', 0.502670407295227), ('infinite network', 0.49481427669525146), ('networks infinite', 0.4919094145298004), ('infinite dimensional systems', 0.48003125190734863), ('lyapunov based', 0.47082510590553284), ('input output stability', 0.4621737599372864)]"
1896,1896,15,1896_quantum algorithms_quantum simulations_quantum simulation_simulation quantum,"['quantum algorithms', 'quantum simulations', 'quantum simulation', 'simulation quantum', 'quantum monte carlo', 'quantum monte', 'hamiltonian simulation', 'commutators', 'quantum systems', 'applications quantum']","['Suzuki Type Estimates for Exponentiated Sums and Generalized Lie-Trotter\n  Formulas in Banach Algebras   The Lie-Trotter formula has been a fundamental tool in quantum mechanics,\nquantum computing, and quantum simulations. The error estimations for the\nLie-Trotter product formula play a crucial role in achieving scalability and\ncomputational efficiency. In this note, we present two error estimates of\nLie-Trotter product formulas, utilizing Jordan product within Banach algebras.\nAdditionally, we introduce two generalized Lie-Trotter formula and provide two\nexplicit estimation formulas. Consequently, the renowned Suzuki symmetrized\napproximation for the exponentiated sums follows directly from our main\nTheorem.\n', 'Error Estimates and Higher Order Trotter Product Formulas in\n  Jordan-Banach Algebras   In quantum computing, Trotter estimates are critical for enabling efficient\nsimulation of quantum systems and quantum dynamics, help implement complex\nquantum algorithms, and provide a systematic way to control approximate errors.\nIn this paper, we extend the analysis of Trotter-Suzuki approximations,\nincluding third and higher orders, to Jordan-Banach algebras. We solve an open\nproblem in our earlier paper on the existence of second-order Trotter formula\nerror estimation in Jordan-Banach algebras. To illustrate our work, we apply\nour formula to simulate Trotter-factorized spins, and show improvements in the\napproximations. Our approach demonstrates the adaptability of Trotter product\nformulas and estimates to non-associative settings, which offers new insights\ninto the applications of Jordan algebra theory to operator dynamics.\n', 'Trotter error bounds and dynamic multi-product formulas for Hamiltonian\n  simulation   Multi-product formulas (MPF) are linear combinations of Trotter circuits\noffering high-quality simulation of Hamiltonian time evolution with fewer\nTrotter steps. Here we report two contributions aimed at making multi-product\nformulas more viable for near-term quantum simulations. First, we extend the\ntheory of Trotter error with commutator scaling developed by Childs, Su, Tran\net al. to multi-product formulas. Our result implies that multi-product\nformulas can achieve a quadratic reduction of Trotter error in 1-norm (nuclear\nnorm) on arbitrary time intervals compared with the regular product formulas\nwithout increasing the required circuit depth or qubit connectivity. The number\nof circuit repetitions grows only by a constant factor. Second, we introduce\ndynamic multi-product formulas with time-dependent coefficients chosen to\nminimize a certain efficiently computable proxy for the Trotter error. We use a\nminimax estimation method to make dynamic multi-product formulas robust to\nuncertainty from algorithmic errors, sampling and hardware noise. We call this\nmethod Minimax MPF and we provide a rigorous bound on its error.\n']","[('quantum algorithms', 0.5411906838417053), ('quantum simulations', 0.46434444189071655), ('quantum simulation', 0.4591327905654907), ('simulation quantum', 0.4523853063583374), ('quantum monte carlo', 0.43587300181388855), ('quantum monte', 0.42546868324279785), ('hamiltonian simulation', 0.42529189586639404), ('commutators', 0.39341309666633606), ('quantum systems', 0.3834659159183502), ('applications quantum', 0.38197192549705505)]"
1897,1897,15,1897_multilevel monte carlo_monte carlo methods_carlo methods_level monte carlo,"['multilevel monte carlo', 'monte carlo methods', 'carlo methods', 'level monte carlo', 'kinetic models', 'monte carlo', 'boltzmann transport', 'particle trajectories', 'kinetic equations', 'multilevel monte']","['A multilevel Monte Carlo method for asymptotic-preserving particle\n  schemes in the diffusive limit   Kinetic equations model distributions of particles in position-velocity phase\nspace. Often, one is interested in studying the long-time behavior of particles\nin high-collisional regimes in which an approximate (advection)-diffusion model\nholds. In this paper we consider the diffusive scaling. Classical\nparticle-based techniques suffer from a strict time-step restriction in this\nlimit, to maintain stability. Asymptotic-preserving schemes avoid this problem,\nbut introduce an additional time discretization error, possibly resulting in an\nunacceptably large bias for larger time steps. Here, we present and analyze a\nmultilevel Monte Carlo scheme that reduces this bias by combining estimates\nusing a hierarchy of different time step sizes. We demonstrate how to correlate\ntrajectories from this scheme, using different time steps. We also present a\nstrategy for selecting the levels in the multilevel scheme. Our approach\nsignificantly reduces the computation required to perform accurate simulations\nof the considered kinetic equations, compared to classical Monte Carlo\napproaches.\n', 'Uncertainty quantification for the BGK model of the Boltzmann equation\n  using multilevel variance reduced Monte Carlo methods   We propose a control variate multilevel Monte Carlo method for the kinetic\nBGK model of the Boltzmann equation subject to random inputs. The method\ncombines a multilevel Monte Carlo technique with the computation of the optimal\ncontrol variate multipliers derived from local or global variance minimization\nproblems. Consistency and convergence analysis for the method equipped with a\nsecond-order positivity-preserving and asymptotic-preserving scheme in space\nand time is also performed. Various numerical examples confirm that the\noptimized multilevel Monte Carlo method outperforms the classical multilevel\nMonte Carlo method especially for problems with discontinuities.\n', 'A Multilevel Monte Carlo Asymptotic-Preserving Particle Method for\n  Kinetic Equations in the Diffusion Limit   We propose a multilevel Monte Carlo method for a particle-based\nasymptotic-preserving scheme for kinetic equations. Kinetic equations model\ntransport and collision of particles in a position-velocity phase-space. With a\ndiffusive scaling, the kinetic equation converges to an advection-diffusion\nequation in the limit of zero mean free path. Classical particle-based\ntechniques suffer from a strict time-step restriction to maintain stability in\nthis limit. Asymptotic-preserving schemes provide a solution to this time step\nrestriction, but introduce a first-order error in the time step size. We\ndemonstrate how the multilevel Monte Carlo method can be used as a bias\nreduction technique to perform accurate simulations in the diffusive regime,\nwhile leveraging the reduced simulation cost given by the asymptotic-preserving\nscheme. We describe how to achieve the necessary correlation between simulation\npaths at different levels and demonstrate the potential of the approach via\nnumerical experiments.\n']","[('multilevel monte carlo', 0.6314797401428223), ('monte carlo methods', 0.57667475938797), ('carlo methods', 0.550129234790802), ('level monte carlo', 0.5046107769012451), ('kinetic models', 0.4777858555316925), ('monte carlo', 0.44057780504226685), ('boltzmann transport', 0.43547165393829346), ('particle trajectories', 0.42179930210113525), ('kinetic equations', 0.4124598801136017), ('multilevel monte', 0.3870351314544678)]"
1898,1898,15,1898_wigner functions_wigner distribution_quantum harmonic oscillator_wigner transform,"['wigner functions', 'wigner distribution', 'quantum harmonic oscillator', 'wigner transform', 'quantum harmonic', 'classical quantum systems', 'equations quantum', 'classical quantum', 'quantum analogue', 'wigner']","['Is the Moyal equation for the Wigner function a quantum analogue of the\n  Liouville equation?   The Moyal equation describes the evolution of the Wigner function of a\nquantum system in the phase space. The right-hand side of the equation contains\nan infinite series with coefficients proportional to powers of the Planck\nconstant. There is an interpretation of the Moyal equation as a quantum\nanalogue of the classical Liouville equation. Indeed, if one uses the notion of\nthe classical passage to the limit as the Planck constant tends to zero, then\nformally the right-hand side of the Moyal equation tends to zero. As a result,\nthe Moyal equation becomes the classical Liouville equation for the\ndistribution function. In this paper, we show that the right side of the Moyal\nequation does not explicitly depend on the Planck constant, and all terms of\nthe series can make a significant contribution. The transition between the\nclassical and quantum descriptions is related not to the Planck constant, but\nto the spatial scale.\n  For a model quantum system with a potential in the form of a\n{\\guillemotleft}quadratic funnel{\\guillemotright}, an exact 3D solution of the\nSchr\\""odinger equation is found and the corresponding Wigner function is\nconstructed in the paper. Using trajectory analysis in the phase space, based\non the representation of the right-hand side of the Moyal equation, it is shown\nthat on the spatial microscale there is an infinite number of\n{\\guillemotleft}trajectories{\\guillemotright} of the particle motion (thereby\nthe concept of a trajectory is indefinite), and when passing to the macroscale,\nall {\\guillemotleft}trajectories{\\guillemotright} concentrate around the\nclassical trajectory.\n', 'Wigner function properties for electromagnetic systems   Using the Wigner-Vlasov formalism, an exact 3D solution of the Schr\\""odinger\nequation for a scalar particle in an electromagnetic field is constructed.\nElectric and magnetic fields are non-uniform. According to the exact expression\nfor the wave function, the search for two types of the Wigner functions is\nconducted. The first function is the usual Wigner function with a modified\nmomentum. The second Wigner function is constructed on the basis of the\nWeyl-Stratonovich transform in papers [Phys. Rev. A 35 2791 (1987)] or [Phys.\nRev. B 99 014423 (2019)]. It turns out that the second function, unlike the\nfirst one, has areas of negative values for wave functions with the Gaussian\ndistribution (Hudson\'s theorem). An example of electromagnetic quantum system\ndescribed by a non-Gaussian wave function has successfully been found. The\nsecond Wigner function is positive over the whole phase space for the\nnon-Gaussian wave function. This result is analogous to the Hudson theorem for\nthe gage-invariant Wigner function.\n  On the one hand, knowing the Wigner functions allows one to find the\ndistribution of the mean momentum vector field and the energy spectrum of the\nquantum system. On the other hand, within the framework of the Wigner-Vlasov\nformalism, the mean momentum distribution and the magnitude of the energy are\ninitially known. Consequently, the mean momentum distributions and energy\nvalues obtained according to the Wigner functions can be compared with the\nexact momentum distribution and energy values. This paper presents this\ncomparison and describes the differences. The Vlasov-Moyal approximation of\naverage acceleration flow has been built in phase space for a quantum system\nwith electromagnetic field. The obtained approximation makes it possible to cut\nthe Vlasov chain off at the second equation and also to analyze the Boltzmann\nH-function evolution.\n', 'The Wigner-Vlasov formalism for time-dependent quantum oscillator   This paper presents a comprehensive investigation of the problem of a\nharmonic oscillator with time-depending frequencies in the framework of the\nVlasov theory and the Wigner function apparatus for quantum systems in the\nphase space. A new method is proposed to find an exact solution of this problem\nusing a relation of the Vlasov equation chain with the Schr\\""odinger equation\nand with the Moyal equation for the Wigner function. A method of averaging the\nenergy function over the Wigner function in the phase space can be used to\nobtain time-dependent energy spectrum for a quantum system. The Vlasov equation\nsolution can be represented in the form of characteristics satisfying the Hill\nequation. A particular case of the Hill equation, namely the Mathieu equation\nwith unstable solutions, has been considered in details. An analysis of the\ndynamics of an unstable quantum system shows that the phase space square\nbounded with the Wigner function level line conserves in time, but the phase\nspace square bounded with the energy function line increases. In this case the\nVlasov equation characteristic is situated on the crosspoint of the Wigner\nfunction level line and the energy function line. This crosspoint moves in time\nwith a trajectory that represents the unstable system dynamics. Each such\ntrajectory has its own energy, and averaging these energies over the Wigner\nfunction results in time-dependent discreet energy spectrum for the whole\nsystem. An explicit expression has been obtained for the Wigner function of the\n4th rank in the generalized phase space $\\left\\{ x,p,\\dot{p},\\ddot{p}\n\\right\\}.$\n']","[('wigner functions', 0.7029975056648254), ('wigner distribution', 0.6050454378128052), ('quantum harmonic oscillator', 0.5898581743240356), ('wigner transform', 0.5775933861732483), ('quantum harmonic', 0.5455856919288635), ('classical quantum systems', 0.5022653341293335), ('equations quantum', 0.49736160039901733), ('classical quantum', 0.49681293964385986), ('quantum analogue', 0.48524370789527893), ('wigner', 0.47809821367263794)]"
1899,1899,15,1899_dimensional standard brownian_dimensional gaussian process_brownian motions_planar brownian,"['dimensional standard brownian', 'dimensional gaussian process', 'brownian motions', 'planar brownian', 'brownian motion independent', 'gaussian process', 'standard brownian', 'standard brownian motion', 'brownian motion', 'brownian']","['Hausdorff and Fourier dimension of graph of continuous additive\n  processes   An additive process is a stochastic process with independent increments and\nthat is continuous in probability. In this paper, we study the almost sure\nHausdorff and Fourier dimension of the graph of continuous additive additive\nprocesses with zero mean. Such processes can be represented as $X_t = B_{V(t)}$\nwhere $B$ is Brownian motion and $V$ is a continuous increasing function. We\nshow that these dimensions depend on the local uniform H\\""{o}lder indices. In\nparticular, if $V$ is locally uniformly bi-Lipschitz, then the Hausdorff\ndimension of the graph will be 3/2. We also show that the Fourier dimension\nalmost surely is positive if $V$ admits at least one point with positive lower\nH\\""{o}lder regularity.\n  It is also possible to estimate the Hausdorff dimension of the graph through\nthe $L^q$ spectrum of $V$. We will show that if $V$ is generated by a\nself-similar measure on ${\\mathbb R}^{1}$ with convex open set condition, the\nHausdorff dimension of the graph can be precisely computed by its $L^q$\nspectrum. An illustrating example of the Cantor Devil Staircase function, the\nHausdorff dimension of the graph is $1+\\frac12\\cdot\\frac{\\log 2}{\\log 3}$.\nMoreover, we will show that the graph of the Brownian staircase surprisingly\nhas Fourier dimension zero almost surely.\n', ""Extensions of Bougerol's identity in law and the associated anticipative\n  path transformations   Let $B=\\{ B_{t}\\} _{t\\ge 0}$ be a one-dimensional standard Brownian motion\nand denote by $A_{t},\\,t\\ge 0$, the quadratic variation of the geometric\nBrownian motion $e^{B_{t}},\\,t\\ge 0$. Bougerol's celebrated identity (1983)\nasserts that, if $\\beta =\\{ \\beta (t)\\} _{t\\ge 0}$ is another Brownian motion\nindependent of $B$, then $\\beta (A_{t})$ is identical in law with $\\sinh B_{t}$\nfor every fixed $t>0$. In this paper, we extend Bougerol's identity to an\nidentity in law for processes up to time $t$, which exhibits a certain\ninvariance of the law of Brownian motion. The extension is described in terms\nof anticipative transforms of $B$ involving $A_{t}$ as an anticipating factor.\nA Girsanov-type formula for those transforms is shown. An extension of a\nvariant of Bougerol's identity is also presented.\n"", 'Irregularity scales for Gaussian processes: Hausdorff dimensions and\n  hitting probabilities   Let $X$ be a $d$-dimensional Gaussian process in $[0,1]$, where the component\nare independent copies of a scalar Gaussian process $X_0$ on $[0,1]$ with a\ngiven general variance function\n$\\gamma^2(r)=\\operatorname{Var}\\left(X_0(r)\\right)$ and a canonical metric\n$\\delta(t,s):=(\\mathbb{E}\\left(X_0(t)-X_0(s)\\right)^2)^{1/2}$ which is\ncommensurate with $\\gamma(t-s)$. Under a weak regularity condition on $\\gamma$,\nreferred to below as $\\mathbf{(C_{0+})}$, which allows $\\gamma$ to be far from\nH\\""older-continuous, we prove that for any Borel set $E\\subset [0,1]$, the\nHausdorff dimension of the image $X(E)$ and of the graph $Gr_E(X)$ are constant\nalmost surely. Furthermore, we show that these constants can be explicitly\nexpressed in terms of $\\dim_{\\delta}(E)$ and $d$. However, when\n$\\mathbf{(C_{0+})}$ is not satisfied, the classical methods may yield different\nupper and lower bounds for the underlying Hausdorff dimensions. This case is\nillustrated via a class of highly irregular processes known as logBm. Even in\nsuch cases, we employ a new method to establish that the Hausdorff dimensions\nof $X(E)$ and $Gr_E(X)$ are almost surely constant. The method uses the\nKarhunen-Lo\\`eve expansion of $X$ to prove that these Hausdorff dimensions are\nmeasurable with respect to the expansion\'s tail sigma-field. Under similarly\nmild conditions on $\\gamma$, we derive upper and lower bounds on the\nprobability that the process $X$ can reach the Borel set $F$ in $\\mathbb{R}^d$\nfrom the Borel set $E$ in $[0,1]$. These bounds are obtained by considering the\nHausdorff measure and the Bessel-Riesz capacity of $E\\times F$ in an\nappropriate metric $\\rho_{\\delta}$ on the product space, relative to\nappropriate orders. Moreover, we demonstrate that the dimension $d$ plays a\ncritical role in determining whether $X\\lvert_E$ hits $F$ or not.\n']","[('dimensional standard brownian', 0.5413936972618103), ('dimensional gaussian process', 0.5300846099853516), ('brownian motions', 0.4994995892047882), ('planar brownian', 0.49512892961502075), ('brownian motion independent', 0.4700795114040375), ('gaussian process', 0.44024261832237244), ('standard brownian', 0.4393186867237091), ('standard brownian motion', 0.42713451385498047), ('brownian motion', 0.4160178601741791), ('brownian', 0.4141608774662018)]"
1900,1900,15,1900_distribution stein_stein operator_stein normal_via stein,"['distribution stein', 'stein operator', 'stein normal', 'via stein', 'stein', 'asymptotic distribution statistics', 'normal approximation', 'approximation probability distribution', 'laplace approximation', 'bound kolmogorov distance']","[""Stein's method of normal approximation: Some recollections and\n  reflections   This paper is a short exposition of Stein's method of normal approximation\nfrom my personal perspective. It focuses mainly on the characterization of the\nnormal distribution and the construction of Stein identities. Through examples,\nit provides glimpses into the many approaches to constructing Stein identities\nand the diverse applications of Stein's method to mathematical problems. It\nalso includes anecdotes of historical interest, including how Stein discovered\nhis method and how I found an unpublished proof of his of the Berry-Esseen\ntheorem.\n"", ""An asymptotic approach to proving sufficiency of Stein characterisations   In extending Stein's method to new target distributions, the first step is to\nfind a Stein operator that suitably characterises the target distribution. In\nthis paper, we introduce a widely applicable technique for proving sufficiency\nof these Stein characterisations, which can be applied when the Stein operators\nare linear differential operators with polynomial coefficients. The approach\ninvolves performing an asymptotic analysis to prove that only one\ncharacteristic function satisfies a certain differential equation associated to\nthe Stein characterisation. We use this approach to prove that all Stein\noperators with linear coefficients characterise their target distribution, and\nverify on a case-by-case basis that all polynomial Stein operators in the\nliterature with coefficients of degree at most two are characterising. For $X$\ndenoting a standard Gaussian random variable and $H_p$ the $p$-th Hermite\npolynomial, we also prove, amongst other examples, that the Stein operators for\n$H_p(X)$, $p=3,4,\\ldots,8$, with coefficients of minimal possible degree\ncharacterise their target distribution, and that the Stein operators for the\nproducts of $p=3,4,\\ldots,8$ independent standard Gaussian random variables are\ncharacterising (in both settings the Stein operators for the cases $p=1,2$ are\nalready known to be characterising). We leverage our Stein characterisations of\n$H_3(X)$ and $H_4(X)$ to derive characterisations of these target distributions\nin terms of iterated Gamma operators from Malliavin calculus, that are natural\nin the context of the Malliavin-Stein method.\n"", ""Edgeworth Expansion by Stein's Method   Edgeworth expansion provides higher-order corrections to the normal\napproximation for a probability distribution. The classical proof of Edgeworth\nexpansion is via characteristic functions. As a powerful method for\ndistributional approximations, Stein's method has also been used to prove\nEdgeworth expansion results. However, these results assume that either the test\nfunction is smooth (which excludes indicator functions of the half line) or\nthat the random variables are continuous (which excludes random variables\nhaving only a continuous component). Thus, how to recover the classical\nEdgeworth expansion result using Stein's method has remained an open problem.\nIn this paper, we develop Stein's method for two-term Edgeworth expansions in a\ngeneral case. Our approach involves repeated use of Stein equations, Stein\nidentities via Stein kernels, and a replacement argument.\n""]","[('distribution stein', 0.6616148948669434), ('stein operator', 0.5789815783500671), ('stein normal', 0.5646209120750427), ('via stein', 0.5525602698326111), ('stein', 0.5170912146568298), ('asymptotic distribution statistics', 0.4085545241832733), ('normal approximation', 0.39546942710876465), ('approximation probability distribution', 0.3923887610435486), ('laplace approximation', 0.38392481207847595), ('bound kolmogorov distance', 0.3795824646949768)]"
1901,1901,15,1901_finite volume discretization_volume discretization_water flow_meshless methods,"['finite volume discretization', 'volume discretization', 'water flow', 'meshless methods', 'linearization methods', 'hydraulic conductivity', 'numerical techniques', 'flow porous media', 'flow porous', 'proposed numerical']","[""Modeling of unsaturated flow through porous media using meshless methods   In this study, we focus on the modelling of infiltration process in porous\nmedia. We use the meshless techniques for efficiently solving the Richards\nequation which describes unsaturated water flow through soils. The design of\napproximate numerical methods for the Richards equation remains computationally\nchallenging and requires the development of efficient numerical techniques.\nThis difficulty is mainly due to the nonlinearity of the unsaturated hydraulic\nconductivity and the capillary pressure function. In this study, we develop a\nnew method based on the localized radial basis function (RBF) and the Kirchhoff\ntransformation technique in order to solve Richards equation in one and\ntwo-dimensional homogeneous medium. Our approach using the multiquadric radial\nbasis function allows us to reduce the computational time and provide accurate\nnumerical solutions. The proposed method does not require mesh generation.\nPicard's iterations are used to linearize the resulting nonlinear problem\nobtained using the Kirchhoff transformation technique. The numerical\nsimulations show the capability of the proposed numerical techniques in\npredicting the dynamics of water through unsaturated soils.\n"", 'LRBF meshless methods for predicting soil moisture distribution in root\n  zone   In this paper, we first propose a coupled numerical model of unsaturated flow\nin soils and plant root water uptake. The Richards equation and different\nformulations are used in the developed numerical model to describe infiltration\nin root zone and to investigate the impact of the plant root on the\ndistribution of soil moisture. The Kirchhoff transformed Richards equation is\nused and the Gardner model is considered for capillary pressure. In our\napproach, we employ a meshless method based on localized radial basis functions\n(LRBF) to solve the resulting system of equations. The LRBF approach is an\naccurate and computationally efficient method that does not require mesh\ngeneration and is flexible in addressing high-dimensional problems with complex\ngeometries. Furthermore, this method leads to a sparse matrix system, which\navoids ill-conditioning issues. We implement the coupled numerical model of\ninfiltration and plant root water uptake for one, two, and three-dimensional\nsoils. Numerical experiments are performed using nontrivial analytical\nsolutions and available experimental data to validate the coupled numerical\nmodel. The numerical results demonstrate the performance and ability of the\nproposed numerical method to predict soil moisture dynamics in root zone.\n', 'Implicit EXP-RBF techniques for modeling unsaturated flow through soils\n  with water uptake by plant roots   Modeling unsaturated flow through soils with water uptake by plan root has\nmany applications in agriculture and water resources management. In this study,\nour aim is to develop efficient numerical techniques for solving the Richards\nequation with a sink term due to plant root water uptake. The Feddes model is\nused for water absorption by plant roots, and the van-Genuchten model is\nemployed for capillary pressure. We introduce a numerical approach that\ncombines the localized exponential radial basis function (EXP-RBF) method for\nspace and the second-order backward differentiation formula (BDF2) for temporal\ndiscretization. The localized RBF methods eliminate the need for mesh\ngeneration and avoid ill-conditioning problems. This approach yields a sparse\nmatrix for the global system, optimizing memory usage and computational time.\nThe proposed implicit EXP-RBF techniques have advantages in terms of accuracy\nand computational efficiency thanks to the use of BDF2 and the localized RBF\nmethod. Modified Picards iteration method for the mixed form of the Richards\nequation is employed to linearize the system. Various numerical experiments are\nconducted to validate the proposed numerical model of infiltration with plant\nroot water absorption. The obtained results conclusively demonstrate the\neffectiveness of the proposed numerical model in accurately predicting soil\nmoisture dynamics under water uptake by plant roots. The proposed numerical\ntechniques can be incorporated in the numerical models where unsaturated flows\nand water uptake by plant roots are involved such as in hydrology, agriculture,\nand water management.\n']","[('finite volume discretization', 0.42972031235694885), ('volume discretization', 0.41082268953323364), ('water flow', 0.4042103588581085), ('meshless methods', 0.3962843120098114), ('linearization methods', 0.39346057176589966), ('hydraulic conductivity', 0.39278972148895264), ('numerical techniques', 0.38125064969062805), ('flow porous media', 0.3645741045475006), ('flow porous', 0.3508395254611969), ('proposed numerical', 0.33848410844802856)]"
1902,1902,15,1902_integer matrices_integer matrix_constraint matrices_constraint matrix,"['integer matrices', 'integer matrix', 'constraint matrices', 'constraint matrix', 'integer programming', 'integer programs', 'dimensional knapsack', 'unimodular matrices', 'unimodular matrix', 'integer linear']","['Integer programs with nearly totally unimodular matrices: the cographic\n  case   It is a notorious open question whether integer programs (IPs), with an\ninteger coefficient matrix $M$ whose subdeterminants are all bounded by a\nconstant $\\Delta$ in absolute value, can be solved in polynomial time. We\nanswer this question in the affirmative if we further require that, by removing\na constant number of rows and columns from $M$, one obtains a submatrix $A$\nthat is the transpose of a network matrix.\n  Our approach focuses on the case where $A$ arises from $M$ after removing $k$\nrows only, where $k$ is a constant. We achieve our result in two main steps,\nthe first related to the theory of IPs and the second related to graph minor\ntheory.\n  First, we derive a strong proximity result for the case where $A$ is a\ngeneral totally unimodular matrix: Given an optimal solution of the linear\nprogramming relaxation, an optimal solution to the IP can be obtained by\nfinding a constant number of augmentations by circuits of $[A\\; I]$.\n  Second, for the case where $A$ is transpose of a network matrix, we\nreformulate the problem as a maximum constrained integer potential problem on a\ngraph $G$. We observe that if $G$ is $2$-connected, then it has no rooted\n$K_{2,t}$-minor for $t = \\Omega(k \\Delta)$. We leverage this to obtain a\ntree-decomposition of $G$ into highly structured graphs for which we can solve\nthe problem locally. This allows us to solve the global problem via dynamic\nprogramming.\n', 'Congruency-Constrained TU Problems Beyond the Bimodular Case   A long-standing open question in Integer Programming is whether integer\nprograms with constraint matrices with bounded subdeterminants are efficiently\nsolvable. An important special case thereof are congruency-constrained integer\nprograms $\\min\\{c^\\top x\\colon\\ Tx\\leq b,\\ \\gamma^\\top x\\equiv r\\pmod{m},\\\nx\\in\\mathbb{Z}^n\\}$ with a totally unimodular constraint matrix $T$. Such\nproblems have been shown to be polynomial-time solvable for $m=2$, which led to\nan efficient algorithm for integer programs with bimodular constraint matrices,\ni.e., full-rank matrices whose $n\\times n$ subdeterminants are bounded by two\nin absolute value. Whereas these advances heavily relied on existing results on\nwell-known combinatorial problems with parity constraints, new approaches are\nneeded beyond the bimodular case, i.e., for $m>2$. We make first progress in\nthis direction through several new techniques. In particular, we show how to\nefficiently decide feasibility of congruency-constrained integer programs with\na totally unimodular constraint matrix for $m=3$. Furthermore, for general $m$,\nour techniques also allow for identifying flat directions of infeasible\nproblems, and deducing bounds on the proximity between solutions of the problem\nand its relaxation.\n', ""Polynomial upper bounds on the number of differing columns of\n  $\\Delta$-modular integer programs   We study integer-valued matrices with bounded determinants. Such matrices\nappear in the theory of integer programs (IP) with bounded determinants. For\nexample, Artmann et al. showed that an IP can be solved in strongly polynomial\ntime if the constraint matrix is bimodular, that is, the determinants are\nbounded in absolute value by two. Determinants are also used to bound the\n$\\ell_1$-distance between IP solutions and solutions of its linear relaxation.\nOne of the first works to quantify the complexity of IPs with bounded\ndeterminants was that of Heller, who identified the maximum number of differing\ncolumns in a totally unimodular matrix. Each extension of Heller's bound to\ngeneral determinants has been super-polynomial in the determinants or the\nnumber of equations. We provide the first column bound that is polynomial in\nboth values. For integer programs with box constraints, our result gives the\nfirst $\\ell_1$-distance bound that is polynomial in the determinants and the\nnumber of equations. Our result can also be used to derive a bound on the\nheight of Graver basis elements that is polynomial in the determinants and the\nnumber of equations. Furthermore, we show a tight bound on the number of\ndiffering columns in a bimodular matrix; this is the first tight bound since\nHeller. Our analysis reveals combinatorial properties of bimodular IPs that may\nbe of independent interest.\n""]","[('integer matrices', 0.5811855792999268), ('integer matrix', 0.5543756484985352), ('constraint matrices', 0.5543084144592285), ('constraint matrix', 0.48272866010665894), ('integer programming', 0.4790968596935272), ('integer programs', 0.46564769744873047), ('dimensional knapsack', 0.43034207820892334), ('unimodular matrices', 0.4241587519645691), ('unimodular matrix', 0.4163268506526947), ('integer linear', 0.39023879170417786)]"
1903,1903,15,1903_skein module_skein theory_kauffman bracket_knot theory,"['skein module', 'skein theory', 'kauffman bracket', 'knot theory', 'knot polynomials', 'skein', 'type skein', 'twisted bundle', 'mathcal torsion', 'incompressible tori']","['Kauffman bracket skein module of the $(3,3,3,3)$-pretzel link exterior   We show that the Kauffman bracket skein module of the $(3,3,3,3)$-pretzel\nlink exterior over $\\mathbb{Q}(q^{\\frac{1}{2}})$ is not finitely generated as a\nmodule over $\\mathbb{Q}(q^{\\frac{1}{2}})[t_1,t_2]$, where $t_1,t_2$ are the\nmeridians of two components. This disproves a finiteness conjecture proposed in\n2021.\n', 'Kauffman Bracket Skein Module of the Connected Sum of Handlebodies: A\n  Counterexample   In this paper we disprove a twenty-two year old theorem about the structure\nof the Kauffman bracket skein module of the connected sum of two handlebodies.\nWe achieve this by analysing handle slidings on compressing discs in a\nhandlebody. We find more relations than previously predicted for the Kauffman\nbracket skein module of the connected sum of handlebodies, when one of them is\nnot a solid torus. Additionally, we speculate on the structure of the Kauffman\nbracket skein module of the connected sum of two solid tori.\n', 'On the Kauffman bracket skein module of $(S^1 \\times S^2) \\ \\# \\ (S^1\n  \\times S^2)$   Determining the structure of the Kauffman bracket skein module of all\n$3$-manifolds over the ring of Laurent polynomials $\\mathbb Z[A^{\\pm 1}]$ is a\nbig open problem in skein theory. Very little is known about the skein module\nof non-prime manifolds over this ring. In this paper, we compute the Kauffman\nbracket skein module of the $3$-manifold $(S^1 \\times S^2) \\ \\# \\ (S^1 \\times\nS^2)$ over the ring $\\mathbb Z[A^{\\pm 1}]$. We do this by analysing the\nsubmodule of handle sliding relations, for which we provide a suitable basis.\nAlong the way we compute the Kauffman bracket skein module of $(S^1 \\times S^2)\n\\ \\# \\ (S^1 \\times D^2)$. We also show that the skein module of $(S^1 \\times\nS^2) \\ \\# \\ (S^1 \\times S^2)$ does not split into the sum of free and torsion\nsubmodules. Furthermore, we illustrate two families of torsion elements in this\nskein module.\n']","[('skein module', 0.5924373269081116), ('skein theory', 0.5676805973052979), ('kauffman bracket', 0.5405994653701782), ('knot theory', 0.5010882019996643), ('knot polynomials', 0.48946261405944824), ('skein', 0.45259371399879456), ('type skein', 0.44572213292121887), ('twisted bundle', 0.3921147882938385), ('mathcal torsion', 0.3842388093471527), ('incompressible tori', 0.3780665993690491)]"
1904,1904,15,1904_berry esseen bound_products random matrices_berry esseen bounds_independent random matrices,"['berry esseen bound', 'products random matrices', 'berry esseen bounds', 'independent random matrices', 'random matrices', 'random matrices let', 'convergence central limit', 'stochastic exponentials', 'esseen bound', 'spectral radius rho']","['Edgeworth expansion and large deviations for the coefficients of\n  products of positive random matrices   Consider the matrix products $G_n: = g_n \\ldots g_1$, where $(g_{n})_{n\\geq\n1}$ is a sequence of independent and identically distributed positive random\n$d\\times d$ matrices. Under the optimal third moment condition, we first\nestablish a Berry-Esseen theorem and an Edgeworth expansion for the $(i,j)$-th\nentry $G_n^{i,j}$ of the matrix $G_n$, where $1 \\leq i, j \\leq d$. Using the\nEdgeworth expansion for $G_n^{i,j}$ under the changed probability measure, we\nthen prove precise upper and lower large deviation asymptotics for the entries\n$G_n^{i,j}$ subject to an exponential moment assumption. As applications, we\ndeduce local limit theorems with large deviations for $G_n^{i,j}$ and upper and\nlower large deviations bounds for the spectral radius $\\rho(G_n)$ of $G_n$. A\nbyproduct of our approach is the local limit theorem for $G_n^{i,j}$ under the\noptimal second moment condition. In the proofs we develop a spectral gap theory\nfor the norm cocycle and for the coefficients, which is of independent\ninterest.\n', ""Berry-Esseen bounds and moderate deviations for the norm, entries and\n  spectral radius of products of positive random matrices   Let $(g_{n})_{n\\geq 1}$ be a sequence of independent and identically\ndistributed positive random $d\\times d$ matrices and consider the matrix\nproduct $G_n: = g_n \\ldots g_1$. Under suitable conditions, we establish the\nBerry-Esseen bounds on the rate of convergence in the central limit theorem and\nmoderate deviation expansions of Cram\\'er type, for the matrix norm $\\| G_n \\|$\nof $G_n$, for its $(i,j)$-th entry $G_n^{i,j}$, and the and for its spectral\nradius $\\rho(G_n)$.\n"", ""Berry-Esseen bound and precise moderate deviations for products of\n  random matrices   Let $(g_{n})_{n\\geq 1}$ be a sequence of independent and identically\ndistributed (i.i.d.) $d\\times d$ real random matrices. For $n\\geq 1$ set $G_n =\ng_n \\ldots g_1$. Given any starting point $x=\\mathbb R v\\in\\mathbb{P}^{d-1}$,\nconsider the Markov chain $X_n^x = \\mathbb R G_n v $ on the projective space\n$\\mathbb P^{d-1}$ and the norm cocycle $\\sigma(G_n, x)= \\log \\frac{|G_n\nv|}{|v|}$, for an arbitrary norm $|\\cdot|$ on $\\mathbb R^{d}$. Under suitable\nconditions we prove a Berry-Esseen type theorem and an Edgeworth expansion for\nthe couple $(X_n^x, \\sigma(G_n, x))$. These results are established using a\nbrand new smoothing inequality on complex plane, the saddle point method and\nadditional spectral gap properties of the transfer operator related to the\nMarkov chain $X_n^x$. Cram\\'{e}r type moderate deviation expansions as well as\na local limit theorem with moderate deviations are proved for the couple\n$(X_n^x, \\sigma(G_n, x))$ with a target function $\\varphi$ on the Markov chain\n$X_n^x$.\n""]","[('berry esseen bound', 0.4899292290210724), ('products random matrices', 0.48020702600479126), ('berry esseen bounds', 0.4671557545661926), ('independent random matrices', 0.4365309774875641), ('random matrices', 0.4210229516029358), ('random matrices let', 0.4084279239177704), ('convergence central limit', 0.38615429401397705), ('stochastic exponentials', 0.35589951276779175), ('esseen bound', 0.34401005506515503), ('spectral radius rho', 0.31459757685661316)]"
1905,1905,15,1905_nonsmooth optimization_semismooth newton_nonsmooth nonconvex optimization_newton methods,"['nonsmooth optimization', 'semismooth newton', 'nonsmooth nonconvex optimization', 'newton methods', 'generalized newton', 'convex composite optimization', 'solving nonsmooth', 'local superlinear convergence', 'semismooth', 'composite optimization']","['On a globally convergent semismooth* Newton method in nonsmooth\n  nonconvex optimization   In this paper we present GSSN, a globalized SCD semismooth* Newton method for\nsolving nonsmooth nonconvex optimization problems. The global convergence\nproperties of the method are ensured by the proximal gradient method, whereas\nlocally superlinear convergence is established via the SCD semismooth* Newton\nmethod under quite weak assumptions. The Newton direction is based on the SC\n(subspace containing) derivative of the subdifferential mapping and can be\ncomputed by the (approximate) solution of an equality-constrained quadratic\nprogram. Special attention is given to the efficient numerical implementation\nof the overall method.\n', 'Two Typical Implementable Semismooth* Newton Methods for Generalized\n  Equations are G-Semismooth Newton Methods   Semismooth* Newton methods have been proposed in recent years targeting\nmulti-valued inclusion problems and have been successfully implemented to deal\nwith several concrete generalized equations. In this paper, we show that two\ntypical implementations of them that are available are exactly the applications\nof G-semismooth Newton methods for solving nonsmooth equations localized from\nthese generalized equations. This new understanding expands the breadth of\nG-semismooth Newton methods in theory, results in a few interesting problems\nregarding the two categories of nonsmooth Newton methods, and more importantly,\nprovides informative observations in facilitating the design and implementation\nof practical Newton-type algorithms for solving generalized equations.\n', 'On the application of the semismooth* Newton method to variational\n  inequalities of the second kind   The paper starts with a concise description of the recently developed\nsemismooth* Newton method for the solution of general inclusions. This method\nis then applied to a class of variational inequalities of the second kind. As a\nresult, one obtains an implementable algorithm exhibiting a local superlinear\nconvergence. Thereafter we suggest several globally convergent hybrid\nalgorithms in which one combines the semismooth* Newton method with selected\nsplitting algorithms for the solution of monotone variational inequalities.\nTheir efficiency is documented by extensive numerical experiments.\n']","[('nonsmooth optimization', 0.6122443079948425), ('semismooth newton', 0.5951319932937622), ('nonsmooth nonconvex optimization', 0.5805391073226929), ('newton methods', 0.5512623190879822), ('generalized newton', 0.5190454125404358), ('convex composite optimization', 0.5159761309623718), ('solving nonsmooth', 0.468085378408432), ('local superlinear convergence', 0.45332029461860657), ('semismooth', 0.4484783709049225), ('composite optimization', 0.43770527839660645)]"
1906,1906,15,1906_minimal surfaces_minimal surface_minimal immersions_compact riemann surface,"['minimal surfaces', 'minimal surface', 'minimal immersions', 'compact riemann surface', 'riemann surface', 'open riemann surface', 'finite total curvature', 'space conformal', 'surfaces finite total', 'riemann surface mathbb']","['A strong parametric h-principle for complete minimal surfaces   We prove a parametric h-principle for complete nonflat conformal minimal\nimmersions of an open Riemann surface $M$ into $\\mathbb R^n$, $n\\geq 3$. It\nfollows that the inclusion of the space of such immersions into the space of\nall nonflat conformal minimal immersions is a weak homotopy equivalence. When\n$M$ is of finite topological type, the inclusion is a genuine homotopy\nequivalence. By a parametric h-principle due to Forstneric and Larusson, the\nspace of complete nonflat conformal minimal immersions therefore has the same\nhomotopy type as the space of continuous maps from $M$ to the punctured null\nquadric. Analogous results hold for holomorphic null curves $M\\to\\mathbb C^n$\nand for full immersions in place of nonflat ones.\n', 'Every nonflat conformal minimal surface is homotopic to a proper one Given an open Riemann surface $M$, we prove that every nonflat conformal minimal immersion $M\\to\\mathbb{R}^n$ ($n\\geq 3$) is homotopic through nonflat conformal minimal immersions $M\\to\\mathbb{R}^n$ to a proper one. If $n\\geq 5$, it may be chosen in addition injective, hence a proper conformal minimal embedding. Prescribing its flux, as a consequence, every nonflat conformal minimal immersion $M\\to\\mathbb{R}^n$ is homotopic to the real part of a proper holomorphic null embedding $M\\to\\mathbb{C}^n$. We also obtain a result for a more general family of holomorphic immersions from an open Riemann surface into $\\mathbb{C}^n$ directed by Oka cones in $\\mathbb{C}^n$.', ""The parametric h-principle for minimal surfaces in $\\mathbb R^n$ and\n  null curves in $\\mathbb C^n$   Let $M$ be an open Riemann surface. It was proved by Alarc\\'on and\nForstneri\\v{c} (arXiv:1408.5315) that every conformal minimal immersion\n$M\\to\\mathbb R^3$ is isotopic to the real part of a holomorphic null curve\n$M\\to\\mathbb C^3$. In this paper, we prove the following much stronger result\nin this direction: for any $n\\geq 3$, the inclusion $\\iota$ of the space of\nreal parts of nonflat null holomorphic immersions $M\\to\\mathbb C^n$ into the\nspace of nonflat conformal minimal immersions $M\\to \\mathbb R^n$ satisfies the\nparametric h-principle with approximation; in particular, it is a weak homotopy\nequivalence. We prove analogous results for several other related maps, and we\ndescribe the homotopy type of the space of all holomorphic immersions\n$M\\to\\mathbb C^n$. For an open Riemann surface $M$ of finite topological type,\nwe obtain optimal results by showing that $\\iota$ and several related maps are\ninclusions of strong deformation retracts; in particular, they are homotopy\nequivalences.\n""]","[('minimal surfaces', 0.5838956832885742), ('minimal surface', 0.5562975406646729), ('minimal immersions', 0.5453838109970093), ('compact riemann surface', 0.49207013845443726), ('riemann surface', 0.4800945520401001), ('open riemann surface', 0.4505111873149872), ('finite total curvature', 0.4484088718891144), ('space conformal', 0.4325776696205139), ('surfaces finite total', 0.42951613664627075), ('riemann surface mathbb', 0.4106893241405487)]"
1907,1907,15,1907_cellular networks_cellular network_coordinated beamforming_minimize total power,"['cellular networks', 'cellular network', 'coordinated beamforming', 'minimize total power', 'efficient optimization', 'radio access network', 'joint beamforming', 'standard cellular', 'cloud radio access', 'outage constrained']","['A Theoretical Performance Bound for Joint Beamformer Design of Wireless\n  Fronthaul and Access Links in Downlink C-RAN   It is known that data rates in standard cellular networks are limited due to\ninter-cell interference. An effective solution of this problem is to use the\nmulti-cell cooperation idea. In Cloud Radio Access Network (C-RAN), which is a\ncandidate solution in 5G and future communication networks, cooperation is\napplied by means of central processors (CPs) connected to simple remote radio\nheads with finite capacity fronthaul links. In this study, we consider a\ndownlink C-RAN with a wireless fronthaul and aim to minimize total power spent\nby jointly designing beamformers for fronthaul and access links. We consider\nthe case where perfect channel state information is not available in the CP. We\nfirst derive a novel theoretical performance bound for the problem defined.\nThen we propose four algorithms with different complexities to show the\ntightness of the bound. The first two algorithms apply successive convex\noptimizations with semi-definite relaxation idea where other two are adapted\nfrom well-known beamforming design methods. The detailed simulations under\nrealistic channel conditions show that as the complexity of the algorithm\nincreases, the corresponding performance becomes closer to the bound.\n', ""QoS-based Beamforming and Compression Design for Cooperative Cellular\n  Networks via Lagrangian Duality   This paper considers the quality-of-service (QoS)-based joint beamforming and\ncompression design problem in the downlink cooperative cellular network, where\nmultiple relay-like base stations (BSs), connected to the central processor via\nrate-limited fronthaul links, cooperatively transmit messages to the users. The\nproblem of interest is formulated as the minimization of the total transmit\npower of the BSs, subject to all users' signal-to-interference-plus-noise ratio\n(SINR) constraints and all BSs' fronthaul rate constraints. In this paper, we\nfirst show that there is no duality gap between the considered joint\noptimization problem and its Lagrangian dual by showing the tightness of its\nsemidefinite relaxation (SDR). Then, we propose an efficient algorithm based on\nthe above duality result for solving the considered problem. The proposed\nalgorithm judiciously exploits the special structure of an enhanced\nKarush-Kuhn-Tucker (KKT) conditions of the considered problem and finds the\nsolution that satisfies the enhanced KKT conditions via two fixed point\niterations. Two key features of the proposed algorithm are: (1) it is able to\ndetect whether the considered problem is feasible or not and find its globally\noptimal solution when it is feasible; (2) it is highly efficient because both\nof the fixed point iterations in the proposed algorithm are linearly convergent\nand evaluating the functions in the fixed point iterations are computationally\ncheap. Numerical results show the global optimality and efficiency of the\nproposed algorithm.\n"", ""Efficiently and Globally Solving Joint Beamforming and Compression\n  Problem in the Cooperative Cellular Network via Lagrangian Duality   Consider the joint beamforming and quantization problem in the cooperative\ncellular network, where multiple relay-like base stations (BSs) connected to\nthe central processor (CP) via rate-limited fronthaul links cooperatively serve\nthe users. This problem can be formulated as the minimization of the total\ntransmit power, subject to all users' signal-to-interference-plus-noise-ratio\n(SINR) constraints and all relay-like BSs' fronthaul rate constraints. In this\npaper, we first show that there is no duality gap between the considered\nproblem and its Lagrangian dual by showing the tightness of the semidefinite\nrelaxation (SDR) of the considered problem. Then we propose an efficient\nalgorithm based on Lagrangian duality for solving the considered problem. The\nproposed algorithm judiciously exploits the special structure of the\nKarush-Kuhn-Tucker (KKT) conditions of the considered problem and finds the\nsolution that satisfies the KKT conditions via two fixed-point iterations. The\nproposed algorithm is highly efficient (as evaluating the functions in both\nfixed-point iterations are computationally cheap) and is guaranteed to find the\nglobal solution of the problem. Simulation results show the efficiency and the\ncorrectness of the proposed algorithm.\n""]","[('cellular networks', 0.48677945137023926), ('cellular network', 0.4793779253959656), ('coordinated beamforming', 0.47615376114845276), ('minimize total power', 0.448354572057724), ('efficient optimization', 0.4353979229927063), ('radio access network', 0.39374932646751404), ('joint beamforming', 0.38416776061058044), ('standard cellular', 0.37053382396698), ('cloud radio access', 0.3497585654258728), ('outage constrained', 0.34963375329971313)]"
1908,1908,15,1908_channel capacity_gaussian channels_gaussian channel_memoryless channels,"['channel capacity', 'gaussian channels', 'gaussian channel', 'memoryless channels', 'shannon limit', 'gaussian noise channel', 'decoding rate', 'gaussian multiple access', 'multiple access channel', 'rate decoding']","['Finite-Blocklength Information Theory   Traditional asymptotic information-theoretic studies of the fundamental\nlimits of wireless communication systems primarily rely on some ideal\nassumptions, such as infinite blocklength and vanishing error probability.\nWhile these assumptions enable tractable mathematical characterizations, they\nfail to capture the stringent requirements of some emerging next-generation\nwireless applications, such as ultra-reliable low latency communication and\nultra-massive machine type communication, in which it is required to support a\nmuch wider range of features including short-packet communication, extremely\nlow latency, and/or low energy consumption. To better support such\napplications, it is important to consider finite-blocklength information\ntheory. In this paper, we present a comprehensive review of the advances in\nthis field, followed by a discussion on the open questions. Specifically, we\ncommence with the fundamental limits of source coding in the non-asymptotic\nregime, with a particular focus on lossless and lossy compression in\npoint-to-point~(P2P) and multiterminal cases. Next, we discuss the fundamental\nlimits of channel coding in P2P channels, multiple access channels, and\nemerging massive access channels. We further introduce recent advances in joint\nsource and channel coding, highlighting its considerable performance advantage\nover separate source and channel coding in the non-asymptotic regime. In each\npart, we review various non-asymptotic achievability bounds, converse bounds,\nand approximations, as well as key ideas behind them, which are essential for\nproviding engineering insights into the design of future wireless communication\nsystems.\n', 'Achievable Information-Energy Region in the Finite Block-Length Regime\n  with Finite Constellations   This paper characterizes an achievable information-energy region of\nsimultaneous information and energy transmission over an additive white\nGaussian noise channel. This analysis is performed in the finite block-length\nregime with finite constellations. More specifically, a method for constructing\na family of codes is proposed and the set of achievable tuples of information\nrate, energy rate, decoding error probability (DEP) and energy outage\nprobability (EOP) is characterized. Using existing converse results, it is\nshown that the construction is information rate, energy rate, and EOP optimal.\nThe achieved DEP is, however, sub-optimal.\n', 'Information-Energy Regions in the Finite Block-Length Regime with Finite\n  Channel Inputs   This paper characterizes the trade-offs between information and energy\ntransmission over an additive white Gaussian noise channel in the finite\nblock-length regime with finite sets of channel input symbols. These trade-offs\nare characterized using impossibility and achievability bounds on the\ninformation transmission rate, energy transmission rate, decoding error\nprobability (DEP) and energy outage probability (EOP) for a finite block-length\ncode. Given a set of channel input symbols, the impossibility results identify\nthe tuples of information rate, energy rate, DEP and EOP that cannot be\nachieved by any code using the given set of channel inputs. A novel method for\nconstructing a family of codes that satisfy a target information rate, energy\nrate, DEP and EOP is also proposed. The achievability bounds identify the set\nof tuples of information rate, energy rate, DEP and EOP that can be\nsimultaneously achieved by the constructed family of codes. The proposed\nconstruction matches the impossibility bounds for the information rate, energy\nrate, and the EOP. However, for a given information rate, energy rate and EOP,\nthe achieved DEP is higher than the impossibility bound due to the choice of\nthe decoding sets made during the code construction.\n']","[('channel capacity', 0.5924021005630493), ('gaussian channels', 0.5447983741760254), ('gaussian channel', 0.5447927713394165), ('memoryless channels', 0.537922739982605), ('shannon limit', 0.5246881246566772), ('gaussian noise channel', 0.49969756603240967), ('decoding rate', 0.4918465316295624), ('gaussian multiple access', 0.4694363474845886), ('multiple access channel', 0.4612162709236145), ('rate decoding', 0.45285898447036743)]"
1909,1909,15,1909_cubic surfaces_singular k3 surfaces_surfaces number_extensions number fields,"['cubic surfaces', 'singular k3 surfaces', 'surfaces number', 'extensions number fields', 'k3 surfaces', 'brauer manin obstruction', 'cubic surface', 'defined number fields', 'number fields', 'quartic surfaces']","['Non-invariance of weak approximation with Brauer-Manin obstruction for\n  surfaces   In this paper, we study the property of weak approximation with Brauer-Manin\nobstruction for surfaces with respect to field extensions of number fields. For\nany nontrivial extension of number fields L/K, assuming a conjecture of M.\nStoll, we construct a smooth, projective, and geometrically connected surface\nover K such that it satisfies weak approximation with Brauer-Manin obstruction\noff all archimedean places, while its base change to L fails. Then we\nillustrate this construction with an explicit unconditional example.\n', 'Non-invariance of the Brauer-Manin obstruction for surfaces   In this paper, we study the properties of weak approximation with\nBrauer-Manin obstruction and the Hasse principle with Brauer-Manin obstruction\nfor surfaces with respect to field extensions of number fields. We assume a\nconjecture of M. Stoll. For any nontrivial extension of number fields $L/K,$ we\nconstruct two kinds of smooth, projective, and geometrically connected surfaces\ndefined over $K.$ For the surface of the first kind, it has a $K$-rational\npoint, and satisfies weak approximation with Brauer-Manin obstruction off\n$\\infty_K,$ while its base change by $L$ does not so off $\\infty_L.$ For the\nsurface of the second kind, it is a counterexample to the Hasse principle\nexplained by the Brauer-Manin obstruction, while the failure of the Hasse\nprinciple of its base change by $L$ cannot be so. We illustrate these\nconstructions with explicit unconditional examples.\n', 'The role of primes of good reduction in the Brauer--Manin obstruction   We discuss the role of primes of good reduction in the existence of the\nBrauer--Manin obstruction to weak approximation for varieties defined over\nnumber fields. Following Bright and Newton, we give some necessaries conditions\non the ramification index that the prime ideal of the number field should\nsatisfy in order to be involved in the Brauer--Manin obstruction to weak\napproximation. To support the results, many examples of transcendental\nBrauer--Manin obstruction to weak approximation on K3 surfaces are given.\n']","[('cubic surfaces', 0.5026895999908447), ('singular k3 surfaces', 0.4769130349159241), ('surfaces number', 0.4562661349773407), ('extensions number fields', 0.4446042776107788), ('k3 surfaces', 0.43758469820022583), ('brauer manin obstruction', 0.43333330750465393), ('cubic surface', 0.41145747900009155), ('defined number fields', 0.4017406105995178), ('number fields', 0.3970797061920166), ('quartic surfaces', 0.39628833532333374)]"
1910,1910,15,1910_graded algebras_grassmann algebra_graded algebra_mathbb _2 graded,"['graded algebras', 'grassmann algebra', 'graded algebra', 'mathbb _2 graded', 'ideal graded', 'graded polynomial', 'basis graded', 'compute graded', 'mathbb graded', 'graded lie']","['Automorphisms and superalgebra structures on the Grassmann algebra   Let $F$ be a field of characteristic zero and let $E$ be the Grassmann\nalgebra of an infinite dimensional $F$-vector space $L$. In this paper we study\nthe superalgebra structures (that is the $\\mathbb{Z}_{2}$-gradings) that the\nalgebra $E$ admits. By using the duality between superalgebras and\nautomorphisms of order $2$ we prove that in many cases the\n$\\mathbb{Z}_{2}$-graded polynomial identities for such structures coincide with\nthe $\\mathbb{Z}_{2}$-graded polynomial identities of the ""typical"" cases\n$E_{\\infty}$, $E_{k^\\ast}$ and $E_{k}$ where the vector space $L$ is\nhomogeneous. Recall that these cases were completely described by Di Vincenzo\nand Da Silva in \\cite{disil}. Moreover we exhibit a wide range of\nnon-homogeneous $\\mathbb{Z}_{2}$-gradings on $E$ that are\n$\\mathbb{Z}_{2}$-isomorphic to $E_{\\infty}$, $E_{k^\\ast}$ and $E_{k}$. In\nparticular we construct a $\\mathbb{Z}_{2}$-grading on $E$ with only one\nhomogeneous generator in $L$ which is $\\mathbb{Z}_{2}$-isomorphic to the\nnatural $\\mathbb{Z}_{2}$-grading on $E$, here denoted by $E_{can}$.\n', '$\\mathbb{Z}$-gradings of full support on the Grassmann algebra   Let $E$ be the infinite dimensional Grassmann algebra over a field $F$ of\ncharacteristic zero. In this paper we investigate the structures of\n$\\mathbb{Z}$-gradings on $E$ of full support. Using methods of elementary\nnumber theory, we describe the $\\mathbb{Z}$-graded polynomial identities for\nthe so-called $2$-induced $\\mathbb{Z}$-gradings on $E$ of full support. As a\nconsequence of this fact we provide examples of $\\mathbb{Z}$-gradings on $E$\nwhich are PI-equivalent but not $\\mathbb{Z}$-isomorphic. This is the first\nexample of graded algebras with infinite support that are PI-equivalent and not\nisomorphic as graded algebras. We also present the notion of central\n$\\mathbb{Z}$-gradings on $E$ and we show that its $\\mathbb{Z}$-graded\npolynomial identities are closely related to the $\\mathbb{Z}_{2}$-graded\npolynomial identities of $\\mathbb{Z}_{2}$-gradings on $E$.\n', '$\\mathbb{Z}$-graded polynomial identities of the Grassmann algebra   Let $F$ be an infinite field of characteristic different from 2, and let $E$\nbe the Grassmann algebra of an infinite dimensional $F$-vector space $L$. In\nthis paper we study the $\\mathbb{Z}$-graded polynomial identities of $E$ with\nrespect to certain $\\mathbb{Z}$-grading such that the vector space $L$ is\nhomogeneous in the grading. More precisely, we construct three types of\n$\\mathbb{Z}$-gradings on $E$, denoted by $E^{\\infty}$, $E^{k^\\ast}$ and\n$E^{k}$, and we give the explicit form of the corresponding $\\mathbb{Z}$-graded\npolynomial identities. We show that the homogeneous superalgebras $E_{\\infty}$,\n$E_{k^\\ast}$ and $E_{k}$ studied in \\cite{disil} can be obtained from\n$E^{\\infty}$, $E^{k^\\ast}$ and $E^{k}$ as quotient gradings. Moreover we\nexhibit several other types of homogeneous $\\mathbb{Z}$-gradings on $E$, and\ndescribe their graded identities.\n']","[('graded algebras', 0.6564455628395081), ('grassmann algebra', 0.6344180703163147), ('graded algebra', 0.6123533248901367), ('mathbb _2 graded', 0.5698092579841614), ('ideal graded', 0.5361759066581726), ('graded polynomial', 0.5205598473548889), ('basis graded', 0.5147208571434021), ('compute graded', 0.5048673748970032), ('mathbb graded', 0.4847913384437561), ('graded lie', 0.47929972410202026)]"
1911,1911,15,1911_weyl sums_weyl inequality_estimates weyl_operators weyl,"['weyl sums', 'weyl inequality', 'estimates weyl', 'operators weyl', 'maximal estimates', 'dimensional weyl', 'sum estimate', 'sums associated', 'maximal estimate', 'weyl']","['Two-dimensional Weyl sums failing square-root cancellation along lines   We show that a certain two-dimensional family of Weyl sums of length $P$\ntakes values as large as $P^{3/4 + o(1)}$ on almost all linear slices of the\nunit torus, contradicting a widely held expectation that Weyl sums should\nexhibit square-root cancellation on generic subvarieties of the unit torus.\nThis is an extension of a result of J. Brandes, S. T. Parsell, C. Poulias, G.\nShakan and R. C. Vaughan (2020) from quadratic and cubic monomials to general\npolynomials of arbitrary degree. The new ingredients of our approach are the\nclassical results of E. Bombieri (1966) on exponential sums along a curve and\nR. J. Duffin and A. C. Schaeffer (1941) on Diophantine approximations by\nrational numbers with prime denominators.\n', '$L^p$ maximal estimates for Weyl sums with $k\\ge3$ on $\\mathbb{T}$   In this paper, we study the $L^p$ maximal estimates for the Weyl sums\n$\\sum_{n=1}^{N}e^{2\\pi i(nx + n^{k}t)}$ with higher-order $k\\ge3$ on\n$\\mathbb{T}$, and obtain the positive and negative results. Especially for the\ncase $k=3$, our result is sharp up to the endpoint. The main idea is to\ninvestigate the structure of the set where large values of Weyl sums are\nachieved by making use of the rational approximation and the refined estimate\nfor the exponential sums.\n', ""Maximal estimates for the Weyl sums on $\\mathbb{T}^{d}$ (with an\n  appendix by Alex Barron)   In this paper, we obtain the maximal estimate for the Weyl sums on the torus\n$\\mathbb{T}^d$ with $d\\geq 2$, which is sharp up to the endpoint. We also\nconsider two variants of this problem which include the maximal estimate along\nthe rational lines and on the generic torus. Applications, which include some\nnew upper bound on the Hausdorff dimension of the sets associated to the large\nvalue of the Weyl sums, reflect the compound phenomenon between the square root\ncancellation and the constructive interference. In the Appendix, an alternate\nproof of Theorem 1.1 inspired by Baker's argument in [1] is given by Barron,\nwhich also improves the $N^{\\epsilon}$ loss in Theorem 1.1, and the\nStrichartz-type estimates for the Weyl sums with logarithmic losses are\nobtained by the same argument.\n""]","[('weyl sums', 0.6776111125946045), ('weyl inequality', 0.6070002913475037), ('estimates weyl', 0.5987199544906616), ('operators weyl', 0.5036052465438843), ('maximal estimates', 0.4481474757194519), ('dimensional weyl', 0.4424247741699219), ('sum estimate', 0.42458248138427734), ('sums associated', 0.4242958128452301), ('maximal estimate', 0.4096047878265381), ('weyl', 0.3797701895236969)]"
1912,1912,15,1912_bounds heat kernel_estimates heat kernels_heat kernel estimates_estimates heat kernel,"['bounds heat kernel', 'estimates heat kernels', 'heat kernel estimates', 'estimates heat kernel', 'heat kernel estimate', 'dirichlet heat kernel', 'heat kernels', 'bounds heat', 'heat kernel associated', 'heat kernel']","['Sharp two-sided heat kernel estimates for Schr\\""{o}dinger operators with\n  decaying potentials   We establish global two-sided heat kernel estimates (for full time and space)\nof the Schr\\""odinger operator $-\\frac{1}{2}\\Delta+V$ on $\\R^d$, where the\npotential $V(x)$ is locally bounded and behaves like $c|x|^{-\\alpha}$ near\ninfinity with $\\alpha\\in (0,2)$ and $c> 0$, or with $\\alpha>0$ and $c<0$.Our\nresults improve all known results in the literature, and it seems that the\ncurrent paper is the first one where consistent two-sided heat kernel bounds\nfor the long range potentials are established.\n', 'Two-sided heat kernel estimates for Schr\\""{o}dinger operators with\n  unbounded potentials   Consider the Schr\\""odinger operator $ \\mathcal L^V=-\\Delta+V $ on $\\R^d$,\nwhere $V:\\R^d\\to [0,\\infty)$ is a nonnegative and locally bounded potential on\n$\\R^d$ so that for all $x\\in \\R^d$ with $|x|\\ge 1$, $c_1g(|x|)\\le V(x)\\le\nc_2g(|x|)$ with some constants $c_1,c_2>0$ and a nondecreasing and strictly\npositive function $g:[0,\\infty)\\to [1,+\\infty)$ that satisfies $g(2r)\\le c_0\ng(r)$ for all $r>0$ and $\\lim_{r\\to \\infty} g(r)=\\infty.$ We establish global\nin time and qualitatively sharp bounds for the heat kernel of the associated\nSchr\\""{o}dinger semigroup by the probabilistic method. In particular, we can\npresent global in space and time two-sided bounds of heat kernel even when the\nSchr\\""{o}dinger semigroup is not intrinsically ultracontractive. Furthermore,\ntwo-sided estimates for the corresponding Green\'s functions are also obtained.\n', 'Uniform Complex Time Heat Kernel Estimates Without Gaussian Bounds   In this paper, first we consider the uniform complex time heat kernel\nestimates of $e^{-z(-\\Delta)^{\\frac{\\alpha}{2}}}$ for $\\alpha>0, z\\in\n\\mathbb{C}^+$. When $\\frac{\\alpha}{2}$ is not an integer, generally the heat\nkernel doest not have the Gaussian upper bounds for real time. Thus the\nPhragm\\\'en-Lindel\\""of methods fail to give the uniform complex time estimates.\nInstead, our first result gives the asymptotic estimates for $P(z, x)$ as $z$\ntending to the imaginary axis. Then we prove the uniform complex time heat\nkernel estimates. Finally we also show the uniform estimates of analytic\nsemigroup generated by $H=(-\\Delta)^{\\frac{\\alpha}{2}}+V$ where $V$ belongs to\nhigher order Kato class.\n']","[('bounds heat kernel', 0.7091272473335266), ('estimates heat kernels', 0.6739336848258972), ('heat kernel estimates', 0.6585491299629211), ('estimates heat kernel', 0.6533366441726685), ('heat kernel estimate', 0.6152596473693848), ('dirichlet heat kernel', 0.6073279976844788), ('heat kernels', 0.5422341823577881), ('bounds heat', 0.5361605882644653), ('heat kernel associated', 0.5328493118286133), ('heat kernel', 0.5228293538093567)]"
1913,1913,15,1913_multiple zeta values_terms multiple zeta_zeta values_multiple zeta,"['multiple zeta values', 'terms multiple zeta', 'zeta values', 'multiple zeta', 'multiple polylogarithms', 'polylogarithms', 'integral identities', 'several integral', 'multiple harmonic sums', 'polylogarithm']","['Iterated integrals on products of one variable multiple polylogarithms   In this paper we show that the iterated integrals on products of one variable\nmultiple polylogarithms from 0 to 1 are actually multiple zeta values if they\nare convergent. In the divergent case, we define regularized iterated integrals\nfrom 0 to 1. By the same method, we show that the regularized iterated\nintegrals are also multiple zeta values. As an application, we give new series\nrepresentations for multiple zeta values and calculate some interesting\nexamples of iterated integrals.\n', ""Explicit Relations between Multiple Zeta Values and Related Variants   In this paper we present some new identities for multiple polylogarithms\n(abbr. MPLs) and multiple harmonic star sums (abbr. MHSSs) by using the methods\nof iterated integral computations of logarithm functions. Then, by applying\nthese formulas obtained, we establish some explicit relations between\nKaneko-Yamamoto type multiple zeta values (abbr. K-Y MZVs), multiple zeta\nvalues (abbr. MZVs) and MPLs. Further, we find some explicit relations between\nMZVs and multiple zeta star values (abbr. MZSVs). Furthermore, we define an\nAp\\'{e}ry-type variant of MZSVs $\\zeta^\\star_B({\\bf k})$ (called multiple zeta\n$B$-star values, abbr. MZBSVs) which involve MHSSs and central binomial\ncoefficients, and establish some explicit connections among MZVs, alternating\nMZVs and MZBSVs by using the method of iterated integrals. Finally, some\ninteresting consequences and illustrative examples are presented.\n"", 'Explicit Relations between Kaneko--Yamamoto Type Multiple Zeta Values\n  and Related Variants   In this paper we first establish several integral identities. These integrals\nare of the form \\[\\int_0^1 x^{an+b} f(x)\\,dx\\quad (a\\in\\{1,2\\},\\\nb\\in\\{-1,-2\\})\\] where $f(x)$ is a single-variable multiple polylogarithm\nfunction or $r$-variable multiple polylogarithm function or Kaneko--Tsumura\nA-function (this is a single-variable multiple polylogarithm function of level\ntwo). We find that these integrals can be expressed in terms of multiple zeta\n(star) values and their related variants (multiple $t$-values, multiple\n$T$-values, multiple $S$-values etc.), and multiple harmonic (star) sums and\ntheir related variants (multiple $T$-harmonic sums, multiple $S$-harmonic sums\netc.). Using these integral identities, we prove many explicit evaluations of\nKaneko--Yamamoto multiple zeta values and their related variants. Further, we\nderive some relations involving multiple zeta (star) values and their related\nvariants.\n']","[('multiple zeta values', 0.6207579374313354), ('terms multiple zeta', 0.6101760268211365), ('zeta values', 0.5787091255187988), ('multiple zeta', 0.5713144540786743), ('multiple polylogarithms', 0.548198401927948), ('polylogarithms', 0.5090649724006653), ('integral identities', 0.4957922697067261), ('several integral', 0.4746694266796112), ('multiple harmonic sums', 0.47352486848831177), ('polylogarithm', 0.4707771837711334)]"
1914,1914,15,1914_groups maximal_maximal subgroups_subgroups maximal_branch groups,"['groups maximal', 'maximal subgroups', 'subgroups maximal', 'branch groups', 'every maximal subgroup', 'maximal subgroup', 'groups acting trees', 'branch group', 'grigorchuk group', 'infinite groups']","['On maximal subgroups of infinite index in branch and weakly branch\n  groups   We generalise a technical tool, originally developed by Pervova for the study\nof maximal subgroups in Grigorchuk and GGS groups, to all weakly branch groups\nsatisfying a natural condition, and in particular to all branch groups. We then\nuse this tool to prove that every maximal subgroup of infinite index of a\nbranch group is also a branch group. As a further application of this result,\nwe show that every maximal subgroup of the Basilica group is of finite index.\n', 'Maximal subgroups of non-torsion Grigorchuk-Gupta-Sidki groups   A Grigorchuk-Gupta-Sidki (GGS-)group is a subgroup of the automorphism group\nof the $p$-adic tree for an odd prime $p$, generated by one rooted automorphism\nand one directed automorphism. Pervova proved that all torsion GGS-groups do\nnot have maximal subgroups of infinite index. Here we extend the result to\nnon-torsion GGS-groups, which include the weakly regular branch, but not\nbranch, GGS-group.\n', 'Subgroup induction property for branch groups   The subgroup induction property is a property of self-similar groups acting\non rooted trees introduced by Grigorchuk and Wilson in 2003 that appears to\nhave strong implications on the structure of the groups possessing it. It was\nfor example used in the proof that the first Grigorchuk group as well as the\nGupta-Sidki 3-group are subgroup separable (locally extended residually finite)\nor to describe their finitely generated subgroups as well as their weakly\nmaximal subgroups. However, until now, there were only two known examples of\ngroups with this property, namely the first Grigorchuk group and the\nGupta-Sidki 3-group.\n  The aim of this article is twofold. First, we investigate various\nconsequences of the subgroup induction property for branch groups, a\nparticularly interesting class of self-similar groups. Notably, we show that\nfinitely generated branch groups with the subgroup induction property must be\ntorsion, just infinite and subgroup separable, and we establish conditions\nunder which all their maximal subgroups are of finite index and all their\nweakly maximal subgroups are closed in the profinite topology. Then, we show\nthat every torsion GGS group has the subgroup induction property, hence\nproviding the first infinite family of examples of groups with this property.\n']","[('groups maximal', 0.6420634984970093), ('maximal subgroups', 0.6270738244056702), ('subgroups maximal', 0.6175369620323181), ('branch groups', 0.6052573323249817), ('every maximal subgroup', 0.590736448764801), ('maximal subgroup', 0.5868551135063171), ('groups acting trees', 0.5569747686386108), ('branch group', 0.5525531768798828), ('grigorchuk group', 0.5317409634590149), ('infinite groups', 0.5162155032157898)]"